Implementation And Testing Of A Hybrid Back And Forth Nudging Ensemble Kalman Filter (HBFNFEnKF) Data Assimilation Method

Ensemble Kalman Filter is a widely used data assimilation method. With the fast developing of data assimilation technology, the most popular way of improving EnKF is combining it with other assimilation method in order to take the advantage of both and create a Hybrid method. Among the Hybrid methods, Hybrid Nudging EnKF(HNEnKF) is designed to reduce the discountinity and unbalance caused by EnKF.Nudging is a traditional assimilation method which can adjust model background state at each integration step in order to achieve a continuous assimilation. The core idea of HNEnKF is to replace empirical weighting operator of Nudging with Kalman gain matrix generated by EnKF, which is more suitable for fast-develop meso-scale weather system. Research has shown that compared with EnKF, HNEnKF is much more smooth and can retain the balance of model state variables, meanwhile, however, the convergence speed of HNEnKF is slow and may result in an insufficiency of convergence. On the other hand, the application and discussion of HNEnKF in complex numerical weather model is far from enough. To enhance the assimilation effect of HNEnKF while retaining the continuity and banlance, a Hybrid Back and Forth Nudging EnKF (HBFNEnKF) method has been designed based on EnKF and Back and Forth Nudging (BFN). The performance of HBFNEnKF, HNEnKF and EnSRF are discussed using shallow water model and WRF model using observation simulation system experiment and drew the following conclusions:(1) Experiments in shallow water model show that HBFNEnKF method retains the continuity and smoothness of HNEnKF, and has the highest convergence speed.Through a single variable observation experiment, the advantage of HBFNEnKF was clear; that is, HBFNEnKF can maintain the balance between different model variables. A scale investigation on the increment field showed that, compared with EnSRF, HBFNEnKF avoids a number of spurious increments at medium and smaller scales.(2) Single point experiment in WRF model showed that HBHNEnKF has stronger assimilation effect than HNEnKF, and both HNEnKF and HBFNEnKF can achieve a more reasonable adjustment on non-observed state variable than EnSRF.(3) Experiment use sounding observation in WRF model showed that compared with EnSRF and HNEnKF, HBFNEnKF can produce a better assimilation result in model dynamic state, but a weaker result on thermo-dynamic relate variables. However, HBFNEnKF can produce a better simulation on precipitation during nature run. When model error are considered, HBFNEnKF can produce better assimilation result than HNEnKF. Meanwhile, HNEnKF and HBFNEnKF can reduce meaningless noises and retain noises which are meaningful for weather system.(4) The effect of Kalman gain matrix’s quality on HNEnKF and HBFNEnKF is significant. Under perfect model condition, Two-way coupled hybrid can help ensemble assimilation produce a better correlation between state variables in turn give a better Kalman gain matrix and a better hybrid assimilation result, on the other hand, when model error are considered, two-way coupled hybrid can bring model error to ensemble members and result in a higer RMSE.