This paper is the first of three dealing with the three-dimensional wind field analysis from dual-Doppler radar data. Here we deal with the first step of the analysis which consists in interpolating and filtering the raw radial velocity fields within each coplane (or common plane simultaneously scanned by the two radars). To carry out such interpolation and filtering, a new method is proposed based on the principles of numerical variational analysis described by Sasaki (1970): the “filtered” representation of the observed field should be both “close” to the data points (in a least-squares sense) and verify some imperative of mathematical regularity. Any method for interpolating and smoothing data is inherently a filtering process. The proposed variational method enables this filtering to be controlled. The presented method is developed for any function of two variables but could be extended to the case of three or more variables.
Numerical simulations substantiate the theoretically predicted filtering characteristics and show an improvement on other filtering schemes. It is found, compared to the classical filtering using the Cressman weighting function, that the variational method brings a substantial improvement of the gain curve (in the sense of a steeper cut-off), when the “regularity” of the second-order derivatives is imposed. It is worth noting that this improvement is achieved without increasing the computing time. It is also emphasized that an elaborate numerical differentiation scheme should be used to estimate the divergence, otherwise the gain curve for this parameter may be different from that for the Cartesian coplane velocities (which may induce distortion in the final three-dimensional wind field).