Evaluation of some infiltration models and hydraulic parameters

The evaluation of infiltration characteristics and some parameters of infiltration models such as sorptivity and final steady infiltration rate in soils are important in agriculture. The aim of this study was to evaluate some of the most common models used to estimate final soil infiltration rate. The equality of final infiltration rate with saturated hydraulic conductivity (Ks) was also tested. Moreover, values of the estimated sorptivity from the Philip’s model were compared to estimates by selected pedotransfer functions (PTFs). The infiltration experiments used the doublering method on soils with two different land uses in the Taleghan watershed of Tehran province, Iran, from September to October, 2007. The infiltration models of Kostiakov-Lewis, Philip two-term and Horton were f itted to observed infiltration data. Some parameters of the models and the coefficient of determination goodness of f it were estimated using MATLAB software. The results showed that, based on comparing measured and model-estimated infiltration rate using root mean squared error (RMSE), Horton’s model gave the best prediction of f inal infiltration rate in the experimental area. Laboratory measured Ks values gave signif icant differences and higher values than estimated final infiltration rates from the selected models. The estimated f inal infiltration rate was not equal to laboratory measured Ks values in the study area. Moreover, the estimated sorptivity factor by Philip’s model was signif icantly different to those estimated by selected PTFs. It is suggested that the applicability of PTFs is limited to specif ic, similar conditions. Additional key words: final infiltration rate, saturated hydraulic conductivity, sorptivity.


Introduction
Infiltration is the term applied to the process of water entry into soil (Hillel, 1980). Evaluation of soil infiltration characteristics and determination of the final steady infiltration rate are required for increased irrigation water use efficiency, the design of irrigation systems, and decreased water and soil losses which are important factors in agriculture. The final steady infiltration rate of a soil is the minimum rate that water enters into the soil (Mbagwu, 1993). Since measuring the final infiltration rate is time consuming, several models have been proposed to determine this parameter. Empirical models such as those of Kostiakov (1932) and Horton (1940), and physical models such as that of Philip (1957) are the most commonly models to estimate final infiltration rate. Singh (1992) stated that the various models can estimate different values of the final soil infiltration rate which seems incorrect as the parameter is soil-dependent. The ability of the models to estimate infiltration rate has been examined by many researchers. Gifford (1976) observed that among the Horton, Kostiakov and Philip's models, the Horton model gave the best fit of infiltration data in mostly semi-arid range lands in Australia, but only under specific conditions. Roohian et al. (2005) suggested that Horton's model gives an acceptable estimate of final infiltration rate under given soil texture conditions. However, complicated factors that influence the final infiltration rate are a major reason for the different applicability of the models. Machiwal et al. (2006) observed infiltration was well described by the Philip's model in wasteland in Kharagpur, India. Navar and Synnott (2000) evaluated the infiltration rates of soils under four land uses in north-eastern Mexico. Among the infiltration models of Horton, Philip, a modified Kostiakov and Green-Ampt, the modified Kostiakov model gave the best fit. Hajabbasi (2006) evaluated the Kostiakov, Horton, and Philip's infiltration models under different tillage and rotations in a clay-loam in North-west Iran and reported that the Horton's model gave the best prediction of infiltration rate in that region.
Soil hydraulic parameters, such as saturated hydraulic conductivity (K s ) and sorptivity (S) are important factors that govern the soil infiltration rate. Several workers have evaluated the Philip's model parameters, transmissivity (A) and sorptivity factors in their experiments (Sutikto et al., 1993;Mohammadi and Refahi, 2006). The A factor in the Philip's model, may approximate to K s for long periods (Swartzendruber and Youngs, 1974;Rawls, 1992). The fit of measured infiltration data to the Philip's model leads to A= K s , as time approaches infinity (Philip, 1969). In Horton's model, the infiltration capacity approximates to a constant minimum (non-zero) rate of i c , as time approaches infinity (Horton, 1940;Hillel, 1998) that can be equal to K s . Mishra et al. (2003) showed that A varied from 50 to 75% of K s values. Mbagwu (1995) also showed that values of the final infiltration rate and K s were not equal over long periods.
Sorptivity is function of soil suction which is important for knowing soil hydraulic properties. This parameter is defined as a physical quantity that shows the capacity of a porous medium for capillary uptake and release of water into soil (Philip, 1957). This parameter can be estimated by defined PTFs as the relationship between soil hydraulic and other more available measured properties (Bouma, 1989) which can be used to estimate hydraulic parameters such as S factor.
The aim of this work was to evaluate the most common models used to estimate the final infiltration rate of soils, and compare values of the estimated final infiltration rate with laboratory measured K s on undisturbed soil columns, and finally, to compare values of the S factor estimated by the Philip's model and PTFs.

Characteristics of the research area
The study was conducted on part of the Taleghan watershed in Iran. Eight points were selected at two sites (36°08' 10.8" N, 50°40' 40.6" E, at 2,236 m asl and 36°08' 58.6" N, 50°43' 12.6" E, at 1,453 m asl, respectively) so the sites had the least difference in soil properties in the area studied. These sites were in rangelands with similar soil surface conditions and homogeneous soils. Soil depth and plant cover at points 1, 2, 3, and 4 were slightly greater than at points 5, 6, 7, and 8. The history of these rangelands showed that they were cropped for several years in the last century at points 3, 4, 7, and 8 using animal tillage. According to the Taleghan watershed study report (1993) the soils are calcareous and are classified as Typic Xerorthents. The depth of the Ap and C horizons were mostly 15 and 30 cm respectively and the boundary between horizons was smooth. The soil structure was massive in the soils studied. Soil texture in this area varied from clay-loam to silty clay loam. Minimum and maximum daily temperatures were approximately -5.6 and 17°C, respectively. Mean annual rainfall varied from 464 to 796 mm and the land had a slope of about 15%.

Soil sampling and analysis
Soil properties were determined by sampling at 0-15 and 15-30 cm soil depths. At each site, 48 undisturbed soil sample cores of 5 cm height and diameter and 98.12 cm 3 volume were taken (four replicates). They were used to measure the saturated hydraulic conductivity (K s ) using the constant head method (Klute and Dirksen, 1986), total porosity (by measuring saturated water content), and initial moisture content (gravimetrically). Darcy's equation was used to calculate the K s value. Additionally, 24 composite soil samples were collected for measurement of soil chemical properties. Organic matter and particle size distribution were measured by the modif ied Walkley-Black wet oxidation method (Allison and Moodie, 1965) and the Bouyoucos hydrometer procedure (Gee and Bauder, 1986). Dry bulk density was determined by the core method (Davies et al., 1973). Infiltration was measured using a doublering infiltrometer (Bouwer et al., 1999), with 25 cm inner diameter and 60 cm outer diameter rings (four replicates at each site) installed in the soil. Grass was carefully cut at the soil surface with shears in the inner and outer rings. A constant water head of approximately 15 cm was kept in both rings and amount of the water drop and the depth of added water were recorded for two hours. The EC of the water used was 0.49 dS m -1 , and sodium (Na) content was 20 mg L -1 . The data were fitted to three chosen infiltration models and the bestfit model selected. The soil Na (in a soil saturation extract) and calcium carbonate content (CaCO 3 ) were measured by flame emission and a volumetric method (Allison and Moodie, 1965), respectively. Soil pH and electrical conductivity (EC) were determined in soil saturation extract using the procedures of Page et al. (1982).

Estimation of infiltration model parameters
In this study, a few commonly used infiltration models, such as Kostiakov-Lewis, Philip two-term, and Horton's model were fitted to the infiltration data. The modelestimated final infiltration rate and sorptivity factor were determined using MATLAB software. The values of the measured final field infiltration rate with the measured K s in the laboratory and estimated S factor, by the Philip's model and PTFs were compared using a t-test (SAS/STAT, 1985).

Kostiakov-Lewis model
The modified Kostiakov model for long time periods is: where a and b are the equation ' s parameters (a > 0 and 0 < b < 1); i(t) and i c are the infiltration rate and presumed final infiltration rate in cm min -1 at time t in min, respectively.

Horton's model
The Horton ' s infiltration model (Horton, 1940) is: where i 0 is the initial infiltration rate in cm min -1 ; t is time; and k is the infiltration decay factor.

Philip two-parameter model
The Philip two-term model (Philip, 1957) is: where A is a transmissivity factor in cm min -1 as a function of soil properties and water content; S is sorptivity which is a function of soil matric potential (cm min -0.5 ).

Sf =
[5] where λ and h b are the Brooks-Corey pore-size distribution index and bubbling pressure head (cm). These parameters are defined based on clay and sand %, and porosity (cm 3 cm -3 ).

Selection of best-fit infiltration model
The results of the soil analyses are shown in Table 1. As expected, the soil analysis results showed that soil texture varied from clay-loam to silty clay loam, the soil pH from 7.7 to 8.0 and the EC from 0.23 to 0.58 dS m -1 at soil depths of 0-15 and 15-30 cm. Thus, there was no salinity or sodicity in soils of the area studied. Table 1 shows there were no notable differences among the soil properties studied. In this study, the goodness of fit of the selected models and their ability to estimate the final soil infiltration rate was evaluated using root mean squared error (RMSE). The R values were high (0.99) and equal for all points. Values of RMSE and i c showed that estimated infiltration rates by the Horton's model, were closer to the measured ones (

Final infiltration rate and K s
The results showed that the saturated hydraulic conductivity, measured in the laboratory, was positively related to the observed final infiltration rate (R = 0.612) (Table 2, Fig. 1). The results showed that measured values of the saturated hydraulic conductivity were significantly higher than the observed final infiltration rate in the field at all 8 points, (P > F = 0.0299, P = 0.05) ( Table 2). Measured K s was approximately 2-3 times the observed final infiltration rate at most sample points.

Estimated sorptivity factor
The sorptivity factor, in the Philip's model, changed from 0.315 to 2.984 among the different sample points (Table 3, Fig. 2). Statistical analysis at p < 0.01 (SAS/STAT, 1985) showed signif icant differences between the sorptivity factor from the Philip's model and the one estimated by PTFs. From Figure 2 it can be seen that sorptivity values estimated by PTFs had high deviations from the Philip's sorptivity factor. Further, the correlation between parameters of the Philip's model (S and A) was poor and the relationship between them was not significant (R = 0.127) (Fig. 3).

Discussion
In this study, the Horton's model gave the best fit of the results for all sample points. The different values of RMSE, for each model, at the different points is probably due to changed conditions at the points such as soil particle size distribution (Table 1), because of a high dependency of infiltration rate on soil texture (Rawls, 1992;Mohammadi and Refahi, 2006). The suitability of the Kostiakov and Philip's models for estimation of the infiltration rate can be site-specific (Mbagwu, 1993). In addition, complicated conditions and regional soil variation can signif icantly affect measured and estimated values. Thus, spatial variations in short distances and probable preferential flow at some points such as P4 can affect the data set obtained and consequently the model parameters. The result of this study agrees with the earlier result of Hajabbasi (2006), who found that the Horton's model is applicable in a clay loam soil of northwest Iran. Thus, the applicability of infiltration models should be tested under different conditions, because the various models can suppose different final infiltration rate values for a soil, which is not correct, while the final infiltration rate is generally a soil-dependent parameter (Singh, 1992;Mishra et al., 2003). In this study, the low predictive ability of the Kostiakov-Lewis model for estimating the final infiltration rate could be because it takes longer to obtain a steady infiltration rate because of a low initial soil moisture content (Navar and Synnott, 2000). It also seems that a longer time duration, more than 2 hours, may be required for application of the Philip's model (Philip, 1969;Mbagwu, 1993). Also, the Philip's two-term model sometimes can not accurately describe the measured field data (Gosh, 1983).
Significant difference between the Philip's sorptivity factor in P4 compared to other sample points may be due to the impossibility of accurately determining the value of the final infiltration rate using the Philip's model. Overall, spatial soil variability is important in infiltration modelling. Significant differences between the observed f inal inf iltration rate and K s can be attributed to the effect of trapped air under field conditions (Radcliffe and Rasmussen, 2000) or disturbed core samples producing preferential flow in the laboratory (Maheshwari, 1996;Mohammadi and Refahi, 2006). Thus, complicated conditions in the field, differences between laboratory and field conditions, and spatial soil variability can be good reasons for the observed results (i.e. Taleghan watershed). Differences between K s and the final infiltration rate (in Table 2) were similar to those of Mohammadi and Refahi (2006).
In this study, the variation in the sorptivity parameter showed no clear pattern in the study region. This agrees with the results of Machiwal et al. (2006). Soils in the field are more heterogeneous than laboratory soil cores and this is a possible reason for the differences. Thus, PTFs should be developed for hydrologic parameters of models on a larger scale than soil core. Also, PTFs derived from one database, in a particular region and condition, is not applicable under all conditions (Kern, 1995;Wösten et al., 2001). Thus, PTFs should be applied to similar conditions to the soils investigated. Moreover, soil pore size distribution is an important factor in Evaluation of some infiltration models and hydraulic parameters 215 spatial variation of Philip's sorptivity parameter (Sharma et al., 1980;Machiwal et al., 2006), whereas total porosity was considered in selected PTFs in this study. Other possible reasons for the difference could be due to variation in soil effective porosity, pore size distribution (Sharma et al., 1980), matric properties, and probable preferential flow. These can be possible reasons for differences between estimated values of sorptivity factor by Philip's equation and PTFs. However, the relationship between the sorptivity factor and effective porosity needs to be evaluated in more detail. Wide variation in model parameters can also be due to non-uniform initial soil moisture. The poor correlation between parameters of Philip's model (S and A) observed in this study, is confirmed by the findings of Talsma (1969).
In conclusion, in this work infiltration models were evaluated. The results showed that Horton's model can be used for estimating final soil infiltration rate. Only, one or some of the infiltration models are better and appropriate for a specific study site. This investigation showed that Horton's model was better than the Kostiakov-Lewis and Philip's model at most sample points in the Taleghan watershed in Iran. Thus, infiltration models should be tested for their ability to estimate the final infiltration rate of each location and it should be documented at each site. It was found that the observed final infiltration rate has no equal concept to the measured saturated hydraulic conductivity for all conditions and sites. Moreover, the determined sorptivity factor is a variable parameter under field conditions and estimated values of this factor by PTFs were significantly different compared with the values obtained for Philip's sorptivity factor. Thus, the use of various models and PTFs is restricted and this problem needs to be considered in these sorts of studies. It is suggested that in the future there is a need to evaluate the parameters of infiltration models and the relationship among them, accurately and for the calibration of PTFs and infiltration models under different conditions. Soil spatial variability has an appreciable effect on infiltration properties and hydraulic parameters that need to be evaluated in more detail.