Interpolating Mean Rainfall Using Thin Plate Smoothing Splines

Abstract Thin plate smoothing splines provide accurate, operationally straightforward and computationally efficient solutions to the problem of the spatial interpolation of annual mean rainfall for a standard period from point data which contains many short period rainfall means. The analyses depend on developing a statistical model of the spatial variation of the observed rainfall means, considered as noisy estimates of standard period means. The error structure of this model has two components which allow separately for strong spatially correlated departures of observed short term means from standard period means and for uncorrelated deficiencies in the representation of standard period mean rainfall by a smooth function of position and elevation. Thin plate splines, with the degree of smoothing determining by minimising generalised cross validation, can estimate this smooth function in two ways. First, the spatially correlated error structure of the data can be accommodated directly by estimating the c...

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