The global MPAS with the 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 costs. One mesh is of 120 km uniform resolution (UR), the other of 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 from both the 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 resolutions. Over the most part of the Earth, the resolutions in the VR mesh is coarser than the UR mesh. The magnitudes of the errors in the VR experiment are found to grow larger than in the UR case shortly after the simulation started. The sensitivities to the errors in the eight-day forecast calculated with the MPAS-SW adjoint model show similar propagating patterns following the 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 primarily come from the coarse resolutions immediately outside the areas with enhanced resolutions. The finding implies that, in simulations under VR, error signals generated in the coarsely resolved regions can be propagated into the finely resolved areas conveyed by wave types allowed in the model, i.e., gravity waves in the case of this study, the rate of which depends on the fluid mean height.