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1 edhill 1.2 \section{Diagnostics--A Flexible Infrastructure}
2     \label{sec:pkg:diagnostics}
3     \begin{rawhtml}
4     <!-- CMIREDIR:package_diagnostics: -->
5     \end{rawhtml}
6 molod 1.1
7     \subsection{Introduction}
8    
9     This section of the documentation describes the Diagnostics Utilities available within the GCM.
10     In addition to
11     a description on how to set and extract diagnostic quantities, this document also provides a
12     comprehensive list of all available diagnostic quantities and a short description of how they are
13     computed. It should be noted that this document is not intended to be a complete documentation
14     of the various packages used in the GCM, and the reader should
15     refer to original publications for further insight.
16    
17    
18     \subsection{Equations}
19     Not relevant.
20    
21     \subsection{Key Subroutines and Parameters}
22     \label{sec:diagnostics:diagover}
23    
24     A large selection of model diagnostics is available in the GCM. At the time of
25     this writing there are 92 different diagnostic quantities which can be enabled for an
26     experiment. As a matter of philosophy, no diagnostic is enabled as default, thus each user must
27     specify the exact diagnostic information required for an experiment. This is accomplished by
28     enabling the specific diagnostic of interest cataloged in the
29     Diagnostic Menu (see Section \ref{sec:diagnostics:menu}).
30     The Diagnostic Menu is a hard-wired enumeration of diagnostic quantities available within the
31     GCM. Diagnostics are internally referred to by their associated number in the Diagnostic
32     Menu. Once a diagnostic is enabled, the GCM will continually increment an array
33     specifically allocated for that diagnostic whenever the associated process for the diagnostic is
34     computed. Separate arrays are used both for the diagnostic quantity and its diagnostic counter
35     which records how many times each diagnostic quantity has been computed. In addition
36     special diagnostics, called
37     ``Counter Diagnostics'', records the frequency of diagnostic updates separately for each
38     model grid location.
39    
40     The diagnostics are computed at various times and places within the GCM.
41     Some diagnostics are computed on the geophysical A-grid (such as
42     those within the Physics routines), while others are computed on the C-grid
43     (those computed during the dynamics time-stepping). Some diagnostics are
44     scalars, while others are vectors. Each of these possibilities requires
45     separate tasks for A-grid to C-grid transformations and coordinate transformations. Due
46     to this complexity, and since the specific diagnostics enabled are User determined at the
47     time of the run,
48     a diagnostic parameter has been developed and implemented into the GCM, defined as GDIAG,
49     which contains information concerning various grid attributes of each diagnostic. The GDIAG
50     array is internally defined as a character*8 variable, and is equivalenced to
51     a character*1 "parse" array in output in order to extract the grid-attribute information.
52     The GDIAG array is described in Table \ref{tab:diagnostics:gdiag.tabl}.
53    
54     \begin{table}
55     \caption{Diagnostic Parsing Array}
56     \label{tab:diagnostics:gdiag.tabl}
57     \begin{center}
58     \begin{tabular}{ |c|c|l| }
59     \hline
60     \multicolumn{3}{|c|}{\bf Diagnostic Parsing Array} \\
61     \hline
62     \hline
63     Array & Value & Description \\
64     \hline
65     parse(1) & $\rightarrow$ S & Scalar Diagnostic \\
66     & $\rightarrow$ U & U-vector component Diagnostic \\
67     & $\rightarrow$ V & V-vector component Diagnostic \\ \hline
68     parse(2) & $\rightarrow$ U & C-Grid U-Point \\
69     & $\rightarrow$ V & C-Grid V-Point \\
70     & $\rightarrow$ M & C-Grid Mass Point \\
71     & $\rightarrow$ Z & C-Grid Vorticity Point \\ \hline
72     parse(3) & $\rightarrow$ R & Computed on the Rotated Grid \\
73     & $\rightarrow$ G & Computed on the Geophysical Grid \\ \hline
74     parse(4) & $\rightarrow$ P & Positive Definite Diagnostic \\ \hline
75     parse(5) & $\rightarrow$ C & Counter Diagnostic \\
76     & $\rightarrow$ D & Disabled Diagnostic for output \\ \hline
77     parse(6-8) & $\rightarrow$ C & 3-digit integer corresponding to \\
78     & & vector or counter component mate \\ \hline
79     \end{tabular}
80     \addcontentsline{lot}{section}{Table 3: Diagnostic Parsing Array}
81     \end{center}
82     \end{table}
83    
84     As an example, consider a diagnostic whose associated GDIAG parameter is equal
85     to ``UUR 002''. From GDIAG we can determine that this diagnostic is a
86     U-vector component located at the C-grid U-point within the Rotated framework.
87     Its corresponding V-component diagnostic is located in Diagnostic \# 002.
88    
89     In this way, each Diagnostic in the model has its attributes (ie. vector or scalar,
90     rotated or geophysical, A-Grid or C-grid, etc.) defined internally. The Output routines
91     use this information in order to determine
92     what type of rotations and/or transformations need to be performed. Thus, all Diagnostic
93     interpolations are done at the time of output rather than during each model dynamic step.
94     In this way the User now has more flexibility
95     in determining the type of gridded data which is output.
96    
97     There are several utilities within the GCM available to users to enable, disable,
98     clear, and retrieve model diagnostics, and may be called from any user-supplied application
99     and/or output routine. The available utilities and the CALL sequences are listed below.
100    
101    
102     {\bf SETDIAG}: This subroutine enables a diagnostic from the Diagnostic Menu, meaning that
103     space is allocated for the diagnostic and the
104     model routines will increment the diagnostic value during execution. This routine is useful when
105     called from either user application routines or user output routines, and is the underlying interface
106     between the user and the desired diagnostic. The diagnostic is referenced by its diagnostic
107     number from the menu, and its calling sequence is given by:
108    
109     \begin{tabbing}
110     XXXXXXXXX\=XXXXXX\= \kill
111     \> CALL SETDIAG (NUM) \\
112     \\
113     where \> NUM \>= Diagnostic number from menu \\
114     \end{tabbing}
115    
116    
117     {\bf GETDIAG}: This subroutine retrieves the value of a model diagnostic. This routine is
118     particulary useful when called from a user output routine, although it can be called from an
119     application routine as well. This routine returns the time-averaged value of the diagnostic by
120     dividing the current accumulated diagnostic value by its corresponding counter. This routine does
121     not change the value of the diagnostic itself, that is, it does not replace the diagnostic with its
122     time-average. The calling sequence for this routine is givin by:
123    
124     \begin{tabbing}
125     XXXXXXXXX\=XXXXXX\= \kill
126     \> CALL GETDIAG (LEV,NUM,QTMP,UNDEF) \\
127     \\
128     where \> LEV \>= Model Level at which the diagnostic is desired \\
129     \> NUM \>= Diagnostic number from menu \\
130     \> QTMP \>= Time-Averaged Diagnostic Output \\
131     \> UNDEF \>= Fill value to be used when diagnostic is undefined \\
132     \end{tabbing}
133    
134     {\bf CLRDIAG}: This subroutine initializes the values of model diagnostics to zero, and is
135     particularly useful when called from user output routines to re-initialize diagnostics during the
136     run. The calling sequence is:
137    
138    
139     \begin{tabbing}
140     XXXXXXXXX\=XXXXXX\= \kill
141     \> CALL CLRDIAG (NUM) \\
142     \\
143     where \> NUM \>= Diagnostic number from menu \\
144     \end{tabbing}
145    
146    
147    
148     {\bf ZAPDIAG}: This entry into subroutine SETDIAG disables model diagnostics, meaning that the
149     diagnostic is no longer available to the user. The memory previously allocated to the diagnostic
150     is released when ZAPDIAG is invoked. The calling sequence is given by:
151    
152    
153     \begin{tabbing}
154     XXXXXXXXX\=XXXXXX\= \kill
155     \> CALL ZAPDIAG (NUM) \\
156     \\
157     where \> NUM \>= Diagnostic number from menu \\
158     \end{tabbing}
159    
160     {\bf DIAGSIZE}: We end this section with a discussion on the manner in which computer memory
161     is allocated for diagnostics.
162     All GCM diagnostic quantities are stored in the single
163     diagnostic array QDIAG which is located in the DIAG COMMON, having the form:
164    
165     \begin{tabbing}
166     XXXXXXXXX\=XXXXXX\= \kill
167     \> COMMON /DIAG/ NDIAG\_MAX,QDIAG(IM,JM,1) \\
168     \\
169     \end{tabbing}
170    
171     where NDIAG\_MAX is an Integer variable which should be
172     set equal to the number of enabled diagnostics, and QDIAG is a three-dimensional
173     array. The first two-dimensions of QDIAG correspond to the horizontal dimension
174     of a given diagnostic, while the third dimension of QDIAG is used to identify
175     specific diagnostic types.
176     In order to minimize the maximum memory requirement used by the model,
177     the default GCM executable is compiled with room for only one horizontal
178     diagnostic array, as shown in the above example.
179     In order for the User to enable more than 1 two-dimensional diagnostic,
180     the size of the DIAG COMMON must be expanded to accomodate the desired diagnostics.
181     This can be accomplished by manually changing the parameter numdiags in the
182     file \filelink{FORWARD\_STEP}{pkg-diagnostics-diagnostics_SIZE.h}, or by allowing the
183     shell script (???????) to make this
184     change based on the choice of diagnostic output made in the namelist.
185    
186     \newpage
187    
188     \subsubsection{GCM Diagnostic Menu}
189     \label{sec:diagnostics:menu}
190    
191     \begin{tabular}{lllll}
192     \hline\hline
193     N & NAME & UNITS & LEVELS & DESCRIPTION \\
194     \hline
195    
196     &\\
197     1 & UFLUX & $Newton/m^2$ & 1
198     &\begin{minipage}[t]{3in}
199     {Surface U-Wind Stress on the atmosphere}
200     \end{minipage}\\
201     2 & VFLUX & $Newton/m^2$ & 1
202     &\begin{minipage}[t]{3in}
203     {Surface V-Wind Stress on the atmosphere}
204     \end{minipage}\\
205     3 & HFLUX & $Watts/m^2$ & 1
206     &\begin{minipage}[t]{3in}
207     {Surface Flux of Sensible Heat}
208     \end{minipage}\\
209     4 & EFLUX & $Watts/m^2$ & 1
210     &\begin{minipage}[t]{3in}
211     {Surface Flux of Latent Heat}
212     \end{minipage}\\
213     5 & QICE & $Watts/m^2$ & 1
214     &\begin{minipage}[t]{3in}
215     {Heat Conduction through Sea-Ice}
216     \end{minipage}\\
217     6 & RADLWG & $Watts/m^2$ & 1
218     &\begin{minipage}[t]{3in}
219     {Net upward LW flux at the ground}
220     \end{minipage}\\
221     7 & RADSWG & $Watts/m^2$ & 1
222     &\begin{minipage}[t]{3in}
223     {Net downward SW flux at the ground}
224     \end{minipage}\\
225     8 & RI & $dimensionless$ & Nrphys
226     &\begin{minipage}[t]{3in}
227     {Richardson Number}
228     \end{minipage}\\
229     9 & CT & $dimensionless$ & 1
230     &\begin{minipage}[t]{3in}
231     {Surface Drag coefficient for T and Q}
232     \end{minipage}\\
233     10 & CU & $dimensionless$ & 1
234     &\begin{minipage}[t]{3in}
235     {Surface Drag coefficient for U and V}
236     \end{minipage}\\
237     11 & ET & $m^2/sec$ & Nrphys
238     &\begin{minipage}[t]{3in}
239     {Diffusivity coefficient for T and Q}
240     \end{minipage}\\
241     12 & EU & $m^2/sec$ & Nrphys
242     &\begin{minipage}[t]{3in}
243     {Diffusivity coefficient for U and V}
244     \end{minipage}\\
245     13 & TURBU & $m/sec/day$ & Nrphys
246     &\begin{minipage}[t]{3in}
247     {U-Momentum Changes due to Turbulence}
248     \end{minipage}\\
249     14 & TURBV & $m/sec/day$ & Nrphys
250     &\begin{minipage}[t]{3in}
251     {V-Momentum Changes due to Turbulence}
252     \end{minipage}\\
253     15 & TURBT & $deg/day$ & Nrphys
254     &\begin{minipage}[t]{3in}
255     {Temperature Changes due to Turbulence}
256     \end{minipage}\\
257     16 & TURBQ & $g/kg/day$ & Nrphys
258     &\begin{minipage}[t]{3in}
259     {Specific Humidity Changes due to Turbulence}
260     \end{minipage}\\
261     17 & MOISTT & $deg/day$ & Nrphys
262     &\begin{minipage}[t]{3in}
263     {Temperature Changes due to Moist Processes}
264     \end{minipage}\\
265     18 & MOISTQ & $g/kg/day$ & Nrphys
266     &\begin{minipage}[t]{3in}
267     {Specific Humidity Changes due to Moist Processes}
268     \end{minipage}\\
269     19 & RADLW & $deg/day$ & Nrphys
270     &\begin{minipage}[t]{3in}
271     {Net Longwave heating rate for each level}
272     \end{minipage}\\
273     20 & RADSW & $deg/day$ & Nrphys
274     &\begin{minipage}[t]{3in}
275     {Net Shortwave heating rate for each level}
276     \end{minipage}\\
277     21 & PREACC & $mm/day$ & 1
278     &\begin{minipage}[t]{3in}
279     {Total Precipitation}
280     \end{minipage}\\
281     22 & PRECON & $mm/day$ & 1
282     &\begin{minipage}[t]{3in}
283     {Convective Precipitation}
284     \end{minipage}\\
285     23 & TUFLUX & $Newton/m^2$ & Nrphys
286     &\begin{minipage}[t]{3in}
287     {Turbulent Flux of U-Momentum}
288     \end{minipage}\\
289     24 & TVFLUX & $Newton/m^2$ & Nrphys
290     &\begin{minipage}[t]{3in}
291     {Turbulent Flux of V-Momentum}
292     \end{minipage}\\
293     25 & TTFLUX & $Watts/m^2$ & Nrphys
294     &\begin{minipage}[t]{3in}
295     {Turbulent Flux of Sensible Heat}
296     \end{minipage}\\
297     26 & TQFLUX & $Watts/m^2$ & Nrphys
298     &\begin{minipage}[t]{3in}
299     {Turbulent Flux of Latent Heat}
300     \end{minipage}\\
301     27 & CN & $dimensionless$ & 1
302     &\begin{minipage}[t]{3in}
303     {Neutral Drag Coefficient}
304     \end{minipage}\\
305     28 & WINDS & $m/sec$ & 1
306     &\begin{minipage}[t]{3in}
307     {Surface Wind Speed}
308     \end{minipage}\\
309     29 & DTSRF & $deg$ & 1
310     &\begin{minipage}[t]{3in}
311     {Air/Surface virtual temperature difference}
312     \end{minipage}\\
313     30 & TG & $deg$ & 1
314     &\begin{minipage}[t]{3in}
315     {Ground temperature}
316     \end{minipage}\\
317     31 & TS & $deg$ & 1
318     &\begin{minipage}[t]{3in}
319     {Surface air temperature (Adiabatic from lowest model layer)}
320     \end{minipage}\\
321     32 & DTG & $deg$ & 1
322     &\begin{minipage}[t]{3in}
323     {Ground temperature adjustment}
324     \end{minipage}\\
325    
326     \end{tabular}
327    
328     \newpage
329     \vspace*{\fill}
330     \begin{tabular}{lllll}
331     \hline\hline
332     N & NAME & UNITS & LEVELS & DESCRIPTION \\
333     \hline
334    
335     &\\
336     33 & QG & $g/kg$ & 1
337     &\begin{minipage}[t]{3in}
338     {Ground specific humidity}
339     \end{minipage}\\
340     34 & QS & $g/kg$ & 1
341     &\begin{minipage}[t]{3in}
342     {Saturation surface specific humidity}
343     \end{minipage}\\
344    
345     &\\
346     35 & TGRLW & $deg$ & 1
347     &\begin{minipage}[t]{3in}
348     {Instantaneous ground temperature used as input to the
349     Longwave radiation subroutine}
350     \end{minipage}\\
351     36 & ST4 & $Watts/m^2$ & 1
352     &\begin{minipage}[t]{3in}
353     {Upward Longwave flux at the ground ($\sigma T^4$)}
354     \end{minipage}\\
355     37 & OLR & $Watts/m^2$ & 1
356     &\begin{minipage}[t]{3in}
357     {Net upward Longwave flux at the top of the model}
358     \end{minipage}\\
359     38 & OLRCLR & $Watts/m^2$ & 1
360     &\begin{minipage}[t]{3in}
361     {Net upward clearsky Longwave flux at the top of the model}
362     \end{minipage}\\
363     39 & LWGCLR & $Watts/m^2$ & 1
364     &\begin{minipage}[t]{3in}
365     {Net upward clearsky Longwave flux at the ground}
366     \end{minipage}\\
367     40 & LWCLR & $deg/day$ & Nrphys
368     &\begin{minipage}[t]{3in}
369     {Net clearsky Longwave heating rate for each level}
370     \end{minipage}\\
371     41 & TLW & $deg$ & Nrphys
372     &\begin{minipage}[t]{3in}
373     {Instantaneous temperature used as input to the Longwave radiation
374     subroutine}
375     \end{minipage}\\
376     42 & SHLW & $g/g$ & Nrphys
377     &\begin{minipage}[t]{3in}
378     {Instantaneous specific humidity used as input to the Longwave radiation
379     subroutine}
380     \end{minipage}\\
381     43 & OZLW & $g/g$ & Nrphys
382     &\begin{minipage}[t]{3in}
383     {Instantaneous ozone used as input to the Longwave radiation
384     subroutine}
385     \end{minipage}\\
386     44 & CLMOLW & $0-1$ & Nrphys
387     &\begin{minipage}[t]{3in}
388     {Maximum overlap cloud fraction used in the Longwave radiation
389     subroutine}
390     \end{minipage}\\
391     45 & CLDTOT & $0-1$ & Nrphys
392     &\begin{minipage}[t]{3in}
393     {Total cloud fraction used in the Longwave and Shortwave radiation
394     subroutines}
395     \end{minipage}\\
396     46 & RADSWT & $Watts/m^2$ & 1
397     &\begin{minipage}[t]{3in}
398     {Incident Shortwave radiation at the top of the atmosphere}
399     \end{minipage}\\
400     47 & CLROSW & $0-1$ & Nrphys
401     &\begin{minipage}[t]{3in}
402     {Random overlap cloud fraction used in the shortwave radiation
403     subroutine}
404     \end{minipage}\\
405     48 & CLMOSW & $0-1$ & Nrphys
406     &\begin{minipage}[t]{3in}
407     {Maximum overlap cloud fraction used in the shortwave radiation
408     subroutine}
409     \end{minipage}\\
410     49 & EVAP & $mm/day$ & 1
411     &\begin{minipage}[t]{3in}
412     {Surface evaporation}
413     \end{minipage}\\
414     \end{tabular}
415     \vfill
416    
417     \newpage
418     \vspace*{\fill}
419     \begin{tabular}{lllll}
420     \hline\hline
421     N & NAME & UNITS & LEVELS & DESCRIPTION \\
422     \hline
423    
424     &\\
425     50 & DUDT & $m/sec/day$ & Nrphys
426     &\begin{minipage}[t]{3in}
427     {Total U-Wind tendency}
428     \end{minipage}\\
429     51 & DVDT & $m/sec/day$ & Nrphys
430     &\begin{minipage}[t]{3in}
431     {Total V-Wind tendency}
432     \end{minipage}\\
433     52 & DTDT & $deg/day$ & Nrphys
434     &\begin{minipage}[t]{3in}
435     {Total Temperature tendency}
436     \end{minipage}\\
437     53 & DQDT & $g/kg/day$ & Nrphys
438     &\begin{minipage}[t]{3in}
439     {Total Specific Humidity tendency}
440     \end{minipage}\\
441     54 & USTAR & $m/sec$ & 1
442     &\begin{minipage}[t]{3in}
443     {Surface USTAR wind}
444     \end{minipage}\\
445     55 & Z0 & $m$ & 1
446     &\begin{minipage}[t]{3in}
447     {Surface roughness}
448     \end{minipage}\\
449     56 & FRQTRB & $0-1$ & Nrphys-1
450     &\begin{minipage}[t]{3in}
451     {Frequency of Turbulence}
452     \end{minipage}\\
453     57 & PBL & $mb$ & 1
454     &\begin{minipage}[t]{3in}
455     {Planetary Boundary Layer depth}
456     \end{minipage}\\
457     58 & SWCLR & $deg/day$ & Nrphys
458     &\begin{minipage}[t]{3in}
459     {Net clearsky Shortwave heating rate for each level}
460     \end{minipage}\\
461     59 & OSR & $Watts/m^2$ & 1
462     &\begin{minipage}[t]{3in}
463     {Net downward Shortwave flux at the top of the model}
464     \end{minipage}\\
465     60 & OSRCLR & $Watts/m^2$ & 1
466     &\begin{minipage}[t]{3in}
467     {Net downward clearsky Shortwave flux at the top of the model}
468     \end{minipage}\\
469     61 & CLDMAS & $kg / m^2$ & Nrphys
470     &\begin{minipage}[t]{3in}
471     {Convective cloud mass flux}
472     \end{minipage}\\
473     62 & UAVE & $m/sec$ & Nrphys
474     &\begin{minipage}[t]{3in}
475     {Time-averaged $u-Wind$}
476     \end{minipage}\\
477     63 & VAVE & $m/sec$ & Nrphys
478     &\begin{minipage}[t]{3in}
479     {Time-averaged $v-Wind$}
480     \end{minipage}\\
481     64 & TAVE & $deg$ & Nrphys
482     &\begin{minipage}[t]{3in}
483     {Time-averaged $Temperature$}
484     \end{minipage}\\
485     65 & QAVE & $g/g$ & Nrphys
486     &\begin{minipage}[t]{3in}
487     {Time-averaged $Specific \, \, Humidity$}
488     \end{minipage}\\
489     66 & PAVE & $mb$ & 1
490     &\begin{minipage}[t]{3in}
491     {Time-averaged $p_{surf} - p_{top}$}
492     \end{minipage}\\
493     67 & QQAVE & $(m/sec)^2$ & Nrphys
494     &\begin{minipage}[t]{3in}
495     {Time-averaged $Turbulent Kinetic Energy$}
496     \end{minipage}\\
497     68 & SWGCLR & $Watts/m^2$ & 1
498     &\begin{minipage}[t]{3in}
499     {Net downward clearsky Shortwave flux at the ground}
500     \end{minipage}\\
501     69 & SDIAG1 & & 1
502     &\begin{minipage}[t]{3in}
503     {User-Defined Surface Diagnostic-1}
504     \end{minipage}\\
505     70 & SDIAG2 & & 1
506     &\begin{minipage}[t]{3in}
507     {User-Defined Surface Diagnostic-2}
508     \end{minipage}\\
509     71 & UDIAG1 & & Nrphys
510     &\begin{minipage}[t]{3in}
511     {User-Defined Upper-Air Diagnostic-1}
512     \end{minipage}\\
513     72 & UDIAG2 & & Nrphys
514     &\begin{minipage}[t]{3in}
515     {User-Defined Upper-Air Diagnostic-2}
516     \end{minipage}\\
517     73 & DIABU & $m/sec/day$ & Nrphys
518     &\begin{minipage}[t]{3in}
519     {Total Diabatic forcing on $u-Wind$}
520     \end{minipage}\\
521     74 & DIABV & $m/sec/day$ & Nrphys
522     &\begin{minipage}[t]{3in}
523     {Total Diabatic forcing on $v-Wind$}
524     \end{minipage}\\
525     75 & DIABT & $deg/day$ & Nrphys
526     &\begin{minipage}[t]{3in}
527     {Total Diabatic forcing on $Temperature$}
528     \end{minipage}\\
529     76 & DIABQ & $g/kg/day$ & Nrphys
530     &\begin{minipage}[t]{3in}
531     {Total Diabatic forcing on $Specific \, \, Humidity$}
532     \end{minipage}\\
533    
534     \end{tabular}
535     \vfill
536    
537     \newpage
538     \vspace*{\fill}
539     \begin{tabular}{lllll}
540     \hline\hline
541     N & NAME & UNITS & LEVELS & DESCRIPTION \\
542     \hline
543    
544     77 & VINTUQ & $m/sec \cdot g/kg$ & 1
545     &\begin{minipage}[t]{3in}
546     {Vertically integrated $u \, q$}
547     \end{minipage}\\
548     78 & VINTVQ & $m/sec \cdot g/kg$ & 1
549     &\begin{minipage}[t]{3in}
550     {Vertically integrated $v \, q$}
551     \end{minipage}\\
552     79 & VINTUT & $m/sec \cdot deg$ & 1
553     &\begin{minipage}[t]{3in}
554     {Vertically integrated $u \, T$}
555     \end{minipage}\\
556     80 & VINTVT & $m/sec \cdot deg$ & 1
557     &\begin{minipage}[t]{3in}
558     {Vertically integrated $v \, T$}
559     \end{minipage}\\
560     81 & CLDFRC & $0-1$ & 1
561     &\begin{minipage}[t]{3in}
562     {Total Cloud Fraction}
563     \end{minipage}\\
564     82 & QINT & $gm/cm^2$ & 1
565     &\begin{minipage}[t]{3in}
566     {Precipitable water}
567     \end{minipage}\\
568     83 & U2M & $m/sec$ & 1
569     &\begin{minipage}[t]{3in}
570     {U-Wind at 2 meters}
571     \end{minipage}\\
572     84 & V2M & $m/sec$ & 1
573     &\begin{minipage}[t]{3in}
574     {V-Wind at 2 meters}
575     \end{minipage}\\
576     85 & T2M & $deg$ & 1
577     &\begin{minipage}[t]{3in}
578     {Temperature at 2 meters}
579     \end{minipage}\\
580     86 & Q2M & $g/kg$ & 1
581     &\begin{minipage}[t]{3in}
582     {Specific Humidity at 2 meters}
583     \end{minipage}\\
584     87 & U10M & $m/sec$ & 1
585     &\begin{minipage}[t]{3in}
586     {U-Wind at 10 meters}
587     \end{minipage}\\
588     88 & V10M & $m/sec$ & 1
589     &\begin{minipage}[t]{3in}
590     {V-Wind at 10 meters}
591     \end{minipage}\\
592     89 & T10M & $deg$ & 1
593     &\begin{minipage}[t]{3in}
594     {Temperature at 10 meters}
595     \end{minipage}\\
596     90 & Q10M & $g/kg$ & 1
597     &\begin{minipage}[t]{3in}
598     {Specific Humidity at 10 meters}
599     \end{minipage}\\
600     91 & DTRAIN & $kg/m^2$ & Nrphys
601     &\begin{minipage}[t]{3in}
602     {Detrainment Cloud Mass Flux}
603     \end{minipage}\\
604     92 & QFILL & $g/kg/day$ & Nrphys
605     &\begin{minipage}[t]{3in}
606     {Filling of negative specific humidity}
607     \end{minipage}\\
608    
609     \end{tabular}
610     \vspace{1.5in}
611     \vfill
612    
613     \newpage
614    
615     \subsubsection{Diagnostic Description}
616    
617     In this section we list and describe the diagnostic quantities available within the
618     GCM. The diagnostics are listed in the order that they appear in the
619     Diagnostic Menu, Section \ref{sec:diagnostics:menu}.
620     In all cases, each diagnostic as currently archived on the output datasets
621     is time-averaged over its diagnostic output frequency:
622    
623     \[
624     {\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t)
625     \]
626     where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the
627     output frequency of the diagnositc, and $\Delta t$ is
628     the timestep over which the diagnostic is updated. For further information on how
629     to set the diagnostic output frequency {\bf NQDIAG}, please see Part III, A User's Guide.
630    
631     {\bf 1) \underline {UFLUX} Surface Zonal Wind Stress on the Atmosphere ($Newton/m^2$) }
632    
633     The zonal wind stress is the turbulent flux of zonal momentum from
634     the surface. See section 3.3 for a description of the surface layer parameterization.
635     \[
636     {\bf UFLUX} = - \rho C_D W_s u \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u
637     \]
638     where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface
639     drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum
640     (see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $u$ is
641     the zonal wind in the lowest model layer.
642     \\
643    
644    
645     {\bf 2) \underline {VFLUX} Surface Meridional Wind Stress on the Atmosphere ($Newton/m^2$) }
646    
647     The meridional wind stress is the turbulent flux of meridional momentum from
648     the surface. See section 3.3 for a description of the surface layer parameterization.
649     \[
650     {\bf VFLUX} = - \rho C_D W_s v \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u
651     \]
652     where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface
653     drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum
654     (see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $v$ is
655     the meridional wind in the lowest model layer.
656     \\
657    
658     {\bf 3) \underline {HFLUX} Surface Flux of Sensible Heat ($Watts/m^2$) }
659    
660     The turbulent flux of sensible heat from the surface to the atmosphere is a function of the
661     gradient of virtual potential temperature and the eddy exchange coefficient:
662     \[
663     {\bf HFLUX} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{surface} - \theta_{Nrphys})
664     \hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t
665     \]
666     where $\rho$ = the atmospheric density at the surface, $c_{p}$ is the specific
667     heat of air, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the
668     magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient
669     for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient
670     for heat and moisture (see diagnostic number 9), and $\theta$ is the potential temperature
671     at the surface and at the bottom model level.
672     \\
673    
674    
675     {\bf 4) \underline {EFLUX} Surface Flux of Latent Heat ($Watts/m^2$) }
676    
677     The turbulent flux of latent heat from the surface to the atmosphere is a function of the
678     gradient of moisture, the potential evapotranspiration fraction and the eddy exchange coefficient:
679     \[
680     {\bf EFLUX} = \rho \beta L C_{H} W_s (q_{surface} - q_{Nrphys})
681     \hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t
682     \]
683     where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of
684     the potential evapotranspiration actually evaporated, L is the latent
685     heat of evaporation, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the
686     magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient
687     for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient
688     for heat and moisture (see diagnostic number 9), and $q_{surface}$ and $q_{Nrphys}$ are the specific
689     humidity at the surface and at the bottom model level, respectively.
690     \\
691    
692     {\bf 5) \underline {QICE} Heat Conduction Through Sea Ice ($Watts/m^2$) }
693    
694     Over sea ice there is an additional source of energy at the surface due to the heat
695     conduction from the relatively warm ocean through the sea ice. The heat conduction
696     through sea ice represents an additional energy source term for the ground temperature equation.
697    
698     \[
699     {\bf QICE} = {C_{ti} \over {H_i}} (T_i-T_g)
700     \]
701    
702     where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to
703     be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and
704     $T_g$ is the temperature of the sea ice.
705    
706     NOTE: QICE is not available through model version 5.3, but is available in subsequent versions.
707     \\
708    
709    
710     {\bf 6) \underline {RADLWG} Net upward Longwave Flux at the surface ($Watts/m^2$)}
711    
712     \begin{eqnarray*}
713     {\bf RADLWG} & = & F_{LW,Nrphys+1}^{Net} \\
714     & = & F_{LW,Nrphys+1}^\uparrow - F_{LW,Nrphys+1}^\downarrow
715     \end{eqnarray*}
716     \\
717     where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$.
718     $F_{LW}^\uparrow$ is
719     the upward Longwave flux and $F_{LW}^\downarrow$ is the downward Longwave flux.
720     \\
721    
722     {\bf 7) \underline {RADSWG} Net downard shortwave Flux at the surface ($Watts/m^2$)}
723    
724     \begin{eqnarray*}
725     {\bf RADSWG} & = & F_{SW,Nrphys+1}^{Net} \\
726     & = & F_{SW,Nrphys+1}^\downarrow - F_{SW,Nrphys+1}^\uparrow
727     \end{eqnarray*}
728     \\
729     where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$.
730     $F_{SW}^\downarrow$ is
731     the downward Shortwave flux and $F_{SW}^\uparrow$ is the upward Shortwave flux.
732     \\
733    
734    
735     \noindent
736     {\bf 8) \underline {RI} Richardson Number} ($dimensionless$)
737    
738     \noindent
739     The non-dimensional stability indicator is the ratio of the buoyancy to the shear:
740     \[
741     {\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } }
742     = { {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } }
743     \]
744     \\
745     where we used the hydrostatic equation:
746     \[
747     {\pp{\Phi}{P^ \kappa}} = c_p \theta_v
748     \]
749     Negative values indicate unstable buoyancy {\bf{AND}} shear, small positive values ($<0.4$)
750     indicate dominantly unstable shear, and large positive values indicate dominantly stable
751     stratification.
752     \\
753    
754     \noindent
755     {\bf 9) \underline {CT} Surface Exchange Coefficient for Temperature and Moisture ($dimensionless$) }
756    
757     \noindent
758     The surface exchange coefficient is obtained from the similarity functions for the stability
759     dependant flux profile relationships:
760     \[
761     {\bf CT} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} =
762     -{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} =
763     { k \over { (\psi_{h} + \psi_{g}) } }
764     \]
765     where $\psi_h$ is the surface layer non-dimensional temperature change and $\psi_g$ is the
766     viscous sublayer non-dimensional temperature or moisture change:
767     \[
768     \psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} \hspace{1cm} and
769     \hspace{1cm} \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} }
770     (h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2}
771     \]
772     and:
773     $h_{0} = 30z_{0}$ with a maximum value over land of 0.01
774    
775     \noindent
776     $\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of
777     the temperature and moisture gradients, specified differently for stable and unstable
778     layers according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the
779     non-dimensional stability parameter, Pr is the Prandtl number for air, $\nu$ is the molecular
780     viscosity, $z_{0}$ is the surface roughness length, $u_*$ is the surface stress velocity
781     (see diagnostic number 67), and the subscript ref refers to a reference value.
782     \\
783    
784     \noindent
785     {\bf 10) \underline {CU} Surface Exchange Coefficient for Momentum ($dimensionless$) }
786    
787     \noindent
788     The surface exchange coefficient is obtained from the similarity functions for the stability
789     dependant flux profile relationships:
790     \[
791     {\bf CU} = {u_* \over W_s} = { k \over \psi_{m} }
792     \]
793     where $\psi_m$ is the surface layer non-dimensional wind shear:
794     \[
795     \psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta}
796     \]
797     \noindent
798     $\phi_m$ is the similarity function of $\zeta$, which expresses the stability dependance of
799     the temperature and moisture gradients, specified differently for stable and unstable layers
800     according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the
801     non-dimensional stability parameter, $u_*$ is the surface stress velocity
802     (see diagnostic number 67), and $W_s$ is the magnitude of the surface layer wind.
803     \\
804    
805     \noindent
806     {\bf 11) \underline {ET} Diffusivity Coefficient for Temperature and Moisture ($m^2/sec$) }
807    
808     \noindent
809     In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat or
810     moisture flux for the atmosphere above the surface layer can be expressed as a turbulent
811     diffusion coefficient $K_h$ times the negative of the gradient of potential temperature
812     or moisture. In the Helfand and Labraga (1988) adaptation of this closure, $K_h$
813     takes the form:
814     \[
815     {\bf ET} = K_h = -{( {\overline{w^{\prime}\theta_v^{\prime}}}) \over {\pp{\theta_v}{z}} }
816     = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) & \mbox{decaying turbulence}
817     \\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right.
818     \]
819     where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm}
820     energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model,
821     which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer
822     depth,
823     $S_H$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and
824     wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium
825     dimensionless buoyancy and wind shear
826     parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$,
827     are functions of the Richardson number.
828    
829     \noindent
830     For the detailed equations and derivations of the modified level 2.5 closure scheme,
831     see Helfand and Labraga, 1988.
832    
833     \noindent
834     In the surface layer, ${\bf {ET}}$ is the exchange coefficient for heat and moisture,
835     in units of $m/sec$, given by:
836     \[
837     {\bf ET_{Nrphys}} = C_t * u_* = C_H W_s
838     \]
839     \noindent
840     where $C_t$ is the dimensionless exchange coefficient for heat and moisture from the
841     surface layer similarity functions (see diagnostic number 9), $u_*$ is the surface
842     friction velocity (see diagnostic number 67), $C_H$ is the heat transfer coefficient,
843     and $W_s$ is the magnitude of the surface layer wind.
844     \\
845    
846     \noindent
847     {\bf 12) \underline {EU} Diffusivity Coefficient for Momentum ($m^2/sec$) }
848    
849     \noindent
850     In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat
851     momentum flux for the atmosphere above the surface layer can be expressed as a turbulent
852     diffusion coefficient $K_m$ times the negative of the gradient of the u-wind.
853     In the Helfand and Labraga (1988) adaptation of this closure, $K_m$
854     takes the form:
855     \[
856     {\bf EU} = K_m = -{( {\overline{u^{\prime}w^{\prime}}}) \over {\pp{U}{z}} }
857     = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) & \mbox{decaying turbulence}
858     \\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right.
859     \]
860     \noindent
861     where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm}
862     energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model,
863     which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer
864     depth,
865     $S_M$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and
866     wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium
867     dimensionless buoyancy and wind shear
868     parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$,
869     are functions of the Richardson number.
870    
871     \noindent
872     For the detailed equations and derivations of the modified level 2.5 closure scheme,
873     see Helfand and Labraga, 1988.
874    
875     \noindent
876     In the surface layer, ${\bf {EU}}$ is the exchange coefficient for momentum,
877     in units of $m/sec$, given by:
878     \[
879     {\bf EU_{Nrphys}} = C_u * u_* = C_D W_s
880     \]
881     \noindent
882     where $C_u$ is the dimensionless exchange coefficient for momentum from the surface layer
883     similarity functions (see diagnostic number 10), $u_*$ is the surface friction velocity
884     (see diagnostic number 67), $C_D$ is the surface drag coefficient, and $W_s$ is the
885     magnitude of the surface layer wind.
886     \\
887    
888     \noindent
889     {\bf 13) \underline {TURBU} Zonal U-Momentum changes due to Turbulence ($m/sec/day$) }
890    
891     \noindent
892     The tendency of U-Momentum due to turbulence is written:
893     \[
894     {\bf TURBU} = {\pp{u}{t}}_{turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})}
895     = {\pp{}{z} }{(K_m \pp{u}{z})}
896     \]
897    
898     \noindent
899     The Helfand and Labraga level 2.5 scheme models the turbulent
900     flux of u-momentum in terms of $K_m$, and the equation has the form of a diffusion
901     equation.
902    
903     \noindent
904     {\bf 14) \underline {TURBV} Meridional V-Momentum changes due to Turbulence ($m/sec/day$) }
905    
906     \noindent
907     The tendency of V-Momentum due to turbulence is written:
908     \[
909     {\bf TURBV} = {\pp{v}{t}}_{turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})}
910     = {\pp{}{z} }{(K_m \pp{v}{z})}
911     \]
912    
913     \noindent
914     The Helfand and Labraga level 2.5 scheme models the turbulent
915     flux of v-momentum in terms of $K_m$, and the equation has the form of a diffusion
916     equation.
917     \\
918    
919     \noindent
920     {\bf 15) \underline {TURBT} Temperature changes due to Turbulence ($deg/day$) }
921    
922     \noindent
923     The tendency of temperature due to turbulence is written:
924     \[
925     {\bf TURBT} = {\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{turb} =
926     P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})}
927     = P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})}
928     \]
929    
930     \noindent
931     The Helfand and Labraga level 2.5 scheme models the turbulent
932     flux of temperature in terms of $K_h$, and the equation has the form of a diffusion
933     equation.
934     \\
935    
936     \noindent
937     {\bf 16) \underline {TURBQ} Specific Humidity changes due to Turbulence ($g/kg/day$) }
938    
939     \noindent
940     The tendency of specific humidity due to turbulence is written:
941     \[
942     {\bf TURBQ} = {\pp{q}{t}}_{turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})}
943     = {\pp{}{z} }{(K_h \pp{q}{z})}
944     \]
945    
946     \noindent
947     The Helfand and Labraga level 2.5 scheme models the turbulent
948     flux of temperature in terms of $K_h$, and the equation has the form of a diffusion
949     equation.
950     \\
951    
952     \noindent
953     {\bf 17) \underline {MOISTT} Temperature Changes Due to Moist Processes ($deg/day$) }
954    
955     \noindent
956     \[
957     {\bf MOISTT} = \left. {\pp{T}{t}}\right|_{c} + \left. {\pp{T}{t}} \right|_{ls}
958     \]
959     where:
960     \[
961     \left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over c_p} \Gamma_s \right)_i
962     \hspace{.4cm} and
963     \hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = {L \over c_p } (q^*-q)
964     \]
965     and
966     \[
967     \Gamma_s = g \eta \pp{s}{p}
968     \]
969    
970     \noindent
971     The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale
972     precipitation processes, or supersaturation rain.
973     The summation refers to contributions from each cloud type called by RAS.
974     The dry static energy is given
975     as $s$, the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is
976     given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc},
977     the description of the convective parameterization. The fractional adjustment, or relaxation
978     parameter, for each cloud type is given as $\alpha$, while
979     $R$ is the rain re-evaporation adjustment.
980     \\
981    
982     \noindent
983     {\bf 18) \underline {MOISTQ} Specific Humidity Changes Due to Moist Processes ($g/kg/day$) }
984    
985     \noindent
986     \[
987     {\bf MOISTQ} = \left. {\pp{q}{t}}\right|_{c} + \left. {\pp{q}{t}} \right|_{ls}
988     \]
989     where:
990     \[
991     \left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over {L}}(\Gamma_h-\Gamma_s) \right)_i
992     \hspace{.4cm} and
993     \hspace{.4cm} \left.{\pp{q}{t}}\right|_{ls} = (q^*-q)
994     \]
995     and
996     \[
997     \Gamma_s = g \eta \pp{s}{p}\hspace{.4cm} and \hspace{.4cm}\Gamma_h = g \eta \pp{h}{p}
998     \]
999     \noindent
1000     The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale
1001     precipitation processes, or supersaturation rain.
1002     The summation refers to contributions from each cloud type called by RAS.
1003     The dry static energy is given as $s$,
1004     the moist static energy is given as $h$,
1005     the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is
1006     given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc},
1007     the description of the convective parameterization. The fractional adjustment, or relaxation
1008     parameter, for each cloud type is given as $\alpha$, while
1009     $R$ is the rain re-evaporation adjustment.
1010     \\
1011    
1012     \noindent
1013     {\bf 19) \underline {RADLW} Heating Rate due to Longwave Radiation ($deg/day$) }
1014    
1015     \noindent
1016     The net longwave heating rate is calculated as the vertical divergence of the
1017     net terrestrial radiative fluxes.
1018     Both the clear-sky and cloudy-sky longwave fluxes are computed within the
1019     longwave routine.
1020     The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first.
1021     For a given cloud fraction,
1022     the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$
1023     to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$,
1024     for the upward and downward radiative fluxes.
1025     (see Section \ref{sec:fizhi:radcloud}).
1026     The cloudy-sky flux is then obtained as:
1027    
1028     \noindent
1029     \[
1030     F_{LW} = C(p,p') \cdot F^{clearsky}_{LW},
1031     \]
1032    
1033     \noindent
1034     Finally, the net longwave heating rate is calculated as the vertical divergence of the
1035     net terrestrial radiative fluxes:
1036     \[
1037     \pp{\rho c_p T}{t} = - {\partial \over \partial z} F_{LW}^{NET} ,
1038     \]
1039     or
1040     \[
1041     {\bf RADLW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F_{LW}^{NET} .
1042     \]
1043    
1044     \noindent
1045     where $g$ is the accelation due to gravity,
1046     $c_p$ is the heat capacity of air at constant pressure,
1047     and
1048     \[
1049     F_{LW}^{NET} = F_{LW}^\uparrow - F_{LW}^\downarrow
1050     \]
1051     \\
1052    
1053    
1054     \noindent
1055     {\bf 20) \underline {RADSW} Heating Rate due to Shortwave Radiation ($deg/day$) }
1056    
1057     \noindent
1058     The net Shortwave heating rate is calculated as the vertical divergence of the
1059     net solar radiative fluxes.
1060     The clear-sky and cloudy-sky shortwave fluxes are calculated separately.
1061     For the clear-sky case, the shortwave fluxes and heating rates are computed with
1062     both CLMO (maximum overlap cloud fraction) and
1063     CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}).
1064     The shortwave routine is then called a second time, for the cloudy-sky case, with the
1065     true time-averaged cloud fractions CLMO
1066     and CLRO being used. In all cases, a normalized incident shortwave flux is used as
1067     input at the top of the atmosphere.
1068    
1069     \noindent
1070     The heating rate due to Shortwave Radiation under cloudy skies is defined as:
1071     \[
1072     \pp{\rho c_p T}{t} = - {\partial \over \partial z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT},
1073     \]
1074     or
1075     \[
1076     {\bf RADSW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} .
1077     \]
1078    
1079     \noindent
1080     where $g$ is the accelation due to gravity,
1081     $c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident
1082     shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and
1083     \[
1084     F(cloudy)_{SW}^{Net} = F(cloudy)_{SW}^\uparrow - F(cloudy)_{SW}^\downarrow
1085     \]
1086     \\
1087    
1088     \noindent
1089     {\bf 21) \underline {PREACC} Total (Large-scale + Convective) Accumulated Precipition ($mm/day$) }
1090    
1091     \noindent
1092     For a change in specific humidity due to moist processes, $\Delta q_{moist}$,
1093     the vertical integral or total precipitable amount is given by:
1094     \[
1095     {\bf PREACC} = \int_{surf}^{top} \rho \Delta q_{moist} dz = - \int_{surf}^{top} \Delta q_{moist}
1096     {dp \over g} = {1 \over g} \int_0^1 \Delta q_{moist} dp
1097     \]
1098     \\
1099    
1100     \noindent
1101     A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes
1102     time step, scaled to $mm/day$.
1103     \\
1104    
1105     \noindent
1106     {\bf 22) \underline {PRECON} Convective Precipition ($mm/day$) }
1107    
1108     \noindent
1109     For a change in specific humidity due to sub-grid scale cumulus convective processes, $\Delta q_{cum}$,
1110     the vertical integral or total precipitable amount is given by:
1111     \[
1112     {\bf PRECON} = \int_{surf}^{top} \rho \Delta q_{cum} dz = - \int_{surf}^{top} \Delta q_{cum}
1113     {dp \over g} = {1 \over g} \int_0^1 \Delta q_{cum} dp
1114     \]
1115     \\
1116    
1117     \noindent
1118     A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes
1119     time step, scaled to $mm/day$.
1120     \\
1121    
1122     \noindent
1123     {\bf 23) \underline {TUFLUX} Turbulent Flux of U-Momentum ($Newton/m^2$) }
1124    
1125     \noindent
1126     The turbulent flux of u-momentum is calculated for $diagnostic \hspace{.2cm} purposes
1127     \hspace{.2cm} only$ from the eddy coefficient for momentum:
1128    
1129     \[
1130     {\bf TUFLUX} = {\rho } {(\overline{u^{\prime}w^{\prime}})} =
1131     {\rho } {(- K_m \pp{U}{z})}
1132     \]
1133    
1134     \noindent
1135     where $\rho$ is the air density, and $K_m$ is the eddy coefficient.
1136     \\
1137    
1138     \noindent
1139     {\bf 24) \underline {TVFLUX} Turbulent Flux of V-Momentum ($Newton/m^2$) }
1140    
1141     \noindent
1142     The turbulent flux of v-momentum is calculated for $diagnostic \hspace{.2cm} purposes
1143     \hspace{.2cm} only$ from the eddy coefficient for momentum:
1144    
1145     \[
1146     {\bf TVFLUX} = {\rho } {(\overline{v^{\prime}w^{\prime}})} =
1147     {\rho } {(- K_m \pp{V}{z})}
1148     \]
1149    
1150     \noindent
1151     where $\rho$ is the air density, and $K_m$ is the eddy coefficient.
1152     \\
1153    
1154    
1155     \noindent
1156     {\bf 25) \underline {TTFLUX} Turbulent Flux of Sensible Heat ($Watts/m^2$) }
1157    
1158     \noindent
1159     The turbulent flux of sensible heat is calculated for $diagnostic \hspace{.2cm} purposes
1160     \hspace{.2cm} only$ from the eddy coefficient for heat and moisture:
1161    
1162     \noindent
1163     \[
1164     {\bf TTFLUX} = c_p {\rho }
1165     P^{\kappa}{(\overline{w^{\prime}\theta^{\prime}})}
1166     = c_p {\rho } P^{\kappa}{(- K_h \pp{\theta_v}{z})}
1167     \]
1168    
1169     \noindent
1170     where $\rho$ is the air density, and $K_h$ is the eddy coefficient.
1171     \\
1172    
1173    
1174     \noindent
1175     {\bf 26) \underline {TQFLUX} Turbulent Flux of Latent Heat ($Watts/m^2$) }
1176    
1177     \noindent
1178     The turbulent flux of latent heat is calculated for $diagnostic \hspace{.2cm} purposes
1179     \hspace{.2cm} only$ from the eddy coefficient for heat and moisture:
1180    
1181     \noindent
1182     \[
1183     {\bf TQFLUX} = {L {\rho } (\overline{w^{\prime}q^{\prime}})} =
1184     {L {\rho }(- K_h \pp{q}{z})}
1185     \]
1186    
1187     \noindent
1188     where $\rho$ is the air density, and $K_h$ is the eddy coefficient.
1189     \\
1190    
1191    
1192     \noindent
1193     {\bf 27) \underline {CN} Neutral Drag Coefficient ($dimensionless$) }
1194    
1195     \noindent
1196     The drag coefficient for momentum obtained by assuming a neutrally stable surface layer:
1197     \[
1198     {\bf CN} = { k \over { \ln({h \over {z_0}})} }
1199     \]
1200    
1201     \noindent
1202     where $k$ is the Von Karman constant, $h$ is the height of the surface layer, and
1203     $z_0$ is the surface roughness.
1204    
1205     \noindent
1206     NOTE: CN is not available through model version 5.3, but is available in subsequent
1207     versions.
1208     \\
1209    
1210     \noindent
1211     {\bf 28) \underline {WINDS} Surface Wind Speed ($meter/sec$) }
1212    
1213     \noindent
1214     The surface wind speed is calculated for the last internal turbulence time step:
1215     \[
1216     {\bf WINDS} = \sqrt{u_{Nrphys}^2 + v_{Nrphys}^2}
1217     \]
1218    
1219     \noindent
1220     where the subscript $Nrphys$ refers to the lowest model level.
1221     \\
1222    
1223     \noindent
1224     {\bf 29) \underline {DTSRF} Air/Surface Virtual Temperature Difference ($deg \hspace{.1cm} K$) }
1225    
1226     \noindent
1227     The air/surface virtual temperature difference measures the stability of the surface layer:
1228     \[
1229     {\bf DTSRF} = (\theta_{v{Nrphys+1}} - \theta{v_{Nrphys}}) P^{\kappa}_{surf}
1230     \]
1231     \noindent
1232     where
1233     \[
1234     \theta_{v{Nrphys+1}} = { T_g \over {P^{\kappa}_{surf}} } (1 + .609 q_{Nrphys+1}) \hspace{1cm}
1235     and \hspace{1cm} q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys})
1236     \]
1237    
1238     \noindent
1239     $\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans),
1240     $q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature
1241     and surface pressure, level $Nrphys$ refers to the lowest model level and level $Nrphys+1$
1242     refers to the surface.
1243     \\
1244    
1245    
1246     \noindent
1247     {\bf 30) \underline {TG} Ground Temperature ($deg \hspace{.1cm} K$) }
1248    
1249     \noindent
1250     The ground temperature equation is solved as part of the turbulence package
1251     using a backward implicit time differencing scheme:
1252     \[
1253     {\bf TG} \hspace{.1cm} is \hspace{.1cm} obtained \hspace{.1cm} from: \hspace{.1cm}
1254     C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{ice} - H - LE
1255     \]
1256    
1257     \noindent
1258     where $R_{sw}$ is the net surface downward shortwave radiative flux, $R_{lw}$ is the
1259     net surface upward longwave radiative flux, $Q_{ice}$ is the heat conduction through
1260     sea ice, $H$ is the upward sensible heat flux, $LE$ is the upward latent heat
1261     flux, and $C_g$ is the total heat capacity of the ground.
1262     $C_g$ is obtained by solving a heat diffusion equation
1263     for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by:
1264     \[
1265     C_g = \sqrt{ {\lambda C_s \over {2 \omega} } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3}
1266     { 86400. \over {2 \pi} } } \, \, .
1267     \]
1268     \noindent
1269     Here, the thermal conductivity, $\lambda$, is equal to $2x10^{-3}$ ${ly\over{ sec}}
1270     {cm \over {^oK}}$,
1271     the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided
1272     by $2 \pi$ $radians/
1273     day$, and the expression for $C_s$, the heat capacity per unit volume at the surface,
1274     is a function of the ground wetness, $W$.
1275     \\
1276    
1277     \noindent
1278     {\bf 31) \underline {TS} Surface Temperature ($deg \hspace{.1cm} K$) }
1279    
1280     \noindent
1281     The surface temperature estimate is made by assuming that the model's lowest
1282     layer is well-mixed, and therefore that $\theta$ is constant in that layer.
1283     The surface temperature is therefore:
1284     \[
1285     {\bf TS} = \theta_{Nrphys} P^{\kappa}_{surf}
1286     \]
1287     \\
1288    
1289     \noindent
1290     {\bf 32) \underline {DTG} Surface Temperature Adjustment ($deg \hspace{.1cm} K$) }
1291    
1292     \noindent
1293     The change in surface temperature from one turbulence time step to the next, solved
1294     using the Ground Temperature Equation (see diagnostic number 30) is calculated:
1295     \[
1296     {\bf DTG} = {T_g}^{n} - {T_g}^{n-1}
1297     \]
1298    
1299     \noindent
1300     where superscript $n$ refers to the new, updated time level, and the superscript $n-1$
1301     refers to the value at the previous turbulence time level.
1302     \\
1303    
1304     \noindent
1305     {\bf 33) \underline {QG} Ground Specific Humidity ($g/kg$) }
1306    
1307     \noindent
1308     The ground specific humidity is obtained by interpolating between the specific
1309     humidity at the lowest model level and the specific humidity of a saturated ground.
1310     The interpolation is performed using the potential evapotranspiration function:
1311     \[
1312     {\bf QG} = q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys})
1313     \]
1314    
1315     \noindent
1316     where $\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans),
1317     and $q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature and surface
1318     pressure.
1319     \\
1320    
1321     \noindent
1322     {\bf 34) \underline {QS} Saturation Surface Specific Humidity ($g/kg$) }
1323    
1324     \noindent
1325     The surface saturation specific humidity is the saturation specific humidity at
1326     the ground temprature and surface pressure:
1327     \[
1328     {\bf QS} = q^*(T_g,P_s)
1329     \]
1330     \\
1331    
1332     \noindent
1333     {\bf 35) \underline {TGRLW} Instantaneous ground temperature used as input to the Longwave
1334     radiation subroutine (deg)}
1335     \[
1336     {\bf TGRLW} = T_g(\lambda , \phi ,n)
1337     \]
1338     \noindent
1339     where $T_g$ is the model ground temperature at the current time step $n$.
1340     \\
1341    
1342    
1343     \noindent
1344     {\bf 36) \underline {ST4} Upward Longwave flux at the surface ($Watts/m^2$) }
1345     \[
1346     {\bf ST4} = \sigma T^4
1347     \]
1348     \noindent
1349     where $\sigma$ is the Stefan-Boltzmann constant and T is the temperature.
1350     \\
1351    
1352     \noindent
1353     {\bf 37) \underline {OLR} Net upward Longwave flux at $p=p_{top}$ ($Watts/m^2$) }
1354     \[
1355     {\bf OLR} = F_{LW,top}^{NET}
1356     \]
1357     \noindent
1358     where top indicates the top of the first model layer.
1359     In the GCM, $p_{top}$ = 0.0 mb.
1360     \\
1361    
1362    
1363     \noindent
1364     {\bf 38) \underline {OLRCLR} Net upward clearsky Longwave flux at $p=p_{top}$ ($Watts/m^2$) }
1365     \[
1366     {\bf OLRCLR} = F(clearsky)_{LW,top}^{NET}
1367     \]
1368     \noindent
1369     where top indicates the top of the first model layer.
1370     In the GCM, $p_{top}$ = 0.0 mb.
1371     \\
1372    
1373     \noindent
1374     {\bf 39) \underline {LWGCLR} Net upward clearsky Longwave flux at the surface ($Watts/m^2$) }
1375    
1376     \noindent
1377     \begin{eqnarray*}
1378     {\bf LWGCLR} & = & F(clearsky)_{LW,Nrphys+1}^{Net} \\
1379     & = & F(clearsky)_{LW,Nrphys+1}^\uparrow - F(clearsky)_{LW,Nrphys+1}^\downarrow
1380     \end{eqnarray*}
1381     where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$.
1382     $F(clearsky)_{LW}^\uparrow$ is
1383     the upward clearsky Longwave flux and the $F(clearsky)_{LW}^\downarrow$ is the downward clearsky Longwave flux.
1384     \\
1385    
1386     \noindent
1387     {\bf 40) \underline {LWCLR} Heating Rate due to Clearsky Longwave Radiation ($deg/day$) }
1388    
1389     \noindent
1390     The net longwave heating rate is calculated as the vertical divergence of the
1391     net terrestrial radiative fluxes.
1392     Both the clear-sky and cloudy-sky longwave fluxes are computed within the
1393     longwave routine.
1394     The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first.
1395     For a given cloud fraction,
1396     the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$
1397     to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$,
1398     for the upward and downward radiative fluxes.
1399     (see Section \ref{sec:fizhi:radcloud}).
1400     The cloudy-sky flux is then obtained as:
1401    
1402     \noindent
1403     \[
1404     F_{LW} = C(p,p') \cdot F^{clearsky}_{LW},
1405     \]
1406    
1407     \noindent
1408     Thus, {\bf LWCLR} is defined as the net longwave heating rate due to the
1409     vertical divergence of the
1410     clear-sky longwave radiative flux:
1411     \[
1412     \pp{\rho c_p T}{t}_{clearsky} = - {\partial \over \partial z} F(clearsky)_{LW}^{NET} ,
1413     \]
1414     or
1415     \[
1416     {\bf LWCLR} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(clearsky)_{LW}^{NET} .
1417     \]
1418    
1419     \noindent
1420     where $g$ is the accelation due to gravity,
1421     $c_p$ is the heat capacity of air at constant pressure,
1422     and
1423     \[
1424     F(clearsky)_{LW}^{Net} = F(clearsky)_{LW}^\uparrow - F(clearsky)_{LW}^\downarrow
1425     \]
1426     \\
1427    
1428    
1429     \noindent
1430     {\bf 41) \underline {TLW} Instantaneous temperature used as input to the Longwave
1431     radiation subroutine (deg)}
1432     \[
1433     {\bf TLW} = T(\lambda , \phi ,level, n)
1434     \]
1435     \noindent
1436     where $T$ is the model temperature at the current time step $n$.
1437     \\
1438    
1439    
1440     \noindent
1441     {\bf 42) \underline {SHLW} Instantaneous specific humidity used as input to
1442     the Longwave radiation subroutine (kg/kg)}
1443     \[
1444     {\bf SHLW} = q(\lambda , \phi , level , n)
1445     \]
1446     \noindent
1447     where $q$ is the model specific humidity at the current time step $n$.
1448     \\
1449    
1450    
1451     \noindent
1452     {\bf 43) \underline {OZLW} Instantaneous ozone used as input to
1453     the Longwave radiation subroutine (kg/kg)}
1454     \[
1455     {\bf OZLW} = {\rm OZ}(\lambda , \phi , level , n)
1456     \]
1457     \noindent
1458     where $\rm OZ$ is the interpolated ozone data set from the climatological monthly
1459     mean zonally averaged ozone data set.
1460     \\
1461    
1462    
1463     \noindent
1464     {\bf 44) \underline {CLMOLW} Maximum Overlap cloud fraction used in LW Radiation ($0-1$) }
1465    
1466     \noindent
1467     {\bf CLMOLW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed
1468     Arakawa/Schubert Convection scheme and will be used in the Longwave Radiation algorithm. These are
1469     convective clouds whose radiative characteristics are assumed to be correlated in the vertical.
1470     For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.
1471     \[
1472     {\bf CLMOLW} = CLMO_{RAS,LW}(\lambda, \phi, level )
1473     \]
1474     \\
1475    
1476    
1477     {\bf 45) \underline {CLDTOT} Total cloud fraction used in LW and SW Radiation ($0-1$) }
1478    
1479     {\bf CLDTOT} is the time-averaged total cloud fraction that has been filled by the Relaxed
1480     Arakawa/Schubert and Large-scale Convection schemes and will be used in the Longwave and Shortwave
1481     Radiation packages.
1482     For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.
1483     \[
1484     {\bf CLDTOT} = F_{RAS} + F_{LS}
1485     \]
1486     \\
1487     where $F_{RAS}$ is the time-averaged cloud fraction due to sub-grid scale convection, and $F_{LS}$ is the
1488     time-averaged cloud fraction due to precipitating and non-precipitating large-scale moist processes.
1489     \\
1490    
1491    
1492     \noindent
1493     {\bf 46) \underline {CLMOSW} Maximum Overlap cloud fraction used in SW Radiation ($0-1$) }
1494    
1495     \noindent
1496     {\bf CLMOSW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed
1497     Arakawa/Schubert Convection scheme and will be used in the Shortwave Radiation algorithm. These are
1498     convective clouds whose radiative characteristics are assumed to be correlated in the vertical.
1499     For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.
1500     \[
1501     {\bf CLMOSW} = CLMO_{RAS,SW}(\lambda, \phi, level )
1502     \]
1503     \\
1504    
1505     \noindent
1506     {\bf 47) \underline {CLROSW} Random Overlap cloud fraction used in SW Radiation ($0-1$) }
1507    
1508     \noindent
1509     {\bf CLROSW} is the time-averaged random overlap cloud fraction that has been filled by the Relaxed
1510     Arakawa/Schubert and Large-scale Convection schemes and will be used in the Shortwave
1511     Radiation algorithm. These are
1512     convective and large-scale clouds whose radiative characteristics are not
1513     assumed to be correlated in the vertical.
1514     For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.
1515     \[
1516     {\bf CLROSW} = CLRO_{RAS,Large Scale,SW}(\lambda, \phi, level )
1517     \]
1518     \\
1519    
1520     \noindent
1521     {\bf 48) \underline {RADSWT} Incident Shortwave radiation at the top of the atmosphere ($Watts/m^2$) }
1522     \[
1523     {\bf RADSWT} = {\frac{S_0}{R_a^2}} \cdot cos \phi_z
1524     \]
1525     \noindent
1526     where $S_0$, is the extra-terrestial solar contant,
1527     $R_a$ is the earth-sun distance in Astronomical Units,
1528     and $cos \phi_z$ is the cosine of the zenith angle.
1529     It should be noted that {\bf RADSWT}, as well as
1530     {\bf OSR} and {\bf OSRCLR},
1531     are calculated at the top of the atmosphere (p=0 mb). However, the
1532     {\bf OLR} and {\bf OLRCLR} diagnostics are currently
1533     calculated at $p= p_{top}$ (0.0 mb for the GCM).
1534     \\
1535    
1536     \noindent
1537     {\bf 49) \underline {EVAP} Surface Evaporation ($mm/day$) }
1538    
1539     \noindent
1540     The surface evaporation is a function of the gradient of moisture, the potential
1541     evapotranspiration fraction and the eddy exchange coefficient:
1542     \[
1543     {\bf EVAP} = \rho \beta K_{h} (q_{surface} - q_{Nrphys})
1544     \]
1545     where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of
1546     the potential evapotranspiration actually evaporated ($\beta=1$ over oceans), $K_{h}$ is the
1547     turbulent eddy exchange coefficient for heat and moisture at the surface in $m/sec$ and
1548     $q{surface}$ and $q_{Nrphys}$ are the specific humidity at the surface (see diagnostic
1549     number 34) and at the bottom model level, respectively.
1550     \\
1551    
1552     \noindent
1553     {\bf 50) \underline {DUDT} Total Zonal U-Wind Tendency ($m/sec/day$) }
1554    
1555     \noindent
1556     {\bf DUDT} is the total time-tendency of the Zonal U-Wind due to Hydrodynamic, Diabatic,
1557     and Analysis forcing.
1558     \[
1559     {\bf DUDT} = \pp{u}{t}_{Dynamics} + \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis}
1560     \]
1561     \\
1562    
1563     \noindent
1564     {\bf 51) \underline {DVDT} Total Zonal V-Wind Tendency ($m/sec/day$) }
1565    
1566     \noindent
1567     {\bf DVDT} is the total time-tendency of the Meridional V-Wind due to Hydrodynamic, Diabatic,
1568     and Analysis forcing.
1569     \[
1570     {\bf DVDT} = \pp{v}{t}_{Dynamics} + \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis}
1571     \]
1572     \\
1573    
1574     \noindent
1575     {\bf 52) \underline {DTDT} Total Temperature Tendency ($deg/day$) }
1576    
1577     \noindent
1578     {\bf DTDT} is the total time-tendency of Temperature due to Hydrodynamic, Diabatic,
1579     and Analysis forcing.
1580     \begin{eqnarray*}
1581     {\bf DTDT} & = & \pp{T}{t}_{Dynamics} + \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\
1582     & + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis}
1583     \end{eqnarray*}
1584     \\
1585    
1586     \noindent
1587     {\bf 53) \underline {DQDT} Total Specific Humidity Tendency ($g/kg/day$) }
1588    
1589     \noindent
1590     {\bf DQDT} is the total time-tendency of Specific Humidity due to Hydrodynamic, Diabatic,
1591     and Analysis forcing.
1592     \[
1593     {\bf DQDT} = \pp{q}{t}_{Dynamics} + \pp{q}{t}_{Moist Processes}
1594     + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis}
1595     \]
1596     \\
1597    
1598     \noindent
1599     {\bf 54) \underline {USTAR} Surface-Stress Velocity ($m/sec$) }
1600    
1601     \noindent
1602     The surface stress velocity, or the friction velocity, is the wind speed at
1603     the surface layer top impeded by the surface drag:
1604     \[
1605     {\bf USTAR} = C_uW_s \hspace{1cm}where: \hspace{.2cm}
1606     C_u = {k \over {\psi_m} }
1607     \]
1608    
1609     \noindent
1610     $C_u$ is the non-dimensional surface drag coefficient (see diagnostic
1611     number 10), and $W_s$ is the surface wind speed (see diagnostic number 28).
1612    
1613     \noindent
1614     {\bf 55) \underline {Z0} Surface Roughness Length ($m$) }
1615    
1616     \noindent
1617     Over the land surface, the surface roughness length is interpolated to the local
1618     time from the monthly mean data of Dorman and Sellers (1989). Over the ocean,
1619     the roughness length is a function of the surface-stress velocity, $u_*$.
1620     \[
1621     {\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}}
1622     \]
1623    
1624     \noindent
1625     where the constants are chosen to interpolate between the reciprocal relation of
1626     Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981)
1627     for moderate to large winds.
1628     \\
1629    
1630     \noindent
1631     {\bf 56) \underline {FRQTRB} Frequency of Turbulence ($0-1$) }
1632    
1633     \noindent
1634     The fraction of time when turbulence is present is defined as the fraction of
1635     time when the turbulent kinetic energy exceeds some minimum value, defined here
1636     to be $0.005 \hspace{.1cm}m^2/sec^2$. When this criterion is met, a counter is
1637     incremented. The fraction over the averaging interval is reported.
1638     \\
1639    
1640     \noindent
1641     {\bf 57) \underline {PBL} Planetary Boundary Layer Depth ($mb$) }
1642    
1643     \noindent
1644     The depth of the PBL is defined by the turbulence parameterization to be the
1645     depth at which the turbulent kinetic energy reduces to ten percent of its surface
1646     value.
1647    
1648     \[
1649     {\bf PBL} = P_{PBL} - P_{surface}
1650     \]
1651    
1652     \noindent
1653     where $P_{PBL}$ is the pressure in $mb$ at which the turbulent kinetic energy
1654     reaches one tenth of its surface value, and $P_s$ is the surface pressure.
1655     \\
1656    
1657     \noindent
1658     {\bf 58) \underline {SWCLR} Clear sky Heating Rate due to Shortwave Radiation ($deg/day$) }
1659    
1660     \noindent
1661     The net Shortwave heating rate is calculated as the vertical divergence of the
1662     net solar radiative fluxes.
1663     The clear-sky and cloudy-sky shortwave fluxes are calculated separately.
1664     For the clear-sky case, the shortwave fluxes and heating rates are computed with
1665     both CLMO (maximum overlap cloud fraction) and
1666     CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}).
1667     The shortwave routine is then called a second time, for the cloudy-sky case, with the
1668     true time-averaged cloud fractions CLMO
1669     and CLRO being used. In all cases, a normalized incident shortwave flux is used as
1670     input at the top of the atmosphere.
1671    
1672     \noindent
1673     The heating rate due to Shortwave Radiation under clear skies is defined as:
1674     \[
1675     \pp{\rho c_p T}{t} = - {\partial \over \partial z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT},
1676     \]
1677     or
1678     \[
1679     {\bf SWCLR} = \frac{g}{c_p } {\partial \over \partial p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} .
1680     \]
1681    
1682     \noindent
1683     where $g$ is the accelation due to gravity,
1684     $c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident
1685     shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and
1686     \[
1687     F(clear)_{SW}^{Net} = F(clear)_{SW}^\uparrow - F(clear)_{SW}^\downarrow
1688     \]
1689     \\
1690    
1691     \noindent
1692     {\bf 59) \underline {OSR} Net upward Shortwave flux at the top of the model ($Watts/m^2$) }
1693     \[
1694     {\bf OSR} = F_{SW,top}^{NET}
1695     \]
1696     \noindent
1697     where top indicates the top of the first model layer used in the shortwave radiation
1698     routine.
1699     In the GCM, $p_{SW_{top}}$ = 0 mb.
1700     \\
1701    
1702     \noindent
1703     {\bf 60) \underline {OSRCLR} Net upward clearsky Shortwave flux at the top of the model ($Watts/m^2$) }
1704     \[
1705     {\bf OSRCLR} = F(clearsky)_{SW,top}^{NET}
1706     \]
1707     \noindent
1708     where top indicates the top of the first model layer used in the shortwave radiation
1709     routine.
1710     In the GCM, $p_{SW_{top}}$ = 0 mb.
1711     \\
1712    
1713    
1714     \noindent
1715     {\bf 61) \underline {CLDMAS} Convective Cloud Mass Flux ($kg/m^2$) }
1716    
1717     \noindent
1718     The amount of cloud mass moved per RAS timestep from all convective clouds is written:
1719     \[
1720     {\bf CLDMAS} = \eta m_B
1721     \]
1722     where $\eta$ is the entrainment, normalized by the cloud base mass flux, and $m_B$ is
1723     the cloud base mass flux. $m_B$ and $\eta$ are defined explicitly in Section \ref{sec:fizhi:mc}, the
1724     description of the convective parameterization.
1725     \\
1726    
1727    
1728    
1729     \noindent
1730     {\bf 62) \underline {UAVE} Time-Averaged Zonal U-Wind ($m/sec$) }
1731    
1732     \noindent
1733     The diagnostic {\bf UAVE} is simply the time-averaged Zonal U-Wind over
1734     the {\bf NUAVE} output frequency. This is contrasted to the instantaneous
1735     Zonal U-Wind which is archived on the Prognostic Output data stream.
1736     \[
1737     {\bf UAVE} = u(\lambda, \phi, level , t)
1738     \]
1739     \\
1740     Note, {\bf UAVE} is computed and stored on the staggered C-grid.
1741     \\
1742    
1743     \noindent
1744     {\bf 63) \underline {VAVE} Time-Averaged Meridional V-Wind ($m/sec$) }
1745    
1746     \noindent
1747     The diagnostic {\bf VAVE} is simply the time-averaged Meridional V-Wind over
1748     the {\bf NVAVE} output frequency. This is contrasted to the instantaneous
1749     Meridional V-Wind which is archived on the Prognostic Output data stream.
1750     \[
1751     {\bf VAVE} = v(\lambda, \phi, level , t)
1752     \]
1753     \\
1754     Note, {\bf VAVE} is computed and stored on the staggered C-grid.
1755     \\
1756    
1757     \noindent
1758     {\bf 64) \underline {TAVE} Time-Averaged Temperature ($Kelvin$) }
1759    
1760     \noindent
1761     The diagnostic {\bf TAVE} is simply the time-averaged Temperature over
1762     the {\bf NTAVE} output frequency. This is contrasted to the instantaneous
1763     Temperature which is archived on the Prognostic Output data stream.
1764     \[
1765     {\bf TAVE} = T(\lambda, \phi, level , t)
1766     \]
1767     \\
1768    
1769     \noindent
1770     {\bf 65) \underline {QAVE} Time-Averaged Specific Humidity ($g/kg$) }
1771    
1772     \noindent
1773     The diagnostic {\bf QAVE} is simply the time-averaged Specific Humidity over
1774     the {\bf NQAVE} output frequency. This is contrasted to the instantaneous
1775     Specific Humidity which is archived on the Prognostic Output data stream.
1776     \[
1777     {\bf QAVE} = q(\lambda, \phi, level , t)
1778     \]
1779     \\
1780    
1781     \noindent
1782     {\bf 66) \underline {PAVE} Time-Averaged Surface Pressure - PTOP ($mb$) }
1783    
1784     \noindent
1785     The diagnostic {\bf PAVE} is simply the time-averaged Surface Pressure - PTOP over
1786     the {\bf NPAVE} output frequency. This is contrasted to the instantaneous
1787     Surface Pressure - PTOP which is archived on the Prognostic Output data stream.
1788     \begin{eqnarray*}
1789     {\bf PAVE} & = & \pi(\lambda, \phi, level , t) \\
1790     & = & p_s(\lambda, \phi, level , t) - p_T
1791     \end{eqnarray*}
1792     \\
1793    
1794    
1795     \noindent
1796     {\bf 67) \underline {QQAVE} Time-Averaged Turbulent Kinetic Energy $(m/sec)^2$ }
1797    
1798     \noindent
1799     The diagnostic {\bf QQAVE} is simply the time-averaged prognostic Turbulent Kinetic Energy
1800     produced by the GCM Turbulence parameterization over
1801     the {\bf NQQAVE} output frequency. This is contrasted to the instantaneous
1802     Turbulent Kinetic Energy which is archived on the Prognostic Output data stream.
1803     \[
1804     {\bf QQAVE} = qq(\lambda, \phi, level , t)
1805     \]
1806     \\
1807     Note, {\bf QQAVE} is computed and stored at the ``mass-point'' locations on the staggered C-grid.
1808     \\
1809    
1810     \noindent
1811     {\bf 68) \underline {SWGCLR} Net downward clearsky Shortwave flux at the surface ($Watts/m^2$) }
1812    
1813     \noindent
1814     \begin{eqnarray*}
1815     {\bf SWGCLR} & = & F(clearsky)_{SW,Nrphys+1}^{Net} \\
1816     & = & F(clearsky)_{SW,Nrphys+1}^\downarrow - F(clearsky)_{SW,Nrphys+1}^\uparrow
1817     \end{eqnarray*}
1818     \noindent
1819     \\
1820     where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$.
1821     $F(clearsky){SW}^\downarrow$ is
1822     the downward clearsky Shortwave flux and $F(clearsky)_{SW}^\uparrow$ is
1823     the upward clearsky Shortwave flux.
1824     \\
1825    
1826     \noindent
1827     {\bf 69) \underline {SDIAG1} User-Defined Surface Diagnostic-1 }
1828    
1829     \noindent
1830     The GCM provides Users with a built-in mechanism for archiving user-defined
1831     diagnostics. The generic diagnostic array QDIAG located in COMMON /DIAG/, and the associated
1832     diagnostic counters and pointers located in COMMON /DIAGP/,
1833     must be accessable in order to use the user-defined diagnostics (see Section \ref{sec:diagnostics:diagover}).
1834     A convenient method for incorporating all necessary COMMON files is to
1835     include the GCM {\em vstate.com} file in the routine which employs the
1836     user-defined diagnostics.
1837    
1838     \noindent
1839     In addition to enabling the user-defined diagnostic (ie., CALL SETDIAG(84)), the User must fill
1840     the QDIAG array with the desired quantity within the User's
1841     application program or within modified GCM subroutines, as well as increment
1842     the diagnostic counter at the time when the diagnostic is updated.
1843     The QDIAG location index for {\bf SDIAG1} and its corresponding counter is
1844     automatically defined as {\bf ISDIAG1} and {\bf NSDIAG1}, respectively, after the
1845     diagnostic has been enabled.
1846     The syntax for its use is given by
1847     \begin{verbatim}
1848     do j=1,jm
1849     do i=1,im
1850     qdiag(i,j,ISDIAG1) = qdiag(i,j,ISDIAG1) + ...
1851     enddo
1852     enddo
1853    
1854     NSDIAG1 = NSDIAG1 + 1
1855     \end{verbatim}
1856     The diagnostics defined in this manner will automatically be archived by the output routines.
1857     \\
1858    
1859     \noindent
1860     {\bf 70) \underline {SDIAG2} User-Defined Surface Diagnostic-2 }
1861    
1862     \noindent
1863     The GCM provides Users with a built-in mechanism for archiving user-defined
1864     diagnostics. For a complete description refer to Diagnostic \#84.
1865     The syntax for using the surface SDIAG2 diagnostic is given by
1866     \begin{verbatim}
1867     do j=1,jm
1868     do i=1,im
1869     qdiag(i,j,ISDIAG2) = qdiag(i,j,ISDIAG2) + ...
1870     enddo
1871     enddo
1872    
1873     NSDIAG2 = NSDIAG2 + 1
1874     \end{verbatim}
1875     The diagnostics defined in this manner will automatically be archived by the output routines.
1876     \\
1877    
1878     \noindent
1879     {\bf 71) \underline {UDIAG1} User-Defined Upper-Air Diagnostic-1 }
1880    
1881     \noindent
1882     The GCM provides Users with a built-in mechanism for archiving user-defined
1883     diagnostics. For a complete description refer to Diagnostic \#84.
1884     The syntax for using the upper-air UDIAG1 diagnostic is given by
1885     \begin{verbatim}
1886     do L=1,Nrphys
1887     do j=1,jm
1888     do i=1,im
1889     qdiag(i,j,IUDIAG1+L-1) = qdiag(i,j,IUDIAG1+L-1) + ...
1890     enddo
1891     enddo
1892     enddo
1893    
1894     NUDIAG1 = NUDIAG1 + 1
1895     \end{verbatim}
1896     The diagnostics defined in this manner will automatically be archived by the
1897     output programs.
1898     \\
1899    
1900     \noindent
1901     {\bf 72) \underline {UDIAG2} User-Defined Upper-Air Diagnostic-2 }
1902    
1903     \noindent
1904     The GCM provides Users with a built-in mechanism for archiving user-defined
1905     diagnostics. For a complete description refer to Diagnostic \#84.
1906     The syntax for using the upper-air UDIAG2 diagnostic is given by
1907     \begin{verbatim}
1908     do L=1,Nrphys
1909     do j=1,jm
1910     do i=1,im
1911     qdiag(i,j,IUDIAG2+L-1) = qdiag(i,j,IUDIAG2+L-1) + ...
1912     enddo
1913     enddo
1914     enddo
1915    
1916     NUDIAG2 = NUDIAG2 + 1
1917     \end{verbatim}
1918     The diagnostics defined in this manner will automatically be archived by the
1919     output programs.
1920     \\
1921    
1922    
1923     \noindent
1924     {\bf 73) \underline {DIABU} Total Diabatic Zonal U-Wind Tendency ($m/sec/day$) }
1925    
1926     \noindent
1927     {\bf DIABU} is the total time-tendency of the Zonal U-Wind due to Diabatic processes
1928     and the Analysis forcing.
1929     \[
1930     {\bf DIABU} = \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis}
1931     \]
1932     \\
1933    
1934     \noindent
1935     {\bf 74) \underline {DIABV} Total Diabatic Meridional V-Wind Tendency ($m/sec/day$) }
1936    
1937     \noindent
1938     {\bf DIABV} is the total time-tendency of the Meridional V-Wind due to Diabatic processes
1939     and the Analysis forcing.
1940     \[
1941     {\bf DIABV} = \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis}
1942     \]
1943     \\
1944    
1945     \noindent
1946     {\bf 75) \underline {DIABT} Total Diabatic Temperature Tendency ($deg/day$) }
1947    
1948     \noindent
1949     {\bf DIABT} is the total time-tendency of Temperature due to Diabatic processes
1950     and the Analysis forcing.
1951     \begin{eqnarray*}
1952     {\bf DIABT} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\
1953     & + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis}
1954     \end{eqnarray*}
1955     \\
1956     If we define the time-tendency of Temperature due to Diabatic processes as
1957     \begin{eqnarray*}
1958     \pp{T}{t}_{Diabatic} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\
1959     & + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence}
1960     \end{eqnarray*}
1961     then, since there are no surface pressure changes due to Diabatic processes, we may write
1962     \[
1963     \pp{T}{t}_{Diabatic} = {p^\kappa \over \pi }\pp{\pi \theta}{t}_{Diabatic}
1964     \]
1965     where $\theta = T/p^\kappa$. Thus, {\bf DIABT} may be written as
1966     \[
1967     {\bf DIABT} = {p^\kappa \over \pi } \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right)
1968     \]
1969     \\
1970    
1971     \noindent
1972     {\bf 76) \underline {DIABQ} Total Diabatic Specific Humidity Tendency ($g/kg/day$) }
1973    
1974     \noindent
1975     {\bf DIABQ} is the total time-tendency of Specific Humidity due to Diabatic processes
1976     and the Analysis forcing.
1977     \[
1978     {\bf DIABQ} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis}
1979     \]
1980     If we define the time-tendency of Specific Humidity due to Diabatic processes as
1981     \[
1982     \pp{q}{t}_{Diabatic} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence}
1983     \]
1984     then, since there are no surface pressure changes due to Diabatic processes, we may write
1985     \[
1986     \pp{q}{t}_{Diabatic} = {1 \over \pi }\pp{\pi q}{t}_{Diabatic}
1987     \]
1988     Thus, {\bf DIABQ} may be written as
1989     \[
1990     {\bf DIABQ} = {1 \over \pi } \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right)
1991     \]
1992     \\
1993    
1994     \noindent
1995     {\bf 77) \underline {VINTUQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) }
1996    
1997     \noindent
1998     The vertically integrated moisture flux due to the zonal u-wind is obtained by integrating
1999     $u q$ over the depth of the atmosphere at each model timestep,
2000     and dividing by the total mass of the column.
2001     \[
2002     {\bf VINTUQ} = \frac{ \int_{surf}^{top} u q \rho dz } { \int_{surf}^{top} \rho dz }
2003     \]
2004     Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have
2005     \[
2006     {\bf VINTUQ} = { \int_0^1 u q dp }
2007     \]
2008     \\
2009    
2010    
2011     \noindent
2012     {\bf 78) \underline {VINTVQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) }
2013    
2014     \noindent
2015     The vertically integrated moisture flux due to the meridional v-wind is obtained by integrating
2016     $v q$ over the depth of the atmosphere at each model timestep,
2017     and dividing by the total mass of the column.
2018     \[
2019     {\bf VINTVQ} = \frac{ \int_{surf}^{top} v q \rho dz } { \int_{surf}^{top} \rho dz }
2020     \]
2021     Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have
2022     \[
2023     {\bf VINTVQ} = { \int_0^1 v q dp }
2024     \]
2025     \\
2026    
2027    
2028     \noindent
2029     {\bf 79) \underline {VINTUT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) }
2030    
2031     \noindent
2032     The vertically integrated heat flux due to the zonal u-wind is obtained by integrating
2033     $u T$ over the depth of the atmosphere at each model timestep,
2034     and dividing by the total mass of the column.
2035     \[
2036     {\bf VINTUT} = \frac{ \int_{surf}^{top} u T \rho dz } { \int_{surf}^{top} \rho dz }
2037     \]
2038     Or,
2039     \[
2040     {\bf VINTUT} = { \int_0^1 u T dp }
2041     \]
2042     \\
2043    
2044     \noindent
2045     {\bf 80) \underline {VINTVT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) }
2046    
2047     \noindent
2048     The vertically integrated heat flux due to the meridional v-wind is obtained by integrating
2049     $v T$ over the depth of the atmosphere at each model timestep,
2050     and dividing by the total mass of the column.
2051     \[
2052     {\bf VINTVT} = \frac{ \int_{surf}^{top} v T \rho dz } { \int_{surf}^{top} \rho dz }
2053     \]
2054     Using $\rho \delta z = -{\delta p \over g} $, we have
2055     \[
2056     {\bf VINTVT} = { \int_0^1 v T dp }
2057     \]
2058     \\
2059    
2060     \noindent
2061     {\bf 81 \underline {CLDFRC} Total 2-Dimensional Cloud Fracton ($0-1$) }
2062    
2063     If we define the
2064     time-averaged random and maximum overlapped cloudiness as CLRO and
2065     CLMO respectively, then the probability of clear sky associated
2066     with random overlapped clouds at any level is (1-CLRO) while the probability of
2067     clear sky associated with maximum overlapped clouds at any level is (1-CLMO).
2068     The total clear sky probability is given by (1-CLRO)*(1-CLMO), thus
2069     the total cloud fraction at each level may be obtained by
2070     1-(1-CLRO)*(1-CLMO).
2071    
2072     At any given level, we may define the clear line-of-site probability by
2073     appropriately accounting for the maximum and random overlap
2074     cloudiness. The clear line-of-site probability is defined to be
2075     equal to the product of the clear line-of-site probabilities
2076     associated with random and maximum overlap cloudiness. The clear
2077     line-of-site probability $C(p,p^{\prime})$ associated with maximum overlap clouds,
2078     from the current pressure $p$
2079     to the model top pressure, $p^{\prime} = p_{top}$, or the model surface pressure, $p^{\prime} = p_{surf}$,
2080     is simply 1.0 minus the largest maximum overlap cloud value along the
2081     line-of-site, ie.
2082    
2083     $$1-MAX_p^{p^{\prime}} \left( CLMO_p \right)$$
2084    
2085     Thus, even in the time-averaged sense it is assumed that the
2086     maximum overlap clouds are correlated in the vertical. The clear
2087     line-of-site probability associated with random overlap clouds is
2088     defined to be the product of the clear sky probabilities at each
2089     level along the line-of-site, ie.
2090    
2091     $$\prod_{p}^{p^{\prime}} \left( 1-CLRO_p \right)$$
2092    
2093     The total cloud fraction at a given level associated with a line-
2094     of-site calculation is given by
2095    
2096     $$1-\left( 1-MAX_p^{p^{\prime}} \left[ CLMO_p \right] \right)
2097     \prod_p^{p^{\prime}} \left( 1-CLRO_p \right)$$
2098    
2099    
2100     \noindent
2101     The 2-dimensional net cloud fraction as seen from the top of the
2102     atmosphere is given by
2103     \[
2104     {\bf CLDFRC} = 1-\left( 1-MAX_{l=l_1}^{Nrphys} \left[ CLMO_l \right] \right)
2105     \prod_{l=l_1}^{Nrphys} \left( 1-CLRO_l \right)
2106     \]
2107     \\
2108     For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.
2109    
2110    
2111     \noindent
2112     {\bf 82) \underline {QINT} Total Precipitable Water ($gm/cm^2$) }
2113    
2114     \noindent
2115     The Total Precipitable Water is defined as the vertical integral of the specific humidity,
2116     given by:
2117     \begin{eqnarray*}
2118     {\bf QINT} & = & \int_{surf}^{top} \rho q dz \\
2119     & = & {\pi \over g} \int_0^1 q dp
2120     \end{eqnarray*}
2121     where we have used the hydrostatic relation
2122     $\rho \delta z = -{\delta p \over g} $.
2123     \\
2124    
2125    
2126     \noindent
2127     {\bf 83) \underline {U2M} Zonal U-Wind at 2 Meter Depth ($m/sec$) }
2128    
2129     \noindent
2130     The u-wind at the 2-meter depth is determined from the similarity theory:
2131     \[
2132     {\bf U2M} = {u_* \over k} \psi_{m_{2m}} {u_{sl} \over {W_s}} =
2133     { \psi_{m_{2m}} \over {\psi_{m_{sl}} }}u_{sl}
2134     \]
2135    
2136     \noindent
2137     where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript
2138     $sl$ refers to the height of the top of the surface layer. If the roughness height
2139     is above two meters, ${\bf U2M}$ is undefined.
2140     \\
2141    
2142     \noindent
2143     {\bf 84) \underline {V2M} Meridional V-Wind at 2 Meter Depth ($m/sec$) }
2144    
2145     \noindent
2146     The v-wind at the 2-meter depth is a determined from the similarity theory:
2147     \[
2148     {\bf V2M} = {u_* \over k} \psi_{m_{2m}} {v_{sl} \over {W_s}} =
2149     { \psi_{m_{2m}} \over {\psi_{m_{sl}} }}v_{sl}
2150     \]
2151    
2152     \noindent
2153     where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript
2154     $sl$ refers to the height of the top of the surface layer. If the roughness height
2155     is above two meters, ${\bf V2M}$ is undefined.
2156     \\
2157    
2158     \noindent
2159     {\bf 85) \underline {T2M} Temperature at 2 Meter Depth ($deg \hspace{.1cm} K$) }
2160    
2161     \noindent
2162     The temperature at the 2-meter depth is a determined from the similarity theory:
2163     \[
2164     {\bf T2M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) =
2165     P^{\kappa}(\theta_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }
2166     (\theta_{sl} - \theta_{surf}))
2167     \]
2168     where:
2169     \[
2170     \theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} }
2171     \]
2172    
2173     \noindent
2174     where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is
2175     the non-dimensional temperature gradient in the viscous sublayer, and the subscript
2176     $sl$ refers to the height of the top of the surface layer. If the roughness height
2177     is above two meters, ${\bf T2M}$ is undefined.
2178     \\
2179    
2180     \noindent
2181     {\bf 86) \underline {Q2M} Specific Humidity at 2 Meter Depth ($g/kg$) }
2182    
2183     \noindent
2184     The specific humidity at the 2-meter depth is determined from the similarity theory:
2185     \[
2186     {\bf Q2M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) =
2187     P^{\kappa}(q_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }
2188     (q_{sl} - q_{surf}))
2189     \]
2190     where:
2191     \[
2192     q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} }
2193     \]
2194    
2195     \noindent
2196     where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is
2197     the non-dimensional temperature gradient in the viscous sublayer, and the subscript
2198     $sl$ refers to the height of the top of the surface layer. If the roughness height
2199     is above two meters, ${\bf Q2M}$ is undefined.
2200     \\
2201    
2202     \noindent
2203     {\bf 87) \underline {U10M} Zonal U-Wind at 10 Meter Depth ($m/sec$) }
2204    
2205     \noindent
2206     The u-wind at the 10-meter depth is an interpolation between the surface wind
2207     and the model lowest level wind using the ratio of the non-dimensional wind shear
2208     at the two levels:
2209     \[
2210     {\bf U10M} = {u_* \over k} \psi_{m_{10m}} {u_{sl} \over {W_s}} =
2211     { \psi_{m_{10m}} \over {\psi_{m_{sl}} }}u_{sl}
2212     \]
2213    
2214     \noindent
2215     where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript
2216     $sl$ refers to the height of the top of the surface layer.
2217     \\
2218    
2219     \noindent
2220     {\bf 88) \underline {V10M} Meridional V-Wind at 10 Meter Depth ($m/sec$) }
2221    
2222     \noindent
2223     The v-wind at the 10-meter depth is an interpolation between the surface wind
2224     and the model lowest level wind using the ratio of the non-dimensional wind shear
2225     at the two levels:
2226     \[
2227     {\bf V10M} = {u_* \over k} \psi_{m_{10m}} {v_{sl} \over {W_s}} =
2228     { \psi_{m_{10m}} \over {\psi_{m_{sl}} }}v_{sl}
2229     \]
2230    
2231     \noindent
2232     where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript
2233     $sl$ refers to the height of the top of the surface layer.
2234     \\
2235    
2236     \noindent
2237     {\bf 89) \underline {T10M} Temperature at 10 Meter Depth ($deg \hspace{.1cm} K$) }
2238    
2239     \noindent
2240     The temperature at the 10-meter depth is an interpolation between the surface potential
2241     temperature and the model lowest level potential temperature using the ratio of the
2242     non-dimensional temperature gradient at the two levels:
2243     \[
2244     {\bf T10M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) =
2245     P^{\kappa}(\theta_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }
2246     (\theta_{sl} - \theta_{surf}))
2247     \]
2248     where:
2249     \[
2250     \theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} }
2251     \]
2252    
2253     \noindent
2254     where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is
2255     the non-dimensional temperature gradient in the viscous sublayer, and the subscript
2256     $sl$ refers to the height of the top of the surface layer.
2257     \\
2258    
2259     \noindent
2260     {\bf 90) \underline {Q10M} Specific Humidity at 10 Meter Depth ($g/kg$) }
2261    
2262     \noindent
2263     The specific humidity at the 10-meter depth is an interpolation between the surface specific
2264     humidity and the model lowest level specific humidity using the ratio of the
2265     non-dimensional temperature gradient at the two levels:
2266     \[
2267     {\bf Q10M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) =
2268     P^{\kappa}(q_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }
2269     (q_{sl} - q_{surf}))
2270     \]
2271     where:
2272     \[
2273     q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} }
2274     \]
2275    
2276     \noindent
2277     where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is
2278     the non-dimensional temperature gradient in the viscous sublayer, and the subscript
2279     $sl$ refers to the height of the top of the surface layer.
2280     \\
2281    
2282     \noindent
2283     {\bf 91) \underline {DTRAIN} Cloud Detrainment Mass Flux ($kg/m^2$) }
2284    
2285     The amount of cloud mass moved per RAS timestep at the cloud detrainment level is written:
2286     \[
2287     {\bf DTRAIN} = \eta_{r_D}m_B
2288     \]
2289     \noindent
2290     where $r_D$ is the detrainment level,
2291     $m_B$ is the cloud base mass flux, and $\eta$
2292     is the entrainment, defined in Section \ref{sec:fizhi:mc}.
2293     \\
2294    
2295     \noindent
2296     {\bf 92) \underline {QFILL} Filling of negative Specific Humidity ($g/kg/day$) }
2297    
2298     \noindent
2299     Due to computational errors associated with the numerical scheme used for
2300     the advection of moisture, negative values of specific humidity may be generated. The
2301     specific humidity is checked for negative values after every dynamics timestep. If negative
2302     values have been produced, a filling algorithm is invoked which redistributes moisture from
2303     below. Diagnostic {\bf QFILL} is equal to the net filling needed
2304     to eliminate negative specific humidity, scaled to a per-day rate:
2305     \[
2306     {\bf QFILL} = q^{n+1}_{final} - q^{n+1}_{initial}
2307     \]
2308     where
2309     \[
2310     q^{n+1} = (\pi q)^{n+1} / \pi^{n+1}
2311     \]
2312    
2313     \subsection{Dos and Donts}
2314    
2315     \subsection{Diagnostics Reference}
2316    

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