where Kˆ *

11 and Kˆ *

22 are the horizontal components of the

contravariant eddy diffusivity multiplied with factor γˆ ρ .

25

The off-diagonal terms are neglected as a practical

simplification. Because the meteorological input parameters

are read in or interpolated at each Δ tsync, we

approximate γˆ ρ to be constant for the duration of a

synchronization time-step for integrating the diffusion

process with the fractional time-step method. The horizontal

diffusion equation is solved with an explicit finite difference

method with a sufficiently small time step to ensure positive

solutions. The reason an implicit scheme is not used here is

to minimize the computer memory requirement for handling

large horizontal grids in the subroutine. For the explicit

scheme, the time-step should be chosen such that numerical

stability and positivity of the solutions are maintained. With

an appropriate Courant number for the horizontal diffusion,

β hdiff , the time-step can be determined with:

 

n1051 - n1052 - n1053 - n1054 - n1055 - n1056 - n1057 - n1058 - n1059 - n1060 - n1061 - n1062 - n1063 - n1064 - n1065 - n1066 - n1067 - n1068 - n1069 - n1070 - n1071 - n1072 - n1073 - n1074 - n1075 - n1076 - n1077 - n1078 - n1079 - n1080 - n1081 - n1082 - n1083 - n1084 - n1085 - n1086 - n1087 - n1088 - n1089 - n1090 - n1091 - n1092 - n1093 - n1094 - n1095 - n1096 - n1097 - n1098 - n1099 - n1100

 

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