The use of ensemble based error statistics for data assimilation and targeted observations

A sub-optimal Kalman Filter called the ensemble transform Kalman Filter (ET KF) is introduced. One difference between the ET KF and other ensemble Kalman Filters is that it uses an ensemble transformation and a normalization to obtain the prediction error covariance matrix associated with a particular deployment of observational resources rapidly.; The performance of ensemble based data assimilation schemes is tested with respect to three different types of forecast model: perfect agency model, resolution error agency model and parameterization error agency model. In all cases, it is found that hybrid ensemble Kalman Filters out perform the data assimilation technique used operationally the National Centers for Environmental Prediction (NCEP), 3D-Var. Further, generating the ensemble using a method similar to the targeting technique currently used by NCEP is competitive with other more computationally expensive hybrid ensemble Kalman Filters.; The ability of the Ensemble Transform Kalman Filter to quantitatively predict the impact of observations on an estimate of the state of a two-dimensional turbulent flow is also explored. Having taken and assimilated observations in the routine observational network, the ET KF is used to determine the two sites which will likely produce the greatest reduction in forecast error variance. The ET KF is then used to estimate the impact of observations on the forecast, by evaluating the signal covariance matrix at the forecast verification time. This estimate is compared to the actual change in the forecast of the flow resulting from taking the two supplemental pseudo-observations, and assimilating them using either 3D-Var or the hybrid. Values of signal realizations are binned to produce a sample variance, and compared to the ET KF signal variance. After applying a statistical correction to the ET KF estimate of signal variance, the corrected estimate is compared to the actual reduction in forecast error variance. The correlations of ET KF signal variance to sample variance and reduction in sample forecast error variance are found to be strong. To quantify the gaussianity of the signal realization distributions, the kurtosis is found for each bin. Using the hybrid to assimilate supplemental observations results in thinner tails in the distribution than when 3D-Var is used, suggesting that there are fewer extreme points, and thus less variable variance estimates. (Abstract shortened by UMI.)...