Additive Gaussian Processes for Blending Gauge and Satellite Rainfall Data

Predicting ground rainfall from satellite estimates is useful as input for many applications, especially for areas with sparse rain gauges. We propose a predictive model based on an Additive Gaussian process (AGP) which can be viewed as the sum of a GP for the influence of the satellite estimate and a GP for the spatial distribution of rainfall between gauges. The hyperparameters for the covariance function estimates maximize the leave-oneout predictive densities. Initial results indicate that the proposed AGP model provides more accurate predictions compared with traditional kriging and inverse weighting methods. I. DATA AND MOTIVATION Spatial estimates of ground rainfall are widely used for scientific applications such as modelling agricultural output and evaluating flood risk. Rain gauges can be sparse, especially in developing countries and in rural areas. Satellite estimates of rainfall provide uniform spatial coverage but are indirect estimates of precipitation, and tend to suffer from systematic bias. The proposed model takes as input satellite measurements for the entire region and gauge observations at specific locations, and can predict the expected monthly gauge rainfall at arbitrary points. The predicted gauge rainfall is a smooth spatial field. This allows for predictions of ground rainfall at new points, for which there have been no gauge observations. Satellite pixels are measured on a grid, and rain gauges are both observed and predicted at arbitrary locations.The satellite estimate of rainfall for a particular location is taken to be the value of the pixel which contains the location. The datasets used are the Tropical Rainfall Measuring Mission (TRMM) 3B43v7 satellite estimates, and gauge observations from a region covering Pakistan and northwest India in which gauges are sparse. Only data from principal monsoon months, July and August, are used. Figure 1 shows an example predictive mean surface Corresponding author: H Strong, University of California, Irvine, Irvine CA [email protected] 1 University of California, Irvine 2 International Research Institute for Climate and Society, Columbia University, New York based on some gauge observations for a particular month. The TRMM input is not shown.