### Sorptivity

The main theoretical infiltration algorithms are based on the work carried out by Philip (1957), when he showed that cumulative absorption or desorption into or out of a horizontal column of soil of uniform properties and initial moisture content was proportional to the square root of time.

Philip also showed that for shorter times of t, vertical one-dimensional infiltration could be described by a rapidly converging power series in t0.5. The coefficient of the leading term of the series (bracketed below) was termed sorptivity.

where:

i = cumulative infiltration (cm)

t = time (minutes)

S = sorptivity (cm/minute^0.5)

A & B = parameters of the second and third terms (cm/minute, cm/minute^1.5).

Philip (1957) and again Talsma (1969) pointed out that sorptivity depended on initial moisture content and on the depth of water over the soil. Talsma varied these parameters in a series of field based experiments to test their effect on sorptivity values.

Measurements of sorptivity were made by Talsma on large samples enclosed with 300 mm diameter, 150 mm high infiltrometer rings pushed 100 mm into the soil.

Water was rapidly ponded in the rings to a depth of about 30 mm and the subsequent drop in water level was noted at regular time increments of 10 to 15 seconds after ponding.

Talsma (1969) proposed methods of measuring sorptivity in the field on undisturbed soil, for subsequent use in analytical applications.

Sorptivities were calculated from the linear portions of initial inflow against the square root of time. Samples of soil for initial and final moisture content were taken close to and inside the rings.

Based on the work by Talsma (1969) the method relied on the reasonable assumptions that:

- during the short time of measurement (1-2 minutes) water flow would remain vertical within the ring infiltrometer, and
- that the first term of the infiltration equation (Philip, 1957) accounted for nearly all of the flow.

Allowing for the accuracy of experimental technique, the first condition, that water flow would remain vertical within the ring infiltrometer, was easily verified, but the second condition was dependent on the magnitude of A relative to S.

Talsma found that plots of I against t0.5 remained essentially linear for at least 1 minute and found that for the wide range of differently textured and structured soils studied, the drop in head during the measuring process was not significant.

Talsma concluded that the accuracy of the ring infiltrometer method of measuring S in situ was quite acceptable, even in soils with high saturated hydraulic conductivity relative to sorptivity. Talsma also concluded that neither the diameter nor shape of the ring affected the results.

In the work carried out on the Giralang catchment by Goyen (1981), perspex rings were used, where possible, in preference to steel ones. This permitted a visual check on the wall/soil interface as well as allowing direct head drop measurements through the wall.

Sorptivities were measured at random sites over the Giralang catchment to add data to the work performed by Talsma in the Canberra region.

**Hydraulic Conductivity**

Hydraulic conductivity, a measurement of the ability of a section of soil profile to conduct water, is reflected in the second term in the infiltration equation by Philip (1957)

Talsma (1969) showed that for a wide range of soils, A could be expressed as follows:

where:

K_{0}=saturated hydraulic conductivity.

K_{0} therefore represents the ability of a soil profile to transmit water when the soil is fully saturated. Ko is therefore only a special case of general hydraulic conductivity.

To apply Philip's infiltration equation it is therefore necessary to obtain measurements of Ko as well as sorptivity for each of the land domains.

Subsequent to reviewing the above Equations (9) and (10), a modified equation, eliminating the need for Equation (10), was cited in a paper by Chong and Green (1979).

In this publication work was described by Talsma and Parlange (1972) and Parlange (1971, 1975, and 1977) where the following equations were developed:

Where X and Y were related to time, t, and accumulative infiltration, i, by the series expansion of Equation (9) and the substitution of Equation (12) and (13) in the result, with rearrangement and truncation after the t1.5 term. The relationships were:

and:

The new equation termed, the "Talsma-Parlange Equation," was therefore as follows:

where:

i = cumulative infiltration

S = sorptivity at a specified antecedent soil moisture content

K_{0} = hydraulic conductivity at water saturation.

Equation (14) was subsequently adopted in place of Equations (9) and (10) and is currently used in the XPRafts loss module.

The method of measurement adopted for Ko follows a similar procedure to measuring sorptivity, only on this occasion the undisturbed core sample held by the infiltrometer ring is removed from the surrounding soil and placed on a wire grid raised above ground level. A 100 mm length of core is adopted for all Ko and S measurements.

In this way zero moisture potential at the base of the core is assured. Water is then ponded on top of the soil until a steady outflow is observed. This flow is then measured at constant head and the saturated hydraulic conductivity calculated as follows:

where:

K_{0} = Saturated hydraulic conductivity (cm/minute)

Q_{W} = volume of water discharged in time t (cm³)

t = time (minutes)

L = length of soil core (cm)

H = hydraulic head, distance from base of core to pondage surface (cm)

Ac =cross-sectional area of core (cm²)

**Storage Capacity**

The same samples used for the determination of saturated hydraulic conductivity can be used to measure water storage capacity in the depth of the sample.

To achieve this the sample is first weighed, then oven dried and re-weighed to deduce moisture content.

In both the hydraulic conductivity and storage capacity sampling procedure two rings can be used, one to obtain the sample and an additional ring containing an imported sample to reinstate the sampling area.

Upper Soil Storage Capacity (USC), as defined below, is an important parameter in the infiltration process using the Australian Representative Basins Model (ARBM) to relate sorptivities of varying initial moisture contents. The following relationship is used in the model as given by Black and Aitken (1977):

where:

S = sorptivity

S_{0} = sorptivity at zero moisture content

US(init) = initial moisture content in upper soil store (mm)

USC = max. moisture content of upper soil store (mm)