A Transparent Method for the Analysis and Quality Evaluation of Irregularly Distributed and Noisy Observational Data

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 integral 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 a twodimensional domain. The basic advantages of the method are on the one 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 weighting functions is required. Furthermore the spatial anisotropy of meteorological fields may be treated 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 especially well suited to model-independent quality assessment procedures and mesoscale objective analyses. It is presently used within the framework of the Mesoscale Alpine Programme.