Evolution of errors in the global multiresolution model for prediction across scales: Shallow water (MPAS–SW)

The global Model for Prediction Across Scales (MPAS) with shallow‐water (SW) dynamics is taken as the forecast model to characterize the errors under a variable‐resolution (VR) mesh. An idealized experiment featuring gravity and Rossby waves triggered by orography is conducted with two meshes consisting of the same number of grid cells, which directly indicates the computational cost. One mesh is of 120‐km uniform resolution (UR), the other has 53–210 km VR. Both simulations are compared with the solutions from a 60‐km uniform high‐resolution (HR) mesh serving as the reference. The differences with respect to the HR results for both UR and VR experiments are manifested as rapidly propagating gravity waves circling the Earth about every two days. These signals are regarded as errors due to insufficient resolution. Over most of the Earth, the resolution of the VR mesh is coarser than that of the UR mesh. The magnitudes of the errors in the VR experiment are found to grow larger than those in the UR case shortly after the simulation starts. The sensitivities to the errors in the eight‐day forecast calculated with the MPAS–SW adjoint model show similar propagation patterns, following a nonlinear state trajectory. The sensitivities under VR suggest that little contribution to the errors throughout the simulation process is made within the finely resolved areas. In the initial conditions under VR, the error signals come primarily from the coarse‐resolution regions immediately outside the areas with enhanced resolution. This finding implies that, in simulations under VR, error signals generated in the coarsely resolved regions can be propagated into the finely resolved areas when conveyed by wave types allowed in the model, that is, gravity waves in the case of this study, the rate of which depends on the fluid mean height.