Estimation of Water Retention Curve for Soils of Bahia , Brazil , Based on Soil Particle-Size Analysis

Soil water retention curve (SWRC) is an important soil attribute because it is a soil quality indicator and is fundamental to study water dynamics in the soil-plant-atmosphere system. Since the conventional SWRC determination is laborious and time-consuming, making it difficult to process a large volume of samples, pedotransfer functions have been used to estimate it by using other soil physical attributes easily determined. Thus, this study aimed to apply Arya-Paris model to SWRC estimation for soils of Bahia state, Brazil, based on soil particle-size analysis, and to compare estimated and determined data of SWRC. Samples were collected from horizons A and AB and/or B and/or C, for a total of 15 soils and 62 horizons. Particle-size was determined by automatic soil particle-size analyzer (PSA) based on -ray attenuation and traditional Bouyoucos’ hydrometer (BH) method. Arya-Paris model showed better SWRC predictions for sandy soils, followed by clayey, loamy, and very clayey soils. Good model performance was observed for all soils together. The α 1 scaling factor provided better predictions, followed by α 3, and α 2 showed unsatisfactory behavior. BH method, using only 7 soil particle-size fractions, gave slightly higher predictions than PSA using 30 soil particle-size fractions.


Introduction
Soil water retention curve (SWRC) expresses the relationship between soil moisture and matric potential (Vieira, 2007) and is an excellent soil physical indicator; however, it is difficult to characterize because of both the time of analysis consumed and the intrinsic influence of hysteresis (Nascimento, Bassoi, & Paz, 2012).SWRC evaluation is essential for estimation of plant available water (Mohammadi, Asadzadeh, & Vanclooster, Particle-size distribution is considered as one of the most fundamental soil physical properties, expressed as clay, silt, and sand percentages.These three fractions directly influence soil properties such as water retention curve, available water capacity, saturated hydraulic conductivity, thermal conductivity, and adsorption properties of chemical substances (D.Wang, Zhao, Hu, & Y. F. Wang, 2008, Minasny & Hartemink, 2011, Botula, Cornelis, Baert, Mafuka, & Ranst, 2013).Arya and Paris (1981) proposed a SWRC estimation model based on the similarity between soil particle-size distribution and water retention curve.Since then, the interest in this model has been constant because it provides a method to transform particle-size distribution into a continuous and complete SWRC (Matula, Mojrova, & Spongrova, 2007;Nimmo, Herkelrath, & Laguna Luna, 2007;Sepaskhah & Raifee, 2008;Chiu, Yan, & Ka, 2012;Fooladmand & Habibi, 2012;Meskini-Vishkaee, Mohammadi, & Vanclooster, 2014).
Thus, the Arya and Paris (1981) model uses the similarity between the functions that describe particle-size distribution and SWRC to indirectly obtain the latter function.Pore size is associated to a certain pore volume determined by the scaling technique (Arya, Van Genutchen, & Shouse, 1999).
In previous work Vaz, Naime, and Silva (2005) evaluated Arya and Paris (1981) model applicability for a set of 104 soil samples from São Paulo and Rio Grande do Sul states, Brazil, and using 30 soil particle-size fractions determined by automatic soil particle-size analyzer (PSA) based on -ray attenuation.The present study aims to analyze Arya and Paris (1981) model feasibility to estimate SWRC for soils of Bahia state, Brazil, based on soil particle-size analysis determined by the same methodology and by traditional Bouyoucos' hydrometer (BH) method, which determines only 7 soil particle-size fractions, and to compare with determined SWRC data.In addition to evaluating different soils, this is the major difference of this study, in which the Arya and Paris (1981) model feasibility to estimate SWRC occurred using only 7 soil particle-size fractions, while Vaz, Iossi, Naime and Silva (2005) used 30 soil particle-size fractions.
Physical analyses were performed at Soil Physical Laboratory of Embrapa Cassava and Fruits, in the municipality of Cruz das Almas, in Bahia state, according to Donagema, Campos, Calderano, Teixeira, and Viana (2011) methods, except for particle-size analysis obtained by grain size analyzer, which was performed at Embrapa Instrumentation, in São Carlos, São Paulo.
Particle-size analysis was performed by two different methods.The first one was the automatic particle-size analyzer (PSA) based on gamma radiation attenuation by scattered particles in sedimentation was utilized (Naime, Vaz, & Macedo, 2001), after chemical dispersion with sodium hydroxide plus mechanical shaking for 15 minutes at 12,000 r.p.m.This technique allows to separate 30 soil particle-size fractions.Results were recorded in file containing cumulative concentration data, in percentage of the initial concentration and particle diameter (μm).Analyzer measurements were made in triplicate and the average value was considered.This same methodology was used by Vaz, Iossi, Naime, and Silva (2005).The second one was the Bouyoucos' hydrometer method using the same kind of dispersion as above, and the total sand fraction separated into five fractions: very coarse sand (2.00-1.00mm), coarse sand (1.00-0.50mm), medium sand (0.50-0.25 mm), fine sand (0.25-0.10 mm), and very fine sand (0.10-0.05 mm), besides silty (0.05-0.002 mm) and clay (< 0.002 mm).Textural classification was obtained by texture triangle (Donagema, Campos, Calderano, Teixeira, & Viana, 2011).
Volumetric cylinder method was utilized to determine soil bulk density by collecting, in each soil profile horizons, two undisturbed soil samples packed in Uhland sampler with approximately 310 cm 3 volume; arithmetic average of two replications was considered for results comparison.Particle density was obtained through the volumetric flask method by using ethanol as penetrating liquid (Donagema, Campos, Calderano, Teixeira, & Viana, 2011), and total porosity was obtained by calculation, according to the following expression: where, TP is the calculated total porosity (m³ m -³), ρ p is soil particle density (kg dm -3 ), and ρ s is soil bulk density (kg dm -3 ).
SWRC was experimentally obtained in laboratory by using tension table and Richards' pressure chambers (Richards, 1949), and estimated by Arya and Paris (1981) model by using soil particle-size data, according to Vaz, Iossi, Naime, and Silva (2005).
Undisturbed soil samples were collected in metal cylinders with approximately 100 cm 3 volume to determine SWRC in laboratory.These samples were slowly saturated by capillarity for 24 hours and subjected to 6 kPa tension on a tension table and to pressures of 10, 33, 100, 300, and 1,500 kPa in the Richards' pressure chambers (Richards, 1949).The soil moisture related to each tension and pressure was determined by drying samples in an oven at 105 o C for 48 hours.
Soil physics has fundamental principles for soil-water relationship understanding.Arya and Paris (1981) model is based on two of these principles.The first one is the capillarity equation, which relates soil water matric potential ( m ), expressed by the capillary rise height, and pore diameter: where, σ (0.0728 N m -1 ) is the water surface tension in the water-air interface; θ is the contact angle (considered near to zero, therefore cos  = 1); ρ w (kg m -3 ) is the water density; g (9.81 m s -2 ) is the gravity acceleration; and r i (m) is the pore radius, considering the international system of units (SI).
The second principle is the soil particle-size distribution and the contribution of each fraction to soil water saturation: where, i are the various fractions of soil particles; ρ s (kg m -3 ) is the soil bulk density; ρ p (kg m -3 ) is the soil particle density; and w i (g g -1 ) is the fraction of soil mass given by the particle-size distribution curve.
The connection between Equations ( 3) and ( 4) for SWRC estimation by Arya and Paris (1981) model is performed by associating the pore radius (r i ) and particle radius (R i ) through the following equation: where, n i is the number of spherical particles of i-th class of soil mass; and e is the void ratio obtained by: The α (alpha) coefficient is defined as a scaling factor, which, according to Basile and D'Urso (1997), represents the empirical fit to pore tortuosity in soils under natural conditions.Arya and Paris (1981) consider 1.38 as the best estimate value for it.Arya and Dierolf (1992), mentioned by Vaz, Iossi, Naime and Silva (2005), obtained 0.938 for α scaling factor.
The soil matric potential is calculated by the combination of Equations 3, 5, 6, and 7: This study utilized the following equations to analyze the α scaling factor: α1 = 0.947 + 0.427e θ 0.129 (Vaz, Iossi, Naime, & Silva, 2005) (9) where, n i is the number of spherical particles of i-th class of soil mass, described by Equation ( 6), and N i is the number of spherical particles necessary to estimate the pore length in the soil natural structure, equal to: Moisture and matric potential values were obtained using an Excel spreadsheet; then, the Genuchten (1980) model was fitted by means of the program SWRC (Dourado-Neto, Nielsen, Hopmans, Reichardt, and Bachi, 2000), according to Equation (2).
As three different alpha scaling factors were utilized to estimate moisture: α 1 (Vaz et al., 2005); α 2 (Vaz et al., 2005); and α 3 (Arya et al., 1999), and as these scaling factors provided different moisture values, each set of moisture values was correlated with the moisture content obtained in laboratory by Richards (1949) method.
The comparison between moisture contents measured (θ measured ) and estimated (θ estimated ) by Arya and Paris (1981) model was performed through simple linear regression fit between the observed values and the estimated values y, by using the 1:1 equation, where y = a + bx.The closer to 0 for a and closer to 1 for b coefficients, the higher the proximity between measured and estimated values.In this kind of relationship the accuracy is greater the lower the dispersion of points in relation to the 1:1 line, which represents a perfect adjustment.
Besides the simple linear regression fit evaluation, the comparison between moisture contents measured (θ measured ) and estimated (θ estimated ) by Arya and Paris (1981) model was performed using the square root of the mean square error (RMSE) based on the following equation: The smaller the RMSE the greater the proximity between measured and estimated values.

Soil Physical Properties
The soil particle-size analysis allowed the observation of 10 out of 13 textural classes present in the texture triangle, ranging from sandy to clayey (Figure 1); only loam, silty-loam, and silty particle-size classes were not found in the evaluated soils.

Clay For clayey was possib in all mois
By analyzi result of α then by α better whe     Note.
(4) Predictions made with soil particle-size data obtained by the Bouyoucos' hydrometer method, using only 7 soil particle-size fractions, were slightly higher than those performed with particle-size analyzer data using 30 soil particle-size fractions.

Figures
Figures 2 values for for both m regression Figure 4. Arya and Figure 5. Arya and