Real-time rainfall forecasting using weather satellite imagery

Taiwan locates at the center of the western Pacific Rim and is particularly vulnerable to threat by typhoons. In average, there are 3.5 typhoons pass through Taiwan annually. Typhoons often draw huge amount and high intensity rainfalls, resulting in high casualties and severe property damages. For example, during the passage of Typhoon Nari in September 2002, more than 700mm rainfall was recorded near the capital city Taipei, causing extensive inundation and tremendous property damages in the city. Recent events and studies indicate that accurate real-time rainfall forecasting is crucial for flood forecasting since most watersheds in Taiwan have short time-of-concentrations (Tc). In this study we propose a real-time rainfall forecasting approach using GMS weather satellite imagery. The approach composes a multi-spectral spatial convolution (MSSC) scheme that yields a 3-hour lead rainfall forecast and a Kalman filtering algorithm for real-time parameter update. Using a single GMS thermal infrared band, the spatial convolution scheme can be expressed by the following equation: [ R(x,y)=sumlimits_{x'=x-ℓ}^x+ℓ {sumlimits_{y'=y-ℓ}^y+ℓ {T({x}',{y}')f(x-{x}',y-{y}')} } =sumlimits_i=1^N {T(i;x,y)f(i;x,y)} ] where R(x,y), T(x,y) and f(x,y) represent rainfall, cloud-top- temperature and kernel function weight at location (x, y). The spatial convolution is carried out within a(2ℓ-1)× (2ℓ-1) moving window. Using rainfall measurements of a network of 37 raingauge stations within the study area and cloud-top-temperatures derived from GMS images, the kernel function weights can be solved by a least square estimator:

[ {R(1)} {R(2)} ďots {R(n)} ]=[ {T(1,1)} & {T(1,2)} & \cdots & {T(1,N)} {T(2,1)} & {T(2,2)} & \cdots & {T(2,N)} ďots & ďots & ddots & ďots {T(n,1)} & {T(n,2)} & \cdots & {T(n,N)} ] [ {f(1)} {f(2)} ďots {f(N)} ] where N is the total number of pixels in the moving window and n is the number of raingauge stations. The above equation can also be expressed as R=T\cdot F, and the least square estimator of the kernel function is TRIAL RESTRICTION. In order to yield rainfall forecast, 3-hour lead accumulative rainfalls are used in the above equation. A multiple bands version of the above matrix equation is also developed using three thermal IR bands of the GMS satellite. During a typhoon event the kernel function may change with time and Kalman filtering is implemented using kernel function weight TRIAL RESTRICTION as the state vector. Results of a cross validation scheme reveal that the correlation between rainfall measurements and real-time forecasted rainfalls by spatial convolution and Kalman filtering ranging from 0.74 to 0.93 in most raingauges, indicating a great potential of real-time rainfall forecasting using weather satellite imagery.