\hypertarget{namespacemom__eos__wright}{}\section{mom\+\_\+eos\+\_\+wright Module Reference} \label{namespacemom__eos__wright}\index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsection{Detailed Description} The equation of state using the Wright 1997 expressions. \subsection*{Data Types} \begin{DoxyCompactItemize} \item interface \hyperlink{interfacemom__eos__wright_1_1calculate__density__derivs__wright}{calculate\+\_\+density\+\_\+derivs\+\_\+wright} \begin{DoxyCompactList}\small\item\em For a given thermodynamic state, return the derivatives of density with temperature and salinity. \end{DoxyCompactList}\item interface \hyperlink{interfacemom__eos__wright_1_1calculate__density__second__derivs__wright}{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+wright} \begin{DoxyCompactList}\small\item\em For a given thermodynamic state, return the second derivatives of density with various combinations of temperature, salinity, and pressure. \end{DoxyCompactList}\item interface \hyperlink{interfacemom__eos__wright_1_1calculate__density__wright}{calculate\+\_\+density\+\_\+wright} \begin{DoxyCompactList}\small\item\em Compute the in situ density of sea water (in \mbox{[}kg m-\/3\mbox{]}), or its anomaly with respect to a reference density, from salinity (in psu), potential temperature (in deg C), and pressure \mbox{[}Pa\mbox{]}, using the expressions from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. \end{DoxyCompactList}\item interface \hyperlink{interfacemom__eos__wright_1_1calculate__spec__vol__wright}{calculate\+\_\+spec\+\_\+vol\+\_\+wright} \begin{DoxyCompactList}\small\item\em Compute the in situ specific volume of sea water (in \mbox{[}m3 kg-\/1\mbox{]}), or an anomaly with respect to a reference specific volume, from salinity (in psu), potential temperature (in deg C), and pressure \mbox{[}Pa\mbox{]}, using the expressions from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Functions/\+Subroutines} \begin{DoxyCompactItemize} \item subroutine \hyperlink{namespacemom__eos__wright_a047725cee226bb5621080176aaff36d6}{calculate\+\_\+density\+\_\+scalar\+\_\+wright} (T, S, pressure, rho, rho\+\_\+ref) \begin{DoxyCompactList}\small\item\em This subroutine computes the in situ density of sea water (rho in \mbox{[}kg m-\/3\mbox{]}) from salinity (S \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__eos__wright_a9d96824061e9c3d438c3d909a00fb7ab}{calculate\+\_\+density\+\_\+array\+\_\+wright} (T, S, pressure, rho, start, npts, rho\+\_\+ref) \begin{DoxyCompactList}\small\item\em This subroutine computes the in situ density of sea water (rho in \mbox{[}kg m-\/3\mbox{]}) from salinity (S \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__eos__wright_aa1577bed7878372af9be62afea06cbf0}{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+wright} (T, S, pressure, specvol, 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{]}. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. If spv\+\_\+ref is present, specvol is an anomaly from spv\+\_\+ref. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__eos__wright_a0e1da760ed0fca53533430d0bd03ee6d}{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+wright} (T, S, pressure, specvol, start, npts, 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{]}. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. If spv\+\_\+ref is present, specvol is an anomaly from spv\+\_\+ref. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__eos__wright_a576d1ff13c93f4a3ffbd483d43a78ab7}{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+wright} (T, S, pressure, drho\+\_\+dT, drho\+\_\+dS, start, npts) \begin{DoxyCompactList}\small\item\em For a given thermodynamic state, return the thermal/haline expansion coefficients. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__eos__wright_a8264a21fbe5809d5290ea388e0b2e64f}{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+wright} (T, S, pressure, drho\+\_\+dT, drho\+\_\+dS) \begin{DoxyCompactList}\small\item\em The scalar version of calculate\+\_\+density\+\_\+derivs which promotes scalar inputs to a 1-\/element array and then demotes the output back to a scalar. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__eos__wright_a218432c80512597414f0c1fe4ae2d97d}{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+wright} (T, S, P, drho\+\_\+ds\+\_\+ds, drho\+\_\+ds\+\_\+dt, drho\+\_\+dt\+\_\+dt, drho\+\_\+ds\+\_\+dp, drho\+\_\+dt\+\_\+dp, start, npts) \begin{DoxyCompactList}\small\item\em Second derivatives of density with respect to temperature, salinity, and pressure. \end{DoxyCompactList}\item subroutine \hyperlink{namespacemom__eos__wright_a74e1c5129ef4414337347a115bcdff10}{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+wright} (T, S, P, drho\+\_\+ds\+\_\+ds, drho\+\_\+ds\+\_\+dt, drho\+\_\+dt\+\_\+dt, drho\+\_\+ds\+\_\+dp, drho\+\_\+dt\+\_\+dp) \begin{DoxyCompactList}\small\item\em Second derivatives of density with respect to temperature, salinity, and pressure for scalar inputs. Inputs promoted to 1-\/element array and output demoted to scalar. \end{DoxyCompactList}\item subroutine, public \hyperlink{namespacemom__eos__wright_a890d098ddbdc76f6cfbf1b7cf19b6388}{calculate\+\_\+specvol\+\_\+derivs\+\_\+wright} (T, S, pressure, d\+S\+V\+\_\+dT, d\+S\+V\+\_\+dS, start, npts) \begin{DoxyCompactList}\small\item\em For a given thermodynamic state, return the partial derivatives of specific volume with temperature and salinity. \end{DoxyCompactList}\item subroutine, public \hyperlink{namespacemom__eos__wright_ab5610ab6dd25f488ff5821dcbde78e0d}{calculate\+\_\+compress\+\_\+wright} (T, S, pressure, rho, drho\+\_\+dp, start, npts) \begin{DoxyCompactList}\small\item\em This subroutine computes the in situ density of sea water (rho in \mbox{[}kg m-\/3\mbox{]}) and the compressibility (drho/dp = C\+\_\+sound$^\wedge$-\/2) (drho\+\_\+dp \mbox{[}s2 m-\/2\mbox{]}) from salinity (sal in psu), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. It uses the expressions from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. Coded by R. Hallberg, 1/01. \end{DoxyCompactList}\item subroutine, public \hyperlink{namespacemom__eos__wright_ac94eaa2504eb4ccb12b41add45e1301e}{int\+\_\+density\+\_\+dz\+\_\+wright} (T, S, z\+\_\+t, z\+\_\+b, rho\+\_\+ref, rho\+\_\+0, G\+\_\+e, HI, dpa, intz\+\_\+dpa, intx\+\_\+dpa, inty\+\_\+dpa, bathyT, dz\+\_\+neglect, use\+Mass\+Wght\+Interp, rho\+\_\+scale, pres\+\_\+scale) \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 \hyperlink{namespacemom__eos__wright_a35402f454f02a3fa680a6d7870931aa6}{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+wright} (T, S, p\+\_\+t, p\+\_\+b, spv\+\_\+ref, HI, dza, intp\+\_\+dza, intx\+\_\+dza, inty\+\_\+dza, halo\+\_\+size, bathyP, d\+P\+\_\+neglect, use\+Mass\+Wght\+Interp, S\+V\+\_\+scale, pres\+\_\+scale) \begin{DoxyCompactList}\small\item\em This subroutine 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. 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}\end{DoxyCompactItemize} \subsection*{Variables} \textbf{ }\par \begin{DoxyCompactItemize} \item \mbox{\Hypertarget{namespacemom__eos__wright_a987d5c090f8875b3f847ffcedfcbbec3}\label{namespacemom__eos__wright_a987d5c090f8875b3f847ffcedfcbbec3}} real, parameter \hyperlink{namespacemom__eos__wright_a987d5c090f8875b3f847ffcedfcbbec3}{a0} = 7.\+057924e-\/4 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a7e7cc154421595caa7f3624fe1ca3673}\label{namespacemom__eos__wright_a7e7cc154421595caa7f3624fe1ca3673}} real, parameter \hyperlink{namespacemom__eos__wright_a7e7cc154421595caa7f3624fe1ca3673}{a1} = 3.\+480336e-\/7 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a4a32a06ae840315cf54baa44822e348d}\label{namespacemom__eos__wright_a4a32a06ae840315cf54baa44822e348d}} real, parameter \hyperlink{namespacemom__eos__wright_a4a32a06ae840315cf54baa44822e348d}{a2} = -\/1.\+112733e-\/7 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_af4229fb5d51c0a7ff4728400c07f8b27}\label{namespacemom__eos__wright_af4229fb5d51c0a7ff4728400c07f8b27}} real, parameter \hyperlink{namespacemom__eos__wright_af4229fb5d51c0a7ff4728400c07f8b27}{b0} = 5.\+790749e8 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a50e15ae674d09fcbb22d050ba02d8a45}\label{namespacemom__eos__wright_a50e15ae674d09fcbb22d050ba02d8a45}} real, parameter \hyperlink{namespacemom__eos__wright_a50e15ae674d09fcbb22d050ba02d8a45}{b1} = 3.\+516535e6 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a7789c35566542d0531bec1e59bfb0142}\label{namespacemom__eos__wright_a7789c35566542d0531bec1e59bfb0142}} real, parameter \hyperlink{namespacemom__eos__wright_a7789c35566542d0531bec1e59bfb0142}{b2} = -\/4.\+002714e4 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a6d60b717365295a1cc748ca0952799dc}\label{namespacemom__eos__wright_a6d60b717365295a1cc748ca0952799dc}} real, parameter \hyperlink{namespacemom__eos__wright_a6d60b717365295a1cc748ca0952799dc}{b3} = 2.\+084372e2 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a56b4d3d9cbd8ef16485d99c207214806}\label{namespacemom__eos__wright_a56b4d3d9cbd8ef16485d99c207214806}} real, parameter \hyperlink{namespacemom__eos__wright_a56b4d3d9cbd8ef16485d99c207214806}{b4} = 5.\+944068e5 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a9db48983c2f40b67bc472fe5f9621a7e}\label{namespacemom__eos__wright_a9db48983c2f40b67bc472fe5f9621a7e}} real, parameter \hyperlink{namespacemom__eos__wright_a9db48983c2f40b67bc472fe5f9621a7e}{b5} = -\/9.\+643486e3 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a218345b2966cffd9e1ef2b17170e8525}\label{namespacemom__eos__wright_a218345b2966cffd9e1ef2b17170e8525}} real, parameter \hyperlink{namespacemom__eos__wright_a218345b2966cffd9e1ef2b17170e8525}{c0} = 1.\+704853e5 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a31d4375b948d86099cb395cab4b9a771}\label{namespacemom__eos__wright_a31d4375b948d86099cb395cab4b9a771}} real, parameter \hyperlink{namespacemom__eos__wright_a31d4375b948d86099cb395cab4b9a771}{c1} = 7.\+904722e2 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a8cac4a7420b6ac57f3c9e1abc251a110}\label{namespacemom__eos__wright_a8cac4a7420b6ac57f3c9e1abc251a110}} real, parameter \hyperlink{namespacemom__eos__wright_a8cac4a7420b6ac57f3c9e1abc251a110}{c2} = -\/7.\+984422 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a4cb9d874402c19becc87294045861267}\label{namespacemom__eos__wright_a4cb9d874402c19becc87294045861267}} real, parameter \hyperlink{namespacemom__eos__wright_a4cb9d874402c19becc87294045861267}{c3} = 5.\+140652e-\/2 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a946198aad59501f936a956f6f9da0861}\label{namespacemom__eos__wright_a946198aad59501f936a956f6f9da0861}} real, parameter \hyperlink{namespacemom__eos__wright_a946198aad59501f936a956f6f9da0861}{c4} = -\/2.\+302158e2 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespacemom__eos__wright_a240d653273908c24302d935f94f32c4c}\label{namespacemom__eos__wright_a240d653273908c24302d935f94f32c4c}} real, parameter \hyperlink{namespacemom__eos__wright_a240d653273908c24302d935f94f32c4c}{c5} = -\/3.\+079464 \begin{DoxyCompactList}\small\item\em Parameters in the Wright equation of state. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Function/\+Subroutine Documentation} \mbox{\Hypertarget{namespacemom__eos__wright_ab5610ab6dd25f488ff5821dcbde78e0d}\label{namespacemom__eos__wright_ab5610ab6dd25f488ff5821dcbde78e0d}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+compress\+\_\+wright@{calculate\+\_\+compress\+\_\+wright}} \index{calculate\+\_\+compress\+\_\+wright@{calculate\+\_\+compress\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+compress\+\_\+wright()}{calculate\_compress\_wright()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+compress\+\_\+wright (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(inout)}]{rho, }\item[{real, dimension(\+:), intent(inout)}]{drho\+\_\+dp, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts }\end{DoxyParamCaption})} This subroutine computes the in situ density of sea water (rho in \mbox{[}kg m-\/3\mbox{]}) and the compressibility (drho/dp = C\+\_\+sound$^\wedge$-\/2) (drho\+\_\+dp \mbox{[}s2 m-\/2\mbox{]}) from salinity (sal in psu), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. It uses the expressions from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. Coded by R. Hallberg, 1/01. \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 in,out} & {\em rho} & In situ density \mbox{[}kg m-\/3\mbox{]}.\\ \hline \mbox{\tt in,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 \end{DoxyParams} Definition at line 380 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 380 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: t\textcolor{comment}{ !< Potential temperature relative to the surface [degC].} 381 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: s\textcolor{comment}{ !< Salinity [PSU].} 382 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 383 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(inout)}, \textcolor{keywordtype}{dimension(:)} :: rho\textcolor{comment}{ !< In situ density [kg m-3].} 384 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(inout)}, \textcolor{keywordtype}{dimension(:)} :: drho\_dp\textcolor{comment}{ !< The partial derivative of density with pressure} 385 \textcolor{comment}{ !! (also the inverse of the square of sound speed)} 386 \textcolor{comment}{ !! [s2 m-2].} 387 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< The starting point in the arrays.} 388 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< The number of values to calculate.} 389 390 \textcolor{comment}{! Coded by R. Hallberg, 1/01} 391 \textcolor{comment}{! Local variables} 392 \textcolor{keywordtype}{real} :: al0, p0, lambda, i\_denom 393 \textcolor{keywordtype}{integer} :: j 394 395 \textcolor{keywordflow}{do} j=start,start+npts-1 396 al0 = (a0 + a1*t(j)) +a2*s(j) 397 p0 = (b0 + b4*s(j)) + t(j) * (b1 + t(j)*((b2 + b3*t(j))) + b5*s(j)) 398 lambda = (c0 +c4*s(j)) + t(j) * (c1 + t(j)*((c2 + c3*t(j))) + c5*s(j)) 399 400 i\_denom = 1.0 / (lambda + al0*(pressure(j) + p0)) 401 rho(j) = (pressure(j) + p0) * i\_denom 402 drho\_dp(j) = lambda * i\_denom * i\_denom 403 \textcolor{keywordflow}{ enddo} \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_a9d96824061e9c3d438c3d909a00fb7ab}\label{namespacemom__eos__wright_a9d96824061e9c3d438c3d909a00fb7ab}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+density\+\_\+array\+\_\+wright@{calculate\+\_\+density\+\_\+array\+\_\+wright}} \index{calculate\+\_\+density\+\_\+array\+\_\+wright@{calculate\+\_\+density\+\_\+array\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+array\+\_\+wright()}{calculate\_density\_array\_wright()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+array\+\_\+wright (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(inout)}]{rho, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts, }\item[{real, intent(in), optional}]{rho\+\_\+ref }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine computes the in situ density of sea water (rho in \mbox{[}kg m-\/3\mbox{]}) from salinity (S \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. \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 in,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\+\_\+ref} & A reference density \mbox{[}kg m-\/3\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 111 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 111 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: t\textcolor{comment}{ !< potential temperature relative to the surface [degC].} 112 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: s\textcolor{comment}{ !< salinity [PSU].} 113 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 114 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(inout)} :: rho\textcolor{comment}{ !< in situ density [kg m-3].} 115 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< the starting point in the arrays.} 116 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< the number of values to calculate.} 117 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A reference density [kg m-3].} 118 119 \textcolor{comment}{! Original coded by R. Hallberg, 7/00, anomaly coded in 3/18.} 120 \textcolor{comment}{! Local variables} 121 \textcolor{keywordtype}{real} :: al0, p0, lambda 122 \textcolor{keywordtype}{real} :: al\_ts, p\_tsp, lam\_ts, pa\_000 123 \textcolor{keywordtype}{integer} :: j 124 125 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(rho\_ref)) pa\_000 = (b0*(1.0 - a0*rho\_ref) - rho\_ref*c0) 126 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(rho\_ref)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=start,start+npts-1 127 al\_ts = a1*t(j) +a2*s(j) 128 al0 = a0 + al\_ts 129 p\_tsp = pressure(j) + (b4*s(j) + t(j) * (b1 + (t(j)*(b2 + b3*t(j)) + b5*s(j)))) 130 lam\_ts = c4*s(j) + t(j) * (c1 + (t(j)*(c2 + c3*t(j)) + c5*s(j))) 131 132 \textcolor{comment}{! The following two expressions are mathematically equivalent.} 133 \textcolor{comment}{! rho(j) = (b0 + p0\_TSp) / ((c0 + lam\_TS) + al0*(b0 + p0\_TSp)) - rho\_ref} 134 rho(j) = (pa\_000 + (p\_tsp - rho\_ref*(p\_tsp*al0 + (b0*al\_ts + lam\_ts)))) / & 135 ( (c0 + lam\_ts) + al0*(b0 + p\_tsp) ) 136 \textcolor{keywordflow}{ enddo} ; \textcolor{keywordflow}{else} ; \textcolor{keywordflow}{do} j=start,start+npts-1 137 al0 = (a0 + a1*t(j)) +a2*s(j) 138 p0 = (b0 + b4*s(j)) + t(j) * (b1 + t(j)*(b2 + b3*t(j)) + b5*s(j)) 139 lambda = (c0 +c4*s(j)) + t(j) * (c1 + t(j)*(c2 + c3*t(j)) + c5*s(j)) 140 rho(j) = (pressure(j) + p0) / (lambda + al0*(pressure(j) + p0)) 141 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} 142 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_a576d1ff13c93f4a3ffbd483d43a78ab7}\label{namespacemom__eos__wright_a576d1ff13c93f4a3ffbd483d43a78ab7}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+wright@{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+wright}} \index{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+wright@{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+wright()}{calculate\_density\_derivs\_array\_wright()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+derivs\+\_\+array\+\_\+wright (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(inout)}]{drho\+\_\+dT, }\item[{real, dimension(\+:), intent(inout)}]{drho\+\_\+dS, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} For a given thermodynamic state, return the thermal/haline expansion coefficients. \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 in,out} & {\em drho\+\_\+dt} & The partial derivative of density with potential temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt in,out} & {\em drho\+\_\+ds} & The partial derivative of density with salinity, in \mbox{[}kg m-\/3 P\+S\+U-\/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 200 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 200 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: t\textcolor{comment}{ !< Potential temperature relative to the} 201 \textcolor{comment}{ !! surface [degC].} 202 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: s\textcolor{comment}{ !< Salinity [PSU].} 203 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 204 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(inout)}, \textcolor{keywordtype}{dimension(:)} :: drho\_dt\textcolor{comment}{ !< The partial derivative of density with potential} 205 \textcolor{comment}{ !! temperature [kg m-3 degC-1].} 206 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(inout)}, \textcolor{keywordtype}{dimension(:)} :: drho\_ds\textcolor{comment}{ !< The partial derivative of density with salinity,} 207 \textcolor{comment}{ !! in [kg m-3 PSU-1].} 208 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< The starting point in the arrays.} 209 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< The number of values to calculate.} 210 211 \textcolor{comment}{! Local variables} 212 \textcolor{keywordtype}{real} :: al0, p0, lambda, i\_denom2 213 \textcolor{keywordtype}{integer} :: j 214 215 \textcolor{keywordflow}{do} j=start,start+npts-1 216 al0 = (a0 + a1*t(j)) + a2*s(j) 217 p0 = (b0 + b4*s(j)) + t(j) * (b1 + t(j)*((b2 + b3*t(j))) + b5*s(j)) 218 lambda = (c0 +c4*s(j)) + t(j) * (c1 + t(j)*((c2 + c3*t(j))) + c5*s(j)) 219 220 i\_denom2 = 1.0 / (lambda + al0*(pressure(j) + p0)) 221 i\_denom2 = i\_denom2 *i\_denom2 222 drho\_dt(j) = i\_denom2 * & 223 (lambda* (b1 + t(j)*(2.0*b2 + 3.0*b3*t(j)) + b5*s(j)) - & 224 (pressure(j)+p0) * ( (pressure(j)+p0)*a1 + & 225 (c1 + t(j)*(c2*2.0 + c3*3.0*t(j)) + c5*s(j)) )) 226 drho\_ds(j) = i\_denom2 * (lambda* (b4 + b5*t(j)) - & 227 (pressure(j)+p0) * ( (pressure(j)+p0)*a2 + (c4 + c5*t(j)) )) 228 \textcolor{keywordflow}{ enddo} 229 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_a8264a21fbe5809d5290ea388e0b2e64f}\label{namespacemom__eos__wright_a8264a21fbe5809d5290ea388e0b2e64f}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+wright@{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+wright}} \index{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+wright@{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+wright()}{calculate\_density\_derivs\_scalar\_wright()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+derivs\+\_\+scalar\+\_\+wright (\begin{DoxyParamCaption}\item[{real, intent(in)}]{T, }\item[{real, intent(in)}]{S, }\item[{real, intent(in)}]{pressure, }\item[{real, intent(out)}]{drho\+\_\+dT, }\item[{real, intent(out)}]{drho\+\_\+dS }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} The scalar version of calculate\+\_\+density\+\_\+derivs which promotes scalar inputs to a 1-\/element array and then demotes the output back to a scalar. \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} & The partial derivative of density with potential temperature \mbox{[}kg m-\/3 deg\+C-\/1\mbox{]}.\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds} & The partial derivative of density with salinity, in \mbox{[}kg m-\/3 P\+S\+U-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 235 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 235 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: t\textcolor{comment}{ !< Potential temperature relative to the surface [degC].} 236 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: s\textcolor{comment}{ !< Salinity [PSU].} 237 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 238 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: drho\_dt\textcolor{comment}{ !< The partial derivative of density with potential} 239 \textcolor{comment}{ !! temperature [kg m-3 degC-1].} 240 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: drho\_ds\textcolor{comment}{ !< The partial derivative of density with salinity,} 241 \textcolor{comment}{ !! in [kg m-3 PSU-1].} 242 243 \textcolor{comment}{! Local variables needed to promote the input/output scalars to 1-element arrays} 244 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(1)} :: t0, s0, p0 245 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(1)} :: drdt0, drds0 246 247 t0(1) = t 248 s0(1) = s 249 p0(1) = pressure 250 \textcolor{keyword}{call }calculate\_density\_derivs\_array\_wright(t0, s0, p0, drdt0, drds0, 1, 1) 251 drho\_dt = drdt0(1) 252 drho\_ds = drds0(1) 253 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_a047725cee226bb5621080176aaff36d6}\label{namespacemom__eos__wright_a047725cee226bb5621080176aaff36d6}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+density\+\_\+scalar\+\_\+wright@{calculate\+\_\+density\+\_\+scalar\+\_\+wright}} \index{calculate\+\_\+density\+\_\+scalar\+\_\+wright@{calculate\+\_\+density\+\_\+scalar\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+scalar\+\_\+wright()}{calculate\_density\_scalar\_wright()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+scalar\+\_\+wright (\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), optional}]{rho\+\_\+ref }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} This subroutine computes the in situ density of sea water (rho in \mbox{[}kg m-\/3\mbox{]}) from salinity (S \mbox{[}P\+SU\mbox{]}), potential temperature (T \mbox{[}degC\mbox{]}), and pressure \mbox{[}Pa\mbox{]}. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. \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\+\_\+ref} & A reference density \mbox{[}kg m-\/3\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 81 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 81 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: t\textcolor{comment}{ !< Potential temperature relative to the surface [degC].} 82 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: s\textcolor{comment}{ !< Salinity [PSU].} 83 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 84 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: rho\textcolor{comment}{ !< In situ density [kg m-3].} 85 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: rho\_ref\textcolor{comment}{ !< A reference density [kg m-3].} 86 87 \textcolor{comment}{! *====================================================================*} 88 \textcolor{comment}{! * This subroutine computes the in situ density of sea water (rho in *} 89 \textcolor{comment}{! * [kg m-3]) from salinity (S [PSU]), potential temperature *} 90 \textcolor{comment}{! * (T [degC]), and pressure [Pa]. It uses the expression from *} 91 \textcolor{comment}{! * Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. *} 92 \textcolor{comment}{! * Coded by R. Hallberg, 7/00 *} 93 \textcolor{comment}{! *====================================================================*} 94 95 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(1)} :: t0, s0, pressure0, rho0 96 97 t0(1) = t 98 s0(1) = s 99 pressure0(1) = pressure 100 101 \textcolor{keyword}{call }calculate\_density\_array\_wright(t0, s0, pressure0, rho0, 1, 1, rho\_ref) 102 rho = rho0(1) 103 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_a218432c80512597414f0c1fe4ae2d97d}\label{namespacemom__eos__wright_a218432c80512597414f0c1fe4ae2d97d}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+wright@{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+wright}} \index{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+wright@{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+wright()}{calculate\_density\_second\_derivs\_array\_wright()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+array\+\_\+wright (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{P, }\item[{real, dimension(\+:), intent(inout)}]{drho\+\_\+ds\+\_\+ds, }\item[{real, dimension(\+:), intent(inout)}]{drho\+\_\+ds\+\_\+dt, }\item[{real, dimension(\+:), intent(inout)}]{drho\+\_\+dt\+\_\+dt, }\item[{real, dimension(\+:), intent(inout)}]{drho\+\_\+ds\+\_\+dp, }\item[{real, dimension(\+:), intent(inout)}]{drho\+\_\+dt\+\_\+dp, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Second derivatives of density with respect to temperature, salinity, and pressure. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & Potential temperature referenced to 0 dbar \mbox{[}degC\mbox{]}\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}\\ \hline \mbox{\tt in} & {\em p} & Pressure \mbox{[}Pa\mbox{]}\\ \hline \mbox{\tt in,out} & {\em drho\+\_\+ds\+\_\+ds} & Partial derivative of beta with respect to S \mbox{[}kg m-\/3 P\+S\+U-\/2\mbox{]}\\ \hline \mbox{\tt in,out} & {\em drho\+\_\+ds\+\_\+dt} & Partial derivative of beta with respcct to T \mbox{[}kg m-\/3 P\+S\+U-\/1 deg\+C-\/1\mbox{]}\\ \hline \mbox{\tt in,out} & {\em drho\+\_\+dt\+\_\+dt} & Partial derivative of alpha with respect to T \mbox{[}kg m-\/3 deg\+C-\/2\mbox{]}\\ \hline \mbox{\tt in,out} & {\em drho\+\_\+ds\+\_\+dp} & Partial derivative of beta with respect to pressure \mbox{[}kg m-\/3 P\+S\+U-\/1 Pa-\/1\mbox{]}\\ \hline \mbox{\tt in,out} & {\em drho\+\_\+dt\+\_\+dp} & Partial derivative of alpha with respect to pressure \mbox{[}kg m-\/3 deg\+C-\/1 Pa-\/1\mbox{]}\\ \hline \mbox{\tt in} & {\em start} & Starting index in T,S,P\\ \hline \mbox{\tt in} & {\em npts} & Number of points to loop over \\ \hline \end{DoxyParams} Definition at line 259 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 259 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in )} :: t\textcolor{comment}{ !< Potential temperature referenced to 0 dbar [degC]} 260 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in )} :: s\textcolor{comment}{ !< Salinity [PSU]} 261 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in )} :: p\textcolor{comment}{ !< Pressure [Pa]} 262 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(inout)} :: drho\_ds\_ds\textcolor{comment}{ !< Partial derivative of beta with respect} 263 \textcolor{comment}{ !! to S [kg m-3 PSU-2]} 264 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(inout)} :: drho\_ds\_dt\textcolor{comment}{ !< Partial derivative of beta with respcct} 265 \textcolor{comment}{ !! to T [kg m-3 PSU-1 degC-1]} 266 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(inout)} :: drho\_dt\_dt\textcolor{comment}{ !< Partial derivative of alpha with respect} 267 \textcolor{comment}{ !! to T [kg m-3 degC-2]} 268 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(inout)} :: drho\_ds\_dp\textcolor{comment}{ !< Partial derivative of beta with respect} 269 \textcolor{comment}{ !! to pressure [kg m-3 PSU-1 Pa-1]} 270 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(inout)} :: drho\_dt\_dp\textcolor{comment}{ !< Partial derivative of alpha with respect} 271 \textcolor{comment}{ !! to pressure [kg m-3 degC-1 Pa-1]} 272 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in )} :: start\textcolor{comment}{ !< Starting index in T,S,P} 273 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in )} :: npts\textcolor{comment}{ !< Number of points to loop over} 274 275 \textcolor{comment}{! Local variables} 276 \textcolor{keywordtype}{real} :: z0, z1, z2, z3, z4, z5, z6 ,z7, z8, z9, z10, z11, z2\_2, z2\_3 277 \textcolor{keywordtype}{integer} :: j 278 \textcolor{comment}{! Based on the above expression with common terms factored, there probably exists a more numerically stable} 279 \textcolor{comment}{! and/or efficient expression} 280 281 \textcolor{keywordflow}{do} j = start,start+npts-1 282 z0 = t(j)*(b1 + b5*s(j) + t(j)*(b2 + b3*t(j))) 283 z1 = (b0 + p(j) + b4*s(j) + z0) 284 z3 = (b1 + b5*s(j) + t(j)*(2.*b2 + 2.*b3*t(j))) 285 z4 = (c0 + c4*s(j) + t(j)*(c1 + c5*s(j) + t(j)*(c2 + c3*t(j)))) 286 z5 = (b1 + b5*s(j) + t(j)*(b2 + b3*t(j)) + t(j)*(b2 + 2.*b3*t(j))) 287 z6 = c1 + c5*s(j) + t(j)*(c2 + c3*t(j)) + t(j)*(c2 + 2.*c3*t(j)) 288 z7 = (c4 + c5*t(j) + a2*z1) 289 z8 = (c1 + c5*s(j) + t(j)*(2.*c2 + 3.*c3*t(j)) + a1*z1) 290 z9 = (a0 + a2*s(j) + a1*t(j)) 291 z10 = (b4 + b5*t(j)) 292 z11 = (z10*z4 - z1*z7) 293 z2 = (c0 + c4*s(j) + t(j)*(c1 + c5*s(j) + t(j)*(c2 + c3*t(j))) + z9*z1) 294 z2\_2 = z2*z2 295 z2\_3 = z2\_2*z2 296 297 drho\_ds\_ds(j) = (z10*(c4 + c5*t(j)) - a2*z10*z1 - z10*z7)/z2\_2 - (2.*(c4 + c5*t(j) + z9*z10 + a2*z1)* z11)/z2\_3 298 drho\_ds\_dt(j) = (z10*z6 - z1*(c5 + a2*z5) + b5*z4 - z5*z7)/z2\_2 - (2.*(z6 + z9*z5 + a1*z1)*z11)/z2\_3 299 drho\_dt\_dt(j) = (z3*z6 - z1*(2.*c2 + 6.*c3*t(j) + a1*z5) + (2.*b2 + 4.*b3*t(j))*z4 - z5*z8)/z2\_2 - & 300 (2.*(z6 + z9*z5 + a1*z1)*(z3*z4 - z1*z8))/z2\_3 301 drho\_ds\_dp(j) = (-c4 - c5*t(j) - 2.*a2*z1)/z2\_2 - (2.*z9*z11)/z2\_3 302 drho\_dt\_dp(j) = (-c1 - c5*s(j) - t(j)*(2.*c2 + 3.*c3*t(j)) - 2.*a1*z1)/z2\_2 - (2.*z9*(z3*z4 - z1*z8))/ z2\_3 303 \textcolor{keywordflow}{ enddo} 304 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_a74e1c5129ef4414337347a115bcdff10}\label{namespacemom__eos__wright_a74e1c5129ef4414337347a115bcdff10}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+wright@{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+wright}} \index{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+wright@{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+wright()}{calculate\_density\_second\_derivs\_scalar\_wright()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+scalar\+\_\+wright (\begin{DoxyParamCaption}\item[{real, intent(in)}]{T, }\item[{real, intent(in)}]{S, }\item[{real, intent(in)}]{P, }\item[{real, intent(out)}]{drho\+\_\+ds\+\_\+ds, }\item[{real, intent(out)}]{drho\+\_\+ds\+\_\+dt, }\item[{real, intent(out)}]{drho\+\_\+dt\+\_\+dt, }\item[{real, intent(out)}]{drho\+\_\+ds\+\_\+dp, }\item[{real, intent(out)}]{drho\+\_\+dt\+\_\+dp }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Second derivatives of density with respect to temperature, salinity, and pressure for scalar inputs. Inputs promoted to 1-\/element array and output demoted to scalar. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em t} & Potential temperature referenced to 0 dbar\\ \hline \mbox{\tt in} & {\em s} & Salinity \mbox{[}P\+SU\mbox{]}\\ \hline \mbox{\tt in} & {\em p} & pressure \mbox{[}Pa\mbox{]}\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+ds} & Partial derivative of beta with respect to S \mbox{[}kg m-\/3 P\+S\+U-\/2\mbox{]}\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+dt} & Partial derivative of beta with respcct to T \mbox{[}kg m-\/3 P\+S\+U-\/1 deg\+C-\/1\mbox{]}\\ \hline \mbox{\tt out} & {\em drho\+\_\+dt\+\_\+dt} & Partial derivative of alpha with respect to T \mbox{[}kg m-\/3 deg\+C-\/2\mbox{]}\\ \hline \mbox{\tt out} & {\em drho\+\_\+ds\+\_\+dp} & Partial derivative of beta with respect to pressure \mbox{[}kg m-\/3 P\+S\+U-\/1 Pa-\/1\mbox{]}\\ \hline \mbox{\tt out} & {\em drho\+\_\+dt\+\_\+dp} & Partial derivative of alpha with respect to pressure \mbox{[}kg m-\/3 deg\+C-\/1 Pa-\/1\mbox{]} \\ \hline \end{DoxyParams} Definition at line 311 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 311 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in )} :: t\textcolor{comment}{ !< Potential temperature referenced to 0 dbar} 312 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in )} :: s\textcolor{comment}{ !< Salinity [PSU]} 313 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in )} :: p\textcolor{comment}{ !< pressure [Pa]} 314 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent( out)} :: drho\_ds\_ds\textcolor{comment}{ !< Partial derivative of beta with respect} 315 \textcolor{comment}{ !! to S [kg m-3 PSU-2]} 316 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent( out)} :: drho\_ds\_dt\textcolor{comment}{ !< Partial derivative of beta with respcct} 317 \textcolor{comment}{ !! to T [kg m-3 PSU-1 degC-1]} 318 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent( out)} :: drho\_dt\_dt\textcolor{comment}{ !< Partial derivative of alpha with respect} 319 \textcolor{comment}{ !! to T [kg m-3 degC-2]} 320 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent( out)} :: drho\_ds\_dp\textcolor{comment}{ !< Partial derivative of beta with respect} 321 \textcolor{comment}{ !! to pressure [kg m-3 PSU-1 Pa-1]} 322 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent( out)} :: drho\_dt\_dp\textcolor{comment}{ !< Partial derivative of alpha with respect} 323 \textcolor{comment}{ !! to pressure [kg m-3 degC-1 Pa-1]} 324 \textcolor{comment}{! Local variables} 325 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(1)} :: t0, s0, p0 326 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(1)} :: drdsds, drdsdt, drdtdt, drdsdp, drdtdp 327 328 t0(1) = t 329 s0(1) = s 330 p0(1) = p 331 \textcolor{keyword}{call }calculate\_density\_second\_derivs\_array\_wright(t0, s0, p0, drdsds, drdsdt, drdtdt, drdsdp, drdtdp, 1, 1) 332 drho\_ds\_ds = drdsds(1) 333 drho\_ds\_dt = drdsdt(1) 334 drho\_dt\_dt = drdtdt(1) 335 drho\_ds\_dp = drdsdp(1) 336 drho\_dt\_dp = drdtdp(1) 337 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_a0e1da760ed0fca53533430d0bd03ee6d}\label{namespacemom__eos__wright_a0e1da760ed0fca53533430d0bd03ee6d}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+wright@{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+wright}} \index{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+wright@{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+wright()}{calculate\_spec\_vol\_array\_wright()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+spec\+\_\+vol\+\_\+array\+\_\+wright (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(inout)}]{specvol, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts, }\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{]}. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. 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 in,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 spv\+\_\+ref} & A reference specific volume \mbox{[}m3 kg-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 172 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 172 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: t\textcolor{comment}{ !< potential temperature relative to the} 173 \textcolor{comment}{ !! surface [degC].} 174 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: s\textcolor{comment}{ !< salinity [PSU].} 175 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 176 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(inout)} :: specvol\textcolor{comment}{ !< in situ specific volume [m3 kg-1].} 177 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< the starting point in the arrays.} 178 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< the number of values to calculate.} 179 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: spv\_ref\textcolor{comment}{ !< A reference specific volume [m3 kg-1].} 180 181 \textcolor{comment}{! Local variables} 182 \textcolor{keywordtype}{real} :: al0, p0, lambda 183 \textcolor{keywordtype}{integer} :: j 184 185 \textcolor{keywordflow}{do} j=start,start+npts-1 186 al0 = (a0 + a1*t(j)) +a2*s(j) 187 p0 = (b0 + b4*s(j)) + t(j) * (b1 + t(j)*((b2 + b3*t(j))) + b5*s(j)) 188 lambda = (c0 +c4*s(j)) + t(j) * (c1 + t(j)*((c2 + c3*t(j))) + c5*s(j)) 189 190 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(spv\_ref)) \textcolor{keywordflow}{then} 191 specvol(j) = (lambda + (al0 - spv\_ref)*(pressure(j) + p0)) / (pressure(j) + p0) 192 \textcolor{keywordflow}{else} 193 specvol(j) = (lambda + al0*(pressure(j) + p0)) / (pressure(j) + p0) 194 \textcolor{keywordflow}{ endif} 195 \textcolor{keywordflow}{ enddo} \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_aa1577bed7878372af9be62afea06cbf0}\label{namespacemom__eos__wright_aa1577bed7878372af9be62afea06cbf0}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+wright@{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+wright}} \index{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+wright@{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+wright()}{calculate\_spec\_vol\_scalar\_wright()}} {\footnotesize\ttfamily subroutine mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+spec\+\_\+vol\+\_\+scalar\+\_\+wright (\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), 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{]}. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-\/740. 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 spv\+\_\+ref} & A reference specific volume \mbox{[}m3 kg-\/1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 151 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 151 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: t\textcolor{comment}{ !< potential temperature relative to the surface [degC].} 152 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: s\textcolor{comment}{ !< salinity [PSU].} 153 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 154 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(out)} :: specvol\textcolor{comment}{ !< in situ specific volume [m3 kg-1].} 155 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: spv\_ref\textcolor{comment}{ !< A reference specific volume [m3 kg-1].} 156 157 \textcolor{comment}{! Local variables} 158 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(1)} :: t0, s0, pressure0, spv0 159 160 t0(1) = t ; s0(1) = s ; pressure0(1) = pressure 161 162 \textcolor{keyword}{call }calculate\_spec\_vol\_array\_wright(t0, s0, pressure0, spv0, 1, 1, spv\_ref) 163 specvol = spv0(1) \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_a890d098ddbdc76f6cfbf1b7cf19b6388}\label{namespacemom__eos__wright_a890d098ddbdc76f6cfbf1b7cf19b6388}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!calculate\+\_\+specvol\+\_\+derivs\+\_\+wright@{calculate\+\_\+specvol\+\_\+derivs\+\_\+wright}} \index{calculate\+\_\+specvol\+\_\+derivs\+\_\+wright@{calculate\+\_\+specvol\+\_\+derivs\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{calculate\+\_\+specvol\+\_\+derivs\+\_\+wright()}{calculate\_specvol\_derivs\_wright()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+specvol\+\_\+derivs\+\_\+wright (\begin{DoxyParamCaption}\item[{real, dimension(\+:), intent(in)}]{T, }\item[{real, dimension(\+:), intent(in)}]{S, }\item[{real, dimension(\+:), intent(in)}]{pressure, }\item[{real, dimension(\+:), intent(inout)}]{d\+S\+V\+\_\+dT, }\item[{real, dimension(\+:), intent(inout)}]{d\+S\+V\+\_\+dS, }\item[{integer, intent(in)}]{start, }\item[{integer, intent(in)}]{npts }\end{DoxyParamCaption})} For a given thermodynamic state, return the partial 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 in,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,out} & {\em dsv\+\_\+ds} & The partial derivative of specific volume with salinity \mbox{[}m3 kg-\/1 / Pa\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 343 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 343 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: t\textcolor{comment}{ !< Potential temperature relative to the surface [degC].} 344 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: s\textcolor{comment}{ !< Salinity [PSU].} 345 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)}, \textcolor{keywordtype}{dimension(:)} :: pressure\textcolor{comment}{ !< pressure [Pa].} 346 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(inout)}, \textcolor{keywordtype}{dimension(:)} :: dsv\_dt\textcolor{comment}{ !< The partial derivative of specific volume with} 347 \textcolor{comment}{ !! potential temperature [m3 kg-1 degC-1].} 348 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(inout)}, \textcolor{keywordtype}{dimension(:)} :: dsv\_ds\textcolor{comment}{ !< The partial derivative of specific volume with} 349 \textcolor{comment}{ !! salinity [m3 kg-1 / Pa].} 350 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: start\textcolor{comment}{ !< The starting point in the arrays.} 351 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: npts\textcolor{comment}{ !< The number of values to calculate.} 352 353 \textcolor{comment}{! Local variables} 354 \textcolor{keywordtype}{real} :: al0, p0, lambda, i\_denom 355 \textcolor{keywordtype}{integer} :: j 356 357 \textcolor{keywordflow}{do} j=start,start+npts-1 358 \textcolor{comment}{! al0 = (a0 + a1*T(j)) + a2*S(j)} 359 p0 = (b0 + b4*s(j)) + t(j) * (b1 + t(j)*((b2 + b3*t(j))) + b5*s(j)) 360 lambda = (c0 +c4*s(j)) + t(j) * (c1 + t(j)*((c2 + c3*t(j))) + c5*s(j)) 361 362 \textcolor{comment}{! SV = al0 + lambda / (pressure(j) + p0)} 363 364 i\_denom = 1.0 / (pressure(j) + p0) 365 dsv\_dt(j) = (a1 + i\_denom * (c1 + t(j)*((2.0*c2 + 3.0*c3*t(j))) + c5*s(j))) - & 366 (i\_denom**2 * lambda) * (b1 + t(j)*((2.0*b2 + 3.0*b3*t(j))) + b5*s(j)) 367 dsv\_ds(j) = (a2 + i\_denom * (c4 + c5*t(j))) - & 368 (i\_denom**2 * lambda) * (b4 + b5*t(j)) 369 \textcolor{keywordflow}{ enddo} 370 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_ac94eaa2504eb4ccb12b41add45e1301e}\label{namespacemom__eos__wright_ac94eaa2504eb4ccb12b41add45e1301e}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!int\+\_\+density\+\_\+dz\+\_\+wright@{int\+\_\+density\+\_\+dz\+\_\+wright}} \index{int\+\_\+density\+\_\+dz\+\_\+wright@{int\+\_\+density\+\_\+dz\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{int\+\_\+density\+\_\+dz\+\_\+wright()}{int\_density\_dz\_wright()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+wright\+::int\+\_\+density\+\_\+dz\+\_\+wright (\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[{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, }\item[{real, intent(in), optional}]{rho\+\_\+scale, }\item[{real, intent(in), optional}]{pres\+\_\+scale }\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$$>$ kg m-\/3\mbox{]} or \mbox{[}kg m-\/3\mbox{]}, that is subtracted out to reduce the magnitude of each of the integrals. (The pressure is calucated as p$\sim$=-\/z$\ast$rho\+\_\+0$\ast$\+G\+\_\+e.)\\ \hline \mbox{\tt in} & {\em rho\+\_\+0} & Density \mbox{[}R $\sim$$>$ 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{\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,out} & {\em dpa} & The change in the pressure anomaly across the\\ \hline \mbox{\tt in,out} & {\em intz\+\_\+dpa} & The integral through the thickness of the layer\\ \hline \mbox{\tt in,out} & {\em intx\+\_\+dpa} & The integral in x of the difference between the\\ \hline \mbox{\tt in,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 \mbox{\tt in} & {\em rho\+\_\+scale} & A multiplicative factor by which to scale density from kg m-\/3 to the desired units \mbox{[}R m3 kg-\/1 $\sim$$>$ 1\mbox{]}\\ \hline \mbox{\tt in} & {\em pres\+\_\+scale} & A multiplicative factor to convert pressure into Pa \mbox{[}Pa T2 R-\/1 L-\/2 $\sim$$>$ 1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 412 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 412 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: hi\textcolor{comment}{ !< The horizontal index type for the arrays.} 413 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 414 \textcolor{keywordtype}{intent(in)} :: t\textcolor{comment}{ !< Potential temperature relative to the surface} 415 \textcolor{comment}{ !! [degC].} 416 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 417 \textcolor{keywordtype}{intent(in)} :: s\textcolor{comment}{ !< Salinity [PSU].} 418 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 419 \textcolor{keywordtype}{intent(in)} :: z\_t\textcolor{comment}{ !< Height at the top of the layer in depth units [Z ~> m].} 420 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 421 \textcolor{keywordtype}{intent(in)} :: z\_b\textcolor{comment}{ !< Height at the top of the layer [Z ~> m].} 422 \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} 423 \textcolor{comment}{ !! out to reduce the magnitude of each of the integrals.} 424 \textcolor{comment}{ !! (The pressure is calucated as p~=-z*rho\_0*G\_e.)} 425 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: rho\_0\textcolor{comment}{ !< Density [R ~> kg m-3] or [kg m-3], that is used} 426 \textcolor{comment}{ !! to calculate the pressure (as p~=-z*rho\_0*G\_e)} 427 \textcolor{comment}{ !! used in the equation of state.} 428 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: g\_e\textcolor{comment}{ !< The Earth's gravitational acceleration} 429 \textcolor{comment}{ !! [L2 Z-1 T-2 ~> m s-2] or [m2 Z-1 s-2 ~> m s-2].} 430 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 431 \textcolor{keywordtype}{intent(inout)} :: dpa\textcolor{comment}{ !< The change in the pressure anomaly across the} 432 \textcolor{comment}{ !! layer [R L2 T-2 ~> Pa] or [Pa].} 433 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 434 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intz\_dpa\textcolor{comment}{ !< The integral through the thickness of the layer} 435 \textcolor{comment}{ !! of the pressure anomaly relative to the anomaly} 436 \textcolor{comment}{ !! at the top of the layer [R Z L2 T-2 ~> Pa m].} 437 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%IsdB:HI%IedB,HI%jsd:HI%jed)}, & 438 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intx\_dpa\textcolor{comment}{ !< The integral in x of the difference between the} 439 \textcolor{comment}{ !! pressure anomaly at the top and bottom of the} 440 \textcolor{comment}{ !! layer divided by the x grid spacing [R L2 T-2 ~> Pa].} 441 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%JsdB:HI%JedB)}, & 442 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: inty\_dpa\textcolor{comment}{ !< The integral in y of the difference between the} 443 \textcolor{comment}{ !! pressure anomaly at the top and bottom of the} 444 \textcolor{comment}{ !! layer divided by the y grid spacing [R L2 T-2 ~> Pa].} 445 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 446 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: bathyt\textcolor{comment}{ !< The depth of the bathymetry [Z ~> m].} 447 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: dz\_neglect\textcolor{comment}{ !< A miniscule thickness change [Z ~> m].} 448 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: usemasswghtinterp\textcolor{comment}{ !< If true, uses mass weighting to} 449 \textcolor{comment}{ !! interpolate T/S for top and bottom integrals.} 450 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: rho\_scale\textcolor{comment}{ !< A multiplicative factor by which to scale density} 451 \textcolor{comment}{ !! from kg m-3 to the desired units [R m3 kg-1 ~> 1]} 452 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: pres\_scale\textcolor{comment}{ !< A multiplicative factor to convert pressure} 453 \textcolor{comment}{ !! into Pa [Pa T2 R-1 L-2 ~> 1].} 454 455 \textcolor{comment}{! Local variables} 456 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)} :: al0\_2d, p0\_2d, lambda\_2d 457 \textcolor{keywordtype}{real} :: al0, p0, lambda 458 \textcolor{keywordtype}{real} :: rho\_anom \textcolor{comment}{! The density anomaly from rho\_ref [kg m-3].} 459 \textcolor{keywordtype}{real} :: eps, eps2, rem 460 \textcolor{keywordtype}{real} :: gxrho \textcolor{comment}{! The gravitational acceleration times density and unit conversion factors [Pa Z-1 ~> kg m-2 s-2]} 461 \textcolor{keywordtype}{real} :: g\_earth \textcolor{comment}{! The gravitational acceleration [m2 Z-1 s-2 ~> m s-2]} 462 \textcolor{keywordtype}{real} :: i\_rho \textcolor{comment}{! The inverse of the Boussinesq density [m3 kg-1]} 463 \textcolor{keywordtype}{real} :: rho\_ref\_mks \textcolor{comment}{! The reference density in MKS units, never rescaled from kg m-3 [kg m-3]} 464 \textcolor{keywordtype}{real} :: p\_ave, i\_al0, i\_lzz 465 \textcolor{keywordtype}{real} :: dz \textcolor{comment}{! The layer thickness [Z ~> m].} 466 \textcolor{keywordtype}{real} :: hwght \textcolor{comment}{! A pressure-thickness below topography [Z ~> m].} 467 \textcolor{keywordtype}{real} :: hl, hr \textcolor{comment}{! Pressure-thicknesses of the columns to the left and right [Z ~> m].} 468 \textcolor{keywordtype}{real} :: idenom \textcolor{comment}{! The inverse of the denominator in the weights [Z-2 ~> m-2].} 469 \textcolor{keywordtype}{real} :: hwt\_ll, hwt\_lr \textcolor{comment}{! hWt\_LA is the weighted influence of A on the left column [nondim].} 470 \textcolor{keywordtype}{real} :: hwt\_rl, hwt\_rr \textcolor{comment}{! hWt\_RA is the weighted influence of A on the right column [nondim].} 471 \textcolor{keywordtype}{real} :: wt\_l, wt\_r \textcolor{comment}{! The linear weights of the left and right columns [nondim].} 472 \textcolor{keywordtype}{real} :: wtt\_l, wtt\_r \textcolor{comment}{! The weights for tracers from the left and right columns [nondim].} 473 \textcolor{keywordtype}{real} :: intz(5) \textcolor{comment}{! The integrals of density with height at the} 474 \textcolor{comment}{! 5 sub-column locations [R L2 T-2 ~> Pa].} 475 \textcolor{keywordtype}{real} :: pa\_to\_rl2\_t2 \textcolor{comment}{! A conversion factor of pressures from Pa to the output units indicated by} 476 \textcolor{comment}{! pres\_scale [R L2 T-2 Pa-1 ~> 1] or [1].} 477 \textcolor{keywordtype}{logical} :: do\_massweight \textcolor{comment}{! Indicates whether to do mass weighting.} 478 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{parameter} :: c1\_3 = 1.0/3.0, c1\_7 = 1.0/7.0 \textcolor{comment}{! Rational constants.} 479 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{parameter} :: c1\_9 = 1.0/9.0, c1\_90 = 1.0/90.0 \textcolor{comment}{! Rational constants.} 480 \textcolor{keywordtype}{integer} :: is, ie, js, je, isq, ieq, jsq, jeq, i, j, m 481 482 \textcolor{comment}{! These array bounds work for the indexing convention of the input arrays, but} 483 \textcolor{comment}{! on the computational domain defined for the output arrays.} 484 isq = hi%IscB ; ieq = hi%IecB 485 jsq = hi%JscB ; jeq = hi%JecB 486 is = hi%isc ; ie = hi%iec 487 js = hi%jsc ; je = hi%jec 488 489 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(pres\_scale)) \textcolor{keywordflow}{then} 490 gxrho = pres\_scale * g\_e * rho\_0 ; g\_earth = pres\_scale * g\_e 491 pa\_to\_rl2\_t2 = 1.0 / pres\_scale 492 \textcolor{keywordflow}{else} 493 gxrho = g\_e * rho\_0 ; g\_earth = g\_e 494 pa\_to\_rl2\_t2 = 1.0 495 \textcolor{keywordflow}{ endif} 496 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(rho\_scale)) \textcolor{keywordflow}{then} 497 g\_earth = g\_earth * rho\_scale 498 rho\_ref\_mks = rho\_ref / rho\_scale ; i\_rho = rho\_scale / rho\_0 499 \textcolor{keywordflow}{else} 500 rho\_ref\_mks = rho\_ref ; i\_rho = 1.0 / rho\_0 501 \textcolor{keywordflow}{ endif} 502 503 do\_massweight = .false. 504 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(usemasswghtinterp)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (usemasswghtinterp) \textcolor{keywordflow}{then} 505 do\_massweight = .true. 506 \textcolor{comment}{! if (.not.present(bathyT)) call MOM\_error(FATAL, "int\_density\_dz\_generic: "//&} 507 \textcolor{comment}{! "bathyT must be present if useMassWghtInterp is present and true.")} 508 \textcolor{comment}{! if (.not.present(dz\_neglect)) call MOM\_error(FATAL, "int\_density\_dz\_generic: "//&} 509 \textcolor{comment}{! "dz\_neglect must be present if useMassWghtInterp is present and true.")} 510 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 511 512 \textcolor{keywordflow}{do} j=jsq,jeq+1 ; \textcolor{keywordflow}{do} i=isq,ieq+1 513 al0\_2d(i,j) = (a0 + a1*t(i,j)) + a2*s(i,j) 514 p0\_2d(i,j) = (b0 + b4*s(i,j)) + t(i,j) * (b1 + t(i,j)*((b2 + b3*t(i,j))) + b5*s(i,j)) 515 lambda\_2d(i,j) = (c0 +c4*s(i,j)) + t(i,j) * (c1 + t(i,j)*((c2 + c3*t(i,j))) + c5*s(i,j)) 516 517 al0 = al0\_2d(i,j) ; p0 = p0\_2d(i,j) ; lambda = lambda\_2d(i,j) 518 519 dz = z\_t(i,j) - z\_b(i,j) 520 p\_ave = -0.5*gxrho*(z\_t(i,j)+z\_b(i,j)) 521 522 i\_al0 = 1.0 / al0 523 i\_lzz = 1.0 / (p0 + (lambda * i\_al0) + p\_ave) 524 eps = 0.5*gxrho*dz*i\_lzz ; eps2 = eps*eps 525 526 \textcolor{comment}{! rho(j) = (pressure(j) + p0) / (lambda + al0*(pressure(j) + p0))} 527 528 rho\_anom = (p0 + p\_ave)*(i\_lzz*i\_al0) - rho\_ref\_mks 529 rem = i\_rho * (lambda * i\_al0**2) * eps2 * & 530 (c1\_3 + eps2*(0.2 + eps2*(c1\_7 + c1\_9*eps2))) 531 dpa(i,j) = pa\_to\_rl2\_t2 * (g\_earth*rho\_anom*dz - 2.0*eps*rem) 532 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intz\_dpa)) & 533 intz\_dpa(i,j) = pa\_to\_rl2\_t2 * (0.5*g\_earth*rho\_anom*dz**2 - dz*(1.0+eps)*rem) 534 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 535 536 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=js,je ; \textcolor{keywordflow}{do} i=isq,ieq 537 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of} 538 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of} 539 \textcolor{comment}{! T & S along the top and bottom integrals, akin to thickness weighting.} 540 hwght = 0.0 541 \textcolor{keywordflow}{if} (do\_massweight) & 542 hwght = max(0., -bathyt(i,j)-z\_t(i+1,j), -bathyt(i+1,j)-z\_t(i,j)) 543 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then} 544 hl = (z\_t(i,j) - z\_b(i,j)) + dz\_neglect 545 hr = (z\_t(i+1,j) - z\_b(i+1,j)) + dz\_neglect 546 hwght = hwght * ( (hl-hr)/(hl+hr) )**2 547 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr ) 548 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom 549 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom 550 \textcolor{keywordflow}{else} 551 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0 552 \textcolor{keywordflow}{ endif} 553 554 intz(1) = dpa(i,j) ; intz(5) = dpa(i+1,j) 555 \textcolor{keywordflow}{do} m=2,4 556 wt\_l = 0.25*\textcolor{keywordtype}{real(5-m)} ; wt\_r = 1.0-wt\_l 557 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr 558 559 al0 = wtt\_l*al0\_2d(i,j) + wtt\_r*al0\_2d(i+1,j) 560 p0 = wtt\_l*p0\_2d(i,j) + wtt\_r*p0\_2d(i+1,j) 561 lambda = wtt\_l*lambda\_2d(i,j) + wtt\_r*lambda\_2d(i+1,j) 562 563 dz = wt\_l*(z\_t(i,j) - z\_b(i,j)) + wt\_r*(z\_t(i+1,j) - z\_b(i+1,j)) 564 p\_ave = -0.5*gxrho*(wt\_l*(z\_t(i,j)+z\_b(i,j)) + & 565 wt\_r*(z\_t(i+1,j)+z\_b(i+1,j))) 566 567 i\_al0 = 1.0 / al0 568 i\_lzz = 1.0 / (p0 + (lambda * i\_al0) + p\_ave) 569 eps = 0.5*gxrho*dz*i\_lzz ; eps2 = eps*eps 570 571 intz(m) = pa\_to\_rl2\_t2 * ( g\_earth*dz*((p0 + p\_ave)*(i\_lzz*i\_al0) - rho\_ref\_mks) - 2.0*eps * & 572 i\_rho * (lambda * i\_al0**2) * eps2 * (c1\_3 + eps2*(0.2 + eps2*(c1\_7 + c1\_9*eps2))) ) 573 \textcolor{keywordflow}{ enddo} 574 \textcolor{comment}{! Use Boole's rule to integrate the values.} 575 intx\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + 12.0*intz(3)) 576 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} 577 578 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dpa)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{do} j=jsq,jeq ; \textcolor{keywordflow}{do} i=is,ie 579 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of} 580 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of} 581 \textcolor{comment}{! T & S along the top and bottom integrals, akin to thickness weighting.} 582 hwght = 0.0 583 \textcolor{keywordflow}{if} (do\_massweight) & 584 hwght = max(0., -bathyt(i,j)-z\_t(i,j+1), -bathyt(i,j+1)-z\_t(i,j)) 585 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then} 586 hl = (z\_t(i,j) - z\_b(i,j)) + dz\_neglect 587 hr = (z\_t(i,j+1) - z\_b(i,j+1)) + dz\_neglect 588 hwght = hwght * ( (hl-hr)/(hl+hr) )**2 589 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr ) 590 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom 591 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom 592 \textcolor{keywordflow}{else} 593 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0 594 \textcolor{keywordflow}{ endif} 595 596 intz(1) = dpa(i,j) ; intz(5) = dpa(i,j+1) 597 \textcolor{keywordflow}{do} m=2,4 598 wt\_l = 0.25*\textcolor{keywordtype}{real(5-m)} ; wt\_r = 1.0-wt\_l 599 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr 600 601 al0 = wtt\_l*al0\_2d(i,j) + wtt\_r*al0\_2d(i,j+1) 602 p0 = wtt\_l*p0\_2d(i,j) + wtt\_r*p0\_2d(i,j+1) 603 lambda = wtt\_l*lambda\_2d(i,j) + wtt\_r*lambda\_2d(i,j+1) 604 605 dz = wt\_l*(z\_t(i,j) - z\_b(i,j)) + wt\_r*(z\_t(i,j+1) - z\_b(i,j+1)) 606 p\_ave = -0.5*gxrho*(wt\_l*(z\_t(i,j)+z\_b(i,j)) + & 607 wt\_r*(z\_t(i,j+1)+z\_b(i,j+1))) 608 609 i\_al0 = 1.0 / al0 610 i\_lzz = 1.0 / (p0 + (lambda * i\_al0) + p\_ave) 611 eps = 0.5*gxrho*dz*i\_lzz ; eps2 = eps*eps 612 613 intz(m) = pa\_to\_rl2\_t2 * ( g\_earth*dz*((p0 + p\_ave)*(i\_lzz*i\_al0) - rho\_ref\_mks) - 2.0*eps * & 614 i\_rho * (lambda * i\_al0**2) * eps2 * (c1\_3 + eps2*(0.2 + eps2*(c1\_7 + c1\_9*eps2))) ) 615 \textcolor{keywordflow}{ enddo} 616 \textcolor{comment}{! Use Boole's rule to integrate the values.} 617 inty\_dpa(i,j) = c1\_90*(7.0*(intz(1)+intz(5)) + 32.0*(intz(2)+intz(4)) + 12.0*intz(3)) 618 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} 619 \end{DoxyCode} \mbox{\Hypertarget{namespacemom__eos__wright_a35402f454f02a3fa680a6d7870931aa6}\label{namespacemom__eos__wright_a35402f454f02a3fa680a6d7870931aa6}} \index{mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}!int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+wright@{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+wright}} \index{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+wright@{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+wright}!mom\+\_\+eos\+\_\+wright@{mom\+\_\+eos\+\_\+wright}} \subsubsection{\texorpdfstring{int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+wright()}{int\_spec\_vol\_dp\_wright()}} {\footnotesize\ttfamily subroutine, public mom\+\_\+eos\+\_\+wright\+::int\+\_\+spec\+\_\+vol\+\_\+dp\+\_\+wright (\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)}]{spv\+\_\+ref, }\item[{type(hor\+\_\+index\+\_\+type), intent(in)}]{HI, }\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, }\item[{real, intent(in), optional}]{S\+V\+\_\+scale, }\item[{real, intent(in), optional}]{pres\+\_\+scale }\end{DoxyParamCaption})} This subroutine 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. 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{\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 spv\+\_\+ref} & A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals \mbox{[}R-\/1 $\sim$$>$ m3 kg-\/1\mbox{]}. The calculation is mathematically identical with different values of spv\+\_\+ref, but this reduces the effects of roundoff.\\ \hline \mbox{\tt in,out} & {\em dza} & The change in the geopotential anomaly across\\ \hline \mbox{\tt in,out} & {\em intp\+\_\+dza} & The integral in pressure through the layer of\\ \hline \mbox{\tt in,out} & {\em intx\+\_\+dza} & The integral in x of the difference between the\\ \hline \mbox{\tt in,out} & {\em inty\+\_\+dza} & The integral in y of the difference between the\\ \hline \mbox{\tt in} & {\em halo\+\_\+size} & The width of halo points on which to calculate dza.\\ \hline \mbox{\tt in} & {\em bathyp} & The pressure at the bathymetry \mbox{[}R L2 T-\/2 $\sim$$>$ 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$$>$ Pa\mbox{]} or \mbox{[}Pa\mbox{]}\\ \hline \mbox{\tt in} & {\em usemasswghtinterp} & If true, uses mass weighting to interpolate T/S for top and bottom integrals.\\ \hline \mbox{\tt in} & {\em sv\+\_\+scale} & A multiplicative factor by which to scale specific volume from m3 kg-\/1 to the desired units \mbox{[}kg m-\/3 R-\/1 $\sim$$>$ 1\mbox{]}\\ \hline \mbox{\tt in} & {\em pres\+\_\+scale} & A multiplicative factor to convert pressure into Pa \mbox{[}Pa T2 R-\/1 L-\/2 $\sim$$>$ 1\mbox{]}. \\ \hline \end{DoxyParams} Definition at line 631 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \begin{DoxyCode} 631 \textcolor{keywordtype}{type}(hor\_index\_type), \textcolor{keywordtype}{intent(in)} :: hi\textcolor{comment}{ !< The ocean's horizontal index type.} 632 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 633 \textcolor{keywordtype}{intent(in)} :: t\textcolor{comment}{ !< Potential temperature relative to the surface} 634 \textcolor{comment}{ !! [degC].} 635 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 636 \textcolor{keywordtype}{intent(in)} :: s\textcolor{comment}{ !< Salinity [PSU].} 637 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 638 \textcolor{keywordtype}{intent(in)} :: p\_t\textcolor{comment}{ !< Pressure at the top of the layer [R L2 T-2 ~> Pa] or [Pa].} 639 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 640 \textcolor{keywordtype}{intent(in)} :: p\_b\textcolor{comment}{ !< Pressure at the top of the layer [R L2 T-2 ~> Pa] or [Pa].} 641 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: spv\_ref\textcolor{comment}{ !< A mean specific volume that is subtracted out} 642 \textcolor{comment}{ !! to reduce the magnitude of each of the integrals [R-1 ~> m3 kg-1].} 643 \textcolor{comment}{ !! The calculation is mathematically identical with different values of} 644 \textcolor{comment}{ !! spv\_ref, but this reduces the effects of roundoff.} 645 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 646 \textcolor{keywordtype}{intent(inout)} :: dza\textcolor{comment}{ !< The change in the geopotential anomaly across} 647 \textcolor{comment}{ !! the layer [T-2 ~> m2 s-2] or [m2 s-2].} 648 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 649 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intp\_dza\textcolor{comment}{ !< The integral in pressure through the layer of} 650 \textcolor{comment}{ !! the geopotential anomaly relative to the anomaly} 651 \textcolor{comment}{ !! at the bottom of the layer [R L4 T-4 ~> Pa m2 s-2]} 652 \textcolor{comment}{ !! or [Pa m2 s-2].} 653 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%IsdB:HI%IedB,HI%jsd:HI%jed)}, & 654 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: intx\_dza\textcolor{comment}{ !< The integral in x of the difference between the} 655 \textcolor{comment}{ !! geopotential anomaly at the top and bottom of} 656 \textcolor{comment}{ !! the layer divided by the x grid spacing} 657 \textcolor{comment}{ !! [L2 T-2 ~> m2 s-2] or [m2 s-2].} 658 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%JsdB:HI%JedB)}, & 659 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(inout)} :: inty\_dza\textcolor{comment}{ !< The integral in y of the difference between the} 660 \textcolor{comment}{ !! geopotential anomaly at the top and bottom of} 661 \textcolor{comment}{ !! the layer divided by the y grid spacing} 662 \textcolor{comment}{ !! [L2 T-2 ~> m2 s-2] or [m2 s-2].} 663 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: halo\_size\textcolor{comment}{ !< The width of halo points on which to calculate} 664 \textcolor{comment}{ !! dza.} 665 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)}, & 666 \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: bathyp\textcolor{comment}{ !< The pressure at the bathymetry [R L2 T-2 ~> Pa] or [Pa]} 667 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: dp\_neglect\textcolor{comment}{ !< A miniscule pressure change with} 668 \textcolor{comment}{ !! the same units as p\_t [R L2 T-2 ~> Pa] or [Pa]} 669 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: usemasswghtinterp\textcolor{comment}{ !< If true, uses mass weighting} 670 \textcolor{comment}{ !! to interpolate T/S for top and bottom integrals.} 671 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: sv\_scale\textcolor{comment}{ !< A multiplicative factor by which to scale specific} 672 \textcolor{comment}{ !! volume from m3 kg-1 to the desired units [kg m-3 R-1 ~> 1]} 673 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: pres\_scale\textcolor{comment}{ !< A multiplicative factor to convert pressure} 674 \textcolor{comment}{ !! into Pa [Pa T2 R-1 L-2 ~> 1].} 675 676 \textcolor{comment}{! Local variables} 677 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(HI%isd:HI%ied,HI%jsd:HI%jed)} :: al0\_2d, p0\_2d, lambda\_2d 678 \textcolor{keywordtype}{real} :: al0 \textcolor{comment}{! A term in the Wright EOS [R-1 ~> m3 kg-1]} 679 \textcolor{keywordtype}{real} :: p0 \textcolor{comment}{! A term in the Wright EOS [R L2 T-2 ~> Pa]} 680 \textcolor{keywordtype}{real} :: lambda \textcolor{comment}{! A term in the Wright EOS [L2 T-2 ~> m2 s-2]} 681 \textcolor{keywordtype}{real} :: al0\_scale \textcolor{comment}{! Scaling factor to convert al0 from MKS units [R-1 kg m-3 ~> 1]} 682 \textcolor{keywordtype}{real} :: p0\_scale \textcolor{comment}{! Scaling factor to convert p0 from MKS units [R L2 T-2 Pa-1 ~> 1]} 683 \textcolor{keywordtype}{real} :: lam\_scale \textcolor{comment}{! Scaling factor to convert lambda from MKS units [L2 s2 T-2 m-2 ~> 1]} 684 \textcolor{keywordtype}{real} :: p\_ave \textcolor{comment}{! The layer average pressure [R L2 T-2 ~> Pa]} 685 \textcolor{keywordtype}{real} :: rem \textcolor{comment}{! [L2 T-2 ~> m2 s-2]} 686 \textcolor{keywordtype}{real} :: eps, eps2 \textcolor{comment}{! A nondimensional ratio and its square [nondim]} 687 \textcolor{keywordtype}{real} :: alpha\_anom \textcolor{comment}{! The depth averaged specific volume anomaly [R-1 ~> m3 kg-1].} 688 \textcolor{keywordtype}{real} :: dp \textcolor{comment}{! The pressure change through a layer [R L2 T-2 ~> Pa].} 689 \textcolor{keywordtype}{real} :: hwght \textcolor{comment}{! A pressure-thickness below topography [R L2 T-2 ~> Pa].} 690 \textcolor{keywordtype}{real} :: hl, hr \textcolor{comment}{! Pressure-thicknesses of the columns to the left and right [R L2 T-2 ~> Pa].} 691 \textcolor{keywordtype}{real} :: idenom \textcolor{comment}{! The inverse of the denominator in the weights [T4 R-2 L-4 ~> Pa-2].} 692 \textcolor{keywordtype}{real} :: hwt\_ll, hwt\_lr \textcolor{comment}{! hWt\_LA is the weighted influence of A on the left column [nondim].} 693 \textcolor{keywordtype}{real} :: hwt\_rl, hwt\_rr \textcolor{comment}{! hWt\_RA is the weighted influence of A on the right column [nondim].} 694 \textcolor{keywordtype}{real} :: wt\_l, wt\_r \textcolor{comment}{! The linear weights of the left and right columns [nondim].} 695 \textcolor{keywordtype}{real} :: wtt\_l, wtt\_r \textcolor{comment}{! The weights for tracers from the left and right columns [nondim].} 696 \textcolor{keywordtype}{real} :: intp(5) \textcolor{comment}{! The integrals of specific volume with pressure at the} 697 \textcolor{comment}{! 5 sub-column locations [L2 T-2 ~> m2 s-2].} 698 \textcolor{keywordtype}{logical} :: do\_massweight \textcolor{comment}{! Indicates whether to do mass weighting.} 699 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{parameter} :: c1\_3 = 1.0/3.0, c1\_7 = 1.0/7.0 \textcolor{comment}{! Rational constants.} 700 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{parameter} :: c1\_9 = 1.0/9.0, c1\_90 = 1.0/90.0 \textcolor{comment}{! Rational constants.} 701 \textcolor{keywordtype}{integer} :: isq, ieq, jsq, jeq, ish, ieh, jsh, jeh, i, j, m, halo 702 703 isq = hi%IscB ; ieq = hi%IecB ; jsq = hi%JscB ; jeq = hi%JecB 704 halo = 0 ; \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(halo\_size)) halo = max(halo\_size,0) 705 ish = hi%isc-halo ; ieh = hi%iec+halo ; jsh = hi%jsc-halo ; jeh = hi%jec+halo 706 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intx\_dza)) \textcolor{keywordflow}{then} ; ish = min(isq,ish) ; ieh = max(ieq+1,ieh);\textcolor{keywordflow}{ endif} 707 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(inty\_dza)) \textcolor{keywordflow}{then} ; jsh = min(jsq,jsh) ; jeh = max(jeq+1,jeh);\textcolor{keywordflow}{ endif} 708 709 710 al0\_scale = 1.0 ; \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(sv\_scale)) al0\_scale = sv\_scale 711 p0\_scale = 1.0 712 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(pres\_scale)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (pres\_scale /= 1.0) \textcolor{keywordflow}{then} 713 p0\_scale = 1.0 / pres\_scale 714 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 715 lam\_scale = al0\_scale * p0\_scale 716 717 do\_massweight = .false. 718 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(usemasswghtinterp)) \textcolor{keywordflow}{then} ; \textcolor{keywordflow}{if} (usemasswghtinterp) \textcolor{keywordflow}{then} 719 do\_massweight = .true. 720 \textcolor{comment}{! if (.not.present(bathyP)) call MOM\_error(FATAL, "int\_spec\_vol\_dp\_generic: "//&} 721 \textcolor{comment}{! "bathyP must be present if useMassWghtInterp is present and true.")} 722 \textcolor{comment}{! if (.not.present(dP\_neglect)) call MOM\_error(FATAL, "int\_spec\_vol\_dp\_generic: "//&} 723 \textcolor{comment}{! "dP\_neglect must be present if useMassWghtInterp is present and true.")} 724 \textcolor{keywordflow}{ endif} ;\textcolor{keywordflow}{ endif} 725 726 \textcolor{comment}{! alpha(j) = (lambda + al0*(pressure(j) + p0)) / (pressure(j) + p0)} 727 \textcolor{keywordflow}{do} j=jsh,jeh ; \textcolor{keywordflow}{do} i=ish,ieh 728 al0\_2d(i,j) = al0\_scale * ( (a0 + a1*t(i,j)) + a2*s(i,j) ) 729 p0\_2d(i,j) = p0\_scale * ( (b0 + b4*s(i,j)) + t(i,j) * (b1 + t(i,j)*((b2 + b3*t(i,j))) + b5*s(i,j)) ) 730 lambda\_2d(i,j) = lam\_scale * ( (c0 + c4*s(i,j)) + t(i,j) * (c1 + t(i,j)*((c2 + c3*t(i,j))) + c5*s(i,j)) ) 731 732 al0 = al0\_2d(i,j) ; p0 = p0\_2d(i,j) ; lambda = lambda\_2d(i,j) 733 dp = p\_b(i,j) - p\_t(i,j) 734 p\_ave = 0.5*(p\_t(i,j)+p\_b(i,j)) 735 736 eps = 0.5 * dp / (p0 + p\_ave) ; eps2 = eps*eps 737 alpha\_anom = al0 + lambda / (p0 + p\_ave) - spv\_ref 738 rem = lambda * eps2 * (c1\_3 + eps2*(0.2 + eps2*(c1\_7 + c1\_9*eps2))) 739 dza(i,j) = alpha\_anom*dp + 2.0*eps*rem 740 \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(intp\_dza)) & 741 intp\_dza(i,j) = 0.5*alpha\_anom*dp**2 - dp*(1.0-eps)*rem 742 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} 743 744 \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 745 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of} 746 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of} 747 \textcolor{comment}{! T & S along the top and bottom integrals, akin to thickness weighting.} 748 hwght = 0.0 749 \textcolor{keywordflow}{if} (do\_massweight) & 750 hwght = max(0., bathyp(i,j)-p\_t(i+1,j), bathyp(i+1,j)-p\_t(i,j)) 751 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then} 752 hl = (p\_b(i,j) - p\_t(i,j)) + dp\_neglect 753 hr = (p\_b(i+1,j) - p\_t(i+1,j)) + dp\_neglect 754 hwght = hwght * ( (hl-hr)/(hl+hr) )**2 755 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr ) 756 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom 757 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom 758 \textcolor{keywordflow}{else} 759 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0 760 \textcolor{keywordflow}{ endif} 761 762 intp(1) = dza(i,j) ; intp(5) = dza(i+1,j) 763 \textcolor{keywordflow}{do} m=2,4 764 wt\_l = 0.25*\textcolor{keywordtype}{real(5-m)} ; wt\_r = 1.0-wt\_l 765 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr 766 767 \textcolor{comment}{! T, S, and p are interpolated in the horizontal. The p interpolation} 768 \textcolor{comment}{! is linear, but for T and S it may be thickness wekghted.} 769 al0 = wtt\_l*al0\_2d(i,j) + wtt\_r*al0\_2d(i+1,j) 770 p0 = wtt\_l*p0\_2d(i,j) + wtt\_r*p0\_2d(i+1,j) 771 lambda = wtt\_l*lambda\_2d(i,j) + wtt\_r*lambda\_2d(i+1,j) 772 773 dp = wt\_l*(p\_b(i,j) - p\_t(i,j)) + wt\_r*(p\_b(i+1,j) - p\_t(i+1,j)) 774 p\_ave = 0.5*(wt\_l*(p\_t(i,j)+p\_b(i,j)) + wt\_r*(p\_t(i+1,j)+p\_b(i+1,j))) 775 776 eps = 0.5 * dp / (p0 + p\_ave) ; eps2 = eps*eps 777 intp(m) = (al0 + lambda / (p0 + p\_ave) - spv\_ref)*dp + 2.0*eps* & 778 lambda * eps2 * (c1\_3 + eps2*(0.2 + eps2*(c1\_7 + c1\_9*eps2))) 779 \textcolor{keywordflow}{ enddo} 780 \textcolor{comment}{! Use Boole's rule to integrate the values.} 781 intx\_dza(i,j) = c1\_90*(7.0*(intp(1)+intp(5)) + 32.0*(intp(2)+intp(4)) + & 782 12.0*intp(3)) 783 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} 784 785 \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 786 \textcolor{comment}{! hWght is the distance measure by which the cell is violation of} 787 \textcolor{comment}{! hydrostatic consistency. For large hWght we bias the interpolation of} 788 \textcolor{comment}{! T & S along the top and bottom integrals, akin to thickness weighting.} 789 hwght = 0.0 790 \textcolor{keywordflow}{if} (do\_massweight) & 791 hwght = max(0., bathyp(i,j)-p\_t(i,j+1), bathyp(i,j+1)-p\_t(i,j)) 792 \textcolor{keywordflow}{if} (hwght > 0.) \textcolor{keywordflow}{then} 793 hl = (p\_b(i,j) - p\_t(i,j)) + dp\_neglect 794 hr = (p\_b(i,j+1) - p\_t(i,j+1)) + dp\_neglect 795 hwght = hwght * ( (hl-hr)/(hl+hr) )**2 796 idenom = 1.0 / ( hwght*(hr + hl) + hl*hr ) 797 hwt\_ll = (hwght*hl + hr*hl) * idenom ; hwt\_lr = (hwght*hr) * idenom 798 hwt\_rr = (hwght*hr + hr*hl) * idenom ; hwt\_rl = (hwght*hl) * idenom 799 \textcolor{keywordflow}{else} 800 hwt\_ll = 1.0 ; hwt\_lr = 0.0 ; hwt\_rr = 1.0 ; hwt\_rl = 0.0 801 \textcolor{keywordflow}{ endif} 802 803 intp(1) = dza(i,j) ; intp(5) = dza(i,j+1) 804 \textcolor{keywordflow}{do} m=2,4 805 wt\_l = 0.25*\textcolor{keywordtype}{real(5-m)} ; wt\_r = 1.0-wt\_l 806 wtt\_l = wt\_l*hwt\_ll + wt\_r*hwt\_rl ; wtt\_r = wt\_l*hwt\_lr + wt\_r*hwt\_rr 807 808 \textcolor{comment}{! T, S, and p are interpolated in the horizontal. The p interpolation} 809 \textcolor{comment}{! is linear, but for T and S it may be thickness wekghted.} 810 al0 = wt\_l*al0\_2d(i,j) + wt\_r*al0\_2d(i,j+1) 811 p0 = wt\_l*p0\_2d(i,j) + wt\_r*p0\_2d(i,j+1) 812 lambda = wt\_l*lambda\_2d(i,j) + wt\_r*lambda\_2d(i,j+1) 813 814 dp = wt\_l*(p\_b(i,j) - p\_t(i,j)) + wt\_r*(p\_b(i,j+1) - p\_t(i,j+1)) 815 p\_ave = 0.5*(wt\_l*(p\_t(i,j)+p\_b(i,j)) + wt\_r*(p\_t(i,j+1)+p\_b(i,j+1))) 816 817 eps = 0.5 * dp / (p0 + p\_ave) ; eps2 = eps*eps 818 intp(m) = (al0 + lambda / (p0 + p\_ave) - spv\_ref)*dp + 2.0*eps* & 819 lambda * eps2 * (c1\_3 + eps2*(0.2 + eps2*(c1\_7 + c1\_9*eps2))) 820 \textcolor{keywordflow}{ enddo} 821 \textcolor{comment}{! Use Boole's rule to integrate the values.} 822 inty\_dza(i,j) = c1\_90*(7.0*(intp(1)+intp(5)) + 32.0*(intp(2)+intp(4)) + & 823 12.0*intp(3)) 824 \textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ enddo} ;\textcolor{keywordflow}{ endif} \end{DoxyCode}