Accuracy Progressive Calculation of Lagrangian Trajectories from a Gridded Velocity Field

Abstract

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