Truncation Error Estimates for Refinement Criteria in Nested and Adaptive Models

Abstract

Truncation error estimates are considered as criteria for fine-grid placement and movement in nested and adaptive finite-difference atmospheric models. A simple method for calculating the truncation error at any time during an integration is described. Two cases using the shallow-water equations and the hydrostatic primitive equations are examined to demonstrate the accuracy of the method and illuminate the relationships among the truncation error, a particular discretization, the equations being solved and the flow physics. The relationship between the truncation error and the solution error is also discussed and it is argued that minimization of the truncation error is the necessary consideration for producing more accurate numerical solutions. Examples of use of the truncation error estimates in adaptive models are also presented.