Mean-preserving interpolation with splines for solar radiation modeling

Abstract

Interpolation is a fundamental process in solar resource assessment that glues consecutive components of the modeling chain. Most interpolation techniques assume that the interpolating function must go through the interpolation points. However, this assumption does not fit with averaged datasets or variables that must be conserved across interpolation. Here I present a mean-preserving splines method for interpolating one-dimensional data that conserves the interpolated field and is appropriate for averaged datasets. It uses second-order polynomial splines to minimize the fluctuations of the interpolated field, restricts the interpolation results to user-provided limits to prevent unphysical values, deals with periodic boundary conditions in the interpolated field, and can work with non-uniform averaging grids. The validity and performance of the method are illustrated against regular second- and third-order splines using relevant case examples in the solar resource assessment realm.