| 1 |
heimbach |
1.6 |
\subsection{KPP: Nonlocal K-Profile Parameterization for |
| 2 |
heimbach |
1.7 |
Vertical Mixing} |
| 3 |
heimbach |
1.1 |
|
| 4 |
edhill |
1.3 |
\label{sec:pkg:kpp} |
| 5 |
|
|
\begin{rawhtml} |
| 6 |
|
|
<!-- CMIREDIR:package_kpp: --> |
| 7 |
|
|
\end{rawhtml} |
| 8 |
heimbach |
1.6 |
|
| 9 |
|
|
Authors: Dimitris Menemenlis and Patrick Heimbach |
| 10 |
|
|
|
| 11 |
|
|
\subsubsection{Introduction |
| 12 |
|
|
\label{sec:pkg:kpp:intro}} |
| 13 |
|
|
|
| 14 |
heimbach |
1.7 |
The nonlocal K-Profile Parameterization (KPP) scheme |
| 15 |
|
|
of \cite{lar-eta:94} unifies the treatment of a variety of |
| 16 |
|
|
unresolved processes involved in vertical mixing. |
| 17 |
|
|
To consider it as one mixing scheme is, in the view of the authors, |
| 18 |
|
|
somewhat misleading since it consists of several entities |
| 19 |
|
|
to deal with distinct mixing processes in the ocean's surface |
| 20 |
|
|
boundary layer, and the interior: |
| 21 |
|
|
% |
| 22 |
|
|
\begin{enumerate} |
| 23 |
|
|
% |
| 24 |
|
|
\item |
| 25 |
|
|
mixing in the interior is goverened by |
| 26 |
|
|
shear instability (modeled as function of the local gradient |
| 27 |
|
|
Richardson number), internal wave activity (assumed constant), |
| 28 |
|
|
and double-diffusion (not implemented here). |
| 29 |
|
|
% |
| 30 |
|
|
\item |
| 31 |
|
|
a boundary layer depth $h$ or \texttt{hbl} is determined |
| 32 |
|
|
at each grid point, based on a critical value of turbulent |
| 33 |
|
|
processes parameterized by a bulk Richardson number; |
| 34 |
|
|
% |
| 35 |
|
|
\item |
| 36 |
|
|
mixing is strongly enhanced in the boundary layer under the |
| 37 |
|
|
stabilizing or destabilizing influence of surface forcing |
| 38 |
|
|
(buoyancy and momentum) enabling boundary layer properties |
| 39 |
|
|
to penetrate well into the thermocline; |
| 40 |
|
|
mixing is represented through a polynomial profile whose |
| 41 |
|
|
coefficients are determined subject to several contraints; |
| 42 |
|
|
% |
| 43 |
|
|
\item |
| 44 |
|
|
the boundary-layer profile is made to agree with similarity |
| 45 |
|
|
theory of turbulence and is matched, in the asymptotic sense |
| 46 |
|
|
(function and derivative agree at the boundary), |
| 47 |
|
|
to the interior thus fixing the polynomial coefficients; |
| 48 |
|
|
matching allows for some fraction of the boundary layer mixing |
| 49 |
|
|
to affect the interior, and vice versa; |
| 50 |
|
|
% |
| 51 |
|
|
\item |
| 52 |
|
|
a ``non-local'' term $\hat{\gamma}$ or \texttt{ghat} |
| 53 |
|
|
which is independent of the vertical property gradient further |
| 54 |
|
|
enhances mixing where the water column is unstable |
| 55 |
|
|
% |
| 56 |
|
|
\end{enumerate} |
| 57 |
|
|
% |
| 58 |
|
|
The scheme has been extensively compared to observations |
| 59 |
|
|
(see e.g. \cite{lar-eta:97}) and is now coomon in many |
| 60 |
|
|
ocean models. |
| 61 |
|
|
|
| 62 |
|
|
The following sections will describe the KPP package |
| 63 |
|
|
configuration and compiling (\ref{sec:pkg:kpp:comp}), |
| 64 |
|
|
the settings and choices of runtime parameters |
| 65 |
|
|
(\ref{sec:pkg:kpp:runtime}), |
| 66 |
|
|
more detailed description of equations to which these |
| 67 |
|
|
parameters relate (\ref{sec:pkg:kpp:equations}), |
| 68 |
|
|
and key subroutines where they are used (\ref{sec:pkg:kpp:subroutines}), |
| 69 |
|
|
and diagnostics output of KPP-derived diffusivities, viscosities |
| 70 |
|
|
and boundary-layer/mixed-layer depths. |
| 71 |
|
|
|
| 72 |
heimbach |
1.6 |
%---------------------------------------------------------------------- |
| 73 |
|
|
|
| 74 |
heimbach |
1.7 |
\subsubsection{KPP configuration and compiling |
| 75 |
|
|
\label{sec:pkg:kpp:comp}} |
| 76 |
heimbach |
1.6 |
|
| 77 |
|
|
As with all MITgcm packages, KPP can be turned on or off at compile time |
| 78 |
|
|
% |
| 79 |
|
|
\begin{itemize} |
| 80 |
|
|
% |
| 81 |
|
|
\item |
| 82 |
|
|
using the \texttt{packages.conf} file by adding \texttt{kpp} to it, |
| 83 |
|
|
% |
| 84 |
|
|
\item |
| 85 |
|
|
or using \texttt{genmake2} adding |
| 86 |
|
|
\texttt{-enable=kpp} or \texttt{-disable=kpp} switches |
| 87 |
|
|
% |
| 88 |
|
|
\end{itemize} |
| 89 |
|
|
(see Section \ref{sect:buildingCode}). |
| 90 |
|
|
|
| 91 |
|
|
Parts of the KPP code can be enabled or disabled at compile time |
| 92 |
|
|
via CPP preprocessor flags. These options are set in |
| 93 |
|
|
\texttt{KPP\_OPTIONS.h}. Table \ref{tab:pkg:kpp:cpp} summarizes them. |
| 94 |
|
|
|
| 95 |
|
|
\begin{table}[h!] |
| 96 |
heimbach |
1.7 |
\centering |
| 97 |
heimbach |
1.6 |
\label{tab:pkg:kpp:cpp} |
| 98 |
|
|
{\footnotesize |
| 99 |
|
|
\begin{tabular}{|l|l|} |
| 100 |
|
|
\hline |
| 101 |
|
|
\textbf{CPP option} & \textbf{Description} \\ |
| 102 |
|
|
\hline \hline |
| 103 |
|
|
\texttt{\_KPP\_RL} & |
| 104 |
|
|
~ \\ |
| 105 |
|
|
\texttt{FRUGAL\_KPP} & |
| 106 |
|
|
~ \\ |
| 107 |
|
|
\texttt{KPP\_SMOOTH\_SHSQ} & |
| 108 |
|
|
~ \\ |
| 109 |
|
|
\texttt{KPP\_SMOOTH\_DVSQ} & |
| 110 |
|
|
~ \\ |
| 111 |
|
|
\texttt{KPP\_SMOOTH\_DENS} & |
| 112 |
|
|
~ \\ |
| 113 |
|
|
\texttt{KPP\_SMOOTH\_VISC} & |
| 114 |
|
|
~ \\ |
| 115 |
|
|
\texttt{KPP\_SMOOTH\_DIFF} & |
| 116 |
|
|
~ \\ |
| 117 |
|
|
\texttt{KPP\_ESTIMATE\_UREF} & |
| 118 |
|
|
~ \\ |
| 119 |
|
|
\texttt{INCLUDE\_DIAGNOSTICS\_INTERFACE\_CODE} & |
| 120 |
|
|
~ \\ |
| 121 |
|
|
\texttt{KPP\_GHAT} & |
| 122 |
|
|
~ \\ |
| 123 |
|
|
\texttt{EXCLUDE\_KPP\_SHEAR\_MIX} & |
| 124 |
|
|
~ \\ |
| 125 |
|
|
\hline |
| 126 |
|
|
\end{tabular} |
| 127 |
|
|
} |
| 128 |
|
|
\caption{~} |
| 129 |
|
|
\end{table} |
| 130 |
|
|
|
| 131 |
|
|
|
| 132 |
|
|
%---------------------------------------------------------------------- |
| 133 |
|
|
|
| 134 |
|
|
\subsubsection{Run-time parameters |
| 135 |
|
|
\label{sec:pkg:kpp:runtime}} |
| 136 |
|
|
|
| 137 |
|
|
Run-time parameters are set in files |
| 138 |
|
|
\texttt{data.pkg} and \texttt{data.kpp} |
| 139 |
|
|
which are read in \texttt{kpp\_readparms.F}. |
| 140 |
|
|
Run-time parameters may be broken into 3 categories: |
| 141 |
|
|
(i) switching on/off the package at runtime, |
| 142 |
|
|
(ii) required MITgcm flags, |
| 143 |
|
|
(iii) package flags and parameters. |
| 144 |
|
|
|
| 145 |
|
|
\paragraph{Enabling the package} |
| 146 |
|
|
~ \\ |
| 147 |
|
|
% |
| 148 |
|
|
The KPP package is switched on at runtime by setting |
| 149 |
|
|
\texttt{useKPP = .TRUE.} in \texttt{data.pkg}. |
| 150 |
|
|
|
| 151 |
|
|
\paragraph{Required MITgcm flags} |
| 152 |
|
|
~ \\ |
| 153 |
|
|
% |
| 154 |
|
|
The following flags/parameters of the MITgcm dynamical |
| 155 |
|
|
kernel need to be set in conjunction with KPP: |
| 156 |
|
|
|
| 157 |
|
|
\begin{tabular}{ll} |
| 158 |
|
|
\texttt{implicitViscosity = .TRUE.} & enable implicit vertical viscosity \\ |
| 159 |
|
|
\texttt{implicitDiffusion = .TRUE.} & enable implicit vertical diffusion \\ |
| 160 |
|
|
\end{tabular} |
| 161 |
|
|
|
| 162 |
|
|
|
| 163 |
|
|
\paragraph{Package flags and parameters} |
| 164 |
|
|
~ \\ |
| 165 |
|
|
% |
| 166 |
heimbach |
1.7 |
Table \ref{tab:pkg:kpp:runtime_flags} summarizes the |
| 167 |
|
|
runtime flags that are set in \texttt{data.pkg}, and |
| 168 |
|
|
their default values. |
| 169 |
|
|
|
| 170 |
heimbach |
1.6 |
\begin{table}[h!] |
| 171 |
heimbach |
1.7 |
\centering |
| 172 |
heimbach |
1.6 |
\label{tab:pkg:kpp:runtime_flags} |
| 173 |
|
|
{\footnotesize |
| 174 |
|
|
\begin{tabular}{|l|c|l|} |
| 175 |
|
|
\hline |
| 176 |
|
|
\textbf{Flag/parameter} & \textbf{default} & \textbf{Description} \\ |
| 177 |
|
|
\hline \hline |
| 178 |
|
|
\multicolumn{3}{|c|}{\textit{I/O related parameters} } \\ |
| 179 |
|
|
\hline |
| 180 |
|
|
kpp\_freq & \texttt{deltaTClock} & |
| 181 |
|
|
Recomputation frequency for KPP fields \\ |
| 182 |
|
|
kpp\_dumpFreq & \texttt{dumpFreq} & |
| 183 |
|
|
Dump frequency of KPP field snapshots \\ |
| 184 |
|
|
kpp\_taveFreq & \texttt{taveFreq} & |
| 185 |
|
|
Averaging and dump frequency of KPP fields \\ |
| 186 |
|
|
KPPmixingMaps & \texttt{.FALSE.} & |
| 187 |
|
|
include KPP diagnostic maps in STDOUT \\ |
| 188 |
|
|
KPPwriteState & \texttt{.FALSE.} & |
| 189 |
|
|
write KPP state to file \\ |
| 190 |
|
|
KPP\_ghatUseTotalDiffus & \texttt{.FALSE.} & |
| 191 |
|
|
if \texttt{.T.} compute non-local term using total vertical diffusivity \\ |
| 192 |
|
|
~ & ~ & |
| 193 |
|
|
if \texttt{.F.} use KPP vertical diffusivity \\ |
| 194 |
|
|
\hline |
| 195 |
|
|
\multicolumn{3}{|c|}{\textit{Genral KPP parameters} } \\ |
| 196 |
|
|
\hline |
| 197 |
|
|
minKPPhbl & \texttt{delRc(1)} & |
| 198 |
|
|
Minimum boundary layer depth \\ |
| 199 |
|
|
epsilon & 0.1 & |
| 200 |
|
|
nondimensional extent of the surface layer \\ |
| 201 |
|
|
vonk & 0.4 & |
| 202 |
|
|
von Karman constant \\ |
| 203 |
|
|
dB\_dz & 5.2E-5 1/s$^2$ & |
| 204 |
|
|
maximum dB/dz in mixed layer hMix \\ |
| 205 |
|
|
concs & 98.96 & |
| 206 |
|
|
~ \\ |
| 207 |
|
|
concv & 1.8 & |
| 208 |
|
|
~ \\ |
| 209 |
|
|
\hline |
| 210 |
|
|
\multicolumn{3}{|c|}{\textit{Boundary layer parameters (S/R \texttt{bldepth})} } \\ |
| 211 |
|
|
\hline |
| 212 |
|
|
Ricr & 0.3 & |
| 213 |
|
|
critical bulk Richardson number \\ |
| 214 |
|
|
cekman & 0.7 & |
| 215 |
|
|
coefficient for Ekman depth \\ |
| 216 |
|
|
cmonob & 1.0 & |
| 217 |
|
|
coefficient for Monin-Obukhov depth \\ |
| 218 |
|
|
concv & 1.8 & |
| 219 |
|
|
ratio of interior to entrainment depth buoyancy frequency \\ |
| 220 |
|
|
hbf & 1.0 & |
| 221 |
|
|
fraction of depth to which absorbed solar radiation contributes \\ |
| 222 |
|
|
~ & ~ & |
| 223 |
|
|
to surface buoyancy forcing \\ |
| 224 |
|
|
Vtc & \texttt{~} & |
| 225 |
|
|
non-dim. coeff. for velocity scale of turbulant velocity shear \\ |
| 226 |
|
|
~ & ~ & |
| 227 |
|
|
( = function of concv,concs,epsilon,vonk,Ricr) \\ |
| 228 |
|
|
\hline |
| 229 |
|
|
\multicolumn{3}{|c|}{\textit{Boundary layer mixing parameters (S/R \texttt{blmix})} } \\ |
| 230 |
|
|
\hline |
| 231 |
|
|
cstar & 10. & |
| 232 |
|
|
proportionality coefficient for nonlocal transport \\ |
| 233 |
|
|
cg & ~ & |
| 234 |
|
|
non-dimensional coefficient for counter-gradient term \\ |
| 235 |
|
|
~ & ~ & |
| 236 |
|
|
( = function of cstar,vonk,concs,epsilon) \\ |
| 237 |
|
|
\hline |
| 238 |
|
|
\multicolumn{3}{|c|}{\textit{Interior mixing parameters (S/R \texttt{Ri\_iwmix})} } \\ |
| 239 |
|
|
\hline |
| 240 |
|
|
Riinfty & 0.7 & |
| 241 |
|
|
gradient Richardson number limit for shear instability \\ |
| 242 |
|
|
BVDQcon & -0.2E-4 1/s$^2$ & |
| 243 |
|
|
Brunt-V\"ai\"sal\"a squared \\ |
| 244 |
|
|
difm0 & 0.005 m$^2$/s & |
| 245 |
|
|
viscosity max. due to shear instability \\ |
| 246 |
|
|
difs0 & 0.005 m$^2$/s & |
| 247 |
|
|
tracer diffusivity max. due to shear instability \\ |
| 248 |
|
|
dift0 & 0.005 m$^2$/s & |
| 249 |
|
|
heat diffusivity max. due to shear instability \\ |
| 250 |
|
|
difmcon & 0.1 & |
| 251 |
|
|
viscosity due to convective instability \\ |
| 252 |
|
|
difscon & 0.1 & |
| 253 |
|
|
tracer diffusivity due to convective instability \\ |
| 254 |
|
|
diftcon & 0.1 & |
| 255 |
|
|
heat diffusivity due to convective instability \\ |
| 256 |
|
|
\hline |
| 257 |
|
|
\multicolumn{3}{|c|}{\textit{Double-diffusive mixing parameters (S/R \texttt{ddmix})} } \\ |
| 258 |
|
|
\hline |
| 259 |
|
|
Rrho0 & not used & |
| 260 |
|
|
limit for double diffusive density ratio \\ |
| 261 |
|
|
dsfmax & not used & |
| 262 |
|
|
maximum diffusivity in case of salt fingering \\ |
| 263 |
|
|
\hline |
| 264 |
|
|
\hline |
| 265 |
|
|
\end{tabular} |
| 266 |
|
|
} |
| 267 |
|
|
\caption{~} |
| 268 |
|
|
\end{table} |
| 269 |
|
|
|
| 270 |
|
|
|
| 271 |
|
|
|
| 272 |
|
|
%---------------------------------------------------------------------- |
| 273 |
|
|
|
| 274 |
|
|
\subsubsection{Equations |
| 275 |
|
|
\label{sec:pkg:kpp:equations}} |
| 276 |
|
|
|
| 277 |
heimbach |
1.7 |
We restrict ourselves to writing out only the essential equations |
| 278 |
|
|
that relate to main processes and parameters mentioned above. |
| 279 |
|
|
We closely follow the notation of \cite{lar-eta:94}. |
| 280 |
|
|
|
| 281 |
|
|
\paragraph{Mixing in the boundary layer} ~ \\ |
| 282 |
|
|
% |
| 283 |
|
|
~ |
| 284 |
|
|
|
| 285 |
|
|
The vertical fluxes $\overline{wx}$ |
| 286 |
|
|
of momentum and tracer properties $X$ |
| 287 |
|
|
is composed of a gradient-flux term (proportional to |
| 288 |
|
|
the vertical property divergence $\partial_z X$), and |
| 289 |
|
|
a ``nonlocal'' term $\gamma_x$ that enhances the |
| 290 |
|
|
gradient-flux mixing coefficient $K_x$ |
| 291 |
|
|
% |
| 292 |
|
|
\begin{equation} |
| 293 |
|
|
\overline{wx}(d) \, = \, -K_x \left( |
| 294 |
|
|
\frac{\partial X}{\partial z} \, - \, \gamma_x \right) |
| 295 |
|
|
\end{equation} |
| 296 |
|
|
|
| 297 |
|
|
\begin{itemize} |
| 298 |
|
|
% |
| 299 |
|
|
\item |
| 300 |
|
|
\textit{Boundary layer mixing profile} \\ |
| 301 |
|
|
% |
| 302 |
|
|
It is expressed as the product of the boundary layer depth $h$, |
| 303 |
|
|
a depth-dependent turbulent velocity scale $w_x(\sigma)$ and a |
| 304 |
|
|
non-dimensional shape function $G(\sigma)$ |
| 305 |
|
|
% |
| 306 |
|
|
\begin{equation} |
| 307 |
|
|
K_x(\sigma) \, = \, h \, w_x(\sigma) \, G(\sigma) |
| 308 |
|
|
\end{equation} |
| 309 |
|
|
% |
| 310 |
|
|
with dimensionless vertical coordinate $\sigma = d/h$. |
| 311 |
|
|
For details of $ w_x(\sigma)$ and $G(\sigma)$ we refer to |
| 312 |
|
|
\cite{lar-eta:94}. |
| 313 |
|
|
|
| 314 |
|
|
% |
| 315 |
|
|
\item |
| 316 |
|
|
\textit{Nonlocal mixing term} \\ |
| 317 |
|
|
% |
| 318 |
|
|
The nonlocal transport term $\gamma$ is nonzero only for |
| 319 |
|
|
tracers in unstable (convective) forcing conditions. |
| 320 |
|
|
Thus, depending on the stability parameter $\zeta = d/L$ |
| 321 |
|
|
(with depth $d$, Monin-Obukhov length scale $L$) |
| 322 |
|
|
it has the following form: |
| 323 |
|
|
% |
| 324 |
|
|
\begin{eqnarray} |
| 325 |
|
|
\begin{array}{cl} |
| 326 |
|
|
\gamma_x \, = \, 0 & \zeta \, \ge \, 0 \\ |
| 327 |
|
|
~ & ~ \\ |
| 328 |
|
|
\left. |
| 329 |
|
|
\begin{array}{c} |
| 330 |
|
|
\gamma_m \, = \, 0 \\ |
| 331 |
|
|
~ \\ |
| 332 |
|
|
\gamma_s \, = \, C_s |
| 333 |
|
|
\frac{\overline{w s_0}}{w_s(\sigma) h} \\ |
| 334 |
|
|
~ \\ |
| 335 |
|
|
\gamma_{\theta} \, = \, C_s |
| 336 |
|
|
\frac{\overline{w \theta_0}+\overline{w \theta_R}}{w_s(\sigma) h} \\ |
| 337 |
|
|
\end{array} |
| 338 |
|
|
\right\} |
| 339 |
|
|
& |
| 340 |
|
|
\zeta \, < \, 0 \\ |
| 341 |
|
|
\end{array} |
| 342 |
|
|
\end{eqnarray} |
| 343 |
|
|
|
| 344 |
|
|
\end{itemize} |
| 345 |
|
|
|
| 346 |
|
|
|
| 347 |
|
|
\paragraph{Mixing in the interior} ~ \\ |
| 348 |
|
|
% |
| 349 |
|
|
~ |
| 350 |
|
|
|
| 351 |
|
|
\paragraph{Implicit time integration} ~ \\ |
| 352 |
|
|
% |
| 353 |
|
|
~ |
| 354 |
|
|
|
| 355 |
heimbach |
1.6 |
%---------------------------------------------------------------------- |
| 356 |
|
|
|
| 357 |
|
|
\subsubsection{Key subroutines |
| 358 |
|
|
\label{sec:pkg:kpp:subroutines}} |
| 359 |
|
|
|
| 360 |
|
|
\paragraph{kpp\_calc:} Top-level routine. \\ |
| 361 |
|
|
~ |
| 362 |
|
|
|
| 363 |
|
|
\paragraph{kpp\_mix:} Intermediate-level routine \\ |
| 364 |
|
|
~ |
| 365 |
|
|
|
| 366 |
|
|
\paragraph{ri\_iwmix:} ~ \\ |
| 367 |
|
|
% |
| 368 |
|
|
Compute interior viscosity and diffusivity coefficients due to |
| 369 |
|
|
% |
| 370 |
|
|
\begin{itemize} |
| 371 |
|
|
% |
| 372 |
|
|
\item |
| 373 |
|
|
shear instability (dependent on a local gradient Richardson number), |
| 374 |
|
|
% |
| 375 |
|
|
\item |
| 376 |
|
|
to background internal wave activity, and |
| 377 |
|
|
% |
| 378 |
|
|
\item |
| 379 |
|
|
to static instability (local Richardson number < 0). |
| 380 |
|
|
% |
| 381 |
|
|
\end{itemize} |
| 382 |
|
|
|
| 383 |
|
|
|
| 384 |
|
|
\paragraph{bldepth:} ~ \\ |
| 385 |
|
|
% |
| 386 |
|
|
The oceanic planetary boundary layer depth, \texttt{hbl}, is determined as |
| 387 |
|
|
the shallowest depth where the bulk Richardson number is |
| 388 |
|
|
equal to the critical value, \texttt{Ricr}. |
| 389 |
|
|
|
| 390 |
|
|
Bulk Richardson numbers are evaluated by computing velocity and |
| 391 |
|
|
buoyancy differences between values at zgrid(kl) < 0 and surface |
| 392 |
|
|
reference values. |
| 393 |
|
|
In this configuration, the reference values are equal to the |
| 394 |
|
|
values in the surface layer. |
| 395 |
|
|
When using a very fine vertical grid, these values should be |
| 396 |
|
|
computed as the vertical average of velocity and buoyancy from |
| 397 |
|
|
the surface down to epsilon*zgrid(kl). |
| 398 |
|
|
|
| 399 |
|
|
When the bulk Richardson number at k exceeds Ricr, hbl is |
| 400 |
|
|
linearly interpolated between grid levels zgrid(k) and zgrid(k-1). |
| 401 |
|
|
|
| 402 |
|
|
The water column and the surface forcing are diagnosed for |
| 403 |
|
|
stable/ustable forcing conditions, and where hbl is relative |
| 404 |
|
|
to grid points (caseA), so that conditional branches can be |
| 405 |
|
|
avoided in later subroutines. |
| 406 |
|
|
|
| 407 |
|
|
\paragraph{blmix:} ~ \\ |
| 408 |
|
|
% |
| 409 |
|
|
Compute boundary layer mixing coefficients. |
| 410 |
|
|
Mixing coefficients within boundary layer depend on surface |
| 411 |
|
|
forcing and the magnitude and gradient of interior mixing below |
| 412 |
|
|
the boundary layer ("matching"). |
| 413 |
|
|
% |
| 414 |
|
|
\begin{enumerate} |
| 415 |
|
|
% |
| 416 |
|
|
\item |
| 417 |
|
|
compute velocity scales at hbl |
| 418 |
|
|
% |
| 419 |
|
|
\item |
| 420 |
|
|
find the interior viscosities and derivatives at hbl |
| 421 |
|
|
% |
| 422 |
|
|
\item |
| 423 |
|
|
compute turbulent velocity scales on the interfaces |
| 424 |
|
|
% |
| 425 |
|
|
\item |
| 426 |
|
|
compute the dimensionless shape functions at the interfaces |
| 427 |
|
|
% |
| 428 |
|
|
\item |
| 429 |
|
|
compute boundary layer diffusivities at the interfaces |
| 430 |
|
|
% |
| 431 |
|
|
\item |
| 432 |
|
|
compute nonlocal transport term |
| 433 |
|
|
% |
| 434 |
|
|
\item |
| 435 |
|
|
find diffusivities at kbl-1 grid level |
| 436 |
|
|
% |
| 437 |
|
|
\end{enumerate} |
| 438 |
|
|
|
| 439 |
heimbach |
1.7 |
\paragraph{kpp\_calc\_diff\_t/\_s, kpp\_calc\_visc:} ~ \\ |
| 440 |
heimbach |
1.6 |
% |
| 441 |
|
|
Add contribution to net diffusivity/viscosity from |
| 442 |
|
|
KPP diffusivity/viscosity. |
| 443 |
|
|
|
| 444 |
heimbach |
1.7 |
\paragraph{kpp\_transport\_t/\_s/\_ptr:} ~ \\ |
| 445 |
heimbach |
1.6 |
% |
| 446 |
|
|
Add non local KPP transport term (ghat) to diffusive |
| 447 |
|
|
temperature/salinity/passive tracer flux. |
| 448 |
|
|
The nonlocal transport term is nonzero only for scalars |
| 449 |
|
|
in unstable (convective) forcing conditions. |
| 450 |
|
|
|
| 451 |
heimbach |
1.7 |
\paragraph{Flow chart:} ~ \\ |
| 452 |
|
|
% |
| 453 |
heimbach |
1.6 |
{\footnotesize |
| 454 |
|
|
\begin{verbatim} |
| 455 |
|
|
|
| 456 |
|
|
C !CALLING SEQUENCE: |
| 457 |
|
|
c ... |
| 458 |
|
|
c kpp_calc (TOP LEVEL ROUTINE) |
| 459 |
|
|
c | |
| 460 |
|
|
c |-- statekpp: o compute all EOS/density-related arrays |
| 461 |
|
|
c | o uses S/R FIND_ALPHA, FIND_BETA, FIND_RHO |
| 462 |
|
|
c | |
| 463 |
|
|
c |-- kppmix |
| 464 |
|
|
c | |--- ri_iwmix (compute interior mixing coefficients due to constant |
| 465 |
|
|
c | | internal wave activity, static instability, |
| 466 |
|
|
c | | and local shear instability). |
| 467 |
|
|
c | | |
| 468 |
|
|
c | |--- bldepth (diagnose boundary layer depth) |
| 469 |
|
|
c | | |
| 470 |
|
|
c | |--- blmix (compute boundary layer diffusivities) |
| 471 |
|
|
c | | |
| 472 |
|
|
c | |--- enhance (enhance diffusivity at interface kbl - 1) |
| 473 |
|
|
c | o |
| 474 |
|
|
c | |
| 475 |
|
|
c |-- swfrac |
| 476 |
|
|
c o |
| 477 |
|
|
|
| 478 |
|
|
\end{verbatim} |
| 479 |
|
|
} |
| 480 |
|
|
|
| 481 |
|
|
%---------------------------------------------------------------------- |
| 482 |
|
|
|
| 483 |
|
|
\subsubsection{KPP diagnostics |
| 484 |
|
|
\label{sec:pkg:kpp:diagnostics}} |
| 485 |
|
|
|
| 486 |
|
|
Diagnostics output is available via the diagnostics package |
| 487 |
|
|
(see Section \ref{sec:pkg:diagnostics}). |
| 488 |
|
|
Available output fields are summarized in |
| 489 |
|
|
Table \ref{tab:pkg:kpp:diagnostics}. |
| 490 |
|
|
|
| 491 |
|
|
\begin{table}[h!] |
| 492 |
heimbach |
1.7 |
\centering |
| 493 |
heimbach |
1.6 |
\label{tab:pkg:kpp:diagnostics} |
| 494 |
|
|
{\footnotesize |
| 495 |
|
|
\begin{verbatim} |
| 496 |
|
|
------------------------------------------------------ |
| 497 |
|
|
<-Name->|Levs|grid|<-- Units -->|<- Tile (max=80c) |
| 498 |
|
|
------------------------------------------------------ |
| 499 |
|
|
KPPviscA| 23 |SM |m^2/s |KPP vertical eddy viscosity coefficient |
| 500 |
|
|
KPPdiffS| 23 |SM |m^2/s |Vertical diffusion coefficient for salt & tracers |
| 501 |
|
|
KPPdiffT| 23 |SM |m^2/s |Vertical diffusion coefficient for heat |
| 502 |
|
|
KPPghat | 23 |SM |s/m^2 |Nonlocal transport coefficient |
| 503 |
|
|
KPPhbl | 1 |SM |m |KPP boundary layer depth, bulk Ri criterion |
| 504 |
|
|
KPPmld | 1 |SM |m |Mixed layer depth, dT=.8degC density criterion |
| 505 |
|
|
KPPfrac | 1 |SM | |Short-wave flux fraction penetrating mixing layer |
| 506 |
|
|
\end{verbatim} |
| 507 |
|
|
} |
| 508 |
|
|
\caption{~} |
| 509 |
|
|
\end{table} |
| 510 |
|
|
|
| 511 |
|
|
%---------------------------------------------------------------------- |
| 512 |
|
|
|
| 513 |
|
|
\subsubsection{Reference experiments} |
| 514 |
|
|
|
| 515 |
|
|
lab\_sea: |
| 516 |
|
|
|
| 517 |
|
|
natl\_box: |
| 518 |
|
|
|
| 519 |
|
|
%---------------------------------------------------------------------- |
| 520 |
|
|
|
| 521 |
|
|
\subsubsection{References} |
| 522 |
heimbach |
1.7 |
|
Parent Directory
| 
Revision Log
| 
Revision Graph