Reduction of computational error is a key issue in computing Lagrangian trajectories 12 using griddedvelocities. Computational accuracy enhances from using the first term (constant 13 velocity scheme), thefirst two terms (linear uncoupled scheme), the first three terms (linear 14 coupled scheme), to using all thefour terms (nonlinear coupled scheme) of the two-dimensional 15 interpolation. A unified ?analyticalform? is presented in this study for different truncations. 16 Ordinary differential equations for predictingLagrangian trajectory are linear using the constant 17 velocity/linear uncoupled schemes (both commonlyused in atmospheric and ocean modeling) 18 linear coupled scheme and nonlinear using the nonlinearcoupled scheme (both proposed in this 19 paper). Location of the Lagrangian drifter inside the grid cell isdetermined by two algebraic 20 equations, which are solved explicitly with the constant velocity/linearuncoupled schemes, and 21 implicitly using the Newton-Raphson iteration method with thelinear/nonlinear coupled 22 schemes. The analytical Stommel ocean model on the f-plane is used toillustrate great accuracy 23 improvement from keeping the first-term to keeping all the terms of thetwo-dimensional 24 interpolation.
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