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\section{Ocean vertical mixing -- |
\subsection{KPP: Nonlocal K-Profile Parameterization for |
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the nonlocal K-profile parameterization scheme KPP |
Diapycnal Mixing} |
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\label{sectionkpp}} |
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\label{sec:pkg:kpp} |
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\begin{rawhtml} |
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<!-- CMIREDIR:package_kpp: --> |
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\end{rawhtml} |
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Authors: Dimitris Menemenlis and Patrick Heimbach |
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\subsubsection{Introduction |
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\label{sec:pkg:kpp:intro}} |
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%---------------------------------------------------------------------- |
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\subsubsection{KPP configuration and compiling} |
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As with all MITgcm packages, KPP can be turned on or off at compile time |
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% |
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\begin{itemize} |
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% |
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\item |
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using the \texttt{packages.conf} file by adding \texttt{kpp} to it, |
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% |
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\item |
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or using \texttt{genmake2} adding |
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\texttt{-enable=kpp} or \texttt{-disable=kpp} switches |
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% |
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\end{itemize} |
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(see Section \ref{sect:buildingCode}). |
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Parts of the KPP code can be enabled or disabled at compile time |
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via CPP preprocessor flags. These options are set in |
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\texttt{KPP\_OPTIONS.h}. Table \ref{tab:pkg:kpp:cpp} summarizes them. |
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\begin{table}[h!] |
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\label{tab:pkg:kpp:cpp} |
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{\footnotesize |
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\begin{tabular}{|l|l|} |
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\hline |
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\textbf{CPP option} & \textbf{Description} \\ |
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\hline \hline |
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\texttt{\_KPP\_RL} & |
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~ \\ |
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\texttt{FRUGAL\_KPP} & |
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~ \\ |
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\texttt{KPP\_SMOOTH\_SHSQ} & |
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~ \\ |
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\texttt{KPP\_SMOOTH\_DVSQ} & |
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~ \\ |
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\texttt{KPP\_SMOOTH\_DENS} & |
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~ \\ |
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\texttt{KPP\_SMOOTH\_VISC} & |
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~ \\ |
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\texttt{KPP\_SMOOTH\_DIFF} & |
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~ \\ |
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\texttt{KPP\_ESTIMATE\_UREF} & |
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~ \\ |
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\texttt{INCLUDE\_DIAGNOSTICS\_INTERFACE\_CODE} & |
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~ \\ |
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\texttt{KPP\_GHAT} & |
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~ \\ |
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\texttt{EXCLUDE\_KPP\_SHEAR\_MIX} & |
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~ \\ |
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\hline |
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\end{tabular} |
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} |
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\caption{~} |
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\end{table} |
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%---------------------------------------------------------------------- |
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\subsubsection{Run-time parameters |
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\label{sec:pkg:kpp:runtime}} |
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Run-time parameters are set in files |
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\texttt{data.pkg} and \texttt{data.kpp} |
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which are read in \texttt{kpp\_readparms.F}. |
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Run-time parameters may be broken into 3 categories: |
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(i) switching on/off the package at runtime, |
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(ii) required MITgcm flags, |
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(iii) package flags and parameters. |
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\paragraph{Enabling the package} |
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~ \\ |
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% |
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The KPP package is switched on at runtime by setting |
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\texttt{useKPP = .TRUE.} in \texttt{data.pkg}. |
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\paragraph{Required MITgcm flags} |
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~ \\ |
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% |
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The following flags/parameters of the MITgcm dynamical |
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kernel need to be set in conjunction with KPP: |
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\begin{tabular}{ll} |
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\texttt{implicitViscosity = .TRUE.} & enable implicit vertical viscosity \\ |
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\texttt{implicitDiffusion = .TRUE.} & enable implicit vertical diffusion \\ |
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\end{tabular} |
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\paragraph{Package flags and parameters} |
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~ \\ |
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% |
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\begin{table}[h!] |
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\label{tab:pkg:kpp:runtime_flags} |
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{\footnotesize |
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\begin{tabular}{|l|c|l|} |
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\hline |
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\textbf{Flag/parameter} & \textbf{default} & \textbf{Description} \\ |
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\hline \hline |
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\multicolumn{3}{|c|}{\textit{I/O related parameters} } \\ |
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\hline |
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kpp\_freq & \texttt{deltaTClock} & |
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Recomputation frequency for KPP fields \\ |
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kpp\_dumpFreq & \texttt{dumpFreq} & |
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Dump frequency of KPP field snapshots \\ |
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kpp\_taveFreq & \texttt{taveFreq} & |
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Averaging and dump frequency of KPP fields \\ |
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KPPmixingMaps & \texttt{.FALSE.} & |
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include KPP diagnostic maps in STDOUT \\ |
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KPPwriteState & \texttt{.FALSE.} & |
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write KPP state to file \\ |
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KPP\_ghatUseTotalDiffus & \texttt{.FALSE.} & |
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if \texttt{.T.} compute non-local term using total vertical diffusivity \\ |
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~ & ~ & |
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if \texttt{.F.} use KPP vertical diffusivity \\ |
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\hline |
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\multicolumn{3}{|c|}{\textit{Genral KPP parameters} } \\ |
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\hline |
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minKPPhbl & \texttt{delRc(1)} & |
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Minimum boundary layer depth \\ |
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epsilon & 0.1 & |
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nondimensional extent of the surface layer \\ |
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vonk & 0.4 & |
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von Karman constant \\ |
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dB\_dz & 5.2E-5 1/s$^2$ & |
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maximum dB/dz in mixed layer hMix \\ |
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concs & 98.96 & |
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~ \\ |
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concv & 1.8 & |
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~ \\ |
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\hline |
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\multicolumn{3}{|c|}{\textit{Boundary layer parameters (S/R \texttt{bldepth})} } \\ |
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\hline |
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Ricr & 0.3 & |
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critical bulk Richardson number \\ |
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cekman & 0.7 & |
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coefficient for Ekman depth \\ |
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cmonob & 1.0 & |
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coefficient for Monin-Obukhov depth \\ |
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concv & 1.8 & |
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ratio of interior to entrainment depth buoyancy frequency \\ |
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hbf & 1.0 & |
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fraction of depth to which absorbed solar radiation contributes \\ |
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~ & ~ & |
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to surface buoyancy forcing \\ |
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Vtc & \texttt{~} & |
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non-dim. coeff. for velocity scale of turbulant velocity shear \\ |
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~ & ~ & |
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( = function of concv,concs,epsilon,vonk,Ricr) \\ |
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\hline |
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\multicolumn{3}{|c|}{\textit{Boundary layer mixing parameters (S/R \texttt{blmix})} } \\ |
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\hline |
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cstar & 10. & |
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proportionality coefficient for nonlocal transport \\ |
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cg & ~ & |
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non-dimensional coefficient for counter-gradient term \\ |
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~ & ~ & |
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( = function of cstar,vonk,concs,epsilon) \\ |
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\hline |
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\multicolumn{3}{|c|}{\textit{Interior mixing parameters (S/R \texttt{Ri\_iwmix})} } \\ |
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\hline |
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Riinfty & 0.7 & |
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gradient Richardson number limit for shear instability \\ |
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BVDQcon & -0.2E-4 1/s$^2$ & |
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Brunt-V\"ai\"sal\"a squared \\ |
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difm0 & 0.005 m$^2$/s & |
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viscosity max. due to shear instability \\ |
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difs0 & 0.005 m$^2$/s & |
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tracer diffusivity max. due to shear instability \\ |
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dift0 & 0.005 m$^2$/s & |
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heat diffusivity max. due to shear instability \\ |
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difmcon & 0.1 & |
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viscosity due to convective instability \\ |
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difscon & 0.1 & |
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tracer diffusivity due to convective instability \\ |
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diftcon & 0.1 & |
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heat diffusivity due to convective instability \\ |
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\hline |
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\multicolumn{3}{|c|}{\textit{Double-diffusive mixing parameters (S/R \texttt{ddmix})} } \\ |
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\hline |
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Rrho0 & not used & |
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limit for double diffusive density ratio \\ |
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dsfmax & not used & |
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maximum diffusivity in case of salt fingering \\ |
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\hline |
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\hline |
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\end{tabular} |
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} |
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\caption{~} |
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\end{table} |
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%---------------------------------------------------------------------- |
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\subsubsection{Equations |
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\label{sec:pkg:kpp:equations}} |
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%---------------------------------------------------------------------- |
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\subsubsection{Key subroutines |
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\label{sec:pkg:kpp:subroutines}} |
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\paragraph{kpp\_calc:} Top-level routine. \\ |
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~ |
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\paragraph{kpp\_mix:} Intermediate-level routine \\ |
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~ |
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\paragraph{ri\_iwmix:} ~ \\ |
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% |
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Compute interior viscosity and diffusivity coefficients due to |
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% |
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\begin{itemize} |
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% |
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\item |
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shear instability (dependent on a local gradient Richardson number), |
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% |
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to background internal wave activity, and |
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% |
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\item |
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to static instability (local Richardson number < 0). |
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% |
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\end{itemize} |
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\paragraph{bldepth:} ~ \\ |
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% |
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The oceanic planetary boundary layer depth, \texttt{hbl}, is determined as |
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the shallowest depth where the bulk Richardson number is |
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equal to the critical value, \texttt{Ricr}. |
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Bulk Richardson numbers are evaluated by computing velocity and |
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buoyancy differences between values at zgrid(kl) < 0 and surface |
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reference values. |
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In this configuration, the reference values are equal to the |
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values in the surface layer. |
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When using a very fine vertical grid, these values should be |
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computed as the vertical average of velocity and buoyancy from |
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the surface down to epsilon*zgrid(kl). |
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When the bulk Richardson number at k exceeds Ricr, hbl is |
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linearly interpolated between grid levels zgrid(k) and zgrid(k-1). |
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The water column and the surface forcing are diagnosed for |
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stable/ustable forcing conditions, and where hbl is relative |
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to grid points (caseA), so that conditional branches can be |
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avoided in later subroutines. |
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\paragraph{blmix:} ~ \\ |
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% |
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Compute boundary layer mixing coefficients. |
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Mixing coefficients within boundary layer depend on surface |
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forcing and the magnitude and gradient of interior mixing below |
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the boundary layer ("matching"). |
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% |
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\begin{enumerate} |
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% |
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\item |
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compute velocity scales at hbl |
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% |
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\item |
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find the interior viscosities and derivatives at hbl |
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% |
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\item |
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compute turbulent velocity scales on the interfaces |
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% |
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compute the dimensionless shape functions at the interfaces |
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% |
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\item |
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compute boundary layer diffusivities at the interfaces |
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% |
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compute nonlocal transport term |
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% |
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\item |
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find diffusivities at kbl-1 grid level |
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% |
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\end{enumerate} |
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\paragraph{kpp\_calc\_diff\_t/s, kpp\_calc\_visc:} ~ \\ |
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% |
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Add contribution to net diffusivity/viscosity from |
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KPP diffusivity/viscosity. |
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\paragraph{kpp\_transport\_t/s/ptr:} ~ \\ |
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% |
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Add non local KPP transport term (ghat) to diffusive |
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temperature/salinity/passive tracer flux. |
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The nonlocal transport term is nonzero only for scalars |
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in unstable (convective) forcing conditions. |
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{\footnotesize |
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\begin{verbatim} |
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C !CALLING SEQUENCE: |
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c ... |
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c kpp_calc (TOP LEVEL ROUTINE) |
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c | |
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c |-- statekpp: o compute all EOS/density-related arrays |
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c | o uses S/R FIND_ALPHA, FIND_BETA, FIND_RHO |
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c | |
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c |-- kppmix |
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c | |--- ri_iwmix (compute interior mixing coefficients due to constant |
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c | | internal wave activity, static instability, |
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c | | and local shear instability). |
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c | | |
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c | |--- bldepth (diagnose boundary layer depth) |
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c | | |
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c | |--- blmix (compute boundary layer diffusivities) |
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c | | |
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c | |--- enhance (enhance diffusivity at interface kbl - 1) |
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c | o |
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c | |
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c |-- swfrac |
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c o |
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\end{verbatim} |
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} |
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%---------------------------------------------------------------------- |
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\subsubsection{KPP diagnostics |
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\label{sec:pkg:kpp:diagnostics}} |
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Diagnostics output is available via the diagnostics package |
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(see Section \ref{sec:pkg:diagnostics}). |
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Available output fields are summarized in |
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Table \ref{tab:pkg:kpp:diagnostics}. |
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\begin{table}[h!] |
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\label{tab:pkg:kpp:diagnostics} |
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{\footnotesize |
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\begin{verbatim} |
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------------------------------------------------------ |
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<-Name->|Levs|grid|<-- Units -->|<- Tile (max=80c) |
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------------------------------------------------------ |
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KPPviscA| 23 |SM |m^2/s |KPP vertical eddy viscosity coefficient |
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KPPdiffS| 23 |SM |m^2/s |Vertical diffusion coefficient for salt & tracers |
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KPPdiffT| 23 |SM |m^2/s |Vertical diffusion coefficient for heat |
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KPPghat | 23 |SM |s/m^2 |Nonlocal transport coefficient |
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KPPhbl | 1 |SM |m |KPP boundary layer depth, bulk Ri criterion |
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KPPmld | 1 |SM |m |Mixed layer depth, dT=.8degC density criterion |
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KPPfrac | 1 |SM | |Short-wave flux fraction penetrating mixing layer |
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\end{verbatim} |
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} |
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\caption{~} |
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\end{table} |
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%---------------------------------------------------------------------- |
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\subsubsection{Reference experiments} |
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lab\_sea: |
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natl\_box: |
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%---------------------------------------------------------------------- |
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\subsubsection{References} |
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