Spatial Modelling of Linear Regression Coefficients for Gauge Measurements Against Satellite Estimates

Satellite imagery provides estimates for the amount of precipitation that has occurred in a region, these estimates are then used in models for predicting future precipitation trends. As these satellite images only provide an estimate for the amount of precipitation that has occurred, it is important that they be accurate estimates. If we assume that a rain gauge correctly measures the amount of precipitation that has occurred in some location over a specified time interval, then we can compare the satellite precipitation estimate to the gauge measurement for the same time interval. By expressing the relationship between the gauge measurement and the satellite precipitation estimate for the same time interval as a linear equation we can then spatially map the coefficients of this linear relationship to inspect the spatial trends of the regression coefficients. We then model the coefficients of the linear equations of each location by a spatial linear model and then use this model to predict the coefficients in location where there are no rain gauges available.