Fronts and nonlinear waves in a simplified shallow-water model of the atmosphere with moisture and convection

We describe a shallow-water type atmospheric model which includes the transport of moisture as well as related precipitation and convection effects. The model combines hydrodynamic nonlinearity of the standard shallow-water model with the intrinsic nonlinearity due to the precipitation threshold. It allows for both theoretical treatment by the method of characteristics and efficient numerical resolution using shock-capturing finite-volume schemes. Linearized in the dynamical sector, the model adequately reproduces the propagation of the edge of precipitation regions (precipitation fronts) found in earlier studies. Results of numerical experiments on simple wave scattering upon a moisture front are in agreement with analytical results and highlight the role of dissipative reflector played by precipitating zones. We also analyze the evolution of a disturbance propagating in a uniformly saturated region and obtain criteria for precipitation front formation. Finally, we simulate wave breaking as an example of essentially nonlinear phenomenon and show how moist effects modify the classical shock formation scenario.