\hypertarget{namespacemom__density__integrals}{}\doxysection{mom\+\_\+density\+\_\+integrals Module Reference} \label{namespacemom__density__integrals}\index{mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsection{Detailed Description} Provides integrals of density. \doxysubsection*{Functions/\+Subroutines} \begin{DoxyCompactItemize} \item subroutine, public \mbox{\hyperlink{namespacemom__density__integrals_ac36ae5f4af2d02df0a1adf41b762e017}{int\+\_\+density\+\_\+dz}} (T, S, z\+\_\+t, z\+\_\+b, rho\+\_\+ref, rho\+\_\+0, G\+\_\+e, HI, E\+OS, US, dpa, intz\+\_\+dpa, intx\+\_\+dpa, inty\+\_\+dpa, bathyT, dz\+\_\+neglect, use\+Mass\+Wght\+Interp) \begin{DoxyCompactList}\small\item\em Calls the appropriate subroutine to calculate analytical and nearly-\/analytical integrals in z across layers of pressure anomalies, which are required for calculating the finite-\/volume form pressure accelerations in a Boussinesq model. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__density__integrals_ad0ff54518bfacf7beebbe4dba687a914}{int\+\_\+density\+\_\+dz\+\_\+generic\+\_\+pcm}} (T, S, z\+\_\+t, z\+\_\+b, rho\+\_\+ref, rho\+\_\+0, G\+\_\+e, HI, E\+OS, US, dpa, intz\+\_\+dpa, intx\+\_\+dpa, inty\+\_\+dpa, bathyT, dz\+\_\+neglect, use\+Mass\+Wght\+Interp) \begin{DoxyCompactList}\small\item\em Calculates (by numerical quadrature) integrals of pressure anomalies across layers, which are required for calculating the finite-\/volume form pressure accelerations in a Boussinesq model. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__density__integrals_a454d4d62eb599716cc3389fb8aa90b4b}{int\+\_\+density\+\_\+dz\+\_\+generic\+\_\+plm}} (k, tv, T\+\_\+t, T\+\_\+b, S\+\_\+t, S\+\_\+b, e, rho\+\_\+ref, rho\+\_\+0, G\+\_\+e, dz\+\_\+subroundoff, bathyT, HI, GV, E\+OS, US, dpa, intz\+\_\+dpa, intx\+\_\+dpa, inty\+\_\+dpa, use\+Mass\+Wght\+Interp) \begin{DoxyCompactList}\small\item\em Compute pressure gradient force integrals by quadrature for the case where T and S are linear profiles. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__density__integrals_a3bf090e5cbb58811b3dd0ee4de80f999}{int\+\_\+density\+\_\+dz\+\_\+generic\+\_\+ppm}} (k, tv, T\+\_\+t, T\+\_\+b, S\+\_\+t, S\+\_\+b, e, rho\+\_\+ref, rho\+\_\+0, G\+\_\+e, dz\+\_\+subroundoff, bathyT, HI, GV, E\+OS, US, dpa, intz\+\_\+dpa, intx\+\_\+dpa, inty\+\_\+dpa, use\+Mass\+Wght\+Interp) \begin{DoxyCompactList}\small\item\em Compute pressure gradient force integrals for layer \char`\"{}k\char`\"{} and the case where T and S are parabolic profiles. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__density__integrals_a759c2ae7aec17c59d532050f68a1e518}{int\+\_\+specific\+\_\+vol\+\_\+dp}} (T, S, p\+\_\+t, p\+\_\+b, alpha\+\_\+ref, HI, E\+OS, US, dza, intp\+\_\+dza, intx\+\_\+dza, inty\+\_\+dza, halo\+\_\+size, bathyP, d\+P\+\_\+tiny, use\+Mass\+Wght\+Interp) \begin{DoxyCompactList}\small\item\em Calls the appropriate subroutine to calculate analytical and nearly-\/analytical integrals in pressure across layers of geopotential anomalies, which are required for calculating the finite-\/volume form pressure accelerations in a non-\/\+Boussinesq model. There are essentially no free assumptions, apart from the use of Boole\textquotesingle{}s rule to do the horizontal integrals, and from a truncation in the series for log(1-\/eps/1+eps) that assumes that $\vert$eps$\vert$ $<$ 0.\+34. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__density__integrals_a86ebdfebaaea2ac0339dcabed482dd11}{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+generic\+\_\+pcm}} (T, S, p\+\_\+t, p\+\_\+b, alpha\+\_\+ref, HI, E\+OS, US, dza, intp\+\_\+dza, intx\+\_\+dza, inty\+\_\+dza, halo\+\_\+size, bathyP, d\+P\+\_\+neglect, use\+Mass\+Wght\+Interp) \begin{DoxyCompactList}\small\item\em This subroutine calculates integrals of specific volume anomalies in pressure across layers, which are required for calculating the finite-\/volume form pressure accelerations in a non-\/\+Boussinesq model. There are essentially no free assumptions, apart from the use of Boole\textquotesingle{}s rule quadrature to do the integrals. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__density__integrals_a71a518f80b5f2ecf83fd9c638cad140d}{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+generic\+\_\+plm}} (T\+\_\+t, T\+\_\+b, S\+\_\+t, S\+\_\+b, p\+\_\+t, p\+\_\+b, alpha\+\_\+ref, d\+P\+\_\+neglect, bathyP, HI, E\+OS, US, dza, intp\+\_\+dza, intx\+\_\+dza, inty\+\_\+dza, use\+Mass\+Wght\+Interp) \begin{DoxyCompactList}\small\item\em This subroutine calculates integrals of specific volume anomalies in pressure across layers, which are required for calculating the finite-\/volume form pressure accelerations in a non-\/\+Boussinesq model. There are essentially no free assumptions, apart from the use of Boole\textquotesingle{}s rule quadrature to do the integrals. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__density__integrals_af9946b0e15d53d8f1fd1ab1c1f81f3a2}{find\+\_\+depth\+\_\+of\+\_\+pressure\+\_\+in\+\_\+cell}} (T\+\_\+t, T\+\_\+b, S\+\_\+t, S\+\_\+b, z\+\_\+t, z\+\_\+b, P\+\_\+t, P\+\_\+tgt, rho\+\_\+ref, G\+\_\+e, E\+OS, US, P\+\_\+b, z\+\_\+out, z\+\_\+tol) \begin{DoxyCompactList}\small\item\em Find the depth at which the reconstructed pressure matches P\+\_\+tgt. \end{DoxyCompactList}\item real function \mbox{\hyperlink{namespacemom__density__integrals_abb8d1f2c24def176a27ef2d30fa373df}{frac\+\_\+dp\+\_\+at\+\_\+pos}} (T\+\_\+t, T\+\_\+b, S\+\_\+t, S\+\_\+b, z\+\_\+t, z\+\_\+b, rho\+\_\+ref, G\+\_\+e, pos, E\+OS) \begin{DoxyCompactList}\small\item\em Returns change in anomalous pressure change from top to non-\/dimensional position pos between z\+\_\+t and z\+\_\+b. \end{DoxyCompactList}\end{DoxyCompactItemize} \doxysubsection{Function/\+Subroutine Documentation} \mbox{\Hypertarget{namespacemom__density__integrals_af9946b0e15d53d8f1fd1ab1c1f81f3a2}\label{namespacemom__density__integrals_af9946b0e15d53d8f1fd1ab1c1f81f3a2}} \index{mom\_density\_integrals@{mom\_density\_integrals}!find\_depth\_of\_pressure\_in\_cell@{find\_depth\_of\_pressure\_in\_cell}} \index{find\_depth\_of\_pressure\_in\_cell@{find\_depth\_of\_pressure\_in\_cell}!mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsubsection{\texorpdfstring{find\_depth\_of\_pressure\_in\_cell()}{find\_depth\_of\_pressure\_in\_cell()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+density\+\_\+integrals\+::find\+\_\+depth\+\_\+of\+\_\+pressure\+\_\+in\+\_\+cell (\begin{DoxyParamCaption}\item[{real, intent(in)}]{T\+\_\+t, }\item[{real, intent(in)}]{T\+\_\+b, }\item[{real, intent(in)}]{S\+\_\+t, }\item[{real, intent(in)}]{S\+\_\+b, }\item[{real, intent(in)}]{z\+\_\+t, }\item[{real, intent(in)}]{z\+\_\+b, }\item[{real, intent(in)}]{P\+\_\+t, }\item[{real, intent(in)}]{P\+\_\+tgt, }\item[{real, intent(in)}]{rho\+\_\+ref, }\item[{real, intent(in)}]{G\+\_\+e, }\item[{type(eos\+\_\+type), pointer}]{E\+OS, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, intent(out)}]{P\+\_\+b, }\item[{real, intent(out)}]{z\+\_\+out, }\item[{real, intent(in), optional}]{z\+\_\+tol }\end{DoxyParamCaption})} Find the depth at which the reconstructed pressure matches P\+\_\+tgt. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em t\+\_\+t} & Potential temperature at the cell top \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em t\+\_\+b} & Potential temperature at the cell bottom \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+t} & Salinity at the cell top \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+b} & Salinity at the cell bottom \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em z\+\_\+t} & Absolute height of top of cell \mbox{[}Z $\sim$$>$ m\mbox{]} (Boussinesq ????) \\ \hline \mbox{\texttt{ in}} & {\em z\+\_\+b} & Absolute height of bottom of cell \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em p\+\_\+t} & Anomalous pressure of top of cell, relative to g$\ast$rho\+\_\+ref$\ast$z\+\_\+t \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em p\+\_\+tgt} & Target pressure at height z\+\_\+out, relative to g$\ast$rho\+\_\+ref$\ast$z\+\_\+out \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+ref} & Reference density with which calculation are anomalous to \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em g\+\_\+e} & Gravitational acceleration \mbox{[}L2 Z-\/1 T-\/2 $\sim$$>$ m s-\/2\mbox{]} \\ \hline & {\em eos} & Equation of state structure \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ out}} & {\em p\+\_\+b} & Pressure at the bottom of the cell \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} \\ \hline \mbox{\texttt{ out}} & {\em z\+\_\+out} & Absolute depth at which anomalous pressure = p\+\_\+tgt \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em z\+\_\+tol} & The tolerance in finding z\+\_\+out \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \end{DoxyParams} Definition at line 1527 of file M\+O\+M\+\_\+density\+\_\+integrals.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1527 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: T\_t\textcolor{comment}{ !< Potential temperature at the cell top [degC]}} \DoxyCodeLine{1528 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: T\_b\textcolor{comment}{ !< Potential temperature at the cell bottom [degC]}} \DoxyCodeLine{1529 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: S\_t\textcolor{comment}{ !< Salinity at the cell top [ppt]}} \DoxyCodeLine{1530 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: S\_b\textcolor{comment}{ !< Salinity at the cell bottom [ppt]}} \DoxyCodeLine{1531 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: z\_t\textcolor{comment}{ !< Absolute height of top of cell [Z ~> m] (Boussinesq ????)}} \DoxyCodeLine{1532 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: z\_b\textcolor{comment}{ !< Absolute height of bottom of cell [Z ~> m]}} \DoxyCodeLine{1533 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: P\_t\textcolor{comment}{ !< Anomalous pressure of top of cell, relative}} \DoxyCodeLine{1534 \textcolor{comment}{ !! to g*rho\_ref*z\_t [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1535 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: P\_tgt\textcolor{comment}{ !< Target pressure at height z\_out, relative}} \DoxyCodeLine{1536 \textcolor{comment}{ !! to g*rho\_ref*z\_out [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1537 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< Reference density with which calculation}} \DoxyCodeLine{1538 \textcolor{comment}{ !! are anomalous to [R ~> kg m-\/3]}} \DoxyCodeLine{1539 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: G\_e\textcolor{comment}{ !< Gravitational acceleration [L2 Z-\/1 T-\/2 ~> m s-\/2]}} \DoxyCodeLine{1540 \textcolor{keywordtype}{type}(EOS\_type), \textcolor{keywordtype}{pointer} :: EOS\textcolor{comment}{ !< Equation of state structure}} \DoxyCodeLine{1541 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{1542 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(out)} :: P\_b\textcolor{comment}{ !< Pressure at the bottom of the cell [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1543 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(out)} :: z\_out\textcolor{comment}{ !< Absolute depth at which anomalous pressure = p\_tgt [Z ~> m]}} \DoxyCodeLine{1544 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: z\_tol\textcolor{comment}{ !< The tolerance in finding z\_out [Z ~> m]}} \DoxyCodeLine{1545 } \DoxyCodeLine{1546 \textcolor{comment}{! Local variables}} \DoxyCodeLine{1547 \textcolor{keywordtype}{ real} :: dp \textcolor{comment}{! Pressure thickness of the layer [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1548 \textcolor{keywordtype}{ real} :: F\_guess, F\_l, F\_r \textcolor{comment}{! Fractional positions [nondim]}} \DoxyCodeLine{1549 \textcolor{keywordtype}{ real} :: GxRho \textcolor{comment}{! The product of the gravitational acceleration and reference density [R L2 Z-\/1 T-\/2 ~> Pa m-\/1]}} \DoxyCodeLine{1550 \textcolor{keywordtype}{ real} :: Pa, Pa\_left, Pa\_right, Pa\_tol \textcolor{comment}{! Pressure anomalies, P = integral of g*(rho-\/rho\_ref) dz [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1551 \textcolor{keywordtype}{character(len=240)} :: msg} \DoxyCodeLine{1552 } \DoxyCodeLine{1553 gxrho = g\_e * rho\_ref} \DoxyCodeLine{1554 } \DoxyCodeLine{1555 \textcolor{comment}{! Anomalous pressure difference across whole cell}} \DoxyCodeLine{1556 dp = frac\_dp\_at\_pos(t\_t, t\_b, s\_t, s\_b, z\_t, z\_b, rho\_ref, g\_e, 1.0, eos)} \DoxyCodeLine{1557 } \DoxyCodeLine{1558 p\_b = p\_t + dp \textcolor{comment}{! Anomalous pressure at bottom of cell}} \DoxyCodeLine{1559 } \DoxyCodeLine{1560 \textcolor{keywordflow}{if} (p\_tgt <= p\_t ) \textcolor{keywordflow}{then}} \DoxyCodeLine{1561 z\_out = z\_t} \DoxyCodeLine{1562 \textcolor{keywordflow}{return}} \DoxyCodeLine{1563 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1564 } \DoxyCodeLine{1565 \textcolor{keywordflow}{if} (p\_tgt >= p\_b) \textcolor{keywordflow}{then}} \DoxyCodeLine{1566 z\_out = z\_b} \DoxyCodeLine{1567 \textcolor{keywordflow}{return}} \DoxyCodeLine{1568 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1569 } \DoxyCodeLine{1570 f\_l = 0.} \DoxyCodeLine{1571 pa\_left = p\_t -\/ p\_tgt \textcolor{comment}{! Pa\_left < 0}} \DoxyCodeLine{1572 f\_r = 1.} \DoxyCodeLine{1573 pa\_right = p\_b -\/ p\_tgt \textcolor{comment}{! Pa\_right > 0}} \DoxyCodeLine{1574 pa\_tol = gxrho * 1.0e-\/5*us\%m\_to\_Z} \DoxyCodeLine{1575 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(z\_tol)) pa\_tol = gxrho * z\_tol} \DoxyCodeLine{1576 } \DoxyCodeLine{1577 f\_guess = f\_l -\/ pa\_left / (pa\_right -\/ pa\_left) * (f\_r -\/ f\_l)} \DoxyCodeLine{1578 pa = pa\_right -\/ pa\_left \textcolor{comment}{! To get into iterative loop}} \DoxyCodeLine{1579 \textcolor{keywordflow}{do} \textcolor{keywordflow}{while} ( abs(pa) > pa\_tol )} \DoxyCodeLine{1580 } \DoxyCodeLine{1581 z\_out = z\_t + ( z\_b -\/ z\_t ) * f\_guess} \DoxyCodeLine{1582 pa = frac\_dp\_at\_pos(t\_t, t\_b, s\_t, s\_b, z\_t, z\_b, rho\_ref, g\_e, f\_guess, eos) -\/ ( p\_tgt -\/ p\_t )} \DoxyCodeLine{1583 } \DoxyCodeLine{1584 \textcolor{keywordflow}{if} (papa\_right) \textcolor{keywordflow}{then}} \DoxyCodeLine{1591 \textcolor{keyword}{write}(msg,*) pa\_left,pa,pa\_right,p\_t-\/p\_tgt,p\_b-\/p\_tgt} \DoxyCodeLine{1592 \textcolor{keyword}{call }mom\_error(fatal, \textcolor{stringliteral}{'find\_depth\_of\_pressure\_in\_cell out of bounds positive: /n'}//msg)} \DoxyCodeLine{1593 \textcolor{keywordflow}{elseif} (pa>0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{1594 pa\_right = pa} \DoxyCodeLine{1595 f\_r = f\_guess} \DoxyCodeLine{1596 \textcolor{keywordflow}{else} \textcolor{comment}{! Pa == 0}} \DoxyCodeLine{1597 \textcolor{keywordflow}{return}} \DoxyCodeLine{1598 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1599 f\_guess = f\_l -\/ pa\_left / (pa\_right -\/ pa\_left) * (f\_r -\/ f\_l)} \DoxyCodeLine{1600 } \DoxyCodeLine{1601 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1602 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__density__integrals_abb8d1f2c24def176a27ef2d30fa373df}\label{namespacemom__density__integrals_abb8d1f2c24def176a27ef2d30fa373df}} \index{mom\_density\_integrals@{mom\_density\_integrals}!frac\_dp\_at\_pos@{frac\_dp\_at\_pos}} \index{frac\_dp\_at\_pos@{frac\_dp\_at\_pos}!mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsubsection{\texorpdfstring{frac\_dp\_at\_pos()}{frac\_dp\_at\_pos()}} {\footnotesize\ttfamily real function mom\+\_\+density\+\_\+integrals\+::frac\+\_\+dp\+\_\+at\+\_\+pos (\begin{DoxyParamCaption}\item[{real, intent(in)}]{T\+\_\+t, }\item[{real, intent(in)}]{T\+\_\+b, }\item[{real, intent(in)}]{S\+\_\+t, }\item[{real, intent(in)}]{S\+\_\+b, }\item[{real, intent(in)}]{z\+\_\+t, }\item[{real, intent(in)}]{z\+\_\+b, }\item[{real, intent(in)}]{rho\+\_\+ref, }\item[{real, intent(in)}]{G\+\_\+e, }\item[{real, intent(in)}]{pos, }\item[{type(eos\+\_\+type), pointer}]{E\+OS }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Returns change in anomalous pressure change from top to non-\/dimensional position pos between z\+\_\+t and z\+\_\+b. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em t\+\_\+t} & Potential temperature at the cell top \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em t\+\_\+b} & Potential temperature at the cell bottom \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+t} & Salinity at the cell top \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+b} & Salinity at the cell bottom \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em z\+\_\+t} & The geometric height at the top of the layer \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em z\+\_\+b} & The geometric height at the bottom of the layer \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+ref} & A mean density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]}, that is subtracted out to reduce the magnitude of each of the integrals. \\ \hline \mbox{\texttt{ in}} & {\em g\+\_\+e} & The Earth\textquotesingle{}s gravitational acceleration \mbox{[}L2 Z-\/1 T-\/2 $\sim$$>$ m s-\/2\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em pos} & The fractional vertical position, 0 to 1 \mbox{[}nondim\mbox{]} \\ \hline & {\em eos} & Equation of state structure \\ \hline \end{DoxyParams} Definition at line 1609 of file M\+O\+M\+\_\+density\+\_\+integrals.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1609 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: T\_t\textcolor{comment}{ !< Potential temperature at the cell top [degC]}} \DoxyCodeLine{1610 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: T\_b\textcolor{comment}{ !< Potential temperature at the cell bottom [degC]}} \DoxyCodeLine{1611 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: S\_t\textcolor{comment}{ !< Salinity at the cell top [ppt]}} \DoxyCodeLine{1612 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: S\_b\textcolor{comment}{ !< Salinity at the cell bottom [ppt]}} \DoxyCodeLine{1613 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: z\_t\textcolor{comment}{ !< The geometric height at the top of the layer [Z ~> m]}} \DoxyCodeLine{1614 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: z\_b\textcolor{comment}{ !< The geometric height at the bottom of the layer [Z ~> m]}} \DoxyCodeLine{1615 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A mean density [R ~> kg m-\/3], that is subtracted out to}} \DoxyCodeLine{1616 \textcolor{comment}{ !! reduce the magnitude of each of the integrals.}} \DoxyCodeLine{1617 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: G\_e\textcolor{comment}{ !< The Earth's gravitational acceleration [L2 Z-\/1 T-\/2 ~> m s-\/2]}} \DoxyCodeLine{1618 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: pos\textcolor{comment}{ !< The fractional vertical position, 0 to 1 [nondim]}} \DoxyCodeLine{1619 \textcolor{keywordtype}{type}(EOS\_type), \textcolor{keywordtype}{pointer} :: EOS\textcolor{comment}{ !< Equation of state structure}} \DoxyCodeLine{1620 \textcolor{keywordtype}{ real} :: fract\_dp\_at\_pos\textcolor{comment}{ !< The change in pressure from the layer top to}} \DoxyCodeLine{1621 \textcolor{comment}{ !! fractional position pos [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1622 \textcolor{comment}{! Local variables}} \DoxyCodeLine{1623 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{parameter} :: C1\_90 = 1.0/90.0 \textcolor{comment}{! A rational constant [nondim]}} \DoxyCodeLine{1624 \textcolor{keywordtype}{ real} :: dz \textcolor{comment}{! Distance from the layer top [Z ~> m]}} \DoxyCodeLine{1625 \textcolor{keywordtype}{ real} :: top\_weight, bottom\_weight \textcolor{comment}{! Fractional weights at quadrature points [nondim]}} \DoxyCodeLine{1626 \textcolor{keywordtype}{ real} :: rho\_ave \textcolor{comment}{! Average density [R ~> kg m-\/3]}} \DoxyCodeLine{1627 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(5)} :: T5 \textcolor{comment}{! Temperatures at quadrature points [degC]}} \DoxyCodeLine{1628 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(5)} :: S5 \textcolor{comment}{! Salinities at quadrature points [ppt]}} \DoxyCodeLine{1629 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(5)} :: p5 \textcolor{comment}{! Pressures at quadrature points [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1630 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(5)} :: rho5 \textcolor{comment}{! Densities at quadrature points [R ~> kg m-\/3]}} \DoxyCodeLine{1631 \textcolor{keywordtype}{integer} :: n} \DoxyCodeLine{1632 } \DoxyCodeLine{1633 \textcolor{keywordflow}{do} n=1,5} \DoxyCodeLine{1634 \textcolor{comment}{! Evaluate density at five quadrature points}} \DoxyCodeLine{1635 bottom\_weight = 0.25*real(n-\/1) * pos} \DoxyCodeLine{1636 top\_weight = 1.0 -\/ bottom\_weight} \DoxyCodeLine{1637 \textcolor{comment}{! Salinity and temperature points are linearly interpolated}} \DoxyCodeLine{1638 s5(n) = top\_weight * s\_t + bottom\_weight * s\_b} \DoxyCodeLine{1639 t5(n) = top\_weight * t\_t + bottom\_weight * t\_b} \DoxyCodeLine{1640 p5(n) = ( top\_weight * z\_t + bottom\_weight * z\_b ) * ( g\_e * rho\_ref )} \DoxyCodeLine{1641 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1642 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, rho5, eos)} \DoxyCodeLine{1643 rho5(:) = rho5(:) \textcolor{comment}{!-\/ rho\_ref ! Work with anomalies relative to rho\_ref}} \DoxyCodeLine{1644 } \DoxyCodeLine{1645 \textcolor{comment}{! Use Boole's rule to estimate the average density}} \DoxyCodeLine{1646 rho\_ave = c1\_90*(7.0*(rho5(1)+rho5(5)) + 32.0*(rho5(2)+rho5(4)) + 12.0*rho5(3))} \DoxyCodeLine{1647 } \DoxyCodeLine{1648 dz = ( z\_t -\/ z\_b ) * pos} \DoxyCodeLine{1649 frac\_dp\_at\_pos = g\_e * dz * rho\_ave} \end{DoxyCode} \mbox{\Hypertarget{namespacemom__density__integrals_ac36ae5f4af2d02df0a1adf41b762e017}\label{namespacemom__density__integrals_ac36ae5f4af2d02df0a1adf41b762e017}} \index{mom\_density\_integrals@{mom\_density\_integrals}!int\_density\_dz@{int\_density\_dz}} \index{int\_density\_dz@{int\_density\_dz}!mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsubsection{\texorpdfstring{int\_density\_dz()}{int\_density\_dz()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+density\+\_\+integrals\+::int\+\_\+density\+\_\+dz (\begin{DoxyParamCaption}\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{T, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{S, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{z\+\_\+t, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{z\+\_\+b, }\item[{real, intent(in)}]{rho\+\_\+ref, }\item[{real, intent(in)}]{rho\+\_\+0, }\item[{real, intent(in)}]{G\+\_\+e, }\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\item[{type(eos\+\_\+type), pointer}]{E\+OS, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(inout)}]{dpa, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(inout), optional}]{intz\+\_\+dpa, }\item[{real, dimension(szib\+\_\+(hi),szj\+\_\+(hi)), intent(inout), optional}]{intx\+\_\+dpa, }\item[{real, dimension(szi\+\_\+(hi),szjb\+\_\+(hi)), intent(inout), optional}]{inty\+\_\+dpa, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in), optional}]{bathyT, }\item[{real, intent(in), optional}]{dz\+\_\+neglect, }\item[{logical, intent(in), optional}]{use\+Mass\+Wght\+Interp }\end{DoxyParamCaption})} Calls the appropriate subroutine to calculate analytical and nearly-\/analytical integrals in z across layers of pressure anomalies, which are required for calculating the finite-\/volume form pressure accelerations in a Boussinesq model. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em hi} & Ocean horizontal index structures for the arrays \\ \hline \mbox{\texttt{ in}} & {\em t} & Potential temperature referenced to the surface \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s} & Salinity \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em z\+\_\+t} & Height at the top of the layer in depth units \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em z\+\_\+b} & Height at the bottom of the layer \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+ref} & A mean density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is subtracted out to reduce the magnitude of each of the integrals. \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+0} & A density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is used to calculate the pressure (as p$\sim$=-\/z$\ast$rho\+\_\+0$\ast$\+G\+\_\+e) used in the equation of state. \\ \hline \mbox{\texttt{ in}} & {\em g\+\_\+e} & The Earth\textquotesingle{}s gravitational acceleration \mbox{[}L2 Z-\/1 T-\/2 $\sim$$>$ m s-\/2\mbox{]} or \mbox{[}m2 Z-\/1 s-\/2 $\sim$$>$ m s-\/2\mbox{]} \\ \hline & {\em eos} & Equation of state structure \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ in,out}} & {\em dpa} & The change in the pressure anomaly \\ \hline \mbox{\texttt{ in,out}} & {\em intz\+\_\+dpa} & The integral through the thickness of the \\ \hline \mbox{\texttt{ in,out}} & {\em intx\+\_\+dpa} & The integral in x of the difference between \\ \hline \mbox{\texttt{ in,out}} & {\em inty\+\_\+dpa} & The integral in y of the difference between \\ \hline \mbox{\texttt{ in}} & {\em bathyt} & The depth of the bathymetry \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em dz\+\_\+neglect} & A minuscule thickness change \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals. \\ \hline \end{DoxyParams} Definition at line 42 of file M\+O\+M\+\_\+density\+\_\+integrals.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{42 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: HI\textcolor{comment}{ !< Ocean horizontal index structures for the arrays}} \DoxyCodeLine{43 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{44 \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature referenced to the surface [degC]}} \DoxyCodeLine{45 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{46 \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [ppt]}} \DoxyCodeLine{47 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{48 \textcolor{keywordtype}{intent(in)} :: z\_t\textcolor{comment}{ !< Height at the top of the layer in depth units [Z ~> m]}} \DoxyCodeLine{49 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{50 \textcolor{keywordtype}{intent(in)} :: z\_b\textcolor{comment}{ !< Height at the bottom of the layer [Z ~> m]}} \DoxyCodeLine{51 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A mean density [R ~> kg m-\/3] or [kg m-\/3], that is}} \DoxyCodeLine{52 \textcolor{comment}{ !! subtracted out to reduce the magnitude of each of the}} \DoxyCodeLine{53 \textcolor{comment}{ !! integrals.}} \DoxyCodeLine{54 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_0\textcolor{comment}{ !< A density [R ~> kg m-\/3] or [kg m-\/3], that is used}} \DoxyCodeLine{55 \textcolor{comment}{ !! to calculate the pressure (as p~=-\/z*rho\_0*G\_e)}} \DoxyCodeLine{56 \textcolor{comment}{ !! used in the equation of state.}} \DoxyCodeLine{57 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: G\_e\textcolor{comment}{ !< The Earth's gravitational acceleration}} \DoxyCodeLine{58 \textcolor{comment}{ !! [L2 Z-\/1 T-\/2 ~> m s-\/2] or [m2 Z-\/1 s-\/2 ~> m s-\/2]}} \DoxyCodeLine{59 \textcolor{keywordtype}{type}(EOS\_type), \textcolor{keywordtype}{pointer} :: EOS\textcolor{comment}{ !< Equation of state structure}} \DoxyCodeLine{60 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{61 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{62 \textcolor{keywordtype}{intent(inout)} :: dpa\textcolor{comment}{ !< The change in the pressure anomaly}} \DoxyCodeLine{63 \textcolor{comment}{ !! across the layer [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{64 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{65 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intz\_dpa\textcolor{comment}{ !< The integral through the thickness of the}} \DoxyCodeLine{66 \textcolor{comment}{ !! layer of the pressure anomaly relative to the}} \DoxyCodeLine{67 \textcolor{comment}{ !! anomaly at the top of the layer [R L2 Z T-\/2 ~> Pa m]}} \DoxyCodeLine{68 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZIB\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{69 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intx\_dpa\textcolor{comment}{ !< The integral in x of the difference between}} \DoxyCodeLine{70 \textcolor{comment}{ !! the pressure anomaly at the top and bottom of the}} \DoxyCodeLine{71 \textcolor{comment}{ !! layer divided by the x grid spacing [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{72 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJB\_(HI))}, \&} \DoxyCodeLine{73 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: inty\_dpa\textcolor{comment}{ !< The integral in y of the difference between}} \DoxyCodeLine{74 \textcolor{comment}{ !! the pressure anomaly at the top and bottom of the}} \DoxyCodeLine{75 \textcolor{comment}{ !! layer divided by the y grid spacing [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{76 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{77 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: bathyT\textcolor{comment}{ !< The depth of the bathymetry [Z ~> m]}} \DoxyCodeLine{78 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: dz\_neglect\textcolor{comment}{ !< A minuscule thickness change [Z ~> m]}} \DoxyCodeLine{79 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: useMassWghtInterp\textcolor{comment}{ !< If true, uses mass weighting to}} \DoxyCodeLine{80 \textcolor{comment}{ !! interpolate T/S for top and bottom integrals.}} \DoxyCodeLine{81 } \DoxyCodeLine{82 \textcolor{keywordflow}{if} (eos\_quadrature(eos)) \textcolor{keywordflow}{then}} \DoxyCodeLine{83 \textcolor{keyword}{call }int\_density\_dz\_generic\_pcm(t, s, z\_t, z\_b, rho\_ref, rho\_0, g\_e, hi, eos, us, dpa, \&} \DoxyCodeLine{84 intz\_dpa, intx\_dpa, inty\_dpa, bathyt, dz\_neglect, usemasswghtinterp)} \DoxyCodeLine{85 \textcolor{keywordflow}{else}} \DoxyCodeLine{86 \textcolor{keyword}{call }analytic\_int\_density\_dz(t, s, z\_t, z\_b, rho\_ref, rho\_0, g\_e, hi, eos, dpa, \&} \DoxyCodeLine{87 intz\_dpa, intx\_dpa, inty\_dpa, bathyt, dz\_neglect, usemasswghtinterp)} \DoxyCodeLine{88 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{89 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__density__integrals_ad0ff54518bfacf7beebbe4dba687a914}\label{namespacemom__density__integrals_ad0ff54518bfacf7beebbe4dba687a914}} \index{mom\_density\_integrals@{mom\_density\_integrals}!int\_density\_dz\_generic\_pcm@{int\_density\_dz\_generic\_pcm}} \index{int\_density\_dz\_generic\_pcm@{int\_density\_dz\_generic\_pcm}!mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsubsection{\texorpdfstring{int\_density\_dz\_generic\_pcm()}{int\_density\_dz\_generic\_pcm()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+density\+\_\+integrals\+::int\+\_\+density\+\_\+dz\+\_\+generic\+\_\+pcm (\begin{DoxyParamCaption}\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in)}]{T, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in)}]{S, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in)}]{z\+\_\+t, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in)}]{z\+\_\+b, }\item[{real, intent(in)}]{rho\+\_\+ref, }\item[{real, intent(in)}]{rho\+\_\+0, }\item[{real, intent(in)}]{G\+\_\+e, }\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\item[{type(eos\+\_\+type), pointer}]{E\+OS, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(inout)}]{dpa, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(inout), optional}]{intz\+\_\+dpa, }\item[{real, dimension( hi \%isdb\+: hi \%iedb, hi \%jsd\+: hi \%jed), intent(inout), optional}]{intx\+\_\+dpa, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsdb\+: hi \%jedb), intent(inout), optional}]{inty\+\_\+dpa, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in), optional}]{bathyT, }\item[{real, intent(in), optional}]{dz\+\_\+neglect, }\item[{logical, intent(in), optional}]{use\+Mass\+Wght\+Interp }\end{DoxyParamCaption})} Calculates (by numerical quadrature) integrals of pressure anomalies across layers, which are required for calculating the finite-\/volume form pressure accelerations in a Boussinesq model. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em hi} & Horizontal index type for input variables. \\ \hline \mbox{\texttt{ in}} & {\em t} & Potential temperature of the layer \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s} & Salinity of the layer \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em z\+\_\+t} & Height at the top of the layer in depth units \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em z\+\_\+b} & Height at the bottom of the layer \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+ref} & A mean density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is subtracted out to reduce the magnitude of each of the integrals. \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+0} & A density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is used to calculate the pressure (as p$\sim$=-\/z$\ast$rho\+\_\+0$\ast$\+G\+\_\+e) used in the equation of state. \\ \hline \mbox{\texttt{ in}} & {\em g\+\_\+e} & The Earth\textquotesingle{}s gravitational acceleration \mbox{[}L2 Z-\/1 T-\/2 $\sim$$>$ m s-\/2\mbox{]} or \mbox{[}m2 Z-\/1 s-\/2 $\sim$$>$ m s-\/2\mbox{]} \\ \hline & {\em eos} & Equation of state structure \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ in,out}} & {\em dpa} & The change in the pressure anomaly \\ \hline \mbox{\texttt{ in,out}} & {\em intz\+\_\+dpa} & The integral through the thickness of the \\ \hline \mbox{\texttt{ in,out}} & {\em intx\+\_\+dpa} & The integral in x of the difference between \\ \hline \mbox{\texttt{ in,out}} & {\em inty\+\_\+dpa} & The integral in y of the difference between \\ \hline \mbox{\texttt{ in}} & {\em bathyt} & The depth of the bathymetry \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em dz\+\_\+neglect} & A minuscule thickness change \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals. \\ \hline \end{DoxyParams} Definition at line 98 of file M\+O\+M\+\_\+density\+\_\+integrals.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{98 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: HI\textcolor{comment}{ !< Horizontal index type for input variables.}} \DoxyCodeLine{99 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{100 \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature of the layer [degC]}} \DoxyCodeLine{101 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{102 \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity of the layer [ppt]}} \DoxyCodeLine{103 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{104 \textcolor{keywordtype}{intent(in)} :: z\_t\textcolor{comment}{ !< Height at the top of the layer in depth units [Z ~> m]}} \DoxyCodeLine{105 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{106 \textcolor{keywordtype}{intent(in)} :: z\_b\textcolor{comment}{ !< Height at the bottom of the layer [Z ~> m]}} \DoxyCodeLine{107 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A mean density [R ~> kg m-\/3] or [kg m-\/3], that is}} \DoxyCodeLine{108 \textcolor{comment}{ !! subtracted out to reduce the magnitude}} \DoxyCodeLine{109 \textcolor{comment}{ !! of each of the integrals.}} \DoxyCodeLine{110 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_0\textcolor{comment}{ !< A density [R ~> kg m-\/3] or [kg m-\/3], that is used}} \DoxyCodeLine{111 \textcolor{comment}{ !! to calculate the pressure (as p~=-\/z*rho\_0*G\_e)}} \DoxyCodeLine{112 \textcolor{comment}{ !! used in the equation of state.}} \DoxyCodeLine{113 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: G\_e\textcolor{comment}{ !< The Earth's gravitational acceleration}} \DoxyCodeLine{114 \textcolor{comment}{ !! [L2 Z-\/1 T-\/2 ~> m s-\/2] or [m2 Z-\/1 s-\/2 ~> m s-\/2]}} \DoxyCodeLine{115 \textcolor{keywordtype}{type}(EOS\_type), \textcolor{keywordtype}{pointer} :: EOS\textcolor{comment}{ !< Equation of state structure}} \DoxyCodeLine{116 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{117 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{118 \textcolor{keywordtype}{intent(inout)} :: dpa\textcolor{comment}{ !< The change in the pressure anomaly}} \DoxyCodeLine{119 \textcolor{comment}{ !! across the layer [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{120 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{121 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intz\_dpa\textcolor{comment}{ !< The integral through the thickness of the}} \DoxyCodeLine{122 \textcolor{comment}{ !! layer of the pressure anomaly relative to the}} \DoxyCodeLine{123 \textcolor{comment}{ !! anomaly at the top of the layer [R L2 Z T-\/2 ~> Pa m]}} \DoxyCodeLine{124 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZIB\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{125 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intx\_dpa\textcolor{comment}{ !< The integral in x of the difference between}} \DoxyCodeLine{126 \textcolor{comment}{ !! the pressure anomaly at the top and bottom of the}} \DoxyCodeLine{127 \textcolor{comment}{ !! layer divided by the x grid spacing [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{128 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJB\_(HI))}, \&} \DoxyCodeLine{129 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: inty\_dpa\textcolor{comment}{ !< The integral in y of the difference between}} \DoxyCodeLine{130 \textcolor{comment}{ !! the pressure anomaly at the top and bottom of the}} \DoxyCodeLine{131 \textcolor{comment}{ !! layer divided by the y grid spacing [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{132 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{133 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: bathyT\textcolor{comment}{ !< The depth of the bathymetry [Z ~> m]}} \DoxyCodeLine{134 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: dz\_neglect\textcolor{comment}{ !< A minuscule thickness change [Z ~> m]}} \DoxyCodeLine{135 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: useMassWghtInterp\textcolor{comment}{ !< If true, uses mass weighting to}} \DoxyCodeLine{136 \textcolor{comment}{ !! interpolate T/S for top and bottom integrals.}} \DoxyCodeLine{137 \textcolor{comment}{! Local variables}} \DoxyCodeLine{138 \textcolor{keywordtype}{ real} :: T5(5), S5(5) \textcolor{comment}{! Temperatures and salinities at five quadrature points [degC] and [ppt]}} \DoxyCodeLine{139 \textcolor{keywordtype}{ real} :: p5(5) \textcolor{comment}{! Pressures at five quadrature points, never rescaled from Pa [Pa]}} \DoxyCodeLine{140 \textcolor{keywordtype}{ real} :: r5(5) \textcolor{comment}{! Densities at five quadrature points [R ~> kg m-\/3] or [kg m-\/3]}} \DoxyCodeLine{141 \textcolor{keywordtype}{ real} :: rho\_anom \textcolor{comment}{! The depth averaged density anomaly [R ~> kg m-\/3] or [kg m-\/3]}} \DoxyCodeLine{142 \textcolor{keywordtype}{ real} :: w\_left, w\_right \textcolor{comment}{! Left and right weights [nondim]}} \DoxyCodeLine{143 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{parameter} :: C1\_90 = 1.0/90.0 \textcolor{comment}{! Rational constants.}} \DoxyCodeLine{144 \textcolor{keywordtype}{ real} :: GxRho \textcolor{comment}{! The gravitational acceleration times density and unit conversion factors [Pa Z-\/1 ~> kg m-\/2 s-\/2]}} \DoxyCodeLine{145 \textcolor{keywordtype}{ real} :: I\_Rho \textcolor{comment}{! The inverse of the Boussinesq density [R-\/1 ~> m3 kg-\/1] or [m3 kg-\/1]}} \DoxyCodeLine{146 \textcolor{keywordtype}{ real} :: rho\_scale \textcolor{comment}{! A scaling factor for densities from kg m-\/3 to R [R m3 kg-\/1 ~> 1]}} \DoxyCodeLine{147 \textcolor{keywordtype}{ real} :: rho\_ref\_mks \textcolor{comment}{! The reference density in MKS units, never rescaled from kg m-\/3 [kg m-\/3]}} \DoxyCodeLine{148 \textcolor{keywordtype}{ real} :: dz \textcolor{comment}{! The layer thickness [Z ~> m]}} \DoxyCodeLine{149 \textcolor{keywordtype}{ real} :: hWght \textcolor{comment}{! A pressure-\/thickness below topography [Z ~> m]}} \DoxyCodeLine{150 \textcolor{keywordtype}{ real} :: hL, hR \textcolor{comment}{! Pressure-\/thicknesses of the columns to the left and right [Z ~> m]}} \DoxyCodeLine{151 \textcolor{keywordtype}{ real} :: iDenom \textcolor{comment}{! The inverse of the denominator in the weights [Z-\/2 ~> m-\/2]}} \DoxyCodeLine{152 \textcolor{keywordtype}{ real} :: hWt\_LL, hWt\_LR \textcolor{comment}{! hWt\_LA is the weighted influence of A on the left column [nondim]}} \DoxyCodeLine{153 \textcolor{keywordtype}{ real} :: hWt\_RL, hWt\_RR \textcolor{comment}{! hWt\_RA is the weighted influence of A on the right column [nondim]}} \DoxyCodeLine{154 \textcolor{keywordtype}{ real} :: wt\_L, wt\_R \textcolor{comment}{! The linear weights of the left and right columns [nondim]}} \DoxyCodeLine{155 \textcolor{keywordtype}{ real} :: wtT\_L, wtT\_R \textcolor{comment}{! The weights for tracers from the left and right columns [nondim]}} \DoxyCodeLine{156 \textcolor{keywordtype}{ real} :: intz(5) \textcolor{comment}{! The gravitational acceleration times the integrals of density}} \DoxyCodeLine{157 \textcolor{comment}{! with height at the 5 sub-\/column locations [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{158 \textcolor{keywordtype}{logical} :: do\_massWeight \textcolor{comment}{! Indicates whether to do mass weighting.}} \DoxyCodeLine{159 \textcolor{keywordtype}{integer} :: is, ie, js, je, Isq, Ieq, Jsq, Jeq, i, j, m, n} \DoxyCodeLine{160 } \DoxyCodeLine{161 \textcolor{comment}{! These array bounds work for the indexing convention of the input arrays, but}} \DoxyCodeLine{162 \textcolor{comment}{! on the computational domain defined for the output arrays.}} \DoxyCodeLine{163 isq = hi\%IscB ; ieq = hi\%IecB} \DoxyCodeLine{164 jsq = hi\%JscB ; jeq = hi\%JecB} \DoxyCodeLine{165 is = hi\%isc ; ie = hi\%iec} \DoxyCodeLine{166 js = hi\%jsc ; je = hi\%jec} \DoxyCodeLine{167 } \DoxyCodeLine{168 rho\_scale = us\%kg\_m3\_to\_R} \DoxyCodeLine{169 gxrho = us\%RL2\_T2\_to\_Pa * g\_e * rho\_0} \DoxyCodeLine{170 rho\_ref\_mks = rho\_ref * us\%R\_to\_kg\_m3} \DoxyCodeLine{171 i\_rho = 1.0 / rho\_0} \DoxyCodeLine{172 } \DoxyCodeLine{173 do\_massweight = .false.} \DoxyCodeLine{174 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(usemasswghtinterp)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (usemasswghtinterp) \textcolor{keywordflow}{then}} \DoxyCodeLine{175 do\_massweight = .true.} \DoxyCodeLine{176 \textcolor{keywordflow}{if} (.not.\textcolor{keyword}{present}(bathyt)) \textcolor{keyword}{call }mom\_error(fatal, \textcolor{stringliteral}{"int\_density\_dz\_generic: "}//\&} \DoxyCodeLine{177 \textcolor{stringliteral}{"bathyT must be present if useMassWghtInterp is present and true."})} \DoxyCodeLine{178 \textcolor{keywordflow}{if} (.not.\textcolor{keyword}{present}(dz\_neglect)) \textcolor{keyword}{call }mom\_error(fatal, \textcolor{stringliteral}{"int\_density\_dz\_generic: "}//\&} \DoxyCodeLine{179 \textcolor{stringliteral}{"dz\_neglect must be present if useMassWghtInterp is present and true."})} \DoxyCodeLine{180 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{181 } \DoxyCodeLine{182 \textcolor{keywordflow}{do} j=jsq,jeq+1 ; \textcolor{keywordflow}{do} i=isq,ieq+1} \DoxyCodeLine{183 dz = z\_t(i,j) -\/ z\_b(i,j)} \DoxyCodeLine{184 \textcolor{keywordflow}{do} n=1,5} \DoxyCodeLine{185 t5(n) = t(i,j) ; s5(n) = s(i,j)} \DoxyCodeLine{186 p5(n) = -\/gxrho*(z\_t(i,j) -\/ 0.25*real(n-\/1)*dz)} \DoxyCodeLine{187 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{188 \textcolor{keywordflow}{if} (rho\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{189 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, 5, eos, rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{190 \textcolor{keywordflow}{else}} \DoxyCodeLine{191 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, 5, eos, rho\_ref=rho\_ref\_mks)} \DoxyCodeLine{192 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{193 } \DoxyCodeLine{194 \textcolor{comment}{! Use Boole's rule to estimate the pressure anomaly change.}} \DoxyCodeLine{195 rho\_anom = c1\_90*(7.0*(r5(1)+r5(5)) + 32.0*(r5(2)+r5(4)) + 12.0*r5(3))} \DoxyCodeLine{196 dpa(i,j) = g\_e*dz*rho\_anom} \DoxyCodeLine{197 \textcolor{comment}{! Use a Boole's-\/rule-\/like fifth-\/order accurate estimate of the double integral of}} \DoxyCodeLine{198 \textcolor{comment}{! the pressure anomaly.}} \DoxyCodeLine{199 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intz\_dpa)) intz\_dpa(i,j) = 0.5*g\_e*dz**2 * \&} \DoxyCodeLine{200 (rho\_anom -\/ c1\_90*(16.0*(r5(4)-\/r5(2)) + 7.0*(r5(5)-\/r5(1))) )} \DoxyCodeLine{201 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{202 } \DoxyCodeLine{203 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=isq,ieq} \DoxyCodeLine{204 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{205 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of}} \DoxyCodeLine{206 \textcolor{comment}{! T \& S along the top and bottom integrals, akin to thickness weighting.}} \DoxyCodeLine{207 hwght = 0.0} \DoxyCodeLine{208 \textcolor{keywordflow}{if} (do\_massweight) \&} \DoxyCodeLine{209 hwght = max(0., -\/bathyt(i,j)-\/z\_t(i+1,j), -\/bathyt(i+1,j)-\/z\_t(i,j))} \DoxyCodeLine{210 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{211 hl = (z\_t(i,j) -\/ z\_b(i,j)) + dz\_neglect} \DoxyCodeLine{212 hr = (z\_t(i+1,j) -\/ z\_b(i+1,j)) + dz\_neglect} \DoxyCodeLine{213 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{214 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{215 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom} \DoxyCodeLine{216 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom} \DoxyCodeLine{217 \textcolor{keywordflow}{else}} \DoxyCodeLine{218 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0} \DoxyCodeLine{219 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{220 } \DoxyCodeLine{221 intz(1) = dpa(i,j) ; intz(5) = dpa(i+1,j)} \DoxyCodeLine{222 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{223 \textcolor{comment}{! T, S, and z are interpolated in the horizontal. The z interpolation}} \DoxyCodeLine{224 \textcolor{comment}{! is linear, but for T and S it may be thickness weighted.}} \DoxyCodeLine{225 wt\_l = 0.25*real(5-\/m) ; wt\_r = 1.0-\/wt\_l} \DoxyCodeLine{226 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr} \DoxyCodeLine{227 dz = wt\_l*(z\_t(i,j) -\/ z\_b(i,j)) + wt\_r*(z\_t(i+1,j) -\/ z\_b(i+1,j))} \DoxyCodeLine{228 t5(1) = wtt\_l*t(i,j) + wtt\_r*t(i+1,j)} \DoxyCodeLine{229 s5(1) = wtt\_l*s(i,j) + wtt\_r*s(i+1,j)} \DoxyCodeLine{230 p5(1) = -\/gxrho*(wt\_l*z\_t(i,j) + wt\_r*z\_t(i+1,j))} \DoxyCodeLine{231 \textcolor{keywordflow}{do} n=2,5} \DoxyCodeLine{232 t5(n) = t5(1) ; s5(n) = s5(1) ; p5(n) = p5(n-\/1) + gxrho*0.25*dz} \DoxyCodeLine{233 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{234 \textcolor{keywordflow}{if} (rho\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{235 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, 5, eos, rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{236 \textcolor{keywordflow}{else}} \DoxyCodeLine{237 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, 5, eos, rho\_ref=rho\_ref\_mks)} \DoxyCodeLine{238 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{239 } \DoxyCodeLine{240 \textcolor{comment}{! Use Boole's rule to estimate the pressure anomaly change.}} \DoxyCodeLine{241 intz(m) = g\_e*dz*( c1\_90*(7.0*(r5(1)+r5(5)) + 32.0*(r5(2)+r5(4)) + 12.0*r5(3)))} \DoxyCodeLine{242 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{243 \textcolor{comment}{! Use Boole's rule to integrate the bottom pressure anomaly values in x.}} \DoxyCodeLine{244 intx\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + \&} \DoxyCodeLine{245 12.0*intz(3))} \DoxyCodeLine{246 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{247 } \DoxyCodeLine{248 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=jsq,jeq ; \textcolor{keywordflow}{do} i=is,ie} \DoxyCodeLine{249 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{250 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of}} \DoxyCodeLine{251 \textcolor{comment}{! T \& S along the top and bottom integrals, akin to thickness weighting.}} \DoxyCodeLine{252 hwght = 0.0} \DoxyCodeLine{253 \textcolor{keywordflow}{if} (do\_massweight) \&} \DoxyCodeLine{254 hwght = max(0., -\/bathyt(i,j)-\/z\_t(i,j+1), -\/bathyt(i,j+1)-\/z\_t(i,j))} \DoxyCodeLine{255 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{256 hl = (z\_t(i,j) -\/ z\_b(i,j)) + dz\_neglect} \DoxyCodeLine{257 hr = (z\_t(i,j+1) -\/ z\_b(i,j+1)) + dz\_neglect} \DoxyCodeLine{258 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{259 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{260 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom} \DoxyCodeLine{261 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom} \DoxyCodeLine{262 \textcolor{keywordflow}{else}} \DoxyCodeLine{263 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0} \DoxyCodeLine{264 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{265 } \DoxyCodeLine{266 intz(1) = dpa(i,j) ; intz(5) = dpa(i,j+1)} \DoxyCodeLine{267 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{268 \textcolor{comment}{! T, S, and z are interpolated in the horizontal. The z interpolation}} \DoxyCodeLine{269 \textcolor{comment}{! is linear, but for T and S it may be thickness weighted.}} \DoxyCodeLine{270 wt\_l = 0.25*real(5-\/m) ; wt\_r = 1.0-\/wt\_l} \DoxyCodeLine{271 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr} \DoxyCodeLine{272 dz = wt\_l*(z\_t(i,j) -\/ z\_b(i,j)) + wt\_r*(z\_t(i,j+1) -\/ z\_b(i,j+1))} \DoxyCodeLine{273 t5(1) = wtt\_l*t(i,j) + wtt\_r*t(i,j+1)} \DoxyCodeLine{274 s5(1) = wtt\_l*s(i,j) + wtt\_r*s(i,j+1)} \DoxyCodeLine{275 p5(1) = -\/gxrho*(wt\_l*z\_t(i,j) + wt\_r*z\_t(i,j+1))} \DoxyCodeLine{276 \textcolor{keywordflow}{do} n=2,5} \DoxyCodeLine{277 t5(n) = t5(1) ; s5(n) = s5(1)} \DoxyCodeLine{278 p5(n) = p5(n-\/1) + gxrho*0.25*dz} \DoxyCodeLine{279 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{280 \textcolor{keywordflow}{if} (rho\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{281 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, 5, eos, rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{282 \textcolor{keywordflow}{else}} \DoxyCodeLine{283 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, 5, eos, rho\_ref=rho\_ref\_mks)} \DoxyCodeLine{284 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{285 } \DoxyCodeLine{286 \textcolor{comment}{! Use Boole's rule to estimate the pressure anomaly change.}} \DoxyCodeLine{287 intz(m) = g\_e*dz*( c1\_90*(7.0*(r5(1)+r5(5)) + 32.0*(r5(2)+r5(4)) + 12.0*r5(3)))} \DoxyCodeLine{288 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{289 \textcolor{comment}{! Use Boole's rule to integrate the values.}} \DoxyCodeLine{290 inty\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + \&} \DoxyCodeLine{291 12.0*intz(3))} \DoxyCodeLine{292 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \end{DoxyCode} \mbox{\Hypertarget{namespacemom__density__integrals_a454d4d62eb599716cc3389fb8aa90b4b}\label{namespacemom__density__integrals_a454d4d62eb599716cc3389fb8aa90b4b}} \index{mom\_density\_integrals@{mom\_density\_integrals}!int\_density\_dz\_generic\_plm@{int\_density\_dz\_generic\_plm}} \index{int\_density\_dz\_generic\_plm@{int\_density\_dz\_generic\_plm}!mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsubsection{\texorpdfstring{int\_density\_dz\_generic\_plm()}{int\_density\_dz\_generic\_plm()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+density\+\_\+integrals\+::int\+\_\+density\+\_\+dz\+\_\+generic\+\_\+plm (\begin{DoxyParamCaption}\item[{integer, intent(in)}]{k, }\item[{type(thermo\+\_\+var\+\_\+ptrs), intent(in)}]{tv, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed, gv \%ke), intent(in)}]{T\+\_\+t, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed, gv \%ke), intent(in)}]{T\+\_\+b, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed, gv \%ke), intent(in)}]{S\+\_\+t, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed, gv \%ke), intent(in)}]{S\+\_\+b, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed, gv \%ke+1), intent(in)}]{e, }\item[{real, intent(in)}]{rho\+\_\+ref, }\item[{real, intent(in)}]{rho\+\_\+0, }\item[{real, intent(in)}]{G\+\_\+e, }\item[{real, intent(in)}]{dz\+\_\+subroundoff, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in)}]{bathyT, }\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\item[{type(verticalgrid\+\_\+type), intent(in)}]{GV, }\item[{type(eos\+\_\+type), pointer}]{E\+OS, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(inout)}]{dpa, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(inout), optional}]{intz\+\_\+dpa, }\item[{real, dimension(szib\+\_\+(hi),szj\+\_\+(hi)), intent(inout), optional}]{intx\+\_\+dpa, }\item[{real, dimension(szi\+\_\+(hi),szjb\+\_\+(hi)), intent(inout), optional}]{inty\+\_\+dpa, }\item[{logical, intent(in), optional}]{use\+Mass\+Wght\+Interp }\end{DoxyParamCaption})} Compute pressure gradient force integrals by quadrature for the case where T and S are linear profiles. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em k} & Layer index to calculate integrals for \\ \hline \mbox{\texttt{ in}} & {\em hi} & Ocean horizontal index structures for the input arrays \\ \hline \mbox{\texttt{ in}} & {\em gv} & Vertical grid structure \\ \hline \mbox{\texttt{ in}} & {\em tv} & Thermodynamic variables \\ \hline \mbox{\texttt{ in}} & {\em t\+\_\+t} & Potential temperature at the cell top \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em t\+\_\+b} & Potential temperature at the cell bottom \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+t} & Salinity at the cell top \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+b} & Salinity at the cell bottom \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em e} & Height of interfaces \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+ref} & A mean density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is subtracted out to reduce the magnitude of each of the integrals. \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+0} & A density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is used to calculate the pressure (as p$\sim$=-\/z$\ast$rho\+\_\+0$\ast$\+G\+\_\+e) used in the equation of state. \\ \hline \mbox{\texttt{ in}} & {\em g\+\_\+e} & The Earth\textquotesingle{}s gravitational acceleration \mbox{[}L2 Z-\/1 T-\/2 $\sim$$>$ m s-\/2\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em dz\+\_\+subroundoff} & A minuscule thickness change \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em bathyt} & The depth of the bathymetry \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline & {\em eos} & Equation of state structure \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ in,out}} & {\em dpa} & The change in the pressure anomaly across the layer \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} \\ \hline \mbox{\texttt{ in,out}} & {\em intz\+\_\+dpa} & The integral through the thickness of the layer of \\ \hline \mbox{\texttt{ in,out}} & {\em intx\+\_\+dpa} & The integral in x of the difference between the \\ \hline \mbox{\texttt{ in,out}} & {\em inty\+\_\+dpa} & The integral in y of the difference between the \\ \hline \mbox{\texttt{ in}} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals. \\ \hline \end{DoxyParams} Definition at line 301 of file M\+O\+M\+\_\+density\+\_\+integrals.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{301 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: k\textcolor{comment}{ !< Layer index to calculate integrals for}} \DoxyCodeLine{302 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: HI\textcolor{comment}{ !< Ocean horizontal index structures for the input arrays}} \DoxyCodeLine{303 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< Vertical grid structure}} \DoxyCodeLine{304 \textcolor{keywordtype}{type}(thermo\_var\_ptrs), \textcolor{keywordtype}{intent(in)} :: tv\textcolor{comment}{ !< Thermodynamic variables}} \DoxyCodeLine{305 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV))}, \&} \DoxyCodeLine{306 \textcolor{keywordtype}{intent(in)} :: T\_t\textcolor{comment}{ !< Potential temperature at the cell top [degC]}} \DoxyCodeLine{307 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV))}, \&} \DoxyCodeLine{308 \textcolor{keywordtype}{intent(in)} :: T\_b\textcolor{comment}{ !< Potential temperature at the cell bottom [degC]}} \DoxyCodeLine{309 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV))}, \&} \DoxyCodeLine{310 \textcolor{keywordtype}{intent(in)} :: S\_t\textcolor{comment}{ !< Salinity at the cell top [ppt]}} \DoxyCodeLine{311 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV))}, \&} \DoxyCodeLine{312 \textcolor{keywordtype}{intent(in)} :: S\_b\textcolor{comment}{ !< Salinity at the cell bottom [ppt]}} \DoxyCodeLine{313 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV)+1)}, \&} \DoxyCodeLine{314 \textcolor{keywordtype}{intent(in)} :: e\textcolor{comment}{ !< Height of interfaces [Z ~> m]}} \DoxyCodeLine{315 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A mean density [R ~> kg m-\/3] or [kg m-\/3], that is subtracted}} \DoxyCodeLine{316 \textcolor{comment}{ !! out to reduce the magnitude of each of the integrals.}} \DoxyCodeLine{317 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_0\textcolor{comment}{ !< A density [R ~> kg m-\/3] or [kg m-\/3], that is used to calculate}} \DoxyCodeLine{318 \textcolor{comment}{ !! the pressure (as p~=-\/z*rho\_0*G\_e) used in the equation of state.}} \DoxyCodeLine{319 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: G\_e\textcolor{comment}{ !< The Earth's gravitational acceleration [L2 Z-\/1 T-\/2 ~> m s-\/2]}} \DoxyCodeLine{320 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: dz\_subroundoff\textcolor{comment}{ !< A minuscule thickness change [Z ~> m]}} \DoxyCodeLine{321 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{322 \textcolor{keywordtype}{intent(in)} :: bathyT\textcolor{comment}{ !< The depth of the bathymetry [Z ~> m]}} \DoxyCodeLine{323 \textcolor{keywordtype}{type}(EOS\_type), \textcolor{keywordtype}{pointer} :: EOS\textcolor{comment}{ !< Equation of state structure}} \DoxyCodeLine{324 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{325 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{326 \textcolor{keywordtype}{intent(inout)} :: dpa\textcolor{comment}{ !< The change in the pressure anomaly across the layer [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{327 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{328 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intz\_dpa\textcolor{comment}{ !< The integral through the thickness of the layer of}} \DoxyCodeLine{329 \textcolor{comment}{ !! the pressure anomaly relative to the anomaly at the}} \DoxyCodeLine{330 \textcolor{comment}{ !! top of the layer [R L2 Z T-\/2 ~> Pa Z]}} \DoxyCodeLine{331 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZIB\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{332 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intx\_dpa\textcolor{comment}{ !< The integral in x of the difference between the}} \DoxyCodeLine{333 \textcolor{comment}{ !! pressure anomaly at the top and bottom of the layer}} \DoxyCodeLine{334 \textcolor{comment}{ !! divided by the x grid spacing [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{335 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJB\_(HI))}, \&} \DoxyCodeLine{336 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: inty\_dpa\textcolor{comment}{ !< The integral in y of the difference between the}} \DoxyCodeLine{337 \textcolor{comment}{ !! pressure anomaly at the top and bottom of the layer}} \DoxyCodeLine{338 \textcolor{comment}{ !! divided by the y grid spacing [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{339 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: useMassWghtInterp\textcolor{comment}{ !< If true, uses mass weighting to}} \DoxyCodeLine{340 \textcolor{comment}{ !! interpolate T/S for top and bottom integrals.}} \DoxyCodeLine{341 } \DoxyCodeLine{342 \textcolor{comment}{! This subroutine calculates (by numerical quadrature) integrals of}} \DoxyCodeLine{343 \textcolor{comment}{! pressure anomalies across layers, which are required for calculating the}} \DoxyCodeLine{344 \textcolor{comment}{! finite-\/volume form pressure accelerations in a Boussinesq model. The one}} \DoxyCodeLine{345 \textcolor{comment}{! potentially dodgy assumption here is that rho\_0 is used both in the denominator}} \DoxyCodeLine{346 \textcolor{comment}{! of the accelerations, and in the pressure used to calculated density (the}} \DoxyCodeLine{347 \textcolor{comment}{! latter being -\/z*rho\_0*G\_e). These two uses could be separated if need be.}} \DoxyCodeLine{348 \textcolor{comment}{!}} \DoxyCodeLine{349 \textcolor{comment}{! It is assumed that the salinity and temperature profiles are linear in the}} \DoxyCodeLine{350 \textcolor{comment}{! vertical. The top and bottom values within each layer are provided and}} \DoxyCodeLine{351 \textcolor{comment}{! a linear interpolation is used to compute intermediate values.}} \DoxyCodeLine{352 } \DoxyCodeLine{353 \textcolor{comment}{! Local variables}} \DoxyCodeLine{354 \textcolor{keywordtype}{ real} :: T5((5*HI\%iscB+1):(5*(HI\%iecB+2))) \textcolor{comment}{! Temperatures along a line of subgrid locations [degC]}} \DoxyCodeLine{355 \textcolor{keywordtype}{ real} :: S5((5*HI\%iscB+1):(5*(HI\%iecB+2))) \textcolor{comment}{! Salinities along a line of subgrid locations [ppt]}} \DoxyCodeLine{356 \textcolor{keywordtype}{ real} :: T25((5*HI\%iscB+1):(5*(HI\%iecB+2))) \textcolor{comment}{! SGS temperature variance along a line of subgrid locations [degC2]}} \DoxyCodeLine{357 \textcolor{keywordtype}{ real} :: TS5((5*HI\%iscB+1):(5*(HI\%iecB+2))) \textcolor{comment}{! SGS temp-\/salt covariance along a line of subgrid locations [degC ppt]}} \DoxyCodeLine{358 \textcolor{keywordtype}{ real} :: S25((5*HI\%iscB+1):(5*(HI\%iecB+2))) \textcolor{comment}{! SGS salinity variance along a line of subgrid locations [ppt2]}} \DoxyCodeLine{359 \textcolor{keywordtype}{ real} :: p5((5*HI\%iscB+1):(5*(HI\%iecB+2))) \textcolor{comment}{! Pressures along a line of subgrid locations, never}} \DoxyCodeLine{360 \textcolor{comment}{! rescaled from Pa [Pa]}} \DoxyCodeLine{361 \textcolor{keywordtype}{ real} :: r5((5*HI\%iscB+1):(5*(HI\%iecB+2))) \textcolor{comment}{! Densities anomalies along a line of subgrid}} \DoxyCodeLine{362 \textcolor{comment}{! locations [R ~> kg m-\/3] or [kg m-\/3]}} \DoxyCodeLine{363 \textcolor{keywordtype}{ real} :: T15((15*HI\%iscB+1):(15*(HI\%iecB+1))) \textcolor{comment}{! Temperatures at an array of subgrid locations [degC]}} \DoxyCodeLine{364 \textcolor{keywordtype}{ real} :: S15((15*HI\%iscB+1):(15*(HI\%iecB+1))) \textcolor{comment}{! Salinities at an array of subgrid locations [ppt]}} \DoxyCodeLine{365 \textcolor{keywordtype}{ real} :: T215((15*HI\%iscB+1):(15*(HI\%iecB+1))) \textcolor{comment}{! SGS temperature variance along a line of subgrid locations [degC2]}} \DoxyCodeLine{366 \textcolor{keywordtype}{ real} :: TS15((15*HI\%iscB+1):(15*(HI\%iecB+1))) \textcolor{comment}{! SGS temp-\/salt covariance along a line of subgrid locations [degC ppt]}} \DoxyCodeLine{367 \textcolor{keywordtype}{ real} :: S215((15*HI\%iscB+1):(15*(HI\%iecB+1))) \textcolor{comment}{! SGS salinity variance along a line of subgrid locations [ppt2]}} \DoxyCodeLine{368 \textcolor{keywordtype}{ real} :: p15((15*HI\%iscB+1):(15*(HI\%iecB+1))) \textcolor{comment}{! Pressures at an array of subgrid locations [Pa]}} \DoxyCodeLine{369 \textcolor{keywordtype}{ real} :: r15((15*HI\%iscB+1):(15*(HI\%iecB+1))) \textcolor{comment}{! Densities at an array of subgrid locations}} \DoxyCodeLine{370 \textcolor{comment}{! [R ~> kg m-\/3] or [kg m-\/3]}} \DoxyCodeLine{371 \textcolor{keywordtype}{ real} :: wt\_t(5), wt\_b(5) \textcolor{comment}{! Top and bottom weights [nondim]}} \DoxyCodeLine{372 \textcolor{keywordtype}{ real} :: rho\_anom \textcolor{comment}{! A density anomaly [R ~> kg m-\/3] or [kg m-\/3]}} \DoxyCodeLine{373 \textcolor{keywordtype}{ real} :: w\_left, w\_right \textcolor{comment}{! Left and right weights [nondim]}} \DoxyCodeLine{374 \textcolor{keywordtype}{ real} :: intz(5) \textcolor{comment}{! The gravitational acceleration times the integrals of density}} \DoxyCodeLine{375 \textcolor{comment}{! with height at the 5 sub-\/column locations [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{376 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{parameter} :: C1\_90 = 1.0/90.0 \textcolor{comment}{! A rational constant [nondim]}} \DoxyCodeLine{377 \textcolor{keywordtype}{ real} :: GxRho \textcolor{comment}{! The gravitational acceleration times density and unit conversion factors [Pa Z-\/1 ~> kg m-\/2 s-\/2]}} \DoxyCodeLine{378 \textcolor{keywordtype}{ real} :: I\_Rho \textcolor{comment}{! The inverse of the Boussinesq density [R-\/1 ~> m3 kg-\/1] or [m3 kg-\/1]}} \DoxyCodeLine{379 \textcolor{keywordtype}{ real} :: rho\_scale \textcolor{comment}{! A scaling factor for densities from kg m-\/3 to R [R m3 kg-\/1 ~> 1]}} \DoxyCodeLine{380 \textcolor{keywordtype}{ real} :: rho\_ref\_mks \textcolor{comment}{! The reference density in MKS units, never rescaled from kg m-\/3 [kg m-\/3]}} \DoxyCodeLine{381 \textcolor{keywordtype}{ real} :: dz(HI\%iscB:HI\%iecB+1) \textcolor{comment}{! Layer thicknesses at tracer points [Z ~> m]}} \DoxyCodeLine{382 \textcolor{keywordtype}{ real} :: dz\_x(5,HI\%iscB:HI\%iecB) \textcolor{comment}{! Layer thicknesses along an x-\/line of subrid locations [Z ~> m]}} \DoxyCodeLine{383 \textcolor{keywordtype}{ real} :: dz\_y(5,HI\%isc:HI\%iec) \textcolor{comment}{! Layer thicknesses along a y-\/line of subrid locations [Z ~> m]}} \DoxyCodeLine{384 \textcolor{keywordtype}{ real} :: massWeightToggle \textcolor{comment}{! A non-\/dimensional toggle factor (0 or 1) [nondim]}} \DoxyCodeLine{385 \textcolor{keywordtype}{ real} :: Ttl, Tbl, Ttr, Tbr \textcolor{comment}{! Temperatures at the velocity cell corners [degC]}} \DoxyCodeLine{386 \textcolor{keywordtype}{ real} :: Stl, Sbl, Str, Sbr \textcolor{comment}{! Salinities at the velocity cell corners [ppt]}} \DoxyCodeLine{387 \textcolor{keywordtype}{ real} :: hWght \textcolor{comment}{! A topographically limited thicknes weight [Z ~> m]}} \DoxyCodeLine{388 \textcolor{keywordtype}{ real} :: hL, hR \textcolor{comment}{! Thicknesses to the left and right [Z ~> m]}} \DoxyCodeLine{389 \textcolor{keywordtype}{ real} :: iDenom \textcolor{comment}{! The denominator of the thickness weight expressions [Z-\/2 ~> m-\/2]}} \DoxyCodeLine{390 \textcolor{keywordtype}{logical} :: use\_stanley\_eos \textcolor{comment}{! True is SGS variance fields exist in tv.}} \DoxyCodeLine{391 \textcolor{keywordtype}{logical} :: use\_varT, use\_varS, use\_covarTS} \DoxyCodeLine{392 \textcolor{keywordtype}{integer} :: Isq, Ieq, Jsq, Jeq, i, j, m, n} \DoxyCodeLine{393 \textcolor{keywordtype}{integer} :: pos} \DoxyCodeLine{394 } \DoxyCodeLine{395 isq = hi\%IscB ; ieq = hi\%IecB ; jsq = hi\%JscB ; jeq = hi\%JecB} \DoxyCodeLine{396 } \DoxyCodeLine{397 rho\_scale = us\%kg\_m3\_to\_R} \DoxyCodeLine{398 gxrho = us\%RL2\_T2\_to\_Pa * g\_e * rho\_0} \DoxyCodeLine{399 rho\_ref\_mks = rho\_ref * us\%R\_to\_kg\_m3} \DoxyCodeLine{400 i\_rho = 1.0 / rho\_0} \DoxyCodeLine{401 massweighttoggle = 0.} \DoxyCodeLine{402 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(usemasswghtinterp)) \textcolor{keywordflow}{then}} \DoxyCodeLine{403 \textcolor{keywordflow}{if} (usemasswghtinterp) massweighttoggle = 1.} \DoxyCodeLine{404 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{405 } \DoxyCodeLine{406 use\_vart = \textcolor{keyword}{associated}(tv\%varT)} \DoxyCodeLine{407 use\_covarts = \textcolor{keyword}{associated}(tv\%covarTS)} \DoxyCodeLine{408 use\_vars = \textcolor{keyword}{associated}(tv\%varS)} \DoxyCodeLine{409 use\_stanley\_eos = use\_vart .or. use\_covarts .or. use\_vars} \DoxyCodeLine{410 t25(:) = 0.} \DoxyCodeLine{411 ts5(:) = 0.} \DoxyCodeLine{412 s25(:) = 0.} \DoxyCodeLine{413 t215(:) = 0.} \DoxyCodeLine{414 ts15(:) = 0.} \DoxyCodeLine{415 s215(:) = 0.} \DoxyCodeLine{416 } \DoxyCodeLine{417 \textcolor{keywordflow}{do} n = 1, 5} \DoxyCodeLine{418 wt\_t(n) = 0.25 * real(5-\/n)} \DoxyCodeLine{419 wt\_b(n) = 1.0 -\/ wt\_t(n)} \DoxyCodeLine{420 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{421 } \DoxyCodeLine{422 \textcolor{comment}{! 1. Compute vertical integrals}} \DoxyCodeLine{423 \textcolor{keywordflow}{do} j=jsq,jeq+1} \DoxyCodeLine{424 \textcolor{keywordflow}{do} i = isq,ieq+1} \DoxyCodeLine{425 dz(i) = e(i,j,k) -\/ e(i,j,k+1)} \DoxyCodeLine{426 \textcolor{keywordflow}{do} n=1,5} \DoxyCodeLine{427 p5(i*5+n) = -\/gxrho*(e(i,j,k) -\/ 0.25*real(n-\/1)*dz(i))} \DoxyCodeLine{428 \textcolor{comment}{! Salinity and temperature points are linearly interpolated}} \DoxyCodeLine{429 s5(i*5+n) = wt\_t(n) * s\_t(i,j,k) + wt\_b(n) * s\_b(i,j,k)} \DoxyCodeLine{430 t5(i*5+n) = wt\_t(n) * t\_t(i,j,k) + wt\_b(n) * t\_b(i,j,k)} \DoxyCodeLine{431 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{432 \textcolor{keywordflow}{if} (use\_vart) t25(i*5+1:i*5+5) = tv\%varT(i,j,k)} \DoxyCodeLine{433 \textcolor{keywordflow}{if} (use\_covarts) ts5(i*5+1:i*5+5) = tv\%covarTS(i,j,k)} \DoxyCodeLine{434 \textcolor{keywordflow}{if} (use\_vars) s25(i*5+1:i*5+5) = tv\%varS(i,j,k)} \DoxyCodeLine{435 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{436 \textcolor{keywordflow}{if} (use\_stanley\_eos) \textcolor{keywordflow}{then}} \DoxyCodeLine{437 \textcolor{keywordflow}{if} (rho\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{438 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, t25, ts5, s25, r5, 1, (ieq-\/isq+2)*5, eos, \&} \DoxyCodeLine{439 rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{440 \textcolor{keywordflow}{else}} \DoxyCodeLine{441 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, t25, ts5, s25, r5, 1, (ieq-\/isq+2)*5, eos, \&} \DoxyCodeLine{442 rho\_ref=rho\_ref\_mks)} \DoxyCodeLine{443 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{444 \textcolor{keywordflow}{else}} \DoxyCodeLine{445 \textcolor{keywordflow}{if} (rho\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{446 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, (ieq-\/isq+2)*5, eos, rho\_ref=rho\_ref\_mks, \&} \DoxyCodeLine{447 scale=rho\_scale)} \DoxyCodeLine{448 \textcolor{keywordflow}{else}} \DoxyCodeLine{449 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, (ieq-\/isq+2)*5, eos, rho\_ref=rho\_ref\_mks)} \DoxyCodeLine{450 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{451 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{452 } \DoxyCodeLine{453 \textcolor{keywordflow}{do} i=isq,ieq+1} \DoxyCodeLine{454 \textcolor{comment}{! Use Boole's rule to estimate the pressure anomaly change.}} \DoxyCodeLine{455 rho\_anom = c1\_90*(7.0*(r5(i*5+1)+r5(i*5+5)) + 32.0*(r5(i*5+2)+r5(i*5+4)) + 12.0*r5(i*5+3))} \DoxyCodeLine{456 dpa(i,j) = g\_e*dz(i)*rho\_anom} \DoxyCodeLine{457 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intz\_dpa)) \textcolor{keywordflow}{then}} \DoxyCodeLine{458 \textcolor{comment}{! Use a Boole's-\/rule-\/like fifth-\/order accurate estimate of}} \DoxyCodeLine{459 \textcolor{comment}{! the double integral of the pressure anomaly.}} \DoxyCodeLine{460 intz\_dpa(i,j) = 0.5*g\_e*dz(i)**2 * \&} \DoxyCodeLine{461 (rho\_anom -\/ c1\_90*(16.0*(r5(i*5+4)-\/r5(i*5+2)) + 7.0*(r5(i*5+5)-\/r5(i*5+1))) )} \DoxyCodeLine{462 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{463 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{464 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! end loops on j}} \DoxyCodeLine{465 } \DoxyCodeLine{466 \textcolor{comment}{! 2. Compute horizontal integrals in the x direction}} \DoxyCodeLine{467 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=hi\%jsc,hi\%jec} \DoxyCodeLine{468 \textcolor{keywordflow}{do} i=isq,ieq} \DoxyCodeLine{469 \textcolor{comment}{! Corner values of T and S}} \DoxyCodeLine{470 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{471 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation}} \DoxyCodeLine{472 \textcolor{comment}{! of T,S along the top and bottom integrals, almost like thickness}} \DoxyCodeLine{473 \textcolor{comment}{! weighting.}} \DoxyCodeLine{474 \textcolor{comment}{! Note: To work in terrain following coordinates we could offset}} \DoxyCodeLine{475 \textcolor{comment}{! this distance by the layer thickness to replicate other models.}} \DoxyCodeLine{476 hwght = massweighttoggle * \&} \DoxyCodeLine{477 max(0., -\/bathyt(i,j)-\/e(i+1,j,k), -\/bathyt(i+1,j)-\/e(i,j,k))} \DoxyCodeLine{478 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{479 hl = (e(i,j,k) -\/ e(i,j,k+1)) + dz\_subroundoff} \DoxyCodeLine{480 hr = (e(i+1,j,k) -\/ e(i+1,j,k+1)) + dz\_subroundoff} \DoxyCodeLine{481 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{482 idenom = 1./( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{483 ttl = ( (hwght*hr)*t\_t(i+1,j,k) + (hwght*hl + hr*hl)*t\_t(i,j,k) ) * idenom} \DoxyCodeLine{484 ttr = ( (hwght*hl)*t\_t(i,j,k) + (hwght*hr + hr*hl)*t\_t(i+1,j,k) ) * idenom} \DoxyCodeLine{485 tbl = ( (hwght*hr)*t\_b(i+1,j,k) + (hwght*hl + hr*hl)*t\_b(i,j,k) ) * idenom} \DoxyCodeLine{486 tbr = ( (hwght*hl)*t\_b(i,j,k) + (hwght*hr + hr*hl)*t\_b(i+1,j,k) ) * idenom} \DoxyCodeLine{487 stl = ( (hwght*hr)*s\_t(i+1,j,k) + (hwght*hl + hr*hl)*s\_t(i,j,k) ) * idenom} \DoxyCodeLine{488 str = ( (hwght*hl)*s\_t(i,j,k) + (hwght*hr + hr*hl)*s\_t(i+1,j,k) ) * idenom} \DoxyCodeLine{489 sbl = ( (hwght*hr)*s\_b(i+1,j,k) + (hwght*hl + hr*hl)*s\_b(i,j,k) ) * idenom} \DoxyCodeLine{490 sbr = ( (hwght*hl)*s\_b(i,j,k) + (hwght*hr + hr*hl)*s\_b(i+1,j,k) ) * idenom} \DoxyCodeLine{491 \textcolor{keywordflow}{else}} \DoxyCodeLine{492 ttl = t\_t(i,j,k); tbl = t\_b(i,j,k); ttr = t\_t(i+1,j,k); tbr = t\_b(i+1,j,k)} \DoxyCodeLine{493 stl = s\_t(i,j,k); sbl = s\_b(i,j,k); str = s\_t(i+1,j,k); sbr = s\_b(i+1,j,k)} \DoxyCodeLine{494 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{495 } \DoxyCodeLine{496 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{497 w\_left = wt\_t(m) ; w\_right = wt\_b(m)} \DoxyCodeLine{498 dz\_x(m,i) = w\_left*(e(i,j,k) -\/ e(i,j,k+1)) + w\_right*(e(i+1,j,k) -\/ e(i+1,j,k+1))} \DoxyCodeLine{499 } \DoxyCodeLine{500 \textcolor{comment}{! Salinity and temperature points are linearly interpolated in}} \DoxyCodeLine{501 \textcolor{comment}{! the horizontal. The subscript (1) refers to the top value in}} \DoxyCodeLine{502 \textcolor{comment}{! the vertical profile while subscript (5) refers to the bottom}} \DoxyCodeLine{503 \textcolor{comment}{! value in the vertical profile.}} \DoxyCodeLine{504 pos = i*15+(m-\/2)*5} \DoxyCodeLine{505 t15(pos+1) = w\_left*ttl + w\_right*ttr} \DoxyCodeLine{506 t15(pos+5) = w\_left*tbl + w\_right*tbr} \DoxyCodeLine{507 } \DoxyCodeLine{508 s15(pos+1) = w\_left*stl + w\_right*str} \DoxyCodeLine{509 s15(pos+5) = w\_left*sbl + w\_right*sbr} \DoxyCodeLine{510 } \DoxyCodeLine{511 p15(pos+1) = -\/gxrho*(w\_left*e(i,j,k) + w\_right*e(i+1,j,k))} \DoxyCodeLine{512 } \DoxyCodeLine{513 \textcolor{comment}{! Pressure}} \DoxyCodeLine{514 \textcolor{keywordflow}{do} n=2,5} \DoxyCodeLine{515 p15(pos+n) = p15(pos+n-\/1) + gxrho*0.25*dz\_x(m,i)} \DoxyCodeLine{516 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{517 } \DoxyCodeLine{518 \textcolor{comment}{! Salinity and temperature (linear interpolation in the vertical)}} \DoxyCodeLine{519 \textcolor{keywordflow}{do} n=2,4} \DoxyCodeLine{520 s15(pos+n) = wt\_t(n) * s15(pos+1) + wt\_b(n) * s15(pos+5)} \DoxyCodeLine{521 t15(pos+n) = wt\_t(n) * t15(pos+1) + wt\_b(n) * t15(pos+5)} \DoxyCodeLine{522 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{523 \textcolor{keywordflow}{if} (use\_vart) t215(pos+1:pos+5) = w\_left*tv\%varT(i,j,k) + w\_right*tv\%varT(i+1,j,k)} \DoxyCodeLine{524 \textcolor{keywordflow}{if} (use\_covarts) ts15(pos+1:pos+5) = w\_left*tv\%covarTS(i,j,k) + w\_right*tv\%covarTS(i+1,j,k)} \DoxyCodeLine{525 \textcolor{keywordflow}{if} (use\_vars) s215(pos+1:pos+5) = w\_left*tv\%varS(i,j,k) + w\_right*tv\%varS(i+1,j,k)} \DoxyCodeLine{526 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{527 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{528 } \DoxyCodeLine{529 \textcolor{keywordflow}{if} (use\_stanley\_eos) \textcolor{keywordflow}{then}} \DoxyCodeLine{530 \textcolor{keywordflow}{if} (rho\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{531 \textcolor{keyword}{call }calculate\_density(t15, s15, p15, t215, ts15, s215, r15, 1, 15*(ieq-\/isq+1), eos, \&} \DoxyCodeLine{532 rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{533 \textcolor{keywordflow}{else}} \DoxyCodeLine{534 \textcolor{keyword}{call }calculate\_density(t15, s15, p15, t215, ts15, s215, r15, 1, 15*(ieq-\/isq+1), eos, \&} \DoxyCodeLine{535 rho\_ref=rho\_ref\_mks)} \DoxyCodeLine{536 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{537 \textcolor{keywordflow}{else}} \DoxyCodeLine{538 \textcolor{keywordflow}{if} (rho\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{539 \textcolor{keyword}{call }calculate\_density(t15, s15, p15, r15, 1, 15*(ieq-\/isq+1), eos, rho\_ref=rho\_ref\_mks, \&} \DoxyCodeLine{540 scale=rho\_scale)} \DoxyCodeLine{541 \textcolor{keywordflow}{else}} \DoxyCodeLine{542 \textcolor{keyword}{call }calculate\_density(t15, s15, p15, r15, 1, 15*(ieq-\/isq+1), eos, rho\_ref=rho\_ref\_mks)} \DoxyCodeLine{543 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{544 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{545 } \DoxyCodeLine{546 \textcolor{keywordflow}{do} i=isq,ieq} \DoxyCodeLine{547 intz(1) = dpa(i,j) ; intz(5) = dpa(i+1,j)} \DoxyCodeLine{548 } \DoxyCodeLine{549 \textcolor{comment}{! Use Boole's rule to estimate the pressure anomaly change.}} \DoxyCodeLine{550 \textcolor{keywordflow}{do} m = 2,4} \DoxyCodeLine{551 pos = i*15+(m-\/2)*5} \DoxyCodeLine{552 intz(m) = g\_e*dz\_x(m,i)*( c1\_90*(7.0*(r15(pos+1)+r15(pos+5)) + 32.0*(r15(pos+2)+r15(pos+4)) + \&} \DoxyCodeLine{553 12.0*r15(pos+3)))} \DoxyCodeLine{554 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{555 \textcolor{comment}{! Use Boole's rule to integrate the bottom pressure anomaly values in x.}} \DoxyCodeLine{556 intx\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + \&} \DoxyCodeLine{557 12.0*intz(3))} \DoxyCodeLine{558 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{559 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{560 } \DoxyCodeLine{561 \textcolor{comment}{! 3. Compute horizontal integrals in the y direction}} \DoxyCodeLine{562 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=jsq,jeq} \DoxyCodeLine{563 \textcolor{keywordflow}{do} i=hi\%isc,hi\%iec} \DoxyCodeLine{564 \textcolor{comment}{! Corner values of T and S}} \DoxyCodeLine{565 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{566 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation}} \DoxyCodeLine{567 \textcolor{comment}{! of T,S along the top and bottom integrals, almost like thickness}} \DoxyCodeLine{568 \textcolor{comment}{! weighting.}} \DoxyCodeLine{569 \textcolor{comment}{! Note: To work in terrain following coordinates we could offset}} \DoxyCodeLine{570 \textcolor{comment}{! this distance by the layer thickness to replicate other models.}} \DoxyCodeLine{571 hwght = massweighttoggle * \&} \DoxyCodeLine{572 max(0., -\/bathyt(i,j)-\/e(i,j+1,k), -\/bathyt(i,j+1)-\/e(i,j,k))} \DoxyCodeLine{573 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{574 hl = (e(i,j,k) -\/ e(i,j,k+1)) + dz\_subroundoff} \DoxyCodeLine{575 hr = (e(i,j+1,k) -\/ e(i,j+1,k+1)) + dz\_subroundoff} \DoxyCodeLine{576 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{577 idenom = 1./( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{578 ttl = ( (hwght*hr)*t\_t(i,j+1,k) + (hwght*hl + hr*hl)*t\_t(i,j,k) ) * idenom} \DoxyCodeLine{579 ttr = ( (hwght*hl)*t\_t(i,j,k) + (hwght*hr + hr*hl)*t\_t(i,j+1,k) ) * idenom} \DoxyCodeLine{580 tbl = ( (hwght*hr)*t\_b(i,j+1,k) + (hwght*hl + hr*hl)*t\_b(i,j,k) ) * idenom} \DoxyCodeLine{581 tbr = ( (hwght*hl)*t\_b(i,j,k) + (hwght*hr + hr*hl)*t\_b(i,j+1,k) ) * idenom} \DoxyCodeLine{582 stl = ( (hwght*hr)*s\_t(i,j+1,k) + (hwght*hl + hr*hl)*s\_t(i,j,k) ) * idenom} \DoxyCodeLine{583 str = ( (hwght*hl)*s\_t(i,j,k) + (hwght*hr + hr*hl)*s\_t(i,j+1,k) ) * idenom} \DoxyCodeLine{584 sbl = ( (hwght*hr)*s\_b(i,j+1,k) + (hwght*hl + hr*hl)*s\_b(i,j,k) ) * idenom} \DoxyCodeLine{585 sbr = ( (hwght*hl)*s\_b(i,j,k) + (hwght*hr + hr*hl)*s\_b(i,j+1,k) ) * idenom} \DoxyCodeLine{586 \textcolor{keywordflow}{else}} \DoxyCodeLine{587 ttl = t\_t(i,j,k); tbl = t\_b(i,j,k); ttr = t\_t(i,j+1,k); tbr = t\_b(i,j+1,k)} \DoxyCodeLine{588 stl = s\_t(i,j,k); sbl = s\_b(i,j,k); str = s\_t(i,j+1,k); sbr = s\_b(i,j+1,k)} \DoxyCodeLine{589 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{590 } \DoxyCodeLine{591 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{592 w\_left = wt\_t(m) ; w\_right = wt\_b(m)} \DoxyCodeLine{593 dz\_y(m,i) = w\_left*(e(i,j,k) -\/ e(i,j,k+1)) + w\_right*(e(i,j+1,k) -\/ e(i,j+1,k+1))} \DoxyCodeLine{594 } \DoxyCodeLine{595 \textcolor{comment}{! Salinity and temperature points are linearly interpolated in}} \DoxyCodeLine{596 \textcolor{comment}{! the horizontal. The subscript (1) refers to the top value in}} \DoxyCodeLine{597 \textcolor{comment}{! the vertical profile while subscript (5) refers to the bottom}} \DoxyCodeLine{598 \textcolor{comment}{! value in the vertical profile.}} \DoxyCodeLine{599 pos = i*15+(m-\/2)*5} \DoxyCodeLine{600 t15(pos+1) = w\_left*ttl + w\_right*ttr} \DoxyCodeLine{601 t15(pos+5) = w\_left*tbl + w\_right*tbr} \DoxyCodeLine{602 } \DoxyCodeLine{603 s15(pos+1) = w\_left*stl + w\_right*str} \DoxyCodeLine{604 s15(pos+5) = w\_left*sbl + w\_right*sbr} \DoxyCodeLine{605 } \DoxyCodeLine{606 p15(pos+1) = -\/gxrho*(w\_left*e(i,j,k) + w\_right*e(i,j+1,k))} \DoxyCodeLine{607 } \DoxyCodeLine{608 \textcolor{comment}{! Pressure}} \DoxyCodeLine{609 \textcolor{keywordflow}{do} n=2,5} \DoxyCodeLine{610 p15(pos+n) = p15(pos+n-\/1) + gxrho*0.25*dz\_y(m,i)} \DoxyCodeLine{611 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{612 } \DoxyCodeLine{613 \textcolor{comment}{! Salinity and temperature (linear interpolation in the vertical)}} \DoxyCodeLine{614 \textcolor{keywordflow}{do} n=2,4} \DoxyCodeLine{615 s15(pos+n) = wt\_t(n) * s15(pos+1) + wt\_b(n) * s15(pos+5)} \DoxyCodeLine{616 t15(pos+n) = wt\_t(n) * t15(pos+1) + wt\_b(n) * t15(pos+5)} \DoxyCodeLine{617 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{618 \textcolor{keywordflow}{if} (use\_vart) t215(pos+1:pos+5) = w\_left*tv\%varT(i,j,k) + w\_right*tv\%varT(i,j+1,k)} \DoxyCodeLine{619 \textcolor{keywordflow}{if} (use\_covarts) ts15(pos+1:pos+5) = w\_left*tv\%covarTS(i,j,k) + w\_right*tv\%covarTS(i,j+1,k)} \DoxyCodeLine{620 \textcolor{keywordflow}{if} (use\_vars) s215(pos+1:pos+5) = w\_left*tv\%varS(i,j,k) + w\_right*tv\%varS(i,j+1,k)} \DoxyCodeLine{621 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{622 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{623 } \DoxyCodeLine{624 \textcolor{keywordflow}{if} (use\_stanley\_eos) \textcolor{keywordflow}{then}} \DoxyCodeLine{625 \textcolor{keywordflow}{if} (rho\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{626 \textcolor{keyword}{call }calculate\_density(t15(15*hi\%isc+1:), s15(15*hi\%isc+1:), p15(15*hi\%isc+1:), \&} \DoxyCodeLine{627 t215(15*hi\%isc+1:), ts15(15*hi\%isc+1:), s215(15*hi\%isc+1:), \&} \DoxyCodeLine{628 r15(15*hi\%isc+1:), 1, 15*(hi\%iec-\/hi\%isc+1), eos, \&} \DoxyCodeLine{629 rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{630 \textcolor{keywordflow}{else}} \DoxyCodeLine{631 \textcolor{keyword}{call }calculate\_density(t15(15*hi\%isc+1:), s15(15*hi\%isc+1:), p15(15*hi\%isc+1:), \&} \DoxyCodeLine{632 t215(15*hi\%isc+1:), ts15(15*hi\%isc+1:), s215(15*hi\%isc+1:), \&} \DoxyCodeLine{633 r15(15*hi\%isc+1:), 1, 15*(hi\%iec-\/hi\%isc+1), eos, rho\_ref=rho\_ref\_mks)} \DoxyCodeLine{634 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{635 \textcolor{keywordflow}{else}} \DoxyCodeLine{636 \textcolor{keywordflow}{if} (rho\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{637 \textcolor{keyword}{call }calculate\_density(t15(15*hi\%isc+1:), s15(15*hi\%isc+1:), p15(15*hi\%isc+1:), \&} \DoxyCodeLine{638 r15(15*hi\%isc+1:), 1, 15*(hi\%iec-\/hi\%isc+1), eos, \&} \DoxyCodeLine{639 rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{640 \textcolor{keywordflow}{else}} \DoxyCodeLine{641 \textcolor{keyword}{call }calculate\_density(t15(15*hi\%isc+1:), s15(15*hi\%isc+1:), p15(15*hi\%isc+1:), \&} \DoxyCodeLine{642 r15(15*hi\%isc+1:), 1, 15*(hi\%iec-\/hi\%isc+1), eos, rho\_ref=rho\_ref\_mks)} \DoxyCodeLine{643 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{644 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{645 } \DoxyCodeLine{646 \textcolor{keywordflow}{do} i=hi\%isc,hi\%iec} \DoxyCodeLine{647 intz(1) = dpa(i,j) ; intz(5) = dpa(i,j+1)} \DoxyCodeLine{648 } \DoxyCodeLine{649 \textcolor{comment}{! Use Boole's rule to estimate the pressure anomaly change.}} \DoxyCodeLine{650 \textcolor{keywordflow}{do} m = 2,4} \DoxyCodeLine{651 pos = i*15+(m-\/2)*5} \DoxyCodeLine{652 intz(m) = g\_e*dz\_y(m,i)*( c1\_90*(7.0*(r15(pos+1)+r15(pos+5)) + \&} \DoxyCodeLine{653 32.0*(r15(pos+2)+r15(pos+4)) + \&} \DoxyCodeLine{654 12.0*r15(pos+3)))} \DoxyCodeLine{655 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{656 \textcolor{comment}{! Use Boole's rule to integrate the values.}} \DoxyCodeLine{657 inty\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + \&} \DoxyCodeLine{658 12.0*intz(3))} \DoxyCodeLine{659 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{660 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{661 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__density__integrals_a3bf090e5cbb58811b3dd0ee4de80f999}\label{namespacemom__density__integrals_a3bf090e5cbb58811b3dd0ee4de80f999}} \index{mom\_density\_integrals@{mom\_density\_integrals}!int\_density\_dz\_generic\_ppm@{int\_density\_dz\_generic\_ppm}} \index{int\_density\_dz\_generic\_ppm@{int\_density\_dz\_generic\_ppm}!mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsubsection{\texorpdfstring{int\_density\_dz\_generic\_ppm()}{int\_density\_dz\_generic\_ppm()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+density\+\_\+integrals\+::int\+\_\+density\+\_\+dz\+\_\+generic\+\_\+ppm (\begin{DoxyParamCaption}\item[{integer, intent(in)}]{k, }\item[{type(thermo\+\_\+var\+\_\+ptrs), intent(in)}]{tv, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi),szk\+\_\+(gv)), intent(in)}]{T\+\_\+t, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi),szk\+\_\+(gv)), intent(in)}]{T\+\_\+b, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi),szk\+\_\+(gv)), intent(in)}]{S\+\_\+t, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi),szk\+\_\+(gv)), intent(in)}]{S\+\_\+b, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi),szk\+\_\+(gv)+1), intent(in)}]{e, }\item[{real, intent(in)}]{rho\+\_\+ref, }\item[{real, intent(in)}]{rho\+\_\+0, }\item[{real, intent(in)}]{G\+\_\+e, }\item[{real, intent(in)}]{dz\+\_\+subroundoff, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{bathyT, }\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\item[{type(verticalgrid\+\_\+type), intent(in)}]{GV, }\item[{type(eos\+\_\+type), pointer}]{E\+OS, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(inout)}]{dpa, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(inout), optional}]{intz\+\_\+dpa, }\item[{real, dimension( hi \%isdb\+: hi \%iedb, hi \%jsd\+: hi \%jed), intent(inout), optional}]{intx\+\_\+dpa, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsdb\+: hi \%jedb), intent(inout), optional}]{inty\+\_\+dpa, }\item[{logical, intent(in), optional}]{use\+Mass\+Wght\+Interp }\end{DoxyParamCaption})} Compute pressure gradient force integrals for layer \char`\"{}k\char`\"{} and the case where T and S are parabolic profiles. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em k} & Layer index to calculate integrals for \\ \hline \mbox{\texttt{ in}} & {\em hi} & Ocean horizontal index structures for the input arrays \\ \hline \mbox{\texttt{ in}} & {\em gv} & Vertical grid structure \\ \hline \mbox{\texttt{ in}} & {\em tv} & Thermodynamic variables \\ \hline \mbox{\texttt{ in}} & {\em t\+\_\+t} & Potential temperature at the cell top \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em t\+\_\+b} & Potential temperature at the cell bottom \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+t} & Salinity at the cell top \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+b} & Salinity at the cell bottom \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em e} & Height of interfaces \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+ref} & A mean density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is subtracted out to reduce the magnitude of each of the integrals. \\ \hline \mbox{\texttt{ in}} & {\em rho\+\_\+0} & A density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is used to calculate the pressure (as p$\sim$=-\/z$\ast$rho\+\_\+0$\ast$\+G\+\_\+e) used in the equation of state. \\ \hline \mbox{\texttt{ in}} & {\em g\+\_\+e} & The Earth\textquotesingle{}s gravitational acceleration \mbox{[}m s-\/2\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em dz\+\_\+subroundoff} & A minuscule thickness change \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em bathyt} & The depth of the bathymetry \mbox{[}Z $\sim$$>$ m\mbox{]} \\ \hline & {\em eos} & Equation of state structure \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ in,out}} & {\em dpa} & The change in the pressure anomaly across the layer \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} \\ \hline \mbox{\texttt{ in,out}} & {\em intz\+\_\+dpa} & The integral through the thickness of the layer of \\ \hline \mbox{\texttt{ in,out}} & {\em intx\+\_\+dpa} & The integral in x of the difference between the \\ \hline \mbox{\texttt{ in,out}} & {\em inty\+\_\+dpa} & The integral in y of the difference between the \\ \hline \mbox{\texttt{ in}} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals. \\ \hline \end{DoxyParams} Definition at line 670 of file M\+O\+M\+\_\+density\+\_\+integrals.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{670 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: k\textcolor{comment}{ !< Layer index to calculate integrals for}} \DoxyCodeLine{671 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: HI\textcolor{comment}{ !< Ocean horizontal index structures for the input arrays}} \DoxyCodeLine{672 \textcolor{keywordtype}{type}(verticalGrid\_type), \textcolor{keywordtype}{intent(in)} :: GV\textcolor{comment}{ !< Vertical grid structure}} \DoxyCodeLine{673 \textcolor{keywordtype}{type}(thermo\_var\_ptrs), \textcolor{keywordtype}{intent(in)} :: tv\textcolor{comment}{ !< Thermodynamic variables}} \DoxyCodeLine{674 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV))}, \&} \DoxyCodeLine{675 \textcolor{keywordtype}{intent(in)} :: T\_t\textcolor{comment}{ !< Potential temperature at the cell top [degC]}} \DoxyCodeLine{676 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV))}, \&} \DoxyCodeLine{677 \textcolor{keywordtype}{intent(in)} :: T\_b\textcolor{comment}{ !< Potential temperature at the cell bottom [degC]}} \DoxyCodeLine{678 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV))}, \&} \DoxyCodeLine{679 \textcolor{keywordtype}{intent(in)} :: S\_t\textcolor{comment}{ !< Salinity at the cell top [ppt]}} \DoxyCodeLine{680 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV))}, \&} \DoxyCodeLine{681 \textcolor{keywordtype}{intent(in)} :: S\_b\textcolor{comment}{ !< Salinity at the cell bottom [ppt]}} \DoxyCodeLine{682 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI),SZK\_(GV)+1)}, \&} \DoxyCodeLine{683 \textcolor{keywordtype}{intent(in)} :: e\textcolor{comment}{ !< Height of interfaces [Z ~> m]}} \DoxyCodeLine{684 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A mean density [R ~> kg m-\/3] or [kg m-\/3], that is}} \DoxyCodeLine{685 \textcolor{comment}{ !! subtracted out to reduce the magnitude of each of the integrals.}} \DoxyCodeLine{686 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: rho\_0\textcolor{comment}{ !< A density [R ~> kg m-\/3] or [kg m-\/3], that is used to calculate}} \DoxyCodeLine{687 \textcolor{comment}{ !! the pressure (as p~=-\/z*rho\_0*G\_e) used in the equation of state.}} \DoxyCodeLine{688 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: G\_e\textcolor{comment}{ !< The Earth's gravitational acceleration [m s-\/2]}} \DoxyCodeLine{689 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: dz\_subroundoff\textcolor{comment}{ !< A minuscule thickness change [Z ~> m]}} \DoxyCodeLine{690 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{691 \textcolor{keywordtype}{intent(in)} :: bathyT\textcolor{comment}{ !< The depth of the bathymetry [Z ~> m]}} \DoxyCodeLine{692 \textcolor{keywordtype}{type}(EOS\_type), \textcolor{keywordtype}{pointer} :: EOS\textcolor{comment}{ !< Equation of state structure}} \DoxyCodeLine{693 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{694 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{695 \textcolor{keywordtype}{intent(inout)} :: dpa\textcolor{comment}{ !< The change in the pressure anomaly across the layer [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{696 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{697 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intz\_dpa\textcolor{comment}{ !< The integral through the thickness of the layer of}} \DoxyCodeLine{698 \textcolor{comment}{ !! the pressure anomaly relative to the anomaly at the}} \DoxyCodeLine{699 \textcolor{comment}{ !! top of the layer [R L2 Z T-\/2 ~> Pa m]}} \DoxyCodeLine{700 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZIB\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{701 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intx\_dpa\textcolor{comment}{ !< The integral in x of the difference between the}} \DoxyCodeLine{702 \textcolor{comment}{ !! pressure anomaly at the top and bottom of the layer}} \DoxyCodeLine{703 \textcolor{comment}{ !! divided by the x grid spacing [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{704 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJB\_(HI))}, \&} \DoxyCodeLine{705 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: inty\_dpa\textcolor{comment}{ !< The integral in y of the difference between the}} \DoxyCodeLine{706 \textcolor{comment}{ !! pressure anomaly at the top and bottom of the layer}} \DoxyCodeLine{707 \textcolor{comment}{ !! divided by the y grid spacing [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{708 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: useMassWghtInterp\textcolor{comment}{ !< If true, uses mass weighting to}} \DoxyCodeLine{709 \textcolor{comment}{ !! interpolate T/S for top and bottom integrals.}} \DoxyCodeLine{710 } \DoxyCodeLine{711 \textcolor{comment}{! This subroutine calculates (by numerical quadrature) integrals of}} \DoxyCodeLine{712 \textcolor{comment}{! pressure anomalies across layers, which are required for calculating the}} \DoxyCodeLine{713 \textcolor{comment}{! finite-\/volume form pressure accelerations in a Boussinesq model. The one}} \DoxyCodeLine{714 \textcolor{comment}{! potentially dodgy assumption here is that rho\_0 is used both in the denominator}} \DoxyCodeLine{715 \textcolor{comment}{! of the accelerations, and in the pressure used to calculated density (the}} \DoxyCodeLine{716 \textcolor{comment}{! latter being -\/z*rho\_0*G\_e). These two uses could be separated if need be.}} \DoxyCodeLine{717 \textcolor{comment}{!}} \DoxyCodeLine{718 \textcolor{comment}{! It is assumed that the salinity and temperature profiles are parabolic in the}} \DoxyCodeLine{719 \textcolor{comment}{! vertical. The top and bottom values within each layer are provided and}} \DoxyCodeLine{720 \textcolor{comment}{! a parabolic interpolation is used to compute intermediate values.}} \DoxyCodeLine{721 } \DoxyCodeLine{722 \textcolor{comment}{! Local variables}} \DoxyCodeLine{723 \textcolor{keywordtype}{ real} :: T5(5) \textcolor{comment}{! Temperatures along a line of subgrid locations [degC]}} \DoxyCodeLine{724 \textcolor{keywordtype}{ real} :: S5(5) \textcolor{comment}{! Salinities along a line of subgrid locations [ppt]}} \DoxyCodeLine{725 \textcolor{keywordtype}{ real} :: T25(5) \textcolor{comment}{! SGS temperature variance along a line of subgrid locations [degC2]}} \DoxyCodeLine{726 \textcolor{keywordtype}{ real} :: TS5(5) \textcolor{comment}{! SGS temperature-\/salinity covariance along a line of subgrid locations [degC ppt]}} \DoxyCodeLine{727 \textcolor{keywordtype}{ real} :: S25(5) \textcolor{comment}{! SGS salinity variance along a line of subgrid locations [ppt2]}} \DoxyCodeLine{728 \textcolor{keywordtype}{ real} :: p5(5) \textcolor{comment}{! Pressures at five quadrature points, never rescaled from Pa [Pa]}} \DoxyCodeLine{729 \textcolor{keywordtype}{ real} :: r5(5) \textcolor{comment}{! Density anomalies from rho\_ref at quadrature points [R ~> kg m-\/3] or [kg m-\/3]}} \DoxyCodeLine{730 \textcolor{keywordtype}{ real} :: wt\_t(5), wt\_b(5) \textcolor{comment}{! Top and bottom weights [nondim]}} \DoxyCodeLine{731 \textcolor{keywordtype}{ real} :: rho\_anom \textcolor{comment}{! The integrated density anomaly [R ~> kg m-\/3] or [kg m-\/3]}} \DoxyCodeLine{732 \textcolor{keywordtype}{ real} :: w\_left, w\_right \textcolor{comment}{! Left and right weights [nondim]}} \DoxyCodeLine{733 \textcolor{keywordtype}{ real} :: intz(5) \textcolor{comment}{! The gravitational acceleration times the integrals of density}} \DoxyCodeLine{734 \textcolor{comment}{! with height at the 5 sub-\/column locations [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{735 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{parameter} :: C1\_90 = 1.0/90.0 \textcolor{comment}{! Rational constants.}} \DoxyCodeLine{736 \textcolor{keywordtype}{ real} :: GxRho \textcolor{comment}{! The gravitational acceleration times density and unit conversion factors [Pa Z-\/1 ~> kg m-\/2 s-\/2]}} \DoxyCodeLine{737 \textcolor{keywordtype}{ real} :: I\_Rho \textcolor{comment}{! The inverse of the Boussinesq density [R-\/1 ~> m3 kg-\/1] or [m3 kg-\/1]}} \DoxyCodeLine{738 \textcolor{keywordtype}{ real} :: rho\_scale \textcolor{comment}{! A scaling factor for densities from kg m-\/3 to R [R m3 kg-\/1 ~> 1]}} \DoxyCodeLine{739 \textcolor{keywordtype}{ real} :: rho\_ref\_mks \textcolor{comment}{! The reference density in MKS units, never rescaled from kg m-\/3 [kg m-\/3]}} \DoxyCodeLine{740 \textcolor{keywordtype}{ real} :: dz \textcolor{comment}{! Layer thicknesses at tracer points [Z ~> m]}} \DoxyCodeLine{741 \textcolor{keywordtype}{ real} :: massWeightToggle \textcolor{comment}{! A non-\/dimensional toggle factor (0 or 1) [nondim]}} \DoxyCodeLine{742 \textcolor{keywordtype}{ real} :: Ttl, Tbl, Tml, Ttr, Tbr, Tmr \textcolor{comment}{! Temperatures at the velocity cell corners [degC]}} \DoxyCodeLine{743 \textcolor{keywordtype}{ real} :: Stl, Sbl, Sml, Str, Sbr, Smr \textcolor{comment}{! Salinities at the velocity cell corners [ppt]}} \DoxyCodeLine{744 \textcolor{keywordtype}{ real} :: s6 \textcolor{comment}{! PPM curvature coefficient for S [ppt]}} \DoxyCodeLine{745 \textcolor{keywordtype}{ real} :: t6 \textcolor{comment}{! PPM curvature coefficient for T [degC]}} \DoxyCodeLine{746 \textcolor{keywordtype}{ real} :: T\_top, T\_mn, T\_bot \textcolor{comment}{! Left edge, cell mean and right edge values used in PPM reconstructions of T}} \DoxyCodeLine{747 \textcolor{keywordtype}{ real} :: S\_top, S\_mn, S\_bot \textcolor{comment}{! Left edge, cell mean and right edge values used in PPM reconstructions of S}} \DoxyCodeLine{748 \textcolor{keywordtype}{ real} :: hWght \textcolor{comment}{! A topographically limited thicknes weight [Z ~> m]}} \DoxyCodeLine{749 \textcolor{keywordtype}{ real} :: hL, hR \textcolor{comment}{! Thicknesses to the left and right [Z ~> m]}} \DoxyCodeLine{750 \textcolor{keywordtype}{ real} :: iDenom \textcolor{comment}{! The denominator of the thickness weight expressions [Z-\/2 ~> m-\/2]}} \DoxyCodeLine{751 \textcolor{keywordtype}{integer} :: Isq, Ieq, Jsq, Jeq, i, j, m, n} \DoxyCodeLine{752 \textcolor{keywordtype}{logical} :: use\_PPM \textcolor{comment}{! If false, assume zero curvature in reconstruction, i.e. PLM}} \DoxyCodeLine{753 \textcolor{keywordtype}{logical} :: use\_stanley\_eos \textcolor{comment}{! True is SGS variance fields exist in tv.}} \DoxyCodeLine{754 \textcolor{keywordtype}{logical} :: use\_varT, use\_varS, use\_covarTS} \DoxyCodeLine{755 } \DoxyCodeLine{756 isq = hi\%IscB ; ieq = hi\%IecB ; jsq = hi\%JscB ; jeq = hi\%JecB} \DoxyCodeLine{757 } \DoxyCodeLine{758 rho\_scale = us\%kg\_m3\_to\_R} \DoxyCodeLine{759 gxrho = us\%RL2\_T2\_to\_Pa * g\_e * rho\_0} \DoxyCodeLine{760 rho\_ref\_mks = rho\_ref * us\%R\_to\_kg\_m3} \DoxyCodeLine{761 i\_rho = 1.0 / rho\_0} \DoxyCodeLine{762 massweighttoggle = 0.} \DoxyCodeLine{763 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(usemasswghtinterp)) \textcolor{keywordflow}{then}} \DoxyCodeLine{764 \textcolor{keywordflow}{if} (usemasswghtinterp) massweighttoggle = 1.} \DoxyCodeLine{765 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{766 } \DoxyCodeLine{767 \textcolor{comment}{! In event PPM calculation is bypassed with use\_PPM=False}} \DoxyCodeLine{768 s6 = 0.} \DoxyCodeLine{769 t6 = 0.} \DoxyCodeLine{770 use\_ppm = .true. \textcolor{comment}{! This is a place-\/holder to allow later re-\/use of this function}} \DoxyCodeLine{771 } \DoxyCodeLine{772 use\_vart = \textcolor{keyword}{associated}(tv\%varT)} \DoxyCodeLine{773 use\_covarts = \textcolor{keyword}{associated}(tv\%covarTS)} \DoxyCodeLine{774 use\_vars = \textcolor{keyword}{associated}(tv\%varS)} \DoxyCodeLine{775 use\_stanley\_eos = use\_vart .or. use\_covarts .or. use\_vars} \DoxyCodeLine{776 t25(:) = 0.} \DoxyCodeLine{777 ts5(:) = 0.} \DoxyCodeLine{778 s25(:) = 0.} \DoxyCodeLine{779 } \DoxyCodeLine{780 \textcolor{keywordflow}{do} n = 1, 5} \DoxyCodeLine{781 wt\_t(n) = 0.25 * real(5-\/n)} \DoxyCodeLine{782 wt\_b(n) = 1.0 -\/ wt\_t(n)} \DoxyCodeLine{783 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{784 } \DoxyCodeLine{785 \textcolor{comment}{! 1. Compute vertical integrals}} \DoxyCodeLine{786 \textcolor{keywordflow}{do} j=jsq,jeq+1 ; \textcolor{keywordflow}{do} i=isq,ieq+1} \DoxyCodeLine{787 \textcolor{keywordflow}{if} (use\_ppm) \textcolor{keywordflow}{then}} \DoxyCodeLine{788 \textcolor{comment}{! Curvature coefficient of the parabolas}} \DoxyCodeLine{789 s6 = 3.0 * ( 2.0*tv\%S(i,j,k) -\/ ( s\_t(i,j,k) + s\_b(i,j,k) ) )} \DoxyCodeLine{790 t6 = 3.0 * ( 2.0*tv\%T(i,j,k) -\/ ( t\_t(i,j,k) + t\_b(i,j,k) ) )} \DoxyCodeLine{791 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{792 dz = e(i,j,k) -\/ e(i,j,k+1)} \DoxyCodeLine{793 \textcolor{keywordflow}{do} n=1,5} \DoxyCodeLine{794 p5(n) = -\/gxrho*(e(i,j,k) -\/ 0.25*real(n-\/1)*dz)} \DoxyCodeLine{795 \textcolor{comment}{! Salinity and temperature points are reconstructed with PPM}} \DoxyCodeLine{796 s5(n) = wt\_t(n) * s\_t(i,j,k) + wt\_b(n) * ( s\_b(i,j,k) + s6 * wt\_t(n) )} \DoxyCodeLine{797 t5(n) = wt\_t(n) * t\_t(i,j,k) + wt\_b(n) * ( t\_b(i,j,k) + t6 * wt\_t(n) )} \DoxyCodeLine{798 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{799 \textcolor{keywordflow}{if} (use\_stanley\_eos) \textcolor{keywordflow}{then}} \DoxyCodeLine{800 \textcolor{keywordflow}{if} (use\_vart) t25(:) = tv\%varT(i,j,k)} \DoxyCodeLine{801 \textcolor{keywordflow}{if} (use\_covarts) ts5(:) = tv\%covarTS(i,j,k)} \DoxyCodeLine{802 \textcolor{keywordflow}{if} (use\_vars) s25(:) = tv\%varS(i,j,k)} \DoxyCodeLine{803 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, t25, ts5, s25, r5, \&} \DoxyCodeLine{804 1, 5, eos, rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{805 \textcolor{keywordflow}{else}} \DoxyCodeLine{806 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, 5, eos, rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{807 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{808 } \DoxyCodeLine{809 \textcolor{comment}{! Use Boole's rule to estimate the pressure anomaly change.}} \DoxyCodeLine{810 rho\_anom = c1\_90*(7.0*(r5(1)+r5(5)) + 32.0*(r5(2)+r5(4)) + 12.0*r5(3))} \DoxyCodeLine{811 dpa(i,j) = g\_e*dz*rho\_anom} \DoxyCodeLine{812 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intz\_dpa)) \textcolor{keywordflow}{then}} \DoxyCodeLine{813 \textcolor{comment}{! Use a Boole's-\/rule-\/like fifth-\/order accurate estimate of}} \DoxyCodeLine{814 \textcolor{comment}{! the double integral of the pressure anomaly.}} \DoxyCodeLine{815 intz\_dpa(i,j) = 0.5*g\_e*dz**2 * \&} \DoxyCodeLine{816 (rho\_anom -\/ c1\_90*(16.0*(r5(4)-\/r5(2)) + 7.0*(r5(5)-\/r5(1))) )} \DoxyCodeLine{817 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{818 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} \textcolor{comment}{! end loops on j and i}} \DoxyCodeLine{819 } \DoxyCodeLine{820 \textcolor{comment}{! 2. Compute horizontal integrals in the x direction}} \DoxyCodeLine{821 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=hi\%jsc,hi\%jec ; \textcolor{keywordflow}{do} i=isq,ieq} \DoxyCodeLine{822 \textcolor{comment}{! Corner values of T and S}} \DoxyCodeLine{823 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{824 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation}} \DoxyCodeLine{825 \textcolor{comment}{! of T,S along the top and bottom integrals, almost like thickness}} \DoxyCodeLine{826 \textcolor{comment}{! weighting.}} \DoxyCodeLine{827 \textcolor{comment}{! Note: To work in terrain following coordinates we could offset}} \DoxyCodeLine{828 \textcolor{comment}{! this distance by the layer thickness to replicate other models.}} \DoxyCodeLine{829 hwght = massweighttoggle * \&} \DoxyCodeLine{830 max(0., -\/bathyt(i,j)-\/e(i+1,j,k), -\/bathyt(i+1,j)-\/e(i,j,k))} \DoxyCodeLine{831 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{832 hl = (e(i,j,k) -\/ e(i,j,k+1)) + dz\_subroundoff} \DoxyCodeLine{833 hr = (e(i+1,j,k) -\/ e(i+1,j,k+1)) + dz\_subroundoff} \DoxyCodeLine{834 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{835 idenom = 1./( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{836 ttl = ( (hwght*hr)*t\_t(i+1,j,k) + (hwght*hl + hr*hl)*t\_t(i,j,k) ) * idenom} \DoxyCodeLine{837 tbl = ( (hwght*hr)*t\_b(i+1,j,k) + (hwght*hl + hr*hl)*t\_b(i,j,k) ) * idenom} \DoxyCodeLine{838 tml = ( (hwght*hr)*tv\%T(i+1,j,k)+ (hwght*hl + hr*hl)*tv\%T(i,j,k) ) * idenom} \DoxyCodeLine{839 ttr = ( (hwght*hl)*t\_t(i,j,k) + (hwght*hr + hr*hl)*t\_t(i+1,j,k) ) * idenom} \DoxyCodeLine{840 tbr = ( (hwght*hl)*t\_b(i,j,k) + (hwght*hr + hr*hl)*t\_b(i+1,j,k) ) * idenom} \DoxyCodeLine{841 tmr = ( (hwght*hl)*tv\%T(i,j,k) + (hwght*hr + hr*hl)*tv\%T(i+1,j,k) ) * idenom} \DoxyCodeLine{842 stl = ( (hwght*hr)*s\_t(i+1,j,k) + (hwght*hl + hr*hl)*s\_t(i,j,k) ) * idenom} \DoxyCodeLine{843 sbl = ( (hwght*hr)*s\_b(i+1,j,k) + (hwght*hl + hr*hl)*s\_b(i,j,k) ) * idenom} \DoxyCodeLine{844 sml = ( (hwght*hr)*tv\%S(i+1,j,k) + (hwght*hl + hr*hl)*tv\%S(i,j,k) ) * idenom} \DoxyCodeLine{845 str = ( (hwght*hl)*s\_t(i,j,k) + (hwght*hr + hr*hl)*s\_t(i+1,j,k) ) * idenom} \DoxyCodeLine{846 sbr = ( (hwght*hl)*s\_b(i,j,k) + (hwght*hr + hr*hl)*s\_b(i+1,j,k) ) * idenom} \DoxyCodeLine{847 smr = ( (hwght*hl)*tv\%S(i,j,k) + (hwght*hr + hr*hl)*tv\%S(i+1,j,k) ) * idenom} \DoxyCodeLine{848 \textcolor{keywordflow}{else}} \DoxyCodeLine{849 ttl = t\_t(i,j,k); tbl = t\_b(i,j,k); ttr = t\_t(i+1,j,k); tbr = t\_b(i+1,j,k)} \DoxyCodeLine{850 tml = tv\%T(i,j,k); tmr = tv\%T(i+1,j,k)} \DoxyCodeLine{851 stl = s\_t(i,j,k); sbl = s\_b(i,j,k); str = s\_t(i+1,j,k); sbr = s\_b(i+1,j,k)} \DoxyCodeLine{852 sml = tv\%S(i,j,k); smr = tv\%S(i+1,j,k)} \DoxyCodeLine{853 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{854 } \DoxyCodeLine{855 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{856 w\_left = wt\_t(m) ; w\_right = wt\_b(m)} \DoxyCodeLine{857 } \DoxyCodeLine{858 \textcolor{comment}{! Salinity and temperature points are linearly interpolated in}} \DoxyCodeLine{859 \textcolor{comment}{! the horizontal. The subscript (1) refers to the top value in}} \DoxyCodeLine{860 \textcolor{comment}{! the vertical profile while subscript (5) refers to the bottom}} \DoxyCodeLine{861 \textcolor{comment}{! value in the vertical profile.}} \DoxyCodeLine{862 t\_top = w\_left*ttl + w\_right*ttr} \DoxyCodeLine{863 t\_mn = w\_left*tml + w\_right*tmr} \DoxyCodeLine{864 t\_bot = w\_left*tbl + w\_right*tbr} \DoxyCodeLine{865 } \DoxyCodeLine{866 s\_top = w\_left*stl + w\_right*str} \DoxyCodeLine{867 s\_mn = w\_left*sml + w\_right*smr} \DoxyCodeLine{868 s\_bot = w\_left*sbl + w\_right*sbr} \DoxyCodeLine{869 } \DoxyCodeLine{870 \textcolor{comment}{! Pressure}} \DoxyCodeLine{871 dz = w\_left*(e(i,j,k) -\/ e(i,j,k+1)) + w\_right*(e(i+1,j,k) -\/ e(i+1,j,k+1))} \DoxyCodeLine{872 p5(1) = -\/gxrho*(w\_left*e(i,j,k) + w\_right*e(i+1,j,k))} \DoxyCodeLine{873 \textcolor{keywordflow}{do} n=2,5} \DoxyCodeLine{874 p5(n) = p5(n-\/1) + gxrho*0.25*dz} \DoxyCodeLine{875 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{876 } \DoxyCodeLine{877 \textcolor{comment}{! Parabolic reconstructions in the vertical for T and S}} \DoxyCodeLine{878 \textcolor{keywordflow}{if} (use\_ppm) \textcolor{keywordflow}{then}} \DoxyCodeLine{879 \textcolor{comment}{! Coefficients of the parabolas}} \DoxyCodeLine{880 s6 = 3.0 * ( 2.0*s\_mn -\/ ( s\_top + s\_bot ) )} \DoxyCodeLine{881 t6 = 3.0 * ( 2.0*t\_mn -\/ ( t\_top + t\_bot ) )} \DoxyCodeLine{882 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{883 \textcolor{keywordflow}{do} n=1,5} \DoxyCodeLine{884 s5(n) = wt\_t(n) * s\_top + wt\_b(n) * ( s\_bot + s6 * wt\_t(n) )} \DoxyCodeLine{885 t5(n) = wt\_t(n) * t\_top + wt\_b(n) * ( t\_bot + t6 * wt\_t(n) )} \DoxyCodeLine{886 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{887 } \DoxyCodeLine{888 \textcolor{keywordflow}{if} (use\_stanley\_eos) \textcolor{keywordflow}{then}} \DoxyCodeLine{889 \textcolor{keywordflow}{if} (use\_vart) t25(:) = w\_left*tv\%varT(i,j,k) + w\_right*tv\%varT(i+1,j,k)} \DoxyCodeLine{890 \textcolor{keywordflow}{if} (use\_covarts) ts5(:) = w\_left*tv\%covarTS(i,j,k) + w\_right*tv\%covarTS(i+1,j,k)} \DoxyCodeLine{891 \textcolor{keywordflow}{if} (use\_vars) s25(:) = w\_left*tv\%varS(i,j,k) + w\_right*tv\%varS(i+1,j,k)} \DoxyCodeLine{892 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, t25, ts5, s25, r5, \&} \DoxyCodeLine{893 1, 5, eos, rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{894 \textcolor{keywordflow}{else}} \DoxyCodeLine{895 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, 5, eos, rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{896 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{897 } \DoxyCodeLine{898 \textcolor{comment}{! Use Boole's rule to estimate the pressure anomaly change.}} \DoxyCodeLine{899 intz(m) = g\_e*dz*( c1\_90*(7.0*(r5(1)+r5(5)) + 32.0*(r5(2)+r5(4)) + 12.0*r5(3)) )} \DoxyCodeLine{900 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! m}} \DoxyCodeLine{901 intz(1) = dpa(i,j) ; intz(5) = dpa(i+1,j)} \DoxyCodeLine{902 } \DoxyCodeLine{903 \textcolor{comment}{! Use Boole's rule to integrate the bottom pressure anomaly values in x.}} \DoxyCodeLine{904 intx\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + 12.0*intz(3))} \DoxyCodeLine{905 } \DoxyCodeLine{906 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{907 } \DoxyCodeLine{908 \textcolor{comment}{! 3. Compute horizontal integrals in the y direction}} \DoxyCodeLine{909 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=jsq,jeq ; \textcolor{keywordflow}{do} i=hi\%isc,hi\%iec} \DoxyCodeLine{910 \textcolor{comment}{! Corner values of T and S}} \DoxyCodeLine{911 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{912 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation}} \DoxyCodeLine{913 \textcolor{comment}{! of T,S along the top and bottom integrals, almost like thickness}} \DoxyCodeLine{914 \textcolor{comment}{! weighting.}} \DoxyCodeLine{915 \textcolor{comment}{! Note: To work in terrain following coordinates we could offset}} \DoxyCodeLine{916 \textcolor{comment}{! this distance by the layer thickness to replicate other models.}} \DoxyCodeLine{917 hwght = massweighttoggle * \&} \DoxyCodeLine{918 max(0., -\/bathyt(i,j)-\/e(i,j+1,k), -\/bathyt(i,j+1)-\/e(i,j,k))} \DoxyCodeLine{919 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{920 hl = (e(i,j,k) -\/ e(i,j,k+1)) + dz\_subroundoff} \DoxyCodeLine{921 hr = (e(i,j+1,k) -\/ e(i,j+1,k+1)) + dz\_subroundoff} \DoxyCodeLine{922 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{923 idenom = 1./( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{924 ttl = ( (hwght*hr)*t\_t(i,j+1,k) + (hwght*hl + hr*hl)*t\_t(i,j,k) ) * idenom} \DoxyCodeLine{925 tbl = ( (hwght*hr)*t\_b(i,j+1,k) + (hwght*hl + hr*hl)*t\_b(i,j,k) ) * idenom} \DoxyCodeLine{926 tml = ( (hwght*hr)*tv\%T(i,j+1,k)+ (hwght*hl + hr*hl)*tv\%T(i,j,k) ) * idenom} \DoxyCodeLine{927 ttr = ( (hwght*hl)*t\_t(i,j,k) + (hwght*hr + hr*hl)*t\_t(i,j+1,k) ) * idenom} \DoxyCodeLine{928 tbr = ( (hwght*hl)*t\_b(i,j,k) + (hwght*hr + hr*hl)*t\_b(i,j+1,k) ) * idenom} \DoxyCodeLine{929 tmr = ( (hwght*hl)*tv\%T(i,j,k) + (hwght*hr + hr*hl)*tv\%T(i,j+1,k) ) * idenom} \DoxyCodeLine{930 stl = ( (hwght*hr)*s\_t(i,j+1,k) + (hwght*hl + hr*hl)*s\_t(i,j,k) ) * idenom} \DoxyCodeLine{931 sbl = ( (hwght*hr)*s\_b(i,j+1,k) + (hwght*hl + hr*hl)*s\_b(i,j,k) ) * idenom} \DoxyCodeLine{932 sml = ( (hwght*hr)*tv\%S(i,j+1,k)+ (hwght*hl + hr*hl)*tv\%S(i,j,k) ) * idenom} \DoxyCodeLine{933 str = ( (hwght*hl)*s\_t(i,j,k) + (hwght*hr + hr*hl)*s\_t(i,j+1,k) ) * idenom} \DoxyCodeLine{934 sbr = ( (hwght*hl)*s\_b(i,j,k) + (hwght*hr + hr*hl)*s\_b(i,j+1,k) ) * idenom} \DoxyCodeLine{935 smr = ( (hwght*hl)*tv\%S(i,j,k) + (hwght*hr + hr*hl)*tv\%S(i,j+1,k) ) * idenom} \DoxyCodeLine{936 \textcolor{keywordflow}{else}} \DoxyCodeLine{937 ttl = t\_t(i,j,k); tbl = t\_b(i,j,k); ttr = t\_t(i,j+1,k); tbr = t\_b(i,j+1,k)} \DoxyCodeLine{938 tml = tv\%T(i,j,k); tmr = tv\%T(i,j+1,k)} \DoxyCodeLine{939 stl = s\_t(i,j,k); sbl = s\_b(i,j,k); str = s\_t(i,j+1,k); sbr = s\_b(i,j+1,k)} \DoxyCodeLine{940 sml = tv\%S(i,j,k); smr = tv\%S(i,j+1,k)} \DoxyCodeLine{941 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{942 } \DoxyCodeLine{943 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{944 w\_left = wt\_t(m) ; w\_right = wt\_b(m)} \DoxyCodeLine{945 } \DoxyCodeLine{946 \textcolor{comment}{! Salinity and temperature points are linearly interpolated in}} \DoxyCodeLine{947 \textcolor{comment}{! the horizontal. The subscript (1) refers to the top value in}} \DoxyCodeLine{948 \textcolor{comment}{! the vertical profile while subscript (5) refers to the bottom}} \DoxyCodeLine{949 \textcolor{comment}{! value in the vertical profile.}} \DoxyCodeLine{950 t\_top = w\_left*ttl + w\_right*ttr} \DoxyCodeLine{951 t\_mn = w\_left*tml + w\_right*tmr} \DoxyCodeLine{952 t\_bot = w\_left*tbl + w\_right*tbr} \DoxyCodeLine{953 } \DoxyCodeLine{954 s\_top = w\_left*stl + w\_right*str} \DoxyCodeLine{955 s\_mn = w\_left*sml + w\_right*smr} \DoxyCodeLine{956 s\_bot = w\_left*sbl + w\_right*sbr} \DoxyCodeLine{957 } \DoxyCodeLine{958 \textcolor{comment}{! Pressure}} \DoxyCodeLine{959 dz = w\_left*(e(i,j,k) -\/ e(i,j,k+1)) + w\_right*(e(i,j+1,k) -\/ e(i,j+1,k+1))} \DoxyCodeLine{960 p5(1) = -\/gxrho*(w\_left*e(i,j,k) + w\_right*e(i,j+1,k))} \DoxyCodeLine{961 \textcolor{keywordflow}{do} n=2,5} \DoxyCodeLine{962 p5(n) = p5(n-\/1) + gxrho*0.25*dz} \DoxyCodeLine{963 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{964 } \DoxyCodeLine{965 \textcolor{comment}{! Parabolic reconstructions in the vertical for T and S}} \DoxyCodeLine{966 \textcolor{keywordflow}{if} (use\_ppm) \textcolor{keywordflow}{then}} \DoxyCodeLine{967 \textcolor{comment}{! Coefficients of the parabolas}} \DoxyCodeLine{968 s6 = 3.0 * ( 2.0*s\_mn -\/ ( s\_top + s\_bot ) )} \DoxyCodeLine{969 t6 = 3.0 * ( 2.0*t\_mn -\/ ( t\_top + t\_bot ) )} \DoxyCodeLine{970 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{971 \textcolor{keywordflow}{do} n=1,5} \DoxyCodeLine{972 s5(n) = wt\_t(n) * s\_top + wt\_b(n) * ( s\_bot + s6 * wt\_t(n) )} \DoxyCodeLine{973 t5(n) = wt\_t(n) * t\_top + wt\_b(n) * ( t\_bot + t6 * wt\_t(n) )} \DoxyCodeLine{974 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{975 } \DoxyCodeLine{976 \textcolor{keywordflow}{if} (use\_stanley\_eos) \textcolor{keywordflow}{then}} \DoxyCodeLine{977 \textcolor{keywordflow}{if} (use\_vart) t25(:) = w\_left*tv\%varT(i,j,k) + w\_right*tv\%varT(i,j+1,k)} \DoxyCodeLine{978 \textcolor{keywordflow}{if} (use\_covarts) ts5(:) = w\_left*tv\%covarTS(i,j,k) + w\_right*tv\%covarTS(i,j+1,k)} \DoxyCodeLine{979 \textcolor{keywordflow}{if} (use\_vars) s25(:) = w\_left*tv\%varS(i,j,k) + w\_right*tv\%varS(i,j+1,k)} \DoxyCodeLine{980 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, t25, ts5, s25, r5, \&} \DoxyCodeLine{981 1, 5, eos, rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{982 \textcolor{keywordflow}{else}} \DoxyCodeLine{983 \textcolor{keyword}{call }calculate\_density(t5, s5, p5, r5, 1, 5, eos, rho\_ref=rho\_ref\_mks, scale=rho\_scale)} \DoxyCodeLine{984 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{985 } \DoxyCodeLine{986 \textcolor{comment}{! Use Boole's rule to estimate the pressure anomaly change.}} \DoxyCodeLine{987 intz(m) = g\_e*dz*( c1\_90*(7.0*(r5(1)+r5(5)) + 32.0*(r5(2)+r5(4)) + 12.0*r5(3)) )} \DoxyCodeLine{988 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! m}} \DoxyCodeLine{989 intz(1) = dpa(i,j) ; intz(5) = dpa(i,j+1)} \DoxyCodeLine{990 } \DoxyCodeLine{991 \textcolor{comment}{! Use Boole's rule to integrate the bottom pressure anomaly values in y.}} \DoxyCodeLine{992 inty\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + 12.0*intz(3))} \DoxyCodeLine{993 } \DoxyCodeLine{994 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{995 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__density__integrals_a86ebdfebaaea2ac0339dcabed482dd11}\label{namespacemom__density__integrals_a86ebdfebaaea2ac0339dcabed482dd11}} \index{mom\_density\_integrals@{mom\_density\_integrals}!int\_spec\_vol\_dp\_generic\_pcm@{int\_spec\_vol\_dp\_generic\_pcm}} \index{int\_spec\_vol\_dp\_generic\_pcm@{int\_spec\_vol\_dp\_generic\_pcm}!mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsubsection{\texorpdfstring{int\_spec\_vol\_dp\_generic\_pcm()}{int\_spec\_vol\_dp\_generic\_pcm()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+density\+\_\+integrals\+::int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+generic\+\_\+pcm (\begin{DoxyParamCaption}\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{T, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{S, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{p\+\_\+t, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{p\+\_\+b, }\item[{real, intent(in)}]{alpha\+\_\+ref, }\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\item[{type(eos\+\_\+type), pointer}]{E\+OS, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(inout)}]{dza, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(inout), optional}]{intp\+\_\+dza, }\item[{real, dimension( hi \%isdb\+: hi \%iedb, hi \%jsd\+: hi \%jed), intent(inout), optional}]{intx\+\_\+dza, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsdb\+: hi \%jedb), intent(inout), optional}]{inty\+\_\+dza, }\item[{integer, intent(in), optional}]{halo\+\_\+size, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in), optional}]{bathyP, }\item[{real, intent(in), optional}]{d\+P\+\_\+neglect, }\item[{logical, intent(in), optional}]{use\+Mass\+Wght\+Interp }\end{DoxyParamCaption})} This subroutine calculates integrals of specific volume anomalies in pressure across layers, which are required for calculating the finite-\/volume form pressure accelerations in a non-\/\+Boussinesq model. There are essentially no free assumptions, apart from the use of Boole\textquotesingle{}s rule quadrature to do the integrals. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em hi} & A horizontal index type structure. \\ \hline \mbox{\texttt{ in}} & {\em t} & Potential temperature of the layer \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s} & Salinity of the layer \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em p\+\_\+t} & Pressure atop the layer \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em p\+\_\+b} & Pressure below the layer \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em alpha\+\_\+ref} & A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals \mbox{[}R-\/1 $\sim$$>$ m3 kg-\/1\mbox{]} The calculation is mathematically identical with different values of alpha\+\_\+ref, but alpha\+\_\+ref alters the effects of roundoff, and answers do change. \\ \hline & {\em eos} & Equation of state structure \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ in,out}} & {\em dza} & The change in the geopotential anomaly \\ \hline \mbox{\texttt{ in,out}} & {\em intp\+\_\+dza} & The integral in pressure through the layer of \\ \hline \mbox{\texttt{ in,out}} & {\em intx\+\_\+dza} & The integral in x of the difference between \\ \hline \mbox{\texttt{ in,out}} & {\em inty\+\_\+dza} & The integral in y of the difference between \\ \hline \mbox{\texttt{ in}} & {\em halo\+\_\+size} & The width of halo points on which to calculate dza. \\ \hline \mbox{\texttt{ in}} & {\em bathyp} & The pressure at the bathymetry \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em dp\+\_\+neglect} & A minuscule pressure change with the same units as p\+\_\+t \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals. \\ \hline \end{DoxyParams} Definition at line 1065 of file M\+O\+M\+\_\+density\+\_\+integrals.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1065 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: HI\textcolor{comment}{ !< A horizontal index type structure.}} \DoxyCodeLine{1066 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1067 \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature of the layer [degC]}} \DoxyCodeLine{1068 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1069 \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity of the layer [ppt]}} \DoxyCodeLine{1070 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1071 \textcolor{keywordtype}{intent(in)} :: p\_t\textcolor{comment}{ !< Pressure atop the layer [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1072 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1073 \textcolor{keywordtype}{intent(in)} :: p\_b\textcolor{comment}{ !< Pressure below the layer [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1074 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: alpha\_ref\textcolor{comment}{ !< A mean specific volume that is subtracted out}} \DoxyCodeLine{1075 \textcolor{comment}{ !! to reduce the magnitude of each of the integrals [R-\/1 ~> m3 kg-\/1]}} \DoxyCodeLine{1076 \textcolor{comment}{ !! The calculation is mathematically identical with different values of}} \DoxyCodeLine{1077 \textcolor{comment}{ !! alpha\_ref, but alpha\_ref alters the effects of roundoff, and}} \DoxyCodeLine{1078 \textcolor{comment}{ !! answers do change.}} \DoxyCodeLine{1079 \textcolor{keywordtype}{type}(EOS\_type), \textcolor{keywordtype}{pointer} :: EOS\textcolor{comment}{ !< Equation of state structure}} \DoxyCodeLine{1080 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{1081 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1082 \textcolor{keywordtype}{intent(inout)} :: dza\textcolor{comment}{ !< The change in the geopotential anomaly}} \DoxyCodeLine{1083 \textcolor{comment}{ !! across the layer [L2 T-\/2 ~> m2 s-\/2] or [m2 s-\/2]}} \DoxyCodeLine{1084 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1085 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intp\_dza\textcolor{comment}{ !< The integral in pressure through the layer of}} \DoxyCodeLine{1086 \textcolor{comment}{ !! the geopotential anomaly relative to the anomaly at the bottom of the}} \DoxyCodeLine{1087 \textcolor{comment}{ !! layer [R L4 T-\/4 ~> Pa m2 s-\/2] or [Pa m2 s-\/2]}} \DoxyCodeLine{1088 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZIB\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1089 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intx\_dza\textcolor{comment}{ !< The integral in x of the difference between}} \DoxyCodeLine{1090 \textcolor{comment}{ !! the geopotential anomaly at the top and bottom of the layer divided}} \DoxyCodeLine{1091 \textcolor{comment}{ !! by the x grid spacing [L2 T-\/2 ~> m2 s-\/2] or [m2 s-\/2]}} \DoxyCodeLine{1092 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJB\_(HI))}, \&} \DoxyCodeLine{1093 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: inty\_dza\textcolor{comment}{ !< The integral in y of the difference between}} \DoxyCodeLine{1094 \textcolor{comment}{ !! the geopotential anomaly at the top and bottom of the layer divided}} \DoxyCodeLine{1095 \textcolor{comment}{ !! by the y grid spacing [L2 T-\/2 ~> m2 s-\/2] or [m2 s-\/2]}} \DoxyCodeLine{1096 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: halo\_size\textcolor{comment}{ !< The width of halo points on which to calculate dza.}} \DoxyCodeLine{1097 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1098 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: bathyP\textcolor{comment}{ !< The pressure at the bathymetry [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1099 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: dP\_neglect\textcolor{comment}{ !< A minuscule pressure change with}} \DoxyCodeLine{1100 \textcolor{comment}{ !! the same units as p\_t [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1101 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: useMassWghtInterp\textcolor{comment}{ !< If true, uses mass weighting}} \DoxyCodeLine{1102 \textcolor{comment}{ !! to interpolate T/S for top and bottom integrals.}} \DoxyCodeLine{1103 } \DoxyCodeLine{1104 \textcolor{comment}{! This subroutine calculates analytical and nearly-\/analytical integrals in}} \DoxyCodeLine{1105 \textcolor{comment}{! pressure across layers of geopotential anomalies, which are required for}} \DoxyCodeLine{1106 \textcolor{comment}{! calculating the finite-\/volume form pressure accelerations in a non-\/Boussinesq}} \DoxyCodeLine{1107 \textcolor{comment}{! model. There are essentially no free assumptions, apart from the use of}} \DoxyCodeLine{1108 \textcolor{comment}{! Boole's rule to do the horizontal integrals, and from a truncation in the}} \DoxyCodeLine{1109 \textcolor{comment}{! series for log(1-\/eps/1+eps) that assumes that |eps| < 0.34.}} \DoxyCodeLine{1110 } \DoxyCodeLine{1111 \textcolor{comment}{! Local variables}} \DoxyCodeLine{1112 \textcolor{keywordtype}{ real} :: T5(5) \textcolor{comment}{! Temperatures at five quadrature points [degC]}} \DoxyCodeLine{1113 \textcolor{keywordtype}{ real} :: S5(5) \textcolor{comment}{! Salinities at five quadrature points [ppt]}} \DoxyCodeLine{1114 \textcolor{keywordtype}{ real} :: p5(5) \textcolor{comment}{! Pressures at five quadrature points, scaled back to Pa if necessary [Pa]}} \DoxyCodeLine{1115 \textcolor{keywordtype}{ real} :: a5(5) \textcolor{comment}{! Specific volumes at five quadrature points [R-\/1 ~> m3 kg-\/1] or [m3 kg-\/1]}} \DoxyCodeLine{1116 \textcolor{keywordtype}{ real} :: alpha\_anom \textcolor{comment}{! The depth averaged specific density anomaly [R-\/1 ~> m3 kg-\/1]}} \DoxyCodeLine{1117 \textcolor{keywordtype}{ real} :: dp \textcolor{comment}{! The pressure change through a layer [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1118 \textcolor{keywordtype}{ real} :: hWght \textcolor{comment}{! A pressure-\/thickness below topography [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1119 \textcolor{keywordtype}{ real} :: hL, hR \textcolor{comment}{! Pressure-\/thicknesses of the columns to the left and right [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1120 \textcolor{keywordtype}{ real} :: alpha\_ref\_mks \textcolor{comment}{! The reference specific volume in MKS units, never rescaled from m3 kg-\/1 [m3 kg-\/1]}} \DoxyCodeLine{1121 \textcolor{keywordtype}{ real} :: iDenom \textcolor{comment}{! The inverse of the denominator in the weights [T4 R-\/2 L-\/4 ~> Pa-\/2]}} \DoxyCodeLine{1122 \textcolor{keywordtype}{ real} :: hWt\_LL, hWt\_LR \textcolor{comment}{! hWt\_LA is the weighted influence of A on the left column [nondim]}} \DoxyCodeLine{1123 \textcolor{keywordtype}{ real} :: hWt\_RL, hWt\_RR \textcolor{comment}{! hWt\_RA is the weighted influence of A on the right column [nondim]}} \DoxyCodeLine{1124 \textcolor{keywordtype}{ real} :: wt\_L, wt\_R \textcolor{comment}{! The linear weights of the left and right columns [nondim]}} \DoxyCodeLine{1125 \textcolor{keywordtype}{ real} :: wtT\_L, wtT\_R \textcolor{comment}{! The weights for tracers from the left and right columns [nondim]}} \DoxyCodeLine{1126 \textcolor{keywordtype}{ real} :: intp(5) \textcolor{comment}{! The integrals of specific volume with pressure at the}} \DoxyCodeLine{1127 \textcolor{comment}{! 5 sub-\/column locations [L2 T-\/2 ~> m2 s-\/2]}} \DoxyCodeLine{1128 \textcolor{keywordtype}{ real} :: RL2\_T2\_to\_Pa \textcolor{comment}{! A unit conversion factor from the rescaled units of pressure to Pa [Pa T2 R-\/1 L-\/2 ~> 1]}} \DoxyCodeLine{1129 \textcolor{keywordtype}{ real} :: SV\_scale \textcolor{comment}{! A multiplicative factor by which to scale specific}} \DoxyCodeLine{1130 \textcolor{comment}{! volume from m3 kg-\/1 to the desired units [kg m-\/3 R-\/1 ~> 1]}} \DoxyCodeLine{1131 \textcolor{keywordtype}{logical} :: do\_massWeight \textcolor{comment}{! Indicates whether to do mass weighting.}} \DoxyCodeLine{1132 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{parameter} :: C1\_90 = 1.0/90.0 \textcolor{comment}{! A rational constant.}} \DoxyCodeLine{1133 \textcolor{keywordtype}{integer} :: Isq, Ieq, Jsq, Jeq, ish, ieh, jsh, jeh, i, j, m, n, halo} \DoxyCodeLine{1134 } \DoxyCodeLine{1135 isq = hi\%IscB ; ieq = hi\%IecB ; jsq = hi\%JscB ; jeq = hi\%JecB} \DoxyCodeLine{1136 halo = 0 ; \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(halo\_size)) halo = max(halo\_size,0)} \DoxyCodeLine{1137 ish = hi\%isc-\/halo ; ieh = hi\%iec+halo ; jsh = hi\%jsc-\/halo ; jeh = hi\%jec+halo} \DoxyCodeLine{1138 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dza)) \textcolor{keywordflow}{then} ; ish = min(isq,ish) ; ieh = max(ieq+1,ieh);\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1139 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dza)) \textcolor{keywordflow}{then} ; jsh = min(jsq,jsh) ; jeh = max(jeq+1,jeh);\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1140 } \DoxyCodeLine{1141 sv\_scale = us\%R\_to\_kg\_m3} \DoxyCodeLine{1142 rl2\_t2\_to\_pa = us\%RL2\_T2\_to\_Pa} \DoxyCodeLine{1143 alpha\_ref\_mks = alpha\_ref * us\%kg\_m3\_to\_R} \DoxyCodeLine{1144 } \DoxyCodeLine{1145 do\_massweight = .false.} \DoxyCodeLine{1146 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(usemasswghtinterp)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (usemasswghtinterp) \textcolor{keywordflow}{then}} \DoxyCodeLine{1147 do\_massweight = .true.} \DoxyCodeLine{1148 \textcolor{keywordflow}{if} (.not.\textcolor{keyword}{present}(bathyp)) \textcolor{keyword}{call }mom\_error(fatal, \textcolor{stringliteral}{"int\_spec\_vol\_dp\_generic: "}//\&} \DoxyCodeLine{1149 \textcolor{stringliteral}{"bathyP must be present if useMassWghtInterp is present and true."})} \DoxyCodeLine{1150 \textcolor{keywordflow}{if} (.not.\textcolor{keyword}{present}(dp\_neglect)) \textcolor{keyword}{call }mom\_error(fatal, \textcolor{stringliteral}{"int\_spec\_vol\_dp\_generic: "}//\&} \DoxyCodeLine{1151 \textcolor{stringliteral}{"dP\_neglect must be present if useMassWghtInterp is present and true."})} \DoxyCodeLine{1152 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1153 } \DoxyCodeLine{1154 \textcolor{keywordflow}{do} j=jsh,jeh ; \textcolor{keywordflow}{do} i=ish,ieh} \DoxyCodeLine{1155 dp = p\_b(i,j) -\/ p\_t(i,j)} \DoxyCodeLine{1156 \textcolor{keywordflow}{do} n=1,5} \DoxyCodeLine{1157 t5(n) = t(i,j) ; s5(n) = s(i,j)} \DoxyCodeLine{1158 p5(n) = rl2\_t2\_to\_pa * (p\_b(i,j) -\/ 0.25*real(n-\/1)*dp)} \DoxyCodeLine{1159 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1160 } \DoxyCodeLine{1161 \textcolor{keywordflow}{if} (sv\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1162 \textcolor{keyword}{call }calculate\_spec\_vol(t5, s5, p5, a5, 1, 5, eos, alpha\_ref\_mks, scale=sv\_scale)} \DoxyCodeLine{1163 \textcolor{keywordflow}{else}} \DoxyCodeLine{1164 \textcolor{keyword}{call }calculate\_spec\_vol(t5, s5, p5, a5, 1, 5, eos, alpha\_ref\_mks)} \DoxyCodeLine{1165 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1166 } \DoxyCodeLine{1167 \textcolor{comment}{! Use Boole's rule to estimate the interface height anomaly change.}} \DoxyCodeLine{1168 alpha\_anom = c1\_90*(7.0*(a5(1)+a5(5)) + 32.0*(a5(2)+a5(4)) + 12.0*a5(3))} \DoxyCodeLine{1169 dza(i,j) = dp*alpha\_anom} \DoxyCodeLine{1170 \textcolor{comment}{! Use a Boole's-\/rule-\/like fifth-\/order accurate estimate of the double integral of}} \DoxyCodeLine{1171 \textcolor{comment}{! the interface height anomaly.}} \DoxyCodeLine{1172 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intp\_dza)) intp\_dza(i,j) = 0.5*dp**2 * \&} \DoxyCodeLine{1173 (alpha\_anom -\/ c1\_90*(16.0*(a5(4)-\/a5(2)) + 7.0*(a5(5)-\/a5(1))) )} \DoxyCodeLine{1174 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1175 } \DoxyCodeLine{1176 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dza)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=hi\%jsc,hi\%jec ; \textcolor{keywordflow}{do} i=isq,ieq} \DoxyCodeLine{1177 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{1178 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of}} \DoxyCodeLine{1179 \textcolor{comment}{! T \& S along the top and bottom integrals, akin to thickness weighting.}} \DoxyCodeLine{1180 hwght = 0.0} \DoxyCodeLine{1181 \textcolor{keywordflow}{if} (do\_massweight) \&} \DoxyCodeLine{1182 hwght = max(0., bathyp(i,j)-\/p\_t(i+1,j), bathyp(i+1,j)-\/p\_t(i,j))} \DoxyCodeLine{1183 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{1184 hl = (p\_b(i,j) -\/ p\_t(i,j)) + dp\_neglect} \DoxyCodeLine{1185 hr = (p\_b(i+1,j) -\/ p\_t(i+1,j)) + dp\_neglect} \DoxyCodeLine{1186 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{1187 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{1188 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom} \DoxyCodeLine{1189 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom} \DoxyCodeLine{1190 \textcolor{keywordflow}{else}} \DoxyCodeLine{1191 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0} \DoxyCodeLine{1192 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1193 } \DoxyCodeLine{1194 intp(1) = dza(i,j) ; intp(5) = dza(i+1,j)} \DoxyCodeLine{1195 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{1196 wt\_l = 0.25*real(5-\/m) ; wt\_r = 1.0-\/wt\_l} \DoxyCodeLine{1197 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr} \DoxyCodeLine{1198 } \DoxyCodeLine{1199 \textcolor{comment}{! T, S, and p are interpolated in the horizontal. The p interpolation}} \DoxyCodeLine{1200 \textcolor{comment}{! is linear, but for T and S it may be thickness weighted.}} \DoxyCodeLine{1201 p5(1) = rl2\_t2\_to\_pa * (wt\_l*p\_b(i,j) + wt\_r*p\_b(i+1,j))} \DoxyCodeLine{1202 dp = wt\_l*(p\_b(i,j) -\/ p\_t(i,j)) + wt\_r*(p\_b(i+1,j) -\/ p\_t(i+1,j))} \DoxyCodeLine{1203 t5(1) = wtt\_l*t(i,j) + wtt\_r*t(i+1,j)} \DoxyCodeLine{1204 s5(1) = wtt\_l*s(i,j) + wtt\_r*s(i+1,j)} \DoxyCodeLine{1205 } \DoxyCodeLine{1206 \textcolor{keywordflow}{do} n=2,5} \DoxyCodeLine{1207 t5(n) = t5(1) ; s5(n) = s5(1) ; p5(n) = p5(n-\/1) -\/ rl2\_t2\_to\_pa * 0.25*dp} \DoxyCodeLine{1208 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1209 \textcolor{keywordflow}{if} (sv\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1210 \textcolor{keyword}{call }calculate\_spec\_vol(t5, s5, p5, a5, 1, 5, eos, alpha\_ref\_mks, scale=sv\_scale)} \DoxyCodeLine{1211 \textcolor{keywordflow}{else}} \DoxyCodeLine{1212 \textcolor{keyword}{call }calculate\_spec\_vol(t5, s5, p5, a5, 1, 5, eos, alpha\_ref\_mks)} \DoxyCodeLine{1213 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1214 } \DoxyCodeLine{1215 \textcolor{comment}{! Use Boole's rule to estimate the interface height anomaly change.}} \DoxyCodeLine{1216 intp(m) = dp*( c1\_90*(7.0*(a5(1)+a5(5)) + 32.0*(a5(2)+a5(4)) + \&} \DoxyCodeLine{1217 12.0*a5(3)))} \DoxyCodeLine{1218 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1219 \textcolor{comment}{! Use Boole's rule to integrate the interface height anomaly values in x.}} \DoxyCodeLine{1220 intx\_dza(i,j) = c1\_90*(7.0*(intp(1)+intp(5)) + 32.0*(intp(2)+intp(4)) + \&} \DoxyCodeLine{1221 12.0*intp(3))} \DoxyCodeLine{1222 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1223 } \DoxyCodeLine{1224 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dza)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=jsq,jeq ; \textcolor{keywordflow}{do} i=hi\%isc,hi\%iec} \DoxyCodeLine{1225 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{1226 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of}} \DoxyCodeLine{1227 \textcolor{comment}{! T \& S along the top and bottom integrals, akin to thickness weighting.}} \DoxyCodeLine{1228 hwght = 0.0} \DoxyCodeLine{1229 \textcolor{keywordflow}{if} (do\_massweight) \&} \DoxyCodeLine{1230 hwght = max(0., bathyp(i,j)-\/p\_t(i,j+1), bathyp(i,j+1)-\/p\_t(i,j))} \DoxyCodeLine{1231 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{1232 hl = (p\_b(i,j) -\/ p\_t(i,j)) + dp\_neglect} \DoxyCodeLine{1233 hr = (p\_b(i,j+1) -\/ p\_t(i,j+1)) + dp\_neglect} \DoxyCodeLine{1234 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{1235 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{1236 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom} \DoxyCodeLine{1237 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom} \DoxyCodeLine{1238 \textcolor{keywordflow}{else}} \DoxyCodeLine{1239 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0} \DoxyCodeLine{1240 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1241 } \DoxyCodeLine{1242 intp(1) = dza(i,j) ; intp(5) = dza(i,j+1)} \DoxyCodeLine{1243 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{1244 wt\_l = 0.25*real(5-\/m) ; wt\_r = 1.0-\/wt\_l} \DoxyCodeLine{1245 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr} \DoxyCodeLine{1246 } \DoxyCodeLine{1247 \textcolor{comment}{! T, S, and p are interpolated in the horizontal. The p interpolation}} \DoxyCodeLine{1248 \textcolor{comment}{! is linear, but for T and S it may be thickness weighted.}} \DoxyCodeLine{1249 p5(1) = rl2\_t2\_to\_pa * (wt\_l*p\_b(i,j) + wt\_r*p\_b(i,j+1))} \DoxyCodeLine{1250 dp = wt\_l*(p\_b(i,j) -\/ p\_t(i,j)) + wt\_r*(p\_b(i,j+1) -\/ p\_t(i,j+1))} \DoxyCodeLine{1251 t5(1) = wtt\_l*t(i,j) + wtt\_r*t(i,j+1)} \DoxyCodeLine{1252 s5(1) = wtt\_l*s(i,j) + wtt\_r*s(i,j+1)} \DoxyCodeLine{1253 \textcolor{keywordflow}{do} n=2,5} \DoxyCodeLine{1254 t5(n) = t5(1) ; s5(n) = s5(1) ; p5(n) = rl2\_t2\_to\_pa * (p5(n-\/1) -\/ 0.25*dp)} \DoxyCodeLine{1255 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1256 \textcolor{keywordflow}{if} (sv\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1257 \textcolor{keyword}{call }calculate\_spec\_vol(t5, s5, p5, a5, 1, 5, eos, alpha\_ref\_mks, scale=sv\_scale)} \DoxyCodeLine{1258 \textcolor{keywordflow}{else}} \DoxyCodeLine{1259 \textcolor{keyword}{call }calculate\_spec\_vol(t5, s5, p5, a5, 1, 5, eos, alpha\_ref\_mks)} \DoxyCodeLine{1260 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1261 } \DoxyCodeLine{1262 \textcolor{comment}{! Use Boole's rule to estimate the interface height anomaly change.}} \DoxyCodeLine{1263 intp(m) = dp*( c1\_90*(7.0*(a5(1)+a5(5)) + 32.0*(a5(2)+a5(4)) + \&} \DoxyCodeLine{1264 12.0*a5(3)))} \DoxyCodeLine{1265 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1266 \textcolor{comment}{! Use Boole's rule to integrate the interface height anomaly values in y.}} \DoxyCodeLine{1267 inty\_dza(i,j) = c1\_90*(7.0*(intp(1)+intp(5)) + 32.0*(intp(2)+intp(4)) + \&} \DoxyCodeLine{1268 12.0*intp(3))} \DoxyCodeLine{1269 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1270 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__density__integrals_a71a518f80b5f2ecf83fd9c638cad140d}\label{namespacemom__density__integrals_a71a518f80b5f2ecf83fd9c638cad140d}} \index{mom\_density\_integrals@{mom\_density\_integrals}!int\_spec\_vol\_dp\_generic\_plm@{int\_spec\_vol\_dp\_generic\_plm}} \index{int\_spec\_vol\_dp\_generic\_plm@{int\_spec\_vol\_dp\_generic\_plm}!mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsubsection{\texorpdfstring{int\_spec\_vol\_dp\_generic\_plm()}{int\_spec\_vol\_dp\_generic\_plm()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+density\+\_\+integrals\+::int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+generic\+\_\+plm (\begin{DoxyParamCaption}\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{T\+\_\+t, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{T\+\_\+b, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{S\+\_\+t, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{S\+\_\+b, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{p\+\_\+t, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{p\+\_\+b, }\item[{real, intent(in)}]{alpha\+\_\+ref, }\item[{real, intent(in)}]{d\+P\+\_\+neglect, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(in)}]{bathyP, }\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\item[{type(eos\+\_\+type), pointer}]{E\+OS, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(inout)}]{dza, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsd\+: hi \%jed), intent(inout), optional}]{intp\+\_\+dza, }\item[{real, dimension( hi \%isdb\+: hi \%iedb, hi \%jsd\+: hi \%jed), intent(inout), optional}]{intx\+\_\+dza, }\item[{real, dimension( hi \%isd\+: hi \%ied, hi \%jsdb\+: hi \%jedb), intent(inout), optional}]{inty\+\_\+dza, }\item[{logical, intent(in), optional}]{use\+Mass\+Wght\+Interp }\end{DoxyParamCaption})} This subroutine calculates integrals of specific volume anomalies in pressure across layers, which are required for calculating the finite-\/volume form pressure accelerations in a non-\/\+Boussinesq model. There are essentially no free assumptions, apart from the use of Boole\textquotesingle{}s rule quadrature to do the integrals. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em hi} & A horizontal index type structure. \\ \hline \mbox{\texttt{ in}} & {\em t\+\_\+t} & Potential temperature at the top of the layer \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em t\+\_\+b} & Potential temperature at the bottom of the layer \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+t} & Salinity at the top the layer \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s\+\_\+b} & Salinity at the bottom the layer \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em p\+\_\+t} & Pressure atop the layer \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em p\+\_\+b} & Pressure below the layer \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em alpha\+\_\+ref} & A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals \mbox{[}R-\/1 $\sim$$>$ m3 kg-\/1\mbox{]} The calculation is mathematically identical with different values of alpha\+\_\+ref, but alpha\+\_\+ref alters the effects of roundoff, and answers do change. \\ \hline \mbox{\texttt{ in}} & {\em dp\+\_\+neglect} & !$<$ A miniscule pressure change with the same units as p\+\_\+t \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em bathyp} & The pressure at the bathymetry \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline & {\em eos} & Equation of state structure \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ in,out}} & {\em dza} & The change in the geopotential anomaly \\ \hline \mbox{\texttt{ in,out}} & {\em intp\+\_\+dza} & The integral in pressure through the layer of \\ \hline \mbox{\texttt{ in,out}} & {\em intx\+\_\+dza} & The integral in x of the difference between \\ \hline \mbox{\texttt{ in,out}} & {\em inty\+\_\+dza} & The integral in y of the difference between \\ \hline \mbox{\texttt{ in}} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals. \\ \hline \end{DoxyParams} Definition at line 1280 of file M\+O\+M\+\_\+density\+\_\+integrals.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1280 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: HI\textcolor{comment}{ !< A horizontal index type structure.}} \DoxyCodeLine{1281 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1282 \textcolor{keywordtype}{intent(in)} :: T\_t\textcolor{comment}{ !< Potential temperature at the top of the layer [degC]}} \DoxyCodeLine{1283 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1284 \textcolor{keywordtype}{intent(in)} :: T\_b\textcolor{comment}{ !< Potential temperature at the bottom of the layer [degC]}} \DoxyCodeLine{1285 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1286 \textcolor{keywordtype}{intent(in)} :: S\_t\textcolor{comment}{ !< Salinity at the top the layer [ppt]}} \DoxyCodeLine{1287 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1288 \textcolor{keywordtype}{intent(in)} :: S\_b\textcolor{comment}{ !< Salinity at the bottom the layer [ppt]}} \DoxyCodeLine{1289 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1290 \textcolor{keywordtype}{intent(in)} :: p\_t\textcolor{comment}{ !< Pressure atop the layer [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1291 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1292 \textcolor{keywordtype}{intent(in)} :: p\_b\textcolor{comment}{ !< Pressure below the layer [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1293 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: alpha\_ref\textcolor{comment}{ !< A mean specific volume that is subtracted out}} \DoxyCodeLine{1294 \textcolor{comment}{ !! to reduce the magnitude of each of the integrals [R-\/1 ~> m3 kg-\/1]}} \DoxyCodeLine{1295 \textcolor{comment}{ !! The calculation is mathematically identical with different values of}} \DoxyCodeLine{1296 \textcolor{comment}{ !! alpha\_ref, but alpha\_ref alters the effects of roundoff, and}} \DoxyCodeLine{1297 \textcolor{comment}{ !! answers do change.}} \DoxyCodeLine{1298 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: dP\_neglect\textcolor{comment}{ ! Pa] or [Pa]}} \DoxyCodeLine{1300 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1301 \textcolor{keywordtype}{intent(in)} :: bathyP\textcolor{comment}{ !< The pressure at the bathymetry [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1302 \textcolor{keywordtype}{type}(EOS\_type), \textcolor{keywordtype}{pointer} :: EOS\textcolor{comment}{ !< Equation of state structure}} \DoxyCodeLine{1303 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{1304 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1305 \textcolor{keywordtype}{intent(inout)} :: dza\textcolor{comment}{ !< The change in the geopotential anomaly}} \DoxyCodeLine{1306 \textcolor{comment}{ !! across the layer [L2 T-\/2 ~> m2 s-\/2]}} \DoxyCodeLine{1307 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1308 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intp\_dza\textcolor{comment}{ !< The integral in pressure through the layer of}} \DoxyCodeLine{1309 \textcolor{comment}{ !! the geopotential anomaly relative to the anomaly at the bottom of the}} \DoxyCodeLine{1310 \textcolor{comment}{ !! layer [R L4 T-\/4 ~> Pa m2 s-\/2] or [Pa m2 s-\/2]}} \DoxyCodeLine{1311 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZIB\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1312 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intx\_dza\textcolor{comment}{ !< The integral in x of the difference between}} \DoxyCodeLine{1313 \textcolor{comment}{ !! the geopotential anomaly at the top and bottom of the layer divided}} \DoxyCodeLine{1314 \textcolor{comment}{ !! by the x grid spacing [L2 T-\/2 ~> m2 s-\/2] or [m2 s-\/2]}} \DoxyCodeLine{1315 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJB\_(HI))}, \&} \DoxyCodeLine{1316 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: inty\_dza\textcolor{comment}{ !< The integral in y of the difference between}} \DoxyCodeLine{1317 \textcolor{comment}{ !! the geopotential anomaly at the top and bottom of the layer divided}} \DoxyCodeLine{1318 \textcolor{comment}{ !! by the y grid spacing [L2 T-\/2 ~> m2 s-\/2] or [m2 s-\/2]}} \DoxyCodeLine{1319 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: useMassWghtInterp\textcolor{comment}{ !< If true, uses mass weighting}} \DoxyCodeLine{1320 \textcolor{comment}{ !! to interpolate T/S for top and bottom integrals.}} \DoxyCodeLine{1321 } \DoxyCodeLine{1322 \textcolor{comment}{! This subroutine calculates analytical and nearly-\/analytical integrals in}} \DoxyCodeLine{1323 \textcolor{comment}{! pressure across layers of geopotential anomalies, which are required for}} \DoxyCodeLine{1324 \textcolor{comment}{! calculating the finite-\/volume form pressure accelerations in a non-\/Boussinesq}} \DoxyCodeLine{1325 \textcolor{comment}{! model. There are essentially no free assumptions, apart from the use of}} \DoxyCodeLine{1326 \textcolor{comment}{! Boole's rule to do the horizontal integrals, and from a truncation in the}} \DoxyCodeLine{1327 \textcolor{comment}{! series for log(1-\/eps/1+eps) that assumes that |eps| < 0.34.}} \DoxyCodeLine{1328 } \DoxyCodeLine{1329 \textcolor{keywordtype}{ real} :: T5(5) \textcolor{comment}{! Temperatures at five quadrature points [degC]}} \DoxyCodeLine{1330 \textcolor{keywordtype}{ real} :: S5(5) \textcolor{comment}{! Salinities at five quadrature points [ppt]}} \DoxyCodeLine{1331 \textcolor{keywordtype}{ real} :: p5(5) \textcolor{comment}{! Pressures at five quadrature points, scaled back to Pa as necessary [Pa]}} \DoxyCodeLine{1332 \textcolor{keywordtype}{ real} :: a5(5) \textcolor{comment}{! Specific volumes at five quadrature points [R-\/1 ~> m3 kg-\/1] or [m3 kg-\/1]}} \DoxyCodeLine{1333 \textcolor{keywordtype}{ real} :: T15(15) \textcolor{comment}{! Temperatures at fifteen interior quadrature points [degC]}} \DoxyCodeLine{1334 \textcolor{keywordtype}{ real} :: S15(15) \textcolor{comment}{! Salinities at fifteen interior quadrature points [ppt]}} \DoxyCodeLine{1335 \textcolor{keywordtype}{ real} :: p15(15) \textcolor{comment}{! Pressures at fifteen quadrature points, scaled back to Pa as necessary [Pa]}} \DoxyCodeLine{1336 \textcolor{keywordtype}{ real} :: a15(15) \textcolor{comment}{! Specific volumes at fifteen quadrature points [R-\/1 ~> m3 kg-\/1] or [m3 kg-\/1]}} \DoxyCodeLine{1337 \textcolor{keywordtype}{ real} :: wt\_t(5), wt\_b(5) \textcolor{comment}{! Weights of top and bottom values at quadrature points [nondim]}} \DoxyCodeLine{1338 \textcolor{keywordtype}{ real} :: T\_top, T\_bot, S\_top, S\_bot, P\_top, P\_bot} \DoxyCodeLine{1339 } \DoxyCodeLine{1340 \textcolor{keywordtype}{ real} :: alpha\_anom \textcolor{comment}{! The depth averaged specific density anomaly [m3 kg-\/1]}} \DoxyCodeLine{1341 \textcolor{keywordtype}{ real} :: dp \textcolor{comment}{! The pressure change through a layer [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1342 \textcolor{keywordtype}{ real} :: dp\_90(2:4) \textcolor{comment}{! The pressure change through a layer divided by 90 [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1343 \textcolor{keywordtype}{ real} :: hWght \textcolor{comment}{! A pressure-\/thickness below topography [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1344 \textcolor{keywordtype}{ real} :: hL, hR \textcolor{comment}{! Pressure-\/thicknesses of the columns to the left and right [R L2 T-\/2 ~> Pa]}} \DoxyCodeLine{1345 \textcolor{keywordtype}{ real} :: alpha\_ref\_mks \textcolor{comment}{! The reference specific volume in MKS units, never rescaled from m3 kg-\/1 [m3 kg-\/1]}} \DoxyCodeLine{1346 \textcolor{keywordtype}{ real} :: iDenom \textcolor{comment}{! The inverse of the denominator in the weights [T4 R-\/2 L-\/4 ~> Pa-\/2]}} \DoxyCodeLine{1347 \textcolor{keywordtype}{ real} :: hWt\_LL, hWt\_LR \textcolor{comment}{! hWt\_LA is the weighted influence of A on the left column [nondim]}} \DoxyCodeLine{1348 \textcolor{keywordtype}{ real} :: hWt\_RL, hWt\_RR \textcolor{comment}{! hWt\_RA is the weighted influence of A on the right column [nondim]}} \DoxyCodeLine{1349 \textcolor{keywordtype}{ real} :: wt\_L, wt\_R \textcolor{comment}{! The linear weights of the left and right columns [nondim]}} \DoxyCodeLine{1350 \textcolor{keywordtype}{ real} :: wtT\_L, wtT\_R \textcolor{comment}{! The weights for tracers from the left and right columns [nondim]}} \DoxyCodeLine{1351 \textcolor{keywordtype}{ real} :: intp(5) \textcolor{comment}{! The integrals of specific volume with pressure at the}} \DoxyCodeLine{1352 \textcolor{comment}{! 5 sub-\/column locations [L2 T-\/2 ~> m2 s-\/2]}} \DoxyCodeLine{1353 \textcolor{keywordtype}{ real} :: RL2\_T2\_to\_Pa \textcolor{comment}{! A unit conversion factor from the rescaled units of pressure to Pa [Pa T2 R-\/1 L-\/2 ~> 1]}} \DoxyCodeLine{1354 \textcolor{keywordtype}{ real} :: SV\_scale \textcolor{comment}{! A multiplicative factor by which to scale specific}} \DoxyCodeLine{1355 \textcolor{comment}{! volume from m3 kg-\/1 to the desired units [kg m-\/3 R-\/1 ~> 1]}} \DoxyCodeLine{1356 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{parameter} :: C1\_90 = 1.0/90.0 \textcolor{comment}{! A rational constant.}} \DoxyCodeLine{1357 \textcolor{keywordtype}{logical} :: do\_massWeight \textcolor{comment}{! Indicates whether to do mass weighting.}} \DoxyCodeLine{1358 \textcolor{keywordtype}{integer} :: Isq, Ieq, Jsq, Jeq, i, j, m, n, pos} \DoxyCodeLine{1359 } \DoxyCodeLine{1360 isq = hi\%IscB ; ieq = hi\%IecB ; jsq = hi\%JscB ; jeq = hi\%JecB} \DoxyCodeLine{1361 } \DoxyCodeLine{1362 do\_massweight = .false.} \DoxyCodeLine{1363 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(usemasswghtinterp)) do\_massweight = usemasswghtinterp} \DoxyCodeLine{1364 } \DoxyCodeLine{1365 sv\_scale = us\%R\_to\_kg\_m3} \DoxyCodeLine{1366 rl2\_t2\_to\_pa = us\%RL2\_T2\_to\_Pa} \DoxyCodeLine{1367 alpha\_ref\_mks = alpha\_ref * us\%kg\_m3\_to\_R} \DoxyCodeLine{1368 } \DoxyCodeLine{1369 \textcolor{keywordflow}{do} n = 1, 5 \textcolor{comment}{! Note that these are reversed from int\_density\_dz.}} \DoxyCodeLine{1370 wt\_t(n) = 0.25 * real(n-\/1)} \DoxyCodeLine{1371 wt\_b(n) = 1.0 -\/ wt\_t(n)} \DoxyCodeLine{1372 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1373 } \DoxyCodeLine{1374 \textcolor{comment}{! 1. Compute vertical integrals}} \DoxyCodeLine{1375 \textcolor{keywordflow}{do} j=jsq,jeq+1; \textcolor{keywordflow}{do} i=isq,ieq+1} \DoxyCodeLine{1376 dp = p\_b(i,j) -\/ p\_t(i,j)} \DoxyCodeLine{1377 \textcolor{keywordflow}{do} n=1,5 \textcolor{comment}{! T, S and p are linearly interpolated in the vertical.}} \DoxyCodeLine{1378 p5(n) = rl2\_t2\_to\_pa * (wt\_t(n) * p\_t(i,j) + wt\_b(n) * p\_b(i,j))} \DoxyCodeLine{1379 s5(n) = wt\_t(n) * s\_t(i,j) + wt\_b(n) * s\_b(i,j)} \DoxyCodeLine{1380 t5(n) = wt\_t(n) * t\_t(i,j) + wt\_b(n) * t\_b(i,j)} \DoxyCodeLine{1381 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1382 \textcolor{keywordflow}{if} (sv\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1383 \textcolor{keyword}{call }calculate\_spec\_vol(t5, s5, p5, a5, 1, 5, eos, alpha\_ref\_mks, scale=sv\_scale)} \DoxyCodeLine{1384 \textcolor{keywordflow}{else}} \DoxyCodeLine{1385 \textcolor{keyword}{call }calculate\_spec\_vol(t5, s5, p5, a5, 1, 5, eos, alpha\_ref\_mks)} \DoxyCodeLine{1386 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1387 } \DoxyCodeLine{1388 \textcolor{comment}{! Use Boole's rule to estimate the interface height anomaly change.}} \DoxyCodeLine{1389 alpha\_anom = c1\_90*((7.0*(a5(1)+a5(5)) + 32.0*(a5(2)+a5(4))) + 12.0*a5(3))} \DoxyCodeLine{1390 dza(i,j) = dp*alpha\_anom} \DoxyCodeLine{1391 \textcolor{comment}{! Use a Boole's-\/rule-\/like fifth-\/order accurate estimate of the double integral of}} \DoxyCodeLine{1392 \textcolor{comment}{! the interface height anomaly.}} \DoxyCodeLine{1393 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intp\_dza)) intp\_dza(i,j) = 0.5*dp**2 * \&} \DoxyCodeLine{1394 (alpha\_anom -\/ c1\_90*(16.0*(a5(4)-\/a5(2)) + 7.0*(a5(5)-\/a5(1))) )} \DoxyCodeLine{1395 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1396 } \DoxyCodeLine{1397 \textcolor{comment}{! 2. Compute horizontal integrals in the x direction}} \DoxyCodeLine{1398 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dza)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=hi\%jsc,hi\%jec ; \textcolor{keywordflow}{do} i=isq,ieq} \DoxyCodeLine{1399 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{1400 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation}} \DoxyCodeLine{1401 \textcolor{comment}{! of T,S along the top and bottom integrals, almost like thickness}} \DoxyCodeLine{1402 \textcolor{comment}{! weighting. Note: To work in terrain following coordinates we could}} \DoxyCodeLine{1403 \textcolor{comment}{! offset this distance by the layer thickness to replicate other models.}} \DoxyCodeLine{1404 hwght = 0.0} \DoxyCodeLine{1405 \textcolor{keywordflow}{if} (do\_massweight) \&} \DoxyCodeLine{1406 hwght = max(0., bathyp(i,j)-\/p\_t(i+1,j), bathyp(i+1,j)-\/p\_t(i,j))} \DoxyCodeLine{1407 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{1408 hl = (p\_b(i,j) -\/ p\_t(i,j)) + dp\_neglect} \DoxyCodeLine{1409 hr = (p\_b(i+1,j) -\/ p\_t(i+1,j)) + dp\_neglect} \DoxyCodeLine{1410 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{1411 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{1412 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom} \DoxyCodeLine{1413 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom} \DoxyCodeLine{1414 \textcolor{keywordflow}{else}} \DoxyCodeLine{1415 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0} \DoxyCodeLine{1416 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1417 } \DoxyCodeLine{1418 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{1419 wt\_l = 0.25*real(5-\/m) ; wt\_r = 1.0-\/wt\_l} \DoxyCodeLine{1420 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr} \DoxyCodeLine{1421 } \DoxyCodeLine{1422 \textcolor{comment}{! T, S, and p are interpolated in the horizontal. The p interpolation}} \DoxyCodeLine{1423 \textcolor{comment}{! is linear, but for T and S it may be thickness weighted.}} \DoxyCodeLine{1424 p\_top = wt\_l*p\_t(i,j) + wt\_r*p\_t(i+1,j)} \DoxyCodeLine{1425 p\_bot = wt\_l*p\_b(i,j) + wt\_r*p\_b(i+1,j)} \DoxyCodeLine{1426 t\_top = wtt\_l*t\_t(i,j) + wtt\_r*t\_t(i+1,j)} \DoxyCodeLine{1427 t\_bot = wtt\_l*t\_b(i,j) + wtt\_r*t\_b(i+1,j)} \DoxyCodeLine{1428 s\_top = wtt\_l*s\_t(i,j) + wtt\_r*s\_t(i+1,j)} \DoxyCodeLine{1429 s\_bot = wtt\_l*s\_b(i,j) + wtt\_r*s\_b(i+1,j)} \DoxyCodeLine{1430 dp\_90(m) = c1\_90*(p\_bot -\/ p\_top)} \DoxyCodeLine{1431 } \DoxyCodeLine{1432 \textcolor{comment}{! Salinity, temperature and pressure with linear interpolation in the vertical.}} \DoxyCodeLine{1433 pos = (m-\/2)*5} \DoxyCodeLine{1434 \textcolor{keywordflow}{do} n=1,5} \DoxyCodeLine{1435 p15(pos+n) = rl2\_t2\_to\_pa * (wt\_t(n) * p\_top + wt\_b(n) * p\_bot)} \DoxyCodeLine{1436 s15(pos+n) = wt\_t(n) * s\_top + wt\_b(n) * s\_bot} \DoxyCodeLine{1437 t15(pos+n) = wt\_t(n) * t\_top + wt\_b(n) * t\_bot} \DoxyCodeLine{1438 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1439 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1440 } \DoxyCodeLine{1441 \textcolor{keywordflow}{if} (sv\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1442 \textcolor{keyword}{call }calculate\_spec\_vol(t15, s15, p15, a15, 1, 15, eos, alpha\_ref\_mks, scale=sv\_scale)} \DoxyCodeLine{1443 \textcolor{keywordflow}{else}} \DoxyCodeLine{1444 \textcolor{keyword}{call }calculate\_spec\_vol(t15, s15, p15, a15, 1, 15, eos, alpha\_ref\_mks)} \DoxyCodeLine{1445 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1446 } \DoxyCodeLine{1447 intp(1) = dza(i,j) ; intp(5) = dza(i+1,j)} \DoxyCodeLine{1448 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{1449 \textcolor{comment}{! Use Boole's rule to estimate the interface height anomaly change.}} \DoxyCodeLine{1450 \textcolor{comment}{! The integrals at the ends of the segment are already known.}} \DoxyCodeLine{1451 pos = (m-\/2)*5} \DoxyCodeLine{1452 intp(m) = dp\_90(m)*((7.0*(a15(pos+1)+a15(pos+5)) + \&} \DoxyCodeLine{1453 32.0*(a15(pos+2)+a15(pos+4))) + 12.0*a15(pos+3))} \DoxyCodeLine{1454 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1455 \textcolor{comment}{! Use Boole's rule to integrate the interface height anomaly values in x.}} \DoxyCodeLine{1456 intx\_dza(i,j) = c1\_90*((7.0*(intp(1)+intp(5)) + 32.0*(intp(2)+intp(4))) + \&} \DoxyCodeLine{1457 12.0*intp(3))} \DoxyCodeLine{1458 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1459 } \DoxyCodeLine{1460 \textcolor{comment}{! 3. Compute horizontal integrals in the y direction}} \DoxyCodeLine{1461 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dza)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=jsq,jeq ; \textcolor{keywordflow}{do} i=hi\%isc,hi\%iec} \DoxyCodeLine{1462 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of}} \DoxyCodeLine{1463 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation}} \DoxyCodeLine{1464 \textcolor{comment}{! of T,S along the top and bottom integrals, like thickness weighting.}} \DoxyCodeLine{1465 hwght = 0.0} \DoxyCodeLine{1466 \textcolor{keywordflow}{if} (do\_massweight) \&} \DoxyCodeLine{1467 hwght = max(0., bathyp(i,j)-\/p\_t(i,j+1), bathyp(i,j+1)-\/p\_t(i,j))} \DoxyCodeLine{1468 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then}} \DoxyCodeLine{1469 hl = (p\_b(i,j) -\/ p\_t(i,j)) + dp\_neglect} \DoxyCodeLine{1470 hr = (p\_b(i,j+1) -\/ p\_t(i,j+1)) + dp\_neglect} \DoxyCodeLine{1471 hwght = hwght * ( (hl-\/hr)/(hl+hr) )**2} \DoxyCodeLine{1472 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr )} \DoxyCodeLine{1473 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom} \DoxyCodeLine{1474 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom} \DoxyCodeLine{1475 \textcolor{keywordflow}{else}} \DoxyCodeLine{1476 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0} \DoxyCodeLine{1477 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1478 } \DoxyCodeLine{1479 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{1480 wt\_l = 0.25*real(5-\/m) ; wt\_r = 1.0-\/wt\_l} \DoxyCodeLine{1481 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr} \DoxyCodeLine{1482 } \DoxyCodeLine{1483 \textcolor{comment}{! T, S, and p are interpolated in the horizontal. The p interpolation}} \DoxyCodeLine{1484 \textcolor{comment}{! is linear, but for T and S it may be thickness weighted.}} \DoxyCodeLine{1485 p\_top = wt\_l*p\_t(i,j) + wt\_r*p\_t(i,j+1)} \DoxyCodeLine{1486 p\_bot = wt\_l*p\_b(i,j) + wt\_r*p\_b(i,j+1)} \DoxyCodeLine{1487 t\_top = wtt\_l*t\_t(i,j) + wtt\_r*t\_t(i,j+1)} \DoxyCodeLine{1488 t\_bot = wtt\_l*t\_b(i,j) + wtt\_r*t\_b(i,j+1)} \DoxyCodeLine{1489 s\_top = wtt\_l*s\_t(i,j) + wtt\_r*s\_t(i,j+1)} \DoxyCodeLine{1490 s\_bot = wtt\_l*s\_b(i,j) + wtt\_r*s\_b(i,j+1)} \DoxyCodeLine{1491 dp\_90(m) = c1\_90*(p\_bot -\/ p\_top)} \DoxyCodeLine{1492 } \DoxyCodeLine{1493 \textcolor{comment}{! Salinity, temperature and pressure with linear interpolation in the vertical.}} \DoxyCodeLine{1494 pos = (m-\/2)*5} \DoxyCodeLine{1495 \textcolor{keywordflow}{do} n=1,5} \DoxyCodeLine{1496 p15(pos+n) = rl2\_t2\_to\_pa * (wt\_t(n) * p\_top + wt\_b(n) * p\_bot)} \DoxyCodeLine{1497 s15(pos+n) = wt\_t(n) * s\_top + wt\_b(n) * s\_bot} \DoxyCodeLine{1498 t15(pos+n) = wt\_t(n) * t\_top + wt\_b(n) * t\_bot} \DoxyCodeLine{1499 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1500 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1501 } \DoxyCodeLine{1502 \textcolor{keywordflow}{if} (sv\_scale /= 1.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{1503 \textcolor{keyword}{call }calculate\_spec\_vol(t15, s15, p15, a15, 1, 15, eos, alpha\_ref\_mks, scale=sv\_scale)} \DoxyCodeLine{1504 \textcolor{keywordflow}{else}} \DoxyCodeLine{1505 \textcolor{keyword}{call }calculate\_spec\_vol(t15, s15, p15, a15, 1, 15, eos, alpha\_ref\_mks)} \DoxyCodeLine{1506 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1507 } \DoxyCodeLine{1508 intp(1) = dza(i,j) ; intp(5) = dza(i,j+1)} \DoxyCodeLine{1509 \textcolor{keywordflow}{do} m=2,4} \DoxyCodeLine{1510 \textcolor{comment}{! Use Boole's rule to estimate the interface height anomaly change.}} \DoxyCodeLine{1511 \textcolor{comment}{! The integrals at the ends of the segment are already known.}} \DoxyCodeLine{1512 pos = (m-\/2)*5} \DoxyCodeLine{1513 intp(m) = dp\_90(m) * ((7.0*(a15(pos+1)+a15(pos+5)) + \&} \DoxyCodeLine{1514 32.0*(a15(pos+2)+a15(pos+4))) + 12.0*a15(pos+3))} \DoxyCodeLine{1515 \textcolor{keywordflow}{ enddo}} \DoxyCodeLine{1516 \textcolor{comment}{! Use Boole's rule to integrate the interface height anomaly values in x.}} \DoxyCodeLine{1517 inty\_dza(i,j) = c1\_90*((7.0*(intp(1)+intp(5)) + 32.0*(intp(2)+intp(4))) + \&} \DoxyCodeLine{1518 12.0*intp(3))} \DoxyCodeLine{1519 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif}} \DoxyCodeLine{1520 } \end{DoxyCode} \mbox{\Hypertarget{namespacemom__density__integrals_a759c2ae7aec17c59d532050f68a1e518}\label{namespacemom__density__integrals_a759c2ae7aec17c59d532050f68a1e518}} \index{mom\_density\_integrals@{mom\_density\_integrals}!int\_specific\_vol\_dp@{int\_specific\_vol\_dp}} \index{int\_specific\_vol\_dp@{int\_specific\_vol\_dp}!mom\_density\_integrals@{mom\_density\_integrals}} \doxysubsubsection{\texorpdfstring{int\_specific\_vol\_dp()}{int\_specific\_vol\_dp()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+density\+\_\+integrals\+::int\+\_\+specific\+\_\+vol\+\_\+dp (\begin{DoxyParamCaption}\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in)}]{T, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in)}]{S, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in)}]{p\+\_\+t, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in)}]{p\+\_\+b, }\item[{real, intent(in)}]{alpha\+\_\+ref, }\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\item[{type(eos\+\_\+type), pointer}]{E\+OS, }\item[{type(unit\+\_\+scale\+\_\+type), intent(in)}]{US, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(inout)}]{dza, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(inout), optional}]{intp\+\_\+dza, }\item[{real, dimension(szib\+\_\+(hi),szj\+\_\+(hi)), intent(inout), optional}]{intx\+\_\+dza, }\item[{real, dimension(szi\+\_\+(hi),szjb\+\_\+(hi)), intent(inout), optional}]{inty\+\_\+dza, }\item[{integer, intent(in), optional}]{halo\+\_\+size, }\item[{real, dimension(szi\+\_\+(hi),szj\+\_\+(hi)), intent(in), optional}]{bathyP, }\item[{real, intent(in), optional}]{d\+P\+\_\+tiny, }\item[{logical, intent(in), optional}]{use\+Mass\+Wght\+Interp }\end{DoxyParamCaption})} Calls the appropriate subroutine to calculate analytical and nearly-\/analytical integrals in pressure across layers of geopotential anomalies, which are required for calculating the finite-\/volume form pressure accelerations in a non-\/\+Boussinesq model. There are essentially no free assumptions, apart from the use of Boole\textquotesingle{}s rule to do the horizontal integrals, and from a truncation in the series for log(1-\/eps/1+eps) that assumes that $\vert$eps$\vert$ $<$ 0.\+34. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em hi} & The horizontal index structure \\ \hline \mbox{\texttt{ in}} & {\em t} & Potential temperature referenced to the surface \mbox{[}degC\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em s} & Salinity \mbox{[}ppt\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em p\+\_\+t} & Pressure at the top of the layer \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em p\+\_\+b} & Pressure at the bottom of the layer \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em alpha\+\_\+ref} & A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals \mbox{[}R-\/1 $\sim$$>$ m3 kg-\/1\mbox{]} The calculation is mathematically identical with different values of alpha\+\_\+ref, but this reduces the effects of roundoff. \\ \hline & {\em eos} & Equation of state structure \\ \hline \mbox{\texttt{ in}} & {\em us} & A dimensional unit scaling type \\ \hline \mbox{\texttt{ in,out}} & {\em dza} & The change in the geopotential anomaly across \\ \hline \mbox{\texttt{ in,out}} & {\em intp\+\_\+dza} & The integral in pressure through the layer of the \\ \hline \mbox{\texttt{ in,out}} & {\em intx\+\_\+dza} & The integral in x of the difference between the \\ \hline \mbox{\texttt{ in,out}} & {\em inty\+\_\+dza} & The integral in y of the difference between the \\ \hline \mbox{\texttt{ in}} & {\em halo\+\_\+size} & The width of halo points on which to calculate dza. \\ \hline \mbox{\texttt{ in}} & {\em bathyp} & The pressure at the bathymetry \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em dp\+\_\+tiny} & A minuscule pressure change with the same units as p\+\_\+t \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals. \\ \hline \end{DoxyParams} Definition at line 1007 of file M\+O\+M\+\_\+density\+\_\+integrals.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{1007 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: HI\textcolor{comment}{ !< The horizontal index structure}} \DoxyCodeLine{1008 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1009 \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature referenced to the surface [degC]}} \DoxyCodeLine{1010 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1011 \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [ppt]}} \DoxyCodeLine{1012 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1013 \textcolor{keywordtype}{intent(in)} :: p\_t\textcolor{comment}{ !< Pressure at the top of the layer [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1014 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1015 \textcolor{keywordtype}{intent(in)} :: p\_b\textcolor{comment}{ !< Pressure at the bottom of the layer [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1016 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{intent(in)} :: alpha\_ref\textcolor{comment}{ !< A mean specific volume that is subtracted out}} \DoxyCodeLine{1017 \textcolor{comment}{ !! to reduce the magnitude of each of the integrals [R-\/1 ~> m3 kg-\/1]}} \DoxyCodeLine{1018 \textcolor{comment}{ !! The calculation is mathematically identical with different values of}} \DoxyCodeLine{1019 \textcolor{comment}{ !! alpha\_ref, but this reduces the effects of roundoff.}} \DoxyCodeLine{1020 \textcolor{keywordtype}{type}(EOS\_type), \textcolor{keywordtype}{pointer} :: EOS\textcolor{comment}{ !< Equation of state structure}} \DoxyCodeLine{1021 \textcolor{keywordtype}{type}(unit\_scale\_type), \textcolor{keywordtype}{intent(in)} :: US\textcolor{comment}{ !< A dimensional unit scaling type}} \DoxyCodeLine{1022 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1023 \textcolor{keywordtype}{intent(inout)} :: dza\textcolor{comment}{ !< The change in the geopotential anomaly across}} \DoxyCodeLine{1024 \textcolor{comment}{ !! the layer [L2 T-\/2 ~> m2 s-\/2] or [m2 s-\/2]}} \DoxyCodeLine{1025 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1026 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intp\_dza\textcolor{comment}{ !< The integral in pressure through the layer of the}} \DoxyCodeLine{1027 \textcolor{comment}{ !! geopotential anomaly relative to the anomaly at the bottom of the}} \DoxyCodeLine{1028 \textcolor{comment}{ !! layer [R L4 T-\/4 ~> Pa m2 s-\/2] or [Pa m2 s-\/2]}} \DoxyCodeLine{1029 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZIB\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1030 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intx\_dza\textcolor{comment}{ !< The integral in x of the difference between the}} \DoxyCodeLine{1031 \textcolor{comment}{ !! geopotential anomaly at the top and bottom of the layer divided by}} \DoxyCodeLine{1032 \textcolor{comment}{ !! the x grid spacing [L2 T-\/2 ~> m2 s-\/2] or [m2 s-\/2]}} \DoxyCodeLine{1033 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJB\_(HI))}, \&} \DoxyCodeLine{1034 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: inty\_dza\textcolor{comment}{ !< The integral in y of the difference between the}} \DoxyCodeLine{1035 \textcolor{comment}{ !! geopotential anomaly at the top and bottom of the layer divided by}} \DoxyCodeLine{1036 \textcolor{comment}{ !! the y grid spacing [L2 T-\/2 ~> m2 s-\/2] or [m2 s-\/2]}} \DoxyCodeLine{1037 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: halo\_size\textcolor{comment}{ !< The width of halo points on which to calculate dza.}} \DoxyCodeLine{1038 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(SZI\_(HI),SZJ\_(HI))}, \&} \DoxyCodeLine{1039 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: bathyP\textcolor{comment}{ !< The pressure at the bathymetry [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1040 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: dP\_tiny\textcolor{comment}{ !< A minuscule pressure change with}} \DoxyCodeLine{1041 \textcolor{comment}{ !! the same units as p\_t [R L2 T-\/2 ~> Pa] or [Pa]}} \DoxyCodeLine{1042 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: useMassWghtInterp\textcolor{comment}{ !< If true, uses mass weighting}} \DoxyCodeLine{1043 \textcolor{comment}{ !! to interpolate T/S for top and bottom integrals.}} \DoxyCodeLine{1044 } \DoxyCodeLine{1045 \textcolor{keywordflow}{if} (eos\_quadrature(eos)) \textcolor{keywordflow}{then}} \DoxyCodeLine{1046 \textcolor{keyword}{call }int\_spec\_vol\_dp\_generic\_pcm(t, s, p\_t, p\_b, alpha\_ref, hi, eos, us, \&} \DoxyCodeLine{1047 dza, intp\_dza, intx\_dza, inty\_dza, halo\_size, \&} \DoxyCodeLine{1048 bathyp, dp\_tiny, usemasswghtinterp)} \DoxyCodeLine{1049 \textcolor{keywordflow}{else}} \DoxyCodeLine{1050 \textcolor{keyword}{call }analytic\_int\_specific\_vol\_dp(t, s, p\_t, p\_b, alpha\_ref, hi, eos, \&} \DoxyCodeLine{1051 dza, intp\_dza, intx\_dza, inty\_dza, halo\_size, \&} \DoxyCodeLine{1052 bathyp, dp\_tiny, usemasswghtinterp)} \DoxyCodeLine{1053 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{1054 } \end{DoxyCode}