Backward Integration of Nonlinear Shallow Water Model: Part I: Solitary Rossby Waves

The inviscid, nonlinear shallow water model developed by Sun was applied to study the inverse of equatorial Rossby solitons, which can be represented by the Korteweg-De Vries equation (KdV equation). The model was integrated forward in time, then the results were used as initial conditions for backward integration by just changing time step from positive to negative. The detailed structure, secondary circulation, and propagating speed of waves from both integrations are in good agreement with analytic solutions. The total mass, energy, and enstrophy are also well conserved. The procedure is much simpler and the results are more accurate than other backward integrations of 2D nonlinear models, which require significant modification of the model and can be contaminated by unwanted diffusion in forward-backward integrations or time-consuming iterative methods. This paper is also different from the numerical method for solving the inverse of the KdV equation.