--- manual/s_phys_pkgs/text/fizhi.tex	2004/01/28 21:00:10	1.5
+++ manual/s_phys_pkgs/text/fizhi.tex	2005/07/14 19:18:02	1.8
@@ -1,4 +1,8 @@
 \section{Fizhi: High-end Atmospheric Physics}
+\label{sec:pkg:fizhi}
+\begin{rawhtml}
+<!-- CMIREDIR:package_fizhi: -->
+\end{rawhtml}
 \input{texinputs/epsf.tex}
 
 \subsection{Introduction}
@@ -888,3 +892,2141 @@
 the model's moisture data is used.  Above 100 mb, the SAGE data is used.  Between 100 and 300 mb,
 a linear interpolation (in pressure) is performed using the data from SAGE and the GCM. 
 
+
+\subsection{Fizhi Diagnostics}
+
+\subsubsection{Fizhi Diagnostic Menu}
+\label{sec:fizhi-diagnostics:menu}
+
+\begin{tabular}{llll}
+\hline\hline
+ NAME & UNITS & LEVELS & DESCRIPTION \\
+\hline
+
+&\\
+ UFLUX    &   $Newton/m^2$  &    1  
+         &\begin{minipage}[t]{3in}
+          {Surface U-Wind Stress on the atmosphere}
+         \end{minipage}\\
+ VFLUX    &   $Newton/m^2$  &    1  
+         &\begin{minipage}[t]{3in}
+          {Surface V-Wind Stress on the atmosphere}
+         \end{minipage}\\
+ HFLUX    &   $Watts/m^2$  &    1  
+         &\begin{minipage}[t]{3in}
+          {Surface Flux of Sensible Heat}
+         \end{minipage}\\
+ EFLUX    &   $Watts/m^2$  &    1  
+         &\begin{minipage}[t]{3in}
+          {Surface Flux of Latent Heat}
+         \end{minipage}\\
+ QICE     &   $Watts/m^2$  &    1  
+         &\begin{minipage}[t]{3in}
+          {Heat Conduction through Sea-Ice}
+         \end{minipage}\\
+ RADLWG   &   $Watts/m^2$ &    1  
+         &\begin{minipage}[t]{3in}
+          {Net upward LW flux at the ground}
+         \end{minipage}\\
+ RADSWG   &   $Watts/m^2$  &    1 
+         &\begin{minipage}[t]{3in}
+          {Net downward SW flux at the ground} 
+         \end{minipage}\\
+ RI       &  $dimensionless$ &  Nrphys 
+         &\begin{minipage}[t]{3in}
+          {Richardson Number}
+         \end{minipage}\\
+ CT       &  $dimensionless$ &  1 
+         &\begin{minipage}[t]{3in}
+          {Surface Drag coefficient for T and Q}
+         \end{minipage}\\
+ CU       & $dimensionless$ &  1 
+     &\begin{minipage}[t]{3in}
+      {Surface Drag coefficient for U and V}
+     \end{minipage}\\
+ ET       &  $m^2/sec$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Diffusivity coefficient for T and Q}
+     \end{minipage}\\
+ EU       &  $m^2/sec$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Diffusivity coefficient for U and V}
+     \end{minipage}\\
+ TURBU    &  $m/sec/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {U-Momentum Changes due to Turbulence}
+     \end{minipage}\\
+ TURBV    &  $m/sec/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {V-Momentum Changes due to Turbulence}
+     \end{minipage}\\
+ TURBT    &  $deg/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Temperature Changes due to Turbulence}
+     \end{minipage}\\
+ TURBQ    &  $g/kg/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Specific Humidity Changes due to Turbulence}
+     \end{minipage}\\
+ MOISTT   &   $deg/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Temperature Changes due to Moist Processes}
+     \end{minipage}\\
+ MOISTQ   &  $g/kg/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Specific Humidity Changes due to Moist Processes}
+     \end{minipage}\\
+ RADLW    &  $deg/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Net Longwave heating rate for each level}
+     \end{minipage}\\
+ RADSW    &  $deg/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Net Shortwave heating rate for each level}
+     \end{minipage}\\
+ PREACC   &  $mm/day$ &  1
+     &\begin{minipage}[t]{3in}
+      {Total Precipitation}
+     \end{minipage}\\
+ PRECON   &  $mm/day$ &  1
+     &\begin{minipage}[t]{3in}
+      {Convective Precipitation}
+     \end{minipage}\\
+ TUFLUX   &  $Newton/m^2$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Turbulent Flux of U-Momentum}
+     \end{minipage}\\
+ TVFLUX   &  $Newton/m^2$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Turbulent Flux of V-Momentum}
+     \end{minipage}\\
+ TTFLUX   &  $Watts/m^2$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Turbulent Flux of Sensible Heat}
+     \end{minipage}\\
+\end{tabular}
+
+\newpage
+\vspace*{\fill}
+\begin{tabular}{llll}
+\hline\hline
+ NAME & UNITS & LEVELS & DESCRIPTION \\
+\hline
+
+&\\
+ TQFLUX   &  $Watts/m^2$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Turbulent Flux of Latent Heat}
+     \end{minipage}\\
+ CN       &  $dimensionless$ &  1
+     &\begin{minipage}[t]{3in}
+      {Neutral Drag Coefficient}
+     \end{minipage}\\
+ WINDS     &  $m/sec$ &  1
+     &\begin{minipage}[t]{3in}
+      {Surface Wind Speed}
+     \end{minipage}\\
+ DTSRF     &  $deg$ &  1
+     &\begin{minipage}[t]{3in}
+      {Air/Surface virtual temperature difference}
+     \end{minipage}\\
+ TG        &  $deg$ &  1
+     &\begin{minipage}[t]{3in}
+      {Ground temperature}
+     \end{minipage}\\
+ TS        &  $deg$ &  1
+     &\begin{minipage}[t]{3in}
+      {Surface air temperature (Adiabatic from lowest model layer)}
+     \end{minipage}\\
+ DTG       &  $deg$ &  1
+     &\begin{minipage}[t]{3in}
+      {Ground temperature adjustment}
+     \end{minipage}\\
+
+ QG        &  $g/kg$ &  1
+     &\begin{minipage}[t]{3in}
+      {Ground specific humidity}
+     \end{minipage}\\
+ QS        &  $g/kg$ &  1
+     &\begin{minipage}[t]{3in}
+      {Saturation surface specific humidity}
+     \end{minipage}\\
+ TGRLW    &    $deg$   &    1  
+     &\begin{minipage}[t]{3in}
+      {Instantaneous ground temperature used as input to the
+       Longwave radiation subroutine} 
+     \end{minipage}\\
+ ST4      &   $Watts/m^2$  &    1  
+     &\begin{minipage}[t]{3in}
+      {Upward Longwave flux at the ground ($\sigma T^4$)}
+     \end{minipage}\\
+ OLR      &   $Watts/m^2$  &    1  
+     &\begin{minipage}[t]{3in}
+      {Net upward Longwave flux at the top of the model}
+     \end{minipage}\\
+ OLRCLR   &   $Watts/m^2$  &    1  
+     &\begin{minipage}[t]{3in}
+      {Net upward clearsky Longwave flux at the top of the model}
+     \end{minipage}\\
+ LWGCLR   &   $Watts/m^2$  &    1  
+     &\begin{minipage}[t]{3in}
+      {Net upward clearsky Longwave flux at the ground}
+     \end{minipage}\\
+ LWCLR    &  $deg/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Net clearsky Longwave heating rate for each level}
+     \end{minipage}\\
+ TLW      &    $deg$   &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Instantaneous temperature used as input to the Longwave radiation
+      subroutine} 
+     \end{minipage}\\
+ SHLW     &    $g/g$   &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Instantaneous specific humidity used as input to the Longwave radiation
+      subroutine} 
+     \end{minipage}\\
+ OZLW     &    $g/g$   &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Instantaneous ozone used as input to the Longwave radiation
+      subroutine} 
+     \end{minipage}\\
+ CLMOLW   &    $0-1$   &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Maximum overlap cloud fraction used in the Longwave radiation
+      subroutine} 
+     \end{minipage}\\
+ CLDTOT   &    $0-1$   &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Total cloud fraction used in the Longwave and Shortwave radiation
+      subroutines} 
+     \end{minipage}\\
+ LWGDOWN  &    $Watts/m^2$   &  1 
+     &\begin{minipage}[t]{3in}
+      {Downwelling Longwave radiation at the ground}
+     \end{minipage}\\
+ GWDT     &    $deg/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Temperature tendency due to Gravity Wave Drag}
+     \end{minipage}\\
+ RADSWT   &    $Watts/m^2$   &  1 
+     &\begin{minipage}[t]{3in}
+      {Incident Shortwave radiation at the top of the atmosphere}
+     \end{minipage}\\
+ TAUCLD   &    $per 100 mb$   &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Counted Cloud Optical Depth (non-dimensional) per 100 mb}
+     \end{minipage}\\
+ TAUCLDC  &    $Number$   &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Cloud Optical Depth Counter}
+     \end{minipage}\\
+\end{tabular}
+\vfill
+
+\newpage
+\vspace*{\fill}
+\begin{tabular}{llll}
+\hline\hline
+ NAME & UNITS & LEVELS & DESCRIPTION \\
+\hline
+
+&\\
+ CLDLOW   &    $0-1$   &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Low-Level ( 1000-700 hPa) Cloud Fraction  (0-1)}
+     \end{minipage}\\
+ EVAP     &    $mm/day$   &  1 
+     &\begin{minipage}[t]{3in}
+      {Surface evaporation}
+     \end{minipage}\\
+ DPDT     &    $hPa/day$ &  1
+     &\begin{minipage}[t]{3in}
+      {Surface Pressure tendency}
+     \end{minipage}\\
+ UAVE     &    $m/sec$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Average U-Wind}
+     \end{minipage}\\
+ VAVE     &    $m/sec$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Average V-Wind}
+     \end{minipage}\\
+ TAVE     &    $deg$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Average Temperature}
+     \end{minipage}\\
+ QAVE     &    $g/kg$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Average Specific Humidity}
+     \end{minipage}\\
+ OMEGA    &    $hPa/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Vertical Velocity}
+     \end{minipage}\\
+ DUDT     &    $m/sec/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Total U-Wind tendency}
+     \end{minipage}\\
+ DVDT     &    $m/sec/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Total V-Wind tendency}
+     \end{minipage}\\
+ DTDT     &    $deg/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Total Temperature tendency}
+     \end{minipage}\\
+ DQDT     &    $g/kg/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Total Specific Humidity tendency}
+     \end{minipage}\\
+ VORT     &    $10^{-4}/sec$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Relative Vorticity}
+     \end{minipage}\\
+ DTLS     &    $deg/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Temperature tendency due to Stratiform Cloud Formation}
+     \end{minipage}\\
+ DQLS     &    $g/kg/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Specific Humidity tendency due to Stratiform Cloud Formation}
+     \end{minipage}\\
+ USTAR    &    $m/sec$ &  1
+     &\begin{minipage}[t]{3in}
+      {Surface USTAR wind}
+     \end{minipage}\\
+ Z0       &    $m$ &  1
+     &\begin{minipage}[t]{3in}
+      {Surface roughness}
+     \end{minipage}\\
+ FRQTRB   &    $0-1$ &  Nrphys-1
+     &\begin{minipage}[t]{3in}
+      {Frequency of Turbulence}
+     \end{minipage}\\
+ PBL      &    $mb$ &  1
+     &\begin{minipage}[t]{3in}
+      {Planetary Boundary Layer depth}
+     \end{minipage}\\
+ SWCLR    &  $deg/day$ &  Nrphys 
+     &\begin{minipage}[t]{3in}
+      {Net clearsky Shortwave heating rate for each level}
+     \end{minipage}\\
+ OSR      &   $Watts/m^2$  &    1 
+     &\begin{minipage}[t]{3in}
+      {Net downward Shortwave flux at the top of the model}
+     \end{minipage}\\
+ OSRCLR   &   $Watts/m^2$  &    1  
+     &\begin{minipage}[t]{3in}
+      {Net downward clearsky Shortwave flux at the top of the model}
+     \end{minipage}\\
+ CLDMAS   &   $kg / m^2$  &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Convective cloud mass flux}
+     \end{minipage}\\
+ UAVE     &   $m/sec$  &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Time-averaged $u-Wind$}
+     \end{minipage}\\
+\end{tabular}
+\vfill
+
+\newpage
+\vspace*{\fill}
+\begin{tabular}{llll}
+\hline\hline
+ NAME & UNITS & LEVELS & DESCRIPTION \\
+\hline
+
+&\\
+ VAVE     &   $m/sec$  &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Time-averaged $v-Wind$}
+     \end{minipage}\\
+ TAVE     &   $deg$  &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Time-averaged $Temperature$}
+     \end{minipage}\\
+ QAVE     &   $g/g$  &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Time-averaged $Specific \, \, Humidity$}
+     \end{minipage}\\
+ RFT      &    $deg/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {Temperature tendency due Rayleigh Friction}
+     \end{minipage}\\
+ PS       &   $mb$  &    1
+     &\begin{minipage}[t]{3in}
+      {Surface Pressure}
+     \end{minipage}\\
+ QQAVE    &   $(m/sec)^2$  &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Time-averaged $Turbulent Kinetic Energy$}
+     \end{minipage}\\
+ SWGCLR   &   $Watts/m^2$  &    1  
+     &\begin{minipage}[t]{3in}
+      {Net downward clearsky Shortwave flux at the ground} 
+     \end{minipage}\\
+ PAVE     &   $mb$  &    1
+     &\begin{minipage}[t]{3in}
+      {Time-averaged Surface Pressure}
+     \end{minipage}\\
+ DIABU    & $m/sec/day$ &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Total Diabatic forcing on $u-Wind$} 
+     \end{minipage}\\
+ DIABV    & $m/sec/day$ &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Total Diabatic forcing on $v-Wind$} 
+     \end{minipage}\\
+ DIABT    & $deg/day$ &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Total Diabatic forcing on $Temperature$} 
+     \end{minipage}\\
+ DIABQ    & $g/kg/day$ &    Nrphys
+     &\begin{minipage}[t]{3in}
+      {Total Diabatic forcing on $Specific \, \, Humidity$} 
+     \end{minipage}\\
+ RFU      &    $m/sec/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {U-Wind tendency due to Rayleigh Friction}
+     \end{minipage}\\
+ RFV      &    $m/sec/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {V-Wind tendency due to Rayleigh Friction}
+     \end{minipage}\\
+ GWDU     &    $m/sec/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {U-Wind tendency due to Gravity Wave Drag}
+     \end{minipage}\\
+ GWDU     &    $m/sec/day$ &  Nrphys
+     &\begin{minipage}[t]{3in}
+      {V-Wind tendency due to Gravity Wave Drag}
+     \end{minipage}\\
+ GWDUS    &    $N/m^2$ &  1
+     &\begin{minipage}[t]{3in}
+      {U-Wind Gravity Wave Drag Stress at Surface}
+     \end{minipage}\\
+ GWDVS    &    $N/m^2$ &  1
+     &\begin{minipage}[t]{3in}
+      {V-Wind Gravity Wave Drag Stress at Surface}
+     \end{minipage}\\
+ GWDUT    &    $N/m^2$ &  1
+     &\begin{minipage}[t]{3in}
+      {U-Wind Gravity Wave Drag Stress at Top}
+     \end{minipage}\\
+ GWDVT    &    $N/m^2$ &  1
+     &\begin{minipage}[t]{3in}
+      {V-Wind Gravity Wave Drag Stress at Top}
+     \end{minipage}\\
+ LZRAD    &    $mg/kg$ &  Nrphys
+         &\begin{minipage}[t]{3in}
+          {Estimated Cloud Liquid Water used in Radiation}
+         \end{minipage}\\
+\end{tabular}
+\vfill
+
+\newpage
+\vspace*{\fill}
+\begin{tabular}{llll}
+\hline\hline
+ NAME & UNITS & LEVELS & DESCRIPTION \\
+\hline
+
+&\\
+ SLP      &   $mb$  &    1
+         &\begin{minipage}[t]{3in}
+          {Time-averaged Sea-level Pressure}
+         \end{minipage}\\
+ CLDFRC  & $0-1$ &    1
+         &\begin{minipage}[t]{3in}
+          {Total Cloud Fraction} 
+         \end{minipage}\\
+ TPW     & $gm/cm^2$ &    1
+         &\begin{minipage}[t]{3in}
+          {Precipitable water} 
+         \end{minipage}\\
+ U2M     & $m/sec$ &    1
+         &\begin{minipage}[t]{3in}
+          {U-Wind at 2 meters}
+         \end{minipage}\\
+ V2M     & $m/sec$ &    1
+         &\begin{minipage}[t]{3in}
+          {V-Wind at 2 meters}
+         \end{minipage}\\
+ T2M     & $deg$ &    1
+         &\begin{minipage}[t]{3in}
+          {Temperature at 2 meters}
+         \end{minipage}\\
+ Q2M     & $g/kg$ &    1
+         &\begin{minipage}[t]{3in}
+          {Specific Humidity at 2 meters}
+         \end{minipage}\\
+ U10M    & $m/sec$ &    1
+         &\begin{minipage}[t]{3in}
+          {U-Wind at 10 meters}
+         \end{minipage}\\
+ V10M    & $m/sec$ &    1
+         &\begin{minipage}[t]{3in}
+          {V-Wind at 10 meters}
+         \end{minipage}\\
+ T10M    & $deg$ &    1
+         &\begin{minipage}[t]{3in}
+          {Temperature at 10 meters}
+         \end{minipage}\\
+ Q10M    & $g/kg$ &    1
+         &\begin{minipage}[t]{3in}
+          {Specific Humidity at 10 meters}
+         \end{minipage}\\
+ DTRAIN  & $kg/m^2$ &    Nrphys
+         &\begin{minipage}[t]{3in}
+          {Detrainment Cloud Mass Flux}
+         \end{minipage}\\
+ QFILL   & $g/kg/day$ &    Nrphys
+         &\begin{minipage}[t]{3in}
+          {Filling of negative specific humidity}
+         \end{minipage}\\
+\end{tabular}
+\vspace{1.5in}
+\vfill
+
+\newpage
+\vspace*{\fill}
+\begin{tabular}{llll}
+\hline\hline
+ NAME & UNITS & LEVELS & DESCRIPTION \\
+\hline
+
+&\\
+ DTCONV   & $deg/sec$ & Nr
+         &\begin{minipage}[t]{3in}
+          {Temp Change due to Convection} 
+         \end{minipage}\\
+ DQCONV   & $g/kg/sec$ & Nr
+         &\begin{minipage}[t]{3in}
+          {Specific Humidity Change due to Convection} 
+         \end{minipage}\\
+ RELHUM   & $percent$ & Nr
+         &\begin{minipage}[t]{3in}
+          {Relative Humidity} 
+         \end{minipage}\\
+ PRECLS   & $g/m^2/sec$ & 1
+         &\begin{minipage}[t]{3in}
+          {Large Scale Precipitation} 
+         \end{minipage}\\
+ ENPREC   & $J/g$ & 1
+         &\begin{minipage}[t]{3in}
+          {Energy of Precipitation (snow, rain Temp)} 
+         \end{minipage}\\
+\end{tabular}
+\vspace{1.5in}
+\vfill
+
+\newpage
+
+\subsubsection{Fizhi Diagnostic Description}
+
+In this section we list and describe the diagnostic quantities available within the 
+GCM.  The diagnostics are listed in the order that they appear in the 
+Diagnostic Menu, Section \ref{sec:fizhi-diagnostics:menu}.
+In all cases, each diagnostic as currently archived on the output datasets
+is time-averaged over its diagnostic output frequency:
+
+\[
+{\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t)
+\]
+where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the 
+output frequency of the diagnostic, and $\Delta t$ is
+the timestep over which the diagnostic is updated.  
+
+{ \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. 
+\[
+{\bf UFLUX} =  - \rho C_D W_s u \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u
+\]
+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.
+\\
+
+
+{ \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. 
+\[
+{\bf VFLUX} =  - \rho C_D W_s v \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u
+\]
+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.
+\\
+
+{ \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.
+\\
+
+
+{ \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.
+\\
+
+{ \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.
+\\
+ 
+
+{ \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.
+\\
+
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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}.
+\[
+{\bf CLMOLW} = CLMO_{RAS,LW}(\lambda, \phi,  level )
+\]
+\\
+ 
+
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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} $.
+\\
+
+
+\noindent
+{ \underline {U2M}  Zonal U-Wind at 2 Meter Depth ($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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \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
+{ \underline {QFILL}  Filling of negative Specific Humidity ($g/kg/day$) }
+
+\noindent
+Due to computational errors associated with the numerical scheme used for
+the advection of moisture, negative values of specific humidity may be generated.  The
+specific humidity is checked for negative values after every dynamics timestep.  If negative
+values have been produced, a filling algorithm is invoked which redistributes moisture from
+below.  Diagnostic {\bf QFILL} is equal to the net filling needed
+to eliminate negative specific humidity, scaled to a per-day rate:
+\[
+{\bf QFILL} = q^{n+1}_{final} - q^{n+1}_{initial}
+\]
+where
+\[
+q^{n+1} = (\pi q)^{n+1} / \pi^{n+1}
+\]
+
+
+\subsection{Key subroutines, parameters and files}
+
+\subsection{Dos and donts}
+
+\subsection{Fizhi Reference}
