Next Article in Journal
Understanding Spatial Variability of Air Quality in Sydney: Part 1—A Suburban Balcony Case Study
Previous Article in Journal
Emissions of a Euro 6b Diesel Passenger Car Retrofitted with a Solid Ammonia Reduction System
Previous Article in Special Issue
An Alternative Bilinear Interpolation Method Between Spherical Grids
Article Menu
Issue 4 (April) cover image

Export Article

Open AccessArticle

Generalized Z-Grid Model for Numerical Weather Prediction

State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, China Meteorological Administration, Beijing 100081, China
Atmosphere 2019, 10(4), 179;
Received: 25 February 2019 / Revised: 27 March 2019 / Accepted: 30 March 2019 / Published: 3 April 2019
PDF [2391 KB, uploaded 17 April 2019]


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. View Full-Text
Keywords: finite volume; C-grid; Z-grid; stability; numerical efficiency; shallow water equations finite volume; C-grid; Z-grid; stability; numerical efficiency; shallow water equations

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Xie, Y. Generalized Z-Grid Model for Numerical Weather Prediction. Atmosphere 2019, 10, 179.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Atmosphere EISSN 2073-4433 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top