where Vw is the volume of water in cm3 and Vt is the total volume in cm3 of a soil sample. At saturation, Ov is equal to the porosity and ranges between 40% and 60%. For many purposes, Ov is multiplied by the soil depth to express soil water as a depth of water that is compatible with the units used to measure rainfall, evaporation, transpiration, and runoff (Hillel, 2004).
Soil water potential energy expresses the ability of soil water to perform work and is of primary importance in determining the state and movement of soil water. Kinetic energy is considered negligible due to the slow movement of soil water. The concept of soil water potential energy expresses the specific potential energy of soil water relative to that of water in a standard reference state. Differences in soil water potential energy occur over a wide range of time and space scales, and knowledge of the relative soil water potential energy allows determination of the condition of soil water compared to the soil system equilibrium state. Consequently, the soil water potential energy state serves as the basis for estimating how much work must be expended by plants to extract a unit amount of water (Hillel, 2004).
Soil water is held in soil pores under surface tension forces and a concave surface extends from particle to particle across each pore channel. The radius of curvature reflects the surface tension on the individual, microscopic air-water interface of a specific pore. The potential energy of water becomes greater as the water content of the pore increases and the radius of curvature of the water film in the pore becomes greater. A water molecule adsorbed in soil is less free to move than a water molecule without adhesion to a surface. A potential energy gradient results, and the related force is directed from higher to lower potential resulting in the energy potential of soil moisture being taken as negative (Hillel, 2004). This concept is applied to both soil wetness and soil water flow in that it defines a gradient indicating a direction of water movement toward a point having the lowest potential. Negative soil water potential is the work required to remove water from the soil by evaporation or transpiration.
The relative concentration of potential energy in soil water at different locations is the characteristic of interest. The major constraint on defining soil water potential is that the absolute potential energy of water cannot be measured. Recognized factors that can change the potential energy of soil water are the adsorption of water onto soil particles, solutes dissolved in soil water, elevation of soil water in the Earth's gravitational field, and applied pressure. The total soil water potential (yt) is the net result of all of these factors and is expressed as yt = yz + ym + yo (4-6)
where yz is the gravitational potential expressing the force gravity has on water, ym is the matric potential, and yo is the osmotic potential (Hillel, 2004). The unit for expressing the soil water potential is the kilopascal (kPa).
The separate potential forces in Equation 4.6 act in different ways for unsaturated soil. An arbitrary reference level is used for determining yz, and selection of the soil surface as the reference pool results in a negative value. Work is needed to withdraw water against the soil matric forces and this produces a negative value for ym. Interacting capillary and adsorptive forces between water and the soil matrix bind water in the soil and lower its potential energy below that of bulk water. Thus, soil water has a pressure lower than atmospheric, a condition known as tension or suction, and a negative pressure potential (Hillel, 2004). The energy differences between pure water and water containing dissolved salts determine yo. It is a negative potential that increases as the solute concentration increases as yo acts to retain or draw water into the soil and to lower the total soil water potential. For unsaturated soils not involving areas with high evaporation and high solute concentrations in the soil water, yo is taken as zero and yt is reduced to two terms.
Numerous instruments are available for measuring either soil wetness or soil water potential. The spatial and temporal resolutions required for soil moisture measurements vary with the data application, and there is no universally recognized standard method of measurement (Hillel, 2004). Soil wetness is determined by direct and indirect methods. Soil water potential is measured by indirect techniques. For hydroclimatic purposes, soil wetness, soil water potential, or both measurements may be important. A brief description of selected measurement methods is presented to illustrate how the data are acquired.
The simplest and most widely used method for measuring soil wetness (0g) is the gravimetric or thermostat-weight technique (Robock et al., 2000; Hillel, 2004). This direct measurement technique is the standard method to which all other methods are compared. A soil sample is removed from the field by coring or augering and transported to a laboratory in a leak-proof container. In the laboratory, the sample is weighed and then dried in an electrically heated oven at 105 °C until the mass stabilizes at a constant value. The difference between the sample weight before and after drying is attributed to the mass of water in the original sample.
The methodology requires simple equipment, but it is destructive to the sample site which becomes unsuitable for a large number of repeated measurements over time. The laboratory procedure is laborious, and a period of at least 24 hours is usually considered necessary for complete oven drying (Hillel, 2004).
Lysimeters are a non-destructive direct method to measure soil moisture, but they are limited to research facilities due to their expense and maintenance requirements. These large soil-filled containers are weighed to determine changes in mass for a specific time and the change is attributed to changes in soil moisture. This procedure requires establishing the wetness of the soil in the container as an initial benchmark for determining later soil wetness. Lysimeters are discussed in more detail in Section 4.6.3 regarding measuring evapotranspiration.
The neutron probe is widely used as an indirect method for measuring soil wetness due to the high efficiency and reliability of the technique. A radioactive source of high-energy neutrons is lowered into an access tube in the soil that provides standardized measuring conditions (Hillel, 2004). The number of neutrons slowed or thermalized by collisions with hydrogen nuclei in the soil water is measured by a detector. There is a fairly linear relationship between the detector count rate and the soil wetness, but the relationship varies from soil to soil. Neutron probe readings are usually calibrated for a given soil against the gravimetric method, but inherent uncertainties with the neutron probe usually limit its utility to measuring moisture differences rather than absolute moisture content (Ward and Robinson, 2000). However, the method is non-destructive and it has the advantage that data are acquired from the same location and depths at each observation.
A number of other instruments are used for indirect measurement of soil wetness. The capacitance probe uses the dielectric constant of the soil as a measure of soil moisture content and provides a non-radioactive alternative to the neutron probe. Time-domain reflectometry (TDR) is another technique for determining soil wetness by measuring the dielectric constant, but this technique employs the soil water response at microwave frequencies. The presence of soil water slows the speed of the electromagnetic wave emitted by the probe (Hillel, 2004). Frequency-domain reflectometry is similar to TDR except that it employs changes in the frequency of microwave signals due to differences in the dielectric properties of the soil with different water content. Gamma densito-metry derives soil moisture content based on the relatively greater gamma radiation attenuation of water compared with other soil components.
Tensiometers are the oldest and most widely used technique for measuring soil matric potential. This technique allows the soil solution to come into equilibrium with a reference pressure indicator by using a liquid-filled permeable ceramic cup connected to a pressure measuring device. The cup is inserted into the soil and water flows between the cup and the soil until the pressure potential inside the cup equalizes that of the soil water. Tensiometers are not affected by the osmotic potential of the soil solution, and they measure the matric potential with good accuracy in the wet range. However, they provide only a point measurement of matric potential and operate between saturation and —80 kPa (Hillel, 2004).
Other approaches for measuring soil matric potential include burying a resistance block of gypsum, nylon fabric, or fiberglass in the soil. Two electrodes are embedded in the porous block. The matric suction of the block comes into equilibrium with the soil water and the resistance across the electrodes varies with the resulting water content of the block (WMO, 1996). Thermocouple psychrometers are used to measure the vapor phase of the soil environment which is assumed to be in equilibrium with the soil matric potential. Neither the resistance block nor the psychrometer is sensitive to wet conditions, but both are well suited to a dry soil environment.
Schneider et al. (2003) demonstrate that a network of heat dissipation sensors can provide a continuous, inexpensive system of soil water profile observations across a range of soil conditions and sites in the Southern Great Plains. The heat dissipation sensors measure soil matric potential from which volumetric water content is estimated.
Challenges encountered in measuring soil wetness and matric potential have encouraged development of techniques for estimating unsaturated soil water conditions. The influence of soil structure and pore size distribution in determining soil moisture characteristics is the physical basis for expecting moisture differences among soil types. The relationship between soil wetness and matric potential is determined experimentally in the laboratory by placing a saturated soil sample on a porous plate and subjecting the sample to a series of suctions or negative pressure heads. Water content is obtained by weighing the soil sample before and after oven drying to determine how much water is retained by the soil at the specific suction (Ward and Robinson, 2000; Hillel, 2004). Soil wetness and matric potential data are used to construct soil moisture characteristic curves that are a graphical representation of the relationship between these variables for a specific soil (Fig. 4.9).
Soil moisture characteristic curves are not unique curves for a given soil type because the equilibrium soil wetness at a given suction is greater during drying than during wetting (Hillel, 2004). The current suction and prior soil conditions are primary factors influencing the equilibrium soil wetness for a given suction, and this dependence on the previous state of the soil water prior to the current equilibrium condition is known as hysteresis. The main contributors to hysteresis are pore irregularity, contact angle between water and the solid walls, entrapped air, and shrinking and swelling (Hillel, 2004). The result is that the wetting curve is drier than the drying curve over a wide range of matric potentials. Hysteresis is a serious practical problem for soils subject to change by both wetting and drying influences. In practice, the problems associated with measuring the moisture characteristic accurately commonly lead to the hysteresis phenomenon being ignored. The drying curve is easier to establish experimentally and is the one most often reported in the literature as the soil moisture characteristic curve or the moisture retention curve (Hillel, 2004).
At the field scale, soil moisture (SM) in the active soil layer is estimated using an alternative form of the water balance (Equation 2.13) as suggested by Robock (2003). Temporal soil moisture variations are expressed as
where Pr is rainfall, Psn is snowmelt, WT is water table contributions, ET is evapotranspiration, and R is runoff. All units are in mm. Soil moisture retention characteristics are incorporated in the algorithm that quantifies evapotranspiration. Water balance soil moisture estimates can be applied to single or multiple layer soils, and the soil moisture estimates are easily incorporated in land surface models. Formulations like Equation 4.7 quantify the soil moisture component driven by atmospheric forcing, but they are less successful at quantifying small-scale soil moisture field variability that appears as a stochastic response to topography, soils, and vegetation (Robock et al., 2000). Nevertheless, Yamaguchi and Shinoda (2002) report success with simple models using limited daily meteorological data that estimate absolute soil moisture amounts in the upper 50 cm soil layer in Sahelian Niger. Regional soil moisture is controlled principally by rainfall, and the models indicate soil moisture variations from intraseasonal to interannual time scales. Braud et al. (2003) use a simplified in situ method to estimate regional soil hydraulic property variability in central Spain. Their method employs a two-layer soil model and representative particle size distributions and infiltration rates based on sample data medians to characterize spatial soil variability. A statistical analysis approach employed by Cosh et al. (2004) reveals the underlying soil type distribution is the most important parameter in accounting for temporal soil moisture variability in southwestern Oklahoma.
Excluding extreme conditions, a fraction of precipitation enters the soil surface by infiltration and is redistributed to successively deeper layers of the soil profile. The infiltrating precipitation replenishes the water stored in the soil that is available to plants, and it determines the water eventually recharging
Fig. 4.10. Infiltration rate shown as a function of time.
Fig. 4.10. Infiltration rate shown as a function of time.
groundwater. Soil water moves in response to a number of forces, and infiltration may involve water movement in one, two, or three dimensions. However, soil water is commonly conceptualized as one-dimensional vertical flow, and this perspective of infiltrated water in the unsaturated zone is emphasized here. Comprehensive treatments of infiltration are found in Ward and Robinson (2000), Hillel (2004), and Rose (2004).
The infiltration rate is the volume flux of water flowing into the soil profile per unit of soil surface area (Hillel, 2004). Horton (1940) defined the soil's infiltration capacity as the condition when the rainfall rate exceeds the infiltration rate. When the rainfall delivery rate is smaller than the infiltration capacity, water infiltrates as fast as it arrives and infiltration is supply controlled. When the delivery rate exceeds the soil's infiltration capacity the infiltration rate determines the flux and the process is soil controlled. The soil can limit the infiltration rate either at the surface or within the soil profile (Hillel, 2004). The infiltration rate generally changes systematically with time during a given rainfall event in response to changes in rainfall intensity and duration and to changing conditions of the soil's surface properties (Fig. 4.10). Surface properties influencing infiltration include soil texture, soil structure, initial soil moisture content, soil chemistry and temperature, the nature of the vegetation cover, and the slope angle of the land. These factors influence the ability of air and water to move through the soil, and they collectively determine the soil's permeability. In addition, conditions affecting infiltration change between rainfall events and this may magnify the complexity of the surface response to infiltration.
Infiltration rates vary from soil to soil and with the presence or absence of vegetation. Coarse-textured soils generally have larger pore spaces than fine-textured soils. Infiltration rates for coarse sand with good structure range as high as 25mmhr~1 while the infiltration rates for clay loams are 8mmhr~1.
Table 4.2. Soil permeability and infiltration rates for selected surface conditions
Permeability class Infiltration rate (mmhr-1)
Infiltration rates for general soil permeability classes are shown in Table 4.2. Poor structure can reduce infiltration rates by 50%. In addition, infiltration rates tend to be high at the beginning of the process and gradually decrease to a nearly constant value as soils become wetter. The decreasing infiltration rate is due to the closure of pore spaces as some soil granules expand in response to wetting and the delay in vertical water movement related to frictional resistance that increases with depth. Final infiltration into sandy soils is about 20mmhr~1 while the expected rate into heavy clay soils is less than 1 mm hr-1 (Hillel, 2004).
Water infiltrates the surface at a given rate as long as the underlying soil profile can conduct the infiltrated water away at a corresponding rate. Soil texture, structure, stratification, and the initial soil water potential gradient are all important contributors to maintaining the necessary water redistribution rate. However, a decrease in the matric suction gradient occurs as infiltration proceeds and the wetted zone deepens (Fig. 4.11). At any given time, wetness decreases with depth at a steeper gradient down to the wetting front, which is a sharp boundary between moistened soil above and initially dry soil at greater depth (Hillel, 2004).
Point infiltration measurements for determining infiltration rate variations with time are made with ring, sprinkler, tension, and furrow infiltrom-eters. These instruments are described by Rawls et al. (1993) and Rose (2004). The purpose of each device is to define the infiltration capacity for a small area by applying a known quantity of water at a specific rate and monitoring changes in soil-water relationships.
The ring infiltrometer illustrates the basic concepts for measuring infiltration. A metal ring with a diameter of 30 to 100 cm and a height of 20 cm is driven into the ground about 5 cm to form an impermeable boundary. Water is applied inside the ring, and intake measurements are recorded until a steady infiltration rate is observed. A double-ring arrangement is used to create a buffer zone to eliminate the effect of lateral spreading of water by capillary forces in unsaturated soils or a correction factor can be applied to the singe-ring data. Measurements from the inner ring are used for determining the infiltration rate. The average of measurements from several sites is recommended due to the high spatial variability of the infiltration capacity. The advantages of the ring infiltrometer are that it requires only a small area for measurements, the device is inexpensive to construct and simple to operate, and it does not have high water requirements (Rawls et al., 1993; Rose, 2004).
Physical, approximate, and empirical models are used to estimate infiltration. Physical models are the most data intensive and have benefited from advances in computer software. Richards' (1931) non-linear equation describing water flow in soils is a physically based infiltration equation that combines Darcy's equation for vertical unsaturated flow in a homogeneous porous medium with the continuity equation. Richards' equation expresses the time-dependent infiltration rate in terms of antecedent soil profile soil moisture conditions, the rate of water delivery at the surface, and the conditions at the bottom of the soil profile (Rawls et al., 1993). The partial differential equation of one-dimensional vertical flow takes the form where 0 is the downward water content gradient, t is time, z is downward vertical flow, K is the hydraulic conductivity, and y is the matric potential gradient. All rainfall infiltrates into the soil when the rainfall intensity is less than or equal to the saturated hydraulic conductivity of the soil profile. High de _ d k (e) dt ~
rainfall intensities that exceed the infiltration rate produce infiltration during the early stages of the event until the soil surface becomes saturated.
Approximate models strive to represent physically based infiltration conditions based on major parameters and a holistic view of the interception process. However, parameter characterization is commonly difficult. A widely used approximate model based on the total amount of water infiltrated was introduced by Green and Ampt (1911) and in its simple form is b f = i c + ^ (4.9)
where f is the infiltration rate, ic is the eventual steady-state flow rate driven by the soil water potential gradient between the wet surface and the drier soil below, b is diffusivity flow of water that moves into the drier soil ahead of the advancing wetting front, and Ss is the volume of water stored in the depth of soil saturated by infiltration. Terms ic and b are constants for given soil texture and moisture conditions, and Equation 4.9 is often used in computer models of infiltration (Ward and Robinson, 2000). The Green and Ampt model provides a reasonable approximation of reality for one-dimensional vertical flow with water supplied under positive hydrostatic pressure to coarse-textured soils that are initially dry and without entrapped air (Hillel, 2004). The time-based equation developed by Philip (1957) is an extension of the Green and Ampt model (Ward and Robinson, 2000).
Empirical infiltration models use parameters estimated from measured infiltration rate-time relationships for a given soil condition. This is a common limitation that hinders the wide-scale application of these models. The Horton (1940) model is widely used in hydrologic modeling and illustrates the nature of empirical infiltration models. It is founded on the concept that infiltration capacity passes through a cycle for each storm starting with a maximum value and decreasing rapidly at first as the surface becomes sealed. Horton's three-parameter model is expressed as fp = fc + (fo - fc)e-kt (4.10)
where fp is the infiltration capacity, fc is the minimum constant infiltration capacity, fo is the maximum infiltration rate at the beginning of the storm event, k is the rate of decrease in the infiltration capacity, and t is time (Rawls et al., 1993). Numerous field experiments have found this relationship is most likely to occur where bare soils are exposed to rainfall as happens in arid and semi-arid areas (Ward and Robinson, 2000).
Rainfall excess models lump infiltration with other surface processes. These models are commonly used for estimating runoff and are discussed in Section 6.10.3.
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