--- manual/s_phys_pkgs/diagnostics.tex 2004/10/12 18:16:03 1.2 +++ manual/s_phys_pkgs/diagnostics.tex 2005/07/14 19:18:01 1.9 @@ -6,14 +6,29 @@ \subsection{Introduction} -This section of the documentation describes the Diagnostics Utilities available within the GCM. -In addition to -a description on how to set and extract diagnostic quantities, this document also provides a -comprehensive list of all available diagnostic quantities and a short description of how they are -computed. It should be noted that this document is not intended to be a complete documentation -of the various packages used in the GCM, and the reader should -refer to original publications for further insight. - +\noindent +This section of the documentation describes the Diagnostics package available within +the GCM. A large selection of model diagnostics is available for output. +In addition to the diagnostic quantities pre-defined in the GCM, there exists +the option, in any experiment, to define a new diagnostic quantity and include it +as part of the diagnostic output with the addition of a single subroutine call in the +routine where the field is computed. As a matter of philosophy, no diagnostic is enabled +as default, thus each user must specify the exact diagnostic information required for an +experiment. This is accomplished by enabling the specific diagnostic of interest cataloged +in the Diagnostic Menu (see Section \ref{sec:diagnostics:menu}). Instructions for enabling +diagnostic output and defining new diagnostic quantities are found in Section +\ref{sec:diagnostics:usersguide} of this document. + +\noindent +The Diagnostic Menu is a hard-wired enumeration of diagnostic quantities available within +the GCM. Once a diagnostic is enabled, the GCM will continually increment an array +specifically allocated for that diagnostic whenever the appropriate quantity is computed. +A counter is defined which records how many times each diagnostic quantity has been +incremented. Several special diagnostics are included in the menu. Quantities refered to +as ``Counter Diagnostics'', are defined for selected diagnostics which record the +frequency at which a diagnostic is incremented separately for each model grid location. +Quantitied refered to as ``User Diagnostics'' are included in the menu to facilitate +defining new diagnostics for a particular experiment. \subsection{Equations} Not relevant. @@ -21,35 +36,16 @@ \subsection{Key Subroutines and Parameters} \label{sec:diagnostics:diagover} -A large selection of model diagnostics is available in the GCM. At the time of -this writing there are 92 different diagnostic quantities which can be enabled for an -experiment. As a matter of philosophy, no diagnostic is enabled as default, thus each user must -specify the exact diagnostic information required for an experiment. This is accomplished by -enabling the specific diagnostic of interest cataloged in the -Diagnostic Menu (see Section \ref{sec:diagnostics:menu}). -The Diagnostic Menu is a hard-wired enumeration of diagnostic quantities available within the -GCM. Diagnostics are internally referred to by their associated number in the Diagnostic -Menu. Once a diagnostic is enabled, the GCM will continually increment an array -specifically allocated for that diagnostic whenever the associated process for the diagnostic is -computed. Separate arrays are used both for the diagnostic quantity and its diagnostic counter -which records how many times each diagnostic quantity has been computed. In addition -special diagnostics, called -``Counter Diagnostics'', records the frequency of diagnostic updates separately for each -model grid location. - -The diagnostics are computed at various times and places within the GCM. -Some diagnostics are computed on the geophysical A-grid (such as -those within the Physics routines), while others are computed on the C-grid -(those computed during the dynamics time-stepping). Some diagnostics are -scalars, while others are vectors. Each of these possibilities requires -separate tasks for A-grid to C-grid transformations and coordinate transformations. Due -to this complexity, and since the specific diagnostics enabled are User determined at the -time of the run, -a diagnostic parameter has been developed and implemented into the GCM, defined as GDIAG, -which contains information concerning various grid attributes of each diagnostic. The GDIAG -array is internally defined as a character*8 variable, and is equivalenced to -a character*1 "parse" array in output in order to extract the grid-attribute information. -The GDIAG array is described in Table \ref{tab:diagnostics:gdiag.tabl}. +\noindent +The diagnostics are computed at various times and places within the GCM. Because the +MIT GCM may employ a staggered grid, diagnostics may be computed at grid box centers, +corners, or edges, and at the middle or edge in the vertical. Some diagnostics are scalars, +while others are components of vectors. An internal array is defined which contains +information concerning various grid attributes of each diagnostic. The GDIAG +array (in common block \\diagnostics in file diagnostics.h) is internally defined as a +character*8 variable, and is equivalenced to a character*1 "parse" array in output in +order to extract the grid-attribute information. The GDIAG array is described in +Table \ref{tab:diagnostics:gdiag.tabl}. \begin{table} \caption{Diagnostic Parsing Array} @@ -68,9 +64,8 @@ parse(2) & $\rightarrow$ U & C-Grid U-Point \\ & $\rightarrow$ V & C-Grid V-Point \\ & $\rightarrow$ M & C-Grid Mass Point \\ - & $\rightarrow$ Z & C-Grid Vorticity Point \\ \hline - parse(3) & $\rightarrow$ R & Computed on the Rotated Grid \\ - & $\rightarrow$ G & Computed on the Geophysical Grid \\ \hline + & $\rightarrow$ Z & C-Grid Vorticity (Corner) Point \\ \hline + parse(3) & $\rightarrow$ R & Not Currently in Use \\ \hline parse(4) & $\rightarrow$ P & Positive Definite Diagnostic \\ \hline parse(5) & $\rightarrow$ C & Counter Diagnostic \\ & $\rightarrow$ D & Disabled Diagnostic for output \\ \hline @@ -81,107 +76,194 @@ \end{center} \end{table} + +\noindent As an example, consider a diagnostic whose associated GDIAG parameter is equal -to ``UUR 002''. From GDIAG we can determine that this diagnostic is a -U-vector component located at the C-grid U-point within the Rotated framework. +to ``UU 002''. From GDIAG we can determine that this diagnostic is a +U-vector component located at the C-grid U-point. Its corresponding V-component diagnostic is located in Diagnostic \# 002. + +\noindent In this way, each Diagnostic in the model has its attributes (ie. vector or scalar, -rotated or geophysical, A-Grid or C-grid, etc.) defined internally. The Output routines -use this information in order to determine -what type of rotations and/or transformations need to be performed. Thus, all Diagnostic -interpolations are done at the time of output rather than during each model dynamic step. -In this way the User now has more flexibility -in determining the type of gridded data which is output. +C-grid location, etc.) defined internally. The Output routines use this information +in order to determine what type of transformations need to be performed. Any +interpolations are done at the time of output rather than during each model step. +In this way the User has flexibility in determining the type of gridded data which +is output. + +\noindent There are several utilities within the GCM available to users to enable, disable, -clear, and retrieve model diagnostics, and may be called from any user-supplied application -and/or output routine. The available utilities and the CALL sequences are listed below. +clear, write and retrieve model diagnostics, and may be called from any routine. +The available utilities and the CALL sequences are listed below. -{\bf SETDIAG}: This subroutine enables a diagnostic from the Diagnostic Menu, meaning that -space is allocated for the diagnostic and the -model routines will increment the diagnostic value during execution. This routine is useful when -called from either user application routines or user output routines, and is the underlying interface -between the user and the desired diagnostic. The diagnostic is referenced by its diagnostic -number from the menu, and its calling sequence is given by: +\noindent +{\bf fill\_diagnostics}: This routine will increment the specified diagnostic +quantity with a field sent through the argument list. + +\noindent \begin{tabbing} XXXXXXXXX\=XXXXXX\= \kill -\> CALL SETDIAG (NUM) \\ +\> call fill\_diagnostics (myThid, chardiag, levflg, nlevs, \\ + bibjflg, bi, bj, arrayin) \\ \\ -where \> NUM \>= Diagnostic number from menu \\ +where \> myThid \>= Current Process(or) \\ + \> chardiag \>= Character *8 expression for diag to fill \\ + \> levflg \>= Integer flag for vertical levels: \\ + \> \> 0 indicates multiple levels incremented in qdiag \\ + \> \> non-0 (any integer) - WHICH single level to increment. \\ + \> \> negative integer - the input data array is single-leveled \\ + \> \> positive integer - the input data array is multi-leveled \\ + \> nlevs \>= indicates Number of levels to be filled (1 if levflg <> 0) \\ + \> \> positive: fill in "nlevs" levels in the same order as \\ + \> \> the input array \\ + \> \> negative: fill in -nlevs levels in reverse order. \\ + \> bibjflg \>= Integer flag to indicate instructions for bi bj loop \\ + \> \> 0 indicates that the bi-bj loop must be done here \\ + \> \> 1 indicates that the bi-bj loop is done OUTSIDE \\ + \> \> 2 indicates that the bi-bj loop is done OUTSIDE \\ + \> \> AND that we have been sent a local array \\ + \> \> 3 indicates that the bi-bj loop is done OUTSIDE \\ + \> \> AND that we have been sent a local array \\ + \> \> AND that the array has the shadow regions \\ + \> bi \>= X-direction process(or) number - used for bibjflg=1-3 \\ + \> bj \>= Y-direction process(or) number - used for bibjflg=1-3 \\ + \> arrayin \>= Field to increment diagnostics array \\ \end{tabbing} -{\bf GETDIAG}: This subroutine retrieves the value of a model diagnostic. This routine is -particulary useful when called from a user output routine, although it can be called from an -application routine as well. This routine returns the time-averaged value of the diagnostic by -dividing the current accumulated diagnostic value by its corresponding counter. This routine does -not change the value of the diagnostic itself, that is, it does not replace the diagnostic with its -time-average. The calling sequence for this routine is givin by: +\noindent +{\bf setdiag}: This subroutine enables a diagnostic from the Diagnostic Menu, meaning +that space is allocated for the diagnostic and the model routines will increment the +diagnostic value during execution. This routine is the underlying interface +between the user and the desired diagnostic. The diagnostic is referenced by its diagnostic +number from the menu, and its calling sequence is given by: +\noindent \begin{tabbing} XXXXXXXXX\=XXXXXX\= \kill -\> CALL GETDIAG (LEV,NUM,QTMP,UNDEF) \\ +\> call setdiag (num) \\ \\ -where \> LEV \>= Model Level at which the diagnostic is desired \\ - \> NUM \>= Diagnostic number from menu \\ - \> QTMP \>= Time-Averaged Diagnostic Output \\ - \> UNDEF \>= Fill value to be used when diagnostic is undefined \\ +where \> num \>= Diagnostic number from menu \\ \end{tabbing} -{\bf CLRDIAG}: This subroutine initializes the values of model diagnostics to zero, and is -particularly useful when called from user output routines to re-initialize diagnostics during the -run. The calling sequence is: - +\noindent +{\bf getdiag}: This subroutine retrieves the value of a model diagnostic. This routine +is particulary useful when called from a user output routine, although it can be called +from any routine. This routine returns the time-averaged value of the diagnostic by +dividing the current accumulated diagnostic value by its corresponding counter. This +routine does not change the value of the diagnostic itself, that is, it does not replace +the diagnostic with its time-average. The calling sequence for this routine is givin by: +\noindent \begin{tabbing} XXXXXXXXX\=XXXXXX\= \kill -\> CALL CLRDIAG (NUM) \\ +\> call getdiag (lev,num,qtmp,undef) \\ \\ -where \> NUM \>= Diagnostic number from menu \\ +where \> lev \>= Model Level at which the diagnostic is desired \\ + \> num \>= Diagnostic number from menu \\ + \> qtmp \>= Time-Averaged Diagnostic Output \\ + \> undef \>= Fill value to be used when diagnostic is undefined \\ \end{tabbing} +\noindent +{\bf clrdiag}: This subroutine initializes the values of model diagnostics to zero, and is +particularly useful when called from user output routines to re-initialize diagnostics +during the run. The calling sequence is: - -{\bf ZAPDIAG}: This entry into subroutine SETDIAG disables model diagnostics, meaning that the -diagnostic is no longer available to the user. The memory previously allocated to the diagnostic -is released when ZAPDIAG is invoked. The calling sequence is given by: - - +\noindent \begin{tabbing} XXXXXXXXX\=XXXXXX\= \kill -\> CALL ZAPDIAG (NUM) \\ +\> call clrdiag (num) \\ \\ -where \> NUM \>= Diagnostic number from menu \\ +where \> num \>= Diagnostic number from menu \\ \end{tabbing} -{\bf DIAGSIZE}: We end this section with a discussion on the manner in which computer memory -is allocated for diagnostics. -All GCM diagnostic quantities are stored in the single -diagnostic array QDIAG which is located in the DIAG COMMON, having the form: +\noindent +{\bf zapdiag}: This entry into subroutine SETDIAG disables model diagnostics, meaning +that the diagnostic is no longer available to the user. The memory previously allocated +to the diagnostic is released when ZAPDIAG is invoked. The calling sequence is given by: +\noindent \begin{tabbing} XXXXXXXXX\=XXXXXX\= \kill -\> COMMON /DIAG/ NDIAG\_MAX,QDIAG(IM,JM,1) \\ +\> call zapdiag (NUM) \\ \\ +where \> num \>= Diagnostic number from menu \\ \end{tabbing} -where NDIAG\_MAX is an Integer variable which should be -set equal to the number of enabled diagnostics, and QDIAG is a three-dimensional -array. The first two-dimensions of QDIAG correspond to the horizontal dimension -of a given diagnostic, while the third dimension of QDIAG is used to identify -specific diagnostic types. -In order to minimize the maximum memory requirement used by the model, -the default GCM executable is compiled with room for only one horizontal -diagnostic array, as shown in the above example. -In order for the User to enable more than 1 two-dimensional diagnostic, -the size of the DIAG COMMON must be expanded to accomodate the desired diagnostics. + +\subsection{Usage Notes} +\label{sec:diagnostics:usersguide} + +\noindent +We begin this section with a discussion on the manner in which computer +memory is allocated for diagnostics. All GCM diagnostic quantities are stored in the +single diagnostic array QDIAG which is located in the file \\ +\filelink{pkg/diagnostics/diagnostics.h}{pkg-diagnostics-diagnostics.h}. +and has the form: + +common /diagnostics/ qdiag(1-Olx,sNx+Olx,1-Olx,sNx+Olx,numdiags,Nsx,Nsy) + +\noindent +where numdiags is an Integer variable which should be set equal to the number of +enabled diagnostics, and qdiag is a three-dimensional array. The first two-dimensions +of qdiag correspond to the horizontal dimension of a given diagnostic, while the third +dimension of qdiag is used to identify diagnostic fields and levels combined. In order +to minimize the memory requirement of the model for diagnostics, the default GCM +executable is compiled with room for only one horizontal diagnostic array, or with +numdiags set to 1. In order for the User to enable more than 1 two-dimensional diagnostic, +the size of the diagnostics common must be expanded to accomodate the desired diagnostics. This can be accomplished by manually changing the parameter numdiags in the -file \filelink{FORWARD\_STEP}{pkg-diagnostics-diagnostics_SIZE.h}, or by allowing the -shell script (???????) to make this -change based on the choice of diagnostic output made in the namelist. +file \filelink{pkg/diagnostics/diagnostics\_SIZE.h}{pkg-diagnostics-diagnostics_SIZE.h}. +numdiags should be set greater than or equal to the sum of all the diagnostics activated +for output each multiplied by the number of levels defined for that diagnostic quantity. +This is illustrated in the example below: + +\noindent +To use the diagnostics package, other than enabling it in packages.conf +and turning the usediagnostics flag in data.pkg to .TRUE., a namelist +must be supplied in the run directory called data.diagnostics. The namelist +will activate a user-defined list of diagnostics quantities to be computed, +specify the frequency of output, the number of levels, and the name of +up to 10 separate output files. A sample data.diagnostics namelist file: + +\noindent +$\#$ Diagnostic Package Choices \\ + $\&$diagnostics\_list \\ + frequency(1) = 10, \ \\ + levels(1,1) = 1.,2.,3.,4.,5., \ \\ + fields(1,1) = 'UVEL ','VVEL ', \ \\ + filename(1) = 'diagout1', \ \\ + frequency(2) = 100, \ \\ + levels(1,2) = 1.,2.,3.,4.,5., \ \\ + fields(1,2) = 'THETA ','SALT ', \ \\ + filename(2) = 'diagout2', \ \\ + $\&$end \ \\ + +\noindent +In this example, there are two output files that will be generated +for each tile and for each output time. The first set of output files +has the prefix diagout1, does time averaging every 10 time steps +(frequency is 10), they will write fields which are multiple-level +fields and output levels 1-5. The names of diagnostics quantities are +UVEL and VVEL. The second set of output files +has the prefix diagout2, does time averaging every 100 time steps, +they include fields which are multiple-level fields, levels output are 1-5, +and the names of diagnostics quantities are THETA and SALT. + +\noindent +In order to define and include as part of the diagnostic output any field +that is desired for a particular experiment, two steps must be taken. The +first is to enable the ``User Diagnostic'' in data.diagnostics. This is +accomplished by setting one of the fields slots to either UDIAG1 through +UDIAG10, for multi-level fields, or SDIAG1 through SDIAG10 for single level +fields. These are listed in the diagnostics menu. The second step is to +add a call to fill\_diagnostics from the subroutine in which the quantity +desired for diagnostic output is computed. \newpage @@ -194,224 +276,88 @@ \hline &\\ -1 & UFLUX & $Newton/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Surface U-Wind Stress on the atmosphere} - \end{minipage}\\ -2 & VFLUX & $Newton/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Surface V-Wind Stress on the atmosphere} - \end{minipage}\\ -3 & HFLUX & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Surface Flux of Sensible Heat} - \end{minipage}\\ -4 & EFLUX & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Surface Flux of Latent Heat} - \end{minipage}\\ -5 & QICE & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Heat Conduction through Sea-Ice} - \end{minipage}\\ -6 & RADLWG & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Net upward LW flux at the ground} - \end{minipage}\\ -7 & RADSWG & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Net downward SW flux at the ground} - \end{minipage}\\ -8 & RI & $dimensionless$ & Nrphys - &\begin{minipage}[t]{3in} - {Richardson Number} - \end{minipage}\\ -9 & CT & $dimensionless$ & 1 - &\begin{minipage}[t]{3in} - {Surface Drag coefficient for T and Q} - \end{minipage}\\ -10 & CU & $dimensionless$ & 1 - &\begin{minipage}[t]{3in} - {Surface Drag coefficient for U and V} - \end{minipage}\\ -11 & ET & $m^2/sec$ & Nrphys - &\begin{minipage}[t]{3in} - {Diffusivity coefficient for T and Q} - \end{minipage}\\ -12 & EU & $m^2/sec$ & Nrphys - &\begin{minipage}[t]{3in} - {Diffusivity coefficient for U and V} - \end{minipage}\\ -13 & TURBU & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {U-Momentum Changes due to Turbulence} - \end{minipage}\\ -14 & TURBV & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {V-Momentum Changes due to Turbulence} - \end{minipage}\\ -15 & TURBT & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Temperature Changes due to Turbulence} - \end{minipage}\\ -16 & TURBQ & $g/kg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Specific Humidity Changes due to Turbulence} - \end{minipage}\\ -17 & MOISTT & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Temperature Changes due to Moist Processes} - \end{minipage}\\ -18 & MOISTQ & $g/kg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Specific Humidity Changes due to Moist Processes} - \end{minipage}\\ -19 & RADLW & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Net Longwave heating rate for each level} - \end{minipage}\\ -20 & RADSW & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Net Shortwave heating rate for each level} - \end{minipage}\\ -21 & PREACC & $mm/day$ & 1 - &\begin{minipage}[t]{3in} - {Total Precipitation} - \end{minipage}\\ -22 & PRECON & $mm/day$ & 1 - &\begin{minipage}[t]{3in} - {Convective Precipitation} - \end{minipage}\\ -23 & TUFLUX & $Newton/m^2$ & Nrphys - &\begin{minipage}[t]{3in} - {Turbulent Flux of U-Momentum} - \end{minipage}\\ -24 & TVFLUX & $Newton/m^2$ & Nrphys - &\begin{minipage}[t]{3in} - {Turbulent Flux of V-Momentum} - \end{minipage}\\ -25 & TTFLUX & $Watts/m^2$ & Nrphys - &\begin{minipage}[t]{3in} - {Turbulent Flux of Sensible Heat} - \end{minipage}\\ -26 & TQFLUX & $Watts/m^2$ & Nrphys - &\begin{minipage}[t]{3in} - {Turbulent Flux of Latent Heat} - \end{minipage}\\ -27 & CN & $dimensionless$ & 1 - &\begin{minipage}[t]{3in} - {Neutral Drag Coefficient} - \end{minipage}\\ -28 & WINDS & $m/sec$ & 1 - &\begin{minipage}[t]{3in} - {Surface Wind Speed} - \end{minipage}\\ -29 & DTSRF & $deg$ & 1 - &\begin{minipage}[t]{3in} - {Air/Surface virtual temperature difference} - \end{minipage}\\ -30 & TG & $deg$ & 1 +84 & SDIAG1 & & 1 &\begin{minipage}[t]{3in} - {Ground temperature} + {User-Defined Surface Diagnostic-1} \end{minipage}\\ -31 & TS & $deg$ & 1 +85 & SDIAG2 & & 1 &\begin{minipage}[t]{3in} - {Surface air temperature (Adiabatic from lowest model layer)} + {User-Defined Surface Diagnostic-2} \end{minipage}\\ -32 & DTG & $deg$ & 1 +86 & UDIAG1 & & Nrphys &\begin{minipage}[t]{3in} - {Ground temperature adjustment} + {User-Defined Upper-Air Diagnostic-1} \end{minipage}\\ - -\end{tabular} - -\newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline - -&\\ -33 & QG & $g/kg$ & 1 +87 & UDIAG2 & & Nrphys &\begin{minipage}[t]{3in} - {Ground specific humidity} + {User-Defined Upper-Air Diagnostic-2} \end{minipage}\\ -34 & QS & $g/kg$ & 1 +124& SDIAG3 & & 1 &\begin{minipage}[t]{3in} - {Saturation surface specific humidity} + {User-Defined Surface Diagnostic-3} \end{minipage}\\ - -&\\ -35 & TGRLW & $deg$ & 1 +125& SDIAG4 & & 1 &\begin{minipage}[t]{3in} - {Instantaneous ground temperature used as input to the - Longwave radiation subroutine} + {User-Defined Surface Diagnostic-4} \end{minipage}\\ -36 & ST4 & $Watts/m^2$ & 1 +126& SDIAG5 & & 1 &\begin{minipage}[t]{3in} - {Upward Longwave flux at the ground ($\sigma T^4$)} + {User-Defined Surface Diagnostic-5} \end{minipage}\\ -37 & OLR & $Watts/m^2$ & 1 +127& SDIAG6 & & 1 &\begin{minipage}[t]{3in} - {Net upward Longwave flux at the top of the model} + {User-Defined Surface Diagnostic-6} \end{minipage}\\ -38 & OLRCLR & $Watts/m^2$ & 1 +128& SDIAG7 & & 1 &\begin{minipage}[t]{3in} - {Net upward clearsky Longwave flux at the top of the model} + {User-Defined Surface Diagnostic-7} \end{minipage}\\ -39 & LWGCLR & $Watts/m^2$ & 1 +129& SDIAG8 & & 1 &\begin{minipage}[t]{3in} - {Net upward clearsky Longwave flux at the ground} + {User-Defined Surface Diagnostic-8} \end{minipage}\\ -40 & LWCLR & $deg/day$ & Nrphys +130& SDIAG9 & & 1 &\begin{minipage}[t]{3in} - {Net clearsky Longwave heating rate for each level} + {User-Defined Surface Diagnostic-9} \end{minipage}\\ -41 & TLW & $deg$ & Nrphys +131& SDIAG10 & & 1 &\begin{minipage}[t]{3in} - {Instantaneous temperature used as input to the Longwave radiation - subroutine} + {User-Defined Surface Diagnostic-1-} \end{minipage}\\ -42 & SHLW & $g/g$ & Nrphys +132& UDIAG3 & & Nrphys &\begin{minipage}[t]{3in} - {Instantaneous specific humidity used as input to the Longwave radiation - subroutine} + {User-Defined Multi-Level Diagnostic-3} \end{minipage}\\ -43 & OZLW & $g/g$ & Nrphys +133& UDIAG4 & & Nrphys &\begin{minipage}[t]{3in} - {Instantaneous ozone used as input to the Longwave radiation - subroutine} + {User-Defined Multi-Level Diagnostic-4} \end{minipage}\\ -44 & CLMOLW & $0-1$ & Nrphys +134& UDIAG5 & & Nrphys &\begin{minipage}[t]{3in} - {Maximum overlap cloud fraction used in the Longwave radiation - subroutine} + {User-Defined Multi-Level Diagnostic-5} \end{minipage}\\ -45 & CLDTOT & $0-1$ & Nrphys +135& UDIAG6 & & Nrphys &\begin{minipage}[t]{3in} - {Total cloud fraction used in the Longwave and Shortwave radiation - subroutines} + {User-Defined Multi-Level Diagnostic-6} \end{minipage}\\ -46 & RADSWT & $Watts/m^2$ & 1 +136& UDIAG7 & & Nrphys &\begin{minipage}[t]{3in} - {Incident Shortwave radiation at the top of the atmosphere} + {User-Defined Multi-Level Diagnostic-7} \end{minipage}\\ -47 & CLROSW & $0-1$ & Nrphys +137& UDIAG8 & & Nrphys &\begin{minipage}[t]{3in} - {Random overlap cloud fraction used in the shortwave radiation - subroutine} + {User-Defined Multi-Level Diagnostic-8} \end{minipage}\\ -48 & CLMOSW & $0-1$ & Nrphys +138& UDIAG9 & & Nrphys &\begin{minipage}[t]{3in} - {Maximum overlap cloud fraction used in the shortwave radiation - subroutine} + {User-Defined Multi-Level Diagnostic-9} \end{minipage}\\ -49 & EVAP & $mm/day$ & 1 +139& UDIAG10 & & Nrphys &\begin{minipage}[t]{3in} - {Surface evaporation} + {User-Defined Multi-Level Diagnostic-10} \end{minipage}\\ \end{tabular} +\vspace{1.5in} \vfill \newpage @@ -422,190 +368,138 @@ \hline &\\ -50 & DUDT & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Total U-Wind tendency} - \end{minipage}\\ -51 & DVDT & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Total V-Wind tendency} - \end{minipage}\\ -52 & DTDT & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Total Temperature tendency} - \end{minipage}\\ -53 & DQDT & $g/kg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Total Specific Humidity tendency} - \end{minipage}\\ -54 & USTAR & $m/sec$ & 1 - &\begin{minipage}[t]{3in} - {Surface USTAR wind} - \end{minipage}\\ -55 & Z0 & $m$ & 1 - &\begin{minipage}[t]{3in} - {Surface roughness} - \end{minipage}\\ -56 & FRQTRB & $0-1$ & Nrphys-1 - &\begin{minipage}[t]{3in} - {Frequency of Turbulence} - \end{minipage}\\ -57 & PBL & $mb$ & 1 - &\begin{minipage}[t]{3in} - {Planetary Boundary Layer depth} - \end{minipage}\\ -58 & SWCLR & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Net clearsky Shortwave heating rate for each level} - \end{minipage}\\ -59 & OSR & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Net downward Shortwave flux at the top of the model} - \end{minipage}\\ -60 & OSRCLR & $Watts/m^2$ & 1 +238& ETAN & $(hPa,m)$ & 1 &\begin{minipage}[t]{3in} - {Net downward clearsky Shortwave flux at the top of the model} + {Perturbation of Surface (pressure, height)} \end{minipage}\\ -61 & CLDMAS & $kg / m^2$ & Nrphys +239& ETANSQ & $(hPa^2,m^2)$ & 1 &\begin{minipage}[t]{3in} - {Convective cloud mass flux} + {Square of Perturbation of Surface (pressure, height)} \end{minipage}\\ -62 & UAVE & $m/sec$ & Nrphys +240& THETA & $deg K$ & Nr &\begin{minipage}[t]{3in} - {Time-averaged $u-Wind$} + {Potential Temperature} \end{minipage}\\ -63 & VAVE & $m/sec$ & Nrphys +241& SALT & $g/kg$ & Nr &\begin{minipage}[t]{3in} - {Time-averaged $v-Wind$} + {Salt (or Water Vapor Mixing Ratio)} \end{minipage}\\ -64 & TAVE & $deg$ & Nrphys +242& UVEL & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Time-averaged $Temperature$} + {U-Velocity} \end{minipage}\\ -65 & QAVE & $g/g$ & Nrphys +243& VVEL & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Time-averaged $Specific \, \, Humidity$} + {V-Velocity} \end{minipage}\\ -66 & PAVE & $mb$ & 1 +244& WVEL & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Time-averaged $p_{surf} - p_{top}$} + {Vertical-Velocity} \end{minipage}\\ -67 & QQAVE & $(m/sec)^2$ & Nrphys +245& THETASQ & $deg^2$ & Nr &\begin{minipage}[t]{3in} - {Time-averaged $Turbulent Kinetic Energy$} + {Square of Potential Temperature} \end{minipage}\\ -68 & SWGCLR & $Watts/m^2$ & 1 +246& SALTSQ & $g^2/{kg}^2$ & Nr &\begin{minipage}[t]{3in} - {Net downward clearsky Shortwave flux at the ground} + {Square of Salt (or Water Vapor Mixing Ratio)} \end{minipage}\\ -69 & SDIAG1 & & 1 +247& UVELSQ & $m^2/sec^2$ & Nr &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-1} + {Square of U-Velocity} \end{minipage}\\ -70 & SDIAG2 & & 1 +248& VVELSQ & $m^2/sec^2$ & Nr &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-2} + {Square of V-Velocity} \end{minipage}\\ -71 & UDIAG1 & & Nrphys +249& WVELSQ & $m^2/sec^2$ & Nr &\begin{minipage}[t]{3in} - {User-Defined Upper-Air Diagnostic-1} + {Square of Vertical-Velocity} \end{minipage}\\ -72 & UDIAG2 & & Nrphys +250& UVELVVEL & $m^2/sec^2$ & Nr &\begin{minipage}[t]{3in} - {User-Defined Upper-Air Diagnostic-2} + {Meridional Transport of Zonal Momentum} \end{minipage}\\ -73 & DIABU & $m/sec/day$ & Nrphys +251& UVELMASS & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Total Diabatic forcing on $u-Wind$} + {Zonal Mass-Weighted Component of Velocity} \end{minipage}\\ -74 & DIABV & $m/sec/day$ & Nrphys +252& VVELMASS & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Total Diabatic forcing on $v-Wind$} + {Meridional Mass-Weighted Component of Velocity} \end{minipage}\\ -75 & DIABT & $deg/day$ & Nrphys +253& WVELMASS & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Total Diabatic forcing on $Temperature$} + {Vertical Mass-Weighted Component of Velocity} \end{minipage}\\ -76 & DIABQ & $g/kg/day$ & Nrphys +254& UTHMASS & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Total Diabatic forcing on $Specific \, \, Humidity$} + {Zonal Mass-Weight Transp of Pot Temp} \end{minipage}\\ - -\end{tabular} -\vfill - -\newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline - -77 & VINTUQ & $m/sec \cdot g/kg$ & 1 +255& VTHMASS & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Vertically integrated $u \, q$} + {Meridional Mass-Weight Transp of Pot Temp} \end{minipage}\\ -78 & VINTVQ & $m/sec \cdot g/kg$ & 1 +256& WTHMASS & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Vertically integrated $v \, q$} + {Vertical Mass-Weight Transp of Pot Temp} \end{minipage}\\ -79 & VINTUT & $m/sec \cdot deg$ & 1 +257& USLTMASS & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Vertically integrated $u \, T$} + {Zonal Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -80 & VINTVT & $m/sec \cdot deg$ & 1 +258& VSLTMASS & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Vertically integrated $v \, T$} + {Meridional Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -81 & CLDFRC & $0-1$ & 1 +259& WSLTMASS & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Total Cloud Fraction} + {Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -82 & QINT & $gm/cm^2$ & 1 +260& UVELTH & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Precipitable water} + {Zonal Transp of Pot Temp} \end{minipage}\\ -83 & U2M & $m/sec$ & 1 +261& VVELTH & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {U-Wind at 2 meters} + {Meridional Transp of Pot Temp} \end{minipage}\\ -84 & V2M & $m/sec$ & 1 +262& WVELTH & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {V-Wind at 2 meters} + {Vertical Transp of Pot Temp} \end{minipage}\\ -85 & T2M & $deg$ & 1 +263& UVELSLT & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Temperature at 2 meters} + {Zonal Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -86 & Q2M & $g/kg$ & 1 +264& VVELSLT & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Specific Humidity at 2 meters} + {Meridional Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -87 & U10M & $m/sec$ & 1 +265& WVELSLT & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {U-Wind at 10 meters} + {Vertical Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -88 & V10M & $m/sec$ & 1 +275& WSLTMASS & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {V-Wind at 10 meters} + {Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -89 & T10M & $deg$ & 1 +298& VISCA4 & $m^4/sec$ & 1 &\begin{minipage}[t]{3in} - {Temperature at 10 meters} + {Biharmonic Viscosity Coefficient} \end{minipage}\\ -90 & Q10M & $g/kg$ & 1 +299& VISCAH & $m^2/sec$ & 1 &\begin{minipage}[t]{3in} - {Specific Humidity at 10 meters} + {Harmonic Viscosity Coefficient} \end{minipage}\\ -91 & DTRAIN & $kg/m^2$ & Nrphys +300& DRHODR & $kg/m^3/{r-unit}$ & Nr &\begin{minipage}[t]{3in} - {Detrainment Cloud Mass Flux} + {Stratification: d.Sigma/dr} \end{minipage}\\ -92 & QFILL & $g/kg/day$ & Nrphys +301& DETADT2 & ${r-unit}^2/s^2$ & 1 &\begin{minipage}[t]{3in} - {Filling of negative specific humidity} + {Square of Eta (Surf.P,SSH) Tendency} \end{minipage}\\ - \end{tabular} \vspace{1.5in} \vfill @@ -624,1691 +518,8 @@ {\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t) \] where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the -output frequency of the diagnositc, and $\Delta t$ is -the timestep over which the diagnostic is updated. For further information on how -to set the diagnostic output frequency {\bf NQDIAG}, please see Part III, A User's Guide. - -{\bf 1) \underline {UFLUX} Surface Zonal Wind Stress on the Atmosphere ($Newton/m^2$) } - -The zonal wind stress is the turbulent flux of zonal momentum from -the surface. See section 3.3 for a description of the surface layer parameterization. -\[ -{\bf UFLUX} = - \rho C_D W_s u \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u -\] -where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface -drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum -(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $u$ is -the zonal wind in the lowest model layer. -\\ - - -{\bf 2) \underline {VFLUX} Surface Meridional Wind Stress on the Atmosphere ($Newton/m^2$) } - -The meridional wind stress is the turbulent flux of meridional momentum from -the surface. See section 3.3 for a description of the surface layer parameterization. -\[ -{\bf VFLUX} = - \rho C_D W_s v \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u -\] -where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface -drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum -(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $v$ is -the meridional wind in the lowest model layer. -\\ - -{\bf 3) \underline {HFLUX} Surface Flux of Sensible Heat ($Watts/m^2$) } - -The turbulent flux of sensible heat from the surface to the atmosphere is a function of the -gradient of virtual potential temperature and the eddy exchange coefficient: -\[ -{\bf HFLUX} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{surface} - \theta_{Nrphys}) -\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t -\] -where $\rho$ = the atmospheric density at the surface, $c_{p}$ is the specific -heat of air, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the -magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient -for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient -for heat and moisture (see diagnostic number 9), and $\theta$ is the potential temperature -at the surface and at the bottom model level. -\\ - - -{\bf 4) \underline {EFLUX} Surface Flux of Latent Heat ($Watts/m^2$) } - -The turbulent flux of latent heat from the surface to the atmosphere is a function of the -gradient of moisture, the potential evapotranspiration fraction and the eddy exchange coefficient: -\[ -{\bf EFLUX} = \rho \beta L C_{H} W_s (q_{surface} - q_{Nrphys}) -\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t -\] -where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of -the potential evapotranspiration actually evaporated, L is the latent -heat of evaporation, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the -magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient -for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient -for heat and moisture (see diagnostic number 9), and $q_{surface}$ and $q_{Nrphys}$ are the specific -humidity at the surface and at the bottom model level, respectively. -\\ - -{\bf 5) \underline {QICE} Heat Conduction Through Sea Ice ($Watts/m^2$) } - -Over sea ice there is an additional source of energy at the surface due to the heat -conduction from the relatively warm ocean through the sea ice. The heat conduction -through sea ice represents an additional energy source term for the ground temperature equation. - -\[ -{\bf QICE} = {C_{ti} \over {H_i}} (T_i-T_g) -\] - -where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to -be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and -$T_g$ is the temperature of the sea ice. - -NOTE: QICE is not available through model version 5.3, but is available in subsequent versions. -\\ - - -{\bf 6) \underline {RADLWG} Net upward Longwave Flux at the surface ($Watts/m^2$)} - -\begin{eqnarray*} -{\bf RADLWG} & = & F_{LW,Nrphys+1}^{Net} \\ - & = & F_{LW,Nrphys+1}^\uparrow - F_{LW,Nrphys+1}^\downarrow -\end{eqnarray*} -\\ -where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. -$F_{LW}^\uparrow$ is -the upward Longwave flux and $F_{LW}^\downarrow$ is the downward Longwave flux. -\\ - -{\bf 7) \underline {RADSWG} Net downard shortwave Flux at the surface ($Watts/m^2$)} - -\begin{eqnarray*} -{\bf RADSWG} & = & F_{SW,Nrphys+1}^{Net} \\ - & = & F_{SW,Nrphys+1}^\downarrow - F_{SW,Nrphys+1}^\uparrow -\end{eqnarray*} -\\ -where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. -$F_{SW}^\downarrow$ is -the downward Shortwave flux and $F_{SW}^\uparrow$ is the upward Shortwave flux. -\\ - - -\noindent -{\bf 8) \underline {RI} Richardson Number} ($dimensionless$) - -\noindent -The non-dimensional stability indicator is the ratio of the buoyancy to the shear: -\[ -{\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } - = { {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } -\] -\\ -where we used the hydrostatic equation: -\[ -{\pp{\Phi}{P^ \kappa}} = c_p \theta_v -\] -Negative values indicate unstable buoyancy {\bf{AND}} shear, small positive values ($<0.4$) -indicate dominantly unstable shear, and large positive values indicate dominantly stable -stratification. -\\ - -\noindent -{\bf 9) \underline {CT} Surface Exchange Coefficient for Temperature and Moisture ($dimensionless$) } - -\noindent -The surface exchange coefficient is obtained from the similarity functions for the stability - dependant flux profile relationships: -\[ -{\bf CT} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} = --{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} = -{ k \over { (\psi_{h} + \psi_{g}) } } -\] -where $\psi_h$ is the surface layer non-dimensional temperature change and $\psi_g$ is the -viscous sublayer non-dimensional temperature or moisture change: -\[ -\psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} \hspace{1cm} and -\hspace{1cm} \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} } -(h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2} -\] -and: -$h_{0} = 30z_{0}$ with a maximum value over land of 0.01 - -\noindent -$\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of -the temperature and moisture gradients, specified differently for stable and unstable -layers according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the -non-dimensional stability parameter, Pr is the Prandtl number for air, $\nu$ is the molecular -viscosity, $z_{0}$ is the surface roughness length, $u_*$ is the surface stress velocity -(see diagnostic number 67), and the subscript ref refers to a reference value. -\\ - -\noindent -{\bf 10) \underline {CU} Surface Exchange Coefficient for Momentum ($dimensionless$) } - -\noindent -The surface exchange coefficient is obtained from the similarity functions for the stability - dependant flux profile relationships: -\[ -{\bf CU} = {u_* \over W_s} = { k \over \psi_{m} } -\] -where $\psi_m$ is the surface layer non-dimensional wind shear: -\[ -\psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta} -\] -\noindent -$\phi_m$ is the similarity function of $\zeta$, which expresses the stability dependance of -the temperature and moisture gradients, specified differently for stable and unstable layers -according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the -non-dimensional stability parameter, $u_*$ is the surface stress velocity -(see diagnostic number 67), and $W_s$ is the magnitude of the surface layer wind. -\\ - -\noindent -{\bf 11) \underline {ET} Diffusivity Coefficient for Temperature and Moisture ($m^2/sec$) } - -\noindent -In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat or -moisture flux for the atmosphere above the surface layer can be expressed as a turbulent -diffusion coefficient $K_h$ times the negative of the gradient of potential temperature -or moisture. In the Helfand and Labraga (1988) adaptation of this closure, $K_h$ -takes the form: -\[ -{\bf ET} = K_h = -{( {\overline{w^{\prime}\theta_v^{\prime}}}) \over {\pp{\theta_v}{z}} } - = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) & \mbox{decaying turbulence} -\\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. -\] -where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} -energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, -which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer -depth, -$S_H$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and -wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium -dimensionless buoyancy and wind shear -parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, -are functions of the Richardson number. - -\noindent -For the detailed equations and derivations of the modified level 2.5 closure scheme, -see Helfand and Labraga, 1988. - -\noindent -In the surface layer, ${\bf {ET}}$ is the exchange coefficient for heat and moisture, -in units of $m/sec$, given by: -\[ -{\bf ET_{Nrphys}} = C_t * u_* = C_H W_s -\] -\noindent -where $C_t$ is the dimensionless exchange coefficient for heat and moisture from the -surface layer similarity functions (see diagnostic number 9), $u_*$ is the surface -friction velocity (see diagnostic number 67), $C_H$ is the heat transfer coefficient, -and $W_s$ is the magnitude of the surface layer wind. -\\ - -\noindent -{\bf 12) \underline {EU} Diffusivity Coefficient for Momentum ($m^2/sec$) } - -\noindent -In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat -momentum flux for the atmosphere above the surface layer can be expressed as a turbulent -diffusion coefficient $K_m$ times the negative of the gradient of the u-wind. -In the Helfand and Labraga (1988) adaptation of this closure, $K_m$ -takes the form: -\[ -{\bf EU} = K_m = -{( {\overline{u^{\prime}w^{\prime}}}) \over {\pp{U}{z}} } - = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) & \mbox{decaying turbulence} -\\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. -\] -\noindent -where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} -energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, -which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer -depth, -$S_M$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and -wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium -dimensionless buoyancy and wind shear -parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, -are functions of the Richardson number. - -\noindent -For the detailed equations and derivations of the modified level 2.5 closure scheme, -see Helfand and Labraga, 1988. - -\noindent -In the surface layer, ${\bf {EU}}$ is the exchange coefficient for momentum, -in units of $m/sec$, given by: -\[ -{\bf EU_{Nrphys}} = C_u * u_* = C_D W_s -\] -\noindent -where $C_u$ is the dimensionless exchange coefficient for momentum from the surface layer -similarity functions (see diagnostic number 10), $u_*$ is the surface friction velocity -(see diagnostic number 67), $C_D$ is the surface drag coefficient, and $W_s$ is the -magnitude of the surface layer wind. -\\ - -\noindent -{\bf 13) \underline {TURBU} Zonal U-Momentum changes due to Turbulence ($m/sec/day$) } - -\noindent -The tendency of U-Momentum due to turbulence is written: -\[ -{\bf TURBU} = {\pp{u}{t}}_{turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})} - = {\pp{}{z} }{(K_m \pp{u}{z})} -\] - -\noindent -The Helfand and Labraga level 2.5 scheme models the turbulent -flux of u-momentum in terms of $K_m$, and the equation has the form of a diffusion -equation. - -\noindent -{\bf 14) \underline {TURBV} Meridional V-Momentum changes due to Turbulence ($m/sec/day$) } - -\noindent -The tendency of V-Momentum due to turbulence is written: -\[ -{\bf TURBV} = {\pp{v}{t}}_{turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})} - = {\pp{}{z} }{(K_m \pp{v}{z})} -\] - -\noindent -The Helfand and Labraga level 2.5 scheme models the turbulent -flux of v-momentum in terms of $K_m$, and the equation has the form of a diffusion -equation. -\\ - -\noindent -{\bf 15) \underline {TURBT} Temperature changes due to Turbulence ($deg/day$) } - -\noindent -The tendency of temperature due to turbulence is written: -\[ -{\bf TURBT} = {\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{turb} = -P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})} - = P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})} -\] - -\noindent -The Helfand and Labraga level 2.5 scheme models the turbulent -flux of temperature in terms of $K_h$, and the equation has the form of a diffusion -equation. -\\ - -\noindent -{\bf 16) \underline {TURBQ} Specific Humidity changes due to Turbulence ($g/kg/day$) } - -\noindent -The tendency of specific humidity due to turbulence is written: -\[ -{\bf TURBQ} = {\pp{q}{t}}_{turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})} - = {\pp{}{z} }{(K_h \pp{q}{z})} -\] - -\noindent -The Helfand and Labraga level 2.5 scheme models the turbulent -flux of temperature in terms of $K_h$, and the equation has the form of a diffusion -equation. -\\ - -\noindent -{\bf 17) \underline {MOISTT} Temperature Changes Due to Moist Processes ($deg/day$) } - -\noindent -\[ -{\bf MOISTT} = \left. {\pp{T}{t}}\right|_{c} + \left. {\pp{T}{t}} \right|_{ls} -\] -where: -\[ -\left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over c_p} \Gamma_s \right)_i -\hspace{.4cm} and -\hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = {L \over c_p } (q^*-q) -\] -and -\[ -\Gamma_s = g \eta \pp{s}{p} -\] - -\noindent -The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale -precipitation processes, or supersaturation rain. -The summation refers to contributions from each cloud type called by RAS. -The dry static energy is given -as $s$, the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is -given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, -the description of the convective parameterization. The fractional adjustment, or relaxation -parameter, for each cloud type is given as $\alpha$, while -$R$ is the rain re-evaporation adjustment. -\\ - -\noindent -{\bf 18) \underline {MOISTQ} Specific Humidity Changes Due to Moist Processes ($g/kg/day$) } - -\noindent -\[ -{\bf MOISTQ} = \left. {\pp{q}{t}}\right|_{c} + \left. {\pp{q}{t}} \right|_{ls} -\] -where: -\[ -\left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over {L}}(\Gamma_h-\Gamma_s) \right)_i -\hspace{.4cm} and -\hspace{.4cm} \left.{\pp{q}{t}}\right|_{ls} = (q^*-q) -\] -and -\[ -\Gamma_s = g \eta \pp{s}{p}\hspace{.4cm} and \hspace{.4cm}\Gamma_h = g \eta \pp{h}{p} -\] -\noindent -The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale -precipitation processes, or supersaturation rain. -The summation refers to contributions from each cloud type called by RAS. -The dry static energy is given as $s$, -the moist static energy is given as $h$, -the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is -given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, -the description of the convective parameterization. The fractional adjustment, or relaxation -parameter, for each cloud type is given as $\alpha$, while -$R$ is the rain re-evaporation adjustment. -\\ - -\noindent -{\bf 19) \underline {RADLW} Heating Rate due to Longwave Radiation ($deg/day$) } - -\noindent -The net longwave heating rate is calculated as the vertical divergence of the -net terrestrial radiative fluxes. -Both the clear-sky and cloudy-sky longwave fluxes are computed within the -longwave routine. -The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. -For a given cloud fraction, -the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ -to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, -for the upward and downward radiative fluxes. -(see Section \ref{sec:fizhi:radcloud}). -The cloudy-sky flux is then obtained as: - -\noindent -\[ -F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, -\] - -\noindent -Finally, the net longwave heating rate is calculated as the vertical divergence of the -net terrestrial radiative fluxes: -\[ -\pp{\rho c_p T}{t} = - {\partial \over \partial z} F_{LW}^{NET} , -\] -or -\[ -{\bf RADLW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F_{LW}^{NET} . -\] - -\noindent -where $g$ is the accelation due to gravity, -$c_p$ is the heat capacity of air at constant pressure, -and -\[ -F_{LW}^{NET} = F_{LW}^\uparrow - F_{LW}^\downarrow -\] -\\ - - -\noindent -{\bf 20) \underline {RADSW} Heating Rate due to Shortwave Radiation ($deg/day$) } - -\noindent -The net Shortwave heating rate is calculated as the vertical divergence of the -net solar radiative fluxes. -The clear-sky and cloudy-sky shortwave fluxes are calculated separately. -For the clear-sky case, the shortwave fluxes and heating rates are computed with -both CLMO (maximum overlap cloud fraction) and -CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). -The shortwave routine is then called a second time, for the cloudy-sky case, with the -true time-averaged cloud fractions CLMO -and CLRO being used. In all cases, a normalized incident shortwave flux is used as -input at the top of the atmosphere. - -\noindent -The heating rate due to Shortwave Radiation under cloudy skies is defined as: -\[ -\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT}, -\] -or -\[ -{\bf RADSW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} . -\] - -\noindent -where $g$ is the accelation due to gravity, -$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident -shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and -\[ -F(cloudy)_{SW}^{Net} = F(cloudy)_{SW}^\uparrow - F(cloudy)_{SW}^\downarrow -\] -\\ - -\noindent -{\bf 21) \underline {PREACC} Total (Large-scale + Convective) Accumulated Precipition ($mm/day$) } - -\noindent -For a change in specific humidity due to moist processes, $\Delta q_{moist}$, -the vertical integral or total precipitable amount is given by: -\[ -{\bf PREACC} = \int_{surf}^{top} \rho \Delta q_{moist} dz = - \int_{surf}^{top} \Delta q_{moist} -{dp \over g} = {1 \over g} \int_0^1 \Delta q_{moist} dp -\] -\\ - -\noindent -A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes -time step, scaled to $mm/day$. -\\ - -\noindent -{\bf 22) \underline {PRECON} Convective Precipition ($mm/day$) } - -\noindent -For a change in specific humidity due to sub-grid scale cumulus convective processes, $\Delta q_{cum}$, -the vertical integral or total precipitable amount is given by: -\[ -{\bf PRECON} = \int_{surf}^{top} \rho \Delta q_{cum} dz = - \int_{surf}^{top} \Delta q_{cum} -{dp \over g} = {1 \over g} \int_0^1 \Delta q_{cum} dp -\] -\\ - -\noindent -A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes -time step, scaled to $mm/day$. -\\ - -\noindent -{\bf 23) \underline {TUFLUX} Turbulent Flux of U-Momentum ($Newton/m^2$) } - -\noindent -The turbulent flux of u-momentum is calculated for $diagnostic \hspace{.2cm} purposes - \hspace{.2cm} only$ from the eddy coefficient for momentum: - -\[ -{\bf TUFLUX} = {\rho } {(\overline{u^{\prime}w^{\prime}})} = -{\rho } {(- K_m \pp{U}{z})} -\] - -\noindent -where $\rho$ is the air density, and $K_m$ is the eddy coefficient. -\\ - -\noindent -{\bf 24) \underline {TVFLUX} Turbulent Flux of V-Momentum ($Newton/m^2$) } - -\noindent -The turbulent flux of v-momentum is calculated for $diagnostic \hspace{.2cm} purposes -\hspace{.2cm} only$ from the eddy coefficient for momentum: - -\[ -{\bf TVFLUX} = {\rho } {(\overline{v^{\prime}w^{\prime}})} = - {\rho } {(- K_m \pp{V}{z})} -\] - -\noindent -where $\rho$ is the air density, and $K_m$ is the eddy coefficient. -\\ - - -\noindent -{\bf 25) \underline {TTFLUX} Turbulent Flux of Sensible Heat ($Watts/m^2$) } - -\noindent -The turbulent flux of sensible heat is calculated for $diagnostic \hspace{.2cm} purposes -\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: - -\noindent -\[ -{\bf TTFLUX} = c_p {\rho } -P^{\kappa}{(\overline{w^{\prime}\theta^{\prime}})} - = c_p {\rho } P^{\kappa}{(- K_h \pp{\theta_v}{z})} -\] - -\noindent -where $\rho$ is the air density, and $K_h$ is the eddy coefficient. -\\ - - -\noindent -{\bf 26) \underline {TQFLUX} Turbulent Flux of Latent Heat ($Watts/m^2$) } - -\noindent -The turbulent flux of latent heat is calculated for $diagnostic \hspace{.2cm} purposes -\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: - -\noindent -\[ -{\bf TQFLUX} = {L {\rho } (\overline{w^{\prime}q^{\prime}})} = -{L {\rho }(- K_h \pp{q}{z})} -\] - -\noindent -where $\rho$ is the air density, and $K_h$ is the eddy coefficient. -\\ - - -\noindent -{\bf 27) \underline {CN} Neutral Drag Coefficient ($dimensionless$) } - -\noindent -The drag coefficient for momentum obtained by assuming a neutrally stable surface layer: -\[ -{\bf CN} = { k \over { \ln({h \over {z_0}})} } -\] - -\noindent -where $k$ is the Von Karman constant, $h$ is the height of the surface layer, and -$z_0$ is the surface roughness. - -\noindent -NOTE: CN is not available through model version 5.3, but is available in subsequent -versions. -\\ - -\noindent -{\bf 28) \underline {WINDS} Surface Wind Speed ($meter/sec$) } - -\noindent -The surface wind speed is calculated for the last internal turbulence time step: -\[ -{\bf WINDS} = \sqrt{u_{Nrphys}^2 + v_{Nrphys}^2} -\] - -\noindent -where the subscript $Nrphys$ refers to the lowest model level. -\\ - -\noindent -{\bf 29) \underline {DTSRF} Air/Surface Virtual Temperature Difference ($deg \hspace{.1cm} K$) } - -\noindent -The air/surface virtual temperature difference measures the stability of the surface layer: -\[ -{\bf DTSRF} = (\theta_{v{Nrphys+1}} - \theta{v_{Nrphys}}) P^{\kappa}_{surf} -\] -\noindent -where -\[ -\theta_{v{Nrphys+1}} = { T_g \over {P^{\kappa}_{surf}} } (1 + .609 q_{Nrphys+1}) \hspace{1cm} -and \hspace{1cm} q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) -\] - -\noindent -$\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), -$q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature -and surface pressure, level $Nrphys$ refers to the lowest model level and level $Nrphys+1$ -refers to the surface. -\\ - - -\noindent -{\bf 30) \underline {TG} Ground Temperature ($deg \hspace{.1cm} K$) } - -\noindent -The ground temperature equation is solved as part of the turbulence package -using a backward implicit time differencing scheme: -\[ -{\bf TG} \hspace{.1cm} is \hspace{.1cm} obtained \hspace{.1cm} from: \hspace{.1cm} -C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{ice} - H - LE -\] - -\noindent -where $R_{sw}$ is the net surface downward shortwave radiative flux, $R_{lw}$ is the -net surface upward longwave radiative flux, $Q_{ice}$ is the heat conduction through -sea ice, $H$ is the upward sensible heat flux, $LE$ is the upward latent heat -flux, and $C_g$ is the total heat capacity of the ground. -$C_g$ is obtained by solving a heat diffusion equation -for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by: -\[ -C_g = \sqrt{ {\lambda C_s \over {2 \omega} } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3} -{ 86400. \over {2 \pi} } } \, \, . -\] -\noindent -Here, the thermal conductivity, $\lambda$, is equal to $2x10^{-3}$ ${ly\over{ sec}} -{cm \over {^oK}}$, -the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided -by $2 \pi$ $radians/ -day$, and the expression for $C_s$, the heat capacity per unit volume at the surface, -is a function of the ground wetness, $W$. -\\ - -\noindent -{\bf 31) \underline {TS} Surface Temperature ($deg \hspace{.1cm} K$) } - -\noindent -The surface temperature estimate is made by assuming that the model's lowest -layer is well-mixed, and therefore that $\theta$ is constant in that layer. -The surface temperature is therefore: -\[ -{\bf TS} = \theta_{Nrphys} P^{\kappa}_{surf} -\] -\\ - -\noindent -{\bf 32) \underline {DTG} Surface Temperature Adjustment ($deg \hspace{.1cm} K$) } - -\noindent -The change in surface temperature from one turbulence time step to the next, solved -using the Ground Temperature Equation (see diagnostic number 30) is calculated: -\[ -{\bf DTG} = {T_g}^{n} - {T_g}^{n-1} -\] - -\noindent -where superscript $n$ refers to the new, updated time level, and the superscript $n-1$ -refers to the value at the previous turbulence time level. -\\ - -\noindent -{\bf 33) \underline {QG} Ground Specific Humidity ($g/kg$) } - -\noindent -The ground specific humidity is obtained by interpolating between the specific -humidity at the lowest model level and the specific humidity of a saturated ground. -The interpolation is performed using the potential evapotranspiration function: -\[ -{\bf QG} = q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) -\] - -\noindent -where $\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), -and $q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature and surface -pressure. -\\ - -\noindent -{\bf 34) \underline {QS} Saturation Surface Specific Humidity ($g/kg$) } - -\noindent -The surface saturation specific humidity is the saturation specific humidity at -the ground temprature and surface pressure: -\[ -{\bf QS} = q^*(T_g,P_s) -\] -\\ - -\noindent -{\bf 35) \underline {TGRLW} Instantaneous ground temperature used as input to the Longwave - radiation subroutine (deg)} -\[ -{\bf TGRLW} = T_g(\lambda , \phi ,n) -\] -\noindent -where $T_g$ is the model ground temperature at the current time step $n$. -\\ - - -\noindent -{\bf 36) \underline {ST4} Upward Longwave flux at the surface ($Watts/m^2$) } -\[ -{\bf ST4} = \sigma T^4 -\] -\noindent -where $\sigma$ is the Stefan-Boltzmann constant and T is the temperature. -\\ - -\noindent -{\bf 37) \underline {OLR} Net upward Longwave flux at $p=p_{top}$ ($Watts/m^2$) } -\[ -{\bf OLR} = F_{LW,top}^{NET} -\] -\noindent -where top indicates the top of the first model layer. -In the GCM, $p_{top}$ = 0.0 mb. -\\ - - -\noindent -{\bf 38) \underline {OLRCLR} Net upward clearsky Longwave flux at $p=p_{top}$ ($Watts/m^2$) } -\[ -{\bf OLRCLR} = F(clearsky)_{LW,top}^{NET} -\] -\noindent -where top indicates the top of the first model layer. -In the GCM, $p_{top}$ = 0.0 mb. -\\ - -\noindent -{\bf 39) \underline {LWGCLR} Net upward clearsky Longwave flux at the surface ($Watts/m^2$) } - -\noindent -\begin{eqnarray*} -{\bf LWGCLR} & = & F(clearsky)_{LW,Nrphys+1}^{Net} \\ - & = & F(clearsky)_{LW,Nrphys+1}^\uparrow - F(clearsky)_{LW,Nrphys+1}^\downarrow -\end{eqnarray*} -where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. -$F(clearsky)_{LW}^\uparrow$ is -the upward clearsky Longwave flux and the $F(clearsky)_{LW}^\downarrow$ is the downward clearsky Longwave flux. -\\ - -\noindent -{\bf 40) \underline {LWCLR} Heating Rate due to Clearsky Longwave Radiation ($deg/day$) } - -\noindent -The net longwave heating rate is calculated as the vertical divergence of the -net terrestrial radiative fluxes. -Both the clear-sky and cloudy-sky longwave fluxes are computed within the -longwave routine. -The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. -For a given cloud fraction, -the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ -to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, -for the upward and downward radiative fluxes. -(see Section \ref{sec:fizhi:radcloud}). -The cloudy-sky flux is then obtained as: - -\noindent -\[ -F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, -\] - -\noindent -Thus, {\bf LWCLR} is defined as the net longwave heating rate due to the -vertical divergence of the -clear-sky longwave radiative flux: -\[ -\pp{\rho c_p T}{t}_{clearsky} = - {\partial \over \partial z} F(clearsky)_{LW}^{NET} , -\] -or -\[ -{\bf LWCLR} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(clearsky)_{LW}^{NET} . -\] - -\noindent -where $g$ is the accelation due to gravity, -$c_p$ is the heat capacity of air at constant pressure, -and -\[ -F(clearsky)_{LW}^{Net} = F(clearsky)_{LW}^\uparrow - F(clearsky)_{LW}^\downarrow -\] -\\ - - -\noindent -{\bf 41) \underline {TLW} Instantaneous temperature used as input to the Longwave - radiation subroutine (deg)} -\[ -{\bf TLW} = T(\lambda , \phi ,level, n) -\] -\noindent -where $T$ is the model temperature at the current time step $n$. -\\ - - -\noindent -{\bf 42) \underline {SHLW} Instantaneous specific humidity used as input to - the Longwave radiation subroutine (kg/kg)} -\[ -{\bf SHLW} = q(\lambda , \phi , level , n) -\] -\noindent -where $q$ is the model specific humidity at the current time step $n$. -\\ - - -\noindent -{\bf 43) \underline {OZLW} Instantaneous ozone used as input to - the Longwave radiation subroutine (kg/kg)} -\[ -{\bf OZLW} = {\rm OZ}(\lambda , \phi , level , n) -\] -\noindent -where $\rm OZ$ is the interpolated ozone data set from the climatological monthly -mean zonally averaged ozone data set. -\\ - - -\noindent -{\bf 44) \underline {CLMOLW} Maximum Overlap cloud fraction used in LW Radiation ($0-1$) } - -\noindent -{\bf CLMOLW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed -Arakawa/Schubert Convection scheme and will be used in the Longwave Radiation algorithm. These are -convective clouds whose radiative characteristics are assumed to be correlated in the vertical. -For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. -\[ -{\bf CLMOLW} = CLMO_{RAS,LW}(\lambda, \phi, level ) -\] -\\ - - -{\bf 45) \underline {CLDTOT} Total cloud fraction used in LW and SW Radiation ($0-1$) } - -{\bf CLDTOT} is the time-averaged total cloud fraction that has been filled by the Relaxed -Arakawa/Schubert and Large-scale Convection schemes and will be used in the Longwave and Shortwave -Radiation packages. -For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. -\[ -{\bf CLDTOT} = F_{RAS} + F_{LS} -\] -\\ -where $F_{RAS}$ is the time-averaged cloud fraction due to sub-grid scale convection, and $F_{LS}$ is the -time-averaged cloud fraction due to precipitating and non-precipitating large-scale moist processes. -\\ - - -\noindent -{\bf 46) \underline {CLMOSW} Maximum Overlap cloud fraction used in SW Radiation ($0-1$) } - -\noindent -{\bf CLMOSW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed -Arakawa/Schubert Convection scheme and will be used in the Shortwave Radiation algorithm. These are -convective clouds whose radiative characteristics are assumed to be correlated in the vertical. -For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. -\[ -{\bf CLMOSW} = CLMO_{RAS,SW}(\lambda, \phi, level ) -\] -\\ - -\noindent -{\bf 47) \underline {CLROSW} Random Overlap cloud fraction used in SW Radiation ($0-1$) } - -\noindent -{\bf CLROSW} is the time-averaged random overlap cloud fraction that has been filled by the Relaxed -Arakawa/Schubert and Large-scale Convection schemes and will be used in the Shortwave -Radiation algorithm. These are -convective and large-scale clouds whose radiative characteristics are not -assumed to be correlated in the vertical. -For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. -\[ -{\bf CLROSW} = CLRO_{RAS,Large Scale,SW}(\lambda, \phi, level ) -\] -\\ - -\noindent -{\bf 48) \underline {RADSWT} Incident Shortwave radiation at the top of the atmosphere ($Watts/m^2$) } -\[ -{\bf RADSWT} = {\frac{S_0}{R_a^2}} \cdot cos \phi_z -\] -\noindent -where $S_0$, is the extra-terrestial solar contant, -$R_a$ is the earth-sun distance in Astronomical Units, -and $cos \phi_z$ is the cosine of the zenith angle. -It should be noted that {\bf RADSWT}, as well as -{\bf OSR} and {\bf OSRCLR}, -are calculated at the top of the atmosphere (p=0 mb). However, the -{\bf OLR} and {\bf OLRCLR} diagnostics are currently -calculated at $p= p_{top}$ (0.0 mb for the GCM). -\\ - -\noindent -{\bf 49) \underline {EVAP} Surface Evaporation ($mm/day$) } - -\noindent -The surface evaporation is a function of the gradient of moisture, the potential -evapotranspiration fraction and the eddy exchange coefficient: -\[ -{\bf EVAP} = \rho \beta K_{h} (q_{surface} - q_{Nrphys}) -\] -where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of -the potential evapotranspiration actually evaporated ($\beta=1$ over oceans), $K_{h}$ is the -turbulent eddy exchange coefficient for heat and moisture at the surface in $m/sec$ and -$q{surface}$ and $q_{Nrphys}$ are the specific humidity at the surface (see diagnostic -number 34) and at the bottom model level, respectively. -\\ - -\noindent -{\bf 50) \underline {DUDT} Total Zonal U-Wind Tendency ($m/sec/day$) } - -\noindent -{\bf DUDT} is the total time-tendency of the Zonal U-Wind due to Hydrodynamic, Diabatic, -and Analysis forcing. -\[ -{\bf DUDT} = \pp{u}{t}_{Dynamics} + \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} -\] -\\ - -\noindent -{\bf 51) \underline {DVDT} Total Zonal V-Wind Tendency ($m/sec/day$) } - -\noindent -{\bf DVDT} is the total time-tendency of the Meridional V-Wind due to Hydrodynamic, Diabatic, -and Analysis forcing. -\[ -{\bf DVDT} = \pp{v}{t}_{Dynamics} + \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} -\] -\\ - -\noindent -{\bf 52) \underline {DTDT} Total Temperature Tendency ($deg/day$) } - -\noindent -{\bf DTDT} is the total time-tendency of Temperature due to Hydrodynamic, Diabatic, -and Analysis forcing. -\begin{eqnarray*} -{\bf DTDT} & = & \pp{T}{t}_{Dynamics} + \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ - & + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} -\end{eqnarray*} -\\ - -\noindent -{\bf 53) \underline {DQDT} Total Specific Humidity Tendency ($g/kg/day$) } - -\noindent -{\bf DQDT} is the total time-tendency of Specific Humidity due to Hydrodynamic, Diabatic, -and Analysis forcing. -\[ -{\bf DQDT} = \pp{q}{t}_{Dynamics} + \pp{q}{t}_{Moist Processes} -+ \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} -\] -\\ - -\noindent -{\bf 54) \underline {USTAR} Surface-Stress Velocity ($m/sec$) } - -\noindent -The surface stress velocity, or the friction velocity, is the wind speed at -the surface layer top impeded by the surface drag: -\[ -{\bf USTAR} = C_uW_s \hspace{1cm}where: \hspace{.2cm} -C_u = {k \over {\psi_m} } -\] - -\noindent -$C_u$ is the non-dimensional surface drag coefficient (see diagnostic -number 10), and $W_s$ is the surface wind speed (see diagnostic number 28). - -\noindent -{\bf 55) \underline {Z0} Surface Roughness Length ($m$) } - -\noindent -Over the land surface, the surface roughness length is interpolated to the local -time from the monthly mean data of Dorman and Sellers (1989). Over the ocean, -the roughness length is a function of the surface-stress velocity, $u_*$. -\[ -{\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}} -\] - -\noindent -where the constants are chosen to interpolate between the reciprocal relation of -Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981) -for moderate to large winds. -\\ - -\noindent -{\bf 56) \underline {FRQTRB} Frequency of Turbulence ($0-1$) } - -\noindent -The fraction of time when turbulence is present is defined as the fraction of -time when the turbulent kinetic energy exceeds some minimum value, defined here -to be $0.005 \hspace{.1cm}m^2/sec^2$. When this criterion is met, a counter is -incremented. The fraction over the averaging interval is reported. -\\ - -\noindent -{\bf 57) \underline {PBL} Planetary Boundary Layer Depth ($mb$) } - -\noindent -The depth of the PBL is defined by the turbulence parameterization to be the -depth at which the turbulent kinetic energy reduces to ten percent of its surface -value. - -\[ -{\bf PBL} = P_{PBL} - P_{surface} -\] - -\noindent -where $P_{PBL}$ is the pressure in $mb$ at which the turbulent kinetic energy -reaches one tenth of its surface value, and $P_s$ is the surface pressure. -\\ - -\noindent -{\bf 58) \underline {SWCLR} Clear sky Heating Rate due to Shortwave Radiation ($deg/day$) } - -\noindent -The net Shortwave heating rate is calculated as the vertical divergence of the -net solar radiative fluxes. -The clear-sky and cloudy-sky shortwave fluxes are calculated separately. -For the clear-sky case, the shortwave fluxes and heating rates are computed with -both CLMO (maximum overlap cloud fraction) and -CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). -The shortwave routine is then called a second time, for the cloudy-sky case, with the -true time-averaged cloud fractions CLMO -and CLRO being used. In all cases, a normalized incident shortwave flux is used as -input at the top of the atmosphere. - -\noindent -The heating rate due to Shortwave Radiation under clear skies is defined as: -\[ -\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT}, -\] -or -\[ -{\bf SWCLR} = \frac{g}{c_p } {\partial \over \partial p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} . -\] - -\noindent -where $g$ is the accelation due to gravity, -$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident -shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and -\[ -F(clear)_{SW}^{Net} = F(clear)_{SW}^\uparrow - F(clear)_{SW}^\downarrow -\] -\\ - -\noindent -{\bf 59) \underline {OSR} Net upward Shortwave flux at the top of the model ($Watts/m^2$) } -\[ -{\bf OSR} = F_{SW,top}^{NET} -\] -\noindent -where top indicates the top of the first model layer used in the shortwave radiation -routine. -In the GCM, $p_{SW_{top}}$ = 0 mb. -\\ - -\noindent -{\bf 60) \underline {OSRCLR} Net upward clearsky Shortwave flux at the top of the model ($Watts/m^2$) } -\[ -{\bf OSRCLR} = F(clearsky)_{SW,top}^{NET} -\] -\noindent -where top indicates the top of the first model layer used in the shortwave radiation -routine. -In the GCM, $p_{SW_{top}}$ = 0 mb. -\\ - - -\noindent -{\bf 61) \underline {CLDMAS} Convective Cloud Mass Flux ($kg/m^2$) } - -\noindent -The amount of cloud mass moved per RAS timestep from all convective clouds is written: -\[ -{\bf CLDMAS} = \eta m_B -\] -where $\eta$ is the entrainment, normalized by the cloud base mass flux, and $m_B$ is -the cloud base mass flux. $m_B$ and $\eta$ are defined explicitly in Section \ref{sec:fizhi:mc}, the -description of the convective parameterization. -\\ - - - -\noindent -{\bf 62) \underline {UAVE} Time-Averaged Zonal U-Wind ($m/sec$) } - -\noindent -The diagnostic {\bf UAVE} is simply the time-averaged Zonal U-Wind over -the {\bf NUAVE} output frequency. This is contrasted to the instantaneous -Zonal U-Wind which is archived on the Prognostic Output data stream. -\[ -{\bf UAVE} = u(\lambda, \phi, level , t) -\] -\\ -Note, {\bf UAVE} is computed and stored on the staggered C-grid. -\\ - -\noindent -{\bf 63) \underline {VAVE} Time-Averaged Meridional V-Wind ($m/sec$) } - -\noindent -The diagnostic {\bf VAVE} is simply the time-averaged Meridional V-Wind over -the {\bf NVAVE} output frequency. This is contrasted to the instantaneous -Meridional V-Wind which is archived on the Prognostic Output data stream. -\[ -{\bf VAVE} = v(\lambda, \phi, level , t) -\] -\\ -Note, {\bf VAVE} is computed and stored on the staggered C-grid. -\\ - -\noindent -{\bf 64) \underline {TAVE} Time-Averaged Temperature ($Kelvin$) } - -\noindent -The diagnostic {\bf TAVE} is simply the time-averaged Temperature over -the {\bf NTAVE} output frequency. This is contrasted to the instantaneous -Temperature which is archived on the Prognostic Output data stream. -\[ -{\bf TAVE} = T(\lambda, \phi, level , t) -\] -\\ - -\noindent -{\bf 65) \underline {QAVE} Time-Averaged Specific Humidity ($g/kg$) } - -\noindent -The diagnostic {\bf QAVE} is simply the time-averaged Specific Humidity over -the {\bf NQAVE} output frequency. This is contrasted to the instantaneous -Specific Humidity which is archived on the Prognostic Output data stream. -\[ -{\bf QAVE} = q(\lambda, \phi, level , t) -\] -\\ - -\noindent -{\bf 66) \underline {PAVE} Time-Averaged Surface Pressure - PTOP ($mb$) } - -\noindent -The diagnostic {\bf PAVE} is simply the time-averaged Surface Pressure - PTOP over -the {\bf NPAVE} output frequency. This is contrasted to the instantaneous -Surface Pressure - PTOP which is archived on the Prognostic Output data stream. -\begin{eqnarray*} -{\bf PAVE} & = & \pi(\lambda, \phi, level , t) \\ - & = & p_s(\lambda, \phi, level , t) - p_T -\end{eqnarray*} -\\ - - -\noindent -{\bf 67) \underline {QQAVE} Time-Averaged Turbulent Kinetic Energy $(m/sec)^2$ } - -\noindent -The diagnostic {\bf QQAVE} is simply the time-averaged prognostic Turbulent Kinetic Energy -produced by the GCM Turbulence parameterization over -the {\bf NQQAVE} output frequency. This is contrasted to the instantaneous -Turbulent Kinetic Energy which is archived on the Prognostic Output data stream. -\[ -{\bf QQAVE} = qq(\lambda, \phi, level , t) -\] -\\ -Note, {\bf QQAVE} is computed and stored at the ``mass-point'' locations on the staggered C-grid. -\\ - -\noindent -{\bf 68) \underline {SWGCLR} Net downward clearsky Shortwave flux at the surface ($Watts/m^2$) } - -\noindent -\begin{eqnarray*} -{\bf SWGCLR} & = & F(clearsky)_{SW,Nrphys+1}^{Net} \\ - & = & F(clearsky)_{SW,Nrphys+1}^\downarrow - F(clearsky)_{SW,Nrphys+1}^\uparrow -\end{eqnarray*} -\noindent -\\ -where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. -$F(clearsky){SW}^\downarrow$ is -the downward clearsky Shortwave flux and $F(clearsky)_{SW}^\uparrow$ is -the upward clearsky Shortwave flux. -\\ - -\noindent -{\bf 69) \underline {SDIAG1} User-Defined Surface Diagnostic-1 } - -\noindent -The GCM provides Users with a built-in mechanism for archiving user-defined -diagnostics. The generic diagnostic array QDIAG located in COMMON /DIAG/, and the associated -diagnostic counters and pointers located in COMMON /DIAGP/, -must be accessable in order to use the user-defined diagnostics (see Section \ref{sec:diagnostics:diagover}). -A convenient method for incorporating all necessary COMMON files is to -include the GCM {\em vstate.com} file in the routine which employs the -user-defined diagnostics. - -\noindent -In addition to enabling the user-defined diagnostic (ie., CALL SETDIAG(84)), the User must fill -the QDIAG array with the desired quantity within the User's -application program or within modified GCM subroutines, as well as increment -the diagnostic counter at the time when the diagnostic is updated. -The QDIAG location index for {\bf SDIAG1} and its corresponding counter is -automatically defined as {\bf ISDIAG1} and {\bf NSDIAG1}, respectively, after the -diagnostic has been enabled. -The syntax for its use is given by -\begin{verbatim} - do j=1,jm - do i=1,im - qdiag(i,j,ISDIAG1) = qdiag(i,j,ISDIAG1) + ... - enddo - enddo - - NSDIAG1 = NSDIAG1 + 1 -\end{verbatim} -The diagnostics defined in this manner will automatically be archived by the output routines. -\\ - -\noindent -{\bf 70) \underline {SDIAG2} User-Defined Surface Diagnostic-2 } - -\noindent -The GCM provides Users with a built-in mechanism for archiving user-defined -diagnostics. For a complete description refer to Diagnostic \#84. -The syntax for using the surface SDIAG2 diagnostic is given by -\begin{verbatim} - do j=1,jm - do i=1,im - qdiag(i,j,ISDIAG2) = qdiag(i,j,ISDIAG2) + ... - enddo - enddo - - NSDIAG2 = NSDIAG2 + 1 -\end{verbatim} -The diagnostics defined in this manner will automatically be archived by the output routines. -\\ - -\noindent -{\bf 71) \underline {UDIAG1} User-Defined Upper-Air Diagnostic-1 } - -\noindent -The GCM provides Users with a built-in mechanism for archiving user-defined -diagnostics. For a complete description refer to Diagnostic \#84. -The syntax for using the upper-air UDIAG1 diagnostic is given by -\begin{verbatim} - do L=1,Nrphys - do j=1,jm - do i=1,im - qdiag(i,j,IUDIAG1+L-1) = qdiag(i,j,IUDIAG1+L-1) + ... - enddo - enddo - enddo - - NUDIAG1 = NUDIAG1 + 1 -\end{verbatim} -The diagnostics defined in this manner will automatically be archived by the -output programs. -\\ - -\noindent -{\bf 72) \underline {UDIAG2} User-Defined Upper-Air Diagnostic-2 } - -\noindent -The GCM provides Users with a built-in mechanism for archiving user-defined -diagnostics. For a complete description refer to Diagnostic \#84. -The syntax for using the upper-air UDIAG2 diagnostic is given by -\begin{verbatim} - do L=1,Nrphys - do j=1,jm - do i=1,im - qdiag(i,j,IUDIAG2+L-1) = qdiag(i,j,IUDIAG2+L-1) + ... - enddo - enddo - enddo - - NUDIAG2 = NUDIAG2 + 1 -\end{verbatim} -The diagnostics defined in this manner will automatically be archived by the -output programs. -\\ - - -\noindent -{\bf 73) \underline {DIABU} Total Diabatic Zonal U-Wind Tendency ($m/sec/day$) } - -\noindent -{\bf DIABU} is the total time-tendency of the Zonal U-Wind due to Diabatic processes -and the Analysis forcing. -\[ -{\bf DIABU} = \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} -\] -\\ - -\noindent -{\bf 74) \underline {DIABV} Total Diabatic Meridional V-Wind Tendency ($m/sec/day$) } - -\noindent -{\bf DIABV} is the total time-tendency of the Meridional V-Wind due to Diabatic processes -and the Analysis forcing. -\[ -{\bf DIABV} = \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} -\] -\\ - -\noindent -{\bf 75) \underline {DIABT} Total Diabatic Temperature Tendency ($deg/day$) } - -\noindent -{\bf DIABT} is the total time-tendency of Temperature due to Diabatic processes -and the Analysis forcing. -\begin{eqnarray*} -{\bf DIABT} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ - & + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} -\end{eqnarray*} -\\ -If we define the time-tendency of Temperature due to Diabatic processes as -\begin{eqnarray*} -\pp{T}{t}_{Diabatic} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ - & + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} -\end{eqnarray*} -then, since there are no surface pressure changes due to Diabatic processes, we may write -\[ -\pp{T}{t}_{Diabatic} = {p^\kappa \over \pi }\pp{\pi \theta}{t}_{Diabatic} -\] -where $\theta = T/p^\kappa$. Thus, {\bf DIABT} may be written as -\[ -{\bf DIABT} = {p^\kappa \over \pi } \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right) -\] -\\ - -\noindent -{\bf 76) \underline {DIABQ} Total Diabatic Specific Humidity Tendency ($g/kg/day$) } - -\noindent -{\bf DIABQ} is the total time-tendency of Specific Humidity due to Diabatic processes -and the Analysis forcing. -\[ -{\bf DIABQ} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} -\] -If we define the time-tendency of Specific Humidity due to Diabatic processes as -\[ -\pp{q}{t}_{Diabatic} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} -\] -then, since there are no surface pressure changes due to Diabatic processes, we may write -\[ -\pp{q}{t}_{Diabatic} = {1 \over \pi }\pp{\pi q}{t}_{Diabatic} -\] -Thus, {\bf DIABQ} may be written as -\[ -{\bf DIABQ} = {1 \over \pi } \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right) -\] -\\ - -\noindent -{\bf 77) \underline {VINTUQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } - -\noindent -The vertically integrated moisture flux due to the zonal u-wind is obtained by integrating -$u q$ over the depth of the atmosphere at each model timestep, -and dividing by the total mass of the column. -\[ -{\bf VINTUQ} = \frac{ \int_{surf}^{top} u q \rho dz } { \int_{surf}^{top} \rho dz } -\] -Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have -\[ -{\bf VINTUQ} = { \int_0^1 u q dp } -\] -\\ - - -\noindent -{\bf 78) \underline {VINTVQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } - -\noindent -The vertically integrated moisture flux due to the meridional v-wind is obtained by integrating -$v q$ over the depth of the atmosphere at each model timestep, -and dividing by the total mass of the column. -\[ -{\bf VINTVQ} = \frac{ \int_{surf}^{top} v q \rho dz } { \int_{surf}^{top} \rho dz } -\] -Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have -\[ -{\bf VINTVQ} = { \int_0^1 v q dp } -\] -\\ - - -\noindent -{\bf 79) \underline {VINTUT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } - -\noindent -The vertically integrated heat flux due to the zonal u-wind is obtained by integrating -$u T$ over the depth of the atmosphere at each model timestep, -and dividing by the total mass of the column. -\[ -{\bf VINTUT} = \frac{ \int_{surf}^{top} u T \rho dz } { \int_{surf}^{top} \rho dz } -\] -Or, -\[ -{\bf VINTUT} = { \int_0^1 u T dp } -\] -\\ - -\noindent -{\bf 80) \underline {VINTVT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } - -\noindent -The vertically integrated heat flux due to the meridional v-wind is obtained by integrating -$v T$ over the depth of the atmosphere at each model timestep, -and dividing by the total mass of the column. -\[ -{\bf VINTVT} = \frac{ \int_{surf}^{top} v T \rho dz } { \int_{surf}^{top} \rho dz } -\] -Using $\rho \delta z = -{\delta p \over g} $, we have -\[ -{\bf VINTVT} = { \int_0^1 v T dp } -\] -\\ - -\noindent -{\bf 81 \underline {CLDFRC} Total 2-Dimensional Cloud Fracton ($0-1$) } - -If we define the -time-averaged random and maximum overlapped cloudiness as CLRO and -CLMO respectively, then the probability of clear sky associated -with random overlapped clouds at any level is (1-CLRO) while the probability of -clear sky associated with maximum overlapped clouds at any level is (1-CLMO). -The total clear sky probability is given by (1-CLRO)*(1-CLMO), thus -the total cloud fraction at each level may be obtained by -1-(1-CLRO)*(1-CLMO). - -At any given level, we may define the clear line-of-site probability by -appropriately accounting for the maximum and random overlap -cloudiness. The clear line-of-site probability is defined to be -equal to the product of the clear line-of-site probabilities -associated with random and maximum overlap cloudiness. The clear -line-of-site probability $C(p,p^{\prime})$ associated with maximum overlap clouds, -from the current pressure $p$ -to the model top pressure, $p^{\prime} = p_{top}$, or the model surface pressure, $p^{\prime} = p_{surf}$, -is simply 1.0 minus the largest maximum overlap cloud value along the -line-of-site, ie. - -$$1-MAX_p^{p^{\prime}} \left( CLMO_p \right)$$ - -Thus, even in the time-averaged sense it is assumed that the -maximum overlap clouds are correlated in the vertical. The clear -line-of-site probability associated with random overlap clouds is -defined to be the product of the clear sky probabilities at each -level along the line-of-site, ie. - -$$\prod_{p}^{p^{\prime}} \left( 1-CLRO_p \right)$$ - -The total cloud fraction at a given level associated with a line- -of-site calculation is given by - -$$1-\left( 1-MAX_p^{p^{\prime}} \left[ CLMO_p \right] \right) - \prod_p^{p^{\prime}} \left( 1-CLRO_p \right)$$ - - -\noindent -The 2-dimensional net cloud fraction as seen from the top of the -atmosphere is given by -\[ -{\bf CLDFRC} = 1-\left( 1-MAX_{l=l_1}^{Nrphys} \left[ CLMO_l \right] \right) - \prod_{l=l_1}^{Nrphys} \left( 1-CLRO_l \right) -\] -\\ -For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. - - -\noindent -{\bf 82) \underline {QINT} Total Precipitable Water ($gm/cm^2$) } - -\noindent -The Total Precipitable Water is defined as the vertical integral of the specific humidity, -given by: -\begin{eqnarray*} -{\bf QINT} & = & \int_{surf}^{top} \rho q dz \\ - & = & {\pi \over g} \int_0^1 q dp -\end{eqnarray*} -where we have used the hydrostatic relation -$\rho \delta z = -{\delta p \over g} $. -\\ - - -\noindent -{\bf 83) \underline {U2M} Zonal U-Wind at 2 Meter Depth ($m/sec$) } - -\noindent -The u-wind at the 2-meter depth is determined from the similarity theory: -\[ -{\bf U2M} = {u_* \over k} \psi_{m_{2m}} {u_{sl} \over {W_s}} = -{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}u_{sl} -\] - -\noindent -where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript -$sl$ refers to the height of the top of the surface layer. If the roughness height -is above two meters, ${\bf U2M}$ is undefined. -\\ - -\noindent -{\bf 84) \underline {V2M} Meridional V-Wind at 2 Meter Depth ($m/sec$) } - -\noindent -The v-wind at the 2-meter depth is a determined from the similarity theory: -\[ -{\bf V2M} = {u_* \over k} \psi_{m_{2m}} {v_{sl} \over {W_s}} = -{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}v_{sl} -\] - -\noindent -where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript -$sl$ refers to the height of the top of the surface layer. If the roughness height -is above two meters, ${\bf V2M}$ is undefined. -\\ - -\noindent -{\bf 85) \underline {T2M} Temperature at 2 Meter Depth ($deg \hspace{.1cm} K$) } - -\noindent -The temperature at the 2-meter depth is a determined from the similarity theory: -\[ -{\bf T2M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) = -P^{\kappa}(\theta_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } -(\theta_{sl} - \theta_{surf})) -\] -where: -\[ -\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } -\] - -\noindent -where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is -the non-dimensional temperature gradient in the viscous sublayer, and the subscript -$sl$ refers to the height of the top of the surface layer. If the roughness height -is above two meters, ${\bf T2M}$ is undefined. -\\ - -\noindent -{\bf 86) \underline {Q2M} Specific Humidity at 2 Meter Depth ($g/kg$) } - -\noindent -The specific humidity at the 2-meter depth is determined from the similarity theory: -\[ -{\bf Q2M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) = -P^{\kappa}(q_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } -(q_{sl} - q_{surf})) -\] -where: -\[ -q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } -\] - -\noindent -where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is -the non-dimensional temperature gradient in the viscous sublayer, and the subscript -$sl$ refers to the height of the top of the surface layer. If the roughness height -is above two meters, ${\bf Q2M}$ is undefined. -\\ - -\noindent -{\bf 87) \underline {U10M} Zonal U-Wind at 10 Meter Depth ($m/sec$) } - -\noindent -The u-wind at the 10-meter depth is an interpolation between the surface wind -and the model lowest level wind using the ratio of the non-dimensional wind shear -at the two levels: -\[ -{\bf U10M} = {u_* \over k} \psi_{m_{10m}} {u_{sl} \over {W_s}} = -{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}u_{sl} -\] - -\noindent -where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript -$sl$ refers to the height of the top of the surface layer. -\\ - -\noindent -{\bf 88) \underline {V10M} Meridional V-Wind at 10 Meter Depth ($m/sec$) } - -\noindent -The v-wind at the 10-meter depth is an interpolation between the surface wind -and the model lowest level wind using the ratio of the non-dimensional wind shear -at the two levels: -\[ -{\bf V10M} = {u_* \over k} \psi_{m_{10m}} {v_{sl} \over {W_s}} = -{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}v_{sl} -\] - -\noindent -where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript -$sl$ refers to the height of the top of the surface layer. -\\ - -\noindent -{\bf 89) \underline {T10M} Temperature at 10 Meter Depth ($deg \hspace{.1cm} K$) } - -\noindent -The temperature at the 10-meter depth is an interpolation between the surface potential -temperature and the model lowest level potential temperature using the ratio of the -non-dimensional temperature gradient at the two levels: -\[ -{\bf T10M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) = -P^{\kappa}(\theta_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } -(\theta_{sl} - \theta_{surf})) -\] -where: -\[ -\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } -\] - -\noindent -where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is -the non-dimensional temperature gradient in the viscous sublayer, and the subscript -$sl$ refers to the height of the top of the surface layer. -\\ - -\noindent -{\bf 90) \underline {Q10M} Specific Humidity at 10 Meter Depth ($g/kg$) } - -\noindent -The specific humidity at the 10-meter depth is an interpolation between the surface specific -humidity and the model lowest level specific humidity using the ratio of the -non-dimensional temperature gradient at the two levels: -\[ -{\bf Q10M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) = -P^{\kappa}(q_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } -(q_{sl} - q_{surf})) -\] -where: -\[ -q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } -\] - -\noindent -where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is -the non-dimensional temperature gradient in the viscous sublayer, and the subscript -$sl$ refers to the height of the top of the surface layer. -\\ - -\noindent -{\bf 91) \underline {DTRAIN} Cloud Detrainment Mass Flux ($kg/m^2$) } - -The amount of cloud mass moved per RAS timestep at the cloud detrainment level is written: -\[ -{\bf DTRAIN} = \eta_{r_D}m_B -\] -\noindent -where $r_D$ is the detrainment level, -$m_B$ is the cloud base mass flux, and $\eta$ -is the entrainment, defined in Section \ref{sec:fizhi:mc}. -\\ - -\noindent -{\bf 92) \underline {QFILL} Filling of negative Specific Humidity ($g/kg/day$) } - -\noindent -Due to computational errors associated with the numerical scheme used for -the advection of moisture, negative values of specific humidity may be generated. The -specific humidity is checked for negative values after every dynamics timestep. If negative -values have been produced, a filling algorithm is invoked which redistributes moisture from -below. Diagnostic {\bf QFILL} is equal to the net filling needed -to eliminate negative specific humidity, scaled to a per-day rate: -\[ -{\bf QFILL} = q^{n+1}_{final} - q^{n+1}_{initial} -\] -where -\[ -q^{n+1} = (\pi q)^{n+1} / \pi^{n+1} -\] +output frequency of the diagnostic, and $\Delta t$ is +the timestep over which the diagnostic is updated. \subsection{Dos and Donts}