An Adaptation of the Barnes Filter Applied to the Objective Analysis of Radar Data

Abstract

Spatial objective analysis is routinely performed in several applications that utilize radar data. Because of their relative simplicity and computational efficiency, one-pass distance-dependent weighted-average (DDWA) schemes that utilize either the Cressman or the Barnes filter are often used in these applications. The DDWA schemes that have traditionally been used do not, however, directly account for two fundamental characteristics of radar data. These are 1) the spacing of radar data depends on direction and 2) radar data density systematically decreases with increasing range. A DDWA scheme based on an adaptation of the Barnes filter is proposed. This scheme, termed the adaptive Barnes (A-B) scheme, explicitly takes into account radar data properties 1 and 2 above. Both theoretical and experimental investigations indicate that two attributes of the A-B scheme, direction-splitting and automatic adaptation to data density, may facilitate the preservation of the maximum amount of meaningful information possible within the confines of one-pass DDWA schemes. It is shown that in the idealized situation of infinite, continuous data and for an analysis in rectangular-Cartesian coordinates, a direction-splitting scheme does not induce phase shifts if the weight function is even in each direction. Moreover, for radar data that are infinite, collected at regular radial, azimuthal, and elevational increments, and collocated with analysis points, the direction-splitting design of the A-B filter removes gradients in the analysis weights. This is a beneficial attribute when considering the treatment of gradient information of rectangular Cartesian data by an analysis system because then postanalysis gradients equal the analysis of gradients. The direction-splitting design of the A-B filter is unable, however, to circumvent the impact of the varying physical distances between adjacent measurements that are inherent to the spherical coordinate system of ground-based weather radars. Because of this, even with the direction-splitting design of the A-B filter postanalysis gradients do not equal the analysis of gradients. Ringing in the response function of a one-dimensional Barnes filter is illustrated. The negative impact of data windows on the main lobe of the response function is found to decrease rapidly as the window is widened relative to the weight function. Unless an analysis point is near a data boundary, in which case both ringing and phase shifting will adversely affect the analysis, window effects are unlikely to be significant in applications of the A-B filter to radar data. The A-B filter has potential drawbacks, the most significant of which is misinterpretations owing to the use of the A-B filter without comprehension of its direction- and range-dependent response function. Despite its drawbacks, the A-B filter has the potential to improve analyses owing to the aforementioned attributes and thus to aid research efforts in areas such as multiple-Doppler wind analyses, pseudo-dual-Doppler analyses, and retrieval studies.