Abstract
Abstract. We present a method to control unbalanced fast dynamics in an ensemble Kalman filter by introducing a weak constraint on the imbalance in a spatially sparse observational network. We show that the balance constraint produces significantly more balanced analyses than ensemble Kalman filters without balance constraints and than filters implementing incremental analysis updates (IAU). Furthermore, our filter with the weak constraint on imbalance produces good rms error statistics which outperform those of ensemble Kalman filters without balance constraints for the fast fields.
Highlights
In data assimilation one seeks to find the best estimation of the state of a dynamical system given a forecast model with possible model error and noisy observations at discrete observation intervals (Kalnay, 2002)
P−1 + h T R −w1 h where we introduced the analysis error covariance P for a standard Kalman filter without any weak constraint which only combines the forecast with direct observations
Besides the variance limiting Kalman filter VLKF-B where we impose a climatic constraint on the imbalance B z, we employ a variance limiting Kalman filter VLKF-hwhere we impose a climatic constraint on the unobserved fast variables {hj }
Summary
In data assimilation one seeks to find the best estimation of the state of a dynamical system given a forecast model with possible model error and noisy observations at discrete observation intervals (Kalnay, 2002) Unbalanced states can be generated by the discontinuous nature of the data assimilation procedure, leading to unphysical readjustment processes of analyses by the subsequent nonlinear forecast model (Bloom et al, 1996; Ourmières et al, 2006). We will incorporate prior information on the amount of imbalance to augment given observational information for the slow variables This implementation of a balance constraint within the data assimilation step eliminates unwanted spurious imbalance, leading to physical analyses states and to an improved analysis skill as measured by the rms error of the fast variables.
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