| 1 |
\section{Fizhi: High-end Atmospheric Physics} |
\subsection{Fizhi: High-end Atmospheric Physics} |
| 2 |
\label{sec:pkg:fizhi} |
\label{sec:pkg:fizhi} |
| 3 |
\begin{rawhtml} |
\begin{rawhtml} |
| 4 |
<!-- CMIREDIR:package_fizhi: --> |
<!-- CMIREDIR:package_fizhi: --> |
| 5 |
\end{rawhtml} |
\end{rawhtml} |
| 6 |
\input{texinputs/epsf.tex} |
\input{texinputs/epsf.tex} |
| 7 |
|
|
| 8 |
\subsection{Introduction} |
\subsubsection{Introduction} |
| 9 |
The fizhi (high-end atmospheric physics) package includes a collection of state-of-the-art |
The fizhi (high-end atmospheric physics) package includes a collection of state-of-the-art |
| 10 |
physical parameterizations for atmospheric radiation, cumulus convection, atmospheric |
physical parameterizations for atmospheric radiation, cumulus convection, atmospheric |
| 11 |
boundary layer turbulence, and land surface processes. |
boundary layer turbulence, and land surface processes. |
| 13 |
% ************************************************************************* |
% ************************************************************************* |
| 14 |
% ************************************************************************* |
% ************************************************************************* |
| 15 |
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| 16 |
\subsection{Equations} |
\subsubsection{Equations} |
| 17 |
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|
| 18 |
\subsubsection{Moist Convective Processes} |
Moist Convective Processes: |
| 19 |
|
|
| 20 |
\paragraph{Sub-grid and Large-scale Convection} |
\paragraph{Sub-grid and Large-scale Convection} |
| 21 |
\label{sec:fizhi:mc} |
\label{sec:fizhi:mc} |
| 186 |
Finally, cloud fractions are time-averaged between calls to the radiation packages. |
Finally, cloud fractions are time-averaged between calls to the radiation packages. |
| 187 |
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| 188 |
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|
| 189 |
\subsubsection{Radiation} |
Radiation: |
| 190 |
|
|
| 191 |
The parameterization of radiative heating in the fizhi package includes effects |
The parameterization of radiative heating in the fizhi package includes effects |
| 192 |
from both shortwave and longwave processes. |
from both shortwave and longwave processes. |
| 428 |
hours). Therefore, in a time-averaged sense, both convective and large-scale |
hours). Therefore, in a time-averaged sense, both convective and large-scale |
| 429 |
cloudiness can exist in a given grid-box. |
cloudiness can exist in a given grid-box. |
| 430 |
|
|
| 431 |
\subsubsection{Turbulence} |
Turbulence: |
| 432 |
|
|
| 433 |
Turbulence is parameterized in the fizhi package to account for its contribution to the |
Turbulence is parameterized in the fizhi package to account for its contribution to the |
| 434 |
vertical exchange of heat, moisture, and momentum. |
vertical exchange of heat, moisture, and momentum. |
| 435 |
The turbulence scheme is invoked every 30 minutes, and employs a backward-implicit iterative |
The turbulence scheme is invoked every 30 minutes, and employs a backward-implicit iterative |
| 673 |
day$, and the expression for $C_s$, the heat capacity per unit volume at the surface, |
day$, and the expression for $C_s$, the heat capacity per unit volume at the surface, |
| 674 |
is a function of the ground wetness, $W$. |
is a function of the ground wetness, $W$. |
| 675 |
|
|
| 676 |
\subsubsection{Land Surface Processes} |
Land Surface Processes: |
| 677 |
|
|
| 678 |
\paragraph{Surface Type} |
\paragraph{Surface Type} |
| 679 |
The fizhi package surface Types are designated using the Koster-Suarez (1992) mosaic |
The fizhi package surface Types are designated using the Koster-Suarez (1992) mosaic |
| 751 |
Modifications are made to account for the presence of snow, and its depth relative |
Modifications are made to account for the presence of snow, and its depth relative |
| 752 |
to the height of the vegetation elements. |
to the height of the vegetation elements. |
| 753 |
|
|
| 754 |
\subsubsection{Gravity Wave Drag} |
Gravity Wave Drag: |
| 755 |
|
|
| 756 |
The fizhi package employs the gravity wave drag scheme of Zhou et al. (1996). |
The fizhi package employs the gravity wave drag scheme of Zhou et al. (1996). |
| 757 |
This scheme is a modified version of Vernekar et al. (1992), |
This scheme is a modified version of Vernekar et al. (1992), |
| 758 |
which was based on Alpert et al. (1988) and Helfand et al. (1987). |
which was based on Alpert et al. (1988) and Helfand et al. (1987). |
| 786 |
convergence (through a reduction in the flux of westerly momentum by transient flow eddies). |
convergence (through a reduction in the flux of westerly momentum by transient flow eddies). |
| 787 |
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|
| 788 |
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|
| 789 |
\subsubsection{Boundary Conditions and other Input Data} |
Boundary Conditions and other Input Data: |
| 790 |
|
|
| 791 |
Required fields which are not explicitly predicted or diagnosed during model execution must |
Required fields which are not explicitly predicted or diagnosed during model execution must |
| 792 |
either be prescribed internally or obtained from external data sets. In the fizhi package these |
either be prescribed internally or obtained from external data sets. In the fizhi package these |
| 894 |
the model's moisture data is used. Above 100 mb, the SAGE data is used. Between 100 and 300 mb, |
the model's moisture data is used. Above 100 mb, the SAGE data is used. Between 100 and 300 mb, |
| 895 |
a linear interpolation (in pressure) is performed using the data from SAGE and the GCM. |
a linear interpolation (in pressure) is performed using the data from SAGE and the GCM. |
| 896 |
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|
|
\subsection{Key subroutines, parameters and files} |
|
| 897 |
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|
| 898 |
\subsection{Dos and donts} |
\subsubsection{Fizhi Diagnostics} |
| 899 |
|
|
| 900 |
|
Fizhi Diagnostic Menu: |
| 901 |
|
\label{sec:fizhi-diagnostics:menu} |
| 902 |
|
|
| 903 |
|
\begin{tabular}{llll} |
| 904 |
|
\hline\hline |
| 905 |
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
| 906 |
|
\hline |
| 907 |
|
|
| 908 |
|
&\\ |
| 909 |
|
UFLUX & $Newton/m^2$ & 1 |
| 910 |
|
&\begin{minipage}[t]{3in} |
| 911 |
|
{Surface U-Wind Stress on the atmosphere} |
| 912 |
|
\end{minipage}\\ |
| 913 |
|
VFLUX & $Newton/m^2$ & 1 |
| 914 |
|
&\begin{minipage}[t]{3in} |
| 915 |
|
{Surface V-Wind Stress on the atmosphere} |
| 916 |
|
\end{minipage}\\ |
| 917 |
|
HFLUX & $Watts/m^2$ & 1 |
| 918 |
|
&\begin{minipage}[t]{3in} |
| 919 |
|
{Surface Flux of Sensible Heat} |
| 920 |
|
\end{minipage}\\ |
| 921 |
|
EFLUX & $Watts/m^2$ & 1 |
| 922 |
|
&\begin{minipage}[t]{3in} |
| 923 |
|
{Surface Flux of Latent Heat} |
| 924 |
|
\end{minipage}\\ |
| 925 |
|
QICE & $Watts/m^2$ & 1 |
| 926 |
|
&\begin{minipage}[t]{3in} |
| 927 |
|
{Heat Conduction through Sea-Ice} |
| 928 |
|
\end{minipage}\\ |
| 929 |
|
RADLWG & $Watts/m^2$ & 1 |
| 930 |
|
&\begin{minipage}[t]{3in} |
| 931 |
|
{Net upward LW flux at the ground} |
| 932 |
|
\end{minipage}\\ |
| 933 |
|
RADSWG & $Watts/m^2$ & 1 |
| 934 |
|
&\begin{minipage}[t]{3in} |
| 935 |
|
{Net downward SW flux at the ground} |
| 936 |
|
\end{minipage}\\ |
| 937 |
|
RI & $dimensionless$ & Nrphys |
| 938 |
|
&\begin{minipage}[t]{3in} |
| 939 |
|
{Richardson Number} |
| 940 |
|
\end{minipage}\\ |
| 941 |
|
CT & $dimensionless$ & 1 |
| 942 |
|
&\begin{minipage}[t]{3in} |
| 943 |
|
{Surface Drag coefficient for T and Q} |
| 944 |
|
\end{minipage}\\ |
| 945 |
|
CU & $dimensionless$ & 1 |
| 946 |
|
&\begin{minipage}[t]{3in} |
| 947 |
|
{Surface Drag coefficient for U and V} |
| 948 |
|
\end{minipage}\\ |
| 949 |
|
ET & $m^2/sec$ & Nrphys |
| 950 |
|
&\begin{minipage}[t]{3in} |
| 951 |
|
{Diffusivity coefficient for T and Q} |
| 952 |
|
\end{minipage}\\ |
| 953 |
|
EU & $m^2/sec$ & Nrphys |
| 954 |
|
&\begin{minipage}[t]{3in} |
| 955 |
|
{Diffusivity coefficient for U and V} |
| 956 |
|
\end{minipage}\\ |
| 957 |
|
TURBU & $m/sec/day$ & Nrphys |
| 958 |
|
&\begin{minipage}[t]{3in} |
| 959 |
|
{U-Momentum Changes due to Turbulence} |
| 960 |
|
\end{minipage}\\ |
| 961 |
|
TURBV & $m/sec/day$ & Nrphys |
| 962 |
|
&\begin{minipage}[t]{3in} |
| 963 |
|
{V-Momentum Changes due to Turbulence} |
| 964 |
|
\end{minipage}\\ |
| 965 |
|
TURBT & $deg/day$ & Nrphys |
| 966 |
|
&\begin{minipage}[t]{3in} |
| 967 |
|
{Temperature Changes due to Turbulence} |
| 968 |
|
\end{minipage}\\ |
| 969 |
|
TURBQ & $g/kg/day$ & Nrphys |
| 970 |
|
&\begin{minipage}[t]{3in} |
| 971 |
|
{Specific Humidity Changes due to Turbulence} |
| 972 |
|
\end{minipage}\\ |
| 973 |
|
MOISTT & $deg/day$ & Nrphys |
| 974 |
|
&\begin{minipage}[t]{3in} |
| 975 |
|
{Temperature Changes due to Moist Processes} |
| 976 |
|
\end{minipage}\\ |
| 977 |
|
MOISTQ & $g/kg/day$ & Nrphys |
| 978 |
|
&\begin{minipage}[t]{3in} |
| 979 |
|
{Specific Humidity Changes due to Moist Processes} |
| 980 |
|
\end{minipage}\\ |
| 981 |
|
RADLW & $deg/day$ & Nrphys |
| 982 |
|
&\begin{minipage}[t]{3in} |
| 983 |
|
{Net Longwave heating rate for each level} |
| 984 |
|
\end{minipage}\\ |
| 985 |
|
RADSW & $deg/day$ & Nrphys |
| 986 |
|
&\begin{minipage}[t]{3in} |
| 987 |
|
{Net Shortwave heating rate for each level} |
| 988 |
|
\end{minipage}\\ |
| 989 |
|
PREACC & $mm/day$ & 1 |
| 990 |
|
&\begin{minipage}[t]{3in} |
| 991 |
|
{Total Precipitation} |
| 992 |
|
\end{minipage}\\ |
| 993 |
|
PRECON & $mm/day$ & 1 |
| 994 |
|
&\begin{minipage}[t]{3in} |
| 995 |
|
{Convective Precipitation} |
| 996 |
|
\end{minipage}\\ |
| 997 |
|
TUFLUX & $Newton/m^2$ & Nrphys |
| 998 |
|
&\begin{minipage}[t]{3in} |
| 999 |
|
{Turbulent Flux of U-Momentum} |
| 1000 |
|
\end{minipage}\\ |
| 1001 |
|
TVFLUX & $Newton/m^2$ & Nrphys |
| 1002 |
|
&\begin{minipage}[t]{3in} |
| 1003 |
|
{Turbulent Flux of V-Momentum} |
| 1004 |
|
\end{minipage}\\ |
| 1005 |
|
TTFLUX & $Watts/m^2$ & Nrphys |
| 1006 |
|
&\begin{minipage}[t]{3in} |
| 1007 |
|
{Turbulent Flux of Sensible Heat} |
| 1008 |
|
\end{minipage}\\ |
| 1009 |
|
\end{tabular} |
| 1010 |
|
|
| 1011 |
|
\newpage |
| 1012 |
|
\vspace*{\fill} |
| 1013 |
|
\begin{tabular}{llll} |
| 1014 |
|
\hline\hline |
| 1015 |
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
| 1016 |
|
\hline |
| 1017 |
|
|
| 1018 |
|
&\\ |
| 1019 |
|
TQFLUX & $Watts/m^2$ & Nrphys |
| 1020 |
|
&\begin{minipage}[t]{3in} |
| 1021 |
|
{Turbulent Flux of Latent Heat} |
| 1022 |
|
\end{minipage}\\ |
| 1023 |
|
CN & $dimensionless$ & 1 |
| 1024 |
|
&\begin{minipage}[t]{3in} |
| 1025 |
|
{Neutral Drag Coefficient} |
| 1026 |
|
\end{minipage}\\ |
| 1027 |
|
WINDS & $m/sec$ & 1 |
| 1028 |
|
&\begin{minipage}[t]{3in} |
| 1029 |
|
{Surface Wind Speed} |
| 1030 |
|
\end{minipage}\\ |
| 1031 |
|
DTSRF & $deg$ & 1 |
| 1032 |
|
&\begin{minipage}[t]{3in} |
| 1033 |
|
{Air/Surface virtual temperature difference} |
| 1034 |
|
\end{minipage}\\ |
| 1035 |
|
TG & $deg$ & 1 |
| 1036 |
|
&\begin{minipage}[t]{3in} |
| 1037 |
|
{Ground temperature} |
| 1038 |
|
\end{minipage}\\ |
| 1039 |
|
TS & $deg$ & 1 |
| 1040 |
|
&\begin{minipage}[t]{3in} |
| 1041 |
|
{Surface air temperature (Adiabatic from lowest model layer)} |
| 1042 |
|
\end{minipage}\\ |
| 1043 |
|
DTG & $deg$ & 1 |
| 1044 |
|
&\begin{minipage}[t]{3in} |
| 1045 |
|
{Ground temperature adjustment} |
| 1046 |
|
\end{minipage}\\ |
| 1047 |
|
|
| 1048 |
|
QG & $g/kg$ & 1 |
| 1049 |
|
&\begin{minipage}[t]{3in} |
| 1050 |
|
{Ground specific humidity} |
| 1051 |
|
\end{minipage}\\ |
| 1052 |
|
QS & $g/kg$ & 1 |
| 1053 |
|
&\begin{minipage}[t]{3in} |
| 1054 |
|
{Saturation surface specific humidity} |
| 1055 |
|
\end{minipage}\\ |
| 1056 |
|
TGRLW & $deg$ & 1 |
| 1057 |
|
&\begin{minipage}[t]{3in} |
| 1058 |
|
{Instantaneous ground temperature used as input to the |
| 1059 |
|
Longwave radiation subroutine} |
| 1060 |
|
\end{minipage}\\ |
| 1061 |
|
ST4 & $Watts/m^2$ & 1 |
| 1062 |
|
&\begin{minipage}[t]{3in} |
| 1063 |
|
{Upward Longwave flux at the ground ($\sigma T^4$)} |
| 1064 |
|
\end{minipage}\\ |
| 1065 |
|
OLR & $Watts/m^2$ & 1 |
| 1066 |
|
&\begin{minipage}[t]{3in} |
| 1067 |
|
{Net upward Longwave flux at the top of the model} |
| 1068 |
|
\end{minipage}\\ |
| 1069 |
|
OLRCLR & $Watts/m^2$ & 1 |
| 1070 |
|
&\begin{minipage}[t]{3in} |
| 1071 |
|
{Net upward clearsky Longwave flux at the top of the model} |
| 1072 |
|
\end{minipage}\\ |
| 1073 |
|
LWGCLR & $Watts/m^2$ & 1 |
| 1074 |
|
&\begin{minipage}[t]{3in} |
| 1075 |
|
{Net upward clearsky Longwave flux at the ground} |
| 1076 |
|
\end{minipage}\\ |
| 1077 |
|
LWCLR & $deg/day$ & Nrphys |
| 1078 |
|
&\begin{minipage}[t]{3in} |
| 1079 |
|
{Net clearsky Longwave heating rate for each level} |
| 1080 |
|
\end{minipage}\\ |
| 1081 |
|
TLW & $deg$ & Nrphys |
| 1082 |
|
&\begin{minipage}[t]{3in} |
| 1083 |
|
{Instantaneous temperature used as input to the Longwave radiation |
| 1084 |
|
subroutine} |
| 1085 |
|
\end{minipage}\\ |
| 1086 |
|
SHLW & $g/g$ & Nrphys |
| 1087 |
|
&\begin{minipage}[t]{3in} |
| 1088 |
|
{Instantaneous specific humidity used as input to the Longwave radiation |
| 1089 |
|
subroutine} |
| 1090 |
|
\end{minipage}\\ |
| 1091 |
|
OZLW & $g/g$ & Nrphys |
| 1092 |
|
&\begin{minipage}[t]{3in} |
| 1093 |
|
{Instantaneous ozone used as input to the Longwave radiation |
| 1094 |
|
subroutine} |
| 1095 |
|
\end{minipage}\\ |
| 1096 |
|
CLMOLW & $0-1$ & Nrphys |
| 1097 |
|
&\begin{minipage}[t]{3in} |
| 1098 |
|
{Maximum overlap cloud fraction used in the Longwave radiation |
| 1099 |
|
subroutine} |
| 1100 |
|
\end{minipage}\\ |
| 1101 |
|
CLDTOT & $0-1$ & Nrphys |
| 1102 |
|
&\begin{minipage}[t]{3in} |
| 1103 |
|
{Total cloud fraction used in the Longwave and Shortwave radiation |
| 1104 |
|
subroutines} |
| 1105 |
|
\end{minipage}\\ |
| 1106 |
|
LWGDOWN & $Watts/m^2$ & 1 |
| 1107 |
|
&\begin{minipage}[t]{3in} |
| 1108 |
|
{Downwelling Longwave radiation at the ground} |
| 1109 |
|
\end{minipage}\\ |
| 1110 |
|
GWDT & $deg/day$ & Nrphys |
| 1111 |
|
&\begin{minipage}[t]{3in} |
| 1112 |
|
{Temperature tendency due to Gravity Wave Drag} |
| 1113 |
|
\end{minipage}\\ |
| 1114 |
|
RADSWT & $Watts/m^2$ & 1 |
| 1115 |
|
&\begin{minipage}[t]{3in} |
| 1116 |
|
{Incident Shortwave radiation at the top of the atmosphere} |
| 1117 |
|
\end{minipage}\\ |
| 1118 |
|
TAUCLD & $per 100 mb$ & Nrphys |
| 1119 |
|
&\begin{minipage}[t]{3in} |
| 1120 |
|
{Counted Cloud Optical Depth (non-dimensional) per 100 mb} |
| 1121 |
|
\end{minipage}\\ |
| 1122 |
|
TAUCLDC & $Number$ & Nrphys |
| 1123 |
|
&\begin{minipage}[t]{3in} |
| 1124 |
|
{Cloud Optical Depth Counter} |
| 1125 |
|
\end{minipage}\\ |
| 1126 |
|
\end{tabular} |
| 1127 |
|
\vfill |
| 1128 |
|
|
| 1129 |
|
\newpage |
| 1130 |
|
\vspace*{\fill} |
| 1131 |
|
\begin{tabular}{llll} |
| 1132 |
|
\hline\hline |
| 1133 |
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
| 1134 |
|
\hline |
| 1135 |
|
|
| 1136 |
|
&\\ |
| 1137 |
|
CLDLOW & $0-1$ & Nrphys |
| 1138 |
|
&\begin{minipage}[t]{3in} |
| 1139 |
|
{Low-Level ( 1000-700 hPa) Cloud Fraction (0-1)} |
| 1140 |
|
\end{minipage}\\ |
| 1141 |
|
EVAP & $mm/day$ & 1 |
| 1142 |
|
&\begin{minipage}[t]{3in} |
| 1143 |
|
{Surface evaporation} |
| 1144 |
|
\end{minipage}\\ |
| 1145 |
|
DPDT & $hPa/day$ & 1 |
| 1146 |
|
&\begin{minipage}[t]{3in} |
| 1147 |
|
{Surface Pressure tendency} |
| 1148 |
|
\end{minipage}\\ |
| 1149 |
|
UAVE & $m/sec$ & Nrphys |
| 1150 |
|
&\begin{minipage}[t]{3in} |
| 1151 |
|
{Average U-Wind} |
| 1152 |
|
\end{minipage}\\ |
| 1153 |
|
VAVE & $m/sec$ & Nrphys |
| 1154 |
|
&\begin{minipage}[t]{3in} |
| 1155 |
|
{Average V-Wind} |
| 1156 |
|
\end{minipage}\\ |
| 1157 |
|
TAVE & $deg$ & Nrphys |
| 1158 |
|
&\begin{minipage}[t]{3in} |
| 1159 |
|
{Average Temperature} |
| 1160 |
|
\end{minipage}\\ |
| 1161 |
|
QAVE & $g/kg$ & Nrphys |
| 1162 |
|
&\begin{minipage}[t]{3in} |
| 1163 |
|
{Average Specific Humidity} |
| 1164 |
|
\end{minipage}\\ |
| 1165 |
|
OMEGA & $hPa/day$ & Nrphys |
| 1166 |
|
&\begin{minipage}[t]{3in} |
| 1167 |
|
{Vertical Velocity} |
| 1168 |
|
\end{minipage}\\ |
| 1169 |
|
DUDT & $m/sec/day$ & Nrphys |
| 1170 |
|
&\begin{minipage}[t]{3in} |
| 1171 |
|
{Total U-Wind tendency} |
| 1172 |
|
\end{minipage}\\ |
| 1173 |
|
DVDT & $m/sec/day$ & Nrphys |
| 1174 |
|
&\begin{minipage}[t]{3in} |
| 1175 |
|
{Total V-Wind tendency} |
| 1176 |
|
\end{minipage}\\ |
| 1177 |
|
DTDT & $deg/day$ & Nrphys |
| 1178 |
|
&\begin{minipage}[t]{3in} |
| 1179 |
|
{Total Temperature tendency} |
| 1180 |
|
\end{minipage}\\ |
| 1181 |
|
DQDT & $g/kg/day$ & Nrphys |
| 1182 |
|
&\begin{minipage}[t]{3in} |
| 1183 |
|
{Total Specific Humidity tendency} |
| 1184 |
|
\end{minipage}\\ |
| 1185 |
|
VORT & $10^{-4}/sec$ & Nrphys |
| 1186 |
|
&\begin{minipage}[t]{3in} |
| 1187 |
|
{Relative Vorticity} |
| 1188 |
|
\end{minipage}\\ |
| 1189 |
|
DTLS & $deg/day$ & Nrphys |
| 1190 |
|
&\begin{minipage}[t]{3in} |
| 1191 |
|
{Temperature tendency due to Stratiform Cloud Formation} |
| 1192 |
|
\end{minipage}\\ |
| 1193 |
|
DQLS & $g/kg/day$ & Nrphys |
| 1194 |
|
&\begin{minipage}[t]{3in} |
| 1195 |
|
{Specific Humidity tendency due to Stratiform Cloud Formation} |
| 1196 |
|
\end{minipage}\\ |
| 1197 |
|
USTAR & $m/sec$ & 1 |
| 1198 |
|
&\begin{minipage}[t]{3in} |
| 1199 |
|
{Surface USTAR wind} |
| 1200 |
|
\end{minipage}\\ |
| 1201 |
|
Z0 & $m$ & 1 |
| 1202 |
|
&\begin{minipage}[t]{3in} |
| 1203 |
|
{Surface roughness} |
| 1204 |
|
\end{minipage}\\ |
| 1205 |
|
FRQTRB & $0-1$ & Nrphys-1 |
| 1206 |
|
&\begin{minipage}[t]{3in} |
| 1207 |
|
{Frequency of Turbulence} |
| 1208 |
|
\end{minipage}\\ |
| 1209 |
|
PBL & $mb$ & 1 |
| 1210 |
|
&\begin{minipage}[t]{3in} |
| 1211 |
|
{Planetary Boundary Layer depth} |
| 1212 |
|
\end{minipage}\\ |
| 1213 |
|
SWCLR & $deg/day$ & Nrphys |
| 1214 |
|
&\begin{minipage}[t]{3in} |
| 1215 |
|
{Net clearsky Shortwave heating rate for each level} |
| 1216 |
|
\end{minipage}\\ |
| 1217 |
|
OSR & $Watts/m^2$ & 1 |
| 1218 |
|
&\begin{minipage}[t]{3in} |
| 1219 |
|
{Net downward Shortwave flux at the top of the model} |
| 1220 |
|
\end{minipage}\\ |
| 1221 |
|
OSRCLR & $Watts/m^2$ & 1 |
| 1222 |
|
&\begin{minipage}[t]{3in} |
| 1223 |
|
{Net downward clearsky Shortwave flux at the top of the model} |
| 1224 |
|
\end{minipage}\\ |
| 1225 |
|
CLDMAS & $kg / m^2$ & Nrphys |
| 1226 |
|
&\begin{minipage}[t]{3in} |
| 1227 |
|
{Convective cloud mass flux} |
| 1228 |
|
\end{minipage}\\ |
| 1229 |
|
UAVE & $m/sec$ & Nrphys |
| 1230 |
|
&\begin{minipage}[t]{3in} |
| 1231 |
|
{Time-averaged $u-Wind$} |
| 1232 |
|
\end{minipage}\\ |
| 1233 |
|
\end{tabular} |
| 1234 |
|
\vfill |
| 1235 |
|
|
| 1236 |
|
\newpage |
| 1237 |
|
\vspace*{\fill} |
| 1238 |
|
\begin{tabular}{llll} |
| 1239 |
|
\hline\hline |
| 1240 |
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
| 1241 |
|
\hline |
| 1242 |
|
|
| 1243 |
|
&\\ |
| 1244 |
|
VAVE & $m/sec$ & Nrphys |
| 1245 |
|
&\begin{minipage}[t]{3in} |
| 1246 |
|
{Time-averaged $v-Wind$} |
| 1247 |
|
\end{minipage}\\ |
| 1248 |
|
TAVE & $deg$ & Nrphys |
| 1249 |
|
&\begin{minipage}[t]{3in} |
| 1250 |
|
{Time-averaged $Temperature$} |
| 1251 |
|
\end{minipage}\\ |
| 1252 |
|
QAVE & $g/g$ & Nrphys |
| 1253 |
|
&\begin{minipage}[t]{3in} |
| 1254 |
|
{Time-averaged $Specific \, \, Humidity$} |
| 1255 |
|
\end{minipage}\\ |
| 1256 |
|
RFT & $deg/day$ & Nrphys |
| 1257 |
|
&\begin{minipage}[t]{3in} |
| 1258 |
|
{Temperature tendency due Rayleigh Friction} |
| 1259 |
|
\end{minipage}\\ |
| 1260 |
|
PS & $mb$ & 1 |
| 1261 |
|
&\begin{minipage}[t]{3in} |
| 1262 |
|
{Surface Pressure} |
| 1263 |
|
\end{minipage}\\ |
| 1264 |
|
QQAVE & $(m/sec)^2$ & Nrphys |
| 1265 |
|
&\begin{minipage}[t]{3in} |
| 1266 |
|
{Time-averaged $Turbulent Kinetic Energy$} |
| 1267 |
|
\end{minipage}\\ |
| 1268 |
|
SWGCLR & $Watts/m^2$ & 1 |
| 1269 |
|
&\begin{minipage}[t]{3in} |
| 1270 |
|
{Net downward clearsky Shortwave flux at the ground} |
| 1271 |
|
\end{minipage}\\ |
| 1272 |
|
PAVE & $mb$ & 1 |
| 1273 |
|
&\begin{minipage}[t]{3in} |
| 1274 |
|
{Time-averaged Surface Pressure} |
| 1275 |
|
\end{minipage}\\ |
| 1276 |
|
DIABU & $m/sec/day$ & Nrphys |
| 1277 |
|
&\begin{minipage}[t]{3in} |
| 1278 |
|
{Total Diabatic forcing on $u-Wind$} |
| 1279 |
|
\end{minipage}\\ |
| 1280 |
|
DIABV & $m/sec/day$ & Nrphys |
| 1281 |
|
&\begin{minipage}[t]{3in} |
| 1282 |
|
{Total Diabatic forcing on $v-Wind$} |
| 1283 |
|
\end{minipage}\\ |
| 1284 |
|
DIABT & $deg/day$ & Nrphys |
| 1285 |
|
&\begin{minipage}[t]{3in} |
| 1286 |
|
{Total Diabatic forcing on $Temperature$} |
| 1287 |
|
\end{minipage}\\ |
| 1288 |
|
DIABQ & $g/kg/day$ & Nrphys |
| 1289 |
|
&\begin{minipage}[t]{3in} |
| 1290 |
|
{Total Diabatic forcing on $Specific \, \, Humidity$} |
| 1291 |
|
\end{minipage}\\ |
| 1292 |
|
RFU & $m/sec/day$ & Nrphys |
| 1293 |
|
&\begin{minipage}[t]{3in} |
| 1294 |
|
{U-Wind tendency due to Rayleigh Friction} |
| 1295 |
|
\end{minipage}\\ |
| 1296 |
|
RFV & $m/sec/day$ & Nrphys |
| 1297 |
|
&\begin{minipage}[t]{3in} |
| 1298 |
|
{V-Wind tendency due to Rayleigh Friction} |
| 1299 |
|
\end{minipage}\\ |
| 1300 |
|
GWDU & $m/sec/day$ & Nrphys |
| 1301 |
|
&\begin{minipage}[t]{3in} |
| 1302 |
|
{U-Wind tendency due to Gravity Wave Drag} |
| 1303 |
|
\end{minipage}\\ |
| 1304 |
|
GWDU & $m/sec/day$ & Nrphys |
| 1305 |
|
&\begin{minipage}[t]{3in} |
| 1306 |
|
{V-Wind tendency due to Gravity Wave Drag} |
| 1307 |
|
\end{minipage}\\ |
| 1308 |
|
GWDUS & $N/m^2$ & 1 |
| 1309 |
|
&\begin{minipage}[t]{3in} |
| 1310 |
|
{U-Wind Gravity Wave Drag Stress at Surface} |
| 1311 |
|
\end{minipage}\\ |
| 1312 |
|
GWDVS & $N/m^2$ & 1 |
| 1313 |
|
&\begin{minipage}[t]{3in} |
| 1314 |
|
{V-Wind Gravity Wave Drag Stress at Surface} |
| 1315 |
|
\end{minipage}\\ |
| 1316 |
|
GWDUT & $N/m^2$ & 1 |
| 1317 |
|
&\begin{minipage}[t]{3in} |
| 1318 |
|
{U-Wind Gravity Wave Drag Stress at Top} |
| 1319 |
|
\end{minipage}\\ |
| 1320 |
|
GWDVT & $N/m^2$ & 1 |
| 1321 |
|
&\begin{minipage}[t]{3in} |
| 1322 |
|
{V-Wind Gravity Wave Drag Stress at Top} |
| 1323 |
|
\end{minipage}\\ |
| 1324 |
|
LZRAD & $mg/kg$ & Nrphys |
| 1325 |
|
&\begin{minipage}[t]{3in} |
| 1326 |
|
{Estimated Cloud Liquid Water used in Radiation} |
| 1327 |
|
\end{minipage}\\ |
| 1328 |
|
\end{tabular} |
| 1329 |
|
\vfill |
| 1330 |
|
|
| 1331 |
|
\newpage |
| 1332 |
|
\vspace*{\fill} |
| 1333 |
|
\begin{tabular}{llll} |
| 1334 |
|
\hline\hline |
| 1335 |
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
| 1336 |
|
\hline |
| 1337 |
|
|
| 1338 |
|
&\\ |
| 1339 |
|
SLP & $mb$ & 1 |
| 1340 |
|
&\begin{minipage}[t]{3in} |
| 1341 |
|
{Time-averaged Sea-level Pressure} |
| 1342 |
|
\end{minipage}\\ |
| 1343 |
|
CLDFRC & $0-1$ & 1 |
| 1344 |
|
&\begin{minipage}[t]{3in} |
| 1345 |
|
{Total Cloud Fraction} |
| 1346 |
|
\end{minipage}\\ |
| 1347 |
|
TPW & $gm/cm^2$ & 1 |
| 1348 |
|
&\begin{minipage}[t]{3in} |
| 1349 |
|
{Precipitable water} |
| 1350 |
|
\end{minipage}\\ |
| 1351 |
|
U2M & $m/sec$ & 1 |
| 1352 |
|
&\begin{minipage}[t]{3in} |
| 1353 |
|
{U-Wind at 2 meters} |
| 1354 |
|
\end{minipage}\\ |
| 1355 |
|
V2M & $m/sec$ & 1 |
| 1356 |
|
&\begin{minipage}[t]{3in} |
| 1357 |
|
{V-Wind at 2 meters} |
| 1358 |
|
\end{minipage}\\ |
| 1359 |
|
T2M & $deg$ & 1 |
| 1360 |
|
&\begin{minipage}[t]{3in} |
| 1361 |
|
{Temperature at 2 meters} |
| 1362 |
|
\end{minipage}\\ |
| 1363 |
|
Q2M & $g/kg$ & 1 |
| 1364 |
|
&\begin{minipage}[t]{3in} |
| 1365 |
|
{Specific Humidity at 2 meters} |
| 1366 |
|
\end{minipage}\\ |
| 1367 |
|
U10M & $m/sec$ & 1 |
| 1368 |
|
&\begin{minipage}[t]{3in} |
| 1369 |
|
{U-Wind at 10 meters} |
| 1370 |
|
\end{minipage}\\ |
| 1371 |
|
V10M & $m/sec$ & 1 |
| 1372 |
|
&\begin{minipage}[t]{3in} |
| 1373 |
|
{V-Wind at 10 meters} |
| 1374 |
|
\end{minipage}\\ |
| 1375 |
|
T10M & $deg$ & 1 |
| 1376 |
|
&\begin{minipage}[t]{3in} |
| 1377 |
|
{Temperature at 10 meters} |
| 1378 |
|
\end{minipage}\\ |
| 1379 |
|
Q10M & $g/kg$ & 1 |
| 1380 |
|
&\begin{minipage}[t]{3in} |
| 1381 |
|
{Specific Humidity at 10 meters} |
| 1382 |
|
\end{minipage}\\ |
| 1383 |
|
DTRAIN & $kg/m^2$ & Nrphys |
| 1384 |
|
&\begin{minipage}[t]{3in} |
| 1385 |
|
{Detrainment Cloud Mass Flux} |
| 1386 |
|
\end{minipage}\\ |
| 1387 |
|
QFILL & $g/kg/day$ & Nrphys |
| 1388 |
|
&\begin{minipage}[t]{3in} |
| 1389 |
|
{Filling of negative specific humidity} |
| 1390 |
|
\end{minipage}\\ |
| 1391 |
|
\end{tabular} |
| 1392 |
|
\vspace{1.5in} |
| 1393 |
|
\vfill |
| 1394 |
|
|
| 1395 |
|
\newpage |
| 1396 |
|
\vspace*{\fill} |
| 1397 |
|
\begin{tabular}{llll} |
| 1398 |
|
\hline\hline |
| 1399 |
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
| 1400 |
|
\hline |
| 1401 |
|
|
| 1402 |
|
&\\ |
| 1403 |
|
DTCONV & $deg/sec$ & Nr |
| 1404 |
|
&\begin{minipage}[t]{3in} |
| 1405 |
|
{Temp Change due to Convection} |
| 1406 |
|
\end{minipage}\\ |
| 1407 |
|
DQCONV & $g/kg/sec$ & Nr |
| 1408 |
|
&\begin{minipage}[t]{3in} |
| 1409 |
|
{Specific Humidity Change due to Convection} |
| 1410 |
|
\end{minipage}\\ |
| 1411 |
|
RELHUM & $percent$ & Nr |
| 1412 |
|
&\begin{minipage}[t]{3in} |
| 1413 |
|
{Relative Humidity} |
| 1414 |
|
\end{minipage}\\ |
| 1415 |
|
PRECLS & $g/m^2/sec$ & 1 |
| 1416 |
|
&\begin{minipage}[t]{3in} |
| 1417 |
|
{Large Scale Precipitation} |
| 1418 |
|
\end{minipage}\\ |
| 1419 |
|
ENPREC & $J/g$ & 1 |
| 1420 |
|
&\begin{minipage}[t]{3in} |
| 1421 |
|
{Energy of Precipitation (snow, rain Temp)} |
| 1422 |
|
\end{minipage}\\ |
| 1423 |
|
\end{tabular} |
| 1424 |
|
\vspace{1.5in} |
| 1425 |
|
\vfill |
| 1426 |
|
|
| 1427 |
|
\newpage |
| 1428 |
|
|
| 1429 |
|
Fizhi Diagnostic Description: |
| 1430 |
|
|
| 1431 |
|
In this section we list and describe the diagnostic quantities available within the |
| 1432 |
|
GCM. The diagnostics are listed in the order that they appear in the |
| 1433 |
|
Diagnostic Menu, Section \ref{sec:fizhi-diagnostics:menu}. |
| 1434 |
|
In all cases, each diagnostic as currently archived on the output datasets |
| 1435 |
|
is time-averaged over its diagnostic output frequency: |
| 1436 |
|
|
| 1437 |
|
\[ |
| 1438 |
|
{\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t) |
| 1439 |
|
\] |
| 1440 |
|
where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the |
| 1441 |
|
output frequency of the diagnostic, and $\Delta t$ is |
| 1442 |
|
the timestep over which the diagnostic is updated. |
| 1443 |
|
|
| 1444 |
|
{ \underline {UFLUX} Surface Zonal Wind Stress on the Atmosphere ($Newton/m^2$) } |
| 1445 |
|
|
| 1446 |
|
The zonal wind stress is the turbulent flux of zonal momentum from |
| 1447 |
|
the surface. |
| 1448 |
|
\[ |
| 1449 |
|
{\bf UFLUX} = - \rho C_D W_s u \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u |
| 1450 |
|
\] |
| 1451 |
|
where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface |
| 1452 |
|
drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum |
| 1453 |
|
(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $u$ is |
| 1454 |
|
the zonal wind in the lowest model layer. |
| 1455 |
|
\\ |
| 1456 |
|
|
| 1457 |
|
|
| 1458 |
|
{ \underline {VFLUX} Surface Meridional Wind Stress on the Atmosphere ($Newton/m^2$) } |
| 1459 |
|
|
| 1460 |
|
The meridional wind stress is the turbulent flux of meridional momentum from |
| 1461 |
|
the surface. |
| 1462 |
|
\[ |
| 1463 |
|
{\bf VFLUX} = - \rho C_D W_s v \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u |
| 1464 |
|
\] |
| 1465 |
|
where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface |
| 1466 |
|
drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum |
| 1467 |
|
(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $v$ is |
| 1468 |
|
the meridional wind in the lowest model layer. |
| 1469 |
|
\\ |
| 1470 |
|
|
| 1471 |
|
{ \underline {HFLUX} Surface Flux of Sensible Heat ($Watts/m^2$) } |
| 1472 |
|
|
| 1473 |
|
The turbulent flux of sensible heat from the surface to the atmosphere is a function of the |
| 1474 |
|
gradient of virtual potential temperature and the eddy exchange coefficient: |
| 1475 |
|
\[ |
| 1476 |
|
{\bf HFLUX} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{surface} - \theta_{Nrphys}) |
| 1477 |
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
| 1478 |
|
\] |
| 1479 |
|
where $\rho$ = the atmospheric density at the surface, $c_{p}$ is the specific |
| 1480 |
|
heat of air, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the |
| 1481 |
|
magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient |
| 1482 |
|
for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient |
| 1483 |
|
for heat and moisture (see diagnostic number 9), and $\theta$ is the potential temperature |
| 1484 |
|
at the surface and at the bottom model level. |
| 1485 |
|
\\ |
| 1486 |
|
|
| 1487 |
|
|
| 1488 |
|
{ \underline {EFLUX} Surface Flux of Latent Heat ($Watts/m^2$) } |
| 1489 |
|
|
| 1490 |
|
The turbulent flux of latent heat from the surface to the atmosphere is a function of the |
| 1491 |
|
gradient of moisture, the potential evapotranspiration fraction and the eddy exchange coefficient: |
| 1492 |
|
\[ |
| 1493 |
|
{\bf EFLUX} = \rho \beta L C_{H} W_s (q_{surface} - q_{Nrphys}) |
| 1494 |
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
| 1495 |
|
\] |
| 1496 |
|
where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of |
| 1497 |
|
the potential evapotranspiration actually evaporated, L is the latent |
| 1498 |
|
heat of evaporation, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the |
| 1499 |
|
magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient |
| 1500 |
|
for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient |
| 1501 |
|
for heat and moisture (see diagnostic number 9), and $q_{surface}$ and $q_{Nrphys}$ are the specific |
| 1502 |
|
humidity at the surface and at the bottom model level, respectively. |
| 1503 |
|
\\ |
| 1504 |
|
|
| 1505 |
|
{ \underline {QICE} Heat Conduction Through Sea Ice ($Watts/m^2$) } |
| 1506 |
|
|
| 1507 |
|
Over sea ice there is an additional source of energy at the surface due to the heat |
| 1508 |
|
conduction from the relatively warm ocean through the sea ice. The heat conduction |
| 1509 |
|
through sea ice represents an additional energy source term for the ground temperature equation. |
| 1510 |
|
|
| 1511 |
|
\[ |
| 1512 |
|
{\bf QICE} = {C_{ti} \over {H_i}} (T_i-T_g) |
| 1513 |
|
\] |
| 1514 |
|
|
| 1515 |
|
where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to |
| 1516 |
|
be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and |
| 1517 |
|
$T_g$ is the temperature of the sea ice. |
| 1518 |
|
|
| 1519 |
|
NOTE: QICE is not available through model version 5.3, but is available in subsequent versions. |
| 1520 |
|
\\ |
| 1521 |
|
|
| 1522 |
|
|
| 1523 |
|
{ \underline {RADLWG} Net upward Longwave Flux at the surface ($Watts/m^2$)} |
| 1524 |
|
|
| 1525 |
|
\begin{eqnarray*} |
| 1526 |
|
{\bf RADLWG} & = & F_{LW,Nrphys+1}^{Net} \\ |
| 1527 |
|
& = & F_{LW,Nrphys+1}^\uparrow - F_{LW,Nrphys+1}^\downarrow |
| 1528 |
|
\end{eqnarray*} |
| 1529 |
|
\\ |
| 1530 |
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
| 1531 |
|
$F_{LW}^\uparrow$ is |
| 1532 |
|
the upward Longwave flux and $F_{LW}^\downarrow$ is the downward Longwave flux. |
| 1533 |
|
\\ |
| 1534 |
|
|
| 1535 |
|
{ \underline {RADSWG} Net downard shortwave Flux at the surface ($Watts/m^2$)} |
| 1536 |
|
|
| 1537 |
|
\begin{eqnarray*} |
| 1538 |
|
{\bf RADSWG} & = & F_{SW,Nrphys+1}^{Net} \\ |
| 1539 |
|
& = & F_{SW,Nrphys+1}^\downarrow - F_{SW,Nrphys+1}^\uparrow |
| 1540 |
|
\end{eqnarray*} |
| 1541 |
|
\\ |
| 1542 |
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
| 1543 |
|
$F_{SW}^\downarrow$ is |
| 1544 |
|
the downward Shortwave flux and $F_{SW}^\uparrow$ is the upward Shortwave flux. |
| 1545 |
|
\\ |
| 1546 |
|
|
| 1547 |
|
|
| 1548 |
|
\noindent |
| 1549 |
|
{ \underline {RI} Richardson Number} ($dimensionless$) |
| 1550 |
|
|
| 1551 |
|
\noindent |
| 1552 |
|
The non-dimensional stability indicator is the ratio of the buoyancy to the shear: |
| 1553 |
|
\[ |
| 1554 |
|
{\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
| 1555 |
|
= { {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
| 1556 |
|
\] |
| 1557 |
|
\\ |
| 1558 |
|
where we used the hydrostatic equation: |
| 1559 |
|
\[ |
| 1560 |
|
{\pp{\Phi}{P^ \kappa}} = c_p \theta_v |
| 1561 |
|
\] |
| 1562 |
|
Negative values indicate unstable buoyancy {\bf{AND}} shear, small positive values ($<0.4$) |
| 1563 |
|
indicate dominantly unstable shear, and large positive values indicate dominantly stable |
| 1564 |
|
stratification. |
| 1565 |
|
\\ |
| 1566 |
|
|
| 1567 |
|
\noindent |
| 1568 |
|
{ \underline {CT} Surface Exchange Coefficient for Temperature and Moisture ($dimensionless$) } |
| 1569 |
|
|
| 1570 |
|
\noindent |
| 1571 |
|
The surface exchange coefficient is obtained from the similarity functions for the stability |
| 1572 |
|
dependant flux profile relationships: |
| 1573 |
|
\[ |
| 1574 |
|
{\bf CT} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} = |
| 1575 |
|
-{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} = |
| 1576 |
|
{ k \over { (\psi_{h} + \psi_{g}) } } |
| 1577 |
|
\] |
| 1578 |
|
where $\psi_h$ is the surface layer non-dimensional temperature change and $\psi_g$ is the |
| 1579 |
|
viscous sublayer non-dimensional temperature or moisture change: |
| 1580 |
|
\[ |
| 1581 |
|
\psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} \hspace{1cm} and |
| 1582 |
|
\hspace{1cm} \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} } |
| 1583 |
|
(h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2} |
| 1584 |
|
\] |
| 1585 |
|
and: |
| 1586 |
|
$h_{0} = 30z_{0}$ with a maximum value over land of 0.01 |
| 1587 |
|
|
| 1588 |
|
\noindent |
| 1589 |
|
$\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of |
| 1590 |
|
the temperature and moisture gradients, specified differently for stable and unstable |
| 1591 |
|
layers according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the |
| 1592 |
|
non-dimensional stability parameter, Pr is the Prandtl number for air, $\nu$ is the molecular |
| 1593 |
|
viscosity, $z_{0}$ is the surface roughness length, $u_*$ is the surface stress velocity |
| 1594 |
|
(see diagnostic number 67), and the subscript ref refers to a reference value. |
| 1595 |
|
\\ |
| 1596 |
|
|
| 1597 |
|
\noindent |
| 1598 |
|
{ \underline {CU} Surface Exchange Coefficient for Momentum ($dimensionless$) } |
| 1599 |
|
|
| 1600 |
|
\noindent |
| 1601 |
|
The surface exchange coefficient is obtained from the similarity functions for the stability |
| 1602 |
|
dependant flux profile relationships: |
| 1603 |
|
\[ |
| 1604 |
|
{\bf CU} = {u_* \over W_s} = { k \over \psi_{m} } |
| 1605 |
|
\] |
| 1606 |
|
where $\psi_m$ is the surface layer non-dimensional wind shear: |
| 1607 |
|
\[ |
| 1608 |
|
\psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta} |
| 1609 |
|
\] |
| 1610 |
|
\noindent |
| 1611 |
|
$\phi_m$ is the similarity function of $\zeta$, which expresses the stability dependance of |
| 1612 |
|
the temperature and moisture gradients, specified differently for stable and unstable layers |
| 1613 |
|
according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the |
| 1614 |
|
non-dimensional stability parameter, $u_*$ is the surface stress velocity |
| 1615 |
|
(see diagnostic number 67), and $W_s$ is the magnitude of the surface layer wind. |
| 1616 |
|
\\ |
| 1617 |
|
|
| 1618 |
|
\noindent |
| 1619 |
|
{ \underline {ET} Diffusivity Coefficient for Temperature and Moisture ($m^2/sec$) } |
| 1620 |
|
|
| 1621 |
|
\noindent |
| 1622 |
|
In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat or |
| 1623 |
|
moisture flux for the atmosphere above the surface layer can be expressed as a turbulent |
| 1624 |
|
diffusion coefficient $K_h$ times the negative of the gradient of potential temperature |
| 1625 |
|
or moisture. In the Helfand and Labraga (1988) adaptation of this closure, $K_h$ |
| 1626 |
|
takes the form: |
| 1627 |
|
\[ |
| 1628 |
|
{\bf ET} = K_h = -{( {\overline{w^{\prime}\theta_v^{\prime}}}) \over {\pp{\theta_v}{z}} } |
| 1629 |
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) & \mbox{decaying turbulence} |
| 1630 |
|
\\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. |
| 1631 |
|
\] |
| 1632 |
|
where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} |
| 1633 |
|
energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, |
| 1634 |
|
which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer |
| 1635 |
|
depth, |
| 1636 |
|
$S_H$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and |
| 1637 |
|
wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium |
| 1638 |
|
dimensionless buoyancy and wind shear |
| 1639 |
|
parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
| 1640 |
|
are functions of the Richardson number. |
| 1641 |
|
|
| 1642 |
|
\noindent |
| 1643 |
|
For the detailed equations and derivations of the modified level 2.5 closure scheme, |
| 1644 |
|
see Helfand and Labraga, 1988. |
| 1645 |
|
|
| 1646 |
|
\noindent |
| 1647 |
|
In the surface layer, ${\bf {ET}}$ is the exchange coefficient for heat and moisture, |
| 1648 |
|
in units of $m/sec$, given by: |
| 1649 |
|
\[ |
| 1650 |
|
{\bf ET_{Nrphys}} = C_t * u_* = C_H W_s |
| 1651 |
|
\] |
| 1652 |
|
\noindent |
| 1653 |
|
where $C_t$ is the dimensionless exchange coefficient for heat and moisture from the |
| 1654 |
|
surface layer similarity functions (see diagnostic number 9), $u_*$ is the surface |
| 1655 |
|
friction velocity (see diagnostic number 67), $C_H$ is the heat transfer coefficient, |
| 1656 |
|
and $W_s$ is the magnitude of the surface layer wind. |
| 1657 |
|
\\ |
| 1658 |
|
|
| 1659 |
|
\noindent |
| 1660 |
|
{ \underline {EU} Diffusivity Coefficient for Momentum ($m^2/sec$) } |
| 1661 |
|
|
| 1662 |
|
\noindent |
| 1663 |
|
In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat |
| 1664 |
|
momentum flux for the atmosphere above the surface layer can be expressed as a turbulent |
| 1665 |
|
diffusion coefficient $K_m$ times the negative of the gradient of the u-wind. |
| 1666 |
|
In the Helfand and Labraga (1988) adaptation of this closure, $K_m$ |
| 1667 |
|
takes the form: |
| 1668 |
|
\[ |
| 1669 |
|
{\bf EU} = K_m = -{( {\overline{u^{\prime}w^{\prime}}}) \over {\pp{U}{z}} } |
| 1670 |
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) & \mbox{decaying turbulence} |
| 1671 |
|
\\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. |
| 1672 |
|
\] |
| 1673 |
|
\noindent |
| 1674 |
|
where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} |
| 1675 |
|
energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, |
| 1676 |
|
which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer |
| 1677 |
|
depth, |
| 1678 |
|
$S_M$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and |
| 1679 |
|
wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium |
| 1680 |
|
dimensionless buoyancy and wind shear |
| 1681 |
|
parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
| 1682 |
|
are functions of the Richardson number. |
| 1683 |
|
|
| 1684 |
|
\noindent |
| 1685 |
|
For the detailed equations and derivations of the modified level 2.5 closure scheme, |
| 1686 |
|
see Helfand and Labraga, 1988. |
| 1687 |
|
|
| 1688 |
|
\noindent |
| 1689 |
|
In the surface layer, ${\bf {EU}}$ is the exchange coefficient for momentum, |
| 1690 |
|
in units of $m/sec$, given by: |
| 1691 |
|
\[ |
| 1692 |
|
{\bf EU_{Nrphys}} = C_u * u_* = C_D W_s |
| 1693 |
|
\] |
| 1694 |
|
\noindent |
| 1695 |
|
where $C_u$ is the dimensionless exchange coefficient for momentum from the surface layer |
| 1696 |
|
similarity functions (see diagnostic number 10), $u_*$ is the surface friction velocity |
| 1697 |
|
(see diagnostic number 67), $C_D$ is the surface drag coefficient, and $W_s$ is the |
| 1698 |
|
magnitude of the surface layer wind. |
| 1699 |
|
\\ |
| 1700 |
|
|
| 1701 |
|
\noindent |
| 1702 |
|
{ \underline {TURBU} Zonal U-Momentum changes due to Turbulence ($m/sec/day$) } |
| 1703 |
|
|
| 1704 |
|
\noindent |
| 1705 |
|
The tendency of U-Momentum due to turbulence is written: |
| 1706 |
|
\[ |
| 1707 |
|
{\bf TURBU} = {\pp{u}{t}}_{turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})} |
| 1708 |
|
= {\pp{}{z} }{(K_m \pp{u}{z})} |
| 1709 |
|
\] |
| 1710 |
|
|
| 1711 |
|
\noindent |
| 1712 |
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
| 1713 |
|
flux of u-momentum in terms of $K_m$, and the equation has the form of a diffusion |
| 1714 |
|
equation. |
| 1715 |
|
|
| 1716 |
|
\noindent |
| 1717 |
|
{ \underline {TURBV} Meridional V-Momentum changes due to Turbulence ($m/sec/day$) } |
| 1718 |
|
|
| 1719 |
|
\noindent |
| 1720 |
|
The tendency of V-Momentum due to turbulence is written: |
| 1721 |
|
\[ |
| 1722 |
|
{\bf TURBV} = {\pp{v}{t}}_{turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})} |
| 1723 |
|
= {\pp{}{z} }{(K_m \pp{v}{z})} |
| 1724 |
|
\] |
| 1725 |
|
|
| 1726 |
|
\noindent |
| 1727 |
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
| 1728 |
|
flux of v-momentum in terms of $K_m$, and the equation has the form of a diffusion |
| 1729 |
|
equation. |
| 1730 |
|
\\ |
| 1731 |
|
|
| 1732 |
|
\noindent |
| 1733 |
|
{ \underline {TURBT} Temperature changes due to Turbulence ($deg/day$) } |
| 1734 |
|
|
| 1735 |
|
\noindent |
| 1736 |
|
The tendency of temperature due to turbulence is written: |
| 1737 |
|
\[ |
| 1738 |
|
{\bf TURBT} = {\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{turb} = |
| 1739 |
|
P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})} |
| 1740 |
|
= P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})} |
| 1741 |
|
\] |
| 1742 |
|
|
| 1743 |
|
\noindent |
| 1744 |
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
| 1745 |
|
flux of temperature in terms of $K_h$, and the equation has the form of a diffusion |
| 1746 |
|
equation. |
| 1747 |
|
\\ |
| 1748 |
|
|
| 1749 |
|
\noindent |
| 1750 |
|
{ \underline {TURBQ} Specific Humidity changes due to Turbulence ($g/kg/day$) } |
| 1751 |
|
|
| 1752 |
|
\noindent |
| 1753 |
|
The tendency of specific humidity due to turbulence is written: |
| 1754 |
|
\[ |
| 1755 |
|
{\bf TURBQ} = {\pp{q}{t}}_{turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})} |
| 1756 |
|
= {\pp{}{z} }{(K_h \pp{q}{z})} |
| 1757 |
|
\] |
| 1758 |
|
|
| 1759 |
|
\noindent |
| 1760 |
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
| 1761 |
|
flux of temperature in terms of $K_h$, and the equation has the form of a diffusion |
| 1762 |
|
equation. |
| 1763 |
|
\\ |
| 1764 |
|
|
| 1765 |
|
\noindent |
| 1766 |
|
{ \underline {MOISTT} Temperature Changes Due to Moist Processes ($deg/day$) } |
| 1767 |
|
|
| 1768 |
|
\noindent |
| 1769 |
|
\[ |
| 1770 |
|
{\bf MOISTT} = \left. {\pp{T}{t}}\right|_{c} + \left. {\pp{T}{t}} \right|_{ls} |
| 1771 |
|
\] |
| 1772 |
|
where: |
| 1773 |
|
\[ |
| 1774 |
|
\left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over c_p} \Gamma_s \right)_i |
| 1775 |
|
\hspace{.4cm} and |
| 1776 |
|
\hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = {L \over c_p } (q^*-q) |
| 1777 |
|
\] |
| 1778 |
|
and |
| 1779 |
|
\[ |
| 1780 |
|
\Gamma_s = g \eta \pp{s}{p} |
| 1781 |
|
\] |
| 1782 |
|
|
| 1783 |
|
\noindent |
| 1784 |
|
The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale |
| 1785 |
|
precipitation processes, or supersaturation rain. |
| 1786 |
|
The summation refers to contributions from each cloud type called by RAS. |
| 1787 |
|
The dry static energy is given |
| 1788 |
|
as $s$, the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is |
| 1789 |
|
given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, |
| 1790 |
|
the description of the convective parameterization. The fractional adjustment, or relaxation |
| 1791 |
|
parameter, for each cloud type is given as $\alpha$, while |
| 1792 |
|
$R$ is the rain re-evaporation adjustment. |
| 1793 |
|
\\ |
| 1794 |
|
|
| 1795 |
|
\noindent |
| 1796 |
|
{ \underline {MOISTQ} Specific Humidity Changes Due to Moist Processes ($g/kg/day$) } |
| 1797 |
|
|
| 1798 |
|
\noindent |
| 1799 |
|
\[ |
| 1800 |
|
{\bf MOISTQ} = \left. {\pp{q}{t}}\right|_{c} + \left. {\pp{q}{t}} \right|_{ls} |
| 1801 |
|
\] |
| 1802 |
|
where: |
| 1803 |
|
\[ |
| 1804 |
|
\left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over {L}}(\Gamma_h-\Gamma_s) \right)_i |
| 1805 |
|
\hspace{.4cm} and |
| 1806 |
|
\hspace{.4cm} \left.{\pp{q}{t}}\right|_{ls} = (q^*-q) |
| 1807 |
|
\] |
| 1808 |
|
and |
| 1809 |
|
\[ |
| 1810 |
|
\Gamma_s = g \eta \pp{s}{p}\hspace{.4cm} and \hspace{.4cm}\Gamma_h = g \eta \pp{h}{p} |
| 1811 |
|
\] |
| 1812 |
|
\noindent |
| 1813 |
|
The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale |
| 1814 |
|
precipitation processes, or supersaturation rain. |
| 1815 |
|
The summation refers to contributions from each cloud type called by RAS. |
| 1816 |
|
The dry static energy is given as $s$, |
| 1817 |
|
the moist static energy is given as $h$, |
| 1818 |
|
the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is |
| 1819 |
|
given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, |
| 1820 |
|
the description of the convective parameterization. The fractional adjustment, or relaxation |
| 1821 |
|
parameter, for each cloud type is given as $\alpha$, while |
| 1822 |
|
$R$ is the rain re-evaporation adjustment. |
| 1823 |
|
\\ |
| 1824 |
|
|
| 1825 |
|
\noindent |
| 1826 |
|
{ \underline {RADLW} Heating Rate due to Longwave Radiation ($deg/day$) } |
| 1827 |
|
|
| 1828 |
|
\noindent |
| 1829 |
|
The net longwave heating rate is calculated as the vertical divergence of the |
| 1830 |
|
net terrestrial radiative fluxes. |
| 1831 |
|
Both the clear-sky and cloudy-sky longwave fluxes are computed within the |
| 1832 |
|
longwave routine. |
| 1833 |
|
The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. |
| 1834 |
|
For a given cloud fraction, |
| 1835 |
|
the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ |
| 1836 |
|
to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, |
| 1837 |
|
for the upward and downward radiative fluxes. |
| 1838 |
|
(see Section \ref{sec:fizhi:radcloud}). |
| 1839 |
|
The cloudy-sky flux is then obtained as: |
| 1840 |
|
|
| 1841 |
|
\noindent |
| 1842 |
|
\[ |
| 1843 |
|
F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, |
| 1844 |
|
\] |
| 1845 |
|
|
| 1846 |
|
\noindent |
| 1847 |
|
Finally, the net longwave heating rate is calculated as the vertical divergence of the |
| 1848 |
|
net terrestrial radiative fluxes: |
| 1849 |
|
\[ |
| 1850 |
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F_{LW}^{NET} , |
| 1851 |
|
\] |
| 1852 |
|
or |
| 1853 |
|
\[ |
| 1854 |
|
{\bf RADLW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F_{LW}^{NET} . |
| 1855 |
|
\] |
| 1856 |
|
|
| 1857 |
|
\noindent |
| 1858 |
|
where $g$ is the accelation due to gravity, |
| 1859 |
|
$c_p$ is the heat capacity of air at constant pressure, |
| 1860 |
|
and |
| 1861 |
|
\[ |
| 1862 |
|
F_{LW}^{NET} = F_{LW}^\uparrow - F_{LW}^\downarrow |
| 1863 |
|
\] |
| 1864 |
|
\\ |
| 1865 |
|
|
| 1866 |
|
|
| 1867 |
|
\noindent |
| 1868 |
|
{ \underline {RADSW} Heating Rate due to Shortwave Radiation ($deg/day$) } |
| 1869 |
|
|
| 1870 |
|
\noindent |
| 1871 |
|
The net Shortwave heating rate is calculated as the vertical divergence of the |
| 1872 |
|
net solar radiative fluxes. |
| 1873 |
|
The clear-sky and cloudy-sky shortwave fluxes are calculated separately. |
| 1874 |
|
For the clear-sky case, the shortwave fluxes and heating rates are computed with |
| 1875 |
|
both CLMO (maximum overlap cloud fraction) and |
| 1876 |
|
CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). |
| 1877 |
|
The shortwave routine is then called a second time, for the cloudy-sky case, with the |
| 1878 |
|
true time-averaged cloud fractions CLMO |
| 1879 |
|
and CLRO being used. In all cases, a normalized incident shortwave flux is used as |
| 1880 |
|
input at the top of the atmosphere. |
| 1881 |
|
|
| 1882 |
|
\noindent |
| 1883 |
|
The heating rate due to Shortwave Radiation under cloudy skies is defined as: |
| 1884 |
|
\[ |
| 1885 |
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT}, |
| 1886 |
|
\] |
| 1887 |
|
or |
| 1888 |
|
\[ |
| 1889 |
|
{\bf RADSW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} . |
| 1890 |
|
\] |
| 1891 |
|
|
| 1892 |
|
\noindent |
| 1893 |
|
where $g$ is the accelation due to gravity, |
| 1894 |
|
$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident |
| 1895 |
|
shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and |
| 1896 |
|
\[ |
| 1897 |
|
F(cloudy)_{SW}^{Net} = F(cloudy)_{SW}^\uparrow - F(cloudy)_{SW}^\downarrow |
| 1898 |
|
\] |
| 1899 |
|
\\ |
| 1900 |
|
|
| 1901 |
|
\noindent |
| 1902 |
|
{ \underline {PREACC} Total (Large-scale + Convective) Accumulated Precipition ($mm/day$) } |
| 1903 |
|
|
| 1904 |
|
\noindent |
| 1905 |
|
For a change in specific humidity due to moist processes, $\Delta q_{moist}$, |
| 1906 |
|
the vertical integral or total precipitable amount is given by: |
| 1907 |
|
\[ |
| 1908 |
|
{\bf PREACC} = \int_{surf}^{top} \rho \Delta q_{moist} dz = - \int_{surf}^{top} \Delta q_{moist} |
| 1909 |
|
{dp \over g} = {1 \over g} \int_0^1 \Delta q_{moist} dp |
| 1910 |
|
\] |
| 1911 |
|
\\ |
| 1912 |
|
|
| 1913 |
|
\noindent |
| 1914 |
|
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes |
| 1915 |
|
time step, scaled to $mm/day$. |
| 1916 |
|
\\ |
| 1917 |
|
|
| 1918 |
|
\noindent |
| 1919 |
|
{ \underline {PRECON} Convective Precipition ($mm/day$) } |
| 1920 |
|
|
| 1921 |
|
\noindent |
| 1922 |
|
For a change in specific humidity due to sub-grid scale cumulus convective processes, $\Delta q_{cum}$, |
| 1923 |
|
the vertical integral or total precipitable amount is given by: |
| 1924 |
|
\[ |
| 1925 |
|
{\bf PRECON} = \int_{surf}^{top} \rho \Delta q_{cum} dz = - \int_{surf}^{top} \Delta q_{cum} |
| 1926 |
|
{dp \over g} = {1 \over g} \int_0^1 \Delta q_{cum} dp |
| 1927 |
|
\] |
| 1928 |
|
\\ |
| 1929 |
|
|
| 1930 |
|
\noindent |
| 1931 |
|
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes |
| 1932 |
|
time step, scaled to $mm/day$. |
| 1933 |
|
\\ |
| 1934 |
|
|
| 1935 |
|
\noindent |
| 1936 |
|
{ \underline {TUFLUX} Turbulent Flux of U-Momentum ($Newton/m^2$) } |
| 1937 |
|
|
| 1938 |
|
\noindent |
| 1939 |
|
The turbulent flux of u-momentum is calculated for $diagnostic \hspace{.2cm} purposes |
| 1940 |
|
\hspace{.2cm} only$ from the eddy coefficient for momentum: |
| 1941 |
|
|
| 1942 |
|
\[ |
| 1943 |
|
{\bf TUFLUX} = {\rho } {(\overline{u^{\prime}w^{\prime}})} = |
| 1944 |
|
{\rho } {(- K_m \pp{U}{z})} |
| 1945 |
|
\] |
| 1946 |
|
|
| 1947 |
|
\noindent |
| 1948 |
|
where $\rho$ is the air density, and $K_m$ is the eddy coefficient. |
| 1949 |
|
\\ |
| 1950 |
|
|
| 1951 |
|
\noindent |
| 1952 |
|
{ \underline {TVFLUX} Turbulent Flux of V-Momentum ($Newton/m^2$) } |
| 1953 |
|
|
| 1954 |
|
\noindent |
| 1955 |
|
The turbulent flux of v-momentum is calculated for $diagnostic \hspace{.2cm} purposes |
| 1956 |
|
\hspace{.2cm} only$ from the eddy coefficient for momentum: |
| 1957 |
|
|
| 1958 |
|
\[ |
| 1959 |
|
{\bf TVFLUX} = {\rho } {(\overline{v^{\prime}w^{\prime}})} = |
| 1960 |
|
{\rho } {(- K_m \pp{V}{z})} |
| 1961 |
|
\] |
| 1962 |
|
|
| 1963 |
|
\noindent |
| 1964 |
|
where $\rho$ is the air density, and $K_m$ is the eddy coefficient. |
| 1965 |
|
\\ |
| 1966 |
|
|
| 1967 |
|
|
| 1968 |
|
\noindent |
| 1969 |
|
{ \underline {TTFLUX} Turbulent Flux of Sensible Heat ($Watts/m^2$) } |
| 1970 |
|
|
| 1971 |
|
\noindent |
| 1972 |
|
The turbulent flux of sensible heat is calculated for $diagnostic \hspace{.2cm} purposes |
| 1973 |
|
\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: |
| 1974 |
|
|
| 1975 |
|
\noindent |
| 1976 |
|
\[ |
| 1977 |
|
{\bf TTFLUX} = c_p {\rho } |
| 1978 |
|
P^{\kappa}{(\overline{w^{\prime}\theta^{\prime}})} |
| 1979 |
|
= c_p {\rho } P^{\kappa}{(- K_h \pp{\theta_v}{z})} |
| 1980 |
|
\] |
| 1981 |
|
|
| 1982 |
|
\noindent |
| 1983 |
|
where $\rho$ is the air density, and $K_h$ is the eddy coefficient. |
| 1984 |
|
\\ |
| 1985 |
|
|
| 1986 |
|
|
| 1987 |
|
\noindent |
| 1988 |
|
{ \underline {TQFLUX} Turbulent Flux of Latent Heat ($Watts/m^2$) } |
| 1989 |
|
|
| 1990 |
|
\noindent |
| 1991 |
|
The turbulent flux of latent heat is calculated for $diagnostic \hspace{.2cm} purposes |
| 1992 |
|
\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: |
| 1993 |
|
|
| 1994 |
|
\noindent |
| 1995 |
|
\[ |
| 1996 |
|
{\bf TQFLUX} = {L {\rho } (\overline{w^{\prime}q^{\prime}})} = |
| 1997 |
|
{L {\rho }(- K_h \pp{q}{z})} |
| 1998 |
|
\] |
| 1999 |
|
|
| 2000 |
|
\noindent |
| 2001 |
|
where $\rho$ is the air density, and $K_h$ is the eddy coefficient. |
| 2002 |
|
\\ |
| 2003 |
|
|
| 2004 |
|
|
| 2005 |
|
\noindent |
| 2006 |
|
{ \underline {CN} Neutral Drag Coefficient ($dimensionless$) } |
| 2007 |
|
|
| 2008 |
|
\noindent |
| 2009 |
|
The drag coefficient for momentum obtained by assuming a neutrally stable surface layer: |
| 2010 |
|
\[ |
| 2011 |
|
{\bf CN} = { k \over { \ln({h \over {z_0}})} } |
| 2012 |
|
\] |
| 2013 |
|
|
| 2014 |
|
\noindent |
| 2015 |
|
where $k$ is the Von Karman constant, $h$ is the height of the surface layer, and |
| 2016 |
|
$z_0$ is the surface roughness. |
| 2017 |
|
|
| 2018 |
|
\noindent |
| 2019 |
|
NOTE: CN is not available through model version 5.3, but is available in subsequent |
| 2020 |
|
versions. |
| 2021 |
|
\\ |
| 2022 |
|
|
| 2023 |
|
\noindent |
| 2024 |
|
{ \underline {WINDS} Surface Wind Speed ($meter/sec$) } |
| 2025 |
|
|
| 2026 |
|
\noindent |
| 2027 |
|
The surface wind speed is calculated for the last internal turbulence time step: |
| 2028 |
|
\[ |
| 2029 |
|
{\bf WINDS} = \sqrt{u_{Nrphys}^2 + v_{Nrphys}^2} |
| 2030 |
|
\] |
| 2031 |
|
|
| 2032 |
|
\noindent |
| 2033 |
|
where the subscript $Nrphys$ refers to the lowest model level. |
| 2034 |
|
\\ |
| 2035 |
|
|
| 2036 |
|
\noindent |
| 2037 |
|
{ \underline {DTSRF} Air/Surface Virtual Temperature Difference ($deg \hspace{.1cm} K$) } |
| 2038 |
|
|
| 2039 |
|
\noindent |
| 2040 |
|
The air/surface virtual temperature difference measures the stability of the surface layer: |
| 2041 |
|
\[ |
| 2042 |
|
{\bf DTSRF} = (\theta_{v{Nrphys+1}} - \theta{v_{Nrphys}}) P^{\kappa}_{surf} |
| 2043 |
|
\] |
| 2044 |
|
\noindent |
| 2045 |
|
where |
| 2046 |
|
\[ |
| 2047 |
|
\theta_{v{Nrphys+1}} = { T_g \over {P^{\kappa}_{surf}} } (1 + .609 q_{Nrphys+1}) \hspace{1cm} |
| 2048 |
|
and \hspace{1cm} q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) |
| 2049 |
|
\] |
| 2050 |
|
|
| 2051 |
|
\noindent |
| 2052 |
|
$\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), |
| 2053 |
|
$q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature |
| 2054 |
|
and surface pressure, level $Nrphys$ refers to the lowest model level and level $Nrphys+1$ |
| 2055 |
|
refers to the surface. |
| 2056 |
|
\\ |
| 2057 |
|
|
| 2058 |
|
|
| 2059 |
|
\noindent |
| 2060 |
|
{ \underline {TG} Ground Temperature ($deg \hspace{.1cm} K$) } |
| 2061 |
|
|
| 2062 |
|
\noindent |
| 2063 |
|
The ground temperature equation is solved as part of the turbulence package |
| 2064 |
|
using a backward implicit time differencing scheme: |
| 2065 |
|
\[ |
| 2066 |
|
{\bf TG} \hspace{.1cm} is \hspace{.1cm} obtained \hspace{.1cm} from: \hspace{.1cm} |
| 2067 |
|
C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{ice} - H - LE |
| 2068 |
|
\] |
| 2069 |
|
|
| 2070 |
|
\noindent |
| 2071 |
|
where $R_{sw}$ is the net surface downward shortwave radiative flux, $R_{lw}$ is the |
| 2072 |
|
net surface upward longwave radiative flux, $Q_{ice}$ is the heat conduction through |
| 2073 |
|
sea ice, $H$ is the upward sensible heat flux, $LE$ is the upward latent heat |
| 2074 |
|
flux, and $C_g$ is the total heat capacity of the ground. |
| 2075 |
|
$C_g$ is obtained by solving a heat diffusion equation |
| 2076 |
|
for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by: |
| 2077 |
|
\[ |
| 2078 |
|
C_g = \sqrt{ {\lambda C_s \over {2 \omega} } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3} |
| 2079 |
|
{ 86400. \over {2 \pi} } } \, \, . |
| 2080 |
|
\] |
| 2081 |
|
\noindent |
| 2082 |
|
Here, the thermal conductivity, $\lambda$, is equal to $2x10^{-3}$ ${ly\over{ sec}} |
| 2083 |
|
{cm \over {^oK}}$, |
| 2084 |
|
the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided |
| 2085 |
|
by $2 \pi$ $radians/ |
| 2086 |
|
day$, and the expression for $C_s$, the heat capacity per unit volume at the surface, |
| 2087 |
|
is a function of the ground wetness, $W$. |
| 2088 |
|
\\ |
| 2089 |
|
|
| 2090 |
|
\noindent |
| 2091 |
|
{ \underline {TS} Surface Temperature ($deg \hspace{.1cm} K$) } |
| 2092 |
|
|
| 2093 |
|
\noindent |
| 2094 |
|
The surface temperature estimate is made by assuming that the model's lowest |
| 2095 |
|
layer is well-mixed, and therefore that $\theta$ is constant in that layer. |
| 2096 |
|
The surface temperature is therefore: |
| 2097 |
|
\[ |
| 2098 |
|
{\bf TS} = \theta_{Nrphys} P^{\kappa}_{surf} |
| 2099 |
|
\] |
| 2100 |
|
\\ |
| 2101 |
|
|
| 2102 |
|
\noindent |
| 2103 |
|
{ \underline {DTG} Surface Temperature Adjustment ($deg \hspace{.1cm} K$) } |
| 2104 |
|
|
| 2105 |
|
\noindent |
| 2106 |
|
The change in surface temperature from one turbulence time step to the next, solved |
| 2107 |
|
using the Ground Temperature Equation (see diagnostic number 30) is calculated: |
| 2108 |
|
\[ |
| 2109 |
|
{\bf DTG} = {T_g}^{n} - {T_g}^{n-1} |
| 2110 |
|
\] |
| 2111 |
|
|
| 2112 |
|
\noindent |
| 2113 |
|
where superscript $n$ refers to the new, updated time level, and the superscript $n-1$ |
| 2114 |
|
refers to the value at the previous turbulence time level. |
| 2115 |
|
\\ |
| 2116 |
|
|
| 2117 |
|
\noindent |
| 2118 |
|
{ \underline {QG} Ground Specific Humidity ($g/kg$) } |
| 2119 |
|
|
| 2120 |
|
\noindent |
| 2121 |
|
The ground specific humidity is obtained by interpolating between the specific |
| 2122 |
|
humidity at the lowest model level and the specific humidity of a saturated ground. |
| 2123 |
|
The interpolation is performed using the potential evapotranspiration function: |
| 2124 |
|
\[ |
| 2125 |
|
{\bf QG} = q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) |
| 2126 |
|
\] |
| 2127 |
|
|
| 2128 |
|
\noindent |
| 2129 |
|
where $\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), |
| 2130 |
|
and $q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature and surface |
| 2131 |
|
pressure. |
| 2132 |
|
\\ |
| 2133 |
|
|
| 2134 |
|
\noindent |
| 2135 |
|
{ \underline {QS} Saturation Surface Specific Humidity ($g/kg$) } |
| 2136 |
|
|
| 2137 |
|
\noindent |
| 2138 |
|
The surface saturation specific humidity is the saturation specific humidity at |
| 2139 |
|
the ground temprature and surface pressure: |
| 2140 |
|
\[ |
| 2141 |
|
{\bf QS} = q^*(T_g,P_s) |
| 2142 |
|
\] |
| 2143 |
|
\\ |
| 2144 |
|
|
| 2145 |
|
\noindent |
| 2146 |
|
{ \underline {TGRLW} Instantaneous ground temperature used as input to the Longwave |
| 2147 |
|
radiation subroutine (deg)} |
| 2148 |
|
\[ |
| 2149 |
|
{\bf TGRLW} = T_g(\lambda , \phi ,n) |
| 2150 |
|
\] |
| 2151 |
|
\noindent |
| 2152 |
|
where $T_g$ is the model ground temperature at the current time step $n$. |
| 2153 |
|
\\ |
| 2154 |
|
|
| 2155 |
|
|
| 2156 |
|
\noindent |
| 2157 |
|
{ \underline {ST4} Upward Longwave flux at the surface ($Watts/m^2$) } |
| 2158 |
|
\[ |
| 2159 |
|
{\bf ST4} = \sigma T^4 |
| 2160 |
|
\] |
| 2161 |
|
\noindent |
| 2162 |
|
where $\sigma$ is the Stefan-Boltzmann constant and T is the temperature. |
| 2163 |
|
\\ |
| 2164 |
|
|
| 2165 |
|
\noindent |
| 2166 |
|
{ \underline {OLR} Net upward Longwave flux at $p=p_{top}$ ($Watts/m^2$) } |
| 2167 |
|
\[ |
| 2168 |
|
{\bf OLR} = F_{LW,top}^{NET} |
| 2169 |
|
\] |
| 2170 |
|
\noindent |
| 2171 |
|
where top indicates the top of the first model layer. |
| 2172 |
|
In the GCM, $p_{top}$ = 0.0 mb. |
| 2173 |
|
\\ |
| 2174 |
|
|
| 2175 |
|
|
| 2176 |
|
\noindent |
| 2177 |
|
{ \underline {OLRCLR} Net upward clearsky Longwave flux at $p=p_{top}$ ($Watts/m^2$) } |
| 2178 |
|
\[ |
| 2179 |
|
{\bf OLRCLR} = F(clearsky)_{LW,top}^{NET} |
| 2180 |
|
\] |
| 2181 |
|
\noindent |
| 2182 |
|
where top indicates the top of the first model layer. |
| 2183 |
|
In the GCM, $p_{top}$ = 0.0 mb. |
| 2184 |
|
\\ |
| 2185 |
|
|
| 2186 |
|
\noindent |
| 2187 |
|
{ \underline {LWGCLR} Net upward clearsky Longwave flux at the surface ($Watts/m^2$) } |
| 2188 |
|
|
| 2189 |
|
\noindent |
| 2190 |
|
\begin{eqnarray*} |
| 2191 |
|
{\bf LWGCLR} & = & F(clearsky)_{LW,Nrphys+1}^{Net} \\ |
| 2192 |
|
& = & F(clearsky)_{LW,Nrphys+1}^\uparrow - F(clearsky)_{LW,Nrphys+1}^\downarrow |
| 2193 |
|
\end{eqnarray*} |
| 2194 |
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
| 2195 |
|
$F(clearsky)_{LW}^\uparrow$ is |
| 2196 |
|
the upward clearsky Longwave flux and the $F(clearsky)_{LW}^\downarrow$ is the downward clearsky Longwave flux. |
| 2197 |
|
\\ |
| 2198 |
|
|
| 2199 |
|
\noindent |
| 2200 |
|
{ \underline {LWCLR} Heating Rate due to Clearsky Longwave Radiation ($deg/day$) } |
| 2201 |
|
|
| 2202 |
|
\noindent |
| 2203 |
|
The net longwave heating rate is calculated as the vertical divergence of the |
| 2204 |
|
net terrestrial radiative fluxes. |
| 2205 |
|
Both the clear-sky and cloudy-sky longwave fluxes are computed within the |
| 2206 |
|
longwave routine. |
| 2207 |
|
The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. |
| 2208 |
|
For a given cloud fraction, |
| 2209 |
|
the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ |
| 2210 |
|
to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, |
| 2211 |
|
for the upward and downward radiative fluxes. |
| 2212 |
|
(see Section \ref{sec:fizhi:radcloud}). |
| 2213 |
|
The cloudy-sky flux is then obtained as: |
| 2214 |
|
|
| 2215 |
|
\noindent |
| 2216 |
|
\[ |
| 2217 |
|
F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, |
| 2218 |
|
\] |
| 2219 |
|
|
| 2220 |
|
\noindent |
| 2221 |
|
Thus, {\bf LWCLR} is defined as the net longwave heating rate due to the |
| 2222 |
|
vertical divergence of the |
| 2223 |
|
clear-sky longwave radiative flux: |
| 2224 |
|
\[ |
| 2225 |
|
\pp{\rho c_p T}{t}_{clearsky} = - {\partial \over \partial z} F(clearsky)_{LW}^{NET} , |
| 2226 |
|
\] |
| 2227 |
|
or |
| 2228 |
|
\[ |
| 2229 |
|
{\bf LWCLR} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(clearsky)_{LW}^{NET} . |
| 2230 |
|
\] |
| 2231 |
|
|
| 2232 |
|
\noindent |
| 2233 |
|
where $g$ is the accelation due to gravity, |
| 2234 |
|
$c_p$ is the heat capacity of air at constant pressure, |
| 2235 |
|
and |
| 2236 |
|
\[ |
| 2237 |
|
F(clearsky)_{LW}^{Net} = F(clearsky)_{LW}^\uparrow - F(clearsky)_{LW}^\downarrow |
| 2238 |
|
\] |
| 2239 |
|
\\ |
| 2240 |
|
|
| 2241 |
|
|
| 2242 |
|
\noindent |
| 2243 |
|
{ \underline {TLW} Instantaneous temperature used as input to the Longwave |
| 2244 |
|
radiation subroutine (deg)} |
| 2245 |
|
\[ |
| 2246 |
|
{\bf TLW} = T(\lambda , \phi ,level, n) |
| 2247 |
|
\] |
| 2248 |
|
\noindent |
| 2249 |
|
where $T$ is the model temperature at the current time step $n$. |
| 2250 |
|
\\ |
| 2251 |
|
|
| 2252 |
|
|
| 2253 |
|
\noindent |
| 2254 |
|
{ \underline {SHLW} Instantaneous specific humidity used as input to |
| 2255 |
|
the Longwave radiation subroutine (kg/kg)} |
| 2256 |
|
\[ |
| 2257 |
|
{\bf SHLW} = q(\lambda , \phi , level , n) |
| 2258 |
|
\] |
| 2259 |
|
\noindent |
| 2260 |
|
where $q$ is the model specific humidity at the current time step $n$. |
| 2261 |
|
\\ |
| 2262 |
|
|
| 2263 |
|
|
| 2264 |
|
\noindent |
| 2265 |
|
{ \underline {OZLW} Instantaneous ozone used as input to |
| 2266 |
|
the Longwave radiation subroutine (kg/kg)} |
| 2267 |
|
\[ |
| 2268 |
|
{\bf OZLW} = {\rm OZ}(\lambda , \phi , level , n) |
| 2269 |
|
\] |
| 2270 |
|
\noindent |
| 2271 |
|
where $\rm OZ$ is the interpolated ozone data set from the climatological monthly |
| 2272 |
|
mean zonally averaged ozone data set. |
| 2273 |
|
\\ |
| 2274 |
|
|
| 2275 |
|
|
| 2276 |
|
\noindent |
| 2277 |
|
{ \underline {CLMOLW} Maximum Overlap cloud fraction used in LW Radiation ($0-1$) } |
| 2278 |
|
|
| 2279 |
|
\noindent |
| 2280 |
|
{\bf CLMOLW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed |
| 2281 |
|
Arakawa/Schubert Convection scheme and will be used in the Longwave Radiation algorithm. These are |
| 2282 |
|
convective clouds whose radiative characteristics are assumed to be correlated in the vertical. |
| 2283 |
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
| 2284 |
|
\[ |
| 2285 |
|
{\bf CLMOLW} = CLMO_{RAS,LW}(\lambda, \phi, level ) |
| 2286 |
|
\] |
| 2287 |
|
\\ |
| 2288 |
|
|
| 2289 |
|
|
| 2290 |
|
{ \underline {CLDTOT} Total cloud fraction used in LW and SW Radiation ($0-1$) } |
| 2291 |
|
|
| 2292 |
|
{\bf CLDTOT} is the time-averaged total cloud fraction that has been filled by the Relaxed |
| 2293 |
|
Arakawa/Schubert and Large-scale Convection schemes and will be used in the Longwave and Shortwave |
| 2294 |
|
Radiation packages. |
| 2295 |
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
| 2296 |
|
\[ |
| 2297 |
|
{\bf CLDTOT} = F_{RAS} + F_{LS} |
| 2298 |
|
\] |
| 2299 |
|
\\ |
| 2300 |
|
where $F_{RAS}$ is the time-averaged cloud fraction due to sub-grid scale convection, and $F_{LS}$ is the |
| 2301 |
|
time-averaged cloud fraction due to precipitating and non-precipitating large-scale moist processes. |
| 2302 |
|
\\ |
| 2303 |
|
|
| 2304 |
|
|
| 2305 |
|
\noindent |
| 2306 |
|
{ \underline {CLMOSW} Maximum Overlap cloud fraction used in SW Radiation ($0-1$) } |
| 2307 |
|
|
| 2308 |
|
\noindent |
| 2309 |
|
{\bf CLMOSW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed |
| 2310 |
|
Arakawa/Schubert Convection scheme and will be used in the Shortwave Radiation algorithm. These are |
| 2311 |
|
convective clouds whose radiative characteristics are assumed to be correlated in the vertical. |
| 2312 |
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
| 2313 |
|
\[ |
| 2314 |
|
{\bf CLMOSW} = CLMO_{RAS,SW}(\lambda, \phi, level ) |
| 2315 |
|
\] |
| 2316 |
|
\\ |
| 2317 |
|
|
| 2318 |
|
\noindent |
| 2319 |
|
{ \underline {CLROSW} Random Overlap cloud fraction used in SW Radiation ($0-1$) } |
| 2320 |
|
|
| 2321 |
|
\noindent |
| 2322 |
|
{\bf CLROSW} is the time-averaged random overlap cloud fraction that has been filled by the Relaxed |
| 2323 |
|
Arakawa/Schubert and Large-scale Convection schemes and will be used in the Shortwave |
| 2324 |
|
Radiation algorithm. These are |
| 2325 |
|
convective and large-scale clouds whose radiative characteristics are not |
| 2326 |
|
assumed to be correlated in the vertical. |
| 2327 |
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
| 2328 |
|
\[ |
| 2329 |
|
{\bf CLROSW} = CLRO_{RAS,Large Scale,SW}(\lambda, \phi, level ) |
| 2330 |
|
\] |
| 2331 |
|
\\ |
| 2332 |
|
|
| 2333 |
|
\noindent |
| 2334 |
|
{ \underline {RADSWT} Incident Shortwave radiation at the top of the atmosphere ($Watts/m^2$) } |
| 2335 |
|
\[ |
| 2336 |
|
{\bf RADSWT} = {\frac{S_0}{R_a^2}} \cdot cos \phi_z |
| 2337 |
|
\] |
| 2338 |
|
\noindent |
| 2339 |
|
where $S_0$, is the extra-terrestial solar contant, |
| 2340 |
|
$R_a$ is the earth-sun distance in Astronomical Units, |
| 2341 |
|
and $cos \phi_z$ is the cosine of the zenith angle. |
| 2342 |
|
It should be noted that {\bf RADSWT}, as well as |
| 2343 |
|
{\bf OSR} and {\bf OSRCLR}, |
| 2344 |
|
are calculated at the top of the atmosphere (p=0 mb). However, the |
| 2345 |
|
{\bf OLR} and {\bf OLRCLR} diagnostics are currently |
| 2346 |
|
calculated at $p= p_{top}$ (0.0 mb for the GCM). |
| 2347 |
|
\\ |
| 2348 |
|
|
| 2349 |
|
\noindent |
| 2350 |
|
{ \underline {EVAP} Surface Evaporation ($mm/day$) } |
| 2351 |
|
|
| 2352 |
|
\noindent |
| 2353 |
|
The surface evaporation is a function of the gradient of moisture, the potential |
| 2354 |
|
evapotranspiration fraction and the eddy exchange coefficient: |
| 2355 |
|
\[ |
| 2356 |
|
{\bf EVAP} = \rho \beta K_{h} (q_{surface} - q_{Nrphys}) |
| 2357 |
|
\] |
| 2358 |
|
where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of |
| 2359 |
|
the potential evapotranspiration actually evaporated ($\beta=1$ over oceans), $K_{h}$ is the |
| 2360 |
|
turbulent eddy exchange coefficient for heat and moisture at the surface in $m/sec$ and |
| 2361 |
|
$q{surface}$ and $q_{Nrphys}$ are the specific humidity at the surface (see diagnostic |
| 2362 |
|
number 34) and at the bottom model level, respectively. |
| 2363 |
|
\\ |
| 2364 |
|
|
| 2365 |
|
\noindent |
| 2366 |
|
{ \underline {DUDT} Total Zonal U-Wind Tendency ($m/sec/day$) } |
| 2367 |
|
|
| 2368 |
|
\noindent |
| 2369 |
|
{\bf DUDT} is the total time-tendency of the Zonal U-Wind due to Hydrodynamic, Diabatic, |
| 2370 |
|
and Analysis forcing. |
| 2371 |
|
\[ |
| 2372 |
|
{\bf DUDT} = \pp{u}{t}_{Dynamics} + \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} |
| 2373 |
|
\] |
| 2374 |
|
\\ |
| 2375 |
|
|
| 2376 |
|
\noindent |
| 2377 |
|
{ \underline {DVDT} Total Zonal V-Wind Tendency ($m/sec/day$) } |
| 2378 |
|
|
| 2379 |
|
\noindent |
| 2380 |
|
{\bf DVDT} is the total time-tendency of the Meridional V-Wind due to Hydrodynamic, Diabatic, |
| 2381 |
|
and Analysis forcing. |
| 2382 |
|
\[ |
| 2383 |
|
{\bf DVDT} = \pp{v}{t}_{Dynamics} + \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} |
| 2384 |
|
\] |
| 2385 |
|
\\ |
| 2386 |
|
|
| 2387 |
|
\noindent |
| 2388 |
|
{ \underline {DTDT} Total Temperature Tendency ($deg/day$) } |
| 2389 |
|
|
| 2390 |
|
\noindent |
| 2391 |
|
{\bf DTDT} is the total time-tendency of Temperature due to Hydrodynamic, Diabatic, |
| 2392 |
|
and Analysis forcing. |
| 2393 |
|
\begin{eqnarray*} |
| 2394 |
|
{\bf DTDT} & = & \pp{T}{t}_{Dynamics} + \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
| 2395 |
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} |
| 2396 |
|
\end{eqnarray*} |
| 2397 |
|
\\ |
| 2398 |
|
|
| 2399 |
|
\noindent |
| 2400 |
|
{ \underline {DQDT} Total Specific Humidity Tendency ($g/kg/day$) } |
| 2401 |
|
|
| 2402 |
|
\noindent |
| 2403 |
|
{\bf DQDT} is the total time-tendency of Specific Humidity due to Hydrodynamic, Diabatic, |
| 2404 |
|
and Analysis forcing. |
| 2405 |
|
\[ |
| 2406 |
|
{\bf DQDT} = \pp{q}{t}_{Dynamics} + \pp{q}{t}_{Moist Processes} |
| 2407 |
|
+ \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} |
| 2408 |
|
\] |
| 2409 |
|
\\ |
| 2410 |
|
|
| 2411 |
|
\noindent |
| 2412 |
|
{ \underline {USTAR} Surface-Stress Velocity ($m/sec$) } |
| 2413 |
|
|
| 2414 |
|
\noindent |
| 2415 |
|
The surface stress velocity, or the friction velocity, is the wind speed at |
| 2416 |
|
the surface layer top impeded by the surface drag: |
| 2417 |
|
\[ |
| 2418 |
|
{\bf USTAR} = C_uW_s \hspace{1cm}where: \hspace{.2cm} |
| 2419 |
|
C_u = {k \over {\psi_m} } |
| 2420 |
|
\] |
| 2421 |
|
|
| 2422 |
|
\noindent |
| 2423 |
|
$C_u$ is the non-dimensional surface drag coefficient (see diagnostic |
| 2424 |
|
number 10), and $W_s$ is the surface wind speed (see diagnostic number 28). |
| 2425 |
|
|
| 2426 |
|
\noindent |
| 2427 |
|
{ \underline {Z0} Surface Roughness Length ($m$) } |
| 2428 |
|
|
| 2429 |
|
\noindent |
| 2430 |
|
Over the land surface, the surface roughness length is interpolated to the local |
| 2431 |
|
time from the monthly mean data of Dorman and Sellers (1989). Over the ocean, |
| 2432 |
|
the roughness length is a function of the surface-stress velocity, $u_*$. |
| 2433 |
|
\[ |
| 2434 |
|
{\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}} |
| 2435 |
|
\] |
| 2436 |
|
|
| 2437 |
|
\noindent |
| 2438 |
|
where the constants are chosen to interpolate between the reciprocal relation of |
| 2439 |
|
Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981) |
| 2440 |
|
for moderate to large winds. |
| 2441 |
|
\\ |
| 2442 |
|
|
| 2443 |
|
\noindent |
| 2444 |
|
{ \underline {FRQTRB} Frequency of Turbulence ($0-1$) } |
| 2445 |
|
|
| 2446 |
|
\noindent |
| 2447 |
|
The fraction of time when turbulence is present is defined as the fraction of |
| 2448 |
|
time when the turbulent kinetic energy exceeds some minimum value, defined here |
| 2449 |
|
to be $0.005 \hspace{.1cm}m^2/sec^2$. When this criterion is met, a counter is |
| 2450 |
|
incremented. The fraction over the averaging interval is reported. |
| 2451 |
|
\\ |
| 2452 |
|
|
| 2453 |
|
\noindent |
| 2454 |
|
{ \underline {PBL} Planetary Boundary Layer Depth ($mb$) } |
| 2455 |
|
|
| 2456 |
|
\noindent |
| 2457 |
|
The depth of the PBL is defined by the turbulence parameterization to be the |
| 2458 |
|
depth at which the turbulent kinetic energy reduces to ten percent of its surface |
| 2459 |
|
value. |
| 2460 |
|
|
| 2461 |
|
\[ |
| 2462 |
|
{\bf PBL} = P_{PBL} - P_{surface} |
| 2463 |
|
\] |
| 2464 |
|
|
| 2465 |
|
\noindent |
| 2466 |
|
where $P_{PBL}$ is the pressure in $mb$ at which the turbulent kinetic energy |
| 2467 |
|
reaches one tenth of its surface value, and $P_s$ is the surface pressure. |
| 2468 |
|
\\ |
| 2469 |
|
|
| 2470 |
|
\noindent |
| 2471 |
|
{ \underline {SWCLR} Clear sky Heating Rate due to Shortwave Radiation ($deg/day$) } |
| 2472 |
|
|
| 2473 |
|
\noindent |
| 2474 |
|
The net Shortwave heating rate is calculated as the vertical divergence of the |
| 2475 |
|
net solar radiative fluxes. |
| 2476 |
|
The clear-sky and cloudy-sky shortwave fluxes are calculated separately. |
| 2477 |
|
For the clear-sky case, the shortwave fluxes and heating rates are computed with |
| 2478 |
|
both CLMO (maximum overlap cloud fraction) and |
| 2479 |
|
CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). |
| 2480 |
|
The shortwave routine is then called a second time, for the cloudy-sky case, with the |
| 2481 |
|
true time-averaged cloud fractions CLMO |
| 2482 |
|
and CLRO being used. In all cases, a normalized incident shortwave flux is used as |
| 2483 |
|
input at the top of the atmosphere. |
| 2484 |
|
|
| 2485 |
|
\noindent |
| 2486 |
|
The heating rate due to Shortwave Radiation under clear skies is defined as: |
| 2487 |
|
\[ |
| 2488 |
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT}, |
| 2489 |
|
\] |
| 2490 |
|
or |
| 2491 |
|
\[ |
| 2492 |
|
{\bf SWCLR} = \frac{g}{c_p } {\partial \over \partial p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} . |
| 2493 |
|
\] |
| 2494 |
|
|
| 2495 |
|
\noindent |
| 2496 |
|
where $g$ is the accelation due to gravity, |
| 2497 |
|
$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident |
| 2498 |
|
shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and |
| 2499 |
|
\[ |
| 2500 |
|
F(clear)_{SW}^{Net} = F(clear)_{SW}^\uparrow - F(clear)_{SW}^\downarrow |
| 2501 |
|
\] |
| 2502 |
|
\\ |
| 2503 |
|
|
| 2504 |
|
\noindent |
| 2505 |
|
{ \underline {OSR} Net upward Shortwave flux at the top of the model ($Watts/m^2$) } |
| 2506 |
|
\[ |
| 2507 |
|
{\bf OSR} = F_{SW,top}^{NET} |
| 2508 |
|
\] |
| 2509 |
|
\noindent |
| 2510 |
|
where top indicates the top of the first model layer used in the shortwave radiation |
| 2511 |
|
routine. |
| 2512 |
|
In the GCM, $p_{SW_{top}}$ = 0 mb. |
| 2513 |
|
\\ |
| 2514 |
|
|
| 2515 |
|
\noindent |
| 2516 |
|
{ \underline {OSRCLR} Net upward clearsky Shortwave flux at the top of the model ($Watts/m^2$) } |
| 2517 |
|
\[ |
| 2518 |
|
{\bf OSRCLR} = F(clearsky)_{SW,top}^{NET} |
| 2519 |
|
\] |
| 2520 |
|
\noindent |
| 2521 |
|
where top indicates the top of the first model layer used in the shortwave radiation |
| 2522 |
|
routine. |
| 2523 |
|
In the GCM, $p_{SW_{top}}$ = 0 mb. |
| 2524 |
|
\\ |
| 2525 |
|
|
| 2526 |
|
|
| 2527 |
|
\noindent |
| 2528 |
|
{ \underline {CLDMAS} Convective Cloud Mass Flux ($kg/m^2$) } |
| 2529 |
|
|
| 2530 |
|
\noindent |
| 2531 |
|
The amount of cloud mass moved per RAS timestep from all convective clouds is written: |
| 2532 |
|
\[ |
| 2533 |
|
{\bf CLDMAS} = \eta m_B |
| 2534 |
|
\] |
| 2535 |
|
where $\eta$ is the entrainment, normalized by the cloud base mass flux, and $m_B$ is |
| 2536 |
|
the cloud base mass flux. $m_B$ and $\eta$ are defined explicitly in Section \ref{sec:fizhi:mc}, the |
| 2537 |
|
description of the convective parameterization. |
| 2538 |
|
\\ |
| 2539 |
|
|
| 2540 |
|
|
| 2541 |
|
|
| 2542 |
|
\noindent |
| 2543 |
|
{ \underline {UAVE} Time-Averaged Zonal U-Wind ($m/sec$) } |
| 2544 |
|
|
| 2545 |
|
\noindent |
| 2546 |
|
The diagnostic {\bf UAVE} is simply the time-averaged Zonal U-Wind over |
| 2547 |
|
the {\bf NUAVE} output frequency. This is contrasted to the instantaneous |
| 2548 |
|
Zonal U-Wind which is archived on the Prognostic Output data stream. |
| 2549 |
|
\[ |
| 2550 |
|
{\bf UAVE} = u(\lambda, \phi, level , t) |
| 2551 |
|
\] |
| 2552 |
|
\\ |
| 2553 |
|
Note, {\bf UAVE} is computed and stored on the staggered C-grid. |
| 2554 |
|
\\ |
| 2555 |
|
|
| 2556 |
|
\noindent |
| 2557 |
|
{ \underline {VAVE} Time-Averaged Meridional V-Wind ($m/sec$) } |
| 2558 |
|
|
| 2559 |
|
\noindent |
| 2560 |
|
The diagnostic {\bf VAVE} is simply the time-averaged Meridional V-Wind over |
| 2561 |
|
the {\bf NVAVE} output frequency. This is contrasted to the instantaneous |
| 2562 |
|
Meridional V-Wind which is archived on the Prognostic Output data stream. |
| 2563 |
|
\[ |
| 2564 |
|
{\bf VAVE} = v(\lambda, \phi, level , t) |
| 2565 |
|
\] |
| 2566 |
|
\\ |
| 2567 |
|
Note, {\bf VAVE} is computed and stored on the staggered C-grid. |
| 2568 |
|
\\ |
| 2569 |
|
|
| 2570 |
|
\noindent |
| 2571 |
|
{ \underline {TAVE} Time-Averaged Temperature ($Kelvin$) } |
| 2572 |
|
|
| 2573 |
|
\noindent |
| 2574 |
|
The diagnostic {\bf TAVE} is simply the time-averaged Temperature over |
| 2575 |
|
the {\bf NTAVE} output frequency. This is contrasted to the instantaneous |
| 2576 |
|
Temperature which is archived on the Prognostic Output data stream. |
| 2577 |
|
\[ |
| 2578 |
|
{\bf TAVE} = T(\lambda, \phi, level , t) |
| 2579 |
|
\] |
| 2580 |
|
\\ |
| 2581 |
|
|
| 2582 |
|
\noindent |
| 2583 |
|
{ \underline {QAVE} Time-Averaged Specific Humidity ($g/kg$) } |
| 2584 |
|
|
| 2585 |
|
\noindent |
| 2586 |
|
The diagnostic {\bf QAVE} is simply the time-averaged Specific Humidity over |
| 2587 |
|
the {\bf NQAVE} output frequency. This is contrasted to the instantaneous |
| 2588 |
|
Specific Humidity which is archived on the Prognostic Output data stream. |
| 2589 |
|
\[ |
| 2590 |
|
{\bf QAVE} = q(\lambda, \phi, level , t) |
| 2591 |
|
\] |
| 2592 |
|
\\ |
| 2593 |
|
|
| 2594 |
|
\noindent |
| 2595 |
|
{ \underline {PAVE} Time-Averaged Surface Pressure - PTOP ($mb$) } |
| 2596 |
|
|
| 2597 |
|
\noindent |
| 2598 |
|
The diagnostic {\bf PAVE} is simply the time-averaged Surface Pressure - PTOP over |
| 2599 |
|
the {\bf NPAVE} output frequency. This is contrasted to the instantaneous |
| 2600 |
|
Surface Pressure - PTOP which is archived on the Prognostic Output data stream. |
| 2601 |
|
\begin{eqnarray*} |
| 2602 |
|
{\bf PAVE} & = & \pi(\lambda, \phi, level , t) \\ |
| 2603 |
|
& = & p_s(\lambda, \phi, level , t) - p_T |
| 2604 |
|
\end{eqnarray*} |
| 2605 |
|
\\ |
| 2606 |
|
|
| 2607 |
|
|
| 2608 |
|
\noindent |
| 2609 |
|
{ \underline {QQAVE} Time-Averaged Turbulent Kinetic Energy $(m/sec)^2$ } |
| 2610 |
|
|
| 2611 |
|
\noindent |
| 2612 |
|
The diagnostic {\bf QQAVE} is simply the time-averaged prognostic Turbulent Kinetic Energy |
| 2613 |
|
produced by the GCM Turbulence parameterization over |
| 2614 |
|
the {\bf NQQAVE} output frequency. This is contrasted to the instantaneous |
| 2615 |
|
Turbulent Kinetic Energy which is archived on the Prognostic Output data stream. |
| 2616 |
|
\[ |
| 2617 |
|
{\bf QQAVE} = qq(\lambda, \phi, level , t) |
| 2618 |
|
\] |
| 2619 |
|
\\ |
| 2620 |
|
Note, {\bf QQAVE} is computed and stored at the ``mass-point'' locations on the staggered C-grid. |
| 2621 |
|
\\ |
| 2622 |
|
|
| 2623 |
|
\noindent |
| 2624 |
|
{ \underline {SWGCLR} Net downward clearsky Shortwave flux at the surface ($Watts/m^2$) } |
| 2625 |
|
|
| 2626 |
|
\noindent |
| 2627 |
|
\begin{eqnarray*} |
| 2628 |
|
{\bf SWGCLR} & = & F(clearsky)_{SW,Nrphys+1}^{Net} \\ |
| 2629 |
|
& = & F(clearsky)_{SW,Nrphys+1}^\downarrow - F(clearsky)_{SW,Nrphys+1}^\uparrow |
| 2630 |
|
\end{eqnarray*} |
| 2631 |
|
\noindent |
| 2632 |
|
\\ |
| 2633 |
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
| 2634 |
|
$F(clearsky){SW}^\downarrow$ is |
| 2635 |
|
the downward clearsky Shortwave flux and $F(clearsky)_{SW}^\uparrow$ is |
| 2636 |
|
the upward clearsky Shortwave flux. |
| 2637 |
|
\\ |
| 2638 |
|
|
| 2639 |
|
\noindent |
| 2640 |
|
{ \underline {DIABU} Total Diabatic Zonal U-Wind Tendency ($m/sec/day$) } |
| 2641 |
|
|
| 2642 |
|
\noindent |
| 2643 |
|
{\bf DIABU} is the total time-tendency of the Zonal U-Wind due to Diabatic processes |
| 2644 |
|
and the Analysis forcing. |
| 2645 |
|
\[ |
| 2646 |
|
{\bf DIABU} = \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} |
| 2647 |
|
\] |
| 2648 |
|
\\ |
| 2649 |
|
|
| 2650 |
|
\noindent |
| 2651 |
|
{ \underline {DIABV} Total Diabatic Meridional V-Wind Tendency ($m/sec/day$) } |
| 2652 |
|
|
| 2653 |
|
\noindent |
| 2654 |
|
{\bf DIABV} is the total time-tendency of the Meridional V-Wind due to Diabatic processes |
| 2655 |
|
and the Analysis forcing. |
| 2656 |
|
\[ |
| 2657 |
|
{\bf DIABV} = \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} |
| 2658 |
|
\] |
| 2659 |
|
\\ |
| 2660 |
|
|
| 2661 |
|
\noindent |
| 2662 |
|
{ \underline {DIABT} Total Diabatic Temperature Tendency ($deg/day$) } |
| 2663 |
|
|
| 2664 |
|
\noindent |
| 2665 |
|
{\bf DIABT} is the total time-tendency of Temperature due to Diabatic processes |
| 2666 |
|
and the Analysis forcing. |
| 2667 |
|
\begin{eqnarray*} |
| 2668 |
|
{\bf DIABT} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
| 2669 |
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} |
| 2670 |
|
\end{eqnarray*} |
| 2671 |
|
\\ |
| 2672 |
|
If we define the time-tendency of Temperature due to Diabatic processes as |
| 2673 |
|
\begin{eqnarray*} |
| 2674 |
|
\pp{T}{t}_{Diabatic} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
| 2675 |
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} |
| 2676 |
|
\end{eqnarray*} |
| 2677 |
|
then, since there are no surface pressure changes due to Diabatic processes, we may write |
| 2678 |
|
\[ |
| 2679 |
|
\pp{T}{t}_{Diabatic} = {p^\kappa \over \pi }\pp{\pi \theta}{t}_{Diabatic} |
| 2680 |
|
\] |
| 2681 |
|
where $\theta = T/p^\kappa$. Thus, {\bf DIABT} may be written as |
| 2682 |
|
\[ |
| 2683 |
|
{\bf DIABT} = {p^\kappa \over \pi } \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right) |
| 2684 |
|
\] |
| 2685 |
|
\\ |
| 2686 |
|
|
| 2687 |
|
\noindent |
| 2688 |
|
{ \underline {DIABQ} Total Diabatic Specific Humidity Tendency ($g/kg/day$) } |
| 2689 |
|
|
| 2690 |
|
\noindent |
| 2691 |
|
{\bf DIABQ} is the total time-tendency of Specific Humidity due to Diabatic processes |
| 2692 |
|
and the Analysis forcing. |
| 2693 |
|
\[ |
| 2694 |
|
{\bf DIABQ} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} |
| 2695 |
|
\] |
| 2696 |
|
If we define the time-tendency of Specific Humidity due to Diabatic processes as |
| 2697 |
|
\[ |
| 2698 |
|
\pp{q}{t}_{Diabatic} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} |
| 2699 |
|
\] |
| 2700 |
|
then, since there are no surface pressure changes due to Diabatic processes, we may write |
| 2701 |
|
\[ |
| 2702 |
|
\pp{q}{t}_{Diabatic} = {1 \over \pi }\pp{\pi q}{t}_{Diabatic} |
| 2703 |
|
\] |
| 2704 |
|
Thus, {\bf DIABQ} may be written as |
| 2705 |
|
\[ |
| 2706 |
|
{\bf DIABQ} = {1 \over \pi } \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right) |
| 2707 |
|
\] |
| 2708 |
|
\\ |
| 2709 |
|
|
| 2710 |
|
\noindent |
| 2711 |
|
{ \underline {VINTUQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } |
| 2712 |
|
|
| 2713 |
|
\noindent |
| 2714 |
|
The vertically integrated moisture flux due to the zonal u-wind is obtained by integrating |
| 2715 |
|
$u q$ over the depth of the atmosphere at each model timestep, |
| 2716 |
|
and dividing by the total mass of the column. |
| 2717 |
|
\[ |
| 2718 |
|
{\bf VINTUQ} = \frac{ \int_{surf}^{top} u q \rho dz } { \int_{surf}^{top} \rho dz } |
| 2719 |
|
\] |
| 2720 |
|
Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have |
| 2721 |
|
\[ |
| 2722 |
|
{\bf VINTUQ} = { \int_0^1 u q dp } |
| 2723 |
|
\] |
| 2724 |
|
\\ |
| 2725 |
|
|
| 2726 |
|
|
| 2727 |
|
\noindent |
| 2728 |
|
{ \underline {VINTVQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } |
| 2729 |
|
|
| 2730 |
|
\noindent |
| 2731 |
|
The vertically integrated moisture flux due to the meridional v-wind is obtained by integrating |
| 2732 |
|
$v q$ over the depth of the atmosphere at each model timestep, |
| 2733 |
|
and dividing by the total mass of the column. |
| 2734 |
|
\[ |
| 2735 |
|
{\bf VINTVQ} = \frac{ \int_{surf}^{top} v q \rho dz } { \int_{surf}^{top} \rho dz } |
| 2736 |
|
\] |
| 2737 |
|
Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have |
| 2738 |
|
\[ |
| 2739 |
|
{\bf VINTVQ} = { \int_0^1 v q dp } |
| 2740 |
|
\] |
| 2741 |
|
\\ |
| 2742 |
|
|
| 2743 |
|
|
| 2744 |
|
\noindent |
| 2745 |
|
{ \underline {VINTUT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } |
| 2746 |
|
|
| 2747 |
|
\noindent |
| 2748 |
|
The vertically integrated heat flux due to the zonal u-wind is obtained by integrating |
| 2749 |
|
$u T$ over the depth of the atmosphere at each model timestep, |
| 2750 |
|
and dividing by the total mass of the column. |
| 2751 |
|
\[ |
| 2752 |
|
{\bf VINTUT} = \frac{ \int_{surf}^{top} u T \rho dz } { \int_{surf}^{top} \rho dz } |
| 2753 |
|
\] |
| 2754 |
|
Or, |
| 2755 |
|
\[ |
| 2756 |
|
{\bf VINTUT} = { \int_0^1 u T dp } |
| 2757 |
|
\] |
| 2758 |
|
\\ |
| 2759 |
|
|
| 2760 |
|
\noindent |
| 2761 |
|
{ \underline {VINTVT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } |
| 2762 |
|
|
| 2763 |
|
\noindent |
| 2764 |
|
The vertically integrated heat flux due to the meridional v-wind is obtained by integrating |
| 2765 |
|
$v T$ over the depth of the atmosphere at each model timestep, |
| 2766 |
|
and dividing by the total mass of the column. |
| 2767 |
|
\[ |
| 2768 |
|
{\bf VINTVT} = \frac{ \int_{surf}^{top} v T \rho dz } { \int_{surf}^{top} \rho dz } |
| 2769 |
|
\] |
| 2770 |
|
Using $\rho \delta z = -{\delta p \over g} $, we have |
| 2771 |
|
\[ |
| 2772 |
|
{\bf VINTVT} = { \int_0^1 v T dp } |
| 2773 |
|
\] |
| 2774 |
|
\\ |
| 2775 |
|
|
| 2776 |
|
\noindent |
| 2777 |
|
{ \underline {CLDFRC} Total 2-Dimensional Cloud Fracton ($0-1$) } |
| 2778 |
|
|
| 2779 |
|
If we define the |
| 2780 |
|
time-averaged random and maximum overlapped cloudiness as CLRO and |
| 2781 |
|
CLMO respectively, then the probability of clear sky associated |
| 2782 |
|
with random overlapped clouds at any level is (1-CLRO) while the probability of |
| 2783 |
|
clear sky associated with maximum overlapped clouds at any level is (1-CLMO). |
| 2784 |
|
The total clear sky probability is given by (1-CLRO)*(1-CLMO), thus |
| 2785 |
|
the total cloud fraction at each level may be obtained by |
| 2786 |
|
1-(1-CLRO)*(1-CLMO). |
| 2787 |
|
|
| 2788 |
|
At any given level, we may define the clear line-of-site probability by |
| 2789 |
|
appropriately accounting for the maximum and random overlap |
| 2790 |
|
cloudiness. The clear line-of-site probability is defined to be |
| 2791 |
|
equal to the product of the clear line-of-site probabilities |
| 2792 |
|
associated with random and maximum overlap cloudiness. The clear |
| 2793 |
|
line-of-site probability $C(p,p^{\prime})$ associated with maximum overlap clouds, |
| 2794 |
|
from the current pressure $p$ |
| 2795 |
|
to the model top pressure, $p^{\prime} = p_{top}$, or the model surface pressure, $p^{\prime} = p_{surf}$, |
| 2796 |
|
is simply 1.0 minus the largest maximum overlap cloud value along the |
| 2797 |
|
line-of-site, ie. |
| 2798 |
|
|
| 2799 |
|
$$1-MAX_p^{p^{\prime}} \left( CLMO_p \right)$$ |
| 2800 |
|
|
| 2801 |
|
Thus, even in the time-averaged sense it is assumed that the |
| 2802 |
|
maximum overlap clouds are correlated in the vertical. The clear |
| 2803 |
|
line-of-site probability associated with random overlap clouds is |
| 2804 |
|
defined to be the product of the clear sky probabilities at each |
| 2805 |
|
level along the line-of-site, ie. |
| 2806 |
|
|
| 2807 |
|
$$\prod_{p}^{p^{\prime}} \left( 1-CLRO_p \right)$$ |
| 2808 |
|
|
| 2809 |
|
The total cloud fraction at a given level associated with a line- |
| 2810 |
|
of-site calculation is given by |
| 2811 |
|
|
| 2812 |
|
$$1-\left( 1-MAX_p^{p^{\prime}} \left[ CLMO_p \right] \right) |
| 2813 |
|
\prod_p^{p^{\prime}} \left( 1-CLRO_p \right)$$ |
| 2814 |
|
|
| 2815 |
|
|
| 2816 |
|
\noindent |
| 2817 |
|
The 2-dimensional net cloud fraction as seen from the top of the |
| 2818 |
|
atmosphere is given by |
| 2819 |
|
\[ |
| 2820 |
|
{\bf CLDFRC} = 1-\left( 1-MAX_{l=l_1}^{Nrphys} \left[ CLMO_l \right] \right) |
| 2821 |
|
\prod_{l=l_1}^{Nrphys} \left( 1-CLRO_l \right) |
| 2822 |
|
\] |
| 2823 |
|
\\ |
| 2824 |
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
| 2825 |
|
|
| 2826 |
|
|
| 2827 |
|
\noindent |
| 2828 |
|
{ \underline {QINT} Total Precipitable Water ($gm/cm^2$) } |
| 2829 |
|
|
| 2830 |
|
\noindent |
| 2831 |
|
The Total Precipitable Water is defined as the vertical integral of the specific humidity, |
| 2832 |
|
given by: |
| 2833 |
|
\begin{eqnarray*} |
| 2834 |
|
{\bf QINT} & = & \int_{surf}^{top} \rho q dz \\ |
| 2835 |
|
& = & {\pi \over g} \int_0^1 q dp |
| 2836 |
|
\end{eqnarray*} |
| 2837 |
|
where we have used the hydrostatic relation |
| 2838 |
|
$\rho \delta z = -{\delta p \over g} $. |
| 2839 |
|
\\ |
| 2840 |
|
|
| 2841 |
|
|
| 2842 |
|
\noindent |
| 2843 |
|
{ \underline {U2M} Zonal U-Wind at 2 Meter Depth ($m/sec$) } |
| 2844 |
|
|
| 2845 |
|
\noindent |
| 2846 |
|
The u-wind at the 2-meter depth is determined from the similarity theory: |
| 2847 |
|
\[ |
| 2848 |
|
{\bf U2M} = {u_* \over k} \psi_{m_{2m}} {u_{sl} \over {W_s}} = |
| 2849 |
|
{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}u_{sl} |
| 2850 |
|
\] |
| 2851 |
|
|
| 2852 |
|
\noindent |
| 2853 |
|
where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript |
| 2854 |
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
| 2855 |
|
is above two meters, ${\bf U2M}$ is undefined. |
| 2856 |
|
\\ |
| 2857 |
|
|
| 2858 |
|
\noindent |
| 2859 |
|
{ \underline {V2M} Meridional V-Wind at 2 Meter Depth ($m/sec$) } |
| 2860 |
|
|
| 2861 |
|
\noindent |
| 2862 |
|
The v-wind at the 2-meter depth is a determined from the similarity theory: |
| 2863 |
|
\[ |
| 2864 |
|
{\bf V2M} = {u_* \over k} \psi_{m_{2m}} {v_{sl} \over {W_s}} = |
| 2865 |
|
{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}v_{sl} |
| 2866 |
|
\] |
| 2867 |
|
|
| 2868 |
|
\noindent |
| 2869 |
|
where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript |
| 2870 |
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
| 2871 |
|
is above two meters, ${\bf V2M}$ is undefined. |
| 2872 |
|
\\ |
| 2873 |
|
|
| 2874 |
|
\noindent |
| 2875 |
|
{ \underline {T2M} Temperature at 2 Meter Depth ($deg \hspace{.1cm} K$) } |
| 2876 |
|
|
| 2877 |
|
\noindent |
| 2878 |
|
The temperature at the 2-meter depth is a determined from the similarity theory: |
| 2879 |
|
\[ |
| 2880 |
|
{\bf T2M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) = |
| 2881 |
|
P^{\kappa}(\theta_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
| 2882 |
|
(\theta_{sl} - \theta_{surf})) |
| 2883 |
|
\] |
| 2884 |
|
where: |
| 2885 |
|
\[ |
| 2886 |
|
\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } |
| 2887 |
|
\] |
| 2888 |
|
|
| 2889 |
|
\noindent |
| 2890 |
|
where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
| 2891 |
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
| 2892 |
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
| 2893 |
|
is above two meters, ${\bf T2M}$ is undefined. |
| 2894 |
|
\\ |
| 2895 |
|
|
| 2896 |
|
\noindent |
| 2897 |
|
{ \underline {Q2M} Specific Humidity at 2 Meter Depth ($g/kg$) } |
| 2898 |
|
|
| 2899 |
|
\noindent |
| 2900 |
|
The specific humidity at the 2-meter depth is determined from the similarity theory: |
| 2901 |
|
\[ |
| 2902 |
|
{\bf Q2M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) = |
| 2903 |
|
P^{\kappa}(q_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
| 2904 |
|
(q_{sl} - q_{surf})) |
| 2905 |
|
\] |
| 2906 |
|
where: |
| 2907 |
|
\[ |
| 2908 |
|
q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } |
| 2909 |
|
\] |
| 2910 |
|
|
| 2911 |
|
\noindent |
| 2912 |
|
where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
| 2913 |
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
| 2914 |
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
| 2915 |
|
is above two meters, ${\bf Q2M}$ is undefined. |
| 2916 |
|
\\ |
| 2917 |
|
|
| 2918 |
|
\noindent |
| 2919 |
|
{ \underline {U10M} Zonal U-Wind at 10 Meter Depth ($m/sec$) } |
| 2920 |
|
|
| 2921 |
|
\noindent |
| 2922 |
|
The u-wind at the 10-meter depth is an interpolation between the surface wind |
| 2923 |
|
and the model lowest level wind using the ratio of the non-dimensional wind shear |
| 2924 |
|
at the two levels: |
| 2925 |
|
\[ |
| 2926 |
|
{\bf U10M} = {u_* \over k} \psi_{m_{10m}} {u_{sl} \over {W_s}} = |
| 2927 |
|
{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}u_{sl} |
| 2928 |
|
\] |
| 2929 |
|
|
| 2930 |
|
\noindent |
| 2931 |
|
where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript |
| 2932 |
|
$sl$ refers to the height of the top of the surface layer. |
| 2933 |
|
\\ |
| 2934 |
|
|
| 2935 |
|
\noindent |
| 2936 |
|
{ \underline {V10M} Meridional V-Wind at 10 Meter Depth ($m/sec$) } |
| 2937 |
|
|
| 2938 |
|
\noindent |
| 2939 |
|
The v-wind at the 10-meter depth is an interpolation between the surface wind |
| 2940 |
|
and the model lowest level wind using the ratio of the non-dimensional wind shear |
| 2941 |
|
at the two levels: |
| 2942 |
|
\[ |
| 2943 |
|
{\bf V10M} = {u_* \over k} \psi_{m_{10m}} {v_{sl} \over {W_s}} = |
| 2944 |
|
{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}v_{sl} |
| 2945 |
|
\] |
| 2946 |
|
|
| 2947 |
|
\noindent |
| 2948 |
|
where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript |
| 2949 |
|
$sl$ refers to the height of the top of the surface layer. |
| 2950 |
|
\\ |
| 2951 |
|
|
| 2952 |
|
\noindent |
| 2953 |
|
{ \underline {T10M} Temperature at 10 Meter Depth ($deg \hspace{.1cm} K$) } |
| 2954 |
|
|
| 2955 |
|
\noindent |
| 2956 |
|
The temperature at the 10-meter depth is an interpolation between the surface potential |
| 2957 |
|
temperature and the model lowest level potential temperature using the ratio of the |
| 2958 |
|
non-dimensional temperature gradient at the two levels: |
| 2959 |
|
\[ |
| 2960 |
|
{\bf T10M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) = |
| 2961 |
|
P^{\kappa}(\theta_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
| 2962 |
|
(\theta_{sl} - \theta_{surf})) |
| 2963 |
|
\] |
| 2964 |
|
where: |
| 2965 |
|
\[ |
| 2966 |
|
\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } |
| 2967 |
|
\] |
| 2968 |
|
|
| 2969 |
|
\noindent |
| 2970 |
|
where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
| 2971 |
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
| 2972 |
|
$sl$ refers to the height of the top of the surface layer. |
| 2973 |
|
\\ |
| 2974 |
|
|
| 2975 |
|
\noindent |
| 2976 |
|
{ \underline {Q10M} Specific Humidity at 10 Meter Depth ($g/kg$) } |
| 2977 |
|
|
| 2978 |
|
\noindent |
| 2979 |
|
The specific humidity at the 10-meter depth is an interpolation between the surface specific |
| 2980 |
|
humidity and the model lowest level specific humidity using the ratio of the |
| 2981 |
|
non-dimensional temperature gradient at the two levels: |
| 2982 |
|
\[ |
| 2983 |
|
{\bf Q10M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) = |
| 2984 |
|
P^{\kappa}(q_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
| 2985 |
|
(q_{sl} - q_{surf})) |
| 2986 |
|
\] |
| 2987 |
|
where: |
| 2988 |
|
\[ |
| 2989 |
|
q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } |
| 2990 |
|
\] |
| 2991 |
|
|
| 2992 |
|
\noindent |
| 2993 |
|
where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
| 2994 |
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
| 2995 |
|
$sl$ refers to the height of the top of the surface layer. |
| 2996 |
|
\\ |
| 2997 |
|
|
| 2998 |
|
\noindent |
| 2999 |
|
{ \underline {DTRAIN} Cloud Detrainment Mass Flux ($kg/m^2$) } |
| 3000 |
|
|
| 3001 |
|
The amount of cloud mass moved per RAS timestep at the cloud detrainment level is written: |
| 3002 |
|
\[ |
| 3003 |
|
{\bf DTRAIN} = \eta_{r_D}m_B |
| 3004 |
|
\] |
| 3005 |
|
\noindent |
| 3006 |
|
where $r_D$ is the detrainment level, |
| 3007 |
|
$m_B$ is the cloud base mass flux, and $\eta$ |
| 3008 |
|
is the entrainment, defined in Section \ref{sec:fizhi:mc}. |
| 3009 |
|
\\ |
| 3010 |
|
|
| 3011 |
|
\noindent |
| 3012 |
|
{ \underline {QFILL} Filling of negative Specific Humidity ($g/kg/day$) } |
| 3013 |
|
|
| 3014 |
|
\noindent |
| 3015 |
|
Due to computational errors associated with the numerical scheme used for |
| 3016 |
|
the advection of moisture, negative values of specific humidity may be generated. The |
| 3017 |
|
specific humidity is checked for negative values after every dynamics timestep. If negative |
| 3018 |
|
values have been produced, a filling algorithm is invoked which redistributes moisture from |
| 3019 |
|
below. Diagnostic {\bf QFILL} is equal to the net filling needed |
| 3020 |
|
to eliminate negative specific humidity, scaled to a per-day rate: |
| 3021 |
|
\[ |
| 3022 |
|
{\bf QFILL} = q^{n+1}_{final} - q^{n+1}_{initial} |
| 3023 |
|
\] |
| 3024 |
|
where |
| 3025 |
|
\[ |
| 3026 |
|
q^{n+1} = (\pi q)^{n+1} / \pi^{n+1} |
| 3027 |
|
\] |
| 3028 |
|
|
| 3029 |
|
|
| 3030 |
|
\subsubsection{Key subroutines, parameters and files} |
| 3031 |
|
|
| 3032 |
|
\subsubsection{Dos and donts} |
| 3033 |
|
|
| 3034 |
\subsection{Fizhi Reference} |
\subsubsection{Fizhi Reference} |
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