--- manual/s_phys_pkgs/diagnostics.tex	2004/10/18 19:43:56	1.7
+++ manual/s_phys_pkgs/diagnostics.tex	2005/07/14 19:18:01	1.9
@@ -276,224 +276,88 @@
 \hline
 
 &\\
-1 & UFLUX    &   $Newton/m^2$  &    1  
+84 & SDIAG1   &             &    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
-         &\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
@@ -504,190 +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
@@ -709,1688 +521,6 @@
 output frequency of the diagnostic, and $\Delta t$ is
 the timestep over which the diagnostic is updated.  
 
-{\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
-\[
-q^{n+1} = (\pi q)^{n+1} / \pi^{n+1}
-\]
-
 \subsection{Dos and Donts}
 
 \subsection{Diagnostics Reference}
