非均质性包气带水力参数反演方法研究
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摘要
包气带是地球表面以下，潜水面以上的地质介质，是地下水与大气水、地表水联系的必经通道，也是圈层间相互作用最为敏感、对人类生存的生态环境影响最为巨大的地带。对包气带进行水分和水质的模拟及预测具有重要意义。
包气带水分及溶质运移模型需要准确的描述包气带的水力参数。室内实验测量水力参数需要花费大量的人力和物力，当研究对象为深层包气带时，获取用于室内实验测量水力参数的非扰动土样会非常困难。因此，通过间接的手段，如建立土壤粒径成分与土壤水力参数关系的土壤传递函数或者通过反演方法来预测土壤水力参数逐渐得到了广泛应用。
Rosetta利用2134个土壤样品，将人工神经网络（Artificial Neural Network）与Bootstrap抽样方法相结合，根据每个土壤样品输入参数由少到多，建立了精度逐渐提高的用于预测土壤水力参数的模型，目前已被广泛用于HYDRUS等软件中，但原Rosetta低估了土壤水力参数在压力水头较大时的含水量值。本论文在重新拟合Rosetta原始含水量-压力水头数据，获得带有权重的土壤水力参数的基础上，通过调整权重，训练带有权重的人工神经网络模型，获得了精度更高，即均方根误差（RMSE）和反应系统误差的平均误差（ME）更小的模型，结果显示带权重的Rosetta H2-H5四个模型中RMSE由0.076至0.044降低到0.072至0.038；ME由0.022至0.013降低到0.0024至0.0061，系统误差得到显著降低。改进的Rosetta模型，改善了原Rosetta模型低估土壤水力参数在压力水头较大时的含水量值的问题。
针对难以获得包气带水分运移数值模拟中所有网格结点上的初始含水量的问题，本论文建立了中子仪测数与土壤粒径成分等因子之间的多元线性回归方程，从而利用已知的含水量与中子仪测数的关系式，计算在自然状态下包气带土壤稳定排水结束时的含水量，取得了良好的效果。
反演方法（inverse method）是根据观测得到的状态信息，如水位或含水量等，反求模型系统的参数，如饱和渗透系数等信息。传统的反演方法通常将模拟区域划分为多个子区域，每个子区域看作均质区域并给定一个等效的水力参数，通过目标函数值的最小化来优化每个子区域上的等效水力参数。为了进一步优化目标函数，常常需要增加子区域，进而增加模拟区域的非均质性，因而反演的参数和运算时间也相应增加。本论文提出一种新的保留多孔介质非均质性的反演方法，将通用的土壤传递函数，如Rosetta，应用于土壤质地的地质统计模型中，通过与数值反演方法相结合，将模拟区分为若干非均质的子区域，每个子区域进行线性和非线性变换，如使用logistic函数变换，模拟区域在整个空间网格上的水力参数都是不同的，因此这种方法可以在保留多孔介质的非均质性，以及水力参数之间连续性的同时，减少反演模型优化的参数，使目标函数进一步优化。以美国亚利桑那州Maricopa场地为例，在地质统计学分析的基础上，利用残余变异函数分析场地土壤质地数据，建立了包气带非均质、空间三维结构、非稳定数值模型。通过矩分析、基于似然函数的模型评价准则如AIC、AICc和BIC等方法得出：新的反演模型要优于子区域为均质的传统反演方法，与采用相同个数的均质子区域相比，均方误差减少了35%，模拟含水量和观测含水量的R2达到了0.92，证明在数值模拟中保留多孔介质非均质性的优越性。
Vadose zone is the geologic media that is located between the surface of the earthand water table of the unconfined aquifer. It is a necessary passage that connectsgroundwater with atmospheric water and surface water. Groundwater can gainrecharge from precipitation and surface water, and discharge to the atmosphere byevapotranspiration through vadose zone, which is a complex body that water, soil andair coexist in this part. When vadose zone is contaminated, water, atmosphere, livingorganisms, etc will also be polluted. Therefore, it is of significance to simulate andforecast water quantity and quality of vadose zone.
Meaningful modeling of vadose zone flow and transport requires accurateknowledge of soil hydraulic properties. However, the expense and amount of laborinvolved in direct measurement of hydraulic properties in the required detail is oftenprohibitive. This is especially the case for deep vadose zones, where it is difficult toacquire undisturbed samples for accurate laboratory measurement of hydraulicproperties. In these cases, indirect methods for estimating hydraulic properties areattractive, such as inverse numerical modeling or application of pedotransferfunctions.
Rosetta is a widely used pedotransfer function to forecast soil hydraulicparameters, and has been used in some softwares, such as HYDRUS. Artificial NeuralNetwork and Bootstrap are coupled in Rosetta and2134soil samples are used to trainand validate the Artificial Neural Network. Rosetta can provide different levels ofaccuracy based on the input data for Rosetta. However, Rosetta underestimates thewater content for soil hydraulic parameters when the pressure head is high. In thedissertation, the weights for each soil water retention parameters were obtained byfitting soil moisture content and pressure head of the original Rosetta data. Then theweights were adjusted and used in original Rosetta code to get new Rosetta model with smaller root mean square error (RMSE) and mean error (ME). Results show thatRMSE is decreased from ranging0.076to0.044to ranging from0.072to0.038inH2-H5model, and ME is decreased from ranging0.022to0.013to ranging from0.0024to0.0061. The new Rosetta model can improve the problem of the originalRosetta, which underestimate soil water content for soil hydraulic parameters whenthe pressure head is high.
It is difficult to get the initial water content for each node in the numericalsimulation of vadose zone. In the dissertation, a multiple linear regression equationwas established between neutron count ratios and soil particle size composition, andthen the equation between soil moisture content and neutron count ratios was used tocompute the water content under natural stable drainage of vadose zone. This watercontent can be used as initial water content in vadose zone modeling, and get goodsimulation results.
Inverse method is to compute the parameters (e.g. saturated hydraulicconductivity) of the model system based on state variables (e.g soil water content).Traditional inverse method is usually to classify the simulation domain into severalsubdomains, and each subdomain is treated as homogeneous and given an equivalentsoil hydraulic parameter. The soil hydraulic parameters are optimized by reducing theobjective functions between observed and simulated state variables. In order to furtherreduce the objective functions, it is customary to increase the number of subdomains,and the number of inverse parameters will increase corresponding. In the dissertation,an inversion approach that combines decomposition of a heterogeneous domain intoheterogeneous subdomains with transformation of pedotransfer function estimates forevery subdomain was proposed. Rather than optimizing hydraulic parameters directly,as is common for approaches that define homogeneous subdomains, the proposedmethod optimizes the sub-domain specific parameters in the transformation functions,thus allowing the subdomains to remain heterogeneous. The approach is demonstratedwith data from a deep semi-arid heterogeneous vadose zone monitoring site near Phoenix, Arizona, for which a geospatial model of soil texture and bulk density wasavailable. Domain decomposition into up to six subdomains was carried out byk-means clustering. Base on moment analysis, and model selection criterion, such asAIC, AICc and BIC, the new model is better than traditional inverse model. Ourresults show that the new approach is better than one that considers the subdomains tobe homogeneous with a reduction in mean-square error of about35%, and R2betweensimulated and observed water content can reach up to0.92, indicating that there ismerit in preserving full subsurface heterogeneity within numerical simulations.
包气带水分及溶质运移模型需要准确的描述包气带的水力参数。室内实验测量水力参数需要花费大量的人力和物力，当研究对象为深层包气带时，获取用于室内实验测量水力参数的非扰动土样会非常困难。因此，通过间接的手段，如建立土壤粒径成分与土壤水力参数关系的土壤传递函数或者通过反演方法来预测土壤水力参数逐渐得到了广泛应用。
Rosetta利用2134个土壤样品，将人工神经网络（Artificial Neural Network）与Bootstrap抽样方法相结合，根据每个土壤样品输入参数由少到多，建立了精度逐渐提高的用于预测土壤水力参数的模型，目前已被广泛用于HYDRUS等软件中，但原Rosetta低估了土壤水力参数在压力水头较大时的含水量值。本论文在重新拟合Rosetta原始含水量-压力水头数据，获得带有权重的土壤水力参数的基础上，通过调整权重，训练带有权重的人工神经网络模型，获得了精度更高，即均方根误差（RMSE）和反应系统误差的平均误差（ME）更小的模型，结果显示带权重的Rosetta H2-H5四个模型中RMSE由0.076至0.044降低到0.072至0.038；ME由0.022至0.013降低到0.0024至0.0061，系统误差得到显著降低。改进的Rosetta模型，改善了原Rosetta模型低估土壤水力参数在压力水头较大时的含水量值的问题。
针对难以获得包气带水分运移数值模拟中所有网格结点上的初始含水量的问题，本论文建立了中子仪测数与土壤粒径成分等因子之间的多元线性回归方程，从而利用已知的含水量与中子仪测数的关系式，计算在自然状态下包气带土壤稳定排水结束时的含水量，取得了良好的效果。
反演方法（inverse method）是根据观测得到的状态信息，如水位或含水量等，反求模型系统的参数，如饱和渗透系数等信息。传统的反演方法通常将模拟区域划分为多个子区域，每个子区域看作均质区域并给定一个等效的水力参数，通过目标函数值的最小化来优化每个子区域上的等效水力参数。为了进一步优化目标函数，常常需要增加子区域，进而增加模拟区域的非均质性，因而反演的参数和运算时间也相应增加。本论文提出一种新的保留多孔介质非均质性的反演方法，将通用的土壤传递函数，如Rosetta，应用于土壤质地的地质统计模型中，通过与数值反演方法相结合，将模拟区分为若干非均质的子区域，每个子区域进行线性和非线性变换，如使用logistic函数变换，模拟区域在整个空间网格上的水力参数都是不同的，因此这种方法可以在保留多孔介质的非均质性，以及水力参数之间连续性的同时，减少反演模型优化的参数，使目标函数进一步优化。以美国亚利桑那州Maricopa场地为例，在地质统计学分析的基础上，利用残余变异函数分析场地土壤质地数据，建立了包气带非均质、空间三维结构、非稳定数值模型。通过矩分析、基于似然函数的模型评价准则如AIC、AICc和BIC等方法得出：新的反演模型要优于子区域为均质的传统反演方法，与采用相同个数的均质子区域相比，均方误差减少了35%，模拟含水量和观测含水量的R2达到了0.92，证明在数值模拟中保留多孔介质非均质性的优越性。
Vadose zone is the geologic media that is located between the surface of the earthand water table of the unconfined aquifer. It is a necessary passage that connectsgroundwater with atmospheric water and surface water. Groundwater can gainrecharge from precipitation and surface water, and discharge to the atmosphere byevapotranspiration through vadose zone, which is a complex body that water, soil andair coexist in this part. When vadose zone is contaminated, water, atmosphere, livingorganisms, etc will also be polluted. Therefore, it is of significance to simulate andforecast water quantity and quality of vadose zone.
Meaningful modeling of vadose zone flow and transport requires accurateknowledge of soil hydraulic properties. However, the expense and amount of laborinvolved in direct measurement of hydraulic properties in the required detail is oftenprohibitive. This is especially the case for deep vadose zones, where it is difficult toacquire undisturbed samples for accurate laboratory measurement of hydraulicproperties. In these cases, indirect methods for estimating hydraulic properties areattractive, such as inverse numerical modeling or application of pedotransferfunctions.
Rosetta is a widely used pedotransfer function to forecast soil hydraulicparameters, and has been used in some softwares, such as HYDRUS. Artificial NeuralNetwork and Bootstrap are coupled in Rosetta and2134soil samples are used to trainand validate the Artificial Neural Network. Rosetta can provide different levels ofaccuracy based on the input data for Rosetta. However, Rosetta underestimates thewater content for soil hydraulic parameters when the pressure head is high. In thedissertation, the weights for each soil water retention parameters were obtained byfitting soil moisture content and pressure head of the original Rosetta data. Then theweights were adjusted and used in original Rosetta code to get new Rosetta model with smaller root mean square error (RMSE) and mean error (ME). Results show thatRMSE is decreased from ranging0.076to0.044to ranging from0.072to0.038inH2-H5model, and ME is decreased from ranging0.022to0.013to ranging from0.0024to0.0061. The new Rosetta model can improve the problem of the originalRosetta, which underestimate soil water content for soil hydraulic parameters whenthe pressure head is high.
It is difficult to get the initial water content for each node in the numericalsimulation of vadose zone. In the dissertation, a multiple linear regression equationwas established between neutron count ratios and soil particle size composition, andthen the equation between soil moisture content and neutron count ratios was used tocompute the water content under natural stable drainage of vadose zone. This watercontent can be used as initial water content in vadose zone modeling, and get goodsimulation results.
Inverse method is to compute the parameters (e.g. saturated hydraulicconductivity) of the model system based on state variables (e.g soil water content).Traditional inverse method is usually to classify the simulation domain into severalsubdomains, and each subdomain is treated as homogeneous and given an equivalentsoil hydraulic parameter. The soil hydraulic parameters are optimized by reducing theobjective functions between observed and simulated state variables. In order to furtherreduce the objective functions, it is customary to increase the number of subdomains,and the number of inverse parameters will increase corresponding. In the dissertation,an inversion approach that combines decomposition of a heterogeneous domain intoheterogeneous subdomains with transformation of pedotransfer function estimates forevery subdomain was proposed. Rather than optimizing hydraulic parameters directly,as is common for approaches that define homogeneous subdomains, the proposedmethod optimizes the sub-domain specific parameters in the transformation functions,thus allowing the subdomains to remain heterogeneous. The approach is demonstratedwith data from a deep semi-arid heterogeneous vadose zone monitoring site near Phoenix, Arizona, for which a geospatial model of soil texture and bulk density wasavailable. Domain decomposition into up to six subdomains was carried out byk-means clustering. Base on moment analysis, and model selection criterion, such asAIC, AICc and BIC, the new model is better than traditional inverse model. Ourresults show that the new approach is better than one that considers the subdomains tobe homogeneous with a reduction in mean-square error of about35%, and R2betweensimulated and observed water content can reach up to0.92, indicating that there ismerit in preserving full subsurface heterogeneity within numerical simulations.
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Schaap MG, Leij FJ, van Genuchten MT. ROSETTA: a computer program for estimating soilhydraulic parameters with hierarchical pedotransfer functions. Journal of Hydrology2001;251:163-176.
Schaap MG, Nemes A, Van Genuchten MT. Comparison of models for indirect estimation of waterretention and available water in surface soils. Vadose Zone Journal2004;3:1455-1463.
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Russo D. Determining soil hydraulic properties by parameter estimation: On the selection of amodel for the hydraulic properties. Water Resources Research1988;24:453-459.
Russo D, Bresler E, Shani U, Parker JC. Analyses of infiltration events in relation to determiningsoil hydraulic properties by inverse problem methodology. Water Resources Research1991;27:1361-1373.
Schaap MG. Description, Analysis, and Interpretation of an Infiltration Experiment in a SemiaridDeep Vadose Zone. Advances in Hydrogeology. Springer,2013, pp.159-183.
Schaap MG, Bouten W. Modeling water retention curves of sandy soils using neural networks.Water Resources Research1996;32:3033-3040.
Schaap MG, Leij FJ. Database-related accuracy and uncertainty of pedotransfer functions. SoilScience1998;163:765-779.
Schaap MG, Leij FJ, van Genuchten MT. Neural network analysis for hierarchical prediction ofsoil hydraulic properties. Soil Science Society of America Journal1998;62:847-855.
Schaap MG, Leij FJ, van Genuchten MT. ROSETTA: a computer program for estimating soilhydraulic parameters with hierarchical pedotransfer functions. Journal of Hydrology2001;251:163-176.
Schaap MG, Nemes A, Van Genuchten MT. Comparison of models for indirect estimation of waterretention and available water in surface soils. Vadose Zone Journal2004;3:1455-1463.
Schaap MG, van Genuchten MT. A modified Mualem-van Genuchten formulation for improveddescription of the hydraulic conductivity near saturation. Vadose Zone Journal2006;5:27-34.
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Schweppe FC. Uncertain dynamic systems. Vol160: Prentice-Hall Englewood Cliffs, NJ,1973.
Seber G, Wild C. Nonlinear regression,1989. Wiley, New York.
Seber GA, Lee AJ. Linear regression analysis. Vol936: John Wiley&Sons,2012.im nek J, Jarvis NJ, Van Genuchten MT, G rden s A. Review and comparison of models fordescribing non-equilibrium and preferential flow and transport in the vadose zone.Journal of Hydrology2003;272:14-35.im nek J, Van Genuchten MT, Sejna M. The HYDRUS-1D software package for simulating theone-dimensional movement of water, heat, and multiple solutes in variably-saturatedmedia. University of California-Riverside Research Reports2005;3:1-240.im nek J, Van Genuchten MT, Sejna M. The HYDRUS software package for simulating thetwo-and three-dimensional movement of water, heat, and multiple solutes invariably-saturated media. Technical manual2006;1.
Stallman RW. Numerical analysis of regional water levels to define aquifer hydrology.Transactions, American Geophysical Union1956;37:451-460.
Tamari S, W sten J, Ruiz-Suarez J. Testing an artificial neural network for predicting soilhydraulic conductivity. Soil Science Society of America Journal1996;60:1732-1741.
Thomasson MJ, Wierenga PJ. Spatial variability of the effective retardation factor in anunsaturated field soil. Journal of Hydrology2003;272:213-225.
Tromp J, Tape C, Liu Q. Seismic tomography, adjoint methods, time reversal and banana‐doughnut kernels. Geophysical Journal International2005;160:195-216.
Tsang CF.非均质介质中地下水流动与深质运移模拟——问题与挑战.地球科学:中国地质大学学报2000;25:443-450.
Van Bavel C, Nielsen D, Davidson J. Calibration and characteristics of two neutron moistureprobes. Soil Science Society of America Journal1961;25:329-334.
Van Bavel C, Underwood N, Swanson R. Soil moisture measurement by neutron moderation. SoilScience1956;82:29-42.
Van Dam J, Stricker J, Droogers P. Inverse method to determine soil hydraulic functions frommultistep outflow experiments. Soil Science Society of America Journal1994;58:647-652.
van Genuchten MT. A Closed-Form Equation for Predicting the Hydraulic Conductivity ofUnsaturated Soils. Soil Science Society of America Journal1980;44:892-898.
Van Genuchten MT, Leij F, Wu L. Characterization and measurement of the hydraulic propertiesof unsaturated porous media. Parts1&2. Proceedings of the International Workshop,Riverside, Calif.,22–24Oct,1997.
Van Genuchten MT, Nielsen D. On describing and predicting the hydraulic properties ofunsaturated soils. Ann. Geophys1985;3:615-628.
Venables WN, Smith DM. the R development core team. An Introduction to R. Notes on R: AProgramming Environment for Data Analysis and Graphics2005.
Vogel T, Van Genuchten MT, Cislerova M. Effect of the shape of the soil hydraulic functions nearsaturation on variably-saturated flow predictions. Advances in Water Resources2000;24:133-144.
Vrugt J, Bouten W, Weerts A. Information content of data for identifying soil hydraulic parametersfrom outflow experiments. Soil Science Society of America Journal2001;65:19-27.
Vrugt JA, Bouten W, Gupta HV, Sorooshian S. Toward improved identifiability of hydrologicmodel parameters: The information content of experimental data. Water ResourcesResearch2002;38:48-1-48-13.
Vrugt JA, Stauffer PH, W hling T, Robinson BA, Vesselinov VV. Inverse modeling of subsurfaceflow and transport properties: A review with new developments. Vadose Zone Journal2008;7:843-864.
W sten J, Pachepsky YA, Rawls W. Pedotransfer functions: bridging the gap between availablebasic soil data and missing soil hydraulic characteristics. Journal of Hydrology2001;251:123-150.
Wang W. Uncertainty analysis of ground water flow and in unsaturated-saturated porousmediam:Maricopa case, Ph.D diss. The University of Arizona, Tucson,2002.
Wang W, Neuman SP, Yao T-m, Wierenga PJ. Simulation of Large-Scale Field InfiltrationExperiments Using a Hierarchy of Models Based on Public, Generic, and Site Data.Vadose Zone Journal2003a;2:297-312.
Whisler F, Watson K. One-dimensional gravity drainage of uniform columns of porous materials.Journal of Hydrology1968;6:277-296.
White MD, Oostrom M. STOMP Subsurface Transport Over Multiple Phases User's Guide.Pacific Northwest National Laboratory,2006.
Yao T, Wierenga PJ, Graham AR, Neuman SP. Neutron probe calibration in a vertically stratifiedvadose zone. Vadose Zone Journal2004;3:1400-1406.
Ye M, Khaleel R, Schaap MG, Zhu J. Simulation of field injection experiments in heterogeneousunsaturated media using cokriging and artificial neural network. Water ResourcesResearch2007;43.
Ye M, Meyer PD, Neuman SP. On model selection criteria in multimodel analysis. WaterResources Research2008;44.
Yeh TCJ, Lee CH, Hsu KC, Wen JC. Fusion of hydrologic and geophysical tomographic surveys.Geosciences Journal2008;12:159-167.
Yeh TCJ, Zhang J. A geostatistical inverse method for variably saturated flow in the vadose zone.Water Resources Research1996;32:2757-2766.
Young M. Results of Field Studies at the Maricopa Environmental Monitoring Site, Arizona.University of Arizona, Tucson,1999.
Zachmann D, Duchateau P, Klute A. The calibration of the Richards flow equation for a drainingcolumn by parameter identification. Soil Science Society of America Journal1981;45:1012-1015.
Zhang J, Yeh TCJ. An iterative geostatistical inverse method for steady flow in the vadose zone.Water Resources Research1997;33:63-71.
Zhang ZF, Ward AL, Gee GW. A combined parameter scaling and inverse technique to upscale theunsaturated hydraulic parameters for heterogeneous soils. Water Resources Research2004;40.
Zimmerman DA, de Marsily G, Gotway CA, Marietta MG, Axness CL, Beauheim RL, et al. Acomparison of seven geostatistically based inverse approaches to estimate transmissivitiesfor modeling advective transport by groundwater flow. Water Resources Research1998;34:1373-1413.
刘建立,徐绍辉,刘慧.估计土壤水分特征曲线的间接方法研究进展.水利学报2004:68-76.
毛德强.地下水反演模型解的唯一性和高精度反演方法研究.博士学位论文.中国地质大学（北京）,北京,2013.
邵明安,王全九,黄明斌.土壤物理学:高等教育出版社,2006.
王大纯,张人权,史毅红,许绍倬,于青春,梁杏.水文地质学基础:地质出版社,1995.
中国地下水科学战略研究小组.中国地下水科学的机遇与挑战.北京:科学出版社,2009.