SOIL WATER RELATIONSHIPS

Transcription

1 CHAPTER 6 SOIL WATER RELATIONSHIPS Roger E. Smith (UDSA-ARS, Fort Collins, Colorado) Arthur W. Warrick (University of Arizona, Tucson, Arizona) Abstract. Basic relations of soil water and soil water flow important in irrigation design are presented, and methods to measure soil water content, pressure head, and conductivity are outlined. The calculation of infiltration rates and the measurement of soil infiltration parameters are discussed, as well as many of the complexities and challenges in applying current understanding to irrigation situations. Keywords. Infiltration, Redistribution, Soil physics, Soil water. 6.1 INTRODUCTION Design and operation of efficient irrigation systems require knowledge of the processes controlling movement and storage of water in soil. This chapter outlines basic concepts of the nature of soil water and the interactive forces that affect the distribution and movement of water in the soil-water-plant system. Methods for measuring the state of soil water, and soil properties that describe water movement and water-holding characteristics of soils are presented and discussed. Methods to measure hydraulic conductivity in both saturated and unsaturated soils are presented and techniques for predicting the unsaturated hydraulic conductivity function from the soil water retention characteristic are discussed. Factors controlling infiltration rates and procedures for measuring infiltration characteristics are also presented and discussed. References are given to allow the reader to pursue any of these topics in greater detail, and to obtain more detailed outlines of measurement methods. 6.2 WATER-HOLDING CHARACTERISTICS OF SOILS Soil water has traditionally been of interest because of its influence on plant growth and crop production as well as runoff processes. A growing plant must be able to balance the atmospheric demand for water with the amount it can extract from the soil. The soil water supply is alternately depleted through evapotranspiration and replenished by irrigation or precipitation. Today soil water is of increasing of concern as a medium through which chemicals may move and potentially harm surface or groundwater.

2 Design and Operation of Farm Irrigation Systems Soil Water Content Soils hold water to the extent that they have porosity, and the water usually shares that pore space with air. Even saturated soil will usually have some air trapped within. The porosity of soil itself is quite variable, in response to both natural and agricultural practices. Soil water content, by weight, is calculated as: Wmoist Wdry Wmoist θ w = = 1 (6.1) Wdry Wdry where θ w = water content expressed on the basis of the dry weight of soil W moist = moist soil weight W dry = oven-dry soil weight. It is common to express soil water contents on a volumetric basis, i.e., the ratio of the soil water volume to the total soil volume. This is done by multiplying the water content on a dry weight basis by the ratio of the soil bulk density, ρ b, and water density, ρ w, as follows: θ = (6.2) w where θ = water content on a volume basis. The soil bulk density (or apparent density), ρ b, is defined as the oven-dry weight of soil per unit volume, as it occurs in the field. In the following discussion, θ will be used to mean volumetric water content Soil Water Potential Soil water content alone is not a satisfactory criterion for describing the availability of water to plants and attempts have been made to describe water availability in terms of the energy state of water. Initially, empirical measurements and relationships were developed, but these gave way to consideration of fundamental mechanisms and expressions. The soil-water-plant system is now treated as a continuous dynamic system where water moves through the soil to plant root surfaces, into roots, through the plant, and into the atmosphere along a path of continuously decreasing potential energy. The removal of soil water depends not only upon its amount and energy state, but also upon the ability of the plant to absorb water and the atmospheric demand for water from the plant. A more detailed discussion of the various potential components can be found in a paper by Rawlins (1976). About the beginning of the 20th century, soil water was arbitrarily classified into different forms such as gravitational water, capillary water, hygroscopic water, etc. (Briggs, 1897, cited by Richards and Wadleigh, 1952). These early groupings have been replaced by a fundamental concept referred to as soil water potential. Soil water does not occur in separable forms within the range of our interest, but does vary in the energy with which it is retained in the soil. The work per unit weight to move an infinitesimal amount of water from some reference state to a given point in the soil is known as the total soil water potential, h T. The usual reference state, arbitrarily defined as having zero potential, is an open air-water interface at some specified elevation and air pressure. Energy must be expended to remove water from an unsaturated soil, so the soil water potential is less than the reference state and thus has a negative sign. The potential gradient, or rate of decrease of potential energy with distance, is the driving force causing soil water flow (Section 6.4). Thus, soil water will move θ w ρ ρ b

3 122 Chapter 6 Soil Water Relationships from a wet area where the potential is near zero, toward a dry region where the potential is lower (a larger negative value). The soil water pressure has dimensions of [M/LT 2 ], and the equivalent potential h T has dimension of length. Other definitions will follow resulting in dimensions of pressure and energy per unit mass. The total soil water potential may be expressed as the sum of three component potentials: h T = h g + h p + h a (6.3) where h T = total soil water potential h g = gravitational potential h p = matric or pressure potential h a = pneumatic potential. Gravitational potential, h g, is the elevation. If z is the height above a defined reference plane, h g = z. The value of h g can be positive (if above the reference) or negative (if below the reference). The value of h p, the pressure (and matric) potential, can be positive or negative and is equal to the soil water pressure head (i.e., the pressure divided by the specific weight). If the soil water pressure is greater than the adjoining gas phase pressure, then h p will be positive. If the pressure of the soil water is less than the adjoining gas phase, h p will be negative. This is due to the attraction of soil surfaces for water, the influence of soil pores, and the curvature of the soil water interface. For this situation, h p is also called the matric potential. It is convenient to consider pressure potential as a continuous function of water content, which is positive in a saturated soil below the water table and negative in unsaturated soil. Since soil water potential is generally negative, it is often given a positive value and referred to as suction or tension. The pneumatic potential, h a, (energy per unit mass) may be expressed as h a = p sa /(ρ g), where p sa is the soil air pressure, ρ is the density of water, and g is gravitational acceleration. Usually the air pressure is considered to be uniform throughout the soil profile and the pneumatic potential is ignored in characterizing soil water flow. Such assumptions are not always justified; see Section 6.4. Two other ways are used to define potential. These are energy per unit volume, h T,v, and energy per unit mass, h T,m. The dimensions of h T,v are pressure, and the relation to h T, above, is h T,v = ρ gh T (6.4a) Similarly, the relationship between h T and h T,m is h T,m = gh T A useful conversion table taken from Hillel (1971) is given here as Table 6.1. Table 6.1. Energy levels of soil water expressed in various units (from Hillel, 1971). Soil Water Potential Soil Water Suction Per Unit Weight Per Unit Mass Per Unit Volume Per Unit Weight Per Unit Volume (mm H 2 O) (joules/kg) (kpa) (mm H 2 O) (kpa) (bars) (6.4b)

4 Design and Operation of Farm Irrigation Systems 123 To avoid confusion among the various expressions for soil water energy status, one must keep in mind that a low potential refers to dry soil and is a large negative number, while a high matric or pressure potential refers to a wet soil with a small negative value of h. A high potential would be 0.10 bar while a low potential would be 15 bars. On the other hand, low suction or tension refers to wet soil with a small positive suction value. High suction or tension means a dry soil and is a large positive number; i.e., a low suction is bars and a high suction is +15 bars. The main incentive for introducing soil water potential, h T, is to describe flow relations based on spatial differences in h T. For a non-equilibrium system, flow will occur from a higher to a lower potential. Flow is influenced by additional factors and these factors are often included as additional components for h T (e.g., Jury et al., 1991). In particular, osmotic effects are often included as an additional osmotic potential component. The osmotic potential is a significant component in saline soils. For coupled flow processes consisting of flow due to osmotic gradients, temperature gradients, pressure gradients, and other gradients, it is not necessary to define a total potential which includes components for each independent part. In fact, Corey and Klute (1985) showed that the inclusion of chemical effects can lead to contradictions with the notion that flow occurs from regions of high to low potentials. (This does not complicate the formulation of coupled flows, but simply says that the same transport coefficients cannot be used for the independent gradient terms for each component.) The Soil Water Retention Characteristic As water is removed from a soil, the matric or pressure potential of the water remaining is decreased (algebraically, e.g., 1 is decreased to 10). If water is added to the soil, the matric potential is increased (such as, 10 to 1). A curve showing the functional relationship between matric potential and soil water content is known as the soil water characteristic or retention curve. Soil water is usually expressed as volumetric water content θ or as volumetric percentage of water. When the relationship is determined by drying a wet soil, the curve is known as either the desorption curve, water retention curve, or water release curve. When the relationship is determined as a dry soil wets, it is called the sorption or imbibition curve. The soil water characteristic is related in an indirect way to the pore size distribution. Water is retained in the soil by a combination of the attraction of particle surfaces for water and the capillary action of water in the soil pores. The matric potential is related to the curvatures of the air-water interfaces, which in turn are affected by the soil pore geometry, the particle aggregation, and the soil water content. At high matric potentials (near zero), most of the soil pores are filled with water and the total porosity and pore size distribution greatly influence the water retained. Inasmuch as soil texture dominates the total porosity and pore size distribution, it has a marked effect on the soil water characteristic. In general, the higher the clay content of a soil, the higher will be the water content at any given potential. Soil aggregation, especially for finetextured soils, tends to increase the number of large pores. Thus, soil structure is important in the amount of water retained at high potentials. When the large pores empty, the water remaining in the soil is held in the smaller interaggregate pores and at the particle contact points. As the soil dries, the amount of particle surface area also affects the water retained, and this is strongly influenced by soil texture. Soil compaction also influences the water characteristic because compaction results in smaller pores, reduced total porosity, and increased interparticle contact in a given soil vol-

5 124 Chapter 6 Soil Water Relationships ume. It is usually the larger pores that are reduced most by compaction, so that the influence of compaction is greater at higher potentials. Examples of soil water characteristics for three soils of different textures are given in Figure 6.1. Some common functional forms for describing this relation are presented in Figure 6.2 and Table 6.2. This table uses scaled water content, Θ, defined as (θ θ r )/(θ s θ r ), where θ s and θ r are known as the saturated and residual water contents, respectively. Water potential is scaled by a parameter α with units [1/L]: h * = αh. Residual water content, θ r, may be thought of as water which cannot be withdrawn from a soil by suction, but in practice is often a fitting parameter. Saturated water content, θ s, is a measurable quantity which is usually less than soil porosity because of entrapped air. Figure 6.1. Generalized water retention relations for three different textured soils. Figure 6.2. Examples of various algebraic forms for describing the soil water retention relationship.

6 Design and Operation of Farm Irrigation Systems 125 Table 6.2. Functional relationships for hydraulic characteristics. Parameter Function (and abbreviation) m k r = K/K s Θ (h * ) Relation Gardner (1958) (GR) m > 0 exp(h * ) Θ = [exp(h*/2)(1 h*/2)] 2/(m+2) van Genuchten (1980) [a] (VG) 0 < m < 1 Brooks and Corey (1964) [b] (BC) Broadbridge and White (1988) (FBW) Θ p [1 (1 Θ 1/m ) m ] 2 Θ = (1 + h * n ) -m m > 0 Θ v Θ = h * -m/(1-m) ; h * >1 = 1 ; 1< h * < ( m 1) Θ (m 1)Θ h m > 1 * = 1 + ln Θ m m Θ (m Θ) Linear [c] None Θ h * = ln Θ [a] Use p = 0.5 and commonly use n = 1/(1 m). [b] Use v = 2m + 3 (sometimes v = 2m + 1 or 2m + 2). [c] Also may have k r (h) = dθ/dh. The significance of the parameters α, n, and m used in Table 6.2 in connection with the van Genuchten (1980) (abbreviated VG) and Brooks and Corey (1964) (BC) functions can best be seen in Figure 6.3, which is a log-log plot of these retention relations for specific values of m. The log slope of the asymptote is mn or m/(1 m), often called the pore-size distribution index, and n determines the degree of curvature in the region near the intercept. The asymptote intercept is 1/α and is often referred to as the air-entry head, h e. As n becomes large, the shoulder curvature near h e becomes sharper, and the VG expression approaches the more simple BC relation as a limit. It should be noted that the BC relation is a special case of the VG expression. A generalized form of the BC relation, called the transitional Brooks-Corey relation (TBC), has been introduced by Smith (1990). This is functionally equivalent to the VG relation but retains the same parameters as the BC expression. The relation of m to n often used in the VG expression (see Table 6.2) is not retained. Figure 6.3. The parameters in the TBC or VG retention relation have specific relationship to the shape of the curve, as illustrated here.

7 126 Chapter 6 Soil Water Relationships The term soil water capacity, C(h), refers to the slope (dθ/dh) of the soil water characteristic at any point on the curve. This value represents the change in water content per unit change in matric potential and represents an important property for soil water storage and release. The soil water characteristic can be used to estimate the amount of water released between any two potentials. Although the soil water potential largely determines the ease with which a plant can obtain water, it is also important to know how much water is in the soil at potentials above a given critical level. This, along with crop water requirements, allows one to estimate the need for irrigation. The soil water potential will decrease as a plant withdraws water. If h c is considered a critical level below which it is not desired to deplete water, then the amount of water available at a potential h 1, h 1 > h c, will be θ(h 1 ) θ(h c ). Many soils swell and shrink with wetting and drying, so that all of the water does not come from a constant volume of soil. This is especially important at high potentials where soil structure influences the characteristic Hysteresis. The soil water characteristics for sorption and desorption will often differ because the water content in a soil at a given potential depends upon the wetting and drying history of the soil. This history dependence in the relationship between potential and water content is called hysteresis. A schematic example of desorption and sorption curves for a soil is given in Figure 6.4. When the desorption curve is obtained by drying an initially saturated sample and the sorption curve is obtained by wetting an initially dry sample, the two moisture characteristics are known as the primary hysteresis loops or main branches (main drying curve, MD, and wetting curve, MW, respectively). If the soil is not completely dry before rewetting or not completely wet before drying, the resulting curves will fall between the two primary curves, and they are known as scanning curves (wetting scanning curve, WS, and drying scanning curve, DS). Wherever the starting point is within the main curves, a drying condition will approach the MD curve, and a wetting condition will approach the MW curve. At any given potential the water content will be greater in a drying soil (desorption) than in a wetting soil (sorption). Field soil is rarely either completely wet before drying, or completely dry before wetting, so measured primary wetting or drying reten- Figure 6.4. Definition diagram of the hysteresis loops which can occur during wetting and drying of a soil.

8 Design and Operation of Farm Irrigation Systems 127 tion curves can be used only with reservation in interpreting soil water status. The water content or potential can only be estimated from measurement of the water content and the main curves, unless the wetting history is accurately known. However, the amount of error involved is relatively small, compared with other errors involved such as soil variability, climatic changes, and plant variabilities. Excellent discussions of hysteresis are given by Jury et al. (1991), Hillel (1971), and Nielsen et al. (1972) Methods of determining the soil water characteristic. The soil water characteristic is usually determined in the laboratory using tension tables or pressure plates (Figure 6.5). In all of the techniques used, a porous membrane or plate hydraulically connects the soil water with water in the lower chamber. The pores in the membrane are small enough that, under the imposed pressure, water but not air can pass through. In all cases P 1 > P 2, so that water is forced from the soil into the lower chamber. At equilibrium, the imposed pressure (expressed in suitable terms) can be considered as the potential of the water remaining in the soil. For high potentials the membrane may be blotter paper, fine sand, sintered glass, porous steel, or similar materials. In this case P 1 is often atmospheric and P 2 is obtained with a hanging water column (Figure 6.5a) or with regulated vacuum. At lower potentials of about 1 bar or less, the pores of these materials are too large to remain water filled and air will pass through the membrane. A fine-pored ceramic is then used as the membrane, P 2 is atmospheric, and P 1 is obtained with compressed gas, usually air or nitrogen. Ceramic membranes are available with bubbling pressures of 100 bars and more. The air entry value of the plate should be somewhat matched to the soil water potential of interest as the finer-pored ceramics necessary for higher pressures tend to restrict flow. In addition to porous ceramics, porous stainless steel and plastic materials can be appropriate for the wet range. Cover to prevent evaporation Soil P 1 Porous Membrane Soil Regulated Pressure P 1 P 2 Hanging Water Column P 2 = atmospheric Figure 6.5. Two methods of determining water retention relations for a soil sample: (left) hanging column and (right) pressure plate.

9 128 Chapter 6 Soil Water Relationships In practice, a sample of soil is placed in the pressure chamber in a retaining ring and saturated overnight. The desired pressure is then applied until outflow ceases and the soil water is considered to be in equilibrium with the applied pressure. The amount of water in the soil is then determined, usually by oven drying. The process is repeated, with a second sample being subjected to a different pressure. The resulting soil water contents are plotted against applied pressure or vacuum, expressed as potential units (usually cm or millibars) to form the water characteristic. Details of apparatus and procedure are given in Dane and Topp (2002). Because the pore size distribution has such a large influence on water retention at high potentials, disturbed samples (dried and sieved) often give erroneous results. Use of so-called undisturbed soil cores is preferable, but even with these, some error is inevitable because of the swelling and shrinking that accompanies wetting and drying of many soils. At low potentials (approaching 15 bars) the soil-specific surface dominates water retention and the error introduced by using disturbed soil samples is quite small. Determining the approximate local soil water characteristic in the field may be done at sites where both soil water potential and water content are measured, using apparatus discussed below Approximate Soil Water Parameters Field capacity and permanent wilting point once were considered to be soil water constants. They are now recognized as very imprecise but qualitatively useful terms. After infiltration ceases, water within the wetted portion of the profile will redistribute under the influence of potential gradients. Downward movement is relatively rapid at first, but decreases rapidly with time. Field capacity refers to the water content in a field soil after the drainage rate has become small and it estimates the net amount of water stored in the soil profile for plant use. While field capacity was formerly accepted as a physical property characterizing each soil, now it is used as only a very rough measure of the soil water content a few days after it has been wetted. For most soils this is a near-optimum condition for growing plants. However, soil water will continue to move downward for many days after irrigation. Figure 6.6 (Gardner et al., 1970) is a good illustration of the continuous nature of profile water redistribution, contradicting the idea of a definable point associated with this common term. Indeed, Gardner et al. (1970), referring to their experiments, stated that the soil exhibited nothing resembling a field capacity. The field capacity concept is perhaps more applicable to coarse than to finetextured soils because in coarse soils most of the pores empty soon after irrigation and the capillary conductivity becomes very small at relatively high potentials. Fine soils, however, retain more water than coarse soils as well as drain longer at significant rates. Any interface of soil layers will inhibit water movement across the interface (more or less, depending on the relative hydraulic properties) and thus restrict redistribution and increase apparent field capacity (see Section 6.5.1). Other factors that may influence soil water redistribution rate are organic matter content, depth of wetting, wetting history, and plant uptake pattern. Even the cultural practices are important: for example, the appropriate field capacity for dryland farming on a soil is probably much lower than for a frequently irrigated farming system.

10 Design and Operation of Farm Irrigation Systems 129 Figure 6.6. After irrigation, redistribution in a soil profile extends for many days, as demonstrated here by measurements of Gardner et al. (1970). The permanent wilting point is the soil water content below which plants growing in the soil remain wilted even when transpiration is nearly eliminated. It represents a condition where the rate of water supply to the plant roots is very low. The water content corresponding to the wilting point applies to the average water content of the bulk soil and not to the soil adjacent to the root surfaces. The soil next to the root surfaces will usually be drier than the bulk soil (Gardner, 1960), because water cannot move toward the root surfaces fast enough to supply plant demands and a water content gradient develops near the root. Like field capacity, permanent wilting is not a soil constant nor a unique soil property. There is no single soil water content at which plants cease to withdraw water. However, for a given soil, the range of water contents for wilting may be quite small, since soil water contents change little with matric potential at very low potentials. Plant wilting is a function of demand as well as soil conditions: plants growing under low atmospheric demand can dry soil to lower water contents than if the demand is high, because more time is allowed for water to move through the soil to the roots. When atmospheric demands are high, plants may temporarily wilt even though soil water contents are considered adequate; an example is sugar beet wilting in midday during the summer. In the wilting range, almost all soil pores are empty of water and the water content is determined largely by the specific surface area and the interparticle contact points. The water content in soil subjected to a pressure potential of 15 bars is closely correlated with the permanent wilting percentage for a wide range of soils (see Romano and Santini, 2002). Because of its simplicity and the availability of reliable equipment, the 15 bar percentage is now commonly used to estimate the permanent wilting point. Formerly, sunflowers were the standard test plant used for determining permanent wilting percentage (Romano and Santini, 2002). The amount of water released by a soil between whatever is considered field capacity and permanent wilting is traditionally called the available water. The term implies that the available water can be used by plants, but this is misleading. If the soil water content approaches the wilting range, especially during periods of high atmos-

11 130 Chapter 6 Soil Water Relationships pheric demands for water or during flowering and pollination, the yield and/or quality of most crops will decrease significantly. This concept is more important for dryland agriculture than for irrigated conditions. Inasmuch as the difference between field capacity and available water can be no more meaningful than either of the terms, available water is only an estimate of the amount of water a crop can use from a soil. Many farmers irrigate when the available water has been depleted a certain amount, depending upon the crop. For high-waterrequiring crops such as potatoes, irrigation may be scheduled at 15% to 25% depletion (85% to 75% available water remaining in the soil); for many other crops, the depletion may go to 50% to 75% before irrigation. This bank-account type of irrigation ignores any relation between depletion and water potential. For a given soil, the degree of depletion allowed before irrigation may be roughly related to potential through the characteristic curve. As with field capacity, available water is a useful concept, providing that its limitations are recognized, such as variations with soil depth, the influence of climatic factors on evapotranspiration, and the effects of soil profile characteristics Methods for Characterizing Soil Water The soil water characteristics at locations in the field may be obtained by water potential measuring devices in combination with soil water measurement. Because of natural soil variability and the variation in soil water content with wetting history (hysteresis), the field-determined water characteristic curve is not precise and is difficult to duplicate. Sorption curves are more difficult and tedious to determine then desorption curves because equilibrium is reached very slowly Measuring water content. Topp and Ferre (2002) and Rawlins (1976) have discussed the various methods and associated error for measuring soil wetness. The discussion here will be limited to those techniques considered most useful in the field. Gravimetric. The accepted standard for soil water measurement is the gravimetric method, which involves weighing a sample of moist soil, drying it to a constant weight at a temperature of 105 to 110 C, and reweighing to determine the amount of water lost on drying. The results are often expressed as the ratio of mass of water lost to mass of dry soil. The required drying time depends upon the soil texture, soil wetness, loading of the oven, sample size, whether the oven is a forced draft or convection type, and other factors. Usually 24 h is sufficient but the required time is obtained by repeatedly weighing a sample after various periods of drying. Microwave ovens have been used to reduce drying times (Horton et al., 1982). The bulk density of soil may be measured by drying and weighing a known volume of soil, or by using the clod, core, or excavation method (Grossman and Reinsch, 2002). The core method is the most commonly used. A cylindrical metal sampler of a known volume is forced into the soil at the desired depth. The resulting soil core is dried and the bulk density is found by dividing the mass by the volume of the cylinder. Samples may be taken at successive depths from the surface by cleaning out the sample hole to the desired depths with an auger and then forcing the sampler into the soil at the bottom of the hole. Alternatively, samples may be taken in a trench by forcing the sampler into the soil horizontally at the desired depth. Obviously, this latter method involves more labor but the sampling zones can be better observed. Excellent core samplers are available commercially. Neutron scattering. The neutron scattering procedure to estimate soil water content has gained wide acceptance in recent years. A source of high energy or fast neutrons is

12 Design and Operation of Farm Irrigation Systems 131 lowered to the desired soil depth into a previously installed access tube. Radiumberyllium has been used, but current equipment uses americium. The fast neutrons are emitted into the soil and gradually lose energy by collision with various atomic nuclei. Hydrogen, present almost entirely in soil water, is the most effective element in the soil in slowing down the neutrons. Thus, the degree of the slowing down of neutrons is a measure of the soil water content. The slowed or thermalized neutrons form a cloud around the source and some of these randomly return to the detector, causing ionization of the gas within the detector and creating an electrical pulse. The number of such pulses is measured over a given interval of time with a scalar or the rate of pulsation can be measured with a ratemeter. The count rate is almost linearly related to the water content. When not in use the radiation source is housed in a shield that contains a material high in hydrogen, such as polyethylene. This material serves as a standard by which proper operation of the instrument can be verified. Inasmuch as instrument variations and source decay occur, it is more satisfactory to use the count ratio method rather than just a count. The ratio of sample count/standard count is plotted versus water content. This eliminates any systematic errors due to instrumentation that may vary from day to day. The volume of soil measured depends upon the energy of the initial fast neutrons and upon the wetness of the soil. With the americium-beryllium source the volume of soil measured is a sphere of about 150 mm diameter in a wet soil and up to 500 mm or more in a dry soil (Grossman and Reinsch, 2002). Neutron scattering has some advantages over the gravimetric method because repeated measurements may be made at the same location and depth, thus minimizing the effect of soil variability on successive measurements. It also determines water content on a volume basis, with the measured soil volume influenced by the instrument used, the soil type, and wetness. Disadvantages of neutron scattering are the initial high investment in equipment, the time required per site because of the need to install access tubes, and the training, licensing, and testing required for possession of a radioactive device. Also, measurements near the soil surface are not accurate because neutrons are lost through the surface, and it is difficult to accurately detect any sharp delineation such as a wetting front or soil layering effect. The manufacturer usually supplies a calibration curve, but one should verify whether it applies to a given soil. If changes in water content are desired, rather than absolute values, a single curve is more widely applicable because the bias will be the same in successive readings. Two calibration procedures have been used: field calibration in natural soil profiles, and laboratory calibration in large prepared soil standards. Calibration should be done with the same type of access tubes as used in the field. For details of the method, see Topp (2002). Time domain reflectometry (TDR). This is a relatively new technique used to measure volumetric soil water content and soil bulk salinity based on the high-frequency electrical properties of soil and water. It offers a variety of advantages including rapid, reliable, and repeatable measurements with a minimum of soil disturbance. In theory, TDR requires no calibration and the soil moisture determination is independent of soil texture, structure, salinity, density, or temperature. In reality, calibration may be necessary for different soil types and TDR probes. Additionally, soil salinity can be evaluated with the technique. More than 50 papers discussing the state-of-the-art developments in TDR are published in the proceedings of a 1994 conference (U.S. Bureau of Mines, 1994).

13 132 Chapter 6 Soil Water Relationships A B Voltage TDR 0 C Coaxial cable t 1 t 2 Time Soil surface L p TDR probe Waveguide Figure 6.7. (a) Installation diagram for time domain reflectometry (TDR) measurement of surface soil water content. (b) The instrument trace and its interpretation, discussed in text. TDR refers to both the overall technique and to the electronic device that generates and measures the electrical signal used to measure the soil water content and salinity. A sketch of a typical TDR probe is given in Figure 6.7a. It consists of a coaxial cable, handle, and two or three parallel metal rods. The metal rods are also referred to as waveguides. A voltage pulse is sent down a cable and the returning signal monitored over time. The velocity of the electrical pulse is proportional to the dielectric coefficient (κ) of the soil in contact with the probes. κ is a dimensionless ratio related to the degree of orientation of dipoles in a material when subjected to an oscillating electric field (see Table 6.3 for some typical values of κ). For soil, κ is considered independent of density, texture, structure, temperature, salts (not necessarily true at very low water contents), and others. This is mainly because changes in κ due to changes in water content are very large compare to changes in κ for the other common constituents in soils. As a result, it is possible to create a calibration curve relating κ to soil water content. Topp et al. (1980) conducted a number of experiments to relate the dielectric constant of a wide variety soil types to volumetric water content. They found a close fit for a variety of soils and soil-like materials using a single polynomial equation: θ = κ κ κ 3 (6.5) This calibration curve is still used, but recent work confirms that it is best to make a calibration curve for each soil and probe to get an optimal fit. Table 6.3. Typical values of dielectric coefficient κ. Material κ (dimensionless) Perfect metal conductor Water 70 to 80 Dry soils 2 to 5 Perfect vacuum 1

14 Design and Operation of Farm Irrigation Systems 133 The velocity, v s, of the electromagnetic wave as it travels through the soil is related to the dielectric constant κ by v s = c κ -0.5 (6.6) where c is the velocity of light. v s is defined as twice the physical length of the probes (2L p ) divided by the time (2t s ) for the wave to travel the length of the probe and back, so that 2 cts = Lp κ (6.7) Therefore, the dielectric constant is a function of the speed of light, the length of the probe, and the wave travel time. The art of finding soil water content with TDR is in knowing how to find the two distance end points on the trace. An ideal trace is given as Figure 6.7b. Point t 1 represents the time when the signal enters the soil and t 2 the time when the wave has traveled to the end of the probe and back to the soil surface. For locating t 1 and t 2, some users choose to pick the numerical maxima and minima of the trace. For purposes of automation and for noisy signals, special procedures are adapted for identifying points on the trace. Also shown on Figure 6.7b is a voltage height C. The value of C is related to the effective conductivity and hence to soil salinity. For nonsaline conditions, recovery height C is nearly to the same level as at t 1 ; for a saline condition the height C will be less. The analysis of the trace in this manner allows for the simultaneous determination of water content and salinity Other methods. The attenuation of a beam of gamma rays of known intensity passed through a soil column is related to the mass of material through which the beam passes. If the soil bulk density remains constant or varies in a known way, the water content may be inferred, or if the water content is known, the soil bulk density may be inferred. This technique has been used primarily in laboratory studies, although a double-tube attenuation unit has been commercially developed for use in the field (Reginato and Van Bavel, 1964). It is potentially accurate but only for carefully controlled conditions. Transient heat pulse measurements have long been used to evaluate soil thermal properties. Water content is closely related to thermal properties. In particular, the volumetric heat capacity, ρ c, is a sum of that due to the water present and the dry soil matrix: ρ c = ρ w θ c w + ρ b c m (6.8) where ρ w = density of the water ρ b = density of the bulk soil θ = volumetric water content c w = mass specific heat of the water c m = mass specific heat of the dry soil. The value of ρ c is found using principles of Fourier heat flow to match temperature rise due to an applied heat pulse. Thus, if the properties of the dry soil are known, then θ follows. A commercially available device is available similar to that described by Bristow et al. (1993).

15 134 Chapter 6 Soil Water Relationships Measuring soil water potential. It is often desirable to measure soil water potential in addition to, or instead of, soil water content. The estimation of soil water potential from water content data via the characteristic curve may not be sufficiently accurate. Tensiometer. Tensiometers are widely used for measuring the higher ranges of soil water potential in the field and laboratory. The name is derived from the term tension that was initially applied to the energy of retention of soil water. Many commercial models are available, or the necessary parts can be purchased and assembled at a significant savings. The theory and use of tensiometers have been discussed by Young and Sisson (2002). Schematic diagrams of tensiometers are shown in Figure 6.8. A tensiometer consists of a porous ceramic cup filled with water and connected through a water-filled tube to a suitable vacuum measuring device. The cup, when saturated with water, must be capable of withstanding air pressures of about 1 bar without leaking air. For normal field applications, the vacuum is measured with a reliable vacuum gauge (Bourdon type). For special conditions where rapid response time is needed, the vacuum measurement is made with pressure transducers and almost no water flow through the cup is required. The pressure transducers can also be used to continuously record the vacuum in the tensiometer, and to read many tensiometers through a switching system. Tensiometers have been used as sensors for automating irrigation systems to maintain a desired soil water range. Tensiometers fitted with a septum and read with a portable pressure transducer attached to a hypodermic needle are also commercially available (see Young and Sisson, 2002). The major criticism of the tensiometer is that it functions reliably only in the wetter soil range at potentials of about 0.8 bar or higher, and its range is limited by the depth Pressure transducer Removable air-tight cap Vacuum guage Barrel Porous cup Figure 6.8. Two types of tensiometer, using a gauge (left) or a pressure transducer (right). With multiple tensiometers, readings may be taken by a single transducer with a needle through septums.

16 Design and Operation of Farm Irrigation Systems 135 of installation. At lower potentials the water inside the tensiometer vaporizes (boils) and readings are not reliable. In drier sandy soils, when hydraulic conductivities are very low, tensiometers may not function properly. Soil water flow away from the cup as the soil dries may be so slow that hydraulic equilibrium with the bulk soil will not be achieved. Under such conditions the bulk soil water potential may be much lower than the tensiometer indicates. If it is necessary to measure water potentials at great depths, tensiometers equipped with integral pressure transducers can be used and only electrical leads need come to the soil surface (Watson, 1967). Porous ceramic blocks. The water content of porous blocks in equilibrium with the soil water may also be used as an approximate measure of soil water potential or soil water content. Two electrodes are imbedded within a gypsum block and the resistance between them measured with an AC ohmmeter (alternating current is used to prevent polarization). Modern resistance blocks utilize an inert material saturated with gypsum. The effect of soil solution salinity levels is masked because the electrolyte within the block is essentially a saturated solution of calcium sulfate. Gypsum blocks are relatively cheap and easy to use. Several companies supply them, as well as inexpensive resistance meters. Even though the accuracy is not good, they do indicate soil water conditions qualitatively and can monitor changes in θ (Topp and Ferre, 2002). Psychrometric methods. A detailed discussion of the use of psychrometry to measure water potential has been given by Andraski and Scanlon (2002). The technique measures the sum of the matric and osmotic potentials. The method most widely adopted for in situ measurement of soil water potential is the measurement of wet-bulb temperature, with a small thermocouple serving as the wet bulb. Water is condensed on the thermocouple by passing a current through it to cool it below the dew point by the Peltier effect. The current is then removed and the wet-bulb temperature is measured. Ambient temperature is also measured with the same thermocouple to allow corrections to be made for temperature effects on the calibration curve. Units are calibrated against potentials of standard solutions. This technique is most useful for measurement of very low potentials, since the dew point temperature is very near to ambient (i.e., high relative humidity) at high potentials. 6.3 SOIL HYDRAULIC CONDUCTIVITY Conductivity and Darcy s Law The basic relationship for describing soil water movement was derived from experiments by Darcy who found in 1856 that the flow rate in porous materials is directly proportional to the hydraulic gradient. This relation was originally set forth by Buckingham (1907), although it is better known as Darcy s law (Swartzendruber, 1969), and may be written as: ΔH q = K (6.9) Δs where q is the volume of water moving through the soil in the s-direction per unit area per unit time and ΔH/Δs is the hydraulic gradient in the same direction. The proportionality factor, K, is the hydraulic conductivity, which depends on properties of both the fluid and the porous medium. H is the hydraulic head which is the sum of the pressure head, h, and the elevation head, z (Section 6.2.2). The negative sign in Equation 6.9 indicates flow is in the direction of decreasing H.

17 136 Chapter 6 Soil Water Relationships Figure 6.9. Unsaturated hydraulic conductivity as a function of water potential (left) and water content (right). As illustrated, K s is less than the fully saturated conductivity since soil naturally traps a small quantity of air within its pores. For a saturated soil K is constant, but for regions of the soil which are only partially saturated the hydraulic conductivity varies significantly with water content, K = K(θ). Since θ is a function of h, we may also write K = K(h). Recall that H = h + z (Section 6.2.2) where z is the vertical distance from the datum. Then for flow in the vertical direction, dh dh q = K( h) + 1 = K ( h) K( h) (6.10) dz dz We noted earlier (Section 6.2.3) that soils are usually not completely saturated in nature because of air entrapment during the wetting process. Thus, even for apparently saturated regions below the water table the volumetric water content may not be equal to total porosity, but to θ s, the water content at residual air saturation. The value of K corresponding to θ s is K s (Figure 6.9, right), which may still be considered constant in regions below the water table and is sometimes referred to as the apparent saturated conductivity. Further discussions will assume K s is effective saturated hydraulic conductivity Measuring Saturated Hydraulic Conductivity Various methods for measuring saturated hydraulic conductivity in the field have been described in detail by Reynolds et al. (2002). There are methods suitable for soils with high water tables, similar to well pumping methods for obtaining aquifer transmissivities, and other methods suitable for unsaturated soils. The reader is referred to Reynolds et al. (2002) or to Bouwer and Jackson (1974) for details concerning these methods. Again all of these methods provide measurement of K s at a point, so, due to field variability, numerous measurements may be required to obtain a field effective K s value. Further, some methods measure the approximate horizontal conductivity, which may differ significantly from the vertical conductivity Unsaturated Hydraulic Conductivity For unsaturated soils the water moves primarily in small pores and through films located around and between solid particles. As the water content decreases, the crosssectional area of the films also decreases and the flow paths become more limited. The

18 Design and Operation of Farm Irrigation Systems 137 result is a hydraulic conductivity function that decreases very rapidly with water content as shown schematically in Figure 6.9(right). Several functions for this relation were given above in Table 6.2. In most cases hysteresis in the K(θ) relationship is small. However, when K = K(h) is used as in Equation 6.10, shown in Figure 6.9(left), hysteresis may be pronounced due to hysteresis in the h(θ) relationship (Figure 6.4) Measuring Unsaturated Hydraulic Conductivity The measurement of unsaturated hydraulic conductivity is considerably more difficult than measuring saturated hydraulic conductivity. Since the K value is dependent on water content, both the hydraulic gradient and water content or potential must be determined for a range of water contents to adequately define the hydraulic conductivity function. Most of the reported measurements for unsaturated soils have been conducted in the laboratory where boundary conditions can be carefully controlled and soil water content and flow rates precisely measured. Field measurements have also been reported but are much more difficult because of the number of variables that must be measured and the variability of soil in the field. A major problem with both field and laboratory methods for determining K(θ) is the time and expense required. Measurement of a single K(θ) function by a well trained technician may require several days. Furthermore, several measurements may be needed to adequately characterize K(θ) for a given soil type because of field variability of the soil properties Laboratory methods. Clothier and Scotter (2002) describe steady state methods for measuring K(θ) based on the defining relationship given in Equation Essentially the method consists of setting up boundary conditions to obtain steady, one-directional flow for adjustable pressure heads. In one method, a soil sample is placed in an airtight cavity between two horizontal porous plates through which water flows into and out of the sample. The average pressure head in the sample is controlled by the air pressure in the cavity. The mean hydraulic gradient between two points in the sample is determined by using tensiometers to measure the difference in pressure head. Alternatively, the potential and the potential gradient may be controlled by changing the elevations of the water source and the outlet. In either case, by measuring the steady state flow rate, q, the conductivity may be calculated directly from Equation 6.9. Then the potential is changed and the procedure repeated for another value of pressure head. Although simple in concept, this method has some disadvantages. Since soil conductivities are small in general, particularly at the lower water contents, long times are required to approach steady flow, especially for imbibition. Also the conductivity function obtained using the above method represents a point determination, or at most a determination for a sampled soil section. In order to incorporate some of the heterogeneities of natural soils in the conductivity function, it is better if conductivity determinations can be made on several rather large soil samples. Transient methods utilize a controlled boundary condition with careful measurements during water movement to infer conductivity relationships by optimization with solution of Richards equations. A good example of such methods is described by Hudson et al. (1996), in which upward flow into a cylindrical soil sample is caused by a fixed flux at the lower boundary, and water content and tension measurements are made with TDR and tensiometer methods, respectively.