基于实码遗传算法的湖泊水质模型参数优化

参数的合理取值决定着模型的模拟效果,因此确定研究区域的模型结构后,需要对模型的参数进行优化.湖泊水质模型(Simulation by means of an Analytical Lake Model,SALMO)利用常微分方程描述湖泊的营养物质循环和食物链动态,考虑了多个生态过程,包含104个参数.由于参数较多,不适宜采用传统参数优化方法进行优化.利用太湖梅梁湾2005年数据,采用实码遗传算法优化了SALMO模型中相对敏感的参数,运用优化后的模型,模拟了梅梁湾2006年的水质.对比分析参数优化前后模型的效果表明遗传算法能高效地对SALMO进行参数优化,优化后的模拟精度得到了显著提高,能更好地模拟梅梁湾的水质变化.

Optimization of lake model salmo based on real-coded genetic algorithm

Model calibration is required in order to make model predictions reliable for a certain area. But model calibration is always difficult, especially when the model contains a large number of parameters. The Lake model SALMO (Simulation by means of an Analytical Lake Model) is based on complex ordinary differential equations which represent the nutrient cycles of PO₄-P, NO₃-N and the food webs consisting of diatoms, green algae, blue-green algae and cladocerans. As the model includes numerous ecological processes, it has 104 constant parameters, making it unsuitable for calibration with conventional methods, such as trial and error, HSY (Hornberger-Spear-Young) and GLUE (Generalized Likelihood Uncertainty Estimation) algorithms. Genetic algorithm (GA) is a biologically motivated global optimization technique based on natural selection, reproduction and mutation. Compared to conventional methods, GA is more efficient for global optimum searches and it has a faster convergence speed. There are two different kinds of GA encoding: binary encoding and real encoding. The binary encoding introduces discretization errors when it encodes a real number, and encoding and decoding operations take more computation time. While real encoded GA works directly on the real number, it is more suitable for dealing with continuous search spaces with large dimensions. Therefor this paper choses a real coded GA to calibrate the sensitive parameters of SALMO. Since the sensitive parameters of SALMO are related to phosphate, zooplankton and three algae (diatoms, green algae, blue-green algae), the objective of the optimization is to minimize the relative errors of these state variables. The implementation of GA begins with determining the following appropriate values of its operators: the population size is 200, the max generation is 400, the crossover probability is 0.8, the mutation probability is 0.05. Two years of water quality data were collected from the Meiliang bay of Taihu lake. Data of 2005 was used for calibration while data of 2006 was used for validation. According to the validation results, the average relative errors of PO₄-P, zooplankton, total algae decrease from 53.9%, 174.6%, 65.4% in the initial unoptimized model to 25.2%, 48.1%, 44.4% in the optimized model. Errors of less than 50% are typically considered as satisfactory results in ecological models. This suggests that the real-coded GA is efficient in the calibration of SALMO. After calibration, SALMO predicted the dynamics of water quality variables well, but the maximum simulated value of blue-green algae is still considerably smaller than the observed value. This may be because SALMO does not consider the benthic recruitment and the migration of blue-green algae driven by wind and hydrodynamic forces. Moreover, the real-coded GA just used one year's data to calibrate SALMO, which may also be a cause of the deviation of the simulated results from the observed values.