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A three-dimensional variational (3DVAR) scheme is developed for retrieving three-dimensional mois- ture in the atmosphere from slant-path measurements of a hypothetical ground-based global positioning system (GPS) observation network. It is assumed that the observed data are in the form of slant-path water vapor (SWV), which is the integrated water vapor along the slant path between the ground receiver and the GPS satellite. The inclusion of a background in the analysis overcomes the under-determinedness problem. An explicit Gaussian-type spatial filter is used to model the background error covariances that can be anisotropic. As a unique aspect of this study, an anisotropic spatial filter based on flow-dependent back- ground error structures is implemented and tested and the filter coefficients are derived from either true background error field or from the increment of an intermediate analysis that is obtained using an isotropic filter. In the latter case, an iterative procedure is involved. A set of experiments is conducted to test the new scheme with hypothetical GPS observations for a dryline case that occurred during the 2002 International H2O Project (IHOP_2002) field experiment. Results illustrate that this system is robust and can properly recover three-dimensional mesoscale moisture structures from GPS SWV data and surface moisture observations. The analysis captures major features in water vapor associated with the dryline even when an isotropic spatial filter is used. The analysis is further improved significantly by the use of flow-dependent background error covariances modeled by an aniso- tropic spatial filter. Sensitivity tests show that surface moisture observations are important for the analysis near ground, and more so when flow-dependent background error covariances are not used. Vertical filtering is necessary for obtaining accurate analysis increments. The retrieved moisture field remains reasonably accurate when the surface moisture observations and GPS SWV data contain errors of typical magnitudes. The positive impact of flow-dependent background error covariances increases when the density of ground-based GPS receiver stations decreases.

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Retrieval of Moisture from Slant-Path Water Vapor Observations of a Hypothetical GPS Network Using a Three-Dimensional Variational Scheme with Anisotropic Background Error