Treatment of parametric model error for MM5 with an ensemble Kalman filter

The effectiveness of the ensemble Kalman filter (EnKF) for a modeling environment of operational complexity is investigated. The model chosen for this purpose is the Penn State/NCAR mesoscale model MM5 with a 36-km horizontal resolution and ~2000 km domain size covering the southern United States and northern Gulf of Mexico. The model has 43 layers in the terrain-following vertical coordinate and is configured to employ the MRF PBL, Grell cumulus, and simple ice microphysics parameterization schemes. The ensemble size for all experiments is chosen as 40 and a 41st member is generated as the truth with the same ensemble statistics. The state initialization is carried out by a climatological perturbation technique. 72-hour experiments are conducted with a 12-hour assimilation interval, using simulated sounding and surface observations of horizontal wind and temperature.

State estimation with perfect-model statistics reveals that the EnKF performs exceptionally well for most variables. The mean error reduction for root-mean difference total energy (RM_DTE), temperature (T), and water vapor mixing ratio (q) over the 6 assimilation times is computed as 75%, 41%, and 25%, respectively. Moreover, for the same three variables, the EnKF achieves an overall error reduction of 87%, 62%, and 44%, respectively, compared to the final (72-hour) pure-forecast error. For T and q, the respective rms error and standard deviation stay relatively close and do not diverge throughout the assimilation experiment indicating that filter divergence is not an issue for the state-only estimation experiment with the EnKF. The EnKF is also found to be more responsive to larger-scale information contained by the observations. Preliminary parameter estimation experiments also produce very encouraging results. Only single-parameter experiments are performed focusing on a constant inserted into the code as the multiplier of the vertical eddy mixing coefficient. Two experiments with initial parameter error of 0.2 and 0.65 are conducted for this purpose, both of which result in the successful estimation of the parameter. In both experiments, the mean estimated parameter value consistently converges to the true value of 1.0 by the end of the 72-hour experiment while exhibiting a satisfactory level of variability. This indicates that a sufficient flow-dependent correlation signal exists between the estimated parameter and the observed variables, leading to the satisfactory performance of the EnKF in retrieving the true parameter value within a 72-hour assimilation experiment. Meanwhile, improvement in the reduction of error remains very limited for the initial error magnitude of 0.2. We conjecture that this is mainly due to the initial-condition error dominating the uncertainty space at this level of initial parametric error. The improvement becomes more pronounced when the initial parameter error is increased to 0.65, when the overall error reduction, compared to the worst case, is 7-8% for RM_DTE and the rms errors of T and q.