Rainfall modeling

Numerical simulation of atmospheric processes leading to the formation of rainfall involve solving equations describing the moist airflow dynamics coupled with the equations describing processes leading to the formation and fallout of precipitation. This chapter discusses the progress of the two elements over the last several decades. On the dynamics side, the evolution of weather and climate modeling featured the key transition from using primitive equations suitable for the simulation of hydrostatic large-scale flows and requiring the use of convection parameterization to applying the nonhydrostatic equations that allow convection-permitting simulations. The latter removes the key uncertainty due convection parameterization that numerical weather prediction and climate communities have been struggled with for decades. The transition benefits from a long history of small-scale modeling using nonhydrostatic equations, either anelastic or compressible. Although both are suitable for modeling mesoscale and small-scale nonhydrostatic dynamics, only compressible equations are valid for the global scale because of the unabbreviated vorticity dynamics, the key element of the extratropical synoptic scale baroclinic waves. Modeling of microphysical processes has traditionally used the Eulerian approach and represented cloud and precipitation fields applying density-like variables. The complexity of modeling approaches evolved from simple bulk single-moment schemes (i.e., predicting the total mass only), through double-moment schemes that predict the total mass together with the total concentration, to sophisticated bin (spectral) microphysics schemes that aim at predicting size distributions of cloud and precipitating liquid and solid particles. More recently, a Lagrangian approach was introduced that applies a set of point particles carried by the flow and growing in response to local conditions. Although considered experimental at this stage, the Lagrangian microphysics provides a compelling alternative for the traditional Eulerian approaches.