Integration of Rainfall via Multiquadric Surfaces over Polygons

Abstract

Hydrologic modeling requires accurate estimation of daily areal rainfall. In many parts of the world, this task is complicated by sparse rain‐gage networks and unreliable or missing data. This paper presents a simple, mathematically elegant, and economical algorithm that exploits the linear nature of multiquadric hyperboloid surface‐fitting equations to derive rain‐gage weights for calculating areal rainfall over polygonal approximants of catchments. In addition, gages are classified according to their statistical characteristics using the covariance biplot. This graphical method identifies the records of those gages that have similar statistical properties, those gages that may be unreliable, and highlights possible outliers in the rainfall record. The concept of spatial multicollinearity (a form of overfitting, or redundancy, defined by the geometry of the gages and the catchment boundary) is introduced and is used to help select a suitable set of gages as candidates for the spatial integration. The approach is illustrated on the Slangspruit catchment in Natal, South Africa.