Research On Adaptive Covariance Inflation Method For Ensemble Filtering Data Assimilation

In the ensemble filtering data assimilation process,the model and sampling errors from imperfect physical parameterization,discrete schemes,and finite ensemble will result in smaller background ensemble spread and underestimated error covariances.Because of the constraint of computational resources,it is difficult to use a large ensemble sample size to reduce sampling errors in high-dimensional ocean or atmospheric models.Here,based on Bayesian theory,we explore a new adaptive covariance inflation method to solve the problem of poor assimilation effect when fewer ensemble members are available.To increase the statistical presentation of a finite background ensemble,the prior probability of inflation obeys the inverse chi-square distribution,and the likelihood function obeys the t distribution,which are used to obtain prior,posterior or mixed covariance inflation schemes.The Lorenz63 model is used to explain the setting of the inflation variance,demonstrate the limitations of the manually tuned inflation scheme,and comparing it with adaptive inflation in terms of effect and computational speed.The results show that the new adaptive inflation method is substantially more efficient than the manually tuned scheme.Different types of model errors were added to each of the two coupled atmosphereocean models,the 5-variable coupled climate model(5VCCM)and the meridional overturned circulation box model(MOCBM),by using different time difference schemes or biased parameters.The performance of the new method is tested by comparing the assimilation quality with other inflation methods using different ensemble sizes within both the perfect and imperfect model frameworks.The results show that in the imperfect model,for the unobserved variables in the 5VCCM,the root mean square error of the new method is reduced by about 31% and 64%,respectively,compared to the other two existing methods at an ensemble sample size of 5.For the MOCBM,the reductions are about 25% and 8.5%,respectively.It is proved that the new inflation method performs better than the existing methods in some cases,with more stability and fewer assimilation errors.In addition,prediction experiments have shown the impact of different adaptive inflation methods on climate prediction.The experimental results show that the new inflation method has the longest effective prediction time.Due to better computing performance and relaxed demand for computational resources,the new method has more potential applications in more complex models for prediction initialization and reanalysis.In a word,the new inflation scheme performs well for a small ensemble size,and it may be more suitable for largescale models.