基于Bayes理论的田间层状土壤水分运动参数识别及不确定性分析
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摘要
土壤水分运动参数是非饱和带水分及污染物运移研究的核心参数,根据点尺度土壤样本的室内稳态试验得到的水分运动参数往往不能准确反映天然条件下田间尺度土壤水分运动特征。本文基于为时2年的田间土壤含水量观测数据(2013年为率定期,2014年为验证期),通过土壤转换函数得到了VGM(van Genuchten-Mualem)模型水力参数的先验分布,建立了反演层状土壤持水和导水特征的贝叶斯模型,采用自适应差分演化(DREAMZS)的采样方法,结合Hydrus_1d模型,对田间尺度土壤水分含量预测模型进行优化及不确定性分析,获得了水分特征参数的后验分布,分析了最优参数组的模拟效果及模型预测的95%的置信区间。结果表明,基于DREAMZS采样的Bayes方法可以实现田间尺度层状土壤水分特征参数的率定及土壤水分动态的模拟预测。率定结果显示饱和导水率Ks最不敏感,饱和含水量θs最为敏感,可识别性较高,室内试验反演得到θs可用于田间土壤水分运动的模拟。随着土壤含水量模拟深度的增加,PUCI(单位平均相对宽度所包含的实测点数据比例)值越大,模型预测的性能越高。模拟结果的不确定性主要由模型结构所引起,所以对模型结构的修改完善是未来提高模型预测的关键。
Soil water movement parameters are the core parameters of water and pollutant migration in un-saturated zone. However, water movement parameters obtained from the indoor steady-state test of the soilsamples at the point scale can't accurately reflect the soil water movement characteristics at the field scaleunder the natural occurring boundary conditions. A Bayesian inference for inversion of soil water retentionand hydraulic parameters, based approach DREAMZS(Differential Evolution Adaptive Metropolis algorithm),was combined with Hydrus_1 d to implement model optimization and uncertainty analysis on the data of soilmoisture content in field observation(2013 for calibration and 2014 for validation). In order to get the pri-or information of the parameters in the van Genuchten-Mualem(VGM) model of the soil hydraulic func-tions, the ROSETTA pedotransfer functions was used. The posterior distribution of the water characteristicparameters was obtained, and modelling performance using the best estimated parameter set and the 95%prediction confidence interval of the model prediction were analyzed. The results show that the Bayes meth-od based on DREAMZSsampling can be used to identify the soil water characteristic parameters and predictthe soil water dynamics at the field scale. The parameter identification results show that the saturated con-ductivity Ksis the least sensitive,and saturated water content θsis the most sensitive and easily identified.The parameter θsestimated from the laboratory experiment can be used for the modeling at the field scale.With the increase of soil depth, the higher the PUCI(Percentage of observations bracketed by the UnitConfidence Interval) value,the higher the performance of the model(reliability and accuracy). The predic-tion uncertainty is mainly caused by model structural uncertainty, and this implies that the effort to im-prove model prediction credibility in future should focus on diagnosis of model structure.
Soil water movement parameters are the core parameters of water and pollutant migration in un-saturated zone. However, water movement parameters obtained from the indoor steady-state test of the soilsamples at the point scale can't accurately reflect the soil water movement characteristics at the field scaleunder the natural occurring boundary conditions. A Bayesian inference for inversion of soil water retentionand hydraulic parameters, based approach DREAMZS(Differential Evolution Adaptive Metropolis algorithm),was combined with Hydrus_1 d to implement model optimization and uncertainty analysis on the data of soilmoisture content in field observation(2013 for calibration and 2014 for validation). In order to get the pri-or information of the parameters in the van Genuchten-Mualem(VGM) model of the soil hydraulic func-tions, the ROSETTA pedotransfer functions was used. The posterior distribution of the water characteristicparameters was obtained, and modelling performance using the best estimated parameter set and the 95%prediction confidence interval of the model prediction were analyzed. The results show that the Bayes meth-od based on DREAMZSsampling can be used to identify the soil water characteristic parameters and predictthe soil water dynamics at the field scale. The parameter identification results show that the saturated con-ductivity Ksis the least sensitive,and saturated water content θsis the most sensitive and easily identified.The parameter θsestimated from the laboratory experiment can be used for the modeling at the field scale.With the increase of soil depth, the higher the PUCI(Percentage of observations bracketed by the UnitConfidence Interval) value,the higher the performance of the model(reliability and accuracy). The predic-tion uncertainty is mainly caused by model structural uncertainty, and this implies that the effort to im-prove model prediction credibility in future should focus on diagnosis of model structure.
引文
[1]W?HLING T,VRUGT J A.Combining multiobjective optimization and Bayesian model averaging to calibrate forecast ensembles of soil hydraulic models[J].Water Resources Research,2008,44(12):181-198.
[2]查元源,周发超,杨金忠.一种由土壤剖面含水率估算土壤水力参数的方法[J].水利学报,2011,42(8):883-891.
[3]李春友,任理,李保国.利用优化方法求算Van Genuchten方程参数[J].水科学进展,2001,12(4):473-478.
[4]CARRERA J,NEUMAN S P.Estimation of aquifer parameters under transient and steady state conditions:1.maximum likelihood method incorporating prior information[J].Water Resources Research,1986,22(2):199-210.
[5]RUSSO D,BRESLER E,SHANI U,et al.Analysis of infiltration events in relation to determining soil hydraulic properties by inverse problems methodology[J].Water Resources Research,1991,27(6):1361-1373.
[6]KOOL J B,PARKER J C.Analysis of the inverse problem for transient unsaturated flow[J].Water Resources Research,1988,24:817-830.
[7]PARKER J C,KOOL J B,van GENUCHTEN M T.Determining soil hydraulic properties from one-step outflow experiments by parameter estimation.Part 2:experimental studies[J].Soil Science Society of America Journal,1985,49:1354-1359.
[8]朱嵩,毛根海,刘国华,等.改进的MCMC方法及其应用[J].水利学报,2009,40(8):1019-1023.
[9]?IM?NEK J,?EJNA M,SAITO H,et al.The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water,Heat,and Multiple Solutes in Variably-Saturated Media:version 4.17[EB/OL].[2017-09-25].https://www.pc-progress.com/Downloads/Pgm_hydrus1D/HYDRUS1D-4.17.pdf.
[10]廖凯华.大沽河流域土壤水资源评价及农业节水灌溉模式研究[D].青岛:青岛大学,2009.
[11]W?HLING T,VRUGT J A.Multiresponse multilayer vadose zone model calibration using Markov chain Monte Carlo simulation and field water retention data[J].Water Resources Research,2011,47(4):W04510,doi:10.1029/2010WR009265.
[12]KAVETSKI D,KUCZERA G,FRANKS S W.Bayesian analysis of input uncertainty in hydrological modeling:1.Theory[J].Water Resources Research,2006,42(3):W03407,doi:10.1029/2005WR004368
[13]SCHARNAGL B,VRUGT J A,VEREECKEN H,et al.Information content of incubation experiments for inverse estimation of pools in the Rothamsted carbon model:a Bayesian perspective[J].Biogeosciences Discussions,2009,6(5):1736-1751.
[14]SCHARNAGL B,VRUGT J A,VEREECKEN H,et al.Inverse modelling of in situ soil water dynamics:investigating the effect of different prior distributions of the soil hydraulic parameters[J].Hydrology&Earth System Sciences,2011,15(10):3043-3059.
[15]LALOY E,VRUGT J A.High-dimensional posterior exploration of hydrologic models using multiple-try DREAM(ZS)and high performance computing[J].Water Resources Research,2012,48(1):182-205.
[16]GELMAN A,RUBIN D B.Inference from iterative simulation using multiple sequences[J].Statistical Science,1992,7(4):457-472.
[17]MOREIRA P H S,van GENUCHTEN M T,ORLANDE H R B,et al.Bayesian estimation of the hydraulic and solute transport properties of a small-scale unsaturated soil column[J].Journal of Hydrology&Hydromechanics,2016,64(1):30-44.
[18]RUSSO D,BOUTON M.Statistical analysis of spatial variability in unsaturated flow parameters[J].Water Resources Research,1992,28(7):1911-1925.
[19]杨金忠.多孔介质中水分及溶质运移的随机理论[M].北京:科学出版社,2000.
[20]山东省环境水文地质总站.山东省青岛市大沽河地下水库勘察报告[R].1987.
[21]JIANG S,JOMAA S,BüTTNER O,et al.Multi-site identification of a distributed hydrological nitrogen model using Bayesian uncertainty analysis[J].Journal of Hydrology,2015,529(20):940-950.
[22]KUMAR S,SEKHAR M,REDDY D V,et al.Estimation of soil hydraulic properties and their uncertainty:comparison between laboratory and field experiment[J].Hydrological Processes,2010,24(23):3426-3435.
[23]王金生,杨志峰,陈家军,等.包气带土壤水分滞留特征研究[J].水利学报,2000(2):1-7.
[24]BECK M B.Water quality modeling:A review of the analysis of uncertainty[J].Water Resources Research,1987,23(8):1393-1442.
[2]查元源,周发超,杨金忠.一种由土壤剖面含水率估算土壤水力参数的方法[J].水利学报,2011,42(8):883-891.
[3]李春友,任理,李保国.利用优化方法求算Van Genuchten方程参数[J].水科学进展,2001,12(4):473-478.
[4]CARRERA J,NEUMAN S P.Estimation of aquifer parameters under transient and steady state conditions:1.maximum likelihood method incorporating prior information[J].Water Resources Research,1986,22(2):199-210.
[5]RUSSO D,BRESLER E,SHANI U,et al.Analysis of infiltration events in relation to determining soil hydraulic properties by inverse problems methodology[J].Water Resources Research,1991,27(6):1361-1373.
[6]KOOL J B,PARKER J C.Analysis of the inverse problem for transient unsaturated flow[J].Water Resources Research,1988,24:817-830.
[7]PARKER J C,KOOL J B,van GENUCHTEN M T.Determining soil hydraulic properties from one-step outflow experiments by parameter estimation.Part 2:experimental studies[J].Soil Science Society of America Journal,1985,49:1354-1359.
[8]朱嵩,毛根海,刘国华,等.改进的MCMC方法及其应用[J].水利学报,2009,40(8):1019-1023.
[9]?IM?NEK J,?EJNA M,SAITO H,et al.The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water,Heat,and Multiple Solutes in Variably-Saturated Media:version 4.17[EB/OL].[2017-09-25].https://www.pc-progress.com/Downloads/Pgm_hydrus1D/HYDRUS1D-4.17.pdf.
[10]廖凯华.大沽河流域土壤水资源评价及农业节水灌溉模式研究[D].青岛:青岛大学,2009.
[11]W?HLING T,VRUGT J A.Multiresponse multilayer vadose zone model calibration using Markov chain Monte Carlo simulation and field water retention data[J].Water Resources Research,2011,47(4):W04510,doi:10.1029/2010WR009265.
[12]KAVETSKI D,KUCZERA G,FRANKS S W.Bayesian analysis of input uncertainty in hydrological modeling:1.Theory[J].Water Resources Research,2006,42(3):W03407,doi:10.1029/2005WR004368
[13]SCHARNAGL B,VRUGT J A,VEREECKEN H,et al.Information content of incubation experiments for inverse estimation of pools in the Rothamsted carbon model:a Bayesian perspective[J].Biogeosciences Discussions,2009,6(5):1736-1751.
[14]SCHARNAGL B,VRUGT J A,VEREECKEN H,et al.Inverse modelling of in situ soil water dynamics:investigating the effect of different prior distributions of the soil hydraulic parameters[J].Hydrology&Earth System Sciences,2011,15(10):3043-3059.
[15]LALOY E,VRUGT J A.High-dimensional posterior exploration of hydrologic models using multiple-try DREAM(ZS)and high performance computing[J].Water Resources Research,2012,48(1):182-205.
[16]GELMAN A,RUBIN D B.Inference from iterative simulation using multiple sequences[J].Statistical Science,1992,7(4):457-472.
[17]MOREIRA P H S,van GENUCHTEN M T,ORLANDE H R B,et al.Bayesian estimation of the hydraulic and solute transport properties of a small-scale unsaturated soil column[J].Journal of Hydrology&Hydromechanics,2016,64(1):30-44.
[18]RUSSO D,BOUTON M.Statistical analysis of spatial variability in unsaturated flow parameters[J].Water Resources Research,1992,28(7):1911-1925.
[19]杨金忠.多孔介质中水分及溶质运移的随机理论[M].北京:科学出版社,2000.
[20]山东省环境水文地质总站.山东省青岛市大沽河地下水库勘察报告[R].1987.
[21]JIANG S,JOMAA S,BüTTNER O,et al.Multi-site identification of a distributed hydrological nitrogen model using Bayesian uncertainty analysis[J].Journal of Hydrology,2015,529(20):940-950.
[22]KUMAR S,SEKHAR M,REDDY D V,et al.Estimation of soil hydraulic properties and their uncertainty:comparison between laboratory and field experiment[J].Hydrological Processes,2010,24(23):3426-3435.
[23]王金生,杨志峰,陈家军,等.包气带土壤水分滞留特征研究[J].水利学报,2000(2):1-7.
[24]BECK M B.Water quality modeling:A review of the analysis of uncertainty[J].Water Resources Research,1987,23(8):1393-1442.