A Quantitative Comparison between Traditional and Line Integral Methods of Derivative Estimation

Abstract

For diagnostic purposes, the ?traditional? approach to estimating derivatives employs objective analysis to provide a gridded field from the original observations, which are typically not uniformly distributed in space. However, there exist other methods involving derivative estimation via line integral (?triangle?) techniques that do not involve a prior mapping of the field onto a uniform grid. It has been suggested that these give improved results. Empirical testing of the differences between wind field derivative estimation using two different schemes is done with prototypical examples of the techniques. Test results verify that the triangle method indeed provides substantial improvements over the traditional scheme. The magnitude of the improvement is shown to depend on the degree of irregularity of the data distribution, as expected. Although the particular prototype methods chosen have the property that the triangle method truncates the amplitude of the input field slightly more than the traditional scheme, the pattern of the field is significantly better using the triangle technique than with the traditional method. An unexpected result is that the improvement by the triangle method over the traditional approach does not diminish as the wavelength of the input field increases. It is shown that this is a consequence of overfitting of the field to the station observations, causing local discontinuities in the field that produce errors in the gradient calculations, even in situations where the distribution of data is uniform. Overall, the test results make it abundantly clear that the traditional method is generally inferior to derivative estimates via the line integral methodology.