A proposed baroclinic wave test case for deep‐ and shallow‐atmosphere dynamical cores

Abstract

Idealised studies of key dynamical features of the atmosphere provide insight into the behaviour of atmospheric models. A very important, well understood, aspect of midlatitude dynamics is baroclinic instability. This can be idealised by perturbing a vertically sheared basic state in geostrophic and hydrostatic balance. An unstable wave mode then results with exponential growth (due to linear dynamics) in time until, eventually, nonlinear effects dominate and the wave breaks. A new, unified, idealised baroclinic instability test case is proposed. This improves on previous ones in three ways. First, it is suitable for both deep‐ and shallow‐atmosphere models. Second, the constant surface pressure and zero surface geopotential of the basic state makes it particularly well‐suited for models employing a pressure‐ or height‐based vertical coordinate. Third, the wave triggering mechanism selectively perturbs the rotational component of the flow; this, together with a vertical tapering, significantly improves dynamic balance.

Using the UM dynamical cores to reproduce idealised 3-D flows

“…These 455 practical tests complement the analysis of normal modes in Thuburn et al (2002a,b), and standardised flow tests (e.g. Ullrich et al, 2013;Wood et al, 2013). The general parameters for the model runs are listed in Table 3.…”

“…Several tests have already been successfully performed using the UM. Most recently, Wood et al (2013) performed a subset of tests detailed in the Dynamical Core Model Intercomparison Project (DCMIP, see http://earthsystemcog.org/ projects/dcmip-2012/) and the deep-atmosphere baroclinic instability test of Ullrich et al (2013). However, these tests evaluate the modelling of specific atmospheric responses, such as gravity waves induced by orography, whereas tests such as Held and Suarez (1994) evaluate the modelled state of the entire atmosphere over long integration times.…”

A semi‐implicit deep‐atmosphere spectral dynamical kernel using a hydrostatic‐pressure coordinate

“…The deep‐atmosphere baroclinic wave test case was first described in Ullrich et al . (). The base state of the baroclinic test case is the same as the aforementioned steady‐state test case, and perturbations on both the zonal and meridional wind are added to trigger the baroclinic wave.…”

Implicit-explicit (IMEX) Runge-Kutta methods for non-hydrostatic atmospheric models

“…With this choice of weighting, a WRMS norm of 1 is considered small for any error-like quantities since 1/w i represents a tolerance on the components Newton's method can be quite expensive, especially when many iterations are needed to achieve convergence, since each iteration involves computing or approximating the Jacobian matrix and performing a linear solve. As an alternative we also consider treating (25) as a linearly implicit system. This Rosenbrock-like approach, used in and 15 Guerra and Ullrich (2016), consists of performing a single iteration of Newton's method, thus limiting the cost of the nonlinear solver.…”

“…The second test case simulates the development of a baroclinic wave over the course of approximately 10 days as described in Ullrich et al (2014). For this test case, we focus on how the methods, splittings, and solvers perform near the maximum stable 5 time step size in a 30 day simulation.…”