Soil Science Society of America Journal 63:788-792 (1999)
© 1999 Soil Science Society of America
DIVISION S-1-SOIL PHYSICS
Measuring Saturated Hydraulic Conductivity using a Generalized Solution for Single-Ring Infiltrometers
L. Wua,
L. Panb,
J. Mitchellc and
B. Sandend
a Dep. of Environmental Sciences, Univ. of California, Riverside, CA 92521 USA
b Earth Sci. Div., Lawrence Berkeley National Lab., Univ. of California, Berkeley, CA 95720 USA
c Kearney Agri. Center, Univ. of California, Parlier, CA 93648 USA
d Univ. of California Coop. Ext., Kern County, Bakersfield, CA 93307 USA
laowu{at}mail.ucr.edu
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ABSTRACT
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Saturated hydraulic conductivity is a measure of the ability of a soil to transmit water and is one of the most important soil parameters. New single-ring infiltrometer methods that use a generalized solution to measure the field saturated hydraulic conductivity (Ks) were developed and tested in this study. The Ks values can be calculated either from the whole cumulative infiltration curve (Method 1) or from the steady-state part of the cumulative infiltration curve by using a correction factor (Method 2). Numerical evaluation showed that the Ks values calculated from the simulated infiltration curves of representative soil textural types were in the range of 87 to 130% of the real Ks values. Field infiltration tests were conducted on an Arlington fine sandy loam (coarse-loamy, mixed, thermic, Haplic Durixeralfs). The geometric means of the Ks values calculated from the field-measured infiltration curves by Method 1 and Method 2 were not significantly different. The geometric mean of the Ks calculated from the detached core samples, however, was about twice that of the Ks calculated from the infiltration curves, which was consistent with earlier findings. Unlike the earlier approaches, Method 1 calculates Ks values from the whole infiltration curve without assuming a fixed relationship
between saturated hydraulic conductivity and matric flux potential 
m.
Abbreviations: SH, single head
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INTRODUCTION
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SATURATED HYDRAULIC CONDUCTIVITY is an important soil parameter that measures the ability of a soil to transmit water. Measurement of field saturated hydraulic conductivity (Ks) is often done by borehole permeameters (Amoozegar and Warrick, 1986; Elrick and Reynolds, 1992). In many cases, however, measurement of the soil surface Ks is essential, especially in infiltration-related applications, such as irrigation management.
Ring infiltrometers are often used for measuring the water intake rate at the soil surface. Water flow from a single-ring infiltrometer into soil is a three-dimensional (3-D) problem (Reynolds and Elrick, 1990). The total flow rate into the soil from a single-ring infiltrometer is a combination of both vertical and horizontal flow (Tricker, 1978). A method to calculate the Ks from data obtained from a pressure or ring infiltrometer for both early-time and steady-state infiltration was developed by Reynolds and Elrick (1990), Elrick and Reynolds (1992), and Elrick et al. (1995). Their steady-state method uses a shape factor that was numerically calculated based on Gardner's (1958) relationship between hydraulic conductivity and matric pressure head. Groenevelt et al. (1996) further extended this concept by developing a method to define the critical time that separates early-time and steady-state infiltration.
By applying scaling theory, Wu and Pan (1997) developed a generalized solution for single-ring infiltrometers. Wu et al. (1997) showed further that the infiltration rate of a single-ring infiltrometer was approximately f times greater than the one-dimensional (1-D) infiltration rate for the same soil, where f is a correction factor that depends on soil initial and boundary conditions and ring geometry. For a relatively small ponded head, the 1-D final infiltration rate of a field soil is approximately equal to the field saturated hydraulic conductivity (Ks), which is valuable information for computer modeling, as well as for irrigation management. The objectives of this research were (i) to develop alternative methods to calculate Ks by best fit of a generalized solution to the infiltration curves that are measured by single-ring infiltrometers, and (ii) to compare and evaluate Ks values calculated from infiltration curves of single-ring infiltrometers with those measured by the single head (SH) method (Elrick and Reynolds, 1992) and detached soil core samples (Klute and Dirksen, 1986).
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Theory
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A generalized infiltration equation developed by Wu and Pan (1997) has essentially the same form as the truncated Philip (1957) model of vertical infiltration. We propose here to measure infiltration curves in the field and then utilize the generalized equation to fit to the data in order to obtain the relevant parameters for estimating Ks. The generalized equation (Wu and Pan, 1997) is
 | (1) |
where
 | (2) |
 | (3) |
 | (4) |
 | (5) |
 | (6) |
where 
= 0 - i. The approximation in Eq. [6] follows from the definition
 | (7) |
and the fact that Ki << Ks under most field soil moisture conditions (Elrick and Reynolds, 1992). In Eq. [1] through [7], a and b are dimensionless constants
from the generalized equation, H is the ponded depth in the ring, d is the ring insertion depth, r is the radius of the ring infiltrometer, Ks and Ki are the hydraulic conductivity at saturated water content (0) and at initial water content (i), h and hi are matric and initial matric pressure heads, and K'(h) is the modified van Genuchten hydraulic conductivity–pressure head function (Wu and Pan, 1997).
There are two ways to calculate Ks by applying the generalized infiltration equation to the measured infiltration curves from a single-ring infiltrometer. Method 1 is based on the cumulative infiltration equation. By integrating Eq. [1] from
, we have
 | (8) |
or
 | (9) |
Substituting Eq. [3] and [6] into [9], we can solve for Ks:
 | (10) |
where
 | (11) |
 | (12) |
 | (13) |
It is relatively easy to measure the initial soil water content, i, at the time of an infiltration test, and 0 can be measured or estimated from the bulk density and particle density.
Method 2 is based on the assumption that the last part of the infiltration event has reached steady state. With this assumption, we can fit the linear equation
 | (14) |
to infiltration data, and Ks can be calculated from
 | (15) |
where A is the slope and c is the intercept from the linear regression, and f, which is defined by Eq. [3], can be estimated by
 | (16) |
since
, as shown later in this paper (Table 2)
; m is the matric flux potential when Gardner's (1958) hydraulic conductivity function is used. Method 2 is similar to the SH method of Elrick and Reynolds (1992), since a in Eq. [15] is very close to 1.
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Table 2 Comparison between  and Ks/m of the test soil and the soils used for developing the generalized infiltration equation
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Materials and methods
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To test the reliability of the Ks measured and calculated from the various methods, numerical tests were conducted to simulate infiltration curves for three representative sandy, loamy, and clayey soils (Table 1)
. The axisymmetric form of the Richards equation was solved numerically using the finite volume (control volume) method (Pan and Wierenga, 1997). The model used a nonlinear, transformed pressure as the dependent variable with a modified Picard method. The hydraulic functions in the Richards equation were van Genuchten's (1980) (h) and K(h) relationships with
. The numerical simulation domain was 100-cm radial by 100-cm depth and was assumed to be homogeneous and isotropic. The initial soil water pressure head (hi) was assumed to be -1000 cm. Due to the differences in Ks and other hydraulic parameters, the time required to reach final infiltration rates for the three different textural soils are different. The simulated infiltration duration here was 1 h, 1 d, and 10 d, respectively, for the representative sand (Berino fine sand: fine-loamy, mixed, thermic Typic Haplargids), sandy clay loam, and clay soil (Yolo clay: fine-silty, mixed, nonacid, thermic Typic Xerorthents). Parameters of the van Genuchten (h) and K(h) relationships for the three representative soils used the values of Wu and Pan (1997). The simulated infiltration curves were used to test Methods 1 and 2, and for comparison with the SH method of Reynolds and Elrick (1990). For Method 1, Eq. [9] was fit to the entire cumulative infiltration curve of each soil to obtain A and B (Fig. 1)
. For Method 2, the last 20 min. of infiltration data from each soil were used to determine parameter A in Eq. [14] (Fig. 2)
. For the SH method, the simulated final infiltration rates of the soils were used to calculate Ks. The values for the sand, loam, and clay soils were assumed to be 0.36, 0.12, and 0.04 cm-1, respectively, for the SH method (Elrick and Reynolds, 1992).
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Table 1 Comparison among the Ks values (cm min.-1) calculated by Method 1 (M1), Method 2 (M2), and the SH method (SH) from the numerically simulated infiltration curves and the real Ks for the three test soils
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Fig. 1 An example of cumulative infiltration curve. The dots are measured data and the line is curve fitted to the generalized equation (Method 1)
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Fig. 2 An example of the cumulative infiltration curve. The linear part of the curve was used to calculate Ks (Method 2)
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The field experiment was conducted at the University of California, Riverside Agricultural Field Experimental Station, Moreno Valley, CA. The soil is classified as an Arlington fine sandy loam and the cover crop was alfalfa. Field infiltration was measured by a single-ring infiltrometer consisting of two components: an infiltration ring (20-cm diam.) and a water supply column that maintains a constant ponded head (H = 5 cm) in the ring. The ring insertion depth was d = 5 cm. Eight undisturbed soil cores (5 cm x 5 cm) were collected on the transect to determine Ks by using the falling head method in the laboratory (Klute and Dirksen, 1986). Water retention characteristics were determined using pressure chambers (Klute, 1986) in the laboratory. Samples were also collected for determining bulk density and soil water content at the time of the infiltration measurements.
The single-ring infiltrometer was equipped with pressure transducers (PG15C03D, MicroSwitch, Freeport, IL)1
, and the transducers were connected to a data logger that recorded the readings in 5-s intervals. Cumulative infiltration was calculated from the pressure transducer readings and the transducer calibration curve. To obtain coefficients A and B, Eq. [9] was fit to the cumulative infiltration curves (Method 1) using SigmaPlot 4.0 (Jandel Scientific, 1997) (Fig. 1). The Ks values were then calculated by Eq. [10]. In the field, it is difficult to establish a constant ponded head at the beginning of an infiltration experiment. With our experimental setup in this soil, it took 
5 min. to establish a constant head. Thus, data from the first 5 min. in our infiltration test were removed before the fitting of Eq. [9] to the cumulative infiltration curves.
For Method 2, Eq. [14] was fit to the last 200 data points to obtain the slope A (Fig. 2). Values of Ks were then calculated from Eq. [15] by dividing A by a, the slope of the generalized Eq. [1], and substituting the value of f determined from Eq. [16]. The correction factor f was 2.33 using H = 5, d = 5, and r = 10 cm, and assuming = 0.12 cm-1 (Elrick and Reynolds, 1992) for the Arlington fine sandy loam soil.
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Results and discussion
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Comparison of the Ks Values from Simulated Infiltration Curves
Table 1 lists the field saturated hydraulic conductivity values for the three soils. For the Berino fine sand, the three methods all overestimated the real Ks, but the estimates were close to the real Ks. Values of Ks found by Method 2 and the SH are close to each other, presumably because the assumed values are close to the
value for the Berino fine sand (Table 2). For the sandy clay loam soil, Method 1 and the SH method estimated almost exactly the same Ks value. Method 2, however, slightly overestimated the real Ks, but only by a few percent. For Yolo clay, Methods 1 and 2 slightly overestimated the real Ks, while the SH method slightly underestimated the real Ks. Overall, Method 2 overestimated the real Ks by <21% for the three soil types, whereas neither Method 1 nor the SH method consistently over- or underestimated the real Ks with respect to soil texture. The differences between the real Ks and the Ks values calculated by the two new methods, however, are all in an acceptable range (87 to 130%). The fitted parameters A and B have very small standard errors (CV < 1%).
Comparison of the Ks Values from Field-Measured Infiltration Curves
Table 3
shows geometric means, maximum, and minimum Ks values calculated from the field-measured infiltration curves or measured from detached core samples. Probability distribution showed that the Ks values have a lognormal distribution. Thus, comparisons of means were conducted using the logarithm-transformed data. The geometric mean of the Ks measured from the core samples was approximately twice that of the field-measured Ks values. This observation is consistent with Bouwer (1966) and Wu et al. (1992), who observed that Ks values from the detached core samples were approximately twice that of the field-measured Ks values at a significance level of P = 0.13 (LSD, based on pooled standard deviation). If a significance level of P = 0.05 were chosen, the geometric means estimated from the four methods would not be significantly different (Table 3).
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Table 3 Geometric means (GM), maximum (Max), and minimum (min) Ks (cm min.-1) calculated from field-measured infiltration curves by Method 1 (M1), Method 2 (M2), single head method (SH), and those measured from core samples
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Our evaluation showed that when different numbers of observations were used, the Ks values calculated by Method 2 were slightly different (Table 4)
. The Ks value from one of the eight cumulative infiltration curves was used to evaluate the dependence of Ks on the observation numbers. The linear fitting for the three cases using the last 100, 150, and 200 observations all had a R2 of 0.999. The Ks values were 3.1 and 5.4% greater, respectively, when the last 150 and 200 observations (longer period from the end of measurement) were used than when the last 100 observations were used.
It is worthwhile to note that the Ks values calculated from Method 2 have a smaller range (see the maximum and minimum values in Table 3) than the Ks values calculated from Method 1. The reason is that like the SH method (Elrick and Reynolds, 1992; Bosch, 1997), Method 2 uses a fixed
value for the whole field. It is expected that variations of
or values exist in a field or in soils with similar texture. Thus, using a single value of
or to calculate Ks for a field or a soil textural class may reduce the actual variability of the Ks.
Sensitivity of Ks to
and
If the infiltration test is sufficiently long, Method 2 can be used to calculate Ks from single-ring infiltration data. In the Ks calculation by Method 2,
was approximated by . Most of the
values were close to the values suggested by Elrick and Reynolds (1992) for calculating Ks with their Guelph permeameter one-depth method (Table 2), indicating that their fixed approach can be used in measuring Ks with single-ring infiltrometers (Bosch, 1997). For the soil in this study, the calculated
is greater (0.24 cm-1) than the value suggested by Elrick and Reynolds (1992) for a sandy loam (0.12 cm-1). However, the difference between the Ks values calculated from the same cumulative infiltration curve was not substantial when these two numbers are used: the Ks using an of 0.12 cm-1 is 20% higher than that of the Ks using an of 0.24 cm-1. Based on the geometry of the ring used in this study, Fig. 3
shows that the computed Ks is slightly less sensitive to when a single-ring infiltrometer is used than when a borehole permeameter method is applied (Elrick and Reynolds, 1992).
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Summary and conclusions
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New methods that use a single-ring infiltrometer to calculate field saturated hydraulic conductivity (Ks) were presented and evaluated in this study. Numerical evaluation indicated that the Ksvalues calculated from single-ring infiltration data (Method 1) were comparable to the real Ks values and the single head (SH) method by Elrick and Reynolds (1992). The advantage of utilizing the generalized equation to calculate Ks is that one can use the whole infiltration curve without segregating early-time and steady-state infiltration components. As well, the method does not require the assumption of a
for a particular field or soil. Method 2 assumes steady-state infiltration and is similar to the SH method. The Ks values calculated by Method 2 from the late part of the numerically simulated infiltration curves were very close to Method 1 and were comparable to the real Ks. The Ks values estimated by Method 2 were slightly smaller when the last 100 data points were used than when the last 150 or 200 data points were used to calculate Ks, but the difference was rather small. Thus, if an infiltration test is reasonably long, the Ks values calculated by Method 2 and the SH method are close to the real Ks. It was further shown that values suggested by Elrick and Reynolds (1992) for soils of different textures and structures can be used in calculating Ks from cumulative infiltration curves.
Ring infiltrometers are most often used to measure the water intake rate at the soil surface (Bouwer, 1986); however, it is difficult to compare the results among different studies in which various sizes of rings are used. Like the SH method (Elrick and Reynolds, 1992), the new methods calculate Ks from ring infiltrometer data, and the correction factor f used for calculating Ks considers ring geometry, enabling comparisons among the measurements from different studies. In addition, single-ring infiltrometers are easy and inexpensive to build, and the infiltration measurement is easy to automate with pressure transducers. Surface disturbance of soil is minimal, which reduces measurement errors substantially. The ring size can be adjusted to match the size of a soil's representative elementary volume.
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NOTES
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1 List of a product does not constitute endorsement by the Univ. of California. 
Received for publication June 8, 1998.
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REFERENCES
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- Amoozegar, A., and A.W. Warrick. 1986. Hydraulic conductivity of saturated soils: Field methods. In A. Klute (ed.) Methods of soil analysis. Part 1. 2nd ed. Agronomy Monogr. 9. ASA and SSSA, Madison, WI.
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- Bouwer H. Rapid field measurement of air entry value and hydraulic conductivity of soil as significant parameters in flow system analysis. Water Resour. Res. 1966;2:729-738.
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- Elrick, D.E., and W.D. Reynolds. 1992. Infiltration from constant-head well permeameters and infiltrometers. p. 1–24. In C.G. Topp et al. (ed). Advances in measurement of soil physical properties: Bringing theory into practice. SSSA Spec. Publ. 30. SSSA, Madison, WI.
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TOP
ABSTRACT
INTRODUCTION
