Inconsistent Finite Differencing Errors in the Variational Adjustment of Horizontal Wind Components

Abstract

Inconsistency in writing a set of partial differential equations in finite difference form results in error in the numerical solution. An example is shown in which horizontal wind components are variationally adjusted to remove the surface pressure tendency. Three Euler-Lagrange equations are solved simultaneously using two different finite difference forms, one of which is consistent and the other inconsistent. Derived quantities (divergence and ω-velocity) are examined using both consistently and inconsistently adjusted horizontal wind components