Alternative methods in the development of pedotransfer functions for soil hydraulic characteristics

Soil hydraulic properties are needed in the modeling of water flow and solute movement in the vadose zone. Pedotransfer functions (PTFs) have received the attention of many researchers for indirect determination of hydraulic properties from basic soil properties as an alternative to direct measurement. The objective of this study was to compare the performance of cascade forward network (CFN), multiple-linear regression (MLR), and seemingly unrelated regression (SUR) methods using prediction capabilities of point and parametric PTFs developed by these methods. The point PTFs estimated field capacity (FC), permanent wilting point (PWP), available water capacity (AWC), and saturated hydraulic conductivity (Ks) and the parametric PTFs estimated the van Genuchten retention parameters. A total of 180 soil samples was extracted from the UNSODA database and divided into two groups as 135 for the development and 45 for the validation of the PTFs. The model performances were evaluated with three statistical tools: the maximum error (ME), the model efficiency (EF), and the D index (D) using the observed and predicted values of a given parameter. Despite the fact that the differences among the three methods in prediction accuracies of the point and parametric PTFs were not statistically significant (p > 0.05) except θ_r and α (p < 0.05) based on the ANOVA test, overall MLR and SUR were somewhat better than CFN in prediction of the point PTFs, whereas CFN performed better than the other two methods in prediction of the parametric PTFs. The F.F values of FC and θ_r for CFN, MLR, and SUR methods were 0.705. 0.805, 0.795 and 0.356, −0.290, −0.290, respectively, which refer to the best and worst predictions. Properties (Ks, θ_r, α) having some difficulty in prediction were better predicted by CFN and SUR methods, where these methods predict all hydraulic properties from basic soil properties simultaneously rather than individually as in MLR. This suggests that multivariate analysis using such functional relationships between hydraulic properties and basic soil properties can be utilized in developing more accurate point and parametric PTFs with less time and effort.     

青海三江源地区土壤容重转换函数的建立与比较

Bulk density (BD) is an important soil physical property and has significant effect on soil water conservation function. Indirect methods, which are called pedotransfer functions (PTFs), have replaced direct measurement and can acquire the missing data of BD during routine soil surveys. In this study, multiple linear regression (MLR) and artificial neuron network (ANN) methods were used to develop PTFs for predicting BD from soil organic carbon (OC), texture and depth in the Three-River Headwater region of Qinghai Province, China. The performances of the developed PTFs were compared with 14 published PTFs using four indexes, the mean error (ME), standard deviation error (SDE), root mean squared error (RMSE) and coefficient of determination (R²). Results showed that the performances of published PTFs developed using exponential regression were better than those developed using linear regression from OC. Alexander (1980)-B, Alexander (1980)-A and Manrique and Jones (1991)-B PTFs, which had good predictions, could be applied for the soils in the study area. The PTFs developed using MLR (MLR-PTFs) and ANN (ANN-PTFs) had better soil BD predictions than most of published PTFs. The ANN-PTFs had better performances than the MLR-PTFs and their performances could be improved when soil texture and depth were added as predictor variables. The idea of developing PTFs or predicting soil BD in the study area could provide reference for other areas and the results could lay foundation for the estimation of soil water retention and carbon pool.     

利用土壤传递函数估算土壤水力学特性研究进展

Characterization of soil hydraulic properties is important to environment management; however, it is well recognized that it is laborious, time-consuming and expensive to directly measure soil hydraulic properties. This paper reviews the development of pedotransfer functions (PTFs) used as an alternative tool to estimate soil hydraulic properties during the last two decades. Modern soil survey techniques like satellite imagery/remote sensing has been used in developing PTFs. Compared to mechanistic approaches, empirical relationships between physical properties and hydraulic properties have received wide preference for predicting soil hydraulic properties. Many PTFs based on different parametric functions can be found in the literature. A number of researchers have pursued a universal function that can describe water retention characteristics of all types of soils, but no single function can be termed generic though van Genuchten (VG) function has been the most widely adopted. Most of the reported parametric PTFs focus on estimation of VG parameters to obtain water retention curve (WRC). A number of physical, morphological and chemical properties have been used as predictor variables in PTFs. Conventionally, regression algorithms/techniques (statistical/neural regression) have been used for calibrating PTFs. However, there are reports of utilizing data mining techniques, e.g., pattern recognition and genetic algorithm. It is inferred that it is critical to refine the data used for calibration to improve the accuracy and reliability of the PTFs. Many statistical indices, including root mean square error (RMSE), index of agreement (d), maximum absolute error (ME), mean absolute error (MAE), coefficient of determination (r²) and correlation coefficient (r), have been used by different researchers to evaluate and validate PTFs. It is argued that being location specific, research interest in PTFs will continue till generic PTFs are developed and validated. In future studies, improved methods will be required to extract information from the existing database.     

沿海滩涂农田耕层土壤饱和导水率间接方法的评价

为筛选和构建适合苏北沿海滩涂围垦农田耕层土壤饱和水力传导率间接估算的土壤转换函数,在典型地块实测土壤饱和导水率和相关土壤基本性质的基础上,分析了11种根据基本土壤性质预测饱和导水率的转换函数方法的适用性,同时探讨了基于人工神经网络方法的土壤转换函数的预测效果。结果表明:滩涂围垦农田耕层土壤平均饱和导水率为10.04 cm/d,属低透水强度;在现有的土壤饱和导水率转换函数中,Vereecken函数是最适合滩涂围垦农区土壤、具有最佳预测精度的转换函数,其预测均方根误差为8.154,其次是Li、Campbell和Rawls函数;以砂粒、粘粒、容重和有机质作为输入因子,基于人工神经网络的土壤转换函数较Vereecken函数其预测均方根误差降至7.920,在输入因子中增加土壤盐分指标可进一步提高饱和导水率的预测精度,其预测均方根误差降为7.634。本文的研究结果显示利用人工神经网络方法建立的转换函数可有效提高滩涂盐渍农田土壤饱和导水率的预测精度。     

Soil water-retention prediction from pedotransfer functions for some Indian soils

This paper discusses the development of pedotransfer functions (PTFs) and uses a multiple nonlinear regression technique to validate point and parametric PTFs for the estimation of a water-retention curve from basic soil properties such as particle-size distribution, bulk density and organic matter content. One hundred soil samples were collected at different depths from different locations in the Pavanje river basin that lies within the southern coastal region of Karnataka, India. Prediction accuracies were evaluated using the coefficient of determination (R ²), root mean square error (RMSE) and mean error (ME) between measured and predicted values. Overall, both point and parametric methods predicted water contents at selected water potentials with considerable accuracy. However, prediction of the soil water-retention curve using PTFs by point estimation method was relatively more successful (best case R ² = 0.983) for the sampled soils. F-tests were also conducted for all cases. For one regression equation, the p-value was zero and for other equation, values were close to zero. Critical comparative analysis was carried out on the performances of the point and parametric methods. Use of the developed PTFs is suggested for the prediction of a water-retention curve for loamy sand and sandy loam soils in this area of the coastal region of southern India.     

Estimating the bulk density in 0– 20 cm of tilled soils in China’s Loess Plateau using support vector machine modeling

ABSTRACT

Pedotransfer functions (PTFs), as an indirect forecasting method, offer an alternative for labor-intensive bulk density (BD) measurements. In order to improve the forecasting accuracies, support vector machine (SVM) method was first used to develop PTFs for predicting BD. Cross-validation and grid-search methods were used to automatically determine the SVM parameters in the forecasting process. Soil texture and organic matter content were selected as input variables based on results of predecessors, coupled with gray correlation theory. And additional properties were added as inputs for improving PTF's accuracy and reliability. The performance of the PTF established by SVM method was compared with artificial neural network (ANN) method and published PTFs using two indexes: root-mean-square error (RMSE) and coefficient of determination(R²). Results showed that the average RMSE of published PTFs was 0.1053, and the R² was 0.4558. The RMSE of ANN–PTF was 0.0638, and the R² was 0.7235. The RMSE of SVM–PTF was 0.0558, and the R² was 0.7658. Apparently, the SVM–PTF had better performance, followed by ANN–PTF. Additionally, performances could be improved when accumulated receiving water was added as predictor variable. Therefore, the first application of SVM data mining techniques in the prediction of soil BD was successful, improved the accuracy of predictions, and enhanced the function of soil PTFs. The idea of developing PTFs using SVM method for predicting soil BD in the study area could provide a reference for other areas.     

Applicability of site-specific pedotransfer functions and rosetta model for the estimation of dynamic soil hydraulic properties under different vegetation covers

Background, Aims, and Scope  During the last decades, different methods have been developed to determine soil hydraulic properties in the field and laboratory. These methodologies are frequently time-consuming and/or expensive. An indirect method, named Pedotransfer Functions (PTFs), was developed to predict soil hydraulic properties using other easily measurable soil (physical and chemical) parameters. This work evaluates the use of the PTFs included in the Rosetta model (Schaap et al. 2001) and compares them with PTFs obtained specifically for soils under two different vegetation covers. Methods  Rosetta software includes two basic types of pedotransfer functions (Class PTF and Continuous PTF), allowing the estimation of van Genuchten water retention parameters using limited (textural classes only) or more extensive (texture, bulk density and one or two water retention measurements) input data. We obtained water retention curves from undisturbed samples using the ‘sand box’ method for potentials between saturation and 20 kPa, and the pressure membrane method for potentials between 100 and 1500 kPa. Physical properties of sampled soils were used as input variables for the Rosetta model and to determine site-specific PTFs. Results  The Rosetta model accurately predicts water content at field capacity, but clearly underestimates it at saturation. Poor agreement between observed and estimated values in terms of root mean square error were obtained for the Rosetta model in comparison with specific PTFs. Discrepancies between both methods are comparable to results obtained by other authors. Conclusions  Site-specific PTFs predicted the van Genuchten parameters better than Rosetta model. Pedotransfers functions have been a useful tool to solve the water retention capacity for soils located in the southern Pyrenees, where the fine particle size and organic matter content are higher. The Rosetta model showed good predictions for the curve parameters, even though the uncertainty of the data predicted was higher than for the site-specific PTFs. Recommendations and Perspectives  The Rosetta model accurately predicts the retention curve parameters when the use is related with wide soil types; nevertheless, if we want to obtain good predictors using a homogenous soil database, specific PTFs are required. ESS-Submission Editor: Prof. Zhihong Xu, PhD (zhihong.xu@griffith.edu.au)     

基于人工神经网络的数据处理和多目标群方法用土壤传递函数(PTFs)估算保水性

Pedotransfer functions(PTFs) have been developed to estimate soil water retention curves(SWRC) by various techniques.In this study PTFs were developed to estimate the parameters(θ s,θ r,α and λ) of the Brooks and Corey model from a data set of 148 samples.Particle and aggregate size distribution fractal parameters(PSDFPs and ASDFPs,respectively) were computed from three fractal models for either particle or aggregate size distribution.The most effective model in each group was determined by sensitivity analysis.Along with the other variables,the selected fractal parameters were employed to estimate SWRC using multi-objective group method of data handling(mGMDH) and different topologies of artificial neural networks(ANNs).The architecture of ANNs for parametric PTFs was different regarding the type of ANN,output layer transfer functions and the number of hidden neurons.Each parameter was estimated using four PTFs by the hierarchical entering of input variables in the PTFs.The inclusion of PSDFPs in the list of inputs improved the accuracy and reliability of parametric PTFs with the exception of θ s.The textural fraction variables in PTF1 for the estimation of α were replaced with PSDFPs in PTF3.The use of ASDFPs as inputs significantly improved α estimates in the model.This result highlights the importance of ASDFPs in developing parametric PTFs.The mGMDH technique performed significantly better than ANNs in most PTFs.     

Predicting Cationic Exchange Capacity in Calcareous Soils of East-Azerbaijan Province,Northwest Iran

The aim of this research is to study the efficiency of pedotransfer functions (PTFs) and artificial neural networks (ANNs) for cationic exchange capacity (CEC) prediction using readily available soil properties. Here, 417 soil samples were collected from the calcareous soils located in East-Azerbaijan province, northwest Iran and readily available soil properties, such as particle size distribution (PSD), organic matter (OM) and calcium carbonate equivalent (CCE), were measured. The entire 417 soil samples were divided into two groups, a training data set (83 soil samples) and test data set (334 soil samples). The performances of several published and derived PTFs and developed neural network algorithms using multilayer perceptron were compared, using a test data set. Results showed that, based on statistics of RMSE and R², PTFs and ANNs had a similar performance, and there was no significant difference in the accuracy of the model results. The result of the sensitivity analysis showed that the ANN models were very sensitive to the clay variable (due to the high variability of the clay). Finally, the models tested in this study could account for 85% of the variations in cationic exchange capacity (CEC) of soils in the studied area.

Abbreviations: ANN: arti?cial neural networks; MLP: multilayer perceptron; MLR: multiple linear regression; PTFs: Pedotransfer Functions; RBF: Radial Basis Function; MAE: mean absolute error; MSE: mean square error; CEC: cationic exchange capacity     

Estimating the water retention curve from soil properties: comparison of linear, nonlinear and concomitant variable methods

The unsaturated soil hydraulic functions involving the soil–water retention curve (SWRC) and the hydraulic conductivity provide useful integrated indices of soil quality. Existing and newly devised methods were used to formulate pedotransfer functions (PTFs) that predict the SWRC from readily available soil data. The PTFs were calibrated using a large soils database from Hungary. The database contains measured soil–water retention data, the dry bulk density, sand, silt and clay percentages, and the organic matter content of 305 soil layers from some 80 soil profiles. A three-parameter van Genuchten type function was fitted to the measured retention data to obtain SWRC parameters for each soil sample in the database. Using a quasi-random procedure, the database was divided into “evaluation” (EVAL) and “test” (TEST) parts containing 225 and 80 soil samples, respectively. Linear PTFs for the SWRC parameters were calculated for the EVAL database. The PTFs used for this purpose particle-size percentages, dry bulk density, organic matter content, and the sand/silt ratio, as well as simple transforms (such as logarithms and products) of these independent variables. Of the various independent variables, the eight most significant were used to calculate the different PTFs. A nonlinear (NL) predictive method was obtained by substituting the linear PTFs directly into the SWRC equation, and subsequently adjusting the PTF parameters to all retention data of the EVAL database. The estimation error (SSQ) and efficiency (EE) were used to compare the effectiveness of the linear and nonlinearly adjusted PTFs. We found that EE of the EVAL and the TEST databases increased by 4 and 7%, respectively, using the second nonlinear optimization approach. To further increase EE, one measured retention data point was used as an additional (concomitant) variable in the PTFs. Using the 20 kPa water retention data point in the linear PTFs improved the EE by about 25% for the TEST data set. Nonlinear adjustment of the concomitant variable PTF using the 20 kPa retention data point as concomitant variable produced the best PTF. This PTF produced EE values of 93 and 88% for the EVAL and TEST soil data sets, respectively.     

Selection of a Suitable Soft Computing Model for Estimation of Soil Cation Exchange Capacity

ABSTRACT

Measuring of soil cation exchange capacity (CEC) is difficult and time-consuming. Therefore, it is essential to develop an indirect approach such as pedotransfer functions (PTFs) to predict this property from more readily available soil data. The aim of this study was to compare multiple linear and nonlinear regression, adaptive neurofuzzy inference system, and an artificial neural network (ANN) model to develop PTFs for predicting soil CEC. One hundred and seventy-one soil samples were used into two subsets for training and testing of the models. The model's prediction capability was evaluated by statistical indicators that include RMSE, R², MBE, and RI. Results showed that the ANN model had the most reliable prediction when compared with other models. This study provides a strong basis for predicting soil CEC and identifying the most determinant properties influencing soil CEC in the north regions of Iran. Analytical framework results could be applied to other parts of the world with similar challenges.

Abbreviations: ANFIS: Adaptive Neuro-Fuzzy Inference System; ANN: Artificial Neural Network; CEC: Cation Exchange Capacity; CV: Coefficient of Variation; FFBP: Feed-Forward Back-Propagation; FIS: Fuzzy Inference System; MBE: Mean Bias Error; MF: Membership Function; MLR: Multiple Linear Regressions; MNLR: Multiple Non-Linear Regressions; MLP: Multi-layer Perceptron; OC: Organic Carbon; PTFs: Pedotransfer Functions; R²: Determination Coefficient; RI: Relative Improvement; RMSE: Root Mean Square Error; SD: Standard Deviation     

时间尺度对草地水土保持效应定量研究的影响

时间尺度效应的定量分析有利于进一步理解植被的水土保持机理。基于福建省长汀县河田镇草覆和裸土侵蚀试验小区2007—2010年的观测数据,分析了次降雨、月、季和年时间尺度下降雨、植被、保水和保土效应这4类参数的变化特征,并建立保水（土）效应RE（SE）的估算模型以探讨诸因素的联系,其中RE（SE）为草覆小区与裸土对照小区的径流深度（土壤流失量）的比值。结果表明:4类参数在各时间尺度呈现不同的量值及变化特性,RE和SE因消除了同类因子的影响在各时间尺度之间及其内部均相对稳定。在次降雨尺度RE较低（< 0.3）区间及月尺度下,降雨和植被的耦合作用导致了较好的保水效应,而在RE略高（0.3～0.4）和较高（> 0.7）区间以及年尺度,降雨因子主导了研究小区的保水效应（R² > 0.78）。从保土效应来看,在次降雨和年尺度主要受降雨或/和植被的影响,绿草叶面积指数能较好地表征研究小区草地的保土正效应（SE < 1,R² > 0.55）,而最大30 min雨强可精确表征研究小区草地的保土负效应（SE > 1,R² > 0.79）。无论保水或保土效应,其估算模型在月和季两个中等时间尺度均存在较大的不确定性（R² ≈0.4）。可见在不同的时间尺度,影响草地水土保持效应的诸要素呈现不同的变化和耦合特征,显示时间尺度在植被水土保持研究中的重要性。     

土壤水力性质的估算——土壤转换函数

利用一些易获得的土壤理化参数可以估算土壤水力性质,这些估算方程统称为土壤转换函数,即PTFs（Pedo-Transfer Functions）。本文综述了目前国内外土壤转换函数研究的概况,并利用在华北地区收集到的实测资料,建立了一些土壤转换函数,通过对部分转换函数作的检验和评估,总体而言,所建立的各类模型的预测效果都比较理想,应用于小比例尺的区域研究是可行的。     

Soil quality indicators under continuous cropping systems in the Argentinean Pampas

Over the last two decades, soil cultivation practices in the southern Argentinean Pampas have been changing from a 7 year cash-crop production system alternated with 2–3 years under pasture, to a continuous cropping system. A better understanding of the impact of the period of time a field has been under continuous cropping on a broad spectrum of soil properties related to soil quality is needed to target for sustainable cropping systems. The objectives of this study were to: (i) assess the relationship between physical and chemical soil parameters related to soil quality and (ii) identify soil quality indicators sensitive to soil changes under continuous cropping systems in the Argentinean Pampas.

Correlation analysis of the 29 soil attributes representing soil physical and chemical properties (independent variables) and years of continuous cropping (dependent variable) resulted in a significant correlation (p < 0.05) in 78 of the 420 soil attribute pairs. We detected a clear relationship between hydraulic conductivity at tension h (K_h) and structural porosity (ρ_e); ρ_e being a simple tool for monitoring soil hydraulic conditions.

Soil tillage practice (till or no-till) affected most of the soil parameters measured in our study. It was not possible to find only one indicator related to the years under continuous cropping regardless of the cultivation practice. We observed a significant relationship between years under continuous cropping and K_h under no-till (NT) and wheat fallow (p < 0.001, R² = 0.70). Under these conditions, K₋₄₀ diminished as the number of years under continuous cropping increased.

The change in mean weight diameter (CMWD) was the only physical parameter related to the number of years under continuous cropping, explaining 36% of the variability in the number of years under continuous cropping (p < 0.001) The combination of three soil quality indicators (CMWD, partial R² = 0.38; slope of the soil water retention curve at its inflexion point (S), partial R² = 0.14 and cation exchange capacity (CEC), partial R² = 0.13) was able to explain, in part, the years under continuous cropping (R² = 0.65; p value > 0.001), a measure related to soil quality.     

Support Vector Machine and Nonlinear Regression Methods for Estimating Saturated Hydraulic Conductivity

Pedotransfer functions (PTFs) are widely used for hydrological calculations based on the known basic properties of soils and sediments. The choice of predictors and the mathematical calculus are of particular importance for the accuracy of calculations. The aim of this study is to compare PTFs with the use of the nonlinear regression (NLR) and support vector machine (SVM) methods, as well as to choose predictor properties for estimating saturated hydraulic conductivity (K_s). K_s was determined in direct laboratory experiments on monoliths of agrosoddy-podzolic soil (Umbric Albeluvisol Abruptic, WRB, 2006) and calculated using PTFs based on the NLR and SVM methods. Six classes of predictor properties were tested for the calculated prognosis: K_s-1 (predictors: the sand, silt, and clay contents); K_s-2 (sand, silt, clay, and soil density); K_s-3 (sand, silt, clay, soil organic matter); K_s-4 (sand, silt, clay, soil density, organic matter); K_s-5 (clay, soil density, organic matter); and K_s-6 (sand, clay, soil density, organic matter). The efficiency of PTFs was determined by comparison with experimental values using the root mean square error (RMSE) and determination coefficient (R²). The results showed that the RMSE for SVM is smaller than the RMSE for NLR in predicting K_s for all classes of PTFs. The SVM method has advantages over the NLR method in terms of simplicity and range of application for predicting K_s using PTFs.     

Prediction of soil saturated water content using evolutionary polynomial regression (EPR)

The measurement of saturated water content (SWC) is necessary in the estimation of soil water retention and unsaturated hydraulic conductivity curves. In several studies, pedotransfer functions (PTFs) were developed to predict SWC. Among them, evolutionary polynomial regression (EPR) is one that can operate on large quantities of data in order to capture nonlinear and complex interactions between the variables of the system. In this study, the evolutionary data-mining technique was used to derive new PTFs and different methods were evaluated, such as the soil porosity method, Rosetta method, and others, for the estimation of SWC. For this purpose, 270 soil samples (3:1 ratio for development and validation) from three data sets were used. Among 190 PTFs provided by EPR, one equation with the highest accuracy and the least number of inputs was selected. The EPR predictions were compared with the experimental results as well as the PTFs proposed in previous studies. Comparison of the statistical indicators showed that the ‘proposed PTF’ and ‘porosity method’ are the best and worst methods for the prediction of SWC, respectively. Also, good predictions were achieved from the proposed approaches by the groups of Scheinost, Vereecken, and Williams.     

Using support vector machines to predict cation exchange capacity of different soil horizons in Qingdao City,China

Agricultural, environmental and ecological modeling requires soil cation exchange capacity (CEC) that is difficult to measure. Pedotransfer functions (PTFs) are thus routinely applied to predict CEC from easily measured physicochemical properties (e.g., texture, soil organic matter, pH). This study developed the support vector machines (SVM)‐based PTFs to predict soil CEC based on 208 soil samples collected from A and B horizons in Qingdao City, Shandong Province, China. The database was randomly split into calibration and validation datasets in proportions of 3:1 using the bootstrap method. The optimal SVM parameters were searched by applying the genetic algorithm (GA). The performance of SVM models was compared to those of multiple stepwise regression (MSR) and artificial neural network (ANN) models. Results show that the accuracy of CEC predicted by SVM improves considerably over those predicted by MSR and ANN. The performance of SVM for B horizon (R² = 0.85) is slightly better than that for A horizon (R² = 0.81). The SVM is a powerful approach in the simulation of nonlinear relationship between CEC and physicochemical properties of widely distributed samples from different soil horizons. Sensitivity analysis was also conducted to explore the influence of each input parameter on the CEC predictions by SVM. The clay content is the most sensitive parameter, followed by soil organic matter and pH, while sand content has the weakest influence. This suggests that clay is the most important predictor for predicting CEC of both soil horizons.     

基于土壤传递函数的土壤持水特性间接估计及其空间变异性研究

A total of 107 soil samples were taken from the city of Qingdao,Shandong Province,China.Soil water retention data at 2.5,6,10,33,100,300,and 1 500 kPa matric potentials were measured using a pressure membrane apparatus.Multiple linear regression (MLR) was used to develop pedotransfer functions (PTFs) for single point estimation and van Genuchten parameter estimation based on readily measurable soil properties,i.e.,MLR-based point (MLRP) PTF and MLR-based parametric (MLRV) PTF.The double cross-validation method was used to evaluate the accuracy of PTF estimates and the stability of the PTFs developed in this study.The performance of MLRP and MLRV PTFs in estimating water contents at matric potentials of 10,33,and 1 500 kPa was compared with that of two existing PTFs,the Rawls PTF and the Vereecken PTF.In addition,geostatistical analyses were conducted to assess the capabilities of these PTFs in describing the spatial variability of soil water retention characteristics.Results showed that among all PTFs only the Vereecken PTF failed to accurately estimate water retention characteristics.Although the MLRP PTF can be used to predict retention characteristics through traditional statistical analyses,it failed to describe the spatial variability of soil water retention characteristics.Although the MLRV and Rawls PTFs failed to describe the spatial variability of water contents at a matric potential of 10 kPa,they can be used to quantify the spatial variability of water contents at matric potentials of 33 and 1 500 kPa.