Soil hydrodynamic properties drive the flow of water in the soil-plant-atmosphere system, and hence control processes such as aquifer recharge or nutrient fluxes between soil and vegetation. Knowledge of soil hydrodynamics is important for modeling physical processes related to soil water content. Despite great advances in measurement methods, it is still difficult to determine soil hydraulic properties accurately, especially for undisturbed soils and in the dry range. However, the measurement of the soil hydraulic properties is time-consuming, labor-intensive and expensive (Merdun, 2010). If the area being evaluated is large enough to exhibit substantial spatial variability of soil water availability, it is costly and time consuming to perform adequate measurements to provide good estimates within the temporal and financial constraints of the project (Givi et al., 2004).

Recently, an alternative, indirect estimation of soil hydraulic properties from widely available or more easily measured basic soil properties using pedotransfer functions (PTFs) has attracted considerable attention of researchers in a variety of fields such as soil scientists, hydrologists, and agricultural and environmental engineers (Minasny et al., 2004; Huang et al., 2010).PTFs are based on physical approaches or on empirical regression equations that link soil physical and/or chemical characteristics, easily measured, to hydrodynamic properties (Bouma, 1989; Hamblin, 1991) that just exist as a narrow relationship among these soil properties.

PTFs are classified in three main groups, i.e., class PTFs (Baker & Ellison, 2008); point PTFs (Ghanbarian-Alavijeh & Millán, 2010); and parametric or function PTFs (Santra & Das, 2008). The classes PTFs are used to estimate an average value of soil hydraulic parameters for each class of soil texture. These PTFs are inexpensively developed; however, their accuracy is less than point and parametric PTFs (Abbasi et al., 2011). Point PTFs functions estimate the water contents at fixed pressure heads, often including the water content at the field water capacity (FWC) and the permanent wilting point (PWP) or the water content at a given matric potential (Givi et al., 2004). Function PTFs predict the parameters of a closed-form analytical equation or empirical parameters of water retention curve models, such as the model of Brooks & Corey (1964) or the van Genuchten equation (Van Genuchten, 1980).

At present, there are two common methods to develop PTFs for point and/or function estimations, which are the Multiple Linear Regression (MLR) method (Merdun et al., 2006) and the Artificial Neural Network (ANN) method (Minasny et al., 2004; Sarmadian & Mehrjardi, 2008). In recent years, the ANN method was used to improve the prediction accuracy of PTFs (Kumar et al., 2010; Rezaei-Arshad et al., 2013; Moghimi et al., 2014; Mukhlisin & Abd Rahman, 2014; Rezaeianzadeh et al., 2014).

An advantage of ANN, as compared to other methods, is that it does not require a priori models. The optimal, possibly nonlinear, relations which link the input data (bulk density, particle-size data, etc.) to output data (soil water retention, FWC, etc.) are obtained and implemented in an iterative calibration procedure (Schaap et al., 2001). As a result, ANN method can typically extract the maximum amount of information from the data. For these reasons, the ANN method had a wide application (Merdun et al., 2006; Yi et al., 2013), and many scholars implicate that the general prediction of ANN is better than the MLR method (Moghimi et al., 2014).

However, this method also has some significant disadvantages which must be taken into consideration (Minasny et al., 2004). First of all, the interpretation of ANN is often difficult and subjective, because the fitting with the transfer function is a black-box approach. In addition, as it is usually the case in optimization, the sets of optimized weighting factors are not mathematically unique because the likelihood of convergence is at the local minimum. Consequently, different initial weight values may yield various results that deviate from the global minimum. Nevertheless, the ANN method showed good prediction function, and it would play a greater role in the prediction of soil hydraulic properties with the improvement of scientific technology.

Najafi & Givi (2006) used the ANN and PTF methods for prediction of soil bulk density. They pointed out that the ANNs are able to predict the soil bulk density better than the PTFs. Amini et al. (2005) estimated the cation exchange capacity (CEC) in the central part of Iran using soil organic matter and clay contents. They used the ANN and five experimental models that were on the basis of regression methods for their predictions. They showed that a neural network PTF with eight hidden neurons was able to predict CEC better than the regression PTFs. Also the ANN model significantly improved the accuracy of the prediction by up to 25%. They concluded that network models are in general more suitable for capturing the non-linearity of the relationship between variables. Jain & Kumar (2006) indicated that the ANN technique can be successfully employed for the purpose of calibration of infiltration equations. They had also found that the ANNs are capable of performing very well in situations of limited data availability. In contrast, Merdun (2010) pointed out that although the differences between regression and ANN models were not statistically significant, regression predicted point and parametric variables of soil hydraulic parameters better than ANN.

In order to make the PTFs as widely applicable as possible, Schaap et al. (2001) developed the Rosetta software by using a large number of soil hydraulic data and corresponding predictive soil properties. The Rosetta model based on ANNs works in a hierarchical approach which employs five different PTFs to predict water retention curves (Schaap et al., 2001).Rosetta software is used widely by many scientists for the estimation of soil water retention (SWR), saturated hydraulic conductivity and unsaturated hydraulic conductivity parameters (Schaap et al., 2001; Givi et al., 2004; Minasny et al., 2004; Stumpp et al., 2009).

Although there are many studies on developing and using PTFs as listed above, there is no universal method for the prediction of soil hydraulic parameters. Moreover, the existing PTFs for the estimation of soil hydraulic properties in the literature were not always applicable in other regions with acceptable accuracy (Cornelis et al., 2001; Wagner et al., 2001; Nemes et al., 2003). So, it is necessary to develop and evaluate the PTFs in different regions. Moreover, there are few studies comparing the performance of different methods simultaneously in the development of PTFs in the study area and its surrounding areas. Therefore, the objectives of this study were (1) to develop and validate the point PTFs using Multi-Layer Perceptron (MLP), MLR and function PTFs using the Rosetta software for the estimation of soil moisture in various matric potentials, and (2) to compare the predictive capabilities of the three methods using selected evaluation criteria in the Gilevan Region of Guilan Province, northern Iran.

In this paper, use of MLR, ANN and Rosetta models, for the prediction of soils water content, was described and compared. Descriptive statistics for soil properties are summarized in Table 1. The studied soils can be classified as clayey, clay loam, silty clay loam and sandy clay loam. In general, clay, silt and sand content were between 18% to 48%, 15% to 45.5%, and 14% to 57% respectively. Average bulk density was 1.42 g/cm³ with values varying between 1.28 to 1.6 g/cm³.

Correlation coefficients among the water content in each potential and soil physical and chemical properties were calculated and are reported in Table 2. From the values of correlation coefficients in Table 2, the soil bulk density (BD), clay and sand content have close relationships with the water content at 10 and 33 kPa at the significance level consistent with other scholars (Nemes & Rawls, 2006) and clay and sand content are only suitable for PTFs developing to predict the water content of 100, 300 and 500 kPa. The water content at 1000 and 1500 kPa were only controlled by clay content. The absolute effect of BD decreased with h_m in agreement with Nemes & Rawls (2006). The correlation coefficient of BD was negative for low h_m and positive for high h_m (i.e. 1000 and 1500 kPa). Dexter et al. (2008) found that BD decreased the SWR at low h_m and increased it at high h_m. Aina & Periaswamy (1985) also found a negative correlation between θ₃₃ kPa and BD for western Nigerian soils. However, Hutson & Cass (1987) reported that BD had a non-significant effect on the SWR. Clay and silt increased the SWR for the major of h_m values due to their effects on water retention surfaces. But the effect of silt was not significant at 0.01. This is in agreement with Hutson & Cass (1987). Aina & Periaswamy (1985) found positive relations of θ₃₃ kPa with silt and clay contents and of θ₁₅₀₀ kPa with clay content. Kern (1995) found that effects of silt content and BD on θ₃₃ kPa and θ₁₅₀₀ kPa and effect of sand content on θ₁₅₀₀ kPa were not significant but that sand content significantly affected θ₃₃ kPa. Nemes & Rawls (2006) reported that sand and silt contents decreased and clay content increased θ_FC and θ_PWP. Dexter et al. (2008) found a positive relation between θ_PWP and clay content. Decreasing effect of sand content on the SWR was obvious and had a descending trend fromθ₁₀ to θ₁₅₀₀ kPa. Its effect on θ₁₀₀₀ and θ₁₅₀₀ kPa was not significant. The influence of CaCO₃ was minor and had no significant effect on SWR. It increased the SWR due to its impacts on aggregation and flocculation (by soluble Ca²⁺). Rajkai & Varallyay (1992) found that CaCO₃ content was the second important independent variable entering PTFs for θ₁₅₀₀ kPa. Khodaverdiloo & Homaee (2004), however, observed that carbonates decrease the SWR at high h_m because the carbonates with clay size behave like silt in water retention. Effect of OC on the SWR was not significant. Increasing effect of organic matter on the SWR is dominant at low h_m. Gupta & Larson (1979) also reported that organic matter highly increases the SWR at low h_m. Bell & van Keulen (1995) found a positive and significant relation between θ_PWP and organic matter in four Mexican soils.

Based on the collected training data, the following PTFs using MLR method were developed and are listed in Table 3.The independent variables were selected at a 0.01 significance level for inclusion in the regression model. The values of adjusted coefficients of determination (R ² _adj) given in Table 3 indicate the range of the dependent variable that is explained by the independent variables. These results show that at low pressure heads, the clay, sand and bulk density are appropriate predictors of water content. At high pressure heads (1000 and 1500 kPa), the clay content was a better predictor. These regression equations and their statistics are shown in Table 3. Table 3 showed that clay content is an important factor for predicting water content at all potential points. Also, the studied soils showed a high water content (saturation ≅ 0.60 cm³/cm³ and wilting point ≅ 0.20 cm³/cm³).This feature can be related to high silt and clay particle size content (e.g., Rawls et al., 2003), which was always greater than 65% for all samples.

Clay type plays an important role in the retention properties of soils. So, soils in the humid tropics can have a much lower capacity to retain water than soils in the temperate regions with the same clay content but with a different type of clays (Christopher et al., 2013). Soils in southern Guilan province are principally dominated by montmorillonite clay (Fig. 2) which is expanding type clay minerals and swell by absorbing substantial amounts of water in its interlayer space. Presence of 2:1 smectitic clays, especially, montmorillonite in these soils was also an important specific soil characteristic that contributed to increase the water retention and hygroscopic water content, i.e., the water content in the driest part of the curve. Fig. 2 illustrates the X-ray difractogram of the clay fraction and shows presence of smectite clay minerals in studied soils.

Comparison among different methods for prediction of soil water content from testing data is presented in Suppl. Figs. S2, S3 and S4 [pdfs online] and summarized in Table 4.

These figures and Table 4 imply that the general prediction was good for the three methods, but the ANN method had excellent performance and the prediction values were close to the measured values.

The RMSE values for the ANN were smaller than that for the derived point PTFs and Rosetta model in all matric potentials. MLR and Rosetta software hold the second and third places, respectively. The RMSE values for the derived point PTFs were smaller than that for the Rosetta model, except kPa that Rosetta model had better estimation than regression (Table 4). The R ² values of ANN for all potentials were greater than regressions and regressions were greater than Rosetta, except kPa that Rosetta model had greater than regression. So, the accuracy of the ANN is better than that of the derived point PTFs and Rosetta model. This result is in line with the work done by Minasny et al. (2004) and Amini et al. (2005). But, with regard to evaluation criteria, our study is more accurate than other mentioned researches, because, selection of inputs and model designing (such as type of learning algorithm, the number of layers and neurons, etc,) is carried out more accurately.

The reason of this superior efficiency of ANNs models compared with the basic regression equations is probably because the PTFs that have derived from various areas have different efficiencies. On the other hand, according to the hypothesis of Schaap et al. (2001), for designing of a neural network we do not need a special equation. They also believe that by creating a suitable equation between input and output data we are able to achieve the best results. Also, due to the occurring of nonlinear equations between dependent variables and predicting variables, the neural network have the better efficiency compared with the basic regression equations. Yi et al. (2013) investigated the accuracy of ANN and analyzed the regression method using correlation coefficient and the RMSE. They reported that the neural network is able to predict the easily measurable soil parameters with more accuracy and less error. Similar results have been reported by Mukhlisin & Abd Rahman (2014) as well. They found that using ANN leads to less RMSE values than the MLR. They also reported that the neural network has not better efficiency than linear regression models in occasion of high stability of data. However, the high accuracy of data leads to more efficiency of neural network and also, shows the proper selection of testing and training data. Analysis of the ANN parameters suggested that more input variables were necessary to improve the prediction of soil parameters (Mermoud & Xu, 2006). The RMSE of the different neurons in hidden layer is plotted in Fig. 3. This figure illustrated that the best model obtained with 10, 5, 8, 4, 10, 9 and 7 neurons for 10, 33, 100, 300, 500, 1000 and 1500 kPa respectively.

The RMSE values of different ANN-PTFs and regression-PTFs were lower in the prediction of volumetric water content at PWP than the others. Likewise, based on MBE values, all these PTFs especially at PWP, showed slight underestimation of volumetric water content. But this underestimation of ANN model was very low and could be ignored. Also, in the evaluation study of Tomasella & Hodnett (2004), the general trend of lower RMSE values at permanent wilting point compared to field capacity conditions was observed for all the PTFs without any exception. Recently, Vereecken et al. (2010), also found that RMSE values at -1500 kPa are generally lower than at -33 kPa. The water content in the wet range of the retention curve is related more to the soil structural properties whereas in the dry range it depends more on the particle size distribution. Thus, the point PTFs were able to describe the water retention at different soil water pressure heads by incorporating different independent variables. The relationships between water retention parameters and basic soil properties are complex; consequently, the performance of point PTFs is better than that of Rosetta model. A similar comparison was made by Tomasella et al. (2003) both of whom reported similar differences between these two types of soil water prediction. The results of our investigation showed that in the reliability test, all the derived PTFs were associated with negative values of the MBE. Therefore, for the independent data set, the derived PTFs tend to underestimate the water retention curve (Table 4). As mentioned earlier, the range in clay content was not the major cause of its low predictive capability. Many authors, as Medina et al. (2002), indicated that clay type plays a vital role in the retention and transmission properties of a given soil. This is why soils in the humid tropics can have a much lower capacity to retain water than soils in the temperate regions with the same clay content but with a different type of clays (Christopher et al., 2013). Soils in southern Guilan province are principally dominated by montmorillonite clay (Fig. 3) which is expanding type clay minerals and swell by absorbing substantial amounts of water in its interlayer space. The prediction errors of these methods increased with increasing water content (high matric potentials) probably because at high matric potentials the water content is more related to the soil structure attributes. Because there was no predictor to adequately explain the soil structure effects on soil water content, and soil bulk density alone seems to be insufficient to represent these effects, the error prediction of the PTFs increased at high matric potentials. Comparison of these values with those obtained for the derived PTFs (Table 4) shows that all of the derived PTFs performed better than the Rosetta package. This may be related to the pedogenic differences between the data sets used to derive the Rosetta package and those for the reliability test. These low adjustments of Rosetta model, especially at–1500 kPa, could be related to the textural properties of these soils. Using a different particle size distribution, as does the Canadian Society of Soils Science (McKeague, 1978), a detailed silt particle-size distribution is obtained, where one can observe that exactly the fine silt content (5–2 μm) was between 57%and 84%. Thus, the hydrodynamic behavior of fine silt content, that could be similar to a clay particle size, would increase the water retention content near to PWP, and this would therefore justify the poor fits of Rosetta, because Rosetta predicts according to USDA textural distribution using three well-differentiated particle sizes (sand, silt and clay).The MBE values show that the Rosetta package overestimated water retention, especially at high pressure heads, except at 100 kPa pressure. This was also reported by Schaap et al. (2001).

With decreasing of matric potential (from 10 kPa to 1500 kPa), correlation coefficient increased in all three methods. In other words, the accuracy of prediction increased with increasing in soil suction. Because soils of study area had low content of organic matter and so, soil structure was very weak. On the other hand, the hydrodynamic behavior of fine silt content, that could be similar to a clay particle size, would increase the water retention content near to permanent wilting point. The content of fine silt of soils was between 57% and 84%.

In this study, multivariate linear regression and neural network model were employed to develop a pedotransfer function for predicting soil moisture using available soil properties. This neural network was consisted of three hidden layers, a sigmoid activation function in hidden and linear function in output layer. Results showed that artificial neural network gave the best model with Levenberg–Marquardt learning algorithm and tangent sigmoid (tansig) transfer function. Multi-Layer Perceptron architecture of different matric potentials according to number of inputs, number of neurons in the hidden layer and output parameter were as: 3-10-1, 3-5-1, 2-8-1, 2-4-1, 2-10-1, 1-9-1 and 1-7-1 for 10, 33, 100, 300, 500, 1000 and 1500 kPa, respectively. The ANN model was more suitable for capturing the non-linearity of the relationship between variables than multivariate regression and Rosetta, and can model non-linear functions and has been shown to perform better than linear regression. With regarding to the evaluation criteria, the results of this study revealed that the ANNs had superiority to the basic regression equations for prediction of mentioned soil parameter. This is a crucial result because, since ANN– PTFs formed from local data produce more accurate predictions than those built from data spread from a wider area, the concept of data conservation becomes a critical factor in ANN–PTFs construction (Baker & Ellison, 2008). However, due to difficulties of direct measurement of soil parameters, we recommend using of neuro-fuzzy models in the future studies for obtaining the logical equations of other soil parameters, especially soil hydraulic properties, in each area.