Assessment of pedotransfer functions for estimating soil water retention curves for the amazon region Avaliação de funções de pedotranferência para estimar curvas de retenção água solo

SUMMARY Knowledge of the soil water retention curve (SWRC) is essential for understanding and modeling hydraulic processes in the soil. However, direct determination of the SWRC is time consuming and costly. In addition, it requires a large number of samples, due to the high spatial and temporal variability of soil hydraulic properties. An alternative is the use of models, called pedotransfer functions (PTFs), which estimate the SWRC from easy-to-measure properties. The aim of this paper was to test the accuracy of 16 point or parametric PTFs reported in the literature on different soils from the south and southeast of the State of ParÆ, Brazil. The PTFs tested were proposed by Pidgeon (1972), Lal (1979), Aina & Periaswamy (1985), Arruda et al. (1987), Dijkerman (1988), Vereecken et al. (1989), Batjes (1996), van den Berg et al. (1997), Tomasella et al. (2000), Hodnett & Tomasella (2002), Oliveira et al. (2002), and Barros (2010). We used a database that includes soil texture (sand, silt, and clay), bulk density, soil organic carbon, soil pH, cation exchange capacity, and the SWRC. Most of the PTFs tested did not show good performance in estimating the SWRC. The parametric PTFs, however, performed better than the point PTFs in assessing the SWRC in the tested region. Among the parametric PTFs, those proposed by Tomasella et al. (2000) achieved the best accuracy in estimating the empirical parameters of the van Genuchten (1980) model, especially when tested in the top soil layer. pH do solo, capacidade de troca cati(cid:244)nica e CRA. A maioria das FPT testadas nªo demonstrou boa acurÆcia para estimar as CRA. As FPT paramØtricas apresentaram melhor desempenho do que as FPT pontuais em estimar a CRA dos solos na regiªo. Entre as FPT paramØtricas, as propostas por Tomasella et al. (2000) obtiveram melhor acurÆcia em estimar os par(cid:226)metros emp(cid:237)ricos do modelo de van Genuchten (1980), principalmente, quando testadas na primeira


INTRODUCTION
The term pedotransfer function (PTF) was first introduced by Bouma (1989) to describe the statistical relationship between easy-to-measure soil properties, such as particle size distribution, bulk density (Bd), soil organic carbon (SOC), and so on, and difficult-tomeasure soil hydraulic properties, such as the SWRC, hydraulic conductivity, etc.According to Vereecken et al. (2010), the PTFs can be classified into two types: parametric PTFs that estimate the empirical parameters of the SWRC (Vereecken et al., 1989;Wösten et al., 1999;Navin et al., 2009;Gould et al., 2012) and point PTFs that are used to estimate soil water content at different matric potentials (Gupta & Larson, 1979;Saxton et al., 1986;Reichert et al., 2009).Papers published in recent years highlight the usefulness of parametric PTFs (Vereecken et al., 2010) because they directly provide the required hydraulic parameters to be used in mathematical models that describe the movement of water and solutes in soil, as well as the soil-plant-atmosphere interactions.
In Brazil, Arruda et al. (1987) were pioneers in relating soil particle size distribution to soil water content.Later, Tomasella & Hodnett (1998) produced functions for Amazonian soils to estimate the empirical parameters of the SWRC proposed by Brooks & Corey (1964).Using data from reports of soil surveys of various locations in Brazil, Tomasella et al. (2000) developed PTFs to estimate the empirical parameters of the van Genuchten SWRC model.In the State of Pernambuco, Brazil, Oliveira et al. (2002) developed PTFs to estimate soil moisture at field capacity (FC) and at the permanent wilting point (PWP).In that same year, Giarola et al. (2002), employing multiple regression analyses, developed PTFs relating soil particle size distribution and content of Fe and Al oxides to the volumetric water content at FC and PWP.The SWRC and the soil resistance to penetration curve were estimated by Silva et al. (2008) using PTFs having soil particle size distribution and soil carbon content as predictive variables.Reichert et al. (2009), using soil texture, SOC, Bd and soil particle density data, developed PTFs to predict soil volumetric moisture at specific matric potentials.Recently, Barros et al. (2013) presented PTFs to estimate the empirical parameters of the van Genuchten model for soils of northeastern Brazil.
The use of PTFs requires some care.PTFs developed for soils of a certain region may not be appropriate in other regions (Tomasella et al., 2003).These differences may influence the accuracy of the estimated parameters or water content.Therefore, the choice of an adequate PTF for a particular region and, or, for particular soil types is essential for the accuracy of the estimations.Recently, some studies have tested the accuracy of PTFs for estimating various soil properties (Abbasi et al., 2011;Botula et al., 2012;Moeys et al., 2012).In this context, the aim of this study was to assess the performance of some PTFs to estimate soil water retention at different matric potentials and also the empirical parameters of the van Genuchten (1980) model for soils of the Brazilian Amazon.

Geographical study area
The study was conducted in the southeast of the State of Pará, Brazil, in three locations, corresponding to the municipalities of Nova Ipixuna, Parauapebas, and Pacajá, with coordinates of 4 o 36' S, 49º 26' W; 5 o 45' S, 49 o 56' W; 3º 40' S, and 50 o 56' W, respectively (WGS 84 coordinates).The locations have a tropical rainforest climate (Kottek et al., 2006).Average annual rainfall is 1,700 mm, with a pronounced dry season lasting 4-5 months, from June to October.Average annual relative humidity is 80 % (INMET, 2012).The landscape is composed of undulating to strongly undulating plateaus developed on the crystalline rocks of the Brazilian shield (Paleoproterozoic era).There is great diversity of rock types in the study area, with predominance of magmatic rocks (granites, granodiorites) in the municipalities of Nova Ipixuna and Pacajá, and metamorphic rocks (gneisses, etc) in Parauapebas (Issler & Guimarães, 1974).

Sampling and data analysis
Samples were collected at three depths (0-5; 10-15, and 40-45 cm), with four replicates for depth, in 27 profiles, for a total of 67 layers, evaluating variations of horizons in the profiles (14 layers with incomplete data were discarded).Bulk samples were collected to determine soil texture, soil organic carbon (SOC), soil pH, and cation exchange capacity (CEC).Undisturbed samples were collected to determine bulk density (ρ b ) and the SWRC (Table 1).
After homogenization, about 1 g of air-dried soil was ground and sieved through a 0.2 mm mesh.Each sample was then transferred to a small tube, placed in a desiccator to remove possible moisture, and weighed before dry combustion analysis was carried out to determine SOC.Soil pH was determined by potentiometry at a soil:water ratio of 1:2.5.
The CEC was obtained by the sum of exchangeable cations, where Ca 2+ and Mg 2+ were extracted with potassium chloride and the contents of K + and Na + were extracted with Mehlich-1 solution (H 2 SO 4 + HCl).Calcium and Mg 2+ were determined by atomic absorption spectrometry and K + and Na + by flame photometry.Potential acidity (H+Al) was extracted  with calcium acetate at pH 7.0 and determined by titration with 0.05 mol L -1 NaOH.
Data for pH and CEC were measured only for the first layer.The PTFs that required pH and CEC as predictors (van den Berg-1 and Hodnett PTFs) were compared to the Tomasella PTFs for the samples representing the first layer (0-5 cm), and these results were discussed separately from those that had been estimated by the other PTFs.

Indicators used to assess the accuracy of the PTFs
The indices used to evaluate the accuracy of the PTFs were the mean error (ME), the root mean square error (RMSE), and the coefficient of determination (R 2 ), represented by equations 1, 2, and 3 below, respectively.In addition, the confidence index (CI) was calculated according to Camargo & Sentelhas (1987), as described in equations 4-6.CI is the product of the Willmott (w) index, given by equation 5, and the Pearson correlation coefficient (r), given by equation 6.
( ) in which n represents the number of observations, O i the observed (measured) water content values, E i the estimated (predicted) water content values, and E and O the mean values of estimated and measured water content.
The ME represents the systematic error in the regression model.The remaining error is attributed to the variance of the model (Baker, 2008).The closer the ME value is to zero, the better the performance of the PTF.Likewise, PTF performance also increases when the calculated RMSE approaches zero (Pachepsky & Rawls, 2004).The R² indicates how the variance of the estimated variable is explained by the variance of the observed variable.The predictive capacity of the PTFs increases with the increase in R 2 .The CI values were interpreted as proposed by Camargo & Sentelhas (1987): CI > 0.85 = optimum PTF accuracy; CI from 0.85 to 0.76 = very good; CI from 0.75 to 0.66 = good; CI from 0.65 to 0.61 = average; CI from 0.60 to 0.51 = tolerable; CI from 0.50 to 0.41 = bad; and CI 0.40 = very bad.

RESULTS AND DISCUSSION
The soil samples showed high amplitude of soil bulk density (ρ b ), soil texture (clay and sand content), and SOC values, as well as a wide range of values for the parameters of the van Genuchten (1980) model.In general, the soil types in the study location are sandy clay and sandy clay loam (Figure 1), which reflects the low residual water content values (θ r ), i.e., low capacity for retaining water at high matric potentials.

Assessment of parametric PTFs for the total data set (all depths)
Assessment of the parametric PTFs for the whole data set (Table 4) shows that the four Tomasella PTFs have better capacity in estimating the parameters of the van Genuchten (1980) model than the other PTFs.There is also a slight advantage for the Barros PTFs compared to the Vereecken PTFs.A more detailed analysis of the Tomasella PTFs shows that a reduction in predictive capacity is observed as the PTF level increases (Table 4, Figure 2).The PTFs that showed the best performance, with a CI classified as "good" for eight of the nine selected potentials, were the Tomasella PTFs, levels 1 and 2 (L 1 and L 2 , Figure 2).The performances of these two PTFs were similar.The L 1 PTF, which uses Bd, clay, silt, fine and coarse sand fractions, and so-called "equivalent moisture" (water content measured at -33 kPa) as predictors, had a slightly higher CI than the L 2 PTF, whose predictors are identical to those of the L 1 PTF, with the exception of Bd, which is replaced by SOC.The L 3 and L 4 PTFs showed unsatisfactory CI performance (Figure 2).Equivalent moisture does not enter as a predictive variable in these two PTFs, which use only texture, Bd, and SOC as predictive variables.Overall, it is observed that the PTFs that use more variables to estimate the SWRC parameters have higher  Eqm: equivalent moisture (m 3 m -3 ); Bd: bulk density (Mg m -3 ); SOC: soil organic carbon (g kg -1 ); CS: coarse sand (g kg -1 ); FS: Fine sand (g kg -1 ); Cl: clay (g kg -1 ); S: Sand (g kg -1 ); Sil: silt (g kg -1 ); CEC: cation exchange capacity (cmol c kg -1 ); pH: pH of the soil; θ s and θ r : saturation and residual water content (m 3 m -3 ), respectively; α and n: empirical parameters of the van Genuchten (1980) model.efficiency (Table 4).This is confirmed by the performance of the various PTFs proposed by Tomasella et al. (2000), and by comparing the Barros and Vereecken PTFs.
The CI values using the criteria proposed by Camargo & Sentelhas (1997) indicate that the Tomasella PTFs have "very good" performance for the L 1 and "good" performance for the L 2 (Table 4).However, for the L 3 and L 4 levels, performance was rated "poor".The Barros PTFs were classified as "poor" (CI = 0.48), while Vereecken PTFs had the lowest CI values (0.40) and were classified as "bad" (Table 4).The evaluation of the PTFs for the total data set showed that the Tomasella PTFs had better overall performance than the Barros PTFs and the Vereecken PTFs.
When the estimated data are plotted against the measured data (Figure 3), it is observed that the grouping of the points around the 1:1 line is increasingly better when moving from the Tomasella PTF L 4 to PTF L 1 , which confirms the better efficiency of PTF L 1 .The Vereecken PTFs showed the highest dispersion around the 1:1 line, producing the worst predictive performance among all the parametric PTFs being tested.
The better predictive capacity of levels 1 and 2 of the Tomasella PTFs is probably related to inclusion of the water content value at the -33 kPa matric potential as an independent variable in the model.This result is consistent with the results of Cresswell & Paydar (2000) and Schaap et al. (2001), who showed that PTF performance was greatly improved when including measurement points of the SWRC as predictive variables.However, the determination of this value using undisturbed samples with volumetric rings is costly and time consuming, which limits its use in a practical and generalized way.Another point that justifies the good performance of the Tomasella PTFs is the fact that these PTFs were developed from soils from various regions of Brazil, including several soils from the Amazon region.The good performance presented by the Tomasella PTFs has also been observed in other studies.Medina et al. (2002) tested several PTFs in soils from Cuba and obtained a better performance of the ME and RMSE values, -0.02 and 0.06 (m 3 m -3 ), respectively, for the L 4 PTFs.The poor performance shown by the Barros PTFs is justified by the fact that these PTFs were designed to predict the empirical parameters of the van Genuchten model for soils of the Brazilian Cerrado (tropical savanna).According to the author, these soils generally have low SOC and clay content in their compositions, but high r b values.For the Vereecken PTFs, a tendency to underestimate the moisture values is observed, especially in the central potentials of the SWRC.This fact is related to the low capacity of the function in estimating the shape parameters of the SWRC (α and n), responsible for the accuracy of the water content predictions near the inflection point of the SWRC.This unsatisfactory result is probably related to the fact that these PTFs were developed for temperate soils (soils from Belgium).Tomasella et al. (2003) had already demonstrated the low predictive ability of the PTFs developed for temperate soils when used on soils from tropical regions.The authors asserted that the performance of these PTFs is affected mainly by the difference in silt content between soil types from different regions.Botula et al. (2012) also found that temperate PTFs in hydrological models for studies in the humid tropics can substantially reduce the quality of the results.

Assessment of parametric PTFs for the surface layer (0-5 cm)
As pH and CEC measurements were available only for the 0-5 cm topsoil, van den Berg-1 and Hodnett PTFs could be tested for this particular soil layer only.The statistical indicators of the performance of these PTFs are shown in table 5 together with those of the  Cl: clay (g kg -1 ); S: Sand (g kg -1 ); Sil: silt (g kg -1 ); Bd: bulk density (Mg m -3 ); CEC: cation exchange capacity (cmol c kg -1 ); SOC: soil organic carbon (g kg -1 ); θ: volumetric water content (m 3 m -3 ); W: gravimetric water content (kg kg -1 ); FC: volumetric water content at field capacity (m 3 m -3 ).
Tomasella PTFs.It is worth noting that the four Tomasella PTFs (L 1 to L 4 ) performed better than the van den Berg-1 and Hodnett PTFs.Furthermore, among the four Tomasella PTFs, an increase in the PTF level reduced its predictive capacity, as was observed for the total data set.An analysis of the Tomasella PTFs tested for the two data sets (total and surface layer) showed that, in general, the PTFs tested for the surface layer had a better performance (Tables 4 and 5, Figures 2 and 4).The function developed by Tomasella (L 1 ) had a "very good" CI when tested for the three depths (Table 4), and an "excellent" CI when tested for the surface layer only (Table 5).This same trend was observed for the other Tomasella PTFs.
The performance indicators for the Hodnett PTFs showed low accuracy.On average, considering matric potentials, the Hodnett PTFs was ranked as having a "average" performance (Table 5).The van den Berg-1 PTFs had ME and RMSE values higher than those observed for the Hodnett PTFs, except for the dry part
of the SWRC, and significantly below the ideal values for the current study.The CI indicated low predictive ability of the van den Berg-1 PTFs, rated as "bad" (Table 5).The low efficiency of the van den Berg-1 PTFs may be attributed to the fact that it was developed for Oxisols (horizons A, AB, and B).Our data set has several soil types, providing large variability to the properties used in the model, which reflects the high RMSE values of the van den Berg-1 PTFs.Oliveira et al. (2002) reported that PTFs have greater predictive ability when the soil properties that comprise the database are homogeneous.The estimated and measured data were plotted on a scatter chart (Figure 5).It is observed that the best fit was obtained for Tomasella PTF L 1 .The Hodnett PTFs have a tendency to overestimate water content values in the points near saturation, while the van den Berg-1 PTFs underestimate water content in the dry part of the SWRC (Figure 5).Both the van den Berg-1 and Hodnett PTFs are characterized by a dispersion of the regression points (Figure 5), which confirms the previous statements about these PTFs.Moreover, it was found that the Hodnett and van den Berg-1 PTFs, despite the addition of CEC and pH to the set of predictive variables, did not have good predictive abilities.

Assessment of point PTFs
Performance analysis of the point PTFs tested indicates that most of them have low predictive capacity (Table 6).For estimations of the water content at the -10 kPa potential, all the PTFs tested showed RMSE values above 0.07 m 3 m -3 (Table 6), which is considered high for this kind of study.In addition,
the CI of the PTFs tested ranged from "bad" to "very poor" (Table 6).Among the point PTFs tested that estimate water content at the -10 kPa potential, the van den Berg-2 PTF had the best predictive ability.It had the lowest RMSE and ME values, and the highest R 2 and CI (Table 6).However, according to Camargo & Sentelhas (1997), this PTF was classified as "tolerable", which confirms its low performance in estimating water content at the -10 kPa potential.The worst performance in estimating water content at the -10 kPa potential was observed for the Pidgeon PTF, which showed the highest RMSE and ME, and a CI rated as "poor".For the -33 kPa potential, the PTF that had the best performance was the Batjes PTF (Table 6).The worst performance was observed for the Aina PTF, with a CI performance rated as "bad".A similar behavior was observed for the water content estimations at -1500 kPa.The PTF with the best performance was the Batjes PTF.However, at this potential, the van den Berg and Oliveira PTFs had similar performance results (Table 6).The worst performance was observed for the Arruda PTFs, followed by the Lal, Aina, and Dijkerman PTFs (CI 0.37).Some PTFs overestimate water content at a given potential and underestimate it at another, as observed for the Oliveira and Aina PTFs (Figures 6 and 7).The Lal PTFs underestimate water content at all three potentials.The Pidgeon PTF overestimates water content at both potentials (Figure 7).
The PTFs that estimate volumetric water content showed better results than those that estimate gravimetric water content, except for the Lal PTFs.There are many reasons that lead to low efficiency of a PTF.Finke et al. (1996) showed that a major source of inaccuracy of a PTF is the spatial variability of soil properties that are transferred to the PTF.The performance of several point PTFs was evaluated by Tomasella & Hodnett (2004) using a database of tropical soils composed of 771 horizons.The authors found that some PTFs had great difficulty in estimating water content at specific potentials, and they attributed this difficulty to their simplicity, i.e., x -: mean of the estimated values (m 3 m -3 ); RMSE: root mean square error; ME: mean error; R 2 : coefficient determination;

PTF
CI: Confidence Index proposed by Camargo & Sentelhas (1987); no: no PTF for that potential.the limited number of predictive variables, which may cause a reduction in the robustness of the PTFs.
Another effect to consider is the type of clay found in soils, given that the mineralogy of the clay fraction determines the amount of water a soil can retain.Furthermore, soil mineralogy is one of the factors responsible for the formation of different types of microstructure, which also affects the SWRC (Gaiser et al., 2000).
2. Among the PTFs tested, those elaborated with homogeneous sets of soils do not show good efficiency for the set of soils that were tested.
3. All parametric PTFs assessed in this study, except for those proposed by Tomasella et al. (2000), levels 1 and 2, showed limited capacity for predicting the SWRC.

Figure 1 .
Figure 1.Textural classification of the soils used to evaluate the PTFs (n = 67).

Figure 2 .
Figure 2. Values of RMSE and confidence index (CI) for the parametric PTFs tested for all soil depths; CI > 0.85 = optimum; CI from 0.85 to 0.76 = very good; CI from 0.75 to 0.66 = good; CI from 0.65 to 0.61 = average; CI from 0.60 to 0.51 = tolerable; CI from 0.50 to 0.41 = bad; CI 0.40 = very bad.

Figure 3 .
Figure 3.Estimated vs measured volumetric water content, and estimation residues for the parametric PTFs tested for all depths (n = 67).

Figure 5 .
Figure 5. Measured vs estimated volumetric water content, and estimation residue for the parametric PTFs tested in the surface soil layer (0-5 cm) (n = 27).

Figure 6 .
Figure 6.Estimated vs measured volumetric water content, and estimation residues of the point PTFs tested for all depths (n = 67).

Table 2 .
Parametric PTFs selected for estimating the parameters of the van Genuchten (1980) function

Table 3 .
Point PTFs selected for estimating water content at specific matric potentials

Table 4 .
Statistical indicators for the parametric PTFs tested for the three depths.n = 67

Table 6 .
Statistical indicators for the point PTFs for predicting volumetric or gravimetric water content.n = 67