Purdue atmospheric models and applications

This article summarizes our research related to geofluid dynamics and numerical modeling. In order to have a better understanding of the motion in the atmosphere, we have been working on various forms of the Navier-Stokes equations, including the linearized and nonlinear systems as well as turbulence parametrization, cumulus parametrization, cloud physics, soil-snow parametrization, atmospheric chemistry, etc. We have also been working on numerical methods in order to solve the equations more accurately. The results show that many weather systems in the initial/growing stage can be qualitatively described by the linearized equations; on the other hand, many developed weather phenomena can be quantitatively reproduced by the nonlinear Purdue Regional Climate Model, when the observational data or reanalysis is used as the initial and lateral boundary conditions. The model can also reveal the detailed structure and physics involved, which sometimes can be misinterpreted by meteorologists according to the incomplete observations. However, it is also noted that systematic biases/errors can exist in the simulations and become difficult to correct. Those errors can be caused by the errors in the initial and boundary conditions, model physics and parametrizations, or inadequate equations or poor numerical methods. When the regional model is coupled with a GCM, it is required that both models should be accurate so as to produce meaningful results. In addition to the Purdue Regional Climate Model, we have presented the results obtained from the nonhydrostatic models, the one-dimensional cloud model, the turbulence-pollution model, the characteristic system of the shallow water equations, etc. Although the numerical model is the most important tool for studying weather and climate, more research should be done on data assimilation, the physics, the numerical method and the mathematic formulation in order to improve the accuracy of the models and have a better understanding of the weather and climate.