\hypertarget{interfacemom__eos__wright_1_1calculate__density__second__derivs__wright}{}\section{mom\+\_\+eos\+\_\+wright\+:\+:calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+wright Interface Reference} \label{interfacemom__eos__wright_1_1calculate__density__second__derivs__wright}\index{mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+wright@{mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+wright}} \subsection{Detailed Description} For a given thermodynamic state, return the second derivatives of density with various combinations of temperature, salinity, and pressure. Definition at line 50 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \subsection*{Private functions} \begin{DoxyCompactItemize} \item subroutine \mbox{\hyperlink{interfacemom__eos__wright_1_1calculate__density__second__derivs__wright_a3cbd28af5f550fefbdfff6247a304839}{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 \mbox{\hyperlink{interfacemom__eos__wright_1_1calculate__density__second__derivs__wright_aa37e6361657a2ce09e9f6cd3cd53ff65}{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}\end{DoxyCompactItemize} \subsection{Detailed Description} For a given thermodynamic state, return the second derivatives of density with various combinations of temperature, salinity, and pressure. Definition at line 50 of file M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90. \subsection{Functions and subroutines} \mbox{\Hypertarget{interfacemom__eos__wright_1_1calculate__density__second__derivs__wright_aa37e6361657a2ce09e9f6cd3cd53ff65}\label{interfacemom__eos__wright_1_1calculate__density__second__derivs__wright_aa37e6361657a2ce09e9f6cd3cd53ff65}} \index{mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+wright@{mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+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\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+wright@{mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+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\+\_\+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{interfacemom__eos__wright_1_1calculate__density__second__derivs__wright_a3cbd28af5f550fefbdfff6247a304839}\label{interfacemom__eos__wright_1_1calculate__density__second__derivs__wright_a3cbd28af5f550fefbdfff6247a304839}} \index{mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+wright@{mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+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\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+wright@{mom\+\_\+eos\+\_\+wright\+::calculate\+\_\+density\+\_\+second\+\_\+derivs\+\_\+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\+\_\+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} The documentation for this interface was generated from the following file\+:\begin{DoxyCompactItemize} \item /home/cermak/src/\+M\+O\+M6.\+devrob/src/equation\+\_\+of\+\_\+state/M\+O\+M\+\_\+\+E\+O\+S\+\_\+\+Wright.\+F90\end{DoxyCompactItemize}