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-revision 1.1 by molod,
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+revision 1.9 by molod,
Thu Jul 14 19:18:01 2005 UTC
 Line 1
- \section{Diagnostics-Flexible model infrastructure for diagnostic (instananeous or time averaged) output}
+ \section{Diagnostics--A Flexible Infrastructure}
+ \label{sec:pkg:diagnostics}
+ \begin{rawhtml}
+ <!-- CMIREDIR:package_diagnostics: -->
+ \end{rawhtml}
  \subsection{Introduction}
- This section of the documentation describes the Diagnostics Utilities available within the GCM.
+ \noindent
- In addition to
+ This section of the documentation describes the Diagnostics package available within
- a description on how to set and extract diagnostic quantities, this document also provides a
+ the GCM.  A large selection of model diagnostics is available for output.
- comprehensive list of all available diagnostic quantities and a short description of how they are
+ In addition to the diagnostic quantities pre-defined in the GCM, there exists
- computed.  It should be noted that this document is not intended to be a complete documentation
+ the option, in any experiment, to define a new diagnostic quantity and include it
- of the various packages used in the GCM, and the reader should
+ as part of the diagnostic output with the addition of a single subroutine call in the
- refer to original publications for further insight.
+ routine where the field is computed. As a matter of philosophy, no diagnostic is enabled
+ as default, thus each user must specify the exact diagnostic information required for an
+ experiment.  This is accomplished by enabling the specific diagnostic of interest cataloged
+ in the Diagnostic Menu (see Section \ref{sec:diagnostics:menu}). Instructions for enabling
+ diagnostic output and defining new diagnostic quantities are found in Section
+ \ref{sec:diagnostics:usersguide} of this document.
+ \noindent
+ The Diagnostic Menu is a hard-wired enumeration of diagnostic quantities available within
+ the GCM. Once a diagnostic is enabled, the GCM will continually increment an array
+ specifically allocated for that diagnostic whenever the appropriate quantity is computed.
+ A counter is defined which records how many times each diagnostic quantity has been
+ incremented.  Several special diagnostics are included in the menu. Quantities refered to
+ as ``Counter Diagnostics'', are defined for selected diagnostics which record the
+ frequency at which a diagnostic is incremented separately for each model grid location.
+ Quantitied refered to as ``User Diagnostics'' are included in the menu to facilitate
+ defining new diagnostics for a particular experiment.
  \subsection{Equations}
  Not relevant.
-Line 17 
 Not relevant.
+Line 36 
 Not relevant.
  \subsection{Key Subroutines and Parameters}
  \label{sec:diagnostics:diagover}
- A large selection of model diagnostics is available in the GCM.  At the time of
+ \noindent
- this writing there are 92 different diagnostic quantities which can be enabled for an
+ The diagnostics are computed at various times and places within the GCM. Because the
- 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,
- 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,
- enabling the specific diagnostic of interest cataloged in the
+ while others are components of vectors. An internal array is defined which contains
- Diagnostic Menu (see Section \ref{sec:diagnostics:menu}).
+ information concerning various grid attributes of each diagnostic. The GDIAG
- 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
- 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
- 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
- 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}.
  \begin{table}
  \caption{Diagnostic Parsing Array}
 Line 64 
 Array & Value & Description \\
    parse(2)   & $\rightarrow$ U &  C-Grid U-Point                    \\
               & $\rightarrow$ V &  C-Grid V-Point                    \\
               & $\rightarrow$ M &  C-Grid Mass Point                 \\
-              & $\rightarrow$ Z &  C-Grid Vorticity Point            \\ \hline
+              & $\rightarrow$ Z &  C-Grid Vorticity (Corner) Point   \\ \hline
-   parse(3)   & $\rightarrow$ R &  Computed on the Rotated Grid      \\
+   parse(3)   & $\rightarrow$ R &  Not Currently in Use              \\ \hline
-              & $\rightarrow$ G &  Computed on the Geophysical Grid  \\ \hline
    parse(4)   & $\rightarrow$ P &  Positive Definite Diagnostic      \\ \hline
    parse(5)   & $\rightarrow$ C &  Counter Diagnostic                \\
               & $\rightarrow$ D &  Disabled Diagnostic for output    \\ \hline
-Line 77 
 Array & Value & Description \\
+Line 76 
 Array & Value & Description \\
  \end{center}
  \end{table}
+ \noindent
  As an example, consider a diagnostic whose associated GDIAG parameter is equal
- to ``UUR 002''.  From GDIAG we can determine that this diagnostic is a
+ to ``UU  002''.  From GDIAG we can determine that this diagnostic is a
- U-vector component located at the C-grid U-point within the Rotated framework.
+ U-vector component located at the C-grid U-point.
  Its corresponding V-component diagnostic is located in Diagnostic \# 002.
+ \noindent
  In this way, each Diagnostic in the model has its attributes (ie. vector or scalar,
- rotated or geophysical, A-Grid or C-grid, etc.) defined internally.  The Output routines
+ C-grid location, etc.) defined internally.  The Output routines use this information
- use this information in order to determine
+ in order to determine what type of transformations need to be performed.  Any
- what type of rotations and/or transformations need to be performed.  Thus, all Diagnostic
+ interpolations are done at the time of output rather than during each model step.
- 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
- In this way the User now has more flexibility
+ is output.
- in determining the type of gridded data which is output.
+ \noindent
  There are several utilities within the GCM available to users to enable, disable,
- 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.
- and/or output routine.  The available utilities and the CALL sequences are listed below.
+ The available utilities and the CALL sequences are listed below.
- {\bf SETDIAG}:  This subroutine enables a diagnostic from the Diagnostic Menu, meaning that
+ \noindent
- space is allocated for the diagnostic and the
+ {\bf fill\_diagnostics}:  This routine will increment the specified diagnostic
- model routines will increment the diagnostic value during execution.  This routine is useful when
+ quantity with a field sent through the argument list.
- 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:
+ \noindent
  \begin{tabbing}
  XXXXXXXXX\=XXXXXX\= \kill
- \>        CALL SETDIAG (NUM) \\
+ \>        call fill\_diagnostics (myThid, chardiag, levflg, nlevs, \\
+                 bibjflg, bi, bj, arrayin) \\
  \\
- where \>  NUM   \>= Diagnostic number from menu \\
+ where \>  myThid   \>= Current Process(or) \\
+       \>  chardiag \>= Character *8 expression for diag to fill \\
+       \>  levflg   \>= Integer flag for vertical levels: \\
+       \>           \> 0 indicates multiple levels incremented in qdiag \\
+       \>           \> non-0 (any integer) - WHICH single level to increment. \\
+       \>           \> negative integer - the input data array is single-leveled \\
+       \>           \> positive integer - the input data array is multi-leveled \\
+       \>  nlevs    \>= indicates Number of levels to be filled (1 if levflg <> 0) \\
+       \>           \> positive: fill in "nlevs" levels in the same order as \\
+       \>           \> the input array \\
+       \>           \> negative: fill in -nlevs levels in reverse order. \\
+       \>  bibjflg  \>= Integer flag to indicate instructions for bi bj loop \\
+       \>           \> 0 indicates that the bi-bj loop must be done here \\
+       \>           \> 1 indicates that the bi-bj loop is done OUTSIDE \\
+       \>           \> 2 indicates that the bi-bj loop is done OUTSIDE \\
+       \>           \>    AND that we have been sent a local array \\
+       \>           \> 3 indicates that the bi-bj loop is done OUTSIDE \\
+       \>           \>    AND that we have been sent a local array \\
+       \>           \>    AND that the array has the shadow regions \\
+       \>  bi       \>= X-direction process(or) number - used for bibjflg=1-3 \\
+       \>  bj       \>= Y-direction process(or) number - used for bibjflg=1-3 \\
+       \>  arrayin  \>= Field to increment diagnostics array \\
  \end{tabbing}
- {\bf GETDIAG}:  This subroutine retrieves the value of a model diagnostic.  This routine is
+ \noindent
- 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
- 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
- dividing the current accumulated diagnostic value by its corresponding counter.  This routine does
+ diagnostic value during execution.  This routine is the underlying interface
- 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
- time-average.  The calling sequence for this routine is givin by:
+ number from the menu, and its calling sequence is given by:
+ \noindent
  \begin{tabbing}
  XXXXXXXXX\=XXXXXX\= \kill
- \>        CALL GETDIAG (LEV,NUM,QTMP,UNDEF) \\
+ \>        call setdiag (num) \\
  \\
- 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 \\
  \end{tabbing}
- {\bf CLRDIAG}:  This subroutine initializes the values of model diagnostics to zero, and is
+ \noindent
- 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
- run.  The calling sequence is:
+ is particulary useful when called from a user output routine, although it can be called
+ from any routine.  This routine returns the time-averaged value of the diagnostic by
+ dividing the current accumulated diagnostic value by its corresponding counter.  This
+ routine does not change the value of the diagnostic itself, that is, it does not replace
+ the diagnostic with its time-average.  The calling sequence for this routine is givin by:
+ \noindent
  \begin{tabbing}
  XXXXXXXXX\=XXXXXX\= \kill
- \>        CALL CLRDIAG (NUM) \\
+ \>        call getdiag (lev,num,qtmp,undef) \\
  \\
- where \>  NUM   \>= Diagnostic number from menu \\
+ where \>  lev   \>= Model Level at which the diagnostic is desired \\
+       \>  num   \>= Diagnostic number from menu \\
+       \>  qtmp  \>= Time-Averaged Diagnostic Output \\
+       \>  undef \>= Fill value to be used when diagnostic is undefined \\
  \end{tabbing}
+ \noindent
+ {\bf clrdiag}:  This subroutine initializes the values of model diagnostics to zero, and is
+ particularly useful when called from user output routines to re-initialize diagnostics
+ during the run.  The calling sequence is:
+ \noindent
- {\bf ZAPDIAG}:  This entry into subroutine SETDIAG disables model diagnostics, meaning that the
- diagnostic is no longer available to the user.  The memory previously allocated to the diagnostic
- is released when ZAPDIAG is invoked.  The calling sequence is given by:
  \begin{tabbing}
  XXXXXXXXX\=XXXXXX\= \kill
- \>        CALL ZAPDIAG (NUM) \\
+ \>        call clrdiag (num) \\
  \\
- where \>  NUM   \>= Diagnostic number from menu \\
+ where \>  num   \>= Diagnostic number from menu \\
  \end{tabbing}
- {\bf DIAGSIZE}:  We end this section with a discussion on the manner in which computer memory
+ \noindent
- is allocated for diagnostics.
+ {\bf zapdiag}:  This entry into subroutine SETDIAG disables model diagnostics, meaning
- All GCM diagnostic quantities are stored in the single
+ that the diagnostic is no longer available to the user.  The memory previously allocated
- diagnostic array QDIAG which is located in the DIAG COMMON, having the form:
+ to the diagnostic is released when ZAPDIAG is invoked.  The calling sequence is given by:
+ \noindent
  \begin{tabbing}
  XXXXXXXXX\=XXXXXX\= \kill
- \>        COMMON /DIAG/ NDIAG\_MAX,QDIAG(IM,JM,1) \\
+ \>        call zapdiag (NUM) \\
  \\
+ where \>  num   \>= Diagnostic number from menu \\
  \end{tabbing}
- where NDIAG\_MAX is an Integer variable which should be
- set equal to the number of enabled diagnostics, and QDIAG is a three-dimensional
+ \subsection{Usage Notes}
- array.  The first two-dimensions of QDIAG correspond to the horizontal dimension
+ \label{sec:diagnostics:usersguide}
- of a given diagnostic, while the third dimension of QDIAG is used to identify
- specific diagnostic types.
+ \noindent
- In order to minimize the maximum memory requirement used by the model,
+ We begin this section with a discussion on the manner in which computer
- the default GCM executable is compiled with room for only one horizontal
+ memory is allocated for diagnostics. All GCM diagnostic quantities are stored in the
- diagnostic array, as shown in the above example.
+ single diagnostic array QDIAG which is located in the file \\
- In order for the User to enable more than 1 two-dimensional diagnostic,
+ \filelink{pkg/diagnostics/diagnostics.h}{pkg-diagnostics-diagnostics.h}.
- the size of the DIAG COMMON must be expanded to accomodate the desired diagnostics.
+ and has the form:
+ common /diagnostics/ qdiag(1-Olx,sNx+Olx,1-Olx,sNx+Olx,numdiags,Nsx,Nsy)
+ \noindent
+ where numdiags is an Integer variable which should be set equal to the number of
+ enabled diagnostics, and qdiag is a three-dimensional array.  The first two-dimensions
+ of qdiag correspond to the horizontal dimension of a given diagnostic, while the third
+ dimension of qdiag is used to identify diagnostic fields and levels combined. In order
+ to minimize the memory requirement of the model for diagnostics, the default GCM
+ executable is compiled with room for only one horizontal diagnostic array, or with
+ numdiags set to 1. In order for the User to enable more than 1 two-dimensional diagnostic,
+ the size of the diagnostics common must be expanded to accomodate the desired diagnostics.
  This can be accomplished by manually changing the parameter numdiags in the
- file \filelink{FORWARD\_STEP}{pkg-diagnostics-diagnostics_SIZE.h}, or by allowing the
+ file \filelink{pkg/diagnostics/diagnostics\_SIZE.h}{pkg-diagnostics-diagnostics_SIZE.h}.
- shell script (???????) to make this
+ numdiags should be set greater than or equal to the sum of all the diagnostics activated
- 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.
+ This is illustrated in the example below:
+ \noindent
+ To use the diagnostics package, other than enabling it in packages.conf
+ and turning the usediagnostics flag in data.pkg to .TRUE., a namelist
+ must be supplied in the run directory called data.diagnostics. The namelist
+ will activate a user-defined list of diagnostics quantities to be computed,
+ specify the frequency of output, the number of levels, and the name of
+ up to 10 separate output files. A sample data.diagnostics namelist file:
+ \noindent
+ $\#$ Diagnostic Package Choices \\
+  $\&$diagnostics\_list \\
+   frequency(1) = 10, \ \\
+    levels(1,1) = 1.,2.,3.,4.,5., \ \\
+    fields(1,1) = 'UVEL    ','VVEL    ', \ \\
+    filename(1) = 'diagout1', \ \\
+   frequency(2) = 100, \ \\
+    levels(1,2) = 1.,2.,3.,4.,5., \ \\
+    fields(1,2) = 'THETA   ','SALT    ', \ \\
+    filename(2) = 'diagout2', \ \\
+  $\&$end \ \\
+ \noindent
+ In this example, there are two output files that will be generated
+ for each tile and for each output time. The first set of output files
+ has the prefix diagout1, does time averaging every 10 time steps
+ (frequency is 10), they will write fields which are multiple-level
+ fields and output levels 1-5. The names of diagnostics quantities are
+ UVEL and VVEL.  The second set of output files
+ has the prefix diagout2, does time averaging every 100 time steps,
+ they include fields which are multiple-level fields, levels output are 1-5,
+ and the names of diagnostics quantities are THETA and SALT.
+ \noindent
+ In order to define and include as part of the diagnostic output any field
+ that is desired for a particular experiment, two steps must be taken. The
+ first is to enable the ``User Diagnostic'' in data.diagnostics. This is
+ accomplished by setting one of the fields slots to either UDIAG1 through
+ UDIAG10, for multi-level fields, or SDIAG1 through SDIAG10 for single level
+ fields. These are listed in the diagnostics menu. The second step is to
+ add a call to fill\_diagnostics from the subroutine in which the quantity
+ desired for diagnostic output is computed.
  \newpage
-Line 190 
 N & NAME & UNITS & LEVELS & DESCRIPTION
+Line 276 
 N & NAME & UNITS & LEVELS & DESCRIPTION
  \hline
  &\\
-& UFLUX    &   $Newton/m^2$  &    1
+& SDIAG1   &             &    1
-          &\begin{minipage}[t]{3in}
-           {Surface U-Wind Stress on the atmosphere}
-          \end{minipage}\\
-& VFLUX    &   $Newton/m^2$  &    1
-          &\begin{minipage}[t]{3in}
-           {Surface V-Wind Stress on the atmosphere}
-          \end{minipage}\\
-& HFLUX    &   $Watts/m^2$  &    1
-          &\begin{minipage}[t]{3in}
-           {Surface Flux of Sensible Heat}
-          \end{minipage}\\
-& EFLUX    &   $Watts/m^2$  &    1
-          &\begin{minipage}[t]{3in}
-           {Surface Flux of Latent Heat}
-          \end{minipage}\\
-& QICE     &   $Watts/m^2$  &    1
-          &\begin{minipage}[t]{3in}
-           {Heat Conduction through Sea-Ice}
-          \end{minipage}\\
-& RADLWG   &   $Watts/m^2$ &    1
-          &\begin{minipage}[t]{3in}
-           {Net upward LW flux at the ground}
-          \end{minipage}\\
-& RADSWG   &   $Watts/m^2$  &    1
-          &\begin{minipage}[t]{3in}
-           {Net downward SW flux at the ground}
-          \end{minipage}\\
-& RI       &  $dimensionless$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Richardson Number}
-          \end{minipage}\\
-& CT       &  $dimensionless$ &  1
-          &\begin{minipage}[t]{3in}
-           {Surface Drag coefficient for T and Q}
-          \end{minipage}\\
-& CU       & $dimensionless$ &  1
-          &\begin{minipage}[t]{3in}
-           {Surface Drag coefficient for U and V}
-          \end{minipage}\\
-& ET       &  $m^2/sec$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Diffusivity coefficient for T and Q}
-          \end{minipage}\\
-& EU       &  $m^2/sec$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Diffusivity coefficient for U and V}
-          \end{minipage}\\
-& TURBU    &  $m/sec/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {U-Momentum Changes due to Turbulence}
-          \end{minipage}\\
-& TURBV    &  $m/sec/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {V-Momentum Changes due to Turbulence}
-          \end{minipage}\\
-& TURBT    &  $deg/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Temperature Changes due to Turbulence}
-          \end{minipage}\\
-& TURBQ    &  $g/kg/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Specific Humidity Changes due to Turbulence}
-          \end{minipage}\\
-& MOISTT   &   $deg/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Temperature Changes due to Moist Processes}
-          \end{minipage}\\
-& MOISTQ   &  $g/kg/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Specific Humidity Changes due to Moist Processes}
-          \end{minipage}\\
-& RADLW    &  $deg/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Net Longwave heating rate for each level}
-          \end{minipage}\\
-& RADSW    &  $deg/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Net Shortwave heating rate for each level}
-          \end{minipage}\\
-& PREACC   &  $mm/day$ &  1
-          &\begin{minipage}[t]{3in}
-           {Total Precipitation}
-          \end{minipage}\\
-& PRECON   &  $mm/day$ &  1
-          &\begin{minipage}[t]{3in}
-           {Convective Precipitation}
-          \end{minipage}\\
-& TUFLUX   &  $Newton/m^2$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Turbulent Flux of U-Momentum}
-          \end{minipage}\\
-& TVFLUX   &  $Newton/m^2$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Turbulent Flux of V-Momentum}
-          \end{minipage}\\
-& TTFLUX   &  $Watts/m^2$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Turbulent Flux of Sensible Heat}
-          \end{minipage}\\
-& TQFLUX   &  $Watts/m^2$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Turbulent Flux of Latent Heat}
-          \end{minipage}\\
-& CN       &  $dimensionless$ &  1
-          &\begin{minipage}[t]{3in}
-           {Neutral Drag Coefficient}
-          \end{minipage}\\
-& WINDS     &  $m/sec$ &  1
-          &\begin{minipage}[t]{3in}
-           {Surface Wind Speed}
-          \end{minipage}\\
-& DTSRF     &  $deg$ &  1
-          &\begin{minipage}[t]{3in}
-           {Air/Surface virtual temperature difference}
-          \end{minipage}\\
-& TG        &  $deg$ &  1
           &\begin{minipage}[t]{3in}
-           {Ground temperature}
+           {User-Defined Surface Diagnostic-1}
           \end{minipage}\\
-& TS        &  $deg$ &  1
+& SDIAG2   &             &    1
           &\begin{minipage}[t]{3in}
-           {Surface air temperature (Adiabatic from lowest model layer)}
+           {User-Defined Surface Diagnostic-2}
           \end{minipage}\\
-& DTG       &  $deg$ &  1
+& UDIAG1   &             &    Nrphys
           &\begin{minipage}[t]{3in}
-           {Ground temperature adjustment}
+           {User-Defined Upper-Air Diagnostic-1}
           \end{minipage}\\
+& UDIAG2   &             &    Nrphys
- \end{tabular}
- \newpage
- \vspace*{\fill}
- \begin{tabular}{lllll}
- \hline\hline
- N & NAME & UNITS & LEVELS & DESCRIPTION \\
- \hline
- &\\
-& QG        &  $g/kg$ &  1
           &\begin{minipage}[t]{3in}
-           {Ground specific humidity}
+           {User-Defined Upper-Air Diagnostic-2}
           \end{minipage}\\
-& QS        &  $g/kg$ &  1
+& SDIAG3   &             &    1
           &\begin{minipage}[t]{3in}
-           {Saturation surface specific humidity}
+           {User-Defined Surface Diagnostic-3}
           \end{minipage}\\
+& SDIAG4   &             &    1
- &\\
-& TGRLW    &    $deg$   &    1
           &\begin{minipage}[t]{3in}
-           {Instantaneous ground temperature used as input to the
+           {User-Defined Surface Diagnostic-4}
-            Longwave radiation subroutine}
           \end{minipage}\\
-& ST4      &   $Watts/m^2$  &    1
+& SDIAG5   &             &    1
           &\begin{minipage}[t]{3in}
-           {Upward Longwave flux at the ground ($\sigma T^4$)}
+           {User-Defined Surface Diagnostic-5}
           \end{minipage}\\
-& OLR      &   $Watts/m^2$  &    1
+& SDIAG6   &             &    1
           &\begin{minipage}[t]{3in}
-           {Net upward Longwave flux at the top of the model}
+           {User-Defined Surface Diagnostic-6}
           \end{minipage}\\
-& OLRCLR   &   $Watts/m^2$  &    1
+& SDIAG7   &             &    1
           &\begin{minipage}[t]{3in}
-           {Net upward clearsky Longwave flux at the top of the model}
+           {User-Defined Surface Diagnostic-7}
           \end{minipage}\\
-& LWGCLR   &   $Watts/m^2$  &    1
+& SDIAG8   &             &    1
           &\begin{minipage}[t]{3in}
-           {Net upward clearsky Longwave flux at the ground}
+           {User-Defined Surface Diagnostic-8}
           \end{minipage}\\
-& LWCLR    &  $deg/day$ &  Nrphys
+& SDIAG9   &             &    1
           &\begin{minipage}[t]{3in}
-           {Net clearsky Longwave heating rate for each level}
+           {User-Defined Surface Diagnostic-9}
           \end{minipage}\\
-& TLW      &    $deg$   &  Nrphys
+& SDIAG10  &             &    1
           &\begin{minipage}[t]{3in}
-           {Instantaneous temperature used as input to the Longwave radiation
+           {User-Defined Surface Diagnostic-1-}
-           subroutine}
           \end{minipage}\\
-& SHLW     &    $g/g$   &  Nrphys
+& UDIAG3   &             &    Nrphys
           &\begin{minipage}[t]{3in}
-           {Instantaneous specific humidity used as input to the Longwave radiation
+           {User-Defined Multi-Level Diagnostic-3}
-           subroutine}
           \end{minipage}\\
-& OZLW     &    $g/g$   &  Nrphys
+& UDIAG4   &             &    Nrphys
           &\begin{minipage}[t]{3in}
-           {Instantaneous ozone used as input to the Longwave radiation
+           {User-Defined Multi-Level Diagnostic-4}
-           subroutine}
           \end{minipage}\\
-& CLMOLW   &    $0-1$   &  Nrphys
+& UDIAG5   &             &    Nrphys
           &\begin{minipage}[t]{3in}
-           {Maximum overlap cloud fraction used in the Longwave radiation
+           {User-Defined Multi-Level Diagnostic-5}
-           subroutine}
           \end{minipage}\\
-& CLDTOT   &    $0-1$   &  Nrphys
+& UDIAG6   &             &    Nrphys
           &\begin{minipage}[t]{3in}
-           {Total cloud fraction used in the Longwave and Shortwave radiation
+           {User-Defined Multi-Level Diagnostic-6}
-           subroutines}
           \end{minipage}\\
-& RADSWT   &    $Watts/m^2$   &  1
+& UDIAG7   &             &    Nrphys
           &\begin{minipage}[t]{3in}
-           {Incident Shortwave radiation at the top of the atmosphere}
+           {User-Defined Multi-Level Diagnostic-7}
           \end{minipage}\\
-& CLROSW   &    $0-1$   &  Nrphys
+& UDIAG8   &             &    Nrphys
           &\begin{minipage}[t]{3in}
-           {Random overlap cloud fraction used in the shortwave radiation
+           {User-Defined Multi-Level Diagnostic-8}
-           subroutine}
           \end{minipage}\\
-& CLMOSW   &    $0-1$   &  Nrphys
+& UDIAG9   &             &    Nrphys
           &\begin{minipage}[t]{3in}
-           {Maximum overlap cloud fraction used in the shortwave radiation
+           {User-Defined Multi-Level Diagnostic-9}
-           subroutine}
           \end{minipage}\\
-& EVAP     &    $mm/day$   &  1
+& UDIAG10  &             &    Nrphys
           &\begin{minipage}[t]{3in}
-           {Surface evaporation}
+           {User-Defined Multi-Level Diagnostic-10}
           \end{minipage}\\
  \end{tabular}
+ \vspace{1.5in}
  \vfill
  \newpage
-Line 418 
 N & NAME & UNITS & LEVELS & DESCRIPTION
+Line 368 
 N & NAME & UNITS & LEVELS & DESCRIPTION
  \hline
  &\\
-& DUDT     &    $m/sec/day$ &  Nrphys
+& ETAN     & $(hPa,m)$ &    1
-          &\begin{minipage}[t]{3in}
-           {Total U-Wind tendency}
-          \end{minipage}\\
-& DVDT     &    $m/sec/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Total V-Wind tendency}
-          \end{minipage}\\
-& DTDT     &    $deg/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Total Temperature tendency}
-          \end{minipage}\\
-& DQDT     &    $g/kg/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Total Specific Humidity tendency}
-          \end{minipage}\\
-& USTAR    &    $m/sec$ &  1
-          &\begin{minipage}[t]{3in}
-           {Surface USTAR wind}
-          \end{minipage}\\
-& Z0       &    $m$ &  1
-          &\begin{minipage}[t]{3in}
-           {Surface roughness}
-          \end{minipage}\\
-& FRQTRB   &    $0-1$ &  Nrphys-1
-          &\begin{minipage}[t]{3in}
-           {Frequency of Turbulence}
-          \end{minipage}\\
-& PBL      &    $mb$ &  1
-          &\begin{minipage}[t]{3in}
-           {Planetary Boundary Layer depth}
-          \end{minipage}\\
-& SWCLR    &  $deg/day$ &  Nrphys
-          &\begin{minipage}[t]{3in}
-           {Net clearsky Shortwave heating rate for each level}
-          \end{minipage}\\
-& OSR      &   $Watts/m^2$  &    1
-          &\begin{minipage}[t]{3in}
-           {Net downward Shortwave flux at the top of the model}
-          \end{minipage}\\
-& OSRCLR   &   $Watts/m^2$  &    1
           &\begin{minipage}[t]{3in}
-           {Net downward clearsky Shortwave flux at the top of the model}
+           {Perturbation of Surface (pressure, height)}
           \end{minipage}\\
-& CLDMAS   &   $kg / m^2$  &    Nrphys
+& ETANSQ   & $(hPa^2,m^2)$ & 1
           &\begin{minipage}[t]{3in}
-           {Convective cloud mass flux}
+           {Square of Perturbation of Surface (pressure, height)}
           \end{minipage}\\
-& UAVE     &   $m/sec$  &    Nrphys
+& THETA    & $deg K$ & Nr
           &\begin{minipage}[t]{3in}
-           {Time-averaged $u-Wind$}
+           {Potential Temperature}
           \end{minipage}\\
-& VAVE     &   $m/sec$  &    Nrphys
+& SALT     & $g/kg$ & Nr
           &\begin{minipage}[t]{3in}
-           {Time-averaged $v-Wind$}
+           {Salt (or Water Vapor Mixing Ratio)}
           \end{minipage}\\
-& TAVE     &   $deg$  &    Nrphys
+& UVEL     & $m/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {Time-averaged $Temperature$}
+           {U-Velocity}
           \end{minipage}\\
-& QAVE     &   $g/g$  &    Nrphys
+& VVEL     & $m/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {Time-averaged $Specific \, \, Humidity$}
+           {V-Velocity}
           \end{minipage}\\
-& PAVE     &   $mb$  &    1
+& WVEL     & $m/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {Time-averaged $p_{surf} - p_{top}$}
+           {Vertical-Velocity}
           \end{minipage}\\
-& QQAVE    &   $(m/sec)^2$  &    Nrphys
+& THETASQ  & $deg^2$ & Nr
           &\begin{minipage}[t]{3in}
-           {Time-averaged $Turbulent Kinetic Energy$}
+           {Square of Potential Temperature}
           \end{minipage}\\
-& SWGCLR   &   $Watts/m^2$  &    1
+& SALTSQ   & $g^2/{kg}^2$ & Nr
           &\begin{minipage}[t]{3in}
-           {Net downward clearsky Shortwave flux at the ground}
+           {Square of Salt (or Water Vapor Mixing Ratio)}
           \end{minipage}\\
-& SDIAG1   &             &    1
+& UVELSQ   & $m^2/sec^2$ & Nr
           &\begin{minipage}[t]{3in}
-           {User-Defined Surface Diagnostic-1}
+           {Square of U-Velocity}
           \end{minipage}\\
-& SDIAG2   &             &    1
+& VVELSQ   & $m^2/sec^2$ & Nr
           &\begin{minipage}[t]{3in}
-           {User-Defined Surface Diagnostic-2}
+           {Square of V-Velocity}
           \end{minipage}\\
-& UDIAG1   &             &    Nrphys
+& WVELSQ   & $m^2/sec^2$ & Nr
           &\begin{minipage}[t]{3in}
-           {User-Defined Upper-Air Diagnostic-1}
+           {Square of Vertical-Velocity}
           \end{minipage}\\
-& UDIAG2   &             &    Nrphys
+& UVELVVEL & $m^2/sec^2$ & Nr
           &\begin{minipage}[t]{3in}
-           {User-Defined Upper-Air Diagnostic-2}
+           {Meridional Transport of Zonal Momentum}
           \end{minipage}\\
-& DIABU    & $m/sec/day$ &    Nrphys
+& UVELMASS & $m/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {Total Diabatic forcing on $u-Wind$}
+           {Zonal Mass-Weighted Component of Velocity}
           \end{minipage}\\
-& DIABV    & $m/sec/day$ &    Nrphys
+& VVELMASS & $m/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {Total Diabatic forcing on $v-Wind$}
+           {Meridional Mass-Weighted Component of Velocity}
           \end{minipage}\\
-& DIABT    & $deg/day$ &    Nrphys
+& WVELMASS & $m/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {Total Diabatic forcing on $Temperature$}
+           {Vertical Mass-Weighted Component of Velocity}
           \end{minipage}\\
-& DIABQ    & $g/kg/day$ &    Nrphys
+& UTHMASS  & $m-deg/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {Total Diabatic forcing on $Specific \, \, Humidity$}
+           {Zonal Mass-Weight Transp of Pot Temp}
           \end{minipage}\\
+& VTHMASS  & $m-deg/sec$ & Nr
- \end{tabular}
- \vfill
- \newpage
- \vspace*{\fill}
- \begin{tabular}{lllll}
- \hline\hline
- N & NAME & UNITS & LEVELS & DESCRIPTION \\
- \hline
-& VINTUQ  & $m/sec \cdot g/kg$ &    1
           &\begin{minipage}[t]{3in}
-           {Vertically integrated $u \, q$}
+           {Meridional Mass-Weight Transp of Pot Temp}
           \end{minipage}\\
-& VINTVQ  & $m/sec \cdot g/kg$ &    1
+& WTHMASS  & $m-deg/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {Vertically integrated $v \, q$}
+           {Vertical Mass-Weight Transp of Pot Temp}
           \end{minipage}\\
-& VINTUT  & $m/sec \cdot deg$ &    1
+& USLTMASS & $m-kg/sec-kg$ & Nr
           &\begin{minipage}[t]{3in}
-           {Vertically integrated $u \, T$}
+           {Zonal Mass-Weight Transp of Salt (or W.Vap Mix Rat.)}
           \end{minipage}\\
-& VINTVT  & $m/sec \cdot deg$ &    1
+& VSLTMASS & $m-kg/sec-kg$ & Nr
           &\begin{minipage}[t]{3in}
-           {Vertically integrated $v \, T$}
+           {Meridional Mass-Weight Transp of Salt (or W.Vap Mix Rat.)}
           \end{minipage}\\
-& CLDFRC  & $0-1$ &    1
+& WSLTMASS & $m-kg/sec-kg$ & Nr
           &\begin{minipage}[t]{3in}
-           {Total Cloud Fraction}
+           {Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)}
           \end{minipage}\\
-& QINT    & $gm/cm^2$ &    1
+& UVELTH   & $m-deg/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {Precipitable water}
+           {Zonal Transp of Pot Temp}
           \end{minipage}\\
-& U2M     & $m/sec$ &    1
+& VVELTH   & $m-deg/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {U-Wind at 2 meters}
+           {Meridional Transp of Pot Temp}
           \end{minipage}\\
-& V2M     & $m/sec$ &    1
+& WVELTH   & $m-deg/sec$ & Nr
           &\begin{minipage}[t]{3in}
-           {V-Wind at 2 meters}
+           {Vertical Transp of Pot Temp}
           \end{minipage}\\
-& T2M     & $deg$ &    1
+& UVELSLT  & $m-kg/sec-kg$ & Nr
           &\begin{minipage}[t]{3in}
-           {Temperature at 2 meters}
+           {Zonal Transp of Salt (or W.Vap Mix Rat.)}
           \end{minipage}\\
-& Q2M     & $g/kg$ &    1
+& VVELSLT  & $m-kg/sec-kg$ & Nr
           &\begin{minipage}[t]{3in}
-           {Specific Humidity at 2 meters}
+           {Meridional Transp of Salt (or W.Vap Mix Rat.)}
           \end{minipage}\\
-& U10M    & $m/sec$ &    1
+& WVELSLT  & $m-kg/sec-kg$ & Nr
           &\begin{minipage}[t]{3in}
-           {U-Wind at 10 meters}
+           {Vertical Transp of Salt (or W.Vap Mix Rat.)}
           \end{minipage}\\
-& V10M    & $m/sec$ &    1
+& WSLTMASS & $m-kg/sec-kg$ & Nr
           &\begin{minipage}[t]{3in}
-           {V-Wind at 10 meters}
+           {Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)}
           \end{minipage}\\
-& T10M    & $deg$ &    1
+& VISCA4   & $m^4/sec$ & 1
           &\begin{minipage}[t]{3in}
-           {Temperature at 10 meters}
+           {Biharmonic Viscosity Coefficient}
           \end{minipage}\\
-& Q10M    & $g/kg$ &    1
+& VISCAH   & $m^2/sec$ & 1
           &\begin{minipage}[t]{3in}
-           {Specific Humidity at 10 meters}
+           {Harmonic Viscosity Coefficient}
           \end{minipage}\\
-& DTRAIN  & $kg/m^2$ &    Nrphys
+& DRHODR   & $kg/m^3/{r-unit}$ & Nr
           &\begin{minipage}[t]{3in}
-           {Detrainment Cloud Mass Flux}
+           {Stratification: d.Sigma/dr}
           \end{minipage}\\
-& QFILL   & $g/kg/day$ &    Nrphys
+& DETADT2  & ${r-unit}^2/s^2$ & 1
           &\begin{minipage}[t]{3in}
-           {Filling of negative specific humidity}
+           {Square of Eta (Surf.P,SSH) Tendency}
           \end{minipage}\\
  \end{tabular}
  \vspace{1.5in}
  \vfill
-Line 620 
 is time-averaged over its diagnostic out
+Line 518 
 is time-averaged over its diagnostic out
  {\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t)
  \]
  where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the
- output frequency of the diagnositc, and $\Delta t$ is
+ output frequency of the diagnostic, and $\Delta t$ is
- 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-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
- \[
- q^{n+1} = (\pi q)^{n+1} / \pi^{n+1}
- \]
  \subsection{Dos and Donts}

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