Horizontal shape matching (HSM) is a variational technique used to obtain an analysis that merges the gradient structure from one data source (e.g., satellite) with a background field. This technique is modeled after the variational methods that fall into two general categories: strong constraint and weak constraint. HSM, which is essentially a specialized filter function, falls in the weak constraint category. Here a technique is demonstrated that effectively tunes the filter to the spatial resolution inherent in the data sources rather than on the absolute error of the data. The HSM equation is developed for satellite gradient insertion including a cloud treatment. The filtering properties of the HSM equation are explored using Fourier analysis, and an approximate numerical solution is shown to be viable for operational use. Applying this technique to a dataset spanning more than a year proves the analysis has a positive effect through the statistical significance of a large sample of comparisons with radiosonde observation data.
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