DIVISION S-l—NOTES

TECHNICAL NOTE: RAPIDMEASUREMENT OF SOIL SORPTIVITY

ROGER E. SMITH*

AbstractA simple and fast method is described for measuring surface soil

sorptivity, 5. Rather than measure the progress of infiltration flux fora long initial period, the cumulative infiltration is measured in theearly stage in which the gravity effect is negligible. The theory behindthe method is sound and simple, and measurements may be taken inonly a few minutes using a small single ring. It is applicable to find5 for both ponded and flux surface boundary conditions.

CHARACTERIZING the spatial variation of soil hydrau-lic properties is important for applications in hy-

drology, soil physics, and site-specific agriculture. Statis-tical characterization of spatial variability requires avery large number of measurements, and most currentmethods for finding saturated conductivity, Ks, sorptiv-ity, 5, and the soil-water retention relation, 6(»|;), aretime-consuming. Sorptivity is usually estimated by tak-ing flux data from disc permeameters or ring infiltromet-ers at early times and fitting a straight line on a plot ofinfiltration vs. Vf, where t is time. (Clothier and White,1982). This is often quite difficult due to the rapid intakeof water at early times, or in the case of the disc permea-meter, the difficulty of observing a dropping water levelin a marriot tube when air bubbles are entering rapidly.I suggest a simple method to quickly find an accuratesorptivity value. While it is unlikely that I am the firstto think of this, I find nothing in the literature in whichsuch a simple measure is proposed or used.

TheoryPhysically based infiltration relations have two basic soil

parameters, plus the initial soil water deficit variable, A6 =9S— 6j, where 9S is effective field saturation and 6; is initial watercontent. One parameter is Ks. The other is either sorptivity,5 (Philip, 1957b), or capillary length scale, G. G and 5 areapproximately but very closely related (White and Sully, 1987)by:

S1 = 2G#SA6Capillary length scale G is defined as (Smith and Parlange,1978)

G = d + k,(h)dh

[1]ige,

[2]where d is the surface water depth; h is the pore water pressurehead, and k,(h) is the relative hydraulic conductivity curve

Roger E. Smith, ARS-USDA, AERC Foothills Campus, ColoradoState Univ., Fort Collins, CO, 80523-1325. Received 20 Nov. 1997.*Corresponding author (roger@lily.aerc.colostate.edu).

Published in Soil Sci. Soc. Am. J. 63:55-57 (1999).

[kr(h) is not a function of KJ. The capillary length scale maybe thought of as the &r-weighted value of capillary head (plussurface water depth). Note that 5 is a function of all theimportant infiltration variables, and a measurement of S isnot only useful for characterizing early stages of infiltration,but for characterizing spatial variations in soil hydraulic char-acteristics.

Ponded ConditionsAt early times of infiltration from a suddenly ponded sur-

face boundary condition, all analytic infiltration equations(Philip, 1957b; Green and Ampt, 1911; Smith and Parlange,1978) are the same and equal to the solution to the absorptionequation (Philip, 1957a). Infiltration flux f ( t ) reduces to

f=SI(2{f) [3]and cumulative infiltrated depth, /, is:

/ = Sit [4]The applicability of the above relations can be determinedusing the time scale, tffav, introduced by Philip (1969):

= S2/K2S [5]

Talsma (1969) suggested that Eq. [3] and [4] were accuratewithin 5% at early times when t < 0.02((grav). Values of thistime scale for the mean characteristics of various soil typespresented by Carsel and Parrish (1988) are given in Table 1.These values should be considered as order of magnitudeestimates only.

Sorptivity may be calculated numerically from the relationK(h) of any soil type. Using a method suggested by Philip(1955), the effect of initial water content, 6; , on S, in scaledterms, is computed and illustrated in Fig. 1 for two relativelydifferent soil types. Here sorptivity is scaled on its maximumvalue (when 61 is a minimum), and initial water content 9j isscaled between 6S and the residual water content, Or. Thisscaled relation may be used with field data on porosity andinitial soil water conditions to adjust measured values of S toa common basis.

Rainfall ConditionsWhen water is supplied at a fixed flux rate, r, a time-based

relation is not the most appropriate descriptor for infiltration(Smith, 1982). Equations [3] and [4] may be combined forearly times to yield a more appropriate relation for infiltrationand sorptivity:

C2

/= ——1 21 [6]

This relation holds at early times, and as soon as the soilsurface ponds and control is exercised by the limit of the soilto infiltrate. Use of this condition to identify sorptivity requiresa relatively high application rate, r, thus a high ratio f/Ks, sothat, as illustrated in Fig. 2, the scaled/(/) curve is interceptedat a point where //A6G is less than about 0.1.

Experimental MethodsEquation [4] suggests a simple measure of S for the early

time or soil ponding when it applies. Talsma (1969) used Eq.

55

56 SOIL SCI. SOC. AM. J., VOL. 63, JANUARY-FEBRUARY 1999

Table 1. Soil type estimates for mean capillary length scale, G,sorptivity, and scaling time, tsfm, based on soil class propertiesfrom Carsel and Parrish (1988).

Texture type class

SandLoamy sandSandy loamLoamSiltSilt loamSandy clay loamClay loamSilty clay loamSandy claySilty clayClay

Mean A,cmls X Vf-f

82540612227869.4

12536172.219.433.311.1

111

Mean Gcm8.29.7

16.538.591.472.424.080.4

15958.9

357223

Sorptivitycm/s"2

0.2280.1660.1180.0850.0690.0790.0690.0550.0380.0290.0270.074

'p..s x 10-6t0.000760.001670.009320.09450.9600.4010.03670.5813.880.7446.060.443

t Reported value equals actual value X 10'.$ Reported value equals actual value X 10"'.

[3] with a standard ring infiltrometer and measured fallingwater levels with a point gauge. Here I suggest an even simplermethod. A small ring is used, with any diameter that is conve-nient for insertion and appropriate for the area of sampling.An insertion depth may be achieved, for small volumes ofwater, such that one-dimensional flow is assured. A volumeof water, V, is applied quickly, and the time, t,, is measuredfrom the application of water to the instant at which half thesurface area, however uneven, is no longer covered by water.Using the depth of water D corresponding to V, local S isfound simply, from Eq. (4), as DNta.

Equation [6] may be used for sprinkler infiltrometer condi-tions, or under circumstances of relatively uniform r for sprin-kler irrigation, to determine local S by identifying the timefor / = r when this equation first applies. Application rate rshould be known and r/Ks sufficiently high. A simple container,a can for instance, may be placed under a rain or sprinklersource and removed at the time local ponding is observed.The volume accumulated in the can is the cumulative depthof ponding, If(r), and with known or measured r = f, S canbe found from Eq. [6]. The procedure is significantly simplifiedcompared with estimating infiltration parameters from runoffplot experiments, since only the depth of infiltration at pond-ing is required. Further, this experiment can be used as asupplement to infiltrometer or plot experiments. Unlike the

— Sandy Soil- - - Clay Loam

0.6 0.8 1

— - - Green-Ampt— Smith-Parlange— Modified Philip

Scaled Initial Water Content, (ere,)/(es-er)Fig. 1. Effect of initial 6 on sorptivity as calculated from soil hydrau-

lic properties.

Scaled Infiltrated Depth, I/GAOFig. 2. Scaled theoretical infiltrability functions/(/) from Green and

Ampt (1911), Smith and Parlange (1978), and Philip (1957b). Mea-surements for S should take place with scaled infiltration depth,/, less than about 0.1, where all functions approach coincidence.

data from runoff measurements, values of S obtained in thisway are independent of effects of surface routing.

Evaluation and DiscussionThe entire measurement in the ponded case can be

done in a very few minutes. Care must be taken in anyring infiltrometer test to drive the ring with minimumside motion. The applied water volume may be mea-sured such that 1 cm water depth is used each time, andthe calculation of S is then even more simple. Largedepths of water on a soil with low values of S shouldbe avoided to minimize the bias in effective G by a largevalue of d in Eq. [2].

If the initial soil water content is also sampled at thesame time, and the same sample used to find the porosityor saturated water content, then A6 may be estimatedand the product GKS obtained (Eq. [1]). For purposesof infiltration variations across a field, however, S makesan excellent statistic. Using Fig. 1, values of A0 may beused to adjust S results. With the advent of GlobalPositioning System (GPS) instruments, sample locationscan be quickly determined and intersample distancesused to evaluate correlation lengths.

Comparative EvaluationThe measurement method was tested in a field experi-

ment on a Valentine loamy sand (mixed, mesic typicUstipsamment) in Eastern Colorado. Our cylinders are10 cm high and 9.75 cm i.d., so that 75 mL provides awater depth of 1 cm. This cylinder size allows insertion,using a small flat board, without excessive force. Weused a small square-tipped spatula to close any gapbetween the soil and the inner cylinder wall createdduring the insertion into the soil. No soil surface isperfectly flat, so we made three time measurements foreach ring: t0, the time when the first soil is exposed bythe falling water; tm, the estimated time when half thesoil surface is exposed; and tz, the time when the lastfree water disappears. The time fm is used for estimatingsorptivity, but the others give an indication of the micro-

NOTES 57

topographic distribution. While there may be some er-ror in visually identifying rm, experience has shown noobservational bias, and the shrinking of the coveredsurface area is usually rapid enough so that such errorsare a few seconds at most.

Sorptivity values were measured in evenly spaced gridcenters across our 72-ha experimental field. From mea-surements to date, this soil is well mixed with poorspatial correlation, and side-by-side samples are foundto be poorly related. Moreover, measurement by an-other device on the same location would not encounterthe same conditions; however, on the same field, severalmeasurements of soil water retention and hydraulic con-ductivity were obtained from near-surface soil samples.Using these measured retention curves and saturatedconductivities evaluated in the laboratory from 11 soilsamples across the field, the mean sorptivity was 0.157.The mean values of 5 from the 124 sorptimeter sampleson the same area was 0.168, with a standard deviationof 0.048. Taking statistical uncertainty into account, suchagreement within a few percent supports the reliabilityof this measurement method. The mean difference is infact smaller than general variation in means from othersamples at a variety of grid scales on this field. Themethod seems superior in most respects to more cum-

bersome methods that rely on obtaining estimates ofthe early slope of the /(?) curve with a mariott reservoir.