Statistical methods for blending satellite and ground observations to improve high-resolution precipitation estimates

Drought and flood management practices require accurate estimates of precipitation in space and time. However, data is sparse in regions with complicated terrain, often in valleys, and of poor quality. Consequently, extreme precipitation events are poorly represented. Satellite-derived rainfall data is an attractive alternative in such regions and is being widely used, though it too fails in representing extreme events due to its dependency on retrieval algorithms and the indirect relationship between satellite infrared observations and precipitation intensities. Thus, it seems appropriate to blend satellite-derived rainfall data of extensive spatial coverage with rain gauge data in order to provide a more robust estimate of precipitation. To this end, in this research we offer four techniques to blend rain gauge data and the Climate Hazards group InfraRed Precipitation (CHIRP) satellite-derived precipitation estimate for Central America and Colombia. In the first two methods, the gauge data is assigned to the closest CHIRP grid point, where the error is defined as r(s) = Yobs(s) - Ysat(s). The spatial structure of r(s) is then modeled using physiographic information (easting, northing, and elevation) by two methods (i) a traditional Co-kriging approach which utilizes a variogram that is calculated in Euclidean space and (ii) a nonparametric method based on local polynomial functional estimation. The models are used to estimate r at all grid points, which is then added to the CHIRP, thus creating an improved satellite estimate. We demonstrate these methods by applying them to pentadal and monthly total precipitation fields during 2009. The models' predictive abilities and their ability to capture extremes are investigated. These blending methods significantly improve upon the satellite-derived estimates and are also competitive in their ability to capture extreme precipitation. The above methods assume satellite-derived precipitation to be unbiased estimates of gauge precipitation, which is far from being the case. Thus the third method, Bayesian Hierarchical Modeling (BHM), is offered. In this approach, first, the gauge observations are modeled as a function of satellite-derived estimates and other variables such as elevation (the satellite estimate coefficient is in effect a bias correction factor). The residual from this first hierarchical model is then subjected to a spatial kriging model. The posterior distributions of all the model parameters are estimated simultaneously in Markov Chain Monte Carlo framework -- consequently, the posterior distributions and uncertainties of the blended precipitation estimates are attained. This approach provides a robust treatment of the uncertainties and the hierarchy enables incorporating all relevant covariates. While the BHM provides a robust confidence interval of the bias correction factor for CHIRP, it is reasonable to assume this bias is not uniform over the domain. Therefore a fourth method is proposed, wherein a GLM is fit to the time series at each point (Yobs(s,t) = beta(s) Ysat(s,t) + epsilon(s,t)), and the satellite coefficients are interpolated using a Co-kriging model similar to the first two methods. This provides a unique bias correction factor for every time frame (pentad, month), and therefore may be applied in near-real-time. To obtain the error field (i.e. residuals epsilon(s,t)) for a specific time frame t, the residuals corresponding to the appropriate time frame are extracted from the GLMs and interpolated, again using a physiographic Co-kriging model. These blended products provide more accurate and representative initial conditions for hydrologic modeling applications that are crucial for modeling and mitigating impacts from climate hazards such as floods and landslides which are of major concern in this region.