Multiresolution Interpolation and Detiding of the ADCP Data

Abstract

To account for the uneven sampling of current measurements collected by acoustic Doppler current profilers (ADCPs), a robust, three-dimensional interpolation scheme based on the multiresolution representation of the regional mean and tidal current fields is proposed. Instead of reconstructing the tidal field by getting bin-averaged time series that rely on heavy sampling or invoking radial basis function expansions, such as using the biharmonic splines with subjectively selected knots, the resolving capability of the proposed scheme relies fundamentally on the scale hierarchy of the resolvable local information constrained by the data. It is demonstrated that the proposed scheme flexibly incorporates the merits of the two conventional techniques. It enforces the resolution of model information while accommodating the local sampling density. Since it is based on a knots network defined by regular grids, attempts at experimentally and subjectively constructing the proper number and locations of controlling nodes are avoided. Constructing multiresolution representation of the current fields in terms of the three-dimensional wavelet basis is implemented by the computationally effective discrete wavelet transform of coefficients of the interpolation equations. Applications of the proposed multiresolution scheme on artificial as well as field datasets of the ADCP measurements demonstrate that it is a promising approach.