A framework for evaluating model error using asymptotic convergence in the Eady model

Abstract

AbstractOperational weather forecasting requires the accurate simulation of atmospheric motions on scales ranging from the synoptic down to tens of kilometres. Weather fronts, characteristic of midlatitude weather systems, are generated through baroclinic instability on the large scale but are anisotropic features in which temperature and winds can vary rapidly on the short scale.We present a framework for evaluating model error in terms of asymptotic convergence using the Eady model. Through rescaling the problem, we are able to approach solutions of a balanced model, given by the semi‐geostrophic equations, using the non‐hydrostatic, incompressible Euler–Boussinesq Eady equations. Using this approach, we are able to validate the numerical implementation and assess the long‐term performance in terms of solution lifecycles.We present results using a finite‐difference method with semi‐implicit time‐stepping and semi‐Lagrangian transport, and show that we are able to proceed past the point of frontal collapse and recover the theoretical convergence rate. We propose that numerical diffusion of potential vorticity after collapse, as a result of insufficient Lagrangian conservation, is detrimental to the long‐term evolution of the solution.