Results from an ideal simulation with known background-error covariances show that the GGF localization function is superior to the optimal Gaspari and Cohn (GC) localization function. Using the output of an ensemble simulation from the NCEP Global Forecast System (GFS) and the NOAA operational EnKF, the localization function for each channel of the AMSU-A radiances is computed by GGF. The GGF localization functions vary from channels, and are generally proportional to the absolute value of the mean sample correlations. When a prominent negative correlation occurs, a local maximum localization value is obtained, resulting in a localization function with multiple local maxima. These results indicate the complexity and large computational cost to tune the localization for the radiances. By implementing the GGF localization function in a subsequent experiment, verifications in both observation and model spaces suggest that GGF localization generally produces smaller error than GC localization, and these advantages persist through 120h forecast lead time.