SUBROUTINE MODESPLIT

After INTERNAL and SUPERBEEUV have estimated $\Delta U$ and $\Delta V$, MODESPLIT is called to update the U, V , W and ETA fields including the effects of all terms in the momentum equations and the equation of continuity, except the atmospheric pressure term.

In MODESPLIT the following steps are taken:

• The contributions in $\Delta U$ and $\Delta V$ are vertically integrated to produce terms $A_x$ and $A_y$ according to equation (55).
• The $U$ and $V$ fields are split into 2-D external or barotropic and 3-D internal or baroclinic parts according to equation (51).
• Then for each call to MODESPLIT N2D steps are used to propagate the depth integrated velocities $U_A$ and $V_A$ and the water level with a $\Theta$-method using DTE = DT/N2D as time step. In each 2D time step the following actions are taken: Estimate the $A_{M2D}$ field through a call to SMAGOR2D, if SMAG is true. Include the effects of horizontal viscosity on the $U_A$ and $V_A$ fields. (Calls to HORVISCUV2DPOM or HORVISCUV2D) In the first substep, a forward method is used as a predictor method. That is: $\eta^*$ = $\eta^n$ + DTE $\times \Delta \eta^n$, where $\Delta \eta^n$ contain the spatially discretized terms of the $\eta$-equation. In the first substep, $U_A^*$ and $V_A^*$ are computed correspondingly with the forward method. In each of the following 2D sub-steps, the leapfrog method is used as predictor for $\eta^*$, $U_A^*$, and $V_A^*$. That is: $\eta^*$ = $\eta^{n-1}$ + $2 \times DTE \times \Delta \eta^n$. The final values at time step $n+1$ are computed with a $\theta$-method according to: $\eta^{n+1}$ = $\eta^{n}$ + $DTE \times ( \Theta_{2D} \Delta \eta^{*} + (1-\Theta_{2D}) \Delta \eta^{n} ).$ $\Theta_{2D}$ must be in the range $0.5 \leq \Theta_{2D} \leq 1$ to ensure stability.

• After the 2D steps, the velocity fields, that have been used to change the water level from ETAP to ETA over the N2D 2D time steps, are saved in the UADV and VADV arrays. It is essential that these non-divergent fields are used in the advection of scalar fields and momentum to maintain the mass balance.
• Estimate the $A_M$ and $A_H$ fields through a call to SMAGOR, if SMAG is true.
• Estimate the horizontal viscosity fluxes in equations (58) and (59) and store these through a call to HORVISCUVPOM if VISCPOM is true, and a call to HORVISCUV otherwise.
• Update the $U_B$, $V_B$, $U$ and $V$ fields taking into account the effects of the Coriolis terms, the horizontal viscosity terms, the $A_x$, $A_y$, $\Delta U$ and $\Delta V$ terms of equations (58) and (59).
• Call VERTVISCUVB to include the effects of vertical viscosity on the momentum.
• Include the effects of surface and bottom stress on the $U_B$, $V_B$, $U$ and $V$ fields.
• Compute the sigma coordinate vertical velocities $W$ from equation (36) using fluxes produced by UADV and VADV and the water levels ETA and ETAP.

If we are running experiments with river runoff, RIVLOG = .TRUE. , the effects of the runoff on the U, V, W and ETA fields are also included in modesplit.f90.