Can an ensemble transform Kalman filter predict the reduction in forecast‐error variance produced by targeted observations?

The ensemble transform Kalman filter (ET KF) is currently used at the National Centers for Environmental Prediction (NCEP) to identify deployments of aircraft‐borne dropwindsondes that are likely to significantly improve 1‐3 day forecasts of winter storms over the continental United States. It is unique among existing targeted observing strategies in that it attempts to predict the reduction in forecast‐error variance associated with each deployment of targeted observations. To achieve this, the ET KF predicts the variance of ‘signals’ for each feasible deployment, where a signal represents the difference between two forecasts, initialized with and without the targeted observations. For linear forecast‐error evolution, the signal variance is equal to the reduction in forecast‐error variance, provided that observation‐ and background‐error covariances are accurately specified and identical to those produced by the operational data‐assimilation scheme. However, background‐error covariances assumed by the ET KF are both imperfect and different from the imperfect error covariances used in NCEP's 3D‐Var data‐assimilation scheme, and hence their signal statistics are likely to differ. In spite of these differences, a linear relationship of positive gradient is found to exist between the ET KF signal variance and the sample variance of NCEP signal realizations at both the targeted analysis and forecast verification times, for 30 forecasts from the 2000 Winter Storm Reconnaissance Program. This relationship enables the NCEP signal variance to be predicted by the ET KF, via a statistical rescaling that corrects the ET KF's current over‐prediction of signal variance magnitude. A monotonically increasing relationship is also found to exist between the NCEP signal variance and the reduction in NCEP forecast‐error variance. The ET KF signal variance predictions can be used to make quantitative estimates of the forecast‐error‐variance reducing effect of targeted observations. Potential benefits include (i) making rapid decisions on when and where to deploy targeted observations, (ii) warning operational data quality‐control schemes against the rejection of observational data if the signal variance is large, and (iii) estimating the likelihood of economic benefit due to any future deployment of observations.