摘要
在我国东北、西北和西南等广大地区,冬季通常会有一层相对稳定的雪被覆盖于冻结土壤表面,雪被覆盖条件下的季节性冻土水分运移和热量传输具有独特的性质,需将雪被和季节性冻融土壤视为一个联合体进行整体研究。同时,水分、热量在雪被-土壤联合体中的运移、存储和转化是自然界水循环中的一个重要环节,在农业、水资源、环境系统中占有极其重要的地位,对农业生产具有重要意义。然而,在理论基础、技术方法、实际应用等各方面,面向农业的雪被覆盖条件下季节性冻土水热运移的研究还存在许多问题亟待解决。
针对雪被覆盖条件下季节性冻土水热运移研究中存在的问题,结合哈尔滨市科技创新人才研究专项资金资助项目“雪被覆盖条件下农田土壤水热耦合运动规律及其数值模拟研究(No.RC2010XK002013)”,本文以雪被-土壤联合体中的水分和热量为研究对象,通过田间试验与理论分析相结合的方法,深入研究了联合体中水热耦合运移的变化规律、数学模型及数值模拟。
本文的主要研究内容、具体方法、分析结果及研究结论如下:
(1)根据野外试验实测资料,运用对比分析和统计分析的方法,对季节性冻土水分运移的驱动力、土壤季节性冻融过程中地面温度的变化规律、地面温度与土壤中温度场的关系、土壤剖面温度、总含水量及液态含水量的变化规律、雪被覆盖对土壤温度、含水量的影响等问题进行了详细探讨。结果表明:季节性冻土水分沿土水势减小的方向运移,地面温度与气温相关性较高且对土壤表层温度影响较大,冻融期日平均地面温度总体上呈开口向上的抛物线型,而地面温度日变化则在不同时期表现出不同的变化规律,土壤已冻层中的总含水量、液态含水量的变化与土壤冻结、融化过程密切相关,季节性冻土区土壤冻融作用导致了土壤水分的重分布,雪被覆盖对土壤与大气之间的热交换具有阻滞作用,对土壤剖面(特别是土壤表层)热状况影响显著,而雪被覆盖仅在融化期才对土壤表层含水量有显著影响。以上分析结果与结论可为数学模型构建及数值模拟计算中合理假设条件的制定、初始及边界条件的简化、水热运移参数的确定等提供重要依据。
(2)运用地统计学的理论与方法,通过季节性冻土水分半方差分析及空间分布图的绘制,分别对季节性冻土区土壤冻融过程中剖面总含水量及液态含水量的空间变异结构和空间分布规律进行了分析和研究。结果表明:季节性冻土总含水量与液态含水量具有良好的空间结构和空间相关性,土壤冻融过程影响两种含水量的空间相关性和变程,受冻融过程影响冻结状态下土壤两种含水量均表现出一定的空间分布规律,土壤融化后表层含水量的空间分布表现出较大的随机性。地统计学理论能够很好的刻画季节性冻土水分的空间变异性,可为冻土水分运移的机理研究提供新的思路。
(3)从季节性冻土水热运移的机理出发,基于质量守恒原理、能量守恒定律、非饱和土壤水流动的达西定律、热传导理论及一定的假设条件构建了季节性冻土水热耦合运移数学模型,运用有限差分法对季节性冻土一维垂向水热耦合运移进行了数值模拟及结果检验。结果表明:一维季节性冻土水热耦合运移的数值模拟结果存在一定误差,但模拟值与实测值的平均相对误差较小,并且土壤剖面含水量和温度模拟值的变化规律与实测值基本一致。数值模拟效果表明本文所建立的季节性冻土水热耦合运移模型合理、参数确定及数值模拟方法比较可靠。
(4)在充分分析雪被-土壤联合体水热运移机理的基础上,根据前人研究成果构建了一维雪被-土壤联合体水热耦合运移模型,制定了模型参数化方案,并进行了数值模拟分析和验证。结果表明:一维雪被-土壤联合体水热耦合运移数值模拟存在较大误差,但模拟值与实测值的绝对误差尚可接受且变化规律相近,本文所建立的一维雪被-土壤联合体水热耦合运移模型及参数化方案尚需进一步改进。
综上所述,对季节性冻土区雪被-土壤联合体水热耦合运移规律、数学模型及数值模拟的研究,不仅能揭示季节性冻土区雪被覆盖条件下的土壤水热耦合运移规律、刻画冻融过程中的土壤水热状况,而且能为季节性冻土区农业土壤水热资源的有效利用,地表水、地下水资源评价,水土保持,环境保护等方面的研究提供理论支撑和科学依据。
Snow cover is a widespread and relatively stable coverage type on soil surface during the winter of vast areas of northeast, northwest and southwest China. Snow cover and seasonal freezing-thawing soil need to be studied unitedly for water movement and heat transfer of seasonal frozen soil have distinctive properties under the coverage condition of snow cover. Movement, storage and transformation of water and heat in snow cover and soil union are the important link of nature water cycle, play an important role in the systems of agriculture, water resources and environment and have significances to agricultural production. However, studies on water-heat movement in seasonal frozen soil under snow cover still have many problems at the aspects of theory basis, technical method, practical application, etc. to be solved, particularly in the studies towards agriculture.
Aiming at the problems in the studies on water-heat movements in seasonal frozen soil under snow cover and combining with the project“Study on farmland soil water-heat coupling movements and numerical simulation under snow cover”(No.RC2010XK002013) subsidized by Harbin Science and Technology Innovation Talents Research Special Funds, the thesis taking the water and heat in snow cover and soil union as study objects, studied the change laws, mathematical model and numerical simulation of water-heat coupling movements in the union by using the methods of field experiments and theory analysis.
The study contents, specific methods, analysis results and conclusions of the thesis are as follows:
(1) On the basis of the data measured in field experiments, some basic topics were studied by using comparison and statistics methods, including the driving force of water movement in seasonal frozen soil, change law of soil surface temperature during seasonal freezing-thawing process, correlation between soil surface and profile temperature, variations of soil profile temperature, total and liquid moisture and the influence of snow cover on soil temperature and moisture. The results indicated that water in seasonal frozen soil moved along the direction on which soil-water potential decreased, soil surface temperature had high correlation with air temperature and strongly affected surface soil temperature, daily average soil surface temperature assumed an upward opening parabola while its daily changes have various laws in different periods, the changes of frozen soil total and liquid moisture have high correlations with soil freezing-thawing process, soil freezing-thawing action redistributed soil water, snow cover blocked the heat exchange between soil and atmosphere and affected surface soil heat condition significantly, but only in thawing period have significant effects on surface soil moisture. All the above results and conclusions can provide an important basis for making reasonable hypothesis, simplifying initial and boundary conditions, ascertaining water-heat movement parameters, etc. of model establishment and numerical simulation.
(2) Spatial variation structures and distributions of soil profile total and liquid moisture during freezing-thawing process were studied according to semivariance and spatial distribution analysis of seasonal frozen soil water using geostatistics. The results indicated that seasonal frozen soil total and liquid moisture have good spatial structures and correlations, freezing-thawing process affected the spatial correlations and ranges of the two type soil moisture, the spatial distributions of the two type soil moisture have good laws affected by freezing-thawing process, after thawing the spatial distributions of surface soil moisture have major randomicity. Geostatistics can effectively characterize the spatial variation of seasonal frozen soil water and provide a new way to study the movement mechanism of frozen soil water.
(3) Seasonal frozen soil water-heat coupling movement model was established based on water-heat movement mechanism, conservation of matter and energy, Darcy’s law, heat conduction theory and some hypotheses. Then the process was simulated numerically using finite difference method and the results were tested. The results indicated that simulation values have some error with the measured values, but the average relative error between them is small and they have the same trend. Therefore, the seasonal frozen soil water-heat coupling model established in the thesis was reasonable. The methods of parameter confirmation and numerical simulation were reliable.
(4) One-dimension snow cover and soil union water-heat movement model and parameterization scheme were established based on water-heat movement mechanism and previous research results. Then numerical simulation analysis and test were conducted. The results indicated that the simulated values have major error with the measured values, but the absolute error between them can be accepted and they have similar trend. Thus, the one-dimension snow cover and soil union water-heat movement model and parameterization scheme need to be improved further.
To conclude, the study on laws, model and numerical simulation of snow cover and soil union water-heat coupling movement in seasonal frozen soil region can not only reveal the soil water-heat movement law with snow cover and characterize the water and heat conditions during soil freezing-thawing process, but also provide theory support and science basis for effective utilization of soil water and heat resources, evaluation of surface and underground water, soil and water conservation, environmental protection, etc. in seasonal frozen soil region.
引文
车涛,李新.2005.1993~2002年中国积雪水资源时空分布与变化特征.冰川冻土,27(1):64~67.
陈军锋,郑秀清,邢述彦,等.2006.地表覆膜对季节性冻融土壤入渗规律的影响.农业工程学报,22(7):18~21.
程国栋.1990.中国冻土研究近今进展.地理学报,45(2):220~223.
戴永久.1995.陆面过程模式及其与GCM耦合模拟研究.中国科学院大气物理研究所博士学论文,287.
樊贵盛,郑秀清,潘光在.1999.地下水埋深对冻融土壤水分入渗特性影响的试验研究.水利学报,(3):21~26.
付强.2006.数据处理方法及其农业应用.北京:科学出版社.
郭占荣,荆恩春,聂振龙,等.2002.冻结期和冻融期土壤水分运移特征分析.水科学进展,13(3):298~302.
何平,程国栋,俞祁浩,等.2000.饱和正冻土中的水、热、力场耦合模型.冰川冻土,22(6):135~138.
侯景儒,黄竞先.1982.地质统计学及其在矿产储量计算中的应用.北京:地质出版社.
侯景儒,郭光裕.1993.矿床统计预测及地质统计学的理论与应用.北京:冶金工业出版社.
胡健伟,汤怀民.1999.微分方程数值方法.北京:科学出版社.
黄兴法,曾德超,练国平.1997.土壤水热盐运动模型的建立与初步验证.农业工程学报,13(3):32~36.
姜秋香,付强,王子龙.2007.黑龙江省西部半干旱区土壤水分空间变异性研究.水土保持学报,21(5):118~122.
金继明.1999.一个用于GCM的简单的雪盖—大气—土壤传输模式(SAST).中国科学院大气物理研究所博士学位论文,54.
荆继红,韩双平,王新忠,等.2007.冻结-冻融过程中水分运移机理.地球学报,28(1):50~54.
雷志栋,杨诗秀,许志荣,等.1985.土壤特性空间变异性初步研究.水利学报,(9):10~21.
雷志栋,杨诗秀,谢森传.1988.土壤水动力学.北京:清华大学出版社.
雷志栋,尚松浩,杨诗秀,等.1998.地下水浅埋条件下越冬期土壤水热迁移的数值模拟.冰川冻土,20(1):51~54.
雷志栋,尚松浩,杨诗秀,等.1999.土壤冻结过程中潜水蒸发规律的模拟研究.水利学报,6:6~9.
李哈滨,伍业刚.1992.景观生态学数量研究方法.刘建国.当代生态学博论.北京:中国科学技术出版社,209~233.
李述训,程国栋.1995.冻土中水热输送问题.兰州:兰州大学出版社.
李述训,南卓铜,赵林.2002a.冻融作用对系统与环境间能量交换的影响.冰川冻土,24(2):109~115.
李述训,南卓铜,赵林.2002b.冻融作用对地气系统能量交换的影响分析.冰川冻土,24(5):506~511.
李述训,吴通华.2004.冻土温度状况研究方法和应用分析.冰川冻土,26(4):377~383.
李杨.2008.季节冻土水分迁移模型研究.吉林大学博士学位论文.
刘来福,曾文艺.1988.数学模型与数学建模.北京:北京师范大学出版社.
陆金甫,关治.1987.偏微分方程数值解法.北京:清华大学出版社.
罗焕炎,陈雨孙.1988.地下水运动的数值模拟.北京:中国建筑工业出版社.
马虹,胡汝骥.1995.积雪对冻土热状况的影响.干旱区地理,18(4):23~27.
毛晓敏,杨诗秀,雷志栋,等.叶尔羌河流域裸地潜水蒸发的数值模拟研究.水科学进展,8(4):313~320.
毛雪松,胡长顺,窦明健,等.2003.正冻土中水分场和温度场耦合过程的动态观测与分析.冰川冻土,23(1):55~59.
毛雪松,胡长顺,侯仲杰.2004.冻土路基温度场室内足尺模型试验.长安大学学报(自然科学版),24(1):30~33.
毛雪松,王秉纲,胡长顺,等.2006a.冻土路基水热迁移问题的理论模型及数值模拟.中外公路, 26(1):23~26.
毛雪松,李宁,王秉纲,等.2006b.多年冻土路基水-热-力耦合理论模型及数值模拟.长安大学学报(自然科学版),26(4):16~19.
毛雪松,王秉纲,胡长顺.2006c.多年冻土路基水分迁移热力学性能分析.路基工程,4:1~4.
苗天德,朱久江,丁伯阳.1995.对饱和多孔介质波动问题中本构关系的探讨.力学学报,27(5):536~543.
潘守文.1989小气候考察的理论基础及其应用.北京:气象出版社.
秦耀东.1998.土壤空间变异研究中的半方差问题.农业工程学报,(4):42~47.
邱国庆,王雅卿.1990.兰州地区黄土的冻结温度.冰川冻土,12(2):105~115.
尚松浩.1997.越冬期土壤冻结融化过程中水热迁移规律及其应用研究.清华大学博士学位论文.
尚松浩,雷志栋,杨诗秀.1997a.冻结条件下土壤水热耦合迁移数值模拟的改进.清华大学学报(自然科学版),37(8):62~64.
尚松浩,雷志栋,杨诗秀.1997b.冬季田间水热状况的数值模拟.灌溉排水学报,16(3):12~17.
尚松浩,雷志栋,杨诗秀.1997c.冬灌对越冬期土壤水分状况影响的数值模拟.农业工程学报,13(3):65~70.
尚松浩,雷志栋,杨诗秀,等.1999.冻融期地下水位变化情况下土壤水分运动的初步研究.农业工程学报,15(2):64~68.
尚松浩,毛晓敏,雷志栋,等.2009.土壤水分动态模拟模型及其应用.北京:科学出版社.
施成熙,粟宗嵩.1984.农业水文学.北京:农业出版社.
苏联科学院西伯利亚分院冻土研究所.1988.普通冻土学.北京:科学出版社.
孙菽芬,李敬阳.2002.用于气候研究的雪盖模型参数化方案敏感性研究.大气科学,26(4):558~576.
孙菽芬.2005.陆面过程的物理、生化机理和参数化模型.北京:气象出版社, 163~176.
孙英君,王劲峰,柏延臣.2004.地统计学方法进展研究.地球科学进展,19(2):268~274.
孙志忠.2005.偏微分方程数值解法.北京:科学出版社.
王仁铎,胡光道.1987.线性地质统计学.北京:地质出版社.
王铁行,胡长顺,王秉纲,等.2000.考虑多种因素的冻土路基温度场有限元方法.中国公路学报,2000,13(4):8~11.
王铁行,胡长顺.2001.冻土路基水分迁移数值模型.中国公路学报,14(4):5~8.
王铁行,胡长顺.2003.多年冻土地区路基温度场和水分迁移场耦合问题研究.土木工程学报,36(12):93~97.
王政权.1999.地统计学及在生态学中的应用.北京:科学出版社.
夏坤.2008.BATS-SAST模式对森林和草地两种下垫面积雪过程的数值模拟.中国气象科学研究院硕士学位论文,3~4.
邢述彦,郑秀清.2003.雪层中水热耦合迁移模型的建立.太原理工大学学报, 34(6):647~650.
徐吉炎,Webster R.1983.土壤调查数据地域统计的最佳估值研究——彰武县土壤表层土全氮量的半方差图和块状Kriging估值.土壤学报,20(4):419~430.
徐学祖,邓友生.1991.冻土中水分迁移的试验研究.北京:科学出版社.
徐学祖,王家澄,张立新.2001.冻土物理学.北京:科学出版社.
杨金凤,郑秀清,孙明.2006.地表覆盖对季节性冻融土壤温度影响研究.太原理工大学学报,37(3):358~360.
杨劲松,姚荣江.2007.黄河三角洲地区土壤水盐空间变异特征研究.地理科学,27(3):348~353.
杨诗秀,雷志栋,朱强,等.1988.土壤冻结条件下水热耦合运移的数值模拟.清华大学学报(自然科学版),28(s1):112~120.
叶佰生,陈肖柏.1990.非饱和土冻结时水热耦合迁移的数值模拟.第四届全国冻土学术会议论文选集.北京:科学出版社,77~79.
原国红.2006.季节冻土水分迁移的机理及数值模拟.吉林大学博士学位论文.
张仁铎.2005.空间变异理论及应用.北京:科学出版社.
郑秀清,樊贵盛.2000.土壤含水率对季节性冻土入渗特性影响的试验研究.农业工程学报,16(6):52~55.
郑秀清,樊贵盛.2001.冻融土壤水热迁移数值模型的建立及仿真分析.系统仿真学报,13(3):308~311.
郑秀清,樊贵盛,邢述彦.2002.水分在季节性非饱和冻融土壤中的运动.北京:地质出版社.
中国科学院兰州冰川冻土研究所.1989.冻土的温度水分应力及其相互作用.兰州:兰州大学出版社.
中央气象局.1955.气象文丛第一号:霜冻、冻土、积雪.财政经济出版社,88.
周石硚,中尾正义,桥本重将,等.2001.水在雪中下渗的数学模拟.水利学报,(1):6~10.
周幼吾,郭东信,邱国庆,等.2000.中国冻土.北京:科学出版社.
Akan A O.1984.Simulation of runoff from snow-covered hillslopes.Water Resources Research,20:707~713.
Anderson E A.1976.A point energy and mass balance model of a snow cover.NOAA Technical Report NWS,19:150.
Bader H P.1992.Modeling temperature distribution,energy and mass flow in a phase-changing snowpack. I: Model and case studies.Cold Reg.Sci.Technol.,20:157~181.
Ball D F,Williams W M.1968.Variability of soil chemical properties in two uncultivated brown earth.J. Soil Sci.,19:379~391.
Bloomsberg G L and Wang S J.1969.Effect of moisture content on permeability of frozen soils.Proc. American Geophysical Union Pacific Northwest Regional Meeting.Portland, OR. Oct., 16~17.
Bristow K L.1983.Simulation of heat and moisture transfer through a surface residue-soil system.Washington State University,Thesis (Ph.D.).
Bristow K L,Campbell G S,Saxton K E.1985.An equation for separating daily solar radiation irradiation into direct and diffuse components.Agric. and For. Meteor,35:123~131.
Brum E,Martin E,Simon V,et al.1989.An energy and mass balance model of snow cover suitable for operational avalanche forecasting.J. Glacial.,35:333~342.
Cambardella C A,Moorman T B,Novak J M, et al.1994.Field-scale variability of soil properties in central Iowa soils.Soil Sci. Soc. Am. J.,58:1501~1511.
Camillo P J,Gurney R J.1986.A resistence parameter for bare soil evaporation models.Soil Science,141(2):95~105.
Campbell G S.1974.A simple method for determining unsaturated conductivity from moisture retention data.Soil Science,117:311~314.
Cressie N A C.1991.Statistics for spatial data.New York:John Wiley&Sons.
Dai Y J,Xue F,Zeng Q C.1998. A land surface model (IAP94) for climate studies part I: implementation and preliminary results of coupled model with IAP GCM. Advances in Atmospheric Sciences,15(1):47~62.
Dai Y J,Zeng Q C.1997.A land surface model (IAP94) for climate studies part I: formulation and validation in off-line experiments.Advances in Atmospheric Sciences,14(4):433~455.
Dirksen C,Miller R D.1966.Closed-system freezing of unsaturated soil.Soil Sci. Soc. Am. Proc.,30:168~173.
Douville H,Mahfouf J F.1995a.A new snow parameterization for the Météo-France climate model. I: Validation in standalone experiments.Climate Dynamics,12(1):21~35.
Douville H,Mahfouf J F.1995b.A new snow parameterization for the Meteo-France climate model. II. Validation in a 3-D GCM experiments.Climate Dynamics,12(1):37~52.
Fernandez A.1998.An energy balance model of seasonal snow evolution.Phys. Chem. Earth,23(5):661~666.
Flerchinger G N,Cooley K R,Deng Y.1994.Impact of spatially and temporally varying snowmelt on subsurface flow in a mountainous watershed.Hydrological Sciences Journal, 39(5):507~533.
Flerchinger G N,Saxton K E.1989a.Simultaneous heat and water model of a freezing snow-residue-soil system I. theory and development.Transactions of the ASAE TAAEAJ,32(2):565~572.
Flerchinger G N,Saxton K E.1989b.Simultaneous heat and water model of freezing snow-residue-soil system II. field verification.Transactions of the ASAE TAAEAJ,32(2):573~578.
Fok Y S.1970.One-dimentional infiltration into layered soil. Jour. of Irrig. and Drain. Div.,ASCE,90(2):121~129.
Fox J D.1992.Incorporating freeze-thaw calculations into a water balance model.Water Resources Research,28(9):2229~2244.
Fremond M,Mikkola M.1991.Thermo-mechanical of freezing soil.Proceedings of the sixth International Symposium on Ground Freezing.Rottendam:Balkema,17~24.
Hanks R J,Ashcroft G L.1984.应用土壤物理学-土壤水和温度的应用.杨诗秀等译.北京:水利电力出版社.
Harlan R L.1973.Analysis of coupled heat-flow transport in partially frozen soil.Water Resources Research,9(5):1314~1323.
Hillel D.1997.Computer Simulation of Soil Water Dynamics. Ottawa, Canada: International Development Research Center.
Hoekstra P.1966.Moisture movement in soil under temperature gradient with the cold-side temperature below freezing.Water Resources Research,2(2):241~250.
Humphrey J H,Skau C M.1974.Variation of snowpack density and structure with environmental conditions.Center of Water Resources Research, Desert Res. Instit. Univ. of Nevada,15.
Idso S B,Jackson R D.1969.Thermal radiation from the atmosphere.Journal of Geophysical Research,74(23):5397~5403.
Issaks E H, Srivastava R M.1989.An introduction to applied geostatistics.New York:Oxford Univ. Press.
Jame Y,Nornm D I.1980.Heat and mass transfer in freezing unsaturated porous medium.Water Resources Research,16(4):811~819.
Jordan R A.1991.One-dimensional temperature model for a snow cover. CRREL, Special Report,1b:1~48.
Journel A G, Huijbregts C J.1978.Mining geostatistics.London:Academic Press.
Kane D L,Hinkel K M,Goering D J, et al.2001.Non-conductive heat transfer associated with frozen soils.Global and Planetary change,29:275~292.
Kane D L,Hinzman L D,Zarling J P.1991.Thermal response of the active layer to climatic warming in a permafrost environment.Cold Regions Science and Technology,19(2):111~122.
Kennedy J,Eberhart R C.1995.Particle swarm optimization.Proceedings of IEEE International Conference on Neural Networks.Piscataway, NJ:IEEE Press,1942-1948
Konrad J M,Morgenstern N R.1982.Prediction of frost heave in the laboratory during transientfreezing.Canadian Geotechnical Journal,19:250~259.
Kung S K J,Steenhuis T S.1986.Heat and moisture transfer in a partly frozen nonheaving soil.Soil Science Society of America Journal,50:1114~1122.
Langham E J.1976.Physics and properties of snowcover. In Handbook of Snow: principle, process, management.Gray D M,Male D H (Eds).Ontraio Canada:Pergamon Press,275~337.
Lehnings M,Bartlet P,Brown B.1998.Operational use of a snowpack model for the avalanche warning service in Switzerland: Model development and first development and first experiences.Nor. Geotech.Inst.,203:169~174.
Li N,Chen B,Chen F X,et al.2000.The coupled heat-moisture-mechanic model of the frozen soil.Cold Regions Science and Technology,31:199~205.
List R J.1951.Smithsonian Meteorological Tables.Washington D.C.:Smithsonian Institute Press,527.
Loth B,Graf H F,Oberhuber J M.1993.Snow cover model for global climate simulations.Journal of Geophysical Research,98(D6):10451~10464.
Lynch-Stieglitz M.1994.The development and validation of a simple snow model for the GISS GCM.J. Clim.,7:1842~1855.
Matheron G.1963.Principles of geostatistics.Economic Geology,58(8):1246~1266.
Matheron G.1971.The Theory of Regionalized Variables and Its Applications.Les Cahiers du Centre de Morphologie Mathematique de Fontainebleau. Ecole Nationale Superieure des Mines de Paris.
Mualem Y.1976.A new model for predicting the hydraulic conductivity of unsaturated porous media.Water Resources Research,12:513~522.
Nakano Y.1987.Transport of water in frozen soil:Ⅵ. Effect of temperature.Advances in Water Resources,10:44~50.
Nakano Y,Tice A R, Oliphant J.1984a.Transport of water in frozen soil:Ⅲ. Experiment on the effects of ice content.Advances in Water Resources,7:28~34.
Nakano Y,Tice A R, Oliphant J.1984b.Transport of water in frozen soil:Ⅳ. Analysis of experimental results on the effects of ice content.Advances in Water Resources,7:58~66.
Nixon J F.1975.The role of convective heat transport in the thawing of frozen soils.Canadian Geotechnical Journal,12:425~429.
O’Neill A D J,Gray D M.1972.Solar radiation penetration through snow.In The Role of Snow and Ice in Hydrology.Proceeding of the Banff Symposia,227~241.
Outcalt S I,Goodwin C,Weller G,Brown J.1975.A digital computer simulation of the annual snow and soil thermal regimes at Barrow, Alaska.Cold Region Research and Engineering Laboratory Research Report,331.
Philip J R,de Vries D A.1957. Moisture movement in porous materials under temperature gradients.Transactions American Geophysical Union,32(2):222~232.
Pitman A J,Yang Z L,Cogley J G,et al.1991.Description of bare essentials of surface transferfor the Bureau of Meteorology Research Centre AGCM.BMRC Res.Rep.,32:117.
Rosenberg N J.1974.The Biological Environment.New York:John Wiley and Sons,495.
Sepaskhah A R,Boersma L.1979.Thermal conductivity of soils as a function temperature and water content.Soil Science Society of America Journal,43:439~444.
Shoop S A and Bigl S R.1997.Moisture migration during freeze and thaw of unsaturated soils: modeling and large scale experiments.Cold Regions Science and Technology,25(1):33~45.
Slater A G,Pitman A J,Desborough C E.1998.The validation of snow parameterization designed for use in General Circulation Model.Inter. J. Clim.,18:595~617.
Smets P,Kennes R.1994.The transferable belief model.Artificial Intelligence.
Sokratov S A,Maeno N.1997.Heat and mass transport in snow under a temperature gradient.Proc. of the 3rd International Conference on Snow Engineering,(3):49~54.
Sud Y C,Mocko D M.1999.New snow-physics to complement SSiB. Part 1: Design and evaluation with ISLSCP initiative 1 datasets.J. Meteor. Soc. Japan,77(1B):335~348.
Sun S F,Jin J M,Wu G X.1999.A snow model design for coupling with GCM.Acta Meteorological Sinica,57(3):293~300.
Sun S F,Jin J M,Xue Y K.1999.A simple snow-atmosphere-soil transfer model.J. Geophys. Res.,104(D16):19587~19598.
Sun S F,Li J Y.2001.A sensitivity study on parameterization scheme of snow internal and interfacial processes in snow model.Advances in Atmospheric Sciences,18(5):910~928.
Talyor G S,Luthin J N.1978.A model for coupled heat and moisture transfer during soil freening.Canadian Geotechnical Journal,18:548~555.
van Genuchten M T.1980.A closed-form equation for predicting hydraulic conductivity of unsaturated soils.Soil Science Society of America Journal,44:892~898.
Verseghy D L.1991.Class a Canadian land surface scheme for GCMS. I. Soil model.Inter. J. Clim.,11(2):111~133.
Vieira S R,Hatfield J L,Nielsen D R et al.1983.Geostatistical theory and application to variability of some agronomical properties.Hilgardia,51:1~75.
Voller V R.1990.Fixed grid techniques for phase change problems: A review.International Journal for Numerical Methods in Engineering,30:875~898.
Wang T H, Hu C S,Li N.2005.Simulation method for calculation stressand deformation of highway embankment on frozen soil area.Cold Regions and Technology, 42:89~95.
Warrach K,Mengelkamp H T,Raschke E.2001.Treatment of frozen soil and snow cover in the land surface model SEWAB.Theoretical and Applied Climatology,69:23~37.
Webster R.1985.Quantitative spatial analysis of soil in the field.Advanced in Soil Science,3:1~71.
Yang Z L,Dickinson R E,Robock A,et al.1997.Validation of the snow submodel of the Biosphere-Atmosphere Transfer Scheme with Russian snow cover and meteorology observation data.J.Clim.,10:353~373.
Zhao Litong,Gray D M et al.1997.Numerical analysis of simultaneous heat and mass transfer during infiltration into frozen ground. Journal of Hydrology,200:345~363.