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\section{Diagnostics--A Flexible Infrastructure} |
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\label{sec:pkg:diagnostics} |
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\begin{rawhtml} |
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<!-- CMIREDIR:package_diagnostics: --> |
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\end{rawhtml} |
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\subsection{Introduction} |
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This section of the documentation describes the Diagnostics package available within |
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the GCM. In addition to a description of how to set and extract diagnostic quantities, |
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this document also provides a comprehensive list of all available diagnostic quantities |
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and a short description of how they are computed. It should be noted that this document |
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is not intended to be a complete documentation of the various packages used in the GCM, |
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and the reader should refer to original publications and the appropriate sections of this |
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documentation for further insight. |
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|
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\subsection{Equations} |
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Not relevant. |
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\subsection{Key Subroutines and Parameters} |
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\label{sec:diagnostics:diagover} |
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A large selection of model diagnostics is available in the GCM. At the time of |
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this writing there are 280 different diagnostic quantities which can be enabled for an |
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experiment. As a matter of philosophy, no diagnostic is enabled as default, thus each |
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user must specify the exact diagnostic information required for an experiment. This |
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is accomplished by enabling the specific diagnostic of interest cataloged in the |
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Diagnostic Menu (see Section \ref{sec:diagnostics:menu}). |
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The Diagnostic Menu is a hard-wired enumeration of diagnostic quantities available within |
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the GCM. Diagnostics are internally referred to by their associated number in the Diagnostic |
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Menu. Once a diagnostic is enabled, the GCM will continually increment an array |
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specifically allocated for that diagnostic whenever the associated process for the |
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diagnostic is computed. Separate arrays are used both for the diagnostic quantity and |
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its diagnostic counter which records how many times each diagnostic quantity has been |
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computed. In addition special diagnostics, called ``Counter Diagnostics'', records the |
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frequency of diagnostic updates separately for each model grid location. |
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|
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The diagnostics are computed at various times and places within the GCM. |
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Some diagnostics are computed on the A-grid (such as those within the fizhi routines), |
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while others are computed on the C-grid (those computed during the dynamics time-stepping). |
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Some diagnostics are scalars, while others are vectors. Each of these possibilities requires |
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separate tasks for A-grid to C-grid transformations and coordinate transformations. Due |
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to this complexity, and since the specific diagnostics enabled are User determined at the |
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time of the run, |
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a diagnostic parameter has been developed and implemented into the GCM, defined as GDIAG, |
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which contains information concerning various grid attributes of each diagnostic. The GDIAG |
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array is internally defined as a character*8 variable, and is equivalenced to |
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a character*1 "parse" array in output in order to extract the grid-attribute information. |
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The GDIAG array is described in Table \ref{tab:diagnostics:gdiag.tabl}. |
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\begin{table} |
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\caption{Diagnostic Parsing Array} |
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\label{tab:diagnostics:gdiag.tabl} |
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\begin{center} |
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\begin{tabular}{ |c|c|l| } |
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\hline |
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\multicolumn{3}{|c|}{\bf Diagnostic Parsing Array} \\ |
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\hline |
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\hline |
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Array & Value & Description \\ |
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\hline |
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parse(1) & $\rightarrow$ S & Scalar Diagnostic \\ |
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& $\rightarrow$ U & U-vector component Diagnostic \\ |
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& $\rightarrow$ V & V-vector component Diagnostic \\ \hline |
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parse(2) & $\rightarrow$ U & C-Grid U-Point \\ |
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& $\rightarrow$ V & C-Grid V-Point \\ |
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& $\rightarrow$ M & C-Grid Mass Point \\ |
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& $\rightarrow$ Z & C-Grid Vorticity (Corner) Point \\ \hline |
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parse(3) & $\rightarrow$ R & Not Currently in Use \\ \hline |
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parse(4) & $\rightarrow$ P & Positive Definite Diagnostic \\ \hline |
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parse(5) & $\rightarrow$ C & Counter Diagnostic \\ |
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& $\rightarrow$ D & Disabled Diagnostic for output \\ \hline |
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parse(6-8) & $\rightarrow$ C & 3-digit integer corresponding to \\ |
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& & vector or counter component mate \\ \hline |
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\end{tabular} |
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\addcontentsline{lot}{section}{Table 3: Diagnostic Parsing Array} |
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\end{center} |
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\end{table} |
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As an example, consider a diagnostic whose associated GDIAG parameter is equal |
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to ``UU 002''. From GDIAG we can determine that this diagnostic is a |
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U-vector component located at the C-grid U-point. |
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Its corresponding V-component diagnostic is located in Diagnostic \# 002. |
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In this way, each Diagnostic in the model has its attributes (ie. vector or scalar, |
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A-Grid or C-grid, etc.) defined internally. The Output routines |
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use this information in order to determine |
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what type of transformations need to be performed. Thus, all Diagnostic |
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interpolations are done at the time of output rather than during each model dynamic step. |
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In this way the User now has more flexibility |
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in determining the type of gridded data which is output. |
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There are several utilities within the GCM available to users to enable, disable, |
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clear, write and retrieve model diagnostics, and may be called from any routine. |
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The available utilities and the CALL sequences are listed below. |
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|
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{\bf fill\_diag}: This routine will increment |
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|
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{\bf setdiag}: This subroutine enables a diagnostic from the Diagnostic Menu, meaning |
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that space is allocated for the diagnostic and the model routines will increment the |
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diagnostic value during execution. This routine is the underlying interface |
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between the user and the desired diagnostic. The diagnostic is referenced by its diagnostic |
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number from the menu, and its calling sequence is given by: |
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\begin{tabbing} |
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XXXXXXXXX\=XXXXXX\= \kill |
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\> call setdiag (num) \\ |
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\\ |
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where \> num \>= Diagnostic number from menu \\ |
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\end{tabbing} |
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|
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{\bf getdiag}: This subroutine retrieves the value of a model diagnostic. This routine |
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is particulary useful when called from a user output routine, although it can be called |
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from any routine. This routine returns the time-averaged value of the diagnostic by |
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dividing the current accumulated diagnostic value by its corresponding counter. This |
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routine does not change the value of the diagnostic itself, that is, it does not replace |
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the diagnostic with its time-average. The calling sequence for this routine is givin by: |
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|
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\begin{tabbing} |
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XXXXXXXXX\=XXXXXX\= \kill |
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\> call getdiag (lev,num,qtmp,undef) \\ |
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\\ |
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where \> lev \>= Model Level at which the diagnostic is desired \\ |
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\> num \>= Diagnostic number from menu \\ |
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\> qtmp \>= Time-Averaged Diagnostic Output \\ |
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\> undef \>= Fill value to be used when diagnostic is undefined \\ |
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\end{tabbing} |
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{\bf clrdiag}: This subroutine initializes the values of model diagnostics to zero, and is |
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particularly useful when called from user output routines to re-initialize diagnostics |
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during the run. The calling sequence is: |
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\begin{tabbing} |
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XXXXXXXXX\=XXXXXX\= \kill |
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\> call clrdiag (num) \\ |
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\\ |
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where \> num \>= Diagnostic number from menu \\ |
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\end{tabbing} |
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{\bf zapdiag}: This entry into subroutine SETDIAG disables model diagnostics, meaning |
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that the diagnostic is no longer available to the user. The memory previously allocated |
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to the diagnostic is released when ZAPDIAG is invoked. The calling sequence is given by: |
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|
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\begin{tabbing} |
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XXXXXXXXX\=XXXXXX\= \kill |
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\> call zapdiag (NUM) \\ |
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\\ |
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where \> num \>= Diagnostic number from menu \\ |
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\end{tabbing} |
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{\bf diagsize}: We end this section with a discussion on the manner in which computer |
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memory is allocated for diagnostics. All GCM diagnostic quantities are stored in the |
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single diagnostic array QDIAG which is located in diagnostics.h, and has the form: |
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|
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common /diagnostics/ qdiag(1-Olx,sNx+Olx,1-Olx,sNx+Olx,numdiags,Nsx,Nsy) |
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|
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where numdiags is an Integer variable which should be |
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set equal to the number of enabled diagnostics, and qdiag is a three-dimensional |
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array. The first two-dimensions of qdiag correspond to the horizontal dimension |
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of a given diagnostic, while the third dimension of qdiag is used to identify |
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specific diagnostic types. |
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In order to minimize the memory requirement of the model for diagnostics, |
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the default GCM executable is compiled with room for only one horizontal |
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diagnostic array, as shown in the above example. |
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In order for the User to enable more than 1 two-dimensional diagnostic, |
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the size of the diagnostics common must be expanded to accomodate the desired diagnostics. |
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This can be accomplished by manually changing the parameter numdiags in the |
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file \filelink{pkg/diagnostics/diagnostics\_SIZE.h}{pkg-diagnostics-diagnostics_SIZE.h}, or by allowing the |
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shell script (???????) to make this |
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change based on the choice of diagnostic output made in the namelist. |
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\subsection{Usage Notes} |
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\label{sec:diagnostics:usersguide} |
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To use the diagnostics package, other than enabling it in packages.conf |
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and turning the usediagnostics flag in data.pkg to .TRUE., a namelist |
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must be supplied in the run directory called data.diagnostics. The namelist |
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will activate a user-defined list of diagnostics quantities to be computed, |
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specify the frequency of output, the number of levels, and the name of |
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up to 10 separate output files. A sample data.diagnostics namelist file: |
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|
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$\#$ Diagnostic Package Choices |
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$\&$diagnostics\_list |
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frequency(1) = 10, \ |
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levels(1,1) = 1.,2.,3.,4.,5., \ |
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fields(1,1) = 'UVEL ','VVEL ', \ |
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filename(1) = 'diagout1', \ |
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frequency(2) = 100, \ |
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levels(1,2) = 1.,2.,3.,4.,5., \ |
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fields(1,2) = 'THETA ','SALT ', \ |
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filename(2) = 'diagout2', \ |
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$\&$end \ |
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|
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In this example, there are two output files that will be generated |
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for each tile and for each output time. The first set of output files |
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has the prefix diagout1, does time averaging every 10 time steps, |
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for fields which are multiple-level fields the levels output are 1-5, |
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and the names of diagnostics quantities are UVEL and VVEL. |
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The second set of output files |
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has the prefix diagout2, does time averaging every 100 time steps, |
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for fields which are multiple-level fields the levels output are 1-5, |
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and the names of diagnostics quantities are THETA and SALT. |
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\newpage |
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\subsubsection{GCM Diagnostic Menu} |
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\label{sec:diagnostics:menu} |
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\begin{tabular}{lllll} |
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\hline\hline |
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N & NAME & UNITS & LEVELS & DESCRIPTION \\ |
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\hline |
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&\\ |
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1 & UFLUX & $Newton/m^2$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Surface U-Wind Stress on the atmosphere} |
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\end{minipage}\\ |
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2 & VFLUX & $Newton/m^2$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Surface V-Wind Stress on the atmosphere} |
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\end{minipage}\\ |
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3 & HFLUX & $Watts/m^2$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Surface Flux of Sensible Heat} |
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\end{minipage}\\ |
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4 & EFLUX & $Watts/m^2$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Surface Flux of Latent Heat} |
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\end{minipage}\\ |
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5 & QICE & $Watts/m^2$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Heat Conduction through Sea-Ice} |
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\end{minipage}\\ |
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6 & RADLWG & $Watts/m^2$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Net upward LW flux at the ground} |
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\end{minipage}\\ |
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7 & RADSWG & $Watts/m^2$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Net downward SW flux at the ground} |
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\end{minipage}\\ |
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8 & RI & $dimensionless$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Richardson Number} |
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\end{minipage}\\ |
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9 & CT & $dimensionless$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Surface Drag coefficient for T and Q} |
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\end{minipage}\\ |
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10 & CU & $dimensionless$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Surface Drag coefficient for U and V} |
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\end{minipage}\\ |
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11 & ET & $m^2/sec$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Diffusivity coefficient for T and Q} |
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\end{minipage}\\ |
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12 & EU & $m^2/sec$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Diffusivity coefficient for U and V} |
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\end{minipage}\\ |
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13 & TURBU & $m/sec/day$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{U-Momentum Changes due to Turbulence} |
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\end{minipage}\\ |
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14 & TURBV & $m/sec/day$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{V-Momentum Changes due to Turbulence} |
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\end{minipage}\\ |
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15 & TURBT & $deg/day$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Temperature Changes due to Turbulence} |
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\end{minipage}\\ |
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16 & TURBQ & $g/kg/day$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Specific Humidity Changes due to Turbulence} |
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\end{minipage}\\ |
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17 & MOISTT & $deg/day$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Temperature Changes due to Moist Processes} |
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\end{minipage}\\ |
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18 & MOISTQ & $g/kg/day$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Specific Humidity Changes due to Moist Processes} |
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\end{minipage}\\ |
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19 & RADLW & $deg/day$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Net Longwave heating rate for each level} |
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\end{minipage}\\ |
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20 & RADSW & $deg/day$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Net Shortwave heating rate for each level} |
293 |
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\end{minipage}\\ |
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21 & PREACC & $mm/day$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Total Precipitation} |
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\end{minipage}\\ |
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22 & PRECON & $mm/day$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Convective Precipitation} |
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\end{minipage}\\ |
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23 & TUFLUX & $Newton/m^2$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Turbulent Flux of U-Momentum} |
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\end{minipage}\\ |
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24 & TVFLUX & $Newton/m^2$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Turbulent Flux of V-Momentum} |
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\end{minipage}\\ |
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25 & TTFLUX & $Watts/m^2$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Turbulent Flux of Sensible Heat} |
313 |
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\end{minipage}\\ |
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26 & TQFLUX & $Watts/m^2$ & Nrphys |
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&\begin{minipage}[t]{3in} |
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{Turbulent Flux of Latent Heat} |
317 |
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\end{minipage}\\ |
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27 & CN & $dimensionless$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Neutral Drag Coefficient} |
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\end{minipage}\\ |
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28 & WINDS & $m/sec$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Surface Wind Speed} |
325 |
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\end{minipage}\\ |
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29 & DTSRF & $deg$ & 1 |
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&\begin{minipage}[t]{3in} |
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{Air/Surface virtual temperature difference} |
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\end{minipage}\\ |
330 |
|
|
30 & TG & $deg$ & 1 |
331 |
|
|
&\begin{minipage}[t]{3in} |
332 |
|
|
{Ground temperature} |
333 |
|
|
\end{minipage}\\ |
334 |
|
|
31 & TS & $deg$ & 1 |
335 |
|
|
&\begin{minipage}[t]{3in} |
336 |
|
|
{Surface air temperature (Adiabatic from lowest model layer)} |
337 |
|
|
\end{minipage}\\ |
338 |
|
|
32 & DTG & $deg$ & 1 |
339 |
|
|
&\begin{minipage}[t]{3in} |
340 |
|
|
{Ground temperature adjustment} |
341 |
|
|
\end{minipage}\\ |
342 |
|
|
|
343 |
|
|
\end{tabular} |
344 |
|
|
|
345 |
|
|
\newpage |
346 |
|
|
\vspace*{\fill} |
347 |
|
|
\begin{tabular}{lllll} |
348 |
|
|
\hline\hline |
349 |
|
|
N & NAME & UNITS & LEVELS & DESCRIPTION \\ |
350 |
|
|
\hline |
351 |
|
|
|
352 |
|
|
&\\ |
353 |
|
|
33 & QG & $g/kg$ & 1 |
354 |
|
|
&\begin{minipage}[t]{3in} |
355 |
|
|
{Ground specific humidity} |
356 |
|
|
\end{minipage}\\ |
357 |
|
|
34 & QS & $g/kg$ & 1 |
358 |
|
|
&\begin{minipage}[t]{3in} |
359 |
|
|
{Saturation surface specific humidity} |
360 |
|
|
\end{minipage}\\ |
361 |
|
|
|
362 |
|
|
&\\ |
363 |
|
|
35 & TGRLW & $deg$ & 1 |
364 |
|
|
&\begin{minipage}[t]{3in} |
365 |
|
|
{Instantaneous ground temperature used as input to the |
366 |
|
|
Longwave radiation subroutine} |
367 |
|
|
\end{minipage}\\ |
368 |
|
|
36 & ST4 & $Watts/m^2$ & 1 |
369 |
|
|
&\begin{minipage}[t]{3in} |
370 |
|
|
{Upward Longwave flux at the ground ($\sigma T^4$)} |
371 |
|
|
\end{minipage}\\ |
372 |
|
|
37 & OLR & $Watts/m^2$ & 1 |
373 |
|
|
&\begin{minipage}[t]{3in} |
374 |
|
|
{Net upward Longwave flux at the top of the model} |
375 |
|
|
\end{minipage}\\ |
376 |
|
|
38 & OLRCLR & $Watts/m^2$ & 1 |
377 |
|
|
&\begin{minipage}[t]{3in} |
378 |
|
|
{Net upward clearsky Longwave flux at the top of the model} |
379 |
|
|
\end{minipage}\\ |
380 |
|
|
39 & LWGCLR & $Watts/m^2$ & 1 |
381 |
|
|
&\begin{minipage}[t]{3in} |
382 |
|
|
{Net upward clearsky Longwave flux at the ground} |
383 |
|
|
\end{minipage}\\ |
384 |
|
|
40 & LWCLR & $deg/day$ & Nrphys |
385 |
|
|
&\begin{minipage}[t]{3in} |
386 |
|
|
{Net clearsky Longwave heating rate for each level} |
387 |
|
|
\end{minipage}\\ |
388 |
|
|
41 & TLW & $deg$ & Nrphys |
389 |
|
|
&\begin{minipage}[t]{3in} |
390 |
|
|
{Instantaneous temperature used as input to the Longwave radiation |
391 |
|
|
subroutine} |
392 |
|
|
\end{minipage}\\ |
393 |
|
|
42 & SHLW & $g/g$ & Nrphys |
394 |
|
|
&\begin{minipage}[t]{3in} |
395 |
|
|
{Instantaneous specific humidity used as input to the Longwave radiation |
396 |
|
|
subroutine} |
397 |
|
|
\end{minipage}\\ |
398 |
|
|
43 & OZLW & $g/g$ & Nrphys |
399 |
|
|
&\begin{minipage}[t]{3in} |
400 |
|
|
{Instantaneous ozone used as input to the Longwave radiation |
401 |
|
|
subroutine} |
402 |
|
|
\end{minipage}\\ |
403 |
|
|
44 & CLMOLW & $0-1$ & Nrphys |
404 |
|
|
&\begin{minipage}[t]{3in} |
405 |
|
|
{Maximum overlap cloud fraction used in the Longwave radiation |
406 |
|
|
subroutine} |
407 |
|
|
\end{minipage}\\ |
408 |
|
|
45 & CLDTOT & $0-1$ & Nrphys |
409 |
|
|
&\begin{minipage}[t]{3in} |
410 |
|
|
{Total cloud fraction used in the Longwave and Shortwave radiation |
411 |
|
|
subroutines} |
412 |
|
|
\end{minipage}\\ |
413 |
|
|
46 & RADSWT & $Watts/m^2$ & 1 |
414 |
|
|
&\begin{minipage}[t]{3in} |
415 |
|
|
{Incident Shortwave radiation at the top of the atmosphere} |
416 |
|
|
\end{minipage}\\ |
417 |
|
|
47 & CLROSW & $0-1$ & Nrphys |
418 |
|
|
&\begin{minipage}[t]{3in} |
419 |
|
|
{Random overlap cloud fraction used in the shortwave radiation |
420 |
|
|
subroutine} |
421 |
|
|
\end{minipage}\\ |
422 |
|
|
48 & CLMOSW & $0-1$ & Nrphys |
423 |
|
|
&\begin{minipage}[t]{3in} |
424 |
|
|
{Maximum overlap cloud fraction used in the shortwave radiation |
425 |
|
|
subroutine} |
426 |
|
|
\end{minipage}\\ |
427 |
|
|
49 & EVAP & $mm/day$ & 1 |
428 |
|
|
&\begin{minipage}[t]{3in} |
429 |
|
|
{Surface evaporation} |
430 |
|
|
\end{minipage}\\ |
431 |
|
|
\end{tabular} |
432 |
|
|
\vfill |
433 |
|
|
|
434 |
|
|
\newpage |
435 |
|
|
\vspace*{\fill} |
436 |
|
|
\begin{tabular}{lllll} |
437 |
|
|
\hline\hline |
438 |
|
|
N & NAME & UNITS & LEVELS & DESCRIPTION \\ |
439 |
|
|
\hline |
440 |
|
|
|
441 |
|
|
&\\ |
442 |
|
|
50 & DUDT & $m/sec/day$ & Nrphys |
443 |
|
|
&\begin{minipage}[t]{3in} |
444 |
|
|
{Total U-Wind tendency} |
445 |
|
|
\end{minipage}\\ |
446 |
|
|
51 & DVDT & $m/sec/day$ & Nrphys |
447 |
|
|
&\begin{minipage}[t]{3in} |
448 |
|
|
{Total V-Wind tendency} |
449 |
|
|
\end{minipage}\\ |
450 |
|
|
52 & DTDT & $deg/day$ & Nrphys |
451 |
|
|
&\begin{minipage}[t]{3in} |
452 |
|
|
{Total Temperature tendency} |
453 |
|
|
\end{minipage}\\ |
454 |
|
|
53 & DQDT & $g/kg/day$ & Nrphys |
455 |
|
|
&\begin{minipage}[t]{3in} |
456 |
|
|
{Total Specific Humidity tendency} |
457 |
|
|
\end{minipage}\\ |
458 |
|
|
54 & USTAR & $m/sec$ & 1 |
459 |
|
|
&\begin{minipage}[t]{3in} |
460 |
|
|
{Surface USTAR wind} |
461 |
|
|
\end{minipage}\\ |
462 |
|
|
55 & Z0 & $m$ & 1 |
463 |
|
|
&\begin{minipage}[t]{3in} |
464 |
|
|
{Surface roughness} |
465 |
|
|
\end{minipage}\\ |
466 |
|
|
56 & FRQTRB & $0-1$ & Nrphys-1 |
467 |
|
|
&\begin{minipage}[t]{3in} |
468 |
|
|
{Frequency of Turbulence} |
469 |
|
|
\end{minipage}\\ |
470 |
|
|
57 & PBL & $mb$ & 1 |
471 |
|
|
&\begin{minipage}[t]{3in} |
472 |
|
|
{Planetary Boundary Layer depth} |
473 |
|
|
\end{minipage}\\ |
474 |
|
|
58 & SWCLR & $deg/day$ & Nrphys |
475 |
|
|
&\begin{minipage}[t]{3in} |
476 |
|
|
{Net clearsky Shortwave heating rate for each level} |
477 |
|
|
\end{minipage}\\ |
478 |
|
|
59 & OSR & $Watts/m^2$ & 1 |
479 |
|
|
&\begin{minipage}[t]{3in} |
480 |
|
|
{Net downward Shortwave flux at the top of the model} |
481 |
|
|
\end{minipage}\\ |
482 |
|
|
60 & OSRCLR & $Watts/m^2$ & 1 |
483 |
|
|
&\begin{minipage}[t]{3in} |
484 |
|
|
{Net downward clearsky Shortwave flux at the top of the model} |
485 |
|
|
\end{minipage}\\ |
486 |
|
|
61 & CLDMAS & $kg / m^2$ & Nrphys |
487 |
|
|
&\begin{minipage}[t]{3in} |
488 |
|
|
{Convective cloud mass flux} |
489 |
|
|
\end{minipage}\\ |
490 |
|
|
62 & UAVE & $m/sec$ & Nrphys |
491 |
|
|
&\begin{minipage}[t]{3in} |
492 |
|
|
{Time-averaged $u-Wind$} |
493 |
|
|
\end{minipage}\\ |
494 |
|
|
63 & VAVE & $m/sec$ & Nrphys |
495 |
|
|
&\begin{minipage}[t]{3in} |
496 |
|
|
{Time-averaged $v-Wind$} |
497 |
|
|
\end{minipage}\\ |
498 |
|
|
64 & TAVE & $deg$ & Nrphys |
499 |
|
|
&\begin{minipage}[t]{3in} |
500 |
|
|
{Time-averaged $Temperature$} |
501 |
|
|
\end{minipage}\\ |
502 |
|
|
65 & QAVE & $g/g$ & Nrphys |
503 |
|
|
&\begin{minipage}[t]{3in} |
504 |
|
|
{Time-averaged $Specific \, \, Humidity$} |
505 |
|
|
\end{minipage}\\ |
506 |
|
|
66 & PAVE & $mb$ & 1 |
507 |
|
|
&\begin{minipage}[t]{3in} |
508 |
|
|
{Time-averaged $p_{surf} - p_{top}$} |
509 |
|
|
\end{minipage}\\ |
510 |
|
|
67 & QQAVE & $(m/sec)^2$ & Nrphys |
511 |
|
|
&\begin{minipage}[t]{3in} |
512 |
|
|
{Time-averaged $Turbulent Kinetic Energy$} |
513 |
|
|
\end{minipage}\\ |
514 |
|
|
68 & SWGCLR & $Watts/m^2$ & 1 |
515 |
|
|
&\begin{minipage}[t]{3in} |
516 |
|
|
{Net downward clearsky Shortwave flux at the ground} |
517 |
|
|
\end{minipage}\\ |
518 |
|
|
69 & SDIAG1 & & 1 |
519 |
|
|
&\begin{minipage}[t]{3in} |
520 |
|
|
{User-Defined Surface Diagnostic-1} |
521 |
|
|
\end{minipage}\\ |
522 |
|
|
70 & SDIAG2 & & 1 |
523 |
|
|
&\begin{minipage}[t]{3in} |
524 |
|
|
{User-Defined Surface Diagnostic-2} |
525 |
|
|
\end{minipage}\\ |
526 |
|
|
71 & UDIAG1 & & Nrphys |
527 |
|
|
&\begin{minipage}[t]{3in} |
528 |
|
|
{User-Defined Upper-Air Diagnostic-1} |
529 |
|
|
\end{minipage}\\ |
530 |
|
|
72 & UDIAG2 & & Nrphys |
531 |
|
|
&\begin{minipage}[t]{3in} |
532 |
|
|
{User-Defined Upper-Air Diagnostic-2} |
533 |
|
|
\end{minipage}\\ |
534 |
|
|
73 & DIABU & $m/sec/day$ & Nrphys |
535 |
|
|
&\begin{minipage}[t]{3in} |
536 |
|
|
{Total Diabatic forcing on $u-Wind$} |
537 |
|
|
\end{minipage}\\ |
538 |
|
|
74 & DIABV & $m/sec/day$ & Nrphys |
539 |
|
|
&\begin{minipage}[t]{3in} |
540 |
|
|
{Total Diabatic forcing on $v-Wind$} |
541 |
|
|
\end{minipage}\\ |
542 |
|
|
75 & DIABT & $deg/day$ & Nrphys |
543 |
|
|
&\begin{minipage}[t]{3in} |
544 |
|
|
{Total Diabatic forcing on $Temperature$} |
545 |
|
|
\end{minipage}\\ |
546 |
|
|
76 & DIABQ & $g/kg/day$ & Nrphys |
547 |
|
|
&\begin{minipage}[t]{3in} |
548 |
|
|
{Total Diabatic forcing on $Specific \, \, Humidity$} |
549 |
|
|
\end{minipage}\\ |
550 |
|
|
|
551 |
|
|
\end{tabular} |
552 |
|
|
\vfill |
553 |
|
|
|
554 |
|
|
\newpage |
555 |
|
|
\vspace*{\fill} |
556 |
|
|
\begin{tabular}{lllll} |
557 |
|
|
\hline\hline |
558 |
|
|
N & NAME & UNITS & LEVELS & DESCRIPTION \\ |
559 |
|
|
\hline |
560 |
|
|
|
561 |
|
|
77 & VINTUQ & $m/sec \cdot g/kg$ & 1 |
562 |
|
|
&\begin{minipage}[t]{3in} |
563 |
|
|
{Vertically integrated $u \, q$} |
564 |
|
|
\end{minipage}\\ |
565 |
|
|
78 & VINTVQ & $m/sec \cdot g/kg$ & 1 |
566 |
|
|
&\begin{minipage}[t]{3in} |
567 |
|
|
{Vertically integrated $v \, q$} |
568 |
|
|
\end{minipage}\\ |
569 |
|
|
79 & VINTUT & $m/sec \cdot deg$ & 1 |
570 |
|
|
&\begin{minipage}[t]{3in} |
571 |
|
|
{Vertically integrated $u \, T$} |
572 |
|
|
\end{minipage}\\ |
573 |
|
|
80 & VINTVT & $m/sec \cdot deg$ & 1 |
574 |
|
|
&\begin{minipage}[t]{3in} |
575 |
|
|
{Vertically integrated $v \, T$} |
576 |
|
|
\end{minipage}\\ |
577 |
|
|
81 & CLDFRC & $0-1$ & 1 |
578 |
|
|
&\begin{minipage}[t]{3in} |
579 |
|
|
{Total Cloud Fraction} |
580 |
|
|
\end{minipage}\\ |
581 |
|
|
82 & QINT & $gm/cm^2$ & 1 |
582 |
|
|
&\begin{minipage}[t]{3in} |
583 |
|
|
{Precipitable water} |
584 |
|
|
\end{minipage}\\ |
585 |
|
|
83 & U2M & $m/sec$ & 1 |
586 |
|
|
&\begin{minipage}[t]{3in} |
587 |
|
|
{U-Wind at 2 meters} |
588 |
|
|
\end{minipage}\\ |
589 |
|
|
84 & V2M & $m/sec$ & 1 |
590 |
|
|
&\begin{minipage}[t]{3in} |
591 |
|
|
{V-Wind at 2 meters} |
592 |
|
|
\end{minipage}\\ |
593 |
|
|
85 & T2M & $deg$ & 1 |
594 |
|
|
&\begin{minipage}[t]{3in} |
595 |
|
|
{Temperature at 2 meters} |
596 |
|
|
\end{minipage}\\ |
597 |
|
|
86 & Q2M & $g/kg$ & 1 |
598 |
|
|
&\begin{minipage}[t]{3in} |
599 |
|
|
{Specific Humidity at 2 meters} |
600 |
|
|
\end{minipage}\\ |
601 |
|
|
87 & U10M & $m/sec$ & 1 |
602 |
|
|
&\begin{minipage}[t]{3in} |
603 |
|
|
{U-Wind at 10 meters} |
604 |
|
|
\end{minipage}\\ |
605 |
|
|
88 & V10M & $m/sec$ & 1 |
606 |
|
|
&\begin{minipage}[t]{3in} |
607 |
|
|
{V-Wind at 10 meters} |
608 |
|
|
\end{minipage}\\ |
609 |
|
|
89 & T10M & $deg$ & 1 |
610 |
|
|
&\begin{minipage}[t]{3in} |
611 |
|
|
{Temperature at 10 meters} |
612 |
|
|
\end{minipage}\\ |
613 |
|
|
90 & Q10M & $g/kg$ & 1 |
614 |
|
|
&\begin{minipage}[t]{3in} |
615 |
|
|
{Specific Humidity at 10 meters} |
616 |
|
|
\end{minipage}\\ |
617 |
|
|
91 & DTRAIN & $kg/m^2$ & Nrphys |
618 |
|
|
&\begin{minipage}[t]{3in} |
619 |
|
|
{Detrainment Cloud Mass Flux} |
620 |
|
|
\end{minipage}\\ |
621 |
|
|
92 & QFILL & $g/kg/day$ & Nrphys |
622 |
|
|
&\begin{minipage}[t]{3in} |
623 |
|
|
{Filling of negative specific humidity} |
624 |
|
|
\end{minipage}\\ |
625 |
|
|
|
626 |
|
|
\end{tabular} |
627 |
|
|
\vspace{1.5in} |
628 |
|
|
\vfill |
629 |
|
|
|
630 |
|
|
\newpage |
631 |
|
|
|
632 |
|
|
\subsubsection{Diagnostic Description} |
633 |
|
|
|
634 |
|
|
In this section we list and describe the diagnostic quantities available within the |
635 |
|
|
GCM. The diagnostics are listed in the order that they appear in the |
636 |
|
|
Diagnostic Menu, Section \ref{sec:diagnostics:menu}. |
637 |
|
|
In all cases, each diagnostic as currently archived on the output datasets |
638 |
|
|
is time-averaged over its diagnostic output frequency: |
639 |
|
|
|
640 |
|
|
\[ |
641 |
|
|
{\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t) |
642 |
|
|
\] |
643 |
|
|
where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the |
644 |
molod |
1.5 |
output frequency of the diagnostic, and $\Delta t$ is |
645 |
|
|
the timestep over which the diagnostic is updated. |
646 |
molod |
1.1 |
|
647 |
|
|
{\bf 1) \underline {UFLUX} Surface Zonal Wind Stress on the Atmosphere ($Newton/m^2$) } |
648 |
|
|
|
649 |
|
|
The zonal wind stress is the turbulent flux of zonal momentum from |
650 |
|
|
the surface. See section 3.3 for a description of the surface layer parameterization. |
651 |
|
|
\[ |
652 |
|
|
{\bf UFLUX} = - \rho C_D W_s u \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u |
653 |
|
|
\] |
654 |
|
|
where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface |
655 |
|
|
drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum |
656 |
|
|
(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $u$ is |
657 |
|
|
the zonal wind in the lowest model layer. |
658 |
|
|
\\ |
659 |
|
|
|
660 |
|
|
|
661 |
|
|
{\bf 2) \underline {VFLUX} Surface Meridional Wind Stress on the Atmosphere ($Newton/m^2$) } |
662 |
|
|
|
663 |
|
|
The meridional wind stress is the turbulent flux of meridional momentum from |
664 |
|
|
the surface. See section 3.3 for a description of the surface layer parameterization. |
665 |
|
|
\[ |
666 |
|
|
{\bf VFLUX} = - \rho C_D W_s v \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u |
667 |
|
|
\] |
668 |
|
|
where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface |
669 |
|
|
drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum |
670 |
|
|
(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $v$ is |
671 |
|
|
the meridional wind in the lowest model layer. |
672 |
|
|
\\ |
673 |
|
|
|
674 |
|
|
{\bf 3) \underline {HFLUX} Surface Flux of Sensible Heat ($Watts/m^2$) } |
675 |
|
|
|
676 |
|
|
The turbulent flux of sensible heat from the surface to the atmosphere is a function of the |
677 |
|
|
gradient of virtual potential temperature and the eddy exchange coefficient: |
678 |
|
|
\[ |
679 |
|
|
{\bf HFLUX} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{surface} - \theta_{Nrphys}) |
680 |
|
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
681 |
|
|
\] |
682 |
|
|
where $\rho$ = the atmospheric density at the surface, $c_{p}$ is the specific |
683 |
|
|
heat of air, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the |
684 |
|
|
magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient |
685 |
|
|
for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient |
686 |
|
|
for heat and moisture (see diagnostic number 9), and $\theta$ is the potential temperature |
687 |
|
|
at the surface and at the bottom model level. |
688 |
|
|
\\ |
689 |
|
|
|
690 |
|
|
|
691 |
|
|
{\bf 4) \underline {EFLUX} Surface Flux of Latent Heat ($Watts/m^2$) } |
692 |
|
|
|
693 |
|
|
The turbulent flux of latent heat from the surface to the atmosphere is a function of the |
694 |
|
|
gradient of moisture, the potential evapotranspiration fraction and the eddy exchange coefficient: |
695 |
|
|
\[ |
696 |
|
|
{\bf EFLUX} = \rho \beta L C_{H} W_s (q_{surface} - q_{Nrphys}) |
697 |
|
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
698 |
|
|
\] |
699 |
|
|
where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of |
700 |
|
|
the potential evapotranspiration actually evaporated, L is the latent |
701 |
|
|
heat of evaporation, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the |
702 |
|
|
magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient |
703 |
|
|
for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient |
704 |
|
|
for heat and moisture (see diagnostic number 9), and $q_{surface}$ and $q_{Nrphys}$ are the specific |
705 |
|
|
humidity at the surface and at the bottom model level, respectively. |
706 |
|
|
\\ |
707 |
|
|
|
708 |
|
|
{\bf 5) \underline {QICE} Heat Conduction Through Sea Ice ($Watts/m^2$) } |
709 |
|
|
|
710 |
|
|
Over sea ice there is an additional source of energy at the surface due to the heat |
711 |
|
|
conduction from the relatively warm ocean through the sea ice. The heat conduction |
712 |
|
|
through sea ice represents an additional energy source term for the ground temperature equation. |
713 |
|
|
|
714 |
|
|
\[ |
715 |
|
|
{\bf QICE} = {C_{ti} \over {H_i}} (T_i-T_g) |
716 |
|
|
\] |
717 |
|
|
|
718 |
|
|
where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to |
719 |
|
|
be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and |
720 |
|
|
$T_g$ is the temperature of the sea ice. |
721 |
|
|
|
722 |
|
|
NOTE: QICE is not available through model version 5.3, but is available in subsequent versions. |
723 |
|
|
\\ |
724 |
|
|
|
725 |
|
|
|
726 |
|
|
{\bf 6) \underline {RADLWG} Net upward Longwave Flux at the surface ($Watts/m^2$)} |
727 |
|
|
|
728 |
|
|
\begin{eqnarray*} |
729 |
|
|
{\bf RADLWG} & = & F_{LW,Nrphys+1}^{Net} \\ |
730 |
|
|
& = & F_{LW,Nrphys+1}^\uparrow - F_{LW,Nrphys+1}^\downarrow |
731 |
|
|
\end{eqnarray*} |
732 |
|
|
\\ |
733 |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
734 |
|
|
$F_{LW}^\uparrow$ is |
735 |
|
|
the upward Longwave flux and $F_{LW}^\downarrow$ is the downward Longwave flux. |
736 |
|
|
\\ |
737 |
|
|
|
738 |
|
|
{\bf 7) \underline {RADSWG} Net downard shortwave Flux at the surface ($Watts/m^2$)} |
739 |
|
|
|
740 |
|
|
\begin{eqnarray*} |
741 |
|
|
{\bf RADSWG} & = & F_{SW,Nrphys+1}^{Net} \\ |
742 |
|
|
& = & F_{SW,Nrphys+1}^\downarrow - F_{SW,Nrphys+1}^\uparrow |
743 |
|
|
\end{eqnarray*} |
744 |
|
|
\\ |
745 |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
746 |
|
|
$F_{SW}^\downarrow$ is |
747 |
|
|
the downward Shortwave flux and $F_{SW}^\uparrow$ is the upward Shortwave flux. |
748 |
|
|
\\ |
749 |
|
|
|
750 |
|
|
|
751 |
|
|
\noindent |
752 |
|
|
{\bf 8) \underline {RI} Richardson Number} ($dimensionless$) |
753 |
|
|
|
754 |
|
|
\noindent |
755 |
|
|
The non-dimensional stability indicator is the ratio of the buoyancy to the shear: |
756 |
|
|
\[ |
757 |
|
|
{\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
758 |
|
|
= { {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
759 |
|
|
\] |
760 |
|
|
\\ |
761 |
|
|
where we used the hydrostatic equation: |
762 |
|
|
\[ |
763 |
|
|
{\pp{\Phi}{P^ \kappa}} = c_p \theta_v |
764 |
|
|
\] |
765 |
|
|
Negative values indicate unstable buoyancy {\bf{AND}} shear, small positive values ($<0.4$) |
766 |
|
|
indicate dominantly unstable shear, and large positive values indicate dominantly stable |
767 |
|
|
stratification. |
768 |
|
|
\\ |
769 |
|
|
|
770 |
|
|
\noindent |
771 |
|
|
{\bf 9) \underline {CT} Surface Exchange Coefficient for Temperature and Moisture ($dimensionless$) } |
772 |
|
|
|
773 |
|
|
\noindent |
774 |
|
|
The surface exchange coefficient is obtained from the similarity functions for the stability |
775 |
|
|
dependant flux profile relationships: |
776 |
|
|
\[ |
777 |
|
|
{\bf CT} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} = |
778 |
|
|
-{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} = |
779 |
|
|
{ k \over { (\psi_{h} + \psi_{g}) } } |
780 |
|
|
\] |
781 |
|
|
where $\psi_h$ is the surface layer non-dimensional temperature change and $\psi_g$ is the |
782 |
|
|
viscous sublayer non-dimensional temperature or moisture change: |
783 |
|
|
\[ |
784 |
|
|
\psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} \hspace{1cm} and |
785 |
|
|
\hspace{1cm} \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} } |
786 |
|
|
(h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2} |
787 |
|
|
\] |
788 |
|
|
and: |
789 |
|
|
$h_{0} = 30z_{0}$ with a maximum value over land of 0.01 |
790 |
|
|
|
791 |
|
|
\noindent |
792 |
|
|
$\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of |
793 |
|
|
the temperature and moisture gradients, specified differently for stable and unstable |
794 |
|
|
layers according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the |
795 |
|
|
non-dimensional stability parameter, Pr is the Prandtl number for air, $\nu$ is the molecular |
796 |
|
|
viscosity, $z_{0}$ is the surface roughness length, $u_*$ is the surface stress velocity |
797 |
|
|
(see diagnostic number 67), and the subscript ref refers to a reference value. |
798 |
|
|
\\ |
799 |
|
|
|
800 |
|
|
\noindent |
801 |
|
|
{\bf 10) \underline {CU} Surface Exchange Coefficient for Momentum ($dimensionless$) } |
802 |
|
|
|
803 |
|
|
\noindent |
804 |
|
|
The surface exchange coefficient is obtained from the similarity functions for the stability |
805 |
|
|
dependant flux profile relationships: |
806 |
|
|
\[ |
807 |
|
|
{\bf CU} = {u_* \over W_s} = { k \over \psi_{m} } |
808 |
|
|
\] |
809 |
|
|
where $\psi_m$ is the surface layer non-dimensional wind shear: |
810 |
|
|
\[ |
811 |
|
|
\psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta} |
812 |
|
|
\] |
813 |
|
|
\noindent |
814 |
|
|
$\phi_m$ is the similarity function of $\zeta$, which expresses the stability dependance of |
815 |
|
|
the temperature and moisture gradients, specified differently for stable and unstable layers |
816 |
|
|
according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the |
817 |
|
|
non-dimensional stability parameter, $u_*$ is the surface stress velocity |
818 |
|
|
(see diagnostic number 67), and $W_s$ is the magnitude of the surface layer wind. |
819 |
|
|
\\ |
820 |
|
|
|
821 |
|
|
\noindent |
822 |
|
|
{\bf 11) \underline {ET} Diffusivity Coefficient for Temperature and Moisture ($m^2/sec$) } |
823 |
|
|
|
824 |
|
|
\noindent |
825 |
|
|
In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat or |
826 |
|
|
moisture flux for the atmosphere above the surface layer can be expressed as a turbulent |
827 |
|
|
diffusion coefficient $K_h$ times the negative of the gradient of potential temperature |
828 |
|
|
or moisture. In the Helfand and Labraga (1988) adaptation of this closure, $K_h$ |
829 |
|
|
takes the form: |
830 |
|
|
\[ |
831 |
|
|
{\bf ET} = K_h = -{( {\overline{w^{\prime}\theta_v^{\prime}}}) \over {\pp{\theta_v}{z}} } |
832 |
|
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) & \mbox{decaying turbulence} |
833 |
|
|
\\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. |
834 |
|
|
\] |
835 |
|
|
where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} |
836 |
|
|
energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, |
837 |
|
|
which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer |
838 |
|
|
depth, |
839 |
|
|
$S_H$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and |
840 |
|
|
wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium |
841 |
|
|
dimensionless buoyancy and wind shear |
842 |
|
|
parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
843 |
|
|
are functions of the Richardson number. |
844 |
|
|
|
845 |
|
|
\noindent |
846 |
|
|
For the detailed equations and derivations of the modified level 2.5 closure scheme, |
847 |
|
|
see Helfand and Labraga, 1988. |
848 |
|
|
|
849 |
|
|
\noindent |
850 |
|
|
In the surface layer, ${\bf {ET}}$ is the exchange coefficient for heat and moisture, |
851 |
|
|
in units of $m/sec$, given by: |
852 |
|
|
\[ |
853 |
|
|
{\bf ET_{Nrphys}} = C_t * u_* = C_H W_s |
854 |
|
|
\] |
855 |
|
|
\noindent |
856 |
|
|
where $C_t$ is the dimensionless exchange coefficient for heat and moisture from the |
857 |
|
|
surface layer similarity functions (see diagnostic number 9), $u_*$ is the surface |
858 |
|
|
friction velocity (see diagnostic number 67), $C_H$ is the heat transfer coefficient, |
859 |
|
|
and $W_s$ is the magnitude of the surface layer wind. |
860 |
|
|
\\ |
861 |
|
|
|
862 |
|
|
\noindent |
863 |
|
|
{\bf 12) \underline {EU} Diffusivity Coefficient for Momentum ($m^2/sec$) } |
864 |
|
|
|
865 |
|
|
\noindent |
866 |
|
|
In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat |
867 |
|
|
momentum flux for the atmosphere above the surface layer can be expressed as a turbulent |
868 |
|
|
diffusion coefficient $K_m$ times the negative of the gradient of the u-wind. |
869 |
|
|
In the Helfand and Labraga (1988) adaptation of this closure, $K_m$ |
870 |
|
|
takes the form: |
871 |
|
|
\[ |
872 |
|
|
{\bf EU} = K_m = -{( {\overline{u^{\prime}w^{\prime}}}) \over {\pp{U}{z}} } |
873 |
|
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) & \mbox{decaying turbulence} |
874 |
|
|
\\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. |
875 |
|
|
\] |
876 |
|
|
\noindent |
877 |
|
|
where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} |
878 |
|
|
energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, |
879 |
|
|
which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer |
880 |
|
|
depth, |
881 |
|
|
$S_M$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and |
882 |
|
|
wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium |
883 |
|
|
dimensionless buoyancy and wind shear |
884 |
|
|
parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
885 |
|
|
are functions of the Richardson number. |
886 |
|
|
|
887 |
|
|
\noindent |
888 |
|
|
For the detailed equations and derivations of the modified level 2.5 closure scheme, |
889 |
|
|
see Helfand and Labraga, 1988. |
890 |
|
|
|
891 |
|
|
\noindent |
892 |
|
|
In the surface layer, ${\bf {EU}}$ is the exchange coefficient for momentum, |
893 |
|
|
in units of $m/sec$, given by: |
894 |
|
|
\[ |
895 |
|
|
{\bf EU_{Nrphys}} = C_u * u_* = C_D W_s |
896 |
|
|
\] |
897 |
|
|
\noindent |
898 |
|
|
where $C_u$ is the dimensionless exchange coefficient for momentum from the surface layer |
899 |
|
|
similarity functions (see diagnostic number 10), $u_*$ is the surface friction velocity |
900 |
|
|
(see diagnostic number 67), $C_D$ is the surface drag coefficient, and $W_s$ is the |
901 |
|
|
magnitude of the surface layer wind. |
902 |
|
|
\\ |
903 |
|
|
|
904 |
|
|
\noindent |
905 |
|
|
{\bf 13) \underline {TURBU} Zonal U-Momentum changes due to Turbulence ($m/sec/day$) } |
906 |
|
|
|
907 |
|
|
\noindent |
908 |
|
|
The tendency of U-Momentum due to turbulence is written: |
909 |
|
|
\[ |
910 |
|
|
{\bf TURBU} = {\pp{u}{t}}_{turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})} |
911 |
|
|
= {\pp{}{z} }{(K_m \pp{u}{z})} |
912 |
|
|
\] |
913 |
|
|
|
914 |
|
|
\noindent |
915 |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
916 |
|
|
flux of u-momentum in terms of $K_m$, and the equation has the form of a diffusion |
917 |
|
|
equation. |
918 |
|
|
|
919 |
|
|
\noindent |
920 |
|
|
{\bf 14) \underline {TURBV} Meridional V-Momentum changes due to Turbulence ($m/sec/day$) } |
921 |
|
|
|
922 |
|
|
\noindent |
923 |
|
|
The tendency of V-Momentum due to turbulence is written: |
924 |
|
|
\[ |
925 |
|
|
{\bf TURBV} = {\pp{v}{t}}_{turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})} |
926 |
|
|
= {\pp{}{z} }{(K_m \pp{v}{z})} |
927 |
|
|
\] |
928 |
|
|
|
929 |
|
|
\noindent |
930 |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
931 |
|
|
flux of v-momentum in terms of $K_m$, and the equation has the form of a diffusion |
932 |
|
|
equation. |
933 |
|
|
\\ |
934 |
|
|
|
935 |
|
|
\noindent |
936 |
|
|
{\bf 15) \underline {TURBT} Temperature changes due to Turbulence ($deg/day$) } |
937 |
|
|
|
938 |
|
|
\noindent |
939 |
|
|
The tendency of temperature due to turbulence is written: |
940 |
|
|
\[ |
941 |
|
|
{\bf TURBT} = {\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{turb} = |
942 |
|
|
P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})} |
943 |
|
|
= P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})} |
944 |
|
|
\] |
945 |
|
|
|
946 |
|
|
\noindent |
947 |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
948 |
|
|
flux of temperature in terms of $K_h$, and the equation has the form of a diffusion |
949 |
|
|
equation. |
950 |
|
|
\\ |
951 |
|
|
|
952 |
|
|
\noindent |
953 |
|
|
{\bf 16) \underline {TURBQ} Specific Humidity changes due to Turbulence ($g/kg/day$) } |
954 |
|
|
|
955 |
|
|
\noindent |
956 |
|
|
The tendency of specific humidity due to turbulence is written: |
957 |
|
|
\[ |
958 |
|
|
{\bf TURBQ} = {\pp{q}{t}}_{turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})} |
959 |
|
|
= {\pp{}{z} }{(K_h \pp{q}{z})} |
960 |
|
|
\] |
961 |
|
|
|
962 |
|
|
\noindent |
963 |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
964 |
|
|
flux of temperature in terms of $K_h$, and the equation has the form of a diffusion |
965 |
|
|
equation. |
966 |
|
|
\\ |
967 |
|
|
|
968 |
|
|
\noindent |
969 |
|
|
{\bf 17) \underline {MOISTT} Temperature Changes Due to Moist Processes ($deg/day$) } |
970 |
|
|
|
971 |
|
|
\noindent |
972 |
|
|
\[ |
973 |
|
|
{\bf MOISTT} = \left. {\pp{T}{t}}\right|_{c} + \left. {\pp{T}{t}} \right|_{ls} |
974 |
|
|
\] |
975 |
|
|
where: |
976 |
|
|
\[ |
977 |
|
|
\left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over c_p} \Gamma_s \right)_i |
978 |
|
|
\hspace{.4cm} and |
979 |
|
|
\hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = {L \over c_p } (q^*-q) |
980 |
|
|
\] |
981 |
|
|
and |
982 |
|
|
\[ |
983 |
|
|
\Gamma_s = g \eta \pp{s}{p} |
984 |
|
|
\] |
985 |
|
|
|
986 |
|
|
\noindent |
987 |
|
|
The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale |
988 |
|
|
precipitation processes, or supersaturation rain. |
989 |
|
|
The summation refers to contributions from each cloud type called by RAS. |
990 |
|
|
The dry static energy is given |
991 |
|
|
as $s$, the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is |
992 |
|
|
given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, |
993 |
|
|
the description of the convective parameterization. The fractional adjustment, or relaxation |
994 |
|
|
parameter, for each cloud type is given as $\alpha$, while |
995 |
|
|
$R$ is the rain re-evaporation adjustment. |
996 |
|
|
\\ |
997 |
|
|
|
998 |
|
|
\noindent |
999 |
|
|
{\bf 18) \underline {MOISTQ} Specific Humidity Changes Due to Moist Processes ($g/kg/day$) } |
1000 |
|
|
|
1001 |
|
|
\noindent |
1002 |
|
|
\[ |
1003 |
|
|
{\bf MOISTQ} = \left. {\pp{q}{t}}\right|_{c} + \left. {\pp{q}{t}} \right|_{ls} |
1004 |
|
|
\] |
1005 |
|
|
where: |
1006 |
|
|
\[ |
1007 |
|
|
\left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over {L}}(\Gamma_h-\Gamma_s) \right)_i |
1008 |
|
|
\hspace{.4cm} and |
1009 |
|
|
\hspace{.4cm} \left.{\pp{q}{t}}\right|_{ls} = (q^*-q) |
1010 |
|
|
\] |
1011 |
|
|
and |
1012 |
|
|
\[ |
1013 |
|
|
\Gamma_s = g \eta \pp{s}{p}\hspace{.4cm} and \hspace{.4cm}\Gamma_h = g \eta \pp{h}{p} |
1014 |
|
|
\] |
1015 |
|
|
\noindent |
1016 |
|
|
The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale |
1017 |
|
|
precipitation processes, or supersaturation rain. |
1018 |
|
|
The summation refers to contributions from each cloud type called by RAS. |
1019 |
|
|
The dry static energy is given as $s$, |
1020 |
|
|
the moist static energy is given as $h$, |
1021 |
|
|
the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is |
1022 |
|
|
given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, |
1023 |
|
|
the description of the convective parameterization. The fractional adjustment, or relaxation |
1024 |
|
|
parameter, for each cloud type is given as $\alpha$, while |
1025 |
|
|
$R$ is the rain re-evaporation adjustment. |
1026 |
|
|
\\ |
1027 |
|
|
|
1028 |
|
|
\noindent |
1029 |
|
|
{\bf 19) \underline {RADLW} Heating Rate due to Longwave Radiation ($deg/day$) } |
1030 |
|
|
|
1031 |
|
|
\noindent |
1032 |
|
|
The net longwave heating rate is calculated as the vertical divergence of the |
1033 |
|
|
net terrestrial radiative fluxes. |
1034 |
|
|
Both the clear-sky and cloudy-sky longwave fluxes are computed within the |
1035 |
|
|
longwave routine. |
1036 |
|
|
The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. |
1037 |
|
|
For a given cloud fraction, |
1038 |
|
|
the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ |
1039 |
|
|
to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, |
1040 |
|
|
for the upward and downward radiative fluxes. |
1041 |
|
|
(see Section \ref{sec:fizhi:radcloud}). |
1042 |
|
|
The cloudy-sky flux is then obtained as: |
1043 |
|
|
|
1044 |
|
|
\noindent |
1045 |
|
|
\[ |
1046 |
|
|
F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, |
1047 |
|
|
\] |
1048 |
|
|
|
1049 |
|
|
\noindent |
1050 |
|
|
Finally, the net longwave heating rate is calculated as the vertical divergence of the |
1051 |
|
|
net terrestrial radiative fluxes: |
1052 |
|
|
\[ |
1053 |
|
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F_{LW}^{NET} , |
1054 |
|
|
\] |
1055 |
|
|
or |
1056 |
|
|
\[ |
1057 |
|
|
{\bf RADLW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F_{LW}^{NET} . |
1058 |
|
|
\] |
1059 |
|
|
|
1060 |
|
|
\noindent |
1061 |
|
|
where $g$ is the accelation due to gravity, |
1062 |
|
|
$c_p$ is the heat capacity of air at constant pressure, |
1063 |
|
|
and |
1064 |
|
|
\[ |
1065 |
|
|
F_{LW}^{NET} = F_{LW}^\uparrow - F_{LW}^\downarrow |
1066 |
|
|
\] |
1067 |
|
|
\\ |
1068 |
|
|
|
1069 |
|
|
|
1070 |
|
|
\noindent |
1071 |
|
|
{\bf 20) \underline {RADSW} Heating Rate due to Shortwave Radiation ($deg/day$) } |
1072 |
|
|
|
1073 |
|
|
\noindent |
1074 |
|
|
The net Shortwave heating rate is calculated as the vertical divergence of the |
1075 |
|
|
net solar radiative fluxes. |
1076 |
|
|
The clear-sky and cloudy-sky shortwave fluxes are calculated separately. |
1077 |
|
|
For the clear-sky case, the shortwave fluxes and heating rates are computed with |
1078 |
|
|
both CLMO (maximum overlap cloud fraction) and |
1079 |
|
|
CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). |
1080 |
|
|
The shortwave routine is then called a second time, for the cloudy-sky case, with the |
1081 |
|
|
true time-averaged cloud fractions CLMO |
1082 |
|
|
and CLRO being used. In all cases, a normalized incident shortwave flux is used as |
1083 |
|
|
input at the top of the atmosphere. |
1084 |
|
|
|
1085 |
|
|
\noindent |
1086 |
|
|
The heating rate due to Shortwave Radiation under cloudy skies is defined as: |
1087 |
|
|
\[ |
1088 |
|
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT}, |
1089 |
|
|
\] |
1090 |
|
|
or |
1091 |
|
|
\[ |
1092 |
|
|
{\bf RADSW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} . |
1093 |
|
|
\] |
1094 |
|
|
|
1095 |
|
|
\noindent |
1096 |
|
|
where $g$ is the accelation due to gravity, |
1097 |
|
|
$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident |
1098 |
|
|
shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and |
1099 |
|
|
\[ |
1100 |
|
|
F(cloudy)_{SW}^{Net} = F(cloudy)_{SW}^\uparrow - F(cloudy)_{SW}^\downarrow |
1101 |
|
|
\] |
1102 |
|
|
\\ |
1103 |
|
|
|
1104 |
|
|
\noindent |
1105 |
|
|
{\bf 21) \underline {PREACC} Total (Large-scale + Convective) Accumulated Precipition ($mm/day$) } |
1106 |
|
|
|
1107 |
|
|
\noindent |
1108 |
|
|
For a change in specific humidity due to moist processes, $\Delta q_{moist}$, |
1109 |
|
|
the vertical integral or total precipitable amount is given by: |
1110 |
|
|
\[ |
1111 |
|
|
{\bf PREACC} = \int_{surf}^{top} \rho \Delta q_{moist} dz = - \int_{surf}^{top} \Delta q_{moist} |
1112 |
|
|
{dp \over g} = {1 \over g} \int_0^1 \Delta q_{moist} dp |
1113 |
|
|
\] |
1114 |
|
|
\\ |
1115 |
|
|
|
1116 |
|
|
\noindent |
1117 |
|
|
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes |
1118 |
|
|
time step, scaled to $mm/day$. |
1119 |
|
|
\\ |
1120 |
|
|
|
1121 |
|
|
\noindent |
1122 |
|
|
{\bf 22) \underline {PRECON} Convective Precipition ($mm/day$) } |
1123 |
|
|
|
1124 |
|
|
\noindent |
1125 |
|
|
For a change in specific humidity due to sub-grid scale cumulus convective processes, $\Delta q_{cum}$, |
1126 |
|
|
the vertical integral or total precipitable amount is given by: |
1127 |
|
|
\[ |
1128 |
|
|
{\bf PRECON} = \int_{surf}^{top} \rho \Delta q_{cum} dz = - \int_{surf}^{top} \Delta q_{cum} |
1129 |
|
|
{dp \over g} = {1 \over g} \int_0^1 \Delta q_{cum} dp |
1130 |
|
|
\] |
1131 |
|
|
\\ |
1132 |
|
|
|
1133 |
|
|
\noindent |
1134 |
|
|
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes |
1135 |
|
|
time step, scaled to $mm/day$. |
1136 |
|
|
\\ |
1137 |
|
|
|
1138 |
|
|
\noindent |
1139 |
|
|
{\bf 23) \underline {TUFLUX} Turbulent Flux of U-Momentum ($Newton/m^2$) } |
1140 |
|
|
|
1141 |
|
|
\noindent |
1142 |
|
|
The turbulent flux of u-momentum is calculated for $diagnostic \hspace{.2cm} purposes |
1143 |
|
|
\hspace{.2cm} only$ from the eddy coefficient for momentum: |
1144 |
|
|
|
1145 |
|
|
\[ |
1146 |
|
|
{\bf TUFLUX} = {\rho } {(\overline{u^{\prime}w^{\prime}})} = |
1147 |
|
|
{\rho } {(- K_m \pp{U}{z})} |
1148 |
|
|
\] |
1149 |
|
|
|
1150 |
|
|
\noindent |
1151 |
|
|
where $\rho$ is the air density, and $K_m$ is the eddy coefficient. |
1152 |
|
|
\\ |
1153 |
|
|
|
1154 |
|
|
\noindent |
1155 |
|
|
{\bf 24) \underline {TVFLUX} Turbulent Flux of V-Momentum ($Newton/m^2$) } |
1156 |
|
|
|
1157 |
|
|
\noindent |
1158 |
|
|
The turbulent flux of v-momentum is calculated for $diagnostic \hspace{.2cm} purposes |
1159 |
|
|
\hspace{.2cm} only$ from the eddy coefficient for momentum: |
1160 |
|
|
|
1161 |
|
|
\[ |
1162 |
|
|
{\bf TVFLUX} = {\rho } {(\overline{v^{\prime}w^{\prime}})} = |
1163 |
|
|
{\rho } {(- K_m \pp{V}{z})} |
1164 |
|
|
\] |
1165 |
|
|
|
1166 |
|
|
\noindent |
1167 |
|
|
where $\rho$ is the air density, and $K_m$ is the eddy coefficient. |
1168 |
|
|
\\ |
1169 |
|
|
|
1170 |
|
|
|
1171 |
|
|
\noindent |
1172 |
|
|
{\bf 25) \underline {TTFLUX} Turbulent Flux of Sensible Heat ($Watts/m^2$) } |
1173 |
|
|
|
1174 |
|
|
\noindent |
1175 |
|
|
The turbulent flux of sensible heat is calculated for $diagnostic \hspace{.2cm} purposes |
1176 |
|
|
\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: |
1177 |
|
|
|
1178 |
|
|
\noindent |
1179 |
|
|
\[ |
1180 |
|
|
{\bf TTFLUX} = c_p {\rho } |
1181 |
|
|
P^{\kappa}{(\overline{w^{\prime}\theta^{\prime}})} |
1182 |
|
|
= c_p {\rho } P^{\kappa}{(- K_h \pp{\theta_v}{z})} |
1183 |
|
|
\] |
1184 |
|
|
|
1185 |
|
|
\noindent |
1186 |
|
|
where $\rho$ is the air density, and $K_h$ is the eddy coefficient. |
1187 |
|
|
\\ |
1188 |
|
|
|
1189 |
|
|
|
1190 |
|
|
\noindent |
1191 |
|
|
{\bf 26) \underline {TQFLUX} Turbulent Flux of Latent Heat ($Watts/m^2$) } |
1192 |
|
|
|
1193 |
|
|
\noindent |
1194 |
|
|
The turbulent flux of latent heat is calculated for $diagnostic \hspace{.2cm} purposes |
1195 |
|
|
\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: |
1196 |
|
|
|
1197 |
|
|
\noindent |
1198 |
|
|
\[ |
1199 |
|
|
{\bf TQFLUX} = {L {\rho } (\overline{w^{\prime}q^{\prime}})} = |
1200 |
|
|
{L {\rho }(- K_h \pp{q}{z})} |
1201 |
|
|
\] |
1202 |
|
|
|
1203 |
|
|
\noindent |
1204 |
|
|
where $\rho$ is the air density, and $K_h$ is the eddy coefficient. |
1205 |
|
|
\\ |
1206 |
|
|
|
1207 |
|
|
|
1208 |
|
|
\noindent |
1209 |
|
|
{\bf 27) \underline {CN} Neutral Drag Coefficient ($dimensionless$) } |
1210 |
|
|
|
1211 |
|
|
\noindent |
1212 |
|
|
The drag coefficient for momentum obtained by assuming a neutrally stable surface layer: |
1213 |
|
|
\[ |
1214 |
|
|
{\bf CN} = { k \over { \ln({h \over {z_0}})} } |
1215 |
|
|
\] |
1216 |
|
|
|
1217 |
|
|
\noindent |
1218 |
|
|
where $k$ is the Von Karman constant, $h$ is the height of the surface layer, and |
1219 |
|
|
$z_0$ is the surface roughness. |
1220 |
|
|
|
1221 |
|
|
\noindent |
1222 |
|
|
NOTE: CN is not available through model version 5.3, but is available in subsequent |
1223 |
|
|
versions. |
1224 |
|
|
\\ |
1225 |
|
|
|
1226 |
|
|
\noindent |
1227 |
|
|
{\bf 28) \underline {WINDS} Surface Wind Speed ($meter/sec$) } |
1228 |
|
|
|
1229 |
|
|
\noindent |
1230 |
|
|
The surface wind speed is calculated for the last internal turbulence time step: |
1231 |
|
|
\[ |
1232 |
|
|
{\bf WINDS} = \sqrt{u_{Nrphys}^2 + v_{Nrphys}^2} |
1233 |
|
|
\] |
1234 |
|
|
|
1235 |
|
|
\noindent |
1236 |
|
|
where the subscript $Nrphys$ refers to the lowest model level. |
1237 |
|
|
\\ |
1238 |
|
|
|
1239 |
|
|
\noindent |
1240 |
|
|
{\bf 29) \underline {DTSRF} Air/Surface Virtual Temperature Difference ($deg \hspace{.1cm} K$) } |
1241 |
|
|
|
1242 |
|
|
\noindent |
1243 |
|
|
The air/surface virtual temperature difference measures the stability of the surface layer: |
1244 |
|
|
\[ |
1245 |
|
|
{\bf DTSRF} = (\theta_{v{Nrphys+1}} - \theta{v_{Nrphys}}) P^{\kappa}_{surf} |
1246 |
|
|
\] |
1247 |
|
|
\noindent |
1248 |
|
|
where |
1249 |
|
|
\[ |
1250 |
|
|
\theta_{v{Nrphys+1}} = { T_g \over {P^{\kappa}_{surf}} } (1 + .609 q_{Nrphys+1}) \hspace{1cm} |
1251 |
|
|
and \hspace{1cm} q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) |
1252 |
|
|
\] |
1253 |
|
|
|
1254 |
|
|
\noindent |
1255 |
|
|
$\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), |
1256 |
|
|
$q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature |
1257 |
|
|
and surface pressure, level $Nrphys$ refers to the lowest model level and level $Nrphys+1$ |
1258 |
|
|
refers to the surface. |
1259 |
|
|
\\ |
1260 |
|
|
|
1261 |
|
|
|
1262 |
|
|
\noindent |
1263 |
|
|
{\bf 30) \underline {TG} Ground Temperature ($deg \hspace{.1cm} K$) } |
1264 |
|
|
|
1265 |
|
|
\noindent |
1266 |
|
|
The ground temperature equation is solved as part of the turbulence package |
1267 |
|
|
using a backward implicit time differencing scheme: |
1268 |
|
|
\[ |
1269 |
|
|
{\bf TG} \hspace{.1cm} is \hspace{.1cm} obtained \hspace{.1cm} from: \hspace{.1cm} |
1270 |
|
|
C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{ice} - H - LE |
1271 |
|
|
\] |
1272 |
|
|
|
1273 |
|
|
\noindent |
1274 |
|
|
where $R_{sw}$ is the net surface downward shortwave radiative flux, $R_{lw}$ is the |
1275 |
|
|
net surface upward longwave radiative flux, $Q_{ice}$ is the heat conduction through |
1276 |
|
|
sea ice, $H$ is the upward sensible heat flux, $LE$ is the upward latent heat |
1277 |
|
|
flux, and $C_g$ is the total heat capacity of the ground. |
1278 |
|
|
$C_g$ is obtained by solving a heat diffusion equation |
1279 |
|
|
for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by: |
1280 |
|
|
\[ |
1281 |
|
|
C_g = \sqrt{ {\lambda C_s \over {2 \omega} } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3} |
1282 |
|
|
{ 86400. \over {2 \pi} } } \, \, . |
1283 |
|
|
\] |
1284 |
|
|
\noindent |
1285 |
|
|
Here, the thermal conductivity, $\lambda$, is equal to $2x10^{-3}$ ${ly\over{ sec}} |
1286 |
|
|
{cm \over {^oK}}$, |
1287 |
|
|
the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided |
1288 |
|
|
by $2 \pi$ $radians/ |
1289 |
|
|
day$, and the expression for $C_s$, the heat capacity per unit volume at the surface, |
1290 |
|
|
is a function of the ground wetness, $W$. |
1291 |
|
|
\\ |
1292 |
|
|
|
1293 |
|
|
\noindent |
1294 |
|
|
{\bf 31) \underline {TS} Surface Temperature ($deg \hspace{.1cm} K$) } |
1295 |
|
|
|
1296 |
|
|
\noindent |
1297 |
|
|
The surface temperature estimate is made by assuming that the model's lowest |
1298 |
|
|
layer is well-mixed, and therefore that $\theta$ is constant in that layer. |
1299 |
|
|
The surface temperature is therefore: |
1300 |
|
|
\[ |
1301 |
|
|
{\bf TS} = \theta_{Nrphys} P^{\kappa}_{surf} |
1302 |
|
|
\] |
1303 |
|
|
\\ |
1304 |
|
|
|
1305 |
|
|
\noindent |
1306 |
|
|
{\bf 32) \underline {DTG} Surface Temperature Adjustment ($deg \hspace{.1cm} K$) } |
1307 |
|
|
|
1308 |
|
|
\noindent |
1309 |
|
|
The change in surface temperature from one turbulence time step to the next, solved |
1310 |
|
|
using the Ground Temperature Equation (see diagnostic number 30) is calculated: |
1311 |
|
|
\[ |
1312 |
|
|
{\bf DTG} = {T_g}^{n} - {T_g}^{n-1} |
1313 |
|
|
\] |
1314 |
|
|
|
1315 |
|
|
\noindent |
1316 |
|
|
where superscript $n$ refers to the new, updated time level, and the superscript $n-1$ |
1317 |
|
|
refers to the value at the previous turbulence time level. |
1318 |
|
|
\\ |
1319 |
|
|
|
1320 |
|
|
\noindent |
1321 |
|
|
{\bf 33) \underline {QG} Ground Specific Humidity ($g/kg$) } |
1322 |
|
|
|
1323 |
|
|
\noindent |
1324 |
|
|
The ground specific humidity is obtained by interpolating between the specific |
1325 |
|
|
humidity at the lowest model level and the specific humidity of a saturated ground. |
1326 |
|
|
The interpolation is performed using the potential evapotranspiration function: |
1327 |
|
|
\[ |
1328 |
|
|
{\bf QG} = q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) |
1329 |
|
|
\] |
1330 |
|
|
|
1331 |
|
|
\noindent |
1332 |
|
|
where $\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), |
1333 |
|
|
and $q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature and surface |
1334 |
|
|
pressure. |
1335 |
|
|
\\ |
1336 |
|
|
|
1337 |
|
|
\noindent |
1338 |
|
|
{\bf 34) \underline {QS} Saturation Surface Specific Humidity ($g/kg$) } |
1339 |
|
|
|
1340 |
|
|
\noindent |
1341 |
|
|
The surface saturation specific humidity is the saturation specific humidity at |
1342 |
|
|
the ground temprature and surface pressure: |
1343 |
|
|
\[ |
1344 |
|
|
{\bf QS} = q^*(T_g,P_s) |
1345 |
|
|
\] |
1346 |
|
|
\\ |
1347 |
|
|
|
1348 |
|
|
\noindent |
1349 |
|
|
{\bf 35) \underline {TGRLW} Instantaneous ground temperature used as input to the Longwave |
1350 |
|
|
radiation subroutine (deg)} |
1351 |
|
|
\[ |
1352 |
|
|
{\bf TGRLW} = T_g(\lambda , \phi ,n) |
1353 |
|
|
\] |
1354 |
|
|
\noindent |
1355 |
|
|
where $T_g$ is the model ground temperature at the current time step $n$. |
1356 |
|
|
\\ |
1357 |
|
|
|
1358 |
|
|
|
1359 |
|
|
\noindent |
1360 |
|
|
{\bf 36) \underline {ST4} Upward Longwave flux at the surface ($Watts/m^2$) } |
1361 |
|
|
\[ |
1362 |
|
|
{\bf ST4} = \sigma T^4 |
1363 |
|
|
\] |
1364 |
|
|
\noindent |
1365 |
|
|
where $\sigma$ is the Stefan-Boltzmann constant and T is the temperature. |
1366 |
|
|
\\ |
1367 |
|
|
|
1368 |
|
|
\noindent |
1369 |
|
|
{\bf 37) \underline {OLR} Net upward Longwave flux at $p=p_{top}$ ($Watts/m^2$) } |
1370 |
|
|
\[ |
1371 |
|
|
{\bf OLR} = F_{LW,top}^{NET} |
1372 |
|
|
\] |
1373 |
|
|
\noindent |
1374 |
|
|
where top indicates the top of the first model layer. |
1375 |
|
|
In the GCM, $p_{top}$ = 0.0 mb. |
1376 |
|
|
\\ |
1377 |
|
|
|
1378 |
|
|
|
1379 |
|
|
\noindent |
1380 |
|
|
{\bf 38) \underline {OLRCLR} Net upward clearsky Longwave flux at $p=p_{top}$ ($Watts/m^2$) } |
1381 |
|
|
\[ |
1382 |
|
|
{\bf OLRCLR} = F(clearsky)_{LW,top}^{NET} |
1383 |
|
|
\] |
1384 |
|
|
\noindent |
1385 |
|
|
where top indicates the top of the first model layer. |
1386 |
|
|
In the GCM, $p_{top}$ = 0.0 mb. |
1387 |
|
|
\\ |
1388 |
|
|
|
1389 |
|
|
\noindent |
1390 |
|
|
{\bf 39) \underline {LWGCLR} Net upward clearsky Longwave flux at the surface ($Watts/m^2$) } |
1391 |
|
|
|
1392 |
|
|
\noindent |
1393 |
|
|
\begin{eqnarray*} |
1394 |
|
|
{\bf LWGCLR} & = & F(clearsky)_{LW,Nrphys+1}^{Net} \\ |
1395 |
|
|
& = & F(clearsky)_{LW,Nrphys+1}^\uparrow - F(clearsky)_{LW,Nrphys+1}^\downarrow |
1396 |
|
|
\end{eqnarray*} |
1397 |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
1398 |
|
|
$F(clearsky)_{LW}^\uparrow$ is |
1399 |
|
|
the upward clearsky Longwave flux and the $F(clearsky)_{LW}^\downarrow$ is the downward clearsky Longwave flux. |
1400 |
|
|
\\ |
1401 |
|
|
|
1402 |
|
|
\noindent |
1403 |
|
|
{\bf 40) \underline {LWCLR} Heating Rate due to Clearsky Longwave Radiation ($deg/day$) } |
1404 |
|
|
|
1405 |
|
|
\noindent |
1406 |
|
|
The net longwave heating rate is calculated as the vertical divergence of the |
1407 |
|
|
net terrestrial radiative fluxes. |
1408 |
|
|
Both the clear-sky and cloudy-sky longwave fluxes are computed within the |
1409 |
|
|
longwave routine. |
1410 |
|
|
The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. |
1411 |
|
|
For a given cloud fraction, |
1412 |
|
|
the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ |
1413 |
|
|
to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, |
1414 |
|
|
for the upward and downward radiative fluxes. |
1415 |
|
|
(see Section \ref{sec:fizhi:radcloud}). |
1416 |
|
|
The cloudy-sky flux is then obtained as: |
1417 |
|
|
|
1418 |
|
|
\noindent |
1419 |
|
|
\[ |
1420 |
|
|
F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, |
1421 |
|
|
\] |
1422 |
|
|
|
1423 |
|
|
\noindent |
1424 |
|
|
Thus, {\bf LWCLR} is defined as the net longwave heating rate due to the |
1425 |
|
|
vertical divergence of the |
1426 |
|
|
clear-sky longwave radiative flux: |
1427 |
|
|
\[ |
1428 |
|
|
\pp{\rho c_p T}{t}_{clearsky} = - {\partial \over \partial z} F(clearsky)_{LW}^{NET} , |
1429 |
|
|
\] |
1430 |
|
|
or |
1431 |
|
|
\[ |
1432 |
|
|
{\bf LWCLR} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(clearsky)_{LW}^{NET} . |
1433 |
|
|
\] |
1434 |
|
|
|
1435 |
|
|
\noindent |
1436 |
|
|
where $g$ is the accelation due to gravity, |
1437 |
|
|
$c_p$ is the heat capacity of air at constant pressure, |
1438 |
|
|
and |
1439 |
|
|
\[ |
1440 |
|
|
F(clearsky)_{LW}^{Net} = F(clearsky)_{LW}^\uparrow - F(clearsky)_{LW}^\downarrow |
1441 |
|
|
\] |
1442 |
|
|
\\ |
1443 |
|
|
|
1444 |
|
|
|
1445 |
|
|
\noindent |
1446 |
|
|
{\bf 41) \underline {TLW} Instantaneous temperature used as input to the Longwave |
1447 |
|
|
radiation subroutine (deg)} |
1448 |
|
|
\[ |
1449 |
|
|
{\bf TLW} = T(\lambda , \phi ,level, n) |
1450 |
|
|
\] |
1451 |
|
|
\noindent |
1452 |
|
|
where $T$ is the model temperature at the current time step $n$. |
1453 |
|
|
\\ |
1454 |
|
|
|
1455 |
|
|
|
1456 |
|
|
\noindent |
1457 |
|
|
{\bf 42) \underline {SHLW} Instantaneous specific humidity used as input to |
1458 |
|
|
the Longwave radiation subroutine (kg/kg)} |
1459 |
|
|
\[ |
1460 |
|
|
{\bf SHLW} = q(\lambda , \phi , level , n) |
1461 |
|
|
\] |
1462 |
|
|
\noindent |
1463 |
|
|
where $q$ is the model specific humidity at the current time step $n$. |
1464 |
|
|
\\ |
1465 |
|
|
|
1466 |
|
|
|
1467 |
|
|
\noindent |
1468 |
|
|
{\bf 43) \underline {OZLW} Instantaneous ozone used as input to |
1469 |
|
|
the Longwave radiation subroutine (kg/kg)} |
1470 |
|
|
\[ |
1471 |
|
|
{\bf OZLW} = {\rm OZ}(\lambda , \phi , level , n) |
1472 |
|
|
\] |
1473 |
|
|
\noindent |
1474 |
|
|
where $\rm OZ$ is the interpolated ozone data set from the climatological monthly |
1475 |
|
|
mean zonally averaged ozone data set. |
1476 |
|
|
\\ |
1477 |
|
|
|
1478 |
|
|
|
1479 |
|
|
\noindent |
1480 |
|
|
{\bf 44) \underline {CLMOLW} Maximum Overlap cloud fraction used in LW Radiation ($0-1$) } |
1481 |
|
|
|
1482 |
|
|
\noindent |
1483 |
|
|
{\bf CLMOLW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed |
1484 |
|
|
Arakawa/Schubert Convection scheme and will be used in the Longwave Radiation algorithm. These are |
1485 |
|
|
convective clouds whose radiative characteristics are assumed to be correlated in the vertical. |
1486 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
1487 |
|
|
\[ |
1488 |
|
|
{\bf CLMOLW} = CLMO_{RAS,LW}(\lambda, \phi, level ) |
1489 |
|
|
\] |
1490 |
|
|
\\ |
1491 |
|
|
|
1492 |
|
|
|
1493 |
|
|
{\bf 45) \underline {CLDTOT} Total cloud fraction used in LW and SW Radiation ($0-1$) } |
1494 |
|
|
|
1495 |
|
|
{\bf CLDTOT} is the time-averaged total cloud fraction that has been filled by the Relaxed |
1496 |
|
|
Arakawa/Schubert and Large-scale Convection schemes and will be used in the Longwave and Shortwave |
1497 |
|
|
Radiation packages. |
1498 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
1499 |
|
|
\[ |
1500 |
|
|
{\bf CLDTOT} = F_{RAS} + F_{LS} |
1501 |
|
|
\] |
1502 |
|
|
\\ |
1503 |
|
|
where $F_{RAS}$ is the time-averaged cloud fraction due to sub-grid scale convection, and $F_{LS}$ is the |
1504 |
|
|
time-averaged cloud fraction due to precipitating and non-precipitating large-scale moist processes. |
1505 |
|
|
\\ |
1506 |
|
|
|
1507 |
|
|
|
1508 |
|
|
\noindent |
1509 |
|
|
{\bf 46) \underline {CLMOSW} Maximum Overlap cloud fraction used in SW Radiation ($0-1$) } |
1510 |
|
|
|
1511 |
|
|
\noindent |
1512 |
|
|
{\bf CLMOSW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed |
1513 |
|
|
Arakawa/Schubert Convection scheme and will be used in the Shortwave Radiation algorithm. These are |
1514 |
|
|
convective clouds whose radiative characteristics are assumed to be correlated in the vertical. |
1515 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
1516 |
|
|
\[ |
1517 |
|
|
{\bf CLMOSW} = CLMO_{RAS,SW}(\lambda, \phi, level ) |
1518 |
|
|
\] |
1519 |
|
|
\\ |
1520 |
|
|
|
1521 |
|
|
\noindent |
1522 |
|
|
{\bf 47) \underline {CLROSW} Random Overlap cloud fraction used in SW Radiation ($0-1$) } |
1523 |
|
|
|
1524 |
|
|
\noindent |
1525 |
|
|
{\bf CLROSW} is the time-averaged random overlap cloud fraction that has been filled by the Relaxed |
1526 |
|
|
Arakawa/Schubert and Large-scale Convection schemes and will be used in the Shortwave |
1527 |
|
|
Radiation algorithm. These are |
1528 |
|
|
convective and large-scale clouds whose radiative characteristics are not |
1529 |
|
|
assumed to be correlated in the vertical. |
1530 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
1531 |
|
|
\[ |
1532 |
|
|
{\bf CLROSW} = CLRO_{RAS,Large Scale,SW}(\lambda, \phi, level ) |
1533 |
|
|
\] |
1534 |
|
|
\\ |
1535 |
|
|
|
1536 |
|
|
\noindent |
1537 |
|
|
{\bf 48) \underline {RADSWT} Incident Shortwave radiation at the top of the atmosphere ($Watts/m^2$) } |
1538 |
|
|
\[ |
1539 |
|
|
{\bf RADSWT} = {\frac{S_0}{R_a^2}} \cdot cos \phi_z |
1540 |
|
|
\] |
1541 |
|
|
\noindent |
1542 |
|
|
where $S_0$, is the extra-terrestial solar contant, |
1543 |
|
|
$R_a$ is the earth-sun distance in Astronomical Units, |
1544 |
|
|
and $cos \phi_z$ is the cosine of the zenith angle. |
1545 |
|
|
It should be noted that {\bf RADSWT}, as well as |
1546 |
|
|
{\bf OSR} and {\bf OSRCLR}, |
1547 |
|
|
are calculated at the top of the atmosphere (p=0 mb). However, the |
1548 |
|
|
{\bf OLR} and {\bf OLRCLR} diagnostics are currently |
1549 |
|
|
calculated at $p= p_{top}$ (0.0 mb for the GCM). |
1550 |
|
|
\\ |
1551 |
|
|
|
1552 |
|
|
\noindent |
1553 |
|
|
{\bf 49) \underline {EVAP} Surface Evaporation ($mm/day$) } |
1554 |
|
|
|
1555 |
|
|
\noindent |
1556 |
|
|
The surface evaporation is a function of the gradient of moisture, the potential |
1557 |
|
|
evapotranspiration fraction and the eddy exchange coefficient: |
1558 |
|
|
\[ |
1559 |
|
|
{\bf EVAP} = \rho \beta K_{h} (q_{surface} - q_{Nrphys}) |
1560 |
|
|
\] |
1561 |
|
|
where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of |
1562 |
|
|
the potential evapotranspiration actually evaporated ($\beta=1$ over oceans), $K_{h}$ is the |
1563 |
|
|
turbulent eddy exchange coefficient for heat and moisture at the surface in $m/sec$ and |
1564 |
|
|
$q{surface}$ and $q_{Nrphys}$ are the specific humidity at the surface (see diagnostic |
1565 |
|
|
number 34) and at the bottom model level, respectively. |
1566 |
|
|
\\ |
1567 |
|
|
|
1568 |
|
|
\noindent |
1569 |
|
|
{\bf 50) \underline {DUDT} Total Zonal U-Wind Tendency ($m/sec/day$) } |
1570 |
|
|
|
1571 |
|
|
\noindent |
1572 |
|
|
{\bf DUDT} is the total time-tendency of the Zonal U-Wind due to Hydrodynamic, Diabatic, |
1573 |
|
|
and Analysis forcing. |
1574 |
|
|
\[ |
1575 |
|
|
{\bf DUDT} = \pp{u}{t}_{Dynamics} + \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} |
1576 |
|
|
\] |
1577 |
|
|
\\ |
1578 |
|
|
|
1579 |
|
|
\noindent |
1580 |
|
|
{\bf 51) \underline {DVDT} Total Zonal V-Wind Tendency ($m/sec/day$) } |
1581 |
|
|
|
1582 |
|
|
\noindent |
1583 |
|
|
{\bf DVDT} is the total time-tendency of the Meridional V-Wind due to Hydrodynamic, Diabatic, |
1584 |
|
|
and Analysis forcing. |
1585 |
|
|
\[ |
1586 |
|
|
{\bf DVDT} = \pp{v}{t}_{Dynamics} + \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} |
1587 |
|
|
\] |
1588 |
|
|
\\ |
1589 |
|
|
|
1590 |
|
|
\noindent |
1591 |
|
|
{\bf 52) \underline {DTDT} Total Temperature Tendency ($deg/day$) } |
1592 |
|
|
|
1593 |
|
|
\noindent |
1594 |
|
|
{\bf DTDT} is the total time-tendency of Temperature due to Hydrodynamic, Diabatic, |
1595 |
|
|
and Analysis forcing. |
1596 |
|
|
\begin{eqnarray*} |
1597 |
|
|
{\bf DTDT} & = & \pp{T}{t}_{Dynamics} + \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
1598 |
|
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} |
1599 |
|
|
\end{eqnarray*} |
1600 |
|
|
\\ |
1601 |
|
|
|
1602 |
|
|
\noindent |
1603 |
|
|
{\bf 53) \underline {DQDT} Total Specific Humidity Tendency ($g/kg/day$) } |
1604 |
|
|
|
1605 |
|
|
\noindent |
1606 |
|
|
{\bf DQDT} is the total time-tendency of Specific Humidity due to Hydrodynamic, Diabatic, |
1607 |
|
|
and Analysis forcing. |
1608 |
|
|
\[ |
1609 |
|
|
{\bf DQDT} = \pp{q}{t}_{Dynamics} + \pp{q}{t}_{Moist Processes} |
1610 |
|
|
+ \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} |
1611 |
|
|
\] |
1612 |
|
|
\\ |
1613 |
|
|
|
1614 |
|
|
\noindent |
1615 |
|
|
{\bf 54) \underline {USTAR} Surface-Stress Velocity ($m/sec$) } |
1616 |
|
|
|
1617 |
|
|
\noindent |
1618 |
|
|
The surface stress velocity, or the friction velocity, is the wind speed at |
1619 |
|
|
the surface layer top impeded by the surface drag: |
1620 |
|
|
\[ |
1621 |
|
|
{\bf USTAR} = C_uW_s \hspace{1cm}where: \hspace{.2cm} |
1622 |
|
|
C_u = {k \over {\psi_m} } |
1623 |
|
|
\] |
1624 |
|
|
|
1625 |
|
|
\noindent |
1626 |
|
|
$C_u$ is the non-dimensional surface drag coefficient (see diagnostic |
1627 |
|
|
number 10), and $W_s$ is the surface wind speed (see diagnostic number 28). |
1628 |
|
|
|
1629 |
|
|
\noindent |
1630 |
|
|
{\bf 55) \underline {Z0} Surface Roughness Length ($m$) } |
1631 |
|
|
|
1632 |
|
|
\noindent |
1633 |
|
|
Over the land surface, the surface roughness length is interpolated to the local |
1634 |
|
|
time from the monthly mean data of Dorman and Sellers (1989). Over the ocean, |
1635 |
|
|
the roughness length is a function of the surface-stress velocity, $u_*$. |
1636 |
|
|
\[ |
1637 |
|
|
{\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}} |
1638 |
|
|
\] |
1639 |
|
|
|
1640 |
|
|
\noindent |
1641 |
|
|
where the constants are chosen to interpolate between the reciprocal relation of |
1642 |
|
|
Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981) |
1643 |
|
|
for moderate to large winds. |
1644 |
|
|
\\ |
1645 |
|
|
|
1646 |
|
|
\noindent |
1647 |
|
|
{\bf 56) \underline {FRQTRB} Frequency of Turbulence ($0-1$) } |
1648 |
|
|
|
1649 |
|
|
\noindent |
1650 |
|
|
The fraction of time when turbulence is present is defined as the fraction of |
1651 |
|
|
time when the turbulent kinetic energy exceeds some minimum value, defined here |
1652 |
|
|
to be $0.005 \hspace{.1cm}m^2/sec^2$. When this criterion is met, a counter is |
1653 |
|
|
incremented. The fraction over the averaging interval is reported. |
1654 |
|
|
\\ |
1655 |
|
|
|
1656 |
|
|
\noindent |
1657 |
|
|
{\bf 57) \underline {PBL} Planetary Boundary Layer Depth ($mb$) } |
1658 |
|
|
|
1659 |
|
|
\noindent |
1660 |
|
|
The depth of the PBL is defined by the turbulence parameterization to be the |
1661 |
|
|
depth at which the turbulent kinetic energy reduces to ten percent of its surface |
1662 |
|
|
value. |
1663 |
|
|
|
1664 |
|
|
\[ |
1665 |
|
|
{\bf PBL} = P_{PBL} - P_{surface} |
1666 |
|
|
\] |
1667 |
|
|
|
1668 |
|
|
\noindent |
1669 |
|
|
where $P_{PBL}$ is the pressure in $mb$ at which the turbulent kinetic energy |
1670 |
|
|
reaches one tenth of its surface value, and $P_s$ is the surface pressure. |
1671 |
|
|
\\ |
1672 |
|
|
|
1673 |
|
|
\noindent |
1674 |
|
|
{\bf 58) \underline {SWCLR} Clear sky Heating Rate due to Shortwave Radiation ($deg/day$) } |
1675 |
|
|
|
1676 |
|
|
\noindent |
1677 |
|
|
The net Shortwave heating rate is calculated as the vertical divergence of the |
1678 |
|
|
net solar radiative fluxes. |
1679 |
|
|
The clear-sky and cloudy-sky shortwave fluxes are calculated separately. |
1680 |
|
|
For the clear-sky case, the shortwave fluxes and heating rates are computed with |
1681 |
|
|
both CLMO (maximum overlap cloud fraction) and |
1682 |
|
|
CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). |
1683 |
|
|
The shortwave routine is then called a second time, for the cloudy-sky case, with the |
1684 |
|
|
true time-averaged cloud fractions CLMO |
1685 |
|
|
and CLRO being used. In all cases, a normalized incident shortwave flux is used as |
1686 |
|
|
input at the top of the atmosphere. |
1687 |
|
|
|
1688 |
|
|
\noindent |
1689 |
|
|
The heating rate due to Shortwave Radiation under clear skies is defined as: |
1690 |
|
|
\[ |
1691 |
|
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT}, |
1692 |
|
|
\] |
1693 |
|
|
or |
1694 |
|
|
\[ |
1695 |
|
|
{\bf SWCLR} = \frac{g}{c_p } {\partial \over \partial p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} . |
1696 |
|
|
\] |
1697 |
|
|
|
1698 |
|
|
\noindent |
1699 |
|
|
where $g$ is the accelation due to gravity, |
1700 |
|
|
$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident |
1701 |
|
|
shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and |
1702 |
|
|
\[ |
1703 |
|
|
F(clear)_{SW}^{Net} = F(clear)_{SW}^\uparrow - F(clear)_{SW}^\downarrow |
1704 |
|
|
\] |
1705 |
|
|
\\ |
1706 |
|
|
|
1707 |
|
|
\noindent |
1708 |
|
|
{\bf 59) \underline {OSR} Net upward Shortwave flux at the top of the model ($Watts/m^2$) } |
1709 |
|
|
\[ |
1710 |
|
|
{\bf OSR} = F_{SW,top}^{NET} |
1711 |
|
|
\] |
1712 |
|
|
\noindent |
1713 |
|
|
where top indicates the top of the first model layer used in the shortwave radiation |
1714 |
|
|
routine. |
1715 |
|
|
In the GCM, $p_{SW_{top}}$ = 0 mb. |
1716 |
|
|
\\ |
1717 |
|
|
|
1718 |
|
|
\noindent |
1719 |
|
|
{\bf 60) \underline {OSRCLR} Net upward clearsky Shortwave flux at the top of the model ($Watts/m^2$) } |
1720 |
|
|
\[ |
1721 |
|
|
{\bf OSRCLR} = F(clearsky)_{SW,top}^{NET} |
1722 |
|
|
\] |
1723 |
|
|
\noindent |
1724 |
|
|
where top indicates the top of the first model layer used in the shortwave radiation |
1725 |
|
|
routine. |
1726 |
|
|
In the GCM, $p_{SW_{top}}$ = 0 mb. |
1727 |
|
|
\\ |
1728 |
|
|
|
1729 |
|
|
|
1730 |
|
|
\noindent |
1731 |
|
|
{\bf 61) \underline {CLDMAS} Convective Cloud Mass Flux ($kg/m^2$) } |
1732 |
|
|
|
1733 |
|
|
\noindent |
1734 |
|
|
The amount of cloud mass moved per RAS timestep from all convective clouds is written: |
1735 |
|
|
\[ |
1736 |
|
|
{\bf CLDMAS} = \eta m_B |
1737 |
|
|
\] |
1738 |
|
|
where $\eta$ is the entrainment, normalized by the cloud base mass flux, and $m_B$ is |
1739 |
|
|
the cloud base mass flux. $m_B$ and $\eta$ are defined explicitly in Section \ref{sec:fizhi:mc}, the |
1740 |
|
|
description of the convective parameterization. |
1741 |
|
|
\\ |
1742 |
|
|
|
1743 |
|
|
|
1744 |
|
|
|
1745 |
|
|
\noindent |
1746 |
|
|
{\bf 62) \underline {UAVE} Time-Averaged Zonal U-Wind ($m/sec$) } |
1747 |
|
|
|
1748 |
|
|
\noindent |
1749 |
|
|
The diagnostic {\bf UAVE} is simply the time-averaged Zonal U-Wind over |
1750 |
|
|
the {\bf NUAVE} output frequency. This is contrasted to the instantaneous |
1751 |
|
|
Zonal U-Wind which is archived on the Prognostic Output data stream. |
1752 |
|
|
\[ |
1753 |
|
|
{\bf UAVE} = u(\lambda, \phi, level , t) |
1754 |
|
|
\] |
1755 |
|
|
\\ |
1756 |
|
|
Note, {\bf UAVE} is computed and stored on the staggered C-grid. |
1757 |
|
|
\\ |
1758 |
|
|
|
1759 |
|
|
\noindent |
1760 |
|
|
{\bf 63) \underline {VAVE} Time-Averaged Meridional V-Wind ($m/sec$) } |
1761 |
|
|
|
1762 |
|
|
\noindent |
1763 |
|
|
The diagnostic {\bf VAVE} is simply the time-averaged Meridional V-Wind over |
1764 |
|
|
the {\bf NVAVE} output frequency. This is contrasted to the instantaneous |
1765 |
|
|
Meridional V-Wind which is archived on the Prognostic Output data stream. |
1766 |
|
|
\[ |
1767 |
|
|
{\bf VAVE} = v(\lambda, \phi, level , t) |
1768 |
|
|
\] |
1769 |
|
|
\\ |
1770 |
|
|
Note, {\bf VAVE} is computed and stored on the staggered C-grid. |
1771 |
|
|
\\ |
1772 |
|
|
|
1773 |
|
|
\noindent |
1774 |
|
|
{\bf 64) \underline {TAVE} Time-Averaged Temperature ($Kelvin$) } |
1775 |
|
|
|
1776 |
|
|
\noindent |
1777 |
|
|
The diagnostic {\bf TAVE} is simply the time-averaged Temperature over |
1778 |
|
|
the {\bf NTAVE} output frequency. This is contrasted to the instantaneous |
1779 |
|
|
Temperature which is archived on the Prognostic Output data stream. |
1780 |
|
|
\[ |
1781 |
|
|
{\bf TAVE} = T(\lambda, \phi, level , t) |
1782 |
|
|
\] |
1783 |
|
|
\\ |
1784 |
|
|
|
1785 |
|
|
\noindent |
1786 |
|
|
{\bf 65) \underline {QAVE} Time-Averaged Specific Humidity ($g/kg$) } |
1787 |
|
|
|
1788 |
|
|
\noindent |
1789 |
|
|
The diagnostic {\bf QAVE} is simply the time-averaged Specific Humidity over |
1790 |
|
|
the {\bf NQAVE} output frequency. This is contrasted to the instantaneous |
1791 |
|
|
Specific Humidity which is archived on the Prognostic Output data stream. |
1792 |
|
|
\[ |
1793 |
|
|
{\bf QAVE} = q(\lambda, \phi, level , t) |
1794 |
|
|
\] |
1795 |
|
|
\\ |
1796 |
|
|
|
1797 |
|
|
\noindent |
1798 |
|
|
{\bf 66) \underline {PAVE} Time-Averaged Surface Pressure - PTOP ($mb$) } |
1799 |
|
|
|
1800 |
|
|
\noindent |
1801 |
|
|
The diagnostic {\bf PAVE} is simply the time-averaged Surface Pressure - PTOP over |
1802 |
|
|
the {\bf NPAVE} output frequency. This is contrasted to the instantaneous |
1803 |
|
|
Surface Pressure - PTOP which is archived on the Prognostic Output data stream. |
1804 |
|
|
\begin{eqnarray*} |
1805 |
|
|
{\bf PAVE} & = & \pi(\lambda, \phi, level , t) \\ |
1806 |
|
|
& = & p_s(\lambda, \phi, level , t) - p_T |
1807 |
|
|
\end{eqnarray*} |
1808 |
|
|
\\ |
1809 |
|
|
|
1810 |
|
|
|
1811 |
|
|
\noindent |
1812 |
|
|
{\bf 67) \underline {QQAVE} Time-Averaged Turbulent Kinetic Energy $(m/sec)^2$ } |
1813 |
|
|
|
1814 |
|
|
\noindent |
1815 |
|
|
The diagnostic {\bf QQAVE} is simply the time-averaged prognostic Turbulent Kinetic Energy |
1816 |
|
|
produced by the GCM Turbulence parameterization over |
1817 |
|
|
the {\bf NQQAVE} output frequency. This is contrasted to the instantaneous |
1818 |
|
|
Turbulent Kinetic Energy which is archived on the Prognostic Output data stream. |
1819 |
|
|
\[ |
1820 |
|
|
{\bf QQAVE} = qq(\lambda, \phi, level , t) |
1821 |
|
|
\] |
1822 |
|
|
\\ |
1823 |
|
|
Note, {\bf QQAVE} is computed and stored at the ``mass-point'' locations on the staggered C-grid. |
1824 |
|
|
\\ |
1825 |
|
|
|
1826 |
|
|
\noindent |
1827 |
|
|
{\bf 68) \underline {SWGCLR} Net downward clearsky Shortwave flux at the surface ($Watts/m^2$) } |
1828 |
|
|
|
1829 |
|
|
\noindent |
1830 |
|
|
\begin{eqnarray*} |
1831 |
|
|
{\bf SWGCLR} & = & F(clearsky)_{SW,Nrphys+1}^{Net} \\ |
1832 |
|
|
& = & F(clearsky)_{SW,Nrphys+1}^\downarrow - F(clearsky)_{SW,Nrphys+1}^\uparrow |
1833 |
|
|
\end{eqnarray*} |
1834 |
|
|
\noindent |
1835 |
|
|
\\ |
1836 |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
1837 |
|
|
$F(clearsky){SW}^\downarrow$ is |
1838 |
|
|
the downward clearsky Shortwave flux and $F(clearsky)_{SW}^\uparrow$ is |
1839 |
|
|
the upward clearsky Shortwave flux. |
1840 |
|
|
\\ |
1841 |
|
|
|
1842 |
|
|
\noindent |
1843 |
|
|
{\bf 69) \underline {SDIAG1} User-Defined Surface Diagnostic-1 } |
1844 |
|
|
|
1845 |
|
|
\noindent |
1846 |
|
|
The GCM provides Users with a built-in mechanism for archiving user-defined |
1847 |
|
|
diagnostics. The generic diagnostic array QDIAG located in COMMON /DIAG/, and the associated |
1848 |
|
|
diagnostic counters and pointers located in COMMON /DIAGP/, |
1849 |
|
|
must be accessable in order to use the user-defined diagnostics (see Section \ref{sec:diagnostics:diagover}). |
1850 |
|
|
A convenient method for incorporating all necessary COMMON files is to |
1851 |
|
|
include the GCM {\em vstate.com} file in the routine which employs the |
1852 |
|
|
user-defined diagnostics. |
1853 |
|
|
|
1854 |
|
|
\noindent |
1855 |
|
|
In addition to enabling the user-defined diagnostic (ie., CALL SETDIAG(84)), the User must fill |
1856 |
|
|
the QDIAG array with the desired quantity within the User's |
1857 |
|
|
application program or within modified GCM subroutines, as well as increment |
1858 |
|
|
the diagnostic counter at the time when the diagnostic is updated. |
1859 |
|
|
The QDIAG location index for {\bf SDIAG1} and its corresponding counter is |
1860 |
|
|
automatically defined as {\bf ISDIAG1} and {\bf NSDIAG1}, respectively, after the |
1861 |
|
|
diagnostic has been enabled. |
1862 |
|
|
The syntax for its use is given by |
1863 |
|
|
\begin{verbatim} |
1864 |
|
|
do j=1,jm |
1865 |
|
|
do i=1,im |
1866 |
|
|
qdiag(i,j,ISDIAG1) = qdiag(i,j,ISDIAG1) + ... |
1867 |
|
|
enddo |
1868 |
|
|
enddo |
1869 |
|
|
|
1870 |
|
|
NSDIAG1 = NSDIAG1 + 1 |
1871 |
|
|
\end{verbatim} |
1872 |
|
|
The diagnostics defined in this manner will automatically be archived by the output routines. |
1873 |
|
|
\\ |
1874 |
|
|
|
1875 |
|
|
\noindent |
1876 |
|
|
{\bf 70) \underline {SDIAG2} User-Defined Surface Diagnostic-2 } |
1877 |
|
|
|
1878 |
|
|
\noindent |
1879 |
|
|
The GCM provides Users with a built-in mechanism for archiving user-defined |
1880 |
|
|
diagnostics. For a complete description refer to Diagnostic \#84. |
1881 |
|
|
The syntax for using the surface SDIAG2 diagnostic is given by |
1882 |
|
|
\begin{verbatim} |
1883 |
|
|
do j=1,jm |
1884 |
|
|
do i=1,im |
1885 |
|
|
qdiag(i,j,ISDIAG2) = qdiag(i,j,ISDIAG2) + ... |
1886 |
|
|
enddo |
1887 |
|
|
enddo |
1888 |
|
|
|
1889 |
|
|
NSDIAG2 = NSDIAG2 + 1 |
1890 |
|
|
\end{verbatim} |
1891 |
|
|
The diagnostics defined in this manner will automatically be archived by the output routines. |
1892 |
|
|
\\ |
1893 |
|
|
|
1894 |
|
|
\noindent |
1895 |
|
|
{\bf 71) \underline {UDIAG1} User-Defined Upper-Air Diagnostic-1 } |
1896 |
|
|
|
1897 |
|
|
\noindent |
1898 |
|
|
The GCM provides Users with a built-in mechanism for archiving user-defined |
1899 |
|
|
diagnostics. For a complete description refer to Diagnostic \#84. |
1900 |
|
|
The syntax for using the upper-air UDIAG1 diagnostic is given by |
1901 |
|
|
\begin{verbatim} |
1902 |
|
|
do L=1,Nrphys |
1903 |
|
|
do j=1,jm |
1904 |
|
|
do i=1,im |
1905 |
|
|
qdiag(i,j,IUDIAG1+L-1) = qdiag(i,j,IUDIAG1+L-1) + ... |
1906 |
|
|
enddo |
1907 |
|
|
enddo |
1908 |
|
|
enddo |
1909 |
|
|
|
1910 |
|
|
NUDIAG1 = NUDIAG1 + 1 |
1911 |
|
|
\end{verbatim} |
1912 |
|
|
The diagnostics defined in this manner will automatically be archived by the |
1913 |
|
|
output programs. |
1914 |
|
|
\\ |
1915 |
|
|
|
1916 |
|
|
\noindent |
1917 |
|
|
{\bf 72) \underline {UDIAG2} User-Defined Upper-Air Diagnostic-2 } |
1918 |
|
|
|
1919 |
|
|
\noindent |
1920 |
|
|
The GCM provides Users with a built-in mechanism for archiving user-defined |
1921 |
|
|
diagnostics. For a complete description refer to Diagnostic \#84. |
1922 |
|
|
The syntax for using the upper-air UDIAG2 diagnostic is given by |
1923 |
|
|
\begin{verbatim} |
1924 |
|
|
do L=1,Nrphys |
1925 |
|
|
do j=1,jm |
1926 |
|
|
do i=1,im |
1927 |
|
|
qdiag(i,j,IUDIAG2+L-1) = qdiag(i,j,IUDIAG2+L-1) + ... |
1928 |
|
|
enddo |
1929 |
|
|
enddo |
1930 |
|
|
enddo |
1931 |
|
|
|
1932 |
|
|
NUDIAG2 = NUDIAG2 + 1 |
1933 |
|
|
\end{verbatim} |
1934 |
|
|
The diagnostics defined in this manner will automatically be archived by the |
1935 |
|
|
output programs. |
1936 |
|
|
\\ |
1937 |
|
|
|
1938 |
|
|
|
1939 |
|
|
\noindent |
1940 |
|
|
{\bf 73) \underline {DIABU} Total Diabatic Zonal U-Wind Tendency ($m/sec/day$) } |
1941 |
|
|
|
1942 |
|
|
\noindent |
1943 |
|
|
{\bf DIABU} is the total time-tendency of the Zonal U-Wind due to Diabatic processes |
1944 |
|
|
and the Analysis forcing. |
1945 |
|
|
\[ |
1946 |
|
|
{\bf DIABU} = \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} |
1947 |
|
|
\] |
1948 |
|
|
\\ |
1949 |
|
|
|
1950 |
|
|
\noindent |
1951 |
|
|
{\bf 74) \underline {DIABV} Total Diabatic Meridional V-Wind Tendency ($m/sec/day$) } |
1952 |
|
|
|
1953 |
|
|
\noindent |
1954 |
|
|
{\bf DIABV} is the total time-tendency of the Meridional V-Wind due to Diabatic processes |
1955 |
|
|
and the Analysis forcing. |
1956 |
|
|
\[ |
1957 |
|
|
{\bf DIABV} = \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} |
1958 |
|
|
\] |
1959 |
|
|
\\ |
1960 |
|
|
|
1961 |
|
|
\noindent |
1962 |
|
|
{\bf 75) \underline {DIABT} Total Diabatic Temperature Tendency ($deg/day$) } |
1963 |
|
|
|
1964 |
|
|
\noindent |
1965 |
|
|
{\bf DIABT} is the total time-tendency of Temperature due to Diabatic processes |
1966 |
|
|
and the Analysis forcing. |
1967 |
|
|
\begin{eqnarray*} |
1968 |
|
|
{\bf DIABT} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
1969 |
|
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} |
1970 |
|
|
\end{eqnarray*} |
1971 |
|
|
\\ |
1972 |
|
|
If we define the time-tendency of Temperature due to Diabatic processes as |
1973 |
|
|
\begin{eqnarray*} |
1974 |
|
|
\pp{T}{t}_{Diabatic} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
1975 |
|
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} |
1976 |
|
|
\end{eqnarray*} |
1977 |
|
|
then, since there are no surface pressure changes due to Diabatic processes, we may write |
1978 |
|
|
\[ |
1979 |
|
|
\pp{T}{t}_{Diabatic} = {p^\kappa \over \pi }\pp{\pi \theta}{t}_{Diabatic} |
1980 |
|
|
\] |
1981 |
|
|
where $\theta = T/p^\kappa$. Thus, {\bf DIABT} may be written as |
1982 |
|
|
\[ |
1983 |
|
|
{\bf DIABT} = {p^\kappa \over \pi } \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right) |
1984 |
|
|
\] |
1985 |
|
|
\\ |
1986 |
|
|
|
1987 |
|
|
\noindent |
1988 |
|
|
{\bf 76) \underline {DIABQ} Total Diabatic Specific Humidity Tendency ($g/kg/day$) } |
1989 |
|
|
|
1990 |
|
|
\noindent |
1991 |
|
|
{\bf DIABQ} is the total time-tendency of Specific Humidity due to Diabatic processes |
1992 |
|
|
and the Analysis forcing. |
1993 |
|
|
\[ |
1994 |
|
|
{\bf DIABQ} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} |
1995 |
|
|
\] |
1996 |
|
|
If we define the time-tendency of Specific Humidity due to Diabatic processes as |
1997 |
|
|
\[ |
1998 |
|
|
\pp{q}{t}_{Diabatic} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} |
1999 |
|
|
\] |
2000 |
|
|
then, since there are no surface pressure changes due to Diabatic processes, we may write |
2001 |
|
|
\[ |
2002 |
|
|
\pp{q}{t}_{Diabatic} = {1 \over \pi }\pp{\pi q}{t}_{Diabatic} |
2003 |
|
|
\] |
2004 |
|
|
Thus, {\bf DIABQ} may be written as |
2005 |
|
|
\[ |
2006 |
|
|
{\bf DIABQ} = {1 \over \pi } \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right) |
2007 |
|
|
\] |
2008 |
|
|
\\ |
2009 |
|
|
|
2010 |
|
|
\noindent |
2011 |
|
|
{\bf 77) \underline {VINTUQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } |
2012 |
|
|
|
2013 |
|
|
\noindent |
2014 |
|
|
The vertically integrated moisture flux due to the zonal u-wind is obtained by integrating |
2015 |
|
|
$u q$ over the depth of the atmosphere at each model timestep, |
2016 |
|
|
and dividing by the total mass of the column. |
2017 |
|
|
\[ |
2018 |
|
|
{\bf VINTUQ} = \frac{ \int_{surf}^{top} u q \rho dz } { \int_{surf}^{top} \rho dz } |
2019 |
|
|
\] |
2020 |
|
|
Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have |
2021 |
|
|
\[ |
2022 |
|
|
{\bf VINTUQ} = { \int_0^1 u q dp } |
2023 |
|
|
\] |
2024 |
|
|
\\ |
2025 |
|
|
|
2026 |
|
|
|
2027 |
|
|
\noindent |
2028 |
|
|
{\bf 78) \underline {VINTVQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } |
2029 |
|
|
|
2030 |
|
|
\noindent |
2031 |
|
|
The vertically integrated moisture flux due to the meridional v-wind is obtained by integrating |
2032 |
|
|
$v q$ over the depth of the atmosphere at each model timestep, |
2033 |
|
|
and dividing by the total mass of the column. |
2034 |
|
|
\[ |
2035 |
|
|
{\bf VINTVQ} = \frac{ \int_{surf}^{top} v q \rho dz } { \int_{surf}^{top} \rho dz } |
2036 |
|
|
\] |
2037 |
|
|
Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have |
2038 |
|
|
\[ |
2039 |
|
|
{\bf VINTVQ} = { \int_0^1 v q dp } |
2040 |
|
|
\] |
2041 |
|
|
\\ |
2042 |
|
|
|
2043 |
|
|
|
2044 |
|
|
\noindent |
2045 |
|
|
{\bf 79) \underline {VINTUT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } |
2046 |
|
|
|
2047 |
|
|
\noindent |
2048 |
|
|
The vertically integrated heat flux due to the zonal u-wind is obtained by integrating |
2049 |
|
|
$u T$ over the depth of the atmosphere at each model timestep, |
2050 |
|
|
and dividing by the total mass of the column. |
2051 |
|
|
\[ |
2052 |
|
|
{\bf VINTUT} = \frac{ \int_{surf}^{top} u T \rho dz } { \int_{surf}^{top} \rho dz } |
2053 |
|
|
\] |
2054 |
|
|
Or, |
2055 |
|
|
\[ |
2056 |
|
|
{\bf VINTUT} = { \int_0^1 u T dp } |
2057 |
|
|
\] |
2058 |
|
|
\\ |
2059 |
|
|
|
2060 |
|
|
\noindent |
2061 |
|
|
{\bf 80) \underline {VINTVT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } |
2062 |
|
|
|
2063 |
|
|
\noindent |
2064 |
|
|
The vertically integrated heat flux due to the meridional v-wind is obtained by integrating |
2065 |
|
|
$v T$ over the depth of the atmosphere at each model timestep, |
2066 |
|
|
and dividing by the total mass of the column. |
2067 |
|
|
\[ |
2068 |
|
|
{\bf VINTVT} = \frac{ \int_{surf}^{top} v T \rho dz } { \int_{surf}^{top} \rho dz } |
2069 |
|
|
\] |
2070 |
|
|
Using $\rho \delta z = -{\delta p \over g} $, we have |
2071 |
|
|
\[ |
2072 |
|
|
{\bf VINTVT} = { \int_0^1 v T dp } |
2073 |
|
|
\] |
2074 |
|
|
\\ |
2075 |
|
|
|
2076 |
|
|
\noindent |
2077 |
|
|
{\bf 81 \underline {CLDFRC} Total 2-Dimensional Cloud Fracton ($0-1$) } |
2078 |
|
|
|
2079 |
|
|
If we define the |
2080 |
|
|
time-averaged random and maximum overlapped cloudiness as CLRO and |
2081 |
|
|
CLMO respectively, then the probability of clear sky associated |
2082 |
|
|
with random overlapped clouds at any level is (1-CLRO) while the probability of |
2083 |
|
|
clear sky associated with maximum overlapped clouds at any level is (1-CLMO). |
2084 |
|
|
The total clear sky probability is given by (1-CLRO)*(1-CLMO), thus |
2085 |
|
|
the total cloud fraction at each level may be obtained by |
2086 |
|
|
1-(1-CLRO)*(1-CLMO). |
2087 |
|
|
|
2088 |
|
|
At any given level, we may define the clear line-of-site probability by |
2089 |
|
|
appropriately accounting for the maximum and random overlap |
2090 |
|
|
cloudiness. The clear line-of-site probability is defined to be |
2091 |
|
|
equal to the product of the clear line-of-site probabilities |
2092 |
|
|
associated with random and maximum overlap cloudiness. The clear |
2093 |
|
|
line-of-site probability $C(p,p^{\prime})$ associated with maximum overlap clouds, |
2094 |
|
|
from the current pressure $p$ |
2095 |
|
|
to the model top pressure, $p^{\prime} = p_{top}$, or the model surface pressure, $p^{\prime} = p_{surf}$, |
2096 |
|
|
is simply 1.0 minus the largest maximum overlap cloud value along the |
2097 |
|
|
line-of-site, ie. |
2098 |
|
|
|
2099 |
|
|
$$1-MAX_p^{p^{\prime}} \left( CLMO_p \right)$$ |
2100 |
|
|
|
2101 |
|
|
Thus, even in the time-averaged sense it is assumed that the |
2102 |
|
|
maximum overlap clouds are correlated in the vertical. The clear |
2103 |
|
|
line-of-site probability associated with random overlap clouds is |
2104 |
|
|
defined to be the product of the clear sky probabilities at each |
2105 |
|
|
level along the line-of-site, ie. |
2106 |
|
|
|
2107 |
|
|
$$\prod_{p}^{p^{\prime}} \left( 1-CLRO_p \right)$$ |
2108 |
|
|
|
2109 |
|
|
The total cloud fraction at a given level associated with a line- |
2110 |
|
|
of-site calculation is given by |
2111 |
|
|
|
2112 |
|
|
$$1-\left( 1-MAX_p^{p^{\prime}} \left[ CLMO_p \right] \right) |
2113 |
|
|
\prod_p^{p^{\prime}} \left( 1-CLRO_p \right)$$ |
2114 |
|
|
|
2115 |
|
|
|
2116 |
|
|
\noindent |
2117 |
|
|
The 2-dimensional net cloud fraction as seen from the top of the |
2118 |
|
|
atmosphere is given by |
2119 |
|
|
\[ |
2120 |
|
|
{\bf CLDFRC} = 1-\left( 1-MAX_{l=l_1}^{Nrphys} \left[ CLMO_l \right] \right) |
2121 |
|
|
\prod_{l=l_1}^{Nrphys} \left( 1-CLRO_l \right) |
2122 |
|
|
\] |
2123 |
|
|
\\ |
2124 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
2125 |
|
|
|
2126 |
|
|
|
2127 |
|
|
\noindent |
2128 |
|
|
{\bf 82) \underline {QINT} Total Precipitable Water ($gm/cm^2$) } |
2129 |
|
|
|
2130 |
|
|
\noindent |
2131 |
|
|
The Total Precipitable Water is defined as the vertical integral of the specific humidity, |
2132 |
|
|
given by: |
2133 |
|
|
\begin{eqnarray*} |
2134 |
|
|
{\bf QINT} & = & \int_{surf}^{top} \rho q dz \\ |
2135 |
|
|
& = & {\pi \over g} \int_0^1 q dp |
2136 |
|
|
\end{eqnarray*} |
2137 |
|
|
where we have used the hydrostatic relation |
2138 |
|
|
$\rho \delta z = -{\delta p \over g} $. |
2139 |
|
|
\\ |
2140 |
|
|
|
2141 |
|
|
|
2142 |
|
|
\noindent |
2143 |
|
|
{\bf 83) \underline {U2M} Zonal U-Wind at 2 Meter Depth ($m/sec$) } |
2144 |
|
|
|
2145 |
|
|
\noindent |
2146 |
|
|
The u-wind at the 2-meter depth is determined from the similarity theory: |
2147 |
|
|
\[ |
2148 |
|
|
{\bf U2M} = {u_* \over k} \psi_{m_{2m}} {u_{sl} \over {W_s}} = |
2149 |
|
|
{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}u_{sl} |
2150 |
|
|
\] |
2151 |
|
|
|
2152 |
|
|
\noindent |
2153 |
|
|
where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript |
2154 |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
2155 |
|
|
is above two meters, ${\bf U2M}$ is undefined. |
2156 |
|
|
\\ |
2157 |
|
|
|
2158 |
|
|
\noindent |
2159 |
|
|
{\bf 84) \underline {V2M} Meridional V-Wind at 2 Meter Depth ($m/sec$) } |
2160 |
|
|
|
2161 |
|
|
\noindent |
2162 |
|
|
The v-wind at the 2-meter depth is a determined from the similarity theory: |
2163 |
|
|
\[ |
2164 |
|
|
{\bf V2M} = {u_* \over k} \psi_{m_{2m}} {v_{sl} \over {W_s}} = |
2165 |
|
|
{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}v_{sl} |
2166 |
|
|
\] |
2167 |
|
|
|
2168 |
|
|
\noindent |
2169 |
|
|
where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript |
2170 |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
2171 |
|
|
is above two meters, ${\bf V2M}$ is undefined. |
2172 |
|
|
\\ |
2173 |
|
|
|
2174 |
|
|
\noindent |
2175 |
|
|
{\bf 85) \underline {T2M} Temperature at 2 Meter Depth ($deg \hspace{.1cm} K$) } |
2176 |
|
|
|
2177 |
|
|
\noindent |
2178 |
|
|
The temperature at the 2-meter depth is a determined from the similarity theory: |
2179 |
|
|
\[ |
2180 |
|
|
{\bf T2M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) = |
2181 |
|
|
P^{\kappa}(\theta_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
2182 |
|
|
(\theta_{sl} - \theta_{surf})) |
2183 |
|
|
\] |
2184 |
|
|
where: |
2185 |
|
|
\[ |
2186 |
|
|
\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } |
2187 |
|
|
\] |
2188 |
|
|
|
2189 |
|
|
\noindent |
2190 |
|
|
where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
2191 |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
2192 |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
2193 |
|
|
is above two meters, ${\bf T2M}$ is undefined. |
2194 |
|
|
\\ |
2195 |
|
|
|
2196 |
|
|
\noindent |
2197 |
|
|
{\bf 86) \underline {Q2M} Specific Humidity at 2 Meter Depth ($g/kg$) } |
2198 |
|
|
|
2199 |
|
|
\noindent |
2200 |
|
|
The specific humidity at the 2-meter depth is determined from the similarity theory: |
2201 |
|
|
\[ |
2202 |
|
|
{\bf Q2M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) = |
2203 |
|
|
P^{\kappa}(q_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
2204 |
|
|
(q_{sl} - q_{surf})) |
2205 |
|
|
\] |
2206 |
|
|
where: |
2207 |
|
|
\[ |
2208 |
|
|
q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } |
2209 |
|
|
\] |
2210 |
|
|
|
2211 |
|
|
\noindent |
2212 |
|
|
where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
2213 |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
2214 |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
2215 |
|
|
is above two meters, ${\bf Q2M}$ is undefined. |
2216 |
|
|
\\ |
2217 |
|
|
|
2218 |
|
|
\noindent |
2219 |
|
|
{\bf 87) \underline {U10M} Zonal U-Wind at 10 Meter Depth ($m/sec$) } |
2220 |
|
|
|
2221 |
|
|
\noindent |
2222 |
|
|
The u-wind at the 10-meter depth is an interpolation between the surface wind |
2223 |
|
|
and the model lowest level wind using the ratio of the non-dimensional wind shear |
2224 |
|
|
at the two levels: |
2225 |
|
|
\[ |
2226 |
|
|
{\bf U10M} = {u_* \over k} \psi_{m_{10m}} {u_{sl} \over {W_s}} = |
2227 |
|
|
{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}u_{sl} |
2228 |
|
|
\] |
2229 |
|
|
|
2230 |
|
|
\noindent |
2231 |
|
|
where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript |
2232 |
|
|
$sl$ refers to the height of the top of the surface layer. |
2233 |
|
|
\\ |
2234 |
|
|
|
2235 |
|
|
\noindent |
2236 |
|
|
{\bf 88) \underline {V10M} Meridional V-Wind at 10 Meter Depth ($m/sec$) } |
2237 |
|
|
|
2238 |
|
|
\noindent |
2239 |
|
|
The v-wind at the 10-meter depth is an interpolation between the surface wind |
2240 |
|
|
and the model lowest level wind using the ratio of the non-dimensional wind shear |
2241 |
|
|
at the two levels: |
2242 |
|
|
\[ |
2243 |
|
|
{\bf V10M} = {u_* \over k} \psi_{m_{10m}} {v_{sl} \over {W_s}} = |
2244 |
|
|
{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}v_{sl} |
2245 |
|
|
\] |
2246 |
|
|
|
2247 |
|
|
\noindent |
2248 |
|
|
where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript |
2249 |
|
|
$sl$ refers to the height of the top of the surface layer. |
2250 |
|
|
\\ |
2251 |
|
|
|
2252 |
|
|
\noindent |
2253 |
|
|
{\bf 89) \underline {T10M} Temperature at 10 Meter Depth ($deg \hspace{.1cm} K$) } |
2254 |
|
|
|
2255 |
|
|
\noindent |
2256 |
|
|
The temperature at the 10-meter depth is an interpolation between the surface potential |
2257 |
|
|
temperature and the model lowest level potential temperature using the ratio of the |
2258 |
|
|
non-dimensional temperature gradient at the two levels: |
2259 |
|
|
\[ |
2260 |
|
|
{\bf T10M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) = |
2261 |
|
|
P^{\kappa}(\theta_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
2262 |
|
|
(\theta_{sl} - \theta_{surf})) |
2263 |
|
|
\] |
2264 |
|
|
where: |
2265 |
|
|
\[ |
2266 |
|
|
\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } |
2267 |
|
|
\] |
2268 |
|
|
|
2269 |
|
|
\noindent |
2270 |
|
|
where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
2271 |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
2272 |
|
|
$sl$ refers to the height of the top of the surface layer. |
2273 |
|
|
\\ |
2274 |
|
|
|
2275 |
|
|
\noindent |
2276 |
|
|
{\bf 90) \underline {Q10M} Specific Humidity at 10 Meter Depth ($g/kg$) } |
2277 |
|
|
|
2278 |
|
|
\noindent |
2279 |
|
|
The specific humidity at the 10-meter depth is an interpolation between the surface specific |
2280 |
|
|
humidity and the model lowest level specific humidity using the ratio of the |
2281 |
|
|
non-dimensional temperature gradient at the two levels: |
2282 |
|
|
\[ |
2283 |
|
|
{\bf Q10M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) = |
2284 |
|
|
P^{\kappa}(q_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
2285 |
|
|
(q_{sl} - q_{surf})) |
2286 |
|
|
\] |
2287 |
|
|
where: |
2288 |
|
|
\[ |
2289 |
|
|
q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } |
2290 |
|
|
\] |
2291 |
|
|
|
2292 |
|
|
\noindent |
2293 |
|
|
where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
2294 |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
2295 |
|
|
$sl$ refers to the height of the top of the surface layer. |
2296 |
|
|
\\ |
2297 |
|
|
|
2298 |
|
|
\noindent |
2299 |
|
|
{\bf 91) \underline {DTRAIN} Cloud Detrainment Mass Flux ($kg/m^2$) } |
2300 |
|
|
|
2301 |
|
|
The amount of cloud mass moved per RAS timestep at the cloud detrainment level is written: |
2302 |
|
|
\[ |
2303 |
|
|
{\bf DTRAIN} = \eta_{r_D}m_B |
2304 |
|
|
\] |
2305 |
|
|
\noindent |
2306 |
|
|
where $r_D$ is the detrainment level, |
2307 |
|
|
$m_B$ is the cloud base mass flux, and $\eta$ |
2308 |
|
|
is the entrainment, defined in Section \ref{sec:fizhi:mc}. |
2309 |
|
|
\\ |
2310 |
|
|
|
2311 |
|
|
\noindent |
2312 |
|
|
{\bf 92) \underline {QFILL} Filling of negative Specific Humidity ($g/kg/day$) } |
2313 |
|
|
|
2314 |
|
|
\noindent |
2315 |
|
|
Due to computational errors associated with the numerical scheme used for |
2316 |
|
|
the advection of moisture, negative values of specific humidity may be generated. The |
2317 |
|
|
specific humidity is checked for negative values after every dynamics timestep. If negative |
2318 |
|
|
values have been produced, a filling algorithm is invoked which redistributes moisture from |
2319 |
|
|
below. Diagnostic {\bf QFILL} is equal to the net filling needed |
2320 |
|
|
to eliminate negative specific humidity, scaled to a per-day rate: |
2321 |
|
|
\[ |
2322 |
|
|
{\bf QFILL} = q^{n+1}_{final} - q^{n+1}_{initial} |
2323 |
|
|
\] |
2324 |
|
|
where |
2325 |
|
|
\[ |
2326 |
|
|
q^{n+1} = (\pi q)^{n+1} / \pi^{n+1} |
2327 |
|
|
\] |
2328 |
|
|
|
2329 |
|
|
\subsection{Dos and Donts} |
2330 |
|
|
|
2331 |
|
|
\subsection{Diagnostics Reference} |
2332 |
|
|
|