A Fast Mean-Preserving Spline for Interpolating Interval Data

Abstract

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. Significance Statement Interpolation is often utilized to mathematically estimate smaller time step values when such data are not readily available, for example, the estimation of daily temperature when only monthly temperature values are available. We propose a novel interpolation method based on linking segments of flexible continuous curves that ensures the average of interpolated result will be the same as the original value, which is important for minimizing interpolation errors. We find that our new method takes significantly less computational time when compared with other existing methods, while retaining a similar degree of precision. Furthermore, we outline an additional procedure for users to specify the minimum and maximum bounds of interpolated results if applicable.