Computing Derivatives from Equally Spaced Data

Abstract

The evaluation of derivatives from equally spaced numerical data can lead to very inexact results. This problem arises, for example, in the measurement of 1 min rainfall rates from U. S. Weather Service raingage records for use in estimating rain attenuation distributions. In the method of computation of derivatives described here, the data are detrended and transformed into the frequency domain by a finite Fourier series. In the frequency domain, most of the noise can be identified and removed by suitable filtering and the derivative computed from the inverse transform of the filtered spectrum. The accuracy of the resulting derivative is expressed as a signal-to-noise ratio. Computation of rain rate as the derivative of the trace on a weighing raingage chart is included as a practical application of this method.