基于遗传算法的四维变分资料同化技术的研究

A Research of Four-Dimensional Variational Data Assimilation Based on Genetic Algorithm

将遗传算法应用于四维变分资料同化问题,提供一种新的较为有效的数值预报初始场优化方法,给出了相应的理论依据和详细算法,并结合变分问题本身的特点,设计合理的遗传编码、遗传操作和遗传参数。同时,以二维的浅水方程模式为例建立基于遗传算法的变分同化模型,并从多方面与伴随模式变分同化方案进行分析比较。数值试验结果表明,基于遗传算法的变分同化方案取得了比较满意的同化效果。

Four-dimensional （4D） variational data assimilation （VDA） has been recognized as one of the effective methods to improve numerical weather predication （NWP） initial field. But, the method still has some shortcomings, for example, 1） the optimization method used in VDA should satisfy continual presumption, while the discontinuity of a forecast model, such as the parameterization physical process, will make the presupposition available no more; 2） the cost function always presents multimodal distribution owning to its non-linear dynamic constraint, whereas the present descent algorithms of VDA only aim at the local optimization; 3） furthermore, the adjoint VDA requires higher computing resource in operation. Therefore, it is necessary to seek for a new algorithm with weaker demand to mathematical properties of cost function and higher skill in searching out the global optimum or proximity, together with less computer time to match with the operational demand. In this context, the genetic algorithm （GA） is applied to 4DVDA. The raitional genetic coding, manipulation and parameters, together with related theoretical basis and detailed procedure are designed based upon the properties of the variational technique. The algorithm will be described as follows in detail： 1） real encoding of the parameters; 2） population initialization with model solutions trajectory and the reciprocal of cost function as fitness equivalent; 3） selection of the intermediate population with roulette wheel method; 4） adoption of self-adaptive and mandatory crossover probability to produce better individuals towards greater fitness; 5） application of the quasi-elitist strategy to directly reproduce parent individuals of higher fitness to next generation for better individual reserved; 6） introduction of the steepest descent method, in order to exert its superiority of calculation velocity and precision, to make the mutation manipulation along with the descent direction; 7） selection of genetic control parameters also playing an important role in GA, whose rationality depends on the solution convergence and quality after running times without number. Thus, it can be seen that in the process of assuring the population diversity, all of the operations make the population evolve towards greater fitness and accelerate the convergence velocity of GA global optimization. As an example, the output of a GA-based VDA model constructed under the constraint of 2-dimensional shallow water equations has been compared with that of a scheme with an adjoint VDA model. The results suggest that the convergence precision of GA-based scheme is in common with that of the adjoint equivalent to great degree. When the assimilation window is 6 hours, the convergence velocity of GA-based method is nearly in agreement with that of the adjoint scheme. If the window increases to 12 hours, the former is superior to the latter. Consequently, the GA-based VDA scheme shows a better performance than the adjoint counterpart with the assimilation time window increasing. The most important is that the GA-based VDA model improves greatly mathematical properties of cost function, only utilizing adaptability information independent of higher-order demands, such as the gradient of cost function. In conclusion, the new method suggests a better performance than the adjoint counterpart based on the present experimental case. The GA-based VDA scheme is of superiority to some degree, which enriches the VDA contents and provides more extensive application prospect for future work.