--- manual/s_phys_pkgs/diagnostics.tex 2004/10/28 22:41:16 1.8 +++ manual/s_phys_pkgs/diagnostics.tex 2005/07/14 19:18:01 1.9 @@ -276,107 +276,89 @@ \hline &\\ -1 & UFLUX & $Newton/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Surface U-Wind Stress on the atmosphere} - \end{minipage}\\ -2 & VFLUX & $Newton/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Surface V-Wind Stress on the atmosphere} - \end{minipage}\\ -3 & HFLUX & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Surface Flux of Sensible Heat} - \end{minipage}\\ -4 & EFLUX & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Surface Flux of Latent Heat} - \end{minipage}\\ -5 & QICE & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Heat Conduction through Sea-Ice} - \end{minipage}\\ -6 & RADLWG & $Watts/m^2$ & 1 +84 & SDIAG1 & & 1 &\begin{minipage}[t]{3in} - {Net upward LW flux at the ground} + {User-Defined Surface Diagnostic-1} \end{minipage}\\ -7 & RADSWG & $Watts/m^2$ & 1 +85 & SDIAG2 & & 1 &\begin{minipage}[t]{3in} - {Net downward SW flux at the ground} + {User-Defined Surface Diagnostic-2} \end{minipage}\\ -8 & RI & $dimensionless$ & Nrphys +86 & UDIAG1 & & Nrphys &\begin{minipage}[t]{3in} - {Richardson Number} + {User-Defined Upper-Air Diagnostic-1} \end{minipage}\\ -9 & CT & $dimensionless$ & 1 +87 & UDIAG2 & & Nrphys &\begin{minipage}[t]{3in} - {Surface Drag coefficient for T and Q} + {User-Defined Upper-Air Diagnostic-2} \end{minipage}\\ -10 & CU & $dimensionless$ & 1 +124& SDIAG3 & & 1 &\begin{minipage}[t]{3in} - {Surface Drag coefficient for U and V} + {User-Defined Surface Diagnostic-3} \end{minipage}\\ -11 & ET & $m^2/sec$ & Nrphys +125& SDIAG4 & & 1 &\begin{minipage}[t]{3in} - {Diffusivity coefficient for T and Q} + {User-Defined Surface Diagnostic-4} \end{minipage}\\ -12 & EU & $m^2/sec$ & Nrphys +126& SDIAG5 & & 1 &\begin{minipage}[t]{3in} - {Diffusivity coefficient for U and V} + {User-Defined Surface Diagnostic-5} \end{minipage}\\ -13 & TURBU & $m/sec/day$ & Nrphys +127& SDIAG6 & & 1 &\begin{minipage}[t]{3in} - {U-Momentum Changes due to Turbulence} + {User-Defined Surface Diagnostic-6} \end{minipage}\\ -14 & TURBV & $m/sec/day$ & Nrphys +128& SDIAG7 & & 1 &\begin{minipage}[t]{3in} - {V-Momentum Changes due to Turbulence} + {User-Defined Surface Diagnostic-7} \end{minipage}\\ -15 & TURBT & $deg/day$ & Nrphys +129& SDIAG8 & & 1 &\begin{minipage}[t]{3in} - {Temperature Changes due to Turbulence} + {User-Defined Surface Diagnostic-8} \end{minipage}\\ -16 & TURBQ & $g/kg/day$ & Nrphys +130& SDIAG9 & & 1 &\begin{minipage}[t]{3in} - {Specific Humidity Changes due to Turbulence} + {User-Defined Surface Diagnostic-9} \end{minipage}\\ -17 & MOISTT & $deg/day$ & Nrphys +131& SDIAG10 & & 1 &\begin{minipage}[t]{3in} - {Temperature Changes due to Moist Processes} + {User-Defined Surface Diagnostic-1-} \end{minipage}\\ -18 & MOISTQ & $g/kg/day$ & Nrphys +132& UDIAG3 & & Nrphys &\begin{minipage}[t]{3in} - {Specific Humidity Changes due to Moist Processes} + {User-Defined Multi-Level Diagnostic-3} \end{minipage}\\ -19 & RADLW & $deg/day$ & Nrphys +133& UDIAG4 & & Nrphys &\begin{minipage}[t]{3in} - {Net Longwave heating rate for each level} + {User-Defined Multi-Level Diagnostic-4} \end{minipage}\\ -20 & RADSW & $deg/day$ & Nrphys +134& UDIAG5 & & Nrphys &\begin{minipage}[t]{3in} - {Net Shortwave heating rate for each level} + {User-Defined Multi-Level Diagnostic-5} \end{minipage}\\ -21 & PREACC & $mm/day$ & 1 +135& UDIAG6 & & Nrphys &\begin{minipage}[t]{3in} - {Total Precipitation} + {User-Defined Multi-Level Diagnostic-6} \end{minipage}\\ -22 & PRECON & $mm/day$ & 1 +136& UDIAG7 & & Nrphys &\begin{minipage}[t]{3in} - {Convective Precipitation} + {User-Defined Multi-Level Diagnostic-7} \end{minipage}\\ -23 & TUFLUX & $Newton/m^2$ & Nrphys +137& UDIAG8 & & Nrphys &\begin{minipage}[t]{3in} - {Turbulent Flux of U-Momentum} + {User-Defined Multi-Level Diagnostic-8} \end{minipage}\\ -24 & TVFLUX & $Newton/m^2$ & Nrphys +138& UDIAG9 & & Nrphys &\begin{minipage}[t]{3in} - {Turbulent Flux of V-Momentum} + {User-Defined Multi-Level Diagnostic-9} \end{minipage}\\ -25 & TTFLUX & $Watts/m^2$ & Nrphys +139& UDIAG10 & & Nrphys &\begin{minipage}[t]{3in} - {Turbulent Flux of Sensible Heat} + {User-Defined Multi-Level Diagnostic-10} \end{minipage}\\ \end{tabular} +\vspace{1.5in} +\vfill \newpage \vspace*{\fill} @@ -386,2524 +368,158 @@ \hline &\\ -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} - \end{minipage}\\ -31 & TS & $deg$ & 1 - &\begin{minipage}[t]{3in} - {Surface air temperature (Adiabatic from lowest model layer)} - \end{minipage}\\ -32 & DTG & $deg$ & 1 - &\begin{minipage}[t]{3in} - {Ground temperature adjustment} - \end{minipage}\\ - -33 & QG & $g/kg$ & 1 - &\begin{minipage}[t]{3in} - {Ground specific humidity} - \end{minipage}\\ -34 & QS & $g/kg$ & 1 - &\begin{minipage}[t]{3in} - {Saturation surface specific humidity} - \end{minipage}\\ -35 & TGRLW & $deg$ & 1 - &\begin{minipage}[t]{3in} - {Instantaneous ground temperature used as input to the - Longwave radiation subroutine} - \end{minipage}\\ -36 & ST4 & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Upward Longwave flux at the ground ($\sigma T^4$)} - \end{minipage}\\ -37 & OLR & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Net upward Longwave flux at the top of the model} - \end{minipage}\\ -38 & OLRCLR & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Net upward clearsky Longwave flux at the top of the model} - \end{minipage}\\ -39 & LWGCLR & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Net upward clearsky Longwave flux at the ground} - \end{minipage}\\ -40 & LWCLR & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Net clearsky Longwave heating rate for each level} - \end{minipage}\\ -41 & TLW & $deg$ & Nrphys - &\begin{minipage}[t]{3in} - {Instantaneous temperature used as input to the Longwave radiation - subroutine} - \end{minipage}\\ -42 & SHLW & $g/g$ & Nrphys - &\begin{minipage}[t]{3in} - {Instantaneous specific humidity used as input to the Longwave radiation - subroutine} - \end{minipage}\\ -43 & OZLW & $g/g$ & Nrphys +238& ETAN & $(hPa,m)$ & 1 &\begin{minipage}[t]{3in} - {Instantaneous ozone used as input to the Longwave radiation - subroutine} + {Perturbation of Surface (pressure, height)} \end{minipage}\\ -44 & CLMOLW & $0-1$ & Nrphys +239& ETANSQ & $(hPa^2,m^2)$ & 1 &\begin{minipage}[t]{3in} - {Maximum overlap cloud fraction used in the Longwave radiation - subroutine} + {Square of Perturbation of Surface (pressure, height)} \end{minipage}\\ -45 & CLDTOT & $0-1$ & Nrphys +240& THETA & $deg K$ & Nr &\begin{minipage}[t]{3in} - {Total cloud fraction used in the Longwave and Shortwave radiation - subroutines} + {Potential Temperature} \end{minipage}\\ -46 & LWGDOWN & $Watts/m^2$ & 1 +241& SALT & $g/kg$ & Nr &\begin{minipage}[t]{3in} - {Downwelling Longwave radiation at the ground} + {Salt (or Water Vapor Mixing Ratio)} \end{minipage}\\ -47 & GWDT & $deg/day$ & Nrphys +242& UVEL & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Temperature tendency due to Gravity Wave Drag} + {U-Velocity} \end{minipage}\\ -48 & RADSWT & $Watts/m^2$ & 1 +243& VVEL & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Incident Shortwave radiation at the top of the atmosphere} + {V-Velocity} \end{minipage}\\ -49 & TAUCLD & $per 100 mb$ & Nrphys +244& WVEL & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Counted Cloud Optical Depth (non-dimensional) per 100 mb} + {Vertical-Velocity} \end{minipage}\\ -50 & TAUCLDC & $Number$ & Nrphys +245& THETASQ & $deg^2$ & Nr &\begin{minipage}[t]{3in} - {Cloud Optical Depth Counter} + {Square of Potential Temperature} \end{minipage}\\ -\end{tabular} -\vfill - -\newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline - -&\\ -51 & CLDLOW & $0-1$ & Nrphys +246& SALTSQ & $g^2/{kg}^2$ & Nr &\begin{minipage}[t]{3in} - {Low-Level ( 1000-700 hPa) Cloud Fraction (0-1)} + {Square of Salt (or Water Vapor Mixing Ratio)} \end{minipage}\\ -52 & EVAP & $mm/day$ & 1 +247& UVELSQ & $m^2/sec^2$ & Nr &\begin{minipage}[t]{3in} - {Surface evaporation} + {Square of U-Velocity} \end{minipage}\\ -53 & DPDT & $hPa/day$ & 1 +248& VVELSQ & $m^2/sec^2$ & Nr &\begin{minipage}[t]{3in} - {Surface Pressure tendency} + {Square of V-Velocity} \end{minipage}\\ -54 & UAVE & $m/sec$ & Nrphys +249& WVELSQ & $m^2/sec^2$ & Nr &\begin{minipage}[t]{3in} - {Average U-Wind} + {Square of Vertical-Velocity} \end{minipage}\\ -55 & VAVE & $m/sec$ & Nrphys +250& UVELVVEL & $m^2/sec^2$ & Nr &\begin{minipage}[t]{3in} - {Average V-Wind} + {Meridional Transport of Zonal Momentum} \end{minipage}\\ -56 & TAVE & $deg$ & Nrphys +251& UVELMASS & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Average Temperature} + {Zonal Mass-Weighted Component of Velocity} \end{minipage}\\ -57 & QAVE & $g/kg$ & Nrphys +252& VVELMASS & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Average Specific Humidity} + {Meridional Mass-Weighted Component of Velocity} \end{minipage}\\ -58 & OMEGA & $hPa/day$ & Nrphys +253& WVELMASS & $m/sec$ & Nr &\begin{minipage}[t]{3in} - {Vertical Velocity} + {Vertical Mass-Weighted Component of Velocity} \end{minipage}\\ -59 & DUDT & $m/sec/day$ & Nrphys +254& UTHMASS & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Total U-Wind tendency} + {Zonal Mass-Weight Transp of Pot Temp} \end{minipage}\\ -60 & DVDT & $m/sec/day$ & Nrphys +255& VTHMASS & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Total V-Wind tendency} + {Meridional Mass-Weight Transp of Pot Temp} \end{minipage}\\ -61 & DTDT & $deg/day$ & Nrphys +256& WTHMASS & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Total Temperature tendency} + {Vertical Mass-Weight Transp of Pot Temp} \end{minipage}\\ -62 & DQDT & $g/kg/day$ & Nrphys +257& USLTMASS & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Total Specific Humidity tendency} + {Zonal Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -63 & VORT & $10^{-4}/sec$ & Nrphys +258& VSLTMASS & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Relative Vorticity} + {Meridional Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -64 & NOT USED & $$ & +259& WSLTMASS & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {} + {Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -65 & DTLS & $deg/day$ & Nrphys +260& UVELTH & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Temperature tendency due to Stratiform Cloud Formation} + {Zonal Transp of Pot Temp} \end{minipage}\\ -66 & DQLS & $g/kg/day$ & Nrphys +261& VVELTH & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Specific Humidity tendency due to Stratiform Cloud Formation} + {Meridional Transp of Pot Temp} \end{minipage}\\ -67 & USTAR & $m/sec$ & 1 +262& WVELTH & $m-deg/sec$ & Nr &\begin{minipage}[t]{3in} - {Surface USTAR wind} + {Vertical Transp of Pot Temp} \end{minipage}\\ -68 & Z0 & $m$ & 1 +263& UVELSLT & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Surface roughness} + {Zonal Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -69 & FRQTRB & $0-1$ & Nrphys-1 +264& VVELSLT & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Frequency of Turbulence} + {Meridional Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -70 & PBL & $mb$ & 1 +265& WVELSLT & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Planetary Boundary Layer depth} + {Vertical Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -71 & SWCLR & $deg/day$ & Nrphys +275& WSLTMASS & $m-kg/sec-kg$ & Nr &\begin{minipage}[t]{3in} - {Net clearsky Shortwave heating rate for each level} + {Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} \end{minipage}\\ -72 & OSR & $Watts/m^2$ & 1 +298& VISCA4 & $m^4/sec$ & 1 &\begin{minipage}[t]{3in} - {Net downward Shortwave flux at the top of the model} + {Biharmonic Viscosity Coefficient} \end{minipage}\\ -73 & OSRCLR & $Watts/m^2$ & 1 +299& VISCAH & $m^2/sec$ & 1 &\begin{minipage}[t]{3in} - {Net downward clearsky Shortwave flux at the top of the model} + {Harmonic Viscosity Coefficient} \end{minipage}\\ -74 & CLDMAS & $kg / m^2$ & Nrphys +300& DRHODR & $kg/m^3/{r-unit}$ & Nr &\begin{minipage}[t]{3in} - {Convective cloud mass flux} + {Stratification: d.Sigma/dr} \end{minipage}\\ -75 & UAVE & $m/sec$ & Nrphys +301& DETADT2 & ${r-unit}^2/s^2$ & 1 &\begin{minipage}[t]{3in} - {Time-averaged $u-Wind$} + {Square of Eta (Surf.P,SSH) Tendency} \end{minipage}\\ \end{tabular} +\vspace{1.5in} \vfill \newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline -&\\ -76 & VAVE & $m/sec$ & Nrphys - &\begin{minipage}[t]{3in} - {Time-averaged $v-Wind$} - \end{minipage}\\ -77 & TAVE & $deg$ & Nrphys - &\begin{minipage}[t]{3in} - {Time-averaged $Temperature$} - \end{minipage}\\ -78 & QAVE & $g/g$ & Nrphys - &\begin{minipage}[t]{3in} - {Time-averaged $Specific \, \, Humidity$} - \end{minipage}\\ -79 & RFT & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Temperature tendency due Rayleigh Friction} - \end{minipage}\\ -80 & PS & $mb$ & 1 - &\begin{minipage}[t]{3in} - {Surface Pressure} - \end{minipage}\\ -81 & QQAVE & $(m/sec)^2$ & Nrphys - &\begin{minipage}[t]{3in} - {Time-averaged $Turbulent Kinetic Energy$} - \end{minipage}\\ -82 & SWGCLR & $Watts/m^2$ & 1 - &\begin{minipage}[t]{3in} - {Net downward clearsky Shortwave flux at the ground} - \end{minipage}\\ -83 & PAVE & $mb$ & 1 - &\begin{minipage}[t]{3in} - {Time-averaged Surface Pressure} - \end{minipage}\\ -84 & SDIAG1 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-1} - \end{minipage}\\ -85 & SDIAG2 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-2} - \end{minipage}\\ -86 & UDIAG1 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Upper-Air Diagnostic-1} - \end{minipage}\\ -87 & UDIAG2 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Upper-Air Diagnostic-2} - \end{minipage}\\ -88 & DIABU & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Total Diabatic forcing on $u-Wind$} - \end{minipage}\\ -89 & DIABV & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Total Diabatic forcing on $v-Wind$} - \end{minipage}\\ -90 & DIABT & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Total Diabatic forcing on $Temperature$} - \end{minipage}\\ -91 & DIABQ & $g/kg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Total Diabatic forcing on $Specific \, \, Humidity$} - \end{minipage}\\ -92 & RFU & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {U-Wind tendency due to Rayleigh Friction} - \end{minipage}\\ -93 & RFV & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {V-Wind tendency due to Rayleigh Friction} - \end{minipage}\\ -94 & GWDU & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {U-Wind tendency due to Gravity Wave Drag} - \end{minipage}\\ -95 & GWDU & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {V-Wind tendency due to Gravity Wave Drag} - \end{minipage}\\ -96 & GWDUS & $N/m^2$ & 1 - &\begin{minipage}[t]{3in} - {U-Wind Gravity Wave Drag Stress at Surface} - \end{minipage}\\ -97 & GWDVS & $N/m^2$ & 1 - &\begin{minipage}[t]{3in} - {V-Wind Gravity Wave Drag Stress at Surface} - \end{minipage}\\ -98 & GWDUT & $N/m^2$ & 1 - &\begin{minipage}[t]{3in} - {U-Wind Gravity Wave Drag Stress at Top} - \end{minipage}\\ -99 & GWDVT & $N/m^2$ & 1 - &\begin{minipage}[t]{3in} - {V-Wind Gravity Wave Drag Stress at Top} - \end{minipage}\\ -100& LZRAD & $mg/kg$ & Nrphys - &\begin{minipage}[t]{3in} - {Estimated Cloud Liquid Water used in Radiation} - \end{minipage}\\ -\end{tabular} -\vfill +\subsubsection{Diagnostic Description} -\newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline +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:diagnostics:menu}. +In all cases, each diagnostic as currently archived on the output datasets +is time-averaged over its diagnostic output frequency: -&\\ -101& SLP & $mb$ & 1 - &\begin{minipage}[t]{3in} - {Time-averaged Sea-level Pressure} - \end{minipage}\\ -102& NOT USED & $$ & - &\begin{minipage}[t]{3in} - {} - \end{minipage}\\ -103& NOT USED & $$ & - &\begin{minipage}[t]{3in} - {} - \end{minipage}\\ -104& NOT USED & $$ & - &\begin{minipage}[t]{3in} - {} - \end{minipage}\\ -105& NOT USED & $$ & - &\begin{minipage}[t]{3in} - {} - \end{minipage}\\ -106& CLDFRC & $0-1$ & 1 - &\begin{minipage}[t]{3in} - {Total Cloud Fraction} - \end{minipage}\\ -107& TPW & $gm/cm^2$ & 1 - &\begin{minipage}[t]{3in} - {Precipitable water} - \end{minipage}\\ -108& U2M & $m/sec$ & 1 - &\begin{minipage}[t]{3in} - {U-Wind at 2 meters} - \end{minipage}\\ -109& V2M & $m/sec$ & 1 - &\begin{minipage}[t]{3in} - {V-Wind at 2 meters} - \end{minipage}\\ -110& T2M & $deg$ & 1 - &\begin{minipage}[t]{3in} - {Temperature at 2 meters} - \end{minipage}\\ -111& Q2M & $g/kg$ & 1 - &\begin{minipage}[t]{3in} - {Specific Humidity at 2 meters} - \end{minipage}\\ -112& U10M & $m/sec$ & 1 - &\begin{minipage}[t]{3in} - {U-Wind at 10 meters} - \end{minipage}\\ -113& V10M & $m/sec$ & 1 - &\begin{minipage}[t]{3in} - {V-Wind at 10 meters} - \end{minipage}\\ -114& T10M & $deg$ & 1 - &\begin{minipage}[t]{3in} - {Temperature at 10 meters} - \end{minipage}\\ -115& Q10M & $g/kg$ & 1 - &\begin{minipage}[t]{3in} - {Specific Humidity at 10 meters} - \end{minipage}\\ -116& DTRAIN & $kg/m^2$ & Nrphys - &\begin{minipage}[t]{3in} - {Detrainment Cloud Mass Flux} - \end{minipage}\\ -117& QFILL & $g/kg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Filling of negative specific humidity} - \end{minipage}\\ -118& NOT USED & $$ & - &\begin{minipage}[t]{3in} - {} - \end{minipage}\\ -119& NOT USED & $$ & - &\begin{minipage}[t]{3in} - {} - \end{minipage}\\ -120& SHAPU & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {U-Wind tendency due to Shapiro Filter} - \end{minipage}\\ -121& SHAPV & $m/sec/day$ & Nrphys - &\begin{minipage}[t]{3in} - {V-Wind tendency due to Shapiro Filter} - \end{minipage}\\ -122& SHAPT & $deg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Temperature tendency due Shapiro Filter} - \end{minipage}\\ -123& SHAPQ & $g/kg/day$ & Nrphys - &\begin{minipage}[t]{3in} - {Specific Humidity tendency due to Shapiro Filter} - \end{minipage}\\ -124& SDIAG3 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-3} - \end{minipage}\\ -125& SDIAG4 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-4} - \end{minipage}\\ -\end{tabular} -\vspace{1.5in} -\vfill - -\newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline - -&\\ -126& SDIAG5 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-5} - \end{minipage}\\ -127& SDIAG6 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-6} - \end{minipage}\\ -128& SDIAG7 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-7} - \end{minipage}\\ -129& SDIAG8 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-8} - \end{minipage}\\ -130& SDIAG9 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-9} - \end{minipage}\\ -131& SDIAG10 & & 1 - &\begin{minipage}[t]{3in} - {User-Defined Surface Diagnostic-1-} - \end{minipage}\\ -132& UDIAG3 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Multi-Level Diagnostic-3} - \end{minipage}\\ -133& UDIAG4 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Multi-Level Diagnostic-4} - \end{minipage}\\ -134& UDIAG5 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Multi-Level Diagnostic-5} - \end{minipage}\\ -135& UDIAG6 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Multi-Level Diagnostic-6} - \end{minipage}\\ -136& UDIAG7 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Multi-Level Diagnostic-7} - \end{minipage}\\ -137& UDIAG8 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Multi-Level Diagnostic-8} - \end{minipage}\\ -138& UDIAG9 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Multi-Level Diagnostic-9} - \end{minipage}\\ -139& UDIAG10 & & Nrphys - &\begin{minipage}[t]{3in} - {User-Defined Multi-Level Diagnostic-10} - \end{minipage}\\ -\end{tabular} -\vspace{1.5in} -\vfill - -\newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline - -&\\ -238& ETAN & $(hPa,m)$ & 1 - &\begin{minipage}[t]{3in} - {Perturbation of Surface (pressure, height)} - \end{minipage}\\ -239& ETANSQ & $(hPa^2,m^2)$ & 1 - &\begin{minipage}[t]{3in} - {Square of Perturbation of Surface (pressure, height)} - \end{minipage}\\ -240& THETA & $deg K$ & Nr - &\begin{minipage}[t]{3in} - {Potential Temperature} - \end{minipage}\\ -241& SALT & $g/kg$ & Nr - &\begin{minipage}[t]{3in} - {Salt (or Water Vapor Mixing Ratio)} - \end{minipage}\\ -242& UVEL & $m/sec$ & Nr - &\begin{minipage}[t]{3in} - {U-Velocity} - \end{minipage}\\ -243& VVEL & $m/sec$ & Nr - &\begin{minipage}[t]{3in} - {V-Velocity} - \end{minipage}\\ -244& WVEL & $m/sec$ & Nr - &\begin{minipage}[t]{3in} - {Vertical-Velocity} - \end{minipage}\\ -245& THETASQ & $deg^2$ & Nr - &\begin{minipage}[t]{3in} - {Square of Potential Temperature} - \end{minipage}\\ -246& SALTSQ & $g^2/{kg}^2$ & Nr - &\begin{minipage}[t]{3in} - {Square of Salt (or Water Vapor Mixing Ratio)} - \end{minipage}\\ -247& UVELSQ & $m^2/sec^2$ & Nr - &\begin{minipage}[t]{3in} - {Square of U-Velocity} - \end{minipage}\\ -248& VVELSQ & $m^2/sec^2$ & Nr - &\begin{minipage}[t]{3in} - {Square of V-Velocity} - \end{minipage}\\ -249& WVELSQ & $m^2/sec^2$ & Nr - &\begin{minipage}[t]{3in} - {Square of Vertical-Velocity} - \end{minipage}\\ -250& UVELVVEL & $m^2/sec^2$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Transport of Zonal Momentum} - \end{minipage}\\ -\end{tabular} -\vspace{1.5in} -\vfill - -\newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline - -&\\ -251& UVELMASS & $m/sec$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Mass-Weighted Component of Velocity} - \end{minipage}\\ -252& VVELMASS & $m/sec$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Mass-Weighted Component of Velocity} - \end{minipage}\\ -253& WVELMASS & $m/sec$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Mass-Weighted Component of Velocity} - \end{minipage}\\ -254& UTHMASS & $m-deg/sec$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Mass-Weight Transp of Pot Temp} - \end{minipage}\\ -255& VTHMASS & $m-deg/sec$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Mass-Weight Transp of Pot Temp} - \end{minipage}\\ -256& WTHMASS & $m-deg/sec$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Mass-Weight Transp of Pot Temp} - \end{minipage}\\ -257& USLTMASS & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} - \end{minipage}\\ -258& VSLTMASS & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} - \end{minipage}\\ -259& WSLTMASS & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} - \end{minipage}\\ -260& UVELTH & $m-deg/sec$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Transp of Pot Temp} - \end{minipage}\\ -261& VVELTH & $m-deg/sec$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Transp of Pot Temp} - \end{minipage}\\ -262& WVELTH & $m-deg/sec$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Transp of Pot Temp} - \end{minipage}\\ -263& UVELSLT & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Transp of Salt (or W.Vap Mix Rat.)} - \end{minipage}\\ -264& VVELSLT & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Transp of Salt (or W.Vap Mix Rat.)} - \end{minipage}\\ -265& WVELSLT & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Transp of Salt (or W.Vap Mix Rat.)} - \end{minipage}\\ -266& UTRAC1 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Transp of Tracer 1} - \end{minipage}\\ -267& VTRAC1 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Transp of Tracer 1} - \end{minipage}\\ -268& WTRAC1 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Transp of Tracer 1} - \end{minipage}\\ -269& UTRAC2 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Transp of Tracer 2} - \end{minipage}\\ -270& VTRAC2 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Transp of Tracer 2} - \end{minipage}\\ -271& WTRAC2 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Transp of Tracer 2} - \end{minipage}\\ -272& UTRAC3 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Transp of Tracer 3} - \end{minipage}\\ -273& VTRAC3 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Transp of Tracer 3} - \end{minipage}\\ -274& WTRAC3 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Transp of Tracer 3} - \end{minipage}\\ -275& WSLTMASS & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Mass-Weight Transp of Salt (or W.Vap Mix Rat.)} - \end{minipage}\\ -\end{tabular} -\vspace{1.5in} -\vfill - -\newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline - -&\\ -275& UTRAC4 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Transp of Tracer 4} - \end{minipage}\\ -276& VTRAC4 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Transp of Tracer 4} - \end{minipage}\\ -277& WTRAC4 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Transp of Tracer 4} - \end{minipage}\\ -278& UTRAC5 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Zonal Transp of Tracer 5} - \end{minipage}\\ -279& VTRAC5 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Meridional Transp of Tracer 5} - \end{minipage}\\ -280& WTRAC5 & $m-kg/sec-kg$ & Nr - &\begin{minipage}[t]{3in} - {Vertical Transp of Tracer 5} - \end{minipage}\\ -281& TRAC1 & $kg/kg$ & Nr - &\begin{minipage}[t]{3in} - {Mass-Weight Tracer 1} - \end{minipage}\\ -282& TRAC2 & $kg/kg$ & Nr - &\begin{minipage}[t]{3in} - {Mass-Weight Tracer 2} - \end{minipage}\\ -283& TRAC3 & $kg/kg$ & Nr - &\begin{minipage}[t]{3in} - {Mass-Weight Tracer 3} - \end{minipage}\\ -284& TRAC4 & $kg/kg$ & Nr - &\begin{minipage}[t]{3in} - {Mass-Weight Tracer 4} - \end{minipage}\\ -285& TRAC5 & $kg/kg$ & Nr - &\begin{minipage}[t]{3in} - {Mass-Weight Tracer 5} - \end{minipage}\\ -286& DICBIOA & $mol/m3/s$ & Nr - &\begin{minipage}[t]{3in} - {Biological Productivity} - \end{minipage}\\ -287& DICCARB & $mol eq/m3/s$ & Nr - &\begin{minipage}[t]{3in} - {Carbonate chg-biol prod and remin} - \end{minipage}\\ -288& DICTFLX & $mol/m3/s$ & 1 - &\begin{minipage}[t]{3in} - {Tendency of DIC due to air-sea exch} - \end{minipage}\\ -289& DICOFLX & $mol/m3/s$ & 1 - &\begin{minipage}[t]{3in} - {Tendency of O2 due to air-sea exch} - \end{minipage}\\ -290& DICCFLX & $mol/m2/s$ & 1 - &\begin{minipage}[t]{3in} - {Flux of CO2 - air-sea exch} - \end{minipage}\\ -291& DICPCO2 & $atm$ & 1 - &\begin{minipage}[t]{3in} - {Partial Pressure of CO2} - \end{minipage}\\ -292& DICPHAV & $dimensionless$ & 1 - &\begin{minipage}[t]{3in} - {Average pH} - \end{minipage}\\ -293& DTCONV & $deg/sec$ & Nr - &\begin{minipage}[t]{3in} - {Temp Change due to Convection} - \end{minipage}\\ -294& DQCONV & $g/kg/sec$ & Nr - &\begin{minipage}[t]{3in} - {Specific Humidity Change due to Convection} - \end{minipage}\\ -295& RELHUM & $percent$ & Nr - &\begin{minipage}[t]{3in} - {Relative Humidity} - \end{minipage}\\ -296& PRECLS & $g/m^2/sec$ & 1 - &\begin{minipage}[t]{3in} - {Large Scale Precipitation} - \end{minipage}\\ -297& ENPREC & $J/g$ & 1 - &\begin{minipage}[t]{3in} - {Energy of Precipitation (snow, rain Temp)} - \end{minipage}\\ -298& VISCA4 & $m^4/sec$ & 1 - &\begin{minipage}[t]{3in} - {Biharmonic Viscosity Coefficient} - \end{minipage}\\ -299& VISCAH & $m^2/sec$ & 1 - &\begin{minipage}[t]{3in} - {Harmonic Viscosity Coefficient} - \end{minipage}\\ -300& DRHODR & $kg/m^3/{r-unit}$ & Nr - &\begin{minipage}[t]{3in} - {Stratification: d.Sigma/dr} - \end{minipage}\\ -\end{tabular} -\vspace{1.5in} -\vfill - -\newpage -\vspace*{\fill} -\begin{tabular}{lllll} -\hline\hline -N & NAME & UNITS & LEVELS & DESCRIPTION \\ -\hline - -&\\ -301& DETADT2 & ${r-unit}^2/s^2$ & 1 - &\begin{minipage}[t]{3in} - {Square of Eta (Surf.P,SSH) Tendency} - \end{minipage}\\ -\end{tabular} -\vspace{1.5in} -\vfill - -\newpage - -\subsubsection{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: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. - -{\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 -\[ -q^{n+1} = (\pi q)^{n+1} / \pi^{n+1} +{\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t) \] +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. \subsection{Dos and Donts}