\hypertarget{namespacemom__entrain__diffusive}{}\doxysection{mom\+\_\+entrain\+\_\+diffusive Module Reference} \label{namespacemom__entrain__diffusive}\index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsection{Detailed Description} Diapycnal mixing and advection in isopycnal mode. By Robert Hallberg, September 1997 -\/ July 2000. This file contains the subroutines that implement diapycnal mixing and advection in isopycnal layers. The main subroutine, calculate\+\_\+entrainment, returns the entrainment by each layer across the interfaces above and below it. These are calculated subject to the constraints that no layers can be driven to neg-\/ ative thickness and that the each layer maintains its target density, using the scheme described in Hallberg (M\+WR 2000). There may or may not be a bulk mixed layer above the isopycnal layers. The solution is iterated until the change in the entrainment between successive iterations is less than some small tolerance. The dual-\/stream entrainment scheme of Mac\+Dougall and Dewar (J\+PO 1997) is used for combined diapycnal advection and diffusion, modified as described in Hallberg (M\+WR 2000) to be solved implicitly in time. Any profile of diffusivities may be used. Diapycnal advection is fundamentally the residual of diapycnal diffusion, so the fully implicit upwind differencing scheme that is used is entirely appropriate. The downward buoyancy flux in each layer is determined from an implicit calculation based on the previously calculated flux of the layer above and an estim-\/ ated flux in the layer below. This flux is subject to the foll-\/ owing conditions\+: (1) the flux in the top and bottom layers are set by the boundary conditions, and (2) no layer may be driven below an Angstrom thickness. If there is a bulk mixed layer, the mixed and buffer layers are treated as Eulerian layers, whose thicknesses only change due to entrainment by the interior layers. \doxysubsection*{Data Types} \begin{DoxyCompactItemize} \item type \mbox{\hyperlink{structmom__entrain__diffusive_1_1entrain__diffusive__cs}{entrain\+\_\+diffusive\+\_\+cs}} \begin{DoxyCompactList}\small\item\em The control structure holding parametes for the M\+O\+M\+\_\+entrain\+\_\+diffusive module. \end{DoxyCompactList}\end{DoxyCompactItemize} \doxysubsection*{Functions/\+Subroutines} \begin{DoxyCompactItemize} \item subroutine, public \mbox{\hyperlink{namespacemom__entrain__diffusive_ae68ab2fa707778de2f92ce179729f2ff}{entrainment\+\_\+diffusive}} (h, tv, fluxes, dt, G, GV, US, CS, ea, eb, kb\+\_\+out, Kd\+\_\+\+Lay, Kd\+\_\+int) \begin{DoxyCompactList}\small\item\em This subroutine calculates ea and eb, the rates at which a layer entrains from the layers above and below. The entrainment rates are proportional to the buoyancy flux in a layer and inversely proportional to the density differences between layers. The scheme that is used here is described in detail in Hallberg, Mon. Wea. Rev. 2000. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__entrain__diffusive_a13bbe9f35e3198470100375d9d016b7a}{f\+\_\+to\+\_\+ent}} (F, h, kb, kmb, j, G, GV, CS, dsp1\+\_\+ds, eakb, Ent\+\_\+bl, ea, eb, do\+\_\+i\+\_\+in) \begin{DoxyCompactList}\small\item\em This subroutine calculates the actual entrainments (ea and eb) and the amount of surface forcing that is applied to each layer if there is no bulk mixed layer. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__entrain__diffusive_a363a25e7823043bb028e920e359733b0}{set\+\_\+ent\+\_\+bl}} (h, dt\+Kd\+\_\+int, tv, kb, kmb, do\+\_\+i, G, GV, US, CS, j, Ent\+\_\+bl, Sref, h\+\_\+bl) \begin{DoxyCompactList}\small\item\em This subroutine sets the average entrainment across each of the interfaces between buffer layers within a timestep. It also causes thin and relatively light interior layers to be entrained by the deepest buffer layer. Also find the initial coordinate potential densities (Sref) of each layer. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__entrain__diffusive_aa2d2f462912ba1e201b1b73e62a905f3}{determine\+\_\+dskb}} (h\+\_\+bl, Sref, Ent\+\_\+bl, E\+\_\+kb, is, ie, kmb, G, GV, limit, d\+Skb, dd\+Skb\+\_\+dE, d\+Slay, dd\+Slay\+\_\+dE, d\+S\+\_\+anom\+\_\+lim, do\+\_\+i\+\_\+in) \begin{DoxyCompactList}\small\item\em This subroutine determines the reference density difference between the bottommost buffer layer and the first interior after the mixing between mixed and buffer layers and mixing with the layer below. Within the mixed and buffer layers, entrainment from the layer above is increased when it is necessary to keep the layers from developing a negative thickness; otherwise it equals Ent\+\_\+bl. At each interface, the upward and downward fluxes average out to Ent\+\_\+bl, unless entrainment by the layer below is larger than twice Ent\+\_\+bl. The density difference across the first interior layer may also be returned. It could also be limited to avoid negative values or values that greatly exceed the density differences across an interface. Additionally, the partial derivatives of d\+Skb and d\+Slay with E\+\_\+kb could also be returned. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__entrain__diffusive_adce1b1ba57f5245f1eda57e7a254d4df}{f\+\_\+kb\+\_\+to\+\_\+ea\+\_\+kb}} (h\+\_\+bl, Sref, Ent\+\_\+bl, I\+\_\+d\+Skbp1, F\+\_\+kb, kmb, i, G, GV, CS, ea\+\_\+kb, tol\+\_\+in) \begin{DoxyCompactList}\small\item\em Given an entrainment from below for layer kb, determine a consistent entrainment from above, such that d\+Skb $\ast$ ea\+\_\+kb = d\+Skbp1 $\ast$ F\+\_\+kb. The input value of ea\+\_\+kb is both the maximum value that can be obtained and the first guess of the iterations. Ideally ea\+\_\+kb should be an under-\/estimate. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__entrain__diffusive_a541b3aadc418110f7359b0ae401e4e78}{determine\+\_\+ea\+\_\+kb}} (h\+\_\+bl, dt\+Kd\+\_\+kb, Sref, I\+\_\+d\+Skbp1, Ent\+\_\+bl, ea\+\_\+kbp1, min\+\_\+eakb, max\+\_\+eakb, kmb, is, ie, do\+\_\+i, G, GV, CS, Ent, error, err\+\_\+min\+\_\+eakb0, err\+\_\+max\+\_\+eakb0, F\+\_\+kb, d\+Fdfm\+\_\+kb) \begin{DoxyCompactList}\small\item\em This subroutine determines the entrainment from above by the top interior layer (labeled kb elsewhere) given an entrainment by the layer below it, constrained to be within the provided bounds. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__entrain__diffusive_ae45dbf976314c3a9e278ebcebedab109}{find\+\_\+maxf\+\_\+kb}} (h\+\_\+bl, Sref, Ent\+\_\+bl, I\+\_\+d\+Skbp1, min\+\_\+ent\+\_\+in, max\+\_\+ent\+\_\+in, kmb, is, ie, G, GV, CS, maxF, ent\+\_\+maxF, do\+\_\+i\+\_\+in, F\+\_\+lim\+\_\+maxent, F\+\_\+thresh) \begin{DoxyCompactList}\small\item\em Maximize F = ent$\ast$ds\+\_\+kb$\ast$\+I\+\_\+d\+Skbp1 in the range min\+\_\+ent $<$ ent $<$ max\+\_\+ent. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__entrain__diffusive_a08d3203366fac7ec13472c79681dea0e}{entrain\+\_\+diffusive\+\_\+init}} (Time, G, GV, US, param\+\_\+file, diag, CS, just\+\_\+read\+\_\+params) \begin{DoxyCompactList}\small\item\em This subroutine initializes the parameters and memory associated with the entrain\+\_\+diffusive module. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__entrain__diffusive_a0e71b47abe1e1889f4b687139615ca14}{entrain\+\_\+diffusive\+\_\+end}} (CS) \begin{DoxyCompactList}\small\item\em This subroutine cleans up and deallocates any memory associated with the entrain\+\_\+diffusive module. \end{DoxyCompactList}\end{DoxyCompactItemize} \doxysubsection{Function/\+Subroutine Documentation} \mbox{\Hypertarget{namespacemom__entrain__diffusive_aa2d2f462912ba1e201b1b73e62a905f3}\label{namespacemom__entrain__diffusive_aa2d2f462912ba1e201b1b73e62a905f3}} \index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}!determine\_dskb@{determine\_dskb}} \index{determine\_dskb@{determine\_dskb}!mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsubsection{\texorpdfstring{determine\_dskb()}{determine\_dskb()}} {\footnotesize\ttfamily subroutine mom\+\_\+entrain\+\_\+diffusive\+::determine\+\_\+dskb (\begin{DoxyParamCaption}\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{h\+\_\+bl, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{Sref, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{Ent\+\_\+bl, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{E\+\_\+kb, }\item[{integer, intent(in)}]{is, }\item[{integer, intent(in)}]{ie, }\item[{integer, intent(in)}]{kmb, }\item[{type(\mbox{\hyperlink{structmom__grid_1_1ocean__grid__type}{ocean\+\_\+grid\+\_\+type}}), intent(in)}]{G, }\item[{type(\mbox{\hyperlink{structmom__verticalgrid_1_1verticalgrid__type}{verticalgrid\+\_\+type}}), intent(in)}]{GV, }\item[{logical, intent(in)}]{limit, }\item[{real, dimension(szi\+\_\+(g)), intent(inout)}]{d\+Skb, }\item[{real, dimension(szi\+\_\+(g)), intent(inout), optional}]{dd\+Skb\+\_\+dE, }\item[{real, dimension(szi\+\_\+(g)), intent(inout), optional}]{d\+Slay, }\item[{real, dimension(szi\+\_\+(g)), intent(inout), optional}]{dd\+Slay\+\_\+dE, }\item[{real, dimension(szi\+\_\+(g)), intent(inout), optional}]{d\+S\+\_\+anom\+\_\+lim, }\item[{logical, dimension(szi\+\_\+(g)), intent(in), optional}]{do\+\_\+i\+\_\+in }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine determines the reference density difference between the bottommost buffer layer and the first interior after the mixing between mixed and buffer layers and mixing with the layer below. Within the mixed and buffer layers, entrainment from the layer above is increased when it is necessary to keep the layers from developing a negative thickness; otherwise it equals Ent\+\_\+bl. At each interface, the upward and downward fluxes average out to Ent\+\_\+bl, unless entrainment by the layer below is larger than twice Ent\+\_\+bl. The density difference across the first interior layer may also be returned. It could also be limited to avoid negative values or values that greatly exceed the density differences across an interface. Additionally, the partial derivatives of d\+Skb and d\+Slay with E\+\_\+kb could also be returned. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em g} & The ocean\textquotesingle{}s grid structure. \\ \hline \mbox{\texttt{ in}} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure. \\ \hline \mbox{\texttt{ in}} & {\em h\+\_\+bl} & Layer thickness \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em sref} & Reference potential density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em ent\+\_\+bl} & The average entrainment upward and downward across each interface around the buffer layers \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em e\+\_\+kb} & The entrainment by the top interior layer \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em is} & The start of the i-\/index range to work on. \\ \hline \mbox{\texttt{ in}} & {\em ie} & The end of the i-\/index range to work on. \\ \hline \mbox{\texttt{ in}} & {\em kmb} & The number of mixed and buffer layers. \\ \hline \mbox{\texttt{ in}} & {\em limit} & If true, limit d\+Skb and d\+Slay to avoid negative values. \\ \hline \mbox{\texttt{ in,out}} & {\em dskb} & The limited potential density difference across the interface between the bottommost buffer layer and the topmost interior layer. \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} d\+Skb $>$ 0. \\ \hline \mbox{\texttt{ in,out}} & {\em ddskb\+\_\+de} & The partial derivative of d\+Skb with E \mbox{[}R H-\/1 $\sim$$>$ kg m-\/4 or m-\/1\mbox{]}. \\ \hline \mbox{\texttt{ in,out}} & {\em dslay} & The limited potential density difference across the topmost interior layer. 0 $<$ d\+Skb \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} \\ \hline \mbox{\texttt{ in,out}} & {\em ddslay\+\_\+de} & The partial derivative of d\+Slay with E \mbox{[}R H-\/1 $\sim$$>$ kg m-\/4 or m-\/1\mbox{]}. \\ \hline \mbox{\texttt{ in,out}} & {\em ds\+\_\+anom\+\_\+lim} & A limiting value to use for the density anomalies below the buffer layer \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em do\+\_\+i\+\_\+in} & If present, determines which columns are worked on. \\ \hline \end{DoxyParams} Definition at line 1199 of file M\+O\+M\+\_\+entrain\+\_\+diffusive.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1201 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure.}} \DoxyCodeLine{1202 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid}} \DoxyCodeLine{1203 \textcolor{comment}{ !! structure.}} \DoxyCodeLine{1204 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: h\_bl\textcolor{comment}{ !< Layer thickness [H \string~> m or kg m-\/2]}} \DoxyCodeLine{1205 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: Sref\textcolor{comment}{ !< Reference potential density [R \string~> kg m-\/3]}} \DoxyCodeLine{1206 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: Ent\_bl\textcolor{comment}{ !< The average entrainment upward and}} \DoxyCodeLine{1207 \textcolor{comment}{ !! downward across each interface}} \DoxyCodeLine{1208 \textcolor{comment}{ !! around the buffer layers [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1209 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: E\_kb\textcolor{comment}{ !< The entrainment by the top interior}} \DoxyCodeLine{1210 \textcolor{comment}{ !! layer [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1211 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: is\textcolor{comment}{ !< The start of the i-\/index range to work on.}} \DoxyCodeLine{1212 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: ie\textcolor{comment}{ !< The end of the i-\/index range to work on.}} \DoxyCodeLine{1213 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: kmb\textcolor{comment}{ !< The number of mixed and buffer layers.}} \DoxyCodeLine{1214 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{intent(in)} :: limit\textcolor{comment}{ !< If true, limit dSkb and dSlay to}} \DoxyCodeLine{1215 \textcolor{comment}{ !! avoid negative values.}} \DoxyCodeLine{1216 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(inout)} :: dSkb\textcolor{comment}{ !< The limited potential density}} \DoxyCodeLine{1217 \textcolor{comment}{ !! difference across the interface}} \DoxyCodeLine{1218 \textcolor{comment}{ !! between the bottommost buffer layer}} \DoxyCodeLine{1219 \textcolor{comment}{ !! and the topmost interior layer. [R \string~> kg m-\/3]}} \DoxyCodeLine{1220 \textcolor{comment}{ !! dSkb > 0.}} \DoxyCodeLine{1221 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: ddSkb\_dE\textcolor{comment}{ !< The partial derivative of dSkb}} \DoxyCodeLine{1222 \textcolor{comment}{ !! with E [R H-\/1 \string~> kg m-\/4 or m-\/1].}} \DoxyCodeLine{1223 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: dSlay\textcolor{comment}{ !< The limited potential density}} \DoxyCodeLine{1224 \textcolor{comment}{ !! difference across the topmost}} \DoxyCodeLine{1225 \textcolor{comment}{ !! interior layer. 0 < dSkb [R \string~> kg m-\/3]}} \DoxyCodeLine{1226 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: ddSlay\_dE\textcolor{comment}{ !< The partial derivative of dSlay}} \DoxyCodeLine{1227 \textcolor{comment}{ !! with E [R H-\/1 \string~> kg m-\/4 or m-\/1].}} \DoxyCodeLine{1228 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: dS\_anom\_lim\textcolor{comment}{ !< A limiting value to use for}} \DoxyCodeLine{1229 \textcolor{comment}{ !! the density anomalies below the}} \DoxyCodeLine{1230 \textcolor{comment}{ !! buffer layer [R \string~> kg m-\/3].}} \DoxyCodeLine{1231 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: do\_i\_in\textcolor{comment}{ !< If present, determines which}} \DoxyCodeLine{1232 \textcolor{comment}{ !! columns are worked on.}} \DoxyCodeLine{1233 } \DoxyCodeLine{1234 \textcolor{comment}{! Note that dSkb, ddSkb\_dE, dSlay, ddSlay\_dE, and dS\_anom\_lim are declared}} \DoxyCodeLine{1235 \textcolor{comment}{! intent inout because they should not change where do\_i\_in is false.}} \DoxyCodeLine{1236 } \DoxyCodeLine{1237 \textcolor{comment}{! This subroutine determines the reference density difference between the}} \DoxyCodeLine{1238 \textcolor{comment}{! bottommost buffer layer and the first interior after the mixing between mixed}} \DoxyCodeLine{1239 \textcolor{comment}{! and buffer layers and mixing with the layer below. Within the mixed and buffer}} \DoxyCodeLine{1240 \textcolor{comment}{! layers, entrainment from the layer above is increased when it is necessary to}} \DoxyCodeLine{1241 \textcolor{comment}{! keep the layers from developing a negative thickness; otherwise it equals}} \DoxyCodeLine{1242 \textcolor{comment}{! Ent\_bl. At each interface, the upward and downward fluxes average out to}} \DoxyCodeLine{1243 \textcolor{comment}{! Ent\_bl, unless entrainment by the layer below is larger than twice Ent\_bl.}} \DoxyCodeLine{1244 \textcolor{comment}{! The density difference across the first interior layer may also be returned.}} \DoxyCodeLine{1245 \textcolor{comment}{! It could also be limited to avoid negative values or values that greatly}} \DoxyCodeLine{1246 \textcolor{comment}{! exceed the density differences across an interface.}} \DoxyCodeLine{1247 \textcolor{comment}{! Additionally, the partial derivatives of dSkb and dSlay with E\_kb could}} \DoxyCodeLine{1248 \textcolor{comment}{! also be returned.}} \DoxyCodeLine{1249 } \DoxyCodeLine{1250 \textcolor{comment}{! Local variables}} \DoxyCodeLine{1251 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))} :: \&} \DoxyCodeLine{1252 b1, c1, \& \textcolor{comment}{! b1 and c1 are variables used by the tridiagonal solver.}} \DoxyCodeLine{1253 S, dS\_dE, \& \textcolor{comment}{! The coordinate density [R \string~> kg m-\/3] and its derivative with E.}} \DoxyCodeLine{1254 ea, dea\_dE, \& \textcolor{comment}{! The entrainment from above and its derivative with E.}} \DoxyCodeLine{1255 eb, deb\_dE \textcolor{comment}{! The entrainment from below and its derivative with E.}} \DoxyCodeLine{1256 \textcolor{keywordtype}{ real} :: deriv\_dSkb(SZI\_(G))} \DoxyCodeLine{1257 \textcolor{keywordtype}{ real} :: d1(SZI\_(G)) \textcolor{comment}{! d1 = 1.0-\/c1 is also used by the tridiagonal solver.}} \DoxyCodeLine{1258 \textcolor{keywordtype}{ real} :: src \textcolor{comment}{! A source term for dS\_dR.}} \DoxyCodeLine{1259 \textcolor{keywordtype}{ real} :: h1 \textcolor{comment}{! The thickness in excess of the minimum that will remain}} \DoxyCodeLine{1260 \textcolor{comment}{! after exchange with the layer below [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1261 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: do\_i} \DoxyCodeLine{1262 \textcolor{keywordtype}{ real} :: h\_neglect \textcolor{comment}{! A thickness that is so small it is usually lost}} \DoxyCodeLine{1263 \textcolor{comment}{! in roundoff and can be neglected [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1264 \textcolor{keywordtype}{ real} :: h\_tr \textcolor{comment}{! h\_tr is h at tracer points with a tiny thickness}} \DoxyCodeLine{1265 \textcolor{comment}{! added to ensure positive definiteness [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1266 \textcolor{keywordtype}{ real} :: b\_denom\_1 \textcolor{comment}{! The first term in the denominator of b1 [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1267 \textcolor{keywordtype}{ real} :: rat} \DoxyCodeLine{1268 \textcolor{keywordtype}{ real} :: dS\_kbp1, IdS\_kbp1} \DoxyCodeLine{1269 \textcolor{keywordtype}{ real} :: deriv\_dSLay} \DoxyCodeLine{1270 \textcolor{keywordtype}{ real} :: Inv\_term \textcolor{comment}{! [nondim]}} \DoxyCodeLine{1271 \textcolor{keywordtype}{ real} :: f1, df1\_drat \textcolor{comment}{! Temporary variables [nondim].}} \DoxyCodeLine{1272 \textcolor{keywordtype}{ real} :: z, dz\_drat, f2, df2\_dz, expz \textcolor{comment}{! Temporary variables [nondim].}} \DoxyCodeLine{1273 \textcolor{keywordtype}{ real} :: eps\_dSLay, eps\_dSkb \textcolor{comment}{! Small nondimensional constants.}} \DoxyCodeLine{1274 \textcolor{keywordtype}{integer} :: i, k} \DoxyCodeLine{1275 } \DoxyCodeLine{1276 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ddslay\_de) .and. .not.\textcolor{keyword}{present}(dslay)) \textcolor{keyword}{call }mom\_error(fatal, \&} \DoxyCodeLine{1277 \textcolor{stringliteral}{"{}In deterimine\_dSkb, ddSLay\_dE may only be present if dSlay is."{}})} \DoxyCodeLine{1278 } \DoxyCodeLine{1279 h\_neglect = gv\%H\_subroundoff} \DoxyCodeLine{1280 } \DoxyCodeLine{1281 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1282 ea(i,kmb+1) = e\_kb(i) ; dea\_de(i,kmb+1) = 1.0} \DoxyCodeLine{1283 s(i,kmb+1) = sref(i,kmb+1) ; ds\_de(i,kmb+1) = 0.0} \DoxyCodeLine{1284 b1(i,kmb+1) = 0.0} \DoxyCodeLine{1285 d1(i) = 1.0} \DoxyCodeLine{1286 do\_i(i) = .true.} \DoxyCodeLine{1287 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1288 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(do\_i\_in)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1289 \textcolor{keywordflow}{do} i=is,ie ; do\_i(i) = do\_i\_in(i) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1290 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1291 \textcolor{keywordflow}{do} k=kmb,1,-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1292 \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1293 \textcolor{comment}{! The do\_i test here is only for efficiency.}} \DoxyCodeLine{1294 \textcolor{comment}{! Determine the entrainment from below for each buffer layer.}} \DoxyCodeLine{1295 \textcolor{keywordflow}{if} (2.0*ent\_bl(i,k+1) > ea(i,k+1)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1296 eb(i,k) = 2.0*ent\_bl(i,k+1) -\/ ea(i,k+1) ; deb\_de(i,k) = -\/dea\_de(i,k+1)} \DoxyCodeLine{1297 \textcolor{keywordflow}{else}} \DoxyCodeLine{1298 eb(i,k) = 0.0 ; deb\_de(i,k) = 0.0} \DoxyCodeLine{1299 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1300 } \DoxyCodeLine{1301 \textcolor{comment}{! Determine the entrainment from above for each buffer layer.}} \DoxyCodeLine{1302 h1 = (h\_bl(i,k) -\/ gv\%Angstrom\_H) + (eb(i,k) -\/ ea(i,k+1))} \DoxyCodeLine{1303 \textcolor{keywordflow}{if} (h1 >= 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1304 ea(i,k) = ent\_bl(i,k) ; dea\_de(i,k) = 0.0} \DoxyCodeLine{1305 \textcolor{keywordflow}{elseif} (ent\_bl(i,k) + 0.5*h1 >= 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1306 ea(i,k) = ent\_bl(i,k) -\/ 0.5*h1} \DoxyCodeLine{1307 dea\_de(i,k) = 0.5*(dea\_de(i,k+1) -\/ deb\_de(i,k))} \DoxyCodeLine{1308 \textcolor{keywordflow}{else}} \DoxyCodeLine{1309 ea(i,k) = -\/h1} \DoxyCodeLine{1310 dea\_de(i,k) = dea\_de(i,k+1) -\/ deb\_de(i,k)} \DoxyCodeLine{1311 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1312 \textcolor{keywordflow}{else}} \DoxyCodeLine{1313 ea(i,k) = 0.0 ; dea\_de(i,k) = 0.0 ; eb(i,k) = 0.0 ; deb\_de(i,k) = 0.0} \DoxyCodeLine{1314 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1315 } \DoxyCodeLine{1316 \textcolor{comment}{! This is the first-\/pass of a tridiagonal solver for S.}} \DoxyCodeLine{1317 h\_tr = h\_bl(i,k) + h\_neglect} \DoxyCodeLine{1318 c1(i,k) = ea(i,k+1) * b1(i,k+1)} \DoxyCodeLine{1319 b\_denom\_1 = (h\_tr + d1(i)*eb(i,k))} \DoxyCodeLine{1320 b1(i,k) = 1.0 / (b\_denom\_1 + ea(i,k))} \DoxyCodeLine{1321 d1(i) = b\_denom\_1 * b1(i,k)} \DoxyCodeLine{1322 } \DoxyCodeLine{1323 s(i,k) = (h\_tr*sref(i,k) + eb(i,k)*s(i,k+1)) * b1(i,k)} \DoxyCodeLine{1324 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1325 \textcolor{keywordflow}{do} k=2,kmb ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1326 s(i,k) = s(i,k) + c1(i,k-\/1)*s(i,k-\/1)} \DoxyCodeLine{1327 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1328 } \DoxyCodeLine{1329 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ddskb\_de) .or. \textcolor{keyword}{present}(ddslay\_de)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1330 \textcolor{comment}{! These two tridiagonal solvers cannot be combined because the solutions for}} \DoxyCodeLine{1331 \textcolor{comment}{! S are required as a source for dS\_dE.}} \DoxyCodeLine{1332 \textcolor{keywordflow}{do} k=kmb,2,-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1333 \textcolor{keywordflow}{if} (do\_i(i) .and. (dea\_de(i,k) -\/ deb\_de(i,k) > 0.0)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1334 src = (((s(i,k+1) -\/ sref(i,k)) * (h\_bl(i,k) + h\_neglect) + \&} \DoxyCodeLine{1335 (s(i,k+1) -\/ s(i,k-\/1)) * ea(i,k)) * deb\_de(i,k) -\/ \&} \DoxyCodeLine{1336 ((sref(i,k) -\/ s(i,k-\/1)) * h\_bl(i,k) + \&} \DoxyCodeLine{1337 (s(i,k+1) -\/ s(i,k-\/1)) * eb(i,k)) * dea\_de(i,k)) / \&} \DoxyCodeLine{1338 ((h\_bl(i,k) + h\_neglect + ea(i,k)) + eb(i,k))} \DoxyCodeLine{1339 \textcolor{keywordflow}{else} ; src = 0.0 ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1340 ds\_de(i,k) = (src + eb(i,k)*ds\_de(i,k+1)) * b1(i,k)} \DoxyCodeLine{1341 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1342 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1343 \textcolor{keywordflow}{if} (do\_i(i) .and. (deb\_de(i,1) < 0.0)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1344 src = (((s(i,2) -\/ sref(i,1)) * (h\_bl(i,1) + h\_neglect)) * deb\_de(i,1)) / \&} \DoxyCodeLine{1345 (h\_bl(i,1) + h\_neglect + eb(i,1))} \DoxyCodeLine{1346 \textcolor{keywordflow}{else} ; src = 0.0 ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1347 ds\_de(i,1) = (src + eb(i,1)*ds\_de(i,2)) * b1(i,1)} \DoxyCodeLine{1348 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1349 \textcolor{keywordflow}{do} k=2,kmb ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1350 ds\_de(i,k) = ds\_de(i,k) + c1(i,k-\/1)*ds\_de(i,k-\/1)} \DoxyCodeLine{1351 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1352 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1353 } \DoxyCodeLine{1354 \textcolor{comment}{! Now, apply any limiting and return the requested variables.}} \DoxyCodeLine{1355 } \DoxyCodeLine{1356 eps\_dskb = 1.0e-\/6 \textcolor{comment}{! Should be a small, nondimensional, positive number.}} \DoxyCodeLine{1357 \textcolor{keywordflow}{if} (.not.limit) \textcolor{keywordflow}{then}} \DoxyCodeLine{1358 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1359 dskb(i) = sref(i,kmb+1) -\/ s(i,kmb)} \DoxyCodeLine{1360 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1361 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ddskb\_de)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1362 ddskb\_de(i) = -\/1.0*ds\_de(i,kmb)} \DoxyCodeLine{1363 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1364 } \DoxyCodeLine{1365 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(dslay)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1366 dslay(i) = 0.5 * (sref(i,kmb+2) -\/ s(i,kmb))} \DoxyCodeLine{1367 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1368 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ddslay\_de)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1369 ddslay\_de(i) = -\/0.5*ds\_de(i,kmb)} \DoxyCodeLine{1370 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1371 \textcolor{keywordflow}{else}} \DoxyCodeLine{1372 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1373 \textcolor{comment}{! Need to ensure that 0 < dSkb <= S\_kb -\/ Sbl}} \DoxyCodeLine{1374 \textcolor{keywordflow}{if} (sref(i,kmb+1) -\/ s(i,kmb) < eps\_dskb*(sref(i,kmb+2) -\/ sref(i,kmb+1))) \textcolor{keywordflow}{then}} \DoxyCodeLine{1375 dskb(i) = eps\_dskb * (sref(i,kmb+2) -\/ sref(i,kmb+1)) ; deriv\_dskb(i) = 0.0} \DoxyCodeLine{1376 \textcolor{keywordflow}{else}} \DoxyCodeLine{1377 dskb(i) = sref(i,kmb+1) -\/ s(i,kmb) ; deriv\_dskb(i) = -\/1.0} \DoxyCodeLine{1378 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1379 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ddskb\_de)) ddskb\_de(i) = deriv\_dskb(i)*ds\_de(i,kmb)} \DoxyCodeLine{1380 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1381 } \DoxyCodeLine{1382 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(dslay)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1383 dz\_drat = 1000.0 \textcolor{comment}{! The limit of large dz\_drat the same as choosing a}} \DoxyCodeLine{1384 \textcolor{comment}{! Heaviside function.}} \DoxyCodeLine{1385 eps\_dslay = 1.0e-\/10 \textcolor{comment}{! Should be \string~= GV\%Angstrom\_H / sqrt(Kd*dt)}} \DoxyCodeLine{1386 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1387 ds\_kbp1 = sref(i,kmb+2) -\/ sref(i,kmb+1)} \DoxyCodeLine{1388 ids\_kbp1 = 1.0 / (sref(i,kmb+2) -\/ sref(i,kmb+1))} \DoxyCodeLine{1389 rat = (sref(i,kmb+1) -\/ s(i,kmb)) * ids\_kbp1} \DoxyCodeLine{1390 \textcolor{comment}{! Need to ensure that 0 < dSLay <= 2*dSkb}} \DoxyCodeLine{1391 \textcolor{keywordflow}{if} (rat < 0.5) \textcolor{keywordflow}{then}} \DoxyCodeLine{1392 \textcolor{comment}{! The coefficients here are chosen so that at rat = 0.5, the value (1.5)}} \DoxyCodeLine{1393 \textcolor{comment}{! and first derivative (-\/0.5) match with the "{}typical"{} case (next).}} \DoxyCodeLine{1394 \textcolor{comment}{! The functional form here is arbitrary.}} \DoxyCodeLine{1395 \textcolor{comment}{! f1 provides a reasonable profile that matches the value and derivative}} \DoxyCodeLine{1396 \textcolor{comment}{! of the "{}typical"{} case at rat = 0.5, and has a maximum of less than 2.}} \DoxyCodeLine{1397 inv\_term = 1.0 / (1.0-\/rat)} \DoxyCodeLine{1398 f1 = 2.0 -\/ 0.125*(inv\_term**2)} \DoxyCodeLine{1399 df1\_drat = -\/ 0.25*(inv\_term**3)} \DoxyCodeLine{1400 } \DoxyCodeLine{1401 \textcolor{comment}{! f2 ensures that dSLay goes to 0 rapidly if rat is significantly}} \DoxyCodeLine{1402 \textcolor{comment}{! negative.}} \DoxyCodeLine{1403 z = dz\_drat * rat + 4.0 \textcolor{comment}{! The 4 here gives f2(0) = 0.982.}} \DoxyCodeLine{1404 \textcolor{keywordflow}{if} (z >= 18.0) \textcolor{keywordflow}{then} ; f2 = 1.0 ; df2\_dz = 0.0} \DoxyCodeLine{1405 \textcolor{keywordflow}{elseif} (z <= -\/58.0) \textcolor{keywordflow}{then} ; f2 = eps\_dslay ; df2\_dz = 0.0} \DoxyCodeLine{1406 \textcolor{keywordflow}{else}} \DoxyCodeLine{1407 expz = exp(z) ; inv\_term = 1.0 / (1.0 + expz)} \DoxyCodeLine{1408 f2 = (eps\_dslay + expz) * inv\_term} \DoxyCodeLine{1409 df2\_dz = (1.0 -\/ eps\_dslay) * expz * inv\_term**2} \DoxyCodeLine{1410 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1411 } \DoxyCodeLine{1412 dslay(i) = dskb(i) * f1 * f2} \DoxyCodeLine{1413 deriv\_dslay = deriv\_dskb(i) * (f1 * f2) -\/ (dskb(i)*ids\_kbp1) * \&} \DoxyCodeLine{1414 (df1\_drat*f2 + f1 * dz\_drat * df2\_dz)} \DoxyCodeLine{1415 \textcolor{keywordflow}{elseif} (dskb(i) <= 3.0*ds\_kbp1) \textcolor{keywordflow}{then}} \DoxyCodeLine{1416 \textcolor{comment}{! This is the "{}typical"{} case.}} \DoxyCodeLine{1417 dslay(i) = 0.5 * (dskb(i) + ds\_kbp1)} \DoxyCodeLine{1418 deriv\_dslay = 0.5 * deriv\_dskb(i) \textcolor{comment}{! = -\/0.5}} \DoxyCodeLine{1419 \textcolor{keywordflow}{else}} \DoxyCodeLine{1420 dslay(i) = 2.0*ds\_kbp1} \DoxyCodeLine{1421 deriv\_dslay = 0.0} \DoxyCodeLine{1422 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1423 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ddslay\_de)) ddslay\_de(i) = deriv\_dslay*ds\_de(i,kmb)} \DoxyCodeLine{1424 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1425 \textcolor{keywordflow}{ endif} \textcolor{comment}{! present(dSlay)}} \DoxyCodeLine{1426 \textcolor{keywordflow}{ endif} \textcolor{comment}{! Not limited.}} \DoxyCodeLine{1427 } \DoxyCodeLine{1428 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ds\_anom\_lim)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1429 ds\_anom\_lim(i) = max(0.0, eps\_dskb * (sref(i,kmb+2) -\/ sref(i,kmb+1)) -\/ \&} \DoxyCodeLine{1430 (sref(i,kmb+1) -\/ s(i,kmb)) )} \DoxyCodeLine{1431 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1432 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__entrain__diffusive_a541b3aadc418110f7359b0ae401e4e78}\label{namespacemom__entrain__diffusive_a541b3aadc418110f7359b0ae401e4e78}} \index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}!determine\_ea\_kb@{determine\_ea\_kb}} \index{determine\_ea\_kb@{determine\_ea\_kb}!mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsubsection{\texorpdfstring{determine\_ea\_kb()}{determine\_ea\_kb()}} {\footnotesize\ttfamily subroutine mom\+\_\+entrain\+\_\+diffusive\+::determine\+\_\+ea\+\_\+kb (\begin{DoxyParamCaption}\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{h\+\_\+bl, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{dt\+Kd\+\_\+kb, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{Sref, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{I\+\_\+d\+Skbp1, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{Ent\+\_\+bl, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{ea\+\_\+kbp1, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{min\+\_\+eakb, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{max\+\_\+eakb, }\item[{integer, intent(in)}]{kmb, }\item[{integer, intent(in)}]{is, }\item[{integer, intent(in)}]{ie, }\item[{logical, dimension(szi\+\_\+(g)), intent(in)}]{do\+\_\+i, }\item[{type(\mbox{\hyperlink{structmom__grid_1_1ocean__grid__type}{ocean\+\_\+grid\+\_\+type}}), intent(in)}]{G, }\item[{type(\mbox{\hyperlink{structmom__verticalgrid_1_1verticalgrid__type}{verticalgrid\+\_\+type}}), intent(in)}]{GV, }\item[{type(\mbox{\hyperlink{structmom__entrain__diffusive_1_1entrain__diffusive__cs}{entrain\+\_\+diffusive\+\_\+cs}}), pointer}]{CS, }\item[{real, dimension( g \%isd\+: g \%ied), intent(inout)}]{Ent, }\item[{real, dimension( g \%isd\+: g \%ied), intent(out), optional}]{error, }\item[{real, dimension( g \%isd\+: g \%ied), intent(in), optional}]{err\+\_\+min\+\_\+eakb0, }\item[{real, dimension( g \%isd\+: g \%ied), intent(in), optional}]{err\+\_\+max\+\_\+eakb0, }\item[{real, dimension( g \%isd\+: g \%ied), intent(out), optional}]{F\+\_\+kb, }\item[{real, dimension( g \%isd\+: g \%ied), intent(out), optional}]{d\+Fdfm\+\_\+kb }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine determines the entrainment from above by the top interior layer (labeled kb elsewhere) given an entrainment by the layer below it, constrained to be within the provided bounds. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em g} & The ocean\textquotesingle{}s grid structure. \\ \hline \mbox{\texttt{ in}} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure. \\ \hline \mbox{\texttt{ in}} & {\em h\+\_\+bl} & Layer thickness, with the top interior layer at k-\/index kmb+1 \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em sref} & The coordinate reference potential density, with the value of the topmost interior layer at layer kmb+1 \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em ent\+\_\+bl} & The average entrainment upward and downward across each interface around the buffer layers \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em i\+\_\+dskbp1} & The inverse of the difference in reference potential density across the base of the uppermost interior layer \mbox{[}R-\/1 $\sim$$>$ m3 kg-\/1\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em dtkd\+\_\+kb} & The diapycnal diffusivity in the top interior layer times the time step \mbox{[}H2 $\sim$$>$ m2 or kg2 m-\/4\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em ea\+\_\+kbp1} & The entrainment from above by layer kb+1 \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em min\+\_\+eakb} & The minimum permissible rate of entrainment \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em max\+\_\+eakb} & The maximum permissible rate of entrainment \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em kmb} & The number of mixed and buffer layers. \\ \hline \mbox{\texttt{ in}} & {\em is} & The start of the i-\/index range to work on. \\ \hline \mbox{\texttt{ in}} & {\em ie} & The end of the i-\/index range to work on. \\ \hline \mbox{\texttt{ in}} & {\em do\+\_\+i} & A logical variable indicating which i-\/points to work on. \\ \hline & {\em cs} & This module\textquotesingle{}s control structure. \\ \hline \mbox{\texttt{ in,out}} & {\em ent} & The entrainment rate of the uppermost interior layer \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. The input value is the first guess. \\ \hline \mbox{\texttt{ out}} & {\em error} & The error (locally defined in this routine) associated with the returned solution. \\ \hline \mbox{\texttt{ in}} & {\em err\+\_\+min\+\_\+eakb0} & The errors (locally defined) associated with min\+\_\+eakb when ea\+\_\+kbp1 = 0, returned from a previous call to this fn. \\ \hline \mbox{\texttt{ in}} & {\em err\+\_\+max\+\_\+eakb0} & The errors (locally defined) associated with min\+\_\+eakb when ea\+\_\+kbp1 = 0, returned from a previous call to this fn. \\ \hline \mbox{\texttt{ out}} & {\em f\+\_\+kb} & The entrainment from below by the uppermost interior layer corresponding to the returned value of Ent \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ out}} & {\em dfdfm\+\_\+kb} & The partial derivative of F\+\_\+kb with ea\+\_\+kbp1 \mbox{[}nondim\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 1571 of file M\+O\+M\+\_\+entrain\+\_\+diffusive.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1574 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure.}} \DoxyCodeLine{1575 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid structure.}} \DoxyCodeLine{1576 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: h\_bl\textcolor{comment}{ !< Layer thickness, with the top interior}} \DoxyCodeLine{1577 \textcolor{comment}{ !! layer at k-\/index kmb+1 [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1578 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: Sref\textcolor{comment}{ !< The coordinate reference potential}} \DoxyCodeLine{1579 \textcolor{comment}{ !! density, with the value of the}} \DoxyCodeLine{1580 \textcolor{comment}{ !! topmost interior layer at layer}} \DoxyCodeLine{1581 \textcolor{comment}{ !! kmb+1 [R \string~> kg m-\/3].}} \DoxyCodeLine{1582 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: Ent\_bl\textcolor{comment}{ !< The average entrainment upward and}} \DoxyCodeLine{1583 \textcolor{comment}{ !! downward across each interface around}} \DoxyCodeLine{1584 \textcolor{comment}{ !! the buffer layers [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1585 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: I\_dSkbp1\textcolor{comment}{ !< The inverse of the difference in}} \DoxyCodeLine{1586 \textcolor{comment}{ !! reference potential density across}} \DoxyCodeLine{1587 \textcolor{comment}{ !! the base of the uppermost interior}} \DoxyCodeLine{1588 \textcolor{comment}{ !! layer [R-\/1 \string~> m3 kg-\/1].}} \DoxyCodeLine{1589 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: dtKd\_kb\textcolor{comment}{ !< The diapycnal diffusivity in the top}} \DoxyCodeLine{1590 \textcolor{comment}{ !! interior layer times the time step}} \DoxyCodeLine{1591 \textcolor{comment}{ !! [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{1592 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: ea\_kbp1\textcolor{comment}{ !< The entrainment from above by layer}} \DoxyCodeLine{1593 \textcolor{comment}{ !! kb+1 [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1594 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: min\_eakb\textcolor{comment}{ !< The minimum permissible rate of}} \DoxyCodeLine{1595 \textcolor{comment}{ !! entrainment [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1596 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: max\_eakb\textcolor{comment}{ !< The maximum permissible rate of}} \DoxyCodeLine{1597 \textcolor{comment}{ !! entrainment [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1598 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: kmb\textcolor{comment}{ !< The number of mixed and buffer layers.}} \DoxyCodeLine{1599 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: is\textcolor{comment}{ !< The start of the i-\/index range to work on.}} \DoxyCodeLine{1600 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: ie\textcolor{comment}{ !< The end of the i-\/index range to work on.}} \DoxyCodeLine{1601 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: do\_i\textcolor{comment}{ !< A logical variable indicating which}} \DoxyCodeLine{1602 \textcolor{comment}{ !! i-\/points to work on.}} \DoxyCodeLine{1603 \textcolor{keywordtype}{type}(entrain\_diffusive\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< This module's control structure.}} \DoxyCodeLine{1604 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(inout)} :: Ent\textcolor{comment}{ !< The entrainment rate of the uppermost}} \DoxyCodeLine{1605 \textcolor{comment}{ !! interior layer [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1606 \textcolor{comment}{ !! The input value is the first guess.}} \DoxyCodeLine{1607 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: error\textcolor{comment}{ !< The error (locally defined in this}} \DoxyCodeLine{1608 \textcolor{comment}{ !! routine) associated with the returned}} \DoxyCodeLine{1609 \textcolor{comment}{ !! solution.}} \DoxyCodeLine{1610 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: err\_min\_eakb0\textcolor{comment}{ !< The errors (locally defined)}} \DoxyCodeLine{1611 \textcolor{comment}{ !! associated with min\_eakb when ea\_kbp1 = 0,}} \DoxyCodeLine{1612 \textcolor{comment}{ !! returned from a previous call to this fn.}} \DoxyCodeLine{1613 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: err\_max\_eakb0\textcolor{comment}{ !< The errors (locally defined)}} \DoxyCodeLine{1614 \textcolor{comment}{ !! associated with min\_eakb when ea\_kbp1 = 0,}} \DoxyCodeLine{1615 \textcolor{comment}{ !! returned from a previous call to this fn.}} \DoxyCodeLine{1616 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: F\_kb\textcolor{comment}{ !< The entrainment from below by the}} \DoxyCodeLine{1617 \textcolor{comment}{ !! uppermost interior layer}} \DoxyCodeLine{1618 \textcolor{comment}{ !! corresponding to the returned}} \DoxyCodeLine{1619 \textcolor{comment}{ !! value of Ent [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1620 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: dFdfm\_kb\textcolor{comment}{ !< The partial derivative of F\_kb with}} \DoxyCodeLine{1621 \textcolor{comment}{ !! ea\_kbp1 [nondim].}} \DoxyCodeLine{1622 } \DoxyCodeLine{1623 \textcolor{comment}{! This subroutine determines the entrainment from above by the top interior}} \DoxyCodeLine{1624 \textcolor{comment}{! layer (labeled kb elsewhere) given an entrainment by the layer below it,}} \DoxyCodeLine{1625 \textcolor{comment}{! constrained to be within the provided bounds.}} \DoxyCodeLine{1626 } \DoxyCodeLine{1627 \textcolor{comment}{! Local variables}} \DoxyCodeLine{1628 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: \&} \DoxyCodeLine{1629 dS\_kb, \& \textcolor{comment}{! The coordinate-\/density difference between the}} \DoxyCodeLine{1630 \textcolor{comment}{! layer kb and deepest buffer layer, limited to}} \DoxyCodeLine{1631 \textcolor{comment}{! ensure that it is positive [R \string~> kg m-\/3].}} \DoxyCodeLine{1632 ds\_lay, \& \textcolor{comment}{! The coordinate-\/density difference across layer}} \DoxyCodeLine{1633 \textcolor{comment}{! kb, limited to ensure that it is positive and not}} \DoxyCodeLine{1634 \textcolor{comment}{! too much bigger than dS\_kb or dS\_kbp1 [R \string~> kg m-\/3].}} \DoxyCodeLine{1635 ddskb\_de, ddslay\_de, \& \textcolor{comment}{! The derivatives of dS\_kb and dS\_Lay with E}} \DoxyCodeLine{1636 \textcolor{comment}{! [R H-\/1 \string~> kg m-\/4 or m-\/1].}} \DoxyCodeLine{1637 derror\_de, \& \textcolor{comment}{! The derivative of err with E [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1638 err, \& \textcolor{comment}{! The "{}error"{} whose zero is being sought [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{1639 e\_min, e\_max, \& \textcolor{comment}{! The minimum and maximum values of E [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1640 error\_mine, error\_maxe \textcolor{comment}{! err when E = E\_min or E = E\_max [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{1641 \textcolor{keywordtype}{ real} :: err\_est \textcolor{comment}{! An estimate of what err will be [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{1642 \textcolor{keywordtype}{ real} :: eL \textcolor{comment}{! 1 or 0, depending on whether increases in E lead}} \DoxyCodeLine{1643 \textcolor{comment}{! to decreases in the entrainment from below by the}} \DoxyCodeLine{1644 \textcolor{comment}{! deepest buffer layer [nondim].}} \DoxyCodeLine{1645 \textcolor{keywordtype}{ real} :: fa \textcolor{comment}{! Temporary variable used to calculate err [nondim].}} \DoxyCodeLine{1646 \textcolor{keywordtype}{ real} :: fk \textcolor{comment}{! Temporary variable used to calculate err [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{1647 \textcolor{keywordtype}{ real} :: fm, fr \textcolor{comment}{! Temporary variables used to calculate err [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1648 \textcolor{keywordtype}{ real} :: tolerance \textcolor{comment}{! The tolerance within which E must be converged [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1649 \textcolor{keywordtype}{ real} :: E\_prev \textcolor{comment}{! The previous value of E [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1650 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: false\_position \textcolor{comment}{! If true, the false position}} \DoxyCodeLine{1651 \textcolor{comment}{! method might be used for the next iteration.}} \DoxyCodeLine{1652 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: redo\_i \textcolor{comment}{! If true, more work is needed on this column.}} \DoxyCodeLine{1653 \textcolor{keywordtype}{logical} :: do\_any} \DoxyCodeLine{1654 \textcolor{keywordtype}{ real} :: large\_err \textcolor{comment}{! A large error measure [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{1655 \textcolor{keywordtype}{integer} :: i, it} \DoxyCodeLine{1656 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{parameter} :: MAXIT = 30} \DoxyCodeLine{1657 } \DoxyCodeLine{1658 \textcolor{keywordflow}{if} (.not.cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{1659 \textcolor{keyword}{call }mom\_error(fatal, \textcolor{stringliteral}{"{}determine\_Ea\_kb should not be called "{}}//\&} \DoxyCodeLine{1660 \textcolor{stringliteral}{"{}unless BULKMIXEDLAYER is defined."{}})} \DoxyCodeLine{1661 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1662 tolerance = cs\%Tolerance\_Ent} \DoxyCodeLine{1663 large\_err = gv\%m\_to\_H**2 * 1.0e30} \DoxyCodeLine{1664 } \DoxyCodeLine{1665 \textcolor{keywordflow}{do} i=is,ie ; redo\_i(i) = do\_i(i) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1666 } \DoxyCodeLine{1667 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1668 \textcolor{comment}{! The first guess of Ent was the value from the previous iteration.}} \DoxyCodeLine{1669 } \DoxyCodeLine{1670 \textcolor{comment}{! These were previously calculated and provide good limits and estimates}} \DoxyCodeLine{1671 \textcolor{comment}{! of the errors there. By construction the errors increase with R*ea\_kbp1.}} \DoxyCodeLine{1672 e\_min(i) = min\_eakb(i) ; e\_max(i) = max\_eakb(i)} \DoxyCodeLine{1673 error\_mine(i) = -\/large\_err ; error\_maxe(i) = large\_err} \DoxyCodeLine{1674 false\_position(i) = .true. \textcolor{comment}{! Used to alternate between false\_position and}} \DoxyCodeLine{1675 \textcolor{comment}{! bisection when Newton's method isn't working.}} \DoxyCodeLine{1676 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(err\_min\_eakb0)) error\_mine(i) = err\_min\_eakb0(i) -\/ e\_min(i) * ea\_kbp1(i)} \DoxyCodeLine{1677 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(err\_max\_eakb0)) error\_maxe(i) = err\_max\_eakb0(i) -\/ e\_max(i) * ea\_kbp1(i)} \DoxyCodeLine{1678 } \DoxyCodeLine{1679 \textcolor{keywordflow}{if} ((error\_maxe(i) <= 0.0) .or. (error\_mine(i) >= 0.0)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1680 \textcolor{comment}{! The root is not bracketed and one of the limiting values should be used.}} \DoxyCodeLine{1681 \textcolor{keywordflow}{if} (error\_maxe(i) <= 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1682 \textcolor{comment}{! The errors decrease with E*ea\_kbp1, so E\_max is the best solution.}} \DoxyCodeLine{1683 ent(i) = e\_max(i) ; err(i) = error\_maxe(i)} \DoxyCodeLine{1684 \textcolor{keywordflow}{else} \textcolor{comment}{! error\_minE >= 0 is equivalent to ea\_kbp1 = 0.0.}} \DoxyCodeLine{1685 ent(i) = e\_min(i) ; err(i) = error\_mine(i)} \DoxyCodeLine{1686 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1687 derror\_de(i) = 0.0} \DoxyCodeLine{1688 redo\_i(i) = .false.} \DoxyCodeLine{1689 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1690 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} \textcolor{comment}{! End of i-\/loop}} \DoxyCodeLine{1691 } \DoxyCodeLine{1692 \textcolor{keywordflow}{do} it = 1,maxit} \DoxyCodeLine{1693 do\_any = .false. ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (redo\_i(i)) do\_any = .true. ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1694 \textcolor{keywordflow}{if} (.not.do\_any) \textcolor{keywordflow}{exit}} \DoxyCodeLine{1695 \textcolor{keyword}{call }determine\_dskb(h\_bl, sref, ent\_bl, ent, is, ie, kmb, g, gv, .true., ds\_kb, \&} \DoxyCodeLine{1696 ddskb\_de, ds\_lay, ddslay\_de, do\_i\_in = redo\_i)} \DoxyCodeLine{1697 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (redo\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1698 \textcolor{comment}{! The correct root is bracketed between E\_min and E\_max.}} \DoxyCodeLine{1699 \textcolor{comment}{! Note the following limits: Ent >= 0 ; fa > 1 ; fk > 0}} \DoxyCodeLine{1700 el = 0.0 ; \textcolor{keywordflow}{if} (2.0*ent\_bl(i,kmb+1) >= ent(i)) el = 1.0} \DoxyCodeLine{1701 fa = (1.0 + el) + ds\_kb(i)*i\_dskbp1(i)} \DoxyCodeLine{1702 fk = dtkd\_kb(i) * (ds\_lay(i)/ds\_kb(i))} \DoxyCodeLine{1703 fm = (ea\_kbp1(i) -\/ h\_bl(i,kmb+1)) + el*2.0*ent\_bl(i,kmb+1)} \DoxyCodeLine{1704 \textcolor{keywordflow}{if} (fm > -\/gv\%Angstrom\_H) fm = fm + gv\%Angstrom\_H \textcolor{comment}{! This could be smooth if need be.}} \DoxyCodeLine{1705 err(i) = (fa * ent(i)**2 -\/ fm * ent(i)) -\/ fk} \DoxyCodeLine{1706 derror\_de(i) = ((2.0*fa + (ddskb\_de(i)*i\_dskbp1(i))*ent(i))*ent(i) -\/ fm) -\/ \&} \DoxyCodeLine{1707 dtkd\_kb(i) * (ddslay\_de(i)*ds\_kb(i) -\/ ddskb\_de(i)*ds\_lay(i))/(ds\_kb(i)**2)} \DoxyCodeLine{1708 } \DoxyCodeLine{1709 \textcolor{keywordflow}{if} (err(i) == 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1710 redo\_i(i) = .false. ; cycle} \DoxyCodeLine{1711 \textcolor{keywordflow}{elseif} (err(i) > 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1712 e\_max(i) = ent(i) ; error\_maxe(i) = err(i)} \DoxyCodeLine{1713 \textcolor{keywordflow}{else}} \DoxyCodeLine{1714 e\_min(i) = ent(i) ; error\_mine(i) = err(i)} \DoxyCodeLine{1715 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1716 } \DoxyCodeLine{1717 e\_prev = ent(i)} \DoxyCodeLine{1718 \textcolor{keywordflow}{if} ((it == 1) .or. (derror\_de(i) <= 0.0)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1719 \textcolor{comment}{! Assuming that the coefficients of the quadratic equation are correct}} \DoxyCodeLine{1720 \textcolor{comment}{! will usually give a very good first guess. Also, if derror\_dE < 0.0,}} \DoxyCodeLine{1721 \textcolor{comment}{! R is on the wrong side of the approximate parabola. In either case,}} \DoxyCodeLine{1722 \textcolor{comment}{! try assuming that the error is approximately a parabola and solve.}} \DoxyCodeLine{1723 fr = sqrt(fm**2 + 4.0*fa*fk)} \DoxyCodeLine{1724 \textcolor{keywordflow}{if} (fm >= 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1725 ent(i) = (fm + fr) / (2.0 * fa)} \DoxyCodeLine{1726 \textcolor{keywordflow}{else}} \DoxyCodeLine{1727 ent(i) = (2.0 * fk) / (fr -\/ fm)} \DoxyCodeLine{1728 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1729 \textcolor{comment}{! But make sure that the root stays bracketed, bisecting if needed.}} \DoxyCodeLine{1730 \textcolor{keywordflow}{if} ((ent(i) > e\_max(i)) .or. (ent(i) < e\_min(i))) \&} \DoxyCodeLine{1731 ent(i) = 0.5*(e\_max(i) + e\_min(i))} \DoxyCodeLine{1732 \textcolor{keywordflow}{elseif} (((e\_max(i)-\/ent(i))*derror\_de(i) > -\/err(i)) .and. \&} \DoxyCodeLine{1733 ((ent(i)-\/e\_min(i))*derror\_de(i) > err(i)) ) \textcolor{keywordflow}{then}} \DoxyCodeLine{1734 \textcolor{comment}{! Use Newton's method for the next estimate, provided it will}} \DoxyCodeLine{1735 \textcolor{comment}{! remain bracketed between Rmin and Rmax.}} \DoxyCodeLine{1736 ent(i) = ent(i) -\/ err(i) / derror\_de(i)} \DoxyCodeLine{1737 \textcolor{keywordflow}{elseif} (false\_position(i) .and. \&} \DoxyCodeLine{1738 (error\_maxe(i) -\/ error\_mine(i) < 0.9*large\_err)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1739 \textcolor{comment}{! Use the false postion method if there are decent error estimates.}} \DoxyCodeLine{1740 ent(i) = e\_min(i) + (e\_max(i)-\/e\_min(i)) * \&} \DoxyCodeLine{1741 (-\/error\_mine(i)/(error\_maxe(i) -\/ error\_mine(i)))} \DoxyCodeLine{1742 false\_position(i) = .false.} \DoxyCodeLine{1743 \textcolor{keywordflow}{else} \textcolor{comment}{! Bisect as a last resort or if the false position method was used last.}} \DoxyCodeLine{1744 ent(i) = 0.5*(e\_max(i) + e\_min(i))} \DoxyCodeLine{1745 false\_position(i) = .true.} \DoxyCodeLine{1746 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1747 } \DoxyCodeLine{1748 \textcolor{keywordflow}{if} (abs(e\_prev -\/ ent(i)) < tolerance) \textcolor{keywordflow}{then}} \DoxyCodeLine{1749 err\_est = err(i) + (ent(i) -\/ e\_prev) * derror\_de(i)} \DoxyCodeLine{1750 \textcolor{keywordflow}{if} ((it > 1) .or. (err\_est*err(i) <= 0.0) .or. \&} \DoxyCodeLine{1751 (abs(err\_est) < abs(tolerance*derror\_de(i)))) redo\_i(i) = .false.} \DoxyCodeLine{1752 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1753 } \DoxyCodeLine{1754 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} \textcolor{comment}{! End of i-\/loop}} \DoxyCodeLine{1755 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! End of iterations to determine Ent(i).}} \DoxyCodeLine{1756 } \DoxyCodeLine{1757 \textcolor{comment}{! Update the value of dS\_kb for consistency with Ent.}} \DoxyCodeLine{1758 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(f\_kb) .or. \textcolor{keyword}{present}(dfdfm\_kb)) \&} \DoxyCodeLine{1759 \textcolor{keyword}{call }determine\_dskb(h\_bl, sref, ent\_bl, ent, is, ie, kmb, g, gv, .true., \&} \DoxyCodeLine{1760 ds\_kb, do\_i\_in = do\_i)} \DoxyCodeLine{1761 } \DoxyCodeLine{1762 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(f\_kb)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1763 f\_kb(i) = ent(i) * (ds\_kb(i) * i\_dskbp1(i))} \DoxyCodeLine{1764 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1765 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(error)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1766 error(i) = err(i)} \DoxyCodeLine{1767 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1768 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(dfdfm\_kb)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1769 \textcolor{comment}{! derror\_dE and ddSkb\_dE are \_not\_ recalculated here, since dFdfm\_kb is}} \DoxyCodeLine{1770 \textcolor{comment}{! only used in Newton's method, and slightly increasing the accuracy of the}} \DoxyCodeLine{1771 \textcolor{comment}{! estimate is unlikely to speed convergence.}} \DoxyCodeLine{1772 \textcolor{keywordflow}{if} (derror\_de(i) > 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1773 dfdfm\_kb(i) = ((ds\_kb(i) + ent(i) * ddskb\_de(i)) * i\_dskbp1(i)) * \&} \DoxyCodeLine{1774 (ent(i) / derror\_de(i))} \DoxyCodeLine{1775 \textcolor{keywordflow}{else} \textcolor{comment}{! Use Adcroft's division by 0 convention.}} \DoxyCodeLine{1776 dfdfm\_kb(i) = 0.0} \DoxyCodeLine{1777 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1778 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1779 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__entrain__diffusive_a0e71b47abe1e1889f4b687139615ca14}\label{namespacemom__entrain__diffusive_a0e71b47abe1e1889f4b687139615ca14}} \index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}!entrain\_diffusive\_end@{entrain\_diffusive\_end}} \index{entrain\_diffusive\_end@{entrain\_diffusive\_end}!mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsubsection{\texorpdfstring{entrain\_diffusive\_end()}{entrain\_diffusive\_end()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+entrain\+\_\+diffusive\+::entrain\+\_\+diffusive\+\_\+end (\begin{DoxyParamCaption}\item[{type(\mbox{\hyperlink{structmom__entrain__diffusive_1_1entrain__diffusive__cs}{entrain\+\_\+diffusive\+\_\+cs}}), pointer}]{CS }\end{DoxyParamCaption})} This subroutine cleans up and deallocates any memory associated with the entrain\+\_\+diffusive module. \begin{DoxyParams}{Parameters} {\em cs} & A pointer to the control structure for this module that will be deallocated. \\ \hline \end{DoxyParams} Definition at line 2147 of file M\+O\+M\+\_\+entrain\+\_\+diffusive.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{2148 \textcolor{keywordtype}{type}(entrain\_diffusive\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< A pointer to the control structure for this}} \DoxyCodeLine{2149 \textcolor{comment}{ !! module that will be deallocated.}} \DoxyCodeLine{2150 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(cs)) \textcolor{keyword}{deallocate}(cs)} \DoxyCodeLine{2151 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__entrain__diffusive_a08d3203366fac7ec13472c79681dea0e}\label{namespacemom__entrain__diffusive_a08d3203366fac7ec13472c79681dea0e}} \index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}!entrain\_diffusive\_init@{entrain\_diffusive\_init}} \index{entrain\_diffusive\_init@{entrain\_diffusive\_init}!mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsubsection{\texorpdfstring{entrain\_diffusive\_init()}{entrain\_diffusive\_init()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+entrain\+\_\+diffusive\+::entrain\+\_\+diffusive\+\_\+init (\begin{DoxyParamCaption}\item[{type(time\+\_\+type), intent(in)}]{Time, }\item[{type(\mbox{\hyperlink{structmom__grid_1_1ocean__grid__type}{ocean\+\_\+grid\+\_\+type}}), intent(in)}]{G, }\item[{type(\mbox{\hyperlink{structmom__verticalgrid_1_1verticalgrid__type}{verticalgrid\+\_\+type}}), intent(in)}]{GV, }\item[{type(\mbox{\hyperlink{structmom__unit__scaling_1_1unit__scale__type}{unit\+\_\+scale\+\_\+type}}), intent(in)}]{US, }\item[{type(\mbox{\hyperlink{structmom__file__parser_1_1param__file__type}{param\+\_\+file\+\_\+type}}), intent(in)}]{param\+\_\+file, }\item[{type(\mbox{\hyperlink{structmom__diag__mediator_1_1diag__ctrl}{diag\+\_\+ctrl}}), intent(inout), target}]{diag, }\item[{type(\mbox{\hyperlink{structmom__entrain__diffusive_1_1entrain__diffusive__cs}{entrain\+\_\+diffusive\+\_\+cs}}), pointer}]{CS, }\item[{logical, intent(in), optional}]{just\+\_\+read\+\_\+params }\end{DoxyParamCaption})} This subroutine initializes the parameters and memory associated with the entrain\+\_\+diffusive module. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em time} & The current model time. \\ \hline \mbox{\texttt{ in}} & {\em g} & The ocean\textquotesingle{}s grid structure. \\ \hline \mbox{\texttt{ in}} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure. \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ in}} & {\em param\+\_\+file} & A structure to parse for run-\/time parameters. \\ \hline \mbox{\texttt{ in,out}} & {\em diag} & A structure that is used to regulate diagnostic output. \\ \hline & {\em cs} & A pointer that is set to point to the control structure. \\ \hline \mbox{\texttt{ in}} & {\em just\+\_\+read\+\_\+params} & If present and true, this call will only read parameters logging them or registering any diagnostics \\ \hline \end{DoxyParams} Definition at line 2080 of file M\+O\+M\+\_\+entrain\+\_\+diffusive.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{2081 \textcolor{keywordtype}{type}(time\_type), \textcolor{keywordtype}{intent(in)} :: Time\textcolor{comment}{ !< The current model time.}} \DoxyCodeLine{2082 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure.}} \DoxyCodeLine{2083 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid structure.}} \DoxyCodeLine{2084 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{2085 \textcolor{keywordtype}{type}(param\_file\_type), \textcolor{keywordtype}{intent(in)} :: param\_file\textcolor{comment}{ !< A structure to parse for run-\/time}} \DoxyCodeLine{2086 \textcolor{comment}{ !! parameters.}} \DoxyCodeLine{2087 \textcolor{keywordtype}{type}(diag\_ctrl), \textcolor{keywordtype}{target}, \textcolor{keywordtype}{intent(inout)} :: diag\textcolor{comment}{ !< A structure that is used to regulate diagnostic}} \DoxyCodeLine{2088 \textcolor{comment}{ !! output.}} \DoxyCodeLine{2089 \textcolor{keywordtype}{type}(entrain\_diffusive\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< A pointer that is set to point to the control}} \DoxyCodeLine{2090 \textcolor{comment}{ !! structure.}} \DoxyCodeLine{2091 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: just\_read\_params\textcolor{comment}{ !< If present and true, this call will}} \DoxyCodeLine{2092 \textcolor{comment}{ !! only read parameters logging them or registering}} \DoxyCodeLine{2093 \textcolor{comment}{ !! any diagnostics}} \DoxyCodeLine{2094 } \DoxyCodeLine{2095 \textcolor{comment}{! Local variables}} \DoxyCodeLine{2096 \textcolor{keywordtype}{ real} :: dt \textcolor{comment}{! The dynamics timestep, used here in the default for TOLERANCE\_ENT, in MKS units [s]}} \DoxyCodeLine{2097 \textcolor{keywordtype}{ real} :: Kd \textcolor{comment}{! A diffusivity used in the default for TOLERANCE\_ENT, in MKS units [m2 s-\/1]}} \DoxyCodeLine{2098 \textcolor{keywordtype}{logical} :: just\_read \textcolor{comment}{! If true, just read parameters but do nothing else.}} \DoxyCodeLine{2099 \textcolor{comment}{! This include declares and sets the variable "{}version"{}.}} \DoxyCodeLine{2100 \textcolor{preprocessor}{\# include "{}version\_variable.h"{}}} \DoxyCodeLine{2101 \textcolor{preprocessor}{} \textcolor{keywordtype}{character(len=40)} :: mdl = \textcolor{stringliteral}{"{}MOM\_entrain\_diffusive"{}} \textcolor{comment}{! This module's name.}} \DoxyCodeLine{2102 } \DoxyCodeLine{2103 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(cs)) \textcolor{keywordflow}{then}} \DoxyCodeLine{2104 \textcolor{keyword}{call }mom\_error(warning, \textcolor{stringliteral}{"{}entrain\_diffusive\_init called with an associated "{}}// \&} \DoxyCodeLine{2105 \textcolor{stringliteral}{"{}control structure."{}})} \DoxyCodeLine{2106 \textcolor{keywordflow}{return}} \DoxyCodeLine{2107 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2108 \textcolor{keyword}{allocate}(cs)} \DoxyCodeLine{2109 } \DoxyCodeLine{2110 just\_read = .false. ; \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(just\_read\_params)) just\_read = just\_read\_params} \DoxyCodeLine{2111 } \DoxyCodeLine{2112 cs\%diag => diag} \DoxyCodeLine{2113 } \DoxyCodeLine{2114 cs\%bulkmixedlayer = (gv\%nkml > 0)} \DoxyCodeLine{2115 } \DoxyCodeLine{2116 \textcolor{comment}{! Set default, read and log parameters}} \DoxyCodeLine{2117 \textcolor{keywordflow}{if} (.not.just\_read) \textcolor{keyword}{call }log\_version(param\_file, mdl, version, \textcolor{stringliteral}{"{}"{}})} \DoxyCodeLine{2118 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"{}MAX\_ENT\_IT"{}}, cs\%max\_ent\_it, \&} \DoxyCodeLine{2119 \textcolor{stringliteral}{"{}The maximum number of iterations that may be used to "{}}//\&} \DoxyCodeLine{2120 \textcolor{stringliteral}{"{}calculate the interior diapycnal entrainment."{}}, default=5, do\_not\_log=just\_read)} \DoxyCodeLine{2121 \textcolor{comment}{! In this module, KD is only used to set the default for TOLERANCE\_ENT. [m2 s-\/1]}} \DoxyCodeLine{2122 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"{}KD"{}}, kd, default=0.0)} \DoxyCodeLine{2123 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"{}DT"{}}, dt, \&} \DoxyCodeLine{2124 \textcolor{stringliteral}{"{}The (baroclinic) dynamics time step."{}}, units = \textcolor{stringliteral}{"{}s"{}}, \&} \DoxyCodeLine{2125 fail\_if\_missing=.true., do\_not\_log=just\_read)} \DoxyCodeLine{2126 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"{}TOLERANCE\_ENT"{}}, cs\%Tolerance\_Ent, \&} \DoxyCodeLine{2127 \textcolor{stringliteral}{"{}The tolerance with which to solve for entrainment values."{}}, \&} \DoxyCodeLine{2128 units=\textcolor{stringliteral}{"{}m"{}}, default=max(100.0*gv\%Angstrom\_m,1.0e-\/4*sqrt(dt*kd)), scale=gv\%m\_to\_H, \&} \DoxyCodeLine{2129 do\_not\_log=just\_read)} \DoxyCodeLine{2130 } \DoxyCodeLine{2131 cs\%Rho\_sig\_off = 1000.0*us\%kg\_m3\_to\_R} \DoxyCodeLine{2132 } \DoxyCodeLine{2133 \textcolor{keywordflow}{if} (.not.just\_read) \textcolor{keywordflow}{then}} \DoxyCodeLine{2134 cs\%id\_Kd = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'Kd\_effective'}, diag\%axesTL, time, \&} \DoxyCodeLine{2135 \textcolor{stringliteral}{'Diapycnal diffusivity as applied'}, \textcolor{stringliteral}{'m2 s-\/1'}, conversion=us\%Z2\_T\_to\_m2\_s)} \DoxyCodeLine{2136 cs\%id\_diff\_work = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'diff\_work'}, diag\%axesTi, time, \&} \DoxyCodeLine{2137 \textcolor{stringliteral}{'Work actually done by diapycnal diffusion across each interface'}, \&} \DoxyCodeLine{2138 \textcolor{stringliteral}{'W m-\/2'}, conversion=us\%RZ3\_T3\_to\_W\_m2)} \DoxyCodeLine{2139 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2140 } \DoxyCodeLine{2141 \textcolor{keywordflow}{if} (just\_read) \textcolor{keyword}{deallocate}(cs)} \DoxyCodeLine{2142 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__entrain__diffusive_ae68ab2fa707778de2f92ce179729f2ff}\label{namespacemom__entrain__diffusive_ae68ab2fa707778de2f92ce179729f2ff}} \index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}!entrainment\_diffusive@{entrainment\_diffusive}} \index{entrainment\_diffusive@{entrainment\_diffusive}!mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsubsection{\texorpdfstring{entrainment\_diffusive()}{entrainment\_diffusive()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+entrain\+\_\+diffusive\+::entrainment\+\_\+diffusive (\begin{DoxyParamCaption}\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed, g \%ke), intent(in)}]{h, }\item[{type(\mbox{\hyperlink{structmom__variables_1_1thermo__var__ptrs}{thermo\+\_\+var\+\_\+ptrs}}), intent(in)}]{tv, }\item[{type(\mbox{\hyperlink{structmom__forcing__type_1_1forcing}{forcing}}), intent(in)}]{fluxes, }\item[{real, intent(in)}]{dt, }\item[{type(\mbox{\hyperlink{structmom__grid_1_1ocean__grid__type}{ocean\+\_\+grid\+\_\+type}}), intent(in)}]{G, }\item[{type(\mbox{\hyperlink{structmom__verticalgrid_1_1verticalgrid__type}{verticalgrid\+\_\+type}}), intent(in)}]{GV, }\item[{type(\mbox{\hyperlink{structmom__unit__scaling_1_1unit__scale__type}{unit\+\_\+scale\+\_\+type}}), intent(in)}]{US, }\item[{type(\mbox{\hyperlink{structmom__entrain__diffusive_1_1entrain__diffusive__cs}{entrain\+\_\+diffusive\+\_\+cs}}), pointer}]{CS, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed, g \%ke), intent(out)}]{ea, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed, g \%ke), intent(out)}]{eb, }\item[{integer, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed), intent(inout), optional}]{kb\+\_\+out, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed, g \%ke), intent(in), optional}]{Kd\+\_\+\+Lay, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed, g \%ke+1), intent(in), optional}]{Kd\+\_\+int }\end{DoxyParamCaption})} This subroutine calculates ea and eb, the rates at which a layer entrains from the layers above and below. The entrainment rates are proportional to the buoyancy flux in a layer and inversely proportional to the density differences between layers. The scheme that is used here is described in detail in Hallberg, Mon. Wea. Rev. 2000. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em g} & The ocean\textquotesingle{}s grid structure. \\ \hline \mbox{\texttt{ in}} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure. \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ in}} & {\em h} & Layer thicknesses \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em tv} & A structure containing pointers to any available thermodynamic fields. Absent fields have N\+U\+LL ptrs. \\ \hline \mbox{\texttt{ in}} & {\em fluxes} & A structure of surface fluxes that may be used. \\ \hline \mbox{\texttt{ in}} & {\em dt} & The time increment \mbox{[}T $\sim$$>$ s\mbox{]}. \\ \hline & {\em cs} & The control structure returned by a previous call to entrain\+\_\+diffusive\+\_\+init. \\ \hline \mbox{\texttt{ out}} & {\em ea} & The amount of fluid entrained from the layer \\ \hline \mbox{\texttt{ out}} & {\em eb} & The amount of fluid entrained from the layer \\ \hline \mbox{\texttt{ in,out}} & {\em kb\+\_\+out} & The index of the lightest layer denser than \\ \hline \mbox{\texttt{ in}} & {\em kd\+\_\+lay} & The diapycnal diffusivity of layers \\ \hline \mbox{\texttt{ in}} & {\em kd\+\_\+int} & The diapycnal diffusivity of interfaces \\ \hline \end{DoxyParams} Definition at line 50 of file M\+O\+M\+\_\+entrain\+\_\+diffusive.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{52 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure.}} \DoxyCodeLine{53 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid structure.}} \DoxyCodeLine{54 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{55 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G))}, \&} \DoxyCodeLine{56 \textcolor{keywordtype}{intent(in)} :: h\textcolor{comment}{ !< Layer thicknesses [H \string~> m or kg m-\/2].}} \DoxyCodeLine{57 \textcolor{keywordtype}{type}(thermo\_var\_ptrs), \textcolor{keywordtype}{intent(in)} :: tv\textcolor{comment}{ !< A structure containing pointers to any available}} \DoxyCodeLine{58 \textcolor{comment}{ !! thermodynamic fields. Absent fields have NULL}} \DoxyCodeLine{59 \textcolor{comment}{ !! ptrs.}} \DoxyCodeLine{60 \textcolor{keywordtype}{type}(forcing), \textcolor{keywordtype}{intent(in)} :: fluxes\textcolor{comment}{ !< A structure of surface fluxes that may}} \DoxyCodeLine{61 \textcolor{comment}{ !! be used.}} \DoxyCodeLine{62 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: dt\textcolor{comment}{ !< The time increment [T \string~> s].}} \DoxyCodeLine{63 \textcolor{keywordtype}{type}(entrain\_diffusive\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< The control structure returned by a previous}} \DoxyCodeLine{64 \textcolor{comment}{ !! call to entrain\_diffusive\_init.}} \DoxyCodeLine{65 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G))}, \&} \DoxyCodeLine{66 \textcolor{keywordtype}{intent(out)} :: ea\textcolor{comment}{ !< The amount of fluid entrained from the layer}} \DoxyCodeLine{67 \textcolor{comment}{ !! above within this time step [H \string~> m or kg m-\/2].}} \DoxyCodeLine{68 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G))}, \&} \DoxyCodeLine{69 \textcolor{keywordtype}{intent(out)} :: eb\textcolor{comment}{ !< The amount of fluid entrained from the layer}} \DoxyCodeLine{70 \textcolor{comment}{ !! below within this time step [H \string~> m or kg m-\/2].}} \DoxyCodeLine{71 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G))}, \&} \DoxyCodeLine{72 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: kb\_out\textcolor{comment}{ !< The index of the lightest layer denser than}} \DoxyCodeLine{73 \textcolor{comment}{ !! the buffer layer.}} \DoxyCodeLine{74 \textcolor{comment}{! At least one of the two following arguments must be present.}} \DoxyCodeLine{75 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G))}, \&} \DoxyCodeLine{76 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: Kd\_Lay\textcolor{comment}{ !< The diapycnal diffusivity of layers}} \DoxyCodeLine{77 \textcolor{comment}{ !! [Z2 T-\/1 \string~> m2 s-\/1].}} \DoxyCodeLine{78 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G)+1)}, \&} \DoxyCodeLine{79 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: Kd\_int\textcolor{comment}{ !< The diapycnal diffusivity of interfaces}} \DoxyCodeLine{80 \textcolor{comment}{ !! [Z2 T-\/1 \string~> m2 s-\/1].}} \DoxyCodeLine{81 } \DoxyCodeLine{82 \textcolor{comment}{! This subroutine calculates ea and eb, the rates at which a layer entrains}} \DoxyCodeLine{83 \textcolor{comment}{! from the layers above and below. The entrainment rates are proportional to}} \DoxyCodeLine{84 \textcolor{comment}{! the buoyancy flux in a layer and inversely proportional to the density}} \DoxyCodeLine{85 \textcolor{comment}{! differences between layers. The scheme that is used here is described in}} \DoxyCodeLine{86 \textcolor{comment}{! detail in Hallberg, Mon. Wea. Rev. 2000.}} \DoxyCodeLine{87 } \DoxyCodeLine{88 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))} :: \&} \DoxyCodeLine{89 dtKd \textcolor{comment}{! The layer diapycnal diffusivity times the time step [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{90 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G)+1)} :: \&} \DoxyCodeLine{91 dtKd\_int \textcolor{comment}{! The diapycnal diffusivity at the interfaces times the time step [H2 \string~> m2 or kg2 m-\/4]}} \DoxyCodeLine{92 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))} :: \&} \DoxyCodeLine{93 F, \& \textcolor{comment}{! The density flux through a layer within a time step divided by the}} \DoxyCodeLine{94 \textcolor{comment}{! density difference across the interface below the layer [H \string~> m or kg m-\/2].}} \DoxyCodeLine{95 maxf, \& \textcolor{comment}{! maxF is the maximum value of F that will not deplete all of the}} \DoxyCodeLine{96 \textcolor{comment}{! layers above or below a layer within a timestep [H \string~> m or kg m-\/2].}} \DoxyCodeLine{97 minf, \& \textcolor{comment}{! minF is the minimum flux that should be expected in the absence of}} \DoxyCodeLine{98 \textcolor{comment}{! interactions between layers [H \string~> m or kg m-\/2].}} \DoxyCodeLine{99 fprev, \&\textcolor{comment}{! The previous estimate of F [H \string~> m or kg m-\/2].}} \DoxyCodeLine{100 dfdfm, \&\textcolor{comment}{! The partial derivative of F with respect to changes in F of the}} \DoxyCodeLine{101 \textcolor{comment}{! neighboring layers. [nondim]}} \DoxyCodeLine{102 h\_guess \textcolor{comment}{! An estimate of the layer thicknesses after entrainment, but}} \DoxyCodeLine{103 \textcolor{comment}{! before the entrainments are adjusted to drive the layer}} \DoxyCodeLine{104 \textcolor{comment}{! densities toward their target values [H \string~> m or kg m-\/2].}} \DoxyCodeLine{105 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G)+1)} :: \&} \DoxyCodeLine{106 Ent\_bl \textcolor{comment}{! The average entrainment upward and downward across}} \DoxyCodeLine{107 \textcolor{comment}{! each interface around the buffer layers [H \string~> m or kg m-\/2].}} \DoxyCodeLine{108 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{allocatable}, \textcolor{keywordtype}{dimension(:,:,:)} :: \&} \DoxyCodeLine{109 Kd\_eff, \& \textcolor{comment}{! The effective diffusivity that actually applies to each}} \DoxyCodeLine{110 \textcolor{comment}{! layer after the effects of boundary conditions are}} \DoxyCodeLine{111 \textcolor{comment}{! considered [Z2 T-\/1 \string~> m2 s-\/1].}} \DoxyCodeLine{112 diff\_work \textcolor{comment}{! The work actually done by diffusion across each}} \DoxyCodeLine{113 \textcolor{comment}{! interface [R Z3 T-\/3 \string~> W m-\/2]. Sum vertically for the total work.}} \DoxyCodeLine{114 } \DoxyCodeLine{115 \textcolor{keywordtype}{ real} :: hm, fm, fr, fk \textcolor{comment}{! Work variables with units of H, H, H, and H2.}} \DoxyCodeLine{116 } \DoxyCodeLine{117 \textcolor{keywordtype}{ real} :: b1(SZI\_(G)) \textcolor{comment}{! b1 and c1 are variables used by the}} \DoxyCodeLine{118 \textcolor{keywordtype}{ real} :: c1(SZI\_(G),SZK\_(G)) \textcolor{comment}{! tridiagonal solver.}} \DoxyCodeLine{119 } \DoxyCodeLine{120 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: \&} \DoxyCodeLine{121 htot, \& \textcolor{comment}{! The total thickness above or below a layer [H \string~> m or kg m-\/2].}} \DoxyCodeLine{122 Rcv, \& \textcolor{comment}{! Value of the coordinate variable (potential density)}} \DoxyCodeLine{123 \textcolor{comment}{! based on the simulated T and S and P\_Ref [R \string~> kg m-\/3].}} \DoxyCodeLine{124 pres, \& \textcolor{comment}{! Reference pressure (P\_Ref) [R L2 T-\/2 \string~> Pa].}} \DoxyCodeLine{125 eakb, \& \textcolor{comment}{! The entrainment from above by the layer below the buffer}} \DoxyCodeLine{126 \textcolor{comment}{! layer (i.e. layer kb) [H \string~> m or kg m-\/2].}} \DoxyCodeLine{127 ea\_kbp1, \& \textcolor{comment}{! The entrainment from above by layer kb+1 [H \string~> m or kg m-\/2].}} \DoxyCodeLine{128 eb\_kmb, \& \textcolor{comment}{! The entrainment from below by the deepest buffer layer [H \string~> m or kg m-\/2].}} \DoxyCodeLine{129 ds\_kb, \& \textcolor{comment}{! The reference potential density difference across the}} \DoxyCodeLine{130 \textcolor{comment}{! interface between the buffer layers and layer kb [R \string~> kg m-\/3].}} \DoxyCodeLine{131 ds\_anom\_lim, \&\textcolor{comment}{! The amount by which dS\_kb is reduced when limits are}} \DoxyCodeLine{132 \textcolor{comment}{! applied [R \string~> kg m-\/3].}} \DoxyCodeLine{133 i\_dskbp1, \& \textcolor{comment}{! The inverse of the potential density difference across the}} \DoxyCodeLine{134 \textcolor{comment}{! interface below layer kb [R-\/1 \string~> m3 kg-\/1].}} \DoxyCodeLine{135 dtkd\_kb, \& \textcolor{comment}{! The diapycnal diffusivity in layer kb times the time step}} \DoxyCodeLine{136 \textcolor{comment}{! [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{137 maxf\_correct, \& \textcolor{comment}{! An amount by which to correct maxF due to excessive}} \DoxyCodeLine{138 \textcolor{comment}{! surface heat loss [H \string~> m or kg m-\/2].}} \DoxyCodeLine{139 zeros, \& \textcolor{comment}{! An array of all zeros. (Usually used with [H \string~> m or kg m-\/2].)}} \DoxyCodeLine{140 max\_eakb, \& \textcolor{comment}{! The maximum value of eakb that might be realized [H \string~> m or kg m-\/2].}} \DoxyCodeLine{141 min\_eakb, \& \textcolor{comment}{! The minimum value of eakb that might be realized [H \string~> m or kg m-\/2].}} \DoxyCodeLine{142 err\_max\_eakb0, \& \textcolor{comment}{! The value of error returned by determine\_Ea\_kb}} \DoxyCodeLine{143 err\_min\_eakb0, \& \textcolor{comment}{! when eakb = min\_eakb and max\_eakb and ea\_kbp1 = 0.}} \DoxyCodeLine{144 err\_eakb0, \& \textcolor{comment}{! A value of error returned by determine\_Ea\_kb.}} \DoxyCodeLine{145 f\_kb, \& \textcolor{comment}{! The value of F in layer kb, or equivalently the entrainment}} \DoxyCodeLine{146 \textcolor{comment}{! from below by layer kb [H \string~> m or kg m-\/2].}} \DoxyCodeLine{147 dfdfm\_kb, \& \textcolor{comment}{! The partial derivative of F with fm [nondim]. See dFdfm.}} \DoxyCodeLine{148 maxf\_kb, \& \textcolor{comment}{! The maximum value of F\_kb that might be realized [H \string~> m or kg m-\/2].}} \DoxyCodeLine{149 eakb\_maxf, \& \textcolor{comment}{! The value of eakb that gives F\_kb=maxF\_kb [H \string~> m or kg m-\/2].}} \DoxyCodeLine{150 f\_kb\_maxent \textcolor{comment}{! The value of F\_kb when eakb = max\_eakb [H \string~> m or kg m-\/2].}} \DoxyCodeLine{151 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))} :: \&} \DoxyCodeLine{152 Sref, \& \textcolor{comment}{! The reference potential density of the mixed and buffer layers,}} \DoxyCodeLine{153 \textcolor{comment}{! and of the two lightest interior layers (kb and kb+1) copied}} \DoxyCodeLine{154 \textcolor{comment}{! into layers kmb+1 and kmb+2 [R \string~> kg m-\/3].}} \DoxyCodeLine{155 h\_bl \textcolor{comment}{! The thicknesses of the mixed and buffer layers, and of the two}} \DoxyCodeLine{156 \textcolor{comment}{! lightest interior layers (kb and kb+1) copied into layers kmb+1}} \DoxyCodeLine{157 \textcolor{comment}{! and kmb+2 [H \string~> m or kg m-\/2].}} \DoxyCodeLine{158 } \DoxyCodeLine{159 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))} :: \&} \DoxyCodeLine{160 ds\_dsp1, \& \textcolor{comment}{! The coordinate variable (sigma-\/2) difference across an}} \DoxyCodeLine{161 \textcolor{comment}{! interface divided by the difference across the interface}} \DoxyCodeLine{162 \textcolor{comment}{! below it. [nondim]}} \DoxyCodeLine{163 dsp1\_ds, \& \textcolor{comment}{! The inverse coordinate variable (sigma-\/2) difference}} \DoxyCodeLine{164 \textcolor{comment}{! across an interface times the difference across the}} \DoxyCodeLine{165 \textcolor{comment}{! interface above it. [nondim]}} \DoxyCodeLine{166 i2p2dsp1\_ds, \& \textcolor{comment}{! 1 / (2 + 2 * ds\_k+1 / ds\_k). [nondim]}} \DoxyCodeLine{167 grats \textcolor{comment}{! 2*(2 + ds\_k+1 / ds\_k + ds\_k / ds\_k+1) =}} \DoxyCodeLine{168 \textcolor{comment}{! 4*ds\_Lay*(1/ds\_k + 1/ds\_k+1). [nondim]}} \DoxyCodeLine{169 } \DoxyCodeLine{170 \textcolor{keywordtype}{ real} :: dRHo \textcolor{comment}{! The change in locally referenced potential density between}} \DoxyCodeLine{171 \textcolor{comment}{! the layers above and below an interface [R \string~> kg m-\/3].}} \DoxyCodeLine{172 \textcolor{keywordtype}{ real} :: g\_2dt \textcolor{comment}{! 0.5 * G\_Earth / dt, times unit conversion factors}} \DoxyCodeLine{173 \textcolor{comment}{! [m3 H-\/2 s-\/2 T-\/1 \string~> m s-\/3 or m7 kg-\/2 s-\/3].}} \DoxyCodeLine{174 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: \&} \DoxyCodeLine{175 pressure, \& \textcolor{comment}{! The pressure at an interface [R L2 T-\/2 \string~> Pa].}} \DoxyCodeLine{176 T\_eos, S\_eos, \& \textcolor{comment}{! The potential temperature and salinity at which to}} \DoxyCodeLine{177 \textcolor{comment}{! evaluate dRho\_dT and dRho\_dS [degC] and [ppt].}} \DoxyCodeLine{178 drho\_dt, drho\_ds \textcolor{comment}{! The partial derivatives of potential density with temperature and}} \DoxyCodeLine{179 \textcolor{comment}{! salinity, [R degC-\/1 \string~> kg m-\/3 degC-\/1] and [R ppt-\/1 \string~> kg m-\/3 ppt-\/1].}} \DoxyCodeLine{180 } \DoxyCodeLine{181 \textcolor{keywordtype}{ real} :: tolerance \textcolor{comment}{! The tolerance within which E must be converged [H \string~> m or kg m-\/2].}} \DoxyCodeLine{182 \textcolor{keywordtype}{ real} :: Angstrom \textcolor{comment}{! The minimum layer thickness [H \string~> m or kg m-\/2].}} \DoxyCodeLine{183 \textcolor{keywordtype}{ real} :: h\_neglect \textcolor{comment}{! A thickness that is so small it is usually lost}} \DoxyCodeLine{184 \textcolor{comment}{! in roundoff and can be neglected [H \string~> m or kg m-\/2].}} \DoxyCodeLine{185 \textcolor{keywordtype}{ real} :: F\_cor \textcolor{comment}{! A correction to the amount of F that is used to}} \DoxyCodeLine{186 \textcolor{comment}{! entrain from the layer above [H \string~> m or kg m-\/2].}} \DoxyCodeLine{187 \textcolor{keywordtype}{ real} :: Kd\_here \textcolor{comment}{! The effective diapycnal diffusivity [H2 s-\/1 \string~> m2 s-\/1 or kg2 m-\/4 s-\/1].}} \DoxyCodeLine{188 \textcolor{keywordtype}{ real} :: h\_avail \textcolor{comment}{! The thickness that is available for entrainment [H \string~> m or kg m-\/2].}} \DoxyCodeLine{189 \textcolor{keywordtype}{ real} :: dS\_kb\_eff \textcolor{comment}{! The value of dS\_kb after limiting is taken into account.}} \DoxyCodeLine{190 \textcolor{keywordtype}{ real} :: Rho\_cor \textcolor{comment}{! The depth-\/integrated potential density anomaly that}} \DoxyCodeLine{191 \textcolor{comment}{! needs to be corrected for [H R \string~> kg m-\/2 or kg2 m-\/5].}} \DoxyCodeLine{192 \textcolor{keywordtype}{ real} :: ea\_cor \textcolor{comment}{! The corrective adjustment to eakb [H \string~> m or kg m-\/2].}} \DoxyCodeLine{193 \textcolor{keywordtype}{ real} :: h1 \textcolor{comment}{! The layer thickness after entrainment through the}} \DoxyCodeLine{194 \textcolor{comment}{! interface below is taken into account [H \string~> m or kg m-\/2].}} \DoxyCodeLine{195 \textcolor{keywordtype}{ real} :: Idt \textcolor{comment}{! The inverse of the time step [T-\/1 \string~> s-\/1].}} \DoxyCodeLine{196 } \DoxyCodeLine{197 \textcolor{keywordtype}{logical} :: do\_any} \DoxyCodeLine{198 \textcolor{keywordtype}{logical} :: do\_entrain\_eakb \textcolor{comment}{! True if buffer layer is entrained}} \DoxyCodeLine{199 \textcolor{keywordtype}{logical} :: do\_i(SZI\_(G)), did\_i(SZI\_(G)), reiterate} \DoxyCodeLine{200 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{dimension(2)} :: EOSdom \textcolor{comment}{! The i-\/computational domain for the equation of state}} \DoxyCodeLine{201 \textcolor{keywordtype}{integer} :: it, i, j, k, is, ie, js, je, nz, K2, kmb} \DoxyCodeLine{202 \textcolor{keywordtype}{integer} :: kb(SZI\_(G)) \textcolor{comment}{! The value of kb in row j.}} \DoxyCodeLine{203 \textcolor{keywordtype}{integer} :: kb\_min \textcolor{comment}{! The minimum value of kb in the current j-\/row.}} \DoxyCodeLine{204 \textcolor{keywordtype}{integer} :: kb\_min\_act \textcolor{comment}{! The minimum active value of kb in the current j-\/row.}} \DoxyCodeLine{205 \textcolor{keywordtype}{integer} :: is1, ie1 \textcolor{comment}{! The minimum and maximum active values of i in the current j-\/row.}} \DoxyCodeLine{206 is = g\%isc ; ie = g\%iec ; js = g\%jsc ; je = g\%jec ; nz = g\%ke} \DoxyCodeLine{207 angstrom = gv\%Angstrom\_H} \DoxyCodeLine{208 h\_neglect = gv\%H\_subroundoff} \DoxyCodeLine{209 } \DoxyCodeLine{210 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(cs)) \textcolor{keyword}{call }mom\_error(fatal, \&} \DoxyCodeLine{211 \textcolor{stringliteral}{"{}MOM\_entrain\_diffusive: Module must be initialized before it is used."{}})} \DoxyCodeLine{212 } \DoxyCodeLine{213 \textcolor{keywordflow}{if} (.not.(\textcolor{keyword}{present}(kd\_lay) .or. \textcolor{keyword}{present}(kd\_int))) \textcolor{keyword}{call }mom\_error(fatal, \&} \DoxyCodeLine{214 \textcolor{stringliteral}{"{}MOM\_entrain\_diffusive: Either Kd\_Lay or Kd\_int must be present in call."{}})} \DoxyCodeLine{215 } \DoxyCodeLine{216 \textcolor{keywordflow}{if} ((.not.cs\%bulkmixedlayer .and. .not.\textcolor{keyword}{associated}(fluxes\%buoy)) .and. \&} \DoxyCodeLine{217 (\textcolor{keyword}{associated}(fluxes\%lprec) .or. \textcolor{keyword}{associated}(fluxes\%evap) .or. \&} \DoxyCodeLine{218 \textcolor{keyword}{associated}(fluxes\%sens) .or. \textcolor{keyword}{associated}(fluxes\%sw))) \textcolor{keywordflow}{then}} \DoxyCodeLine{219 \textcolor{keywordflow}{if} (is\_root\_pe()) \textcolor{keyword}{call }mom\_error(note, \textcolor{stringliteral}{"{}Calculate\_Entrainment: \&}} \DoxyCodeLine{220 \textcolor{stringliteral}{}\textcolor{stringliteral}{ \&The code to handle evaporation and precipitation without \&}} \DoxyCodeLine{221 \textcolor{stringliteral}{}\textcolor{stringliteral}{ \&a bulk mixed layer has not been implemented."{}})} \DoxyCodeLine{222 \textcolor{keywordflow}{if} (is\_root\_pe()) \textcolor{keyword}{call }mom\_error(fatal, \&} \DoxyCodeLine{223 \textcolor{stringliteral}{"{}Either define BULKMIXEDLAYER in MOM\_input or use fluxes\%buoy \&}} \DoxyCodeLine{224 \textcolor{stringliteral}{}\textcolor{stringliteral}{ \&and a linear equation of state to drive the model."{}})} \DoxyCodeLine{225 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{226 } \DoxyCodeLine{227 tolerance = cs\%Tolerance\_Ent} \DoxyCodeLine{228 kmb = gv\%nk\_rho\_varies} \DoxyCodeLine{229 k2 = max(kmb+1,2) ; kb\_min = k2} \DoxyCodeLine{230 \textcolor{keywordflow}{if} (.not. cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{231 kb(:) = 1} \DoxyCodeLine{232 \textcolor{comment}{! These lines fill in values that are arbitrary, but needed because}} \DoxyCodeLine{233 \textcolor{comment}{! they are used to normalize the buoyancy flux in layer nz.}} \DoxyCodeLine{234 \textcolor{keywordflow}{do} i=is,ie ; ds\_dsp1(i,nz) = 2.0 ; dsp1\_ds(i,nz) = 0.5 ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{235 \textcolor{keywordflow}{else}} \DoxyCodeLine{236 kb(:) = 0} \DoxyCodeLine{237 \textcolor{keywordflow}{do} i=is,ie ; ds\_dsp1(i,nz) = 0.0 ; dsp1\_ds(i,nz) = 0.0 ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{238 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{239 } \DoxyCodeLine{240 \textcolor{keywordflow}{if} (cs\%id\_diff\_work > 0) \textcolor{keyword}{allocate}(diff\_work(g\%isd:g\%ied,g\%jsd:g\%jed,nz+1))} \DoxyCodeLine{241 \textcolor{keywordflow}{if} (cs\%id\_Kd > 0) \textcolor{keyword}{allocate}(kd\_eff(g\%isd:g\%ied,g\%jsd:g\%jed,nz))} \DoxyCodeLine{242 } \DoxyCodeLine{243 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(tv\%eqn\_of\_state)) \textcolor{keywordflow}{then}} \DoxyCodeLine{244 pres(:) = tv\%P\_Ref} \DoxyCodeLine{245 \textcolor{keywordflow}{else}} \DoxyCodeLine{246 pres(:) = 0.0} \DoxyCodeLine{247 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{248 eosdom(:) = eos\_domain(g\%HI)} \DoxyCodeLine{249 } \DoxyCodeLine{250 \textcolor{comment}{!\$OMP parallel do default(none) shared(is,ie,js,je,nz,Kd\_Lay,G,GV,US,dt,CS,h,tv, \&}} \DoxyCodeLine{251 \textcolor{comment}{!\$OMP kmb,Angstrom,fluxes,K2,h\_neglect,tolerance, \&}} \DoxyCodeLine{252 \textcolor{comment}{!\$OMP ea,eb,Kd\_int,Kd\_eff,EOSdom,diff\_work,g\_2dt, kb\_out) \&}} \DoxyCodeLine{253 \textcolor{comment}{!\$OMP firstprivate(kb,ds\_dsp1,dsp1\_ds,pres,kb\_min) \&}} \DoxyCodeLine{254 \textcolor{comment}{!\$OMP private(dtKd,dtKd\_int,do\_i,Ent\_bl,dtKd\_kb,h\_bl, \&}} \DoxyCodeLine{255 \textcolor{comment}{!\$OMP I2p2dsp1\_ds,grats,htot,max\_eakb,I\_dSkbp1, \&}} \DoxyCodeLine{256 \textcolor{comment}{!\$OMP zeros,maxF\_kb,maxF,ea\_kbp1,eakb,Sref, \&}} \DoxyCodeLine{257 \textcolor{comment}{!\$OMP maxF\_correct,do\_any,do\_entrain\_eakb, \&}} \DoxyCodeLine{258 \textcolor{comment}{!\$OMP err\_min\_eakb0,err\_max\_eakb0,eakb\_maxF, \&}} \DoxyCodeLine{259 \textcolor{comment}{!\$OMP min\_eakb,err\_eakb0,F,minF,hm,fk,F\_kb\_maxent,\&}} \DoxyCodeLine{260 \textcolor{comment}{!\$OMP F\_kb,is1,ie1,kb\_min\_act,dFdfm\_kb,b1,dFdfm, \&}} \DoxyCodeLine{261 \textcolor{comment}{!\$OMP Fprev,fm,fr,c1,reiterate,eb\_kmb,did\_i, \&}} \DoxyCodeLine{262 \textcolor{comment}{!\$OMP h\_avail,h\_guess,dS\_kb,Rcv,F\_cor,dS\_kb\_eff, \&}} \DoxyCodeLine{263 \textcolor{comment}{!\$OMP Rho\_cor,ea\_cor,h1,Idt,Kd\_here,pressure, \&}} \DoxyCodeLine{264 \textcolor{comment}{!\$OMP T\_eos,S\_eos,dRho\_dT,dRho\_dS,dRho,dS\_anom\_lim)}} \DoxyCodeLine{265 \textcolor{keywordflow}{do} j=js,je} \DoxyCodeLine{266 \textcolor{keywordflow}{do} i=is,ie ; kb(i) = 1 ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{267 } \DoxyCodeLine{268 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(kd\_lay)) \textcolor{keywordflow}{then}} \DoxyCodeLine{269 \textcolor{keywordflow}{do} k=1,nz ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{270 dtkd(i,k) = gv\%Z\_to\_H**2 * (dt * kd\_lay(i,j,k))} \DoxyCodeLine{271 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{272 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(kd\_int)) \textcolor{keywordflow}{then}} \DoxyCodeLine{273 \textcolor{keywordflow}{do} k=1,nz+1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{274 dtkd\_int(i,k) = gv\%Z\_to\_H**2 * (dt * kd\_int(i,j,k))} \DoxyCodeLine{275 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{276 \textcolor{keywordflow}{else}} \DoxyCodeLine{277 \textcolor{keywordflow}{do} k=2,nz ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{278 dtkd\_int(i,k) = gv\%Z\_to\_H**2 * (0.5 * dt * (kd\_lay(i,j,k-\/1) + kd\_lay(i,j,k)))} \DoxyCodeLine{279 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{280 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{281 \textcolor{keywordflow}{else} \textcolor{comment}{! Kd\_int must be present, or there already would have been an error.}} \DoxyCodeLine{282 \textcolor{keywordflow}{do} k=1,nz ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{283 dtkd(i,k) = gv\%Z\_to\_H**2 * (0.5 * dt * (kd\_int(i,j,k)+kd\_int(i,j,k+1)))} \DoxyCodeLine{284 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{285 \textcolor{keywordflow}{dO} k=1,nz+1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{286 dtkd\_int(i,k) = gv\%Z\_to\_H**2 * (dt * kd\_int(i,j,k))} \DoxyCodeLine{287 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{288 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{289 } \DoxyCodeLine{290 \textcolor{keywordflow}{do} i=is,ie ; do\_i(i) = (g\%mask2dT(i,j) > 0.5) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{291 \textcolor{keywordflow}{do} i=is,ie ; ds\_dsp1(i,nz) = 0.0 ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{292 \textcolor{keywordflow}{do} i=is,ie ; dsp1\_ds(i,nz) = 0.0 ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{293 } \DoxyCodeLine{294 \textcolor{keywordflow}{do} k=2,nz-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{295 ds\_dsp1(i,k) = gv\%g\_prime(k) / gv\%g\_prime(k+1)} \DoxyCodeLine{296 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{297 } \DoxyCodeLine{298 \textcolor{keywordflow}{if} (cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{299 \textcolor{comment}{! This subroutine determines the averaged entrainment across each}} \DoxyCodeLine{300 \textcolor{comment}{! interface and causes thin and relatively light interior layers to be}} \DoxyCodeLine{301 \textcolor{comment}{! entrained by the deepest buffer layer. This also determines kb.}} \DoxyCodeLine{302 \textcolor{keyword}{call }set\_ent\_bl(h, dtkd\_int, tv, kb, kmb, do\_i, g, gv, us, cs, j, ent\_bl, sref, h\_bl)} \DoxyCodeLine{303 } \DoxyCodeLine{304 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{305 dtkd\_kb(i) = 0.0 ; \textcolor{keywordflow}{if} (kb(i) < nz) dtkd\_kb(i) = dtkd(i,kb(i))} \DoxyCodeLine{306 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{307 \textcolor{keywordflow}{else}} \DoxyCodeLine{308 \textcolor{keywordflow}{do} i=is,ie ; ent\_bl(i,kmb+1) = 0.0 ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{309 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{310 } \DoxyCodeLine{311 \textcolor{keywordflow}{do} k=2,nz-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{312 dsp1\_ds(i,k) = 1.0 / ds\_dsp1(i,k)} \DoxyCodeLine{313 i2p2dsp1\_ds(i,k) = 0.5/(1.0+dsp1\_ds(i,k))} \DoxyCodeLine{314 grats(i,k) = 2.0*(2.0+(dsp1\_ds(i,k)+ds\_dsp1(i,k)))} \DoxyCodeLine{315 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{316 } \DoxyCodeLine{317 \textcolor{comment}{! Determine the maximum flux, maxF, for each of the isopycnal layers.}} \DoxyCodeLine{318 \textcolor{comment}{! Also determine when the fluxes start entraining}} \DoxyCodeLine{319 \textcolor{comment}{! from various buffer or mixed layers, where appropriate.}} \DoxyCodeLine{320 \textcolor{keywordflow}{if} (cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{321 kb\_min = nz} \DoxyCodeLine{322 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{323 htot(i) = h(i,j,1) -\/ angstrom} \DoxyCodeLine{324 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{325 \textcolor{keywordflow}{do} k=2,kmb ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{326 htot(i) = htot(i) + (h(i,j,k) -\/ angstrom)} \DoxyCodeLine{327 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{328 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{329 max\_eakb(i) = max(ent\_bl(i,kmb+1) + 0.5*htot(i), htot(i))} \DoxyCodeLine{330 i\_dskbp1(i) = 1.0 / (sref(i,kmb+2) -\/ sref(i,kmb+1))} \DoxyCodeLine{331 zeros(i) = 0.0} \DoxyCodeLine{332 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{333 } \DoxyCodeLine{334 \textcolor{comment}{! Find the maximum amount of entrainment from below that the top}} \DoxyCodeLine{335 \textcolor{comment}{! interior layer could exhibit (maxF(i,kb)), approximating that}} \DoxyCodeLine{336 \textcolor{comment}{! entrainment by (eakb*max(dS\_kb/dSkbp1,0)). eakb is in the range}} \DoxyCodeLine{337 \textcolor{comment}{! from 0 to max\_eakb.}} \DoxyCodeLine{338 \textcolor{keyword}{call }find\_maxf\_kb(h\_bl, sref, ent\_bl, i\_dskbp1, zeros, max\_eakb, kmb, \&} \DoxyCodeLine{339 is, ie, g, gv, cs, maxf\_kb, eakb\_maxf, do\_i, f\_kb\_maxent)} \DoxyCodeLine{340 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (kb(i) <= nz) \textcolor{keywordflow}{then}} \DoxyCodeLine{341 maxf(i,kb(i)) = max(0.0, maxf\_kb(i), f\_kb\_maxent(i))} \DoxyCodeLine{342 \textcolor{keywordflow}{if} ((maxf\_kb(i) > f\_kb\_maxent(i)) .and. (eakb\_maxf(i) >= htot(i))) \&} \DoxyCodeLine{343 max\_eakb(i) = eakb\_maxf(i)} \DoxyCodeLine{344 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{345 } \DoxyCodeLine{346 \textcolor{keywordflow}{do} i=is,ie ; ea\_kbp1(i) = 0.0 ; eakb(i) = max\_eakb(i) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{347 \textcolor{keyword}{call }determine\_ea\_kb(h\_bl, dtkd\_kb, sref, i\_dskbp1, ent\_bl, ea\_kbp1, \&} \DoxyCodeLine{348 max\_eakb, max\_eakb, kmb, is, ie, do\_i, g, gv, cs, eakb, \&} \DoxyCodeLine{349 error=err\_max\_eakb0, f\_kb=f\_kb)} \DoxyCodeLine{350 } \DoxyCodeLine{351 \textcolor{comment}{! The maximum value of F(kb) between htot and max\_eakb determines}} \DoxyCodeLine{352 \textcolor{comment}{! what maxF(kb+1) should be.}} \DoxyCodeLine{353 \textcolor{keywordflow}{do} i=is,ie ; min\_eakb(i) = min(htot(i), max\_eakb(i)) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{354 \textcolor{keyword}{call }find\_maxf\_kb(h\_bl, sref, ent\_bl, i\_dskbp1, min\_eakb, max\_eakb, \&} \DoxyCodeLine{355 kmb, is, ie, g, gv, cs, f\_kb\_maxent, do\_i\_in = do\_i)} \DoxyCodeLine{356 } \DoxyCodeLine{357 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{358 do\_entrain\_eakb = .false.} \DoxyCodeLine{359 \textcolor{comment}{! If error\_max\_eakb0 < 0, then buffer layers are always all entrained}} \DoxyCodeLine{360 \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (err\_max\_eakb0(i) < 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{361 do\_entrain\_eakb = .true.} \DoxyCodeLine{362 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{363 } \DoxyCodeLine{364 \textcolor{keywordflow}{if} (do\_entrain\_eakb) \textcolor{keywordflow}{then}} \DoxyCodeLine{365 eakb(i) = max\_eakb(i) ; min\_eakb(i) = max\_eakb(i)} \DoxyCodeLine{366 \textcolor{keywordflow}{else}} \DoxyCodeLine{367 eakb(i) = 0.0 ; min\_eakb(i) = 0.0} \DoxyCodeLine{368 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{369 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{370 } \DoxyCodeLine{371 \textcolor{comment}{! Find the amount of entrainment of the buffer layers that would occur}} \DoxyCodeLine{372 \textcolor{comment}{! if there were no entrainment by the deeper interior layers. Also find}} \DoxyCodeLine{373 \textcolor{comment}{! how much entrainment of the deeper layers would occur.}} \DoxyCodeLine{374 \textcolor{keyword}{call }determine\_ea\_kb(h\_bl, dtkd\_kb, sref, i\_dskbp1, ent\_bl, ea\_kbp1, \&} \DoxyCodeLine{375 zeros, max\_eakb, kmb, is, ie, do\_i, g, gv, cs, min\_eakb, \&} \DoxyCodeLine{376 error=err\_min\_eakb0, f\_kb=f\_kb, err\_max\_eakb0=err\_max\_eakb0)} \DoxyCodeLine{377 \textcolor{comment}{! Error\_min\_eakb0 should be \string~0 unless error\_max\_eakb0 < 0.}} \DoxyCodeLine{378 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} ((kb(i)kb(i))) kb\_min = kb(i) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{379 \textcolor{keywordflow}{else}} \DoxyCodeLine{380 \textcolor{comment}{! Without a bulk mixed layer, surface fluxes are applied in this}} \DoxyCodeLine{381 \textcolor{comment}{! subroutine. (Otherwise, they are handled in mixedlayer.)}} \DoxyCodeLine{382 \textcolor{comment}{! Initially the maximum flux in layer zero is given by the surface}} \DoxyCodeLine{383 \textcolor{comment}{! buoyancy flux. It will later be limited if the surface flux is}} \DoxyCodeLine{384 \textcolor{comment}{! too large. Here buoy is the surface buoyancy flux.}} \DoxyCodeLine{385 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{386 maxf(i,1) = 0.0} \DoxyCodeLine{387 htot(i) = h(i,j,1) -\/ angstrom} \DoxyCodeLine{388 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{389 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(fluxes\%buoy)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{390 maxf(i,1) = gv\%Z\_to\_H * (dt*fluxes\%buoy(i,j)) / gv\%g\_prime(2)} \DoxyCodeLine{391 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{392 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{393 } \DoxyCodeLine{394 \textcolor{comment}{! The following code calculates the maximum flux, maxF, for the interior}} \DoxyCodeLine{395 \textcolor{comment}{! layers.}} \DoxyCodeLine{396 \textcolor{keywordflow}{do} k=kb\_min,nz-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{397 \textcolor{keywordflow}{if} ((k == kb(i)+1) .and. cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{398 maxf(i,k) = ds\_dsp1(i,k)*(f\_kb\_maxent(i) + htot(i))} \DoxyCodeLine{399 htot(i) = htot(i) + (h(i,j,k) -\/ angstrom)} \DoxyCodeLine{400 \textcolor{keywordflow}{elseif} (k > kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{401 maxf(i,k) = ds\_dsp1(i,k)*(maxf(i,k-\/1) + htot(i))} \DoxyCodeLine{402 htot(i) = htot(i) + (h(i,j,k) -\/ angstrom)} \DoxyCodeLine{403 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{404 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{405 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{406 maxf(i,nz) = 0.0} \DoxyCodeLine{407 \textcolor{keywordflow}{if} (.not.cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{408 maxf\_correct(i) = max(0.0, -\/(maxf(i,nz-\/1) + htot(i)))} \DoxyCodeLine{409 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{410 htot(i) = h(i,j,nz) -\/ angstrom} \DoxyCodeLine{411 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{412 \textcolor{keywordflow}{if} (.not.cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{413 do\_any = .false. ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (maxf\_correct(i) > 0.0) do\_any = .true. ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{414 \textcolor{keywordflow}{if} (do\_any) \textcolor{keywordflow}{then}} \DoxyCodeLine{415 \textcolor{keywordflow}{do} k=nz-\/1,1,-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{416 maxf(i,k) = maxf(i,k) + maxf\_correct(i)} \DoxyCodeLine{417 maxf\_correct(i) = maxf\_correct(i) * dsp1\_ds(i,k)} \DoxyCodeLine{418 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{419 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{420 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{421 \textcolor{keywordflow}{do} k=nz-\/1,kb\_min,-\/1 ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{422 \textcolor{keywordflow}{if} (k >= kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{423 maxf(i,k) = min(maxf(i,k),dsp1\_ds(i,k+1)*maxf(i,k+1) + htot(i))} \DoxyCodeLine{424 htot(i) = htot(i) + (h(i,j,k) -\/ angstrom)} \DoxyCodeLine{425 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{426 \textcolor{keywordflow}{if} (k == kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{427 \textcolor{keywordflow}{if} ((maxf(i,k) < f\_kb(i)) .or. (maxf(i,k) < maxf\_kb(i)) \&} \DoxyCodeLine{428 .and. (eakb\_maxf(i) <= max\_eakb(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{429 \textcolor{comment}{! In this case, too much was being entrained by the topmost interior}} \DoxyCodeLine{430 \textcolor{comment}{! layer, even with the minimum initial estimate. The buffer layer}} \DoxyCodeLine{431 \textcolor{comment}{! will always entrain the maximum amount.}} \DoxyCodeLine{432 f\_kb(i) = maxf(i,k)} \DoxyCodeLine{433 \textcolor{keywordflow}{if} ((f\_kb(i) <= maxf\_kb(i)) .and. (eakb\_maxf(i) <= max\_eakb(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{434 eakb(i) = eakb\_maxf(i)} \DoxyCodeLine{435 \textcolor{keywordflow}{else}} \DoxyCodeLine{436 eakb(i) = max\_eakb(i)} \DoxyCodeLine{437 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{438 \textcolor{keyword}{call }f\_kb\_to\_ea\_kb(h\_bl, sref, ent\_bl, i\_dskbp1, f\_kb, kmb, i, \&} \DoxyCodeLine{439 g, gv, cs, eakb, angstrom)} \DoxyCodeLine{440 \textcolor{keywordflow}{if} ((eakb(i) < max\_eakb(i)) .or. (eakb(i) < min\_eakb(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{441 \textcolor{keyword}{call }determine\_ea\_kb(h\_bl, dtkd\_kb, sref, i\_dskbp1, ent\_bl, zeros, \&} \DoxyCodeLine{442 eakb, eakb, kmb, i, i, do\_i, g, gv, cs, eakb, \&} \DoxyCodeLine{443 error=err\_eakb0)} \DoxyCodeLine{444 \textcolor{keywordflow}{if} (eakb(i) < max\_eakb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{445 max\_eakb(i) = eakb(i) ; err\_max\_eakb0(i) = err\_eakb0(i)} \DoxyCodeLine{446 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{447 \textcolor{keywordflow}{if} (eakb(i) < min\_eakb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{448 min\_eakb(i) = eakb(i) ; err\_min\_eakb0(i) = err\_eakb0(i)} \DoxyCodeLine{449 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{450 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{451 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{452 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{453 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{454 \textcolor{keywordflow}{if} (.not.cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{455 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{456 maxf(i,1) = min(maxf(i,1),dsp1\_ds(i,2)*maxf(i,2) + htot(i))} \DoxyCodeLine{457 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{458 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{459 } \DoxyCodeLine{460 \textcolor{comment}{! The following code provides an initial estimate of the flux in}} \DoxyCodeLine{461 \textcolor{comment}{! each layer, F. The initial guess for the layer diffusive flux is}} \DoxyCodeLine{462 \textcolor{comment}{! the smaller of a forward discretization or the maximum diffusive}} \DoxyCodeLine{463 \textcolor{comment}{! flux starting from zero thickness in one time step without}} \DoxyCodeLine{464 \textcolor{comment}{! considering adjacent layers.}} \DoxyCodeLine{465 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{466 f(i,1) = maxf(i,1)} \DoxyCodeLine{467 f(i,nz) = maxf(i,nz) ; minf(i,nz) = 0.0} \DoxyCodeLine{468 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{469 \textcolor{keywordflow}{do} k=nz-\/1,k2,-\/1} \DoxyCodeLine{470 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{471 \textcolor{keywordflow}{if} ((k==kb(i)) .and. (do\_i(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{472 eakb(i) = min\_eakb(i)} \DoxyCodeLine{473 minf(i,k) = 0.0} \DoxyCodeLine{474 \textcolor{keywordflow}{elseif} ((k>kb(i)) .and. (do\_i(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{475 \textcolor{comment}{! Here the layer flux is estimated, assuming no entrainment from}} \DoxyCodeLine{476 \textcolor{comment}{! the surrounding layers. The estimate is a forward (steady) flux,}} \DoxyCodeLine{477 \textcolor{comment}{! limited by the maximum flux for a layer starting with zero}} \DoxyCodeLine{478 \textcolor{comment}{! thickness. This is often a good guess and leads to few iterations.}} \DoxyCodeLine{479 hm = h(i,j,k) + h\_neglect} \DoxyCodeLine{480 \textcolor{comment}{! Note: Tried sqrt((0.5*ds\_dsp1(i,k))*dtKd(i,k)) for the second limit,}} \DoxyCodeLine{481 \textcolor{comment}{! but it usually doesn't work as well.}} \DoxyCodeLine{482 f(i,k) = min(maxf(i,k), sqrt(ds\_dsp1(i,k)*dtkd(i,k)), \&} \DoxyCodeLine{483 0.5*(ds\_dsp1(i,k)+1.0) * (dtkd(i,k) / hm))} \DoxyCodeLine{484 } \DoxyCodeLine{485 \textcolor{comment}{! Calculate the minimum flux that can be expected if there is no entrainment}} \DoxyCodeLine{486 \textcolor{comment}{! from the neighboring layers. The 0.9 is used to give used to give a 10\%}} \DoxyCodeLine{487 \textcolor{comment}{! known error tolerance.}} \DoxyCodeLine{488 fk = dtkd(i,k) * grats(i,k)} \DoxyCodeLine{489 minf(i,k) = min(maxf(i,k), \&} \DoxyCodeLine{490 0.9*(i2p2dsp1\_ds(i,k) * fk / (hm + sqrt(hm*hm + fk))))} \DoxyCodeLine{491 \textcolor{keywordflow}{if} (k==kb(i)) minf(i,k) = 0.0 \textcolor{comment}{! BACKWARD COMPATIBILITY -\/ DELETE LATER?}} \DoxyCodeLine{492 \textcolor{keywordflow}{else}} \DoxyCodeLine{493 f(i,k) = 0.0} \DoxyCodeLine{494 minf(i,k) = 0.0} \DoxyCodeLine{495 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{496 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! end of i loop}} \DoxyCodeLine{497 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! end of k loop}} \DoxyCodeLine{498 } \DoxyCodeLine{499 \textcolor{comment}{! This is where the fluxes are actually calculated.}} \DoxyCodeLine{500 } \DoxyCodeLine{501 is1 = ie+1 ; ie1 = is-\/1} \DoxyCodeLine{502 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then} ; is1 = i ; \textcolor{keywordflow}{exit} ;\textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{503 \textcolor{keywordflow}{do} i=ie,is,-\/1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then} ; ie1 = i ; \textcolor{keywordflow}{exit} ;\textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{504 } \DoxyCodeLine{505 \textcolor{keywordflow}{if} (cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{506 kb\_min\_act = nz} \DoxyCodeLine{507 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{508 \textcolor{keywordflow}{if} (do\_i(i) .and. (kb(i) < kb\_min\_act)) kb\_min\_act = kb(i)} \DoxyCodeLine{509 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{510 \textcolor{comment}{! Solve for the entrainment rate from above in the topmost interior}} \DoxyCodeLine{511 \textcolor{comment}{! layer, eakb, such that}} \DoxyCodeLine{512 \textcolor{comment}{! eakb*dS\_implicit = dt*Kd*dS\_layer\_implicit / h\_implicit.}} \DoxyCodeLine{513 \textcolor{keywordflow}{do} i=is1,ie1} \DoxyCodeLine{514 ea\_kbp1(i) = 0.0} \DoxyCodeLine{515 \textcolor{keywordflow}{if} (do\_i(i) .and. (kb(i) < nz)) \&} \DoxyCodeLine{516 ea\_kbp1(i) = dsp1\_ds(i,kb(i)+1)*f(i,kb(i)+1)} \DoxyCodeLine{517 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{518 \textcolor{keyword}{call }determine\_ea\_kb(h\_bl, dtkd\_kb, sref, i\_dskbp1, ent\_bl, ea\_kbp1, min\_eakb, \&} \DoxyCodeLine{519 max\_eakb, kmb, is1, ie1, do\_i, g, gv, cs, eakb, f\_kb=f\_kb, \&} \DoxyCodeLine{520 err\_max\_eakb0=err\_max\_eakb0, err\_min\_eakb0=err\_min\_eakb0, \&} \DoxyCodeLine{521 dfdfm\_kb=dfdfm\_kb)} \DoxyCodeLine{522 \textcolor{keywordflow}{else}} \DoxyCodeLine{523 kb\_min\_act = kb\_min} \DoxyCodeLine{524 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{525 } \DoxyCodeLine{526 \textcolor{keywordflow}{do} it=0,cs\%max\_ent\_it-\/1} \DoxyCodeLine{527 \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{528 \textcolor{keywordflow}{if} (.not.cs\%bulkmixedlayer) f(i,1) = min(f(i,1),maxf(i,1))} \DoxyCodeLine{529 b1(i) = 1.0} \DoxyCodeLine{530 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} \textcolor{comment}{! end of i loop}} \DoxyCodeLine{531 } \DoxyCodeLine{532 \textcolor{comment}{! F\_kb has already been found for this iteration, either above or at}} \DoxyCodeLine{533 \textcolor{comment}{! the end of the code for the previous iteration.}} \DoxyCodeLine{534 \textcolor{keywordflow}{do} k=kb\_min\_act,nz-\/1 ; \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i) .and. (k>=kb(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{535 \textcolor{comment}{! Calculate the flux in layer k.}} \DoxyCodeLine{536 \textcolor{keywordflow}{if} (cs\%bulkmixedlayer .and. (k==kb(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{537 f(i,k) = f\_kb(i)} \DoxyCodeLine{538 dfdfm(i,k) = dfdfm\_kb(i)} \DoxyCodeLine{539 \textcolor{keywordflow}{else} \textcolor{comment}{! k > kb(i)}} \DoxyCodeLine{540 fprev(i,k) = f(i,k)} \DoxyCodeLine{541 fm = (f(i,k-\/1) -\/ h(i,j,k)) + dsp1\_ds(i,k+1)*f(i,k+1)} \DoxyCodeLine{542 fk = grats(i,k)*dtkd(i,k)} \DoxyCodeLine{543 fr = sqrt(fm*fm + fk)} \DoxyCodeLine{544 } \DoxyCodeLine{545 \textcolor{keywordflow}{if} (fm>=0) \textcolor{keywordflow}{then}} \DoxyCodeLine{546 f(i,k) = min(maxf(i,k), i2p2dsp1\_ds(i,k) * (fm+fr))} \DoxyCodeLine{547 \textcolor{keywordflow}{else}} \DoxyCodeLine{548 f(i,k) = min(maxf(i,k), i2p2dsp1\_ds(i,k) * (fk / (-\/1.0*fm+fr)))} \DoxyCodeLine{549 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{550 } \DoxyCodeLine{551 \textcolor{keywordflow}{if} ((f(i,k) >= maxf(i,k)) .or. (fr == 0.0)) \textcolor{keywordflow}{then}} \DoxyCodeLine{552 dfdfm(i,k) = 0.0} \DoxyCodeLine{553 \textcolor{keywordflow}{else}} \DoxyCodeLine{554 dfdfm(i,k) = i2p2dsp1\_ds(i,k) * ((fr + fm) / fr)} \DoxyCodeLine{555 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{556 } \DoxyCodeLine{557 \textcolor{keywordflow}{if} (k > k2) \textcolor{keywordflow}{then}} \DoxyCodeLine{558 \textcolor{comment}{! This is part of a tridiagonal solver for the actual flux.}} \DoxyCodeLine{559 c1(i,k) = dfdfm(i,k-\/1)*(dsp1\_ds(i,k)*b1(i))} \DoxyCodeLine{560 b1(i) = 1.0 / (1.0 -\/ c1(i,k)*dfdfm(i,k))} \DoxyCodeLine{561 f(i,k) = min(b1(i)*(f(i,k)-\/fprev(i,k)) + fprev(i,k), maxf(i,k))} \DoxyCodeLine{562 \textcolor{keywordflow}{if} (f(i,k) >= maxf(i,k)) dfdfm(i,k) = 0.0} \DoxyCodeLine{563 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{564 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{565 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{566 } \DoxyCodeLine{567 \textcolor{keywordflow}{do} k=nz-\/2,kb\_min\_act,-\/1 ; \textcolor{keywordflow}{do} i=is1,ie1} \DoxyCodeLine{568 \textcolor{keywordflow}{if} (do\_i(i) .and. (k > kb(i))) \&} \DoxyCodeLine{569 f(i,k) = min((f(i,k)+c1(i,k+1)*(f(i,k+1)-\/fprev(i,k+1))),maxf(i,k))} \DoxyCodeLine{570 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{571 } \DoxyCodeLine{572 \textcolor{keywordflow}{if} (cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{573 \textcolor{keywordflow}{do} i=is1,ie1} \DoxyCodeLine{574 \textcolor{keywordflow}{if} (do\_i(i) .and. (kb(i) < nz)) \textcolor{keywordflow}{then}} \DoxyCodeLine{575 \textcolor{comment}{! F will be increased to minF later.}} \DoxyCodeLine{576 ea\_kbp1(i) = dsp1\_ds(i,kb(i)+1)*max(f(i,kb(i)+1), minf(i,kb(i)+1))} \DoxyCodeLine{577 \textcolor{keywordflow}{else}} \DoxyCodeLine{578 ea\_kbp1(i) = 0.0} \DoxyCodeLine{579 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{580 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{581 \textcolor{keyword}{call }determine\_ea\_kb(h\_bl, dtkd\_kb, sref, i\_dskbp1, ent\_bl, ea\_kbp1, min\_eakb, \&} \DoxyCodeLine{582 max\_eakb, kmb, is1, ie1, do\_i, g, gv, cs, eakb, f\_kb=f\_kb, \&} \DoxyCodeLine{583 err\_max\_eakb0=err\_max\_eakb0, err\_min\_eakb0=err\_min\_eakb0, \&} \DoxyCodeLine{584 dfdfm\_kb=dfdfm\_kb)} \DoxyCodeLine{585 \textcolor{keywordflow}{do} i=is1,ie1} \DoxyCodeLine{586 \textcolor{keywordflow}{if} (do\_i(i) .and. (kb(i) < nz)) f(i,kb(i)) = f\_kb(i)} \DoxyCodeLine{587 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{588 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{589 } \DoxyCodeLine{590 \textcolor{comment}{! Determine whether to do another iteration.}} \DoxyCodeLine{591 \textcolor{keywordflow}{if} (it < cs\%max\_ent\_it-\/1) \textcolor{keywordflow}{then}} \DoxyCodeLine{592 } \DoxyCodeLine{593 reiterate = .false.} \DoxyCodeLine{594 \textcolor{keywordflow}{if} (cs\%bulkmixedlayer) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{595 eb\_kmb(i) = max(2.0*ent\_bl(i,kmb+1) -\/ eakb(i), 0.0)} \DoxyCodeLine{596 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{597 \textcolor{keywordflow}{do} i=is1,ie1} \DoxyCodeLine{598 did\_i(i) = do\_i(i) ; do\_i(i) = .false.} \DoxyCodeLine{599 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{600 \textcolor{keywordflow}{do} k=kb\_min\_act,nz-\/1 ; \textcolor{keywordflow}{do} i=is1,ie1} \DoxyCodeLine{601 \textcolor{keywordflow}{if} (did\_i(i) .and. (k >= kb(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{602 \textcolor{keywordflow}{if} (f(i,k) < minf(i,k)) \textcolor{keywordflow}{then}} \DoxyCodeLine{603 f(i,k) = minf(i,k)} \DoxyCodeLine{604 do\_i(i) = .true. ; reiterate = .true.} \DoxyCodeLine{605 \textcolor{keywordflow}{elseif} (k > kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{606 \textcolor{keywordflow}{if} ((abs(f(i,k) -\/ fprev(i,k)) > tolerance) .or. \&} \DoxyCodeLine{607 ((h(i,j,k) + ((1.0+dsp1\_ds(i,k))*f(i,k) -\/ \&} \DoxyCodeLine{608 (f(i,k-\/1) + dsp1\_ds(i,k+1)*f(i,k+1)))) < 0.9*angstrom)) \textcolor{keywordflow}{then}} \DoxyCodeLine{609 do\_i(i) = .true. ; reiterate = .true.} \DoxyCodeLine{610 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{611 \textcolor{keywordflow}{else} \textcolor{comment}{! (k == kb(i))}} \DoxyCodeLine{612 \textcolor{comment}{! A more complicated test is required for the layer beneath the buffer layer,}} \DoxyCodeLine{613 \textcolor{comment}{! since its flux may be partially used to entrain directly from the mixed layer.}} \DoxyCodeLine{614 \textcolor{comment}{! Negative fluxes should not occur with the bulk mixed layer.}} \DoxyCodeLine{615 \textcolor{keywordflow}{if} (h(i,j,k) + ((f(i,k) + eakb(i)) -\/ \&} \DoxyCodeLine{616 (eb\_kmb(i) + dsp1\_ds(i,k+1)*f(i,k+1))) < 0.9*angstrom) \textcolor{keywordflow}{then}} \DoxyCodeLine{617 do\_i(i) = .true. ; reiterate = .true.} \DoxyCodeLine{618 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{619 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{620 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{621 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{622 \textcolor{keywordflow}{if} (.not.reiterate) \textcolor{keywordflow}{exit}} \DoxyCodeLine{623 \textcolor{keywordflow}{ endif} \textcolor{comment}{! end of if (it < CS\%max\_ent\_it-\/1)}} \DoxyCodeLine{624 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! end of it loop}} \DoxyCodeLine{625 \textcolor{comment}{! This is the end of the section that might be iterated.}} \DoxyCodeLine{626 } \DoxyCodeLine{627 } \DoxyCodeLine{628 \textcolor{keywordflow}{if} (it == (cs\%max\_ent\_it)) \textcolor{keywordflow}{then}} \DoxyCodeLine{629 \textcolor{comment}{! Limit the flux so that the layer below is not depleted.}} \DoxyCodeLine{630 \textcolor{comment}{! This should only be applied to the last iteration.}} \DoxyCodeLine{631 \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{632 f(i,nz-\/1) = max(f(i,nz-\/1), min(minf(i,nz-\/1), 0.0))} \DoxyCodeLine{633 \textcolor{keywordflow}{if} (kb(i) >= nz-\/1) \textcolor{keywordflow}{then} ; ea\_kbp1(i) = 0.0 ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{634 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{635 \textcolor{keywordflow}{do} k=nz-\/2,kb\_min\_act,-\/1 ; \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{636 \textcolor{keywordflow}{if} (k>kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{637 f(i,k) = min(max(minf(i,k),f(i,k)), (dsp1\_ds(i,k+1)*f(i,k+1) + \&} \DoxyCodeLine{638 max(((f(i,k+1)-\/dsp1\_ds(i,k+2)*f(i,k+2)) + \&} \DoxyCodeLine{639 (h(i,j,k+1) -\/ angstrom)), 0.5*(h(i,j,k+1)-\/angstrom))))} \DoxyCodeLine{640 \textcolor{keywordflow}{elseif} (k==kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{641 ea\_kbp1(i) = dsp1\_ds(i,k+1)*f(i,k+1)} \DoxyCodeLine{642 h\_avail = dsp1\_ds(i,k+1)*f(i,k+1) + max(0.5*(h(i,j,k+1)-\/angstrom), \&} \DoxyCodeLine{643 ((f(i,k+1)-\/dsp1\_ds(i,k+2)*f(i,k+2)) + (h(i,j,k+1) -\/ angstrom)))} \DoxyCodeLine{644 \textcolor{keywordflow}{if} ((f(i,k) > 0.0) .and. (f(i,k) > h\_avail)) \textcolor{keywordflow}{then}} \DoxyCodeLine{645 f\_kb(i) = max(0.0, h\_avail)} \DoxyCodeLine{646 f(i,k) = f\_kb(i)} \DoxyCodeLine{647 \textcolor{keywordflow}{if} ((f\_kb(i) < maxf\_kb(i)) .and. (eakb\_maxf(i) <= eakb(i))) \&} \DoxyCodeLine{648 eakb(i) = eakb\_maxf(i)} \DoxyCodeLine{649 \textcolor{keyword}{call }f\_kb\_to\_ea\_kb(h\_bl, sref, ent\_bl, i\_dskbp1, f\_kb, kmb, i, \&} \DoxyCodeLine{650 g, gv, cs, eakb)} \DoxyCodeLine{651 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{652 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{653 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{654 } \DoxyCodeLine{655 } \DoxyCodeLine{656 \textcolor{keywordflow}{if} (cs\%bulkmixedlayer) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is1,ie1} \DoxyCodeLine{657 \textcolor{keywordflow}{if} (do\_i(i) .and. (kb(i) < nz)) \textcolor{keywordflow}{then}} \DoxyCodeLine{658 h\_avail = eakb(i) + max(0.5*(h\_bl(i,kmb+1)-\/angstrom), \&} \DoxyCodeLine{659 (f\_kb(i)-\/ea\_kbp1(i)) + (h\_bl(i,kmb+1)-\/angstrom))} \DoxyCodeLine{660 \textcolor{comment}{! Ensure that 0 < eb\_kmb < h\_avail.}} \DoxyCodeLine{661 ent\_bl(i,kmb+1) = min(ent\_bl(i,kmb+1),0.5*(eakb(i) + h\_avail))} \DoxyCodeLine{662 } \DoxyCodeLine{663 eb\_kmb(i) = max(2.0*ent\_bl(i,kmb+1) -\/ eakb(i), 0.0)} \DoxyCodeLine{664 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{665 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{666 } \DoxyCodeLine{667 \textcolor{comment}{! Limit the flux so that the layer above is not depleted.}} \DoxyCodeLine{668 \textcolor{keywordflow}{do} k=kb\_min\_act+1,nz-\/1 ; \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{669 \textcolor{keywordflow}{if} ((.not.cs\%bulkmixedlayer) .or. (k > kb(i)+1)) \textcolor{keywordflow}{then}} \DoxyCodeLine{670 f(i,k) = min(f(i,k), ds\_dsp1(i,k)*( ((f(i,k-\/1) + \&} \DoxyCodeLine{671 dsp1\_ds(i,k-\/1)*f(i,k-\/1)) -\/ f(i,k-\/2)) + (h(i,j,k-\/1) -\/ angstrom)))} \DoxyCodeLine{672 f(i,k) = max(f(i,k),min(minf(i,k),0.0))} \DoxyCodeLine{673 \textcolor{keywordflow}{elseif} (k == kb(i)+1) \textcolor{keywordflow}{then}} \DoxyCodeLine{674 f(i,k) = min(f(i,k), ds\_dsp1(i,k)*( ((f(i,k-\/1) + eakb(i)) -\/ \&} \DoxyCodeLine{675 eb\_kmb(i)) + (h(i,j,k-\/1) -\/ angstrom)))} \DoxyCodeLine{676 f(i,k) = max(f(i,k),min(minf(i,k),0.0))} \DoxyCodeLine{677 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{678 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{679 \textcolor{keywordflow}{ endif} \textcolor{comment}{! (it == (CS\%max\_ent\_it))}} \DoxyCodeLine{680 } \DoxyCodeLine{681 \textcolor{keyword}{call }f\_to\_ent(f, h, kb, kmb, j, g, gv, cs, dsp1\_ds, eakb, ent\_bl, ea, eb)} \DoxyCodeLine{682 } \DoxyCodeLine{683 \textcolor{comment}{! Calculate the layer thicknesses after the entrainment to constrain the}} \DoxyCodeLine{684 \textcolor{comment}{! corrective fluxes.}} \DoxyCodeLine{685 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(tv\%eqn\_of\_state)) \textcolor{keywordflow}{then}} \DoxyCodeLine{686 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{687 h\_guess(i,1) = (h(i,j,1) -\/ angstrom) + (eb(i,j,1) -\/ ea(i,j,2))} \DoxyCodeLine{688 h\_guess(i,nz) = (h(i,j,nz) -\/ angstrom) + (ea(i,j,nz) -\/ eb(i,j,nz-\/1))} \DoxyCodeLine{689 \textcolor{keywordflow}{if} (h\_guess(i,1) < 0.0) h\_guess(i,1) = 0.0} \DoxyCodeLine{690 \textcolor{keywordflow}{if} (h\_guess(i,nz) < 0.0) h\_guess(i,nz) = 0.0} \DoxyCodeLine{691 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{692 \textcolor{keywordflow}{do} k=2,nz-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{693 h\_guess(i,k) = (h(i,j,k) -\/ angstrom) + ((ea(i,j,k) -\/ eb(i,j,k-\/1)) + \&} \DoxyCodeLine{694 (eb(i,j,k) -\/ ea(i,j,k+1)))} \DoxyCodeLine{695 \textcolor{keywordflow}{if} (h\_guess(i,k) < 0.0) h\_guess(i,k) = 0.0} \DoxyCodeLine{696 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{697 \textcolor{keywordflow}{if} (cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{698 \textcolor{keyword}{call }determine\_dskb(h\_bl, sref, ent\_bl, eakb, is, ie, kmb, g, gv, \&} \DoxyCodeLine{699 .true., ds\_kb, ds\_anom\_lim=ds\_anom\_lim)} \DoxyCodeLine{700 \textcolor{keywordflow}{do} k=nz-\/1,kb\_min,-\/1} \DoxyCodeLine{701 \textcolor{keyword}{call }calculate\_density(tv\%T(:,j,k), tv\%S(:,j,k), pres, rcv, tv\%eqn\_of\_state, eosdom)} \DoxyCodeLine{702 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{703 \textcolor{keywordflow}{if} ((k>kb(i)) .and. (f(i,k) > 0.0)) \textcolor{keywordflow}{then}} \DoxyCodeLine{704 \textcolor{comment}{! Within a time step, a layer may entrain no more than its}} \DoxyCodeLine{705 \textcolor{comment}{! thickness for correction. This limitation should apply}} \DoxyCodeLine{706 \textcolor{comment}{! extremely rarely, but precludes undesirable behavior.}} \DoxyCodeLine{707 \textcolor{comment}{! Note: Corrected a sign/logic error \& factor of 2 error, and}} \DoxyCodeLine{708 \textcolor{comment}{! the layers tracked the target density better, mostly due to}} \DoxyCodeLine{709 \textcolor{comment}{! the factor of 2 error.}} \DoxyCodeLine{710 f\_cor = h(i,j,k) * min(1.0 , max(-\/ds\_dsp1(i,k), \&} \DoxyCodeLine{711 (gv\%Rlay(k) -\/ rcv(i)) / (gv\%Rlay(k+1)-\/gv\%Rlay(k))) )} \DoxyCodeLine{712 } \DoxyCodeLine{713 \textcolor{comment}{! Ensure that (1) Entrainments are positive, (2) Corrections in}} \DoxyCodeLine{714 \textcolor{comment}{! a layer cannot deplete the layer itself (very generously), and}} \DoxyCodeLine{715 \textcolor{comment}{! (3) a layer can take no more than a quarter the mass of its}} \DoxyCodeLine{716 \textcolor{comment}{! neighbor.}} \DoxyCodeLine{717 \textcolor{keywordflow}{if} (f\_cor > 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{718 f\_cor = min(f\_cor, 0.9*f(i,k), ds\_dsp1(i,k)*0.5*h\_guess(i,k), \&} \DoxyCodeLine{719 0.25*h\_guess(i,k+1))} \DoxyCodeLine{720 \textcolor{keywordflow}{else}} \DoxyCodeLine{721 f\_cor = -\/min(-\/f\_cor, 0.9*f(i,k), 0.5*h\_guess(i,k), \&} \DoxyCodeLine{722 0.25*ds\_dsp1(i,k)*h\_guess(i,k-\/1) )} \DoxyCodeLine{723 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{724 } \DoxyCodeLine{725 ea(i,j,k) = ea(i,j,k) -\/ dsp1\_ds(i,k)*f\_cor} \DoxyCodeLine{726 eb(i,j,k) = eb(i,j,k) + f\_cor} \DoxyCodeLine{727 \textcolor{keywordflow}{elseif} ((k==kb(i)) .and. (f(i,k) > 0.0)) \textcolor{keywordflow}{then}} \DoxyCodeLine{728 \textcolor{comment}{! Rho\_cor is the density anomaly that needs to be corrected,}} \DoxyCodeLine{729 \textcolor{comment}{! taking into account that the true potential density of the}} \DoxyCodeLine{730 \textcolor{comment}{! deepest buffer layer is not exactly what is returned as dS\_kb.}} \DoxyCodeLine{731 ds\_kb\_eff = 2.0*ds\_kb(i) -\/ ds\_anom\_lim(i) \textcolor{comment}{! Could be negative!!!}} \DoxyCodeLine{732 rho\_cor = h(i,j,k) * (gv\%Rlay(k)-\/rcv(i)) + eakb(i)*ds\_anom\_lim(i)} \DoxyCodeLine{733 } \DoxyCodeLine{734 \textcolor{comment}{! Ensure that -\/.9*eakb < ea\_cor < .9*eakb}} \DoxyCodeLine{735 \textcolor{keywordflow}{if} (abs(rho\_cor) < abs(0.9*eakb(i)*ds\_kb\_eff)) \textcolor{keywordflow}{then}} \DoxyCodeLine{736 ea\_cor = -\/rho\_cor / ds\_kb\_eff} \DoxyCodeLine{737 \textcolor{keywordflow}{else}} \DoxyCodeLine{738 ea\_cor = sign(0.9*eakb(i),-\/rho\_cor*ds\_kb\_eff)} \DoxyCodeLine{739 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{740 } \DoxyCodeLine{741 \textcolor{keywordflow}{if} (ea\_cor > 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{742 \textcolor{comment}{! Ensure that -\/F\_cor < 0.5*h\_guess}} \DoxyCodeLine{743 ea\_cor = min(ea\_cor, 0.5*(max\_eakb(i) -\/ eakb(i)), \&} \DoxyCodeLine{744 0.5*h\_guess(i,k) / (ds\_kb(i) * i\_dskbp1(i)))} \DoxyCodeLine{745 \textcolor{keywordflow}{else}} \DoxyCodeLine{746 \textcolor{comment}{! Ensure that -\/ea\_cor < 0.5*h\_guess \& F\_cor < 0.25*h\_guess(k+1)}} \DoxyCodeLine{747 ea\_cor = -\/min(-\/ea\_cor, 0.5*h\_guess(i,k), \&} \DoxyCodeLine{748 0.25*h\_guess(i,k+1) / (ds\_kb(i) * i\_dskbp1(i)))} \DoxyCodeLine{749 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{750 } \DoxyCodeLine{751 ea(i,j,k) = ea(i,j,k) + ea\_cor} \DoxyCodeLine{752 eb(i,j,k) = eb(i,j,k) -\/ (ds\_kb(i) * i\_dskbp1(i)) * ea\_cor} \DoxyCodeLine{753 \textcolor{keywordflow}{elseif} (k < kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{754 \textcolor{comment}{! Repetative, unless ea(kb) has been corrected.}} \DoxyCodeLine{755 ea(i,j,k) = ea(i,j,k+1)} \DoxyCodeLine{756 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{757 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{758 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{759 \textcolor{keywordflow}{do} k=kb\_min-\/1,k2,-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{760 ea(i,j,k) = ea(i,j,k+1)} \DoxyCodeLine{761 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{762 } \DoxyCodeLine{763 \textcolor{comment}{! Repetative, unless ea(kb) has been corrected.}} \DoxyCodeLine{764 k=kmb} \DoxyCodeLine{765 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{766 \textcolor{comment}{! Do not adjust eb through the base of the buffer layers, but it}} \DoxyCodeLine{767 \textcolor{comment}{! may be necessary to change entrainment from above.}} \DoxyCodeLine{768 h1 = (h(i,j,k) -\/ angstrom) + (eb(i,j,k) -\/ ea(i,j,k+1))} \DoxyCodeLine{769 ea(i,j,k) = max(ent\_bl(i,k), ent\_bl(i,k)-\/0.5*h1, -\/h1)} \DoxyCodeLine{770 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{771 \textcolor{keywordflow}{do} k=kmb-\/1,2,-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{772 \textcolor{comment}{! Determine the entrainment from below for each buffer layer.}} \DoxyCodeLine{773 eb(i,j,k) = max(2.0*ent\_bl(i,k+1) -\/ ea(i,j,k+1), 0.0)} \DoxyCodeLine{774 } \DoxyCodeLine{775 \textcolor{comment}{! Determine the entrainment from above for each buffer layer.}} \DoxyCodeLine{776 h1 = (h(i,j,k) -\/ angstrom) + (eb(i,j,k) -\/ ea(i,j,k+1))} \DoxyCodeLine{777 ea(i,j,k) = max(ent\_bl(i,k), ent\_bl(i,k)-\/0.5*h1, -\/h1)} \DoxyCodeLine{778 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{779 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{780 eb(i,j,1) = max(2.0*ent\_bl(i,2) -\/ ea(i,j,2), 0.0)} \DoxyCodeLine{781 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{782 } \DoxyCodeLine{783 \textcolor{keywordflow}{else} \textcolor{comment}{! not bulkmixedlayer}} \DoxyCodeLine{784 \textcolor{keywordflow}{do} k=k2,nz-\/1;} \DoxyCodeLine{785 \textcolor{keyword}{call }calculate\_density(tv\%T(:,j,k), tv\%S(:,j,k), pres, rcv, tv\%eqn\_of\_state, eosdom)} \DoxyCodeLine{786 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (f(i,k) > 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{787 \textcolor{comment}{! Within a time step, a layer may entrain no more than}} \DoxyCodeLine{788 \textcolor{comment}{! its thickness for correction. This limitation should}} \DoxyCodeLine{789 \textcolor{comment}{! apply extremely rarely, but precludes undesirable}} \DoxyCodeLine{790 \textcolor{comment}{! behavior.}} \DoxyCodeLine{791 f\_cor = h(i,j,k) * min(dsp1\_ds(i,k) , max(-\/1.0, \&} \DoxyCodeLine{792 (gv\%Rlay(k) -\/ rcv(i)) / (gv\%Rlay(k+1)-\/gv\%Rlay(k))) )} \DoxyCodeLine{793 } \DoxyCodeLine{794 \textcolor{comment}{! Ensure that (1) Entrainments are positive, (2) Corrections in}} \DoxyCodeLine{795 \textcolor{comment}{! a layer cannot deplete the layer itself (very generously), and}} \DoxyCodeLine{796 \textcolor{comment}{! (3) a layer can take no more than a quarter the mass of its}} \DoxyCodeLine{797 \textcolor{comment}{! neighbor.}} \DoxyCodeLine{798 \textcolor{keywordflow}{if} (f\_cor >= 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{799 f\_cor = min(f\_cor, 0.9*f(i,k), 0.5*dsp1\_ds(i,k)*h\_guess(i,k), \&} \DoxyCodeLine{800 0.25*h\_guess(i,k+1))} \DoxyCodeLine{801 \textcolor{keywordflow}{else}} \DoxyCodeLine{802 f\_cor = -\/min(-\/f\_cor, 0.9*f(i,k), 0.5*h\_guess(i,k), \&} \DoxyCodeLine{803 0.25*ds\_dsp1(i,k)*h\_guess(i,k-\/1) )} \DoxyCodeLine{804 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{805 } \DoxyCodeLine{806 ea(i,j,k) = ea(i,j,k) -\/ dsp1\_ds(i,k)*f\_cor} \DoxyCodeLine{807 eb(i,j,k) = eb(i,j,k) + f\_cor} \DoxyCodeLine{808 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{809 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{810 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{811 } \DoxyCodeLine{812 \textcolor{keywordflow}{ endif} \textcolor{comment}{! associated(tv\%eqn\_of\_state))}} \DoxyCodeLine{813 } \DoxyCodeLine{814 \textcolor{keywordflow}{if} (cs\%id\_Kd > 0) \textcolor{keywordflow}{then}} \DoxyCodeLine{815 idt = gv\%H\_to\_Z**2 / dt} \DoxyCodeLine{816 \textcolor{keywordflow}{do} k=2,nz-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{817 \textcolor{keywordflow}{if} (k 0) \textcolor{keywordflow}{then}} \DoxyCodeLine{831 g\_2dt = 0.5 * gv\%H\_to\_Z**2*us\%L\_to\_Z**2 * (gv\%g\_Earth / dt)} \DoxyCodeLine{832 \textcolor{keywordflow}{do} i=is,ie ; diff\_work(i,j,1) = 0.0 ; diff\_work(i,j,nz+1) = 0.0 ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{833 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(tv\%eqn\_of\_state)) \textcolor{keywordflow}{then}} \DoxyCodeLine{834 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(fluxes\%p\_surf)) \textcolor{keywordflow}{then}} \DoxyCodeLine{835 \textcolor{keywordflow}{do} i=is,ie ; pressure(i) = fluxes\%p\_surf(i,j) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{836 \textcolor{keywordflow}{else}} \DoxyCodeLine{837 \textcolor{keywordflow}{do} i=is,ie ; pressure(i) = 0.0 ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{838 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{839 \textcolor{keywordflow}{do} k=2,nz} \DoxyCodeLine{840 \textcolor{keywordflow}{do} i=is,ie ; pressure(i) = pressure(i) + (gv\%g\_Earth*gv\%H\_to\_RZ)*h(i,j,k-\/1) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{841 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{842 \textcolor{keywordflow}{if} (k==kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{843 t\_eos(i) = 0.5*(tv\%T(i,j,kmb) + tv\%T(i,j,k))} \DoxyCodeLine{844 s\_eos(i) = 0.5*(tv\%S(i,j,kmb) + tv\%S(i,j,k))} \DoxyCodeLine{845 \textcolor{keywordflow}{else}} \DoxyCodeLine{846 t\_eos(i) = 0.5*(tv\%T(i,j,k-\/1) + tv\%T(i,j,k))} \DoxyCodeLine{847 s\_eos(i) = 0.5*(tv\%S(i,j,k-\/1) + tv\%S(i,j,k))} \DoxyCodeLine{848 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{849 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{850 \textcolor{keyword}{call }calculate\_density\_derivs(t\_eos, s\_eos, pressure, drho\_dt, drho\_ds, \&} \DoxyCodeLine{851 tv\%eqn\_of\_state, eosdom)} \DoxyCodeLine{852 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{853 \textcolor{keywordflow}{if} ((k>kmb) .and. (k 0) \textcolor{keyword}{call }post\_data(cs\%id\_Kd, kd\_eff, cs\%diag)} \DoxyCodeLine{885 \textcolor{keywordflow}{if} (cs\%id\_Kd > 0) \textcolor{keyword}{deallocate}(kd\_eff)} \DoxyCodeLine{886 \textcolor{keywordflow}{if} (cs\%id\_diff\_work > 0) \textcolor{keyword}{call }post\_data(cs\%id\_diff\_work, diff\_work, cs\%diag)} \DoxyCodeLine{887 \textcolor{keywordflow}{if} (cs\%id\_diff\_work > 0) \textcolor{keyword}{deallocate}(diff\_work)} \DoxyCodeLine{888 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__entrain__diffusive_adce1b1ba57f5245f1eda57e7a254d4df}\label{namespacemom__entrain__diffusive_adce1b1ba57f5245f1eda57e7a254d4df}} \index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}!f\_kb\_to\_ea\_kb@{f\_kb\_to\_ea\_kb}} \index{f\_kb\_to\_ea\_kb@{f\_kb\_to\_ea\_kb}!mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsubsection{\texorpdfstring{f\_kb\_to\_ea\_kb()}{f\_kb\_to\_ea\_kb()}} {\footnotesize\ttfamily subroutine mom\+\_\+entrain\+\_\+diffusive\+::f\+\_\+kb\+\_\+to\+\_\+ea\+\_\+kb (\begin{DoxyParamCaption}\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{h\+\_\+bl, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{Sref, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{Ent\+\_\+bl, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{I\+\_\+d\+Skbp1, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{F\+\_\+kb, }\item[{integer, intent(in)}]{kmb, }\item[{integer, intent(in)}]{i, }\item[{type(\mbox{\hyperlink{structmom__grid_1_1ocean__grid__type}{ocean\+\_\+grid\+\_\+type}}), intent(in)}]{G, }\item[{type(\mbox{\hyperlink{structmom__verticalgrid_1_1verticalgrid__type}{verticalgrid\+\_\+type}}), intent(in)}]{GV, }\item[{type(\mbox{\hyperlink{structmom__entrain__diffusive_1_1entrain__diffusive__cs}{entrain\+\_\+diffusive\+\_\+cs}}), pointer}]{CS, }\item[{real, dimension( g \%isd\+: g \%ied), intent(inout)}]{ea\+\_\+kb, }\item[{real, intent(in), optional}]{tol\+\_\+in }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Given an entrainment from below for layer kb, determine a consistent entrainment from above, such that d\+Skb $\ast$ ea\+\_\+kb = d\+Skbp1 $\ast$ F\+\_\+kb. The input value of ea\+\_\+kb is both the maximum value that can be obtained and the first guess of the iterations. Ideally ea\+\_\+kb should be an under-\/estimate. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em g} & The ocean\textquotesingle{}s grid structure \\ \hline \mbox{\texttt{ in}} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure \\ \hline \mbox{\texttt{ in}} & {\em h\+\_\+bl} & Layer thickness, with the top interior \\ \hline \mbox{\texttt{ in}} & {\em sref} & The coordinate reference potential density, \\ \hline \mbox{\texttt{ in}} & {\em ent\+\_\+bl} & The average entrainment upward and downward \\ \hline \mbox{\texttt{ in}} & {\em i\+\_\+dskbp1} & The inverse of the difference in reference potential density across the base of the uppermost interior layer \mbox{[}R-\/1 $\sim$$>$ m3 kg-\/1\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em f\+\_\+kb} & The entrainment from below by the uppermost interior layer \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em kmb} & The number of mixed and buffer layers. \\ \hline \mbox{\texttt{ in}} & {\em i} & The i-\/index to work on \\ \hline & {\em cs} & This module\textquotesingle{}s control structure. \\ \hline \mbox{\texttt{ in,out}} & {\em ea\+\_\+kb} & The entrainment from above by the layer below the buffer layer (i.\+e. layer kb) \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em tol\+\_\+in} & A tolerance for the iterative determination of the entrainment \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 1439 of file M\+O\+M\+\_\+entrain\+\_\+diffusive.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1441 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure}} \DoxyCodeLine{1442 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid structure}} \DoxyCodeLine{1443 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \&} \DoxyCodeLine{1444 \textcolor{keywordtype}{intent(in)} :: h\_bl\textcolor{comment}{ !< Layer thickness, with the top interior}} \DoxyCodeLine{1445 \textcolor{comment}{ !! layer at k-\/index kmb+1 [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1446 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \&} \DoxyCodeLine{1447 \textcolor{keywordtype}{intent(in)} :: Sref\textcolor{comment}{ !< The coordinate reference potential density,}} \DoxyCodeLine{1448 \textcolor{comment}{ !! with the value of the topmost interior layer}} \DoxyCodeLine{1449 \textcolor{comment}{ !! at index kmb+1 [R \string~> kg m-\/3].}} \DoxyCodeLine{1450 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \&} \DoxyCodeLine{1451 \textcolor{keywordtype}{intent(in)} :: Ent\_bl\textcolor{comment}{ !< The average entrainment upward and downward}} \DoxyCodeLine{1452 \textcolor{comment}{ !! across each interface around the buffer layers,}} \DoxyCodeLine{1453 \textcolor{comment}{ !! [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1454 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: I\_dSkbp1\textcolor{comment}{ !< The inverse of the difference in reference}} \DoxyCodeLine{1455 \textcolor{comment}{ !! potential density across the base of the}} \DoxyCodeLine{1456 \textcolor{comment}{ !! uppermost interior layer [R-\/1 \string~> m3 kg-\/1].}} \DoxyCodeLine{1457 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: F\_kb\textcolor{comment}{ !< The entrainment from below by the}} \DoxyCodeLine{1458 \textcolor{comment}{ !! uppermost interior layer [H \string~> m or kg m-\/2]}} \DoxyCodeLine{1459 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: kmb\textcolor{comment}{ !< The number of mixed and buffer layers.}} \DoxyCodeLine{1460 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: i\textcolor{comment}{ !< The i-\/index to work on}} \DoxyCodeLine{1461 \textcolor{keywordtype}{type}(entrain\_diffusive\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< This module's control structure.}} \DoxyCodeLine{1462 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(inout)} :: ea\_kb\textcolor{comment}{ !< The entrainment from above by the layer below}} \DoxyCodeLine{1463 \textcolor{comment}{ !! the buffer layer (i.e. layer kb) [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1464 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: tol\_in\textcolor{comment}{ !< A tolerance for the iterative determination}} \DoxyCodeLine{1465 \textcolor{comment}{ !! of the entrainment [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1466 } \DoxyCodeLine{1467 \textcolor{keywordtype}{ real} :: max\_ea, min\_ea} \DoxyCodeLine{1468 \textcolor{keywordtype}{ real} :: err, err\_min, err\_max} \DoxyCodeLine{1469 \textcolor{keywordtype}{ real} :: derr\_dea} \DoxyCodeLine{1470 \textcolor{keywordtype}{ real} :: val, tolerance, tol1} \DoxyCodeLine{1471 \textcolor{keywordtype}{ real} :: ea\_prev} \DoxyCodeLine{1472 \textcolor{keywordtype}{ real} :: dS\_kbp1} \DoxyCodeLine{1473 \textcolor{keywordtype}{logical} :: bisect\_next, Newton} \DoxyCodeLine{1474 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: dS\_kb} \DoxyCodeLine{1475 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: maxF, ent\_maxF, zeros} \DoxyCodeLine{1476 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: ddSkb\_dE} \DoxyCodeLine{1477 \textcolor{keywordtype}{integer} :: it} \DoxyCodeLine{1478 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{parameter} :: MAXIT = 30} \DoxyCodeLine{1479 } \DoxyCodeLine{1480 ds\_kbp1 = sref(i,kmb+2) -\/ sref(i,kmb+1)} \DoxyCodeLine{1481 max\_ea = ea\_kb(i) ; min\_ea = 0.0} \DoxyCodeLine{1482 val = ds\_kbp1 * f\_kb(i)} \DoxyCodeLine{1483 err\_min = -\/val} \DoxyCodeLine{1484 } \DoxyCodeLine{1485 tolerance = cs\%Tolerance\_Ent} \DoxyCodeLine{1486 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(tol\_in)) tolerance = tol\_in} \DoxyCodeLine{1487 bisect\_next = .true.} \DoxyCodeLine{1488 } \DoxyCodeLine{1489 \textcolor{keyword}{call }determine\_dskb(h\_bl, sref, ent\_bl, ea\_kb, i, i, kmb, g, gv, .true., \&} \DoxyCodeLine{1490 ds\_kb, ddskb\_de)} \DoxyCodeLine{1491 } \DoxyCodeLine{1492 err = ds\_kb(i) * ea\_kb(i) -\/ val} \DoxyCodeLine{1493 derr\_dea = ds\_kb(i) + ddskb\_de(i) * ea\_kb(i)} \DoxyCodeLine{1494 \textcolor{comment}{! Return if Newton's method on the first guess would give a tolerably small}} \DoxyCodeLine{1495 \textcolor{comment}{! change in the value of ea\_kb.}} \DoxyCodeLine{1496 \textcolor{keywordflow}{if} ((err <= 0.0) .and. (abs(err) <= tolerance*abs(derr\_dea))) \textcolor{keywordflow}{return}} \DoxyCodeLine{1497 } \DoxyCodeLine{1498 \textcolor{keywordflow}{if} (err == 0.0) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{return} \textcolor{comment}{! The exact solution on the first guess...}} \DoxyCodeLine{1499 \textcolor{keywordflow}{elseif} (err > 0.0) \textcolor{keywordflow}{then} \textcolor{comment}{! The root is properly bracketed.}} \DoxyCodeLine{1500 max\_ea = ea\_kb(i) ; err\_max = err} \DoxyCodeLine{1501 \textcolor{comment}{! Use Newton's method (if it stays bounded) or the false position method}} \DoxyCodeLine{1502 \textcolor{comment}{! to find the next value.}} \DoxyCodeLine{1503 \textcolor{keywordflow}{if} ((derr\_dea > 0.0) .and. (derr\_dea*(ea\_kb(i) -\/ min\_ea) > err) .and. \&} \DoxyCodeLine{1504 (derr\_dea*(max\_ea -\/ ea\_kb(i)) > -\/1.0*err)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1505 ea\_kb(i) = ea\_kb(i) -\/ err / derr\_dea} \DoxyCodeLine{1506 \textcolor{keywordflow}{else} \textcolor{comment}{! Use the bisection for the next guess.}} \DoxyCodeLine{1507 ea\_kb(i) = 0.5*(max\_ea+min\_ea)} \DoxyCodeLine{1508 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1509 \textcolor{keywordflow}{else}} \DoxyCodeLine{1510 \textcolor{comment}{! Try to bracket the root first. If unable to bracket the root, return}} \DoxyCodeLine{1511 \textcolor{comment}{! the maximum.}} \DoxyCodeLine{1512 zeros(i) = 0.0} \DoxyCodeLine{1513 \textcolor{keyword}{call }find\_maxf\_kb(h\_bl, sref, ent\_bl, i\_dskbp1, zeros, ea\_kb, \&} \DoxyCodeLine{1514 kmb, i, i, g, gv, cs, maxf, ent\_maxf, f\_thresh = f\_kb)} \DoxyCodeLine{1515 err\_max = ds\_kbp1 * maxf(i) -\/ val} \DoxyCodeLine{1516 \textcolor{comment}{! If err\_max is negative, there is no good solution, so use the maximum}} \DoxyCodeLine{1517 \textcolor{comment}{! value of F in the valid range.}} \DoxyCodeLine{1518 \textcolor{keywordflow}{if} (err\_max <= 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1519 ea\_kb(i) = ent\_maxf(i) ; \textcolor{keywordflow}{return}} \DoxyCodeLine{1520 \textcolor{keywordflow}{else}} \DoxyCodeLine{1521 max\_ea = ent\_maxf(i)} \DoxyCodeLine{1522 ea\_kb(i) = 0.5*(max\_ea+min\_ea) \textcolor{comment}{! Use bisection for the next guess.}} \DoxyCodeLine{1523 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1524 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1525 } \DoxyCodeLine{1526 \textcolor{comment}{! Exit if the range between max\_ea and min\_ea already acceptable.}} \DoxyCodeLine{1527 \textcolor{comment}{! if (abs(max\_ea -\/ min\_ea) < 0.1*tolerance) return}} \DoxyCodeLine{1528 } \DoxyCodeLine{1529 \textcolor{keywordflow}{do} it = 1, maxit} \DoxyCodeLine{1530 \textcolor{keyword}{call }determine\_dskb(h\_bl, sref, ent\_bl, ea\_kb, i, i, kmb, g, gv, .true., \&} \DoxyCodeLine{1531 ds\_kb, ddskb\_de)} \DoxyCodeLine{1532 } \DoxyCodeLine{1533 err = ds\_kb(i) * ea\_kb(i) -\/ val} \DoxyCodeLine{1534 derr\_dea = ds\_kb(i) + ddskb\_de(i) * ea\_kb(i)} \DoxyCodeLine{1535 } \DoxyCodeLine{1536 ea\_prev = ea\_kb(i)} \DoxyCodeLine{1537 \textcolor{comment}{! Use Newton's method or the false position method to find the next value.}} \DoxyCodeLine{1538 newton = .false.} \DoxyCodeLine{1539 \textcolor{keywordflow}{if} (err > 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1540 max\_ea = ea\_kb(i) ; err\_max = err} \DoxyCodeLine{1541 \textcolor{keywordflow}{if} ((derr\_dea > 0.0) .and. (derr\_dea*(ea\_kb(i)-\/min\_ea) > err)) newton = .true.} \DoxyCodeLine{1542 \textcolor{keywordflow}{else}} \DoxyCodeLine{1543 min\_ea = ea\_kb(i) ; err\_min = err} \DoxyCodeLine{1544 \textcolor{keywordflow}{if} ((derr\_dea > 0.0) .and. (derr\_dea*(ea\_kb(i)-\/max\_ea) < err)) newton = .true.} \DoxyCodeLine{1545 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1546 } \DoxyCodeLine{1547 \textcolor{keywordflow}{if} (newton) \textcolor{keywordflow}{then}} \DoxyCodeLine{1548 ea\_kb(i) = ea\_kb(i) -\/ err / derr\_dea} \DoxyCodeLine{1549 \textcolor{keywordflow}{elseif} (bisect\_next) \textcolor{keywordflow}{then} \textcolor{comment}{! Use bisection to reduce the range.}} \DoxyCodeLine{1550 ea\_kb(i) = 0.5*(max\_ea+min\_ea)} \DoxyCodeLine{1551 bisect\_next = .false.} \DoxyCodeLine{1552 \textcolor{keywordflow}{else} \textcolor{comment}{! Use the false-\/position method for the next guess.}} \DoxyCodeLine{1553 ea\_kb(i) = min\_ea + (max\_ea-\/min\_ea) * (err\_min/(err\_min -\/ err\_max))} \DoxyCodeLine{1554 bisect\_next = .true.} \DoxyCodeLine{1555 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1556 } \DoxyCodeLine{1557 tol1 = tolerance ; \textcolor{keywordflow}{if} (err > 0.0) tol1 = 0.099*tolerance} \DoxyCodeLine{1558 \textcolor{keywordflow}{if} (ds\_kb(i) <= ds\_kbp1) \textcolor{keywordflow}{then}} \DoxyCodeLine{1559 \textcolor{keywordflow}{if} (abs(ea\_kb(i) -\/ ea\_prev) <= tol1) \textcolor{keywordflow}{return}} \DoxyCodeLine{1560 \textcolor{keywordflow}{else}} \DoxyCodeLine{1561 \textcolor{keywordflow}{if} (ds\_kbp1*abs(ea\_kb(i) -\/ ea\_prev) <= ds\_kb(i)*tol1) \textcolor{keywordflow}{return}} \DoxyCodeLine{1562 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1563 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1564 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__entrain__diffusive_a13bbe9f35e3198470100375d9d016b7a}\label{namespacemom__entrain__diffusive_a13bbe9f35e3198470100375d9d016b7a}} \index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}!f\_to\_ent@{f\_to\_ent}} \index{f\_to\_ent@{f\_to\_ent}!mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsubsection{\texorpdfstring{f\_to\_ent()}{f\_to\_ent()}} {\footnotesize\ttfamily subroutine mom\+\_\+entrain\+\_\+diffusive\+::f\+\_\+to\+\_\+ent (\begin{DoxyParamCaption}\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{F, }\item[{real, dimension(szi\+\_\+(g),szj\+\_\+(g),szk\+\_\+(g)), intent(in)}]{h, }\item[{integer, dimension(szi\+\_\+(g)), intent(in)}]{kb, }\item[{integer, intent(in)}]{kmb, }\item[{integer, intent(in)}]{j, }\item[{type(\mbox{\hyperlink{structmom__grid_1_1ocean__grid__type}{ocean\+\_\+grid\+\_\+type}}), intent(in)}]{G, }\item[{type(\mbox{\hyperlink{structmom__verticalgrid_1_1verticalgrid__type}{verticalgrid\+\_\+type}}), intent(in)}]{GV, }\item[{type(\mbox{\hyperlink{structmom__entrain__diffusive_1_1entrain__diffusive__cs}{entrain\+\_\+diffusive\+\_\+cs}}), intent(in)}]{CS, }\item[{real, dimension( g \%isd\+: g \%ied, g \%ke), intent(in)}]{dsp1\+\_\+ds, }\item[{real, dimension( g \%isd\+: g \%ied), intent(in)}]{eakb, }\item[{real, dimension( g \%isd\+: g \%ied, g \%ke), intent(in)}]{Ent\+\_\+bl, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed, g \%ke), intent(inout)}]{ea, }\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed, g \%ke), intent(inout)}]{eb, }\item[{logical, dimension( g \%isd\+: g \%ied), intent(in), optional}]{do\+\_\+i\+\_\+in }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine calculates the actual entrainments (ea and eb) and the amount of surface forcing that is applied to each layer if there is no bulk mixed layer. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em g} & The ocean\textquotesingle{}s grid structure \\ \hline \mbox{\texttt{ in}} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure \\ \hline \mbox{\texttt{ in}} & {\em f} & The density flux through a layer within a time step divided by the density difference across the interface below the layer \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em h} & Layer thicknesses \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em kb} & The index of the lightest layer denser than the deepest buffer layer. \\ \hline \mbox{\texttt{ in}} & {\em kmb} & The number of mixed and buffer layers. \\ \hline \mbox{\texttt{ in}} & {\em j} & The meridional index upon which to work. \\ \hline \mbox{\texttt{ in}} & {\em cs} & This module\textquotesingle{}s control structure. \\ \hline \mbox{\texttt{ in}} & {\em dsp1\+\_\+ds} & The ratio of coordinate variable differences across the interfaces below a layer over the difference across the interface above the layer. \\ \hline \mbox{\texttt{ in}} & {\em eakb} & The entrainment from above by the layer below the buffer layer \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em ent\+\_\+bl} & The average entrainment upward and downward across each interface around the buffer layers \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in,out}} & {\em ea} & The amount of fluid entrained from the layer \\ \hline \mbox{\texttt{ in,out}} & {\em eb} & The amount of fluid entrained from the layer \\ \hline \mbox{\texttt{ in}} & {\em do\+\_\+i\+\_\+in} & Indicates which i-\/points to work on. \\ \hline \end{DoxyParams} Definition at line 894 of file M\+O\+M\+\_\+entrain\+\_\+diffusive.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{895 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure}} \DoxyCodeLine{896 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid structure}} \DoxyCodeLine{897 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: F\textcolor{comment}{ !< The density flux through a layer within}} \DoxyCodeLine{898 \textcolor{comment}{ !! a time step divided by the density}} \DoxyCodeLine{899 \textcolor{comment}{ !! difference across the interface below}} \DoxyCodeLine{900 \textcolor{comment}{ !! the layer [H \string~> m or kg m-\/2].}} \DoxyCodeLine{901 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G))}, \&} \DoxyCodeLine{902 \textcolor{keywordtype}{intent(in)} :: h\textcolor{comment}{ !< Layer thicknesses [H \string~> m or kg m-\/2]}} \DoxyCodeLine{903 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: kb\textcolor{comment}{ !< The index of the lightest layer denser than}} \DoxyCodeLine{904 \textcolor{comment}{ !! the deepest buffer layer.}} \DoxyCodeLine{905 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: kmb\textcolor{comment}{ !< The number of mixed and buffer layers.}} \DoxyCodeLine{906 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: j\textcolor{comment}{ !< The meridional index upon which to work.}} \DoxyCodeLine{907 \textcolor{keywordtype}{type}(entrain\_diffusive\_CS), \textcolor{keywordtype}{intent(in)} :: CS\textcolor{comment}{ !< This module's control structure.}} \DoxyCodeLine{908 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: dsp1\_ds\textcolor{comment}{ !< The ratio of coordinate variable}} \DoxyCodeLine{909 \textcolor{comment}{ !! differences across the interfaces below}} \DoxyCodeLine{910 \textcolor{comment}{ !! a layer over the difference across the}} \DoxyCodeLine{911 \textcolor{comment}{ !! interface above the layer.}} \DoxyCodeLine{912 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: eakb\textcolor{comment}{ !< The entrainment from above by the layer}} \DoxyCodeLine{913 \textcolor{comment}{ !! below the buffer layer [H \string~> m or kg m-\/2].}} \DoxyCodeLine{914 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(in)} :: Ent\_bl\textcolor{comment}{ !< The average entrainment upward and}} \DoxyCodeLine{915 \textcolor{comment}{ !! downward across each interface around}} \DoxyCodeLine{916 \textcolor{comment}{ !! the buffer layers [H \string~> m or kg m-\/2].}} \DoxyCodeLine{917 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G))}, \&} \DoxyCodeLine{918 \textcolor{keywordtype}{intent(inout)} :: ea\textcolor{comment}{ !< The amount of fluid entrained from the layer}} \DoxyCodeLine{919 \textcolor{comment}{ !! above within this time step [H \string~> m or kg m-\/2].}} \DoxyCodeLine{920 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G))}, \&} \DoxyCodeLine{921 \textcolor{keywordtype}{intent(inout)} :: eb\textcolor{comment}{ !< The amount of fluid entrained from the layer}} \DoxyCodeLine{922 \textcolor{comment}{ !! below within this time step [H \string~> m or kg m-\/2].}} \DoxyCodeLine{923 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \&} \DoxyCodeLine{924 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: do\_i\_in\textcolor{comment}{ !< Indicates which i-\/points to work on.}} \DoxyCodeLine{925 \textcolor{comment}{! This subroutine calculates the actual entrainments (ea and eb) and the}} \DoxyCodeLine{926 \textcolor{comment}{! amount of surface forcing that is applied to each layer if there is no bulk}} \DoxyCodeLine{927 \textcolor{comment}{! mixed layer.}} \DoxyCodeLine{928 } \DoxyCodeLine{929 \textcolor{keywordtype}{ real} :: h1 \textcolor{comment}{! The thickness in excess of the minimum that will remain}} \DoxyCodeLine{930 \textcolor{comment}{! after exchange with the layer below [H \string~> m or kg m-\/2].}} \DoxyCodeLine{931 \textcolor{keywordtype}{logical} :: do\_i(SZI\_(G))} \DoxyCodeLine{932 \textcolor{keywordtype}{integer} :: i, k, is, ie, nz} \DoxyCodeLine{933 } \DoxyCodeLine{934 is = g\%isc ; ie = g\%iec ; nz = g\%ke} \DoxyCodeLine{935 } \DoxyCodeLine{936 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(do\_i\_in)) \textcolor{keywordflow}{then}} \DoxyCodeLine{937 \textcolor{keywordflow}{do} i=is,ie ; do\_i(i) = do\_i\_in(i) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{938 \textcolor{keywordflow}{do} i=g\%isc,g\%iec ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{939 is = i ; \textcolor{keywordflow}{exit}} \DoxyCodeLine{940 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{941 \textcolor{keywordflow}{do} i=g\%iec,g\%isc,-\/1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{942 ie = i ; \textcolor{keywordflow}{exit}} \DoxyCodeLine{943 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{944 \textcolor{keywordflow}{else}} \DoxyCodeLine{945 \textcolor{keywordflow}{do} i=is,ie ; do\_i(i) = .true. ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{946 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{947 } \DoxyCodeLine{948 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{949 ea(i,j,nz) = 0.0 ; eb(i,j,nz) = 0.0} \DoxyCodeLine{950 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{951 \textcolor{keywordflow}{if} (cs\%bulkmixedlayer) \textcolor{keywordflow}{then}} \DoxyCodeLine{952 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{953 eb(i,j,kmb) = max(2.0*ent\_bl(i,kmb+1) -\/ eakb(i), 0.0)} \DoxyCodeLine{954 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{955 \textcolor{keywordflow}{do} k=nz-\/1,kmb+1,-\/1 ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{956 \textcolor{keywordflow}{if} (k > kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{957 \textcolor{comment}{! With a bulk mixed layer, surface buoyancy fluxes are applied}} \DoxyCodeLine{958 \textcolor{comment}{! elsewhere, so F should always be nonnegative.}} \DoxyCodeLine{959 ea(i,j,k) = dsp1\_ds(i,k)*f(i,k)} \DoxyCodeLine{960 eb(i,j,k) = f(i,k)} \DoxyCodeLine{961 \textcolor{keywordflow}{elseif} (k == kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{962 ea(i,j,k) = eakb(i)} \DoxyCodeLine{963 eb(i,j,k) = f(i,k)} \DoxyCodeLine{964 \textcolor{keywordflow}{elseif} (k == kb(i)-\/1) \textcolor{keywordflow}{then}} \DoxyCodeLine{965 ea(i,j,k) = ea(i,j,k+1)} \DoxyCodeLine{966 eb(i,j,k) = eb(i,j,kmb)} \DoxyCodeLine{967 \textcolor{keywordflow}{else}} \DoxyCodeLine{968 ea(i,j,k) = ea(i,j,k+1)} \DoxyCodeLine{969 \textcolor{comment}{! Add the entrainment of the thin interior layers to eb going}} \DoxyCodeLine{970 \textcolor{comment}{! up into the buffer layer.}} \DoxyCodeLine{971 eb(i,j,k) = eb(i,j,k+1) + max(0.0, h(i,j,k+1) -\/ gv\%Angstrom\_H)} \DoxyCodeLine{972 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{973 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{974 k = kmb} \DoxyCodeLine{975 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{976 \textcolor{comment}{! Adjust the previously calculated entrainment from below by the deepest}} \DoxyCodeLine{977 \textcolor{comment}{! buffer layer to account for entrainment of thin interior layers .}} \DoxyCodeLine{978 \textcolor{keywordflow}{if} (kb(i) > kmb+1) \&} \DoxyCodeLine{979 eb(i,j,k) = eb(i,j,k+1) + max(0.0, h(i,j,k+1) -\/ gv\%Angstrom\_H)} \DoxyCodeLine{980 } \DoxyCodeLine{981 \textcolor{comment}{! Determine the entrainment from above for each buffer layer.}} \DoxyCodeLine{982 h1 = (h(i,j,k) -\/ gv\%Angstrom\_H) + (eb(i,j,k) -\/ ea(i,j,k+1))} \DoxyCodeLine{983 ea(i,j,k) = max(ent\_bl(i,k), ent\_bl(i,k)-\/0.5*h1, -\/h1)} \DoxyCodeLine{984 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{985 \textcolor{keywordflow}{do} k=kmb-\/1,2,-\/1 ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{986 \textcolor{comment}{! Determine the entrainment from below for each buffer layer.}} \DoxyCodeLine{987 eb(i,j,k) = max(2.0*ent\_bl(i,k+1) -\/ ea(i,j,k+1), 0.0)} \DoxyCodeLine{988 } \DoxyCodeLine{989 \textcolor{comment}{! Determine the entrainment from above for each buffer layer.}} \DoxyCodeLine{990 h1 = (h(i,j,k) -\/ gv\%Angstrom\_H) + (eb(i,j,k) -\/ ea(i,j,k+1))} \DoxyCodeLine{991 ea(i,j,k) = max(ent\_bl(i,k), ent\_bl(i,k)-\/0.5*h1, -\/h1)} \DoxyCodeLine{992 \textcolor{comment}{! if (h1 >= 0.0) then ; ea(i,j,k) = Ent\_bl(i,K)}} \DoxyCodeLine{993 \textcolor{comment}{! elseif (Ent\_bl(i,K)+0.5*h1 >= 0.0) then ; ea(i,j,k) = Ent\_bl(i,K)-\/0.5*h1}} \DoxyCodeLine{994 \textcolor{comment}{! else ; ea(i,j,k) = -\/h1 ; endif}} \DoxyCodeLine{995 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{996 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{997 eb(i,j,1) = max(2.0*ent\_bl(i,2) -\/ ea(i,j,2), 0.0)} \DoxyCodeLine{998 ea(i,j,1) = 0.0} \DoxyCodeLine{999 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1000 \textcolor{keywordflow}{else} \textcolor{comment}{! not BULKMIXEDLAYER}} \DoxyCodeLine{1001 \textcolor{comment}{! Calculate the entrainment by each layer from above and below.}} \DoxyCodeLine{1002 \textcolor{comment}{! Entrainment is always positive, but F may be negative due to}} \DoxyCodeLine{1003 \textcolor{comment}{! surface buoyancy fluxes.}} \DoxyCodeLine{1004 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1005 ea(i,j,1) = 0.0 ; eb(i,j,1) = max(f(i,1),0.0)} \DoxyCodeLine{1006 ea(i,j,2) = dsp1\_ds(i,2)*f(i,2) -\/ min(f(i,1),0.0)} \DoxyCodeLine{1007 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1008 } \DoxyCodeLine{1009 \textcolor{keywordflow}{do} k=2,nz-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1010 eb(i,j,k) = max(f(i,k),0.0)} \DoxyCodeLine{1011 ea(i,j,k+1) = dsp1\_ds(i,k+1)*f(i,k+1) -\/ (f(i,k)-\/eb(i,j,k))} \DoxyCodeLine{1012 \textcolor{keywordflow}{if} (ea(i,j,k+1) < 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1013 eb(i,j,k) = eb(i,j,k) -\/ ea(i,j,k+1)} \DoxyCodeLine{1014 ea(i,j,k+1) = 0.0} \DoxyCodeLine{1015 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1016 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1017 \textcolor{keywordflow}{ endif} \textcolor{comment}{! end BULKMIXEDLAYER}} \end{DoxyCode} \mbox{\Hypertarget{namespacemom__entrain__diffusive_ae45dbf976314c3a9e278ebcebedab109}\label{namespacemom__entrain__diffusive_ae45dbf976314c3a9e278ebcebedab109}} \index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}!find\_maxf\_kb@{find\_maxf\_kb}} \index{find\_maxf\_kb@{find\_maxf\_kb}!mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsubsection{\texorpdfstring{find\_maxf\_kb()}{find\_maxf\_kb()}} {\footnotesize\ttfamily subroutine mom\+\_\+entrain\+\_\+diffusive\+::find\+\_\+maxf\+\_\+kb (\begin{DoxyParamCaption}\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{h\+\_\+bl, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{Sref, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(in)}]{Ent\+\_\+bl, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{I\+\_\+d\+Skbp1, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{min\+\_\+ent\+\_\+in, }\item[{real, dimension(szi\+\_\+(g)), intent(in)}]{max\+\_\+ent\+\_\+in, }\item[{integer, intent(in)}]{kmb, }\item[{integer, intent(in)}]{is, }\item[{integer, intent(in)}]{ie, }\item[{type(\mbox{\hyperlink{structmom__grid_1_1ocean__grid__type}{ocean\+\_\+grid\+\_\+type}}), intent(in)}]{G, }\item[{type(\mbox{\hyperlink{structmom__verticalgrid_1_1verticalgrid__type}{verticalgrid\+\_\+type}}), intent(in)}]{GV, }\item[{type(\mbox{\hyperlink{structmom__entrain__diffusive_1_1entrain__diffusive__cs}{entrain\+\_\+diffusive\+\_\+cs}}), pointer}]{CS, }\item[{real, dimension( g \%isd\+: g \%ied), intent(out)}]{maxF, }\item[{real, dimension( g \%isd\+: g \%ied), intent(out), optional}]{ent\+\_\+maxF, }\item[{logical, dimension( g \%isd\+: g \%ied), intent(in), optional}]{do\+\_\+i\+\_\+in, }\item[{real, dimension( g \%isd\+: g \%ied), intent(out), optional}]{F\+\_\+lim\+\_\+maxent, }\item[{real, dimension( g \%isd\+: g \%ied), intent(in), optional}]{F\+\_\+thresh }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Maximize F = ent$\ast$ds\+\_\+kb$\ast$\+I\+\_\+d\+Skbp1 in the range min\+\_\+ent $<$ ent $<$ max\+\_\+ent. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em g} & The ocean\textquotesingle{}s grid structure. \\ \hline \mbox{\texttt{ in}} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure. \\ \hline \mbox{\texttt{ in}} & {\em h\+\_\+bl} & Layer thickness \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em sref} & Reference potential density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em ent\+\_\+bl} & The average entrainment upward and \\ \hline \mbox{\texttt{ in}} & {\em i\+\_\+dskbp1} & The inverse of the difference in reference potential density across the base of the uppermost interior layer \mbox{[}R-\/1 $\sim$$>$ m3 kg-\/1\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em min\+\_\+ent\+\_\+in} & The minimum value of ent to search, \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em max\+\_\+ent\+\_\+in} & The maximum value of ent to search, \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em kmb} & The number of mixed and buffer layers. \\ \hline \mbox{\texttt{ in}} & {\em is} & The start of the i-\/index range to work on. \\ \hline \mbox{\texttt{ in}} & {\em ie} & The end of the i-\/index range to work on. \\ \hline & {\em cs} & This module\textquotesingle{}s control structure. \\ \hline \mbox{\texttt{ out}} & {\em maxf} & The maximum value of F = ent$\ast$ds\+\_\+kb$\ast$\+I\+\_\+d\+Skbp1 found in the range min\+\_\+ent $<$ ent $<$ max\+\_\+ent \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ out}} & {\em ent\+\_\+maxf} & The value of ent at that maximum \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \mbox{\texttt{ in}} & {\em do\+\_\+i\+\_\+in} & A logical array indicating which columns \\ \hline \mbox{\texttt{ out}} & {\em f\+\_\+lim\+\_\+maxent} & If present, do not apply the limit in \\ \hline \mbox{\texttt{ in}} & {\em f\+\_\+thresh} & If F\+\_\+thresh is present, return the first \\ \hline \end{DoxyParams} Definition at line 1783 of file M\+O\+M\+\_\+entrain\+\_\+diffusive.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1786 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure.}} \DoxyCodeLine{1787 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid structure.}} \DoxyCodeLine{1788 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \&} \DoxyCodeLine{1789 \textcolor{keywordtype}{intent(in)} :: h\_bl\textcolor{comment}{ !< Layer thickness [H \string~> m or kg m-\/2]}} \DoxyCodeLine{1790 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \&} \DoxyCodeLine{1791 \textcolor{keywordtype}{intent(in)} :: Sref\textcolor{comment}{ !< Reference potential density [R \string~> kg m-\/3].}} \DoxyCodeLine{1792 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \&} \DoxyCodeLine{1793 \textcolor{keywordtype}{intent(in)} :: Ent\_bl\textcolor{comment}{ !< The average entrainment upward and}} \DoxyCodeLine{1794 \textcolor{comment}{ !! downward across each interface around}} \DoxyCodeLine{1795 \textcolor{comment}{ !! the buffer layers [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1796 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: I\_dSkbp1\textcolor{comment}{ !< The inverse of the difference in}} \DoxyCodeLine{1797 \textcolor{comment}{ !! reference potential density across the}} \DoxyCodeLine{1798 \textcolor{comment}{ !! base of the uppermost interior layer}} \DoxyCodeLine{1799 \textcolor{comment}{ !! [R-\/1 \string~> m3 kg-\/1].}} \DoxyCodeLine{1800 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: min\_ent\_in\textcolor{comment}{ !< The minimum value of ent to search,}} \DoxyCodeLine{1801 \textcolor{comment}{ !! [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1802 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: max\_ent\_in\textcolor{comment}{ !< The maximum value of ent to search,}} \DoxyCodeLine{1803 \textcolor{comment}{ !! [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1804 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: kmb\textcolor{comment}{ !< The number of mixed and buffer layers.}} \DoxyCodeLine{1805 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: is\textcolor{comment}{ !< The start of the i-\/index range to work on.}} \DoxyCodeLine{1806 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: ie\textcolor{comment}{ !< The end of the i-\/index range to work on.}} \DoxyCodeLine{1807 \textcolor{keywordtype}{type}(entrain\_diffusive\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< This module's control structure.}} \DoxyCodeLine{1808 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(out)} :: maxF\textcolor{comment}{ !< The maximum value of F}} \DoxyCodeLine{1809 \textcolor{comment}{ !! = ent*ds\_kb*I\_dSkbp1 found in the range}} \DoxyCodeLine{1810 \textcolor{comment}{ !! min\_ent < ent < max\_ent [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1811 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \&} \DoxyCodeLine{1812 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: ent\_maxF\textcolor{comment}{ !< The value of ent at that maximum [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1813 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \&} \DoxyCodeLine{1814 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: do\_i\_in\textcolor{comment}{ !< A logical array indicating which columns}} \DoxyCodeLine{1815 \textcolor{comment}{ !! to work on.}} \DoxyCodeLine{1816 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \&} \DoxyCodeLine{1817 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: F\_lim\_maxent\textcolor{comment}{ !< If present, do not apply the limit in}} \DoxyCodeLine{1818 \textcolor{comment}{ !! finding the maximum value, but return the}} \DoxyCodeLine{1819 \textcolor{comment}{ !! limited value at ent=max\_ent\_in in this}} \DoxyCodeLine{1820 \textcolor{comment}{ !! array [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1821 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \&} \DoxyCodeLine{1822 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: F\_thresh\textcolor{comment}{ !< If F\_thresh is present, return the first}} \DoxyCodeLine{1823 \textcolor{comment}{ !! value found that has F > F\_thresh, or}} \DoxyCodeLine{1824 \textcolor{comment}{ !! the maximum.}} \DoxyCodeLine{1825 } \DoxyCodeLine{1826 \textcolor{comment}{! Maximize F = ent*ds\_kb*I\_dSkbp1 in the range min\_ent < ent < max\_ent.}} \DoxyCodeLine{1827 \textcolor{comment}{! ds\_kb may itself be limited to positive values in determine\_dSkb, which gives}} \DoxyCodeLine{1828 \textcolor{comment}{! the prospect of two local maxima in the range -\/ one at max\_ent\_in with that}} \DoxyCodeLine{1829 \textcolor{comment}{! minimum value of ds\_kb, and the other due to the unlimited (potentially}} \DoxyCodeLine{1830 \textcolor{comment}{! negative) value. It is faster to find the true maximum by first finding the}} \DoxyCodeLine{1831 \textcolor{comment}{! unlimited maximum and comparing it to the limited value at max\_ent\_in.}} \DoxyCodeLine{1832 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: \&} \DoxyCodeLine{1833 ent, \&} \DoxyCodeLine{1834 minent, maxent, ent\_best, \&} \DoxyCodeLine{1835 F\_max\_ent\_in, \&} \DoxyCodeLine{1836 F\_maxent, F\_minent, F, F\_best, \&} \DoxyCodeLine{1837 dF\_dent, dF\_dE\_max, dF\_dE\_min, dF\_dE\_best, \&} \DoxyCodeLine{1838 dS\_kb, dS\_kb\_lim, ddSkb\_dE, dS\_anom\_lim, \&} \DoxyCodeLine{1839 chg\_prev, chg\_pre\_prev} \DoxyCodeLine{1840 \textcolor{keywordtype}{ real} :: dF\_dE\_mean, maxslope, minslope} \DoxyCodeLine{1841 \textcolor{keywordtype}{ real} :: tolerance} \DoxyCodeLine{1842 \textcolor{keywordtype}{ real} :: ratio\_select\_end} \DoxyCodeLine{1843 \textcolor{keywordtype}{ real} :: rat, max\_chg, min\_chg, chg1, chg2, chg} \DoxyCodeLine{1844 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: do\_i, last\_it, need\_bracket, may\_use\_best} \DoxyCodeLine{1845 \textcolor{keywordtype}{logical} :: doany, OK1, OK2, bisect, new\_min\_bound} \DoxyCodeLine{1846 \textcolor{keywordtype}{integer} :: i, it, is1, ie1} \DoxyCodeLine{1847 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{parameter} :: MAXIT = 20} \DoxyCodeLine{1848 } \DoxyCodeLine{1849 tolerance = cs\%Tolerance\_Ent} \DoxyCodeLine{1850 } \DoxyCodeLine{1851 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(do\_i\_in)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1852 \textcolor{keywordflow}{do} i=is,ie ; do\_i(i) = do\_i\_in(i) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1853 \textcolor{keywordflow}{else}} \DoxyCodeLine{1854 \textcolor{keywordflow}{do} i=is,ie ; do\_i(i) = .true. ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1855 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1856 } \DoxyCodeLine{1857 \textcolor{comment}{! The most likely value is at max\_ent.}} \DoxyCodeLine{1858 \textcolor{keyword}{call }determine\_dskb(h\_bl, sref, ent\_bl, max\_ent\_in, is, ie, kmb, g, gv, .false., \&} \DoxyCodeLine{1859 ds\_kb, ddskb\_de, ds\_anom\_lim=ds\_anom\_lim)} \DoxyCodeLine{1860 ie1 = is-\/1 ; doany = .false.} \DoxyCodeLine{1861 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1862 ds\_kb\_lim(i) = ds\_kb(i) + ds\_anom\_lim(i)} \DoxyCodeLine{1863 f\_max\_ent\_in(i) = max\_ent\_in(i)*ds\_kb\_lim(i)*i\_dskbp1(i)} \DoxyCodeLine{1864 maxent(i) = max\_ent\_in(i) ; minent(i) = min\_ent\_in(i)} \DoxyCodeLine{1865 \textcolor{keywordflow}{if} ((abs(maxent(i) -\/ minent(i)) < tolerance) .or. (.not.do\_i(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{1866 f\_best(i) = max\_ent\_in(i)*ds\_kb(i)*i\_dskbp1(i)} \DoxyCodeLine{1867 ent\_best(i) = max\_ent\_in(i) ; ent(i) = max\_ent\_in(i)} \DoxyCodeLine{1868 do\_i(i) = .false.} \DoxyCodeLine{1869 \textcolor{keywordflow}{else}} \DoxyCodeLine{1870 f\_maxent(i) = maxent(i) * ds\_kb(i) * i\_dskbp1(i)} \DoxyCodeLine{1871 df\_de\_max(i) = (ds\_kb(i) + maxent(i)*ddskb\_de(i)) * i\_dskbp1(i)} \DoxyCodeLine{1872 doany = .true. ; last\_it(i) = .false. ; need\_bracket(i) = .true.} \DoxyCodeLine{1873 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1874 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1875 } \DoxyCodeLine{1876 \textcolor{keywordflow}{if} (doany) \textcolor{keywordflow}{then}} \DoxyCodeLine{1877 ie1 = is-\/1 ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) ie1 = i ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1878 \textcolor{keywordflow}{do} i=ie1,is,-\/1 ; \textcolor{keywordflow}{if} (do\_i(i)) is1 = i ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1879 \textcolor{comment}{! Find the value of F and its derivative at min\_ent.}} \DoxyCodeLine{1880 \textcolor{keyword}{call }determine\_dskb(h\_bl, sref, ent\_bl, minent, is1, ie1, kmb, g, gv, .false., \&} \DoxyCodeLine{1881 ds\_kb, ddskb\_de, do\_i\_in = do\_i)} \DoxyCodeLine{1882 \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1883 f\_minent(i) = minent(i) * ds\_kb(i) * i\_dskbp1(i)} \DoxyCodeLine{1884 df\_de\_min(i) = (ds\_kb(i) + minent(i)*ddskb\_de(i)) * i\_dskbp1(i)} \DoxyCodeLine{1885 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1886 } \DoxyCodeLine{1887 ratio\_select\_end = 0.9} \DoxyCodeLine{1888 \textcolor{keywordflow}{do} it=1,maxit} \DoxyCodeLine{1889 ratio\_select\_end = 0.5*ratio\_select\_end} \DoxyCodeLine{1890 \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1891 \textcolor{keywordflow}{if} (need\_bracket(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1892 df\_de\_mean = (f\_maxent(i) -\/ f\_minent(i)) / (maxent(i) -\/ minent(i))} \DoxyCodeLine{1893 maxslope = max(df\_de\_mean, df\_de\_min(i), df\_de\_max(i))} \DoxyCodeLine{1894 minslope = min(df\_de\_mean, df\_de\_min(i), df\_de\_max(i))} \DoxyCodeLine{1895 \textcolor{keywordflow}{if} (f\_minent(i) >= f\_maxent(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1896 \textcolor{keywordflow}{if} (df\_de\_min(i) > 0.0) \textcolor{keywordflow}{then} ; rat = 0.02 \textcolor{comment}{! A small step should bracket the soln.}} \DoxyCodeLine{1897 \textcolor{keywordflow}{elseif} (maxslope < ratio\_select\_end*minslope) \textcolor{keywordflow}{then}} \DoxyCodeLine{1898 \textcolor{comment}{! The maximum of F is at minent.}} \DoxyCodeLine{1899 f\_best(i) = f\_minent(i) ; ent\_best(i) = minent(i) ; rat = 0.0} \DoxyCodeLine{1900 do\_i(i) = .false.} \DoxyCodeLine{1901 \textcolor{keywordflow}{else} ; rat = 0.382 ;\textcolor{keywordflow}{ endif} \textcolor{comment}{! Use the golden ratio}} \DoxyCodeLine{1902 \textcolor{keywordflow}{else}} \DoxyCodeLine{1903 \textcolor{keywordflow}{if} (df\_de\_max(i) < 0.0) \textcolor{keywordflow}{then} ; rat = 0.98 \textcolor{comment}{! A small step should bracket the soln.}} \DoxyCodeLine{1904 \textcolor{keywordflow}{elseif} (minslope > ratio\_select\_end*maxslope) \textcolor{keywordflow}{then}} \DoxyCodeLine{1905 \textcolor{comment}{! The maximum of F is at maxent.}} \DoxyCodeLine{1906 f\_best(i) = f\_maxent(i) ; ent\_best(i) = maxent(i) ; rat = 1.0} \DoxyCodeLine{1907 do\_i(i) = .false.} \DoxyCodeLine{1908 \textcolor{keywordflow}{else} ; rat = 0.618 ;\textcolor{keywordflow}{ endif} \textcolor{comment}{! Use the golden ratio}} \DoxyCodeLine{1909 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1910 } \DoxyCodeLine{1911 \textcolor{keywordflow}{if} (rat >= 0.0) ent(i) = rat*maxent(i) + (1.0-\/rat)*minent(i)} \DoxyCodeLine{1912 \textcolor{keywordflow}{if} (((maxent(i) -\/ minent(i)) < tolerance) .or. (it==maxit)) \&} \DoxyCodeLine{1913 last\_it(i) = .true.} \DoxyCodeLine{1914 \textcolor{keywordflow}{else} \textcolor{comment}{! The maximum is bracketed by minent, ent\_best, and maxent.}} \DoxyCodeLine{1915 chg1 = 2.0*(maxent(i) -\/ minent(i)) ; chg2 = chg1} \DoxyCodeLine{1916 \textcolor{keywordflow}{if} (df\_de\_best(i) > 0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1917 max\_chg = maxent(i) -\/ ent\_best(i) ; min\_chg = 0.0} \DoxyCodeLine{1918 \textcolor{keywordflow}{else}} \DoxyCodeLine{1919 max\_chg = 0.0 ; min\_chg = minent(i) -\/ ent\_best(i) \textcolor{comment}{! < 0}} \DoxyCodeLine{1920 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1921 \textcolor{keywordflow}{if} (max\_chg -\/ min\_chg < 2.0*tolerance) last\_it(i) = .true.} \DoxyCodeLine{1922 \textcolor{keywordflow}{if} (df\_de\_max(i) /= df\_de\_best(i)) \&} \DoxyCodeLine{1923 chg1 = (maxent(i) -\/ ent\_best(i))*df\_de\_best(i) / \&} \DoxyCodeLine{1924 (df\_de\_best(i) -\/ df\_de\_max(i))} \DoxyCodeLine{1925 \textcolor{keywordflow}{if} (df\_de\_min(i) /= df\_de\_best(i)) \&} \DoxyCodeLine{1926 chg2 = (minent(i) -\/ ent\_best(i))*df\_de\_best(i) / \&} \DoxyCodeLine{1927 (df\_de\_best(i) -\/ df\_de\_min(i))} \DoxyCodeLine{1928 ok1 = ((chg1 < max\_chg) .and. (chg1 > min\_chg))} \DoxyCodeLine{1929 ok2 = ((chg2 < max\_chg) .and. (chg2 > min\_chg))} \DoxyCodeLine{1930 \textcolor{keywordflow}{if} (.not.(ok1 .or. ok2)) \textcolor{keywordflow}{then} ; bisect = .true. ; \textcolor{keywordflow}{else}} \DoxyCodeLine{1931 \textcolor{keywordflow}{if} (ok1 .and. ok2) \textcolor{keywordflow}{then} \textcolor{comment}{! Take the acceptable smaller change.}} \DoxyCodeLine{1932 chg = chg1 ; \textcolor{keywordflow}{if} (abs(chg2) < abs(chg1)) chg = chg2} \DoxyCodeLine{1933 \textcolor{keywordflow}{elseif} (ok1) \textcolor{keywordflow}{then} ; chg = chg1} \DoxyCodeLine{1934 \textcolor{keywordflow}{else} ; chg = chg2 ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1935 \textcolor{keywordflow}{if} (abs(chg) > 0.5*abs(chg\_pre\_prev(i))) \textcolor{keywordflow}{then} ; bisect = .true.} \DoxyCodeLine{1936 \textcolor{keywordflow}{else} ; bisect = .false. ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1937 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1938 chg\_pre\_prev(i) = chg\_prev(i)} \DoxyCodeLine{1939 \textcolor{keywordflow}{if} (bisect) \textcolor{keywordflow}{then}} \DoxyCodeLine{1940 \textcolor{keywordflow}{if} (df\_de\_best(i) > 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1941 ent(i) = 0.5*(maxent(i) + ent\_best(i))} \DoxyCodeLine{1942 chg\_prev(i) = 0.5*(maxent(i) -\/ ent\_best(i))} \DoxyCodeLine{1943 \textcolor{keywordflow}{else}} \DoxyCodeLine{1944 ent(i) = 0.5*(minent(i) + ent\_best(i))} \DoxyCodeLine{1945 chg\_prev(i) = 0.5*(minent(i) -\/ ent\_best(i))} \DoxyCodeLine{1946 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1947 \textcolor{keywordflow}{else}} \DoxyCodeLine{1948 \textcolor{keywordflow}{if} (abs(chg) < tolerance) chg = sign(tolerance,chg)} \DoxyCodeLine{1949 ent(i) = ent\_best(i) + chg} \DoxyCodeLine{1950 chg\_prev(i) = chg} \DoxyCodeLine{1951 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1952 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1953 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1954 } \DoxyCodeLine{1955 \textcolor{keywordflow}{if} (mod(it,3) == 0) \textcolor{keywordflow}{then} \textcolor{comment}{! Re-\/determine the loop bounds.}} \DoxyCodeLine{1956 ie1 = is-\/1 ; \textcolor{keywordflow}{do} i=is1,ie ; \textcolor{keywordflow}{if} (do\_i(i)) ie1 = i ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1957 \textcolor{keywordflow}{do} i=ie1,is,-\/1 ; \textcolor{keywordflow}{if} (do\_i(i)) is1 = i ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1958 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1959 } \DoxyCodeLine{1960 \textcolor{keyword}{call }determine\_dskb(h\_bl, sref, ent\_bl, ent, is1, ie1, kmb, g, gv, .false., \&} \DoxyCodeLine{1961 ds\_kb, ddskb\_de, do\_i\_in = do\_i)} \DoxyCodeLine{1962 \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1963 f(i) = ent(i)*ds\_kb(i)*i\_dskbp1(i)} \DoxyCodeLine{1964 df\_dent(i) = (ds\_kb(i) + ent(i)*ddskb\_de(i)) * i\_dskbp1(i)} \DoxyCodeLine{1965 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1966 } \DoxyCodeLine{1967 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(f\_thresh)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1968 \textcolor{keywordflow}{if} (f(i) >= f\_thresh(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1969 f\_best(i) = f(i) ; ent\_best(i) = ent(i) ; do\_i(i) = .false.} \DoxyCodeLine{1970 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1971 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1972 } \DoxyCodeLine{1973 doany = .false.} \DoxyCodeLine{1974 \textcolor{keywordflow}{do} i=is1,ie1 ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1975 \textcolor{keywordflow}{if} (.not.last\_it(i)) doany = .true.} \DoxyCodeLine{1976 \textcolor{keywordflow}{if} (last\_it(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1977 \textcolor{keywordflow}{if} (need\_bracket(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1978 \textcolor{keywordflow}{if} ((f(i) > f\_maxent(i)) .and. (f(i) > f\_minent(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{1979 f\_best(i) = f(i) ; ent\_best(i) = ent(i)} \DoxyCodeLine{1980 \textcolor{keywordflow}{elseif} (f\_maxent(i) > f\_minent(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1981 f\_best(i) = f\_maxent(i) ; ent\_best(i) = maxent(i)} \DoxyCodeLine{1982 \textcolor{keywordflow}{else}} \DoxyCodeLine{1983 f\_best(i) = f\_minent(i) ; ent\_best(i) = minent(i)} \DoxyCodeLine{1984 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1985 \textcolor{keywordflow}{elseif} (f(i) > f\_best(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1986 f\_best(i) = f(i) ; ent\_best(i) = ent(i)} \DoxyCodeLine{1987 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1988 do\_i(i) = .false.} \DoxyCodeLine{1989 \textcolor{keywordflow}{elseif} (need\_bracket(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1990 \textcolor{keywordflow}{if} ((f(i) > f\_maxent(i)) .and. (f(i) > f\_minent(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{1991 need\_bracket(i) = .false. \textcolor{comment}{! The maximum is now bracketed.}} \DoxyCodeLine{1992 chg\_prev(i) = (maxent(i) -\/ minent(i))} \DoxyCodeLine{1993 chg\_pre\_prev(i) = 2.0*chg\_prev(i)} \DoxyCodeLine{1994 ent\_best(i) = ent(i) ; f\_best(i) = f(i) ; df\_de\_best(i) = df\_dent(i)} \DoxyCodeLine{1995 \textcolor{keywordflow}{elseif} ((f(i) <= f\_maxent(i)) .and. (f(i) > f\_minent(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{1996 new\_min\_bound = .true. \textcolor{comment}{! We have a new minimum bound.}} \DoxyCodeLine{1997 \textcolor{keywordflow}{elseif} ((f(i) <= f\_maxent(i)) .and. (f(i) > f\_minent(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{1998 new\_min\_bound = .false. \textcolor{comment}{! We have a new maximum bound.}} \DoxyCodeLine{1999 \textcolor{keywordflow}{else} \textcolor{comment}{! This case would bracket a minimum. Wierd.}} \DoxyCodeLine{2000 \textcolor{comment}{! Unless the derivative indicates that there is a maximum near the}} \DoxyCodeLine{2001 \textcolor{comment}{! lower bound, try keeping the end with the larger value of F}} \DoxyCodeLine{2002 \textcolor{comment}{! in a tie keep the minimum as the answer here will be compared}} \DoxyCodeLine{2003 \textcolor{comment}{! with the maximum input value later.}} \DoxyCodeLine{2004 new\_min\_bound = .true.} \DoxyCodeLine{2005 \textcolor{keywordflow}{if} (df\_de\_min(i) > 0.0 .or. (f\_minent(i) >= f\_maxent(i))) \&} \DoxyCodeLine{2006 new\_min\_bound = .false.} \DoxyCodeLine{2007 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2008 \textcolor{keywordflow}{if} (need\_bracket(i)) \textcolor{keywordflow}{then} \textcolor{comment}{! Still not bracketed.}} \DoxyCodeLine{2009 \textcolor{keywordflow}{if} (new\_min\_bound) \textcolor{keywordflow}{then}} \DoxyCodeLine{2010 minent(i) = ent(i) ; f\_minent(i) = f(i) ; df\_de\_min(i) = df\_dent(i)} \DoxyCodeLine{2011 \textcolor{keywordflow}{else}} \DoxyCodeLine{2012 maxent(i) = ent(i) ; f\_maxent(i) = f(i) ; df\_de\_max(i) = df\_dent(i)} \DoxyCodeLine{2013 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2014 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2015 \textcolor{keywordflow}{else} \textcolor{comment}{! The root was previously bracketed.}} \DoxyCodeLine{2016 \textcolor{keywordflow}{if} (f(i) >= f\_best(i)) \textcolor{keywordflow}{then} \textcolor{comment}{! There is a new maximum.}} \DoxyCodeLine{2017 \textcolor{keywordflow}{if} (ent(i) > ent\_best(i)) \textcolor{keywordflow}{then} \textcolor{comment}{! Replace minent with ent\_prev.}} \DoxyCodeLine{2018 minent(i) = ent\_best(i) ; f\_minent(i) = f\_best(i) ; df\_de\_min(i) = df\_de\_best(i)} \DoxyCodeLine{2019 \textcolor{keywordflow}{else} \textcolor{comment}{! Replace maxent with ent\_best.}} \DoxyCodeLine{2020 maxent(i) = ent\_best(i) ; f\_maxent(i) = f\_best(i) ; df\_de\_max(i) = df\_de\_best(i)} \DoxyCodeLine{2021 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2022 ent\_best(i) = ent(i) ; f\_best(i) = f(i) ; df\_de\_best(i) = df\_dent(i)} \DoxyCodeLine{2023 \textcolor{keywordflow}{else}} \DoxyCodeLine{2024 \textcolor{keywordflow}{if} (ent(i) < ent\_best(i)) \textcolor{keywordflow}{then} \textcolor{comment}{! Replace the minent with ent.}} \DoxyCodeLine{2025 minent(i) = ent(i) ; f\_minent(i) = f(i) ; df\_de\_min(i) = df\_dent(i)} \DoxyCodeLine{2026 \textcolor{keywordflow}{else} \textcolor{comment}{! Replace maxent with ent\_prev.}} \DoxyCodeLine{2027 maxent(i) = ent(i) ; f\_maxent(i) = f(i) ; df\_de\_max(i) = df\_dent(i)} \DoxyCodeLine{2028 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2029 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2030 \textcolor{keywordflow}{if} ((maxent(i) -\/ minent(i)) <= tolerance) do\_i(i) = .false. \textcolor{comment}{! Done.}} \DoxyCodeLine{2031 \textcolor{keywordflow}{ endif} \textcolor{comment}{! need\_bracket.}} \DoxyCodeLine{2032 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{2033 \textcolor{keywordflow}{if} (.not.doany) \textcolor{keywordflow}{exit}} \DoxyCodeLine{2034 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{2035 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2036 } \DoxyCodeLine{2037 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(f\_lim\_maxent)) \textcolor{keywordflow}{then}} \DoxyCodeLine{2038 \textcolor{comment}{! Return the unlimited maximum in maxF, and the limited value of F at maxent.}} \DoxyCodeLine{2039 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{2040 maxf(i) = f\_best(i)} \DoxyCodeLine{2041 f\_lim\_maxent(i) = f\_max\_ent\_in(i)} \DoxyCodeLine{2042 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ent\_maxf)) ent\_maxf(i) = ent\_best(i)} \DoxyCodeLine{2043 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{2044 \textcolor{keywordflow}{else}} \DoxyCodeLine{2045 \textcolor{comment}{! Now compare the two? potential maxima using the limited value of dF\_kb.}} \DoxyCodeLine{2046 doany = .false.} \DoxyCodeLine{2047 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{2048 may\_use\_best(i) = (ent\_best(i) /= max\_ent\_in(i))} \DoxyCodeLine{2049 \textcolor{keywordflow}{if} (may\_use\_best(i)) doany = .true.} \DoxyCodeLine{2050 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{2051 \textcolor{keywordflow}{if} (doany) \textcolor{keywordflow}{then}} \DoxyCodeLine{2052 \textcolor{comment}{! For efficiency, could save previous value of dS\_anom\_lim\_best?}} \DoxyCodeLine{2053 \textcolor{keyword}{call }determine\_dskb(h\_bl, sref, ent\_bl, ent\_best, is, ie, kmb, g, gv, .true., \&} \DoxyCodeLine{2054 ds\_kb\_lim)} \DoxyCodeLine{2055 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{2056 f\_best(i) = ent\_best(i)*ds\_kb\_lim(i)*i\_dskbp1(i)} \DoxyCodeLine{2057 \textcolor{comment}{! The second test seems necessary because of roundoff differences that}} \DoxyCodeLine{2058 \textcolor{comment}{! can arise during compilation.}} \DoxyCodeLine{2059 \textcolor{keywordflow}{if} ((f\_best(i) > f\_max\_ent\_in(i)) .and. (may\_use\_best(i))) \textcolor{keywordflow}{then}} \DoxyCodeLine{2060 maxf(i) = f\_best(i)} \DoxyCodeLine{2061 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ent\_maxf)) ent\_maxf(i) = ent\_best(i)} \DoxyCodeLine{2062 \textcolor{keywordflow}{else}} \DoxyCodeLine{2063 maxf(i) = f\_max\_ent\_in(i)} \DoxyCodeLine{2064 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ent\_maxf)) ent\_maxf(i) = max\_ent\_in(i)} \DoxyCodeLine{2065 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2066 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{2067 \textcolor{keywordflow}{else}} \DoxyCodeLine{2068 \textcolor{comment}{! All of the maxima are at the maximum entrainment.}} \DoxyCodeLine{2069 \textcolor{keywordflow}{do} i=is,ie ; maxf(i) = f\_max\_ent\_in(i) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{2070 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(ent\_maxf)) \textcolor{keywordflow}{then}} \DoxyCodeLine{2071 \textcolor{keywordflow}{do} i=is,ie ; ent\_maxf(i) = max\_ent\_in(i) ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{2072 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2073 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2074 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{2075 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__entrain__diffusive_a363a25e7823043bb028e920e359733b0}\label{namespacemom__entrain__diffusive_a363a25e7823043bb028e920e359733b0}} \index{mom\_entrain\_diffusive@{mom\_entrain\_diffusive}!set\_ent\_bl@{set\_ent\_bl}} \index{set\_ent\_bl@{set\_ent\_bl}!mom\_entrain\_diffusive@{mom\_entrain\_diffusive}} \doxysubsubsection{\texorpdfstring{set\_ent\_bl()}{set\_ent\_bl()}} {\footnotesize\ttfamily subroutine mom\+\_\+entrain\+\_\+diffusive\+::set\+\_\+ent\+\_\+bl (\begin{DoxyParamCaption}\item[{real, dimension( g \%isd\+: g \%ied, g \%jsd\+: g \%jed, g \%ke), intent(in)}]{h, }\item[{real, dimension( g \%isd\+: g \%ied, g \%ke+1), intent(in)}]{dt\+Kd\+\_\+int, }\item[{type(\mbox{\hyperlink{structmom__variables_1_1thermo__var__ptrs}{thermo\+\_\+var\+\_\+ptrs}}), intent(in)}]{tv, }\item[{integer, dimension( g \%isd\+: g \%ied), intent(inout)}]{kb, }\item[{integer, intent(in)}]{kmb, }\item[{logical, dimension( g \%isd\+: g \%ied), intent(in)}]{do\+\_\+i, }\item[{type(\mbox{\hyperlink{structmom__grid_1_1ocean__grid__type}{ocean\+\_\+grid\+\_\+type}}), intent(in)}]{G, }\item[{type(\mbox{\hyperlink{structmom__verticalgrid_1_1verticalgrid__type}{verticalgrid\+\_\+type}}), intent(in)}]{GV, }\item[{type(\mbox{\hyperlink{structmom__unit__scaling_1_1unit__scale__type}{unit\+\_\+scale\+\_\+type}}), intent(in)}]{US, }\item[{type(\mbox{\hyperlink{structmom__entrain__diffusive_1_1entrain__diffusive__cs}{entrain\+\_\+diffusive\+\_\+cs}}), pointer}]{CS, }\item[{integer, intent(in)}]{j, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)+1), intent(out)}]{Ent\+\_\+bl, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(out)}]{Sref, }\item[{real, dimension(szi\+\_\+(g),szk\+\_\+(g)), intent(out)}]{h\+\_\+bl }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine sets the average entrainment across each of the interfaces between buffer layers within a timestep. It also causes thin and relatively light interior layers to be entrained by the deepest buffer layer. Also find the initial coordinate potential densities (Sref) of each layer. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em g} & The ocean\textquotesingle{}s grid structure. \\ \hline \mbox{\texttt{ in}} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure. \\ \hline \mbox{\texttt{ in}} & {\em h} & Layer thicknesses \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em dtkd\+\_\+int} & The diapycnal diffusivity across \\ \hline \mbox{\texttt{ in}} & {\em tv} & A structure containing pointers to any available thermodynamic fields. Absent fields have N\+U\+LL ptrs. \\ \hline \mbox{\texttt{ in,out}} & {\em kb} & The index of the lightest layer denser than the buffer layer or 1 if there is no buffer layer. \\ \hline \mbox{\texttt{ in}} & {\em kmb} & The number of mixed and buffer layers. \\ \hline \mbox{\texttt{ in}} & {\em do\+\_\+i} & A logical variable indicating which i-\/points to work on. \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline & {\em cs} & This module\textquotesingle{}s control structure. \\ \hline \mbox{\texttt{ in}} & {\em j} & The meridional index upon which to work. \\ \hline \mbox{\texttt{ out}} & {\em ent\+\_\+bl} & The average entrainment upward and \\ \hline \mbox{\texttt{ out}} & {\em sref} & The coordinate potential density minus 1000 for each layer \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]}. \\ \hline \mbox{\texttt{ out}} & {\em h\+\_\+bl} & The thickness of each layer \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 1024 of file M\+O\+M\+\_\+entrain\+\_\+diffusive.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1025 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure.}} \DoxyCodeLine{1026 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid structure.}} \DoxyCodeLine{1027 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZJ\_(G),SZK\_(G))}, \&} \DoxyCodeLine{1028 \textcolor{keywordtype}{intent(in)} :: h\textcolor{comment}{ !< Layer thicknesses [H \string~> m or kg m-\/2]}} \DoxyCodeLine{1029 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G)+1)}, \&} \DoxyCodeLine{1030 \textcolor{keywordtype}{intent(in)} :: dtKd\_int\textcolor{comment}{ !< The diapycnal diffusivity across}} \DoxyCodeLine{1031 \textcolor{comment}{ !! each interface times the time step}} \DoxyCodeLine{1032 \textcolor{comment}{ !! [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{1033 \textcolor{keywordtype}{type}(thermo\_var\_ptrs), \textcolor{keywordtype}{intent(in)} :: tv\textcolor{comment}{ !< A structure containing pointers to any}} \DoxyCodeLine{1034 \textcolor{comment}{ !! available thermodynamic fields. Absent}} \DoxyCodeLine{1035 \textcolor{comment}{ !! fields have NULL ptrs.}} \DoxyCodeLine{1036 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(inout)} :: kb\textcolor{comment}{ !< The index of the lightest layer denser}} \DoxyCodeLine{1037 \textcolor{comment}{ !! than the buffer layer or 1 if there is}} \DoxyCodeLine{1038 \textcolor{comment}{ !! no buffer layer.}} \DoxyCodeLine{1039 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: kmb\textcolor{comment}{ !< The number of mixed and buffer layers.}} \DoxyCodeLine{1040 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{dimension(SZI\_(G))}, \textcolor{keywordtype}{intent(in)} :: do\_i\textcolor{comment}{ !< A logical variable indicating which}} \DoxyCodeLine{1041 \textcolor{comment}{ !! i-\/points to work on.}} \DoxyCodeLine{1042 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{1043 \textcolor{keywordtype}{type}(entrain\_diffusive\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< This module's control structure.}} \DoxyCodeLine{1044 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: j\textcolor{comment}{ !< The meridional index upon which to work.}} \DoxyCodeLine{1045 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G)+1)}, \&} \DoxyCodeLine{1046 \textcolor{keywordtype}{intent(out)} :: Ent\_bl\textcolor{comment}{ !< The average entrainment upward and}} \DoxyCodeLine{1047 \textcolor{comment}{ !! downward across each interface around}} \DoxyCodeLine{1048 \textcolor{comment}{ !! the buffer layers [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1049 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(out)} :: Sref\textcolor{comment}{ !< The coordinate potential density minus}} \DoxyCodeLine{1050 \textcolor{comment}{ !! 1000 for each layer [R \string~> kg m-\/3].}} \DoxyCodeLine{1051 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G),SZK\_(G))}, \textcolor{keywordtype}{intent(out)} :: h\_bl\textcolor{comment}{ !< The thickness of each layer [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1052 } \DoxyCodeLine{1053 \textcolor{comment}{! This subroutine sets the average entrainment across each of the interfaces}} \DoxyCodeLine{1054 \textcolor{comment}{! between buffer layers within a timestep. It also causes thin and relatively}} \DoxyCodeLine{1055 \textcolor{comment}{! light interior layers to be entrained by the deepest buffer layer.}} \DoxyCodeLine{1056 \textcolor{comment}{! Also find the initial coordinate potential densities (Sref) of each layer.}} \DoxyCodeLine{1057 \textcolor{comment}{! Does there need to be limiting when the layers below are all thin?}} \DoxyCodeLine{1058 } \DoxyCodeLine{1059 \textcolor{comment}{! Local variables}} \DoxyCodeLine{1060 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G))} :: \&} \DoxyCodeLine{1061 b1, d1, \& \textcolor{comment}{! Variables used by the tridiagonal solver [H-\/1 \string~> m-\/1 or m2 kg-\/1] and [nondim].}} \DoxyCodeLine{1062 Rcv, \& \textcolor{comment}{! Value of the coordinate variable (potential density)}} \DoxyCodeLine{1063 \textcolor{comment}{! based on the simulated T and S and P\_Ref [R \string~> kg m-\/3].}} \DoxyCodeLine{1064 pres, \& \textcolor{comment}{! Reference pressure (P\_Ref) [R L2 T-\/2 \string~> Pa].}} \DoxyCodeLine{1065 frac\_rem, \& \textcolor{comment}{! The fraction of the diffusion remaining [nondim].}} \DoxyCodeLine{1066 h\_interior \textcolor{comment}{! The interior thickness available for entrainment [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1067 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(G), SZK\_(G))} :: \&} \DoxyCodeLine{1068 S\_est \textcolor{comment}{! An estimate of the coordinate potential density -\/ 1000 after}} \DoxyCodeLine{1069 \textcolor{comment}{! entrainment for each layer [R \string~> kg m-\/3].}} \DoxyCodeLine{1070 \textcolor{keywordtype}{ real} :: max\_ent \textcolor{comment}{! The maximum possible entrainment [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1071 \textcolor{keywordtype}{ real} :: dh \textcolor{comment}{! An available thickness [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1072 \textcolor{keywordtype}{ real} :: Kd\_x\_dt \textcolor{comment}{! The diffusion that remains after thin layers are}} \DoxyCodeLine{1073 \textcolor{comment}{! entrained [H2 \string~> m2 or kg2 m-\/4].}} \DoxyCodeLine{1074 \textcolor{keywordtype}{ real} :: h\_neglect \textcolor{comment}{! A thickness that is so small it is usually lost}} \DoxyCodeLine{1075 \textcolor{comment}{! in roundoff and can be neglected [H \string~> m or kg m-\/2].}} \DoxyCodeLine{1076 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{dimension(2)} :: EOSdom \textcolor{comment}{! The i-\/computational domain for the equation of state}} \DoxyCodeLine{1077 \textcolor{keywordtype}{integer} :: i, k, is, ie, nz} \DoxyCodeLine{1078 is = g\%isc ; ie = g\%iec ; nz = g\%ke} \DoxyCodeLine{1079 } \DoxyCodeLine{1080 \textcolor{comment}{! max\_ent = 1.0e14*GV\%Angstrom\_H ! This is set to avoid roundoff problems.}} \DoxyCodeLine{1081 max\_ent = 1.0e4*gv\%m\_to\_H} \DoxyCodeLine{1082 h\_neglect = gv\%H\_subroundoff} \DoxyCodeLine{1083 } \DoxyCodeLine{1084 \textcolor{keywordflow}{do} i=is,ie ; pres(i) = tv\%P\_Ref ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1085 eosdom(:) = eos\_domain(g\%HI)} \DoxyCodeLine{1086 \textcolor{keywordflow}{do} k=1,kmb} \DoxyCodeLine{1087 \textcolor{keyword}{call }calculate\_density(tv\%T(:,j,k), tv\%S(:,j,k), pres, rcv, tv\%eqn\_of\_state, eosdom)} \DoxyCodeLine{1088 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1089 h\_bl(i,k) = h(i,j,k) + h\_neglect} \DoxyCodeLine{1090 sref(i,k) = rcv(i) -\/ cs\%Rho\_sig\_off} \DoxyCodeLine{1091 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1092 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1093 } \DoxyCodeLine{1094 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1095 h\_interior(i) = 0.0 ; ent\_bl(i,1) = 0.0} \DoxyCodeLine{1096 \textcolor{comment}{! if (kb(i) > nz) Ent\_bl(i,Kmb+1) = 0.0}} \DoxyCodeLine{1097 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1098 } \DoxyCodeLine{1099 \textcolor{keywordflow}{do} k=2,kmb ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1100 \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1101 ent\_bl(i,k) = min(2.0 * dtkd\_int(i,k) / (h(i,j,k-\/1) + h(i,j,k) + h\_neglect), \&} \DoxyCodeLine{1102 max\_ent)} \DoxyCodeLine{1103 \textcolor{keywordflow}{else} ; ent\_bl(i,k) = 0.0 ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1104 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1105 } \DoxyCodeLine{1106 \textcolor{comment}{! Determine the coordinate density of the bottommost buffer layer if there}} \DoxyCodeLine{1107 \textcolor{comment}{! is no entrainment from the layers below. This is a partial solver, based}} \DoxyCodeLine{1108 \textcolor{comment}{! on the first pass of a tridiagonal solver, as the values in the upper buffer}} \DoxyCodeLine{1109 \textcolor{comment}{! layers are not needed.}} \DoxyCodeLine{1110 } \DoxyCodeLine{1111 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1112 b1(i) = 1.0 / (h\_bl(i,1) + ent\_bl(i,2))} \DoxyCodeLine{1113 d1(i) = h\_bl(i,1) * b1(i) \textcolor{comment}{! = 1.0 -\/ Ent\_bl(i,2)*b1(i)}} \DoxyCodeLine{1114 s\_est(i,1) = (h\_bl(i,1)*sref(i,1)) * b1(i)} \DoxyCodeLine{1115 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1116 \textcolor{keywordflow}{do} k=2,kmb-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1117 b1(i) = 1.0 / ((h\_bl(i,k) + ent\_bl(i,k+1)) + d1(i)*ent\_bl(i,k))} \DoxyCodeLine{1118 d1(i) = (h\_bl(i,k) + d1(i)*ent\_bl(i,k)) * b1(i) \textcolor{comment}{! = 1.0 -\/ Ent\_bl(i,K+1)*b1(i)}} \DoxyCodeLine{1119 s\_est(i,k) = (h\_bl(i,k)*sref(i,k) + ent\_bl(i,k)*s\_est(i,k-\/1)) * b1(i)} \DoxyCodeLine{1120 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1121 \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1122 s\_est(i,kmb) = (h\_bl(i,kmb)*sref(i,kmb) + ent\_bl(i,kmb)*s\_est(i,kmb-\/1)) / \&} \DoxyCodeLine{1123 (h\_bl(i,kmb) + d1(i)*ent\_bl(i,kmb))} \DoxyCodeLine{1124 frac\_rem(i) = 1.0} \DoxyCodeLine{1125 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1126 } \DoxyCodeLine{1127 \textcolor{comment}{! Entrain any thin interior layers that are lighter (in the coordinate}} \DoxyCodeLine{1128 \textcolor{comment}{! potential density) than the deepest buffer layer will be, and adjust kb.}} \DoxyCodeLine{1129 \textcolor{keywordflow}{do} i=is,ie ; kb(i) = nz+1 ; \textcolor{keywordflow}{if} (do\_i(i)) kb(i) = kmb+1 ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1130 } \DoxyCodeLine{1131 \textcolor{keywordflow}{do} k=kmb+1,nz ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1132 \textcolor{keywordflow}{if} ((k == kb(i)) .and. (s\_est(i,kmb) > (gv\%Rlay(k) -\/ cs\%Rho\_sig\_off))) \textcolor{keywordflow}{then}} \DoxyCodeLine{1133 \textcolor{keywordflow}{if} (4.0*dtkd\_int(i,kmb+1)*frac\_rem(i) > \&} \DoxyCodeLine{1134 (h\_bl(i,kmb) + h(i,j,k)) * (h(i,j,k) -\/ gv\%Angstrom\_H)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1135 \textcolor{comment}{! Entrain this layer into the buffer layer and move kb down.}} \DoxyCodeLine{1136 dh = max((h(i,j,k) -\/ gv\%Angstrom\_H), 0.0)} \DoxyCodeLine{1137 \textcolor{keywordflow}{if} (dh > 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1138 frac\_rem(i) = frac\_rem(i) -\/ ((h\_bl(i,kmb) + h(i,j,k)) * dh) / \&} \DoxyCodeLine{1139 (4.0*dtkd\_int(i,kmb+1))} \DoxyCodeLine{1140 sref(i,kmb) = (h\_bl(i,kmb)*sref(i,kmb) + dh*(gv\%Rlay(k)-\/cs\%Rho\_sig\_off)) / \&} \DoxyCodeLine{1141 (h\_bl(i,kmb) + dh)} \DoxyCodeLine{1142 h\_bl(i,kmb) = h\_bl(i,kmb) + dh} \DoxyCodeLine{1143 s\_est(i,kmb) = (h\_bl(i,kmb)*sref(i,kmb) + ent\_bl(i,kmb)*s\_est(i,kmb-\/1)) / \&} \DoxyCodeLine{1144 (h\_bl(i,kmb) + d1(i)*ent\_bl(i,kmb))} \DoxyCodeLine{1145 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1146 kb(i) = kb(i) + 1} \DoxyCodeLine{1147 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1148 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1149 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1150 } \DoxyCodeLine{1151 \textcolor{comment}{! This is where variables are be set up with a different vertical grid}} \DoxyCodeLine{1152 \textcolor{comment}{! in which the (newly?) massless layers are taken out.}} \DoxyCodeLine{1153 \textcolor{keywordflow}{do} k=nz,kmb+1,-\/1 ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{1154 \textcolor{keywordflow}{if} (k >= kb(i)) h\_interior(i) = h\_interior(i) + (h(i,j,k)-\/gv\%Angstrom\_H)} \DoxyCodeLine{1155 \textcolor{keywordflow}{if} (k==kb(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1156 h\_bl(i,kmb+1) = h(i,j,k) ; sref(i,kmb+1) = gv\%Rlay(k) -\/ cs\%Rho\_sig\_off} \DoxyCodeLine{1157 \textcolor{keywordflow}{elseif} (k==kb(i)+1) \textcolor{keywordflow}{then}} \DoxyCodeLine{1158 h\_bl(i,kmb+2) = h(i,j,k) ; sref(i,kmb+2) = gv\%Rlay(k) -\/ cs\%Rho\_sig\_off} \DoxyCodeLine{1159 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1160 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1161 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (kb(i) >= nz) \textcolor{keywordflow}{then}} \DoxyCodeLine{1162 h\_bl(i,kmb+1) = h(i,j,nz)} \DoxyCodeLine{1163 sref(i,kmb+1) = gv\%Rlay(nz) -\/ cs\%Rho\_sig\_off} \DoxyCodeLine{1164 h\_bl(i,kmb+2) = gv\%Angstrom\_H} \DoxyCodeLine{1165 sref(i,kmb+2) = sref(i,kmb+1) + (gv\%Rlay(nz) -\/ gv\%Rlay(nz-\/1))} \DoxyCodeLine{1166 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1167 } \DoxyCodeLine{1168 \textcolor{comment}{! Perhaps we should revisit the way that the average entrainment between the}} \DoxyCodeLine{1169 \textcolor{comment}{! buffer layer and the interior is calculated so that it is not unduly}} \DoxyCodeLine{1170 \textcolor{comment}{! limited when the layers are less than sqrt(Kd * dt) thick?}} \DoxyCodeLine{1171 \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (do\_i(i)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1172 kd\_x\_dt = frac\_rem(i) * dtkd\_int(i,kmb+1)} \DoxyCodeLine{1173 \textcolor{keywordflow}{if} ((kd\_x\_dt <= 0.0) .or. (h\_interior(i) <= 0.0)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1174 ent\_bl(i,kmb+1) = 0.0} \DoxyCodeLine{1175 \textcolor{keywordflow}{else}} \DoxyCodeLine{1176 \textcolor{comment}{! If the combined layers are exceptionally thin, use sqrt(Kd*dt) as the}} \DoxyCodeLine{1177 \textcolor{comment}{! estimate of the thickness in the denominator of the thickness diffusion.}} \DoxyCodeLine{1178 ent\_bl(i,kmb+1) = min(0.5*h\_interior(i), sqrt(kd\_x\_dt), \&} \DoxyCodeLine{1179 kd\_x\_dt / (0.5*(h\_bl(i,kmb) + h\_bl(i,kmb+1))))} \DoxyCodeLine{1180 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1181 \textcolor{keywordflow}{else}} \DoxyCodeLine{1182 ent\_bl(i,kmb+1) = 0.0} \DoxyCodeLine{1183 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1184 } \end{DoxyCode}