Flow-adaptive moderation of spurious ensemble correlations and its use in ensemble-based data assimilation

Many ensemble Kalman filter (EnKF) data assimilation (DA) schemes reduce the effect of spurious ensemble correlations caused by small ensemble size by multiplying the correlations by mode ration functions. Moderation functions envelop true error correlation functions. Ideal moderation functions would adapt to variations in the movement and width of true error correlation functions. Here, we describe a new method in which flow-dependent moderation functions are built from powers of smoothed ensemble correlations. The approach imparts to the moderation function movement and width information retained by the smoothed ensemble correlations. Spurious smoothed ensemble correlations are attenuated by raising them to a power. Simple systems were used to compare DA performance using such Smoothed ENsemble COrrelations Raised to a Power (SENCORP) moderation functions against DA performance using optimally tuned but non-adaptive moderation functions. The simple systems considered feature propagating error correlation functions and error correlation functions with variable width. It was found that when significant spatio-temporal variations in the true error correlation function are present, SENCORP moderation functions are superior to non-adaptive moderation functions. In the absence of spatio-temporal variations, the DA performance of SENCORP moderation functions was found to be statistically indistinguishable from the DA performance of non-adaptive moderation functions. An example using a primitive equation global model is given to illustrate how the method could be used to improve the performance of a local ensemble Kalman filter/smoother, particularly when larger observation volumes are used, to better account for error propagation and/or observations that represent vertically averaged variables. Published in 2007 by John Wiley & Sons, Ltd.