摘录自《流域水文模型参数不确定性量化理论方法与应用》第5章。

概述

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参数识别研究
基于优化思想的参数识别思路
基于不确定分析的参数识别思路
前提是可识别性 水文模型模型参数不可识别性严重
基于贝叶斯理论 使用先验分布即未知参数的分布信息 如RSA GLUE

根据贝叶斯理论，参数的先验分布 p ( θ ) p(\theta) p(θ)、样本信息和后验分布具有如下关系：
p ( θ ∣ y ) = p ( y ∣ θ ) p ( θ ) p ( y ) p(\theta|y) = \frac{p(y|\theta)p(\theta)}{p(y)} p(θ∣y)=p(y)p(y∣θ)p(θ)​

水文模型常用不确定性分析方法

GLUE方法

该方法是基于Hornberger和Spear提出的RSA方法发展起来的，其结合蒙特卡罗随机取样和贝叶斯理论，对不同参数组合的模型进行不确定性分析，是目前应用较为广泛的方法。

GLUE方法的一个很重要的观点是：导致模型模拟结果的好坏不是模型的单个参数，而是模型参数的组合。

主要步骤为：

  1. 似然判据的定义。
  2. 确定参数的初始范围和先验分布函数。
  3. 加权参数组的似然判据值。
  4. 当有新的数据时，利用贝叶斯函数，以递推方式更新加权后的似然判据值。

GLUE方法的缺陷：

  1. 需要确定每个参数的取值范围，根据参数的物理意义或个人的主观经验来定。
  2. 需要确定获取参数样本空间的方法，在大多数GLUE方法的应用中都是采用Monte Carlo方法计算，在参数取值范围内随机抽样，是均匀分布；
  3. 方法要确定似然函数（即似然度的计算方法）以及似然函数的临界值，判别“可接受”和“不可接受”的结果。

贝叶斯方法

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综合分析各种不确定性来源的方法
基于贝叶斯理论框架的水文预报系统 BFS
贝叶斯总误差分析方法 BATEA
贝叶斯不确定性估计量 IBUNE
单个不确定性来源的分析方法
贝叶斯递归估计方法
MCMC
贝叶斯模型平均方法 BMA
AM算法
并行自适应的Metropolis PAM 算法

贝叶斯方法用于不确定性分析方法的参数识别的思想已经得到广泛认可，但由于巨大的计算量，只适应参数个数较少的情况，当参数个数超过3~5个时，即使采用高性能计算机进行模拟，也面临着计算复杂性的问题。

其他方法

美国环保部网站提供了70多个模型评价方法，总结如下：

基于代理模型和MCMC的分析方法

Maokov Chain Monte Carlo ：MCMC

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MCMC采样算法
Metropolis-Hastings算法
Gibbs算法
自适应的Metropolis算法

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