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6    
7  \subsection{Introduction}  \subsection{Introduction}
8    
9  This section of the documentation describes the Diagnostics Utilities available within  \noindent
10  the GCM.  In addition to a description on how to set and extract diagnostic quantities,  This section of the documentation describes the Diagnostics package available within
11  this document also provides a comprehensive list of all available diagnostic quantities  the GCM.  A large selection of model diagnostics is available for output.  
12  and a short description of how they are computed.  It should be noted that this document  In addition to the diagnostic quantities pre-defined in the GCM, there exists
13  is not intended to be a complete documentation of the various packages used in the GCM,  the option, in any experiment, to define a new diagnostic quantity and include it
14  and the reader should refer to original publications and the appropriate sections of this  as part of the diagnostic output with the addition of a single subroutine call in the
15  documentation for further insight.  routine where the field is computed. As a matter of philosophy, no diagnostic is enabled
16    as default, thus each user must specify the exact diagnostic information required for an
17    experiment.  This is accomplished by enabling the specific diagnostic of interest cataloged
18    in the Diagnostic Menu (see Section \ref{sec:diagnostics:menu}). Instructions for enabling
19    diagnostic output and defining new diagnostic quantities are found in Section
20    \ref{sec:diagnostics:usersguide} of this document.
21    
22    \noindent
23    The Diagnostic Menu is a hard-wired enumeration of diagnostic quantities available within
24    the GCM. Once a diagnostic is enabled, the GCM will continually increment an array
25    specifically allocated for that diagnostic whenever the appropriate quantity is computed.  
26    A counter is defined which records how many times each diagnostic quantity has been
27    incremented.  Several special diagnostics are included in the menu. Quantities refered to
28    as ``Counter Diagnostics'', are defined for selected diagnostics which record the
29    frequency at which a diagnostic is incremented separately for each model grid location.
30    Quantitied refered to as ``User Diagnostics'' are included in the menu to facilitate
31    defining new diagnostics for a particular experiment.
32    
33  \subsection{Equations}  \subsection{Equations}
34  Not relevant.  Not relevant.
# Line 20  Not relevant. Line 36  Not relevant.
36  \subsection{Key Subroutines and Parameters}  \subsection{Key Subroutines and Parameters}
37  \label{sec:diagnostics:diagover}  \label{sec:diagnostics:diagover}
38    
39  A large selection of model diagnostics is available in the GCM.  At the time of  \noindent
40  this writing there are 280 different diagnostic quantities which can be enabled for an  The diagnostics are computed at various times and places within the GCM. Because the
41  experiment.  As a matter of philosophy, no diagnostic is enabled as default, thus each user must  MIT GCM may employ a staggered grid, diagnostics may be computed at grid box centers,
42  specify the exact diagnostic information required for an experiment.  This is accomplished by  corners, or edges, and at the middle or edge in the vertical. Some diagnostics are scalars,
43  enabling the specific diagnostic of interest cataloged in the  while others are components of vectors. An internal array is defined which contains
44  Diagnostic Menu (see Section \ref{sec:diagnostics:menu}).  information concerning various grid attributes of each diagnostic. The GDIAG
45  The Diagnostic Menu is a hard-wired enumeration of diagnostic quantities available within the  array (in common block \\diagnostics in file diagnostics.h) is internally defined as a
46  GCM.  Diagnostics are internally referred to by their associated number in the Diagnostic  character*8 variable, and is equivalenced to a character*1 "parse" array in output in
47  Menu.  Once a diagnostic is enabled, the GCM will continually increment an array  order to extract the grid-attribute information.  The GDIAG array is described in
48  specifically allocated for that diagnostic whenever the associated process for the diagnostic is  Table \ref{tab:diagnostics:gdiag.tabl}.
 computed.  Separate arrays are used both for the diagnostic quantity and its diagnostic counter  
 which records how many times each diagnostic quantity has been computed.  In addition  
 special diagnostics, called  
 ``Counter Diagnostics'', records the frequency of diagnostic updates separately for each  
 model grid location.  
   
 The diagnostics are computed at various times and places within the GCM.    
 Some diagnostics are computed on the geophysical A-grid (such as  
 those within the Physics routines), while others are computed on the C-grid  
 (those computed during the dynamics time-stepping).  Some diagnostics are  
 scalars, while others are vectors.  Each of these possibilities requires  
 separate tasks for A-grid to C-grid transformations and coordinate transformations.  Due  
 to this complexity, and since the specific diagnostics enabled are User determined at the  
 time of the run,  
 a diagnostic parameter has been developed and implemented into the GCM, defined as GDIAG,  
 which contains information concerning various grid attributes of each diagnostic.  The GDIAG  
 array is internally defined as a character*8 variable, and is equivalenced to  
 a character*1 "parse" array in output in order to extract the grid-attribute information.  
 The GDIAG array is described in Table \ref{tab:diagnostics:gdiag.tabl}.  
49    
50  \begin{table}  \begin{table}
51  \caption{Diagnostic Parsing Array}  \caption{Diagnostic Parsing Array}
# Line 79  Array & Value & Description \\ Line 76  Array & Value & Description \\
76  \end{center}  \end{center}
77  \end{table}  \end{table}
78    
79    
80    \noindent
81  As an example, consider a diagnostic whose associated GDIAG parameter is equal  As an example, consider a diagnostic whose associated GDIAG parameter is equal
82  to ``UU  002''.  From GDIAG we can determine that this diagnostic is a  to ``UU  002''.  From GDIAG we can determine that this diagnostic is a
83  U-vector component located at the C-grid U-point.  U-vector component located at the C-grid U-point.
84  Its corresponding V-component diagnostic is located in Diagnostic \# 002.  Its corresponding V-component diagnostic is located in Diagnostic \# 002.
85    
86    
87    \noindent
88  In this way, each Diagnostic in the model has its attributes (ie. vector or scalar,  In this way, each Diagnostic in the model has its attributes (ie. vector or scalar,
89  A-Grid or C-grid, etc.) defined internally.  The Output routines  C-grid location, etc.) defined internally.  The Output routines use this information
90  use this information in order to determine  in order to determine what type of transformations need to be performed.  Any
91  what type of transformations need to be performed.  Thus, all Diagnostic  interpolations are done at the time of output rather than during each model step.
92  interpolations are done at the time of output rather than during each model dynamic step.  In this way the User has flexibility in determining the type of gridded data which
93  In this way the User now has more flexibility  is output.
 in determining the type of gridded data which is output.  
94    
95    
96    \noindent
97  There are several utilities within the GCM available to users to enable, disable,  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  clear, write and retrieve model diagnostics, and may be called from any routine.  
99  and/or output routine.  The available utilities and the CALL sequences are listed below.  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  \noindent
103  space is allocated for the diagnostic and the  {\bf fill\_diagnostics}:  This routine will increment the specified diagnostic
104  model routines will increment the diagnostic value during execution.  This routine is useful when  quantity with a field sent through the argument list.
105  called from either user application routines or user output routines, and is the underlying interface  
 between the user and the desired diagnostic.  The diagnostic is referenced by its diagnostic  
 number from the menu, and its calling sequence is given by:  
106    
107    \noindent
108  \begin{tabbing}  \begin{tabbing}
109  XXXXXXXXX\=XXXXXX\= \kill  XXXXXXXXX\=XXXXXX\= \kill
110  \>        CALL SETDIAG (NUM) \\  \>        call fill\_diagnostics (myThid, chardiag, levflg, nlevs, \\
111                    bibjflg, bi, bj, arrayin) \\
112  \\  \\
113  where \>  NUM   \>= Diagnostic number from menu \\  where \>  myThid   \>= Current Process(or) \\
114          \>  chardiag \>= Character *8 expression for diag to fill \\
115          \>  levflg   \>= Integer flag for vertical levels: \\
116          \>           \> 0 indicates multiple levels incremented in qdiag \\
117          \>           \> non-0 (any integer) - WHICH single level to increment. \\
118          \>           \> negative integer - the input data array is single-leveled \\
119          \>           \> positive integer - the input data array is multi-leveled \\
120          \>  nlevs    \>= indicates Number of levels to be filled (1 if levflg <> 0) \\
121          \>           \> positive: fill in "nlevs" levels in the same order as \\
122          \>           \> the input array \\
123          \>           \> negative: fill in -nlevs levels in reverse order. \\
124          \>  bibjflg  \>= Integer flag to indicate instructions for bi bj loop \\
125          \>           \> 0 indicates that the bi-bj loop must be done here \\
126          \>           \> 1 indicates that the bi-bj loop is done OUTSIDE \\
127          \>           \> 2 indicates that the bi-bj loop is done OUTSIDE \\
128          \>           \>    AND that we have been sent a local array \\
129          \>           \> 3 indicates that the bi-bj loop is done OUTSIDE \\
130          \>           \>    AND that we have been sent a local array \\
131          \>           \>    AND that the array has the shadow regions \\
132          \>  bi       \>= X-direction process(or) number - used for bibjflg=1-3 \\
133          \>  bj       \>= Y-direction process(or) number - used for bibjflg=1-3 \\
134          \>  arrayin  \>= Field to increment diagnostics array \\
135  \end{tabbing}  \end{tabbing}
136    
137    
138  {\bf GETDIAG}:  This subroutine retrieves the value of a model diagnostic.  This routine is  \noindent
139  particulary useful when called from a user output routine, although it can be called from an  {\bf setdiag}:  This subroutine enables a diagnostic from the Diagnostic Menu, meaning
140  application routine as well.  This routine returns the time-averaged value of the diagnostic by  that space is allocated for the diagnostic and the model routines will increment the
141  dividing the current accumulated diagnostic value by its corresponding counter.  This routine does  diagnostic value during execution.  This routine is the underlying interface
142  not change the value of the diagnostic itself, that is, it does not replace the diagnostic with its  between the user and the desired diagnostic.  The diagnostic is referenced by its diagnostic
143  time-average.  The calling sequence for this routine is givin by:  number from the menu, and its calling sequence is given by:
144    
145    \noindent
146  \begin{tabbing}  \begin{tabbing}
147  XXXXXXXXX\=XXXXXX\= \kill  XXXXXXXXX\=XXXXXX\= \kill
148  \>        CALL GETDIAG (LEV,NUM,QTMP,UNDEF) \\  \>        call setdiag (num) \\
149  \\  \\
150  where \>  LEV   \>= Model Level at which the diagnostic is desired \\  where \>  num   \>= Diagnostic number from menu \\
       \>  NUM   \>= Diagnostic number from menu \\  
       \>  QTMP  \>= Time-Averaged Diagnostic Output \\  
       \>  UNDEF \>= Fill value to be used when diagnostic is undefined \\  
151  \end{tabbing}  \end{tabbing}
152    
153  {\bf CLRDIAG}:  This subroutine initializes the values of model diagnostics to zero, and is  \noindent
154  particularly useful when called from user output routines to re-initialize diagnostics during the  {\bf getdiag}:  This subroutine retrieves the value of a model diagnostic.  This routine
155  run.  The calling sequence is:  is particulary useful when called from a user output routine, although it can be called
156    from any routine.  This routine returns the time-averaged value of the diagnostic by
157    dividing the current accumulated diagnostic value by its corresponding counter.  This
158    routine does not change the value of the diagnostic itself, that is, it does not replace
159    the diagnostic with its time-average.  The calling sequence for this routine is givin by:
160    
161    \noindent
162  \begin{tabbing}  \begin{tabbing}
163  XXXXXXXXX\=XXXXXX\= \kill  XXXXXXXXX\=XXXXXX\= \kill
164  \>        CALL CLRDIAG (NUM) \\  \>        call getdiag (lev,num,qtmp,undef) \\
165  \\  \\
166  where \>  NUM   \>= Diagnostic number from menu \\  where \>  lev   \>= Model Level at which the diagnostic is desired \\
167          \>  num   \>= Diagnostic number from menu \\
168          \>  qtmp  \>= Time-Averaged Diagnostic Output \\
169          \>  undef \>= Fill value to be used when diagnostic is undefined \\
170  \end{tabbing}  \end{tabbing}
171    
172    \noindent
173    {\bf clrdiag}:  This subroutine initializes the values of model diagnostics to zero, and is
174    particularly useful when called from user output routines to re-initialize diagnostics
175    during the run.  The calling sequence is:
176    
177    \noindent
178    \begin{tabbing}
179    XXXXXXXXX\=XXXXXX\= \kill
180    \>        call clrdiag (num) \\
181    \\
182    where \>  num   \>= Diagnostic number from menu \\
183    \end{tabbing}
184    
185  {\bf ZAPDIAG}:  This entry into subroutine SETDIAG disables model diagnostics, meaning that the  \noindent
186  diagnostic is no longer available to the user.  The memory previously allocated to the diagnostic  {\bf zapdiag}:  This entry into subroutine SETDIAG disables model diagnostics, meaning
187  is released when ZAPDIAG is invoked.  The calling sequence is given by:  that the diagnostic is no longer available to the user.  The memory previously allocated
188    to the diagnostic is released when ZAPDIAG is invoked.  The calling sequence is given by:
189    
190    \noindent
191  \begin{tabbing}  \begin{tabbing}
192  XXXXXXXXX\=XXXXXX\= \kill  XXXXXXXXX\=XXXXXX\= \kill
193  \>        CALL ZAPDIAG (NUM) \\  \>        call zapdiag (NUM) \\
194  \\  \\
195  where \>  NUM   \>= Diagnostic number from menu \\  where \>  num   \>= Diagnostic number from menu \\
196  \end{tabbing}  \end{tabbing}
197    
198  {\bf DIAGSIZE}:  We end this section with a discussion on the manner in which computer memory    
199  is allocated for diagnostics.    \subsection{Usage Notes}
200  All GCM diagnostic quantities are stored in the single  \label{sec:diagnostics:usersguide}
201  diagnostic array QDIAG which is located in diagnostics.h, and has the form:  
202    \noindent
203    We begin this section with a discussion on the manner in which computer
204    memory is allocated for diagnostics. All GCM diagnostic quantities are stored in the
205    single diagnostic array QDIAG which is located in the file \\
206    \filelink{pkg/diagnostics/diagnostics.h}{pkg-diagnostics-diagnostics.h}.
207    and has the form:
208    
209  common /diagnostics/ qdiag(1-Olx,sNx+Olx,1-Olx,sNx+Olx,numdiags,Nsx,Nsy)  common /diagnostics/ qdiag(1-Olx,sNx+Olx,1-Olx,sNx+Olx,numdiags,Nsx,Nsy)
210    
211  where numdiags is an Integer variable which should be  \noindent
212  set equal to the number of enabled diagnostics, and QDIAG is a three-dimensional  where numdiags is an Integer variable which should be set equal to the number of
213  array.  The first two-dimensions of QDIAG correspond to the horizontal dimension  enabled diagnostics, and qdiag is a three-dimensional array.  The first two-dimensions
214  of a given diagnostic, while the third dimension of QDIAG is used to identify  of qdiag correspond to the horizontal dimension of a given diagnostic, while the third
215  specific diagnostic types.  dimension of qdiag is used to identify diagnostic fields and levels combined. In order
216  In order to minimize the memory requirement of the model for diagnostics,  to minimize the memory requirement of the model for diagnostics, the default GCM
217  the default GCM executable is compiled with room for only one horizontal  executable is compiled with room for only one horizontal diagnostic array, or with
218  diagnostic array, as shown in the above example.    numdiags set to 1. In order for the User to enable more than 1 two-dimensional diagnostic,
 In order for the User to enable more than 1 two-dimensional diagnostic,  
219  the size of the diagnostics common must be expanded to accomodate the desired diagnostics.  the size of the diagnostics common must be expanded to accomodate the desired diagnostics.
220  This can be accomplished by manually changing the parameter numdiags in the  This can be accomplished by manually changing the parameter numdiags in the
221  file \filelink{pkg/diagnostics/diagnostics\_SIZE.h}{pkg-diagnostics-diagnostics_SIZE.h}, or by allowing the  file \filelink{pkg/diagnostics/diagnostics\_SIZE.h}{pkg-diagnostics-diagnostics\_SIZE.h}.
222  shell script (???????) to make this  numdiags should be set greater than or equal to the sum of all the diagnostics activated
223  change based on the choice of diagnostic output made in the namelist.  for output each multiplied by the number of levels defined for that diagnostic quantity.
224    This is illustrated in the example below:
225    
226  \subsection{Usage Notes}  \noindent
 \label{sec:diagnostics:usersguide}  
227  To use the diagnostics package, other than enabling it in packages.conf  To use the diagnostics package, other than enabling it in packages.conf
228  and turning the usediagnostics flag in data.pkg to .TRUE., a namelist  and turning the usediagnostics flag in data.pkg to .TRUE., a namelist
229  must be supplied in the run directory called data.diagnostics. The namelist  must be supplied in the run directory called data.diagnostics. The namelist
# Line 186  will activate a user-defined list of dia Line 231  will activate a user-defined list of dia
231  specify the frequency of output, the number of levels, and the name of  specify the frequency of output, the number of levels, and the name of
232  up to 10 separate output files. A sample data.diagnostics namelist file:  up to 10 separate output files. A sample data.diagnostics namelist file:
233    
234  \begin{verbatim}  \noindent
235  \# Diagnostic Package Choices  $\#$ Diagnostic Package Choices \\
236   \&diagnostics_list   $\&$diagnostics\_list \\
237    frequency(1) = 10, \    frequency(1) = 10, \ \\
238     levels(1,1) = 1.,2.,3.,4.,5., \     levels(1,1) = 1.,2.,3.,4.,5., \ \\
239     fields(1,1) = 'UVEL    ','VVEL    ', \     fields(1,1) = 'UVEL    ','VVEL    ', \ \\
240     filename(1) = 'diagout1', \     filename(1) = 'diagout1', \ \\
241    frequency(2) = 100, \    frequency(2) = 100, \ \\
242     levels(1,2) = 1.,2.,3.,4.,5., \     levels(1,2) = 1.,2.,3.,4.,5., \ \\
243     fields(1,2) = 'THETA   ','SALT    ', \     fields(1,2) = 'THETA   ','SALT    ', \ \\
244     filename(2) = 'diagout2', \     filename(2) = 'diagout2', \ \\
245   \&end \   $\&$end \ \\
 \end{verbatim}  
246    
247    \noindent
248  In this example, there are two output files that will be generated  In this example, there are two output files that will be generated
249  for each tile and for each output time. The first set of output files  for each tile and for each output time. The first set of output files
250  has the prefix diagout1, does time averaging every 10 time steps,  has the prefix diagout1, does time averaging every 10 time steps
251  for fields which are multiple-level fields the levels output are 1-5,  (frequency is 10), they will write fields which are multiple-level
252  and the names of diagnostics quantities are UVEL and VVEL.  fields and output levels 1-5. The names of diagnostics quantities are
253  The second set of output files  UVEL and VVEL.  The second set of output files
254  has the prefix diagout2, does time averaging every 100 time steps,  has the prefix diagout2, does time averaging every 100 time steps,
255  for fields which are multiple-level fields the levels output are 1-5,  they include fields which are multiple-level fields, levels output are 1-5,
256  and the names of diagnostics quantities are THETA and SALT.  and the names of diagnostics quantities are THETA and SALT.
257    
258    \noindent
259    In order to define and include as part of the diagnostic output any field
260    that is desired for a particular experiment, two steps must be taken. The
261    first is to enable the ``User Diagnostic'' in data.diagnostics. This is
262    accomplished by setting one of the fields slots to either UDIAG1 through
263    UDIAG10, for multi-level fields, or SDIAG1 through SDIAG10 for single level
264    fields. These are listed in the diagnostics menu. The second step is to
265    add a call to fill\_diagnostics from the subroutine in which the quantity
266    desired for diagnostic output is computed.
267    
268  \newpage  \newpage
269    
270  \subsubsection{GCM Diagnostic Menu}  \subsubsection{GCM Diagnostic Menu}
271  \label{sec:diagnostics:menu}  \label{sec:diagnostics:menu}
272    
273  \begin{tabular}{lllll}  \begin{tabular}{llll}
274  \hline\hline  \hline\hline
275  N & NAME & UNITS & LEVELS & DESCRIPTION \\   NAME & UNITS & LEVELS & DESCRIPTION \\
276  \hline  \hline
277    
278  &\\  &\\
279  1 & UFLUX    &   $Newton/m^2$  &    1     SDIAG1   &             &    1  
          &\begin{minipage}[t]{3in}  
           {Surface U-Wind Stress on the atmosphere}  
          \end{minipage}\\  
 2 & VFLUX    &   $Newton/m^2$  &    1    
280           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
281            {Surface V-Wind Stress on the atmosphere}            {User-Defined Surface Diagnostic-1}
          \end{minipage}\\  
 3 & HFLUX    &   $Watts/m^2$  &    1    
          &\begin{minipage}[t]{3in}  
           {Surface Flux of Sensible Heat}  
282           \end{minipage}\\           \end{minipage}\\
283  4 & EFLUX    &   $Watts/m^2$  &    1     SDIAG2   &             &    1  
284           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
285            {Surface Flux of Latent Heat}            {User-Defined Surface Diagnostic-2}
286           \end{minipage}\\           \end{minipage}\\
287  5 & QICE     &   $Watts/m^2$  &    1     UDIAG1   &             &    Nrphys
288           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
289            {Heat Conduction through Sea-Ice}            {User-Defined Upper-Air Diagnostic-1}
290           \end{minipage}\\           \end{minipage}\\
291  6 & RADLWG   &   $Watts/m^2$ &    1     UDIAG2   &             &    Nrphys
292           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
293            {Net upward LW flux at the ground}            {User-Defined Upper-Air Diagnostic-2}
294           \end{minipage}\\           \end{minipage}\\
295  7 & RADSWG   &   $Watts/m^2$  &    1   SDIAG3   &             &    1  
296           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
297            {Net downward SW flux at the ground}            {User-Defined Surface Diagnostic-3}
298           \end{minipage}\\           \end{minipage}\\
299  8 & RI       &  $dimensionless$ &  Nrphys   SDIAG4   &             &    1  
300           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
301            {Richardson Number}            {User-Defined Surface Diagnostic-4}
302           \end{minipage}\\           \end{minipage}\\
303  9 & CT       &  $dimensionless$ &  1   SDIAG5   &             &    1  
304           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
305            {Surface Drag coefficient for T and Q}            {User-Defined Surface Diagnostic-5}
306           \end{minipage}\\           \end{minipage}\\
307  10 & CU       & $dimensionless$ &  1   SDIAG6   &             &    1  
308           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
309            {Surface Drag coefficient for U and V}            {User-Defined Surface Diagnostic-6}
310           \end{minipage}\\           \end{minipage}\\
311  11 & ET       &  $m^2/sec$ &  Nrphys   SDIAG7   &             &    1  
312           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
313            {Diffusivity coefficient for T and Q}            {User-Defined Surface Diagnostic-7}
314           \end{minipage}\\           \end{minipage}\\
315  12 & EU       &  $m^2/sec$ &  Nrphys   SDIAG8   &             &    1  
316           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
317            {Diffusivity coefficient for U and V}            {User-Defined Surface Diagnostic-8}
318           \end{minipage}\\           \end{minipage}\\
319  13 & TURBU    &  $m/sec/day$ &  Nrphys   SDIAG9   &             &    1  
320           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
321            {U-Momentum Changes due to Turbulence}            {User-Defined Surface Diagnostic-9}
322           \end{minipage}\\           \end{minipage}\\
323  14 & TURBV    &  $m/sec/day$ &  Nrphys   SDIAG10  &             &    1  
324           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
325            {V-Momentum Changes due to Turbulence}            {User-Defined Surface Diagnostic-1-}
326           \end{minipage}\\           \end{minipage}\\
327  15 & TURBT    &  $deg/day$ &  Nrphys   UDIAG3   &             &    Nrphys  
328           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
329            {Temperature Changes due to Turbulence}            {User-Defined Multi-Level Diagnostic-3}
330           \end{minipage}\\           \end{minipage}\\
331  16 & TURBQ    &  $g/kg/day$ &  Nrphys   UDIAG4   &             &    Nrphys  
332           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
333            {Specific Humidity Changes due to Turbulence}            {User-Defined Multi-Level Diagnostic-4}
334           \end{minipage}\\           \end{minipage}\\
335  17 & MOISTT   &   $deg/day$ &  Nrphys   UDIAG5   &             &    Nrphys  
336           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
337            {Temperature Changes due to Moist Processes}            {User-Defined Multi-Level Diagnostic-5}
338           \end{minipage}\\           \end{minipage}\\
339  18 & MOISTQ   &  $g/kg/day$ &  Nrphys   UDIAG6   &             &    Nrphys  
340           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
341            {Specific Humidity Changes due to Moist Processes}            {User-Defined Multi-Level Diagnostic-6}
342           \end{minipage}\\           \end{minipage}\\
343  19 & RADLW    &  $deg/day$ &  Nrphys   UDIAG7   &             &    Nrphys  
344           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
345            {Net Longwave heating rate for each level}            {User-Defined Multi-Level Diagnostic-7}
346           \end{minipage}\\           \end{minipage}\\
347  20 & RADSW    &  $deg/day$ &  Nrphys   UDIAG8   &             &    Nrphys  
348           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
349            {Net Shortwave heating rate for each level}            {User-Defined Multi-Level Diagnostic-8}
350           \end{minipage}\\           \end{minipage}\\
351  21 & PREACC   &  $mm/day$ &  1   UDIAG9   &             &    Nrphys  
352           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
353            {Total Precipitation}            {User-Defined Multi-Level Diagnostic-9}
354           \end{minipage}\\           \end{minipage}\\
355  22 & PRECON   &  $mm/day$ &  1   UDIAG10  &             &    Nrphys  
356           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
357            {Convective Precipitation}            {User-Defined Multi-Level Diagnostic-10}
358           \end{minipage}\\           \end{minipage}\\
359  23 & TUFLUX   &  $Newton/m^2$ &  Nrphys   SDIAGC   &             &    1  
360           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
361            {Turbulent Flux of U-Momentum}            {User-Defined Counted Surface Diagnostic}
362           \end{minipage}\\           \end{minipage}\\
363  24 & TVFLUX   &  $Newton/m^2$ &  Nrphys   SDIAGCC  &             &    1  
364           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
365            {Turbulent Flux of V-Momentum}            {User-Defined Counted Surface Diagnostic Counter}
366           \end{minipage}\\           \end{minipage}\\
367  25 & TTFLUX   &  $Watts/m^2$ &  Nrphys   ETAN     & $(hPa,m)$ &    1
368           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
369            {Turbulent Flux of Sensible Heat}            {Perturbation of Surface (pressure, height)}
370           \end{minipage}\\           \end{minipage}\\
371  26 & TQFLUX   &  $Watts/m^2$ &  Nrphys   ETANSQ   & $(hPa^2,m^2)$ & 1
372           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
373            {Turbulent Flux of Latent Heat}            {Square of Perturbation of Surface (pressure, height)}
374           \end{minipage}\\           \end{minipage}\\
375  27 & CN       &  $dimensionless$ &  1   DETADT2  & ${r-unit}^2/s^2$ & 1
376           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
377            {Neutral Drag Coefficient}            {Square of Eta (Surf.P,SSH) Tendency}
378           \end{minipage}\\           \end{minipage}\\
379  28 & WINDS     &  $m/sec$ &  1   THETA    & $deg K$ & Nr
380           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
381            {Surface Wind Speed}            {Potential Temperature}
382           \end{minipage}\\           \end{minipage}\\
383  29 & DTSRF     &  $deg$ &  1   SST      & $deg K$ & 1
384           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
385            {Air/Surface virtual temperature difference}            {Sea Surface Temperature}
386           \end{minipage}\\           \end{minipage}\\
387  30 & TG        &  $deg$ &  1   SALT     & $g/kg$ & Nr
388           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
389            {Ground temperature}            {Salt (or Water Vapor Mixing Ratio)}
390           \end{minipage}\\           \end{minipage}\\
391  31 & TS        &  $deg$ &  1   SSS      & $g/kg$ & 1
392           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
393            {Surface air temperature (Adiabatic from lowest model layer)}            {Sea Surface Salinity}
394           \end{minipage}\\           \end{minipage}\\
395  32 & DTG       &  $deg$ &  1   SALTanom & $g/kg$ & Nr
396           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
397            {Ground temperature adjustment}            {Salt anomaly (=SALT-35)}
398           \end{minipage}\\           \end{minipage}\\
   
399  \end{tabular}  \end{tabular}
400    \vspace{1.5in}
401    \vfill
402    
403  \newpage  \newpage
404  \vspace*{\fill}  \vspace*{\fill}
405  \begin{tabular}{lllll}  \begin{tabular}{llll}
406  \hline\hline  \hline\hline
407  N & NAME & UNITS & LEVELS & DESCRIPTION \\   NAME & UNITS & LEVELS & DESCRIPTION \\
408  \hline  \hline
409    
410  &\\  &\\
411  33 & QG        &  $g/kg$ &  1   UVEL     & $m/sec$ & Nr
412           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
413            {Ground specific humidity}            {U-Velocity}
414           \end{minipage}\\           \end{minipage}\\
415  34 & QS        &  $g/kg$ &  1   VVEL     & $m/sec$ & Nr
416           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
417            {Saturation surface specific humidity}            {V-Velocity}
418           \end{minipage}\\           \end{minipage}\\
419     UVEL\_k2  & $m/sec$ & 1
 &\\  
 35 & TGRLW    &    $deg$   &    1    
420           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
421            {Instantaneous ground temperature used as input to the            {U-Velocity}
            Longwave radiation subroutine}  
422           \end{minipage}\\           \end{minipage}\\
423  36 & ST4      &   $Watts/m^2$  &    1     VVEL\_k2  & $m/sec$ & 1
424           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
425            {Upward Longwave flux at the ground ($\sigma T^4$)}            {V-Velocity}
426           \end{minipage}\\           \end{minipage}\\
427  37 & OLR      &   $Watts/m^2$  &    1     WVEL     & $m/sec$ & Nr
428           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
429            {Net upward Longwave flux at the top of the model}            {Vertical-Velocity}
430           \end{minipage}\\           \end{minipage}\\
431  38 & OLRCLR   &   $Watts/m^2$  &    1     THETASQ  & $deg^2$ & Nr
432           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
433            {Net upward clearsky Longwave flux at the top of the model}            {Square of Potential Temperature}
434           \end{minipage}\\           \end{minipage}\\
435  39 & LWGCLR   &   $Watts/m^2$  &    1     SALTSQ   & $g^2/{kg}^2$ & Nr
436           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
437            {Net upward clearsky Longwave flux at the ground}            {Square of Salt (or Water Vapor Mixing Ratio)}
438           \end{minipage}\\           \end{minipage}\\
439  40 & LWCLR    &  $deg/day$ &  Nrphys   SALTSQan & $g^2/{kg}^2$ & Nr
440           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
441            {Net clearsky Longwave heating rate for each level}            {Square of Salt anomaly (=SALT-35)}
442           \end{minipage}\\           \end{minipage}\\
443  41 & TLW      &    $deg$   &  Nrphys   UVELSQ   & $m^2/sec^2$ & Nr
444           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
445            {Instantaneous temperature used as input to the Longwave radiation            {Square of U-Velocity}
           subroutine}  
446           \end{minipage}\\           \end{minipage}\\
447  42 & SHLW     &    $g/g$   &  Nrphys   VVELSQ   & $m^2/sec^2$ & Nr
448           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
449            {Instantaneous specific humidity used as input to the Longwave radiation            {Square of V-Velocity}
           subroutine}  
450           \end{minipage}\\           \end{minipage}\\
451  43 & OZLW     &    $g/g$   &  Nrphys   WVELSQ   & $m^2/sec^2$ & Nr
452           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
453            {Instantaneous ozone used as input to the Longwave radiation            {Square of Vertical-Velocity}
           subroutine}  
454           \end{minipage}\\           \end{minipage}\\
455  44 & CLMOLW   &    $0-1$   &  Nrphys   UV\_VEL\_C & $m^2/sec^2$ & Nr
456           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
457            {Maximum overlap cloud fraction used in the Longwave radiation            {Meridional Transport of Zonal Momentum (cell center)}
           subroutine}  
458           \end{minipage}\\           \end{minipage}\\
459  45 & CLDTOT   &    $0-1$   &  Nrphys   UV\_VEL\_Z & $m^2/sec^2$ & Nr
460           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
461            {Total cloud fraction used in the Longwave and Shortwave radiation            {Meridional Transport of Zonal Momentum (corner)}
           subroutines}  
462           \end{minipage}\\           \end{minipage}\\
463  46 & RADSWT   &    $Watts/m^2$   &  1   WU\_VEL   & $m^2/sec^2$ & Nr
464           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
465            {Incident Shortwave radiation at the top of the atmosphere}            {Vertical Transport of Zonal Momentum (cell center)}
466           \end{minipage}\\           \end{minipage}\\
467  47 & CLROSW   &    $0-1$   &  Nrphys   WV\_VEL   & $m^2/sec^2$ & Nr
468           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
469            {Random overlap cloud fraction used in the shortwave radiation            {Vertical Transport of Meridional Momentum (cell center)}
           subroutine}  
470           \end{minipage}\\           \end{minipage}\\
471  48 & CLMOSW   &    $0-1$   &  Nrphys   UVELMASS & $m/sec$ & Nr
472           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
473            {Maximum overlap cloud fraction used in the shortwave radiation            {Zonal Mass-Weighted Component of Velocity}
           subroutine}  
474           \end{minipage}\\           \end{minipage}\\
475  49 & EVAP     &    $mm/day$   &  1   VVELMASS & $m/sec$ & Nr
476           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
477            {Surface evaporation}            {Meridional Mass-Weighted Component of Velocity}
478           \end{minipage}\\           \end{minipage}\\
479  \end{tabular}   WVELMASS & $m/sec$ & Nr
 \vfill  
   
 \newpage  
 \vspace*{\fill}  
 \begin{tabular}{lllll}  
 \hline\hline  
 N & NAME & UNITS & LEVELS & DESCRIPTION \\  
 \hline  
   
 &\\  
 50 & DUDT     &    $m/sec/day$ &  Nrphys  
480           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
481            {Total U-Wind tendency}            {Vertical Mass-Weighted Component of Velocity}
482           \end{minipage}\\           \end{minipage}\\
483  51 & DVDT     &    $m/sec/day$ &  Nrphys   UTHMASS  & $m-deg/sec$ & Nr
484           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
485            {Total V-Wind tendency}            {Zonal Mass-Weight Transp of Pot Temp}
486           \end{minipage}\\           \end{minipage}\\
487  52 & DTDT     &    $deg/day$ &  Nrphys   VTHMASS  & $m-deg/sec$ & Nr
488           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
489            {Total Temperature tendency}            {Meridional Mass-Weight Transp of Pot Temp}
490           \end{minipage}\\           \end{minipage}\\
491  53 & DQDT     &    $g/kg/day$ &  Nrphys   WTHMASS  & $m-deg/sec$ & Nr
492           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
493            {Total Specific Humidity tendency}            {Vertical Mass-Weight Transp of Pot Temp}
494           \end{minipage}\\           \end{minipage}\\
495  54 & USTAR    &    $m/sec$ &  1   USLTMASS & $m-kg/sec-kg$ & Nr
496           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
497            {Surface USTAR wind}            {Zonal Mass-Weight Transp of Salt (or W.Vap Mix Rat.)}
498           \end{minipage}\\           \end{minipage}\\
499  55 & Z0       &    $m$ &  1   VSLTMASS & $m-kg/sec-kg$ & Nr
500           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
501            {Surface roughness}            {Meridional Mass-Weight Transp of Salt (or W.Vap Mix Rat.)}
502           \end{minipage}\\           \end{minipage}\\
503  56 & FRQTRB   &    $0-1$ &  Nrphys-1   WSLTMASS & $m-kg/sec-kg$ & Nr
504           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
505            {Frequency of Turbulence}            {Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)}
506           \end{minipage}\\           \end{minipage}\\
507  57 & PBL      &    $mb$ &  1   UVELTH   & $m-deg/sec$ & Nr
508           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
509            {Planetary Boundary Layer depth}            {Zonal Transp of Pot Temp}
510           \end{minipage}\\           \end{minipage}\\
511  58 & SWCLR    &  $deg/day$ &  Nrphys   VVELTH   & $m-deg/sec$ & Nr
512           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
513            {Net clearsky Shortwave heating rate for each level}            {Meridional Transp of Pot Temp}
514           \end{minipage}\\           \end{minipage}\\
515  59 & OSR      &   $Watts/m^2$  &    1   WVELTH   & $m-deg/sec$ & Nr
516           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
517            {Net downward Shortwave flux at the top of the model}            {Vertical Transp of Pot Temp}
518           \end{minipage}\\           \end{minipage}\\
519  60 & OSRCLR   &   $Watts/m^2$  &    1     UVELSLT  & $m-kg/sec-kg$ & Nr
520           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
521            {Net downward clearsky Shortwave flux at the top of the model}            {Zonal Transp of Salt (or W.Vap Mix Rat.)}
522           \end{minipage}\\           \end{minipage}\\
523  61 & CLDMAS   &   $kg / m^2$  &    Nrphys   VVELSLT  & $m-kg/sec-kg$ & Nr
524           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
525            {Convective cloud mass flux}            {Meridional Transp of Salt (or W.Vap Mix Rat.)}
526           \end{minipage}\\           \end{minipage}\\
527  62 & UAVE     &   $m/sec$  &    Nrphys   WVELSLT  & $m-kg/sec-kg$ & Nr
528           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
529            {Time-averaged $u-Wind$}            {Vertical Transp of Salt (or W.Vap Mix Rat.)}
530           \end{minipage}\\           \end{minipage}\\
531  63 & VAVE     &   $m/sec$  &    Nrphys  \end{tabular}
532    \vspace{1.5in}
533    \vfill
534    
535    \newpage
536    \vspace*{\fill}
537    \begin{tabular}{llll}
538    \hline\hline
539     NAME & UNITS & LEVELS & DESCRIPTION \\
540    \hline
541    
542    &\\
543     RHOAnoma & $kg/m^3  $  &  Nr  
544           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
545            {Time-averaged $v-Wind$}            {Density Anomaly (=Rho-rhoConst)}
546           \end{minipage}\\           \end{minipage}\\
547  64 & TAVE     &   $deg$  &    Nrphys   RHOANOSQ & $kg^2/m^6$  &  Nr  
548           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
549            {Time-averaged $Temperature$}            {Square of Density Anomaly (=(Rho-rhoConst))}
550           \end{minipage}\\           \end{minipage}\\
551  65 & QAVE     &   $g/g$  &    Nrphys   URHOMASS & $kg/m^2/s$  &  Nr  
552           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
553            {Time-averaged $Specific \, \, Humidity$}            {Zonal Transport of Density}
554           \end{minipage}\\           \end{minipage}\\
555  66 & PAVE     &   $mb$  &    1   VRHOMASS & $kg/m^2/s$  &  Nr  
556           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
557            {Time-averaged $p_{surf} - p_{top}$}            {Meridional Transport of Density}
558           \end{minipage}\\           \end{minipage}\\
559  67 & QQAVE    &   $(m/sec)^2$  &    Nrphys   WRHOMASS & $kg/m^2/s$  &  Nr  
560           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
561            {Time-averaged $Turbulent Kinetic Energy$}            {Vertical Transport of Potential Density}
562           \end{minipage}\\           \end{minipage}\\
563  68 & SWGCLR   &   $Watts/m^2$  &    1     PHIHYD   & $m^2/s^2 $  &  Nr  
564           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
565            {Net downward clearsky Shortwave flux at the ground}            {Hydrostatic (ocean) pressure / (atmos) geo-Potential}
566           \end{minipage}\\           \end{minipage}\\
567  69 & SDIAG1   &             &    1     PHIHYDSQ & $m^4/s^4 $  &  Nr  
568           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
569            {User-Defined Surface Diagnostic-1}            {Square of Hyd. (ocean) press / (atmos) geoPotential}
570           \end{minipage}\\           \end{minipage}\\
571  70 & SDIAG2   &             &    1     PHIBOT   & $m^2/s^2 $  &  Nr  
572           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
573            {User-Defined Surface Diagnostic-2}            {ocean bottom pressure / top. atmos geo-Potential}
574           \end{minipage}\\           \end{minipage}\\
575  71 & UDIAG1   &             &    Nrphys   PHIBOTSQ & $m^4/s^4 $  &  Nr  
576           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
577            {User-Defined Upper-Air Diagnostic-1}            {Square of ocean bottom pressure / top. geo-Potential}
578           \end{minipage}\\           \end{minipage}\\
579  72 & UDIAG2   &             &    Nrphys   DRHODR   & $kg/m^3/{r-unit}$ & Nr
580           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
581            {User-Defined Upper-Air Diagnostic-2}            {Stratification: d.Sigma/dr}
582           \end{minipage}\\           \end{minipage}\\
583  73 & DIABU    & $m/sec/day$ &    Nrphys   VISCA4   & $m^4/sec$ & 1
584           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
585            {Total Diabatic forcing on $u-Wind$}            {Biharmonic Viscosity Coefficient}
586           \end{minipage}\\           \end{minipage}\\
587  74 & DIABV    & $m/sec/day$ &    Nrphys   VISCAH   & $m^2/sec$ & 1
588           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
589            {Total Diabatic forcing on $v-Wind$}            {Harmonic Viscosity Coefficient}
590           \end{minipage}\\           \end{minipage}\\
591  75 & DIABT    & $deg/day$ &    Nrphys   TAUX     & $N/m^2        $ & 1
592           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
593            {Total Diabatic forcing on $Temperature$}            {zonal surface wind stress, >0 increases uVel}
594           \end{minipage}\\           \end{minipage}\\
595  76 & DIABQ    & $g/kg/day$ &    Nrphys   TAUY     & $N/m^2        $ & 1
596           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
597            {Total Diabatic forcing on $Specific \, \, Humidity$}            {meridional surf. wind stress, >0 increases vVel}
598           \end{minipage}\\           \end{minipage}\\
599     TFLUX    & $W/m^2        $ & 1
 \end{tabular}  
 \vfill  
   
 \newpage  
 \vspace*{\fill}  
 \begin{tabular}{lllll}  
 \hline\hline  
 N & NAME & UNITS & LEVELS & DESCRIPTION \\  
 \hline  
   
 77 & VINTUQ  & $m/sec \cdot g/kg$ &    1  
600           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
601            {Vertically integrated $u \, q$}            {net surface heat flux, >0 increases theta}
602           \end{minipage}\\           \end{minipage}\\
603  78 & VINTVQ  & $m/sec \cdot g/kg$ &    1   TRELAX   & $W/m^2        $ & 1
604           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
605            {Vertically integrated $v \, q$}            {surface temperature relaxation, >0 increases theta}
606           \end{minipage}\\           \end{minipage}\\
607  79 & VINTUT  & $m/sec \cdot deg$ &    1   TICE     & $W/m^2        $ & 1
608           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
609            {Vertically integrated $u \, T$}            {heat from melt/freeze of sea-ice, >0 increases theta}
610           \end{minipage}\\           \end{minipage}\\
611  80 & VINTVT  & $m/sec \cdot deg$ &    1   SFLUX    & $g/m^2/s      $ & 1
612           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
613            {Vertically integrated $v \, T$}            {net surface salt flux, >0 increases salt}
614           \end{minipage}\\           \end{minipage}\\
615  81 & CLDFRC  & $0-1$ &    1   SRELAX   & $g/m^2/s      $ & 1
616           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
617            {Total Cloud Fraction}            {surface salinity relaxation, >0 increases salt}
618           \end{minipage}\\           \end{minipage}\\
619  82 & QINT    & $gm/cm^2$ &    1   PRESSURE & $Pa           $ & Nr
620           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
621            {Precipitable water}            {Atmospheric Pressure (Pa)}
622           \end{minipage}\\           \end{minipage}\\
623  83 & U2M     & $m/sec$ &    1   ADVr\_TH  & $K.Pa.m^2/s   $ & Nr
624           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
625            {U-Wind at 2 meters}            {Vertical   Advective Flux of Pot.Temperature}
626           \end{minipage}\\           \end{minipage}\\
627  84 & V2M     & $m/sec$ &    1   ADVx\_TH  & $K.Pa.m^2/s   $ & Nr
628           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
629            {V-Wind at 2 meters}            {Zonal      Advective Flux of Pot.Temperature}
630           \end{minipage}\\           \end{minipage}\\
631  85 & T2M     & $deg$ &    1   ADVy\_TH  & $K.Pa.m^2/s   $ & Nr
632           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
633            {Temperature at 2 meters}            {Meridional Advective Flux of Pot.Temperature}
634           \end{minipage}\\           \end{minipage}\\
635  86 & Q2M     & $g/kg$ &    1   DFrE\_TH  & $K.Pa.m^2/s   $ & Nr
636           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
637            {Specific Humidity at 2 meters}            {Vertical Diffusive Flux of Pot.Temperature (Explicit part)}
638           \end{minipage}\\           \end{minipage}\\
639  87 & U10M    & $m/sec$ &    1   DIFx\_TH  & $K.Pa.m^2/s   $ & Nr
640           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
641            {U-Wind at 10 meters}            {Zonal      Diffusive Flux of Pot.Temperature}
642           \end{minipage}\\           \end{minipage}\\
643  88 & V10M    & $m/sec$ &    1   DIFy\_TH  & $K.Pa.m^2/s   $ & Nr
644           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
645            {V-Wind at 10 meters}            {Meridional Diffusive Flux of Pot.Temperature}
646           \end{minipage}\\           \end{minipage}\\
647  89 & T10M    & $deg$ &    1   DFrI\_TH  & $K.Pa.m^2/s   $ & Nr
648           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
649            {Temperature at 10 meters}            {Vertical Diffusive Flux of Pot.Temperature (Implicit part)}
650           \end{minipage}\\           \end{minipage}\\
651  90 & Q10M    & $g/kg$ &    1   ADVr\_SLT & $g/kg.Pa.m^2/s$ & Nr
652           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
653            {Specific Humidity at 10 meters}            {Vertical   Advective Flux of Water-Vapor}
654           \end{minipage}\\           \end{minipage}\\
655  91 & DTRAIN  & $kg/m^2$ &    Nrphys   ADVx\_SLT & $g/kg.Pa.m^2/s$ & Nr
656           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
657            {Detrainment Cloud Mass Flux}            {Zonal      Advective Flux of Water-Vapor}
658           \end{minipage}\\           \end{minipage}\\
659  92 & QFILL   & $g/kg/day$ &    Nrphys   ADVy\_SLT & $g/kg.Pa.m^2/s$ & Nr
660           &\begin{minipage}[t]{3in}           &\begin{minipage}[t]{3in}
661            {Filling of negative specific humidity}            {Meridional Advective Flux of Water-Vapor}
662           \end{minipage}\\           \end{minipage}\\
663    \end{tabular}
664    \vspace{1.5in}
665    \vfill
666    
667    \newpage
668    \vspace*{\fill}
669    \begin{tabular}{llll}
670    \hline\hline
671     NAME & UNITS & LEVELS & DESCRIPTION \\
672    \hline
673    
674    &\\
675     DFrE\_SLT & $g/kg.Pa.m^2/s$ & Nr
676             &\begin{minipage}[t]{3in}
677              {Vertical Diffusive Flux of Water-Vapor (Explicit part)}
678             \end{minipage}\\
679     DIFx\_SLT & $g/kg.Pa.m^2/s$ & Nr
680             &\begin{minipage}[t]{3in}
681              {Zonal      Diffusive Flux of Water-Vapor}
682             \end{minipage}\\
683     DIFy\_SLT & $g/kg.Pa.m^2/s$ & Nr
684             &\begin{minipage}[t]{3in}
685              {Meridional Diffusive Flux of Water-Vapor}
686             \end{minipage}\\
687     DFrI\_SLT & $g/kg.Pa.m^2/s$ & Nr
688             &\begin{minipage}[t]{3in}
689              {Vertical Diffusive Flux of Water-Vapor (Implicit part)}
690             \end{minipage}\\
691  \end{tabular}  \end{tabular}
692  \vspace{1.5in}  \vspace{1.5in}
693  \vfill  \vfill
# Line 651  is time-averaged over its diagnostic out Line 706  is time-averaged over its diagnostic out
706  {\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t)  {\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t)
707  \]  \]
708  where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the  where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the
709  output frequency of the diagnositc, and $\Delta t$ is  output frequency of the diagnostic, and $\Delta t$ is
710  the timestep over which the diagnostic is updated.  For further information on how  the timestep over which the diagnostic is updated.  
 to set the diagnostic output frequency {\bf NQDIAG}, please see Part III, A User's Guide.  
   
 {\bf 1)  \underline {UFLUX} Surface Zonal Wind Stress on the Atmosphere ($Newton/m^2$) }  
   
 The zonal wind stress is the turbulent flux of zonal momentum from  
 the surface. See section 3.3 for a description of the surface layer parameterization.  
 \[  
 {\bf UFLUX} =  - \rho C_D W_s u \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u  
 \]  
 where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface  
 drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum  
 (see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $u$ is  
 the zonal wind in the lowest model layer.  
 \\  
   
   
 {\bf 2)  \underline {VFLUX} Surface Meridional Wind Stress on the Atmosphere ($Newton/m^2$) }  
   
 The meridional wind stress is the turbulent flux of meridional momentum from  
 the surface. See section 3.3 for a description of the surface layer parameterization.  
 \[  
 {\bf VFLUX} =  - \rho C_D W_s v \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u  
 \]  
 where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface  
 drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum  
 (see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $v$ is  
 the meridional wind in the lowest model layer.  
 \\  
   
 {\bf 3)  \underline {HFLUX} Surface Flux of Sensible Heat ($Watts/m^2$) }  
   
 The turbulent flux of sensible heat from the surface to the atmosphere is a function of the  
 gradient of virtual potential temperature and the eddy exchange coefficient:  
 \[  
 {\bf HFLUX} =  P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{surface} - \theta_{Nrphys})  
 \hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t  
 \]  
 where $\rho$ = the atmospheric density at the surface, $c_{p}$ is the specific  
 heat of air, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the  
 magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient  
 for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient  
 for heat and moisture (see diagnostic number 9), and $\theta$ is the potential temperature  
 at the surface and at the bottom model level.  
 \\  
   
   
 {\bf 4)  \underline {EFLUX} Surface Flux of Latent Heat ($Watts/m^2$) }  
   
 The turbulent flux of latent heat from the surface to the atmosphere is a function of the  
 gradient of moisture, the potential evapotranspiration fraction and the eddy exchange coefficient:  
 \[  
 {\bf EFLUX} =  \rho \beta L C_{H} W_s (q_{surface} - q_{Nrphys})  
 \hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t  
 \]  
 where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of  
 the potential evapotranspiration actually evaporated, L is the latent  
 heat of evaporation, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the  
 magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient  
 for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient  
 for heat and moisture (see diagnostic number 9), and $q_{surface}$ and $q_{Nrphys}$ are the specific  
 humidity at the surface and at the bottom model level, respectively.  
 \\  
   
 {\bf 5)  \underline {QICE} Heat Conduction Through Sea Ice ($Watts/m^2$) }  
   
 Over sea ice there is an additional source of energy at the surface due to the heat  
 conduction from the relatively warm ocean through the sea ice. The heat conduction  
 through sea ice represents an additional energy source term for the ground temperature equation.  
   
 \[  
 {\bf QICE} = {C_{ti} \over {H_i}} (T_i-T_g)  
 \]  
   
 where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to  
 be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and  
 $T_g$ is the temperature of the sea ice.  
   
 NOTE: QICE is not available through model version 5.3, but is available in subsequent versions.  
 \\  
   
   
 {\bf 6) \underline {RADLWG} Net upward Longwave Flux at the surface ($Watts/m^2$)}  
   
 \begin{eqnarray*}  
 {\bf RADLWG} & =  & F_{LW,Nrphys+1}^{Net} \\  
              & =  & F_{LW,Nrphys+1}^\uparrow - F_{LW,Nrphys+1}^\downarrow  
 \end{eqnarray*}  
 \\  
 where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$.  
 $F_{LW}^\uparrow$ is  
 the upward Longwave flux and $F_{LW}^\downarrow$ is the downward Longwave flux.  
 \\  
   
 {\bf 7) \underline {RADSWG} Net downard shortwave Flux at the surface ($Watts/m^2$)}  
   
 \begin{eqnarray*}  
 {\bf RADSWG} & =  & F_{SW,Nrphys+1}^{Net} \\  
              & =  & F_{SW,Nrphys+1}^\downarrow - F_{SW,Nrphys+1}^\uparrow  
 \end{eqnarray*}  
 \\  
 where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$.  
 $F_{SW}^\downarrow$ is  
 the downward Shortwave flux and $F_{SW}^\uparrow$ is the upward Shortwave flux.  
 \\  
   
   
 \noindent  
 {\bf 8)  \underline {RI} Richardson Number} ($dimensionless$)  
   
 \noindent  
 The non-dimensional stability indicator is the ratio of the buoyancy to the shear:  
 \[  
 {\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } }  
  =  {  {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } }  
 \]  
 \\  
 where we used the hydrostatic equation:  
 \[  
 {\pp{\Phi}{P^ \kappa}} = c_p \theta_v  
 \]  
 Negative values indicate unstable buoyancy {\bf{AND}} shear, small positive values ($<0.4$)  
 indicate dominantly unstable shear, and large positive values indicate dominantly stable  
 stratification.  
 \\  
   
 \noindent  
 {\bf 9)  \underline {CT}  Surface Exchange Coefficient for Temperature and Moisture ($dimensionless$) }  
   
 \noindent  
 The surface exchange coefficient is obtained from the similarity functions for the stability  
  dependant flux profile relationships:  
 \[  
 {\bf CT} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} =  
 -{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} =  
 { k \over { (\psi_{h} + \psi_{g}) } }  
 \]  
 where $\psi_h$ is the surface layer non-dimensional temperature change and $\psi_g$ is the  
 viscous sublayer non-dimensional temperature or moisture change:  
 \[  
 \psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} \hspace{1cm} and  
 \hspace{1cm} \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} }  
 (h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2}  
 \]  
 and:  
 $h_{0} = 30z_{0}$ with a maximum value over land of 0.01  
   
 \noindent  
 $\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of  
 the temperature and moisture gradients, specified differently for stable and unstable  
 layers according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the  
 non-dimensional stability parameter, Pr is the Prandtl number for air, $\nu$ is the molecular  
 viscosity, $z_{0}$ is the surface roughness length, $u_*$ is the surface stress velocity  
 (see diagnostic number 67), and the subscript ref refers to a reference value.  
 \\  
   
 \noindent  
 {\bf 10)  \underline {CU}  Surface Exchange Coefficient for Momentum ($dimensionless$) }  
   
 \noindent  
 The surface exchange coefficient is obtained from the similarity functions for the stability  
  dependant flux profile relationships:  
 \[  
 {\bf CU} = {u_* \over W_s} = { k \over \psi_{m} }  
 \]  
 where $\psi_m$ is the surface layer non-dimensional wind shear:  
 \[  
 \psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta}  
 \]  
 \noindent  
 $\phi_m$ is the similarity function of $\zeta$, which expresses the stability dependance of  
 the temperature and moisture gradients, specified differently for stable and unstable layers  
 according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the  
 non-dimensional stability parameter, $u_*$ is the surface stress velocity  
 (see diagnostic number 67), and $W_s$ is the magnitude of the surface layer wind.  
 \\  
   
 \noindent  
 {\bf 11)  \underline {ET}  Diffusivity Coefficient for Temperature and Moisture ($m^2/sec$) }  
   
 \noindent  
 In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat or  
 moisture flux for the atmosphere above the surface layer can be expressed as a turbulent  
 diffusion coefficient $K_h$ times the negative of the gradient of potential temperature  
 or moisture. In the Helfand and Labraga (1988) adaptation of this closure, $K_h$  
 takes the form:  
 \[  
 {\bf ET} = K_h = -{( {\overline{w^{\prime}\theta_v^{\prime}}}) \over {\pp{\theta_v}{z}} }  
  = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) & \mbox{decaying turbulence}  
 \\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right.  
 \]  
 where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm}  
 energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model,  
 which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer  
 depth,  
 $S_H$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and  
 wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium  
 dimensionless buoyancy and wind shear  
 parameters.   Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$,  
 are functions of the Richardson number.  
   
 \noindent  
 For the detailed equations and derivations of the modified level 2.5 closure scheme,  
 see Helfand and Labraga, 1988.  
   
 \noindent  
 In the surface layer, ${\bf {ET}}$ is the exchange coefficient for heat and moisture,  
 in units of $m/sec$, given by:  
 \[  
 {\bf ET_{Nrphys}} =  C_t * u_* = C_H W_s  
 \]  
 \noindent  
 where $C_t$ is the dimensionless exchange coefficient for heat and moisture from the  
 surface layer similarity functions (see diagnostic number 9), $u_*$ is the surface  
 friction velocity (see diagnostic number 67), $C_H$ is the heat transfer coefficient,  
 and $W_s$ is the magnitude of the surface layer wind.  
 \\  
   
 \noindent  
 {\bf 12)  \underline {EU}  Diffusivity Coefficient for Momentum ($m^2/sec$) }  
   
 \noindent    
 In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat  
 momentum flux for the atmosphere above the surface layer can be expressed as a turbulent  
 diffusion coefficient $K_m$ times the negative of the gradient of the u-wind.  
 In the Helfand and Labraga (1988) adaptation of this closure, $K_m$  
 takes the form:  
 \[  
 {\bf EU} = K_m = -{( {\overline{u^{\prime}w^{\prime}}}) \over {\pp{U}{z}} }  
  = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) & \mbox{decaying turbulence}  
 \\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right.  
 \]  
 \noindent  
 where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm}  
 energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model,  
 which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer  
 depth,  
 $S_M$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and  
 wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium  
 dimensionless buoyancy and wind shear  
 parameters.   Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$,  
 are functions of the Richardson number.  
   
 \noindent  
 For the detailed equations and derivations of the modified level 2.5 closure scheme,  
 see Helfand and Labraga, 1988.  
   
 \noindent  
 In the surface layer, ${\bf {EU}}$ is the exchange coefficient for momentum,  
 in units of $m/sec$, given by:  
 \[  
 {\bf EU_{Nrphys}} = C_u * u_* = C_D W_s  
 \]  
 \noindent  
 where $C_u$ is the dimensionless exchange coefficient for momentum from the surface layer  
 similarity functions (see diagnostic number 10), $u_*$ is the surface friction velocity  
 (see diagnostic number 67), $C_D$ is the surface drag coefficient, and $W_s$ is the  
 magnitude of the surface layer wind.  
 \\  
   
 \noindent  
 {\bf 13)  \underline {TURBU}  Zonal U-Momentum changes due to Turbulence ($m/sec/day$) }  
   
 \noindent  
 The tendency of U-Momentum due to turbulence is written:  
 \[  
 {\bf TURBU} = {\pp{u}{t}}_{turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})}  
  = {\pp{}{z} }{(K_m \pp{u}{z})}  
 \]  
   
 \noindent  
 The Helfand and Labraga level 2.5 scheme models the turbulent  
 flux of u-momentum in terms of $K_m$, and the equation has the form of a diffusion  
 equation.  
   
 \noindent  
 {\bf 14)  \underline {TURBV}  Meridional V-Momentum changes due to Turbulence ($m/sec/day$) }  
   
 \noindent  
 The tendency of V-Momentum due to turbulence is written:  
 \[  
 {\bf TURBV} = {\pp{v}{t}}_{turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})}  
  = {\pp{}{z} }{(K_m \pp{v}{z})}  
 \]  
   
 \noindent  
 The Helfand and Labraga level 2.5 scheme models the turbulent  
 flux of v-momentum in terms of $K_m$, and the equation has the form of a diffusion  
 equation.  
 \\  
   
 \noindent  
 {\bf 15)  \underline {TURBT}  Temperature changes due to Turbulence ($deg/day$) }  
   
 \noindent  
 The tendency of temperature due to turbulence is written:  
 \[  
 {\bf TURBT} = {\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{turb} =  
 P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})}  
  = P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})}  
 \]  
   
 \noindent  
 The Helfand and Labraga level 2.5 scheme models the turbulent  
 flux of temperature in terms of $K_h$, and the equation has the form of a diffusion  
 equation.  
 \\  
   
 \noindent  
 {\bf 16)  \underline {TURBQ}  Specific Humidity changes due to Turbulence ($g/kg/day$) }  
   
 \noindent  
 The tendency of specific humidity due to turbulence is written:  
 \[  
 {\bf TURBQ} = {\pp{q}{t}}_{turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})}  
  = {\pp{}{z} }{(K_h \pp{q}{z})}  
 \]  
   
 \noindent  
 The Helfand and Labraga level 2.5 scheme models the turbulent  
 flux of temperature in terms of $K_h$, and the equation has the form of a diffusion  
 equation.  
 \\  
   
 \noindent  
 {\bf 17)  \underline {MOISTT} Temperature Changes Due to Moist Processes ($deg/day$) }  
   
 \noindent  
 \[  
 {\bf MOISTT} = \left. {\pp{T}{t}}\right|_{c} + \left. {\pp{T}{t}} \right|_{ls}  
 \]  
 where:  
 \[  
 \left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over c_p} \Gamma_s \right)_i  
 \hspace{.4cm} and  
 \hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = {L \over c_p } (q^*-q)  
 \]  
 and  
 \[  
 \Gamma_s = g \eta \pp{s}{p}  
 \]  
   
 \noindent  
 The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale  
 precipitation processes, or supersaturation rain.  
 The summation refers to contributions from each cloud type called by RAS.    
 The dry static energy is given  
 as $s$, the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is  
 given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc},  
 the description of the convective parameterization.  The fractional adjustment, or relaxation  
 parameter, for each cloud type is given as $\alpha$, while  
 $R$ is the rain re-evaporation adjustment.  
 \\  
   
 \noindent  
 {\bf 18)  \underline {MOISTQ} Specific Humidity Changes Due to Moist Processes ($g/kg/day$) }  
   
 \noindent  
 \[  
 {\bf MOISTQ} = \left. {\pp{q}{t}}\right|_{c} + \left. {\pp{q}{t}} \right|_{ls}  
 \]  
 where:  
 \[  
 \left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over {L}}(\Gamma_h-\Gamma_s) \right)_i  
 \hspace{.4cm} and  
 \hspace{.4cm} \left.{\pp{q}{t}}\right|_{ls} = (q^*-q)  
 \]  
 and  
 \[  
 \Gamma_s = g \eta \pp{s}{p}\hspace{.4cm} and \hspace{.4cm}\Gamma_h = g \eta \pp{h}{p}  
 \]  
 \noindent  
 The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale  
 precipitation processes, or supersaturation rain.  
 The summation refers to contributions from each cloud type called by RAS.    
 The dry static energy is given as $s$,  
 the moist static energy is given as $h$,  
 the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is  
 given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc},  
 the description of the convective parameterization.  The fractional adjustment, or relaxation  
 parameter, for each cloud type is given as $\alpha$, while  
 $R$ is the rain re-evaporation adjustment.  
 \\  
   
 \noindent  
 {\bf 19)  \underline {RADLW} Heating Rate due to Longwave Radiation ($deg/day$) }  
   
 \noindent  
 The net longwave heating rate is calculated as the vertical divergence of the  
 net terrestrial radiative fluxes.  
 Both the clear-sky and cloudy-sky longwave fluxes are computed within the  
 longwave routine.  
 The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first.  
 For a given cloud fraction,  
 the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$  
 to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$,  
 for the upward and downward radiative fluxes.  
 (see Section \ref{sec:fizhi:radcloud}).  
 The cloudy-sky flux is then obtained as:  
     
 \noindent  
 \[  
 F_{LW} = C(p,p') \cdot F^{clearsky}_{LW},  
 \]  
   
 \noindent  
 Finally, the net longwave heating rate is calculated as the vertical divergence of the  
 net terrestrial radiative fluxes:  
 \[  
 \pp{\rho c_p T}{t} = - {\partial \over \partial z} F_{LW}^{NET} ,  
 \]  
 or  
 \[  
 {\bf RADLW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F_{LW}^{NET} .  
 \]  
   
 \noindent  
 where $g$ is the accelation due to gravity,  
 $c_p$ is the heat capacity of air at constant pressure,  
 and  
 \[  
 F_{LW}^{NET} = F_{LW}^\uparrow - F_{LW}^\downarrow  
 \]  
 \\  
   
   
 \noindent  
 {\bf 20)  \underline {RADSW} Heating Rate due to Shortwave Radiation ($deg/day$) }  
   
 \noindent  
 The net Shortwave heating rate is calculated as the vertical divergence of the  
 net solar radiative fluxes.  
 The clear-sky and cloudy-sky shortwave fluxes are calculated separately.  
 For the clear-sky case, the shortwave fluxes and heating rates are computed with  
 both CLMO (maximum overlap cloud fraction) and  
 CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}).  
 The shortwave routine is then called a second time, for the cloudy-sky case, with the  
 true time-averaged cloud fractions CLMO  
 and CLRO being used.  In all cases, a normalized incident shortwave flux is used as  
 input at the top of the atmosphere.  
   
 \noindent  
 The heating rate due to Shortwave Radiation under cloudy skies is defined as:  
 \[  
 \pp{\rho c_p T}{t} = - {\partial \over \partial z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT},  
 \]  
 or  
 \[  
 {\bf RADSW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} .  
 \]  
   
 \noindent  
 where $g$ is the accelation due to gravity,  
 $c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident  
 shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and  
 \[  
 F(cloudy)_{SW}^{Net} = F(cloudy)_{SW}^\uparrow - F(cloudy)_{SW}^\downarrow  
 \]  
 \\  
   
 \noindent  
 {\bf 21)  \underline {PREACC} Total (Large-scale + Convective) Accumulated Precipition ($mm/day$) }  
   
 \noindent  
 For a change in specific humidity due to moist processes, $\Delta q_{moist}$,  
 the vertical integral or total precipitable amount is given by:    
 \[  
 {\bf PREACC} = \int_{surf}^{top} \rho \Delta q_{moist} dz = - \int_{surf}^{top} \Delta  q_{moist}  
 {dp \over g} = {1 \over g} \int_0^1 \Delta q_{moist} dp  
 \]  
 \\  
   
 \noindent  
 A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes  
 time step, scaled to $mm/day$.  
 \\  
   
 \noindent  
 {\bf 22)  \underline {PRECON} Convective Precipition ($mm/day$) }  
   
 \noindent  
 For a change in specific humidity due to sub-grid scale cumulus convective processes, $\Delta q_{cum}$,  
 the vertical integral or total precipitable amount is given by:    
 \[  
 {\bf PRECON} = \int_{surf}^{top} \rho \Delta q_{cum} dz = - \int_{surf}^{top} \Delta  q_{cum}  
 {dp \over g} = {1 \over g} \int_0^1 \Delta q_{cum} dp  
 \]  
 \\  
   
 \noindent  
 A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes  
 time step, scaled to $mm/day$.  
 \\  
   
 \noindent  
 {\bf 23)  \underline {TUFLUX}  Turbulent Flux of U-Momentum ($Newton/m^2$) }  
   
 \noindent  
 The turbulent flux of u-momentum is calculated for $diagnostic \hspace{.2cm} purposes  
  \hspace{.2cm} only$ from the eddy coefficient for momentum:  
   
 \[  
 {\bf TUFLUX} =  {\rho } {(\overline{u^{\prime}w^{\prime}})} =    
 {\rho } {(- K_m \pp{U}{z})}  
 \]  
   
 \noindent  
 where $\rho$ is the air density, and $K_m$ is the eddy coefficient.  
 \\  
   
 \noindent  
 {\bf 24)  \underline {TVFLUX}  Turbulent Flux of V-Momentum ($Newton/m^2$) }  
   
 \noindent  
 The turbulent flux of v-momentum is calculated for $diagnostic \hspace{.2cm} purposes  
 \hspace{.2cm} only$ from the eddy coefficient for momentum:  
   
 \[  
 {\bf TVFLUX} =  {\rho } {(\overline{v^{\prime}w^{\prime}})} =  
  {\rho } {(- K_m \pp{V}{z})}  
 \]  
   
 \noindent  
 where $\rho$ is the air density, and $K_m$ is the eddy coefficient.  
 \\  
   
   
 \noindent  
 {\bf 25)  \underline {TTFLUX}  Turbulent Flux of Sensible Heat ($Watts/m^2$) }  
   
 \noindent  
 The turbulent flux of sensible heat is calculated for $diagnostic \hspace{.2cm} purposes  
 \hspace{.2cm} only$ from the eddy coefficient for heat and moisture:  
   
 \noindent  
 \[  
 {\bf TTFLUX} = c_p {\rho }    
 P^{\kappa}{(\overline{w^{\prime}\theta^{\prime}})}  
  = c_p  {\rho } P^{\kappa}{(- K_h \pp{\theta_v}{z})}  
 \]  
   
 \noindent  
 where $\rho$ is the air density, and $K_h$ is the eddy coefficient.  
 \\  
   
   
 \noindent  
 {\bf 26)  \underline {TQFLUX}  Turbulent Flux of Latent Heat ($Watts/m^2$) }  
   
 \noindent  
 The turbulent flux of latent heat is calculated for $diagnostic \hspace{.2cm} purposes  
 \hspace{.2cm} only$ from the eddy coefficient for heat and moisture:  
   
 \noindent  
 \[  
 {\bf TQFLUX} = {L {\rho } (\overline{w^{\prime}q^{\prime}})} =  
 {L {\rho }(- K_h \pp{q}{z})}  
 \]  
   
 \noindent  
 where $\rho$ is the air density, and $K_h$ is the eddy coefficient.  
 \\  
   
   
 \noindent  
 {\bf 27)  \underline {CN}  Neutral Drag Coefficient ($dimensionless$) }  
   
 \noindent  
 The drag coefficient for momentum obtained by assuming a neutrally stable surface layer:  
 \[  
 {\bf CN} = { k \over { \ln({h \over {z_0}})} }  
 \]  
   
 \noindent  
 where $k$ is the Von Karman constant, $h$ is the height of the surface layer, and  
 $z_0$ is the surface roughness.  
   
 \noindent  
 NOTE: CN is not available through model version 5.3, but is available in subsequent  
 versions.  
 \\  
   
 \noindent  
 {\bf 28)  \underline {WINDS}  Surface Wind Speed ($meter/sec$) }  
   
 \noindent  
 The surface wind speed is calculated for the last internal turbulence time step:  
 \[  
 {\bf WINDS} = \sqrt{u_{Nrphys}^2 + v_{Nrphys}^2}  
 \]  
   
 \noindent  
 where the subscript $Nrphys$ refers to the lowest model level.  
 \\  
   
 \noindent  
 {\bf 29)  \underline {DTSRF}  Air/Surface Virtual Temperature Difference ($deg \hspace{.1cm} K$) }  
   
 \noindent  
 The air/surface virtual temperature difference measures the stability of the surface layer:  
 \[  
 {\bf DTSRF} = (\theta_{v{Nrphys+1}} - \theta{v_{Nrphys}}) P^{\kappa}_{surf}  
 \]  
 \noindent  
 where  
 \[  
 \theta_{v{Nrphys+1}} = { T_g \over {P^{\kappa}_{surf}} } (1 + .609 q_{Nrphys+1}) \hspace{1cm}  
 and \hspace{1cm} q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys})  
 \]  
   
 \noindent  
 $\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans),  
 $q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature  
 and surface pressure, level $Nrphys$ refers to the lowest model level and level $Nrphys+1$  
 refers to the surface.  
 \\  
   
   
 \noindent  
 {\bf 30)  \underline {TG}  Ground Temperature ($deg \hspace{.1cm} K$) }  
   
 \noindent  
 The ground temperature equation is solved as part of the turbulence package  
 using a backward implicit time differencing scheme:  
 \[  
 {\bf TG} \hspace{.1cm} is \hspace{.1cm} obtained \hspace{.1cm} from: \hspace{.1cm}  
 C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{ice} - H - LE  
 \]  
   
 \noindent  
 where $R_{sw}$ is the net surface downward shortwave radiative flux, $R_{lw}$ is the  
 net surface upward longwave radiative flux, $Q_{ice}$ is the heat conduction through  
 sea ice, $H$ is the upward sensible heat flux, $LE$ is the upward latent heat  
 flux, and $C_g$ is the total heat capacity of the ground.  
 $C_g$ is obtained by solving a heat diffusion equation  
 for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by:  
 \[  
 C_g = \sqrt{ {\lambda C_s \over {2 \omega} } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3}  
 { 86400. \over {2 \pi} } } \, \, .  
 \]  
 \noindent  
 Here, the thermal conductivity, $\lambda$, is equal to $2x10^{-3}$ ${ly\over{ sec}}  
 {cm \over {^oK}}$,  
 the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided  
 by $2 \pi$ $radians/  
 day$, and the expression for $C_s$, the heat capacity per unit volume at the surface,  
 is a function of the ground wetness, $W$.  
 \\  
   
 \noindent  
 {\bf 31)  \underline {TS}  Surface Temperature ($deg \hspace{.1cm} K$) }  
   
 \noindent  
 The surface temperature estimate is made by assuming that the model's lowest  
 layer is well-mixed, and therefore that $\theta$ is constant in that layer.  
 The surface temperature is therefore:  
 \[  
 {\bf TS} = \theta_{Nrphys} P^{\kappa}_{surf}  
 \]  
 \\  
   
 \noindent  
 {\bf 32)  \underline {DTG}  Surface Temperature Adjustment ($deg \hspace{.1cm} K$) }  
   
 \noindent  
 The change in surface temperature from one turbulence time step to the next, solved  
 using the Ground Temperature Equation (see diagnostic number 30) is calculated:  
 \[  
 {\bf DTG} = {T_g}^{n} - {T_g}^{n-1}  
 \]  
   
 \noindent  
 where superscript $n$ refers to the new, updated time level, and the superscript $n-1$  
 refers to the value at the previous turbulence time level.  
 \\  
   
 \noindent  
 {\bf 33)  \underline {QG}  Ground Specific Humidity ($g/kg$) }  
   
 \noindent  
 The ground specific humidity is obtained by interpolating between the specific  
 humidity at the lowest model level and the specific humidity of a saturated ground.  
 The interpolation is performed using the potential evapotranspiration function:  
 \[  
 {\bf QG} = q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys})  
 \]  
   
 \noindent  
 where $\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans),  
 and $q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature and surface  
 pressure.  
 \\  
   
 \noindent  
 {\bf 34)  \underline {QS}  Saturation Surface Specific Humidity ($g/kg$) }  
   
 \noindent  
 The surface saturation specific humidity is the saturation specific humidity at  
 the ground temprature and surface pressure:  
 \[  
 {\bf QS} = q^*(T_g,P_s)  
 \]  
 \\  
   
 \noindent  
 {\bf 35)  \underline {TGRLW} Instantaneous ground temperature used as input to the Longwave  
  radiation subroutine (deg)}  
 \[  
 {\bf TGRLW}  = T_g(\lambda , \phi ,n)  
 \]  
 \noindent  
 where $T_g$ is the model ground temperature at the current time step $n$.  
 \\  
   
   
 \noindent  
 {\bf 36)  \underline {ST4} Upward Longwave flux at the surface ($Watts/m^2$) }  
 \[  
 {\bf ST4} = \sigma T^4  
 \]  
 \noindent  
 where $\sigma$ is the Stefan-Boltzmann constant and T is the temperature.  
 \\  
   
 \noindent  
 {\bf 37)  \underline {OLR} Net upward Longwave flux at $p=p_{top}$ ($Watts/m^2$) }  
 \[  
 {\bf OLR}  =  F_{LW,top}^{NET}  
 \]  
 \noindent  
 where top indicates the top of the first model layer.  
 In the GCM, $p_{top}$ = 0.0 mb.  
 \\  
   
   
 \noindent  
 {\bf 38)  \underline {OLRCLR} Net upward clearsky Longwave flux at $p=p_{top}$ ($Watts/m^2$) }  
 \[  
 {\bf OLRCLR}  =  F(clearsky)_{LW,top}^{NET}  
 \]  
 \noindent  
 where top indicates the top of the first model layer.  
 In the GCM, $p_{top}$ = 0.0 mb.  
 \\  
   
 \noindent  
 {\bf 39)  \underline {LWGCLR} Net upward clearsky Longwave flux at the surface ($Watts/m^2$) }  
   
 \noindent  
 \begin{eqnarray*}  
 {\bf LWGCLR} & =  & F(clearsky)_{LW,Nrphys+1}^{Net} \\  
              & =  & F(clearsky)_{LW,Nrphys+1}^\uparrow - F(clearsky)_{LW,Nrphys+1}^\downarrow  
 \end{eqnarray*}  
 where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$.  
 $F(clearsky)_{LW}^\uparrow$ is  
 the upward clearsky Longwave flux and the $F(clearsky)_{LW}^\downarrow$ is the downward clearsky Longwave flux.  
 \\  
   
 \noindent  
 {\bf 40)  \underline {LWCLR} Heating Rate due to Clearsky Longwave Radiation ($deg/day$) }  
   
 \noindent  
 The net longwave heating rate is calculated as the vertical divergence of the  
 net terrestrial radiative fluxes.  
 Both the clear-sky and cloudy-sky longwave fluxes are computed within the  
 longwave routine.  
 The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first.  
 For a given cloud fraction,  
 the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$  
 to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$,  
 for the upward and downward radiative fluxes.  
 (see Section \ref{sec:fizhi:radcloud}).  
 The cloudy-sky flux is then obtained as:  
     
 \noindent  
 \[  
 F_{LW} = C(p,p') \cdot F^{clearsky}_{LW},  
 \]  
   
 \noindent  
 Thus, {\bf LWCLR} is defined as the net longwave heating rate due to the  
 vertical divergence of the  
 clear-sky longwave radiative flux:  
 \[  
 \pp{\rho c_p T}{t}_{clearsky} = - {\partial \over \partial z} F(clearsky)_{LW}^{NET} ,  
 \]  
 or  
 \[  
 {\bf LWCLR} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(clearsky)_{LW}^{NET} .  
 \]  
   
 \noindent  
 where $g$ is the accelation due to gravity,  
 $c_p$ is the heat capacity of air at constant pressure,  
 and  
 \[  
 F(clearsky)_{LW}^{Net} = F(clearsky)_{LW}^\uparrow - F(clearsky)_{LW}^\downarrow  
 \]  
 \\  
   
   
 \noindent  
 {\bf 41)  \underline {TLW} Instantaneous temperature used as input to the Longwave  
  radiation subroutine (deg)}  
 \[  
 {\bf TLW}  = T(\lambda , \phi ,level, n)  
 \]  
 \noindent  
 where $T$ is the model temperature at the current time step $n$.  
 \\  
   
   
 \noindent  
 {\bf 42)  \underline {SHLW} Instantaneous specific humidity used as input to  
  the Longwave radiation subroutine (kg/kg)}  
 \[  
 {\bf SHLW}  = q(\lambda , \phi , level , n)  
 \]  
 \noindent  
 where $q$ is the model specific humidity at the current time step $n$.  
 \\  
   
   
 \noindent  
 {\bf 43)  \underline {OZLW} Instantaneous ozone used as input to  
  the Longwave radiation subroutine (kg/kg)}  
 \[  
 {\bf OZLW}  = {\rm OZ}(\lambda , \phi , level , n)  
 \]  
 \noindent  
 where $\rm OZ$ is the interpolated ozone data set from the climatological monthly  
 mean zonally averaged ozone data set.  
 \\  
   
   
 \noindent  
 {\bf 44) \underline {CLMOLW} Maximum Overlap cloud fraction used in LW Radiation ($0-1$) }  
   
 \noindent  
 {\bf CLMOLW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed  
 Arakawa/Schubert Convection scheme and will be used in the Longwave Radiation algorithm.  These are  
 convective clouds whose radiative characteristics are assumed to be correlated in the vertical.  
 For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.  
 \[  
 {\bf CLMOLW} = CLMO_{RAS,LW}(\lambda, \phi,  level )  
 \]  
 \\  
   
   
 {\bf 45) \underline {CLDTOT} Total cloud fraction used in LW and SW Radiation ($0-1$) }  
   
 {\bf CLDTOT} is the time-averaged total cloud fraction that has been filled by the Relaxed  
 Arakawa/Schubert and Large-scale Convection schemes and will be used in the Longwave and Shortwave  
 Radiation packages.  
 For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.  
 \[  
 {\bf CLDTOT} = F_{RAS} + F_{LS}  
 \]  
 \\  
 where $F_{RAS}$ is the time-averaged cloud fraction due to sub-grid scale convection, and $F_{LS}$ is the  
 time-averaged cloud fraction due to precipitating and non-precipitating large-scale moist processes.  
 \\  
   
   
 \noindent  
 {\bf 46) \underline {CLMOSW} Maximum Overlap cloud fraction used in SW Radiation ($0-1$) }  
   
 \noindent  
 {\bf CLMOSW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed  
 Arakawa/Schubert Convection scheme and will be used in the Shortwave Radiation algorithm.  These are  
 convective clouds whose radiative characteristics are assumed to be correlated in the vertical.  
 For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.  
 \[  
 {\bf CLMOSW} = CLMO_{RAS,SW}(\lambda, \phi,  level )  
 \]  
 \\  
   
 \noindent  
 {\bf 47) \underline {CLROSW} Random Overlap cloud fraction used in SW Radiation ($0-1$) }  
   
 \noindent  
 {\bf CLROSW} is the time-averaged random overlap cloud fraction that has been filled by the Relaxed  
 Arakawa/Schubert and Large-scale Convection schemes and will be used in the Shortwave  
 Radiation algorithm.  These are  
 convective and large-scale clouds whose radiative characteristics are not  
 assumed to be correlated in the vertical.  
 For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.  
 \[  
 {\bf CLROSW} = CLRO_{RAS,Large Scale,SW}(\lambda, \phi,  level )  
 \]  
 \\  
   
 \noindent  
 {\bf 48)  \underline {RADSWT} Incident Shortwave radiation at the top of the atmosphere ($Watts/m^2$) }  
 \[  
 {\bf RADSWT} = {\frac{S_0}{R_a^2}} \cdot cos \phi_z  
 \]  
 \noindent  
 where $S_0$, is the extra-terrestial solar contant,  
 $R_a$ is the earth-sun distance in Astronomical Units,  
 and $cos \phi_z$ is the cosine of the zenith angle.  
 It should be noted that {\bf RADSWT}, as well as  
 {\bf OSR} and {\bf OSRCLR},  
 are calculated at the top of the atmosphere (p=0 mb).  However, the  
 {\bf OLR} and {\bf OLRCLR} diagnostics are currently  
 calculated at $p= p_{top}$ (0.0 mb for the GCM).  
 \\  
     
 \noindent  
 {\bf 49)  \underline {EVAP}  Surface Evaporation ($mm/day$) }  
   
 \noindent  
 The surface evaporation is a function of the gradient of moisture, the potential  
 evapotranspiration fraction and the eddy exchange coefficient:  
 \[  
 {\bf EVAP} =  \rho \beta K_{h} (q_{surface} - q_{Nrphys})  
 \]  
 where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of  
 the potential evapotranspiration actually evaporated ($\beta=1$ over oceans), $K_{h}$ is the  
 turbulent eddy exchange coefficient for heat and moisture at the surface in $m/sec$ and  
 $q{surface}$ and $q_{Nrphys}$ are the specific humidity at the surface (see diagnostic  
 number 34) and at the bottom model level, respectively.  
 \\  
   
 \noindent  
 {\bf 50)  \underline {DUDT} Total Zonal U-Wind Tendency  ($m/sec/day$) }  
   
 \noindent  
 {\bf DUDT} is the total time-tendency of the Zonal U-Wind due to Hydrodynamic, Diabatic,  
 and Analysis forcing.  
 \[  
 {\bf DUDT} = \pp{u}{t}_{Dynamics} + \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis}  
 \]  
 \\  
   
 \noindent  
 {\bf 51)  \underline {DVDT} Total Zonal V-Wind Tendency  ($m/sec/day$) }  
   
 \noindent  
 {\bf DVDT} is the total time-tendency of the Meridional V-Wind due to Hydrodynamic, Diabatic,  
 and Analysis forcing.  
 \[  
 {\bf DVDT} = \pp{v}{t}_{Dynamics} + \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis}  
 \]  
 \\  
   
 \noindent  
 {\bf 52)  \underline {DTDT} Total Temperature Tendency  ($deg/day$) }  
   
 \noindent  
 {\bf DTDT} is the total time-tendency of Temperature due to Hydrodynamic, Diabatic,  
 and Analysis forcing.  
 \begin{eqnarray*}  
 {\bf DTDT} & = & \pp{T}{t}_{Dynamics} + \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\  
            & + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis}  
 \end{eqnarray*}  
 \\  
   
 \noindent  
 {\bf 53)  \underline {DQDT} Total Specific Humidity Tendency  ($g/kg/day$) }  
   
 \noindent  
 {\bf DQDT} is the total time-tendency of Specific Humidity due to Hydrodynamic, Diabatic,  
 and Analysis forcing.  
 \[  
 {\bf DQDT} = \pp{q}{t}_{Dynamics} + \pp{q}{t}_{Moist Processes}  
 + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis}  
 \]  
 \\  
     
 \noindent  
 {\bf 54)  \underline {USTAR}  Surface-Stress Velocity ($m/sec$) }  
   
 \noindent  
 The surface stress velocity, or the friction velocity, is the wind speed at  
 the surface layer top impeded by the surface drag:  
 \[  
 {\bf USTAR} = C_uW_s \hspace{1cm}where: \hspace{.2cm}  
 C_u = {k \over {\psi_m} }  
 \]  
   
 \noindent  
 $C_u$ is the non-dimensional surface drag coefficient (see diagnostic  
 number 10), and $W_s$ is the surface wind speed (see diagnostic number 28).  
   
 \noindent  
 {\bf 55)  \underline {Z0}  Surface Roughness Length ($m$) }  
   
 \noindent  
 Over the land surface, the surface roughness length is interpolated to the local  
 time from the monthly mean data of Dorman and Sellers (1989). Over the ocean,  
 the roughness length is a function of the surface-stress velocity, $u_*$.  
 \[  
 {\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}}  
 \]  
   
 \noindent  
 where the constants are chosen to interpolate between the reciprocal relation of  
 Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981)  
 for moderate to large winds.  
 \\  
   
 \noindent  
 {\bf 56)  \underline {FRQTRB}  Frequency of Turbulence ($0-1$) }  
   
 \noindent  
 The fraction of time when turbulence is present is defined as the fraction of  
 time when the turbulent kinetic energy exceeds some minimum value, defined here  
 to be $0.005 \hspace{.1cm}m^2/sec^2$. When this criterion is met, a counter is  
 incremented. The fraction over the averaging interval is reported.  
 \\  
   
 \noindent  
 {\bf 57)  \underline {PBL}  Planetary Boundary Layer Depth ($mb$) }  
   
 \noindent  
 The depth of the PBL is defined by the turbulence parameterization to be the  
 depth at which the turbulent kinetic energy reduces to ten percent of its surface  
 value.  
   
 \[  
 {\bf PBL} = P_{PBL} - P_{surface}  
 \]  
   
 \noindent  
 where $P_{PBL}$ is the pressure in $mb$ at which the turbulent kinetic energy  
 reaches one tenth of its surface value, and $P_s$ is the surface pressure.  
 \\  
   
 \noindent  
 {\bf 58)  \underline {SWCLR} Clear sky Heating Rate due to Shortwave Radiation ($deg/day$) }  
   
 \noindent  
 The net Shortwave heating rate is calculated as the vertical divergence of the  
 net solar radiative fluxes.  
 The clear-sky and cloudy-sky shortwave fluxes are calculated separately.  
 For the clear-sky case, the shortwave fluxes and heating rates are computed with  
 both CLMO (maximum overlap cloud fraction) and  
 CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}).  
 The shortwave routine is then called a second time, for the cloudy-sky case, with the  
 true time-averaged cloud fractions CLMO  
 and CLRO being used.  In all cases, a normalized incident shortwave flux is used as  
 input at the top of the atmosphere.  
   
 \noindent  
 The heating rate due to Shortwave Radiation under clear skies is defined as:  
 \[  
 \pp{\rho c_p T}{t} = - {\partial \over \partial z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT},  
 \]  
 or  
 \[  
 {\bf SWCLR} = \frac{g}{c_p } {\partial \over \partial p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} .  
 \]  
   
 \noindent  
 where $g$ is the accelation due to gravity,  
 $c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident  
 shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and  
 \[  
 F(clear)_{SW}^{Net} = F(clear)_{SW}^\uparrow - F(clear)_{SW}^\downarrow  
 \]  
 \\  
   
 \noindent  
 {\bf 59)  \underline {OSR} Net upward Shortwave flux at the top of the model ($Watts/m^2$) }  
 \[  
 {\bf OSR}  =  F_{SW,top}^{NET}  
 \]                                                                                        
 \noindent  
 where top indicates the top of the first model layer used in the shortwave radiation  
 routine.  
 In the GCM, $p_{SW_{top}}$ = 0 mb.  
 \\  
   
 \noindent  
 {\bf 60)  \underline {OSRCLR} Net upward clearsky Shortwave flux at the top of the model ($Watts/m^2$) }  
 \[  
 {\bf OSRCLR}  =  F(clearsky)_{SW,top}^{NET}  
 \]  
 \noindent  
 where top indicates the top of the first model layer used in the shortwave radiation  
 routine.  
 In the GCM, $p_{SW_{top}}$ = 0 mb.  
 \\  
   
   
 \noindent  
 {\bf 61)  \underline {CLDMAS} Convective Cloud Mass Flux ($kg/m^2$) }  
   
 \noindent  
 The amount of cloud mass moved per RAS timestep from all convective clouds is written:  
 \[  
 {\bf CLDMAS} = \eta m_B  
 \]  
 where $\eta$ is the entrainment, normalized by the cloud base mass flux, and $m_B$ is  
 the cloud base mass flux. $m_B$ and $\eta$ are defined explicitly in Section \ref{sec:fizhi:mc}, the  
 description of the convective parameterization.  
 \\  
   
   
   
 \noindent  
 {\bf 62)  \underline {UAVE} Time-Averaged Zonal U-Wind ($m/sec$) }  
   
 \noindent  
 The diagnostic {\bf UAVE} is simply the time-averaged Zonal U-Wind over  
 the {\bf NUAVE} output frequency.  This is contrasted to the instantaneous  
 Zonal U-Wind which is archived on the Prognostic Output data stream.  
 \[  
 {\bf UAVE} = u(\lambda, \phi, level , t)  
 \]  
 \\  
 Note, {\bf UAVE} is computed and stored on the staggered C-grid.  
 \\  
   
 \noindent  
 {\bf 63)  \underline {VAVE} Time-Averaged Meridional V-Wind ($m/sec$) }  
   
 \noindent  
 The diagnostic {\bf VAVE} is simply the time-averaged Meridional V-Wind over  
 the {\bf NVAVE} output frequency.  This is contrasted to the instantaneous  
 Meridional V-Wind which is archived on the Prognostic Output data stream.  
 \[  
 {\bf VAVE} = v(\lambda, \phi, level , t)  
 \]  
 \\  
 Note, {\bf VAVE} is computed and stored on the staggered C-grid.  
 \\  
   
 \noindent  
 {\bf 64)  \underline {TAVE} Time-Averaged Temperature ($Kelvin$) }  
   
 \noindent  
 The diagnostic {\bf TAVE} is simply the time-averaged Temperature over  
 the {\bf NTAVE} output frequency.  This is contrasted to the instantaneous  
 Temperature which is archived on the Prognostic Output data stream.  
 \[  
 {\bf TAVE} = T(\lambda, \phi, level , t)  
 \]  
 \\  
   
 \noindent  
 {\bf 65)  \underline {QAVE} Time-Averaged Specific Humidity ($g/kg$) }  
   
 \noindent  
 The diagnostic {\bf QAVE} is simply the time-averaged Specific Humidity over  
 the {\bf NQAVE} output frequency.  This is contrasted to the instantaneous  
 Specific Humidity which is archived on the Prognostic Output data stream.  
 \[  
 {\bf QAVE} = q(\lambda, \phi, level , t)  
 \]  
 \\  
   
 \noindent  
 {\bf 66)  \underline {PAVE} Time-Averaged Surface Pressure - PTOP ($mb$) }  
   
 \noindent  
 The diagnostic {\bf PAVE} is simply the time-averaged Surface Pressure - PTOP over  
 the {\bf NPAVE} output frequency.  This is contrasted to the instantaneous  
 Surface Pressure - PTOP which is archived on the Prognostic Output data stream.  
 \begin{eqnarray*}  
 {\bf PAVE} & =  & \pi(\lambda, \phi, level , t) \\  
            & =  & p_s(\lambda, \phi, level , t) - p_T  
 \end{eqnarray*}  
 \\  
   
   
 \noindent  
 {\bf 67)  \underline {QQAVE} Time-Averaged Turbulent Kinetic Energy $(m/sec)^2$ }  
   
 \noindent  
 The diagnostic {\bf QQAVE} is simply the time-averaged prognostic Turbulent Kinetic Energy  
 produced by the GCM Turbulence parameterization over  
 the {\bf NQQAVE} output frequency.  This is contrasted to the instantaneous  
 Turbulent Kinetic Energy which is archived on the Prognostic Output data stream.  
 \[  
 {\bf QQAVE} = qq(\lambda, \phi, level , t)  
 \]  
 \\  
 Note, {\bf QQAVE} is computed and stored at the ``mass-point'' locations on the staggered C-grid.  
 \\  
   
 \noindent  
 {\bf 68)  \underline {SWGCLR} Net downward clearsky Shortwave flux at the surface ($Watts/m^2$) }  
   
 \noindent  
 \begin{eqnarray*}  
 {\bf SWGCLR} & =  & F(clearsky)_{SW,Nrphys+1}^{Net} \\  
              & =  & F(clearsky)_{SW,Nrphys+1}^\downarrow - F(clearsky)_{SW,Nrphys+1}^\uparrow  
 \end{eqnarray*}  
 \noindent  
 \\  
 where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$.  
 $F(clearsky){SW}^\downarrow$ is  
 the downward clearsky Shortwave flux and $F(clearsky)_{SW}^\uparrow$ is  
 the upward clearsky Shortwave flux.  
 \\  
   
 \noindent  
 {\bf 69)  \underline {SDIAG1} User-Defined Surface Diagnostic-1 }  
   
 \noindent  
 The GCM provides Users with a built-in mechanism for archiving user-defined  
 diagnostics.  The generic diagnostic array QDIAG located in COMMON /DIAG/, and the associated  
 diagnostic counters and pointers located in COMMON /DIAGP/,  
 must be accessable in order to use the user-defined diagnostics (see Section \ref{sec:diagnostics:diagover}).    
 A convenient method for incorporating all necessary COMMON files is to  
 include the GCM {\em vstate.com} file in the routine which employs the  
 user-defined diagnostics.  
   
 \noindent  
 In addition to enabling the user-defined diagnostic (ie., CALL SETDIAG(84)), the User must fill  
 the QDIAG array with the desired quantity within the User's  
 application program or within modified GCM subroutines, as well as increment  
 the diagnostic counter at the time when the diagnostic is updated.    
 The QDIAG location index for {\bf SDIAG1} and its corresponding counter is  
 automatically defined as {\bf ISDIAG1} and {\bf NSDIAG1}, respectively, after the  
 diagnostic has been enabled.    
 The syntax for its use is given by  
 \begin{verbatim}  
       do j=1,jm  
       do i=1,im  
       qdiag(i,j,ISDIAG1) = qdiag(i,j,ISDIAG1) + ...  
       enddo  
       enddo  
   
       NSDIAG1 = NSDIAG1 + 1  
 \end{verbatim}  
 The diagnostics defined in this manner will automatically be archived by the output routines.  
 \\  
   
 \noindent  
 {\bf 70)  \underline {SDIAG2} User-Defined Surface Diagnostic-2 }  
   
 \noindent  
 The GCM provides Users with a built-in mechanism for archiving user-defined  
 diagnostics.  For a complete description refer to Diagnostic \#84.  
 The syntax for using the surface SDIAG2 diagnostic is given by  
 \begin{verbatim}  
       do j=1,jm  
       do i=1,im  
       qdiag(i,j,ISDIAG2) = qdiag(i,j,ISDIAG2) + ...  
       enddo  
       enddo  
   
       NSDIAG2 = NSDIAG2 + 1  
 \end{verbatim}  
 The diagnostics defined in this manner will automatically be archived by the output routines.  
 \\  
   
 \noindent  
 {\bf 71)  \underline {UDIAG1} User-Defined Upper-Air Diagnostic-1 }  
   
 \noindent  
 The GCM provides Users with a built-in mechanism for archiving user-defined  
 diagnostics.  For a complete description refer to Diagnostic \#84.  
 The syntax for using the upper-air UDIAG1 diagnostic is given by  
 \begin{verbatim}  
       do L=1,Nrphys  
       do j=1,jm  
       do i=1,im  
       qdiag(i,j,IUDIAG1+L-1) = qdiag(i,j,IUDIAG1+L-1) + ...  
       enddo  
       enddo  
       enddo  
   
       NUDIAG1 = NUDIAG1 + 1  
 \end{verbatim}  
 The diagnostics defined in this manner will automatically be archived by the  
 output programs.  
 \\  
   
 \noindent  
 {\bf 72)  \underline {UDIAG2} User-Defined Upper-Air Diagnostic-2 }  
   
 \noindent  
 The GCM provides Users with a built-in mechanism for archiving user-defined  
 diagnostics.  For a complete description refer to Diagnostic \#84.  
 The syntax for using the upper-air UDIAG2 diagnostic is given by  
 \begin{verbatim}  
       do L=1,Nrphys  
       do j=1,jm  
       do i=1,im  
       qdiag(i,j,IUDIAG2+L-1) = qdiag(i,j,IUDIAG2+L-1) + ...  
       enddo  
       enddo  
       enddo  
   
       NUDIAG2 = NUDIAG2 + 1  
 \end{verbatim}  
 The diagnostics defined in this manner will automatically be archived by the  
 output programs.  
 \\  
   
   
 \noindent  
 {\bf 73)  \underline {DIABU} Total Diabatic Zonal U-Wind Tendency  ($m/sec/day$) }  
   
 \noindent  
 {\bf DIABU} is the total time-tendency of the Zonal U-Wind due to Diabatic processes  
 and the Analysis forcing.  
 \[  
 {\bf DIABU} = \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis}  
 \]  
 \\  
   
 \noindent  
 {\bf 74)  \underline {DIABV} Total Diabatic Meridional V-Wind Tendency  ($m/sec/day$) }  
   
 \noindent  
 {\bf DIABV} is the total time-tendency of the Meridional V-Wind due to Diabatic processes  
 and the Analysis forcing.  
 \[  
 {\bf DIABV} = \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis}  
 \]  
 \\  
   
 \noindent  
 {\bf 75)  \underline {DIABT} Total Diabatic Temperature Tendency  ($deg/day$) }  
   
 \noindent  
 {\bf DIABT} is the total time-tendency of Temperature due to Diabatic processes  
 and the Analysis forcing.  
 \begin{eqnarray*}  
 {\bf DIABT} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\  
            & + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis}  
 \end{eqnarray*}  
 \\  
 If we define the time-tendency of Temperature due to Diabatic processes as  
 \begin{eqnarray*}  
 \pp{T}{t}_{Diabatic} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\  
                      & + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence}  
 \end{eqnarray*}  
 then, since there are no surface pressure changes due to Diabatic processes, we may write  
 \[  
 \pp{T}{t}_{Diabatic} = {p^\kappa \over \pi }\pp{\pi \theta}{t}_{Diabatic}  
 \]  
 where $\theta = T/p^\kappa$.  Thus, {\bf DIABT} may be written as  
 \[  
 {\bf DIABT} = {p^\kappa \over \pi } \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right)  
 \]  
 \\  
   
 \noindent  
 {\bf 76)  \underline {DIABQ} Total Diabatic Specific Humidity Tendency  ($g/kg/day$) }  
   
 \noindent  
 {\bf DIABQ} is the total time-tendency of Specific Humidity due to Diabatic processes  
 and the Analysis forcing.  
 \[  
 {\bf DIABQ} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis}  
 \]  
 If we define the time-tendency of Specific Humidity due to Diabatic processes as  
 \[  
 \pp{q}{t}_{Diabatic} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence}  
 \]  
 then, since there are no surface pressure changes due to Diabatic processes, we may write  
 \[  
 \pp{q}{t}_{Diabatic} = {1 \over \pi }\pp{\pi q}{t}_{Diabatic}  
 \]  
 Thus, {\bf DIABQ} may be written as  
 \[  
 {\bf DIABQ} = {1 \over \pi } \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right)  
 \]  
 \\  
   
 \noindent  
 {\bf 77)  \underline {VINTUQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) }  
   
 \noindent  
 The vertically integrated moisture flux due to the zonal u-wind is obtained by integrating  
 $u q$ over the depth of the atmosphere at each model timestep,  
 and dividing by the total mass of the column.  
 \[  
 {\bf VINTUQ} = \frac{ \int_{surf}^{top} u q \rho dz  } { \int_{surf}^{top} \rho dz  }  
 \]  
 Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have  
 \[  
 {\bf VINTUQ} = { \int_0^1 u q dp  }  
 \]  
 \\  
   
   
 \noindent  
 {\bf 78)  \underline {VINTVQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) }  
   
 \noindent  
 The vertically integrated moisture flux due to the meridional v-wind is obtained by integrating  
 $v q$ over the depth of the atmosphere at each model timestep,  
 and dividing by the total mass of the column.  
 \[  
 {\bf VINTVQ} = \frac{ \int_{surf}^{top} v q \rho dz  } { \int_{surf}^{top} \rho dz  }  
 \]  
 Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have  
 \[  
 {\bf VINTVQ} = { \int_0^1 v q dp  }  
 \]  
 \\  
   
   
 \noindent  
 {\bf 79)  \underline {VINTUT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) }  
   
 \noindent  
 The vertically integrated heat flux due to the zonal u-wind is obtained by integrating  
 $u T$ over the depth of the atmosphere at each model timestep,  
 and dividing by the total mass of the column.  
 \[  
 {\bf VINTUT} = \frac{ \int_{surf}^{top} u T \rho dz  } { \int_{surf}^{top} \rho dz  }  
 \]  
 Or,  
 \[  
 {\bf VINTUT} = { \int_0^1 u T dp  }  
 \]  
 \\  
   
 \noindent  
 {\bf 80)  \underline {VINTVT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) }  
   
 \noindent  
 The vertically integrated heat flux due to the meridional v-wind is obtained by integrating  
 $v T$ over the depth of the atmosphere at each model timestep,  
 and dividing by the total mass of the column.  
 \[  
 {\bf VINTVT} = \frac{ \int_{surf}^{top} v T \rho dz  } { \int_{surf}^{top} \rho dz  }  
 \]  
 Using $\rho \delta z = -{\delta p \over g} $, we have  
 \[  
 {\bf VINTVT} = { \int_0^1 v T dp  }  
 \]  
 \\  
   
 \noindent  
 {\bf 81 \underline {CLDFRC} Total 2-Dimensional Cloud Fracton ($0-1$) }  
   
 If we define the  
 time-averaged random and maximum overlapped cloudiness as CLRO and  
 CLMO respectively, then the probability of clear sky associated  
 with random overlapped clouds at any level is (1-CLRO) while the probability of  
 clear sky associated with maximum overlapped clouds at any level is (1-CLMO).  
 The total clear sky probability is given by (1-CLRO)*(1-CLMO), thus  
 the total cloud fraction at each  level may be obtained by  
 1-(1-CLRO)*(1-CLMO).  
   
 At any given level, we may define the clear line-of-site probability by  
 appropriately accounting for the maximum and random overlap  
 cloudiness.  The clear line-of-site probability is defined to be  
 equal to the product of the clear line-of-site probabilities  
 associated with random and maximum overlap cloudiness.  The clear  
 line-of-site probability $C(p,p^{\prime})$ associated with maximum overlap clouds,  
 from the current pressure $p$  
 to the model top pressure, $p^{\prime} = p_{top}$, or the model surface pressure, $p^{\prime} = p_{surf}$,  
 is simply 1.0 minus the largest maximum overlap cloud value along  the  
 line-of-site, ie.  
   
 $$1-MAX_p^{p^{\prime}} \left( CLMO_p \right)$$  
   
 Thus, even in the time-averaged sense it is assumed that the  
 maximum overlap clouds are correlated in the vertical.  The clear  
 line-of-site probability associated with random overlap clouds is  
 defined to be the product of the clear sky probabilities at each  
 level along the line-of-site, ie.  
   
 $$\prod_{p}^{p^{\prime}} \left( 1-CLRO_p \right)$$  
   
 The total cloud fraction at a given level associated with a line-  
 of-site calculation is given by  
   
 $$1-\left( 1-MAX_p^{p^{\prime}} \left[ CLMO_p \right] \right)  
     \prod_p^{p^{\prime}} \left( 1-CLRO_p \right)$$  
   
   
 \noindent  
 The 2-dimensional net cloud fraction as seen from the top of the  
 atmosphere is given by  
 \[  
 {\bf CLDFRC} = 1-\left( 1-MAX_{l=l_1}^{Nrphys} \left[ CLMO_l \right] \right)  
     \prod_{l=l_1}^{Nrphys} \left( 1-CLRO_l \right)  
 \]  
 \\  
 For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}.  
   
   
 \noindent  
 {\bf 82)  \underline {QINT} Total Precipitable Water ($gm/cm^2$) }  
   
 \noindent  
 The Total Precipitable Water is defined as the vertical integral of the specific humidity,  
 given by:  
 \begin{eqnarray*}  
 {\bf QINT} & = & \int_{surf}^{top} \rho q dz \\  
            & = & {\pi \over g} \int_0^1 q dp  
 \end{eqnarray*}  
 where we have used the hydrostatic relation  
 $\rho \delta z = -{\delta p \over g} $.  
 \\  
   
   
 \noindent  
 {\bf 83)  \underline {U2M}  Zonal U-Wind at 2 Meter Depth ($m/sec$) }  
   
 \noindent  
 The u-wind at the 2-meter depth is determined from the similarity theory:  
 \[  
 {\bf U2M} = {u_* \over k} \psi_{m_{2m}} {u_{sl} \over {W_s}} =  
 { \psi_{m_{2m}} \over {\psi_{m_{sl}} }}u_{sl}  
 \]  
   
 \noindent  
 where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript  
 $sl$ refers to the height of the top of the surface layer. If the roughness height  
 is above two meters, ${\bf U2M}$ is undefined.  
 \\  
   
 \noindent  
 {\bf 84)  \underline {V2M}  Meridional V-Wind at 2 Meter Depth ($m/sec$) }  
   
 \noindent  
 The v-wind at the 2-meter depth is a determined from the similarity theory:  
 \[  
 {\bf V2M} = {u_* \over k} \psi_{m_{2m}} {v_{sl} \over {W_s}} =  
 { \psi_{m_{2m}} \over {\psi_{m_{sl}} }}v_{sl}  
 \]  
   
 \noindent  
 where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript  
 $sl$ refers to the height of the top of the surface layer. If the roughness height  
 is above two meters, ${\bf V2M}$ is undefined.  
 \\  
   
 \noindent  
 {\bf 85)  \underline {T2M}  Temperature at 2 Meter Depth ($deg \hspace{.1cm} K$) }  
   
 \noindent  
 The temperature at the 2-meter depth is a determined from the similarity theory:  
 \[  
 {\bf T2M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) =  
 P^{\kappa}(\theta_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }  
 (\theta_{sl} - \theta_{surf}))  
 \]  
 where:  
 \[  
 \theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} }  
 \]  
   
 \noindent  
 where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is  
 the non-dimensional temperature gradient in the viscous sublayer, and the subscript  
 $sl$ refers to the height of the top of the surface layer. If the roughness height  
 is above two meters, ${\bf T2M}$ is undefined.  
 \\  
   
 \noindent  
 {\bf 86)  \underline {Q2M}  Specific Humidity at 2 Meter Depth ($g/kg$) }  
   
 \noindent  
 The specific humidity at the 2-meter depth is determined from the similarity theory:  
 \[  
 {\bf Q2M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) =  
 P^{\kappa}(q_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }  
 (q_{sl} - q_{surf}))  
 \]  
 where:  
 \[  
 q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} }  
 \]  
   
 \noindent  
 where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is  
 the non-dimensional temperature gradient in the viscous sublayer, and the subscript  
 $sl$ refers to the height of the top of the surface layer. If the roughness height  
 is above two meters, ${\bf Q2M}$ is undefined.  
 \\  
   
 \noindent  
 {\bf 87)  \underline {U10M}  Zonal U-Wind at 10 Meter Depth ($m/sec$) }  
   
 \noindent  
 The u-wind at the 10-meter depth is an interpolation between the surface wind  
 and the model lowest level wind using the ratio of the non-dimensional wind shear  
 at the two levels:  
 \[  
 {\bf U10M} = {u_* \over k} \psi_{m_{10m}} {u_{sl} \over {W_s}} =  
 { \psi_{m_{10m}} \over {\psi_{m_{sl}} }}u_{sl}  
 \]  
   
 \noindent  
 where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript  
 $sl$ refers to the height of the top of the surface layer.  
 \\  
   
 \noindent  
 {\bf 88)  \underline {V10M}  Meridional V-Wind at 10 Meter Depth ($m/sec$) }  
   
 \noindent  
 The v-wind at the 10-meter depth is an interpolation between the surface wind  
 and the model lowest level wind using the ratio of the non-dimensional wind shear  
 at the two levels:  
 \[  
 {\bf V10M} = {u_* \over k} \psi_{m_{10m}} {v_{sl} \over {W_s}} =  
 { \psi_{m_{10m}} \over {\psi_{m_{sl}} }}v_{sl}  
 \]  
   
 \noindent  
 where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript  
 $sl$ refers to the height of the top of the surface layer.  
 \\  
   
 \noindent  
 {\bf 89)  \underline {T10M}  Temperature at 10 Meter Depth ($deg \hspace{.1cm} K$) }  
   
 \noindent  
 The temperature at the 10-meter depth is an interpolation between the surface potential  
 temperature and the model lowest level potential temperature using the ratio of the  
 non-dimensional temperature gradient at the two levels:  
 \[  
 {\bf T10M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) =  
 P^{\kappa}(\theta_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }  
 (\theta_{sl} - \theta_{surf}))  
 \]  
 where:  
 \[  
 \theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} }  
 \]  
   
 \noindent  
 where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is  
 the non-dimensional temperature gradient in the viscous sublayer, and the subscript  
 $sl$ refers to the height of the top of the surface layer.  
 \\  
   
 \noindent  
 {\bf 90)  \underline {Q10M}  Specific Humidity at 10 Meter Depth ($g/kg$) }  
   
 \noindent  
 The specific humidity at the 10-meter depth is an interpolation between the surface specific  
 humidity and the model lowest level specific humidity using the ratio of the  
 non-dimensional temperature gradient at the two levels:  
 \[  
 {\bf Q10M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) =  
 P^{\kappa}(q_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }  
 (q_{sl} - q_{surf}))  
 \]  
 where:  
 \[  
 q_* =  - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} }  
 \]  
   
 \noindent  
 where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is  
 the non-dimensional temperature gradient in the viscous sublayer, and the subscript  
 $sl$ refers to the height of the top of the surface layer.  
 \\  
   
 \noindent  
 {\bf 91)  \underline {DTRAIN} Cloud Detrainment Mass Flux ($kg/m^2$) }  
   
 The amount of cloud mass moved per RAS timestep at the cloud detrainment level is written:  
 \[  
 {\bf DTRAIN} = \eta_{r_D}m_B  
 \]  
 \noindent  
 where $r_D$ is the detrainment level,  
 $m_B$ is the cloud base mass flux, and $\eta$  
 is the entrainment, defined in Section \ref{sec:fizhi:mc}.  
 \\  
   
 \noindent  
 {\bf 92)  \underline {QFILL}  Filling of negative Specific Humidity ($g/kg/day$) }  
   
 \noindent  
 Due to computational errors associated with the numerical scheme used for  
 the advection of moisture, negative values of specific humidity may be generated.  The  
 specific humidity is checked for negative values after every dynamics timestep.  If negative  
 values have been produced, a filling algorithm is invoked which redistributes moisture from  
 below.  Diagnostic {\bf QFILL} is equal to the net filling needed  
 to eliminate negative specific humidity, scaled to a per-day rate:  
 \[  
 {\bf QFILL} = q^{n+1}_{final} - q^{n+1}_{initial}  
 \]  
 where  
 \[  
 q^{n+1} = (\pi q)^{n+1} / \pi^{n+1}  
 \]  
711    
712  \subsection{Dos and Donts}  \subsection{Dos and Donts}
713    

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