Strategies to Overcome Filter Divergence in the DRP-4-DVar Approach

This paper discusses an important issue related to filter divergence in the dimension-reduced projection,four-dimensional variational data assimilation(DRP-4-DVar) approach.Idealized experiments with the Lorenz-96 model over a period of 200 days showed that the amplitudes of the root mean square errors(RMSEs) reached the same levels as those of the state variables after approximately 100 days because of the accumulation of sampling errors following the cycle of assimilation.Strategies to reduce sampling errors are critical to ensure the quality of ensemble-based assimilation.Numerical experiments showed that localization and reducing observational errors can alleviate,but cannot completely overcome,the filter divergence in the DRP-4-DVar approach,while the method of perturbing observations and the inflation technique can efficiently eliminate the filter divergence problem.

Comparison between gradient based UCODE2005 and the ensemble Kalman Filter for transient groundwater flow inverse modeling

Gradient based UCODE_2005 and data assimilation based on the Ensemble Kalman Filter(EnKF) are two different inverse methods. A synthetic two-dimensional flow case with four no-flow boundaries is used to compare the UCODE_2005 with the Ensemble Kalman Filter(EnKF) for their efficiency to inversely calculate and calibrate a hydraulic conductivity field based on hydraulic head data. A zonal, random heterogeneous conductivity field is calibrated by assimilating the time series of heads observed in monitoring wells. The study results indicate that the two inverse methods, UCODE_2005 and EnKF, could be used to calibrate the hydraulic conductivity field to a certain degree. More available observations and information about the conductivity field, more accurate inverse results will be obtained for the UCODE_2005. On the other hand, for a realistic zonal heterogeneous hydraulic conductivity field, EnKF can only efficiently determine the hydraulic conductivity field at the first several assimilated time steps. The results obtained by the UCODE_2005 look better than those by the EnKF. This is possibly due to the fact that the UCODE_2005 uses observed head data at every time step, while EnKF can only use observed heads at first several steps due to the filter divergence problem.