A physically based satellite rainfall estimation method using fluid dynamics modelling

A cloud motion winds (CMW) method is presented for improving quantitative rainfall estimation advection schemes that use both infrared (IR) and passive microwave (PMW) satellite data. Advection schemes are used to provide quantitative rainfall estimates by combining more direct PMW rainfall estimates with more frequent IR cloud top temperature measures using a two-step technique: (1) PMW estimates are transported along CMW trajectories calculated with an advection scheme at subpixel resolution; and (2) PMW estimates are calibrated using the IR gradient along those trajectories. These schemes outperform traditional methods of satellite rainfall estimation but no clear physical basis for the procedure has yet been described. Here, the physical basis for the image processing techniques used in advection techniques is described. It is shown that geostationary satellite-derived CMW from IR sensors can be modelled in terms of fluid dynamics using Navier-Stokes equations. This approach allows for modelling the problem as equivalent to the flow of a brightness temperature field, also providing subpixel resolution and unlimited rotation/deformation possibilities. The method is illustrated with rainfall estimates from a numerical weather prediction (NWP) model and with 3-hourly PMW products as simulation data, obtaining consistent results.