Investigating the Application of Generalized Gaspari-Cohn Correlation Function in Vertical Localization

Assimilation of column-integrated observations such as precipitable water vapor (PWV) remains challenging when vertical moisture profile constraints (e.g., radiosondes) are unavailable. Ensemble data assimilation systems typically employ Gaspari–Cohn (GC) localization (e.g., in DART) to limit the spatial influence of observations and reduce spurious correlations arising from finite ensemble size. However, GC assumes homogeneous and isotropic correlations and does not represent physically driven vertical inhomogeneity, such as transient moisture structures associated with convection or moisture transport. Consequently, vertically displaced but dynamically sensitive layers may be underrepresented during PWV assimilation. The generalized Gaspari–Cohn (GenGC) localization function introduced by Gilpin et al. (2023) relaxes these assumptions by allowing localization parameters to vary spatially, enabling inhomogeneous and anisotropic correlation structures. This flexibility is particularly relevant for PWV assimilation, where the vertical distribution of moisture sensitivity can vary substantially with atmospheric state.

Sensitivity of water vapor mixing ratio (qvapor) to PWV was analyzed for Tucson, Flagstaff, Albuquerque, and Santa Teresa at 12 UTC during July–September 2021. These sensitivities were used to estimate the appropriate vertical influence of PWV assimilation and to construct a vertically varying GenGC localization. The performance of GenGC was evaluated relative to a standard GC localization with a fixed vertical radius of 3.5 km. These four locations in the Southwest US are chosen since they are impacted by the North American monsoon. To date, forecasting the monsoon precipitation is still challenging even with convective-permitting models coupled with data assimilation (Risanto et al. 2026 – in review).

Global Positioning System PWV (GPS-PWV) observations from Tucson and Flagstaff for three summer days in 2021 were assimilated into a convective-permitting (1.8 km) WRF ensemble with 40 members. HRRRv4 provided initial and boundary conditions. PWV was assimilated at 12 UTC using both GC and GenGC vertical localization, and radiosonde observations are used for independent verification.

Initial results indicate that qvapor exhibits strongest sensitivity to PWV from the surface up to approximately 6 km MSL, motivating a GenGC localization that extends vertical influence on this level. PWV analyses produced using GenGC were generally closer to observations than those using GC, reflecting the inclusion of moisture adjustments above 3.5 km MSL. In some cases, GenGC also improved near-surface qvapor relative to GC; however, larger positive qvapor biases were found above ~5 km MSL. Further investigation is required to assess the robustness of these results.

Future work will expand the number of cases and implement GenGC directly within the DART framework to evaluate its broader applicability for assimilating PWV and related datasets.