| 276 |
\hline |
\hline |
| 277 |
|
|
| 278 |
&\\ |
&\\ |
| 279 |
1 & UFLUX & $Newton/m^2$ & 1 |
84 & SDIAG1 & & 1 |
| 280 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 281 |
{Surface U-Wind Stress on the atmosphere} |
{User-Defined Surface Diagnostic-1} |
|
\end{minipage}\\ |
|
|
2 & VFLUX & $Newton/m^2$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Surface V-Wind Stress on the atmosphere} |
|
|
\end{minipage}\\ |
|
|
3 & HFLUX & $Watts/m^2$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Surface Flux of Sensible Heat} |
|
|
\end{minipage}\\ |
|
|
4 & EFLUX & $Watts/m^2$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Surface Flux of Latent Heat} |
|
|
\end{minipage}\\ |
|
|
5 & QICE & $Watts/m^2$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Heat Conduction through Sea-Ice} |
|
|
\end{minipage}\\ |
|
|
6 & RADLWG & $Watts/m^2$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Net upward LW flux at the ground} |
|
|
\end{minipage}\\ |
|
|
7 & RADSWG & $Watts/m^2$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Net downward SW flux at the ground} |
|
|
\end{minipage}\\ |
|
|
8 & RI & $dimensionless$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Richardson Number} |
|
|
\end{minipage}\\ |
|
|
9 & CT & $dimensionless$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Surface Drag coefficient for T and Q} |
|
|
\end{minipage}\\ |
|
|
10 & CU & $dimensionless$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Surface Drag coefficient for U and V} |
|
|
\end{minipage}\\ |
|
|
11 & ET & $m^2/sec$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Diffusivity coefficient for T and Q} |
|
|
\end{minipage}\\ |
|
|
12 & EU & $m^2/sec$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Diffusivity coefficient for U and V} |
|
|
\end{minipage}\\ |
|
|
13 & TURBU & $m/sec/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{U-Momentum Changes due to Turbulence} |
|
|
\end{minipage}\\ |
|
|
14 & TURBV & $m/sec/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{V-Momentum Changes due to Turbulence} |
|
|
\end{minipage}\\ |
|
|
15 & TURBT & $deg/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Temperature Changes due to Turbulence} |
|
|
\end{minipage}\\ |
|
|
16 & TURBQ & $g/kg/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Specific Humidity Changes due to Turbulence} |
|
|
\end{minipage}\\ |
|
|
17 & MOISTT & $deg/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Temperature Changes due to Moist Processes} |
|
|
\end{minipage}\\ |
|
|
18 & MOISTQ & $g/kg/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Specific Humidity Changes due to Moist Processes} |
|
|
\end{minipage}\\ |
|
|
19 & RADLW & $deg/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Net Longwave heating rate for each level} |
|
|
\end{minipage}\\ |
|
|
20 & RADSW & $deg/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Net Shortwave heating rate for each level} |
|
|
\end{minipage}\\ |
|
|
21 & PREACC & $mm/day$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Total Precipitation} |
|
|
\end{minipage}\\ |
|
|
22 & PRECON & $mm/day$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Convective Precipitation} |
|
|
\end{minipage}\\ |
|
|
23 & TUFLUX & $Newton/m^2$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Turbulent Flux of U-Momentum} |
|
|
\end{minipage}\\ |
|
|
24 & TVFLUX & $Newton/m^2$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Turbulent Flux of V-Momentum} |
|
|
\end{minipage}\\ |
|
|
25 & TTFLUX & $Watts/m^2$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Turbulent Flux of Sensible Heat} |
|
|
\end{minipage}\\ |
|
|
26 & TQFLUX & $Watts/m^2$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Turbulent Flux of Latent Heat} |
|
|
\end{minipage}\\ |
|
|
27 & CN & $dimensionless$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Neutral Drag Coefficient} |
|
|
\end{minipage}\\ |
|
|
28 & WINDS & $m/sec$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Surface Wind Speed} |
|
|
\end{minipage}\\ |
|
|
29 & DTSRF & $deg$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Air/Surface virtual temperature difference} |
|
|
\end{minipage}\\ |
|
|
30 & TG & $deg$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Ground temperature} |
|
| 282 |
\end{minipage}\\ |
\end{minipage}\\ |
| 283 |
31 & TS & $deg$ & 1 |
85 & SDIAG2 & & 1 |
| 284 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 285 |
{Surface air temperature (Adiabatic from lowest model layer)} |
{User-Defined Surface Diagnostic-2} |
| 286 |
\end{minipage}\\ |
\end{minipage}\\ |
| 287 |
32 & DTG & $deg$ & 1 |
86 & UDIAG1 & & Nrphys |
| 288 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 289 |
{Ground temperature adjustment} |
{User-Defined Upper-Air Diagnostic-1} |
| 290 |
\end{minipage}\\ |
\end{minipage}\\ |
| 291 |
|
87 & UDIAG2 & & Nrphys |
|
\end{tabular} |
|
|
|
|
|
\newpage |
|
|
\vspace*{\fill} |
|
|
\begin{tabular}{lllll} |
|
|
\hline\hline |
|
|
N & NAME & UNITS & LEVELS & DESCRIPTION \\ |
|
|
\hline |
|
|
|
|
|
&\\ |
|
|
33 & QG & $g/kg$ & 1 |
|
| 292 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 293 |
{Ground specific humidity} |
{User-Defined Upper-Air Diagnostic-2} |
| 294 |
\end{minipage}\\ |
\end{minipage}\\ |
| 295 |
34 & QS & $g/kg$ & 1 |
124& SDIAG3 & & 1 |
| 296 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 297 |
{Saturation surface specific humidity} |
{User-Defined Surface Diagnostic-3} |
| 298 |
\end{minipage}\\ |
\end{minipage}\\ |
| 299 |
|
125& SDIAG4 & & 1 |
|
&\\ |
|
|
35 & TGRLW & $deg$ & 1 |
|
| 300 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 301 |
{Instantaneous ground temperature used as input to the |
{User-Defined Surface Diagnostic-4} |
|
Longwave radiation subroutine} |
|
| 302 |
\end{minipage}\\ |
\end{minipage}\\ |
| 303 |
36 & ST4 & $Watts/m^2$ & 1 |
126& SDIAG5 & & 1 |
| 304 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 305 |
{Upward Longwave flux at the ground ($\sigma T^4$)} |
{User-Defined Surface Diagnostic-5} |
| 306 |
\end{minipage}\\ |
\end{minipage}\\ |
| 307 |
37 & OLR & $Watts/m^2$ & 1 |
127& SDIAG6 & & 1 |
| 308 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 309 |
{Net upward Longwave flux at the top of the model} |
{User-Defined Surface Diagnostic-6} |
| 310 |
\end{minipage}\\ |
\end{minipage}\\ |
| 311 |
38 & OLRCLR & $Watts/m^2$ & 1 |
128& SDIAG7 & & 1 |
| 312 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 313 |
{Net upward clearsky Longwave flux at the top of the model} |
{User-Defined Surface Diagnostic-7} |
| 314 |
\end{minipage}\\ |
\end{minipage}\\ |
| 315 |
39 & LWGCLR & $Watts/m^2$ & 1 |
129& SDIAG8 & & 1 |
| 316 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 317 |
{Net upward clearsky Longwave flux at the ground} |
{User-Defined Surface Diagnostic-8} |
| 318 |
\end{minipage}\\ |
\end{minipage}\\ |
| 319 |
40 & LWCLR & $deg/day$ & Nrphys |
130& SDIAG9 & & 1 |
| 320 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 321 |
{Net clearsky Longwave heating rate for each level} |
{User-Defined Surface Diagnostic-9} |
| 322 |
\end{minipage}\\ |
\end{minipage}\\ |
| 323 |
41 & TLW & $deg$ & Nrphys |
131& SDIAG10 & & 1 |
| 324 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 325 |
{Instantaneous temperature used as input to the Longwave radiation |
{User-Defined Surface Diagnostic-1-} |
|
subroutine} |
|
| 326 |
\end{minipage}\\ |
\end{minipage}\\ |
| 327 |
42 & SHLW & $g/g$ & Nrphys |
132& UDIAG3 & & Nrphys |
| 328 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 329 |
{Instantaneous specific humidity used as input to the Longwave radiation |
{User-Defined Multi-Level Diagnostic-3} |
|
subroutine} |
|
| 330 |
\end{minipage}\\ |
\end{minipage}\\ |
| 331 |
43 & OZLW & $g/g$ & Nrphys |
133& UDIAG4 & & Nrphys |
| 332 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 333 |
{Instantaneous ozone used as input to the Longwave radiation |
{User-Defined Multi-Level Diagnostic-4} |
|
subroutine} |
|
| 334 |
\end{minipage}\\ |
\end{minipage}\\ |
| 335 |
44 & CLMOLW & $0-1$ & Nrphys |
134& UDIAG5 & & Nrphys |
| 336 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 337 |
{Maximum overlap cloud fraction used in the Longwave radiation |
{User-Defined Multi-Level Diagnostic-5} |
|
subroutine} |
|
| 338 |
\end{minipage}\\ |
\end{minipage}\\ |
| 339 |
45 & CLDTOT & $0-1$ & Nrphys |
135& UDIAG6 & & Nrphys |
| 340 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 341 |
{Total cloud fraction used in the Longwave and Shortwave radiation |
{User-Defined Multi-Level Diagnostic-6} |
|
subroutines} |
|
| 342 |
\end{minipage}\\ |
\end{minipage}\\ |
| 343 |
46 & RADSWT & $Watts/m^2$ & 1 |
136& UDIAG7 & & Nrphys |
| 344 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 345 |
{Incident Shortwave radiation at the top of the atmosphere} |
{User-Defined Multi-Level Diagnostic-7} |
| 346 |
\end{minipage}\\ |
\end{minipage}\\ |
| 347 |
47 & CLROSW & $0-1$ & Nrphys |
137& UDIAG8 & & Nrphys |
| 348 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 349 |
{Random overlap cloud fraction used in the shortwave radiation |
{User-Defined Multi-Level Diagnostic-8} |
|
subroutine} |
|
| 350 |
\end{minipage}\\ |
\end{minipage}\\ |
| 351 |
48 & CLMOSW & $0-1$ & Nrphys |
138& UDIAG9 & & Nrphys |
| 352 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 353 |
{Maximum overlap cloud fraction used in the shortwave radiation |
{User-Defined Multi-Level Diagnostic-9} |
|
subroutine} |
|
| 354 |
\end{minipage}\\ |
\end{minipage}\\ |
| 355 |
49 & EVAP & $mm/day$ & 1 |
139& UDIAG10 & & Nrphys |
| 356 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 357 |
{Surface evaporation} |
{User-Defined Multi-Level Diagnostic-10} |
| 358 |
\end{minipage}\\ |
\end{minipage}\\ |
| 359 |
\end{tabular} |
\end{tabular} |
| 360 |
|
\vspace{1.5in} |
| 361 |
\vfill |
\vfill |
| 362 |
|
|
| 363 |
\newpage |
\newpage |
| 368 |
\hline |
\hline |
| 369 |
|
|
| 370 |
&\\ |
&\\ |
| 371 |
50 & DUDT & $m/sec/day$ & Nrphys |
238& ETAN & $(hPa,m)$ & 1 |
|
&\begin{minipage}[t]{3in} |
|
|
{Total U-Wind tendency} |
|
|
\end{minipage}\\ |
|
|
51 & DVDT & $m/sec/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Total V-Wind tendency} |
|
|
\end{minipage}\\ |
|
|
52 & DTDT & $deg/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Total Temperature tendency} |
|
|
\end{minipage}\\ |
|
|
53 & DQDT & $g/kg/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Total Specific Humidity tendency} |
|
|
\end{minipage}\\ |
|
|
54 & USTAR & $m/sec$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Surface USTAR wind} |
|
|
\end{minipage}\\ |
|
|
55 & Z0 & $m$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Surface roughness} |
|
|
\end{minipage}\\ |
|
|
56 & FRQTRB & $0-1$ & Nrphys-1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Frequency of Turbulence} |
|
|
\end{minipage}\\ |
|
|
57 & PBL & $mb$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Planetary Boundary Layer depth} |
|
|
\end{minipage}\\ |
|
|
58 & SWCLR & $deg/day$ & Nrphys |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Net clearsky Shortwave heating rate for each level} |
|
|
\end{minipage}\\ |
|
|
59 & OSR & $Watts/m^2$ & 1 |
|
|
&\begin{minipage}[t]{3in} |
|
|
{Net downward Shortwave flux at the top of the model} |
|
|
\end{minipage}\\ |
|
|
60 & OSRCLR & $Watts/m^2$ & 1 |
|
| 372 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 373 |
{Net downward clearsky Shortwave flux at the top of the model} |
{Perturbation of Surface (pressure, height)} |
| 374 |
\end{minipage}\\ |
\end{minipage}\\ |
| 375 |
61 & CLDMAS & $kg / m^2$ & Nrphys |
239& ETANSQ & $(hPa^2,m^2)$ & 1 |
| 376 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 377 |
{Convective cloud mass flux} |
{Square of Perturbation of Surface (pressure, height)} |
| 378 |
\end{minipage}\\ |
\end{minipage}\\ |
| 379 |
62 & UAVE & $m/sec$ & Nrphys |
240& THETA & $deg K$ & Nr |
| 380 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 381 |
{Time-averaged $u-Wind$} |
{Potential Temperature} |
| 382 |
\end{minipage}\\ |
\end{minipage}\\ |
| 383 |
63 & VAVE & $m/sec$ & Nrphys |
241& SALT & $g/kg$ & Nr |
| 384 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 385 |
{Time-averaged $v-Wind$} |
{Salt (or Water Vapor Mixing Ratio)} |
| 386 |
\end{minipage}\\ |
\end{minipage}\\ |
| 387 |
64 & TAVE & $deg$ & Nrphys |
242& UVEL & $m/sec$ & Nr |
| 388 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 389 |
{Time-averaged $Temperature$} |
{U-Velocity} |
| 390 |
\end{minipage}\\ |
\end{minipage}\\ |
| 391 |
65 & QAVE & $g/g$ & Nrphys |
243& VVEL & $m/sec$ & Nr |
| 392 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 393 |
{Time-averaged $Specific \, \, Humidity$} |
{V-Velocity} |
| 394 |
\end{minipage}\\ |
\end{minipage}\\ |
| 395 |
66 & PAVE & $mb$ & 1 |
244& WVEL & $m/sec$ & Nr |
| 396 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 397 |
{Time-averaged $p_{surf} - p_{top}$} |
{Vertical-Velocity} |
| 398 |
\end{minipage}\\ |
\end{minipage}\\ |
| 399 |
67 & QQAVE & $(m/sec)^2$ & Nrphys |
245& THETASQ & $deg^2$ & Nr |
| 400 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 401 |
{Time-averaged $Turbulent Kinetic Energy$} |
{Square of Potential Temperature} |
| 402 |
\end{minipage}\\ |
\end{minipage}\\ |
| 403 |
68 & SWGCLR & $Watts/m^2$ & 1 |
246& SALTSQ & $g^2/{kg}^2$ & Nr |
| 404 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 405 |
{Net downward clearsky Shortwave flux at the ground} |
{Square of Salt (or Water Vapor Mixing Ratio)} |
| 406 |
\end{minipage}\\ |
\end{minipage}\\ |
| 407 |
69 & SDIAG1 & & 1 |
247& UVELSQ & $m^2/sec^2$ & Nr |
| 408 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 409 |
{User-Defined Surface Diagnostic-1} |
{Square of U-Velocity} |
| 410 |
\end{minipage}\\ |
\end{minipage}\\ |
| 411 |
70 & SDIAG2 & & 1 |
248& VVELSQ & $m^2/sec^2$ & Nr |
| 412 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 413 |
{User-Defined Surface Diagnostic-2} |
{Square of V-Velocity} |
| 414 |
\end{minipage}\\ |
\end{minipage}\\ |
| 415 |
71 & UDIAG1 & & Nrphys |
249& WVELSQ & $m^2/sec^2$ & Nr |
| 416 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 417 |
{User-Defined Upper-Air Diagnostic-1} |
{Square of Vertical-Velocity} |
| 418 |
\end{minipage}\\ |
\end{minipage}\\ |
| 419 |
72 & UDIAG2 & & Nrphys |
250& UVELVVEL & $m^2/sec^2$ & Nr |
| 420 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 421 |
{User-Defined Upper-Air Diagnostic-2} |
{Meridional Transport of Zonal Momentum} |
| 422 |
\end{minipage}\\ |
\end{minipage}\\ |
| 423 |
73 & DIABU & $m/sec/day$ & Nrphys |
251& UVELMASS & $m/sec$ & Nr |
| 424 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 425 |
{Total Diabatic forcing on $u-Wind$} |
{Zonal Mass-Weighted Component of Velocity} |
| 426 |
\end{minipage}\\ |
\end{minipage}\\ |
| 427 |
74 & DIABV & $m/sec/day$ & Nrphys |
252& VVELMASS & $m/sec$ & Nr |
| 428 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 429 |
{Total Diabatic forcing on $v-Wind$} |
{Meridional Mass-Weighted Component of Velocity} |
| 430 |
\end{minipage}\\ |
\end{minipage}\\ |
| 431 |
75 & DIABT & $deg/day$ & Nrphys |
253& WVELMASS & $m/sec$ & Nr |
| 432 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 433 |
{Total Diabatic forcing on $Temperature$} |
{Vertical Mass-Weighted Component of Velocity} |
| 434 |
\end{minipage}\\ |
\end{minipage}\\ |
| 435 |
76 & DIABQ & $g/kg/day$ & Nrphys |
254& UTHMASS & $m-deg/sec$ & Nr |
| 436 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 437 |
{Total Diabatic forcing on $Specific \, \, Humidity$} |
{Zonal Mass-Weight Transp of Pot Temp} |
| 438 |
\end{minipage}\\ |
\end{minipage}\\ |
| 439 |
|
255& VTHMASS & $m-deg/sec$ & Nr |
|
\end{tabular} |
|
|
\vfill |
|
|
|
|
|
\newpage |
|
|
\vspace*{\fill} |
|
|
\begin{tabular}{lllll} |
|
|
\hline\hline |
|
|
N & NAME & UNITS & LEVELS & DESCRIPTION \\ |
|
|
\hline |
|
|
|
|
|
77 & VINTUQ & $m/sec \cdot g/kg$ & 1 |
|
| 440 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 441 |
{Vertically integrated $u \, q$} |
{Meridional Mass-Weight Transp of Pot Temp} |
| 442 |
\end{minipage}\\ |
\end{minipage}\\ |
| 443 |
78 & VINTVQ & $m/sec \cdot g/kg$ & 1 |
256& WTHMASS & $m-deg/sec$ & Nr |
| 444 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 445 |
{Vertically integrated $v \, q$} |
{Vertical Mass-Weight Transp of Pot Temp} |
| 446 |
\end{minipage}\\ |
\end{minipage}\\ |
| 447 |
79 & VINTUT & $m/sec \cdot deg$ & 1 |
257& USLTMASS & $m-kg/sec-kg$ & Nr |
| 448 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 449 |
{Vertically integrated $u \, T$} |
{Zonal Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} |
| 450 |
\end{minipage}\\ |
\end{minipage}\\ |
| 451 |
80 & VINTVT & $m/sec \cdot deg$ & 1 |
258& VSLTMASS & $m-kg/sec-kg$ & Nr |
| 452 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 453 |
{Vertically integrated $v \, T$} |
{Meridional Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} |
| 454 |
\end{minipage}\\ |
\end{minipage}\\ |
| 455 |
81 & CLDFRC & $0-1$ & 1 |
259& WSLTMASS & $m-kg/sec-kg$ & Nr |
| 456 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 457 |
{Total Cloud Fraction} |
{Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} |
| 458 |
\end{minipage}\\ |
\end{minipage}\\ |
| 459 |
82 & QINT & $gm/cm^2$ & 1 |
260& UVELTH & $m-deg/sec$ & Nr |
| 460 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 461 |
{Precipitable water} |
{Zonal Transp of Pot Temp} |
| 462 |
\end{minipage}\\ |
\end{minipage}\\ |
| 463 |
83 & U2M & $m/sec$ & 1 |
261& VVELTH & $m-deg/sec$ & Nr |
| 464 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 465 |
{U-Wind at 2 meters} |
{Meridional Transp of Pot Temp} |
| 466 |
\end{minipage}\\ |
\end{minipage}\\ |
| 467 |
84 & V2M & $m/sec$ & 1 |
262& WVELTH & $m-deg/sec$ & Nr |
| 468 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 469 |
{V-Wind at 2 meters} |
{Vertical Transp of Pot Temp} |
| 470 |
\end{minipage}\\ |
\end{minipage}\\ |
| 471 |
85 & T2M & $deg$ & 1 |
263& UVELSLT & $m-kg/sec-kg$ & Nr |
| 472 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 473 |
{Temperature at 2 meters} |
{Zonal Transp of Salt (or W.Vap Mix Rat.)} |
| 474 |
\end{minipage}\\ |
\end{minipage}\\ |
| 475 |
86 & Q2M & $g/kg$ & 1 |
264& VVELSLT & $m-kg/sec-kg$ & Nr |
| 476 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 477 |
{Specific Humidity at 2 meters} |
{Meridional Transp of Salt (or W.Vap Mix Rat.)} |
| 478 |
\end{minipage}\\ |
\end{minipage}\\ |
| 479 |
87 & U10M & $m/sec$ & 1 |
265& WVELSLT & $m-kg/sec-kg$ & Nr |
| 480 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 481 |
{U-Wind at 10 meters} |
{Vertical Transp of Salt (or W.Vap Mix Rat.)} |
| 482 |
\end{minipage}\\ |
\end{minipage}\\ |
| 483 |
88 & V10M & $m/sec$ & 1 |
275& WSLTMASS & $m-kg/sec-kg$ & Nr |
| 484 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 485 |
{V-Wind at 10 meters} |
{Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} |
| 486 |
\end{minipage}\\ |
\end{minipage}\\ |
| 487 |
89 & T10M & $deg$ & 1 |
298& VISCA4 & $m^4/sec$ & 1 |
| 488 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 489 |
{Temperature at 10 meters} |
{Biharmonic Viscosity Coefficient} |
| 490 |
\end{minipage}\\ |
\end{minipage}\\ |
| 491 |
90 & Q10M & $g/kg$ & 1 |
299& VISCAH & $m^2/sec$ & 1 |
| 492 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 493 |
{Specific Humidity at 10 meters} |
{Harmonic Viscosity Coefficient} |
| 494 |
\end{minipage}\\ |
\end{minipage}\\ |
| 495 |
91 & DTRAIN & $kg/m^2$ & Nrphys |
300& DRHODR & $kg/m^3/{r-unit}$ & Nr |
| 496 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 497 |
{Detrainment Cloud Mass Flux} |
{Stratification: d.Sigma/dr} |
| 498 |
\end{minipage}\\ |
\end{minipage}\\ |
| 499 |
92 & QFILL & $g/kg/day$ & Nrphys |
301& DETADT2 & ${r-unit}^2/s^2$ & 1 |
| 500 |
&\begin{minipage}[t]{3in} |
&\begin{minipage}[t]{3in} |
| 501 |
{Filling of negative specific humidity} |
{Square of Eta (Surf.P,SSH) Tendency} |
| 502 |
\end{minipage}\\ |
\end{minipage}\\ |
|
|
|
| 503 |
\end{tabular} |
\end{tabular} |
| 504 |
\vspace{1.5in} |
\vspace{1.5in} |
| 505 |
\vfill |
\vfill |
| 521 |
output frequency of the diagnostic, and $\Delta t$ is |
output frequency of the diagnostic, and $\Delta t$ is |
| 522 |
the timestep over which the diagnostic is updated. |
the timestep over which the diagnostic is updated. |
| 523 |
|
|
|
{\bf 1) \underline {UFLUX} Surface Zonal Wind Stress on the Atmosphere ($Newton/m^2$) } |
|
|
|
|
|
The zonal wind stress is the turbulent flux of zonal momentum from |
|
|
the surface. See section 3.3 for a description of the surface layer parameterization. |
|
|
\[ |
|
|
{\bf UFLUX} = - \rho C_D W_s u \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u |
|
|
\] |
|
|
where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface |
|
|
drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum |
|
|
(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $u$ is |
|
|
the zonal wind in the lowest model layer. |
|
|
\\ |
|
|
|
|
|
|
|
|
{\bf 2) \underline {VFLUX} Surface Meridional Wind Stress on the Atmosphere ($Newton/m^2$) } |
|
|
|
|
|
The meridional wind stress is the turbulent flux of meridional momentum from |
|
|
the surface. See section 3.3 for a description of the surface layer parameterization. |
|
|
\[ |
|
|
{\bf VFLUX} = - \rho C_D W_s v \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u |
|
|
\] |
|
|
where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface |
|
|
drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum |
|
|
(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $v$ is |
|
|
the meridional wind in the lowest model layer. |
|
|
\\ |
|
|
|
|
|
{\bf 3) \underline {HFLUX} Surface Flux of Sensible Heat ($Watts/m^2$) } |
|
|
|
|
|
The turbulent flux of sensible heat from the surface to the atmosphere is a function of the |
|
|
gradient of virtual potential temperature and the eddy exchange coefficient: |
|
|
\[ |
|
|
{\bf HFLUX} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{surface} - \theta_{Nrphys}) |
|
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
|
|
\] |
|
|
where $\rho$ = the atmospheric density at the surface, $c_{p}$ is the specific |
|
|
heat of air, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the |
|
|
magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient |
|
|
for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient |
|
|
for heat and moisture (see diagnostic number 9), and $\theta$ is the potential temperature |
|
|
at the surface and at the bottom model level. |
|
|
\\ |
|
|
|
|
|
|
|
|
{\bf 4) \underline {EFLUX} Surface Flux of Latent Heat ($Watts/m^2$) } |
|
|
|
|
|
The turbulent flux of latent heat from the surface to the atmosphere is a function of the |
|
|
gradient of moisture, the potential evapotranspiration fraction and the eddy exchange coefficient: |
|
|
\[ |
|
|
{\bf EFLUX} = \rho \beta L C_{H} W_s (q_{surface} - q_{Nrphys}) |
|
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
|
|
\] |
|
|
where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of |
|
|
the potential evapotranspiration actually evaporated, L is the latent |
|
|
heat of evaporation, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the |
|
|
magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient |
|
|
for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient |
|
|
for heat and moisture (see diagnostic number 9), and $q_{surface}$ and $q_{Nrphys}$ are the specific |
|
|
humidity at the surface and at the bottom model level, respectively. |
|
|
\\ |
|
|
|
|
|
{\bf 5) \underline {QICE} Heat Conduction Through Sea Ice ($Watts/m^2$) } |
|
|
|
|
|
Over sea ice there is an additional source of energy at the surface due to the heat |
|
|
conduction from the relatively warm ocean through the sea ice. The heat conduction |
|
|
through sea ice represents an additional energy source term for the ground temperature equation. |
|
|
|
|
|
\[ |
|
|
{\bf QICE} = {C_{ti} \over {H_i}} (T_i-T_g) |
|
|
\] |
|
|
|
|
|
where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to |
|
|
be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and |
|
|
$T_g$ is the temperature of the sea ice. |
|
|
|
|
|
NOTE: QICE is not available through model version 5.3, but is available in subsequent versions. |
|
|
\\ |
|
|
|
|
|
|
|
|
{\bf 6) \underline {RADLWG} Net upward Longwave Flux at the surface ($Watts/m^2$)} |
|
|
|
|
|
\begin{eqnarray*} |
|
|
{\bf RADLWG} & = & F_{LW,Nrphys+1}^{Net} \\ |
|
|
& = & F_{LW,Nrphys+1}^\uparrow - F_{LW,Nrphys+1}^\downarrow |
|
|
\end{eqnarray*} |
|
|
\\ |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
|
|
$F_{LW}^\uparrow$ is |
|
|
the upward Longwave flux and $F_{LW}^\downarrow$ is the downward Longwave flux. |
|
|
\\ |
|
|
|
|
|
{\bf 7) \underline {RADSWG} Net downard shortwave Flux at the surface ($Watts/m^2$)} |
|
|
|
|
|
\begin{eqnarray*} |
|
|
{\bf RADSWG} & = & F_{SW,Nrphys+1}^{Net} \\ |
|
|
& = & F_{SW,Nrphys+1}^\downarrow - F_{SW,Nrphys+1}^\uparrow |
|
|
\end{eqnarray*} |
|
|
\\ |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
|
|
$F_{SW}^\downarrow$ is |
|
|
the downward Shortwave flux and $F_{SW}^\uparrow$ is the upward Shortwave flux. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 8) \underline {RI} Richardson Number} ($dimensionless$) |
|
|
|
|
|
\noindent |
|
|
The non-dimensional stability indicator is the ratio of the buoyancy to the shear: |
|
|
\[ |
|
|
{\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
|
|
= { {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
|
|
\] |
|
|
\\ |
|
|
where we used the hydrostatic equation: |
|
|
\[ |
|
|
{\pp{\Phi}{P^ \kappa}} = c_p \theta_v |
|
|
\] |
|
|
Negative values indicate unstable buoyancy {\bf{AND}} shear, small positive values ($<0.4$) |
|
|
indicate dominantly unstable shear, and large positive values indicate dominantly stable |
|
|
stratification. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 9) \underline {CT} Surface Exchange Coefficient for Temperature and Moisture ($dimensionless$) } |
|
|
|
|
|
\noindent |
|
|
The surface exchange coefficient is obtained from the similarity functions for the stability |
|
|
dependant flux profile relationships: |
|
|
\[ |
|
|
{\bf CT} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} = |
|
|
-{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} = |
|
|
{ k \over { (\psi_{h} + \psi_{g}) } } |
|
|
\] |
|
|
where $\psi_h$ is the surface layer non-dimensional temperature change and $\psi_g$ is the |
|
|
viscous sublayer non-dimensional temperature or moisture change: |
|
|
\[ |
|
|
\psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} \hspace{1cm} and |
|
|
\hspace{1cm} \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} } |
|
|
(h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2} |
|
|
\] |
|
|
and: |
|
|
$h_{0} = 30z_{0}$ with a maximum value over land of 0.01 |
|
|
|
|
|
\noindent |
|
|
$\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of |
|
|
the temperature and moisture gradients, specified differently for stable and unstable |
|
|
layers according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the |
|
|
non-dimensional stability parameter, Pr is the Prandtl number for air, $\nu$ is the molecular |
|
|
viscosity, $z_{0}$ is the surface roughness length, $u_*$ is the surface stress velocity |
|
|
(see diagnostic number 67), and the subscript ref refers to a reference value. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 10) \underline {CU} Surface Exchange Coefficient for Momentum ($dimensionless$) } |
|
|
|
|
|
\noindent |
|
|
The surface exchange coefficient is obtained from the similarity functions for the stability |
|
|
dependant flux profile relationships: |
|
|
\[ |
|
|
{\bf CU} = {u_* \over W_s} = { k \over \psi_{m} } |
|
|
\] |
|
|
where $\psi_m$ is the surface layer non-dimensional wind shear: |
|
|
\[ |
|
|
\psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta} |
|
|
\] |
|
|
\noindent |
|
|
$\phi_m$ is the similarity function of $\zeta$, which expresses the stability dependance of |
|
|
the temperature and moisture gradients, specified differently for stable and unstable layers |
|
|
according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the |
|
|
non-dimensional stability parameter, $u_*$ is the surface stress velocity |
|
|
(see diagnostic number 67), and $W_s$ is the magnitude of the surface layer wind. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 11) \underline {ET} Diffusivity Coefficient for Temperature and Moisture ($m^2/sec$) } |
|
|
|
|
|
\noindent |
|
|
In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat or |
|
|
moisture flux for the atmosphere above the surface layer can be expressed as a turbulent |
|
|
diffusion coefficient $K_h$ times the negative of the gradient of potential temperature |
|
|
or moisture. In the Helfand and Labraga (1988) adaptation of this closure, $K_h$ |
|
|
takes the form: |
|
|
\[ |
|
|
{\bf ET} = K_h = -{( {\overline{w^{\prime}\theta_v^{\prime}}}) \over {\pp{\theta_v}{z}} } |
|
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) & \mbox{decaying turbulence} |
|
|
\\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. |
|
|
\] |
|
|
where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} |
|
|
energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, |
|
|
which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer |
|
|
depth, |
|
|
$S_H$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and |
|
|
wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium |
|
|
dimensionless buoyancy and wind shear |
|
|
parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
|
|
are functions of the Richardson number. |
|
|
|
|
|
\noindent |
|
|
For the detailed equations and derivations of the modified level 2.5 closure scheme, |
|
|
see Helfand and Labraga, 1988. |
|
|
|
|
|
\noindent |
|
|
In the surface layer, ${\bf {ET}}$ is the exchange coefficient for heat and moisture, |
|
|
in units of $m/sec$, given by: |
|
|
\[ |
|
|
{\bf ET_{Nrphys}} = C_t * u_* = C_H W_s |
|
|
\] |
|
|
\noindent |
|
|
where $C_t$ is the dimensionless exchange coefficient for heat and moisture from the |
|
|
surface layer similarity functions (see diagnostic number 9), $u_*$ is the surface |
|
|
friction velocity (see diagnostic number 67), $C_H$ is the heat transfer coefficient, |
|
|
and $W_s$ is the magnitude of the surface layer wind. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 12) \underline {EU} Diffusivity Coefficient for Momentum ($m^2/sec$) } |
|
|
|
|
|
\noindent |
|
|
In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat |
|
|
momentum flux for the atmosphere above the surface layer can be expressed as a turbulent |
|
|
diffusion coefficient $K_m$ times the negative of the gradient of the u-wind. |
|
|
In the Helfand and Labraga (1988) adaptation of this closure, $K_m$ |
|
|
takes the form: |
|
|
\[ |
|
|
{\bf EU} = K_m = -{( {\overline{u^{\prime}w^{\prime}}}) \over {\pp{U}{z}} } |
|
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) & \mbox{decaying turbulence} |
|
|
\\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. |
|
|
\] |
|
|
\noindent |
|
|
where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} |
|
|
energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, |
|
|
which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer |
|
|
depth, |
|
|
$S_M$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and |
|
|
wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium |
|
|
dimensionless buoyancy and wind shear |
|
|
parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
|
|
are functions of the Richardson number. |
|
|
|
|
|
\noindent |
|
|
For the detailed equations and derivations of the modified level 2.5 closure scheme, |
|
|
see Helfand and Labraga, 1988. |
|
|
|
|
|
\noindent |
|
|
In the surface layer, ${\bf {EU}}$ is the exchange coefficient for momentum, |
|
|
in units of $m/sec$, given by: |
|
|
\[ |
|
|
{\bf EU_{Nrphys}} = C_u * u_* = C_D W_s |
|
|
\] |
|
|
\noindent |
|
|
where $C_u$ is the dimensionless exchange coefficient for momentum from the surface layer |
|
|
similarity functions (see diagnostic number 10), $u_*$ is the surface friction velocity |
|
|
(see diagnostic number 67), $C_D$ is the surface drag coefficient, and $W_s$ is the |
|
|
magnitude of the surface layer wind. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 13) \underline {TURBU} Zonal U-Momentum changes due to Turbulence ($m/sec/day$) } |
|
|
|
|
|
\noindent |
|
|
The tendency of U-Momentum due to turbulence is written: |
|
|
\[ |
|
|
{\bf TURBU} = {\pp{u}{t}}_{turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})} |
|
|
= {\pp{}{z} }{(K_m \pp{u}{z})} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
|
|
flux of u-momentum in terms of $K_m$, and the equation has the form of a diffusion |
|
|
equation. |
|
|
|
|
|
\noindent |
|
|
{\bf 14) \underline {TURBV} Meridional V-Momentum changes due to Turbulence ($m/sec/day$) } |
|
|
|
|
|
\noindent |
|
|
The tendency of V-Momentum due to turbulence is written: |
|
|
\[ |
|
|
{\bf TURBV} = {\pp{v}{t}}_{turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})} |
|
|
= {\pp{}{z} }{(K_m \pp{v}{z})} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
|
|
flux of v-momentum in terms of $K_m$, and the equation has the form of a diffusion |
|
|
equation. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 15) \underline {TURBT} Temperature changes due to Turbulence ($deg/day$) } |
|
|
|
|
|
\noindent |
|
|
The tendency of temperature due to turbulence is written: |
|
|
\[ |
|
|
{\bf TURBT} = {\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{turb} = |
|
|
P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})} |
|
|
= P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
|
|
flux of temperature in terms of $K_h$, and the equation has the form of a diffusion |
|
|
equation. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 16) \underline {TURBQ} Specific Humidity changes due to Turbulence ($g/kg/day$) } |
|
|
|
|
|
\noindent |
|
|
The tendency of specific humidity due to turbulence is written: |
|
|
\[ |
|
|
{\bf TURBQ} = {\pp{q}{t}}_{turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})} |
|
|
= {\pp{}{z} }{(K_h \pp{q}{z})} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
|
|
flux of temperature in terms of $K_h$, and the equation has the form of a diffusion |
|
|
equation. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 17) \underline {MOISTT} Temperature Changes Due to Moist Processes ($deg/day$) } |
|
|
|
|
|
\noindent |
|
|
\[ |
|
|
{\bf MOISTT} = \left. {\pp{T}{t}}\right|_{c} + \left. {\pp{T}{t}} \right|_{ls} |
|
|
\] |
|
|
where: |
|
|
\[ |
|
|
\left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over c_p} \Gamma_s \right)_i |
|
|
\hspace{.4cm} and |
|
|
\hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = {L \over c_p } (q^*-q) |
|
|
\] |
|
|
and |
|
|
\[ |
|
|
\Gamma_s = g \eta \pp{s}{p} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale |
|
|
precipitation processes, or supersaturation rain. |
|
|
The summation refers to contributions from each cloud type called by RAS. |
|
|
The dry static energy is given |
|
|
as $s$, the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is |
|
|
given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, |
|
|
the description of the convective parameterization. The fractional adjustment, or relaxation |
|
|
parameter, for each cloud type is given as $\alpha$, while |
|
|
$R$ is the rain re-evaporation adjustment. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 18) \underline {MOISTQ} Specific Humidity Changes Due to Moist Processes ($g/kg/day$) } |
|
|
|
|
|
\noindent |
|
|
\[ |
|
|
{\bf MOISTQ} = \left. {\pp{q}{t}}\right|_{c} + \left. {\pp{q}{t}} \right|_{ls} |
|
|
\] |
|
|
where: |
|
|
\[ |
|
|
\left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over {L}}(\Gamma_h-\Gamma_s) \right)_i |
|
|
\hspace{.4cm} and |
|
|
\hspace{.4cm} \left.{\pp{q}{t}}\right|_{ls} = (q^*-q) |
|
|
\] |
|
|
and |
|
|
\[ |
|
|
\Gamma_s = g \eta \pp{s}{p}\hspace{.4cm} and \hspace{.4cm}\Gamma_h = g \eta \pp{h}{p} |
|
|
\] |
|
|
\noindent |
|
|
The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale |
|
|
precipitation processes, or supersaturation rain. |
|
|
The summation refers to contributions from each cloud type called by RAS. |
|
|
The dry static energy is given as $s$, |
|
|
the moist static energy is given as $h$, |
|
|
the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is |
|
|
given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, |
|
|
the description of the convective parameterization. The fractional adjustment, or relaxation |
|
|
parameter, for each cloud type is given as $\alpha$, while |
|
|
$R$ is the rain re-evaporation adjustment. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 19) \underline {RADLW} Heating Rate due to Longwave Radiation ($deg/day$) } |
|
|
|
|
|
\noindent |
|
|
The net longwave heating rate is calculated as the vertical divergence of the |
|
|
net terrestrial radiative fluxes. |
|
|
Both the clear-sky and cloudy-sky longwave fluxes are computed within the |
|
|
longwave routine. |
|
|
The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. |
|
|
For a given cloud fraction, |
|
|
the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ |
|
|
to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, |
|
|
for the upward and downward radiative fluxes. |
|
|
(see Section \ref{sec:fizhi:radcloud}). |
|
|
The cloudy-sky flux is then obtained as: |
|
|
|
|
|
\noindent |
|
|
\[ |
|
|
F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
Finally, the net longwave heating rate is calculated as the vertical divergence of the |
|
|
net terrestrial radiative fluxes: |
|
|
\[ |
|
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F_{LW}^{NET} , |
|
|
\] |
|
|
or |
|
|
\[ |
|
|
{\bf RADLW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F_{LW}^{NET} . |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $g$ is the accelation due to gravity, |
|
|
$c_p$ is the heat capacity of air at constant pressure, |
|
|
and |
|
|
\[ |
|
|
F_{LW}^{NET} = F_{LW}^\uparrow - F_{LW}^\downarrow |
|
|
\] |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 20) \underline {RADSW} Heating Rate due to Shortwave Radiation ($deg/day$) } |
|
|
|
|
|
\noindent |
|
|
The net Shortwave heating rate is calculated as the vertical divergence of the |
|
|
net solar radiative fluxes. |
|
|
The clear-sky and cloudy-sky shortwave fluxes are calculated separately. |
|
|
For the clear-sky case, the shortwave fluxes and heating rates are computed with |
|
|
both CLMO (maximum overlap cloud fraction) and |
|
|
CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). |
|
|
The shortwave routine is then called a second time, for the cloudy-sky case, with the |
|
|
true time-averaged cloud fractions CLMO |
|
|
and CLRO being used. In all cases, a normalized incident shortwave flux is used as |
|
|
input at the top of the atmosphere. |
|
|
|
|
|
\noindent |
|
|
The heating rate due to Shortwave Radiation under cloudy skies is defined as: |
|
|
\[ |
|
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT}, |
|
|
\] |
|
|
or |
|
|
\[ |
|
|
{\bf RADSW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} . |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $g$ is the accelation due to gravity, |
|
|
$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident |
|
|
shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and |
|
|
\[ |
|
|
F(cloudy)_{SW}^{Net} = F(cloudy)_{SW}^\uparrow - F(cloudy)_{SW}^\downarrow |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 21) \underline {PREACC} Total (Large-scale + Convective) Accumulated Precipition ($mm/day$) } |
|
|
|
|
|
\noindent |
|
|
For a change in specific humidity due to moist processes, $\Delta q_{moist}$, |
|
|
the vertical integral or total precipitable amount is given by: |
|
|
\[ |
|
|
{\bf PREACC} = \int_{surf}^{top} \rho \Delta q_{moist} dz = - \int_{surf}^{top} \Delta q_{moist} |
|
|
{dp \over g} = {1 \over g} \int_0^1 \Delta q_{moist} dp |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes |
|
|
time step, scaled to $mm/day$. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 22) \underline {PRECON} Convective Precipition ($mm/day$) } |
|
|
|
|
|
\noindent |
|
|
For a change in specific humidity due to sub-grid scale cumulus convective processes, $\Delta q_{cum}$, |
|
|
the vertical integral or total precipitable amount is given by: |
|
|
\[ |
|
|
{\bf PRECON} = \int_{surf}^{top} \rho \Delta q_{cum} dz = - \int_{surf}^{top} \Delta q_{cum} |
|
|
{dp \over g} = {1 \over g} \int_0^1 \Delta q_{cum} dp |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes |
|
|
time step, scaled to $mm/day$. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 23) \underline {TUFLUX} Turbulent Flux of U-Momentum ($Newton/m^2$) } |
|
|
|
|
|
\noindent |
|
|
The turbulent flux of u-momentum is calculated for $diagnostic \hspace{.2cm} purposes |
|
|
\hspace{.2cm} only$ from the eddy coefficient for momentum: |
|
|
|
|
|
\[ |
|
|
{\bf TUFLUX} = {\rho } {(\overline{u^{\prime}w^{\prime}})} = |
|
|
{\rho } {(- K_m \pp{U}{z})} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\rho$ is the air density, and $K_m$ is the eddy coefficient. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 24) \underline {TVFLUX} Turbulent Flux of V-Momentum ($Newton/m^2$) } |
|
|
|
|
|
\noindent |
|
|
The turbulent flux of v-momentum is calculated for $diagnostic \hspace{.2cm} purposes |
|
|
\hspace{.2cm} only$ from the eddy coefficient for momentum: |
|
|
|
|
|
\[ |
|
|
{\bf TVFLUX} = {\rho } {(\overline{v^{\prime}w^{\prime}})} = |
|
|
{\rho } {(- K_m \pp{V}{z})} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\rho$ is the air density, and $K_m$ is the eddy coefficient. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 25) \underline {TTFLUX} Turbulent Flux of Sensible Heat ($Watts/m^2$) } |
|
|
|
|
|
\noindent |
|
|
The turbulent flux of sensible heat is calculated for $diagnostic \hspace{.2cm} purposes |
|
|
\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: |
|
|
|
|
|
\noindent |
|
|
\[ |
|
|
{\bf TTFLUX} = c_p {\rho } |
|
|
P^{\kappa}{(\overline{w^{\prime}\theta^{\prime}})} |
|
|
= c_p {\rho } P^{\kappa}{(- K_h \pp{\theta_v}{z})} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\rho$ is the air density, and $K_h$ is the eddy coefficient. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 26) \underline {TQFLUX} Turbulent Flux of Latent Heat ($Watts/m^2$) } |
|
|
|
|
|
\noindent |
|
|
The turbulent flux of latent heat is calculated for $diagnostic \hspace{.2cm} purposes |
|
|
\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: |
|
|
|
|
|
\noindent |
|
|
\[ |
|
|
{\bf TQFLUX} = {L {\rho } (\overline{w^{\prime}q^{\prime}})} = |
|
|
{L {\rho }(- K_h \pp{q}{z})} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\rho$ is the air density, and $K_h$ is the eddy coefficient. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 27) \underline {CN} Neutral Drag Coefficient ($dimensionless$) } |
|
|
|
|
|
\noindent |
|
|
The drag coefficient for momentum obtained by assuming a neutrally stable surface layer: |
|
|
\[ |
|
|
{\bf CN} = { k \over { \ln({h \over {z_0}})} } |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $k$ is the Von Karman constant, $h$ is the height of the surface layer, and |
|
|
$z_0$ is the surface roughness. |
|
|
|
|
|
\noindent |
|
|
NOTE: CN is not available through model version 5.3, but is available in subsequent |
|
|
versions. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 28) \underline {WINDS} Surface Wind Speed ($meter/sec$) } |
|
|
|
|
|
\noindent |
|
|
The surface wind speed is calculated for the last internal turbulence time step: |
|
|
\[ |
|
|
{\bf WINDS} = \sqrt{u_{Nrphys}^2 + v_{Nrphys}^2} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where the subscript $Nrphys$ refers to the lowest model level. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 29) \underline {DTSRF} Air/Surface Virtual Temperature Difference ($deg \hspace{.1cm} K$) } |
|
|
|
|
|
\noindent |
|
|
The air/surface virtual temperature difference measures the stability of the surface layer: |
|
|
\[ |
|
|
{\bf DTSRF} = (\theta_{v{Nrphys+1}} - \theta{v_{Nrphys}}) P^{\kappa}_{surf} |
|
|
\] |
|
|
\noindent |
|
|
where |
|
|
\[ |
|
|
\theta_{v{Nrphys+1}} = { T_g \over {P^{\kappa}_{surf}} } (1 + .609 q_{Nrphys+1}) \hspace{1cm} |
|
|
and \hspace{1cm} q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
$\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), |
|
|
$q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature |
|
|
and surface pressure, level $Nrphys$ refers to the lowest model level and level $Nrphys+1$ |
|
|
refers to the surface. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 30) \underline {TG} Ground Temperature ($deg \hspace{.1cm} K$) } |
|
|
|
|
|
\noindent |
|
|
The ground temperature equation is solved as part of the turbulence package |
|
|
using a backward implicit time differencing scheme: |
|
|
\[ |
|
|
{\bf TG} \hspace{.1cm} is \hspace{.1cm} obtained \hspace{.1cm} from: \hspace{.1cm} |
|
|
C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{ice} - H - LE |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $R_{sw}$ is the net surface downward shortwave radiative flux, $R_{lw}$ is the |
|
|
net surface upward longwave radiative flux, $Q_{ice}$ is the heat conduction through |
|
|
sea ice, $H$ is the upward sensible heat flux, $LE$ is the upward latent heat |
|
|
flux, and $C_g$ is the total heat capacity of the ground. |
|
|
$C_g$ is obtained by solving a heat diffusion equation |
|
|
for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by: |
|
|
\[ |
|
|
C_g = \sqrt{ {\lambda C_s \over {2 \omega} } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3} |
|
|
{ 86400. \over {2 \pi} } } \, \, . |
|
|
\] |
|
|
\noindent |
|
|
Here, the thermal conductivity, $\lambda$, is equal to $2x10^{-3}$ ${ly\over{ sec}} |
|
|
{cm \over {^oK}}$, |
|
|
the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided |
|
|
by $2 \pi$ $radians/ |
|
|
day$, and the expression for $C_s$, the heat capacity per unit volume at the surface, |
|
|
is a function of the ground wetness, $W$. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 31) \underline {TS} Surface Temperature ($deg \hspace{.1cm} K$) } |
|
|
|
|
|
\noindent |
|
|
The surface temperature estimate is made by assuming that the model's lowest |
|
|
layer is well-mixed, and therefore that $\theta$ is constant in that layer. |
|
|
The surface temperature is therefore: |
|
|
\[ |
|
|
{\bf TS} = \theta_{Nrphys} P^{\kappa}_{surf} |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 32) \underline {DTG} Surface Temperature Adjustment ($deg \hspace{.1cm} K$) } |
|
|
|
|
|
\noindent |
|
|
The change in surface temperature from one turbulence time step to the next, solved |
|
|
using the Ground Temperature Equation (see diagnostic number 30) is calculated: |
|
|
\[ |
|
|
{\bf DTG} = {T_g}^{n} - {T_g}^{n-1} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where superscript $n$ refers to the new, updated time level, and the superscript $n-1$ |
|
|
refers to the value at the previous turbulence time level. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 33) \underline {QG} Ground Specific Humidity ($g/kg$) } |
|
|
|
|
|
\noindent |
|
|
The ground specific humidity is obtained by interpolating between the specific |
|
|
humidity at the lowest model level and the specific humidity of a saturated ground. |
|
|
The interpolation is performed using the potential evapotranspiration function: |
|
|
\[ |
|
|
{\bf QG} = q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), |
|
|
and $q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature and surface |
|
|
pressure. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 34) \underline {QS} Saturation Surface Specific Humidity ($g/kg$) } |
|
|
|
|
|
\noindent |
|
|
The surface saturation specific humidity is the saturation specific humidity at |
|
|
the ground temprature and surface pressure: |
|
|
\[ |
|
|
{\bf QS} = q^*(T_g,P_s) |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 35) \underline {TGRLW} Instantaneous ground temperature used as input to the Longwave |
|
|
radiation subroutine (deg)} |
|
|
\[ |
|
|
{\bf TGRLW} = T_g(\lambda , \phi ,n) |
|
|
\] |
|
|
\noindent |
|
|
where $T_g$ is the model ground temperature at the current time step $n$. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 36) \underline {ST4} Upward Longwave flux at the surface ($Watts/m^2$) } |
|
|
\[ |
|
|
{\bf ST4} = \sigma T^4 |
|
|
\] |
|
|
\noindent |
|
|
where $\sigma$ is the Stefan-Boltzmann constant and T is the temperature. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 37) \underline {OLR} Net upward Longwave flux at $p=p_{top}$ ($Watts/m^2$) } |
|
|
\[ |
|
|
{\bf OLR} = F_{LW,top}^{NET} |
|
|
\] |
|
|
\noindent |
|
|
where top indicates the top of the first model layer. |
|
|
In the GCM, $p_{top}$ = 0.0 mb. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 38) \underline {OLRCLR} Net upward clearsky Longwave flux at $p=p_{top}$ ($Watts/m^2$) } |
|
|
\[ |
|
|
{\bf OLRCLR} = F(clearsky)_{LW,top}^{NET} |
|
|
\] |
|
|
\noindent |
|
|
where top indicates the top of the first model layer. |
|
|
In the GCM, $p_{top}$ = 0.0 mb. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 39) \underline {LWGCLR} Net upward clearsky Longwave flux at the surface ($Watts/m^2$) } |
|
|
|
|
|
\noindent |
|
|
\begin{eqnarray*} |
|
|
{\bf LWGCLR} & = & F(clearsky)_{LW,Nrphys+1}^{Net} \\ |
|
|
& = & F(clearsky)_{LW,Nrphys+1}^\uparrow - F(clearsky)_{LW,Nrphys+1}^\downarrow |
|
|
\end{eqnarray*} |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
|
|
$F(clearsky)_{LW}^\uparrow$ is |
|
|
the upward clearsky Longwave flux and the $F(clearsky)_{LW}^\downarrow$ is the downward clearsky Longwave flux. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 40) \underline {LWCLR} Heating Rate due to Clearsky Longwave Radiation ($deg/day$) } |
|
|
|
|
|
\noindent |
|
|
The net longwave heating rate is calculated as the vertical divergence of the |
|
|
net terrestrial radiative fluxes. |
|
|
Both the clear-sky and cloudy-sky longwave fluxes are computed within the |
|
|
longwave routine. |
|
|
The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. |
|
|
For a given cloud fraction, |
|
|
the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ |
|
|
to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, |
|
|
for the upward and downward radiative fluxes. |
|
|
(see Section \ref{sec:fizhi:radcloud}). |
|
|
The cloudy-sky flux is then obtained as: |
|
|
|
|
|
\noindent |
|
|
\[ |
|
|
F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
Thus, {\bf LWCLR} is defined as the net longwave heating rate due to the |
|
|
vertical divergence of the |
|
|
clear-sky longwave radiative flux: |
|
|
\[ |
|
|
\pp{\rho c_p T}{t}_{clearsky} = - {\partial \over \partial z} F(clearsky)_{LW}^{NET} , |
|
|
\] |
|
|
or |
|
|
\[ |
|
|
{\bf LWCLR} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(clearsky)_{LW}^{NET} . |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $g$ is the accelation due to gravity, |
|
|
$c_p$ is the heat capacity of air at constant pressure, |
|
|
and |
|
|
\[ |
|
|
F(clearsky)_{LW}^{Net} = F(clearsky)_{LW}^\uparrow - F(clearsky)_{LW}^\downarrow |
|
|
\] |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 41) \underline {TLW} Instantaneous temperature used as input to the Longwave |
|
|
radiation subroutine (deg)} |
|
|
\[ |
|
|
{\bf TLW} = T(\lambda , \phi ,level, n) |
|
|
\] |
|
|
\noindent |
|
|
where $T$ is the model temperature at the current time step $n$. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 42) \underline {SHLW} Instantaneous specific humidity used as input to |
|
|
the Longwave radiation subroutine (kg/kg)} |
|
|
\[ |
|
|
{\bf SHLW} = q(\lambda , \phi , level , n) |
|
|
\] |
|
|
\noindent |
|
|
where $q$ is the model specific humidity at the current time step $n$. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 43) \underline {OZLW} Instantaneous ozone used as input to |
|
|
the Longwave radiation subroutine (kg/kg)} |
|
|
\[ |
|
|
{\bf OZLW} = {\rm OZ}(\lambda , \phi , level , n) |
|
|
\] |
|
|
\noindent |
|
|
where $\rm OZ$ is the interpolated ozone data set from the climatological monthly |
|
|
mean zonally averaged ozone data set. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 44) \underline {CLMOLW} Maximum Overlap cloud fraction used in LW Radiation ($0-1$) } |
|
|
|
|
|
\noindent |
|
|
{\bf CLMOLW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed |
|
|
Arakawa/Schubert Convection scheme and will be used in the Longwave Radiation algorithm. These are |
|
|
convective clouds whose radiative characteristics are assumed to be correlated in the vertical. |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
|
|
\[ |
|
|
{\bf CLMOLW} = CLMO_{RAS,LW}(\lambda, \phi, level ) |
|
|
\] |
|
|
\\ |
|
|
|
|
|
|
|
|
{\bf 45) \underline {CLDTOT} Total cloud fraction used in LW and SW Radiation ($0-1$) } |
|
|
|
|
|
{\bf CLDTOT} is the time-averaged total cloud fraction that has been filled by the Relaxed |
|
|
Arakawa/Schubert and Large-scale Convection schemes and will be used in the Longwave and Shortwave |
|
|
Radiation packages. |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
|
|
\[ |
|
|
{\bf CLDTOT} = F_{RAS} + F_{LS} |
|
|
\] |
|
|
\\ |
|
|
where $F_{RAS}$ is the time-averaged cloud fraction due to sub-grid scale convection, and $F_{LS}$ is the |
|
|
time-averaged cloud fraction due to precipitating and non-precipitating large-scale moist processes. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 46) \underline {CLMOSW} Maximum Overlap cloud fraction used in SW Radiation ($0-1$) } |
|
|
|
|
|
\noindent |
|
|
{\bf CLMOSW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed |
|
|
Arakawa/Schubert Convection scheme and will be used in the Shortwave Radiation algorithm. These are |
|
|
convective clouds whose radiative characteristics are assumed to be correlated in the vertical. |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
|
|
\[ |
|
|
{\bf CLMOSW} = CLMO_{RAS,SW}(\lambda, \phi, level ) |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 47) \underline {CLROSW} Random Overlap cloud fraction used in SW Radiation ($0-1$) } |
|
|
|
|
|
\noindent |
|
|
{\bf CLROSW} is the time-averaged random overlap cloud fraction that has been filled by the Relaxed |
|
|
Arakawa/Schubert and Large-scale Convection schemes and will be used in the Shortwave |
|
|
Radiation algorithm. These are |
|
|
convective and large-scale clouds whose radiative characteristics are not |
|
|
assumed to be correlated in the vertical. |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
|
|
\[ |
|
|
{\bf CLROSW} = CLRO_{RAS,Large Scale,SW}(\lambda, \phi, level ) |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 48) \underline {RADSWT} Incident Shortwave radiation at the top of the atmosphere ($Watts/m^2$) } |
|
|
\[ |
|
|
{\bf RADSWT} = {\frac{S_0}{R_a^2}} \cdot cos \phi_z |
|
|
\] |
|
|
\noindent |
|
|
where $S_0$, is the extra-terrestial solar contant, |
|
|
$R_a$ is the earth-sun distance in Astronomical Units, |
|
|
and $cos \phi_z$ is the cosine of the zenith angle. |
|
|
It should be noted that {\bf RADSWT}, as well as |
|
|
{\bf OSR} and {\bf OSRCLR}, |
|
|
are calculated at the top of the atmosphere (p=0 mb). However, the |
|
|
{\bf OLR} and {\bf OLRCLR} diagnostics are currently |
|
|
calculated at $p= p_{top}$ (0.0 mb for the GCM). |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 49) \underline {EVAP} Surface Evaporation ($mm/day$) } |
|
|
|
|
|
\noindent |
|
|
The surface evaporation is a function of the gradient of moisture, the potential |
|
|
evapotranspiration fraction and the eddy exchange coefficient: |
|
|
\[ |
|
|
{\bf EVAP} = \rho \beta K_{h} (q_{surface} - q_{Nrphys}) |
|
|
\] |
|
|
where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of |
|
|
the potential evapotranspiration actually evaporated ($\beta=1$ over oceans), $K_{h}$ is the |
|
|
turbulent eddy exchange coefficient for heat and moisture at the surface in $m/sec$ and |
|
|
$q{surface}$ and $q_{Nrphys}$ are the specific humidity at the surface (see diagnostic |
|
|
number 34) and at the bottom model level, respectively. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 50) \underline {DUDT} Total Zonal U-Wind Tendency ($m/sec/day$) } |
|
|
|
|
|
\noindent |
|
|
{\bf DUDT} is the total time-tendency of the Zonal U-Wind due to Hydrodynamic, Diabatic, |
|
|
and Analysis forcing. |
|
|
\[ |
|
|
{\bf DUDT} = \pp{u}{t}_{Dynamics} + \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 51) \underline {DVDT} Total Zonal V-Wind Tendency ($m/sec/day$) } |
|
|
|
|
|
\noindent |
|
|
{\bf DVDT} is the total time-tendency of the Meridional V-Wind due to Hydrodynamic, Diabatic, |
|
|
and Analysis forcing. |
|
|
\[ |
|
|
{\bf DVDT} = \pp{v}{t}_{Dynamics} + \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 52) \underline {DTDT} Total Temperature Tendency ($deg/day$) } |
|
|
|
|
|
\noindent |
|
|
{\bf DTDT} is the total time-tendency of Temperature due to Hydrodynamic, Diabatic, |
|
|
and Analysis forcing. |
|
|
\begin{eqnarray*} |
|
|
{\bf DTDT} & = & \pp{T}{t}_{Dynamics} + \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
|
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} |
|
|
\end{eqnarray*} |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 53) \underline {DQDT} Total Specific Humidity Tendency ($g/kg/day$) } |
|
|
|
|
|
\noindent |
|
|
{\bf DQDT} is the total time-tendency of Specific Humidity due to Hydrodynamic, Diabatic, |
|
|
and Analysis forcing. |
|
|
\[ |
|
|
{\bf DQDT} = \pp{q}{t}_{Dynamics} + \pp{q}{t}_{Moist Processes} |
|
|
+ \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 54) \underline {USTAR} Surface-Stress Velocity ($m/sec$) } |
|
|
|
|
|
\noindent |
|
|
The surface stress velocity, or the friction velocity, is the wind speed at |
|
|
the surface layer top impeded by the surface drag: |
|
|
\[ |
|
|
{\bf USTAR} = C_uW_s \hspace{1cm}where: \hspace{.2cm} |
|
|
C_u = {k \over {\psi_m} } |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
$C_u$ is the non-dimensional surface drag coefficient (see diagnostic |
|
|
number 10), and $W_s$ is the surface wind speed (see diagnostic number 28). |
|
|
|
|
|
\noindent |
|
|
{\bf 55) \underline {Z0} Surface Roughness Length ($m$) } |
|
|
|
|
|
\noindent |
|
|
Over the land surface, the surface roughness length is interpolated to the local |
|
|
time from the monthly mean data of Dorman and Sellers (1989). Over the ocean, |
|
|
the roughness length is a function of the surface-stress velocity, $u_*$. |
|
|
\[ |
|
|
{\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where the constants are chosen to interpolate between the reciprocal relation of |
|
|
Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981) |
|
|
for moderate to large winds. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 56) \underline {FRQTRB} Frequency of Turbulence ($0-1$) } |
|
|
|
|
|
\noindent |
|
|
The fraction of time when turbulence is present is defined as the fraction of |
|
|
time when the turbulent kinetic energy exceeds some minimum value, defined here |
|
|
to be $0.005 \hspace{.1cm}m^2/sec^2$. When this criterion is met, a counter is |
|
|
incremented. The fraction over the averaging interval is reported. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 57) \underline {PBL} Planetary Boundary Layer Depth ($mb$) } |
|
|
|
|
|
\noindent |
|
|
The depth of the PBL is defined by the turbulence parameterization to be the |
|
|
depth at which the turbulent kinetic energy reduces to ten percent of its surface |
|
|
value. |
|
|
|
|
|
\[ |
|
|
{\bf PBL} = P_{PBL} - P_{surface} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $P_{PBL}$ is the pressure in $mb$ at which the turbulent kinetic energy |
|
|
reaches one tenth of its surface value, and $P_s$ is the surface pressure. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 58) \underline {SWCLR} Clear sky Heating Rate due to Shortwave Radiation ($deg/day$) } |
|
|
|
|
|
\noindent |
|
|
The net Shortwave heating rate is calculated as the vertical divergence of the |
|
|
net solar radiative fluxes. |
|
|
The clear-sky and cloudy-sky shortwave fluxes are calculated separately. |
|
|
For the clear-sky case, the shortwave fluxes and heating rates are computed with |
|
|
both CLMO (maximum overlap cloud fraction) and |
|
|
CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). |
|
|
The shortwave routine is then called a second time, for the cloudy-sky case, with the |
|
|
true time-averaged cloud fractions CLMO |
|
|
and CLRO being used. In all cases, a normalized incident shortwave flux is used as |
|
|
input at the top of the atmosphere. |
|
|
|
|
|
\noindent |
|
|
The heating rate due to Shortwave Radiation under clear skies is defined as: |
|
|
\[ |
|
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT}, |
|
|
\] |
|
|
or |
|
|
\[ |
|
|
{\bf SWCLR} = \frac{g}{c_p } {\partial \over \partial p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} . |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $g$ is the accelation due to gravity, |
|
|
$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident |
|
|
shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and |
|
|
\[ |
|
|
F(clear)_{SW}^{Net} = F(clear)_{SW}^\uparrow - F(clear)_{SW}^\downarrow |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 59) \underline {OSR} Net upward Shortwave flux at the top of the model ($Watts/m^2$) } |
|
|
\[ |
|
|
{\bf OSR} = F_{SW,top}^{NET} |
|
|
\] |
|
|
\noindent |
|
|
where top indicates the top of the first model layer used in the shortwave radiation |
|
|
routine. |
|
|
In the GCM, $p_{SW_{top}}$ = 0 mb. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 60) \underline {OSRCLR} Net upward clearsky Shortwave flux at the top of the model ($Watts/m^2$) } |
|
|
\[ |
|
|
{\bf OSRCLR} = F(clearsky)_{SW,top}^{NET} |
|
|
\] |
|
|
\noindent |
|
|
where top indicates the top of the first model layer used in the shortwave radiation |
|
|
routine. |
|
|
In the GCM, $p_{SW_{top}}$ = 0 mb. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 61) \underline {CLDMAS} Convective Cloud Mass Flux ($kg/m^2$) } |
|
|
|
|
|
\noindent |
|
|
The amount of cloud mass moved per RAS timestep from all convective clouds is written: |
|
|
\[ |
|
|
{\bf CLDMAS} = \eta m_B |
|
|
\] |
|
|
where $\eta$ is the entrainment, normalized by the cloud base mass flux, and $m_B$ is |
|
|
the cloud base mass flux. $m_B$ and $\eta$ are defined explicitly in Section \ref{sec:fizhi:mc}, the |
|
|
description of the convective parameterization. |
|
|
\\ |
|
|
|
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 62) \underline {UAVE} Time-Averaged Zonal U-Wind ($m/sec$) } |
|
|
|
|
|
\noindent |
|
|
The diagnostic {\bf UAVE} is simply the time-averaged Zonal U-Wind over |
|
|
the {\bf NUAVE} output frequency. This is contrasted to the instantaneous |
|
|
Zonal U-Wind which is archived on the Prognostic Output data stream. |
|
|
\[ |
|
|
{\bf UAVE} = u(\lambda, \phi, level , t) |
|
|
\] |
|
|
\\ |
|
|
Note, {\bf UAVE} is computed and stored on the staggered C-grid. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 63) \underline {VAVE} Time-Averaged Meridional V-Wind ($m/sec$) } |
|
|
|
|
|
\noindent |
|
|
The diagnostic {\bf VAVE} is simply the time-averaged Meridional V-Wind over |
|
|
the {\bf NVAVE} output frequency. This is contrasted to the instantaneous |
|
|
Meridional V-Wind which is archived on the Prognostic Output data stream. |
|
|
\[ |
|
|
{\bf VAVE} = v(\lambda, \phi, level , t) |
|
|
\] |
|
|
\\ |
|
|
Note, {\bf VAVE} is computed and stored on the staggered C-grid. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 64) \underline {TAVE} Time-Averaged Temperature ($Kelvin$) } |
|
|
|
|
|
\noindent |
|
|
The diagnostic {\bf TAVE} is simply the time-averaged Temperature over |
|
|
the {\bf NTAVE} output frequency. This is contrasted to the instantaneous |
|
|
Temperature which is archived on the Prognostic Output data stream. |
|
|
\[ |
|
|
{\bf TAVE} = T(\lambda, \phi, level , t) |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 65) \underline {QAVE} Time-Averaged Specific Humidity ($g/kg$) } |
|
|
|
|
|
\noindent |
|
|
The diagnostic {\bf QAVE} is simply the time-averaged Specific Humidity over |
|
|
the {\bf NQAVE} output frequency. This is contrasted to the instantaneous |
|
|
Specific Humidity which is archived on the Prognostic Output data stream. |
|
|
\[ |
|
|
{\bf QAVE} = q(\lambda, \phi, level , t) |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 66) \underline {PAVE} Time-Averaged Surface Pressure - PTOP ($mb$) } |
|
|
|
|
|
\noindent |
|
|
The diagnostic {\bf PAVE} is simply the time-averaged Surface Pressure - PTOP over |
|
|
the {\bf NPAVE} output frequency. This is contrasted to the instantaneous |
|
|
Surface Pressure - PTOP which is archived on the Prognostic Output data stream. |
|
|
\begin{eqnarray*} |
|
|
{\bf PAVE} & = & \pi(\lambda, \phi, level , t) \\ |
|
|
& = & p_s(\lambda, \phi, level , t) - p_T |
|
|
\end{eqnarray*} |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 67) \underline {QQAVE} Time-Averaged Turbulent Kinetic Energy $(m/sec)^2$ } |
|
|
|
|
|
\noindent |
|
|
The diagnostic {\bf QQAVE} is simply the time-averaged prognostic Turbulent Kinetic Energy |
|
|
produced by the GCM Turbulence parameterization over |
|
|
the {\bf NQQAVE} output frequency. This is contrasted to the instantaneous |
|
|
Turbulent Kinetic Energy which is archived on the Prognostic Output data stream. |
|
|
\[ |
|
|
{\bf QQAVE} = qq(\lambda, \phi, level , t) |
|
|
\] |
|
|
\\ |
|
|
Note, {\bf QQAVE} is computed and stored at the ``mass-point'' locations on the staggered C-grid. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 68) \underline {SWGCLR} Net downward clearsky Shortwave flux at the surface ($Watts/m^2$) } |
|
|
|
|
|
\noindent |
|
|
\begin{eqnarray*} |
|
|
{\bf SWGCLR} & = & F(clearsky)_{SW,Nrphys+1}^{Net} \\ |
|
|
& = & F(clearsky)_{SW,Nrphys+1}^\downarrow - F(clearsky)_{SW,Nrphys+1}^\uparrow |
|
|
\end{eqnarray*} |
|
|
\noindent |
|
|
\\ |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
|
|
$F(clearsky){SW}^\downarrow$ is |
|
|
the downward clearsky Shortwave flux and $F(clearsky)_{SW}^\uparrow$ is |
|
|
the upward clearsky Shortwave flux. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 69) \underline {SDIAG1} User-Defined Surface Diagnostic-1 } |
|
|
|
|
|
\noindent |
|
|
The GCM provides Users with a built-in mechanism for archiving user-defined |
|
|
diagnostics. The generic diagnostic array QDIAG located in COMMON /DIAG/, and the associated |
|
|
diagnostic counters and pointers located in COMMON /DIAGP/, |
|
|
must be accessable in order to use the user-defined diagnostics (see Section \ref{sec:diagnostics:diagover}). |
|
|
A convenient method for incorporating all necessary COMMON files is to |
|
|
include the GCM {\em vstate.com} file in the routine which employs the |
|
|
user-defined diagnostics. |
|
|
|
|
|
\noindent |
|
|
In addition to enabling the user-defined diagnostic (ie., CALL SETDIAG(84)), the User must fill |
|
|
the QDIAG array with the desired quantity within the User's |
|
|
application program or within modified GCM subroutines, as well as increment |
|
|
the diagnostic counter at the time when the diagnostic is updated. |
|
|
The QDIAG location index for {\bf SDIAG1} and its corresponding counter is |
|
|
automatically defined as {\bf ISDIAG1} and {\bf NSDIAG1}, respectively, after the |
|
|
diagnostic has been enabled. |
|
|
The syntax for its use is given by |
|
|
\begin{verbatim} |
|
|
do j=1,jm |
|
|
do i=1,im |
|
|
qdiag(i,j,ISDIAG1) = qdiag(i,j,ISDIAG1) + ... |
|
|
enddo |
|
|
enddo |
|
|
|
|
|
NSDIAG1 = NSDIAG1 + 1 |
|
|
\end{verbatim} |
|
|
The diagnostics defined in this manner will automatically be archived by the output routines. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 70) \underline {SDIAG2} User-Defined Surface Diagnostic-2 } |
|
|
|
|
|
\noindent |
|
|
The GCM provides Users with a built-in mechanism for archiving user-defined |
|
|
diagnostics. For a complete description refer to Diagnostic \#84. |
|
|
The syntax for using the surface SDIAG2 diagnostic is given by |
|
|
\begin{verbatim} |
|
|
do j=1,jm |
|
|
do i=1,im |
|
|
qdiag(i,j,ISDIAG2) = qdiag(i,j,ISDIAG2) + ... |
|
|
enddo |
|
|
enddo |
|
|
|
|
|
NSDIAG2 = NSDIAG2 + 1 |
|
|
\end{verbatim} |
|
|
The diagnostics defined in this manner will automatically be archived by the output routines. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 71) \underline {UDIAG1} User-Defined Upper-Air Diagnostic-1 } |
|
|
|
|
|
\noindent |
|
|
The GCM provides Users with a built-in mechanism for archiving user-defined |
|
|
diagnostics. For a complete description refer to Diagnostic \#84. |
|
|
The syntax for using the upper-air UDIAG1 diagnostic is given by |
|
|
\begin{verbatim} |
|
|
do L=1,Nrphys |
|
|
do j=1,jm |
|
|
do i=1,im |
|
|
qdiag(i,j,IUDIAG1+L-1) = qdiag(i,j,IUDIAG1+L-1) + ... |
|
|
enddo |
|
|
enddo |
|
|
enddo |
|
|
|
|
|
NUDIAG1 = NUDIAG1 + 1 |
|
|
\end{verbatim} |
|
|
The diagnostics defined in this manner will automatically be archived by the |
|
|
output programs. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 72) \underline {UDIAG2} User-Defined Upper-Air Diagnostic-2 } |
|
|
|
|
|
\noindent |
|
|
The GCM provides Users with a built-in mechanism for archiving user-defined |
|
|
diagnostics. For a complete description refer to Diagnostic \#84. |
|
|
The syntax for using the upper-air UDIAG2 diagnostic is given by |
|
|
\begin{verbatim} |
|
|
do L=1,Nrphys |
|
|
do j=1,jm |
|
|
do i=1,im |
|
|
qdiag(i,j,IUDIAG2+L-1) = qdiag(i,j,IUDIAG2+L-1) + ... |
|
|
enddo |
|
|
enddo |
|
|
enddo |
|
|
|
|
|
NUDIAG2 = NUDIAG2 + 1 |
|
|
\end{verbatim} |
|
|
The diagnostics defined in this manner will automatically be archived by the |
|
|
output programs. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 73) \underline {DIABU} Total Diabatic Zonal U-Wind Tendency ($m/sec/day$) } |
|
|
|
|
|
\noindent |
|
|
{\bf DIABU} is the total time-tendency of the Zonal U-Wind due to Diabatic processes |
|
|
and the Analysis forcing. |
|
|
\[ |
|
|
{\bf DIABU} = \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 74) \underline {DIABV} Total Diabatic Meridional V-Wind Tendency ($m/sec/day$) } |
|
|
|
|
|
\noindent |
|
|
{\bf DIABV} is the total time-tendency of the Meridional V-Wind due to Diabatic processes |
|
|
and the Analysis forcing. |
|
|
\[ |
|
|
{\bf DIABV} = \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 75) \underline {DIABT} Total Diabatic Temperature Tendency ($deg/day$) } |
|
|
|
|
|
\noindent |
|
|
{\bf DIABT} is the total time-tendency of Temperature due to Diabatic processes |
|
|
and the Analysis forcing. |
|
|
\begin{eqnarray*} |
|
|
{\bf DIABT} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
|
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} |
|
|
\end{eqnarray*} |
|
|
\\ |
|
|
If we define the time-tendency of Temperature due to Diabatic processes as |
|
|
\begin{eqnarray*} |
|
|
\pp{T}{t}_{Diabatic} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
|
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} |
|
|
\end{eqnarray*} |
|
|
then, since there are no surface pressure changes due to Diabatic processes, we may write |
|
|
\[ |
|
|
\pp{T}{t}_{Diabatic} = {p^\kappa \over \pi }\pp{\pi \theta}{t}_{Diabatic} |
|
|
\] |
|
|
where $\theta = T/p^\kappa$. Thus, {\bf DIABT} may be written as |
|
|
\[ |
|
|
{\bf DIABT} = {p^\kappa \over \pi } \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right) |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 76) \underline {DIABQ} Total Diabatic Specific Humidity Tendency ($g/kg/day$) } |
|
|
|
|
|
\noindent |
|
|
{\bf DIABQ} is the total time-tendency of Specific Humidity due to Diabatic processes |
|
|
and the Analysis forcing. |
|
|
\[ |
|
|
{\bf DIABQ} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} |
|
|
\] |
|
|
If we define the time-tendency of Specific Humidity due to Diabatic processes as |
|
|
\[ |
|
|
\pp{q}{t}_{Diabatic} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} |
|
|
\] |
|
|
then, since there are no surface pressure changes due to Diabatic processes, we may write |
|
|
\[ |
|
|
\pp{q}{t}_{Diabatic} = {1 \over \pi }\pp{\pi q}{t}_{Diabatic} |
|
|
\] |
|
|
Thus, {\bf DIABQ} may be written as |
|
|
\[ |
|
|
{\bf DIABQ} = {1 \over \pi } \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right) |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 77) \underline {VINTUQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } |
|
|
|
|
|
\noindent |
|
|
The vertically integrated moisture flux due to the zonal u-wind is obtained by integrating |
|
|
$u q$ over the depth of the atmosphere at each model timestep, |
|
|
and dividing by the total mass of the column. |
|
|
\[ |
|
|
{\bf VINTUQ} = \frac{ \int_{surf}^{top} u q \rho dz } { \int_{surf}^{top} \rho dz } |
|
|
\] |
|
|
Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have |
|
|
\[ |
|
|
{\bf VINTUQ} = { \int_0^1 u q dp } |
|
|
\] |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 78) \underline {VINTVQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } |
|
|
|
|
|
\noindent |
|
|
The vertically integrated moisture flux due to the meridional v-wind is obtained by integrating |
|
|
$v q$ over the depth of the atmosphere at each model timestep, |
|
|
and dividing by the total mass of the column. |
|
|
\[ |
|
|
{\bf VINTVQ} = \frac{ \int_{surf}^{top} v q \rho dz } { \int_{surf}^{top} \rho dz } |
|
|
\] |
|
|
Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have |
|
|
\[ |
|
|
{\bf VINTVQ} = { \int_0^1 v q dp } |
|
|
\] |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 79) \underline {VINTUT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } |
|
|
|
|
|
\noindent |
|
|
The vertically integrated heat flux due to the zonal u-wind is obtained by integrating |
|
|
$u T$ over the depth of the atmosphere at each model timestep, |
|
|
and dividing by the total mass of the column. |
|
|
\[ |
|
|
{\bf VINTUT} = \frac{ \int_{surf}^{top} u T \rho dz } { \int_{surf}^{top} \rho dz } |
|
|
\] |
|
|
Or, |
|
|
\[ |
|
|
{\bf VINTUT} = { \int_0^1 u T dp } |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 80) \underline {VINTVT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } |
|
|
|
|
|
\noindent |
|
|
The vertically integrated heat flux due to the meridional v-wind is obtained by integrating |
|
|
$v T$ over the depth of the atmosphere at each model timestep, |
|
|
and dividing by the total mass of the column. |
|
|
\[ |
|
|
{\bf VINTVT} = \frac{ \int_{surf}^{top} v T \rho dz } { \int_{surf}^{top} \rho dz } |
|
|
\] |
|
|
Using $\rho \delta z = -{\delta p \over g} $, we have |
|
|
\[ |
|
|
{\bf VINTVT} = { \int_0^1 v T dp } |
|
|
\] |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 81 \underline {CLDFRC} Total 2-Dimensional Cloud Fracton ($0-1$) } |
|
|
|
|
|
If we define the |
|
|
time-averaged random and maximum overlapped cloudiness as CLRO and |
|
|
CLMO respectively, then the probability of clear sky associated |
|
|
with random overlapped clouds at any level is (1-CLRO) while the probability of |
|
|
clear sky associated with maximum overlapped clouds at any level is (1-CLMO). |
|
|
The total clear sky probability is given by (1-CLRO)*(1-CLMO), thus |
|
|
the total cloud fraction at each level may be obtained by |
|
|
1-(1-CLRO)*(1-CLMO). |
|
|
|
|
|
At any given level, we may define the clear line-of-site probability by |
|
|
appropriately accounting for the maximum and random overlap |
|
|
cloudiness. The clear line-of-site probability is defined to be |
|
|
equal to the product of the clear line-of-site probabilities |
|
|
associated with random and maximum overlap cloudiness. The clear |
|
|
line-of-site probability $C(p,p^{\prime})$ associated with maximum overlap clouds, |
|
|
from the current pressure $p$ |
|
|
to the model top pressure, $p^{\prime} = p_{top}$, or the model surface pressure, $p^{\prime} = p_{surf}$, |
|
|
is simply 1.0 minus the largest maximum overlap cloud value along the |
|
|
line-of-site, ie. |
|
|
|
|
|
$$1-MAX_p^{p^{\prime}} \left( CLMO_p \right)$$ |
|
|
|
|
|
Thus, even in the time-averaged sense it is assumed that the |
|
|
maximum overlap clouds are correlated in the vertical. The clear |
|
|
line-of-site probability associated with random overlap clouds is |
|
|
defined to be the product of the clear sky probabilities at each |
|
|
level along the line-of-site, ie. |
|
|
|
|
|
$$\prod_{p}^{p^{\prime}} \left( 1-CLRO_p \right)$$ |
|
|
|
|
|
The total cloud fraction at a given level associated with a line- |
|
|
of-site calculation is given by |
|
|
|
|
|
$$1-\left( 1-MAX_p^{p^{\prime}} \left[ CLMO_p \right] \right) |
|
|
\prod_p^{p^{\prime}} \left( 1-CLRO_p \right)$$ |
|
|
|
|
|
|
|
|
\noindent |
|
|
The 2-dimensional net cloud fraction as seen from the top of the |
|
|
atmosphere is given by |
|
|
\[ |
|
|
{\bf CLDFRC} = 1-\left( 1-MAX_{l=l_1}^{Nrphys} \left[ CLMO_l \right] \right) |
|
|
\prod_{l=l_1}^{Nrphys} \left( 1-CLRO_l \right) |
|
|
\] |
|
|
\\ |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 82) \underline {QINT} Total Precipitable Water ($gm/cm^2$) } |
|
|
|
|
|
\noindent |
|
|
The Total Precipitable Water is defined as the vertical integral of the specific humidity, |
|
|
given by: |
|
|
\begin{eqnarray*} |
|
|
{\bf QINT} & = & \int_{surf}^{top} \rho q dz \\ |
|
|
& = & {\pi \over g} \int_0^1 q dp |
|
|
\end{eqnarray*} |
|
|
where we have used the hydrostatic relation |
|
|
$\rho \delta z = -{\delta p \over g} $. |
|
|
\\ |
|
|
|
|
|
|
|
|
\noindent |
|
|
{\bf 83) \underline {U2M} Zonal U-Wind at 2 Meter Depth ($m/sec$) } |
|
|
|
|
|
\noindent |
|
|
The u-wind at the 2-meter depth is determined from the similarity theory: |
|
|
\[ |
|
|
{\bf U2M} = {u_* \over k} \psi_{m_{2m}} {u_{sl} \over {W_s}} = |
|
|
{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}u_{sl} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
|
|
is above two meters, ${\bf U2M}$ is undefined. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 84) \underline {V2M} Meridional V-Wind at 2 Meter Depth ($m/sec$) } |
|
|
|
|
|
\noindent |
|
|
The v-wind at the 2-meter depth is a determined from the similarity theory: |
|
|
\[ |
|
|
{\bf V2M} = {u_* \over k} \psi_{m_{2m}} {v_{sl} \over {W_s}} = |
|
|
{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}v_{sl} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
|
|
is above two meters, ${\bf V2M}$ is undefined. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 85) \underline {T2M} Temperature at 2 Meter Depth ($deg \hspace{.1cm} K$) } |
|
|
|
|
|
\noindent |
|
|
The temperature at the 2-meter depth is a determined from the similarity theory: |
|
|
\[ |
|
|
{\bf T2M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) = |
|
|
P^{\kappa}(\theta_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
|
|
(\theta_{sl} - \theta_{surf})) |
|
|
\] |
|
|
where: |
|
|
\[ |
|
|
\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
|
|
is above two meters, ${\bf T2M}$ is undefined. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 86) \underline {Q2M} Specific Humidity at 2 Meter Depth ($g/kg$) } |
|
|
|
|
|
\noindent |
|
|
The specific humidity at the 2-meter depth is determined from the similarity theory: |
|
|
\[ |
|
|
{\bf Q2M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) = |
|
|
P^{\kappa}(q_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
|
|
(q_{sl} - q_{surf})) |
|
|
\] |
|
|
where: |
|
|
\[ |
|
|
q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
|
|
is above two meters, ${\bf Q2M}$ is undefined. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 87) \underline {U10M} Zonal U-Wind at 10 Meter Depth ($m/sec$) } |
|
|
|
|
|
\noindent |
|
|
The u-wind at the 10-meter depth is an interpolation between the surface wind |
|
|
and the model lowest level wind using the ratio of the non-dimensional wind shear |
|
|
at the two levels: |
|
|
\[ |
|
|
{\bf U10M} = {u_* \over k} \psi_{m_{10m}} {u_{sl} \over {W_s}} = |
|
|
{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}u_{sl} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript |
|
|
$sl$ refers to the height of the top of the surface layer. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 88) \underline {V10M} Meridional V-Wind at 10 Meter Depth ($m/sec$) } |
|
|
|
|
|
\noindent |
|
|
The v-wind at the 10-meter depth is an interpolation between the surface wind |
|
|
and the model lowest level wind using the ratio of the non-dimensional wind shear |
|
|
at the two levels: |
|
|
\[ |
|
|
{\bf V10M} = {u_* \over k} \psi_{m_{10m}} {v_{sl} \over {W_s}} = |
|
|
{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}v_{sl} |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript |
|
|
$sl$ refers to the height of the top of the surface layer. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 89) \underline {T10M} Temperature at 10 Meter Depth ($deg \hspace{.1cm} K$) } |
|
|
|
|
|
\noindent |
|
|
The temperature at the 10-meter depth is an interpolation between the surface potential |
|
|
temperature and the model lowest level potential temperature using the ratio of the |
|
|
non-dimensional temperature gradient at the two levels: |
|
|
\[ |
|
|
{\bf T10M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) = |
|
|
P^{\kappa}(\theta_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
|
|
(\theta_{sl} - \theta_{surf})) |
|
|
\] |
|
|
where: |
|
|
\[ |
|
|
\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
|
|
$sl$ refers to the height of the top of the surface layer. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 90) \underline {Q10M} Specific Humidity at 10 Meter Depth ($g/kg$) } |
|
|
|
|
|
\noindent |
|
|
The specific humidity at the 10-meter depth is an interpolation between the surface specific |
|
|
humidity and the model lowest level specific humidity using the ratio of the |
|
|
non-dimensional temperature gradient at the two levels: |
|
|
\[ |
|
|
{\bf Q10M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) = |
|
|
P^{\kappa}(q_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
|
|
(q_{sl} - q_{surf})) |
|
|
\] |
|
|
where: |
|
|
\[ |
|
|
q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } |
|
|
\] |
|
|
|
|
|
\noindent |
|
|
where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
|
|
$sl$ refers to the height of the top of the surface layer. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 91) \underline {DTRAIN} Cloud Detrainment Mass Flux ($kg/m^2$) } |
|
|
|
|
|
The amount of cloud mass moved per RAS timestep at the cloud detrainment level is written: |
|
|
\[ |
|
|
{\bf DTRAIN} = \eta_{r_D}m_B |
|
|
\] |
|
|
\noindent |
|
|
where $r_D$ is the detrainment level, |
|
|
$m_B$ is the cloud base mass flux, and $\eta$ |
|
|
is the entrainment, defined in Section \ref{sec:fizhi:mc}. |
|
|
\\ |
|
|
|
|
|
\noindent |
|
|
{\bf 92) \underline {QFILL} Filling of negative Specific Humidity ($g/kg/day$) } |
|
|
|
|
|
\noindent |
|
|
Due to computational errors associated with the numerical scheme used for |
|
|
the advection of moisture, negative values of specific humidity may be generated. The |
|
|
specific humidity is checked for negative values after every dynamics timestep. If negative |
|
|
values have been produced, a filling algorithm is invoked which redistributes moisture from |
|
|
below. Diagnostic {\bf QFILL} is equal to the net filling needed |
|
|
to eliminate negative specific humidity, scaled to a per-day rate: |
|
|
\[ |
|
|
{\bf QFILL} = q^{n+1}_{final} - q^{n+1}_{initial} |
|
|
\] |
|
|
where |
|
|
\[ |
|
|
q^{n+1} = (\pi q)^{n+1} / \pi^{n+1} |
|
|
\] |
|
|
|
|
| 524 |
\subsection{Dos and Donts} |
\subsection{Dos and Donts} |
| 525 |
|
|
| 526 |
\subsection{Diagnostics Reference} |
\subsection{Diagnostics Reference} |
Parent Directory
| 
Revision Log
| 
Revision Graph
| 
Patch