土壤水分特性的分形特征与传递函数研究
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摘要
研究土壤特性的空间变异性对于推动农业、土壤和水科学等学科的发展和应用具有重要的科学意义。研究尺度不同时,土壤特性的空间变异特征有较大差异,主要影响因素和过程也不一定完全相同,多尺度分析能更深入地揭示土壤特性空间变异性的机理。此外,不同土层土壤水力特性参数的空间变异性及其与影响因素的尺度相关性不一定完全相同,不同土层土壤特性空间变异性之间可能存在某种程度的相互关系。为此,论文依托国家科技支撑计划项目(2006BAD11B04)和国家自然科学基金项目(50879072),以杨凌地区为例,利用多重分形方法研究分析不同土层土壤含水率、土壤电导率、土壤基本物理特性、土壤粒径分布分形维数、土壤水分特征曲线和土壤入渗特性的空间变异性;利用联合多重分形方法研究分析田间土壤粒径分布分形维数、土壤水分特征曲线、土壤入渗特性等土壤水分运动参数与影响因素在多尺度上的相关性,并基于上述分析得出的联合多重分形结论建立考虑尺度效应的田间尺度上上述参数的土壤传递函数;探索了田间尺度向区域尺度转换的方法,即将田间尺度上得出的联合多重分形结论应用到区域尺度上,建立区域尺度上土壤水分运动参数的土壤传递函数;同时探讨分析不同土层土壤含水率、土壤电导率、土壤基本物理特性、土壤粒径分布分形维数、土壤水分特征曲线空间变异性之间的相互关系。主要得出以下结论:
(1)研究区域内土壤含水率、土壤电导率、砂粒含量、粘粒含量、有机质含量、稳定入渗率、前30min累积入渗量和van Genuchten模型参数α的多重分形特征比较明显;粗粉粒含量、土壤容重、土壤粒径分布分形维数、van Genuchten模型参数n和θs的多重分形特征不明显。
(2)利用多重分形方法研究分析了土壤含水率、土壤电导率、土壤基本物理特性、土壤粒径分布分形维数、van Genuchten模型参数和土壤入渗特性的空间变异性,确定了引起上述研究对象空间变异性的局部信息,可为分析上述参数的空间变异性及尺度效应和深入揭示其空间变异机理等提供方法借鉴和参考。
研究区域内土壤含水率和土壤电导率的空间变异性都分别随土壤含水率和土壤电导率平均值的增大而减弱。土壤含水率和土壤电导率的平均值不同时,土壤含水率和土壤电导率空间变异性的尺度效应都有所差异。土壤含水率和土壤电导率的平均值较大时,随着采样面积的增大,土壤含水率的空间变异性逐渐增强,土壤电导率的空间变异性很弱;土壤含水率和土壤电导率的平均值较小时,随着采样面积的增大,土壤含水率和土壤电导率的空间变异性较强,且空间分布中都存在斑块结构。
土壤基本物理特性的多重分形分析表明,砂粒含量和粘粒含量的空间变异性较强,粗粉粒含量和有机质含量的空间变异性次之,土壤容重的空间变异性最弱;0～20cm土层和20～40cm土层砂粒含量的空间变异性都是由砂粒含量的高值分布造成的,不同土层粘粒含量、有机质含量和粗粉粒含量的空间变异性都是由对应变量的低值分布造成的。
不同土层土壤粒径分布分形维数的空间变异性都很弱。0～20cm土层和20～40cm土层van Genuchten模型参数α的空间变异性较强,且分别是由其低值和高值分布引起的;参数n和θs的空间变异性较弱。稳定入渗率和前30min累积入渗量的空间变异性较强,其中前30min累积入渗量的空间变异性是由其高值分布造成的。
(3)利用联合多重分形方法研究分析了田间土壤粒径分布分形维数、van Genuchten模型参数α和n、土壤入渗特性与影响因素在多尺度上的相关性,发现上述参数与影响因素的相关性具有尺度依赖性,在单一尺度和多尺度上的相关性特征并不完全相同。基于得出的联合多重分形结论建立了考虑尺度效应的田间尺度上上述参数的土壤传递函数,验证分析表明建立的土壤传递函数具有较强的理论基础,预测精度较高,可用于估算田间尺度上的上述参数。
不同土层土壤粒径分布分形维数与土壤颗粒组成的相关特征相似,但土壤粒径分布分形维数与土壤颗粒组成在田间单一尺度和多尺度上的相关特征有所差异。田间单一尺度上,0～20cm和20～40cm土层土壤粒径分布分形维数与粘粒含量、砂粒含量、粗粉粒含量的相关程度依次降低;联合多重分形分析表明,田间多尺度上,不同土层土壤粒径分布分形维数与粘粒含量、粗粉粒含量、砂粒含量的相关程度依次降低。基于联合多重分形结论建立的考虑尺度效应的田间尺度上0～20cm和20～40cm土层土壤粒径分布分形维数的土壤传递函数具有较强的理论基础和适应性,预测精度很高,预测值的RMSE分别为0.0134和0.0117,可用于估算田间尺度上的土壤粒径分布分形维数。
不同土层van Genuchten模型参数α、n与影响因素之间的相关特征不完全相同;van Genuchten模型参数α、n与影响因素相关的相关性特征,在田间单一尺度和多尺度上不完全相同。田间单一尺度上,0～20cm土层van Genuchten模型参数α与砂粒含量、粗粉粒含量之间的相关性最显著,参数n与砂粒含量、有机质含量之间的相关性最显著;20～40cm土层参数α与有机质含量之间的相关性最显著,参数n与砂粒含量、粗粉粒含量、有机质含量之间的相关性最显著。联合多重分形分析表明,田间多尺度上,0～20cm土层参数α与砂粒含量、粗粉粒含量之间的相关性最显著,参数n与砂粒含量、粘粒含量、有机质含量之间的相关性最显著;20～40cm土层参数α与土壤容重、有机质含量之间的相关性最显著,参数n与粗粉粒含量、砂粒含量、有机质含量之间的相关性最显著。基于联合多重分形结论建立的考虑尺度效应的田间尺度上不同土层van Genuchten模型参数α、n的土壤传递函数具有较强的理论基础,预测精度较高,其中利用0～20cm土层van Genuchten模型参数α、n的土壤传递函数预测的土壤含水量的RMSE为0.0386,利用20～40cm土层van Genuchten模型参数α、n的土壤传递函数预测的土壤含水量的RMSE为0.0473,可用于估算田间尺度上的van Genuchten模型参数α和n。
土壤入渗特性与影响因素在田间单一尺度和多尺度上的相关特征并不完全相同。田间单一尺度上,稳定入渗率、前30min累积入渗量分别都与粗粉粒含量和粘粒含量的相关程度最高;联合多重分形分析表明,田间多尺度上,稳定入渗率与土壤容重、粗粉粒含量和粘粒含量之间的相关程度最高,前30min累积入渗量与粗粉粒含量和粘粒含量之间的相关程度最高。基于联合多重分形结论建立的考虑尺度效应的田间尺度上稳定入渗率和前30分钟累积入渗量的土壤传递函数具有较强的理论基础,预测精度较高,稳定入渗率和前30分钟累积入渗量土壤传递函数预测值的RMSE分别为0.1432和0.8019,可用于估算田间尺度上的土壤入渗特性。
(4)探索了田间尺度向区域尺度转换的问题,即将田间尺度上土壤粒径分布分形维数、van Genuchten模型参数α和n、土壤入渗特性与影响因素之间的联合多重分形分析得出的结论进行尺度扩展,应用到区域尺度上,建立考虑尺度效应的区域尺度上上述参数的土壤传递函数。结果表明,可以将在田间尺度上得出的联合多重分形结论应用到区域尺度上,建立区域尺度上上述参数的土壤传递函数,基于此建立的土壤传递函数的预测精度较高,可用于估算较大尺度上的上述参数,这可为构建考虑尺度效应的区域尺度上上述参数的土壤传递函数提供方法借鉴和参考。
区域尺度上,0～20cm土层和20～40cm土层土壤粒径分布分形维数的土壤传递函数的预测精度很高,预测值的RMSE分别为0.0129和0.0111。不同土层van Genuchten模型参数α、n土壤传递函数的预测精度较高,其中利用0～20cm土层和20～40cm土层van Genuchten模型参数α、n的土壤传递函数预测的土壤含水量的RMSE分别为0.0270和0.0304。稳定入渗率和前30分钟累积入渗量土壤传递函数的预测精度较高,预测值的RMSE分别为0.1855和0.9823。这说明建立的土壤传递函数可用于估算较大尺度上的上述参数,且具有较强的理论基础,可为构建考虑尺度效应的区域尺度上上述参数的土壤传递函数提供方法借鉴和。
(5)利用联合多重分形方法研究分析了不同土层土壤特性空间变异性之间的相互关系,研究结果可为探讨不同土层土壤特性空间变异性之间的相互关系提供方法借鉴。研究区域内0～20cm土层土壤含水率、土壤容重、van Genuchten模型参数n和θs的空间变异性与20～40cm土层对应变量空间变异性之间的相互关系非常密切;0～20cm土层土壤电导率、砂粒含量、粘粒含量、有机质含量、土壤粒径分布分形维数和van Genuchten模型参数α与20～40cm土层对应变量空间变异性之间的相互关系比较密切;0～20cm土层粗粉粒含量的空间变异性与20～40cm土层粗粉粒含量空间变异性之间的相互关系不密切。
论文研究结果可为研究揭示造成空间变异性的局部信息和深入分析研究对象的空间变异性机理等提供方法借鉴;可为识别在多尺度上对土壤水分运动参数都具有显著影响的因素,以及基于多尺度分析得出的结论建立考虑尺度效应的土壤水分运动参数的土壤传递函数等提供方法借鉴和参考;可为探索田间尺度向区域尺度的转换问题,即利用田间尺度上土壤水分运动参数与影响因素的联合多重分形结论,构建考虑尺度效应的区域尺度土壤水分运动参数的土壤传递函数提供方法借鉴和理论依据;可为深入分析不同土层土壤特性空间变异性之间的相互关系提供方法借鉴,同时也可为其它区域类似研究提供方法借鉴和参考。鉴于该研究的复杂性和时间限制,还需在以下几个方面展开深入研究:土壤特性的空间变异性是一个复杂问题,论文对造成土壤特性空间变异性的机理和物理解释还不够深入,在时间方面的变异性研究也尚且不足;研究区域和研究尺度不同时,论文中的一些规律和趋势有待于进一步研究和验证;基于田间尺度上土壤水分运动参数与影响因素的联合多重分形结论建立区域尺度上土壤水分运动参数土壤传递函数的可行性还有待于进一步研究;论文只是分析了上下两层土壤特性空间变异性之间的相互关系,多层土壤特性空间变异性之间的相互关系还有待于进一步深入分析;进一步研究离心机法测定土壤水分特征曲线过程中土壤容重的变化,对土壤水分特征曲线与影响因素尺度相关性的影响;如何将研究区域内土壤特性的时空变异性与作物生长有机结合起来,实施“精准农业”有待于进一步研究。
Study on spatial variability of soil properties had great significance in promoting the development and application of agriculture, soil and water science. When scale was different, spatial variability of soil properties was different, main factors and processes were also different, and mechanism of spatial variability of soil properties could be disclosed deeply with multi-scale analysis. Furthermore, spatial variability of soil properties in different soil layers and scale correlation between them and factors were not necessarily identical, and correlation of different degree between spatial variability of soil properties in different soil layers could exist. So the paper depended on National Key Technology R&D Program(2006BAD11B04) and National Natural Science Foundation of China(50879072), and firstly studied spatial variability of soil water, soil electrical conductivity, soil basic physical properties, fractal dimension of soil particle-size distribution, soil water retention curve in different soil layers and soil infiltration characteristics at the multiple scales with multifractal method; then studied scale dependency between fractal dimension of soil particle-size distribution, soil water retention curve and soil infiltration characteristics and their factors at the multiple scales with joint multifractal method, and established their pedo-transfer functions considering scale effect based on conclusions educed with joint multifractal analysis at the field scale; explored conversion from field scale to region scale, namely, conclusions educed with joint multifractal analysis at the field scale were applied at the region scale, and established pedo-transfer functions of soil water movement parameters at the region scale; at the same time, analyzed correlation between spatial variability of soil water, soil electrical conductivity, soil basic physical properties, fractal dimension of soil particle-size distribution, soil water retention curve in different soil layers. The main conclusions were as follows:
(1)In the studied area, the multifractal characteristics of soil water, soil electrical conductivity, sand content, clay content, organic matter content, stable infiltration rate, cumulative infiltration within initial 30 min and parameterαin van Genuchten model were obvious, and the multifractal characteristics of silt content, bulk density, fractal dimension of soil particle-size distribution, parameter n andθs in van Genuchten model were not obvious.
(2)Spatial variability of soil water, soil electrical conductivity, soil basic physical properties, fractal dimension of soil particle-size distribution, van Genuchten model parameters and soil infiltration characteristics were studied with multifractal method, and local information that caused their spatial variability were also identified, which could provided methods reference for studying spatial variability, its scale effect and disclosing spatial variability mechanism of parameters mentioned above.
Spatial variability of soil water and electrical conductivity decreased with the increase of average of water content and electrical conductivity. When average of water content and electrical conductivity was different, scale effect of soil water content and electrical conductivity was obviously different. As sampling area increased, when average of soil water content and electrical conductivity were high, spatial variability of soil water became large, spatial variability of soil electrical conductivity was very weak; when average of soil water content and electrical conductivity were low, spatial variability of soil water and electrical conductivity was high, and their spatial distribution had obvious patch structure.
Multifractal analysis of soil basic physical properties showed that spatial variability of sand and clay was strong, spatial variability of silt and organic matter content took second place, and spatial variability of bulk density was weakest; spatial variability of sand content in 0～20cm and 20～40cm soil layer was caused by its high value, and spatial variability of clay, organic matter and silt content was caused respectively by their low value.
Spatial variability of fractal dimension of soil particle-size distribution was very weak. Spatial variability parameterαin van Genuchten model in 0～20cm and 20～40cm soil layer was strong, its spatial variability were caused recpectively by its low and high value, and parameter n andθs in van Genuchten model were weak. Spatial variability of stable infiltration rate and cumulative infiltration within initial 30 min were strong, and spatial variability of cumulative infiltration within initial 30 min was caused by its high value.
(3)Correlation characteristics between fractal dimensions of soil particle-size distribution, parameterαandnin van Genuchten model and soil infiltration and factors at the multiple scales were studied with joint multifractal method, which showed that correlation characteristics between parameters mentioned above and factors had scale dependency, and their correlation characteristics were not completely same at the single and multiple scales. Pedo-transfer functions of parameters mentioned above considering scale effect at the field scale that were established based on conclusions educed through joint multifractal analysis between them and factors. Validation anslysis showed that these pedo-transfer functions had strong theoretical foundation, high precision, and could be used to estimate parameters mentioned above at the field scale.
Correlation characteristics between fractal dimensions of soil particle-size distribution and soil particle composition in different soil layers were same, however, correlation characteristics between fractal dimensions of soil particle-size distribution and soil particle composition were different at the single and multiple scales in the field. At the single scale, in 0～20cm and 20～40cm soil layers, correlation degree between fractal dimension of soil particle-size distribution and clay content was highest, correlation degree between fractal dimension of soil particle-size distribution and sand content took second place, and correlation degree between fractal dimension of soil particle-size distribution and silt content was lowest; at the multiple scales, in 0～20cm and 20～40cm soil layers, correlation degree between fractal dimension of soil particle-size distribution and clay content was highest, correlation degree between fractal dimension of soil particle-size distribution and silt content took second place, and correlation degree between fractal dimension of soil particle-size distribution and sand content was lowest. Pedo-transfer functions of fractal dimension of soil particle-size distribution in 0～20cm and 20～40cm soil layers parameters considering scale effect at the field scale that were established based on conclusions educed through joint multifractal analysis had strong theoretical foundation, application, high precision, RMSE of fractal dimension of soil particle-size distribution predicited with pedo-transfer functions was repectively 0.0134 and 0.0117, and these pedo-transfer functions could be used to estimate fractal dimension of soil particle-size distribution at the field scale.
Correlation characteristics between parameterαand n in van Genuchten model and factors in different soil layers were different, and correlation characteristics parameterαand n in van Genuchten model and soil basic physical properties were also different at the single and multiple scales in the field. At the single scale, in 0～20cm soil layer, correlations between parameterαand sand and silt content were remarkable, and correlations between parametern and sand and organic matter were significant; in 20～40cm soil layers, correlation between parameterαand organic matter was significant, and correlations between parametern and sand, silt and organic matter were remarkable. At the multiple scales, in 0～20cm soil layer, correlations between parameterαand sand and silt content were remarkable, and correlations between parametern and sand, clay and organic matter content were remarkable; in 20～40cm soil layers, correlations between parameterαand bulk density and organic matter content were significant, and parametern and silt, sand and organic matter content were significant. Pedo-transfer functions of parameterαandnin van Genuchten model in 0～20cm and 20～40cm soil layers considering scale effect at the field scale that were established based on conclusions educed through joint multifractal analysis had strong theoretical foundation and high precision, RMSE of soil water predicited with pedo-transfer functions of parameterαandnin van Genuchten model in 0～20cm and 20～40cm soil layers was respectively 0.0386 and 0.0473, and thes pedo-transfer functions could be used to estimate fractal dimension of parameterαandnin van Genuchten model at the field scale.
Correlation characteristics between soil infiltration characteristics and factors were different at the single and multiple scales in the field. At the single scale, correlations between stable infiltration rate and silt and clay content were most significant, and correlations between cumulative infiltration within initial 30 min and silt and clay content were also most remarkable; at the multiple scales, correlations between stable infiltration rate and bulk density, silt and clay content were most remarkable, and orrelations between cumulative infiltration within initial 30 min and silt and clay content were also most significant. Pedo-transfer functions of stable infiltration rate and cumulative infiltration within initial 30 min considering scale effect at the field scale that were established based on conclusions educed through joint multifractal analysis had strong theoretical foundation and high precision, RMSE of stable infiltration rate and cumulative infiltration within initial 30 min predicited with pedo-transfer functions was respectively 0.1432 and 0.8019, and these pedo-transfer functions could be used to estimate soil infiltration characteristics fractal dimension of parameterαandnin van Genuchten model at the field scale.
(4)Conclusions educed through joint multifractal analysis between fractal dimensions of soil particle-size distribution, parameterαand n in van Genuchten model and soil infiltration characteristics and factors at the field scale were applied at the region scale, based on conclusions mentioned above, pedo-transfer functions of fractal dimensions of soil particle-size distribution, parameterαand n in van Genuchten model and soil infiltration characteristics considering scale effect at the region scale were established. The results showed conclusions educed through joint multifractal analysis at the field scale could be applied at the region scale, and established pedo-transfer functions of fractal dimensions of soil particle-size distribution, parameterαandnin van Genuchten model and soil infiltration characteristics at the region scale based on these conclusions, which had also high precision and could be used to estimate fractal dimensions of soil particle-size distribution, parameterαandnin van Genuchten model and soil infiltration characteristics at the large scale. The result could provide methods reference for constructing pedo-transfer functions of parameters mention above.
At the region scale, forecasting precision of pedo-transfer functions of fractal dimensions of soil particle-size distribution in 0～20cm and 20～40cm soil layers were very high, and RMSE were respectively 0.0129 and 0.0111. Forecasting precision of pedo-transfer functions of parameterαand n in van Genuchten model in different soil layer were high, RMSE of soil water content forecasted based on pedo-transfer functions of parameterαandnin van Genuchten model in 0～20cm and 20～40cm was respectively 0.0270 and 0.0304. Forecasting precision of pedo-transfer functions of stable infiltration rate and cumulative infiltration within initial 30 min were high, and RMSE were respectively 0.1855 and 0.9823. The results showed that established pedo-transfer functions could be used to estimate parameters mention above at the large scale,and had strong theoretical foundation, which could provide references for constructing pedo-transfer functions of parameters mention above considering scale effect at the large scale. In order to improve them applicability and precision, it was necessary to establish pedo-transfer functions based on conclusions educed at the multiple scales.
(5)Relationship between spatial variability of soil properties in different soil layers were studied with joint multifractal method, and results could provide method reference for exploring correlation between spatial variability of different soil properties in different soil layers.
In studied area, relationship between spatial variability of soil water, bulk density, parameterθs and n in van Genuchten model in 0～20cm soil layer and their spatial variability in 20～40cm soil layer were very close; relationship between spatial variability of soil electrical conductivity, sand content, clay content, organic matter content, fractal dimension of soil particle-size distribution and parameterαin van Genuchten model in 0～20cm soil layer and their spatial variability in 20～40cm soil layer were close; relationship between spatial variability of silt content in 0～20cm soil layer and its spatial variability in 20～40cm soil layer was not close.
The results provided method reference for disclosing local information leading to spatial variability of soil properties and analyzing deeply mechanism of spatial variability of soil properties; supplied method reference for identifying factors that had significant effects on soil water movement parameters at the different scale and establishing pedo-transfer functions of soil water movement parameters considering scale effect based on conclusions educed with muti-scale analysis; provided method reference for exploreing conversion from field scale to region scale, namely, constructing pedo-transfer functions of soil water movement parameters considering scale effect at the region scale based on conclusions educed through joint multifractal analysis; supplied method reference for analyzing deep correlation between spatial variability of soil properties in different soil layers and carrying out similar study at the other region. Given the complexity of the study and time constraints, questions that need be studied deep in future included: spatial variability of soil properties was a comples problem, physical explanation on factors and processes leading to spatial variability of soil properties was not thorough enough, and studies on temporal variability of soil properties was also not enough; when study area and scale were different, law and trendency in the paper need be further studied and validated; feasibility of constructing pedo-transfer functions of soil water movement parameters considering scale effect at the region scale based on conclusions educed through joint multifractal analysis at the field scale needed to be further studied; the paper only analyzed correlation between spatial variability of soil properties in the upper and lower soil layer, and correlation between spatial variability of soil properties in different soil layer needed to be analyzed deep; bulk density of sample would change in the process of measuring soil water retention curve was measured with centrifuge method, which could had some effects on conclusions, so scale correlation between soil water retention curve and factors need to be further validated; it need further study how to combine spatial and temporal variability of soil properties and crop growth in the studied area and implement“precision agriculture”.
(1)研究区域内土壤含水率、土壤电导率、砂粒含量、粘粒含量、有机质含量、稳定入渗率、前30min累积入渗量和van Genuchten模型参数α的多重分形特征比较明显;粗粉粒含量、土壤容重、土壤粒径分布分形维数、van Genuchten模型参数n和θs的多重分形特征不明显。
(2)利用多重分形方法研究分析了土壤含水率、土壤电导率、土壤基本物理特性、土壤粒径分布分形维数、van Genuchten模型参数和土壤入渗特性的空间变异性,确定了引起上述研究对象空间变异性的局部信息,可为分析上述参数的空间变异性及尺度效应和深入揭示其空间变异机理等提供方法借鉴和参考。
研究区域内土壤含水率和土壤电导率的空间变异性都分别随土壤含水率和土壤电导率平均值的增大而减弱。土壤含水率和土壤电导率的平均值不同时,土壤含水率和土壤电导率空间变异性的尺度效应都有所差异。土壤含水率和土壤电导率的平均值较大时,随着采样面积的增大,土壤含水率的空间变异性逐渐增强,土壤电导率的空间变异性很弱;土壤含水率和土壤电导率的平均值较小时,随着采样面积的增大,土壤含水率和土壤电导率的空间变异性较强,且空间分布中都存在斑块结构。
土壤基本物理特性的多重分形分析表明,砂粒含量和粘粒含量的空间变异性较强,粗粉粒含量和有机质含量的空间变异性次之,土壤容重的空间变异性最弱;0～20cm土层和20～40cm土层砂粒含量的空间变异性都是由砂粒含量的高值分布造成的,不同土层粘粒含量、有机质含量和粗粉粒含量的空间变异性都是由对应变量的低值分布造成的。
不同土层土壤粒径分布分形维数的空间变异性都很弱。0～20cm土层和20～40cm土层van Genuchten模型参数α的空间变异性较强,且分别是由其低值和高值分布引起的;参数n和θs的空间变异性较弱。稳定入渗率和前30min累积入渗量的空间变异性较强,其中前30min累积入渗量的空间变异性是由其高值分布造成的。
(3)利用联合多重分形方法研究分析了田间土壤粒径分布分形维数、van Genuchten模型参数α和n、土壤入渗特性与影响因素在多尺度上的相关性,发现上述参数与影响因素的相关性具有尺度依赖性,在单一尺度和多尺度上的相关性特征并不完全相同。基于得出的联合多重分形结论建立了考虑尺度效应的田间尺度上上述参数的土壤传递函数,验证分析表明建立的土壤传递函数具有较强的理论基础,预测精度较高,可用于估算田间尺度上的上述参数。
不同土层土壤粒径分布分形维数与土壤颗粒组成的相关特征相似,但土壤粒径分布分形维数与土壤颗粒组成在田间单一尺度和多尺度上的相关特征有所差异。田间单一尺度上,0～20cm和20～40cm土层土壤粒径分布分形维数与粘粒含量、砂粒含量、粗粉粒含量的相关程度依次降低;联合多重分形分析表明,田间多尺度上,不同土层土壤粒径分布分形维数与粘粒含量、粗粉粒含量、砂粒含量的相关程度依次降低。基于联合多重分形结论建立的考虑尺度效应的田间尺度上0～20cm和20～40cm土层土壤粒径分布分形维数的土壤传递函数具有较强的理论基础和适应性,预测精度很高,预测值的RMSE分别为0.0134和0.0117,可用于估算田间尺度上的土壤粒径分布分形维数。
不同土层van Genuchten模型参数α、n与影响因素之间的相关特征不完全相同;van Genuchten模型参数α、n与影响因素相关的相关性特征,在田间单一尺度和多尺度上不完全相同。田间单一尺度上,0～20cm土层van Genuchten模型参数α与砂粒含量、粗粉粒含量之间的相关性最显著,参数n与砂粒含量、有机质含量之间的相关性最显著;20～40cm土层参数α与有机质含量之间的相关性最显著,参数n与砂粒含量、粗粉粒含量、有机质含量之间的相关性最显著。联合多重分形分析表明,田间多尺度上,0～20cm土层参数α与砂粒含量、粗粉粒含量之间的相关性最显著,参数n与砂粒含量、粘粒含量、有机质含量之间的相关性最显著;20～40cm土层参数α与土壤容重、有机质含量之间的相关性最显著,参数n与粗粉粒含量、砂粒含量、有机质含量之间的相关性最显著。基于联合多重分形结论建立的考虑尺度效应的田间尺度上不同土层van Genuchten模型参数α、n的土壤传递函数具有较强的理论基础,预测精度较高,其中利用0～20cm土层van Genuchten模型参数α、n的土壤传递函数预测的土壤含水量的RMSE为0.0386,利用20～40cm土层van Genuchten模型参数α、n的土壤传递函数预测的土壤含水量的RMSE为0.0473,可用于估算田间尺度上的van Genuchten模型参数α和n。
土壤入渗特性与影响因素在田间单一尺度和多尺度上的相关特征并不完全相同。田间单一尺度上,稳定入渗率、前30min累积入渗量分别都与粗粉粒含量和粘粒含量的相关程度最高;联合多重分形分析表明,田间多尺度上,稳定入渗率与土壤容重、粗粉粒含量和粘粒含量之间的相关程度最高,前30min累积入渗量与粗粉粒含量和粘粒含量之间的相关程度最高。基于联合多重分形结论建立的考虑尺度效应的田间尺度上稳定入渗率和前30分钟累积入渗量的土壤传递函数具有较强的理论基础,预测精度较高,稳定入渗率和前30分钟累积入渗量土壤传递函数预测值的RMSE分别为0.1432和0.8019,可用于估算田间尺度上的土壤入渗特性。
(4)探索了田间尺度向区域尺度转换的问题,即将田间尺度上土壤粒径分布分形维数、van Genuchten模型参数α和n、土壤入渗特性与影响因素之间的联合多重分形分析得出的结论进行尺度扩展,应用到区域尺度上,建立考虑尺度效应的区域尺度上上述参数的土壤传递函数。结果表明,可以将在田间尺度上得出的联合多重分形结论应用到区域尺度上,建立区域尺度上上述参数的土壤传递函数,基于此建立的土壤传递函数的预测精度较高,可用于估算较大尺度上的上述参数,这可为构建考虑尺度效应的区域尺度上上述参数的土壤传递函数提供方法借鉴和参考。
区域尺度上,0～20cm土层和20～40cm土层土壤粒径分布分形维数的土壤传递函数的预测精度很高,预测值的RMSE分别为0.0129和0.0111。不同土层van Genuchten模型参数α、n土壤传递函数的预测精度较高,其中利用0～20cm土层和20～40cm土层van Genuchten模型参数α、n的土壤传递函数预测的土壤含水量的RMSE分别为0.0270和0.0304。稳定入渗率和前30分钟累积入渗量土壤传递函数的预测精度较高,预测值的RMSE分别为0.1855和0.9823。这说明建立的土壤传递函数可用于估算较大尺度上的上述参数,且具有较强的理论基础,可为构建考虑尺度效应的区域尺度上上述参数的土壤传递函数提供方法借鉴和。
(5)利用联合多重分形方法研究分析了不同土层土壤特性空间变异性之间的相互关系,研究结果可为探讨不同土层土壤特性空间变异性之间的相互关系提供方法借鉴。研究区域内0～20cm土层土壤含水率、土壤容重、van Genuchten模型参数n和θs的空间变异性与20～40cm土层对应变量空间变异性之间的相互关系非常密切;0～20cm土层土壤电导率、砂粒含量、粘粒含量、有机质含量、土壤粒径分布分形维数和van Genuchten模型参数α与20～40cm土层对应变量空间变异性之间的相互关系比较密切;0～20cm土层粗粉粒含量的空间变异性与20～40cm土层粗粉粒含量空间变异性之间的相互关系不密切。
论文研究结果可为研究揭示造成空间变异性的局部信息和深入分析研究对象的空间变异性机理等提供方法借鉴;可为识别在多尺度上对土壤水分运动参数都具有显著影响的因素,以及基于多尺度分析得出的结论建立考虑尺度效应的土壤水分运动参数的土壤传递函数等提供方法借鉴和参考;可为探索田间尺度向区域尺度的转换问题,即利用田间尺度上土壤水分运动参数与影响因素的联合多重分形结论,构建考虑尺度效应的区域尺度土壤水分运动参数的土壤传递函数提供方法借鉴和理论依据;可为深入分析不同土层土壤特性空间变异性之间的相互关系提供方法借鉴,同时也可为其它区域类似研究提供方法借鉴和参考。鉴于该研究的复杂性和时间限制,还需在以下几个方面展开深入研究:土壤特性的空间变异性是一个复杂问题,论文对造成土壤特性空间变异性的机理和物理解释还不够深入,在时间方面的变异性研究也尚且不足;研究区域和研究尺度不同时,论文中的一些规律和趋势有待于进一步研究和验证;基于田间尺度上土壤水分运动参数与影响因素的联合多重分形结论建立区域尺度上土壤水分运动参数土壤传递函数的可行性还有待于进一步研究;论文只是分析了上下两层土壤特性空间变异性之间的相互关系,多层土壤特性空间变异性之间的相互关系还有待于进一步深入分析;进一步研究离心机法测定土壤水分特征曲线过程中土壤容重的变化,对土壤水分特征曲线与影响因素尺度相关性的影响;如何将研究区域内土壤特性的时空变异性与作物生长有机结合起来,实施“精准农业”有待于进一步研究。
Study on spatial variability of soil properties had great significance in promoting the development and application of agriculture, soil and water science. When scale was different, spatial variability of soil properties was different, main factors and processes were also different, and mechanism of spatial variability of soil properties could be disclosed deeply with multi-scale analysis. Furthermore, spatial variability of soil properties in different soil layers and scale correlation between them and factors were not necessarily identical, and correlation of different degree between spatial variability of soil properties in different soil layers could exist. So the paper depended on National Key Technology R&D Program(2006BAD11B04) and National Natural Science Foundation of China(50879072), and firstly studied spatial variability of soil water, soil electrical conductivity, soil basic physical properties, fractal dimension of soil particle-size distribution, soil water retention curve in different soil layers and soil infiltration characteristics at the multiple scales with multifractal method; then studied scale dependency between fractal dimension of soil particle-size distribution, soil water retention curve and soil infiltration characteristics and their factors at the multiple scales with joint multifractal method, and established their pedo-transfer functions considering scale effect based on conclusions educed with joint multifractal analysis at the field scale; explored conversion from field scale to region scale, namely, conclusions educed with joint multifractal analysis at the field scale were applied at the region scale, and established pedo-transfer functions of soil water movement parameters at the region scale; at the same time, analyzed correlation between spatial variability of soil water, soil electrical conductivity, soil basic physical properties, fractal dimension of soil particle-size distribution, soil water retention curve in different soil layers. The main conclusions were as follows:
(1)In the studied area, the multifractal characteristics of soil water, soil electrical conductivity, sand content, clay content, organic matter content, stable infiltration rate, cumulative infiltration within initial 30 min and parameterαin van Genuchten model were obvious, and the multifractal characteristics of silt content, bulk density, fractal dimension of soil particle-size distribution, parameter n andθs in van Genuchten model were not obvious.
(2)Spatial variability of soil water, soil electrical conductivity, soil basic physical properties, fractal dimension of soil particle-size distribution, van Genuchten model parameters and soil infiltration characteristics were studied with multifractal method, and local information that caused their spatial variability were also identified, which could provided methods reference for studying spatial variability, its scale effect and disclosing spatial variability mechanism of parameters mentioned above.
Spatial variability of soil water and electrical conductivity decreased with the increase of average of water content and electrical conductivity. When average of water content and electrical conductivity was different, scale effect of soil water content and electrical conductivity was obviously different. As sampling area increased, when average of soil water content and electrical conductivity were high, spatial variability of soil water became large, spatial variability of soil electrical conductivity was very weak; when average of soil water content and electrical conductivity were low, spatial variability of soil water and electrical conductivity was high, and their spatial distribution had obvious patch structure.
Multifractal analysis of soil basic physical properties showed that spatial variability of sand and clay was strong, spatial variability of silt and organic matter content took second place, and spatial variability of bulk density was weakest; spatial variability of sand content in 0～20cm and 20～40cm soil layer was caused by its high value, and spatial variability of clay, organic matter and silt content was caused respectively by their low value.
Spatial variability of fractal dimension of soil particle-size distribution was very weak. Spatial variability parameterαin van Genuchten model in 0～20cm and 20～40cm soil layer was strong, its spatial variability were caused recpectively by its low and high value, and parameter n andθs in van Genuchten model were weak. Spatial variability of stable infiltration rate and cumulative infiltration within initial 30 min were strong, and spatial variability of cumulative infiltration within initial 30 min was caused by its high value.
(3)Correlation characteristics between fractal dimensions of soil particle-size distribution, parameterαandnin van Genuchten model and soil infiltration and factors at the multiple scales were studied with joint multifractal method, which showed that correlation characteristics between parameters mentioned above and factors had scale dependency, and their correlation characteristics were not completely same at the single and multiple scales. Pedo-transfer functions of parameters mentioned above considering scale effect at the field scale that were established based on conclusions educed through joint multifractal analysis between them and factors. Validation anslysis showed that these pedo-transfer functions had strong theoretical foundation, high precision, and could be used to estimate parameters mentioned above at the field scale.
Correlation characteristics between fractal dimensions of soil particle-size distribution and soil particle composition in different soil layers were same, however, correlation characteristics between fractal dimensions of soil particle-size distribution and soil particle composition were different at the single and multiple scales in the field. At the single scale, in 0～20cm and 20～40cm soil layers, correlation degree between fractal dimension of soil particle-size distribution and clay content was highest, correlation degree between fractal dimension of soil particle-size distribution and sand content took second place, and correlation degree between fractal dimension of soil particle-size distribution and silt content was lowest; at the multiple scales, in 0～20cm and 20～40cm soil layers, correlation degree between fractal dimension of soil particle-size distribution and clay content was highest, correlation degree between fractal dimension of soil particle-size distribution and silt content took second place, and correlation degree between fractal dimension of soil particle-size distribution and sand content was lowest. Pedo-transfer functions of fractal dimension of soil particle-size distribution in 0～20cm and 20～40cm soil layers parameters considering scale effect at the field scale that were established based on conclusions educed through joint multifractal analysis had strong theoretical foundation, application, high precision, RMSE of fractal dimension of soil particle-size distribution predicited with pedo-transfer functions was repectively 0.0134 and 0.0117, and these pedo-transfer functions could be used to estimate fractal dimension of soil particle-size distribution at the field scale.
Correlation characteristics between parameterαand n in van Genuchten model and factors in different soil layers were different, and correlation characteristics parameterαand n in van Genuchten model and soil basic physical properties were also different at the single and multiple scales in the field. At the single scale, in 0～20cm soil layer, correlations between parameterαand sand and silt content were remarkable, and correlations between parametern and sand and organic matter were significant; in 20～40cm soil layers, correlation between parameterαand organic matter was significant, and correlations between parametern and sand, silt and organic matter were remarkable. At the multiple scales, in 0～20cm soil layer, correlations between parameterαand sand and silt content were remarkable, and correlations between parametern and sand, clay and organic matter content were remarkable; in 20～40cm soil layers, correlations between parameterαand bulk density and organic matter content were significant, and parametern and silt, sand and organic matter content were significant. Pedo-transfer functions of parameterαandnin van Genuchten model in 0～20cm and 20～40cm soil layers considering scale effect at the field scale that were established based on conclusions educed through joint multifractal analysis had strong theoretical foundation and high precision, RMSE of soil water predicited with pedo-transfer functions of parameterαandnin van Genuchten model in 0～20cm and 20～40cm soil layers was respectively 0.0386 and 0.0473, and thes pedo-transfer functions could be used to estimate fractal dimension of parameterαandnin van Genuchten model at the field scale.
Correlation characteristics between soil infiltration characteristics and factors were different at the single and multiple scales in the field. At the single scale, correlations between stable infiltration rate and silt and clay content were most significant, and correlations between cumulative infiltration within initial 30 min and silt and clay content were also most remarkable; at the multiple scales, correlations between stable infiltration rate and bulk density, silt and clay content were most remarkable, and orrelations between cumulative infiltration within initial 30 min and silt and clay content were also most significant. Pedo-transfer functions of stable infiltration rate and cumulative infiltration within initial 30 min considering scale effect at the field scale that were established based on conclusions educed through joint multifractal analysis had strong theoretical foundation and high precision, RMSE of stable infiltration rate and cumulative infiltration within initial 30 min predicited with pedo-transfer functions was respectively 0.1432 and 0.8019, and these pedo-transfer functions could be used to estimate soil infiltration characteristics fractal dimension of parameterαandnin van Genuchten model at the field scale.
(4)Conclusions educed through joint multifractal analysis between fractal dimensions of soil particle-size distribution, parameterαand n in van Genuchten model and soil infiltration characteristics and factors at the field scale were applied at the region scale, based on conclusions mentioned above, pedo-transfer functions of fractal dimensions of soil particle-size distribution, parameterαand n in van Genuchten model and soil infiltration characteristics considering scale effect at the region scale were established. The results showed conclusions educed through joint multifractal analysis at the field scale could be applied at the region scale, and established pedo-transfer functions of fractal dimensions of soil particle-size distribution, parameterαandnin van Genuchten model and soil infiltration characteristics at the region scale based on these conclusions, which had also high precision and could be used to estimate fractal dimensions of soil particle-size distribution, parameterαandnin van Genuchten model and soil infiltration characteristics at the large scale. The result could provide methods reference for constructing pedo-transfer functions of parameters mention above.
At the region scale, forecasting precision of pedo-transfer functions of fractal dimensions of soil particle-size distribution in 0～20cm and 20～40cm soil layers were very high, and RMSE were respectively 0.0129 and 0.0111. Forecasting precision of pedo-transfer functions of parameterαand n in van Genuchten model in different soil layer were high, RMSE of soil water content forecasted based on pedo-transfer functions of parameterαandnin van Genuchten model in 0～20cm and 20～40cm was respectively 0.0270 and 0.0304. Forecasting precision of pedo-transfer functions of stable infiltration rate and cumulative infiltration within initial 30 min were high, and RMSE were respectively 0.1855 and 0.9823. The results showed that established pedo-transfer functions could be used to estimate parameters mention above at the large scale,and had strong theoretical foundation, which could provide references for constructing pedo-transfer functions of parameters mention above considering scale effect at the large scale. In order to improve them applicability and precision, it was necessary to establish pedo-transfer functions based on conclusions educed at the multiple scales.
(5)Relationship between spatial variability of soil properties in different soil layers were studied with joint multifractal method, and results could provide method reference for exploring correlation between spatial variability of different soil properties in different soil layers.
In studied area, relationship between spatial variability of soil water, bulk density, parameterθs and n in van Genuchten model in 0～20cm soil layer and their spatial variability in 20～40cm soil layer were very close; relationship between spatial variability of soil electrical conductivity, sand content, clay content, organic matter content, fractal dimension of soil particle-size distribution and parameterαin van Genuchten model in 0～20cm soil layer and their spatial variability in 20～40cm soil layer were close; relationship between spatial variability of silt content in 0～20cm soil layer and its spatial variability in 20～40cm soil layer was not close.
The results provided method reference for disclosing local information leading to spatial variability of soil properties and analyzing deeply mechanism of spatial variability of soil properties; supplied method reference for identifying factors that had significant effects on soil water movement parameters at the different scale and establishing pedo-transfer functions of soil water movement parameters considering scale effect based on conclusions educed with muti-scale analysis; provided method reference for exploreing conversion from field scale to region scale, namely, constructing pedo-transfer functions of soil water movement parameters considering scale effect at the region scale based on conclusions educed through joint multifractal analysis; supplied method reference for analyzing deep correlation between spatial variability of soil properties in different soil layers and carrying out similar study at the other region. Given the complexity of the study and time constraints, questions that need be studied deep in future included: spatial variability of soil properties was a comples problem, physical explanation on factors and processes leading to spatial variability of soil properties was not thorough enough, and studies on temporal variability of soil properties was also not enough; when study area and scale were different, law and trendency in the paper need be further studied and validated; feasibility of constructing pedo-transfer functions of soil water movement parameters considering scale effect at the region scale based on conclusions educed through joint multifractal analysis at the field scale needed to be further studied; the paper only analyzed correlation between spatial variability of soil properties in the upper and lower soil layer, and correlation between spatial variability of soil properties in different soil layer needed to be analyzed deep; bulk density of sample would change in the process of measuring soil water retention curve was measured with centrifuge method, which could had some effects on conclusions, so scale correlation between soil water retention curve and factors need to be further validated; it need further study how to combine spatial and temporal variability of soil properties and crop growth in the studied area and implement“precision agriculture”.
引文
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