\hypertarget{namespacemom__eos__linear}{}\section{mom\+\_\+eos\+\_\+linear Module Reference} \label{namespacemom__eos__linear}\index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsection{Detailed Description} A simple linear equation of state for sea water with constant coefficients. \subsection*{Data Types} \begin{DoxyCompactItemize} \item interface \mbox{\hyperlink{interfacemom__eos__linear_1_1calculate__density__derivs__linear}{calculate\+\_\+density\+\_\+derivs\+\_\+linear}} \begin{DoxyCompactList}\small\item\em For a given thermodynamic state, return the derivatives of density with temperature and salinity using the simple linear equation of state. \end{DoxyCompactList}\item interface \mbox{\hyperlink{interfacemom__eos__linear_1_1calculate__density__linear}{calculate\+\_\+density\+\_\+linear}} \begin{DoxyCompactList}\small\item\em Compute the density of sea water (in kg/m$^\wedge$3), or its anomaly from a reference density, using a simple linear equation of state from salinity (in psu), potential temperature (in deg C) and pressure \mbox{[}Pa\mbox{]}. \end{DoxyCompactList}\item interface \mbox{\hyperlink{interfacemom__eos__linear_1_1calculate__density__second__derivs__linear}{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+linear}} \begin{DoxyCompactList}\small\item\em For a given thermodynamic state, return the second derivatives of density with various combinations of temperature, salinity, and pressure. Note that with a simple linear equation of state these second derivatives are all 0. \end{DoxyCompactList}\item interface \mbox{\hyperlink{interfacemom__eos__linear_1_1calculate__spec__vol__linear}{calculate\+\_\+spec\+\_\+vol\+\_\+linear}} \begin{DoxyCompactList}\small\item\em Compute the specific volume of sea water (in m$^\wedge$3/kg), or its anomaly from a reference value, using a simple linear equation of state from salinity (in psu), potential temperature (in deg C) and pressure \mbox{[}Pa\mbox{]}. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Functions/\+Subroutines} \begin{DoxyCompactItemize} \item subroutine, public \mbox{\hyperlink{namespacemom__eos__linear_a39e8258b3b0ddd5d176061b48a151648}{calculate\+\_\+density\+\_\+scalar\+\_\+linear}} (T, S, pressure, rho, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS, rho\+\_\+ref) \begin{DoxyCompactList}\small\item\em This subroutine computes the density of sea water with a trivial linear equation of state (in \mbox{[}kg m-\/3\mbox{]}) from salinity (sal \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__eos__linear_ae31468c3395f4bade9a2ca58ccfc83a0}{calculate\+\_\+density\+\_\+array\+\_\+linear}} (T, S, pressure, rho, start, npts, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS, rho\+\_\+ref) \begin{DoxyCompactList}\small\item\em This subroutine computes the density of sea water with a trivial linear equation of state (in kg/m$^\wedge$3) from salinity (sal in psu), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__eos__linear_a64c38d475860e8ae042d221af8d7195a}{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+linear}} (T, S, pressure, specvol, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS, spv\+\_\+ref) \begin{DoxyCompactList}\small\item\em This subroutine computes the in situ specific volume of sea water (specvol in \mbox{[}m3 kg-\/1\mbox{]}) from salinity (S \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}) and pressure \mbox{[}Pa\mbox{]}, using a trivial linear equation of state for density. If spv\+\_\+ref is present, specvol is an anomaly from spv\+\_\+ref. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__eos__linear_ab3b2951f265e375bd27a2eace7a91a87}{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+linear}} (T, S, pressure, specvol, start, npts, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS, spv\+\_\+ref) \begin{DoxyCompactList}\small\item\em This subroutine computes the in situ specific volume of sea water (specvol in \mbox{[}m3 kg-\/1\mbox{]}) from salinity (S \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}) and pressure \mbox{[}Pa\mbox{]}, using a trivial linear equation of state for density. If spv\+\_\+ref is present, specvol is an anomaly from spv\+\_\+ref. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__eos__linear_a366576999aae16f01b503a5aca78353e}{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+linear}} (T, S, pressure, drho\+\_\+d\+T\+\_\+out, drho\+\_\+d\+S\+\_\+out, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS, start, npts) \begin{DoxyCompactList}\small\item\em This subroutine calculates the partial derivatives of density $\ast$ with potential temperature and salinity. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__eos__linear_a1f03feeee904430da4980f23e59a992b}{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+linear}} (T, S, pressure, drho\+\_\+d\+T\+\_\+out, drho\+\_\+d\+S\+\_\+out, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS) \begin{DoxyCompactList}\small\item\em This subroutine calculates the partial derivatives of density $\ast$ with potential temperature and salinity for a single point. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__eos__linear_a80a174894f52db0aa1cdb2b267d70e76}{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+linear}} (T, S, pressure, drho\+\_\+d\+S\+\_\+dS, drho\+\_\+d\+S\+\_\+dT, drho\+\_\+d\+T\+\_\+dT, drho\+\_\+d\+S\+\_\+dP, drho\+\_\+d\+T\+\_\+dP) \begin{DoxyCompactList}\small\item\em This subroutine calculates the five, partial second derivatives of density w.\+r.\+t. potential temperature and salinity and pressure which for a linear equation of state should all be 0. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespacemom__eos__linear_adb222e7164a10bf7ce8e30d22a58ba46}{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+linear}} (T, S, pressure, drho\+\_\+d\+S\+\_\+dS, drho\+\_\+d\+S\+\_\+dT, drho\+\_\+d\+T\+\_\+dT, drho\+\_\+d\+S\+\_\+dP, drho\+\_\+d\+T\+\_\+dP, start, npts) \begin{DoxyCompactList}\small\item\em This subroutine calculates the five, partial second derivatives of density w.\+r.\+t. potential temperature and salinity and pressure which for a linear equation of state should all be 0. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__eos__linear_ac104dedf6f20ab794c2c430462ace217}{calculate\+\_\+specvol\+\_\+derivs\+\_\+linear}} (T, S, pressure, d\+S\+V\+\_\+dT, d\+S\+V\+\_\+dS, start, npts, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS) \begin{DoxyCompactList}\small\item\em Calculate the derivatives of specific volume with temperature and salinity. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__eos__linear_a2d051ebfb3ee1ef96888c74c09a1a6ca}{calculate\+\_\+compress\+\_\+linear}} (T, S, pressure, rho, drho\+\_\+dp, start, npts, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS) \begin{DoxyCompactList}\small\item\em This subroutine computes the in situ density of sea water (rho) and the compressibility (drho/dp == C\+\_\+sound$^\wedge$-\/2) at the given salinity, potential temperature, and pressure. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacemom__eos__linear_a4da51fc5de5654041e08fb43a8b0283c}{int\+\_\+density\+\_\+dz\+\_\+linear}} (T, S, z\+\_\+t, z\+\_\+b, rho\+\_\+ref, rho\+\_\+0\+\_\+pres, G\+\_\+e, HI, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS, dpa, intz\+\_\+dpa, intx\+\_\+dpa, inty\+\_\+dpa, bathyT, dz\+\_\+neglect, use\+Mass\+Wght\+Interp) \begin{DoxyCompactList}\small\item\em This subroutine calculates analytical and nearly-\/analytical 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__eos__linear_ac9a31e315e6cb02f8f270de7c877f688}{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+linear}} (T, S, p\+\_\+t, p\+\_\+b, alpha\+\_\+ref, HI, Rho\+\_\+\+T0\+\_\+\+S0, d\+Rho\+\_\+dT, d\+Rho\+\_\+dS, dza, intp\+\_\+dza, intx\+\_\+dza, inty\+\_\+dza, halo\+\_\+size, bathyP, d\+P\+\_\+neglect, use\+Mass\+Wght\+Interp) \begin{DoxyCompactList}\small\item\em Calculates 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. Specific volume is assumed to vary linearly between adjacent points. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Function/\+Subroutine Documentation} \mbox{\Hypertarget{namespacemom__eos__linear_a2d051ebfb3ee1ef96888c74c09a1a6ca}\label{namespacemom__eos__linear_a2d051ebfb3ee1ef96888c74c09a1a6ca}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+compress\+\_\+linear@{calculate\+\_\+compress\+\_\+linear}} \index{calculate\+\_\+compress\+\_\+linear@{calculate\+\_\+compress\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+compress\+\_\+linear()}{calculate\_compress\_linear()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+compress\+\_\+linear (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(out)}]{rho, }\item[{real, dimension(\+:), intent(out)}]{drho\+\_\+dp, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts, }\item[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS }\end{DoxyParamCaption})} This subroutine computes the in situ density of sea water (rho) and the compressibility (drho/dp == C\+\_\+sound$^\wedge$-\/2) at the given salinity, potential temperature, and pressure. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & Potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em rho} & In situ density \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+dp} & The partial derivative of density with pressure (also the inverse of the square of sound speed) \mbox{[}s2 m-\/2\mbox{]}.\\ \hline \mbox{\tt in} & {\em start} & The starting point in the arrays.\\ \hline \mbox{\tt in} & {\em npts} & The number of values to calculate.\\ \hline \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivative of density with temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivative of density with salinity \mbox{[}kg m-\/3 ppt-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 301 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 301 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: T\textcolor{comment}{ !< Potential temperature relative to the surface} 302 \textcolor{comment}{ !! [degC].} 303 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: S\textcolor{comment}{ !< Salinity [PSU].} 304 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 305 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)}, \textcolor{keywordtype}{dimension(:)} :: rho\textcolor{comment}{ !< In situ density [kg m-3].} 306 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)}, \textcolor{keywordtype}{dimension(:)} :: drho\_dp\textcolor{comment}{ !< The partial derivative of density with pressure} 307 \textcolor{comment}{ !! (also the inverse of the square of sound speed)} 308 \textcolor{comment}{ !! [s2 m-2].} 309 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< The starting point in the arrays.} 310 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< The number of values to calculate.} 311 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [kg m-3].} 312 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivative of density with} 313 \textcolor{comment}{ !! temperature [kg m-3 degC-1].} 314 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivative of density with} 315 \textcolor{comment}{ !! salinity [kg m-3 ppt-1].} 316 \textcolor{comment}{! Local variables} 317 \textcolor{keywordtype}{integer} :: j 318 319 \textcolor{keywordflow}{do} j=start,start+npts-1 320 rho(j) = rho\_t0\_s0 + drho\_dt*t(j) + drho\_ds*s(j) 321 drho\_dp(j) = 0.0 322 \textcolor{keywordflow}{ enddo} \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_ae31468c3395f4bade9a2ca58ccfc83a0}\label{namespacemom__eos__linear_ae31468c3395f4bade9a2ca58ccfc83a0}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+density\+\_\+array\+\_\+linear@{calculate\+\_\+density\+\_\+array\+\_\+linear}} \index{calculate\+\_\+density\+\_\+array\+\_\+linear@{calculate\+\_\+density\+\_\+array\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+array\+\_\+linear()}{calculate\_density\_array\_linear()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+density\+\_\+array\+\_\+linear (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(out)}]{rho, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts, }\item[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS, }\item[{real, intent(in), optional}]{rho\+\_\+ref }\end{DoxyParamCaption})} This subroutine computes the density of sea water with a trivial linear equation of state (in kg/m$^\wedge$3) from salinity (sal in psu), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em rho} & in situ density \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em start} & the starting point in the arrays.\\ \hline \mbox{\tt in} & {\em npts} & the number of values to calculate.\\ \hline \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivatives of density with temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivatives of density with salinity in \mbox{[}kg m-\/3 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em rho\+\_\+ref} & A reference density \mbox{[}kg m-\/3\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 82 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 82 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< potential temperature relative to the surface [degC].} 83 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< salinity [PSU].} 84 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 85 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(out)} :: rho\textcolor{comment}{ !< in situ density [kg m-3].} 86 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< the starting point in the arrays.} 87 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< the number of values to calculate.} 88 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [kg m-3].} 89 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivatives of density with temperature} 90 \textcolor{comment}{ !! [kg m-3 degC-1].} 91 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivatives of density with salinity} 92 \textcolor{comment}{ !! in [kg m-3 ppt-1].} 93 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A reference density [kg m-3].} 94 \textcolor{comment}{! Local variables} 95 \textcolor{keywordtype}{integer} :: j 96 97 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(rho\_ref)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=start,start+npts-1 98 rho(j) = (rho\_t0\_s0 - rho\_ref) + (drho\_dt*t(j) + drho\_ds*s(j)) 99 \textcolor{keywordflow}{ enddo} ; \textcolor{keywordflow}{else} ; \textcolor{keywordflow}{do} j=start,start+npts-1 100 rho(j) = rho\_t0\_s0 + drho\_dt*t(j) + drho\_ds*s(j) 101 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} 102 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_a366576999aae16f01b503a5aca78353e}\label{namespacemom__eos__linear_a366576999aae16f01b503a5aca78353e}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+linear@{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+linear}} \index{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+linear@{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+linear()}{calculate\_density\_derivs\_array\_linear()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+linear (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(out)}]{drho\+\_\+d\+T\+\_\+out, }\item[{real, dimension(\+:), intent(out)}]{drho\+\_\+d\+S\+\_\+out, }\item[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine calculates the partial derivatives of density $\ast$ with potential temperature and salinity. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & Potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & Pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+dt\+\_\+out} & The partial derivative of density with potential temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+out} & The partial derivative of density with salinity \mbox{[}kg m-\/3 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivative of density with temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivative of density with salinity \mbox{[}kg m-\/3 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em start} & The starting point in the arrays.\\ \hline \mbox{\tt in} & {\em npts} & The number of values to calculate. \\ \hline \end{DoxyParams} Definition at line 165 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 165 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: T\textcolor{comment}{ !< Potential temperature relative to the surface} 166 \textcolor{comment}{ !! [degC].} 167 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: S\textcolor{comment}{ !< Salinity [PSU].} 168 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: pressure\textcolor{comment}{ !< Pressure [Pa].} 169 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)}, \textcolor{keywordtype}{dimension(:)} :: drho\_dT\_out\textcolor{comment}{ !< The partial derivative of density with} 170 \textcolor{comment}{ !! potential temperature [kg m-3 degC-1].} 171 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)}, \textcolor{keywordtype}{dimension(:)} :: drho\_dS\_out\textcolor{comment}{ !< The partial derivative of density with} 172 \textcolor{comment}{ !! salinity [kg m-3 ppt-1].} 173 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [kg m-3].} 174 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivative of density with temperature [kg m-3 degC-1].} 175 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivative of density with salinity [kg m-3 ppt-1].} 176 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< The starting point in the arrays.} 177 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< The number of values to calculate.} 178 \textcolor{comment}{! Local variables} 179 \textcolor{keywordtype}{integer} :: j 180 181 \textcolor{keywordflow}{do} j=start,start+npts-1 182 drho\_dt\_out(j) = drho\_dt 183 drho\_ds\_out(j) = drho\_ds 184 \textcolor{keywordflow}{ enddo} 185 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_a1f03feeee904430da4980f23e59a992b}\label{namespacemom__eos__linear_a1f03feeee904430da4980f23e59a992b}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+linear@{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+linear}} \index{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+linear@{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+linear()}{calculate\_density\_derivs\_scalar\_linear()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+linear (\begin{DoxyParamCaption}\item[{real, intent(in)}]{T, }\item[{real, intent(in)}]{S, }\item[{real, intent(in)}]{pressure, }\item[{real, intent(out)}]{drho\+\_\+d\+T\+\_\+out, }\item[{real, intent(out)}]{drho\+\_\+d\+S\+\_\+out, }\item[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS }\end{DoxyParamCaption})} This subroutine calculates the partial derivatives of density $\ast$ with potential temperature and salinity for a single point. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & Potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+dt\+\_\+out} & The partial derivative of density with potential temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+out} & The partial derivative of density with salinity \mbox{[}kg m-\/3 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivatives of density with temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivatives of density with salinity \mbox{[}kg m-\/3 ppt-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 192 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 192 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature relative to the surface} 193 \textcolor{comment}{ !! [degC].} 194 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [PSU].} 195 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 196 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: drho\_dT\_out\textcolor{comment}{ !< The partial derivative of density with} 197 \textcolor{comment}{ !! potential temperature [kg m-3 degC-1].} 198 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: drho\_dS\_out\textcolor{comment}{ !< The partial derivative of density with} 199 \textcolor{comment}{ !! salinity [kg m-3 ppt-1].} 200 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [kg m-3].} 201 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivatives of density with temperature [kg m-3 degC-1].} 202 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivatives of density with salinity [kg m-3 ppt-1].} 203 drho\_dt\_out = drho\_dt 204 drho\_ds\_out = drho\_ds 205 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_a39e8258b3b0ddd5d176061b48a151648}\label{namespacemom__eos__linear_a39e8258b3b0ddd5d176061b48a151648}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+density\+\_\+scalar\+\_\+linear@{calculate\+\_\+density\+\_\+scalar\+\_\+linear}} \index{calculate\+\_\+density\+\_\+scalar\+\_\+linear@{calculate\+\_\+density\+\_\+scalar\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+scalar\+\_\+linear()}{calculate\_density\_scalar\_linear()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+density\+\_\+scalar\+\_\+linear (\begin{DoxyParamCaption}\item[{real, intent(in)}]{T, }\item[{real, intent(in)}]{S, }\item[{real, intent(in)}]{pressure, }\item[{real, intent(out)}]{rho, }\item[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS, }\item[{real, intent(in), optional}]{rho\+\_\+ref }\end{DoxyParamCaption})} This subroutine computes the density of sea water with a trivial linear equation of state (in \mbox{[}kg m-\/3\mbox{]}) from salinity (sal \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & Potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em rho} & In situ density \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivatives of density with temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivatives of density with salinity in \mbox{[}kg m-\/3 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em rho\+\_\+ref} & A reference density \mbox{[}kg m-\/3\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 58 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 58 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature relative to the surface [degC].} 59 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [PSU].} 60 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 61 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: rho\textcolor{comment}{ !< In situ density [kg m-3].} 62 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [kg m-3].} 63 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivatives of density with temperature} 64 \textcolor{comment}{ !! [kg m-3 degC-1].} 65 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivatives of density with salinity} 66 \textcolor{comment}{ !! in [kg m-3 ppt-1].} 67 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A reference density [kg m-3].} 68 69 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(rho\_ref)) \textcolor{keywordflow}{then} 70 rho = (rho\_t0\_s0 - rho\_ref) + (drho\_dt*t + drho\_ds*s) 71 \textcolor{keywordflow}{else} 72 rho = rho\_t0\_s0 + drho\_dt*t + drho\_ds*s 73 \textcolor{keywordflow}{ endif} 74 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_adb222e7164a10bf7ce8e30d22a58ba46}\label{namespacemom__eos__linear_adb222e7164a10bf7ce8e30d22a58ba46}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+linear@{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+linear}} \index{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+linear@{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+linear()}{calculate\_density\_second\_derivs\_array\_linear()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+linear (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(out)}]{drho\+\_\+d\+S\+\_\+dS, }\item[{real, dimension(\+:), intent(out)}]{drho\+\_\+d\+S\+\_\+dT, }\item[{real, dimension(\+:), intent(out)}]{drho\+\_\+d\+T\+\_\+dT, }\item[{real, dimension(\+:), intent(out)}]{drho\+\_\+d\+S\+\_\+dP, }\item[{real, dimension(\+:), intent(out)}]{drho\+\_\+d\+T\+\_\+dP, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine calculates the five, partial second derivatives of density w.\+r.\+t. potential temperature and salinity and pressure which for a linear equation of state should all be 0. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & Potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+ds} & The second derivative of density with salinity \mbox{[}kg m-\/3 P\+S\+U-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+dt} & The second derivative of density with temperature and salinity \mbox{[}kg m-\/3 ppt-\/1 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+dt\+\_\+dt} & The second derivative of density with temperature \mbox{[}kg m-\/3 deg\+C-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+dp} & The second derivative of density with salinity and pressure \mbox{[}kg m-\/3 P\+S\+U-\/1 Pa-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+dt\+\_\+dp} & The second derivative of density with temperature and pressure \mbox{[}kg m-\/3 deg\+C-\/1 Pa-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em start} & The starting point in the arrays.\\ \hline \mbox{\tt in} & {\em npts} & The number of values to calculate. \\ \hline \end{DoxyParams} Definition at line 238 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 238 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature relative to the surface [degC].} 239 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [PSU].} 240 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 241 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(out)} :: drho\_dS\_dS\textcolor{comment}{ !< The second derivative of density with} 242 \textcolor{comment}{ !! salinity [kg m-3 PSU-2].} 243 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(out)} :: drho\_dS\_dT\textcolor{comment}{ !< The second derivative of density with} 244 \textcolor{comment}{ !! temperature and salinity [kg m-3 ppt-1 degC-1].} 245 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(out)} :: drho\_dT\_dT\textcolor{comment}{ !< The second derivative of density with} 246 \textcolor{comment}{ !! temperature [kg m-3 degC-2].} 247 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(out)} :: drho\_dS\_dP\textcolor{comment}{ !< The second derivative of density with} 248 \textcolor{comment}{ !! salinity and pressure [kg m-3 PSU-1 Pa-1].} 249 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(out)} :: drho\_dT\_dP\textcolor{comment}{ !< The second derivative of density with} 250 \textcolor{comment}{ !! temperature and pressure [kg m-3 degC-1 Pa-1].} 251 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< The starting point in the arrays.} 252 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< The number of values to calculate.} 253 \textcolor{comment}{! Local variables} 254 \textcolor{keywordtype}{integer} :: j 255 \textcolor{keywordflow}{do} j=start,start+npts-1 256 drho\_ds\_ds(j) = 0. 257 drho\_ds\_dt(j) = 0. 258 drho\_dt\_dt(j) = 0. 259 drho\_ds\_dp(j) = 0. 260 drho\_dt\_dp(j) = 0. 261 \textcolor{keywordflow}{ enddo} 262 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_a80a174894f52db0aa1cdb2b267d70e76}\label{namespacemom__eos__linear_a80a174894f52db0aa1cdb2b267d70e76}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+linear@{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+linear}} \index{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+linear@{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+linear()}{calculate\_density\_second\_derivs\_scalar\_linear()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+linear (\begin{DoxyParamCaption}\item[{real, intent(in)}]{T, }\item[{real, intent(in)}]{S, }\item[{real, intent(in)}]{pressure, }\item[{real, intent(out)}]{drho\+\_\+d\+S\+\_\+dS, }\item[{real, intent(out)}]{drho\+\_\+d\+S\+\_\+dT, }\item[{real, intent(out)}]{drho\+\_\+d\+T\+\_\+dT, }\item[{real, intent(out)}]{drho\+\_\+d\+S\+\_\+dP, }\item[{real, intent(out)}]{drho\+\_\+d\+T\+\_\+dP }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine calculates the five, partial second derivatives of density w.\+r.\+t. potential temperature and salinity and pressure which for a linear equation of state should all be 0. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & Potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+ds} & The second derivative of density with salinity \mbox{[}kg m-\/3 P\+S\+U-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+dt} & The second derivative of density with temperature and salinity \mbox{[}kg m-\/3 ppt-\/1 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+dt\+\_\+dt} & The second derivative of density with temperature \mbox{[}kg m-\/3 deg\+C-\/2\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+dp} & The second derivative of density with salinity and pressure \mbox{[}kg m-\/3 P\+S\+U-\/1 Pa-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+dt\+\_\+dp} & The second derivative of density with temperature and pressure \mbox{[}kg m-\/3 deg\+C-\/1 Pa-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 212 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 212 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature relative to the surface [degC].} 213 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [PSU].} 214 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 215 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: drho\_dS\_dS\textcolor{comment}{ !< The second derivative of density with} 216 \textcolor{comment}{ !! salinity [kg m-3 PSU-2].} 217 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: drho\_dS\_dT\textcolor{comment}{ !< The second derivative of density with} 218 \textcolor{comment}{ !! temperature and salinity [kg m-3 ppt-1 degC-1].} 219 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: drho\_dT\_dT\textcolor{comment}{ !< The second derivative of density with} 220 \textcolor{comment}{ !! temperature [kg m-3 degC-2].} 221 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: drho\_dS\_dP\textcolor{comment}{ !< The second derivative of density with} 222 \textcolor{comment}{ !! salinity and pressure [kg m-3 PSU-1 Pa-1].} 223 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: drho\_dT\_dP\textcolor{comment}{ !< The second derivative of density with} 224 \textcolor{comment}{ !! temperature and pressure [kg m-3 degC-1 Pa-1].} 225 226 drho\_ds\_ds = 0. 227 drho\_ds\_dt = 0. 228 drho\_dt\_dt = 0. 229 drho\_ds\_dp = 0. 230 drho\_dt\_dp = 0. 231 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_ab3b2951f265e375bd27a2eace7a91a87}\label{namespacemom__eos__linear_ab3b2951f265e375bd27a2eace7a91a87}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+linear@{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+linear}} \index{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+linear@{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+linear()}{calculate\_spec\_vol\_array\_linear()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+linear (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(out)}]{specvol, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts, }\item[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS, }\item[{real, intent(in), optional}]{spv\+\_\+ref }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine computes the in situ specific volume of sea water (specvol in \mbox{[}m3 kg-\/1\mbox{]}) from salinity (S \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}) and pressure \mbox{[}Pa\mbox{]}, using a trivial linear equation of state for density. If spv\+\_\+ref is present, specvol is an anomaly from spv\+\_\+ref. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & Pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em specvol} & in situ specific volume \mbox{[}m3 kg-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em start} & the starting point in the arrays.\\ \hline \mbox{\tt in} & {\em npts} & the number of values to calculate.\\ \hline \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivatives of density with temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivatives of density with salinity \mbox{[}kg m-\/3 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em spv\+\_\+ref} & A reference specific volume \mbox{[}m3 kg-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 138 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 138 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< potential temperature relative to the surface} 139 \textcolor{comment}{ !! [degC].} 140 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [PSU].} 141 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< Pressure [Pa].} 142 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(out)} :: specvol\textcolor{comment}{ !< in situ specific volume [m3 kg-1].} 143 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< the starting point in the arrays.} 144 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< the number of values to calculate.} 145 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [kg m-3].} 146 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivatives of density with temperature [kg m-3 degC-1].} 147 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivatives of density with salinity [kg m-3 ppt-1].} 148 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: spv\_ref\textcolor{comment}{ !< A reference specific volume [m3 kg-1].} 149 \textcolor{comment}{! Local variables} 150 \textcolor{keywordtype}{integer} :: j 151 152 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(spv\_ref)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=start,start+npts-1 153 specvol(j) = ((1.0 - rho\_t0\_s0*spv\_ref) + spv\_ref*(drho\_dt*t(j) + drho\_ds*s(j))) / & 154 ( rho\_t0\_s0 + (drho\_dt*t(j) + drho\_ds*s(j))) 155 \textcolor{keywordflow}{ enddo} ; \textcolor{keywordflow}{else} ; \textcolor{keywordflow}{do} j=start,start+npts-1 156 specvol(j) = 1.0 / ( rho\_t0\_s0 + (drho\_dt*t(j) + drho\_ds*s(j))) 157 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} 158 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_a64c38d475860e8ae042d221af8d7195a}\label{namespacemom__eos__linear_a64c38d475860e8ae042d221af8d7195a}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+linear@{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+linear}} \index{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+linear@{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+linear()}{calculate\_spec\_vol\_scalar\_linear()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+linear (\begin{DoxyParamCaption}\item[{real, intent(in)}]{T, }\item[{real, intent(in)}]{S, }\item[{real, intent(in)}]{pressure, }\item[{real, intent(out)}]{specvol, }\item[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS, }\item[{real, intent(in), optional}]{spv\+\_\+ref }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine computes the in situ specific volume of sea water (specvol in \mbox{[}m3 kg-\/1\mbox{]}) from salinity (S \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}) and pressure \mbox{[}Pa\mbox{]}, using a trivial linear equation of state for density. If spv\+\_\+ref is present, specvol is an anomaly from spv\+\_\+ref. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & Pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em specvol} & In situ specific volume \mbox{[}m3 kg-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivatives of density with temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivatives of density with salinity \mbox{[}kg m-\/3 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em spv\+\_\+ref} & A reference specific volume \mbox{[}m3 kg-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 111 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 111 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< potential temperature relative to the surface} 112 \textcolor{comment}{ !! [degC].} 113 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [PSU].} 114 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< Pressure [Pa].} 115 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: specvol\textcolor{comment}{ !< In situ specific volume [m3 kg-1].} 116 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [kg m-3].} 117 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivatives of density with temperature [kg m-3 degC-1].} 118 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivatives of density with salinity [kg m-3 ppt-1].} 119 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: spv\_ref\textcolor{comment}{ !< A reference specific volume [m3 kg-1].} 120 \textcolor{comment}{! Local variables} 121 \textcolor{keywordtype}{integer} :: j 122 123 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(spv\_ref)) \textcolor{keywordflow}{then} 124 specvol = ((1.0 - rho\_t0\_s0*spv\_ref) + spv\_ref*(drho\_dt*t + drho\_ds*s)) / & 125 ( rho\_t0\_s0 + (drho\_dt*t + drho\_ds*s)) 126 \textcolor{keywordflow}{else} 127 specvol = 1.0 / ( rho\_t0\_s0 + (drho\_dt*t + drho\_ds*s)) 128 \textcolor{keywordflow}{ endif} 129 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_ac104dedf6f20ab794c2c430462ace217}\label{namespacemom__eos__linear_ac104dedf6f20ab794c2c430462ace217}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!calculate\+\_\+specvol\+\_\+derivs\+\_\+linear@{calculate\+\_\+specvol\+\_\+derivs\+\_\+linear}} \index{calculate\+\_\+specvol\+\_\+derivs\+\_\+linear@{calculate\+\_\+specvol\+\_\+derivs\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{calculate\+\_\+specvol\+\_\+derivs\+\_\+linear()}{calculate\_specvol\_derivs\_linear()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+linear\+::calculate\+\_\+specvol\+\_\+derivs\+\_\+linear (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(out)}]{d\+S\+V\+\_\+dT, }\item[{real, dimension(\+:), intent(out)}]{d\+S\+V\+\_\+dS, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts, }\item[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS }\end{DoxyParamCaption})} Calculate the derivatives of specific volume with temperature and salinity. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & Potential temperature relative to the surface \mbox{[}degC\mbox{]}.\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em pressure} & pressure \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt out} & {\em dsv\+\_\+ds} & The partial derivative of specific volume with salinity \mbox{[}m3 kg-\/1 P\+S\+U-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em dsv\+\_\+dt} & The partial derivative of specific volume with potential temperature \mbox{[}m3 kg-\/1 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em start} & The starting point in the arrays.\\ \hline \mbox{\tt in} & {\em npts} & The number of values to calculate.\\ \hline \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivative of density with temperature, \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivative of density with salinity \mbox{[}kg m-\/3 ppt-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 268 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 268 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: T\textcolor{comment}{ !< Potential temperature relative to the surface} 269 \textcolor{comment}{ !! [degC].} 270 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: S\textcolor{comment}{ !< Salinity [PSU].} 271 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 272 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)}, \textcolor{keywordtype}{dimension(:)} :: dSV\_dS\textcolor{comment}{ !< The partial derivative of specific volume with} 273 \textcolor{comment}{ !! salinity [m3 kg-1 PSU-1].} 274 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)}, \textcolor{keywordtype}{dimension(:)} :: dSV\_dT\textcolor{comment}{ !< The partial derivative of specific volume with} 275 \textcolor{comment}{ !! potential temperature [m3 kg-1 degC-1].} 276 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< The starting point in the arrays.} 277 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< The number of values to calculate.} 278 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [kg m-3].} 279 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivative of density with} 280 \textcolor{comment}{ !! temperature, [kg m-3 degC-1].} 281 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivative of density with} 282 \textcolor{comment}{ !! salinity [kg m-3 ppt-1].} 283 \textcolor{comment}{! Local variables} 284 \textcolor{keywordtype}{real} :: I\_rho2 285 \textcolor{keywordtype}{integer} :: j 286 287 \textcolor{keywordflow}{do} j=start,start+npts-1 288 \textcolor{comment}{! Sv = 1.0 / (Rho\_T0\_S0 + dRho\_dT*T(j) + dRho\_dS*S(j))} 289 i\_rho2 = 1.0 / (rho\_t0\_s0 + (drho\_dt*t(j) + drho\_ds*s(j)))**2 290 dsv\_dt(j) = -drho\_dt * i\_rho2 291 dsv\_ds(j) = -drho\_ds * i\_rho2 292 \textcolor{keywordflow}{ enddo} 293 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_a4da51fc5de5654041e08fb43a8b0283c}\label{namespacemom__eos__linear_a4da51fc5de5654041e08fb43a8b0283c}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!int\+\_\+density\+\_\+dz\+\_\+linear@{int\+\_\+density\+\_\+dz\+\_\+linear}} \index{int\+\_\+density\+\_\+dz\+\_\+linear@{int\+\_\+density\+\_\+dz\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{int\+\_\+density\+\_\+dz\+\_\+linear()}{int\_density\_dz\_linear()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+linear\+::int\+\_\+density\+\_\+dz\+\_\+linear (\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\+\_\+pres, }\item[{real, intent(in)}]{G\+\_\+e, }\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\item[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS, }\item[{real, dimension(hi\%isd\+:hi\%ied,hi\%jsd\+:hi\%jed), intent(out)}]{dpa, }\item[{real, dimension(hi\%isd\+:hi\%ied,hi\%jsd\+:hi\%jed), intent(out), optional}]{intz\+\_\+dpa, }\item[{real, dimension(hi\%isdb\+:hi\%iedb,hi\%jsd\+:hi\%jed), intent(out), optional}]{intx\+\_\+dpa, }\item[{real, dimension(hi\%isd\+:hi\%ied,hi\%jsdb\+:hi\%jedb), intent(out), 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})} This subroutine calculates analytical and nearly-\/analytical 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{\tt in} & {\em hi} & The horizontal index type for the arrays.\\ \hline \mbox{\tt in} & {\em t} & Potential temperature relative to the surface\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt in} & {\em z\+\_\+t} & Height at the top of the layer in depth units \mbox{[}Z $\sim$$>$ m\mbox{]}.\\ \hline \mbox{\tt in} & {\em z\+\_\+b} & Height at the top of the layer \mbox{[}Z $\sim$$>$ m\mbox{]}.\\ \hline \mbox{\tt in} & {\em rho\+\_\+ref} & A mean density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is subtracted out to reduce the magnitude of each of the integrals.\\ \hline \mbox{\tt in} & {\em rho\+\_\+0\+\_\+pres} & A density \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]}, used to calculate the pressure (as p$\sim$=-\/z$\ast$rho\+\_\+0\+\_\+pres$\ast$\+G\+\_\+e) used in the equation of state. rho\+\_\+0\+\_\+pres is not used.\\ \hline \mbox{\tt 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 \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivative of density with temperature, \mbox{[}R deg\+C-\/1 $\sim$$>$ kg m-\/3 deg\+C-\/1\mbox{]} or \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivative of density with salinity, in \mbox{[}R ppt-\/1 $\sim$$>$ kg m-\/3 ppt-\/1\mbox{]} or \mbox{[}kg m-\/3 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em dpa} & The change in the pressure anomaly across the\\ \hline \mbox{\tt out} & {\em intz\+\_\+dpa} & The integral through the thickness of the layer\\ \hline \mbox{\tt out} & {\em intx\+\_\+dpa} & The integral in x of the difference between the\\ \hline \mbox{\tt out} & {\em inty\+\_\+dpa} & The integral in y of the difference between the\\ \hline \mbox{\tt in} & {\em bathyt} & The depth of the bathymetry \mbox{[}Z $\sim$$>$ m\mbox{]}.\\ \hline \mbox{\tt in} & {\em dz\+\_\+neglect} & A miniscule thickness change \mbox{[}Z $\sim$$>$ m\mbox{]}.\\ \hline \mbox{\tt in} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals. \\ \hline \end{DoxyParams} Definition at line 331 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 331 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: HI\textcolor{comment}{ !< The horizontal index type for the arrays.} 332 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 333 \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature relative to the surface} 334 \textcolor{comment}{ !! [degC].} 335 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 336 \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [PSU].} 337 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 338 \textcolor{keywordtype}{intent(in)} :: z\_t\textcolor{comment}{ !< Height at the top of the layer in depth units [Z ~> m].} 339 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 340 \textcolor{keywordtype}{intent(in)} :: z\_b\textcolor{comment}{ !< Height at the top of the layer [Z ~> m].} 341 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A mean density [R ~> kg m-3] or [kg m-3], that} 342 \textcolor{comment}{ !! is subtracted out to reduce the magnitude of} 343 \textcolor{comment}{ !! each of the integrals.} 344 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: rho\_0\_pres\textcolor{comment}{ !< A density [R ~> kg m-3], used to calculate} 345 \textcolor{comment}{ !! the pressure (as p~=-z*rho\_0\_pres*G\_e) used in} 346 \textcolor{comment}{ !! the equation of state. rho\_0\_pres is not used.} 347 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: G\_e\textcolor{comment}{ !< The Earth's gravitational acceleration} 348 \textcolor{comment}{ !! [L2 Z-1 T-2 ~> m s-2] or [m2 Z-1 s-2 ~> m s-2].} 349 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [R ~> kg m-3] or [kg m-3].} 350 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivative of density with temperature,} 351 \textcolor{comment}{ !! [R degC-1 ~> kg m-3 degC-1] or [kg m-3 degC-1].} 352 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivative of density with salinity,} 353 \textcolor{comment}{ !! in [R ppt-1 ~> kg m-3 ppt-1] or [kg m-3 ppt-1].} 354 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 355 \textcolor{keywordtype}{intent(out)} :: dpa\textcolor{comment}{ !< The change in the pressure anomaly across the} 356 \textcolor{comment}{ !! layer [R L2 T-2 ~> Pa] or [Pa].} 357 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 358 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: intz\_dpa\textcolor{comment}{ !< The integral through the thickness of the layer} 359 \textcolor{comment}{ !! of the pressure anomaly relative to the anomaly} 360 \textcolor{comment}{ !! at the top of the layer [R L2 Z T-2 ~> Pa Z] or [Pa Z].} 361 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%IsdB:HI%IedB,HI%jsd:HI%jed)}, & 362 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: intx\_dpa\textcolor{comment}{ !< The integral in x of the difference between the} 363 \textcolor{comment}{ !! pressure anomaly at the top and bottom of the} 364 \textcolor{comment}{ !! layer divided by the x grid spacing [R L2 T-2 ~> Pa] or [Pa].} 365 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%JsdB:HI%JedB)}, & 366 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: inty\_dpa\textcolor{comment}{ !< The integral in y of the difference between the} 367 \textcolor{comment}{ !! pressure anomaly at the top and bottom of the} 368 \textcolor{comment}{ !! layer divided by the y grid spacing [R L2 T-2 ~> Pa] or [Pa].} 369 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 370 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: bathyT\textcolor{comment}{ !< The depth of the bathymetry [Z ~> m].} 371 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: dz\_neglect\textcolor{comment}{ !< A miniscule thickness change [Z ~> m].} 372 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: useMassWghtInterp\textcolor{comment}{ !< If true, uses mass weighting to} 373 \textcolor{comment}{ !! interpolate T/S for top and bottom integrals.} 374 375 \textcolor{comment}{! Local variables} 376 \textcolor{keywordtype}{real} :: rho\_anom \textcolor{comment}{! The density anomaly from rho\_ref [R ~> kg m-3].} 377 \textcolor{keywordtype}{real} :: raL, raR \textcolor{comment}{! rho\_anom to the left and right [R ~> kg m-3].} 378 \textcolor{keywordtype}{real} :: dz, dzL, dzR \textcolor{comment}{! Layer thicknesses [Z ~> m].} 379 \textcolor{keywordtype}{real} :: hWght \textcolor{comment}{! A pressure-thickness below topography [Z ~> m].} 380 \textcolor{keywordtype}{real} :: hL, hR \textcolor{comment}{! Pressure-thicknesses of the columns to the left and right [Z ~> m].} 381 \textcolor{keywordtype}{real} :: iDenom \textcolor{comment}{! The inverse of the denominator in the weights [Z-2 ~> m-2].} 382 \textcolor{keywordtype}{real} :: hWt\_LL, hWt\_LR \textcolor{comment}{! hWt\_LA is the weighted influence of A on the left column [nondim].} 383 \textcolor{keywordtype}{real} :: hWt\_RL, hWt\_RR \textcolor{comment}{! hWt\_RA is the weighted influence of A on the right column [nondim].} 384 \textcolor{keywordtype}{real} :: wt\_L, wt\_R \textcolor{comment}{! The linear weights of the left and right columns [nondim].} 385 \textcolor{keywordtype}{real} :: wtT\_L, wtT\_R \textcolor{comment}{! The weights for tracers from the left and right columns [nondim].} 386 \textcolor{keywordtype}{real} :: intz(5) \textcolor{comment}{! The integrals of density with height at the} 387 \textcolor{comment}{! 5 sub-column locations [R L2 T-2 ~> Pa] or [Pa].} 388 \textcolor{keywordtype}{logical} :: do\_massWeight \textcolor{comment}{! Indicates whether to do mass weighting.} 389 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{parameter} :: C1\_6 = 1.0/6.0, c1\_90 = 1.0/90.0 \textcolor{comment}{! Rational constants.} 390 \textcolor{keywordtype}{integer} :: is, ie, js, je, Isq, Ieq, Jsq, Jeq, i, j, m 391 392 \textcolor{comment}{! These array bounds work for the indexing convention of the input arrays, but} 393 \textcolor{comment}{! on the computational domain defined for the output arrays.} 394 isq = hi%IscB ; ieq = hi%IecB 395 jsq = hi%JscB ; jeq = hi%JecB 396 is = hi%isc ; ie = hi%iec 397 js = hi%jsc ; je = hi%jec 398 399 do\_massweight = .false. 400 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(usemasswghtinterp)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (usemasswghtinterp) \textcolor{keywordflow}{then} 401 do\_massweight = .true. 402 \textcolor{comment}{! if (.not.present(bathyT)) call MOM\_error(FATAL, "int\_density\_dz\_generic: "//&} 403 \textcolor{comment}{! "bathyT must be present if useMassWghtInterp is present and true.")} 404 \textcolor{comment}{! if (.not.present(dz\_neglect)) call MOM\_error(FATAL, "int\_density\_dz\_generic: "//&} 405 \textcolor{comment}{! "dz\_neglect must be present if useMassWghtInterp is present and true.")} 406 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 407 408 \textcolor{keywordflow}{do} j=jsq,jeq+1 ; \textcolor{keywordflow}{do} i=isq,ieq+1 409 dz = z\_t(i,j) - z\_b(i,j) 410 rho\_anom = (rho\_t0\_s0 - rho\_ref) + drho\_dt*t(i,j) + drho\_ds*s(i,j) 411 dpa(i,j) = g\_e*rho\_anom*dz 412 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intz\_dpa)) intz\_dpa(i,j) = 0.5*g\_e*rho\_anom*dz**2 413 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 414 415 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=isq,ieq 416 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of} 417 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of} 418 \textcolor{comment}{! T & S along the top and bottom integrals, akin to thickness weighting.} 419 hwght = 0.0 420 \textcolor{keywordflow}{if} (do\_massweight) & 421 hwght = max(0., -bathyt(i,j)-z\_t(i+1,j), -bathyt(i+1,j)-z\_t(i,j)) 422 423 \textcolor{keywordflow}{if} (hwght <= 0.0) \textcolor{keywordflow}{then} 424 dzl = z\_t(i,j) - z\_b(i,j) ; dzr = z\_t(i+1,j) - z\_b(i+1,j) 425 ral = (rho\_t0\_s0 - rho\_ref) + (drho\_dt*t(i,j) + drho\_ds*s(i,j)) 426 rar = (rho\_t0\_s0 - rho\_ref) + (drho\_dt*t(i+1,j) + drho\_ds*s(i+1,j)) 427 428 intx\_dpa(i,j) = g\_e*c1\_6 * (dzl*(2.0*ral + rar) + dzr*(2.0*rar + ral)) 429 \textcolor{keywordflow}{else} 430 hl = (z\_t(i,j) - z\_b(i,j)) + dz\_neglect 431 hr = (z\_t(i+1,j) - z\_b(i+1,j)) + dz\_neglect 432 hwght = hwght * ( (hl-hr)/(hl+hr) )**2 433 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr ) 434 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom 435 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom 436 437 intz(1) = dpa(i,j) ; intz(5) = dpa(i+1,j) 438 \textcolor{keywordflow}{do} m=2,4 439 wt\_l = 0.25*\textcolor{keywordtype}{real(5-m)} ; wt\_R = 1.0-wt\_l 440 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr 441 442 dz = wt\_l*(z\_t(i,j) - z\_b(i,j)) + wt\_r*(z\_t(i+1,j) - z\_b(i+1,j)) 443 rho\_anom = (rho\_t0\_s0 - rho\_ref) + & 444 (drho\_dt * (wtt\_l*t(i,j) + wtt\_r*t(i+1,j)) + & 445 drho\_ds * (wtt\_l*s(i,j) + wtt\_r*s(i+1,j))) 446 intz(m) = g\_e*rho\_anom*dz 447 \textcolor{keywordflow}{ enddo} 448 \textcolor{comment}{! Use Boole's rule to integrate the values.} 449 intx\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + & 450 12.0*intz(3)) 451 \textcolor{keywordflow}{ endif} 452 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} 453 454 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=jsq,jeq ; \textcolor{keywordflow}{do} i=is,ie 455 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of} 456 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of} 457 \textcolor{comment}{! T & S along the top and bottom integrals, akin to thickness weighting.} 458 hwght = 0.0 459 \textcolor{keywordflow}{if} (do\_massweight) & 460 hwght = max(0., -bathyt(i,j)-z\_t(i,j+1), -bathyt(i,j+1)-z\_t(i,j)) 461 462 \textcolor{keywordflow}{if} (hwght <= 0.0) \textcolor{keywordflow}{then} 463 dzl = z\_t(i,j) - z\_b(i,j) ; dzr = z\_t(i,j+1) - z\_b(i,j+1) 464 ral = (rho\_t0\_s0 - rho\_ref) + (drho\_dt*t(i,j) + drho\_ds*s(i,j)) 465 rar = (rho\_t0\_s0 - rho\_ref) + (drho\_dt*t(i,j+1) + drho\_ds*s(i,j+1)) 466 467 inty\_dpa(i,j) = g\_e*c1\_6 * (dzl*(2.0*ral + rar) + dzr*(2.0*rar + ral)) 468 \textcolor{keywordflow}{else} 469 hl = (z\_t(i,j) - z\_b(i,j)) + dz\_neglect 470 hr = (z\_t(i,j+1) - z\_b(i,j+1)) + dz\_neglect 471 hwght = hwght * ( (hl-hr)/(hl+hr) )**2 472 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr ) 473 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom 474 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom 475 476 intz(1) = dpa(i,j) ; intz(5) = dpa(i,j+1) 477 \textcolor{keywordflow}{do} m=2,4 478 wt\_l = 0.25*\textcolor{keywordtype}{real(5-m)} ; wt\_R = 1.0-wt\_l 479 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr 480 481 dz = wt\_l*(z\_t(i,j) - z\_b(i,j)) + wt\_r*(z\_t(i,j+1) - z\_b(i,j+1)) 482 rho\_anom = (rho\_t0\_s0 - rho\_ref) + & 483 (drho\_dt * (wtt\_l*t(i,j) + wtt\_r*t(i,j+1)) + & 484 drho\_ds * (wtt\_l*s(i,j) + wtt\_r*s(i,j+1))) 485 intz(m) = g\_e*rho\_anom*dz 486 \textcolor{keywordflow}{ enddo} 487 \textcolor{comment}{! Use Boole's rule to integrate the values.} 488 inty\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + & 489 12.0*intz(3)) 490 \textcolor{keywordflow}{ endif} 491 492 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__linear_ac9a31e315e6cb02f8f270de7c877f688}\label{namespacemom__eos__linear_ac9a31e315e6cb02f8f270de7c877f688}} \index{mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}!int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+linear@{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+linear}} \index{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+linear@{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+linear}!mom\+\_\+eos\+\_\+linear@{mom\+\_\+eos\+\_\+linear}} \subsubsection{\texorpdfstring{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+linear()}{int\_spec\_vol\_dp\_linear()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+linear\+::int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+linear (\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[{real, intent(in)}]{Rho\+\_\+\+T0\+\_\+\+S0, }\item[{real, intent(in)}]{d\+Rho\+\_\+dT, }\item[{real, intent(in)}]{d\+Rho\+\_\+dS, }\item[{real, dimension(hi\%isd\+:hi\%ied,hi\%jsd\+:hi\%jed), intent(out)}]{dza, }\item[{real, dimension(hi\%isd\+:hi\%ied,hi\%jsd\+:hi\%jed), intent(out), optional}]{intp\+\_\+dza, }\item[{real, dimension(hi\%isdb\+:hi\%iedb,hi\%jsd\+:hi\%jed), intent(out), optional}]{intx\+\_\+dza, }\item[{real, dimension(hi\%isd\+:hi\%ied,hi\%jsdb\+:hi\%jedb), intent(out), 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})} Calculates 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. Specific volume is assumed to vary linearly between adjacent points. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em hi} & The ocean\textquotesingle{}s horizontal index type.\\ \hline \mbox{\tt in} & {\em t} & Potential temperature relative to the surface\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}.\\ \hline \mbox{\tt 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{\tt in} & {\em p\+\_\+b} & Pressure at the top of the layer \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]}.\\ \hline \mbox{\tt in} & {\em alpha\+\_\+ref} & A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals \mbox{[}R-\/1 $\sim$$>$ m3 kg-\/1\mbox{]}. The calculation is mathematically identical with different values of alpha\+\_\+ref, but this reduces the effects of roundoff.\\ \hline \mbox{\tt in} & {\em rho\+\_\+t0\+\_\+s0} & The density at T=0, S=0 \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+dt} & The derivative of density with temperature \mbox{[}R deg\+C-\/1 $\sim$$>$ kg m-\/3 deg\+C-\/1\mbox{]} or \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in} & {\em drho\+\_\+ds} & The derivative of density with salinity, in \mbox{[}R ppt-\/1 $\sim$$>$ kg m-\/3 ppt-\/1\mbox{]} or \mbox{[}kg m-\/3 ppt-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em dza} & The change in the geopotential anomaly across\\ \hline \mbox{\tt out} & {\em intp\+\_\+dza} & The integral in pressure through the layer of the\\ \hline \mbox{\tt out} & {\em intx\+\_\+dza} & The integral in x of the difference between the\\ \hline \mbox{\tt out} & {\em inty\+\_\+dza} & The integral in y of the difference between the\\ \hline \mbox{\tt in} & {\em halo\+\_\+size} & The width of halo points on which to calculate dza.\\ \hline \mbox{\tt in} & {\em bathyp} & The pressure at the bathymetry \mbox{[}R L2 T-\/2 $\sim$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]}\\ \hline \mbox{\tt 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{\tt in} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals. \\ \hline \end{DoxyParams} Definition at line 502 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+linear.\+F90. \begin{DoxyCode} 502 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: HI\textcolor{comment}{ !< The ocean's horizontal index type.} 503 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 504 \textcolor{keywordtype}{intent(in)} :: T\textcolor{comment}{ !< Potential temperature relative to the surface} 505 \textcolor{comment}{ !! [degC].} 506 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 507 \textcolor{keywordtype}{intent(in)} :: S\textcolor{comment}{ !< Salinity [PSU].} 508 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 509 \textcolor{keywordtype}{intent(in)} :: p\_t\textcolor{comment}{ !< Pressure at the top of the layer [R L2 T-2 ~> Pa] or [Pa].} 510 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 511 \textcolor{keywordtype}{intent(in)} :: p\_b\textcolor{comment}{ !< Pressure at the top of the layer [R L2 T-2 ~> Pa] or [Pa].} 512 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: alpha\_ref\textcolor{comment}{ !< A mean specific volume that is subtracted out} 513 \textcolor{comment}{ !! to reduce the magnitude of each of the integrals [R-1 ~> m3 kg-1].} 514 \textcolor{comment}{ !! The calculation is mathematically identical with different values of} 515 \textcolor{comment}{ !! alpha\_ref, but this reduces the effects of roundoff.} 516 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: Rho\_T0\_S0\textcolor{comment}{ !< The density at T=0, S=0 [R ~> kg m-3] or [kg m-3].} 517 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dT\textcolor{comment}{ !< The derivative of density with temperature} 518 \textcolor{comment}{ !! [R degC-1 ~> kg m-3 degC-1] or [kg m-3 degC-1].} 519 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: dRho\_dS\textcolor{comment}{ !< The derivative of density with salinity,} 520 \textcolor{comment}{ !! in [R ppt-1 ~> kg m-3 ppt-1] or [kg m-3 ppt-1].} 521 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 522 \textcolor{keywordtype}{intent(out)} :: dza\textcolor{comment}{ !< The change in the geopotential anomaly across} 523 \textcolor{comment}{ !! the layer [L2 T-2 ~> m2 s-2] or [m2 s-2].} 524 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 525 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: intp\_dza\textcolor{comment}{ !< The integral in pressure through the layer of the} 526 \textcolor{comment}{ !! geopotential anomaly relative to the anomaly at the} 527 \textcolor{comment}{ !! bottom of the layer [R L4 T-4 ~> Pa m2 s-2] or [Pa m2 s-2].} 528 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%IsdB:HI%IedB,HI%jsd:HI%jed)}, & 529 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: intx\_dza\textcolor{comment}{ !< The integral in x of the difference between the} 530 \textcolor{comment}{ !! geopotential anomaly at the top and bottom of} 531 \textcolor{comment}{ !! the layer divided by the x grid spacing} 532 \textcolor{comment}{ !! [L2 T-2 ~> m2 s-2] or [m2 s-2].} 533 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%JsdB:HI%JedB)}, & 534 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(out)} :: inty\_dza\textcolor{comment}{ !< The integral in y of the difference between the} 535 \textcolor{comment}{ !! geopotential anomaly at the top and bottom of} 536 \textcolor{comment}{ !! the layer divided by the y grid spacing} 537 \textcolor{comment}{ !! [L2 T-2 ~> m2 s-2] or [m2 s-2].} 538 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: halo\_size\textcolor{comment}{ !< The width of halo points on which to calculate dza.} 539 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 540 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: bathyP\textcolor{comment}{ !< The pressure at the bathymetry [R L2 T-2 ~> Pa] or [Pa]} 541 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: dP\_neglect\textcolor{comment}{ !< A miniscule pressure change with} 542 \textcolor{comment}{ !! the same units as p\_t [R L2 T-2 ~> Pa] or [Pa]} 543 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: useMassWghtInterp\textcolor{comment}{ !< If true, uses mass weighting} 544 \textcolor{comment}{ !! to interpolate T/S for top and bottom integrals.} 545 \textcolor{comment}{! Local variables} 546 \textcolor{keywordtype}{real} :: dRho\_TS \textcolor{comment}{! The density anomaly due to T and S [R ~> kg m-3] or [kg m-3].} 547 \textcolor{keywordtype}{real} :: alpha\_anom \textcolor{comment}{! The specific volume anomaly from 1/rho\_ref [R-1 ~> m3 kg-1] or [m3 kg-1].} 548 \textcolor{keywordtype}{real} :: aaL, aaR \textcolor{comment}{! The specific volume anomaly to the left and right [R-1 ~> m3 kg-1] or [m3 kg-1].} 549 \textcolor{keywordtype}{real} :: dp, dpL, dpR \textcolor{comment}{! Layer pressure thicknesses [R L2 T-2 ~> Pa] or [Pa].} 550 \textcolor{keywordtype}{real} :: hWght \textcolor{comment}{! A pressure-thickness below topography [R L2 T-2 ~> Pa] or [Pa].} 551 \textcolor{keywordtype}{real} :: hL, hR \textcolor{comment}{! Pressure-thicknesses of the columns to the left and right [R L2 T-2 ~> Pa] or [Pa].} 552 \textcolor{keywordtype}{real} :: iDenom \textcolor{comment}{! The inverse of the denominator in the weights [T4 R-2 L-2 ~> Pa-2] or [Pa-2].} 553 \textcolor{keywordtype}{real} :: hWt\_LL, hWt\_LR \textcolor{comment}{! hWt\_LA is the weighted influence of A on the left column [nondim].} 554 \textcolor{keywordtype}{real} :: hWt\_RL, hWt\_RR \textcolor{comment}{! hWt\_RA is the weighted influence of A on the right column [nondim].} 555 \textcolor{keywordtype}{real} :: wt\_L, wt\_R \textcolor{comment}{! The linear weights of the left and right columns [nondim].} 556 \textcolor{keywordtype}{real} :: wtT\_L, wtT\_R \textcolor{comment}{! The weights for tracers from the left and right columns [nondim].} 557 \textcolor{keywordtype}{real} :: intp(5) \textcolor{comment}{! The integrals of specific volume with pressure at the} 558 \textcolor{comment}{! 5 sub-column locations [L2 T-2 ~> m2 s-2] or [m2 s-2].} 559 \textcolor{keywordtype}{logical} :: do\_massWeight \textcolor{comment}{! Indicates whether to do mass weighting.} 560 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{parameter} :: C1\_6 = 1.0/6.0, c1\_90 = 1.0/90.0 \textcolor{comment}{! Rational constants.} 561 \textcolor{keywordtype}{integer} :: Isq, Ieq, Jsq, Jeq, ish, ieh, jsh, jeh, i, j, m, halo 562 563 isq = hi%IscB ; ieq = hi%IecB ; jsq = hi%JscB ; jeq = hi%JecB 564 halo = 0 ; \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(halo\_size)) halo = max(halo\_size,0) 565 ish = hi%isc-halo ; ieh = hi%iec+halo ; jsh = hi%jsc-halo ; jeh = hi%jec+halo 566 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dza)) \textcolor{keywordflow}{then} ; ish = min(isq,ish) ; ieh = max(ieq+1,ieh);\textcolor{keywordflow}{ endif} 567 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dza)) \textcolor{keywordflow}{then} ; jsh = min(jsq,jsh) ; jeh = max(jeq+1,jeh);\textcolor{keywordflow}{ endif} 568 569 do\_massweight = .false. 570 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(usemasswghtinterp)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (usemasswghtinterp) \textcolor{keywordflow}{then} 571 do\_massweight = .true. 572 \textcolor{comment}{! if (.not.present(bathyP)) call MOM\_error(FATAL, "int\_spec\_vol\_dp\_generic: "//&} 573 \textcolor{comment}{! "bathyP must be present if useMassWghtInterp is present and true.")} 574 \textcolor{comment}{! if (.not.present(dP\_neglect)) call MOM\_error(FATAL, "int\_spec\_vol\_dp\_generic: "//&} 575 \textcolor{comment}{! "dP\_neglect must be present if useMassWghtInterp is present and true.")} 576 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 577 578 \textcolor{keywordflow}{do} j=jsh,jeh ; \textcolor{keywordflow}{do} i=ish,ieh 579 dp = p\_b(i,j) - p\_t(i,j) 580 drho\_ts = drho\_dt*t(i,j) + drho\_ds*s(i,j) 581 \textcolor{comment}{! alpha\_anom = 1.0/(Rho\_T0\_S0 + dRho\_TS)) - alpha\_ref} 582 alpha\_anom = ((1.0-rho\_t0\_s0*alpha\_ref) - drho\_ts*alpha\_ref) / (rho\_t0\_s0 + drho\_ts) 583 dza(i,j) = alpha\_anom*dp 584 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intp\_dza)) intp\_dza(i,j) = 0.5*alpha\_anom*dp**2 585 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 586 587 \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 588 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of} 589 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of} 590 \textcolor{comment}{! T & S along the top and bottom integrals, akin to thickness weighting.} 591 hwght = 0.0 592 \textcolor{keywordflow}{if} (do\_massweight) & 593 hwght = max(0., bathyp(i,j)-p\_t(i+1,j), bathyp(i+1,j)-p\_t(i,j)) 594 595 \textcolor{keywordflow}{if} (hwght <= 0.0) \textcolor{keywordflow}{then} 596 dpl = p\_b(i,j) - p\_t(i,j) ; dpr = p\_b(i+1,j) - p\_t(i+1,j) 597 drho\_ts = drho\_dt*t(i,j) + drho\_ds*s(i,j) 598 aal = ((1.0 - rho\_t0\_s0*alpha\_ref) - drho\_ts*alpha\_ref) / (rho\_t0\_s0 + drho\_ts) 599 drho\_ts = drho\_dt*t(i+1,j) + drho\_ds*s(i+1,j) 600 aar = ((1.0 - rho\_t0\_s0*alpha\_ref) - drho\_ts*alpha\_ref) / (rho\_t0\_s0 + drho\_ts) 601 602 intx\_dza(i,j) = c1\_6 * (2.0*(dpl*aal + dpr*aar) + (dpl*aar + dpr*aal)) 603 \textcolor{keywordflow}{else} 604 hl = (p\_b(i,j) - p\_t(i,j)) + dp\_neglect 605 hr = (p\_b(i+1,j) - p\_t(i+1,j)) + dp\_neglect 606 hwght = hwght * ( (hl-hr)/(hl+hr) )**2 607 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr ) 608 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom 609 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom 610 611 intp(1) = dza(i,j) ; intp(5) = dza(i+1,j) 612 \textcolor{keywordflow}{do} m=2,4 613 wt\_l = 0.25*\textcolor{keywordtype}{real(5-m)} ; wt\_R = 1.0-wt\_l 614 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr 615 616 \textcolor{comment}{! T, S, and p are interpolated in the horizontal. The p interpolation} 617 \textcolor{comment}{! is linear, but for T and S it may be thickness wekghted.} 618 dp = wt\_l*(p\_b(i,j) - p\_t(i,j)) + wt\_r*(p\_b(i+1,j) - p\_t(i+1,j)) 619 620 drho\_ts = drho\_dt*(wtt\_l*t(i,j) + wtt\_r*t(i+1,j)) + & 621 drho\_ds*(wtt\_l*s(i,j) + wtt\_r*s(i+1,j)) 622 \textcolor{comment}{! alpha\_anom = 1.0/(Rho\_T0\_S0 + dRho\_TS)) - alpha\_ref} 623 alpha\_anom = ((1.0-rho\_t0\_s0*alpha\_ref) - drho\_ts*alpha\_ref) / (rho\_t0\_s0 + drho\_ts) 624 intp(m) = alpha\_anom*dp 625 \textcolor{keywordflow}{ enddo} 626 \textcolor{comment}{! Use Boole's rule to integrate the interface height anomaly values in y.} 627 intx\_dza(i,j) = c1\_90*(7.0*(intp(1)+intp(5)) + 32.0*(intp(2)+intp(4)) + & 628 12.0*intp(3)) 629 \textcolor{keywordflow}{ endif} 630 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} 631 632 \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 633 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of} 634 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of} 635 \textcolor{comment}{! T & S along the top and bottom integrals, akin to thickness weighting.} 636 hwght = 0.0 637 \textcolor{keywordflow}{if} (do\_massweight) & 638 hwght = max(0., bathyp(i,j)-p\_t(i,j+1), bathyp(i,j+1)-p\_t(i,j)) 639 640 \textcolor{keywordflow}{if} (hwght <= 0.0) \textcolor{keywordflow}{then} 641 dpl = p\_b(i,j) - p\_t(i,j) ; dpr = p\_b(i,j+1) - p\_t(i,j+1) 642 drho\_ts = drho\_dt*t(i,j) + drho\_ds*s(i,j) 643 aal = ((1.0 - rho\_t0\_s0*alpha\_ref) - drho\_ts*alpha\_ref) / (rho\_t0\_s0 + drho\_ts) 644 drho\_ts = drho\_dt*t(i,j+1) + drho\_ds*s(i,j+1) 645 aar = ((1.0 - rho\_t0\_s0*alpha\_ref) - drho\_ts*alpha\_ref) / (rho\_t0\_s0 + drho\_ts) 646 647 inty\_dza(i,j) = c1\_6 * (2.0*(dpl*aal + dpr*aar) + (dpl*aar + dpr*aal)) 648 \textcolor{keywordflow}{else} 649 hl = (p\_b(i,j) - p\_t(i,j)) + dp\_neglect 650 hr = (p\_b(i,j+1) - p\_t(i,j+1)) + dp\_neglect 651 hwght = hwght * ( (hl-hr)/(hl+hr) )**2 652 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr ) 653 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom 654 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom 655 656 intp(1) = dza(i,j) ; intp(5) = dza(i,j+1) 657 \textcolor{keywordflow}{do} m=2,4 658 wt\_l = 0.25*\textcolor{keywordtype}{real(5-m)} ; wt\_R = 1.0-wt\_l 659 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr 660 661 \textcolor{comment}{! T, S, and p are interpolated in the horizontal. The p interpolation} 662 \textcolor{comment}{! is linear, but for T and S it may be thickness wekghted.} 663 dp = wt\_l*(p\_b(i,j) - p\_t(i,j)) + wt\_r*(p\_b(i,j+1) - p\_t(i,j+1)) 664 665 drho\_ts = drho\_dt*(wtt\_l*t(i,j) + wtt\_r*t(i,j+1)) + & 666 drho\_ds*(wtt\_l*s(i,j) + wtt\_r*s(i,j+1)) 667 \textcolor{comment}{! alpha\_anom = 1.0/(Rho\_T0\_S0 + dRho\_TS)) - alpha\_ref} 668 alpha\_anom = ((1.0-rho\_t0\_s0*alpha\_ref) - drho\_ts*alpha\_ref) / (rho\_t0\_s0 + drho\_ts) 669 intp(m) = alpha\_anom*dp 670 \textcolor{keywordflow}{ enddo} 671 \textcolor{comment}{! Use Boole's rule to integrate the interface height anomaly values in y.} 672 inty\_dza(i,j) = c1\_90*(7.0*(intp(1)+intp(5)) + 32.0*(intp(2)+intp(4)) + & 673 12.0*intp(3)) 674 \textcolor{keywordflow}{ endif} 675 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} \end{DoxyCode}