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