An adaptive spatial model for precipitation data from multiple satellites over large regions

Satellite measurements have of late become an important source of information for climate features such as precipitation due to their near-global coverage. In this article, we look at a precipitation dataset during a 3-hour window over tropical South America that has information from two satellites. We develop a flexible hierarchical model to combine instantaneous rainrate measurements from those satellites while accounting for their potential heterogeneity. The research of Bani K. Mallick and Avishek Chakraborty was supported by National Science Foundation grant DMS 0914951. Research of Marc G. Genton was partially supported by NSF grants DMS-1007504 and DMS-1100492. The research in this article was also partially supported by Award No. KUSC1-016-04 made by King Abdullah University of Science and Technology (KAUST). A. Chakraborty (B) · H. Sang · B.K. Mallick Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA e-mail: [email protected] H. Sang e-mail: [email protected] B.K. Mallick e-mail: [email protected] S. De SAS Research & Development (India) Pvt. Ltd, Pune 411013, India e-mail: [email protected] K.P. Bowman Department of Atmospheric Sciences, Texas A&M University, College Station, TX 77843-3150, USA e-mail: [email protected] M.G. Genton CEMSE Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia e-mail: [email protected] Conceptually, we envision an underlying precipitation surface that influences the observed rain as well as absence of it. The surface is specified using a mean function centered at a set of knot locations, to capture the local patterns in the rainrate, combined with a residual Gaussian process to account for global correlation across sites. To improve over the commonly used pre-fixed knot choices, an efficient reversible jump scheme is used to allow the number of such knots as well as the order and support of associated polynomial terms to be chosen adaptively. To facilitate computation over a large region, a reduced rank approximation for the parent Gaussian process is employed.