Generalized Z-Grid Model for Numerical Weather Prediction

Abstract

Z-grid finite volume models conserve all-scalar quantities as well as energy and potential enstrophy and yield better dispersion relations for shallow water equations than other finite volume models, such as C-grid and C-D grid models; however, they are more expensive to implement. During each time integration, a Z-grid model must solve Poisson equations to convert its vorticity and divergence to a stream function and velocity potential, respectively. To optimally utilize these conversions, we propose a model in which the stability and possibly accuracy on the sphere are improved by introducing more stencils, such that a generalized Z-grid model can utilize longer time-integration steps and reduce computing time. Further, we analyzed the proposed model’s dispersion relation and compared it to that of the original Z-grid model for a linearly rotating shallow water equation, an important property for numerical models solving primitive equations. The analysis results suggest a means of balancing stability and dispersion. Our numerical results also show that the proposed Z-grid model for a shallow water equation is more stable and efficient than the original Z-grid model, increasing the time steps by more than 1.4 times.

Positive Definite Advection Transport Algorithm for Conservation Law Equations on Nonuniform Irregular Grids

“…for regular grids, and discretation (6) is the first order. For an irregular grid, the discretation of (6) prevents step (3) from reaching first order.…”

“…In fact, for the nonuniform grid, many existing numerical schemes cannot achieve the design accuracy. In [6], Xie studies such precision problems. Numerical solutions on spheres are the key to developing global atmospheric models.…”

Resolution Sensitivity of the GRIST Nonhydrostatic Model From 120 to 5 km (3.75 km) During the DYAMOND Winter

“…In response to a broad need for unified weather and climate modeling, GRIST was developed as one of several tentative projects (cf., Xie, 2019; Yu et al., 2019) to explore the possibility of unification. The development of this model system boosts the creation of a new model architecture that facilitates unified weather and climate modeling.…”