# EVALUACION DE LA ECUACION DE INFILTRACION DE GREEN Y AMPT EN ALGUNOS SUELOS AGRICOLAS DE MEXICO, USANDO INFORMACION DEL USDA Y UN METODO MODIFICADO DE BROOKS Y COREY.

EVALUATION OF GREEN-AMPT INFILTRATION EQUATION IN SOME AGRICULTURAL SOILS IN MEXICO, USING USDA INFORMATION AND A MODIFIED METHOD FROM BROOKS AND COREY

AVALIACAO DA EQUACAO DE INFILTRACAO DE GREEN-AMPT EM ALGUNS SOLOS AGRICOLAS DO MEXICO, USANDO INFORMACAO DO USDA E UM METODO MODIFICADO DE BROOKS E COREY

The surface irrigation method is the one most frequently used to apply water in the different districts and irrigation units in Mexico, used in 92% of the area under irrigation (Rendon et al, 2003). However, it is the method with the lowest application efficiency, which means that a large part of the water volume applied is lost. Thus, it is essential to increase the efficiency of application of this irrigation method. For this purpose, it is necessary to have a detailed understanding of the infiltration process, since it allows to calculate an optimal irrigation time and increase the efficiency of application. However, the complex infiltration process can only be approximately described through mathematical equations.

A simple theoretical approach, although useful, was suggested for the infiltration process in 1911 by Green and Ampt in their classical article about the flow of air and water through soils (Green and Ampt, 1911). The Green-Ampt infiltration model can be used to represent the infiltration of water in surface irrigation (Killen and Slack, 1987), in addition to being useful for to design sub-superficial agricultural drains, to represent the wetting patterns for surface emitters in trickle and sprinkler irrigation and to estimate the superficial runoff in watersheds (DeBoer and Chu, 2001; Schmidt and Govindaraju, 2003; Sepaskhah and Chitsaz, 2004; Baiamonte and Singh, 2015).

The combination of simplifying water infiltration hypotheses introduced by Green and Ampt (1911) leads to the following equation (Fuentes, 2007; Rendon et al., 2012):

I(t) = [K.sub.s]t + [gamma]1n(1+1/[gamma])with [gamma] = (h+[[psi].sub.f])([[theta].sub.s]-[[theta].sub.i]) (1)

where I(t): amount of infiltration (cumulative infiltrated depth; cm) in time t(h); [[psi].sub.f]: wetting front capillary pressure head (cm); h: water depth on the surface (cm); [[theta].sub.s]: soil water content at saturation ([cm.sup.3] x [cm.sup.-3]); [[theta].sub.i]: initial soil water content ([cm.sup.3] x [cm.sup.-3]); and Ks: hydraulic conductivity at saturation (cm x [h.sup.-1]).

The wetting front capillary pressure can be obtained from the integration of the Brooks and Corey equation of relative hydraulic conductivity (Brooks and Corey, 1964), through the expression (Brakensiek, 1977; Rawls et al., 1983; Ogden and Saghafian, 1997):

[[psi].sub.f] = 2+3[lambda]/1+3[lambda]([[psi].sub.b]/2), (2)

where [[psi].sub.b]: bubbling pressure and [lambda]: poresize distribution index.

From the laboratory experimentation with many types of soils, the authors (Brooks and Corey, 1964; Corey and Brooks, 2009) concluded that [[psi].sub.f] can be expressed as a logarithmic function of effective saturation (Se)

[S.sub.e] = [[[[psi].sub.b]/[psi]].sup.[lambda]] for [psi] [greater than or equal to][[psi].sub.e] (3)

where Se: effective saturation, [[psi].sub.b]: bubbling pressure, [psi]: capillary pressure that corresponds to moisture [theta], and [[psi].sub.e]: air entry pressure.

The effective saturation is the relationship between available moisture and the maximum moisture content possible, expressed as

[S.sub.e] = [theta]-[[theta].sub.r]/[eta]-[[theta].sub.r] (4)

where [theta]: soil water content, [[theta].sub.r]: residual soil water content, and [eta]: total soil porosity.

According to Corey and Brooks (2009), [[theta].sub.r], [[psi].sub.b] and [[psi].sub.e] are curve fitting parameters determined from a plot of the capillary pressure as a function of Se on a log-log plot. The parameter [[theta].sub.r] is defined as that saturation value which provides the best fit to straight line, for saturations greater than a critical capillary pressure called [[psi].sub.e]. The exponent [lambda] is the negative of the slope straight line. The intercept at the ordinate where ln([S.sub.e])=0 defines ln([[[psi].sub.b]), and the point where the measured curve intersects the straight line determines ln([[psi].sub.e]). Some researchers assume that the bubbling pressure [[psi].sub.b] and the air entry pressure [[psi].sub.e] are similar (Brakensiek, 1977; Saxton and Rawls, 2006).

For the design of surface irrigation in Mexico, Fuentes (2007) and Rendon et al. (2012) suggest using the parameters of the Green-Ampt function obtained by researchers of the United States Department of Agriculture (USDA) and reported by Brakensiek et al. (1981) and Rawls and Brakensiek (1982). A more complete and recent database that integrates and complements the prior studies, was generated from the study of 5000 soil horizons in the USA and reported by Rawls et al. (1983); however, the standard deviation of their values for a same textural class is very broad. To overcome this problem, the wetting front capillary pressure for a soil of well-identified texture can be obtained through the bubbling pressure in function of the soil water content at saturation (Saxton et al., 1986) and the contents of sand, clay and organic matter (Saxton and Rawls, 2006).

The application of the Green-Ampt equation in Mexico with the values of the parameters reported by the USDA researchers, as suggested by some researchers and government institutions (Fuentes, 2007; Rendon et al., 2012), does not guarantee a good representation of water infiltration due to the heterogeneity of the soils in the country. Therefore, the objective of this research was to obtain the parameters [K.sub.s] and [[psi].sub.f] of the GreenAmpt Eq. 1 with information from the USDA and from a laboratory procedure in some soils of agricultural importance in Mexico, and to evaluate their accuracy through the comparison of the accumulated infiltration depths estimated with field measurements to determine the most appropriate for soils in Mexico.

Materials and Methods

Soils studied

The determination of the parameters was carried out in ten soil samples from soils with agricultural use, seven of them under irrigation and three under rainfall. Sampling was performed in the Mexican states of Michoacan, Oaxaca, Sinaloa, Estado de Mexico, Sonora and Baja California.

Five samples were taken in the state of Michoacan: two samples (Samples 1 and 2) in an agricultural and three samples (Samples 8, 9 and 10) in a rain fed agricultural zone within a small micro-basin (El Malacate) with forestry as primary land use. Each of the remaining five samples corresponded to one of the other previously mentioned states and were collected from irrigated agricultural areas.

Determinations performed in the soils

In each case, five samples of soil were taken from the terrain, at a depth of 30cm and were mixed to form a homogeneous compound sample.

To find the parameters of the Green-Ampt equation in each of the samples, the following were determined: texture, initial soil water content (9i), soil water content at saturation ([[theta].sub.s]), residual soil water content ([[theta].sub.r]), particle soil density ([[rho].sub.s]), bulk soil density ([[rho].sub.b]), saturated hydraulic conductivity ([K.sub.s]) and the water retention curve.

The saturated hydraulic conductivity was determined in laboratory with a permeameter under constant hydraulic head and applying the Darcy law. We used this method because it is employed as a reference to evaluate the accuracy of other methods (Dirksen, 2009) and because the determination of the parameter in the field is difficult to obtain due to the entrance of atmospheric air into the soils (Faybishenko, 2009). The texture and real density were found applying the AS-09 and AS-04 methods, respectively, from the Norma Oficial Mexicana NOM-021-SEMARNAT-2000 (SEMARNAT, 2016). The apparent density was determined with the test tube method, using 50g of dry sieved soil.

The water retention curve was obtained by following the procedure indicated in the AS-06 method of NOM-021-SEMARNAT-2000. The volumetric moisture content was determined at tensions of 0.01, 0.05, 0.1, 0.2, 0.33, 0.5, 1.0, 3.0, 5.0, 7.0, 9.0, 11.0, 12.0, 13.0, 15, 16.0 and 17.0atm, using a pressure cooker for low tensions and a pressure membrane for high tensions.

To calculate effective saturation with Eq. 4, the residual soil water content obtained at 17atm of tension was considered, and total porosity obtained as a function of ps and pb.

For the application of Eq. 1 soil water content at saturation, referred to a soil tension of 0atm, was used.

Green-Ampt models analyzed

The difference between the models that are described hereafter consisted in the way of obtaining parameters [K.sub.s] and [[psi].sub.f] of Eq. 1, since in every case a [[theta].sub.s] was used which resulted from laboratory determinations, and [[theta].sub.i] is a variable that takes the value of the moisture content prior to the infiltration.

Model from the water retention curve

This model was called 'retention curve', where the [K.sub.S] was taken up again from the data obtained in the laboratory with the permeameter under constant hydraulic head method and the parameter [[psi].sub.f] was obtained by solving Eqs. 2, 3 and 4 with information from the water retention curve.

The pressure in the wetting front capillary pressure was obtained from the water retention curve of the soil in a similar way as done by Brooks and Corey (1964) and Brakensiek (1977); the difference in the method applied in our study is that we used a retention curve in a range of 0.01 to 17atm, as pointed out above, and that parameters [[psi].sub.b] and [lambda] were obtained by solving simultaneously Eqs. 3 and 4 by the method of minimum squares instead of a graphic method.

The reason to use a water retention curve in such a broad range of tensions instead of using a curve in a much smaller range, from 0 to 0.5atm as Brooks and Corey (1964) and Brakensiek (1977) did, was because of the limitations of Mexican laboratories that do not allow measuring soil moisture at such low tensions nor distinguishing moisture differentials with small tension differentials.

Model based on data reported by Rawls et al. (1983)

This model was called this way because the values of parameters [K.sub.s] and [[psi].sub.f] were taken from the study carried out by Rawls et al. (1983).

Model based on the equation reported by Saxton et al. (1986)

This model was based on the equation found by Saxton et al. (1986) to calculate parameter [[psi].sub.b] as a function of the soil water content at saturation [[theta].sub.s].

With the [[psi].sub.b] value obtained, Eqs. 3 and 4 were solved by the minimum squares method to obtain the value of [lambda], using the information from the retention curve, and then Eq. 2 was applied to obtain the value of parameter [[psi].sub.f]. The value of [K.sub.s] obtained from the laboratory determination was used.

Model based on the equations obtained by Saxton and Rawls

This model was called 'Saxton and Rawls' because the equations found by Saxton and Rawls (2006) to calculate the parameter [[psi].sub.b] and one of the two contemplated values of [K.sub.s], were used, as a function of the content of clay, sand and organic matter.

The calculation of parameter [lambda] was similar to that performed in the method denominated Saxton et al. (1986). The other value of [K.sub.S] employed was taken from the laboratory result.

Evaluation of the Green-Ampt models

The representativeness of the models considered was evaluated by comparing their results to those obtained from an infiltration test performed through the double ring infiltrometer method. The comparison was made in the soil of the experimental agricultural field of the Universidad Autonoma Chapingo (UACh; Sample 5) and in the three soils of the micro-basin of the state of Michoacan (Samples 8, 9 and 10).

Prior to the beginning of the infiltration test, a small soil sample was taken with a drill to determine the initial moisture content in the four sites analyzed.

The evaluation of the degree of accuracy in the estimation of the infiltrated depth from the models analyzed was carried out with the standard error (SE), average error (AE) and relative error (RE). It is considered that the model has a good accuracy to predict the observed values as the values of the statistical parameters SE, AE and RE approach zero (Gutierrez and de la Vara, 2009).

Results and Discussion

The analyzed soils correspond to six of the twelve textural classes that the USDA considers, covering from loam to clay (Table I).

Table I shows that the total porosity ([eta]) of Sample 8 is quite similar to the mean reported by a soil in the USA with the same texture (Rawls et al., 1983); in contrast, the rest of the soils studied (Samples 1, 2, 3, 4, 5, 6, 7, 9 and 10) presented higher total porosity values than the mean values corresponding to soils with equivalent texture. In general, the total porosity values found are more similar to the higher limits of the intervals of total porosity in Rawls et al. 1983. However, although the total porosity of the samples analyzed is relatively high, the values are within the interval described in the literature, where it is mentioned that the porosity of a soil can reach up to 60% and can further increase in the presence of organic matter (Flint et al., 2009; Stolf et al., 2011).

The values obtained for effective porosity ([[theta].sub.e]) turned out to be similar to the mean values found in soils of the same texture in the USA in Samples 6, 7, 10. In Samples 1, 2, 8 and 9 they were lower (89.6, 71.4, 12.8 and 43.3%, respectively) and in Samples 3, 4 and 5 they were higher (36.4, 29.4 and 33.3%, respectively). The differences in Samples 1 and 2 are notable, and the very small [[theta].sub.e] values in Table I are attributed to their high residual humidity.

In Samples 1 and 2 the soil water content at saturation turned out to be >100%. These high contents of moisture are attributed to the percentage of clay in the samples (>70 %). The class to which these clays belong to is inferred to be montmorillonites, due to the behavior shown during the determination of water retention curves and according to the place where the samples were extracted. According to the Edaphology of the Digital Map of Mexico (INEGI, 2016), Samples 1 and 2 were obtained from a soil belonging to the order of vertisols, which are characterized by having montmorillonite clays, of type 2:1. This class of clay has the capacity of expanding to many times its original volume when water is added. This behavior, analogous to that of a hydrogel, explains the high percentage of saturation moisture in these samples.

Table II shows the values found for parameters [[psi].sub.f] and [K.sub.s] from the Green-Ampt equation, obtained for the models of retention curve and Rawls et al. (1983). The order in which the results are presented corresponds to the increasing fineness of the textures found in the soils studied, so as to ease their analysis. The results from these models are reported in the same table because it would be expected for those of the retention curve to be the most precise ones and because the Rawls et al. (1983) model is the one suggested for Mexico. Notable differences are seen in the values of in all the soil textures analyzed. In nine out of the ten soils, the retention curve model found values that were within the range that the Rawls et al. (1983) model reports, and in most of the cases they were higher than the mean values.

Concerning the values of saturated hydraulic conductivity presented in Table II, in nine of the ten samples analyzed they were higher in the retention curve model and the difference was noticeable in five of the soils analyzed. The discrepancy could be due to differences in the physical properties of the soils and because in our study the parameter was determined with the constant head per-meameter method and making use of altered samples; in contrast, in the study carried out by Rawls et al. (1983), the saturated hydraulic conductivity was obtained through a semi-empirical equation as a function of some physical characteristics of the soil and which has adjustment errors, using the following equation (Brutsaert, 1967):

[K.sub.s] = [alpha][[[theta].sup.2.sub.e]/[[psi].sup.2.sub.b]] [[[lambda].sup.2]/([lambda]+1)([lambda]+2)] (5)

where [alpha]: constant that represents the effects of various fluid constants and of the acceleration of gravity, and is equal to 21[cm.sup.3] x [s.sup.-1] (Rawls et al., 1983).

In Table III, the wetted front capillary pressure and the saturated hydraulic conductivity of the Saxton et al. (1986) and Saxton and Rawls (2006) models are shown. In columns 4, 5 and 6 only the values for Samples 5, 6, 7, 8, 9 and 10 are included, as they were not calculated for the rest of the samples because their organic matter content, a necessary piece of data to apply the Saxton and Rawls (2006) equations, was not determined (see Table I).

The values of parameter [[psi].sub.f] turned out to be different in the four models (Tables II and III). The values of parameter KS obtained in the laboratory also turned out to be different, as well as those calculated with the Saxton and Rawls (2006) equations, particularly in the soils of Samples 8, 9 and 10.

This behavior can be attributed to the fact that these soils have high organic matter contents, as they are agricultural soils in a micro-basin with predominately forestry use, a situation that is not contemplated by the mentioned equations because the average value of the analyzed USA soils was 0.6 and 2.8% for the horizons B-C and A, respectively (Saxton and Rawls, 2006). In Figure 1, the evolution of the accumulated infiltration depth obtained with the double ring infiltrometer (Sample 5, measured at the experimental field at UACh) and with the four models considered in an agricultural soil of Sandy clay loam texture is presented. In the figure, two Saxton and Rawls (2006) models are shown; the one indicated by Saxton and Rawls 1 (2006) used the value of parameter KS calculated with the Saxton and Rawls (2006) equations (column 5 of Table III), and the one labelled as Saxton and Rawls 2 (2006) used the value obtained in the laboratory (column 6 of Table III).

In Figure 1 it can be appreciated that the retention curve model underestimated the results but it was the one that best represented the amount of infiltration, followed in decreasing order of accuracy by the Saxton and Rawls 2 (2006) model, which also underestimated them, Saxton and Rawls 1 (2006) with overestimation, Saxton et al. (1986) with overestimation and Rawls et al. (1983) with an important underestimation. It must be emphasized that the results of the Saxton and Rawls 2 (2006) model turned out to be quite similar to those of the retention curve, with the disadvantage that during long periods of time the infiltration amount is made slightly slower and is more distant from the measured values. The Saxton and Rawls 1 (2006) model had a greater error in the estimation of accumulated infiltrated depth than the Saxton and Rawls 2 (2006) model because the calculation of the hydraulic conductivity at saturation was calculated as a function of the soil water content at saturation, at field capacity and permanent wilting point, which in turn were obtained with empirical equations found for USA soils (Teh and Iba, 2010).

The better approximation of the Saxton and Rawls (2006) models compared to those of Saxton et al. (1986) and Rawls et al. (1983) can be explained because they contemplate the particular characteristics of a soil from its texture and its organic matter content, in addition to being sustained by a larger database. Instead, the use of average values of parameter [[psi].sub.f] from a textural class in the Rawls et al. (1983) model generates strong errors because the range of variation of its values is very broad (column 4 of Table II).

The statistical descriptors SE (cm), AE (cm) and RE (%) allow specifying the power of estimation and quantifying the errors made with the application of each one of the Green-Ampt models analyzed in the soils from Samples 5, 8, 9 and 10. (Table IV). It is clear that the Rawls et al. (1983) model suggested for Mexico is inadequate because in the four soils evaluated there had very high values for the three descriptors: from 3.97 to 82.14cm in SE, from -3.37 to -64.45cm in AE, and from -49.0 to -91.0% in RE. The Saxton et al. (1986) model improved substantially the estimation of the infiltration amount because it included the parameter 9S, a property that is characteristic of a soil, sustained by the analysis of a much broader database. The retention curve and Saxton and Rawls 2 (2006) models were the best and can be considered similar in their predictive quality, except in the soil from Sample 9, where the retention curve model overestimated the results to a lower degree.

In the four evaluated soils, all the Green-Ampt models considered had a lower accuracy in the soil of Sample 10, which has a high content of organic matter and Silty loam texture. Because of the physical characteristics of this soil, it could be said that the flow is applied in piston flow and the other hypotheses suggested by Green-Ampt, so the decrease in the quality of performance from the models is attributed to the use of an altered sample of soil, which could not be the most advisable way to estimate the hydraulic conductivity at saturation in the laboratory for soils with high contents of organic matter, and to the use of equations and a database that also do not contemplate soils with high contents of organic matter.

The good accuracy of the retention curve model suggests that the hypotheses suggested by Green-Ampt are fulfilled in the evaluated soils and that the procedures followed in this model to obtain parameters [[psi].sub.f], [K.sub.S] and [[theta].sub.S] are adequate.

The Saxton and Rawls 2 (2006) model resulted in a similar accuracy to that of the retention curve; however, once the parameter [[psi].sub.b] is estimated, the water retention curve is required to calculate the parameter [lambda] and with them the parameter [[psi].sub.f], and in addition it used the parameter [K.sub.S] obtained in the laboratory and not the one estimated with the empirical equations found by Saxton and Rawls (2006). If the Saxton and Rawls 1 (2006) model, in which the parameter [K.sub.S] was estimated as a function of the texture and the content of organic matter, had been found to be more accurate, the value of [lambda] could be obtained through an inverse process using an infiltration test executed in the field. The inconvenience of obtaining the values for [K.sub.S] and [[psi].sub.f] inversely is that there is a risk of not representing the hydrodynamic characteristics of the soils if there is not enough experience, since these parameters could satisfy only one numerical solution, so that in order to guarantee a good result one must fully identify the parameter to be optimized (Hopmans and Simunek, 2009).

The results from the performed evaluations suggest the need to obtain values from the parameters of the Green-Ampt equation that are suited to the characteristics of soils in Mexico, so as to reach more accurate estimations of the infiltration. According to the results found in this study, the water retention curve must be used to obtain parameter [[psi].sub.f], as was done in the retention curve method, and this curve could be generated taking into consideration the physical properties of the soils, as was done by Rajkai et al. (2004), considering the sand, clay and organic matter contents, and the bulk density from the soils representative of the country to minimize the costs of the studies. Another alternative could be the study of empirical functional relations to obtain [[psi].sub.f] directly as a function of sand and clay contents and the porosity of the soil; these equations have to be specific for soil uses to improve the representativeness of their characteristics (Rawls et al., 1989; King et al., 1999).

Conclusions

It is a challenge to obtain the adequate values of the parameters of the Green-Ampt equation, especially the wetting front capillary pressure head, because of the field and laboratory studies demands, and due to the analysis of information and costs implied. The parameters of the wetting front capillary pressure head and the saturated hydraulic conductivity from the Green-Ampt equations were determined with different procedures in Mexican agricultural soils of six textural classes, and their representativeness evaluated through the comparison of the estimated infiltration depths compared to those obtained in the field with a double ring infiltrometer. The mean values found by Rawls et al. (1983) by texture class, and recommended for soils in Mexico, turned out to be inadequate, with a drastic underestimation of the measured infiltration depths, while the most representative values were those obtained from the water retention curve in the case of the wetting front capillary pressure head and with the constant head permeameter for the saturated hydraulic conductivity.

Finally, obtaining the parameters from the Green-Ampt equation from agricultural soils in Mexico is recommended, and the adaptation of the Brooks and Corey method that was made in this study is suggested to obtain the wetting front capillary pressure head.

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Jorge Victor Prado Hernandez, Fermin Pascual Ramirez, David Cristobal Acevedo, Mauricio Carrillo Garcia, F. Raul Hernandez Saucedo y Antonio Martinez Ruiz

Jorge Victor Prado Hernandez (Corresponding author). Irrigation Engineer, Universidad Autonoma Chapingo (UACh), Mexico. Master of Science in Hydrociences, Colegio de Posgraduados (COLPOS), Mexico. Doctor of Agricultural Engineering, UACh. Professor-Researcher, UACh, Mexico. Address: Soil Department, UACh. Mexico-Texcoco highway, km 38.5, Chapingo, Estado de Mexico. C.P. 56230, Mexico. e-mail: vpradohdez@gmail.com

Fermin Pascual Ramirez. Irrigation Engineer, UACh, Mexico. Master and Doctor in Hydrociencias, COLPOS, Mexico. Professor, Institute for Research on Ecosystems and Sustainability (TIES), CONACYT-UNAM, Campus Morelia, Mexico.

David Cristobal Acevedo. Agricultural Engineer, UACh. Master and Doctor in Hyrociencias, COLPOS, Mexico. Professor-Researcher, UACh, Mexico.

Mauricio Carrillo Garcia. Civil Engineer and Master in Engineering, Universidad Nacional Autonoma de Mexico (UNAM). Ph.D., University of Arizona, USA. Professor-Researcher, UACh, Mexico.

F. Raul Hernandez Saucedo. Irrigation Engineer, UACh, Mexico. Master in Hidrociencias, COLPOS, Mexico. Professor-Researcher, UACh, Mexico.

Antonio Martinez Ruiz. Irrigation Engineer and Master in Agricultural Engineering, UACh, Mexico. Doctoral Candidate, UACh, Mexico.

Caption: Figure 1. Accumulated infiltration depth in the soil from Sample 5.
```TABLE I
CHARACTERISTICS OF THE ANALYZED SOILS

Sample   State of origin   Sand (%)   Clay (%)   Silt (%)

1        Michoacan           8.9        71.8       19.3
2        Michoacan           8.9        73.8       17.3
3        Oaxaca              54.9       21.8       23.3
4        Sinaloa             36.9       37.8       25.3
5        Mexico              48.9       25.8       25.3
6        Baja California     40.3       23.4       36.3
7        Sonora              18.3      37.72       44.0
8        Michoacan           32.0       32.5       35.5
9        Michoacan           28.0       25.0       47.0
10       Michoacan           34.0       15.6       50.4

Texture          [eta]       [[theta].sub.e]
Sample                     ([cm.sup.3]      ([cm.sup.3]
[cm.sup.-3])    [cm.sup.-3])

1        Clay                  0.50            0.04
2        Clay                  0.59            0.11
3        Sandy clay loam       0.57            0.45
4        Clay loam             0.50            0.40
5        Sandy clay loam       0.55            0.44
6        Loam                  0.52            0.41
7        Silty clay loam       0.54            0.42
8        Clay loam             0.48            0.274
9        Loam                  0.57            0.246
10       Silty loam            0.81            0.477

[[theta].sub.s]
Sample     ([cm.sup.3]     OM (%)
[cm.sup.-3])

1             1.35           --
2             1.40           --
3             0.66           --
4             0.75           --
5             0.72          1.75
6             0.80          0.75
7             0.83          1.61
8             0.48          4.80
9             0.57          7.30
10            0.81          8.40

TABLE II
GREEN-AMPT PARAMETERS OBTAINED WITH THE RETENTION
CURVE (RC) AND RAWLS et al. (1983) MODELS

[[psi].sub.f] (cm)     [K.sub.s](cm x [h.sup.-1])

Sample    RC     Rawls et al. (1983)    RC     Rawls et al.

(1983)
6        63.90    8.89 (1.33-59.38)    0.78        0.68
9        40.50    8.89 (1.33-59.38)    17.00       0.68
10       69.10   16.68 (2.92-95.39)    19.00       1.30
3        9.81    21.85 (4.42-108.0)    2.48        0.30
5        10.60   21.85 (4.42-108.0)    1.20        0.30
4        9.98    20.88 (4.79-91.10)    0.36        0.20
8        53.00   20.88 (4.79-91.10)    6.72        0.20
7        86.74   27.30 (5.67-131.5)    0.93        0.20
1        91.67   31.63 (6.39-156.5)    0.10        0.20
2        7.40    31.63 (6.39-156.5)    0.19        0.06

The values in column 3 correspond to the textural class.
Number in parenthesis is [+ or -] standard deviation.

TABLE III
VALUES OF [[psi].sub.f] Y [K.sub.s] USED BY THE SAXTON et al.
(1986) AND SAXTON AND RAWLS (2006) MODELS

Saxton et al. (1986)

Sample   [[psi].sub.f] (cm)   KS from laboratory
(mm x [h.sup.-1])

1              166.90                0.10
2              157.20                0.19
3               9.14                 2.48
4              50.20                 0.36
5              29.57                 1.20
6              21.22                 0.78
7              34.30                 0.93
8              57.81                 6.72
9              82.20                17.00
10             145.92               19.00

Saxton and Rawls (2006)

Sample   [[psi].sub.f]    [K.sub.S] from      [K.sub.S] from
(cm)           laboratory          laboratory
(mm x [h.sup.-1])   (mm x [h.sup.-1])

1             --                --                  --
2             --                --                  --
3             --                --                  --
4             --                --                  --
5            28.44             0.61                1.20
6            42.26             0.61                0.78
7            66.32             0.17                0.93
8            51.26             0.25                6.72
9            63.03             0.45                17.00
10           57.14             0.93                19.00

TABLE IV
STATISTICAL PARAMETERS OF THE ESTIMATED INFILTRATED DEPTH

Sample 5               Sample 8
Model
SE     AE      RE      SE     AE      RE

Retention curve         1.32   -1.05   -15.0   1.03   0.52     6.0
Rawls et al. (1983)     3.97   -3.37   -49.0   9.19   -7.89   -90.0
Saxton et al. (1986)    2.24   1.94    28.0    2.85   2.21    25.0
Saxton and Rawls 1      1.32   1.79    26.0    8.48   -7.28   -83.0
(2006)
Saxton and Rawls 2      2.08   -1.00   -14.0   0.92   0.39     5.0
(2006)

Sample 9                 Sample 10
Model
SE       AE      RE      SE       AE      RE

Retention curve         3.41     0.63     1.0    10.60   -8.33    -12.0
Rawls et al. (1983)     52.07   -43.60   -94.0   82.14   -64.45   -91.0
Saxton et al. (1986)    18.89   15.45    33.0    20.76   16.84    24.0
Saxton and Rawls 1      49.90   -41.71   -90.0   77.72   -60.87   -86.0
(2006)
Saxton and Rawls 2      7.38     5.19    11.0    9.89    -7.75    -11.0
(2006)
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