潜水面动态蒸发的砂柱实验研究
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摘要
潜水蒸发是浅层地下水消耗的主要途径,是地下水向土壤水和大气水转化的主要形式,也是四水转化的重要环节。研究潜水蒸发对于探讨四水转化机理、农田灌溉、盐碱地防治以及水资源评价等都有重要的意义。本文结合国家自然基金课题,采用理论分析与室内实验相结合的方法,研究潜水面的动态变化过程,所作研究和初步成果如下:
(1)通过参阅国内外文献资料,总结了确定土壤水分特征曲线各种方法的优缺点。在测定地大粗砂的干密度、粒径分布和饱和渗透系数的常规实验的基础上,采用自主设计的砂柱实验这种新型试验方法测定了地大粗砂的土壤水分特征曲线,试验结果显示其呈很好的“S”型曲线。能够利用van-Genuchten模型拟合试验结果,通过与压力膜仪法实测的土壤水分特征曲线的对比分析,指出两种方法确定土壤水分特征曲线的优点和存在的不足之处。相比而言,砂柱实验确定土壤水分特征曲线具有方法简单、精确度高、实验成本低的优势。
(2)在分析潜水蒸发影响因素及现有观测方法的基础上,以质量守恒定律为原理,通过初始饱和的砂柱实验,研究不同蒸发历时,潜水蒸发量及潜水蒸发系数随埋深的变化,实验中潜水蒸发主要受到埋深以及大气蒸发能力的影响,随着埋深的增加,大气蒸发能力影响减弱,潜水蒸发量和蒸发系数都会减小。指数公式C= 23.331e-0.8464D可以较好地拟合实测潜水蒸发系数随埋深的变化。
(3)以土壤水动力学理论为指导,建立潜水动态蒸发的数学模型,使用Hydrus-1D软件对砂柱动态蒸发实验进行模拟。模型计算的潜水蒸发量和实测的潜水蒸发量除个别观测点处误差较大外,其他各点相对误差较小,其宏观形态拟合效果较好,模型整体上能够较好的模拟潜水动态蒸发的变化过程,数值模拟值与实测值的趋势基本一致,可满足精度的要求。
(4)由于受客观条件的限制,实验尚存在一些不足之处需要改进,文中提出了改进的建议。
Phreatic evaporation is the main depletion way of shallow groundwater, it is the main form for groundwater to turn into the soil water and atmospheric water and also an important part of transformation in four-water. The study of phreatic is of great importance for four- water transformation mechanism, irrigation, saline control and evaluation of water resources.Surpporting by the National Natural Science Foundation,this paper takes the method of theoretical analysis combining with laboratory to study the dynamic evaporation process of the water table, the research and preliminary results are as follows:
(1) By referring internal and external literatures, the paper summarizes the advantages and disadvantages of the methods of determining the soil water characteristic curve. Based on some conventional experiments including density, particle-size distribution, saturated hydraulic conductivity coefficient, we develop a laboratory experiment of sand column to measure the soil water characteristic curve. It turns out that the curve presents“S”well. At the same time, we see that van Genuchten model is able to match the measured moisture-suction data of the sand material used in the experiments well. Furthermore, pressure-membrane apparatus is applied to determine the soil water characteristic curve,from which inherent advantages and deficiencies of the methods are analyzed. Based on the analysis and comparisons, the laboratory experiment of sand column provides great accuracy, low cost, simple operate in determining the soil water characteristic curve.
(2) On the basis of analysis of Phreatic evaporation and the existing observation methods ,according to the principle of conservation of mass, By the experiment of initial saturated sand column to study the changes of Phreatic evaporation and the evaporation coefficient with depth in different evaporation duration, Phreatic evaporation in the experiment was mainly influenced by the depth and the aatmospheric evaporation, with the increase of depth,the influence of atmospheric evaporation increases too, Phreatic evaporation and the evaporation coefficient will both decrease. Index formula C = 23.331e-0.8464D can better fit the measured evaporation coefficient changing with depth.
(3) To soil water dynamics theory, we established a mathematical model of Phreatic dynamic evaporation,using Hydrus-1D to simulate the dynamic evaporation of the sand column experiments. Except for some specific points, the Model calculation and the measured evaporation have less error,the macroscopic morphology was well fitted ,so the model can better simulate the overall change process of Phreatic dynamic evaporation, the trends of numerical simulation and measured are identical and the requirements of precision can be satisfied.
(4) Due to objective conditions, there are still some shortcomings in the experiments needed to be improved, the paper has put forward some suggestions for further improvement.
(1)通过参阅国内外文献资料,总结了确定土壤水分特征曲线各种方法的优缺点。在测定地大粗砂的干密度、粒径分布和饱和渗透系数的常规实验的基础上,采用自主设计的砂柱实验这种新型试验方法测定了地大粗砂的土壤水分特征曲线,试验结果显示其呈很好的“S”型曲线。能够利用van-Genuchten模型拟合试验结果,通过与压力膜仪法实测的土壤水分特征曲线的对比分析,指出两种方法确定土壤水分特征曲线的优点和存在的不足之处。相比而言,砂柱实验确定土壤水分特征曲线具有方法简单、精确度高、实验成本低的优势。
(2)在分析潜水蒸发影响因素及现有观测方法的基础上,以质量守恒定律为原理,通过初始饱和的砂柱实验,研究不同蒸发历时,潜水蒸发量及潜水蒸发系数随埋深的变化,实验中潜水蒸发主要受到埋深以及大气蒸发能力的影响,随着埋深的增加,大气蒸发能力影响减弱,潜水蒸发量和蒸发系数都会减小。指数公式C= 23.331e-0.8464D可以较好地拟合实测潜水蒸发系数随埋深的变化。
(3)以土壤水动力学理论为指导,建立潜水动态蒸发的数学模型,使用Hydrus-1D软件对砂柱动态蒸发实验进行模拟。模型计算的潜水蒸发量和实测的潜水蒸发量除个别观测点处误差较大外,其他各点相对误差较小,其宏观形态拟合效果较好,模型整体上能够较好的模拟潜水动态蒸发的变化过程,数值模拟值与实测值的趋势基本一致,可满足精度的要求。
(4)由于受客观条件的限制,实验尚存在一些不足之处需要改进,文中提出了改进的建议。
Phreatic evaporation is the main depletion way of shallow groundwater, it is the main form for groundwater to turn into the soil water and atmospheric water and also an important part of transformation in four-water. The study of phreatic is of great importance for four- water transformation mechanism, irrigation, saline control and evaluation of water resources.Surpporting by the National Natural Science Foundation,this paper takes the method of theoretical analysis combining with laboratory to study the dynamic evaporation process of the water table, the research and preliminary results are as follows:
(1) By referring internal and external literatures, the paper summarizes the advantages and disadvantages of the methods of determining the soil water characteristic curve. Based on some conventional experiments including density, particle-size distribution, saturated hydraulic conductivity coefficient, we develop a laboratory experiment of sand column to measure the soil water characteristic curve. It turns out that the curve presents“S”well. At the same time, we see that van Genuchten model is able to match the measured moisture-suction data of the sand material used in the experiments well. Furthermore, pressure-membrane apparatus is applied to determine the soil water characteristic curve,from which inherent advantages and deficiencies of the methods are analyzed. Based on the analysis and comparisons, the laboratory experiment of sand column provides great accuracy, low cost, simple operate in determining the soil water characteristic curve.
(2) On the basis of analysis of Phreatic evaporation and the existing observation methods ,according to the principle of conservation of mass, By the experiment of initial saturated sand column to study the changes of Phreatic evaporation and the evaporation coefficient with depth in different evaporation duration, Phreatic evaporation in the experiment was mainly influenced by the depth and the aatmospheric evaporation, with the increase of depth,the influence of atmospheric evaporation increases too, Phreatic evaporation and the evaporation coefficient will both decrease. Index formula C = 23.331e-0.8464D can better fit the measured evaporation coefficient changing with depth.
(3) To soil water dynamics theory, we established a mathematical model of Phreatic dynamic evaporation,using Hydrus-1D to simulate the dynamic evaporation of the sand column experiments. Except for some specific points, the Model calculation and the measured evaporation have less error,the macroscopic morphology was well fitted ,so the model can better simulate the overall change process of Phreatic dynamic evaporation, the trends of numerical simulation and measured are identical and the requirements of precision can be satisfied.
(4) Due to objective conditions, there are still some shortcomings in the experiments needed to be improved, the paper has put forward some suggestions for further improvement.
引文
Brooks R H, Corey A T. Hydraulic properties of porous media. Colorado State University, Fort Collins, Colorado, 1964. 1～27.
David P. Groeneveld, Remotely-sensed groundwater evapotranspiration from alkali scrub affected by declining water table. Journal of Hydrology ,2008 (358).294～303
Gardner W R and Fireman M. Laboratory Study of Evaporation from Soil Column in the Presence of a Water Table.Soil.Sci.,1958,85(5).244～249.
Gardner W R, Hillel D, Benyamini Post irrigation movement of soil water: I? Redistribution ? Water Resources Research, 1970a.851～861.
Gardner W R, Hillel D, Benyamini Y. Post irrigation movement of soil water:Ⅱ. Simultaneous redistribution and evaporation. Water Resources Research, 1970b, 6. 148～153
Howell T A,Schneider A D,Jensen M E. History of lysimeter design and use for vapotrans-piration measurements In Proceedings of the International Symposium on Lysimeters for Evapotranspiration and Environmental Measurements, eds IR Div,ASAE.1991.1～9
Kusras W P, JM Nonmain. Use of remote sensing for evapotransporation monitoring over land surfaces. Hydrological Sciences Journal, 1996,41(4):255～266
Laura K. Lautz, Erratum. Estimating groundwater evapotranspiration rates using diurnal water-table fluctuations in a semi-arid riparian zone, Hydrogeology Journal 2008(16).483～497
M.Th.Van Genuchten. A Closed-Form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society American Journal,1980,44.892～898
Maceo C. Martinet,1Enrique R. Vivoni, James R. Cleverly,et al, On groundwater fluctuations, evapotranspiration, and understory removal in riparian corridors. WATER RESOURCES RESEARCH, 2009(45)
Marek T H, et al. Design and construction of large weighing monolithic lysimeters. Trans.ASAE.1988,31(2):477～484
Philip J R. Plant water relation: some physical aspects. Ann. Rev.Plant Physiol,1966,17.45～268.
Rassam D W, Cook F J. Numerical simulations of water flow and solute transport applied to acid sulfate soils. Journal of Irrigation and Drainage Engineering. 2002,128(2).107～115
Richards L A,Gardners W R.Ogata G. Physical processes determining water loss from soil. Soil Sci Aner Proc,1956(20):310～314
Russo D. Determining soil hydraulic properties by parameter estimation: on the selection of a model for the hydraulic properties. Water Resources Research, 1988, 24. 453～459
Simunek J, M Sejna, MTh Van Genuchten. The Hydrus-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media. 1998
The HYDRUS Code for Simulating the One-Dimensional Movement of Water,Heat and Multiple Solutes in Variably Saturated Porous Media[S].Version 7.0.
U.S.DEPARTEMENT OF AGRICUTURE RICERSIDE,CALIFORNIA,The HYDRUS-1D Software Package of Simulating the One-Dimensinal movement of water , Heat and Multiple Solutes in Variably-Saturated Media, Version 2.0 . 1998.10
Van Genuchten MTh. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 1980, 44.892～898.
Xun hong Chen, Long cang Shu. Groundwater evapotranspiration captured by seasonally pumped wells in river valleys, Journal of Hydrology 2006(318). 334～347
Youngs E G. Infiltration measurements—A review. Hydrological Processes, 1991,5:309～320
阿维里扬诺夫.防治灌溉土地盐渍化的水平排水.娄溥礼译.北京:中国工业出版社,1963
曹红霞,康绍忠,武海霞.同一质地(重壤土)土壤水分特征曲线的研究.西北农林大
学学报(自然科学版). 2002,30(1):9～12
陈添斐,王旭升,董佩.测定沙土水分特征曲线的一种简易方法.工程勘察,2010,2:33～36
樊自立,陈亚宁,李和平等.中国西北干旱区生态地下水埋深适宜深度的确定.干旱区资源与环境, 2008,22(2):1～5
付秋萍,张江辉,王全九. E0值对潜水蒸发计算精度影响分析.干旱区地理, 2007,30(6): 820～825
付秋萍,张江辉,王全九.常用潜水蒸发经验公式在新疆地区适用性研究.干旱地区农业研究, 2008,26(3):182～188
甘东科,靳孟贵,朱中道等.郑州市地下水均衡场地中渗透仪潜水蒸发规律分析.安全与环境工程,2004,11(1):47～50
宫兆宁,宫辉力,邓伟等.浅埋条件下地下水-土壤-植物-大气连续体中水分运移研究综述. 农业环境科学学报,2006,25:65～73
顾志杰,周洪贵,郭择德.野外试验场场址土壤蒸发量的计算.辐射防护,2000,12(l-2):110～113
侯毅凯.非饱和土壤水分运动参数自动测定系统的应用研究:[硕士学位论文].河北:河工程大学,2007
胡和平等.用直接估算法确定区域潜水蒸发量.灌溉排水,1999,18(2):22～25
胡建锋.不同地下水埋深条件下农田潜水蒸发规律.山西水利科技,2005,(4) :24～31
胡顺军,田长彦,宋郁东.裸地与怪柳生长条件下潜水蒸发计算模型.科学通报, 2006,50(增刊Ⅰ):36～41
金晓媚,万力,Z.Bob.Su .遥感与区域地面蒸散量.北京:地质出版社,2008
瞿兴业,张友义,苏锦星等.地下水蒸发与埋深关系指数n=3的非稳定渗流排水计算.水利学报,1983(9):48～53
孔凡哲,王晓赞.利用土壤水吸力计算潜水蒸发初探.水文,1997,17(3):44～47
雷志栋,杨诗秀,倪光恒,等.地下水位埋深类型与土壤水分动态特征.水利学报,1992(2):1～6
雷志栋,杨诗秀,谢森传.土壤水动力学.北京:清华大学出版社,1988
雷志栋,杨诗秀,谢森传.田间土壤水量平衡与定位通量法的应用.水利学报,1988,5:1～7
李宝庆等.禹城站四水转化试验研究概要.中国科学院禹城综合试验站年报(1988—1990). 北京:气象出版社,1991
李艳,胡顺军,宋郁东.渭干河灌区潜水蒸发规律实验分析.干旱区资源与环境,2004,18(3):92～96
李毅,王文焰,王全九等.温度势梯度下土壤水平一维水盐运动特征的实验研究.农业工程学报,2002,18(6):4～8
刘昌明.土壤-植物-大气系统水分运行的界面过程研究.地理学报,1997,52(4):366～373
刘昌明.自然地理界面过程与水文界面分析.北京:气象出版社,1993
马英杰,王志朋.定水位条件下层状土壤潜水蒸发关系研究.水利学报, 2005,增刊:310～313
毛晓敏,李民,沈言俐等.叶尔羌河流域潜水蒸发规律试验分析.干旱区地理, 1998,21(3):: 44～50
毛晓敏,杨诗秀,雷志栋.叶尔羌河流域裸地潜水蒸发的数值模拟研究.水科学进展,1997,8(4):313～320.
尚松浩,毛晓敏,雷志栋等.计算潜水蒸发系数的反Logistic公式.灌溉排水,1999,18(2):18～21
沈立昌.关于潜水蒸发量经验公式探讨.水利学报,1985(7):34～40
沈立昌.潜水蒸发新经验公式.徐州市水利科学研究所,1983
沈振荣等.水资源科学实验与研究-大气水、地表水、土壤水、地下水相互转化关系.北京:中国科学技术出版社,1992
唐海行,苏逸深,张和平.潜水蒸发的实验研究及其经验公式的改进.水利学报,1989,20(10):37～44.
孔凡泽,王晓赞.有作物的潜水蒸发规律试验研究和理论分析(1).中国水利水电学报,2008,27(4):3～5
王振龙,刘森,李瑞.淮北平原有无作物生长条件下潜水蒸发规律实验.农业工程学报, 2009,25(6):26～32
夏卫生,雷廷武等.土壤水分动力学参数研究与评价.灌溉排水,2002,21:72～75
徐建立,刘绍辉,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(2):68～76
闫华,周顺新.作物生长条件下潜水蒸发的数值模拟研究.中国农村水利水电, 2002,(9): 15～18
叶水庭,施鑫源,苗晓芳.用潜水蒸发经验公式计算给水度问题的分析.水文地质工程地质,1980(4):46～48
张德强,邵景力,李慈君等.地下水浅埋区土壤水的矿化度变化规律及其影响因素浅析.水文地质工程地质,2004 (1):52～56
张光辉.试论在我国北方应用零通量面法计算地下水入渗补给量问题.水文地质工程地质,1988 (2)
张蔚榛.地下水与土壤水动力学.北京:中国水利水电出版社,1996
张振华,史文娟等.干旱区潜水蒸发的影响因素和计算方法分析.水资源与水工学报,2008,10(6):78～80
赵成义,胡顺军,刘国庆等.潜水蒸发经验公式分段拟合研究.水土保持学报,2000,14(5):122～126
赵华,张友义.地下水蒸发影响下农田排水沟(管)间距的非稳定渗流数值解.水利学报,1986(11):35～38
周延辉,李宝庆,赵家义.大型多功能蒸渗仪的研制.中国科学院禹城试验站年报(1988～1990).北京:气象出版社,1991. 55～62
David P. Groeneveld, Remotely-sensed groundwater evapotranspiration from alkali scrub affected by declining water table. Journal of Hydrology ,2008 (358).294～303
Gardner W R and Fireman M. Laboratory Study of Evaporation from Soil Column in the Presence of a Water Table.Soil.Sci.,1958,85(5).244～249.
Gardner W R, Hillel D, Benyamini Post irrigation movement of soil water: I? Redistribution ? Water Resources Research, 1970a.851～861.
Gardner W R, Hillel D, Benyamini Y. Post irrigation movement of soil water:Ⅱ. Simultaneous redistribution and evaporation. Water Resources Research, 1970b, 6. 148～153
Howell T A,Schneider A D,Jensen M E. History of lysimeter design and use for vapotrans-piration measurements In Proceedings of the International Symposium on Lysimeters for Evapotranspiration and Environmental Measurements, eds IR Div,ASAE.1991.1～9
Kusras W P, JM Nonmain. Use of remote sensing for evapotransporation monitoring over land surfaces. Hydrological Sciences Journal, 1996,41(4):255～266
Laura K. Lautz, Erratum. Estimating groundwater evapotranspiration rates using diurnal water-table fluctuations in a semi-arid riparian zone, Hydrogeology Journal 2008(16).483～497
M.Th.Van Genuchten. A Closed-Form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society American Journal,1980,44.892～898
Maceo C. Martinet,1Enrique R. Vivoni, James R. Cleverly,et al, On groundwater fluctuations, evapotranspiration, and understory removal in riparian corridors. WATER RESOURCES RESEARCH, 2009(45)
Marek T H, et al. Design and construction of large weighing monolithic lysimeters. Trans.ASAE.1988,31(2):477～484
Philip J R. Plant water relation: some physical aspects. Ann. Rev.Plant Physiol,1966,17.45～268.
Rassam D W, Cook F J. Numerical simulations of water flow and solute transport applied to acid sulfate soils. Journal of Irrigation and Drainage Engineering. 2002,128(2).107～115
Richards L A,Gardners W R.Ogata G. Physical processes determining water loss from soil. Soil Sci Aner Proc,1956(20):310～314
Russo D. Determining soil hydraulic properties by parameter estimation: on the selection of a model for the hydraulic properties. Water Resources Research, 1988, 24. 453～459
Simunek J, M Sejna, MTh Van Genuchten. The Hydrus-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media. 1998
The HYDRUS Code for Simulating the One-Dimensional Movement of Water,Heat and Multiple Solutes in Variably Saturated Porous Media[S].Version 7.0.
U.S.DEPARTEMENT OF AGRICUTURE RICERSIDE,CALIFORNIA,The HYDRUS-1D Software Package of Simulating the One-Dimensinal movement of water , Heat and Multiple Solutes in Variably-Saturated Media, Version 2.0 . 1998.10
Van Genuchten MTh. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 1980, 44.892～898.
Xun hong Chen, Long cang Shu. Groundwater evapotranspiration captured by seasonally pumped wells in river valleys, Journal of Hydrology 2006(318). 334～347
Youngs E G. Infiltration measurements—A review. Hydrological Processes, 1991,5:309～320
阿维里扬诺夫.防治灌溉土地盐渍化的水平排水.娄溥礼译.北京:中国工业出版社,1963
曹红霞,康绍忠,武海霞.同一质地(重壤土)土壤水分特征曲线的研究.西北农林大
学学报(自然科学版). 2002,30(1):9～12
陈添斐,王旭升,董佩.测定沙土水分特征曲线的一种简易方法.工程勘察,2010,2:33～36
樊自立,陈亚宁,李和平等.中国西北干旱区生态地下水埋深适宜深度的确定.干旱区资源与环境, 2008,22(2):1～5
付秋萍,张江辉,王全九. E0值对潜水蒸发计算精度影响分析.干旱区地理, 2007,30(6): 820～825
付秋萍,张江辉,王全九.常用潜水蒸发经验公式在新疆地区适用性研究.干旱地区农业研究, 2008,26(3):182～188
甘东科,靳孟贵,朱中道等.郑州市地下水均衡场地中渗透仪潜水蒸发规律分析.安全与环境工程,2004,11(1):47～50
宫兆宁,宫辉力,邓伟等.浅埋条件下地下水-土壤-植物-大气连续体中水分运移研究综述. 农业环境科学学报,2006,25:65～73
顾志杰,周洪贵,郭择德.野外试验场场址土壤蒸发量的计算.辐射防护,2000,12(l-2):110～113
侯毅凯.非饱和土壤水分运动参数自动测定系统的应用研究:[硕士学位论文].河北:河工程大学,2007
胡和平等.用直接估算法确定区域潜水蒸发量.灌溉排水,1999,18(2):22～25
胡建锋.不同地下水埋深条件下农田潜水蒸发规律.山西水利科技,2005,(4) :24～31
胡顺军,田长彦,宋郁东.裸地与怪柳生长条件下潜水蒸发计算模型.科学通报, 2006,50(增刊Ⅰ):36～41
金晓媚,万力,Z.Bob.Su .遥感与区域地面蒸散量.北京:地质出版社,2008
瞿兴业,张友义,苏锦星等.地下水蒸发与埋深关系指数n=3的非稳定渗流排水计算.水利学报,1983(9):48～53
孔凡哲,王晓赞.利用土壤水吸力计算潜水蒸发初探.水文,1997,17(3):44～47
雷志栋,杨诗秀,倪光恒,等.地下水位埋深类型与土壤水分动态特征.水利学报,1992(2):1～6
雷志栋,杨诗秀,谢森传.土壤水动力学.北京:清华大学出版社,1988
雷志栋,杨诗秀,谢森传.田间土壤水量平衡与定位通量法的应用.水利学报,1988,5:1～7
李宝庆等.禹城站四水转化试验研究概要.中国科学院禹城综合试验站年报(1988—1990). 北京:气象出版社,1991
李艳,胡顺军,宋郁东.渭干河灌区潜水蒸发规律实验分析.干旱区资源与环境,2004,18(3):92～96
李毅,王文焰,王全九等.温度势梯度下土壤水平一维水盐运动特征的实验研究.农业工程学报,2002,18(6):4～8
刘昌明.土壤-植物-大气系统水分运行的界面过程研究.地理学报,1997,52(4):366～373
刘昌明.自然地理界面过程与水文界面分析.北京:气象出版社,1993
马英杰,王志朋.定水位条件下层状土壤潜水蒸发关系研究.水利学报, 2005,增刊:310～313
毛晓敏,李民,沈言俐等.叶尔羌河流域潜水蒸发规律试验分析.干旱区地理, 1998,21(3):: 44～50
毛晓敏,杨诗秀,雷志栋.叶尔羌河流域裸地潜水蒸发的数值模拟研究.水科学进展,1997,8(4):313～320.
尚松浩,毛晓敏,雷志栋等.计算潜水蒸发系数的反Logistic公式.灌溉排水,1999,18(2):18～21
沈立昌.关于潜水蒸发量经验公式探讨.水利学报,1985(7):34～40
沈立昌.潜水蒸发新经验公式.徐州市水利科学研究所,1983
沈振荣等.水资源科学实验与研究-大气水、地表水、土壤水、地下水相互转化关系.北京:中国科学技术出版社,1992
唐海行,苏逸深,张和平.潜水蒸发的实验研究及其经验公式的改进.水利学报,1989,20(10):37～44.
孔凡泽,王晓赞.有作物的潜水蒸发规律试验研究和理论分析(1).中国水利水电学报,2008,27(4):3～5
王振龙,刘森,李瑞.淮北平原有无作物生长条件下潜水蒸发规律实验.农业工程学报, 2009,25(6):26～32
夏卫生,雷廷武等.土壤水分动力学参数研究与评价.灌溉排水,2002,21:72～75
徐建立,刘绍辉,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(2):68～76
闫华,周顺新.作物生长条件下潜水蒸发的数值模拟研究.中国农村水利水电, 2002,(9): 15～18
叶水庭,施鑫源,苗晓芳.用潜水蒸发经验公式计算给水度问题的分析.水文地质工程地质,1980(4):46～48
张德强,邵景力,李慈君等.地下水浅埋区土壤水的矿化度变化规律及其影响因素浅析.水文地质工程地质,2004 (1):52～56
张光辉.试论在我国北方应用零通量面法计算地下水入渗补给量问题.水文地质工程地质,1988 (2)
张蔚榛.地下水与土壤水动力学.北京:中国水利水电出版社,1996
张振华,史文娟等.干旱区潜水蒸发的影响因素和计算方法分析.水资源与水工学报,2008,10(6):78～80
赵成义,胡顺军,刘国庆等.潜水蒸发经验公式分段拟合研究.水土保持学报,2000,14(5):122～126
赵华,张友义.地下水蒸发影响下农田排水沟(管)间距的非稳定渗流数值解.水利学报,1986(11):35～38
周延辉,李宝庆,赵家义.大型多功能蒸渗仪的研制.中国科学院禹城试验站年报(1988～1990).北京:气象出版社,1991. 55～62