| 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".
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