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浙江大学学报（农业与生命科学版）
浙江大学学报(农业与生命科学版)  2016, Vol. 42 Issue (5): 598-    DOI: 10.3785/j.issn.1008-9209.2016.11.091
资源与环境科学     
优化法与贝叶斯估计法在非饱和水力参数反演中的比较
柯凤乔,满俊,曾令藻*,吴劳生
浙江大学环境与资源学院土水资源与环境研究所,杭州310058
Comparative study on inversion of the unsaturated hydraulic parameters using optimization and Bayesian estimation methods
KE Fengqiao, MAN Jun, ZENG Lingzao*, WU Laosheng
Institute of Soil Water Resources and Environment, College of Environmental & Resource Sciences, Zhejiang University, Hangzhou 310058, China
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摘要： 非饱和土壤水分运动模型在农业生产和环境保护等领域中具有重要的指导意义。非饱和土壤水力参数的准确获取是利用模型进行可靠预测的前提。传统的参数反演研究大多基于优化方法,只能获取一组最优参数,不能量化其中的不确定性。最新发展的一种基于贝叶斯参数估计理论的马尔科夫链蒙特卡罗算法(Markov Chain Monte Carlo, MCMC)—DREAM(ZS),可以有效进行参数反演,且准确量化不确定性。我们在获取水头观测值的基础上,利用MCMC和Levenberg-Marquardt (LM)非线性优化算法分别对非饱和土壤水力参数进行反演,通过数值模拟与一维沙柱入渗实验比较了2种方法对于分层异质的水力参数估计与水头预测的准确性。结果表明：1)LM优化方法使用广泛,求解速度较快,但受参数初始值影响较大,预测结果与观测值存在一定的偏差,同时由于只能给出一个单一的反演结果,无法量化结果的不确定性。2)与基于优化的反演方法相比,MCMC反演方法不仅能够更好地得出参数的单一估计值,同时预测结果与观测值也具有更好的一致性;更重要的是可以给出未知参数的后验分布,从而准确量化非饱和水力参数的不确定性,避免了基于单一参数反演结果进行预测的风险。但是相对于LM优化方法,MCMC计算量大大增加。
Abstract: The model of water movement in variably saturated flow is of guiding significance in agricultural production and environmental protection. The accurate acquisition of soil hydraulic parameters is the precondition of reliable prediction. Based on searching for one set of parameters that best fit the measurements, traditional optimization methods can not quantify the uncertainty of parameters. Now, a newly developed Markov Chain Monte Carlo (MCMC) algorithm, i.e., DREAM(ZS) was adopted for efficient estimation and accurate uncertainty quantification of soil hydraulic parameters. With the measurements obtained from a one dimensional sand column infiltration experiment, the soil hydraulic parameters were estimated by two approaches, i.e., the MCMC algorithm and the Levenberg-Marquardt (LM) nonlinear optimization algorithm. Then the two approaches were compared in terms of parameter estimation and state prediction. It can be concluded that: 　　1) The LM algorithm can provide a single set of model parameter estimations with only a few model runs. However, this method is sensitive to the initial guess of parameters, and the obtained predictions occasionally deviate from the measurements. 2) The MCMC algorithm can provide state predictions which better fit measurements. More importantly, it accurately quantifies the uncertainty of parameters, which can avoid the potential risk introduced by making predictions via a single estimated value.
出版日期: 2016-09-20
CLC:  S 121　  
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柯凤乔
满俊
曾令藻
吴劳生

引用本文:

柯凤乔,满俊,曾令藻,吴劳生. 优化法与贝叶斯估计法在非饱和水力参数反演中的比较[J]. 浙江大学学报(农业与生命科学版), 2016, 42(5): 598-.

KE Fengqiao, MAN Jun, ZENG Lingzao, WU Laosheng. Comparative study on inversion of the unsaturated hydraulic parameters using optimization and Bayesian estimation methods. Journal of Zhejiang University (Agriculture and Life Sciences), 2016, 42(5): 598-.

链接本文:

http://www.zjujournals.com/agr/CN/10.3785/j.issn.1008-9209.2016.11.091    或    http://www.zjujournals.com/agr/CN/Y2016/V42/I5/598

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