Evolutionary Algorithm-Based Error Parameterization Methods for Data Assimilation

Yulong Bai Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, and College of Physics and Electrical Engineering, Northwest Normal University, Lanzhou, China

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Xin Li Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, China

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Abstract

The methods of parameterizing model errors have a substantial effect on the accuracy of ensemble data assimilation. After a review of the current error-handling methods, a new blending error parameterization method was designed to combine the advantages of multiplicative inflation and additive inflation. Motivated by evolutionary algorithm concepts that have been developed in the control engineering field for years, the authors propose a new data assimilation method coupled with crossover principles of genetic algorithms based on ensemble transform Kalman filters (ETKFs). The numerical experiments were developed based on the classic nonlinear model (i.e., the Lorenz model). Convex crossover, affine crossover, direction-based crossover, and blending crossover data assimilation systems were consequently designed. When focusing on convex crossover and affine crossover data assimilation problems, the error adjustment factors were investigated with respect to four aspects, which were the initial conditions of the Lorenz model, the number of ensembles, observation covariance, and the observation interval. A new data assimilation system, coupled with genetic algorithms, is proposed to solve the difficult problem of the error adjustment factor search, which is usually performed using trial-and-error methods. The results show that all of the methods can adaptively obtain the best error factors within the constraints of the fitness function.

Corresponding author address: Yulong Bai, College of Physics and Electrical Engineering, Northwest Normal University, Lanzhou 730070, China. E-mail: yulongbai@gmail.com

Abstract

The methods of parameterizing model errors have a substantial effect on the accuracy of ensemble data assimilation. After a review of the current error-handling methods, a new blending error parameterization method was designed to combine the advantages of multiplicative inflation and additive inflation. Motivated by evolutionary algorithm concepts that have been developed in the control engineering field for years, the authors propose a new data assimilation method coupled with crossover principles of genetic algorithms based on ensemble transform Kalman filters (ETKFs). The numerical experiments were developed based on the classic nonlinear model (i.e., the Lorenz model). Convex crossover, affine crossover, direction-based crossover, and blending crossover data assimilation systems were consequently designed. When focusing on convex crossover and affine crossover data assimilation problems, the error adjustment factors were investigated with respect to four aspects, which were the initial conditions of the Lorenz model, the number of ensembles, observation covariance, and the observation interval. A new data assimilation system, coupled with genetic algorithms, is proposed to solve the difficult problem of the error adjustment factor search, which is usually performed using trial-and-error methods. The results show that all of the methods can adaptively obtain the best error factors within the constraints of the fitness function.

Corresponding author address: Yulong Bai, College of Physics and Electrical Engineering, Northwest Normal University, Lanzhou 730070, China. E-mail: yulongbai@gmail.com
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