where 



Tx(I,J) = (At/AX){gD(I,J)/a&(J)}, 



7y(I,J) = (At/A$){gD(I,J)/a^(J)}, 



v^iJ) = (At/AX){l/a0(J)}, 



Uy(J) = (At/A*){l/a^(J)},. 



6jjU^(I,J) = U^d-^/J) - U^(I-^,J), 



6yV^(I,J) = V^(I,J+J)e(j4) - V^(I,J-J)0(J-i), 



a = radius of the Earth, 



f(J) = 2flsin('i>o+JA4>), 



F = forcing and friction terms, 



X,f = coupling terms. 



The forcing and coupling terms will be discussed in the next section. 

 The coupling terms in (42) and (43) or (44) aind (45) are of opposite 

 mode relative to the other terms. 



Upon replacing the total depth, D, by the equivalent depth, 

 eH2^H2/D, interchanging modes of all field variables and coupling 

 terms, and using the proper forcing terms, (42) through (45) are also 

 representations of the implicit formulation for the internal mode 

 computation . 



The explicit coding of the external mode momentum equation at 

 odd time steps is 



23 



