灰色关联及非线性规划法构建传递函数估算黑土水力参数
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摘要
土壤水分特征曲线和饱和导水率是重要的水力参数,为了简便准确获取这些参数,以松嫩平原黑土区南部为研究区域,采集136个采样点土样用于测定不同土层土壤水分特征曲线、饱和导水率以及土壤理化性质,并运用灰色关联分析确定影响土壤水力参数的主要土壤理化性质,采用非线性规划构建土壤分形维数、有机质、干容重、土壤颗粒组成与土壤水分特征曲线、饱和导水率之间的土壤传递函数,并通过与现有土壤传递函数对比分析进行精度验证。结果表明:1)土壤分形维数是估算土壤水分特征曲线模型参数和饱和导水率的主要参数之一,同时,干容重和有机质含量也在不同土层土壤传递函数中起到重要的作用;2)通过验证分析,不同土层各参数平均绝对误差接近于0,均方根误差值也都较小,其中在不同土层土壤传递函数估算的土壤含水率均方根误差分别为0.022、0.017cm~3/cm~3;3)对比分析其他已存的土壤水分特征曲线和饱和导水率的土壤传递函数,该文构建的土壤传递函数均方根误差值均较小,决定系数值都在0.66以上,表明估算精度较高,均好于其他方法估算精度,具有良好的区域适应性。综上,所构建的土壤水分特征曲线和饱和导水率土壤传递函数可以用于松嫩平原黑土区土壤水力参数估算。
Soil water characteristic curve and saturated hydraulic conductivity are important parameters for constructing soil moisture and solute transport models, both of which are affected by soil texture, bulk density, organic matter content, porosity, etc. In order to simply and accurately obtain the 2 parameters above, a total of 136 soil sampling points in the southern part of the black soil area in the Songnen Plain were designed, and the soil samples in 2 layers of these sampling points were collected to measure the soil water characteristic curve, saturated hydraulic conductivity and soil physical and chemical properties, the grey correlation analysis was used to determine the main soil physical and chemical properties affecting soil hydraulic parameters.The results showed: 1) in 0-20 cm soil layer, the residual moisture content of van Genuchten model had the higher correlation with fractal dimension, dry bulk density and organic matter content, and the correlation between parameter pore distribution index and fractal dimension, dry bulk density and clay content was the highest. The parameter of reciprocal soil air influx had the higher correlation with sand content, dry bulk density and fractal dimension. In soil layer from 20 to 40 cm, the parameter of residual moisture content of van Genuchten model had the higher correlation with sand content, dry bulk density and organic matter content; the parameter pore distribution index and fractal dimensions had the highest correlation; The correlation between fractal dimension, organic matter content and silt content and parameter pore distribution index was the highest, and the correlation between parameter reciprocal soil air influx and sand content, fractal dimension and organic matter content was the highest. 2) The correlation between soil saturated hydraulic conductivity and soil organic matter, dry bulk density and fractal dimension in 0-40 cm soil layer was higher. 3) The pedo-transfer functions of the soil water characteristic curve and the saturated hydraulic conductivity based on soil fractal dimension, organic matter, dry bulk density and soil particle composition were established by using the nonlinear optimal programming method. The accuracy of the pedo-transfer functions established in the study was verified by comparing with the existing common pedo-transfer functions. The results showed that soil fractal dimension was one of the primary parameters in constructing soil pedo-transfer functions to predict soil water characteristic curve and saturated hydraulic conductivity. In addition, soil dry bulk density and organic matter content also played an important role in pedo-transfer functions of different soil layers. Based on the verification analysis, the mean absolute errors of the estimated soil hydraulic parameters in different soil layers were all close to 0, and the root mean square error values of the predicted soil hydraulic parameters in different soil layers were also small. Specially, the root mean square errors of soil moisture content estimated by pedo-transfer functions established in the study were 0.022 and 0.017 cm3/cm3 in different soil layers, respectively. On the basis of comparing with the other existing common pedo-transfer functions of soil water characteristic curve and saturated hydraulic conductivity, the pedo-transfer functions of soil hydraulic parameters established in the study had high estimation accuracy, the root mean square error values were small; the determination coefficient values were all above 0.66, which was better than the other existing common pedo-transfer functions. In summary, the pedo-transfer functions of the soil water characteristic curve and saturated water conductivity established in the study can be used to estimate the soil hydraulic parameters in the black soil area of the Songnen Plain, and also provide technical support for acquisition of regional soil hydraulic properties.
Soil water characteristic curve and saturated hydraulic conductivity are important parameters for constructing soil moisture and solute transport models, both of which are affected by soil texture, bulk density, organic matter content, porosity, etc. In order to simply and accurately obtain the 2 parameters above, a total of 136 soil sampling points in the southern part of the black soil area in the Songnen Plain were designed, and the soil samples in 2 layers of these sampling points were collected to measure the soil water characteristic curve, saturated hydraulic conductivity and soil physical and chemical properties, the grey correlation analysis was used to determine the main soil physical and chemical properties affecting soil hydraulic parameters.The results showed: 1) in 0-20 cm soil layer, the residual moisture content of van Genuchten model had the higher correlation with fractal dimension, dry bulk density and organic matter content, and the correlation between parameter pore distribution index and fractal dimension, dry bulk density and clay content was the highest. The parameter of reciprocal soil air influx had the higher correlation with sand content, dry bulk density and fractal dimension. In soil layer from 20 to 40 cm, the parameter of residual moisture content of van Genuchten model had the higher correlation with sand content, dry bulk density and organic matter content; the parameter pore distribution index and fractal dimensions had the highest correlation; The correlation between fractal dimension, organic matter content and silt content and parameter pore distribution index was the highest, and the correlation between parameter reciprocal soil air influx and sand content, fractal dimension and organic matter content was the highest. 2) The correlation between soil saturated hydraulic conductivity and soil organic matter, dry bulk density and fractal dimension in 0-40 cm soil layer was higher. 3) The pedo-transfer functions of the soil water characteristic curve and the saturated hydraulic conductivity based on soil fractal dimension, organic matter, dry bulk density and soil particle composition were established by using the nonlinear optimal programming method. The accuracy of the pedo-transfer functions established in the study was verified by comparing with the existing common pedo-transfer functions. The results showed that soil fractal dimension was one of the primary parameters in constructing soil pedo-transfer functions to predict soil water characteristic curve and saturated hydraulic conductivity. In addition, soil dry bulk density and organic matter content also played an important role in pedo-transfer functions of different soil layers. Based on the verification analysis, the mean absolute errors of the estimated soil hydraulic parameters in different soil layers were all close to 0, and the root mean square error values of the predicted soil hydraulic parameters in different soil layers were also small. Specially, the root mean square errors of soil moisture content estimated by pedo-transfer functions established in the study were 0.022 and 0.017 cm3/cm3 in different soil layers, respectively. On the basis of comparing with the other existing common pedo-transfer functions of soil water characteristic curve and saturated hydraulic conductivity, the pedo-transfer functions of soil hydraulic parameters established in the study had high estimation accuracy, the root mean square error values were small; the determination coefficient values were all above 0.66, which was better than the other existing common pedo-transfer functions. In summary, the pedo-transfer functions of the soil water characteristic curve and saturated water conductivity established in the study can be used to estimate the soil hydraulic parameters in the black soil area of the Songnen Plain, and also provide technical support for acquisition of regional soil hydraulic properties.
引文
[1]Merdun H,Cinar O,Meral R,et al.Comparison of artificial neural network and regression pedotransfer functions for prediction of soil water retention and saturated hydraulic conductivity[J].Soil and Tillage Research,2006,90(1):108-116.
[2]廖凯华,徐绍辉,吴吉春,等.不同土壤转换函数预测砂土非饱和导水率的对比分析[J].水科学进展,2013,24(4):560-567.Liao Kaihua,Xu Shaohui,Wu Jichun,et al.Estimating unsaturated hydraulic conductivity of sandy soils using different pedotransfer functions[J].Advances in Water Science,2013,24(4):560-567.(in Chinese with English abstract)
[3]Zeleke T B,Si B C.Characterizing scale-dependent spatial relationships between soil properties using multifractal techniques[J].Geoderma,2006,134(3):440-452.
[4]刘继龙,马孝义,张振华,等.基于联合多重分形的土壤水分特征曲线土壤传递函数[J].农业机械学报,2012,34(3):51-55.Liu Jilong,Ma Xiaoyi,Zhang Zhenhua,et al.Pedotransfer functions of soil water retention curve based on joint multifractal[J].Transactions of the Chinese Society for Agricultural Machinery,2012,34(3):51-55.(in Chinese with English abstract)
[5]黄元仿,李韵珠.土壤水力性质的估算-土壤转换函数[J].土壤学报,2002,39(4):517-523.Huang Yuanfang,Li Yunzhu.Estimation of soil hydraulic properties-pedo-transfer functions[J].Acta Pedologica Sinica,2002,39(4):517-523.(in Chinese with English abstract)
[6]Liu Z X,Shu Q S,Wang Z Y.Apply pedo-transfer functions to simulate spatial heterogeneity of cinnamon soil water retention characteristics in western liaoning province[J].Water Resources Management,2007,21(10):1751-1762.
[7]Schaap M G,Leij F J,van Genuchten M T.Neural network analysis for hierarchical prediction of soil hydraulic properties[J].Soil Science Society of America Journal,1998,62(4):847-855.
[8]Minasny B,Mcbratney A.The neuro-m method for fitting neural network parametric pedotransfer functions[J].Soil Science Society of America Journal,2002,66(2):352-361.
[9]Li Y,Chen D,White R E,et al.Estimating soil hydraulic properties of Fengqiu County soils in the North China Plain using pedo-transfer functions[J].Geoderma,2007,138(3):261-271.
[10]Vereecken H,Maes J,Feyen J,et al.Estimating the soil moisture retention characte ristic from texture,bulk density,and carbon content[J].Soil Science,1989,148(6):389-403.
[11]Schaap M G,Leij F J,Genuchten M Th.ROSET TA:Acomputer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions[J].Journal of Hydrology,2001,251(3):163-176.
[12]Wosten J H M,Lilly A,Nemes A,et al.Development and use of a database of hydraulic properties of Europ pean soil[J].Geoderma,1999,90(3):169-185.
[13]孙美,张晓琳,冯绍元,等.基于交叉验证的农田土壤饱和导水率传递函数研究[J].农业机械学报,2014,45(10):147-152.Sun Mei,Zhang Xiaolin,Feng Shaoyuan,et al.Pedo-transfer function for saturated hydraulic conductivity of agricultural soil based on cross-validation[J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(10):147-152.(in Chinese with English abstract)
[14]孙丽,刘廷玺,段利民,等.科尔沁沙丘-草甸相间地区表土饱和导水率的土壤传递函数[J].土壤学报,2015,52(1):68-76.Sun Li,Liu Tingxi,Duan Limin,et al.Prediction of saturated hydralic conductivity of surface soil in sand-dune-andmeadow inte rlaced region of Horqin with pedo-transfer functions method.[J].Acta Pedologica Sinica,2015,52(1):68-76.(in Chinese with English abstract)
[15]Campbell G S.Soil physics with basic:Transport models for soil-plant system[J].Journal of Hydrology,1987,90(3):359-360.
[16]Cosby B J,Hornberger G M,Clapp R B,et al.A statistical exploration of the relationships of soil moisture characteristics to the physical properties of soils[J].Water Resources Research,1984,20(6):682-690.
[17]Saxton K E,Rawls W J,Romberger J S,et al.Estimating generalized soil-water characteri-stics from texture[J].Soil Science Society of America Journal,1986,50(4):1031-1036.
[18]王子龙,陈伟杰,付强,等.基于优先级指数的土壤采样设计方法研究[J].农业机械学报,2018,49(7):244-251.Wang Zilong,Chen Weijie,Fu Qiang,et al.Method of soil sampling design based on priority index[J].Transactions of the Chinese Society for Agricultural Machinery,2018,49(7):244-251.(in Chinese with English abstract)
[19]王国梁,周生路,赵其国.土壤颗粒的体积分形维数及其在土地利用中的应用[J].土壤学报,2005,42(4):545-550.Wang Guoliang,Zhou Shenglu,Zhao Qiguo.Volume fractal dimension of particles and it’s applications to land use[J].Acta Pedologica Sinica,2005,42(4):545-550.(in Chinese with English abstract)
[20]中华人民共和国农业部.土壤检测第6部分:土壤有机质测定:NY/T 1121.6-2006[S].北京:中国农业出版社,2006.
[21]Wim M Cornelis,Jan Ronsyn,Marc Van Meirvenne.Evaluation of pedotransfer functions for predicting the soil moisture retention curve[J].Soil Science,2001(65):638-648.
[22]陈俊英,柴红阳,Leionid G,等.再生水水质对斥水和亲水土壤水分特征曲线的影响[J].农业工程学报,2018,34(11):121-127.Chen Junying,Cai Hongyang,Leionid G,et al.Impact of treated waste water quality on repellent and wettable soil water characteristic curve[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2018,34(11):121-127.(in Chinese with English abstract)
[23]姚姣转,刘廷玺,王天帅,等.科尔沁沙地土壤水分特征曲线传递函数的构建与评估[J].农业工程学报,2014,30(20):98-108.Yao Jiaozhuan,Liu Tingxi,Wang Tianshuai,et al.Development and evaluation of pedo-transfer functions of soil water characteristic curves in Horqin sandy land[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2014,30(20):98-108.(in Chinese with English abstract)
[24]van Genuchten M T.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J]Soil Science Society of America Journal,1980,44(44):892-898.
[25]郭向红,孙西欢,马娟娟.基于混合遗传算法估计van Genuchten方程参数[J].水科学进展,2009,20(5):677-682.Guo Xianghong,Sun Xihuan,Ma Juanjuan.Parametric estimation of the van Genuchten's equation based on hybrid genetic algorithm[J].Advances in Water Science,2009,20(5):677-682.(in Chinese with English abstract)
[26]付强,蒋睿奇,王子龙,等.基于改进萤火虫算法的土壤水分特征曲线参数优化[J].农业工程学报,2015,31(11):117-122.Fu Qiang,Jiang Ruiqi,Wang Zilong,et al.Optimization of soil water characteristic curves parameters by modified firefly algorithm[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(11):117-122.(in Chinese with English abstract)
[27]付强,颜培儒,李天霄,等.冻融期不同覆盖和气象因子对土壤导热率和热通量的影响[J].农业工程学报,2017,33(20):98-105.Fu Qiang,Yan Peiru,Li Tianxiao,et al.Influence of different coverage and meteorological factors on soil thermal conductivity and heat flux during freezing and thawing period[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2017,33(20):98-105.(in Chinese with English abstract)
[28]Deng J L.Introduction to Grey-system theory[J].The Journal of Grey System,1989,1(1):1-24.
[29]朱安宁,张佳宝,陈效民,等.封丘地区土壤传递函数的研究[J].土壤学报,2003,40(1):53-58.Zhu Anning,Zhang Jiabao,Chen Xiaomin,et al.Study on pedo-transfer function in Fengqiu[J].Acta Pedologica Sinica,2003,40(1):53-58.(in Chinese with English abstract)
[30]郑子成,李卫,李廷轩,等.基于分形理论的土壤水分特征曲线研究[J].农业机械学报,2012,43(5):49-54.Zheng Zicheng,Li Wei,Li Tingxuan,et al.Soil water retention curve based on fractal theory in greenhouse soil[J].Transactions of the Chinese Society for Agricultural Machinery,2012,43(5):49-54.(in Chinese with English abstract)
[31]徐绍辉,刘建立.估计不同质地土壤水分特征曲线的分形方法[J].水利学报,2003,34(1):78-82.Xu Shaohui,Liu Jianli.Fractal approach for estimating soil water retention curves of various textures[J].Journal of Hydraulic Engineering,2003,34(1):78-82.(in Chinese with English abstract)
[32]赵云鹏,白一茹,王幼奇,等.宁夏引黄灌区土壤饱和导水率空间分异特征[J].北方园艺,2017(8):166-171.Zhao Yunpeng,Bai Yiru,Wang Youqi,et al.Spatial variability of soil saturated hydraulic conductivity in the yellow river irrigated area in ningxia[J].Northern Horticulture,2017(8):166-171.(in Chinese with English abstract)
[33]李孝良,陈效民,周炼川,等.西南喀斯特地区土壤饱和导水率及其影响因素研究[J].灌溉排水学报,2008,27(5):74-76.Li Xiaoliang,Chen Xiaomin,Zhou Lianchuan,et al.Soil saturated hydraulic conductivity and its influential factors in southwest karst region of china[J].Journal of Irrigation and Drainage,2008,27(5):74-76.(in Chinese with English abstract)
[34]赵春雷,邵明安,贾小旭.黄土高原北部坡面尺度土壤饱和导水率分布与模拟[J].水科学进展,2014,25(6):806-815.Zhao Chunlei,Shao Ming'an,Jia Xiaoxu.Distribution and simulation of saturated soil hydraulic conductivity at a slope of northern loess plateau[J].Advances in Water Science,2014,25(6):806-815.(in Chinese with English abstract)
[35]张耀方,赵世伟,王子龙,等.黄土高原土壤团聚体胶结物质的分布及作用综述[J].中国水土保持科学,2015,13(5):145-150.Zhang Yaofang,Zhao Shiwei,Wang Zilong,et al Distribution and function of cementing materials of soil aggregates on the Loess plateau,western China[J].Science of Soil and Water Conservation,2015,13(5):145-150.(in Chinese with English abstract)
[2]廖凯华,徐绍辉,吴吉春,等.不同土壤转换函数预测砂土非饱和导水率的对比分析[J].水科学进展,2013,24(4):560-567.Liao Kaihua,Xu Shaohui,Wu Jichun,et al.Estimating unsaturated hydraulic conductivity of sandy soils using different pedotransfer functions[J].Advances in Water Science,2013,24(4):560-567.(in Chinese with English abstract)
[3]Zeleke T B,Si B C.Characterizing scale-dependent spatial relationships between soil properties using multifractal techniques[J].Geoderma,2006,134(3):440-452.
[4]刘继龙,马孝义,张振华,等.基于联合多重分形的土壤水分特征曲线土壤传递函数[J].农业机械学报,2012,34(3):51-55.Liu Jilong,Ma Xiaoyi,Zhang Zhenhua,et al.Pedotransfer functions of soil water retention curve based on joint multifractal[J].Transactions of the Chinese Society for Agricultural Machinery,2012,34(3):51-55.(in Chinese with English abstract)
[5]黄元仿,李韵珠.土壤水力性质的估算-土壤转换函数[J].土壤学报,2002,39(4):517-523.Huang Yuanfang,Li Yunzhu.Estimation of soil hydraulic properties-pedo-transfer functions[J].Acta Pedologica Sinica,2002,39(4):517-523.(in Chinese with English abstract)
[6]Liu Z X,Shu Q S,Wang Z Y.Apply pedo-transfer functions to simulate spatial heterogeneity of cinnamon soil water retention characteristics in western liaoning province[J].Water Resources Management,2007,21(10):1751-1762.
[7]Schaap M G,Leij F J,van Genuchten M T.Neural network analysis for hierarchical prediction of soil hydraulic properties[J].Soil Science Society of America Journal,1998,62(4):847-855.
[8]Minasny B,Mcbratney A.The neuro-m method for fitting neural network parametric pedotransfer functions[J].Soil Science Society of America Journal,2002,66(2):352-361.
[9]Li Y,Chen D,White R E,et al.Estimating soil hydraulic properties of Fengqiu County soils in the North China Plain using pedo-transfer functions[J].Geoderma,2007,138(3):261-271.
[10]Vereecken H,Maes J,Feyen J,et al.Estimating the soil moisture retention characte ristic from texture,bulk density,and carbon content[J].Soil Science,1989,148(6):389-403.
[11]Schaap M G,Leij F J,Genuchten M Th.ROSET TA:Acomputer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions[J].Journal of Hydrology,2001,251(3):163-176.
[12]Wosten J H M,Lilly A,Nemes A,et al.Development and use of a database of hydraulic properties of Europ pean soil[J].Geoderma,1999,90(3):169-185.
[13]孙美,张晓琳,冯绍元,等.基于交叉验证的农田土壤饱和导水率传递函数研究[J].农业机械学报,2014,45(10):147-152.Sun Mei,Zhang Xiaolin,Feng Shaoyuan,et al.Pedo-transfer function for saturated hydraulic conductivity of agricultural soil based on cross-validation[J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(10):147-152.(in Chinese with English abstract)
[14]孙丽,刘廷玺,段利民,等.科尔沁沙丘-草甸相间地区表土饱和导水率的土壤传递函数[J].土壤学报,2015,52(1):68-76.Sun Li,Liu Tingxi,Duan Limin,et al.Prediction of saturated hydralic conductivity of surface soil in sand-dune-andmeadow inte rlaced region of Horqin with pedo-transfer functions method.[J].Acta Pedologica Sinica,2015,52(1):68-76.(in Chinese with English abstract)
[15]Campbell G S.Soil physics with basic:Transport models for soil-plant system[J].Journal of Hydrology,1987,90(3):359-360.
[16]Cosby B J,Hornberger G M,Clapp R B,et al.A statistical exploration of the relationships of soil moisture characteristics to the physical properties of soils[J].Water Resources Research,1984,20(6):682-690.
[17]Saxton K E,Rawls W J,Romberger J S,et al.Estimating generalized soil-water characteri-stics from texture[J].Soil Science Society of America Journal,1986,50(4):1031-1036.
[18]王子龙,陈伟杰,付强,等.基于优先级指数的土壤采样设计方法研究[J].农业机械学报,2018,49(7):244-251.Wang Zilong,Chen Weijie,Fu Qiang,et al.Method of soil sampling design based on priority index[J].Transactions of the Chinese Society for Agricultural Machinery,2018,49(7):244-251.(in Chinese with English abstract)
[19]王国梁,周生路,赵其国.土壤颗粒的体积分形维数及其在土地利用中的应用[J].土壤学报,2005,42(4):545-550.Wang Guoliang,Zhou Shenglu,Zhao Qiguo.Volume fractal dimension of particles and it’s applications to land use[J].Acta Pedologica Sinica,2005,42(4):545-550.(in Chinese with English abstract)
[20]中华人民共和国农业部.土壤检测第6部分:土壤有机质测定:NY/T 1121.6-2006[S].北京:中国农业出版社,2006.
[21]Wim M Cornelis,Jan Ronsyn,Marc Van Meirvenne.Evaluation of pedotransfer functions for predicting the soil moisture retention curve[J].Soil Science,2001(65):638-648.
[22]陈俊英,柴红阳,Leionid G,等.再生水水质对斥水和亲水土壤水分特征曲线的影响[J].农业工程学报,2018,34(11):121-127.Chen Junying,Cai Hongyang,Leionid G,et al.Impact of treated waste water quality on repellent and wettable soil water characteristic curve[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2018,34(11):121-127.(in Chinese with English abstract)
[23]姚姣转,刘廷玺,王天帅,等.科尔沁沙地土壤水分特征曲线传递函数的构建与评估[J].农业工程学报,2014,30(20):98-108.Yao Jiaozhuan,Liu Tingxi,Wang Tianshuai,et al.Development and evaluation of pedo-transfer functions of soil water characteristic curves in Horqin sandy land[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2014,30(20):98-108.(in Chinese with English abstract)
[24]van Genuchten M T.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J]Soil Science Society of America Journal,1980,44(44):892-898.
[25]郭向红,孙西欢,马娟娟.基于混合遗传算法估计van Genuchten方程参数[J].水科学进展,2009,20(5):677-682.Guo Xianghong,Sun Xihuan,Ma Juanjuan.Parametric estimation of the van Genuchten's equation based on hybrid genetic algorithm[J].Advances in Water Science,2009,20(5):677-682.(in Chinese with English abstract)
[26]付强,蒋睿奇,王子龙,等.基于改进萤火虫算法的土壤水分特征曲线参数优化[J].农业工程学报,2015,31(11):117-122.Fu Qiang,Jiang Ruiqi,Wang Zilong,et al.Optimization of soil water characteristic curves parameters by modified firefly algorithm[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(11):117-122.(in Chinese with English abstract)
[27]付强,颜培儒,李天霄,等.冻融期不同覆盖和气象因子对土壤导热率和热通量的影响[J].农业工程学报,2017,33(20):98-105.Fu Qiang,Yan Peiru,Li Tianxiao,et al.Influence of different coverage and meteorological factors on soil thermal conductivity and heat flux during freezing and thawing period[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2017,33(20):98-105.(in Chinese with English abstract)
[28]Deng J L.Introduction to Grey-system theory[J].The Journal of Grey System,1989,1(1):1-24.
[29]朱安宁,张佳宝,陈效民,等.封丘地区土壤传递函数的研究[J].土壤学报,2003,40(1):53-58.Zhu Anning,Zhang Jiabao,Chen Xiaomin,et al.Study on pedo-transfer function in Fengqiu[J].Acta Pedologica Sinica,2003,40(1):53-58.(in Chinese with English abstract)
[30]郑子成,李卫,李廷轩,等.基于分形理论的土壤水分特征曲线研究[J].农业机械学报,2012,43(5):49-54.Zheng Zicheng,Li Wei,Li Tingxuan,et al.Soil water retention curve based on fractal theory in greenhouse soil[J].Transactions of the Chinese Society for Agricultural Machinery,2012,43(5):49-54.(in Chinese with English abstract)
[31]徐绍辉,刘建立.估计不同质地土壤水分特征曲线的分形方法[J].水利学报,2003,34(1):78-82.Xu Shaohui,Liu Jianli.Fractal approach for estimating soil water retention curves of various textures[J].Journal of Hydraulic Engineering,2003,34(1):78-82.(in Chinese with English abstract)
[32]赵云鹏,白一茹,王幼奇,等.宁夏引黄灌区土壤饱和导水率空间分异特征[J].北方园艺,2017(8):166-171.Zhao Yunpeng,Bai Yiru,Wang Youqi,et al.Spatial variability of soil saturated hydraulic conductivity in the yellow river irrigated area in ningxia[J].Northern Horticulture,2017(8):166-171.(in Chinese with English abstract)
[33]李孝良,陈效民,周炼川,等.西南喀斯特地区土壤饱和导水率及其影响因素研究[J].灌溉排水学报,2008,27(5):74-76.Li Xiaoliang,Chen Xiaomin,Zhou Lianchuan,et al.Soil saturated hydraulic conductivity and its influential factors in southwest karst region of china[J].Journal of Irrigation and Drainage,2008,27(5):74-76.(in Chinese with English abstract)
[34]赵春雷,邵明安,贾小旭.黄土高原北部坡面尺度土壤饱和导水率分布与模拟[J].水科学进展,2014,25(6):806-815.Zhao Chunlei,Shao Ming'an,Jia Xiaoxu.Distribution and simulation of saturated soil hydraulic conductivity at a slope of northern loess plateau[J].Advances in Water Science,2014,25(6):806-815.(in Chinese with English abstract)
[35]张耀方,赵世伟,王子龙,等.黄土高原土壤团聚体胶结物质的分布及作用综述[J].中国水土保持科学,2015,13(5):145-150.Zhang Yaofang,Zhao Shiwei,Wang Zilong,et al Distribution and function of cementing materials of soil aggregates on the Loess plateau,western China[J].Science of Soil and Water Conservation,2015,13(5):145-150.(in Chinese with English abstract)