非线性气候动力学模型的参数估计方法研究

Nonlinear parameter estimation has been widely applied in the field of meteorology. It is one of the key technologies to build numerical weather prediction models and climate prediction models, as well as statistical prediction models. So, it has a very important scientific significance and application value to study the method of nonlinear parameter estimation. To solve this problem, the linearization techniques have often been used in the traditional parameter estimation methods, which will inevitably result in the loss of parameter estimation precision. Meanwhile, the estimated results of the intelligent approaches mainly depend on the selection of a variety of factors in these algorithms. In view of the deficiencies of the existing nonlinear parameter estimation methods, this project intends to carry out an exploratory study focusing on three key scientific problems in nonlinear parameter estimation. Firstly, on the basis of the vector difference and skewness index difference, a new quantitative approach for evaluating the performance of parameter estimation method will be presented. Meanwhile, in order to improve the convergence rate of the new parameter estimation method, a group search mode with a damping constraint mechanism will be investigated and tested. Secondly, the project will present a novel scheme for the nonlinear parameter estimation with model errors, and investigate quantitative relationships between the samples, used in parameter estimation tests, and the parameter estimation precision, as well as the convergence rate of the new method. Finally, the project will put forward a new theory and methods of nonlinear parameter estimation, which will improve the performance of the evaluation method in parameter estimation and present an optimization parameters search mode. A rapid and accurate identification for unknown parameters in nonlinear dynamical systems can be achieved by implementing this project.

非线性参数估计在气象领域中有着广泛的应用，它既是建立数值天气预报模式和气候动力模式的关键技术之一，又是气象统计预报的关键。因而，研究非线性参数估计方法具有非常重要的科学意义和应用价值。传统的非线性参数估计主要采取线性化方法进行求解，必然会造成参数估计精度的损失，而智能化方法的估计结果对算法中各种因子的选择具有很强的依赖性。针对现有非线性参数估计方法存在的不足，本项目拟围绕非线性参数估计中的三个关键科学问题展开探索性研究，首先，基于向量差和偏态指数差研究定量评估参数估计效果的新方法。同时，发展一种具有阻尼约束机制的群搜索方式来提高新算法的收敛速度，进而探讨存在模型误差时的非线性参数估计方案，并尝试揭示样本量与算法的估计精度及收敛速度之间的定量关系。项目将提出一套非线性参数估计的新理论和新方法，改进参数估计结果的定量评价方法，优化参数的搜索方式，实现快速准确地识别非线性动力系统中的未知参数。

非线性参数估计在气象领域中有着广泛的应用，它既是建立数值天气预报模式和气候动力模式的关键技术之一，又是气象统计预报的关键。因而，研究非线性参数估计方法具有非常重要的科学意义和应用价值。传统的非线性参数估计主要采取线性化方法进行求解，必然会造成参数估计精度的损失，而智能化方法的估计结果对算法中各种因子的选择具有很强的依赖性。参数估计算法的优劣主要取决于三个关键点：一是对参数估计效果的定量评价方法和技术（常被称之为适应值函数）研究；二是参数的搜索方式和方法研究；三是存在模型误差时的非线性参数估计。本项目围绕非线性参数估计中的这三个关键科学问题展开探索性研究，提出了评估参数估计效果的新适应值函数，改进了参数的搜索方式，揭示了样本量与参数估计精度及算法收敛速度之间的定量关系，最终提出一套非线性参数识别新方法。同时，将项目成果应用于短期气候预测模型的参数估计中，建立了基于演化算法的短期气候预测系统，并已经在国家级和省级气候预测业务中推广应用。