\hypertarget{namespacemom__diapyc__energy__req}{}\section{mom\+\_\+diapyc\+\_\+energy\+\_\+req Module Reference} \label{namespacemom__diapyc__energy__req}\index{mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}} \subsection{Detailed Description} Calculates the energy requirements of mixing. \subsection*{Data Types} \begin{DoxyCompactItemize} \item type \mbox{\hyperlink{structmom__diapyc__energy__req_1_1diapyc__energy__req__cs}{diapyc\+\_\+energy\+\_\+req\+\_\+cs}} \begin{DoxyCompactList}\small\item\em This control structure holds parameters for the M\+O\+M\+\_\+diapyc\+\_\+energy\+\_\+req module. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Functions/\+Subroutines} \begin{DoxyCompactItemize} \item subroutine, public \mbox{\hyperlink{namespacemom__diapyc__energy__req_a0bf0dd1f3ae4f7f66fb000322f18064e}{diapyc\+\_\+energy\+\_\+req\+\_\+test}} (h\+\_\+3d, dt, tv, G, GV, US, CS, Kd\+\_\+int) \begin{DoxyCompactList}\small\item\em This subroutine helps test the accuracy of the diapycnal mixing energy requirement code by writing diagnostics, possibly using an intensely mixing test profile of diffusivity. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__diapyc__energy__req_aca27fbd2a716b8565b0b754a417479d5}{diapyc\+\_\+energy\+\_\+req\+\_\+calc}} (h\+\_\+in, T\+\_\+in, S\+\_\+in, Kd, energy\+\_\+\+Kd, dt, tv, G, GV, US, may\+\_\+print, CS) \begin{DoxyCompactList}\small\item\em This subroutine uses a substantially refactored tridiagonal equation for diapycnal mixing of temperature and salinity to estimate the potential energy change due to diapycnal mixing in a column of water. It does this estimate 4 different ways, all of which should be equivalent, but reports only one. The various estimates are taken because they will later be used as templates for other bits of code. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__diapyc__energy__req_a2bed511a4b1df9de0e2230c24389bc82}{find\+\_\+pe\+\_\+chg}} (Kddt\+\_\+h0, d\+Kddt\+\_\+h, hp\+\_\+a, hp\+\_\+b, Th\+\_\+a, Sh\+\_\+a, Th\+\_\+b, Sh\+\_\+b, d\+T\+\_\+to\+\_\+d\+P\+E\+\_\+a, d\+S\+\_\+to\+\_\+d\+P\+E\+\_\+a, d\+T\+\_\+to\+\_\+d\+P\+E\+\_\+b, d\+S\+\_\+to\+\_\+d\+P\+E\+\_\+b, pres\+\_\+Z, d\+T\+\_\+to\+\_\+d\+Col\+Ht\+\_\+a, d\+S\+\_\+to\+\_\+d\+Col\+Ht\+\_\+a, d\+T\+\_\+to\+\_\+d\+Col\+Ht\+\_\+b, d\+S\+\_\+to\+\_\+d\+Col\+Ht\+\_\+b, P\+E\+\_\+chg, d\+P\+Ec\+\_\+d\+Kd, d\+P\+E\+\_\+max, d\+P\+Ec\+\_\+d\+Kd\+\_\+0, Col\+Ht\+\_\+cor) \begin{DoxyCompactList}\small\item\em This subroutine calculates the change in potential energy and or derivatives for several changes in an interfaces\textquotesingle{}s diapycnal diffusivity times a timestep. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__diapyc__energy__req_afb1736a09e8f04ae84f561924e157691}{find\+\_\+pe\+\_\+chg\+\_\+orig}} (Kddt\+\_\+h, h\+\_\+k, b\+\_\+den\+\_\+1, d\+Te\+\_\+term, d\+Se\+\_\+term, d\+T\+\_\+km1\+\_\+t2, d\+S\+\_\+km1\+\_\+t2, d\+T\+\_\+to\+\_\+d\+P\+E\+\_\+k, d\+S\+\_\+to\+\_\+d\+P\+E\+\_\+k, d\+T\+\_\+to\+\_\+d\+P\+Ea, d\+S\+\_\+to\+\_\+d\+P\+Ea, pres\+\_\+Z, d\+T\+\_\+to\+\_\+d\+Col\+Ht\+\_\+k, d\+S\+\_\+to\+\_\+d\+Col\+Ht\+\_\+k, d\+T\+\_\+to\+\_\+d\+Col\+Hta, d\+S\+\_\+to\+\_\+d\+Col\+Hta, P\+E\+\_\+chg, d\+P\+Ec\+\_\+d\+Kd, d\+P\+E\+\_\+max, d\+P\+Ec\+\_\+d\+Kd\+\_\+0) \begin{DoxyCompactList}\small\item\em This subroutine calculates the change in potential energy and or derivatives for several changes in an interfaces\textquotesingle{}s diapycnal diffusivity times a timestep using the original form used in the first version of e\+P\+BL. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__diapyc__energy__req_a63b127bfd78461d8df3449591792b224}{diapyc\+\_\+energy\+\_\+req\+\_\+init}} (Time, G, GV, US, param\+\_\+file, diag, CS) \begin{DoxyCompactList}\small\item\em Initialize parameters and allocate memory associated with the diapycnal energy requirement module. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__diapyc__energy__req_aa4cb9f1b90a245e34ddd4182943a21c6}{diapyc\+\_\+energy\+\_\+req\+\_\+end}} (CS) \begin{DoxyCompactList}\small\item\em Clean up and deallocate memory associated with the diapycnal energy requirement module. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Function/\+Subroutine Documentation} \mbox{\Hypertarget{namespacemom__diapyc__energy__req_aca27fbd2a716b8565b0b754a417479d5}\label{namespacemom__diapyc__energy__req_aca27fbd2a716b8565b0b754a417479d5}} \index{mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}!diapyc\+\_\+energy\+\_\+req\+\_\+calc@{diapyc\+\_\+energy\+\_\+req\+\_\+calc}} \index{diapyc\+\_\+energy\+\_\+req\+\_\+calc@{diapyc\+\_\+energy\+\_\+req\+\_\+calc}!mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}} \subsubsection{\texorpdfstring{diapyc\+\_\+energy\+\_\+req\+\_\+calc()}{diapyc\_energy\_req\_calc()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+diapyc\+\_\+energy\+\_\+req\+::diapyc\+\_\+energy\+\_\+req\+\_\+calc (\begin{DoxyParamCaption}\item[{real, dimension(gv\%ke), intent(in)}]{h\+\_\+in, }\item[{real, dimension(gv\%ke), intent(in)}]{T\+\_\+in, }\item[{real, dimension(gv\%ke), intent(in)}]{S\+\_\+in, }\item[{real, dimension(gv\%ke+1), intent(in)}]{Kd, }\item[{real, intent(out)}]{energy\+\_\+\+Kd, }\item[{real, intent(in)}]{dt, }\item[{type(thermo\+\_\+var\+\_\+ptrs), intent(inout)}]{tv, }\item[{type(ocean\+\_\+grid\+\_\+type), intent(in)}]{G, }\item[{type(verticalgrid\+\_\+type), intent(in)}]{GV, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{logical, intent(in), optional}]{may\+\_\+print, }\item[{type(\mbox{\hyperlink{structmom__diapyc__energy__req_1_1diapyc__energy__req__cs}{diapyc\+\_\+energy\+\_\+req\+\_\+cs}}), optional, pointer}]{CS }\end{DoxyParamCaption})} This subroutine uses a substantially refactored tridiagonal equation for diapycnal mixing of temperature and salinity to estimate the potential energy change due to diapycnal mixing in a column of water. It does this estimate 4 different ways, all of which should be equivalent, but reports only one. The various estimates are taken because they will later be used as templates for other bits of code. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em g} & The ocean\textquotesingle{}s grid structure.\\ \hline \mbox{\tt in} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure.\\ \hline \mbox{\tt in} & {\em us} & A dimensional unit scaling type\\ \hline \mbox{\tt in} & {\em h\+\_\+in} & Layer thickness before entrainment, \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em t\+\_\+in} & The layer temperatures \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s\+\_\+in} & The layer salinities \mbox{[}ppt\mbox{]}.\\ \hline \mbox{\tt in} & {\em kd} & The interfaces diapycnal diffusivities \mbox{[}Z2 T-\/1 $\sim$$>$ m2 s-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt} & The amount of time covered by this call \mbox{[}T $\sim$$>$ s\mbox{]}.\\ \hline \mbox{\tt out} & {\em energy\+\_\+kd} & The column-\/integrated rate of energy consumption by diapycnal diffusion \mbox{[}R Z L2 T-\/3 $\sim$$>$ W m-\/2\mbox{]}.\\ \hline \mbox{\tt in,out} & {\em tv} & A structure containing pointers to any available thermodynamic fields. Absent fields have N\+U\+LL ptrs.\\ \hline \mbox{\tt in} & {\em may\+\_\+print} & If present and true, write out diagnostics of energy use.\\ \hline & {\em cs} & This module\textquotesingle{}s control structure. \\ \hline \end{DoxyParams} Definition at line 122 of file M\+O\+M\+\_\+diapyc\+\_\+energy\+\_\+req.\+F90. \begin{DoxyCode} 122 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure.} 123 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid structure.} 124 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type} 125 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke)}, \textcolor{keywordtype}{intent(in)} :: h\_in\textcolor{comment}{ !< Layer thickness before entrainment,} 126 \textcolor{comment}{ !! [H ~> m or kg m-2].} 127 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke)}, \textcolor{keywordtype}{intent(in)} :: T\_in\textcolor{comment}{ !< The layer temperatures [degC].} 128 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke)}, \textcolor{keywordtype}{intent(in)} :: S\_in\textcolor{comment}{ !< The layer salinities [ppt].} 129 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke+1)}, \textcolor{keywordtype}{intent(in)} :: Kd\textcolor{comment}{ !< The interfaces diapycnal diffusivities} 130 \textcolor{comment}{ !! [Z2 T-1 ~> m2 s-1].} 131 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dt\textcolor{comment}{ !< The amount of time covered by this call [T ~> s].} 132 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: energy\_Kd\textcolor{comment}{ !< The column-integrated rate of energy} 133 \textcolor{comment}{ !! consumption by diapycnal diffusion [R Z L2 T-3 ~> W m-2].} 134 \textcolor{keywordtype}{type}(thermo\_var\_ptrs), \textcolor{keywordtype}{intent(inout)} :: tv\textcolor{comment}{ !< A structure containing pointers to any} 135 \textcolor{comment}{ !! available thermodynamic fields.} 136 \textcolor{comment}{ !! Absent fields have NULL ptrs.} 137 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: may\_print\textcolor{comment}{ !< If present and true, write out diagnostics} 138 \textcolor{comment}{ !! of energy use.} 139 \textcolor{keywordtype}{type}(diapyc\_energy\_req\_CS), & 140 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< This module's control structure.} 141 142 \textcolor{comment}{! This subroutine uses a substantially refactored tridiagonal equation for} 143 \textcolor{comment}{! diapycnal mixing of temperature and salinity to estimate the potential energy} 144 \textcolor{comment}{! change due to diapycnal mixing in a column of water. It does this estimate} 145 \textcolor{comment}{! 4 different ways, all of which should be equivalent, but reports only one.} 146 \textcolor{comment}{! The various estimates are taken because they will later be used as templates} 147 \textcolor{comment}{! for other bits of code.} 148 149 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke)} :: & 150 p\_lay, & \textcolor{comment}{! Average pressure of a layer [R L2 T-2 ~> Pa].} 151 dSV\_dT, & \textcolor{comment}{! Partial derivative of specific volume with temperature [R-1 degC-1 ~> m3 kg-1 degC-1].} 152 dSV\_dS, & \textcolor{comment}{! Partial derivative of specific volume with salinity [R-1 ppt-1 ~> m3 kg-1 ppt-1].} 153 T0, S0, & \textcolor{comment}{! Initial temperatures and salinities [degC] and [ppt].} 154 Te, Se, & \textcolor{comment}{! Running incomplete estimates of the new temperatures and salinities [degC] and [ppt].} 155 Te\_a, Se\_a, & \textcolor{comment}{! Running incomplete estimates of the new temperatures and salinities [degC] and [ppt].} 156 Te\_b, Se\_b, & \textcolor{comment}{! Running incomplete estimates of the new temperatures and salinities [degC] and [ppt].} 157 Tf, Sf, & \textcolor{comment}{! New final values of the temperatures and salinities [degC] and [ppt].} 158 dTe, dSe, & \textcolor{comment}{! Running (1-way) estimates of temperature and salinity change [degC] and [ppt].} 159 dTe\_a, dSe\_a, & \textcolor{comment}{! Running (1-way) estimates of temperature and salinity change [degC] and [ppt].} 160 dTe\_b, dSe\_b, & \textcolor{comment}{! Running (1-way) estimates of temperature and salinity change [degC] and [ppt].} 161 Th\_a, & \textcolor{comment}{! An effective temperature times a thickness in the layer above, including implicit} 162 \textcolor{comment}{! mixing effects with other yet higher layers [degC H ~> degC m or degC kg m-2].} 163 sh\_a, & \textcolor{comment}{! An effective salinity times a thickness in the layer above, including implicit} 164 \textcolor{comment}{! mixing effects with other yet higher layers [ppt H ~> ppt m or ppt kg m-2].} 165 th\_b, & \textcolor{comment}{! An effective temperature times a thickness in the layer below, including implicit} 166 \textcolor{comment}{! mixing effects with other yet lower layers [degC H ~> degC m or degC kg m-2].} 167 sh\_b, & \textcolor{comment}{! An effective salinity times a thickness in the layer below, including implicit} 168 \textcolor{comment}{! mixing effects with other yet lower layers [ppt H ~> ppt m or ppt kg m-2].} 169 dt\_to\_dpe, & \textcolor{comment}{! Partial derivative of column potential energy with the temperature and salinity} 170 ds\_to\_dpe, & \textcolor{comment}{! changes within a layer [R Z L2 T-2 degC-1 ~> J m-2 degC-1] and [R Z L2 T-2 ppt-1 ~> J m-2 ppt-1].} 171 dt\_to\_dcolht, & \textcolor{comment}{! Partial derivatives of the total column height with the temperature} 172 ds\_to\_dcolht, & \textcolor{comment}{! and salinity changes within a layer [Z degC-1 ~> m degC-1] and [Z ppt-1 ~> m ppt-1].} 173 dt\_to\_dcolht\_a, & \textcolor{comment}{! Partial derivatives of the total column height with the temperature} 174 ds\_to\_dcolht\_a, & \textcolor{comment}{! and salinity changes within a layer, including the implicit effects} 175 \textcolor{comment}{! of mixing with layers higher in the water colun [Z degC-1 ~> m degC-1] and [Z ppt-1 ~> m ppt-1].} 176 dt\_to\_dcolht\_b, & \textcolor{comment}{! Partial derivatives of the total column height with the temperature} 177 ds\_to\_dcolht\_b, & \textcolor{comment}{! and salinity changes within a layer, including the implicit effects} 178 \textcolor{comment}{! of mixing with layers lower in the water colun [Z degC-1 ~> m degC-1] and [Z ppt-1 ~> m ppt-1].} 179 dt\_to\_dpe\_a, & \textcolor{comment}{! Partial derivatives of column potential energy with the temperature} 180 ds\_to\_dpe\_a, & \textcolor{comment}{! and salinity changes within a layer, including the implicit effects} 181 \textcolor{comment}{! of mixing with layers higher in the water column, in} 182 \textcolor{comment}{! units of [R Z L2 T-2 degC-1 ~> J m-2 degC-1] and [R Z L2 T-2 ppt-1 ~> J m-2 ppt-1].} 183 dt\_to\_dpe\_b, & \textcolor{comment}{! Partial derivatives of column potential energy with the temperature} 184 ds\_to\_dpe\_b, & \textcolor{comment}{! and salinity changes within a layer, including the implicit effects} 185 \textcolor{comment}{! of mixing with layers lower in the water column, in} 186 \textcolor{comment}{! units of [R Z L2 T-2 degC-1 ~> J m-2 degC-1] and [R Z L2 T-2 ppt-1 ~> J m-2 ppt-1].} 187 hp\_a, & \textcolor{comment}{! An effective pivot thickness of the layer including the effects} 188 \textcolor{comment}{! of coupling with layers above [H ~> m or kg m-2]. This is the first term} 189 \textcolor{comment}{! in the denominator of b1 in a downward-oriented tridiagonal solver.} 190 hp\_b, & \textcolor{comment}{! An effective pivot thickness of the layer including the effects} 191 \textcolor{comment}{! of coupling with layers below [H ~> m or kg m-2]. This is the first term} 192 \textcolor{comment}{! in the denominator of b1 in an upward-oriented tridiagonal solver.} 193 c1\_a, & \textcolor{comment}{! c1\_a is used by a downward-oriented tridiagonal solver [nondim].} 194 c1\_b, & \textcolor{comment}{! c1\_b is used by an upward-oriented tridiagonal solver [nondim].} 195 h\_tr \textcolor{comment}{! h\_tr is h at tracer points with a h\_neglect added to} 196 \textcolor{comment}{! ensure positive definiteness [H ~> m or kg m-2].} 197 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke+1)} :: & 198 pres, & \textcolor{comment}{! Interface pressures [R L2 T-2 ~> Pa].} 199 pres\_Z, & \textcolor{comment}{! Interface pressures with a rescaling factor to convert interface height} 200 \textcolor{comment}{! movements into changes in column potential energy [R L2 T-2 m Z-1 ~> J m-3].} 201 z\_int, & \textcolor{comment}{! Interface heights relative to the surface [H ~> m or kg m-2].} 202 n2, & \textcolor{comment}{! An estimate of the buoyancy frequency [T-2 ~> s-2].} 203 kddt\_h, & \textcolor{comment}{! The diapycnal diffusivity times a timestep divided by the} 204 \textcolor{comment}{! average thicknesses around a layer [H ~> m or kg m-2].} 205 kddt\_h\_a, & \textcolor{comment}{! The value of Kddt\_h for layers above the central point in the} 206 \textcolor{comment}{! tridiagonal solver [H ~> m or kg m-2].} 207 kddt\_h\_b, & \textcolor{comment}{! The value of Kddt\_h for layers below the central point in the} 208 \textcolor{comment}{! tridiagonal solver [H ~> m or kg m-2].} 209 kd\_so\_far \textcolor{comment}{! The value of Kddt\_h that has been applied already in} 210 \textcolor{comment}{! calculating the energy changes [H ~> m or kg m-2].} 211 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke+1,4)} :: & 212 PE\_chg\_k, & \textcolor{comment}{! The integrated potential energy change within a timestep due} 213 \textcolor{comment}{! to the diffusivity at interface K for 4 different orders of} 214 \textcolor{comment}{! accumulating the diffusivities [R Z L2 T-2 ~> J m-2].} 215 colht\_cor\_k \textcolor{comment}{! The correction to the potential energy change due to} 216 \textcolor{comment}{! changes in the net column height [R Z L2 T-2 ~> J m-2].} 217 \textcolor{keywordtype}{real} :: & 218 b1 \textcolor{comment}{! b1 is used by the tridiagonal solver [H-1 ~> m-1 or m2 kg-1].} 219 \textcolor{keywordtype}{real} :: & 220 I\_b1 \textcolor{comment}{! The inverse of b1 [H ~> m or kg m-2].} 221 \textcolor{keywordtype}{real} :: Kd0 \textcolor{comment}{! The value of Kddt\_h that has already been applied [H ~> m or kg m-2].} 222 \textcolor{keywordtype}{real} :: dKd \textcolor{comment}{! The change in the value of Kddt\_h [H ~> m or kg m-2].} 223 \textcolor{keywordtype}{real} :: h\_neglect \textcolor{comment}{! A thickness that is so small it is usually lost} 224 \textcolor{comment}{! in roundoff and can be neglected [H ~> m or kg m-2].} 225 \textcolor{keywordtype}{real} :: dTe\_term \textcolor{comment}{! A diffusivity-independent term related to the temperature} 226 \textcolor{comment}{! change in the layer below the interface [degC H ~> degC m or degC kg m-2].} 227 \textcolor{keywordtype}{real} :: dSe\_term \textcolor{comment}{! A diffusivity-independent term related to the salinity} 228 \textcolor{comment}{! change in the layer below the interface [ppt H ~> ppt m or ppt kg m-2].} 229 \textcolor{keywordtype}{real} :: Kddt\_h\_guess \textcolor{comment}{! A guess of the final value of Kddt\_h [H ~> m or kg m-2].} 230 \textcolor{keywordtype}{real} :: dMass \textcolor{comment}{! The mass per unit area within a layer [R Z ~> kg m-2].} 231 \textcolor{keywordtype}{real} :: dPres \textcolor{comment}{! The hydrostatic pressure change across a layer [R L2 T-2 ~> Pa].} 232 \textcolor{keywordtype}{real} :: dMKE\_max \textcolor{comment}{! The maximum amount of mean kinetic energy that could be} 233 \textcolor{comment}{! converted to turbulent kinetic energy if the velocity in} 234 \textcolor{comment}{! the layer below an interface were homogenized with all of} 235 \textcolor{comment}{! the water above the interface [R Z L2 T-2 ~> J m-2 = kg s-2].} 236 \textcolor{keywordtype}{real} :: rho\_here \textcolor{comment}{! The in-situ density [R ~> kg m-3].} 237 \textcolor{keywordtype}{real} :: PE\_change \textcolor{comment}{! The change in column potential energy from applying Kddt\_h at the} 238 \textcolor{comment}{! present interface [R L2 Z T-2 ~> J m-2].} 239 \textcolor{keywordtype}{real} :: ColHt\_cor \textcolor{comment}{! The correction to PE\_chg that is made due to a net} 240 \textcolor{comment}{! change in the column height [R L2 Z T-2 ~> J m-2].} 241 \textcolor{keywordtype}{real} :: htot \textcolor{comment}{! A running sum of thicknesses [H ~> m or kg m-2].} 242 \textcolor{keywordtype}{real} :: dTe\_t2, dT\_km1\_t2, dT\_k\_t2 \textcolor{comment}{! Temporary arrays describing temperature changes [degC].} 243 \textcolor{keywordtype}{real} :: dSe\_t2, dS\_km1\_t2, dS\_k\_t2 \textcolor{comment}{! Temporary arrays describing salinity changes [ppt].} 244 \textcolor{keywordtype}{logical} :: do\_print 245 246 \textcolor{comment}{! The following are a bunch of diagnostic arrays for debugging purposes.} 247 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke)} :: & 248 Ta, Sa, Tb, Sb 249 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke+1)} :: & 250 dPEa\_dKd, dPEa\_dKd\_est, dPEa\_dKd\_err, dPEa\_dKd\_trunc, dPEa\_dKd\_err\_norm, & 251 dPEb\_dKd, dPEb\_dKd\_est, dPEb\_dKd\_err, dPEb\_dKd\_trunc, dPEb\_dKd\_err\_norm 252 \textcolor{keywordtype}{real} :: PE\_chg\_tot1A, PE\_chg\_tot2A, T\_chg\_totA 253 \textcolor{keywordtype}{real} :: PE\_chg\_tot1B, PE\_chg\_tot2B, T\_chg\_totB 254 \textcolor{keywordtype}{real} :: PE\_chg\_tot1C, PE\_chg\_tot2C, T\_chg\_totC 255 \textcolor{keywordtype}{real} :: PE\_chg\_tot1D, PE\_chg\_tot2D, T\_chg\_totD 256 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke+1)} :: dPEchg\_dKd 257 \textcolor{keywordtype}{real} :: PE\_chg(6) 258 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(6)} :: dT\_k\_itt, dS\_k\_itt, dT\_km1\_itt, dS\_km1\_itt 259 260 \textcolor{keywordtype}{integer} :: k, nz, itt, max\_itt, k\_cent 261 \textcolor{keywordtype}{logical} :: surface\_BL, bottom\_BL, central, halves, debug 262 \textcolor{keywordtype}{logical} :: old\_PE\_calc 263 nz = g%ke 264 h\_neglect = gv%H\_subroundoff 265 266 debug = .true. 267 268 surface\_bl = .true. ; bottom\_bl = .true. ; halves = .true. 269 central = .true. ; k\_cent = nz/2 270 271 do\_print = .false. ; \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(may\_print) .and. \textcolor{keyword}{present}(cs)) do\_print = may\_print 272 273 dpea\_dkd(:) = 0.0 ; dpea\_dkd\_est(:) = 0.0 ; dpea\_dkd\_err(:) = 0.0 274 dpea\_dkd\_err\_norm(:) = 0.0 ; dpea\_dkd\_trunc(:) = 0.0 275 dpeb\_dkd(:) = 0.0 ; dpeb\_dkd\_est(:) = 0.0 ; dpeb\_dkd\_err(:) = 0.0 276 dpeb\_dkd\_err\_norm(:) = 0.0 ; dpeb\_dkd\_trunc(:) = 0.0 277 278 htot = 0.0 ; pres(1) = 0.0 ; pres\_z(1) = 0.0 ; z\_int(1) = 0.0 279 \textcolor{keywordflow}{do} k=1,nz 280 t0(k) = t\_in(k) ; s0(k) = s\_in(k) 281 h\_tr(k) = h\_in(k) 282 htot = htot + h\_tr(k) 283 pres(k+1) = pres(k) + (gv%g\_Earth * gv%H\_to\_RZ) * h\_tr(k) 284 pres\_z(k+1) = pres(k+1) 285 p\_lay(k) = 0.5*(pres(k) + pres(k+1)) 286 z\_int(k+1) = z\_int(k) - h\_tr(k) 287 \textcolor{keywordflow}{ enddo} 288 \textcolor{keywordflow}{do} k=1,nz 289 h\_tr(k) = max(h\_tr(k), 1e-15*htot) 290 \textcolor{keywordflow}{ enddo} 291 292 \textcolor{comment}{! Introduce a diffusive flux variable, Kddt\_h(K) = ea(k) = eb(k-1)} 293 294 kddt\_h(1) = 0.0 ; kddt\_h(nz+1) = 0.0 295 \textcolor{keywordflow}{do} k=2,nz 296 kddt\_h(k) = min((gv%Z\_to\_H**2*dt)*kd(k) / (0.5*(h\_tr(k-1) + h\_tr(k))), 1e3*htot) 297 \textcolor{keywordflow}{ enddo} 298 299 \textcolor{comment}{! Solve the tridiagonal equations for new temperatures.} 300 301 \textcolor{keyword}{call }calculate\_specific\_vol\_derivs(t0, s0, p\_lay, dsv\_dt, dsv\_ds, tv%eqn\_of\_state) 302 303 \textcolor{keywordflow}{do} k=1,nz 304 dmass = gv%H\_to\_RZ * h\_tr(k) 305 dpres = (gv%g\_Earth * gv%H\_to\_RZ) * h\_tr(k) 306 dt\_to\_dpe(k) = (dmass * (pres(k) + 0.5*dpres)) * dsv\_dt(k) 307 ds\_to\_dpe(k) = (dmass * (pres(k) + 0.5*dpres)) * dsv\_ds(k) 308 dt\_to\_dcolht(k) = dmass * dsv\_dt(k) * cs%ColHt\_scaling 309 ds\_to\_dcolht(k) = dmass * dsv\_ds(k) * cs%ColHt\_scaling 310 \textcolor{keywordflow}{ enddo} 311 312 \textcolor{comment}{! PE\_chg\_k(1) = 0.0 ; PE\_chg\_k(nz+1) = 0.0} 313 \textcolor{comment}{! PEchg(:) = 0.0} 314 pe\_chg\_k(:,:) = 0.0 ; colht\_cor\_k(:,:) = 0.0 315 dpechg\_dkd(:) = 0.0 316 317 \textcolor{keywordflow}{if} (surface\_bl) \textcolor{keywordflow}{then} \textcolor{comment}{! This version is appropriate for a surface boundary layer.} 318 old\_pe\_calc = .false. 319 320 \textcolor{comment}{! Set up values appropriate for no diffusivity.} 321 \textcolor{keywordflow}{do} k=1,nz 322 hp\_a(k) = h\_tr(k) ; hp\_b(k) = h\_tr(k) 323 dt\_to\_dpe\_a(k) = dt\_to\_dpe(k) ; ds\_to\_dpe\_a(k) = ds\_to\_dpe(k) 324 dt\_to\_dpe\_b(k) = dt\_to\_dpe(k) ; ds\_to\_dpe\_b(k) = ds\_to\_dpe(k) 325 dt\_to\_dcolht\_a(k) = dt\_to\_dcolht(k) ; ds\_to\_dcolht\_a(k) = ds\_to\_dcolht(k) 326 dt\_to\_dcolht\_b(k) = dt\_to\_dcolht(k) ; ds\_to\_dcolht\_b(k) = ds\_to\_dcolht(k) 327 \textcolor{keywordflow}{ enddo} 328 329 \textcolor{keywordflow}{do} k=2,nz 330 \textcolor{comment}{! At this point, Kddt\_h(K) will be unknown because its value may depend} 331 \textcolor{comment}{! on how much energy is available.} 332 333 \textcolor{comment}{! Precalculate some temporary expressions that are independent of Kddt\_h\_guess.} 334 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 335 \textcolor{keywordflow}{if} (k==2) \textcolor{keywordflow}{then} 336 dt\_km1\_t2 = (t0(k)-t0(k-1)) 337 ds\_km1\_t2 = (s0(k)-s0(k-1)) 338 dte\_t2 = 0.0 ; dse\_t2 = 0.0 339 \textcolor{keywordflow}{else} 340 dte\_t2 = kddt\_h(k-1) * ((t0(k-2) - t0(k-1)) + dte(k-2)) 341 dse\_t2 = kddt\_h(k-1) * ((s0(k-2) - s0(k-1)) + dse(k-2)) 342 dt\_km1\_t2 = (t0(k)-t0(k-1)) - & 343 (kddt\_h(k-1) / hp\_a(k-1)) * ((t0(k-2) - t0(k-1)) + dte(k-2)) 344 ds\_km1\_t2 = (s0(k)-s0(k-1)) - & 345 (kddt\_h(k-1) / hp\_a(k-1)) * ((s0(k-2) - s0(k-1)) + dse(k-2)) 346 \textcolor{keywordflow}{ endif} 347 dte\_term = dte\_t2 + hp\_a(k-1) * (t0(k-1)-t0(k)) 348 dse\_term = dse\_t2 + hp\_a(k-1) * (s0(k-1)-s0(k)) 349 \textcolor{keywordflow}{else} 350 \textcolor{keywordflow}{if} (k<=2) \textcolor{keywordflow}{then} 351 th\_a(k-1) = h\_tr(k-1) * t0(k-1) ; sh\_a(k-1) = h\_tr(k-1) * s0(k-1) 352 \textcolor{keywordflow}{else} 353 th\_a(k-1) = h\_tr(k-1) * t0(k-1) + kddt\_h(k-1) * te(k-2) 354 sh\_a(k-1) = h\_tr(k-1) * s0(k-1) + kddt\_h(k-1) * se(k-2) 355 \textcolor{keywordflow}{ endif} 356 th\_b(k) = h\_tr(k) * t0(k) ; sh\_b(k) = h\_tr(k) * s0(k) 357 \textcolor{keywordflow}{ endif} 358 359 360 \textcolor{comment}{! Find the energy change due to a guess at the strength of diffusion at interface K.} 361 362 kddt\_h\_guess = kddt\_h(k) 363 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 364 \textcolor{keyword}{call }find\_pe\_chg\_orig(kddt\_h\_guess, h\_tr(k), hp\_a(k-1), & 365 dte\_term, dse\_term, dt\_km1\_t2, ds\_km1\_t2, & 366 dt\_to\_dpe(k), ds\_to\_dpe(k), dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), & 367 pres\_z(k), dt\_to\_dcolht(k), ds\_to\_dcolht(k), & 368 dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 369 pe\_chg\_k(k,1), dpea\_dkd(k)) 370 \textcolor{keywordflow}{else} 371 \textcolor{keyword}{call }find\_pe\_chg(0.0, kddt\_h\_guess, hp\_a(k-1), hp\_b(k), & 372 th\_a(k-1), sh\_a(k-1), th\_b(k), sh\_b(k), & 373 dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 374 pres\_z(k), dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 375 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 376 pe\_chg=pe\_chg\_k(k,1), dpec\_dkd=dpea\_dkd(k), & 377 colht\_cor=colht\_cor\_k(k,1)) 378 \textcolor{keywordflow}{ endif} 379 380 \textcolor{keywordflow}{if} (debug) \textcolor{keywordflow}{then} 381 \textcolor{keywordflow}{do} itt=1,5 382 kddt\_h\_guess = (1.0+0.01*(itt-3))*kddt\_h(k) 383 384 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 385 \textcolor{keyword}{call }find\_pe\_chg\_orig(kddt\_h\_guess, h\_tr(k), hp\_a(k-1), & 386 dte\_term, dse\_term, dt\_km1\_t2, ds\_km1\_t2, & 387 dt\_to\_dpe(k), ds\_to\_dpe(k), dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), & 388 pres\_z(k), dt\_to\_dcolht(k), ds\_to\_dcolht(k), & 389 dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 390 pe\_chg=pe\_chg(itt)) 391 \textcolor{keywordflow}{else} 392 \textcolor{keyword}{call }find\_pe\_chg(0.0, kddt\_h\_guess, hp\_a(k-1), hp\_b(k), & 393 th\_a(k-1), sh\_a(k-1), th\_b(k), sh\_b(k), & 394 dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 395 pres\_z(k), dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 396 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 397 pe\_chg=pe\_chg(itt)) 398 \textcolor{keywordflow}{ endif} 399 \textcolor{keywordflow}{ enddo} 400 \textcolor{comment}{! Compare with a 4th-order finite difference estimate.} 401 dpea\_dkd\_est(k) = (4.0*(pe\_chg(4)-pe\_chg(2))/(0.02*kddt\_h(k)) - & 402 (pe\_chg(5)-pe\_chg(1))/(0.04*kddt\_h(k))) / 3.0 403 dpea\_dkd\_trunc(k) = (pe\_chg(4)-pe\_chg(2))/(0.02*kddt\_h(k)) - & 404 (pe\_chg(5)-pe\_chg(1))/(0.04*kddt\_h(k)) 405 dpea\_dkd\_err(k) = (dpea\_dkd\_est(k) - dpea\_dkd(k)) 406 dpea\_dkd\_err\_norm(k) = (dpea\_dkd\_est(k) - dpea\_dkd(k)) / & 407 (abs(dpea\_dkd\_est(k)) + abs(dpea\_dkd(k)) + 1e-100*us%RZ\_to\_kg\_m2*us %L\_T\_to\_m\_s**2) 408 \textcolor{keywordflow}{ endif} 409 410 \textcolor{comment}{! At this point, the final value of Kddt\_h(K) is known, so the estimated} 411 \textcolor{comment}{! properties for layer k-1 can be calculated.} 412 413 b1 = 1.0 / (hp\_a(k-1) + kddt\_h(k)) 414 c1\_a(k) = kddt\_h(k) * b1 415 \textcolor{keywordflow}{if} (k==2) \textcolor{keywordflow}{then} 416 te(1) = b1*(h\_tr(1)*t0(1)) 417 se(1) = b1*(h\_tr(1)*s0(1)) 418 \textcolor{keywordflow}{else} 419 te(k-1) = b1 * (h\_tr(k-1) * t0(k-1) + kddt\_h(k-1) * te(k-2)) 420 se(k-1) = b1 * (h\_tr(k-1) * s0(k-1) + kddt\_h(k-1) * se(k-2)) 421 \textcolor{keywordflow}{ endif} 422 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 423 dte(k-1) = b1 * ( kddt\_h(k)*(t0(k)-t0(k-1)) + dte\_t2 ) 424 dse(k-1) = b1 * ( kddt\_h(k)*(s0(k)-s0(k-1)) + dse\_t2 ) 425 \textcolor{keywordflow}{ endif} 426 427 hp\_a(k) = h\_tr(k) + (hp\_a(k-1) * b1) * kddt\_h(k) 428 dt\_to\_dpe\_a(k) = dt\_to\_dpe(k) + c1\_a(k)*dt\_to\_dpe\_a(k-1) 429 ds\_to\_dpe\_a(k) = ds\_to\_dpe(k) + c1\_a(k)*ds\_to\_dpe\_a(k-1) 430 dt\_to\_dcolht\_a(k) = dt\_to\_dcolht(k) + c1\_a(k)*dt\_to\_dcolht\_a(k-1) 431 ds\_to\_dcolht\_a(k) = ds\_to\_dcolht(k) + c1\_a(k)*ds\_to\_dcolht\_a(k-1) 432 433 \textcolor{keywordflow}{ enddo} 434 435 b1 = 1.0 / (hp\_a(nz)) 436 tf(nz) = b1 * (h\_tr(nz) * t0(nz) + kddt\_h(nz) * te(nz-1)) 437 sf(nz) = b1 * (h\_tr(nz) * s0(nz) + kddt\_h(nz) * se(nz-1)) 438 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 439 dte(nz) = b1 * kddt\_h(nz) * ((t0(nz-1)-t0(nz)) + dte(nz-1)) 440 dse(nz) = b1 * kddt\_h(nz) * ((s0(nz-1)-s0(nz)) + dse(nz-1)) 441 \textcolor{keywordflow}{ endif} 442 443 \textcolor{keywordflow}{do} k=nz-1,1,-1 444 tf(k) = te(k) + c1\_a(k+1)*tf(k+1) 445 sf(k) = se(k) + c1\_a(k+1)*sf(k+1) 446 \textcolor{keywordflow}{ enddo} 447 448 \textcolor{keywordflow}{if} (debug) \textcolor{keywordflow}{then} 449 \textcolor{keywordflow}{do} k=1,nz ; ta(k) = tf(k) ; sa(k) = sf(k) ;\textcolor{keywordflow}{ enddo} 450 pe\_chg\_tot1a = 0.0 ; pe\_chg\_tot2a = 0.0 ; t\_chg\_tota = 0.0 451 \textcolor{keywordflow}{do} k=1,nz 452 pe\_chg\_tot1a = pe\_chg\_tot1a + (dt\_to\_dpe(k) * (tf(k) - t0(k)) + & 453 ds\_to\_dpe(k) * (sf(k) - s0(k))) 454 t\_chg\_tota = t\_chg\_tota + h\_tr(k) * (tf(k) - t0(k)) 455 \textcolor{keywordflow}{ enddo} 456 \textcolor{keywordflow}{do} k=2,nz 457 pe\_chg\_tot2a = pe\_chg\_tot2a + (pe\_chg\_k(k,1) - colht\_cor\_k(k,1)) 458 \textcolor{keywordflow}{ enddo} 459 \textcolor{keywordflow}{ endif} 460 461 \textcolor{keywordflow}{ endif} 462 463 \textcolor{keywordflow}{if} (bottom\_bl) \textcolor{keywordflow}{then} \textcolor{comment}{! This version is appropriate for a bottom boundary layer.} 464 old\_pe\_calc = .false. 465 466 \textcolor{comment}{! Set up values appropriate for no diffusivity.} 467 \textcolor{keywordflow}{do} k=1,nz 468 hp\_a(k) = h\_tr(k) ; hp\_b(k) = h\_tr(k) 469 dt\_to\_dpe\_a(k) = dt\_to\_dpe(k) ; ds\_to\_dpe\_a(k) = ds\_to\_dpe(k) 470 dt\_to\_dpe\_b(k) = dt\_to\_dpe(k) ; ds\_to\_dpe\_b(k) = ds\_to\_dpe(k) 471 dt\_to\_dcolht\_a(k) = dt\_to\_dcolht(k) ; ds\_to\_dcolht\_a(k) = ds\_to\_dcolht(k) 472 dt\_to\_dcolht\_b(k) = dt\_to\_dcolht(k) ; ds\_to\_dcolht\_b(k) = ds\_to\_dcolht(k) 473 \textcolor{keywordflow}{ enddo} 474 475 \textcolor{keywordflow}{do} k=nz,2,-1 \textcolor{comment}{! Loop over interior interfaces.} 476 \textcolor{comment}{! At this point, Kddt\_h(K) will be unknown because its value may depend} 477 \textcolor{comment}{! on how much energy is available.} 478 479 \textcolor{comment}{! Precalculate some temporary expressions that are independent of Kddt\_h\_guess.} 480 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 481 \textcolor{keywordflow}{if} (k==nz) \textcolor{keywordflow}{then} 482 dt\_k\_t2 = (t0(k-1)-t0(k)) 483 ds\_k\_t2 = (s0(k-1)-s0(k)) 484 dte\_t2 = 0.0 ; dse\_t2 = 0.0 485 \textcolor{keywordflow}{else} 486 dte\_t2 = kddt\_h(k+1) * ((t0(k+1) - t0(k)) + dte(k+1)) 487 dse\_t2 = kddt\_h(k+1) * ((s0(k+1) - s0(k)) + dse(k+1)) 488 dt\_k\_t2 = (t0(k-1)-t0(k)) - & 489 (kddt\_h(k+1)/ hp\_b(k)) * ((t0(k+1) - t0(k)) + dte(k+1)) 490 ds\_k\_t2 = (s0(k-1)-s0(k)) - & 491 (kddt\_h(k+1)/ hp\_b(k)) * ((s0(k+1) - s0(k)) + dse(k+1)) 492 \textcolor{keywordflow}{ endif} 493 dte\_term = dte\_t2 + hp\_b(k) * (t0(k)-t0(k-1)) 494 dse\_term = dse\_t2 + hp\_b(k) * (s0(k)-s0(k-1)) 495 \textcolor{keywordflow}{else} 496 th\_a(k-1) = h\_tr(k-1) * t0(k-1) ; sh\_a(k-1) = h\_tr(k-1) * s0(k-1) 497 \textcolor{keywordflow}{if} (k>=nz) \textcolor{keywordflow}{then} 498 th\_b(k) = h\_tr(k) * t0(k) ; sh\_b(k) = h\_tr(k) * s0(k) 499 \textcolor{keywordflow}{else} 500 th\_b(k) = h\_tr(k) * t0(k) + kddt\_h(k+1) * te(k+1) 501 sh\_b(k) = h\_tr(k) * s0(k) + kddt\_h(k+1) * se(k+1) 502 \textcolor{keywordflow}{ endif} 503 \textcolor{keywordflow}{ endif} 504 505 \textcolor{comment}{! Find the energy change due to a guess at the strength of diffusion at interface K.} 506 kddt\_h\_guess = kddt\_h(k) 507 508 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 509 \textcolor{keyword}{call }find\_pe\_chg\_orig(kddt\_h\_guess, h\_tr(k-1), hp\_b(k), & 510 dte\_term, dse\_term, dt\_k\_t2, ds\_k\_t2, & 511 dt\_to\_dpe(k-1), ds\_to\_dpe(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 512 pres\_z(k), dt\_to\_dcolht(k-1), ds\_to\_dcolht(k-1), & 513 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 514 pe\_chg=pe\_chg\_k(k,2), dpec\_dkd=dpeb\_dkd(k)) 515 \textcolor{keywordflow}{else} 516 \textcolor{keyword}{call }find\_pe\_chg(0.0, kddt\_h\_guess, hp\_a(k-1), hp\_b(k), & 517 th\_a(k-1), sh\_a(k-1), th\_b(k), sh\_b(k), & 518 dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 519 pres\_z(k), dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 520 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 521 pe\_chg=pe\_chg\_k(k,2), dpec\_dkd=dpeb\_dkd(k), & 522 colht\_cor=colht\_cor\_k(k,2)) 523 \textcolor{keywordflow}{ endif} 524 525 \textcolor{keywordflow}{if} (debug) \textcolor{keywordflow}{then} 526 \textcolor{comment}{! Compare with a 4th-order finite difference estimate.} 527 \textcolor{keywordflow}{do} itt=1,5 528 kddt\_h\_guess = (1.0+0.01*(itt-3))*kddt\_h(k) 529 530 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 531 \textcolor{keyword}{call }find\_pe\_chg\_orig(kddt\_h\_guess, h\_tr(k-1), hp\_b(k), & 532 dte\_term, dse\_term, dt\_k\_t2, ds\_k\_t2, & 533 dt\_to\_dpe(k-1), ds\_to\_dpe(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 534 pres\_z(k), dt\_to\_dcolht(k-1), ds\_to\_dcolht(k-1), & 535 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 536 pe\_chg=pe\_chg(itt)) 537 \textcolor{keywordflow}{else} 538 \textcolor{keyword}{call }find\_pe\_chg(0.0, kddt\_h\_guess, hp\_a(k-1), hp\_b(k), & 539 th\_a(k-1), sh\_a(k-1), th\_b(k), sh\_b(k), & 540 dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 541 pres\_z(k), dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 542 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 543 pe\_chg=pe\_chg(itt)) 544 \textcolor{keywordflow}{ endif} 545 \textcolor{keywordflow}{ enddo} 546 547 dpeb\_dkd\_est(k) = (4.0*(pe\_chg(4)-pe\_chg(2))/(0.02*kddt\_h(k)) - & 548 (pe\_chg(5)-pe\_chg(1))/(0.04*kddt\_h(k))) / 3.0 549 dpeb\_dkd\_trunc(k) = (pe\_chg(4)-pe\_chg(2))/(0.02*kddt\_h(k)) - & 550 (pe\_chg(5)-pe\_chg(1))/(0.04*kddt\_h(k)) 551 dpeb\_dkd\_err(k) = (dpeb\_dkd\_est(k) - dpeb\_dkd(k)) 552 dpeb\_dkd\_err\_norm(k) = (dpeb\_dkd\_est(k) - dpeb\_dkd(k)) / & 553 (abs(dpeb\_dkd\_est(k)) + abs(dpeb\_dkd(k)) + 1e-100*us%RZ\_to\_kg\_m2*us %L\_T\_to\_m\_s**2) 554 \textcolor{keywordflow}{ endif} 555 556 \textcolor{comment}{! At this point, the final value of Kddt\_h(K) is known, so the estimated} 557 \textcolor{comment}{! properties for layer k can be calculated.} 558 559 b1 = 1.0 / (hp\_b(k) + kddt\_h(k)) 560 c1\_b(k) = kddt\_h(k) * b1 561 \textcolor{keywordflow}{if} (k==nz) \textcolor{keywordflow}{then} 562 te(nz) = b1* (h\_tr(nz)*t0(nz)) 563 se(nz) = b1* (h\_tr(nz)*s0(nz)) 564 \textcolor{keywordflow}{else} 565 te(k) = b1 * (h\_tr(k) * t0(k) + kddt\_h(k+1) * te(k+1)) 566 se(k) = b1 * (h\_tr(k) * s0(k) + kddt\_h(k+1) * se(k+1)) 567 \textcolor{keywordflow}{ endif} 568 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 569 dte(k) = b1 * ( kddt\_h(k)*(t0(k-1)-t0(k)) + dte\_t2 ) 570 dse(k) = b1 * ( kddt\_h(k)*(s0(k-1)-s0(k)) + dse\_t2 ) 571 \textcolor{keywordflow}{ endif} 572 573 hp\_b(k-1) = h\_tr(k-1) + (hp\_b(k) * b1) * kddt\_h(k) 574 dt\_to\_dpe\_b(k-1) = dt\_to\_dpe(k-1) + c1\_b(k)*dt\_to\_dpe\_b(k) 575 ds\_to\_dpe\_b(k-1) = ds\_to\_dpe(k-1) + c1\_b(k)*ds\_to\_dpe\_b(k) 576 dt\_to\_dcolht\_b(k-1) = dt\_to\_dcolht(k-1) + c1\_b(k)*dt\_to\_dcolht\_b(k) 577 ds\_to\_dcolht\_b(k-1) = ds\_to\_dcolht(k-1) + c1\_b(k)*ds\_to\_dcolht\_b(k) 578 579 \textcolor{keywordflow}{ enddo} 580 581 b1 = 1.0 / (hp\_b(1)) 582 tf(1) = b1 * (h\_tr(1) * t0(1) + kddt\_h(2) * te(2)) 583 sf(1) = b1 * (h\_tr(1) * s0(1) + kddt\_h(2) * se(2)) 584 \textcolor{keywordflow}{if} (old\_pe\_calc) \textcolor{keywordflow}{then} 585 dte(1) = b1 * kddt\_h(2) * ((t0(2)-t0(1)) + dte(2)) 586 dse(1) = b1 * kddt\_h(2) * ((s0(2)-s0(1)) + dse(2)) 587 \textcolor{keywordflow}{ endif} 588 589 \textcolor{keywordflow}{do} k=2,nz 590 tf(k) = te(k) + c1\_b(k)*tf(k-1) 591 sf(k) = se(k) + c1\_b(k)*sf(k-1) 592 \textcolor{keywordflow}{ enddo} 593 594 \textcolor{keywordflow}{if} (debug) \textcolor{keywordflow}{then} 595 \textcolor{keywordflow}{do} k=1,nz ; tb(k) = tf(k) ; sb(k) = sf(k) ;\textcolor{keywordflow}{ enddo} 596 pe\_chg\_tot1b = 0.0 ; pe\_chg\_tot2b = 0.0 ; t\_chg\_totb = 0.0 597 \textcolor{keywordflow}{do} k=1,nz 598 pe\_chg\_tot1b = pe\_chg\_tot1b + (dt\_to\_dpe(k) * (tf(k) - t0(k)) + & 599 ds\_to\_dpe(k) * (sf(k) - s0(k))) 600 t\_chg\_totb = t\_chg\_totb + h\_tr(k) * (tf(k) - t0(k)) 601 \textcolor{keywordflow}{ enddo} 602 \textcolor{keywordflow}{do} k=2,nz 603 pe\_chg\_tot2b = pe\_chg\_tot2b + (pe\_chg\_k(k,2) - colht\_cor\_k(k,2)) 604 \textcolor{keywordflow}{ enddo} 605 \textcolor{keywordflow}{ endif} 606 607 \textcolor{keywordflow}{ endif} 608 609 \textcolor{keywordflow}{if} (central) \textcolor{keywordflow}{then} 610 611 \textcolor{comment}{! Set up values appropriate for no diffusivity.} 612 \textcolor{keywordflow}{do} k=1,nz 613 hp\_a(k) = h\_tr(k) ; hp\_b(k) = h\_tr(k) 614 dt\_to\_dpe\_a(k) = dt\_to\_dpe(k) ; ds\_to\_dpe\_a(k) = ds\_to\_dpe(k) 615 dt\_to\_dpe\_b(k) = dt\_to\_dpe(k) ; ds\_to\_dpe\_b(k) = ds\_to\_dpe(k) 616 dt\_to\_dcolht\_a(k) = dt\_to\_dcolht(k) ; ds\_to\_dcolht\_a(k) = ds\_to\_dcolht(k) 617 dt\_to\_dcolht\_b(k) = dt\_to\_dcolht(k) ; ds\_to\_dcolht\_b(k) = ds\_to\_dcolht(k) 618 \textcolor{keywordflow}{ enddo} 619 620 \textcolor{comment}{! Calculate the dependencies on layers above.} 621 kddt\_h\_a(1) = 0.0 622 \textcolor{keywordflow}{do} k=2,nz \textcolor{comment}{! Loop over interior interfaces.} 623 \textcolor{comment}{! First calculate some terms that are independent of the change in Kddt\_h(K).} 624 kd0 = 0.0 \textcolor{comment}{! This might need to be changed - it is the already applied value of Kddt\_h(K).} 625 \textcolor{keywordflow}{if} (k<=2) \textcolor{keywordflow}{then} 626 th\_a(k-1) = h\_tr(k-1) * t0(k-1) ; sh\_a(k-1) = h\_tr(k-1) * s0(k-1) 627 \textcolor{keywordflow}{else} 628 th\_a(k-1) = h\_tr(k-1) * t0(k-1) + kddt\_h(k-1) * te\_a(k-2) 629 sh\_a(k-1) = h\_tr(k-1) * s0(k-1) + kddt\_h(k-1) * se\_a(k-2) 630 \textcolor{keywordflow}{ endif} 631 th\_b(k) = h\_tr(k) * t0(k) ; sh\_b(k) = h\_tr(k) * s0(k) 632 633 kddt\_h\_a(k) = 0.0 ; \textcolor{keywordflow}{if} (k < k\_cent) kddt\_h\_a(k) = kddt\_h(k) 634 dkd = kddt\_h\_a(k) 635 636 \textcolor{keyword}{call }find\_pe\_chg(kd0, dkd, hp\_a(k-1), hp\_b(k), & 637 th\_a(k-1), sh\_a(k-1), th\_b(k), sh\_b(k), & 638 dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 639 pres\_z(k), dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 640 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 641 pe\_chg=pe\_change, colht\_cor=colht\_cor) 642 pe\_chg\_k(k,3) = pe\_change 643 colht\_cor\_k(k,3) = colht\_cor 644 645 b1 = 1.0 / (hp\_a(k-1) + kddt\_h\_a(k)) 646 c1\_a(k) = kddt\_h\_a(k) * b1 647 \textcolor{keywordflow}{if} (k==2) \textcolor{keywordflow}{then} 648 te\_a(1) = b1*(h\_tr(1)*t0(1)) 649 se\_a(1) = b1*(h\_tr(1)*s0(1)) 650 \textcolor{keywordflow}{else} 651 te\_a(k-1) = b1 * (h\_tr(k-1) * t0(k-1) + kddt\_h\_a(k-1) * te\_a(k-2)) 652 se\_a(k-1) = b1 * (h\_tr(k-1) * s0(k-1) + kddt\_h\_a(k-1) * se\_a(k-2)) 653 \textcolor{keywordflow}{ endif} 654 655 hp\_a(k) = h\_tr(k) + (hp\_a(k-1) * b1) * kddt\_h\_a(k) 656 dt\_to\_dpe\_a(k) = dt\_to\_dpe(k) + c1\_a(k)*dt\_to\_dpe\_a(k-1) 657 ds\_to\_dpe\_a(k) = ds\_to\_dpe(k) + c1\_a(k)*ds\_to\_dpe\_a(k-1) 658 dt\_to\_dcolht\_a(k) = dt\_to\_dcolht(k) + c1\_a(k)*dt\_to\_dcolht\_a(k-1) 659 ds\_to\_dcolht\_a(k) = ds\_to\_dcolht(k) + c1\_a(k)*ds\_to\_dcolht\_a(k-1) 660 \textcolor{keywordflow}{ enddo} 661 662 \textcolor{comment}{! Calculate the dependencies on layers below.} 663 kddt\_h\_b(nz+1) = 0.0 664 \textcolor{keywordflow}{do} k=nz,2,-1 \textcolor{comment}{! Loop over interior interfaces.} 665 \textcolor{comment}{! First calculate some terms that are independent of the change in Kddt\_h(K).} 666 kd0 = 0.0 \textcolor{comment}{! This might need to be changed - it is the already applied value of Kddt\_h(K).} 667 \textcolor{comment}{! if (K<=2) then} 668 th\_a(k-1) = h\_tr(k-1) * t0(k-1) ; sh\_a(k-1) = h\_tr(k-1) * s0(k-1) 669 \textcolor{comment}{! else} 670 \textcolor{comment}{! Th\_a(k-1) = h\_tr(k-1) * T0(k-1) + Kddt\_h(K-1) * Te\_a(k-2)} 671 \textcolor{comment}{! Sh\_a(k-1) = h\_tr(k-1) * S0(k-1) + Kddt\_h(K-1) * Se\_a(k-2)} 672 \textcolor{comment}{! endif} 673 \textcolor{keywordflow}{if} (k>=nz) \textcolor{keywordflow}{then} 674 th\_b(k) = h\_tr(k) * t0(k) ; sh\_b(k) = h\_tr(k) * s0(k) 675 \textcolor{keywordflow}{else} 676 th\_b(k) = h\_tr(k) * t0(k) + kddt\_h(k+1) * te\_b(k+1) 677 sh\_b(k) = h\_tr(k) * s0(k) + kddt\_h(k+1) * se\_b(k+1) 678 \textcolor{keywordflow}{ endif} 679 680 kddt\_h\_b(k) = 0.0 ; \textcolor{keywordflow}{if} (k > k\_cent) kddt\_h\_b(k) = kddt\_h(k) 681 dkd = kddt\_h\_b(k) 682 683 \textcolor{keyword}{call }find\_pe\_chg(kd0, dkd, hp\_a(k-1), hp\_b(k), & 684 th\_a(k-1), sh\_a(k-1), th\_b(k), sh\_b(k), & 685 dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 686 pres\_z(k), dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 687 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 688 pe\_chg=pe\_change, colht\_cor=colht\_cor) 689 pe\_chg\_k(k,3) = pe\_chg\_k(k,3) + pe\_change 690 colht\_cor\_k(k,3) = colht\_cor\_k(k,3) + colht\_cor 691 692 b1 = 1.0 / (hp\_b(k) + kddt\_h\_b(k)) 693 c1\_b(k) = kddt\_h\_b(k) * b1 694 \textcolor{keywordflow}{if} (k==nz) \textcolor{keywordflow}{then} 695 te\_b(k) = b1 * (h\_tr(k)*t0(k)) 696 se\_b(k) = b1 * (h\_tr(k)*s0(k)) 697 \textcolor{keywordflow}{else} 698 te\_b(k) = b1 * (h\_tr(k) * t0(k) + kddt\_h\_b(k+1) * te\_b(k+1)) 699 se\_b(k) = b1 * (h\_tr(k) * s0(k) + kddt\_h\_b(k+1) * se\_b(k+1)) 700 \textcolor{keywordflow}{ endif} 701 702 hp\_b(k-1) = h\_tr(k-1) + (hp\_b(k) * b1) * kddt\_h\_b(k) 703 dt\_to\_dpe\_b(k-1) = dt\_to\_dpe(k-1) + c1\_b(k)*dt\_to\_dpe\_b(k) 704 ds\_to\_dpe\_b(k-1) = ds\_to\_dpe(k-1) + c1\_b(k)*ds\_to\_dpe\_b(k) 705 dt\_to\_dcolht\_b(k-1) = dt\_to\_dcolht(k-1) + c1\_b(k)*dt\_to\_dcolht\_b(k) 706 ds\_to\_dcolht\_b(k-1) = ds\_to\_dcolht(k-1) + c1\_b(k)*ds\_to\_dcolht\_b(k) 707 708 \textcolor{keywordflow}{ enddo} 709 710 \textcolor{comment}{! Calculate the final solution for the layers surrounding interface K\_cent} 711 k = k\_cent 712 713 \textcolor{comment}{! First calculate some terms that are independent of the change in Kddt\_h(K).} 714 kd0 = 0.0 \textcolor{comment}{! This might need to be changed - it is the already applied value of Kddt\_h(K).} 715 \textcolor{keywordflow}{if} (k<=2) \textcolor{keywordflow}{then} 716 th\_a(k-1) = h\_tr(k-1) * t0(k-1) ; sh\_a(k-1) = h\_tr(k-1) * s0(k-1) 717 \textcolor{keywordflow}{else} 718 th\_a(k-1) = h\_tr(k-1) * t0(k-1) + kddt\_h(k-1) * te\_a(k-2) 719 sh\_a(k-1) = h\_tr(k-1) * s0(k-1) + kddt\_h(k-1) * se\_a(k-2) 720 \textcolor{keywordflow}{ endif} 721 \textcolor{keywordflow}{if} (k>=nz) \textcolor{keywordflow}{then} 722 th\_b(k) = h\_tr(k) * t0(k) ; sh\_b(k) = h\_tr(k) * s0(k) 723 \textcolor{keywordflow}{else} 724 th\_b(k) = h\_tr(k) * t0(k) + kddt\_h(k+1) * te\_b(k+1) 725 sh\_b(k) = h\_tr(k) * s0(k) + kddt\_h(k+1) * se\_b(k+1) 726 \textcolor{keywordflow}{ endif} 727 728 dkd = kddt\_h(k) 729 730 \textcolor{keyword}{call }find\_pe\_chg(kd0, dkd, hp\_a(k-1), hp\_b(k), & 731 th\_a(k-1), sh\_a(k-1), th\_b(k), sh\_b(k), & 732 dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 733 pres\_z(k), dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 734 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 735 pe\_chg=pe\_change, colht\_cor=colht\_cor) 736 pe\_chg\_k(k,3) = pe\_chg\_k(k,3) + pe\_change 737 colht\_cor\_k(k,3) = colht\_cor\_k(k,3) + colht\_cor 738 739 740 \textcolor{comment}{! To derive the following, first to a partial update for the estimated} 741 \textcolor{comment}{! temperatures and salinities in the layers around this interface:} 742 \textcolor{comment}{! b1\_a = 1.0 / (hp\_a(k-1) + Kddt\_h(K))} 743 \textcolor{comment}{! b1\_b = 1.0 / (hp\_b(k) + Kddt\_h(K))} 744 \textcolor{comment}{! Te\_up(k) = Th\_b(k) * b1\_b ; Se\_up(k) = Sh\_b(k) * b1\_b} 745 \textcolor{comment}{! Te\_up(k-1) = Th\_a(k-1) * b1\_a ; Se\_up(k-1) = Sh\_a(k-1) * b1\_a} 746 \textcolor{comment}{! Find the final values of T & S for both layers around K\_cent, using that} 747 \textcolor{comment}{! c1\_a(K) = Kddt\_h(K) * b1\_a ; c1\_b(K) = Kddt\_h(K) * b1\_b} 748 \textcolor{comment}{! Tf(K\_cent-1) = Te\_up(K\_cent-1) + c1\_a(K\_cent)*Tf(K\_cent)} 749 \textcolor{comment}{! Tf(K\_cent) = Te\_up(K\_cent) + c1\_b(K\_cent)*Tf(K\_cent-1)} 750 \textcolor{comment}{! but further exploiting the expressions for c1\_a and c1\_b to avoid} 751 \textcolor{comment}{! subtraction in the denominator, and use only a single division.} 752 b1 = 1.0 / (hp\_a(k-1)*hp\_b(k) + kddt\_h(k)*(hp\_a(k-1) + hp\_b(k))) 753 tf(k-1) = ((hp\_b(k) + kddt\_h(k)) * th\_a(k-1) + kddt\_h(k) * th\_b(k) ) * b1 754 sf(k-1) = ((hp\_b(k) + kddt\_h(k)) * sh\_a(k-1) + kddt\_h(k) * sh\_b(k) ) * b1 755 tf(k) = (kddt\_h(k) * th\_a(k-1) + (hp\_a(k-1) + kddt\_h(k)) * th\_b(k) ) * b1 756 sf(k) = (kddt\_h(k) * sh\_a(k-1) + (hp\_a(k-1) + kddt\_h(k)) * sh\_b(k) ) * b1 757 758 c1\_a(k) = kddt\_h(k) / (hp\_a(k-1) + kddt\_h(k)) 759 c1\_b(k) = kddt\_h(k) / (hp\_b(k) + kddt\_h(k)) 760 761 \textcolor{comment}{! Now update the other layer working outward from k\_cent to determine the final} 762 \textcolor{comment}{! temperatures and salinities.} 763 \textcolor{keywordflow}{do} k=k\_cent-2,1,-1 764 tf(k) = te\_a(k) + c1\_a(k+1)*tf(k+1) 765 sf(k) = se\_a(k) + c1\_a(k+1)*sf(k+1) 766 \textcolor{keywordflow}{ enddo} 767 \textcolor{keywordflow}{do} k=k\_cent+1,nz 768 tf(k) = te\_b(k) + c1\_b(k)*tf(k-1) 769 sf(k) = se\_b(k) + c1\_b(k)*sf(k-1) 770 \textcolor{keywordflow}{ enddo} 771 772 \textcolor{keywordflow}{if} (debug) \textcolor{keywordflow}{then} 773 pe\_chg\_tot1c = 0.0 ; pe\_chg\_tot2c = 0.0 ; t\_chg\_totc = 0.0 774 \textcolor{keywordflow}{do} k=1,nz 775 pe\_chg\_tot1c = pe\_chg\_tot1c + (dt\_to\_dpe(k) * (tf(k) - t0(k)) + & 776 ds\_to\_dpe(k) * (sf(k) - s0(k))) 777 t\_chg\_totc = t\_chg\_totc + h\_tr(k) * (tf(k) - t0(k)) 778 \textcolor{keywordflow}{ enddo} 779 \textcolor{keywordflow}{do} k=2,nz 780 pe\_chg\_tot2c = pe\_chg\_tot2c + (pe\_chg\_k(k,3) - colht\_cor\_k(k,3)) 781 \textcolor{keywordflow}{ enddo} 782 \textcolor{keywordflow}{ endif} 783 784 \textcolor{keywordflow}{ endif} 785 786 \textcolor{keywordflow}{if} (halves) \textcolor{keywordflow}{then} 787 788 \textcolor{comment}{! Set up values appropriate for no diffusivity.} 789 \textcolor{keywordflow}{do} k=1,nz 790 hp\_a(k) = h\_tr(k) ; hp\_b(k) = h\_tr(k) 791 dt\_to\_dpe\_a(k) = dt\_to\_dpe(k) ; ds\_to\_dpe\_a(k) = ds\_to\_dpe(k) 792 dt\_to\_dpe\_b(k) = dt\_to\_dpe(k) ; ds\_to\_dpe\_b(k) = ds\_to\_dpe(k) 793 dt\_to\_dcolht\_a(k) = dt\_to\_dcolht(k) ; ds\_to\_dcolht\_a(k) = ds\_to\_dcolht(k) 794 dt\_to\_dcolht\_b(k) = dt\_to\_dcolht(k) ; ds\_to\_dcolht\_b(k) = ds\_to\_dcolht(k) 795 \textcolor{keywordflow}{ enddo} 796 \textcolor{keywordflow}{do} k=1,nz+1 797 kd\_so\_far(k) = 0.0 798 \textcolor{keywordflow}{ enddo} 799 800 \textcolor{comment}{! Calculate the dependencies on layers above.} 801 kddt\_h\_a(1) = 0.0 802 \textcolor{keywordflow}{do} k=2,nz \textcolor{comment}{! Loop over interior interfaces.} 803 \textcolor{comment}{! First calculate some terms that are independent of the change in Kddt\_h(K).} 804 kd0 = kd\_so\_far(k) 805 \textcolor{keywordflow}{if} (k<=2) \textcolor{keywordflow}{then} 806 th\_a(k-1) = h\_tr(k-1) * t0(k-1) ; sh\_a(k-1) = h\_tr(k-1) * s0(k-1) 807 \textcolor{keywordflow}{else} 808 th\_a(k-1) = h\_tr(k-1) * t0(k-1) + kd\_so\_far(k-1) * te(k-2) 809 sh\_a(k-1) = h\_tr(k-1) * s0(k-1) + kd\_so\_far(k-1) * se(k-2) 810 \textcolor{keywordflow}{ endif} 811 th\_b(k) = h\_tr(k) * t0(k) ; sh\_b(k) = h\_tr(k) * s0(k) 812 813 dkd = 0.5 * kddt\_h(k) - kd\_so\_far(k) 814 815 \textcolor{keyword}{call }find\_pe\_chg(kd0, dkd, hp\_a(k-1), hp\_b(k), & 816 th\_a(k-1), sh\_a(k-1), th\_b(k), sh\_b(k), & 817 dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 818 pres\_z(k), dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 819 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 820 pe\_chg=pe\_change, colht\_cor=colht\_cor) 821 822 pe\_chg\_k(k,4) = pe\_change 823 colht\_cor\_k(k,4) = colht\_cor 824 825 kd\_so\_far(k) = kd\_so\_far(k) + dkd 826 827 b1 = 1.0 / (hp\_a(k-1) + kd\_so\_far(k)) 828 c1\_a(k) = kd\_so\_far(k) * b1 829 \textcolor{keywordflow}{if} (k==2) \textcolor{keywordflow}{then} 830 te(1) = b1*(h\_tr(1)*t0(1)) 831 se(1) = b1*(h\_tr(1)*s0(1)) 832 \textcolor{keywordflow}{else} 833 te(k-1) = b1 * (h\_tr(k-1) * t0(k-1) + kd\_so\_far(k-1) * te(k-2)) 834 se(k-1) = b1 * (h\_tr(k-1) * s0(k-1) + kd\_so\_far(k-1) * se(k-2)) 835 \textcolor{keywordflow}{ endif} 836 837 hp\_a(k) = h\_tr(k) + (hp\_a(k-1) * b1) * kd\_so\_far(k) 838 dt\_to\_dpe\_a(k) = dt\_to\_dpe(k) + c1\_a(k)*dt\_to\_dpe\_a(k-1) 839 ds\_to\_dpe\_a(k) = ds\_to\_dpe(k) + c1\_a(k)*ds\_to\_dpe\_a(k-1) 840 dt\_to\_dcolht\_a(k) = dt\_to\_dcolht(k) + c1\_a(k)*dt\_to\_dcolht\_a(k-1) 841 ds\_to\_dcolht\_a(k) = ds\_to\_dcolht(k) + c1\_a(k)*ds\_to\_dcolht\_a(k-1) 842 \textcolor{keywordflow}{ enddo} 843 844 \textcolor{comment}{! Calculate the dependencies on layers below.} 845 \textcolor{keywordflow}{do} k=nz,2,-1 \textcolor{comment}{! Loop over interior interfaces.} 846 \textcolor{comment}{! First calculate some terms that are independent of the change in Kddt\_h(K).} 847 kd0 = kd\_so\_far(k) 848 \textcolor{keywordflow}{if} (k<=2) \textcolor{keywordflow}{then} 849 th\_a(k-1) = h\_tr(k-1) * t0(k-1) ; sh\_a(k-1) = h\_tr(k-1) * s0(k-1) 850 \textcolor{keywordflow}{else} 851 th\_a(k-1) = h\_tr(k-1) * t0(k-1) + kd\_so\_far(k-1) * te(k-2) 852 sh\_a(k-1) = h\_tr(k-1) * s0(k-1) + kd\_so\_far(k-1) * se(k-2) 853 \textcolor{keywordflow}{ endif} 854 \textcolor{keywordflow}{if} (k>=nz) \textcolor{keywordflow}{then} 855 th\_b(k) = h\_tr(k) * t0(k) ; sh\_b(k) = h\_tr(k) * s0(k) 856 \textcolor{keywordflow}{else} 857 th\_b(k) = h\_tr(k) * t0(k) + kd\_so\_far(k+1) * te(k+1) 858 sh\_b(k) = h\_tr(k) * s0(k) + kd\_so\_far(k+1) * se(k+1) 859 \textcolor{keywordflow}{ endif} 860 861 dkd = kddt\_h(k) - kd\_so\_far(k) 862 863 \textcolor{keyword}{call }find\_pe\_chg(kd0, dkd, hp\_a(k-1), hp\_b(k), & 864 th\_a(k-1), sh\_a(k-1), th\_b(k), sh\_b(k), & 865 dt\_to\_dpe\_a(k-1), ds\_to\_dpe\_a(k-1), dt\_to\_dpe\_b(k), ds\_to\_dpe\_b(k), & 866 pres\_z(k), dt\_to\_dcolht\_a(k-1), ds\_to\_dcolht\_a(k-1), & 867 dt\_to\_dcolht\_b(k), ds\_to\_dcolht\_b(k), & 868 pe\_chg=pe\_change, colht\_cor=colht\_cor) 869 870 pe\_chg\_k(k,4) = pe\_chg\_k(k,4) + pe\_change 871 colht\_cor\_k(k,4) = colht\_cor\_k(k,4) + colht\_cor 872 873 874 kd\_so\_far(k) = kd\_so\_far(k) + dkd 875 876 b1 = 1.0 / (hp\_b(k) + kd\_so\_far(k)) 877 c1\_b(k) = kd\_so\_far(k) * b1 878 \textcolor{keywordflow}{if} (k==nz) \textcolor{keywordflow}{then} 879 te(k) = b1 * (h\_tr(k)*t0(k)) 880 se(k) = b1 * (h\_tr(k)*s0(k)) 881 \textcolor{keywordflow}{else} 882 te(k) = b1 * (h\_tr(k) * t0(k) + kd\_so\_far(k+1) * te(k+1)) 883 se(k) = b1 * (h\_tr(k) * s0(k) + kd\_so\_far(k+1) * se(k+1)) 884 \textcolor{keywordflow}{ endif} 885 886 hp\_b(k-1) = h\_tr(k-1) + (hp\_b(k) * b1) * kd\_so\_far(k) 887 dt\_to\_dpe\_b(k-1) = dt\_to\_dpe(k-1) + c1\_b(k)*dt\_to\_dpe\_b(k) 888 ds\_to\_dpe\_b(k-1) = ds\_to\_dpe(k-1) + c1\_b(k)*ds\_to\_dpe\_b(k) 889 dt\_to\_dcolht\_b(k-1) = dt\_to\_dcolht(k-1) + c1\_b(k)*dt\_to\_dcolht\_b(k) 890 ds\_to\_dcolht\_b(k-1) = ds\_to\_dcolht(k-1) + c1\_b(k)*ds\_to\_dcolht\_b(k) 891 892 \textcolor{keywordflow}{ enddo} 893 894 \textcolor{comment}{! Now update the other layer working down from the top to determine the} 895 \textcolor{comment}{! final temperatures and salinities.} 896 b1 = 1.0 / (hp\_b(1)) 897 tf(1) = b1 * (h\_tr(1) * t0(1) + kddt\_h(2) * te(2)) 898 sf(1) = b1 * (h\_tr(1) * s0(1) + kddt\_h(2) * se(2)) 899 \textcolor{keywordflow}{do} k=2,nz 900 tf(k) = te(k) + c1\_b(k)*tf(k-1) 901 sf(k) = se(k) + c1\_b(k)*sf(k-1) 902 \textcolor{keywordflow}{ enddo} 903 904 \textcolor{keywordflow}{if} (debug) \textcolor{keywordflow}{then} 905 pe\_chg\_tot1d = 0.0 ; pe\_chg\_tot2d = 0.0 ; t\_chg\_totd = 0.0 906 \textcolor{keywordflow}{do} k=1,nz 907 pe\_chg\_tot1d = pe\_chg\_tot1d + (dt\_to\_dpe(k) * (tf(k) - t0(k)) + & 908 ds\_to\_dpe(k) * (sf(k) - s0(k))) 909 t\_chg\_totd = t\_chg\_totd + h\_tr(k) * (tf(k) - t0(k)) 910 \textcolor{keywordflow}{ enddo} 911 \textcolor{keywordflow}{do} k=2,nz 912 pe\_chg\_tot2d = pe\_chg\_tot2d + (pe\_chg\_k(k,4) - colht\_cor\_k(k,4)) 913 \textcolor{keywordflow}{ enddo} 914 \textcolor{keywordflow}{ endif} 915 916 \textcolor{keywordflow}{ endif} 917 918 energy\_kd = 0.0 ; \textcolor{keywordflow}{do} k=2,nz ; energy\_kd = energy\_kd + pe\_chg\_k(k,1) ;\textcolor{keywordflow}{ enddo} 919 energy\_kd = energy\_kd / dt 920 921 \textcolor{keywordflow}{if} (do\_print) \textcolor{keywordflow}{then} 922 \textcolor{keywordflow}{if} (cs%id\_ERt>0) \textcolor{keyword}{call }post\_data(cs%id\_ERt, pe\_chg\_k(:,1), cs%diag) 923 \textcolor{keywordflow}{if} (cs%id\_ERb>0) \textcolor{keyword}{call }post\_data(cs%id\_ERb, pe\_chg\_k(:,2), cs%diag) 924 \textcolor{keywordflow}{if} (cs%id\_ERc>0) \textcolor{keyword}{call }post\_data(cs%id\_ERc, pe\_chg\_k(:,3), cs%diag) 925 \textcolor{keywordflow}{if} (cs%id\_ERh>0) \textcolor{keyword}{call }post\_data(cs%id\_ERh, pe\_chg\_k(:,4), cs%diag) 926 \textcolor{keywordflow}{if} (cs%id\_Kddt>0) \textcolor{keyword}{call }post\_data(cs%id\_Kddt, kddt\_h, cs%diag) 927 \textcolor{keywordflow}{if} (cs%id\_Kd>0) \textcolor{keyword}{call }post\_data(cs%id\_Kd, kd, cs%diag) 928 \textcolor{keywordflow}{if} (cs%id\_h>0) \textcolor{keyword}{call }post\_data(cs%id\_h, h\_tr, cs%diag) 929 \textcolor{keywordflow}{if} (cs%id\_zInt>0) \textcolor{keyword}{call }post\_data(cs%id\_zInt, z\_int, cs%diag) 930 \textcolor{keywordflow}{if} (cs%id\_CHCt>0) \textcolor{keyword}{call }post\_data(cs%id\_CHCt, colht\_cor\_k(:,1), cs%diag) 931 \textcolor{keywordflow}{if} (cs%id\_CHCb>0) \textcolor{keyword}{call }post\_data(cs%id\_CHCb, colht\_cor\_k(:,2), cs%diag) 932 \textcolor{keywordflow}{if} (cs%id\_CHCc>0) \textcolor{keyword}{call }post\_data(cs%id\_CHCc, colht\_cor\_k(:,3), cs%diag) 933 \textcolor{keywordflow}{if} (cs%id\_CHCh>0) \textcolor{keyword}{call }post\_data(cs%id\_CHCh, colht\_cor\_k(:,4), cs%diag) 934 \textcolor{keywordflow}{if} (cs%id\_T0>0) \textcolor{keyword}{call }post\_data(cs%id\_T0, t0, cs%diag) 935 \textcolor{keywordflow}{if} (cs%id\_Tf>0) \textcolor{keyword}{call }post\_data(cs%id\_Tf, tf, cs%diag) 936 \textcolor{keywordflow}{if} (cs%id\_S0>0) \textcolor{keyword}{call }post\_data(cs%id\_S0, s0, cs%diag) 937 \textcolor{keywordflow}{if} (cs%id\_Sf>0) \textcolor{keyword}{call }post\_data(cs%id\_Sf, sf, cs%diag) 938 \textcolor{keywordflow}{if} (cs%id\_N2\_0>0) \textcolor{keywordflow}{then} 939 n2(1) = 0.0 ; n2(nz+1) = 0.0 940 \textcolor{keywordflow}{do} k=2,nz 941 \textcolor{keyword}{call }calculate\_density(0.5*(t0(k-1) + t0(k)), 0.5*(s0(k-1) + s0(k)), & 942 pres(k), rho\_here, tv%eqn\_of\_state) 943 n2(k) = ((us%L\_to\_Z**2*gv%g\_Earth) * rho\_here / (0.5*gv%H\_to\_Z*(h\_tr(k-1) + h\_tr(k)))) * & 944 ( 0.5*(dsv\_dt(k-1) + dsv\_dt(k)) * (t0(k-1) - t0(k)) + & 945 0.5*(dsv\_ds(k-1) + dsv\_ds(k)) * (s0(k-1) - s0(k)) ) 946 \textcolor{keywordflow}{ enddo} 947 \textcolor{keyword}{call }post\_data(cs%id\_N2\_0, n2, cs%diag) 948 \textcolor{keywordflow}{ endif} 949 \textcolor{keywordflow}{if} (cs%id\_N2\_f>0) \textcolor{keywordflow}{then} 950 n2(1) = 0.0 ; n2(nz+1) = 0.0 951 \textcolor{keywordflow}{do} k=2,nz 952 \textcolor{keyword}{call }calculate\_density(0.5*(tf(k-1) + tf(k)), 0.5*(sf(k-1) + sf(k)), & 953 pres(k), rho\_here, tv%eqn\_of\_state) 954 n2(k) = ((us%L\_to\_Z**2*gv%g\_Earth) * rho\_here / (0.5*gv%H\_to\_Z*(h\_tr(k-1) + h\_tr(k)))) * & 955 ( 0.5*(dsv\_dt(k-1) + dsv\_dt(k)) * (tf(k-1) - tf(k)) + & 956 0.5*(dsv\_ds(k-1) + dsv\_ds(k)) * (sf(k-1) - sf(k)) ) 957 \textcolor{keywordflow}{ enddo} 958 \textcolor{keyword}{call }post\_data(cs%id\_N2\_f, n2, cs%diag) 959 \textcolor{keywordflow}{ endif} 960 \textcolor{keywordflow}{ endif} 961 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__diapyc__energy__req_aa4cb9f1b90a245e34ddd4182943a21c6}\label{namespacemom__diapyc__energy__req_aa4cb9f1b90a245e34ddd4182943a21c6}} \index{mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}!diapyc\+\_\+energy\+\_\+req\+\_\+end@{diapyc\+\_\+energy\+\_\+req\+\_\+end}} \index{diapyc\+\_\+energy\+\_\+req\+\_\+end@{diapyc\+\_\+energy\+\_\+req\+\_\+end}!mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}} \subsubsection{\texorpdfstring{diapyc\+\_\+energy\+\_\+req\+\_\+end()}{diapyc\_energy\_req\_end()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+diapyc\+\_\+energy\+\_\+req\+::diapyc\+\_\+energy\+\_\+req\+\_\+end (\begin{DoxyParamCaption}\item[{type(\mbox{\hyperlink{structmom__diapyc__energy__req_1_1diapyc__energy__req__cs}{diapyc\+\_\+energy\+\_\+req\+\_\+cs}}), pointer}]{CS }\end{DoxyParamCaption})} Clean up and deallocate memory associated with the diapycnal energy requirement module. \begin{DoxyParams}{Parameters} {\em cs} & Diapycnal energy requirement control structure that will be deallocated in this subroutine. \\ \hline \end{DoxyParams} Definition at line 1352 of file M\+O\+M\+\_\+diapyc\+\_\+energy\+\_\+req.\+F90. \begin{DoxyCode} 1352 \textcolor{keywordtype}{type}(diapyc\_energy\_req\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< Diapycnal energy requirement control structure that} 1353 \textcolor{comment}{ !! will be deallocated in this subroutine.} 1354 \textcolor{keywordflow}{if} (\textcolor{keyword}{associated}(cs)) \textcolor{keyword}{deallocate}(cs) \end{DoxyCode} \mbox{\Hypertarget{namespacemom__diapyc__energy__req_a63b127bfd78461d8df3449591792b224}\label{namespacemom__diapyc__energy__req_a63b127bfd78461d8df3449591792b224}} \index{mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}!diapyc\+\_\+energy\+\_\+req\+\_\+init@{diapyc\+\_\+energy\+\_\+req\+\_\+init}} \index{diapyc\+\_\+energy\+\_\+req\+\_\+init@{diapyc\+\_\+energy\+\_\+req\+\_\+init}!mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}} \subsubsection{\texorpdfstring{diapyc\+\_\+energy\+\_\+req\+\_\+init()}{diapyc\_energy\_req\_init()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+diapyc\+\_\+energy\+\_\+req\+::diapyc\+\_\+energy\+\_\+req\+\_\+init (\begin{DoxyParamCaption}\item[{type(time\+\_\+type), intent(in)}]{Time, }\item[{type(ocean\+\_\+grid\+\_\+type), intent(in)}]{G, }\item[{type(verticalgrid\+\_\+type), intent(in)}]{GV, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{type(param\+\_\+file\+\_\+type), intent(in)}]{param\+\_\+file, }\item[{type(diag\+\_\+ctrl), intent(inout), target}]{diag, }\item[{type(\mbox{\hyperlink{structmom__diapyc__energy__req_1_1diapyc__energy__req__cs}{diapyc\+\_\+energy\+\_\+req\+\_\+cs}}), pointer}]{CS }\end{DoxyParamCaption})} Initialize parameters and allocate memory associated with the diapycnal energy requirement module. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em time} & model time\\ \hline \mbox{\tt in} & {\em g} & model grid structure\\ \hline \mbox{\tt in} & {\em gv} & ocean vertical grid structure\\ \hline \mbox{\tt in} & {\em us} & A dimensional unit scaling type\\ \hline \mbox{\tt in} & {\em param\+\_\+file} & file to parse for parameter values\\ \hline \mbox{\tt in,out} & {\em diag} & structure to regulate diagnostic output\\ \hline & {\em cs} & module control structure \\ \hline \end{DoxyParams} Definition at line 1270 of file M\+O\+M\+\_\+diapyc\+\_\+energy\+\_\+req.\+F90. \begin{DoxyCode} 1270 \textcolor{keywordtype}{type}(time\_type), \textcolor{keywordtype}{intent(in)} :: Time\textcolor{comment}{ !< model time} 1271 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< model grid structure} 1272 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< ocean vertical grid structure} 1273 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type} 1274 \textcolor{keywordtype}{type}(param\_file\_type), \textcolor{keywordtype}{intent(in)} :: param\_file\textcolor{comment}{ !< file to parse for parameter values} 1275 \textcolor{keywordtype}{type}(diag\_ctrl), \textcolor{keywordtype}{target}, \textcolor{keywordtype}{intent(inout)} :: diag\textcolor{comment}{ !< structure to regulate diagnostic output} 1276 \textcolor{keywordtype}{type}(diapyc\_energy\_req\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< module control structure} 1277 1278 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{save} :: init\_calls = 0 1279 \textcolor{comment}{! This include declares and sets the variable "version".} 1280 \textcolor{preprocessor}{#include "version\_variable.h"} 1281 \textcolor{preprocessor}{} \textcolor{keywordtype}{character(len=40)} :: mdl = \textcolor{stringliteral}{"MOM\_diapyc\_energy\_req"} \textcolor{comment}{! This module's name.} 1282 \textcolor{keywordtype}{character(len=256)} :: mesg \textcolor{comment}{! Message for error messages.} 1283 1284 \textcolor{keywordflow}{if} (.not.\textcolor{keyword}{associated}(cs)) \textcolor{keywordflow}{then} ; \textcolor{keyword}{allocate}(cs) 1285 \textcolor{keywordflow}{else} ; \textcolor{keywordflow}{return} ;\textcolor{keywordflow}{ endif} 1286 1287 cs%initialized = .true. 1288 cs%diag => diag 1289 1290 \textcolor{comment}{! Read all relevant parameters and write them to the model log.} 1291 \textcolor{keyword}{call }log\_version(param\_file, mdl, version, \textcolor{stringliteral}{""}) 1292 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"ENERGY\_REQ\_KH\_SCALING"}, cs%test\_Kh\_scaling, & 1293 \textcolor{stringliteral}{"A scaling factor for the diapycnal diffusivity used in "}//& 1294 \textcolor{stringliteral}{"testing the energy requirements."}, default=1.0, units=\textcolor{stringliteral}{"nondim"}) 1295 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"ENERGY\_REQ\_COL\_HT\_SCALING"}, cs%ColHt\_scaling, & 1296 \textcolor{stringliteral}{"A scaling factor for the column height change correction "}//& 1297 \textcolor{stringliteral}{"used in testing the energy requirements."}, default=1.0, units=\textcolor{stringliteral}{"nondim"}) 1298 \textcolor{keyword}{call }get\_param(param\_file, mdl, \textcolor{stringliteral}{"ENERGY\_REQ\_USE\_TEST\_PROFILE"}, & 1299 cs%use\_test\_Kh\_profile, & 1300 \textcolor{stringliteral}{"If true, use the internal test diffusivity profile in "}//& 1301 \textcolor{stringliteral}{"place of any that might be passed in as an argument."}, default=.false.) 1302 1303 cs%id\_ERt = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_ERt'}, diag%axesZi, time, & 1304 \textcolor{stringliteral}{"Diffusivity Energy Requirements, top-down"}, & 1305 \textcolor{stringliteral}{"J m-2"}, conversion=us%RZ\_to\_kg\_m2*us%L\_T\_to\_m\_s**2) 1306 cs%id\_ERb = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_ERb'}, diag%axesZi, time, & 1307 \textcolor{stringliteral}{"Diffusivity Energy Requirements, bottom-up"}, & 1308 \textcolor{stringliteral}{"J m-2"}, conversion=us%RZ\_to\_kg\_m2*us%L\_T\_to\_m\_s**2) 1309 cs%id\_ERc = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_ERc'}, diag%axesZi, time, & 1310 \textcolor{stringliteral}{"Diffusivity Energy Requirements, center-last"}, & 1311 \textcolor{stringliteral}{"J m-2"}, conversion=us%RZ\_to\_kg\_m2*us%L\_T\_to\_m\_s**2) 1312 cs%id\_ERh = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_ERh'}, diag%axesZi, time, & 1313 \textcolor{stringliteral}{"Diffusivity Energy Requirements, halves"}, & 1314 \textcolor{stringliteral}{"J m-2"}, conversion=us%RZ\_to\_kg\_m2*us%L\_T\_to\_m\_s**2) 1315 cs%id\_Kddt = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_Kddt'}, diag%axesZi, time, & 1316 \textcolor{stringliteral}{"Implicit diffusive coupling coefficient"}, \textcolor{stringliteral}{"m"}, conversion=gv%H\_to\_m) 1317 cs%id\_Kd = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_Kd'}, diag%axesZi, time, & 1318 \textcolor{stringliteral}{"Diffusivity in test"}, \textcolor{stringliteral}{"m2 s-1"}, conversion=us%Z\_to\_m**2) 1319 cs%id\_h = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_h\_lay'}, diag%axesZL, time, & 1320 \textcolor{stringliteral}{"Test column layer thicknesses"}, \textcolor{stringliteral}{"m"}, conversion=gv%H\_to\_m) 1321 cs%id\_zInt = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_z\_int'}, diag%axesZi, time, & 1322 \textcolor{stringliteral}{"Test column layer interface heights"}, \textcolor{stringliteral}{"m"}, conversion=gv%H\_to\_m) 1323 cs%id\_CHCt = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_CHCt'}, diag%axesZi, time, & 1324 \textcolor{stringliteral}{"Column Height Correction to Energy Requirements, top-down"}, & 1325 \textcolor{stringliteral}{"J m-2"}, conversion=us%RZ\_to\_kg\_m2*us%L\_T\_to\_m\_s**2) 1326 cs%id\_CHCb = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_CHCb'}, diag%axesZi, time, & 1327 \textcolor{stringliteral}{"Column Height Correction to Energy Requirements, bottom-up"}, & 1328 \textcolor{stringliteral}{"J m-2"}, conversion=us%RZ\_to\_kg\_m2*us%L\_T\_to\_m\_s**2) 1329 cs%id\_CHCc = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_CHCc'}, diag%axesZi, time, & 1330 \textcolor{stringliteral}{"Column Height Correction to Energy Requirements, center-last"}, & 1331 \textcolor{stringliteral}{"J m-2"}, conversion=us%RZ\_to\_kg\_m2*us%L\_T\_to\_m\_s**2) 1332 cs%id\_CHCh = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_CHCh'}, diag%axesZi, time, & 1333 \textcolor{stringliteral}{"Column Height Correction to Energy Requirements, halves"}, & 1334 \textcolor{stringliteral}{"J m-2"}, conversion=us%RZ\_to\_kg\_m2*us%L\_T\_to\_m\_s**2) 1335 cs%id\_T0 = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_T0'}, diag%axesZL, time, & 1336 \textcolor{stringliteral}{"Temperature before mixing"}, \textcolor{stringliteral}{"deg C"}) 1337 cs%id\_Tf = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_Tf'}, diag%axesZL, time, & 1338 \textcolor{stringliteral}{"Temperature after mixing"}, \textcolor{stringliteral}{"deg C"}) 1339 cs%id\_S0 = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_S0'}, diag%axesZL, time, & 1340 \textcolor{stringliteral}{"Salinity before mixing"}, \textcolor{stringliteral}{"g kg-1"}) 1341 cs%id\_Sf = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_Sf'}, diag%axesZL, time, & 1342 \textcolor{stringliteral}{"Salinity after mixing"}, \textcolor{stringliteral}{"g kg-1"}) 1343 cs%id\_N2\_0 = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_N2\_0'}, diag%axesZi, time, & 1344 \textcolor{stringliteral}{"Squared buoyancy frequency before mixing"}, \textcolor{stringliteral}{"second-2"}, conversion=us%s\_to\_T**2) 1345 cs%id\_N2\_f = register\_diag\_field(\textcolor{stringliteral}{'ocean\_model'}, \textcolor{stringliteral}{'EnReqTest\_N2\_f'}, diag%axesZi, time, & 1346 \textcolor{stringliteral}{"Squared buoyancy frequency after mixing"}, \textcolor{stringliteral}{"second-2"}, conversion=us%s\_to\_T**2) 1347 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__diapyc__energy__req_a0bf0dd1f3ae4f7f66fb000322f18064e}\label{namespacemom__diapyc__energy__req_a0bf0dd1f3ae4f7f66fb000322f18064e}} \index{mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}!diapyc\+\_\+energy\+\_\+req\+\_\+test@{diapyc\+\_\+energy\+\_\+req\+\_\+test}} \index{diapyc\+\_\+energy\+\_\+req\+\_\+test@{diapyc\+\_\+energy\+\_\+req\+\_\+test}!mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}} \subsubsection{\texorpdfstring{diapyc\+\_\+energy\+\_\+req\+\_\+test()}{diapyc\_energy\_req\_test()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+diapyc\+\_\+energy\+\_\+req\+::diapyc\+\_\+energy\+\_\+req\+\_\+test (\begin{DoxyParamCaption}\item[{real, dimension(g\%isd\+:g\%ied,g\%jsd\+:g\%jed,gv\%ke), intent(in)}]{h\+\_\+3d, }\item[{real, intent(in)}]{dt, }\item[{type(thermo\+\_\+var\+\_\+ptrs), intent(inout)}]{tv, }\item[{type(ocean\+\_\+grid\+\_\+type), intent(in)}]{G, }\item[{type(verticalgrid\+\_\+type), intent(in)}]{GV, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{type(\mbox{\hyperlink{structmom__diapyc__energy__req_1_1diapyc__energy__req__cs}{diapyc\+\_\+energy\+\_\+req\+\_\+cs}}), pointer}]{CS, }\item[{real, dimension(g\%isd\+:g\%ied,g\%jsd\+:g\%jed,gv\%ke+1), intent(in), optional}]{Kd\+\_\+int }\end{DoxyParamCaption})} This subroutine helps test the accuracy of the diapycnal mixing energy requirement code by writing diagnostics, possibly using an intensely mixing test profile of diffusivity. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em g} & The ocean\textquotesingle{}s grid structure.\\ \hline \mbox{\tt in} & {\em gv} & The ocean\textquotesingle{}s vertical grid structure.\\ \hline \mbox{\tt in} & {\em us} & A dimensional unit scaling type\\ \hline \mbox{\tt in} & {\em h\+\_\+3d} & Layer thickness before entrainment \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in,out} & {\em tv} & A structure containing pointers to any available thermodynamic fields. Absent fields have N\+U\+LL ptrs.\\ \hline \mbox{\tt in} & {\em dt} & The amount of time covered by this call \mbox{[}T $\sim$$>$ s\mbox{]}.\\ \hline & {\em cs} & This module\textquotesingle{}s control structure.\\ \hline \mbox{\tt in} & {\em kd\+\_\+int} & Interface diffusivities \mbox{[}Z2 T-\/1 $\sim$$>$ m2 s-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 50 of file M\+O\+M\+\_\+diapyc\+\_\+energy\+\_\+req.\+F90. \begin{DoxyCode} 50 \textcolor{keywordtype}{type}(ocean\_grid\_type), \textcolor{keywordtype}{intent(in)} :: G\textcolor{comment}{ !< The ocean's grid structure.} 51 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< The ocean's vertical grid structure.} 52 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type} 53 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(G%isd:G%ied,G%jsd:G%jed,GV%ke)}, & 54 \textcolor{keywordtype}{intent(in)} :: h\_3d\textcolor{comment}{ !< Layer thickness before entrainment [H ~> m or kg m-2].} 55 \textcolor{keywordtype}{type}(thermo\_var\_ptrs), \textcolor{keywordtype}{intent(inout)} :: tv\textcolor{comment}{ !< A structure containing pointers to any} 56 \textcolor{comment}{ !! available thermodynamic fields.} 57 \textcolor{comment}{ !! Absent fields have NULL ptrs.} 58 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dt\textcolor{comment}{ !< The amount of time covered by this call [T ~> s].} 59 \textcolor{keywordtype}{type}(diapyc\_energy\_req\_CS), \textcolor{keywordtype}{pointer} :: CS\textcolor{comment}{ !< This module's control structure.} 60 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(G%isd:G%ied,G%jsd:G%jed,GV%ke+1)}, & 61 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: Kd\_int\textcolor{comment}{ !< Interface diffusivities [Z2 T-1 ~> m2 s-1].} 62 63 \textcolor{comment}{! Local variables} 64 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke)} :: & 65 T0, S0, & \textcolor{comment}{! T0 & S0 are columns of initial temperatures and salinities [degC] and g/kg.} 66 h\_col \textcolor{comment}{! h\_col is a column of thicknesses h at tracer points [H ~> m or kg m-2].} 67 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(GV%ke+1)} :: & 68 Kd, & \textcolor{comment}{! A column of diapycnal diffusivities at interfaces [Z2 T-1 ~> m2 s-1].} 69 h\_top, h\_bot \textcolor{comment}{! Distances from the top or bottom [H ~> m or kg m-2].} 70 \textcolor{keywordtype}{real} :: ustar, absf, htot 71 \textcolor{keywordtype}{real} :: energy\_Kd \textcolor{comment}{! The energy used by diapycnal mixing [W m-2].} 72 \textcolor{keywordtype}{real} :: tmp1 \textcolor{comment}{! A temporary array.} 73 \textcolor{keywordtype}{integer} :: i, j, k, is, ie, js, je, nz, itt 74 \textcolor{keywordtype}{logical} :: may\_print 75 is = g%isc ; ie = g%iec ; js = g%jsc ; je = g%jec ; nz = g%ke 76 77 \textcolor{keywordflow}{if} (.not. \textcolor{keyword}{associated}(cs)) \textcolor{keyword}{call }mom\_error(fatal, \textcolor{stringliteral}{"diapyc\_energy\_req\_test: "}// & 78 \textcolor{stringliteral}{"Module must be initialized before it is used."}) 79 80 \textcolor{comment}{!$OMP do} 81 \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=is,ie ; \textcolor{keywordflow}{if} (g%mask2dT(i,j) > 0.5) \textcolor{keywordflow}{then} 82 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(kd\_int) .and. .not.cs%use\_test\_Kh\_profile) \textcolor{keywordflow}{then} 83 \textcolor{keywordflow}{do} k=1,nz+1 ; kd(k) = cs%test\_Kh\_scaling*kd\_int(i,j,k) ;\textcolor{keywordflow}{ enddo} 84 \textcolor{keywordflow}{else} 85 htot = 0.0 ; h\_top(1) = 0.0 86 \textcolor{keywordflow}{do} k=1,nz 87 t0(k) = tv%T(i,j,k) ; s0(k) = tv%S(i,j,k) 88 h\_col(k) = h\_3d(i,j,k) 89 h\_top(k+1) = h\_top(k) + h\_col(k) 90 \textcolor{keywordflow}{ enddo} 91 htot = h\_top(nz+1) 92 h\_bot(nz+1) = 0.0 93 \textcolor{keywordflow}{do} k=nz,1,-1 94 h\_bot(k) = h\_bot(k+1) + h\_col(k) 95 \textcolor{keywordflow}{ enddo} 96 97 ustar = 0.01*us%m\_to\_Z*us%T\_to\_s \textcolor{comment}{! Change this to being an input parameter?} 98 absf = 0.25*((abs(g%CoriolisBu(i-1,j-1)) + abs(g%CoriolisBu(i,j))) + & 99 (abs(g%CoriolisBu(i-1,j-1)) + abs(g%CoriolisBu(i,j)))) 100 kd(1) = 0.0 ; kd(nz+1) = 0.0 101 \textcolor{keywordflow}{do} k=2,nz 102 tmp1 = h\_top(k) * h\_bot(k) * gv%H\_to\_Z 103 kd(k) = cs%test\_Kh\_scaling * & 104 ustar * 0.41 * (tmp1*ustar) / (absf*tmp1 + htot*ustar) 105 \textcolor{keywordflow}{ enddo} 106 \textcolor{keywordflow}{ endif} 107 may\_print = is\_root\_pe() .and. (i==ie) .and. (j==je) 108 \textcolor{keyword}{call }diapyc\_energy\_req\_calc(h\_col, t0, s0, kd, energy\_kd, dt, tv, g, gv, us, & 109 may\_print=may\_print, cs=cs) 110 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 111 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__diapyc__energy__req_a2bed511a4b1df9de0e2230c24389bc82}\label{namespacemom__diapyc__energy__req_a2bed511a4b1df9de0e2230c24389bc82}} \index{mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}!find\+\_\+pe\+\_\+chg@{find\+\_\+pe\+\_\+chg}} \index{find\+\_\+pe\+\_\+chg@{find\+\_\+pe\+\_\+chg}!mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}} \subsubsection{\texorpdfstring{find\+\_\+pe\+\_\+chg()}{find\_pe\_chg()}} {\footnotesize\ttfamily subroutine mom\+\_\+diapyc\+\_\+energy\+\_\+req\+::find\+\_\+pe\+\_\+chg (\begin{DoxyParamCaption}\item[{real, intent(in)}]{Kddt\+\_\+h0, }\item[{real, intent(in)}]{d\+Kddt\+\_\+h, }\item[{real, intent(in)}]{hp\+\_\+a, }\item[{real, intent(in)}]{hp\+\_\+b, }\item[{real, intent(in)}]{Th\+\_\+a, }\item[{real, intent(in)}]{Sh\+\_\+a, }\item[{real, intent(in)}]{Th\+\_\+b, }\item[{real, intent(in)}]{Sh\+\_\+b, }\item[{real, intent(in)}]{d\+T\+\_\+to\+\_\+d\+P\+E\+\_\+a, }\item[{real, intent(in)}]{d\+S\+\_\+to\+\_\+d\+P\+E\+\_\+a, }\item[{real, intent(in)}]{d\+T\+\_\+to\+\_\+d\+P\+E\+\_\+b, }\item[{real, intent(in)}]{d\+S\+\_\+to\+\_\+d\+P\+E\+\_\+b, }\item[{real, intent(in)}]{pres\+\_\+Z, }\item[{real, intent(in)}]{d\+T\+\_\+to\+\_\+d\+Col\+Ht\+\_\+a, }\item[{real, intent(in)}]{d\+S\+\_\+to\+\_\+d\+Col\+Ht\+\_\+a, }\item[{real, intent(in)}]{d\+T\+\_\+to\+\_\+d\+Col\+Ht\+\_\+b, }\item[{real, intent(in)}]{d\+S\+\_\+to\+\_\+d\+Col\+Ht\+\_\+b, }\item[{real, intent(out), optional}]{P\+E\+\_\+chg, }\item[{real, intent(out), optional}]{d\+P\+Ec\+\_\+d\+Kd, }\item[{real, intent(out), optional}]{d\+P\+E\+\_\+max, }\item[{real, intent(out), optional}]{d\+P\+Ec\+\_\+d\+Kd\+\_\+0, }\item[{real, intent(out), optional}]{Col\+Ht\+\_\+cor }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine calculates the change in potential energy and or derivatives for several changes in an interfaces\textquotesingle{}s diapycnal diffusivity times a timestep. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em kddt\+\_\+h0} & The previously used diffusivity at an interface times the time step and divided by the average of the thicknesses around the interface \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em dkddt\+\_\+h} & The trial change in the diffusivity at an interface times the time step and divided by the average of the thicknesses around the interface \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em hp\+\_\+a} & The effective pivot thickness of the layer above the interface, given by h\+\_\+k plus a term that is a fraction (determined from the tridiagonal solver) of Kddt\+\_\+h for the interface above \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em hp\+\_\+b} & The effective pivot thickness of the layer below the interface, given by h\+\_\+k plus a term that is a fraction (determined from the tridiagonal solver) of Kddt\+\_\+h for the interface above \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em th\+\_\+a} & An effective temperature times a thickness in the layer above, including implicit mixing effects with other yet higher layers \mbox{[}degC H $\sim$$>$ degC m or degC kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em sh\+\_\+a} & An effective salinity times a thickness in the layer above, including implicit mixing effects with other yet higher layers \mbox{[}ppt H $\sim$$>$ ppt m or ppt kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em th\+\_\+b} & An effective temperature times a thickness in the layer below, including implicit mixing effects with other yet lower layers \mbox{[}degC H $\sim$$>$ degC m or degC kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em sh\+\_\+b} & An effective salinity times a thickness in the layer below, including implicit mixing effects with other yet lower layers \mbox{[}ppt H $\sim$$>$ ppt m or ppt kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt\+\_\+to\+\_\+dpe\+\_\+a} & A factor (pres\+\_\+lay$\ast$mass\+\_\+lay$\ast$d\+Spec\+\_\+vol/dT) relating a layer\textquotesingle{}s temperature change to the change in column potential energy, including all implicit diffusive changes in the temperatures of all the layers above \mbox{[}R Z L2 T-\/2 deg\+C-\/1 $\sim$$>$ J m-\/2 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em ds\+\_\+to\+\_\+dpe\+\_\+a} & A factor (pres\+\_\+lay$\ast$mass\+\_\+lay$\ast$d\+Spec\+\_\+vol/dS) relating a layer\textquotesingle{}s salinity change to the change in column potential energy, including all implicit diffusive changes in the salinities of all the layers above \mbox{[}R Z L2 T-\/2 ppt-\/1 $\sim$$>$ J m-\/2 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt\+\_\+to\+\_\+dpe\+\_\+b} & A factor (pres\+\_\+lay$\ast$mass\+\_\+lay$\ast$d\+Spec\+\_\+vol/dT) relating a layer\textquotesingle{}s temperature change to the change in column potential energy, including all implicit diffusive changes in the temperatures of all the layers below \mbox{[}R Z L2 T-\/2 deg\+C-\/1 $\sim$$>$ J m-\/2 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em ds\+\_\+to\+\_\+dpe\+\_\+b} & A factor (pres\+\_\+lay$\ast$mass\+\_\+lay$\ast$d\+Spec\+\_\+vol/dS) relating a layer\textquotesingle{}s salinity change to the change in column potential energy, including all implicit diffusive changes in the salinities of all the layers below \mbox{[}R Z L2 T-\/2 ppt-\/1 $\sim$$>$ J m-\/2 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em pres\+\_\+z} & The hydrostatic interface pressure, which is used to relate the changes in column thickness to the energy that is radiated as gravity waves and unavailable to drive mixing \mbox{[}R L2 T-\/2 m Z-\/1 $\sim$$>$ J m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt\+\_\+to\+\_\+dcolht\+\_\+a} & A factor (mass\+\_\+lay$\ast$d\+S\+Col\+Htc\+\_\+vol/dT) relating a layer\textquotesingle{}s temperature change to the change in column height, including all implicit diffusive changes in the temperatures of all the layers above \mbox{[}Z deg\+C-\/1 $\sim$$>$ m deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em ds\+\_\+to\+\_\+dcolht\+\_\+a} & A factor (mass\+\_\+lay$\ast$d\+S\+Col\+Htc\+\_\+vol/dS) relating a layer\textquotesingle{}s salinity change to the change in column height, including all implicit diffusive changes in the salinities of all the layers above \mbox{[}Z ppt-\/1 $\sim$$>$ m ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt\+\_\+to\+\_\+dcolht\+\_\+b} & A factor (mass\+\_\+lay$\ast$d\+S\+Col\+Htc\+\_\+vol/dT) relating a layer\textquotesingle{}s temperature change to the change in column height, including all implicit diffusive changes in the temperatures of all the layers below \mbox{[}Z deg\+C-\/1 $\sim$$>$ m deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em ds\+\_\+to\+\_\+dcolht\+\_\+b} & A factor (mass\+\_\+lay$\ast$d\+S\+Col\+Htc\+\_\+vol/dS) relating a layer\textquotesingle{}s salinity change to the change in column height, including all implicit diffusive changes in the salinities of all the layers below \mbox{[}Z ppt-\/1 $\sim$$>$ m ppt-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em pe\+\_\+chg} & The change in column potential energy from applying Kddt\+\_\+h at the present interface \mbox{[}R Z L2 T-\/2 $\sim$$>$ J m-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em dpec\+\_\+dkd} & The partial derivative of P\+E\+\_\+chg with Kddt\+\_\+h, \mbox{[}R Z L2 T-\/2 H-\/1 $\sim$$>$ J m-\/3 or J kg-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em dpe\+\_\+max} & The maximum change in column potential energy that could be realizedd by applying a huge value of Kddt\+\_\+h at the present interface \mbox{[}R Z L2 T-\/2 $\sim$$>$ J m-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em dpec\+\_\+dkd\+\_\+0} & The partial derivative of P\+E\+\_\+chg with Kddt\+\_\+h in the limit where Kddt\+\_\+h = 0 \mbox{[}R Z L2 T-\/2 H-\/1 $\sim$$>$ J m-\/3 or J kg-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em colht\+\_\+cor} & The correction to P\+E\+\_\+chg that is made due to a net change in the column height \mbox{[}R Z L2 T-\/2 $\sim$$>$ J m-\/2\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 970 of file M\+O\+M\+\_\+diapyc\+\_\+energy\+\_\+req.\+F90. \begin{DoxyCode} 970 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Kddt\_h0\textcolor{comment}{ !< The previously used diffusivity at an interface times} 971 \textcolor{comment}{ !! the time step and divided by the average of the} 972 \textcolor{comment}{ !! thicknesses around the interface [H ~> m or kg m-2].} 973 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dKddt\_h\textcolor{comment}{ !< The trial change in the diffusivity at an interface times} 974 \textcolor{comment}{ !! the time step and divided by the average of the} 975 \textcolor{comment}{ !! thicknesses around the interface [H ~> m or kg m-2].} 976 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: hp\_a\textcolor{comment}{ !< The effective pivot thickness of the layer above the} 977 \textcolor{comment}{ !! interface, given by h\_k plus a term that} 978 \textcolor{comment}{ !! is a fraction (determined from the tridiagonal solver) of} 979 \textcolor{comment}{ !! Kddt\_h for the interface above [H ~> m or kg m-2].} 980 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: hp\_b\textcolor{comment}{ !< The effective pivot thickness of the layer below the} 981 \textcolor{comment}{ !! interface, given by h\_k plus a term that} 982 \textcolor{comment}{ !! is a fraction (determined from the tridiagonal solver) of} 983 \textcolor{comment}{ !! Kddt\_h for the interface above [H ~> m or kg m-2].} 984 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Th\_a\textcolor{comment}{ !< An effective temperature times a thickness in the layer} 985 \textcolor{comment}{ !! above, including implicit mixing effects with other} 986 \textcolor{comment}{ !! yet higher layers [degC H ~> degC m or degC kg m-2].} 987 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Sh\_a\textcolor{comment}{ !< An effective salinity times a thickness in the layer} 988 \textcolor{comment}{ !! above, including implicit mixing effects with other} 989 \textcolor{comment}{ !! yet higher layers [ppt H ~> ppt m or ppt kg m-2].} 990 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Th\_b\textcolor{comment}{ !< An effective temperature times a thickness in the layer} 991 \textcolor{comment}{ !! below, including implicit mixing effects with other} 992 \textcolor{comment}{ !! yet lower layers [degC H ~> degC m or degC kg m-2].} 993 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Sh\_b\textcolor{comment}{ !< An effective salinity times a thickness in the layer} 994 \textcolor{comment}{ !! below, including implicit mixing effects with other} 995 \textcolor{comment}{ !! yet lower layers [ppt H ~> ppt m or ppt kg m-2].} 996 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dT\_to\_dPE\_a\textcolor{comment}{ !< A factor (pres\_lay*mass\_lay*dSpec\_vol/dT) relating} 997 \textcolor{comment}{ !! a layer's temperature change to the change in column} 998 \textcolor{comment}{ !! potential energy, including all implicit diffusive changes} 999 \textcolor{comment}{ !! in the temperatures of all the layers above [R Z L2 T-2 degC-1 ~> J m-2 degC-1].} 1000 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dS\_to\_dPE\_a\textcolor{comment}{ !< A factor (pres\_lay*mass\_lay*dSpec\_vol/dS) relating} 1001 \textcolor{comment}{ !! a layer's salinity change to the change in column} 1002 \textcolor{comment}{ !! potential energy, including all implicit diffusive changes} 1003 \textcolor{comment}{ !! in the salinities of all the layers above [R Z L2 T-2 ppt-1 ~> J m-2 ppt-1].} 1004 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dT\_to\_dPE\_b\textcolor{comment}{ !< A factor (pres\_lay*mass\_lay*dSpec\_vol/dT) relating} 1005 \textcolor{comment}{ !! a layer's temperature change to the change in column} 1006 \textcolor{comment}{ !! potential energy, including all implicit diffusive changes} 1007 \textcolor{comment}{ !! in the temperatures of all the layers below [R Z L2 T-2 degC-1 ~> J m-2 degC-1].} 1008 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dS\_to\_dPE\_b\textcolor{comment}{ !< A factor (pres\_lay*mass\_lay*dSpec\_vol/dS) relating} 1009 \textcolor{comment}{ !! a layer's salinity change to the change in column} 1010 \textcolor{comment}{ !! potential energy, including all implicit diffusive changes} 1011 \textcolor{comment}{ !! in the salinities of all the layers below [R Z L2 T-2 ppt-1 ~> J m-2 ppt-1].} 1012 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: pres\_Z\textcolor{comment}{ !< The hydrostatic interface pressure, which is used to relate} 1013 \textcolor{comment}{ !! the changes in column thickness to the energy that is radiated} 1014 \textcolor{comment}{ !! as gravity waves and unavailable to drive mixing [R L2 T-2 m Z-1 ~> J m-3].} 1015 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dT\_to\_dColHt\_a\textcolor{comment}{ !< A factor (mass\_lay*dSColHtc\_vol/dT) relating} 1016 \textcolor{comment}{ !! a layer's temperature change to the change in column} 1017 \textcolor{comment}{ !! height, including all implicit diffusive changes} 1018 \textcolor{comment}{ !! in the temperatures of all the layers above [Z degC-1 ~> m degC-1].} 1019 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dS\_to\_dColHt\_a\textcolor{comment}{ !< A factor (mass\_lay*dSColHtc\_vol/dS) relating} 1020 \textcolor{comment}{ !! a layer's salinity change to the change in column} 1021 \textcolor{comment}{ !! height, including all implicit diffusive changes} 1022 \textcolor{comment}{ !! in the salinities of all the layers above [Z ppt-1 ~> m ppt-1].} 1023 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dT\_to\_dColHt\_b\textcolor{comment}{ !< A factor (mass\_lay*dSColHtc\_vol/dT) relating} 1024 \textcolor{comment}{ !! a layer's temperature change to the change in column} 1025 \textcolor{comment}{ !! height, including all implicit diffusive changes} 1026 \textcolor{comment}{ !! in the temperatures of all the layers below [Z degC-1 ~> m degC-1].} 1027 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dS\_to\_dColHt\_b\textcolor{comment}{ !< A factor (mass\_lay*dSColHtc\_vol/dS) relating} 1028 \textcolor{comment}{ !! a layer's salinity change to the change in column} 1029 \textcolor{comment}{ !! height, including all implicit diffusive changes} 1030 \textcolor{comment}{ !! in the salinities of all the layers below [Z ppt-1 ~> m ppt-1].} 1031 1032 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: PE\_chg\textcolor{comment}{ !< The change in column potential energy from applying} 1033 \textcolor{comment}{ !! Kddt\_h at the present interface [R Z L2 T-2 ~> J m-2].} 1034 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: dPEc\_dKd\textcolor{comment}{ !< The partial derivative of PE\_chg with Kddt\_h,} 1035 \textcolor{comment}{ !! [R Z L2 T-2 H-1 ~> J m-3 or J kg-1].} 1036 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: dPE\_max\textcolor{comment}{ !< The maximum change in column potential energy that could} 1037 \textcolor{comment}{ !! be realizedd by applying a huge value of Kddt\_h at the} 1038 \textcolor{comment}{ !! present interface [R Z L2 T-2 ~> J m-2].} 1039 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: dPEc\_dKd\_0\textcolor{comment}{ !< The partial derivative of PE\_chg with Kddt\_h in the} 1040 \textcolor{comment}{ !! limit where Kddt\_h = 0 [R Z L2 T-2 H-1 ~> J m-3 or J kg-1].} 1041 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: ColHt\_cor\textcolor{comment}{ !< The correction to PE\_chg that is made due to a net} 1042 \textcolor{comment}{ !! change in the column height [R Z L2 T-2 ~> J m-2].} 1043 1044 \textcolor{keywordtype}{real} :: hps \textcolor{comment}{! The sum of the two effective pivot thicknesses [H ~> m or kg m-2].} 1045 \textcolor{keywordtype}{real} :: bdt1 \textcolor{comment}{! A product of the two pivot thicknesses plus a diffusive term [H2 ~> m2 or kg2 m-4].} 1046 \textcolor{keywordtype}{real} :: dT\_c \textcolor{comment}{! The core term in the expressions for the temperature changes [degC H2 ~> degC m2 or degC kg2 m-4].} 1047 \textcolor{keywordtype}{real} :: dS\_c \textcolor{comment}{! The core term in the expressions for the salinity changes [psu H2 ~> psu m2 or psu kg2 m-4].} 1048 \textcolor{keywordtype}{real} :: PEc\_core \textcolor{comment}{! The diffusivity-independent core term in the expressions} 1049 \textcolor{comment}{! for the potential energy changes [R L2 T-2 ~> J m-3].} 1050 \textcolor{keywordtype}{real} :: ColHt\_core \textcolor{comment}{! The diffusivity-independent core term in the expressions} 1051 \textcolor{comment}{! for the column height changes [R L2 T-2 ~> J m-3].} 1052 \textcolor{keywordtype}{real} :: ColHt\_chg \textcolor{comment}{! The change in the column height [Z ~> m].} 1053 \textcolor{keywordtype}{real} :: y1 \textcolor{comment}{! A local temporary term, in [H-3] or [H-4] in various contexts.} 1054 1055 \textcolor{comment}{! The expression for the change in potential energy used here is derived} 1056 \textcolor{comment}{! from the expression for the final estimates of the changes in temperature} 1057 \textcolor{comment}{! and salinities, and then extensively manipulated to get it into its most} 1058 \textcolor{comment}{! succint form. The derivation is not necessarily obvious, but it demonstrably} 1059 \textcolor{comment}{! works by comparison with separate calculations of the energy changes after} 1060 \textcolor{comment}{! the tridiagonal solver for the final changes in temperature and salinity are} 1061 \textcolor{comment}{! applied.} 1062 1063 hps = hp\_a + hp\_b 1064 bdt1 = hp\_a * hp\_b + kddt\_h0 * hps 1065 dt\_c = hp\_a * th\_b - hp\_b * th\_a 1066 ds\_c = hp\_a * sh\_b - hp\_b * sh\_a 1067 pec\_core = hp\_b * (dt\_to\_dpe\_a * dt\_c + ds\_to\_dpe\_a * ds\_c) - & 1068 hp\_a * (dt\_to\_dpe\_b * dt\_c + ds\_to\_dpe\_b * ds\_c) 1069 colht\_core = hp\_b * (dt\_to\_dcolht\_a * dt\_c + ds\_to\_dcolht\_a * ds\_c) - & 1070 hp\_a * (dt\_to\_dcolht\_b * dt\_c + ds\_to\_dcolht\_b * ds\_c) 1071 1072 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(pe\_chg)) \textcolor{keywordflow}{then} 1073 \textcolor{comment}{! Find the change in column potential energy due to the change in the} 1074 \textcolor{comment}{! diffusivity at this interface by dKddt\_h.} 1075 y1 = dkddt\_h / (bdt1 * (bdt1 + dkddt\_h * hps)) 1076 pe\_chg = pec\_core * y1 1077 colht\_chg = colht\_core * y1 1078 \textcolor{keywordflow}{if} (colht\_chg < 0.0) pe\_chg = pe\_chg - pres\_z * colht\_chg 1079 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(colht\_cor)) colht\_cor = -pres\_z * min(colht\_chg, 0.0) 1080 \textcolor{keywordflow}{elseif} (\textcolor{keyword}{present}(colht\_cor)) \textcolor{keywordflow}{then} 1081 y1 = dkddt\_h / (bdt1 * (bdt1 + dkddt\_h * hps)) 1082 colht\_cor = -pres\_z * min(colht\_core * y1, 0.0) 1083 \textcolor{keywordflow}{ endif} 1084 1085 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(dpec\_dkd)) \textcolor{keywordflow}{then} 1086 \textcolor{comment}{! Find the derivative of the potential energy change with dKddt\_h.} 1087 y1 = 1.0 / (bdt1 + dkddt\_h * hps)**2 1088 dpec\_dkd = pec\_core * y1 1089 colht\_chg = colht\_core * y1 1090 \textcolor{keywordflow}{if} (colht\_chg < 0.0) dpec\_dkd = dpec\_dkd - pres\_z * colht\_chg 1091 \textcolor{keywordflow}{ endif} 1092 1093 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(dpe\_max)) \textcolor{keywordflow}{then} 1094 \textcolor{comment}{! This expression is the limit of PE\_chg for infinite dKddt\_h.} 1095 y1 = 1.0 / (bdt1 * hps) 1096 dpe\_max = pec\_core * y1 1097 colht\_chg = colht\_core * y1 1098 \textcolor{keywordflow}{if} (colht\_chg < 0.0) dpe\_max = dpe\_max - pres\_z * colht\_chg 1099 \textcolor{keywordflow}{ endif} 1100 1101 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(dpec\_dkd\_0)) \textcolor{keywordflow}{then} 1102 \textcolor{comment}{! This expression is the limit of dPEc\_dKd for dKddt\_h = 0.} 1103 y1 = 1.0 / bdt1**2 1104 dpec\_dkd\_0 = pec\_core * y1 1105 colht\_chg = colht\_core * y1 1106 \textcolor{keywordflow}{if} (colht\_chg < 0.0) dpec\_dkd\_0 = dpec\_dkd\_0 - pres\_z * colht\_chg 1107 \textcolor{keywordflow}{ endif} 1108 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__diapyc__energy__req_afb1736a09e8f04ae84f561924e157691}\label{namespacemom__diapyc__energy__req_afb1736a09e8f04ae84f561924e157691}} \index{mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}!find\+\_\+pe\+\_\+chg\+\_\+orig@{find\+\_\+pe\+\_\+chg\+\_\+orig}} \index{find\+\_\+pe\+\_\+chg\+\_\+orig@{find\+\_\+pe\+\_\+chg\+\_\+orig}!mom\+\_\+diapyc\+\_\+energy\+\_\+req@{mom\+\_\+diapyc\+\_\+energy\+\_\+req}} \subsubsection{\texorpdfstring{find\+\_\+pe\+\_\+chg\+\_\+orig()}{find\_pe\_chg\_orig()}} {\footnotesize\ttfamily subroutine mom\+\_\+diapyc\+\_\+energy\+\_\+req\+::find\+\_\+pe\+\_\+chg\+\_\+orig (\begin{DoxyParamCaption}\item[{real, intent(in)}]{Kddt\+\_\+h, }\item[{real, intent(in)}]{h\+\_\+k, }\item[{real, intent(in)}]{b\+\_\+den\+\_\+1, }\item[{real, intent(in)}]{d\+Te\+\_\+term, }\item[{real, intent(in)}]{d\+Se\+\_\+term, }\item[{real, intent(in)}]{d\+T\+\_\+km1\+\_\+t2, }\item[{real, intent(in)}]{d\+S\+\_\+km1\+\_\+t2, }\item[{real, intent(in)}]{d\+T\+\_\+to\+\_\+d\+P\+E\+\_\+k, }\item[{real, intent(in)}]{d\+S\+\_\+to\+\_\+d\+P\+E\+\_\+k, }\item[{real, intent(in)}]{d\+T\+\_\+to\+\_\+d\+P\+Ea, }\item[{real, intent(in)}]{d\+S\+\_\+to\+\_\+d\+P\+Ea, }\item[{real, intent(in)}]{pres\+\_\+Z, }\item[{real, intent(in)}]{d\+T\+\_\+to\+\_\+d\+Col\+Ht\+\_\+k, }\item[{real, intent(in)}]{d\+S\+\_\+to\+\_\+d\+Col\+Ht\+\_\+k, }\item[{real, intent(in)}]{d\+T\+\_\+to\+\_\+d\+Col\+Hta, }\item[{real, intent(in)}]{d\+S\+\_\+to\+\_\+d\+Col\+Hta, }\item[{real, intent(out), optional}]{P\+E\+\_\+chg, }\item[{real, intent(out), optional}]{d\+P\+Ec\+\_\+d\+Kd, }\item[{real, intent(out), optional}]{d\+P\+E\+\_\+max, }\item[{real, intent(out), optional}]{d\+P\+Ec\+\_\+d\+Kd\+\_\+0 }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine calculates the change in potential energy and or derivatives for several changes in an interfaces\textquotesingle{}s diapycnal diffusivity times a timestep using the original form used in the first version of e\+P\+BL. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em kddt\+\_\+h} & The diffusivity at an interface times the time step and divided by the average of the thicknesses around the interface \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em h\+\_\+k} & The thickness of the layer below the interface \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em b\+\_\+den\+\_\+1} & The first term in the denominator of the pivot for the tridiagonal solver, given by h\+\_\+k plus a term that is a fraction (determined from the tridiagonal solver) of Kddt\+\_\+h for the interface above \mbox{[}H $\sim$$>$ m or kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em dte\+\_\+term} & A diffusivity-\/independent term related to the temperature change in the layer below the interface \mbox{[}degC H $\sim$$>$ degC m or degC kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em dse\+\_\+term} & A diffusivity-\/independent term related to the salinity change in the layer below the interface \mbox{[}ppt H $\sim$$>$ ppt m or ppt kg m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt\+\_\+km1\+\_\+t2} & A diffusivity-\/independent term related to the temperature change in the layer above the interface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em ds\+\_\+km1\+\_\+t2} & A diffusivity-\/independent term related to the salinity change in the layer above the interface \mbox{[}ppt\mbox{]}.\\ \hline \mbox{\tt in} & {\em pres\+\_\+z} & The hydrostatic interface pressure, which is used to relate the changes in column thickness to the energy that is radiated as gravity waves and unavailable to drive mixing \mbox{[}R L2 T-\/2 $\sim$$>$ J m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt\+\_\+to\+\_\+dpe\+\_\+k} & A factor (pres\+\_\+lay$\ast$mass\+\_\+lay$\ast$d\+Spec\+\_\+vol/dT) relating a layer\textquotesingle{}s temperature change to the change in column potential energy, including all implicit diffusive changes in the temperatures of all the layers below \mbox{[}R Z L2 T-\/2 deg\+C-\/1 $\sim$$>$ J m-\/2 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em ds\+\_\+to\+\_\+dpe\+\_\+k} & A factor (pres\+\_\+lay$\ast$mass\+\_\+lay$\ast$d\+Spec\+\_\+vol/dS) relating a layer\textquotesingle{}s salinity change to the change in column potential energy, including all implicit diffusive changes in the salinities of all the layers below \mbox{[}R Z L2 T-\/2 ppt-\/1 $\sim$$>$ J m-\/2 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt\+\_\+to\+\_\+dpea} & A factor (pres\+\_\+lay$\ast$mass\+\_\+lay$\ast$d\+Spec\+\_\+vol/dT) relating a layer\textquotesingle{}s temperature change to the change in column potential energy, including all implicit diffusive changes in the temperatures of all the layers above \mbox{[}R Z L2 T-\/2 deg\+C-\/1 $\sim$$>$ J m-\/2 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em ds\+\_\+to\+\_\+dpea} & A factor (pres\+\_\+lay$\ast$mass\+\_\+lay$\ast$d\+Spec\+\_\+vol/dS) relating a layer\textquotesingle{}s salinity change to the change in column potential energy, including all implicit diffusive changes in the salinities of all the layers above \mbox{[}R Z L2 T-\/2 ppt-\/1 $\sim$$>$ J m-\/2 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt\+\_\+to\+\_\+dcolht\+\_\+k} & A factor (mass\+\_\+lay$\ast$d\+S\+Col\+Htc\+\_\+vol/dT) relating a layer\textquotesingle{}s temperature change to the change in column height, including all implicit diffusive changes in the temperatures of all the layers below \mbox{[}Z deg\+C-\/1 $\sim$$>$ m deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em ds\+\_\+to\+\_\+dcolht\+\_\+k} & A factor (mass\+\_\+lay$\ast$d\+S\+Col\+Htc\+\_\+vol/dS) relating a layer\textquotesingle{}s salinity change to the change in column height, including all implicit diffusive changes in the salinities of all the layers below \mbox{[}Z ppt-\/1 $\sim$$>$ m ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em dt\+\_\+to\+\_\+dcolhta} & A factor (mass\+\_\+lay$\ast$d\+S\+Col\+Htc\+\_\+vol/dT) relating a layer\textquotesingle{}s temperature change to the change in column height, including all implicit diffusive changes in the temperatures of all the layers above \mbox{[}Z deg\+C-\/1 $\sim$$>$ m deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em ds\+\_\+to\+\_\+dcolhta} & A factor (mass\+\_\+lay$\ast$d\+S\+Col\+Htc\+\_\+vol/dS) relating a layer\textquotesingle{}s salinity change to the change in column height, including all implicit diffusive changes in the salinities of all the layers above \mbox{[}Z ppt-\/1 $\sim$$>$ m ppt-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em pe\+\_\+chg} & The change in column potential energy from applying Kddt\+\_\+h at the present interface \mbox{[}R Z L2 T-\/2 $\sim$$>$ J m-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em dpec\+\_\+dkd} & The partial derivative of P\+E\+\_\+chg with Kddt\+\_\+h, \mbox{[}R Z L2 T-\/2 H-\/1 $\sim$$>$ J m-\/3 or J kg-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em dpe\+\_\+max} & The maximum change in column potential energy that could be realized by applying a huge value of Kddt\+\_\+h at the present interface \mbox{[}R Z L2 T-\/2 $\sim$$>$ J m-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em dpec\+\_\+dkd\+\_\+0} & The partial derivative of P\+E\+\_\+chg with Kddt\+\_\+h in the limit where Kddt\+\_\+h = 0 \mbox{[}R Z L2 T-\/2 H-\/1 $\sim$$>$ J m-\/3 or J kg-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 1120 of file M\+O\+M\+\_\+diapyc\+\_\+energy\+\_\+req.\+F90. \begin{DoxyCode} 1120 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Kddt\_h\textcolor{comment}{ !< The diffusivity at an interface times the time step and} 1121 \textcolor{comment}{ !! divided by the average of the thicknesses around the} 1122 \textcolor{comment}{ !! interface [H ~> m or kg m-2].} 1123 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: h\_k\textcolor{comment}{ !< The thickness of the layer below the interface [H ~> m or kg m-2].} 1124 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: b\_den\_1\textcolor{comment}{ !< The first term in the denominator of the pivot} 1125 \textcolor{comment}{ !! for the tridiagonal solver, given by h\_k plus a term that} 1126 \textcolor{comment}{ !! is a fraction (determined from the tridiagonal solver) of} 1127 \textcolor{comment}{ !! Kddt\_h for the interface above [H ~> m or kg m-2].} 1128 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dTe\_term\textcolor{comment}{ !< A diffusivity-independent term related to the temperature change} 1129 \textcolor{comment}{ !! in the layer below the interface [degC H ~> degC m or degC kg m-2].} 1130 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dSe\_term\textcolor{comment}{ !< A diffusivity-independent term related to the salinity change} 1131 \textcolor{comment}{ !! in the layer below the interface [ppt H ~> ppt m or ppt kg m-2].} 1132 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dT\_km1\_t2\textcolor{comment}{ !< A diffusivity-independent term related to the} 1133 \textcolor{comment}{ !! temperature change in the layer above the interface [degC].} 1134 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dS\_km1\_t2\textcolor{comment}{ !< A diffusivity-independent term related to the} 1135 \textcolor{comment}{ !! salinity change in the layer above the interface [ppt].} 1136 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: pres\_Z\textcolor{comment}{ !< The hydrostatic interface pressure, which is used to relate} 1137 \textcolor{comment}{ !! the changes in column thickness to the energy that is radiated} 1138 \textcolor{comment}{ !! as gravity waves and unavailable to drive mixing [R L2 T-2 ~> J m-3].} 1139 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dT\_to\_dPE\_k\textcolor{comment}{ !< A factor (pres\_lay*mass\_lay*dSpec\_vol/dT) relating} 1140 \textcolor{comment}{ !! a layer's temperature change to the change in column} 1141 \textcolor{comment}{ !! potential energy, including all implicit diffusive changes} 1142 \textcolor{comment}{ !! in the temperatures of all the layers below [R Z L2 T-2 degC-1 ~> J m-2 degC-1].} 1143 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dS\_to\_dPE\_k\textcolor{comment}{ !< A factor (pres\_lay*mass\_lay*dSpec\_vol/dS) relating} 1144 \textcolor{comment}{ !! a layer's salinity change to the change in column} 1145 \textcolor{comment}{ !! potential energy, including all implicit diffusive changes} 1146 \textcolor{comment}{ !! in the salinities of all the layers below [R Z L2 T-2 ppt-1 ~> J m-2 ppt-1].} 1147 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dT\_to\_dPEa\textcolor{comment}{ !< A factor (pres\_lay*mass\_lay*dSpec\_vol/dT) relating} 1148 \textcolor{comment}{ !! a layer's temperature change to the change in column} 1149 \textcolor{comment}{ !! potential energy, including all implicit diffusive changes} 1150 \textcolor{comment}{ !! in the temperatures of all the layers above [R Z L2 T-2 degC-1 ~> J m-2 degC-1].} 1151 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dS\_to\_dPEa\textcolor{comment}{ !< A factor (pres\_lay*mass\_lay*dSpec\_vol/dS) relating} 1152 \textcolor{comment}{ !! a layer's salinity change to the change in column} 1153 \textcolor{comment}{ !! potential energy, including all implicit diffusive changes} 1154 \textcolor{comment}{ !! in the salinities of all the layers above [R Z L2 T-2 ppt-1 ~> J m-2 ppt-1].} 1155 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dT\_to\_dColHt\_k\textcolor{comment}{ !< A factor (mass\_lay*dSColHtc\_vol/dT) relating} 1156 \textcolor{comment}{ !! a layer's temperature change to the change in column} 1157 \textcolor{comment}{ !! height, including all implicit diffusive changes} 1158 \textcolor{comment}{ !! in the temperatures of all the layers below [Z degC-1 ~> m degC-1].} 1159 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dS\_to\_dColHt\_k\textcolor{comment}{ !< A factor (mass\_lay*dSColHtc\_vol/dS) relating} 1160 \textcolor{comment}{ !! a layer's salinity change to the change in column} 1161 \textcolor{comment}{ !! height, including all implicit diffusive changes} 1162 \textcolor{comment}{ !! in the salinities of all the layers below [Z ppt-1 ~> m ppt-1].} 1163 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dT\_to\_dColHta\textcolor{comment}{ !< A factor (mass\_lay*dSColHtc\_vol/dT) relating} 1164 \textcolor{comment}{ !! a layer's temperature change to the change in column} 1165 \textcolor{comment}{ !! height, including all implicit diffusive changes} 1166 \textcolor{comment}{ !! in the temperatures of all the layers above [Z degC-1 ~> m degC-1].} 1167 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dS\_to\_dColHta\textcolor{comment}{ !< A factor (mass\_lay*dSColHtc\_vol/dS) relating} 1168 \textcolor{comment}{ !! a layer's salinity change to the change in column} 1169 \textcolor{comment}{ !! height, including all implicit diffusive changes} 1170 \textcolor{comment}{ !! in the salinities of all the layers above [Z ppt-1 ~> m ppt-1].} 1171 1172 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: PE\_chg\textcolor{comment}{ !< The change in column potential energy from applying} 1173 \textcolor{comment}{ !! Kddt\_h at the present interface [R Z L2 T-2 ~> J m-2].} 1174 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: dPEc\_dKd\textcolor{comment}{ !< The partial derivative of PE\_chg with Kddt\_h,} 1175 \textcolor{comment}{ !! [R Z L2 T-2 H-1 ~> J m-3 or J kg-1].} 1176 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: dPE\_max\textcolor{comment}{ !< The maximum change in column potential energy that could} 1177 \textcolor{comment}{ !! be realized by applying a huge value of Kddt\_h at the} 1178 \textcolor{comment}{ !! present interface [R Z L2 T-2 ~> J m-2].} 1179 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: dPEc\_dKd\_0\textcolor{comment}{ !< The partial derivative of PE\_chg with Kddt\_h in the} 1180 \textcolor{comment}{ !! limit where Kddt\_h = 0 [R Z L2 T-2 H-1 ~> J m-3 or J kg-1].} 1181 1182 \textcolor{comment}{! This subroutine determines the total potential energy change due to mixing} 1183 \textcolor{comment}{! at an interface, including all of the implicit effects of the prescribed} 1184 \textcolor{comment}{! mixing at interfaces above. Everything here is derived by careful manipulation} 1185 \textcolor{comment}{! of the robust tridiagonal solvers used for tracers by MOM6. The results are} 1186 \textcolor{comment}{! positive for mixing in a stably stratified environment.} 1187 \textcolor{comment}{! The comments describing these arguments are for a downward mixing pass, but} 1188 \textcolor{comment}{! this routine can also be used for an upward pass with the sense of direction} 1189 \textcolor{comment}{! reversed.} 1190 1191 \textcolor{keywordtype}{real} :: b1 \textcolor{comment}{! b1 is used by the tridiagonal solver [H-1 ~> m-1 or m2 kg-1].} 1192 \textcolor{keywordtype}{real} :: b1Kd \textcolor{comment}{! Temporary array [nondim]} 1193 \textcolor{keywordtype}{real} :: ColHt\_chg \textcolor{comment}{! The change in column thickness [Z ~> m].} 1194 \textcolor{keywordtype}{real} :: dColHt\_max \textcolor{comment}{! The change in column thickness for infinite diffusivity [Z ~> m].} 1195 \textcolor{keywordtype}{real} :: dColHt\_dKd \textcolor{comment}{! The partial derivative of column thickness with Kddt\_h [Z H-1 ~> 1 or m3 kg-1].} 1196 \textcolor{keywordtype}{real} :: dT\_k, dT\_km1 \textcolor{comment}{! Temporary arrays [degC].} 1197 \textcolor{keywordtype}{real} :: dS\_k, dS\_km1 \textcolor{comment}{! Temporary arrays [ppt].} 1198 \textcolor{keywordtype}{real} :: I\_Kr\_denom \textcolor{comment}{! Temporary arrays [H-2 ~> m-2 or m4 kg-2].} 1199 \textcolor{keywordtype}{real} :: dKr\_dKd \textcolor{comment}{! Nondimensional temporary array [nondim].} 1200 \textcolor{keywordtype}{real} :: ddT\_k\_dKd, ddT\_km1\_dKd \textcolor{comment}{! Temporary arrays [degC H-1 ~> m-1 or m2 kg-1].} 1201 \textcolor{keywordtype}{real} :: ddS\_k\_dKd, ddS\_km1\_dKd \textcolor{comment}{! Temporary arrays [ppt H-1 ~> ppt m-1 or ppt m2 kg-1].} 1202 1203 b1 = 1.0 / (b\_den\_1 + kddt\_h) 1204 b1kd = kddt\_h*b1 1205 1206 \textcolor{comment}{! Start with the temperature change in layer k-1 due to the diffusivity at} 1207 \textcolor{comment}{! interface K without considering the effects of changes in layer k.} 1208 1209 \textcolor{comment}{! Calculate the change in PE due to the diffusion at interface K} 1210 \textcolor{comment}{! if Kddt\_h(K+1) = 0.} 1211 i\_kr\_denom = 1.0 / (h\_k*b\_den\_1 + (b\_den\_1 + h\_k)*kddt\_h) 1212 1213 dt\_k = (kddt\_h*i\_kr\_denom) * dte\_term 1214 ds\_k = (kddt\_h*i\_kr\_denom) * dse\_term 1215 1216 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(pe\_chg)) \textcolor{keywordflow}{then} 1217 \textcolor{comment}{! Find the change in energy due to diffusion with strength Kddt\_h at this interface.} 1218 \textcolor{comment}{! Increment the temperature changes in layer k-1 due the changes in layer k.} 1219 dt\_km1 = b1kd * ( dt\_k + dt\_km1\_t2 ) 1220 ds\_km1 = b1kd * ( ds\_k + ds\_km1\_t2 ) 1221 1222 pe\_chg = (dt\_to\_dpe\_k * dt\_k + dt\_to\_dpea * dt\_km1) + & 1223 (ds\_to\_dpe\_k * ds\_k + ds\_to\_dpea * ds\_km1) 1224 colht\_chg = (dt\_to\_dcolht\_k * dt\_k + dt\_to\_dcolhta * dt\_km1) + & 1225 (ds\_to\_dcolht\_k * ds\_k + ds\_to\_dcolhta * ds\_km1) 1226 \textcolor{keywordflow}{if} (colht\_chg < 0.0) pe\_chg = pe\_chg - pres\_z * colht\_chg 1227 \textcolor{keywordflow}{ endif} 1228 1229 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(dpec\_dkd)) \textcolor{keywordflow}{then} 1230 \textcolor{comment}{! Find the derivatives of the temperature and salinity changes with Kddt\_h.} 1231 dkr\_dkd = (h\_k*b\_den\_1) * i\_kr\_denom**2 1232 1233 ddt\_k\_dkd = dkr\_dkd * dte\_term 1234 dds\_k\_dkd = dkr\_dkd * dse\_term 1235 ddt\_km1\_dkd = (b1**2 * b\_den\_1) * ( dt\_k + dt\_km1\_t2 ) + b1kd * ddt\_k\_dkd 1236 dds\_km1\_dkd = (b1**2 * b\_den\_1) * ( ds\_k + ds\_km1\_t2 ) + b1kd * dds\_k\_dkd 1237 1238 \textcolor{comment}{! Calculate the partial derivative of Pe\_chg with Kddt\_h.} 1239 dpec\_dkd = (dt\_to\_dpe\_k * ddt\_k\_dkd + dt\_to\_dpea * ddt\_km1\_dkd) + & 1240 (ds\_to\_dpe\_k * dds\_k\_dkd + ds\_to\_dpea * dds\_km1\_dkd) 1241 dcolht\_dkd = (dt\_to\_dcolht\_k * ddt\_k\_dkd + dt\_to\_dcolhta * ddt\_km1\_dkd) + & 1242 (ds\_to\_dcolht\_k * dds\_k\_dkd + ds\_to\_dcolhta * dds\_km1\_dkd) 1243 \textcolor{keywordflow}{if} (dcolht\_dkd < 0.0) dpec\_dkd = dpec\_dkd - pres\_z * dcolht\_dkd 1244 \textcolor{keywordflow}{ endif} 1245 1246 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(dpe\_max)) \textcolor{keywordflow}{then} 1247 \textcolor{comment}{! This expression is the limit of PE\_chg for infinite Kddt\_h.} 1248 dpe\_max = (dt\_to\_dpea * dt\_km1\_t2 + ds\_to\_dpea * ds\_km1\_t2) + & 1249 ((dt\_to\_dpe\_k + dt\_to\_dpea) * dte\_term + & 1250 (ds\_to\_dpe\_k + ds\_to\_dpea) * dse\_term) / (b\_den\_1 + h\_k) 1251 dcolht\_max = (dt\_to\_dcolhta * dt\_km1\_t2 + ds\_to\_dcolhta * ds\_km1\_t2) + & 1252 ((dt\_to\_dcolht\_k + dt\_to\_dcolhta) * dte\_term + & 1253 (ds\_to\_dcolht\_k + ds\_to\_dcolhta) * dse\_term) / (b\_den\_1 + h\_k) 1254 \textcolor{keywordflow}{if} (dcolht\_max < 0.0) dpe\_max = dpe\_max - pres\_z*dcolht\_max 1255 \textcolor{keywordflow}{ endif} 1256 1257 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(dpec\_dkd\_0)) \textcolor{keywordflow}{then} 1258 \textcolor{comment}{! This expression is the limit of dPEc\_dKd for Kddt\_h = 0.} 1259 dpec\_dkd\_0 = (dt\_to\_dpea * dt\_km1\_t2 + ds\_to\_dpea * ds\_km1\_t2) / (b\_den\_1) + & 1260 (dt\_to\_dpe\_k * dte\_term + ds\_to\_dpe\_k * dse\_term) / (h\_k*b\_den\_1) 1261 dcolht\_dkd = (dt\_to\_dcolhta * dt\_km1\_t2 + ds\_to\_dcolhta * ds\_km1\_t2) / (b\_den\_1) + & 1262 (dt\_to\_dcolht\_k * dte\_term + ds\_to\_dcolht\_k * dse\_term) / (h\_k*b\_den\_1) 1263 \textcolor{keywordflow}{if} (dcolht\_dkd < 0.0) dpec\_dkd\_0 = dpec\_dkd\_0 - pres\_z*dcolht\_dkd 1264 \textcolor{keywordflow}{ endif} 1265 \end{DoxyCode}