Dry and Moist Idealized Experiments with a Two-Dimensional Spectral Element Model

Abstract

Abstract A nonhydrostatic, fully compressible spectral element (SE) model is evaluated in a series of two-dimensional idealized simulations. A dry formulation of the model is evaluated for a linear hydrostatic mountain-wave case, and a version with moisture is tested for a squall line. In the SE method, two setup parameters control the spatial resolution: the number of elements (h) and the polynomial order (p) of the basis functions. In this paper, the h−p parameter space is systematically explored, with the average horizontal resolution (Δx) varying from 0.2 to 10 km in 91 simulations. The dry experiments are evaluated using an analytic solution. The ratio of Δx/a < 0.2, where a is the mountain half-width, is sufficient to accurately resolve the mountain wave. Accuracy, computational cost, and convergence to the analytic solution are evaluated and compared to a second-order finite-difference (FD) model. The increase in computational cost by refining the spatial resolution yields a significant accuracy gain for the SE, with only a marginal improvement for the FD model. The squall line is evaluated across the control parameter space by assessing three integrated quantities: total precipitation accumulation, maximum vertical velocity, and maximum precipitation rate. The squall line is adequately resolved with Δx < 2 km and p > 5. There is little variation in metrics due to the varying nodal spacing within an element at the same average Δx. When the spatial resolution is refined, the analyzed metrics no longer converge. The nonlinear nature of moist convection is responsible for this resolution dependence as a result of localized buoyancy sources, evident in the vertical velocity spectrum.