Atmospheric Data Assimilation with an Ensemble Kalman Filter: Results with Real Observations

Abstract

An ensemble Kalman filter (EnKF) has been implemented for atmospheric data assimilation. It assimilates observations from a fairly complete observational network with a forecast model that includes a standard operational set of physical parameterizations. To obtain reasonable results with a limited number of ensemble members, severe horizontal and vertical covariance localizations have been used. It is observed that the error growth in the data assimilation cycle is mainly due to model error. An isotropic parameterization, similar to the forecast-error parameterization in variational algorithms, is used to represent model error. After some adjustment, it is possible to obtain innovation statistics that agree with the ensemble-based estimate of the innovation amplitudes for winds and temperature. Currently, no model error is added for the humidity variable, and, consequently, the ensemble spread for humidity is too small. After about 5 days of cycling, fairly stable global filter statistics are obtained with no sign of filter divergence. The quality of the ensemble mean background field, as verified using radiosonde observations, is similar to that obtained using a 3D variational procedure. In part, this is likely due to the form chosen for the parameterized model error. Nevertheless, the degree of similarity is surprising given that the background-error statistics used by the two procedures are rather different, with generally larger background errors being used by the variational scheme. A set of 5-day integrations has been started from the ensemble of initial conditions provided by the EnKF. For the middle and lower troposphere, the growth rates of the perturbations are somewhat smaller than the growth rate of the actual ensemble mean error. For the upper levels, the perturbation patterns decay for about 3 days as a consequence of diffusive model dynamics. These decaying perturbations tend to severely underestimate the actual error that grows rapidly near the model top.

State and parameter estimation

“…It is an attractive alternative to the more mature 4DVAR method. Very encouraging results have been obtained by a number of researchers for large-scale models (e.g., Houtekamer et al 2005;Whitaker et al 2004). Tests with perfect prediction models with simulated Doppler radar data at the convective scale with EnKF have also produced very encouraging success in recent studies.…”

“…Previous studies using the EnKF method have achieved encouraging success for applications at large scale through convective scale (e.g., Houtekamer et al 2005;Whitaker et al 2004;Snyder and Zhang 2003;Tong and Xue 2005b, TX05 hereafter;Xue et al 2006, hereafter XTD06).…”

“…On the other hand, the deficiency in the NWP models, which is commonly referred to as model error, has received less attention until recently, because the characteristics of model error are little known and its statistical properties are poorly understood (Dee 1995;Houtekamer et al 2005). Model error can arise from many sources such as insufficient resolution in time and/or space, misrepresentation of the physical and sub-grid scale processes, and the use of non-physical model boundaries and/or external forcing.…”

“…It has been observed in certain EnKF studies that model error can dominate the error growth in data assimilation cycles and must be parameterized to prevent the filter from diverging from its truth state (Houtekamer et al 2005). One way to account for model error within the EnKF system is to add the so-called additive error to the model state by assuming an error model (Lawson and Hansen 2005).…”

“…One way to account for model error within the EnKF system is to add the so-called additive error to the model state by assuming an error model (Lawson and Hansen 2005). Houtekamer et al (2005) used additive errors by assuming model error covariance that has the same functional form as the forecast error covariance used in a 3DVAR system. Their experiments using a global model showed that the added model errors increased the ensemble spread to the level of ensemble mean error.…”