Accuracy progressive calculation of Lagrangian trajectories from gridded velocity field

Abstract

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