A Fast Mean-Preserving Spline for Interpolating Interval Data

Abstract

Interpolation of interval data where the mean is preserved, e.g., estimating smoothed, pseudodaily meteorological variables based on monthly means, is a common problem in the geosciences. Existing methods for mean-preserving interpolation are computationally intensive and/or do not readily accommodate bounded interpolation, where the interpolated data cannot exceed a threshold value. Here we present a mean-preserving, continuous, easily implementable, and computationally efficient method for interpolating one-dimensional interval data. Our new algorithm provides a straightforward solution to the interpolation problem by utilizing Hermite cubic splines and midinterval control points to interpolate interval data into smaller partitions. We further include adjustment schemes to restrict the interpolated result to user-specified minimum and maximum bounds. Our method is fast, portable, and broadly applicable to a range of geoscientific data, including interpolating unbounded time series such as mean temperature, and bounded data including mean wind speed or cloud-cover fraction.