Bayesian model averaging(BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization(EM) and the Markov Chain Monte Carlo(MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the addi-tional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA(referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algo-rithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is al-most equivalent to that for EM.
贝叶斯模型平均(Bayesian model averaging,BMA)是最近提出的一种用于多模式集合预报的统计方法.进行贝叶斯模型平均需要准确估算模型集合中每个竞争模型的权重与方差,经常采用的方法是期望最大化(Expectation-Maximization,EM)方法与马尔可夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)方法,两种方法各有优劣.本文首先对BMA的(对数)似然函数进行改进使之无需BMA权重之和为1的显式约束,并利用一种有限记忆的拟牛顿优化算法(LBFGS-B)对其进行极大化,由此提出了一种求解贝叶斯模型平均的新方法(BMA-BFGS).采用三个陆面模式进行的土壤湿度多模式数值模拟试验表明:在计算精度方面,BMA-BFGS的精度与MCMC方法几乎一致,优于EM算法;在计算耗时性方面,BMA-BFGS的计算耗时与EM算法相当,远小于MCMC方法.
The purpose of this paper is to provide a robust and flexible implementation of a proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method(PODEn4DVar) through Rlocalization.With R-localization,the implementation of the local PODEn4DVar analysis can be coded for parallelization with enhanced assimilation precision.The feasibility and effectiveness of the PODEn4DVar local implementation with R-localization are demonstrated in a two-dimensional shallow-water equation model with simulated observations(OSSEs) in comparison with the original version of the PODEn4DVar with B-localization and that without localization.The performance of the PODEn4DVar with localization shows a significant improvement over the scheme with no localization,particularly under the imperfect model scenario.Moreover,the R-localization scheme is capable of outperforming the Blocalization case to a certain extent.Further,the assimilation experiments also demonstrate that PODEn4DVar with R-localization is most efficient due to its easy parallel implementation.
In this study,the Chinese carbon cyle dataassimilation system Tan-Tracker is developed based on the atmospheric chemical transport model(GEOS-Chem)platform.Tan-Tracker is a dual-pass data-assimilation system in which both CO2concentrations and CO2fluxes are simultaneously assimilated from atmospheric observations.It has several advantages,including its advanced data-assimilation method,its highly efficient computing performance,and its simultaneous assimilation of CO2concentrations and CO2fluxes.Preliminary observing system simulation experiments demonstrate its robust performance with high assimilation precision,making full use of observations.The Tan-Tracker system can only assimilate in situ observations for the moment.In the future,we hope to extend Tan-Tracker with functions for using satellite measurements,which will form the quasioperational Chinese carbon cycle data-assimilation system.
