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A scale-dependent localization (SDL) method was formulated and implemented in the Gridpoint Statistical Interpolation (GSI)-based four-dimensional ensemble-variational (4DEnVar) system for NCEP FV3-based Global Forecast System (GFS). SDL applies different localization to different scales of ensemble covariances, while performing a single-step simultaneous assimilation of all available observations. Two SDL variants with (SDL-Cross) and without (SDL-NoCross) considering cross-wave-band covariances were examined. The performance of two- and three-wave-band SDL experiments (W2 and W3, respectively) was evaluated through 1-month cycled data assimilation experiments. SDL improves global forecasts to 5 days over scale-invariant localization including the operationally tuned level-dependent scale-invariant localization (W1-Ope). The W3 SDL-Cross experiment shows more accurate tropical storm–track forecasts at shorter lead times than W1-Ope. Compared to the W2 SDL experiments, the W3 SDL counterparts applying tighter horizontal localization at medium-scale wave band generally show improved global forecasts below 100 hPa, but degraded global forecasts above 50 hPa. While the outperformance of the W3 SDL-NoCross experiment versus the W2 SDL-NoCross experiment below 100 hPa lasts for 5 days, that of the W3 SDL-Cross experiment versus the W2 SDL-Cross experiment lasts for 3 days. Due to local spatial averaging of ensemble covariances that may alleviate sampling error, the SDL-NoCross experiments show slightly better forecasts than the SDL-Cross experiments at shorter lead times. However, the SDL-Cross experiments outperform the SDL-NoCross experiments at longer lead times, likely from retention of more heterogeneity of ensemble covariances and resultant analyses with improved balance. Relative performance of tropical storm–track forecasts in the W2 and W3 SDL experiments are generally consistent with that of global forecasts.

A Simultaneous Multiscale Data Assimilation Using Scale-Dependent Localization in GSI-Based Hybrid 4DEnVar for NCEP FV3-Based GFS