A transparent method for the analysis and quality evaluation of irregulary distributed and noisy observational data

Abstract

Observational errors may have a serious impact on objective analyses. Before conducting an objective analysis. that is, interpolating irregularly spaced observations to a uniform grid, the data should be checked thoroughly for errors. For this procedure a piecewise functional fitting approach is proposed, which is based on a variational algorithm. As for thin-plate splines, an intergral of squares of second temporal and/or spatial derivatives is minimized. The second derivatives are obtained from overlapping finite elements using a polynomial approach. In a slightly different mode, the same approach may also be used to interpolate the observational data to a regular grid. The method is formulated for and applied to scalar and vector quantities in a one- and two-dimentional domain. The basic advantages of the method are on a the hand the fact that no first guess or (prognostic) model field is necessary and on the other hand that no a priori knowledge about structure or explicitly. One of the most valuable features of the method is its simplicity. For a single station it is possible to recalculate by hand each step, which may make the procedure transparent. The comparatively inexpensive computational effort renders it especiallly well suited to model-independent quality assesment procedures and mesoscale objective analyses. It is presently used within the framework of the Mesoscale Alpine Programme.