冻土冰/水含量同腔共射原位测定方法创新与冻融模型检验
|
摘要
在农业生产活动中,由于季节冻土影响着越冬期表层士壤水的入渗性质以及春季伊始农田耕作的最佳时间与效果,人们对农田季节冻土周期变化规律的研究愈加关注。目前冻土相关的很多基础性研究结论仍然是在实验室内借助于人工模拟环境条件取得的,这是因为农田环境下准确、可靠观测冻土关键变量——未冻水含量与含冰量的传感方法与技术相对落后,同时也制约了各种土壤冻融理论模型的适用性检验与修正。为此,本文以介电理论与中子核物理理论为基础,结合创新性的测量方法与试验设计,首先在同腔共射原位测定冻土冰/水含量关键技术难题上取得突破,然后依据土壤冻结特征曲线与土壤水分特征曲线的相似性,通过原位测定土壤冻结特征曲线来估算土壤水分特征曲线,进而估算导水参数。在上述研究成果的基础上对土壤冻融模型进行了检验,通过分析模型预测值与实测值的差异,评价了冻融解析模型的适用性。本文研究工作依托于国家自然科学基金委与德国科学基金会国际合作组项目“中德精细农业中的先进传感科学与技术合作小组”(批准号：GZ494)、国家自然科学基金项目“基于土壤冻融信息获取新方法的复杂农田冻融模型检验与参数解译”(批准号：31171458)与教育部博士点基金“农田季节性冻融过程冰、水复合测量方法与冻融模型检验”(批准号：20110008110046),主要研究内容和结论包括：
1.根据土壤冻融与干湿过程的介电等价性原理,综合考虑冻土介电混合模型以及液态水的介电温度效应,实现原位测定冻土未冻水含量。此外,中子散射法测定的是土壤中氢原子含量,试验结果也证实了前人给出的中子散射仪在冻土中的测量值反映了冰与水总量的结论。
2.试验结果证实了介电管式传感器产生的甚高频电磁辐射与中子散射仪的中子辐射均可穿透PVC管。依据该结果将两种传感器的探头设计成相同尺寸,实现了两种传感器同腔共射原位测定冰/水含量。冻融法测定介电管式传感器的辐射影响半径的试验结果表明该传感器辐射半径(5～8cm)略小于中子散射仪的辐射半径(10～20cm)。
3.在农田环境下冻土未冻水含量的原位测定结果表明：由本文研制的传感器测定的未冻水含量变化不仅真实反映了越冬期土壤冻结锋/融化锋的动态变化,同时为原位测定土壤冻结特征曲线提供了一种新的传感技术。它的技术优势还体现在使用单一传感探头可测定多个土壤剖面,消除了多传感器之间的互换误差。将该方法原位估算的土壤水分特征曲线与标准的压力板方法获得的土壤水分特征曲线相比较,其相似性与差异(R2=0.837,RMSE=131kPa)可满足估算土壤导水相关参数的要求。
4.农田环境下同腔共射法在未冻土壤中的交叉检验结果表明：两种仪器具有良好的互换性(R2>0.95,RMSE<0.02cm3cm-3)。在冻土中的试验结果表明：该方法能够原位测定冻土未冻水含量和总含水量,通过简单计算进而得到冻土含冰量。由于土壤冻融过程伴随着水分迁移,同腔共射法原位测定冻土冰／水含量显著提高了测量的准确性。获取的冻融信息不仅可为农田越冬期管理(尤其对确定冬灌和春耕时间)提供技术支持,且适用于农田尺度土壤剖面水分的常年监测。
5.在单一未冻水含量测定和冰／水含量均测定两种情况下分别对土壤冻融模型的适用性进行了检验,农田测量结果与模型预测结果的比较表明：冻土冰／水含量的同腔共射原位测定能够直接得到未冻土和冻土水分迁移的相关参数,较单一未冻水测定而言有效提高模型的预测精度。
The annual freeze-thaw cycle of soil has attracted increasing attention because it can significantly impacts agricultural services in cold regions, such as water infiltration and runoff over winter and optimal time for tillage in early spring. Many previous studies have only concerned the fundamental of freeze-thaw cycle under laboratory condition because of the difficulty for the in situ measurements of liquid soil water content (LSWC) and soil ice content (SIC) in field, and the latter is more challenging. The shortage of field-based data resulted in the limitation of the wide applicability of soil freeze-thaw models developed. For this, a co-tube-radiation method was innovatively proposed for in situ determination of LSWC and SIC. The soil moisture characteristic curve (SMCC) was deduced from soil freezing characteristic curve (SFCC) determined in situ based on the similarity between the two curves, and the parameters in SMCC were estimated as well. Based on this, a freeze-thaw model was validated and evaluated by the comparison between the model-simulated data and the measured data. This study was financially supported by the Chinese-German Center for Scientific Promotion under Project No. GZ494, National Natural Science Foundation of China under Project No.31171458and the Doctoral Promotion Fund of the Educational Ministry of China under Project No.20110008110046. The major research works and conclusions of this study can be briefly summarized as follows:
1. Based on the equivalence of dielectric properties between soil drying-wetting and freezing-thawing processes, dielectric mixing model and temperature effect on permittivity of liquid water in frozen soil, the in-situ determination of LSWC is feasible. Moreover, the neutron probe is proportional to amount of hydrogen in soil, which is independent of the status whether the soil is frozen. Thus, the total soil water content (TSWC) can be measured either in frozen or unfrozen soil.
2. A co-tube-radiation method was innovatively proposed. Theoretical analysis and experimental results indicate that both the electromagnetic radiation from tube-based dielectric probe and neutron radiation of neutron moisture meter can penetrate through the PVC tube. By uniting the probe size of both instruments, it is possible that the two instruments can be used in a common access PVC tube. A method was used for determination of radius of sensitivity (ROS) of dielectric tube sensor based on the equivalence of dielectric properties between soil drying-wetting and freezing-thawing processes. According to the experiment results, the ROS of dielectric tube sensor is5-8cm, which is close to the ROS of neutron moisture meter (10-20cm).
3. The field experiment showed that the LSWC was determined in-situ. The variations of LSWC can reflect the dynamics of freezing/thawing front over winter. Based on this, the soil freezing characteristic curve (SFCC) was also determined in-situ. Moreovers, the soil moisture characteristic curve (SMCC) can be deduced from SFCC based on the similarity between them. The parameters of SMCC can be estimated through SFCC, which were compared with those determined from pressure plate method (reference). The coefficient of determination (R2=0.837) and RMSE (131kPa) showed a good agreement between the characteristic curves from the two methods.
4. The cross-check results showed that both instruments had good interconvertibility (R2>0.95) with considerably low error (RMSE<0.02cm3cm-3). The co-tube-radiation experiment in the field indicated that the proposed method can determine LSWC and TSWC, and thus SIC. The measuring accuracy was significantly improved even accompanying with water migration during freezing-thawing process. This method can provide technical support to field management for winter irrigation and tillagement in spring and can be used to monitor the soil water dynamics throughout the year.
5. The PDE model was validated by two groups of data. One group only measured LSWC and the other measured both LSWC and SIC. The filed experiment showed that the latter group can yield higher accuracy compared with the former group and the influences from the ignored items in PDE model was analyzed. Besides, it was proved from the experiment that the snowcover is very effective at insulating the soil, decreasing the frost penetrating velocity and therefore increasing moisture migration to the freezing front.
1.根据土壤冻融与干湿过程的介电等价性原理,综合考虑冻土介电混合模型以及液态水的介电温度效应,实现原位测定冻土未冻水含量。此外,中子散射法测定的是土壤中氢原子含量,试验结果也证实了前人给出的中子散射仪在冻土中的测量值反映了冰与水总量的结论。
2.试验结果证实了介电管式传感器产生的甚高频电磁辐射与中子散射仪的中子辐射均可穿透PVC管。依据该结果将两种传感器的探头设计成相同尺寸,实现了两种传感器同腔共射原位测定冰/水含量。冻融法测定介电管式传感器的辐射影响半径的试验结果表明该传感器辐射半径(5～8cm)略小于中子散射仪的辐射半径(10～20cm)。
3.在农田环境下冻土未冻水含量的原位测定结果表明：由本文研制的传感器测定的未冻水含量变化不仅真实反映了越冬期土壤冻结锋/融化锋的动态变化,同时为原位测定土壤冻结特征曲线提供了一种新的传感技术。它的技术优势还体现在使用单一传感探头可测定多个土壤剖面,消除了多传感器之间的互换误差。将该方法原位估算的土壤水分特征曲线与标准的压力板方法获得的土壤水分特征曲线相比较,其相似性与差异(R2=0.837,RMSE=131kPa)可满足估算土壤导水相关参数的要求。
4.农田环境下同腔共射法在未冻土壤中的交叉检验结果表明：两种仪器具有良好的互换性(R2>0.95,RMSE<0.02cm3cm-3)。在冻土中的试验结果表明：该方法能够原位测定冻土未冻水含量和总含水量,通过简单计算进而得到冻土含冰量。由于土壤冻融过程伴随着水分迁移,同腔共射法原位测定冻土冰／水含量显著提高了测量的准确性。获取的冻融信息不仅可为农田越冬期管理(尤其对确定冬灌和春耕时间)提供技术支持,且适用于农田尺度土壤剖面水分的常年监测。
5.在单一未冻水含量测定和冰／水含量均测定两种情况下分别对土壤冻融模型的适用性进行了检验,农田测量结果与模型预测结果的比较表明：冻土冰／水含量的同腔共射原位测定能够直接得到未冻土和冻土水分迁移的相关参数,较单一未冻水测定而言有效提高模型的预测精度。
The annual freeze-thaw cycle of soil has attracted increasing attention because it can significantly impacts agricultural services in cold regions, such as water infiltration and runoff over winter and optimal time for tillage in early spring. Many previous studies have only concerned the fundamental of freeze-thaw cycle under laboratory condition because of the difficulty for the in situ measurements of liquid soil water content (LSWC) and soil ice content (SIC) in field, and the latter is more challenging. The shortage of field-based data resulted in the limitation of the wide applicability of soil freeze-thaw models developed. For this, a co-tube-radiation method was innovatively proposed for in situ determination of LSWC and SIC. The soil moisture characteristic curve (SMCC) was deduced from soil freezing characteristic curve (SFCC) determined in situ based on the similarity between the two curves, and the parameters in SMCC were estimated as well. Based on this, a freeze-thaw model was validated and evaluated by the comparison between the model-simulated data and the measured data. This study was financially supported by the Chinese-German Center for Scientific Promotion under Project No. GZ494, National Natural Science Foundation of China under Project No.31171458and the Doctoral Promotion Fund of the Educational Ministry of China under Project No.20110008110046. The major research works and conclusions of this study can be briefly summarized as follows:
1. Based on the equivalence of dielectric properties between soil drying-wetting and freezing-thawing processes, dielectric mixing model and temperature effect on permittivity of liquid water in frozen soil, the in-situ determination of LSWC is feasible. Moreover, the neutron probe is proportional to amount of hydrogen in soil, which is independent of the status whether the soil is frozen. Thus, the total soil water content (TSWC) can be measured either in frozen or unfrozen soil.
2. A co-tube-radiation method was innovatively proposed. Theoretical analysis and experimental results indicate that both the electromagnetic radiation from tube-based dielectric probe and neutron radiation of neutron moisture meter can penetrate through the PVC tube. By uniting the probe size of both instruments, it is possible that the two instruments can be used in a common access PVC tube. A method was used for determination of radius of sensitivity (ROS) of dielectric tube sensor based on the equivalence of dielectric properties between soil drying-wetting and freezing-thawing processes. According to the experiment results, the ROS of dielectric tube sensor is5-8cm, which is close to the ROS of neutron moisture meter (10-20cm).
3. The field experiment showed that the LSWC was determined in-situ. The variations of LSWC can reflect the dynamics of freezing/thawing front over winter. Based on this, the soil freezing characteristic curve (SFCC) was also determined in-situ. Moreovers, the soil moisture characteristic curve (SMCC) can be deduced from SFCC based on the similarity between them. The parameters of SMCC can be estimated through SFCC, which were compared with those determined from pressure plate method (reference). The coefficient of determination (R2=0.837) and RMSE (131kPa) showed a good agreement between the characteristic curves from the two methods.
4. The cross-check results showed that both instruments had good interconvertibility (R2>0.95) with considerably low error (RMSE<0.02cm3cm-3). The co-tube-radiation experiment in the field indicated that the proposed method can determine LSWC and TSWC, and thus SIC. The measuring accuracy was significantly improved even accompanying with water migration during freezing-thawing process. This method can provide technical support to field management for winter irrigation and tillagement in spring and can be used to monitor the soil water dynamics throughout the year.
5. The PDE model was validated by two groups of data. One group only measured LSWC and the other measured both LSWC and SIC. The filed experiment showed that the latter group can yield higher accuracy compared with the former group and the influences from the ignored items in PDE model was analyzed. Besides, it was proved from the experiment that the snowcover is very effective at insulating the soil, decreasing the frost penetrating velocity and therefore increasing moisture migration to the freezing front.
引文
Anderson, D. M., Tice, A. R.,1973. The unfrozen interfacial phase in frozen soil water systems. Ecological Studies 4,107-125.
Azmatch, T. F., Sego, D. C., Arenson, L. U., Biggar, K.W.,2012. Using soil freezing characteristic curve to estimate the hydraulic conductivity function of partially frozen soils. Cold Reg. Sci. Technol.83-84: 103-109.
Baker, J. M.,2006.'Water Relations in Frozen Soil', Encyclopedia of Soil Science,1:1,1858-1859.
Baker, T. H. W., Davis, J. L., Hayhoe, H. N., Topp, G C.,1982. Locating the frozen-unfrozen interface in soils using time-domain reflectometry. Can. Geotech. J.,19,511-517.
Baker J. M., Lascano, R. J.,1989. The spatial sensitivity of time domain reflectometry. Soil Science 147(5),378-384.
Ball, J. A. R.,2002. Characteristic impedance of unbalanced TDR probes. IEEE Trans. Instrum. Meas., 51(3),532-536.
Birchak, J. R., Gardner, C. G, Hipp, J. E., Victor, M.,1974. High dielectric constant microwave probes for sensing soil moisture. Proceedings of the IEEE 62,93-98.
Bittelli, M., Flury, M., Campbell, G.S.,2003. A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media. Water Resour. Res.39:1041.
Bittelli, M., Flury, M., Roth, K.,2004. Use of dielectric spectroscopy to estimate ice content in frozen porous media. Water Resour. Res.40(4):W04212. doi:10.1029/2003 WR002343.
Bronfenbrener, L., Korin, E.,2002. Experimental studies of water crystallization in porous media. Chemical Engineering and Processing 41,357-363.
Campbell, G. S.1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Sci.117:311-314.
Cary, J. W., Mayland, H. F.,1972. Salt and water movement in unsaturated frozen soil, Soil Sci. Soc. Am. J.,36,549-555.
Dean, T. J., Bell, J. P., Baty, A. J. B.,1987. Soil moisture measurement by an improved capacitance technique, Part I. Sensor design and performance. Journal of Hydrology 93,67-78.
Decker, M., Zeng, X.,2006. An empirical formulation of soil ice fraction based on in situ observations. Geophysical Research letters,33, L05402, doi:10.1029/2005GL024914.
De Vries, D. A.,1963. Thermal properties of soils. In Physics of plant environment. W. R. van Wijk, ed. North-Holland, Amsterdam, the Netherlands.
Dirksen, C., Miller, R. D.,1966. Closed-system freezing of unsaturated soil, Soil Sci. Soc. Amer. Proa, 30,168-173.
Evett, S. R.,2003. Soil water measurements by neutron thermalization. In Encyclopedia of Water Science, eds. B.A. Stewart and T.A. Howell,889-893. New York, NY:Marcel Dekker, Inc.
Evett, S. R., Schwartz, R. C., Casanova, J. J., Heng, L. K.,2012. Review:Soil water sensing for water balance ET and WUE. Agric. Water Manage.104:1-9.
Evett, S. R., Schwartz, R. C., Tolk, J. A., Howell, T. A.,2009. Soil profile water content determination: Spatotemporal variability of electromagnetic and neutron probe sensors in access tubes. Vadose Zone J. 8:926-941.
Flerchinger, G. N.,1991. Sensitivity of soil freezing simulated by the SHAW model. T ASAE,34(6), 2381-2389.
Flerchinger, G. N., Saxton, K. E.,1989a. Simultaneous heat and water model of a freezing snow-residue-soil system. Part Ⅰ. Theory and development. Trans. Am. Soc. Agric. Eng.,32,565-571.
Flerchinger, G. N., Saxton, K. E.,1989b. Simultaneous heat and water model of a freezing snow-residue-soil system. Part Ⅱ. Field verification. Trans. Am. Soc. Agric. Eng.,32,573-578.
Flerchinger, G.N., M.S. Seyfried, and S. P. Hardegree.2006. Using soil freezing characteristics to model multi-season soil water dynamics. Vadose Zone J.5:1143-1153.
Fuchs, M., Campbell, G. S., Papendick, R. I.,1978. An analysis of sensible and latent heat flow in a partially frozen unsaturated soil, Soil Sci. Soc. Am. J.,42,379-385.
Gaskin, G. C., Miller, J. D.,1996. Measurement of soil water content using a simplified impedance measuring technique. J. Agric. Engang. Res.63:153-160.
Guymon, G.L., Luthin, J.N.,1974. A coupled heat and moisture transport model for arctic soils. Water Resour. Res.,10,995-1001.
Hansson, K., Simunek, J., Mizoguchi, M., Lundin, L. C., van Genuchten M. T.,2004. Water flow and heat transport in frozen soil:Numerical solution and freeze/thaw applications, Vadose Zone J.,3,693- 704.
Harlan, R.L.,1973. Analysis of coupled heat-fluid transport in partially frozen soil, Water Resour. Res., 9,1314-1323.
Hayhoe, H. N., Bailey, W. G.,1985. Monitoring changes in total and unfrozen water content in seasonally frozen soil using time domain reflectometry and neutron moderation techniques. Water Resour. Res.21,1077-1084.
Hayhoe, H. N., Topp, G. C.,1983. Measurement of soil water contents and frozen soil depth during a thaw using time domain reflectometry. Atmos.-Ocean,21 (3):299-311.
Jame, Y. W., Norum, D. I.,1980. Heat and mass transfer in a freezing unsaturated porous medium. Water Resour. Res.,16,811-819.
Jansson, P. E., Karlberg, L.,2001. Coupled heat and mass transfer model for soil-plant-atmosphere systems, TRITAAMI Rep.3087, R. Inst. of Technol., Stockholm.
Jordan, R. A.,1991. One dimensional temperature model for a snow cover:Technical Documentation for SNTHERM.89, Spec. Rep.91-16, Cold Reg. Res. and Eng. Lab., U.S. Army Corps of Eng., Hanover, N.H.
Kahimba, F. C., Sri Ranjan, R.,2007. Soil temperature correction of field TDR readings obtained under near freezing conditions. Canadian Biosystems Engineering 49,19-26.
Kelleners, T. J., Norton, J.B.,2012. Determining water retention in seasonally frozen soils using Hydra impedance sensors. Soil Sci. Soc. Am. J.76:36-50.
Kimball, B. A., Jackson, R. D., Reginato, R. J., Nakayama, F. S., Idso, S. B.,1976. Comparison of Field-measured and Calculated Soil-heat Fluxes. Soil Science Society of America Journal 40(1),18-25.
Knight, J. H.,1992. Sensitivity of time domain reflectometry measurements to lateral variations in soil water content. Water resources research 28,2345-2352.
Knight, J. H., Ferr6, P. A., Rudolph, D. L., Kachanoski, R. G.,1997. A numerical analysis of the effects of coatings and gaps upon relative dielectric permittivity measurement with time domain reflectometry. Water Resour. Res.33:1455-1460.
Koopmans, R. W. R., Miller, R. D.,1966. Soil freezing and soil water characteristic curves. Soil Sci. Soc. Am. Proc.30,680-685.
Kozlowski, T.,2003a. A comprehensive method of determining the soil unfrozen water curves:1 Application of the term of convolution. Cold Regions Science and Technology 36,71-79.
Kozlowski, T.,2003b. A comprehensive method of determining the soil unfrozen water curves:2. Stages of the phase change process in frozen soil-water system. Cold Regions Science and Technology 36,81-92.
Li, Q., Sun, S.,2008. Development of the universal and simplified soil model coupling heat and water transport. Science in China Series D:Earth Sciences 51(1),88-102.
Li, Q., Sun, S., Xue, Y.,2010. Analyses and development of a hierarchy of frozen soil models for cold region study. Journal of Geophysical Research 115, D03107.
Liu, G., Si, B. C.,2011. Soil ice content measurement using a heat pulse probe method. Can. J. Soil Sci. 91,235-246.
Lovell, C. W.,1957. Temperature effects on phase composition and strength of Partially-frozen soil. Highway Research Board Bulletin 168,74-95.
Luo, W., Skaggs, R. W. Chescheir, G. M.2000. DRAINMOD modifications fro cold conditions. Transactions of the ASAE 43(6),1569-1582.
Ma, D., Sun, Y., Wang, M., Gao, Y.,2006. three-dimensional numerical modeling of a four-pin probe for soil water content. Aust. J. Soil Res.44:183-189.
Nissen, H. H., Moldrup, P., Olesen, T., Jensen, O. K..,2001. Time domain reflectometry sensitivity to lateral variations in bulk soil electrical conductivity. Soil Sci. Soc. Am. J.65:1351-1360.
Oliphant, J.L.,1985. A model for dielectric constants of frozen soils. Freezing and thawing of soil-water systems. Am. Sot. Civil Eng. New York, pp.46-57.
Or, D., Wraith, J. M.,1999. Temperature effects on soil bulk dielectric permittivity measured by time domain reflectometry:a physical model. Water Resources Research 35,371-383.
Patterson, D.E., Smith, M.W.,1980. The use of time domain reflectometery for the measurement of unfrozen water content in frozen soils. Cold Regions Science and Technology 3,205-210.
Patterson, D. E., Smith, M. W.,1981. The measurement of unfrozen water content by time domain retlectometry:Results from laboratory tests. Can. Georech. J.18:131-144.
Pepin, S., Livingstone, N. J., Hook, W. R.,1995. Temperature-dependent measurement errors in the time domain reflectometry determinations of soil water. Soil Science Society of America Journal 59 (1), 38-43.
Regalado, C. M.,2003. Time domain reflectometry models as a tool to understand the dielectric response of volcanic soils. Geoderma 117,313-330.
Roth, K. R., Schulin, R., Fluhler, H., Attinger, W.,1990. Calibration of time domain reflectometry for water content measurement using a composite dielectric approach. Water Resour. Res.,26,2267-2273.
Rouse, W. R.,1984. Microclimate of arctic tree line 2. Soil microclimate of Tundra and Forest, Water Resour. Res.,20(1),67-73.
Schwank, M., Green, T. R., Matzler, C., Benedickter, H., Fluhler, H.,2006. Laboratory characterization of a commercial capacitance sensor for estimating permittivity and inferring soil water content. Vadose Zone J.5:1048-1064.
Seyfried, M. S., Murdock, M. D.,1996. Calibration of time domain reflectometry for measurement of liquid water content in frozen soils. Soil Sci.161:87-98.
Seyfried, M. S., Murdock, M. D.,2001. Response of new soil water sensor to variable soil water content and temperature. Soil Science Society of America Journal 65,28-34.
Sheppard, M. I., Kay, B. D., Loch, J. P. G.,1981. The coupled transport of water and heat in freezing soils:A field study. Can. J. Soil Sci.,61,417-429.
Shoop, S. A., Bigl, S. R.,1997. Moisture migration during freeze and thaw of unsaturated soils: Modeling and large scale experiments, Cold Reg. Sci. Technol.,25,33-45.
Skierucha, W.,1999. The influence of temperature on soil dielectric permittivity and the TDR determined soil moisture (in Polish). Acta Agrophysica 22,163-172.
Skierucha, W.,2009. Temperature dependence of time domain reflectometry measured soil dielectric permittivity. Journal of Plant Nutrition and Soil Science 172,186-193.
Smith M. W., Patterson, D. E.,1984. Determining the unfrozen water content in soils by Time-Domain Reflectometry. ATMOSPHERE-OCEAN 22(2),261-263.
Spaans, E. J. A., Baker, J. M.,1995. Examining the use of time domain reflectometry for measuring liquid water content in frozen soil. Water Resour. Res.31,2917-2925.
Spaans, E. J. A., Baker, J. M.,1996. The soil freezing characteristic:Its measurement and similarity to the soil moisture characteristic. Soil Sci. Soc. Am. J.60:13-19.
Stein, J., Kane, D. L.,1983. Monitoring the unfrozen water content of soil and snow using time domain reflectometry. Water Resources Research 19(6),1573-1584.
Sun, Y., Schulze Lammers, P., Ma, D.,2004. Evaluation of a combined penetrometer for simultaneous measurement of penetration resistance and soil water content. J. Plant Nutr. Soil Sci.167:745-751.
Sun, Y., Ma, D., Lin, J., Schulze Lammers, P., Damerow, L.,2005. An improved Frequency domain technique for determining soil water content. Pedosphere.15(6):805-812.
Sun, Y, Ma, D., Schulze Lammers, P., Schmittmann, O., Rose, M.,2006. On-the-go measurement of soil water content and mechanical resistance by a combined horizontal penetrometer. Soil Till. Res.86, 209-217.
Taylor, G. S., Luthin, J. N.,1978. A model for coupled heat and moisture transfer during soil freezing, Can. Geotech. J.,15,548-555.
Tice, A. R., Burrous, C. M., Anderson, D. M.,1978. Determination of unfrozen water in frozen soil by pulsed nuclear magnetic resonance. Proceedings, Third International Conference on Permafrost. Ottawa: National Research Council of Canada, p.149-155.
Tice, A. R., Oliphant, J. L., Nakano, Y., Jenkins, T. F.,1982. Relationship between the ice and unfrozen water phases in frozen soil as determined by pulsed nuclear magnetic resonance and physical desorption data. CRREL Report, vol.82-15. US. Army. Cold Regions Research and Engineering Lab (CRREL).
Tien L. C., Churchill S. W.,1965. Freezing Front Motion and Heat Transfer Outside an Infinite, Isothermal Cylinder. A.1.Ch.E. Journal,11,790-793.
Tinga, W. R., Voss, W. A.G., Blossey, D. F.,1973. Generalized approach to multiphase dielectric mixture theory. J. Appl. Phys.44(9),3897-3902.
Topp, G.C., Davis, J. L., Annan, A.P.,1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour. Res.16:574-582.
Turov, V. V., Leboda, R.,1999. Application of 1H NMR spectroscopy method for determination of characteristics of thin layers of water adsorbed on the surface of dispersed and porous adsorbents. Advances in Colloid and Interface Science 79,173-211.
Van Genuchten, M. Th.,1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J.44:892-898.
Watanabe, K., Mizoguchi, M.,2002. Amount of unfrozen water in frozen porous media saturated with solution. Cold Regions Seience and Technology 34,103-110.
Watanabe, K., Wake, T.,2009. Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR. Cold Regions Science and Technology 59,34-41.
Whalley,W. R., Cope, R. E., Nicholl, C. J.,Whitmore, A. P.,2004. In-field calibration of a dielectric soil moisture meter for use in an access tube. Soil Use and Management 20,203-206.
Willatt, S. T.,1979. Changes in water content in and under frozen soil in Iowa. U.S.A. Geoderma,22, 323-331.
Willis, W. O., Carlson, C. W., Alessi, J. Haas, H. J.,1961. Depth of freezing and spring run-off as related to fall soil-moisture level. Can. J. of Soil Sci.41:115-123.
Yoshikawa, K., Overduin, P. P.,2005. Comparing unfrozen water content measurements of frozen soil using recently developed commercial sensors. Cold Regions Science and Technology 42,250-256.
Zegelin, S. J., White, I., Jenkins, D. R.,1989. Improved field probes for soil water content and electrical conductivity measurement using time domain reflectometry. Water resources research 25,2367-2376.
Zhang, X., Sun, S. F., Xue, Y. K.,2007. Development and testing of a frozen soil parameterization for cold region studies, J. Hydrometeorol.,8,690-701.
Zhao, L., Cray, D. M., Male, D. H.,1997. Numerical analysis of simultaneous heat and water transfer during infiltration into frozen ground, J. Hydrol.,200,345-363.
Zhou, Y., Zhou, G.,2010. Numerical simulation of coupled heat-fluid transport in freezing soils using finite volume method. Heat Mass Transfer 46:989-998.
范寿康,卢春兰,李平辉.微波技术与微波电路.北京：机械工业出版社,2003.
胡和平,杨诗秀,雷志栋,1992.土壤冻结时水热迁移规律的数值模拟.水利学报,7：1-8.
马祖罗夫гп.冻土物理力学性质[M].梁惠生,伍期建译.北京：煤炭工业出版社,1980.
沈振荣,张瑜芳,杨诗秀,等.水资源科学实验与研究[M].北京：中国科学技术出版社,1992.253-256.
尚松浩,雷志栋,杨诗秀,1997.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.
孙宇瑞.土壤探针阻抗计算方法的理论分析与试验研究.土壤学报,2002,39(1)：120-126.
孙宇瑞.非饱和土壤介电特性测量理论与方法研究[D].北京：中国农业大学,2000
徐学祖,邓友生.冻土中水分迁移的试验研究[M].北京：科学出版社,1991
徐学祖,王家澄,张立新,冻土物理学[M].北京：科学出版社,2009
杨诗秀,雷志栋,朱强,等.1998.土壤冻结条件下水热耦合运移的数值模拟.清华大学学报,1988,28(s1)：112-120.
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.
Azmatch, T. F., Sego, D. C., Arenson, L. U., Biggar, K.W.,2012. Using soil freezing characteristic curve to estimate the hydraulic conductivity function of partially frozen soils. Cold Reg. Sci. Technol.83-84: 103-109.
Baker, J. M.,2006.'Water Relations in Frozen Soil', Encyclopedia of Soil Science,1:1,1858-1859.
Baker, T. H. W., Davis, J. L., Hayhoe, H. N., Topp, G C.,1982. Locating the frozen-unfrozen interface in soils using time-domain reflectometry. Can. Geotech. J.,19,511-517.
Baker J. M., Lascano, R. J.,1989. The spatial sensitivity of time domain reflectometry. Soil Science 147(5),378-384.
Ball, J. A. R.,2002. Characteristic impedance of unbalanced TDR probes. IEEE Trans. Instrum. Meas., 51(3),532-536.
Birchak, J. R., Gardner, C. G, Hipp, J. E., Victor, M.,1974. High dielectric constant microwave probes for sensing soil moisture. Proceedings of the IEEE 62,93-98.
Bittelli, M., Flury, M., Campbell, G.S.,2003. A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media. Water Resour. Res.39:1041.
Bittelli, M., Flury, M., Roth, K.,2004. Use of dielectric spectroscopy to estimate ice content in frozen porous media. Water Resour. Res.40(4):W04212. doi:10.1029/2003 WR002343.
Bronfenbrener, L., Korin, E.,2002. Experimental studies of water crystallization in porous media. Chemical Engineering and Processing 41,357-363.
Campbell, G. S.1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Sci.117:311-314.
Cary, J. W., Mayland, H. F.,1972. Salt and water movement in unsaturated frozen soil, Soil Sci. Soc. Am. J.,36,549-555.
Dean, T. J., Bell, J. P., Baty, A. J. B.,1987. Soil moisture measurement by an improved capacitance technique, Part I. Sensor design and performance. Journal of Hydrology 93,67-78.
Decker, M., Zeng, X.,2006. An empirical formulation of soil ice fraction based on in situ observations. Geophysical Research letters,33, L05402, doi:10.1029/2005GL024914.
De Vries, D. A.,1963. Thermal properties of soils. In Physics of plant environment. W. R. van Wijk, ed. North-Holland, Amsterdam, the Netherlands.
Dirksen, C., Miller, R. D.,1966. Closed-system freezing of unsaturated soil, Soil Sci. Soc. Amer. Proa, 30,168-173.
Evett, S. R.,2003. Soil water measurements by neutron thermalization. In Encyclopedia of Water Science, eds. B.A. Stewart and T.A. Howell,889-893. New York, NY:Marcel Dekker, Inc.
Evett, S. R., Schwartz, R. C., Casanova, J. J., Heng, L. K.,2012. Review:Soil water sensing for water balance ET and WUE. Agric. Water Manage.104:1-9.
Evett, S. R., Schwartz, R. C., Tolk, J. A., Howell, T. A.,2009. Soil profile water content determination: Spatotemporal variability of electromagnetic and neutron probe sensors in access tubes. Vadose Zone J. 8:926-941.
Flerchinger, G. N.,1991. Sensitivity of soil freezing simulated by the SHAW model. T ASAE,34(6), 2381-2389.
Flerchinger, G. N., Saxton, K. E.,1989a. Simultaneous heat and water model of a freezing snow-residue-soil system. Part Ⅰ. Theory and development. Trans. Am. Soc. Agric. Eng.,32,565-571.
Flerchinger, G. N., Saxton, K. E.,1989b. Simultaneous heat and water model of a freezing snow-residue-soil system. Part Ⅱ. Field verification. Trans. Am. Soc. Agric. Eng.,32,573-578.
Flerchinger, G.N., M.S. Seyfried, and S. P. Hardegree.2006. Using soil freezing characteristics to model multi-season soil water dynamics. Vadose Zone J.5:1143-1153.
Fuchs, M., Campbell, G. S., Papendick, R. I.,1978. An analysis of sensible and latent heat flow in a partially frozen unsaturated soil, Soil Sci. Soc. Am. J.,42,379-385.
Gaskin, G. C., Miller, J. D.,1996. Measurement of soil water content using a simplified impedance measuring technique. J. Agric. Engang. Res.63:153-160.
Guymon, G.L., Luthin, J.N.,1974. A coupled heat and moisture transport model for arctic soils. Water Resour. Res.,10,995-1001.
Hansson, K., Simunek, J., Mizoguchi, M., Lundin, L. C., van Genuchten M. T.,2004. Water flow and heat transport in frozen soil:Numerical solution and freeze/thaw applications, Vadose Zone J.,3,693- 704.
Harlan, R.L.,1973. Analysis of coupled heat-fluid transport in partially frozen soil, Water Resour. Res., 9,1314-1323.
Hayhoe, H. N., Bailey, W. G.,1985. Monitoring changes in total and unfrozen water content in seasonally frozen soil using time domain reflectometry and neutron moderation techniques. Water Resour. Res.21,1077-1084.
Hayhoe, H. N., Topp, G. C.,1983. Measurement of soil water contents and frozen soil depth during a thaw using time domain reflectometry. Atmos.-Ocean,21 (3):299-311.
Jame, Y. W., Norum, D. I.,1980. Heat and mass transfer in a freezing unsaturated porous medium. Water Resour. Res.,16,811-819.
Jansson, P. E., Karlberg, L.,2001. Coupled heat and mass transfer model for soil-plant-atmosphere systems, TRITAAMI Rep.3087, R. Inst. of Technol., Stockholm.
Jordan, R. A.,1991. One dimensional temperature model for a snow cover:Technical Documentation for SNTHERM.89, Spec. Rep.91-16, Cold Reg. Res. and Eng. Lab., U.S. Army Corps of Eng., Hanover, N.H.
Kahimba, F. C., Sri Ranjan, R.,2007. Soil temperature correction of field TDR readings obtained under near freezing conditions. Canadian Biosystems Engineering 49,19-26.
Kelleners, T. J., Norton, J.B.,2012. Determining water retention in seasonally frozen soils using Hydra impedance sensors. Soil Sci. Soc. Am. J.76:36-50.
Kimball, B. A., Jackson, R. D., Reginato, R. J., Nakayama, F. S., Idso, S. B.,1976. Comparison of Field-measured and Calculated Soil-heat Fluxes. Soil Science Society of America Journal 40(1),18-25.
Knight, J. H.,1992. Sensitivity of time domain reflectometry measurements to lateral variations in soil water content. Water resources research 28,2345-2352.
Knight, J. H., Ferr6, P. A., Rudolph, D. L., Kachanoski, R. G.,1997. A numerical analysis of the effects of coatings and gaps upon relative dielectric permittivity measurement with time domain reflectometry. Water Resour. Res.33:1455-1460.
Koopmans, R. W. R., Miller, R. D.,1966. Soil freezing and soil water characteristic curves. Soil Sci. Soc. Am. Proc.30,680-685.
Kozlowski, T.,2003a. A comprehensive method of determining the soil unfrozen water curves:1 Application of the term of convolution. Cold Regions Science and Technology 36,71-79.
Kozlowski, T.,2003b. A comprehensive method of determining the soil unfrozen water curves:2. Stages of the phase change process in frozen soil-water system. Cold Regions Science and Technology 36,81-92.
Li, Q., Sun, S.,2008. Development of the universal and simplified soil model coupling heat and water transport. Science in China Series D:Earth Sciences 51(1),88-102.
Li, Q., Sun, S., Xue, Y.,2010. Analyses and development of a hierarchy of frozen soil models for cold region study. Journal of Geophysical Research 115, D03107.
Liu, G., Si, B. C.,2011. Soil ice content measurement using a heat pulse probe method. Can. J. Soil Sci. 91,235-246.
Lovell, C. W.,1957. Temperature effects on phase composition and strength of Partially-frozen soil. Highway Research Board Bulletin 168,74-95.
Luo, W., Skaggs, R. W. Chescheir, G. M.2000. DRAINMOD modifications fro cold conditions. Transactions of the ASAE 43(6),1569-1582.
Ma, D., Sun, Y., Wang, M., Gao, Y.,2006. three-dimensional numerical modeling of a four-pin probe for soil water content. Aust. J. Soil Res.44:183-189.
Nissen, H. H., Moldrup, P., Olesen, T., Jensen, O. K..,2001. Time domain reflectometry sensitivity to lateral variations in bulk soil electrical conductivity. Soil Sci. Soc. Am. J.65:1351-1360.
Oliphant, J.L.,1985. A model for dielectric constants of frozen soils. Freezing and thawing of soil-water systems. Am. Sot. Civil Eng. New York, pp.46-57.
Or, D., Wraith, J. M.,1999. Temperature effects on soil bulk dielectric permittivity measured by time domain reflectometry:a physical model. Water Resources Research 35,371-383.
Patterson, D.E., Smith, M.W.,1980. The use of time domain reflectometery for the measurement of unfrozen water content in frozen soils. Cold Regions Science and Technology 3,205-210.
Patterson, D. E., Smith, M. W.,1981. The measurement of unfrozen water content by time domain retlectometry:Results from laboratory tests. Can. Georech. J.18:131-144.
Pepin, S., Livingstone, N. J., Hook, W. R.,1995. Temperature-dependent measurement errors in the time domain reflectometry determinations of soil water. Soil Science Society of America Journal 59 (1), 38-43.
Regalado, C. M.,2003. Time domain reflectometry models as a tool to understand the dielectric response of volcanic soils. Geoderma 117,313-330.
Roth, K. R., Schulin, R., Fluhler, H., Attinger, W.,1990. Calibration of time domain reflectometry for water content measurement using a composite dielectric approach. Water Resour. Res.,26,2267-2273.
Rouse, W. R.,1984. Microclimate of arctic tree line 2. Soil microclimate of Tundra and Forest, Water Resour. Res.,20(1),67-73.
Schwank, M., Green, T. R., Matzler, C., Benedickter, H., Fluhler, H.,2006. Laboratory characterization of a commercial capacitance sensor for estimating permittivity and inferring soil water content. Vadose Zone J.5:1048-1064.
Seyfried, M. S., Murdock, M. D.,1996. Calibration of time domain reflectometry for measurement of liquid water content in frozen soils. Soil Sci.161:87-98.
Seyfried, M. S., Murdock, M. D.,2001. Response of new soil water sensor to variable soil water content and temperature. Soil Science Society of America Journal 65,28-34.
Sheppard, M. I., Kay, B. D., Loch, J. P. G.,1981. The coupled transport of water and heat in freezing soils:A field study. Can. J. Soil Sci.,61,417-429.
Shoop, S. A., Bigl, S. R.,1997. Moisture migration during freeze and thaw of unsaturated soils: Modeling and large scale experiments, Cold Reg. Sci. Technol.,25,33-45.
Skierucha, W.,1999. The influence of temperature on soil dielectric permittivity and the TDR determined soil moisture (in Polish). Acta Agrophysica 22,163-172.
Skierucha, W.,2009. Temperature dependence of time domain reflectometry measured soil dielectric permittivity. Journal of Plant Nutrition and Soil Science 172,186-193.
Smith M. W., Patterson, D. E.,1984. Determining the unfrozen water content in soils by Time-Domain Reflectometry. ATMOSPHERE-OCEAN 22(2),261-263.
Spaans, E. J. A., Baker, J. M.,1995. Examining the use of time domain reflectometry for measuring liquid water content in frozen soil. Water Resour. Res.31,2917-2925.
Spaans, E. J. A., Baker, J. M.,1996. The soil freezing characteristic:Its measurement and similarity to the soil moisture characteristic. Soil Sci. Soc. Am. J.60:13-19.
Stein, J., Kane, D. L.,1983. Monitoring the unfrozen water content of soil and snow using time domain reflectometry. Water Resources Research 19(6),1573-1584.
Sun, Y., Schulze Lammers, P., Ma, D.,2004. Evaluation of a combined penetrometer for simultaneous measurement of penetration resistance and soil water content. J. Plant Nutr. Soil Sci.167:745-751.
Sun, Y., Ma, D., Lin, J., Schulze Lammers, P., Damerow, L.,2005. An improved Frequency domain technique for determining soil water content. Pedosphere.15(6):805-812.
Sun, Y, Ma, D., Schulze Lammers, P., Schmittmann, O., Rose, M.,2006. On-the-go measurement of soil water content and mechanical resistance by a combined horizontal penetrometer. Soil Till. Res.86, 209-217.
Taylor, G. S., Luthin, J. N.,1978. A model for coupled heat and moisture transfer during soil freezing, Can. Geotech. J.,15,548-555.
Tice, A. R., Burrous, C. M., Anderson, D. M.,1978. Determination of unfrozen water in frozen soil by pulsed nuclear magnetic resonance. Proceedings, Third International Conference on Permafrost. Ottawa: National Research Council of Canada, p.149-155.
Tice, A. R., Oliphant, J. L., Nakano, Y., Jenkins, T. F.,1982. Relationship between the ice and unfrozen water phases in frozen soil as determined by pulsed nuclear magnetic resonance and physical desorption data. CRREL Report, vol.82-15. US. Army. Cold Regions Research and Engineering Lab (CRREL).
Tien L. C., Churchill S. W.,1965. Freezing Front Motion and Heat Transfer Outside an Infinite, Isothermal Cylinder. A.1.Ch.E. Journal,11,790-793.
Tinga, W. R., Voss, W. A.G., Blossey, D. F.,1973. Generalized approach to multiphase dielectric mixture theory. J. Appl. Phys.44(9),3897-3902.
Topp, G.C., Davis, J. L., Annan, A.P.,1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour. Res.16:574-582.
Turov, V. V., Leboda, R.,1999. Application of 1H NMR spectroscopy method for determination of characteristics of thin layers of water adsorbed on the surface of dispersed and porous adsorbents. Advances in Colloid and Interface Science 79,173-211.
Van Genuchten, M. Th.,1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J.44:892-898.
Watanabe, K., Mizoguchi, M.,2002. Amount of unfrozen water in frozen porous media saturated with solution. Cold Regions Seience and Technology 34,103-110.
Watanabe, K., Wake, T.,2009. Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR. Cold Regions Science and Technology 59,34-41.
Whalley,W. R., Cope, R. E., Nicholl, C. J.,Whitmore, A. P.,2004. In-field calibration of a dielectric soil moisture meter for use in an access tube. Soil Use and Management 20,203-206.
Willatt, S. T.,1979. Changes in water content in and under frozen soil in Iowa. U.S.A. Geoderma,22, 323-331.
Willis, W. O., Carlson, C. W., Alessi, J. Haas, H. J.,1961. Depth of freezing and spring run-off as related to fall soil-moisture level. Can. J. of Soil Sci.41:115-123.
Yoshikawa, K., Overduin, P. P.,2005. Comparing unfrozen water content measurements of frozen soil using recently developed commercial sensors. Cold Regions Science and Technology 42,250-256.
Zegelin, S. J., White, I., Jenkins, D. R.,1989. Improved field probes for soil water content and electrical conductivity measurement using time domain reflectometry. Water resources research 25,2367-2376.
Zhang, X., Sun, S. F., Xue, Y. K.,2007. Development and testing of a frozen soil parameterization for cold region studies, J. Hydrometeorol.,8,690-701.
Zhao, L., Cray, D. M., Male, D. H.,1997. Numerical analysis of simultaneous heat and water transfer during infiltration into frozen ground, J. Hydrol.,200,345-363.
Zhou, Y., Zhou, G.,2010. Numerical simulation of coupled heat-fluid transport in freezing soils using finite volume method. Heat Mass Transfer 46:989-998.
范寿康,卢春兰,李平辉.微波技术与微波电路.北京：机械工业出版社,2003.
胡和平,杨诗秀,雷志栋,1992.土壤冻结时水热迁移规律的数值模拟.水利学报,7：1-8.
马祖罗夫гп.冻土物理力学性质[M].梁惠生,伍期建译.北京：煤炭工业出版社,1980.
沈振荣,张瑜芳,杨诗秀,等.水资源科学实验与研究[M].北京：中国科学技术出版社,1992.253-256.
尚松浩,雷志栋,杨诗秀,1997.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.
孙宇瑞.土壤探针阻抗计算方法的理论分析与试验研究.土壤学报,2002,39(1)：120-126.
孙宇瑞.非饱和土壤介电特性测量理论与方法研究[D].北京：中国农业大学,2000
徐学祖,邓友生.冻土中水分迁移的试验研究[M].北京：科学出版社,1991
徐学祖,王家澄,张立新,冻土物理学[M].北京：科学出版社,2009
杨诗秀,雷志栋,朱强,等.1998.土壤冻结条件下水热耦合运移的数值模拟.清华大学学报,1988,28(s1)：112-120.
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.