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Estimating soil water retention in a selected range of soil pores using tension disc infiltrometer data
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Soil & Tillage Research 97 (2007) 107–116 www.elsevier.com/locate/still
Estimating soil water retention in a selected range of soil pores using tension disc infiltrometer data Youngman Yoon, Jeong-Gyu Kim, Seunghun Hyun * Division of Environmental Science and Ecological Engineering, Korea University, Seoul 136-713, Republic of Korea Received 16 March 2007; received in revised form 11 September 2007; accepted 11 September 2007
Abstract The hydraulic properties of soil, such as soil moisture characteristic and pore size distribution, are very important for the interpretation of the physical characteristics of soil and the management of agricultural practices. The current standard methods employing pressure chamber, however, are often time-consuming and difficult to carry out. In this study, we proposed a simple approach to estimate the soil moisture retention and soil pore size, with sufficient accuracy, using steady-state infiltration data. First, the tension disc infiltration data was interpreted using Wooding’s analytical solution to obtain the K(h) function, from which Ks (saturated hydraulic conductivity) was optimized. The Ks value was then used as an initial input data for the Brooks–Corey model fit to obtain the water retention parameters aBC and b, and the soil water retention characteristics within a selected range of soil pores of 9–450 mm were predicted. The proposed approach was tested for three differently textured soils in laboratory test and one undisturbed field soils. The measurement was replicated for three to five times for each soil. The validity of this method was confirmed by showing good linear regression relationship with data sets obtained by standard pressure chamber method, yielding slopes being close to unity and r2 values being >0.86. This observation strongly suggests that the proposed method can be applied for the in situ measurement of water retention and pore size in field soils. The results of this work will enable us to easily determine the temporal changes of hydrodynamic nature of soil using tension disc infiltrometer technique. # 2007 Elsevier B.V. All rights reserved. Keywords: Water retention; Pore size distribution; Tension disc infiltrometer; Unsaturated hydraulic conductivity
1. Introduction Assessing the movement of soil water is a principal component in soil management practice for minimizing the potential of groundwater contamination from soilapplied chemicals. One of the key factors influencing the movement of soil water is the distribution of various sizes of soil pores. Given that there is a strong relationship between pore size and soil water behavior, obtaining the pore size distribution (PSD) of field soil is an important step in understanding the dynamic
* Corresponding author. Tel.: +82 2 3290 3068; fax: +82 2 953 0737. E-mail address: [email protected] (S. Hyun). 0167-1987/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.still.2007.09.003
processes of the movement of water and solutes in soil (Ankeny et al., 1991; Hillel, 1998). The soil structure and PSD are dynamically changed by various environmental factors, such as tillage practice, wetting– drying processes and biological activity (Azooz et al., 1996; Leij et al., 2002) and thus the timely quantification of the temporal dynamic of the PSD may have important applications. However, since soil porous systems are complicated and are three-dimensionally structured with a variety of sizes, shapes and connectivities, soil pores are very difficult to observe and characterize. In addition, the required experimental equipments (e.g., pressure chamber method) and methodologies conventionally used for analyzing soil structure are very expensive and time-consuming.
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From this perspective, the literature is replete with attempts to develop methods describing the geometry and associated properties of the pore space naturally occurring in soils (Campbell, 1974; Kosugi, 1999; Leij et al., 2002). There are two major experimental approaches currently available for the determination of soil pore sizes and their distribution; the forced fluid intrusion and water desorption methods. The soil pore fluid intrusion method has been generally obtained by observing the relationship between the pore size and pressure required to intrude fluids into pores. The soil pore size can be most rapidly determined over a wide range (105 to 10 nm) with the application of mercury in the intrusion fluid method. The soil pore size obtained by this method has some uncertainty as a result of the possibility of aggregate collapse during the measurement due to the high surface tension of mercury (Dullien and Batra, 1970). The principle and assumptions for measuring the soil pore size using the water desorption method is similar to those for the fluid intrusion method. Based on the theoretical assumption of a cylindrical pore shape and the contact angle of the water with the soil, the volume of water desorbed from different soil pore sizes at the corresponding equilibrium matrix potential can be measured. In this method, however, substantial amount of time with elaborate instruments are required to establish equilibrium between the water content and the associated exerted pressure. Therefore, developing an easier and timesaving technique to describing the properties of soil pore distribution is required, with acceptable accuracy. A tension disc infiltrometer is a useful instrument that offers a rapid method for estimating the hydraulic properties and structural characteristics of soil with minimum disturbance of the soil structure (Perroux and White, 1988; Ankeny et al., 1991; Reynolds and Elrick, 1991; Haw and Rao, 2004; Ramos et al., 2006). The technique has become increasingly popular for the in situ measurement of near saturated hydraulic properties (pressure head, h < 35 cm). A sequence of steadystate flow rates through the soil is measured by setting a sequence pressure heads (h) imposed on the soil surface. The most widely used method estimating the parameters based on the use of a tension disc infiltrometer is to apply an approximate unconfined steady-state solution infiltration from a surface circular source (Wooding, 1968). Alternative methods include the determination of the sorptivity and macroscopic capillary length and numerical inversion (White et al., 1992; Vogeler et al., 1996). While Wooding’s method requires the tension infiltrometer to reach a steady-state rate, the other methods need the accurate measurement
of the transition infiltration rate for a pre-selected tension. In Wooding’s solution, the unknown hydraulic parameters can be solved by measuring either the steady-state infiltration rate at a fixed disc radius with multiple supply tension (Ankeny et al., 1991) or at a fixed tension with variable disc radii (Smettem and Clothier, 1989). Many studies have documented the efficacy of the infiltrometer technique for characterizing the water flow through various field soil profiles (Logsdon et al., 1993; Timlin et al., 1994; Ramos et al., 2006), but no attempt has been made to relate tension disc infiltrometer data with the soil water retention or the pore size distribution. This research was conducted to propose a simple theoretical approach to estimating soil moisture characteristic curve (SMCC) and pore size distribution (PSD), using the hydraulic conductivity function obtained from the tension disc infiltrometer data. Laboratory tests were performed to describe soil moisture retention within a selected range of soil pores from three differently textured soils (sandy, sandy loam, and sandy clay loam soils). The method was further tested for an undisturbed agricultural sandy loam soil in the field. In order to prove the validity of the results from both laboratory and field tests, the SMCC and PSD of each soil estimated by the proposed method were compared with data set independently measured by the conventional standard pressure chamber method. Also discussed is the limitation of the proposed approach. 1.1. Theory Using a multiple regression analysis of soil water retention data, Campbell (1974) developed an equation to describe water retention, as follows: h ¼ he
u us
b (1)
where u is the volume wetness (L3 L3), us the saturated volume wetness (L3 L3), h the matrix potential (L), he the air-entry potential (L) of soil and b the waterretention parameter, which is also related to the pore size distribution (Brooks and Corey, 1964). Similar to the prediction of unsaturated soil hydraulic conductivity (K) proposed by Brooks and Corey (1964), the following hydraulic conductivity function was proposed by Campbell (1974) under the condition of h < he: K ¼ Ks
uðhÞ us
2bþ3 (2)
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where Ks is the saturated hydraulic conductivity (L T1). By assuming the effect of the residual volumetric water content to be negligible (i.e., u (h) ur or ur ffi 0), the effective saturation (Se(h), L3 L3) would be equal to u(h)/us and thus can be expressed in terms of the matrix potential as follows: Se ðhÞ ¼
uðhÞ ur uðhÞ ffi us us u r
(3)
By rearranging Eq. (1), the effective saturation (Se(h) ffi u(h)/us) will be given as: Se ðhÞ ¼
uðhÞ ¼ jaBC hj1=b us
(4)
where aBC is the reverse of an air entry potential (he1, L1). Through substitution of Eq. (4) into Eq. (2), the relationship between K and h can be obtained as follows: KðhÞ ¼ K s jaBC hj23=b
(5)
2. Materials and methods 2.1. Soils The three differently textured soils used in the laboratory study were collected from Korea University Agricultural Farm located in Kyonggi, Korea; K1, K2 and K3 for sand, sandy loam and sandy clayey loam soils, respectively, according to USDA textural classification system (Gee and Or, 2002). Each soil was poured into three pots (15 cm of height and 30 cm of diameter) and stabilized by irrigation for 1 month, prior to use in the laboratory study. In situ field tests were conducted for an undisturbed agricultural surface soil of Bonryang series, which is also located in Kyonggi,
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Korea. Selected soil properties related to hydraulic properties were measured and are summarized in Table 1. Particle size analysis was preformed using a pipette method (Gee and Or, 2002). Bulk density and particle density were determined by core method (Grossman and Reinsch, 2002) and liquid displacement method (Flint and Flint, 2002a), respectively. Porosity was determined by gravimetric method with water saturation (Flint and Flint, 2002b). Also reported in Table 1 is information with regard to soil classification according to the USDA taxonomy system. 2.2. Tension disc infiltrometer experiment 2.2.1. Measurement of steady-state infiltration rate The tension disc infiltrometer used in this study was purchased from Soil Measurement Systems (Tucson, AZ). The supplied pressure head was controlled by a bubble tower (i.e., Mariotte bottle). Six successive pressure heads: 0, 1.0, 3.0, 5.0, 7.0 9.0, and 15 cm were applied and the steady-state infiltration rates were measured. Due to the geometry of the instrument, the pressure range that can be used is restricted to about 20 cm (smaller than the reported air-entry value of disc membrane). A sequential stepwise decrease of the supply pressure head was adopted to reduce the measurement errors potentially caused by hysteresis (Reynolds and Elrick, 1991). A 1.5 cm long thin-walled PVC ring (radius = 4.5 cm) with a sharp cutting edge at the base was inserted straightly on the soil surface. The progressive drainage from the infiltration front occurs from the layer closest to the disc. The drainage from a disc can be influenced by the contact between the disc membrane and soil surface, since direct contact with the soil surface may cause an imperfect and irregular measurement due to the roughness of the soil surface. To smooth out possible
Table 1 Selected physical characteristics of the soils used in these experiments Soils
K1 K2 K3 Bonryang a
Soil ordera
Alfisols Inceptisols Inceptisols Entisols
Subgroupsa
Ochreptic Fragiudalfs Fluvaquentic Endoaquepts Fluvaquentic Endoaquepts Typic Udifluvents
Particle contentb Sand
Silt
Clay
88 71 53 60
5 12 20 30
7 17 27 10
Textural classb
Bd c
Pd d
he
S SL SCL SL
1.41 1.32 1.23 1.37
2.65 2.65 2.65 2.65
0.470 0.502 0.545 0.486
Soil classification according to USDA taxonomy system. Particle size was analyzed by pipette method (Gee and Or, 2002) and defined according to the USDA textural class system. Size-fraction percentages are presented (%, w/w). c Soil bulk density (g cm3) measured by core method (Grossman and Reinsch, 2002). d Soil particle density (g cm3) measured by liquid displacement method (Flint and Flint, 2002a,b). e Soil porosity (cm3 cm3) measured by gravimetric method with water saturation (Flint and Flint, 2002a,b). b
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irregularities at the soil surface and to ensure hydraulic contact between the disc and the underlying soil, 1 cmthickness of coarse sand having mesh size of 20, tamped lightly inside PVC ring, was layered between the disc and soil surface. Three to five replicate infiltration runs were performed for each of the four soils. 2.2.2. Calculation of unsaturated hydraulic conductivity Wooding’s analytical solution was used to interpret the steady-state infiltration data: QðhÞ ¼ KðhÞprd2 þ 4FðhÞr d
(6)
where Q(h) is the steady state infiltration rate (L3 T1), F(h) the matrix flux potential (L2 T1) and rd is the disc radius (L). The first and the second terms on the right side represent the effect of gravitational forces and the effect of capillary forces, respectively. Assuming an exponential relationship between K and h, Eq. (6) can be rewritten by: QðhÞ ¼ KðhÞprd2 þ KðhÞ
4r d aG
(8)
For the estimation of the two unknowns (aG and Ks), Q(h) was measured at a fixed disc radius with multiple supply tensions (Ankeny et al., 1991; Reynolds and Elrick, 1991). To this end, the reverse of capillary length in Gardner’s exponential model (aG) was assumed to be constant in interval between two adjacent supply pressure heads and was determined from the piecewise slope as follows (aGiþð1=2Þ ): lnðQi =Qiþ1 Þ hi hiþ1
i ¼ 1; 2; . . . ; n
(10)
where n is the number of supply pressure heads used, and the subscript i + (1/2) indicates the middle value of two adjacent supply pressure heads; that is, hi + (1/ 2) = (hi + hi + 1)/2. In a same sense, the unsaturated hydraulic conductivity (Ki + (1/2)) at the middle value of two adjacent supply pressure heads (hi + (1/2)) can
ðprd2
Qiþð1=2Þ þ ð4r d =aGiþð1=2Þ ÞÞ
(11)
where
Qiþð1=2Þ
lnðQi Þ þ lnðQiþ1 Þ ¼ exp 2
(12)
The saturated hydraulic conductivity Ks, was estimated by fitting the measured K(h) data to Gardner’s model (Eq. (8)). 2.3. Estimation of SMCC and PSD from K(h) function 2.3.1. Optimization of water retention parameters The model parameters, aBC and b, in Eq. (5) were optimized by adjusting those values until global minimum was found for the following objective function, SSR ¼
By substituting Eq. (8) into Eq. (7) the relationship between Q(h) and the supply tension will be given by: 4r d 2 QðhÞ ¼ K s prd þ (9) expðaG hÞ aG
aGiþð1=2Þ ¼
K iþð1=2Þ ¼
(7)
In this approach, the parameter aG has been defined by Gardner (1958): KðhÞ ¼ K s expðaG hÞ
also be obtained by:
n X
2
½Kðh j Þ K 0 ðh j Þ
(13)
j¼1
where SSR is the sum of squared residuals between the experimental (K(hj)) and model (K0 (hj)) prediction; here, h is actually hi + (1/2) as shown in Eq. (11) In this optimization process, the Ks value estimated from K(h) function was used as a matching point. 2.3.2. Estimation of SMCC and PSD The soil moisture characteristic curve is a plot of u versus h. The effective water saturation (Se(h)) is equivalent to the fraction of total pore space filled with water (u(h)/us), which can be obtained by inputting the values of aBC and b into Eq. (4). Therefore, the soil moisture characteristic curve (SMCC, u(h)) can be obtained by multiplying the effective water saturation by the saturated volume wetness (=us Se(h)): uðhÞ ¼ us jaBC hj1=b
(14)
In addition, the effective water saturation (Se(h)) corresponds to the fraction of the accumulative volume of a water-filled soil pore at a given matric pressure (h). Assuming the pores have a capillary tube shape and the contact angle of water to the pore to be zero, the largest water-filled soil pore, with a radius, r, at a given h, can be expressed by applying the following well known
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Fig. 1. (A–D) The unsaturated hydraulic conductivity (K(h)) of all soils used in this study, as determined using a tension disc infiltrometer data and Wooding’s analytical solution. Data points are the average of replicates and the standard error between measurements is shown by the error bar. The solid line is the Gardner’s exponential model fit with the coefficient of determinant (r2) being >0.90.
capillarity equation: rðhÞ ¼
2g rw gh
(15)
where g is the surface tension (kg s2) of water, rw the density of water (kg m3) and g is the gravitational acceleration (9.81 m s2). Therefore, the cumulative fraction of the pore space filled with water at a given h, can be plotted with respect to the soil pore size by equating capillarity equation (r(h)) and the degree of water saturation (u(h)). 2.4. Determination of SMCC using conventional pressure chamber method To verify the validity of the results obtained using the proposed method, the SMCC and PSD of the tested soils were independently measured by the conventional water-desorption technique, where the volume of water drained from an initially saturated soil at consecutive pressures is used to calculate the pore size. Following measurement of the steady-state infiltration rate, soil cores were taken from the soil beneath the disc, three cores from each in the case of laboratory tests and five cores for the field tests. These soil cores (50 mm in height and 72 mm in diameter) were laid on a ceramic plate, with a bubbling pressure of 10 m water
(ffi1.0 bar). The pressure chamber was modified to obtain the exact reading of the supply pressure head by adapting a 230 cm-water column. The prepared soil cores were water-saturated from the base, and allowed to reach equilibrium for 2 days. A supply pressure head (h) between 6 and 200 cm was regulated by the height of the water level and higher pressures (up to 333 cm) were attained using a pressure regulator. For each pressure increment, the volume wetness (u) of the soil sample was calculated by multiplying the gravimetric water content by the soil bulk density. The fraction of the total pores occupied by water at a given pressure, therefore, was determined by dividing the volume wetness by the porosity. The size of the water-filled soil pore was also calculated using the capillarity equation as describe earlier. 3. Results 3.1. K(h) function from tension disc infiltration The K(h) values determined in four soils using the tension disc infiltrometer at the matric potential of 0.5, 2.0, 4.0, 6.0, 8.0, and 12 cm are presented in Fig. 1. Also shown in Fig. 1 are the Gardner’s exponential model fits (r2 > 0.90) as a solid line for each soil. The fitted Ks values estimated for K1 (sandy), K2 (sandy loam), and K3 (sandy clay loam) soils were
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24.63 3.25, 2.81 0.27, 0.904 0.105 cm h1, respectively, and varied only within 15% of the independently measured value for respective soil using the constant-head method. The Ks value tends to increase greatly with coarse texture because of an increase in the number and size of water-conductive pores; the magnitude of hydraulic conductivity is proportional to the second power of effective particle size (Hubbert, 1940). The magnitude of Ks estimated for three laboratory soils increases exponentially with increasing sand content of soils (r2 = 0.962; regression not shown here). Under the given operation range of pressure potential, the K(h) curve of each soil varied within the two orders of magnitude with the values gradually decreasing as the pressure head became more negative, but no inflection point was attained. The measurement of K(h) under near saturated conditions showed greater fluctuation among replicates compared to less saturated condition (i.e., greater error bars at the lower suction range), especially for sandy soil (Fig. 1A). The amount of water retained with lower matrix suction is strongly affected by soil structure such as capillarity and pore size distribution, both of which will in turn influence the magnitude of Ks. The relatively greater variability of the K(h) measured near saturated conditions indicates the presence of an irregular distribution of macro-pores possibly with entrapped air (Mohanty et al., 1996). The result of undisturbed agricultural Bonryang soil in the field test is shown in Fig. 1D. The Ks value of the Bonryang soil was 0.4962 0.0253 cm h1, one order of magnitude higher than the previously reported value of 0.054 cm h1 by Um et al. (1995), who measured K(u) function using internal drain method employing a scaled water content. This difference is most likely due to the difference in the measurement methods employed and the possible seasonal dynamic change in the soil structure. Agricultural soils frequently exhibit extensive spatial and temporal changes in pore characteristics, causing experimental variation in determining K(h) function (Perroux and White, 1988). In order for better agricultural soil management, it has been well recognized that spatial and temporal replication of soil parameter measurement is required to obtain reliable hydrologic characterization of field soils. 3.2. Soil moisture characteristic curve (SMCC) and pore size distribution (PSD) The soil moisture characteristic curves (SMCC, u (h)) of the three soils with different textures, measured by the conventional pressure chamber method for the
Fig. 2. (A) The soil moisture characteristics curve of K1, K2 and K3 soils for the range of matric potential (h) < he, and (B) the cumulative pore volume ratio of the three soils obtained from the laboratory tests.
matrix potential (h) range from 6 to 333 cm, are shown in Fig. 2A, along with the predicted lines by Eq. (14). Also included in Fig. 2B are the measured cumulative pore size distributions (PSD) and corresponding predicted lines for each soil. The values of the parameters of each soil, including aBC, b, and us, used in the proposed method are listed in Table 2. Note that predicted lines for Fig. 2A were obtained by plugging the parameters aBC and b into Eq. (14); u(h) = us øaBC hø1/b, where u(h) increases asymptotically when soil water potential (h) approaches zero. Due to the geometric restraint of this model, the predictive volumetric water content may be flawed as the soil matrix potential exceed over the limit of air-entry point (he). The dimensionless parameter ‘b’ is the inverse of pore size distribution index, l, as denoted by Brooks and Corey (1964). Theoretically, l approaches infinity for a porous medium with a uniform pore size distribution, whereas it is close to zero for a porous medium with a wide range of pore sizes. That is, the value of parameter b will be smaller for a soil with a relatively uniform pore size distribution. Among soils used in this study, K1 soil can be assumed to have a
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Table 2 The value of soil parameters related to soil moisture retention characteristics Soils
Textural class a
Ks b
K1 K2 K3 Bonryang
S SL SCL SL
24.63 2.81 0.90 0.50
a b c d e f
aG c (3.25)f (0.27) (0.10) (0.02)
0.22 0.11 0.40 0.10
be
aBC d (0.05) (0.02) (0.08) (0.01)
0.30 0.14 0.46 0.12
(0.04) (0.00) (0.01) (0.00)
2.60 4.54 9.60 3.11
(0.11) (0.19) (0.74) (0.10)
Soil textural classification using the USDA scheme (Gee and Or, 2002), S: sandy soil, SL: sandy loam, SCL: sandy clay loam. Saturated hydraulic conductivity (cm h1) obtained by fitting K(h) data to Gardner’s model. Gardner’s model parameter. Brooks–Corey parameter; the reverse of the air entry pressure (he1, cm1). Water retention parameter, which is related to the pore size distribution. Standard error.
uniform distribution of larger pores, based on its smaller b and larger Ks values. The b values of the four soils was found to be linearly correlated with the clay content (%) (r2 = 0.947; a = 0.001, the regression not shown here), suggesting that the presence of more clay induces a broader range of soil pore size. For field study with an undisturbed Bonryang soil, the measured SMCC and calculated PSD (shown as circles) using the conventional technique are shown in
Fig. 3. (a) The soil moisture characteristics curve of Bonryang soil for the range of matric potential (h) < he, and (b) the cumulative soil pore volume ratio. Measured data are shown as closed circles. Predicted lines are shown as solid lines.
Fig. 3, along with the predicted lines (shown as solid line). The proposed method described well the soil water retention for the pressure head (h) range > 20 cm; however, in the higher matrix potentials range of h < 20 cm, the volume wetness of the soil was overestimated (Fig. 3a). Likewise, the subsequent predicted line for the cumulative soil water retained in the corresponding range of pore diameters (i.e., >200 mm) was also overestimated (Fig. 3b). As pointed out earlier, the deviations of the model prediction are most likely due to the nature of Eq. (14), which describes the asymptotical increase in the volume wetness with decreasing matric potential between water molecule and soil matrix. In reality, however, the soil volume wetness (u(h)) should be smaller than soil porosity, no matter how small the matrix potential is acting between the soil pores and water molecules. When all the pores are fully filled with water, the soil water content should reach the value of saturated volume wetness (us), shown as a closed square in Fig. 3a. In addition, it has also been reported that, as the soil wetness (u) approaches saturation, the impact of the structural pores on the water retention and hydraulic conductivity cannot be adequately accounted for by models that assume homogeneous porous media (Ross and Smettem, 1993; Poulsen et al., 2004), which is a case of undisturbed field soil condition. For example, the water retention at lower matrix suction (e.g., close to air-entry pressure) mainly depends on the soil structure, including factors such as the capillarity and pore size. On the other hands, at higher suction, water retention is increasingly due to adsorption, so it is less influenced by the structure, but more by the soil texture and surface area. 3.3. Validation Fig. 4 presents the correlation of the data set of cumulative pore size distributions obtained from both
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the accumulate pore volume ratio as approaching to the point of 0.9 (Fig. 4b), is due to overestimation of water retention at lower pressure head.
4. Discussion
Fig. 4. Correlation between the measured and predicted of pore size distributions of (A) the three soils used obtained from laboratory tests and (B) Bonryang soils from a field test. The solid line is a linear regression fit. The dashed line is a 1:1 line. For graph (A), the regression line was constructed using all the results obtained for the three soils with different textures.
the pressure chamber (denoted as measured) and the proposed method (denoted as predicted) for laboratory and field tests. The validation of the proposed method was accomplished by providing a result of linear regression analysis of two data sets, as shown by the solid line. As a reference, 1:1 matching lines are also shown as dotted lines. The regression line for the laboratory test was constructed using all three soils together. The slopes of both regressed lines are close to unity and have a small intercept; the coefficients of determination (r2) were 0.941 and 0.866 for the laboratory and field tests, respectively, at a significant level of a = 0.01. The r2 value represents the closeness of the predicted data to the regressed line. Therefore, >94% of the laboratory data for the three soils with different textures, and >86% of the undisturbed field soil data, were successfully predicted using the proposed method. The high correlation between the two data sets strongly supports the validity of the proposed approach. The relatively poor prediction of
In this study the Ks value was estimated from K(h) function and was further used as an initial input data for optimizing water retention parameters. Although there are arguments that Ks may not be a suitable matching point for soils rich in macropores due to susceptibility of the magnitude of Ks to macropore flow (Schaap and Leij, 2000), it has been frequently used for estimating soil parameters as it is relatively easily measurable (van Genuchten and Nielsen, 1985; Luckner et al., 1989). The major concern arises from the likelihood that Ks would be a significant scaling factor controlling the overall accuracy of the optimization procedures. The hydraulic conductivity is generally predicted by many mathematical functions in which (1) the analytical solution of water flow through soil pore system is derived and (2) easily obtainable soil data such as parameters estimated from water retention data or Ks are incorporated (Mualem, 1976; van Genuchten, 1980; Poulsen et al., 2004). However, the uncertainty of the K(h) function inferred from the water retention data is subject to error with respect to the parameters acquired by optimization processes (Kool et al., 1985). In our laboratory study where the reverse estimation processes (that is, estimating water retention parameter from K(h) function) were explored for three differently textured soils, good estimations were found, even though there were clearly a certain range of error in the determination of K(h), which are shown by the error bars in Fig. 1. Frequent use of the PSD model for the prediction of K(h) from water retention parameters has implicated a relationship between the hydraulic conductivity and soil properties determining the nature of soil’s water retention (Mualem, 1976; Kosugi, 1999; Schaap and Leij, 2000; Poulsen et al., 2004). Theoretically, the hydraulic conductivity is derived by integration of the elementary pore domains represented by a specific pore radius since hydraulic conductivity of soil at given water content is composed of flow in pores that are filled with water at that water content. In this sense, it can be also reasonably presumed that the concept of reversely using the hydraulic conductivity data to predict soil water retention parameters is acceptable, as long as the water retention parameters keep their original physical meaning and water retention hysteresis is minimal.
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The theoretical approach of this work was essentially based on the assumption of homogeneous soil hydraulic properties within the zone of influence of the infiltrometer measurements under the tension. However, since the soil porous system is fragile and very sensitive to overburden pressure that may alter the geometry of the soil pores and capillary tube depending on the distance to which the wetting front advances during the time taken to establish steady-flow conditions, the extension of this basic assumption toward soils with heterogeneous structural features (e.g., waterrepellency, fissures, cracks, bio-channels and other preferential flow features) and strong aggregation should be questionable. In addition, the disc infiltrometer can be mostly used to measure water flow rates at the soil surface; thus the application of this method to extended depth of soils is also limited. In summary, so far, it has been an important part of soil physics for decades to predict hydraulic conductivity by fitting the water retention model to measured data, which yields values of parameters for K(h) function (van Genuchten, 1980; Ross and Smettem, 1993; Schaap and Leij, 2000; Poulsen et al., 2004). In this study, we provided theoretical approach to estimating the water retention from K(h) function and tested the proposed method for both laboratory and field studies. The hydraulic measurement using each instrument has its own reliable range of matric potential. Due to the geometry of tension infiltrometer, the K(h) function could be obtained in the matric potential (h) range only from 0.5 to 12 cm under which range water retention parameters were also estimated. While the range of matric potential (h) which can be supplied for pressure chamber method was between 6 and 333 cm; lower matric potential was unable to be achieved because of the instrumental restriction. However, even though there is a limited overlapped matric potential, the soil water retention characteristic (u(h)) for an extend range of matric potential was well predicted using parameters obtained from limited range of K(h) function. The observation suggests that the proposed approach provides a relatively simple and reliable alternative method for determining soil water retention in a selected range (9–450 mm) of pore size in homogeneous one-layered surface soils, only requiring tension disc infiltrometer data at multiple tensions and stepwise mathematical manipulation. The result of this work strongly suggests the application of tension disc infiltrometer technique for the in situ measurement of temporal change of soil hydraulic properties of soils, such as water retention and pore size.
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References Ankeny, M.D., Ahmed, M., Kaspar, T.C., Horton, R., 1991. Simple field method for determining unsaturated hydraulic conductivity. Soil Sci. Soc. Am. J. 55, 467–470. Azooz, R.H., Arshad, M.A., Franzluebbers, A.J., 1996. Pore size distribution and hydraulic conductivity affected by tillage in northwestern Canada. Soil Sci. Soc. Am. J. 60, 1197–1201. Brooks, R.H., Corey, A.T., 1964. Hydraulic properties of porous media. Hydrology Paper No. 3. Colorado State Univ., Fort Collins, CO, USA. Campbell, G.S., 1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Sci. 117, 311– 314. Dullien, F.A.L., Batra, V.K., 1970. Determination of the structure of porous media. Ind. Eng. Chem. 62, 25–53. Flint, A.L., Flint, L.E., 2002a. Particle density. In: Dane, J.H., Topp, G.C. (Eds.), Method of Soil Analysis: Part 4-Physical Methods. Amer. Soc. Agron., Madison, WI, USA, pp. 230–234. Flint, L.E., Flint, A.L., 2002b. Porosity. In: Dane, J.H., Topp, G.C. (Eds.), Method of Soil Analysis: Part 4-Physical Methods. Amer. Soc. Agron., Madison, WI, USA, pp. 243–244. Gardner, W.R., 1958. Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation form a water table. Soil Sci. 85, 228–232. Gee, G.W., Or, D., 2002. Particle-size analysis. In: Dane, J.H., Topp, G.C. (Eds.), Method of Soil Analysis: Part 4-Physical Methods. Amer. Soc. Agron., Madison, WI, USA, pp. 272–277. Grossman, R.B., Reinsch, T.G., 2002. Bulk density and linear extensibility. In: Dane, J.H., Topp, G.C. (Eds.), Method of Soil Analysis: Part 4-Physical Methods. Amer. Soc. Agron., Madison, WI, USA, pp. 207–210. Haw, N.W., Rao, P.S.C., 2004. The effect of vertically decreasing macropore fractions on simulations of non-equilibrium solute transport. Vadose Zone J. 3, 1300–1308. Hillel, D., 1998. Environmental Soil Physics. Academic Press, New York. Hubbert, M.K., 1940. The theory of ground-water motion. J. Geol. 48, 785–944. Kosugi, K., 1999. General model for unsaturated hydraulic conductivity for soils with lognormal pore-size distribution. Soil Sci. Soc. Am. J. 63, 270–277. Kool, J.B., Parker, J.C., van Genuchten, M.Th., 1985. Determining soil hydraulic properties from one-step outflow experiments by parameter estimation: I. Theory and numerical studies. Soil Sci. Soc. Am. J. 49, 1348–1354. Leij, F.J., Ghezzehei, T.A., Or, D., 2002. Analytical models for soil pore-size distribution after tillage. Soil Sci. Soc. Am. J. 66, 1104– 1114. Logsdon, S.D., McCoy, E.L., Allmaras, R.R., Linden, D.R., 1993. Macropore characterization by indirect methods. J. Soil Sci. 155, 316–324. Luckner, L., van Genuchten, M.Th., Nielsen, D.R., 1989. A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface. Water Resour. Res. 25, 2187–2193. Mohanty, B.P., Skaggs, T.H., Ankeny, M.D., 1996. Infiltration and macro porosity under a row crop agricultural field in a glacial till soil. J. Soil Sci. 161, 205–213. Mualem, Y., 1976. A new model predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12, 513–522. Perroux, K.M., White, I., 1988. Designs for disc permeameters. Soil Sci. Soc. Am. J. 52, 1205–1215.
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Poulsen, T.G., Moldrup, P., Wosten, H., Jacobsen, O.H., 2004. Predicting three-region unsaturated hydraulic conductivity from three soil-water retention points. Soil Sci. 169, 157–167. Ramos, T.B., Goncalves, M.C., Martins, J.C., van Genuchten, M.Th., Pires, F.P., 2006. Estimation of soil hydraulic properties from numerical inversion of tension disk infiltrometer data. Vadose Zone J. 5, 684–696. Reynolds, W.D., Elrick, D.E., 1991. Determination of hydraulic conductivity using a tension infiltrometer. Soil Sci. Soc. Am. J. 55, 633–639. Ross, P.J., Smettem, K.R.J., 1993. Describing soil hydraulic properties with sums of simple functions. Soil Sci. Soc. Am. J. 57, 26–29. Schaap, M.G., Leij, F.J., 2000. Improved prediction of unsaturated hydraulic conductivity with the Mualem-van Genuchten model. Soil Sci. Soc. Am. J. 64, 843–851. Smettem, K.R.J., Clothier, B.E., 1989. Measuring unsaturated sorptivity and hydraulic conductivity using multi-disc permeameters. J. Soil Sci. 40, 563–568. Timlin, D.J., Ahuja, L.R., Ankeny, M.D., 1994. Comparison of three field methods to characterize apparent macropore conductivity. Soil Sci. Soc. Am. J. 58, 278–284.
Um, K.-C., Song, K.-C., Ryu, K.-S., Sohn, Y.-G., Lee, S.-E., 1995. The estimation model of soil moisture characteristics curve using scaling factor. J. Kor. Soc. Soil Sci. Fer. 28, 227–232. van Genuchten, M.Th., 1980. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898. van Genuchten, M.Th., Nielsen, D.R., 1985. On describing and predicting the hydraulic properties of unsaturated soils. Ann. Geophys. 3, 615–628. Vogeler, I., Clothier, B.E., Green, S.R., Scotter, D.R., Tillman, R.W., 1996. Characterizing water and solute movement by time domain reflectometry and disk permeametry. Soil Sci. Soc. Am. J. 60, 5– 12. White, I., Sully, M.J., Perroux, K.M., 1992. Measurement of surface soil hydraulic properties: disk permeameters, tension infiltrometers, and other techniques. In: Topp, G.C., et al. (Eds.), Advances in Measurement of Soil Physical Properties: Bringing Theory Into Practice. SSSA Spec. Pub. 30. SSSA, Madison, WI, pp. 69–103. Wooding, R.A., 1968. Steady infiltration from a shallow circular pond. Water Resour. Res. 4, 1259–1273.
Soil & Tillage Research 97 (2007) 107–116 www.elsevier.com/locate/still
Estimating soil water retention in a selected range of soil pores using tension disc infiltrometer data Youngman Yoon, Jeong-Gyu Kim, Seunghun Hyun * Division of Environmental Science and Ecological Engineering, Korea University, Seoul 136-713, Republic of Korea Received 16 March 2007; received in revised form 11 September 2007; accepted 11 September 2007
Abstract The hydraulic properties of soil, such as soil moisture characteristic and pore size distribution, are very important for the interpretation of the physical characteristics of soil and the management of agricultural practices. The current standard methods employing pressure chamber, however, are often time-consuming and difficult to carry out. In this study, we proposed a simple approach to estimate the soil moisture retention and soil pore size, with sufficient accuracy, using steady-state infiltration data. First, the tension disc infiltration data was interpreted using Wooding’s analytical solution to obtain the K(h) function, from which Ks (saturated hydraulic conductivity) was optimized. The Ks value was then used as an initial input data for the Brooks–Corey model fit to obtain the water retention parameters aBC and b, and the soil water retention characteristics within a selected range of soil pores of 9–450 mm were predicted. The proposed approach was tested for three differently textured soils in laboratory test and one undisturbed field soils. The measurement was replicated for three to five times for each soil. The validity of this method was confirmed by showing good linear regression relationship with data sets obtained by standard pressure chamber method, yielding slopes being close to unity and r2 values being >0.86. This observation strongly suggests that the proposed method can be applied for the in situ measurement of water retention and pore size in field soils. The results of this work will enable us to easily determine the temporal changes of hydrodynamic nature of soil using tension disc infiltrometer technique. # 2007 Elsevier B.V. All rights reserved. Keywords: Water retention; Pore size distribution; Tension disc infiltrometer; Unsaturated hydraulic conductivity
1. Introduction Assessing the movement of soil water is a principal component in soil management practice for minimizing the potential of groundwater contamination from soilapplied chemicals. One of the key factors influencing the movement of soil water is the distribution of various sizes of soil pores. Given that there is a strong relationship between pore size and soil water behavior, obtaining the pore size distribution (PSD) of field soil is an important step in understanding the dynamic
* Corresponding author. Tel.: +82 2 3290 3068; fax: +82 2 953 0737. E-mail address: [email protected] (S. Hyun). 0167-1987/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.still.2007.09.003
processes of the movement of water and solutes in soil (Ankeny et al., 1991; Hillel, 1998). The soil structure and PSD are dynamically changed by various environmental factors, such as tillage practice, wetting– drying processes and biological activity (Azooz et al., 1996; Leij et al., 2002) and thus the timely quantification of the temporal dynamic of the PSD may have important applications. However, since soil porous systems are complicated and are three-dimensionally structured with a variety of sizes, shapes and connectivities, soil pores are very difficult to observe and characterize. In addition, the required experimental equipments (e.g., pressure chamber method) and methodologies conventionally used for analyzing soil structure are very expensive and time-consuming.
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From this perspective, the literature is replete with attempts to develop methods describing the geometry and associated properties of the pore space naturally occurring in soils (Campbell, 1974; Kosugi, 1999; Leij et al., 2002). There are two major experimental approaches currently available for the determination of soil pore sizes and their distribution; the forced fluid intrusion and water desorption methods. The soil pore fluid intrusion method has been generally obtained by observing the relationship between the pore size and pressure required to intrude fluids into pores. The soil pore size can be most rapidly determined over a wide range (105 to 10 nm) with the application of mercury in the intrusion fluid method. The soil pore size obtained by this method has some uncertainty as a result of the possibility of aggregate collapse during the measurement due to the high surface tension of mercury (Dullien and Batra, 1970). The principle and assumptions for measuring the soil pore size using the water desorption method is similar to those for the fluid intrusion method. Based on the theoretical assumption of a cylindrical pore shape and the contact angle of the water with the soil, the volume of water desorbed from different soil pore sizes at the corresponding equilibrium matrix potential can be measured. In this method, however, substantial amount of time with elaborate instruments are required to establish equilibrium between the water content and the associated exerted pressure. Therefore, developing an easier and timesaving technique to describing the properties of soil pore distribution is required, with acceptable accuracy. A tension disc infiltrometer is a useful instrument that offers a rapid method for estimating the hydraulic properties and structural characteristics of soil with minimum disturbance of the soil structure (Perroux and White, 1988; Ankeny et al., 1991; Reynolds and Elrick, 1991; Haw and Rao, 2004; Ramos et al., 2006). The technique has become increasingly popular for the in situ measurement of near saturated hydraulic properties (pressure head, h < 35 cm). A sequence of steadystate flow rates through the soil is measured by setting a sequence pressure heads (h) imposed on the soil surface. The most widely used method estimating the parameters based on the use of a tension disc infiltrometer is to apply an approximate unconfined steady-state solution infiltration from a surface circular source (Wooding, 1968). Alternative methods include the determination of the sorptivity and macroscopic capillary length and numerical inversion (White et al., 1992; Vogeler et al., 1996). While Wooding’s method requires the tension infiltrometer to reach a steady-state rate, the other methods need the accurate measurement
of the transition infiltration rate for a pre-selected tension. In Wooding’s solution, the unknown hydraulic parameters can be solved by measuring either the steady-state infiltration rate at a fixed disc radius with multiple supply tension (Ankeny et al., 1991) or at a fixed tension with variable disc radii (Smettem and Clothier, 1989). Many studies have documented the efficacy of the infiltrometer technique for characterizing the water flow through various field soil profiles (Logsdon et al., 1993; Timlin et al., 1994; Ramos et al., 2006), but no attempt has been made to relate tension disc infiltrometer data with the soil water retention or the pore size distribution. This research was conducted to propose a simple theoretical approach to estimating soil moisture characteristic curve (SMCC) and pore size distribution (PSD), using the hydraulic conductivity function obtained from the tension disc infiltrometer data. Laboratory tests were performed to describe soil moisture retention within a selected range of soil pores from three differently textured soils (sandy, sandy loam, and sandy clay loam soils). The method was further tested for an undisturbed agricultural sandy loam soil in the field. In order to prove the validity of the results from both laboratory and field tests, the SMCC and PSD of each soil estimated by the proposed method were compared with data set independently measured by the conventional standard pressure chamber method. Also discussed is the limitation of the proposed approach. 1.1. Theory Using a multiple regression analysis of soil water retention data, Campbell (1974) developed an equation to describe water retention, as follows: h ¼ he
u us
b (1)
where u is the volume wetness (L3 L3), us the saturated volume wetness (L3 L3), h the matrix potential (L), he the air-entry potential (L) of soil and b the waterretention parameter, which is also related to the pore size distribution (Brooks and Corey, 1964). Similar to the prediction of unsaturated soil hydraulic conductivity (K) proposed by Brooks and Corey (1964), the following hydraulic conductivity function was proposed by Campbell (1974) under the condition of h < he: K ¼ Ks
uðhÞ us
2bþ3 (2)
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where Ks is the saturated hydraulic conductivity (L T1). By assuming the effect of the residual volumetric water content to be negligible (i.e., u (h) ur or ur ffi 0), the effective saturation (Se(h), L3 L3) would be equal to u(h)/us and thus can be expressed in terms of the matrix potential as follows: Se ðhÞ ¼
uðhÞ ur uðhÞ ffi us us u r
(3)
By rearranging Eq. (1), the effective saturation (Se(h) ffi u(h)/us) will be given as: Se ðhÞ ¼
uðhÞ ¼ jaBC hj1=b us
(4)
where aBC is the reverse of an air entry potential (he1, L1). Through substitution of Eq. (4) into Eq. (2), the relationship between K and h can be obtained as follows: KðhÞ ¼ K s jaBC hj23=b
(5)
2. Materials and methods 2.1. Soils The three differently textured soils used in the laboratory study were collected from Korea University Agricultural Farm located in Kyonggi, Korea; K1, K2 and K3 for sand, sandy loam and sandy clayey loam soils, respectively, according to USDA textural classification system (Gee and Or, 2002). Each soil was poured into three pots (15 cm of height and 30 cm of diameter) and stabilized by irrigation for 1 month, prior to use in the laboratory study. In situ field tests were conducted for an undisturbed agricultural surface soil of Bonryang series, which is also located in Kyonggi,
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Korea. Selected soil properties related to hydraulic properties were measured and are summarized in Table 1. Particle size analysis was preformed using a pipette method (Gee and Or, 2002). Bulk density and particle density were determined by core method (Grossman and Reinsch, 2002) and liquid displacement method (Flint and Flint, 2002a), respectively. Porosity was determined by gravimetric method with water saturation (Flint and Flint, 2002b). Also reported in Table 1 is information with regard to soil classification according to the USDA taxonomy system. 2.2. Tension disc infiltrometer experiment 2.2.1. Measurement of steady-state infiltration rate The tension disc infiltrometer used in this study was purchased from Soil Measurement Systems (Tucson, AZ). The supplied pressure head was controlled by a bubble tower (i.e., Mariotte bottle). Six successive pressure heads: 0, 1.0, 3.0, 5.0, 7.0 9.0, and 15 cm were applied and the steady-state infiltration rates were measured. Due to the geometry of the instrument, the pressure range that can be used is restricted to about 20 cm (smaller than the reported air-entry value of disc membrane). A sequential stepwise decrease of the supply pressure head was adopted to reduce the measurement errors potentially caused by hysteresis (Reynolds and Elrick, 1991). A 1.5 cm long thin-walled PVC ring (radius = 4.5 cm) with a sharp cutting edge at the base was inserted straightly on the soil surface. The progressive drainage from the infiltration front occurs from the layer closest to the disc. The drainage from a disc can be influenced by the contact between the disc membrane and soil surface, since direct contact with the soil surface may cause an imperfect and irregular measurement due to the roughness of the soil surface. To smooth out possible
Table 1 Selected physical characteristics of the soils used in these experiments Soils
K1 K2 K3 Bonryang a
Soil ordera
Alfisols Inceptisols Inceptisols Entisols
Subgroupsa
Ochreptic Fragiudalfs Fluvaquentic Endoaquepts Fluvaquentic Endoaquepts Typic Udifluvents
Particle contentb Sand
Silt
Clay
88 71 53 60
5 12 20 30
7 17 27 10
Textural classb
Bd c
Pd d
he
S SL SCL SL
1.41 1.32 1.23 1.37
2.65 2.65 2.65 2.65
0.470 0.502 0.545 0.486
Soil classification according to USDA taxonomy system. Particle size was analyzed by pipette method (Gee and Or, 2002) and defined according to the USDA textural class system. Size-fraction percentages are presented (%, w/w). c Soil bulk density (g cm3) measured by core method (Grossman and Reinsch, 2002). d Soil particle density (g cm3) measured by liquid displacement method (Flint and Flint, 2002a,b). e Soil porosity (cm3 cm3) measured by gravimetric method with water saturation (Flint and Flint, 2002a,b). b
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irregularities at the soil surface and to ensure hydraulic contact between the disc and the underlying soil, 1 cmthickness of coarse sand having mesh size of 20, tamped lightly inside PVC ring, was layered between the disc and soil surface. Three to five replicate infiltration runs were performed for each of the four soils. 2.2.2. Calculation of unsaturated hydraulic conductivity Wooding’s analytical solution was used to interpret the steady-state infiltration data: QðhÞ ¼ KðhÞprd2 þ 4FðhÞr d
(6)
where Q(h) is the steady state infiltration rate (L3 T1), F(h) the matrix flux potential (L2 T1) and rd is the disc radius (L). The first and the second terms on the right side represent the effect of gravitational forces and the effect of capillary forces, respectively. Assuming an exponential relationship between K and h, Eq. (6) can be rewritten by: QðhÞ ¼ KðhÞprd2 þ KðhÞ
4r d aG
(8)
For the estimation of the two unknowns (aG and Ks), Q(h) was measured at a fixed disc radius with multiple supply tensions (Ankeny et al., 1991; Reynolds and Elrick, 1991). To this end, the reverse of capillary length in Gardner’s exponential model (aG) was assumed to be constant in interval between two adjacent supply pressure heads and was determined from the piecewise slope as follows (aGiþð1=2Þ ): lnðQi =Qiþ1 Þ hi hiþ1
i ¼ 1; 2; . . . ; n
(10)
where n is the number of supply pressure heads used, and the subscript i + (1/2) indicates the middle value of two adjacent supply pressure heads; that is, hi + (1/ 2) = (hi + hi + 1)/2. In a same sense, the unsaturated hydraulic conductivity (Ki + (1/2)) at the middle value of two adjacent supply pressure heads (hi + (1/2)) can
ðprd2
Qiþð1=2Þ þ ð4r d =aGiþð1=2Þ ÞÞ
(11)
where
Qiþð1=2Þ
lnðQi Þ þ lnðQiþ1 Þ ¼ exp 2
(12)
The saturated hydraulic conductivity Ks, was estimated by fitting the measured K(h) data to Gardner’s model (Eq. (8)). 2.3. Estimation of SMCC and PSD from K(h) function 2.3.1. Optimization of water retention parameters The model parameters, aBC and b, in Eq. (5) were optimized by adjusting those values until global minimum was found for the following objective function, SSR ¼
By substituting Eq. (8) into Eq. (7) the relationship between Q(h) and the supply tension will be given by: 4r d 2 QðhÞ ¼ K s prd þ (9) expðaG hÞ aG
aGiþð1=2Þ ¼
K iþð1=2Þ ¼
(7)
In this approach, the parameter aG has been defined by Gardner (1958): KðhÞ ¼ K s expðaG hÞ
also be obtained by:
n X
2
½Kðh j Þ K 0 ðh j Þ
(13)
j¼1
where SSR is the sum of squared residuals between the experimental (K(hj)) and model (K0 (hj)) prediction; here, h is actually hi + (1/2) as shown in Eq. (11) In this optimization process, the Ks value estimated from K(h) function was used as a matching point. 2.3.2. Estimation of SMCC and PSD The soil moisture characteristic curve is a plot of u versus h. The effective water saturation (Se(h)) is equivalent to the fraction of total pore space filled with water (u(h)/us), which can be obtained by inputting the values of aBC and b into Eq. (4). Therefore, the soil moisture characteristic curve (SMCC, u(h)) can be obtained by multiplying the effective water saturation by the saturated volume wetness (=us Se(h)): uðhÞ ¼ us jaBC hj1=b
(14)
In addition, the effective water saturation (Se(h)) corresponds to the fraction of the accumulative volume of a water-filled soil pore at a given matric pressure (h). Assuming the pores have a capillary tube shape and the contact angle of water to the pore to be zero, the largest water-filled soil pore, with a radius, r, at a given h, can be expressed by applying the following well known
Y. Yoon et al. / Soil & Tillage Research 97 (2007) 107–116
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Fig. 1. (A–D) The unsaturated hydraulic conductivity (K(h)) of all soils used in this study, as determined using a tension disc infiltrometer data and Wooding’s analytical solution. Data points are the average of replicates and the standard error between measurements is shown by the error bar. The solid line is the Gardner’s exponential model fit with the coefficient of determinant (r2) being >0.90.
capillarity equation: rðhÞ ¼
2g rw gh
(15)
where g is the surface tension (kg s2) of water, rw the density of water (kg m3) and g is the gravitational acceleration (9.81 m s2). Therefore, the cumulative fraction of the pore space filled with water at a given h, can be plotted with respect to the soil pore size by equating capillarity equation (r(h)) and the degree of water saturation (u(h)). 2.4. Determination of SMCC using conventional pressure chamber method To verify the validity of the results obtained using the proposed method, the SMCC and PSD of the tested soils were independently measured by the conventional water-desorption technique, where the volume of water drained from an initially saturated soil at consecutive pressures is used to calculate the pore size. Following measurement of the steady-state infiltration rate, soil cores were taken from the soil beneath the disc, three cores from each in the case of laboratory tests and five cores for the field tests. These soil cores (50 mm in height and 72 mm in diameter) were laid on a ceramic plate, with a bubbling pressure of 10 m water
(ffi1.0 bar). The pressure chamber was modified to obtain the exact reading of the supply pressure head by adapting a 230 cm-water column. The prepared soil cores were water-saturated from the base, and allowed to reach equilibrium for 2 days. A supply pressure head (h) between 6 and 200 cm was regulated by the height of the water level and higher pressures (up to 333 cm) were attained using a pressure regulator. For each pressure increment, the volume wetness (u) of the soil sample was calculated by multiplying the gravimetric water content by the soil bulk density. The fraction of the total pores occupied by water at a given pressure, therefore, was determined by dividing the volume wetness by the porosity. The size of the water-filled soil pore was also calculated using the capillarity equation as describe earlier. 3. Results 3.1. K(h) function from tension disc infiltration The K(h) values determined in four soils using the tension disc infiltrometer at the matric potential of 0.5, 2.0, 4.0, 6.0, 8.0, and 12 cm are presented in Fig. 1. Also shown in Fig. 1 are the Gardner’s exponential model fits (r2 > 0.90) as a solid line for each soil. The fitted Ks values estimated for K1 (sandy), K2 (sandy loam), and K3 (sandy clay loam) soils were
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24.63 3.25, 2.81 0.27, 0.904 0.105 cm h1, respectively, and varied only within 15% of the independently measured value for respective soil using the constant-head method. The Ks value tends to increase greatly with coarse texture because of an increase in the number and size of water-conductive pores; the magnitude of hydraulic conductivity is proportional to the second power of effective particle size (Hubbert, 1940). The magnitude of Ks estimated for three laboratory soils increases exponentially with increasing sand content of soils (r2 = 0.962; regression not shown here). Under the given operation range of pressure potential, the K(h) curve of each soil varied within the two orders of magnitude with the values gradually decreasing as the pressure head became more negative, but no inflection point was attained. The measurement of K(h) under near saturated conditions showed greater fluctuation among replicates compared to less saturated condition (i.e., greater error bars at the lower suction range), especially for sandy soil (Fig. 1A). The amount of water retained with lower matrix suction is strongly affected by soil structure such as capillarity and pore size distribution, both of which will in turn influence the magnitude of Ks. The relatively greater variability of the K(h) measured near saturated conditions indicates the presence of an irregular distribution of macro-pores possibly with entrapped air (Mohanty et al., 1996). The result of undisturbed agricultural Bonryang soil in the field test is shown in Fig. 1D. The Ks value of the Bonryang soil was 0.4962 0.0253 cm h1, one order of magnitude higher than the previously reported value of 0.054 cm h1 by Um et al. (1995), who measured K(u) function using internal drain method employing a scaled water content. This difference is most likely due to the difference in the measurement methods employed and the possible seasonal dynamic change in the soil structure. Agricultural soils frequently exhibit extensive spatial and temporal changes in pore characteristics, causing experimental variation in determining K(h) function (Perroux and White, 1988). In order for better agricultural soil management, it has been well recognized that spatial and temporal replication of soil parameter measurement is required to obtain reliable hydrologic characterization of field soils. 3.2. Soil moisture characteristic curve (SMCC) and pore size distribution (PSD) The soil moisture characteristic curves (SMCC, u (h)) of the three soils with different textures, measured by the conventional pressure chamber method for the
Fig. 2. (A) The soil moisture characteristics curve of K1, K2 and K3 soils for the range of matric potential (h) < he, and (B) the cumulative pore volume ratio of the three soils obtained from the laboratory tests.
matrix potential (h) range from 6 to 333 cm, are shown in Fig. 2A, along with the predicted lines by Eq. (14). Also included in Fig. 2B are the measured cumulative pore size distributions (PSD) and corresponding predicted lines for each soil. The values of the parameters of each soil, including aBC, b, and us, used in the proposed method are listed in Table 2. Note that predicted lines for Fig. 2A were obtained by plugging the parameters aBC and b into Eq. (14); u(h) = us øaBC hø1/b, where u(h) increases asymptotically when soil water potential (h) approaches zero. Due to the geometric restraint of this model, the predictive volumetric water content may be flawed as the soil matrix potential exceed over the limit of air-entry point (he). The dimensionless parameter ‘b’ is the inverse of pore size distribution index, l, as denoted by Brooks and Corey (1964). Theoretically, l approaches infinity for a porous medium with a uniform pore size distribution, whereas it is close to zero for a porous medium with a wide range of pore sizes. That is, the value of parameter b will be smaller for a soil with a relatively uniform pore size distribution. Among soils used in this study, K1 soil can be assumed to have a
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Table 2 The value of soil parameters related to soil moisture retention characteristics Soils
Textural class a
Ks b
K1 K2 K3 Bonryang
S SL SCL SL
24.63 2.81 0.90 0.50
a b c d e f
aG c (3.25)f (0.27) (0.10) (0.02)
0.22 0.11 0.40 0.10
be
aBC d (0.05) (0.02) (0.08) (0.01)
0.30 0.14 0.46 0.12
(0.04) (0.00) (0.01) (0.00)
2.60 4.54 9.60 3.11
(0.11) (0.19) (0.74) (0.10)
Soil textural classification using the USDA scheme (Gee and Or, 2002), S: sandy soil, SL: sandy loam, SCL: sandy clay loam. Saturated hydraulic conductivity (cm h1) obtained by fitting K(h) data to Gardner’s model. Gardner’s model parameter. Brooks–Corey parameter; the reverse of the air entry pressure (he1, cm1). Water retention parameter, which is related to the pore size distribution. Standard error.
uniform distribution of larger pores, based on its smaller b and larger Ks values. The b values of the four soils was found to be linearly correlated with the clay content (%) (r2 = 0.947; a = 0.001, the regression not shown here), suggesting that the presence of more clay induces a broader range of soil pore size. For field study with an undisturbed Bonryang soil, the measured SMCC and calculated PSD (shown as circles) using the conventional technique are shown in
Fig. 3. (a) The soil moisture characteristics curve of Bonryang soil for the range of matric potential (h) < he, and (b) the cumulative soil pore volume ratio. Measured data are shown as closed circles. Predicted lines are shown as solid lines.
Fig. 3, along with the predicted lines (shown as solid line). The proposed method described well the soil water retention for the pressure head (h) range > 20 cm; however, in the higher matrix potentials range of h < 20 cm, the volume wetness of the soil was overestimated (Fig. 3a). Likewise, the subsequent predicted line for the cumulative soil water retained in the corresponding range of pore diameters (i.e., >200 mm) was also overestimated (Fig. 3b). As pointed out earlier, the deviations of the model prediction are most likely due to the nature of Eq. (14), which describes the asymptotical increase in the volume wetness with decreasing matric potential between water molecule and soil matrix. In reality, however, the soil volume wetness (u(h)) should be smaller than soil porosity, no matter how small the matrix potential is acting between the soil pores and water molecules. When all the pores are fully filled with water, the soil water content should reach the value of saturated volume wetness (us), shown as a closed square in Fig. 3a. In addition, it has also been reported that, as the soil wetness (u) approaches saturation, the impact of the structural pores on the water retention and hydraulic conductivity cannot be adequately accounted for by models that assume homogeneous porous media (Ross and Smettem, 1993; Poulsen et al., 2004), which is a case of undisturbed field soil condition. For example, the water retention at lower matrix suction (e.g., close to air-entry pressure) mainly depends on the soil structure, including factors such as the capillarity and pore size. On the other hands, at higher suction, water retention is increasingly due to adsorption, so it is less influenced by the structure, but more by the soil texture and surface area. 3.3. Validation Fig. 4 presents the correlation of the data set of cumulative pore size distributions obtained from both
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the accumulate pore volume ratio as approaching to the point of 0.9 (Fig. 4b), is due to overestimation of water retention at lower pressure head.
4. Discussion
Fig. 4. Correlation between the measured and predicted of pore size distributions of (A) the three soils used obtained from laboratory tests and (B) Bonryang soils from a field test. The solid line is a linear regression fit. The dashed line is a 1:1 line. For graph (A), the regression line was constructed using all the results obtained for the three soils with different textures.
the pressure chamber (denoted as measured) and the proposed method (denoted as predicted) for laboratory and field tests. The validation of the proposed method was accomplished by providing a result of linear regression analysis of two data sets, as shown by the solid line. As a reference, 1:1 matching lines are also shown as dotted lines. The regression line for the laboratory test was constructed using all three soils together. The slopes of both regressed lines are close to unity and have a small intercept; the coefficients of determination (r2) were 0.941 and 0.866 for the laboratory and field tests, respectively, at a significant level of a = 0.01. The r2 value represents the closeness of the predicted data to the regressed line. Therefore, >94% of the laboratory data for the three soils with different textures, and >86% of the undisturbed field soil data, were successfully predicted using the proposed method. The high correlation between the two data sets strongly supports the validity of the proposed approach. The relatively poor prediction of
In this study the Ks value was estimated from K(h) function and was further used as an initial input data for optimizing water retention parameters. Although there are arguments that Ks may not be a suitable matching point for soils rich in macropores due to susceptibility of the magnitude of Ks to macropore flow (Schaap and Leij, 2000), it has been frequently used for estimating soil parameters as it is relatively easily measurable (van Genuchten and Nielsen, 1985; Luckner et al., 1989). The major concern arises from the likelihood that Ks would be a significant scaling factor controlling the overall accuracy of the optimization procedures. The hydraulic conductivity is generally predicted by many mathematical functions in which (1) the analytical solution of water flow through soil pore system is derived and (2) easily obtainable soil data such as parameters estimated from water retention data or Ks are incorporated (Mualem, 1976; van Genuchten, 1980; Poulsen et al., 2004). However, the uncertainty of the K(h) function inferred from the water retention data is subject to error with respect to the parameters acquired by optimization processes (Kool et al., 1985). In our laboratory study where the reverse estimation processes (that is, estimating water retention parameter from K(h) function) were explored for three differently textured soils, good estimations were found, even though there were clearly a certain range of error in the determination of K(h), which are shown by the error bars in Fig. 1. Frequent use of the PSD model for the prediction of K(h) from water retention parameters has implicated a relationship between the hydraulic conductivity and soil properties determining the nature of soil’s water retention (Mualem, 1976; Kosugi, 1999; Schaap and Leij, 2000; Poulsen et al., 2004). Theoretically, the hydraulic conductivity is derived by integration of the elementary pore domains represented by a specific pore radius since hydraulic conductivity of soil at given water content is composed of flow in pores that are filled with water at that water content. In this sense, it can be also reasonably presumed that the concept of reversely using the hydraulic conductivity data to predict soil water retention parameters is acceptable, as long as the water retention parameters keep their original physical meaning and water retention hysteresis is minimal.
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The theoretical approach of this work was essentially based on the assumption of homogeneous soil hydraulic properties within the zone of influence of the infiltrometer measurements under the tension. However, since the soil porous system is fragile and very sensitive to overburden pressure that may alter the geometry of the soil pores and capillary tube depending on the distance to which the wetting front advances during the time taken to establish steady-flow conditions, the extension of this basic assumption toward soils with heterogeneous structural features (e.g., waterrepellency, fissures, cracks, bio-channels and other preferential flow features) and strong aggregation should be questionable. In addition, the disc infiltrometer can be mostly used to measure water flow rates at the soil surface; thus the application of this method to extended depth of soils is also limited. In summary, so far, it has been an important part of soil physics for decades to predict hydraulic conductivity by fitting the water retention model to measured data, which yields values of parameters for K(h) function (van Genuchten, 1980; Ross and Smettem, 1993; Schaap and Leij, 2000; Poulsen et al., 2004). In this study, we provided theoretical approach to estimating the water retention from K(h) function and tested the proposed method for both laboratory and field studies. The hydraulic measurement using each instrument has its own reliable range of matric potential. Due to the geometry of tension infiltrometer, the K(h) function could be obtained in the matric potential (h) range only from 0.5 to 12 cm under which range water retention parameters were also estimated. While the range of matric potential (h) which can be supplied for pressure chamber method was between 6 and 333 cm; lower matric potential was unable to be achieved because of the instrumental restriction. However, even though there is a limited overlapped matric potential, the soil water retention characteristic (u(h)) for an extend range of matric potential was well predicted using parameters obtained from limited range of K(h) function. The observation suggests that the proposed approach provides a relatively simple and reliable alternative method for determining soil water retention in a selected range (9–450 mm) of pore size in homogeneous one-layered surface soils, only requiring tension disc infiltrometer data at multiple tensions and stepwise mathematical manipulation. The result of this work strongly suggests the application of tension disc infiltrometer technique for the in situ measurement of temporal change of soil hydraulic properties of soils, such as water retention and pore size.
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