81
CHAPTER 8 WATER REQUIREMENTS Richard G. Allen (University of Idaho, Kimberly, Idaho) James L. Wright (USDA-ARS, Kimberly, Idaho) William O. Pruitt (University of California, Davis, California) Luis S. Pereira (University of Lisbon, Lisbon, Portugal) Marvin E. Jensen (USDA-ARS, Fort Collins, Colorado) Abstract. Evapotranspiration (ET) calculation guidelines are based on the crop co- efficient-reference evapotranspiration method (K c ET ref ). Equations for the ASCE- EWRI standardized Penman-Monteith method are provided for grass and alfalfa ref- erences, where the grass reference standardization follows the FAO Penman-Monteith procedure. Linearized FAO-style crop coefficients from FAO-56 and curvilinear coef- ficients from Wright are presented as both mean and as dual (basal) crop coefficients. ET coefficients for landscape utilize a decoupled procedure similar to that summa- rized by the Irrigation Association Water Management Committee. Guidelines for calculating irrigation water requirements and peak system design rates are described. Keywords. Evapotranspiration, Evaporation, Penman, Penman-Monteith, Irriga- tion requirement, Effective precipitation, Crop coefficient, Landscape coefficient. 8.1 INTRODUCTION Evapotranspiration (ET) from vegetation is the primary water requirement for agri- cultural crops. The quantification of ET is necessary for design and sizing of irrigation system components, for operating irrigation and water resources systems, for conduct- ing water balances, and for conducting hydrologic analyses. Many types of systems are available for measuring ET, although direct measurement of ET is generally diffi- cult or expensive. The primary focus of this chapter is estimation of ET using histori- cal or real-time weather data, because design and operation of irrigation systems gen- erally requires long and often continuous records of irrigation water requirements. Most standard, operational procedures for determining ET utilize the crop coeffi- cient (K c )-reference evapotranspiration (ET ref ) approach due to its simplicity, repro- ducibility, relatively good accuracy, and transportability among locations and cli- mates. Two families of K c curves are presented: the linear procedure of the FAO-56 Irrigation and Drainage Paper (Allen et al., 1998) and the curvilinear procedure of

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Page 1: Design and Operation of Farm Irrigation Systemsirrigationtoolbox.com/IrrigationToolBox/Section 2... · Design and Operation of Farm Irrigation Systems 209 Wright (1982). In addition,

CHAPTER 8

WATER REQUIREMENTS Richard G. Allen (University of Idaho,

Kimberly, Idaho) James L. Wright (USDA-ARS,

Kimberly, Idaho) William O. Pruitt (University of California,

Davis, California) Luis S. Pereira (University of Lisbon,

Lisbon, Portugal) Marvin E. Jensen (USDA-ARS,

Fort Collins, Colorado) Abstract. Evapotranspiration (ET) calculation guidelines are based on the crop co-

efficient-reference evapotranspiration method (Kc ETref). Equations for the ASCE-EWRI standardized Penman-Monteith method are provided for grass and alfalfa ref-erences, where the grass reference standardization follows the FAO Penman-Monteith procedure. Linearized FAO-style crop coefficients from FAO-56 and curvilinear coef-ficients from Wright are presented as both mean and as dual (basal) crop coefficients. ET coefficients for landscape utilize a decoupled procedure similar to that summa-rized by the Irrigation Association Water Management Committee. Guidelines for calculating irrigation water requirements and peak system design rates are described.

Keywords. Evapotranspiration, Evaporation, Penman, Penman-Monteith, Irriga-tion requirement, Effective precipitation, Crop coefficient, Landscape coefficient.

8.1 INTRODUCTION Evapotranspiration (ET) from vegetation is the primary water requirement for agri-

cultural crops. The quantification of ET is necessary for design and sizing of irrigation system components, for operating irrigation and water resources systems, for conduct-ing water balances, and for conducting hydrologic analyses. Many types of systems are available for measuring ET, although direct measurement of ET is generally diffi-cult or expensive. The primary focus of this chapter is estimation of ET using histori-cal or real-time weather data, because design and operation of irrigation systems gen-erally requires long and often continuous records of irrigation water requirements.

Most standard, operational procedures for determining ET utilize the crop coeffi-cient (Kc)-reference evapotranspiration (ETref) approach due to its simplicity, repro-ducibility, relatively good accuracy, and transportability among locations and cli-mates. Two families of Kc curves are presented: the linear procedure of the FAO-56 Irrigation and Drainage Paper (Allen et al., 1998) and the curvilinear procedure of

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Design and Operation of Farm Irrigation Systems 209

Wright (1982). In addition, within each family, two types of Kc are defined: mean or time-averaged Kc used for irrigation systems design and general planning, and dual Kc where basal transpiration and evaporation from soil are separated to increase accuracy. Two reference ET types are defined and described: clipped cool-season grass and full-cover alfalfa, since these are both in common usage within the U.S.

Numerous ETref equations have been introduced during the past 50 years. Many of these have been described and evaluated in prior literature (Jensen 1974; Burman et al. 1980; Hatfield and Fuchs, 1990; Jensen et al. 1990). The three reference ET equations described in this chapter are the Penman-Monteith (PM) equation, the classical Pen-man equation and the 1985 Hargreaves equation. These equations are considered to be the most commonly used methods today and are appropriate and applicable to irriga-tion systems design and operation under a wide range of application situations and climates. The PM equation has been standardized to both clipped grass and alfalfa references by ASCE-EWRI (2005), and is considered to be the best method when a full complement of weather data is available (solar radiation, air temperature, humid-ity, and wind speed data). The 1985 Hargreaves equation and the PM equation with estimated weather data are recommended when only air temperature data are avail-able. The FAO-24 pan evaporation method is also useful for situations where good-quality pan evaporation data are measured in conjunction with some weather data. That method is described in Doorenbos and Pruitt (1977), Jensen et al. (1990), and Allen et al. (1998).

Other methods for estimating ET include crop simulation computer models that “grow” and simulate the evaporation and transpiration components of ET separately. These may also simulate the photosynthesis and respiration of plants (Ritchie and Ot-ter, 1985, Jones et al., 1987). Complex ET models include “multi-layer” resistance equations that consider the effects of stomatal, leaf boundary, and aerodynamic char-acteristics for various portions of the plant canopy (Shuttleworth and Wallace, 1985; Dolman, 1993; Huntingford et al., 1995). However, data and time requirements to prepare model parameters for new or localized applications often place these models outside the realm of irrigation systems design and operation. The Kc-ETref method is a tried and true method that empirically incorporates many of the physiological and aerodynamic variables governing crop evapotranspiration. The Kc-ETref method, when applied carefully, can produce estimates of ET that are sufficiently accurate for irriga-tion systems design and operation (Allen et al., 2005c).

8.2 DEFINITIONS Several important quantities are defined in this section. Most of these definitions

are common to agricultural literature. 8.2.1 Evapotranspiration

The term evapotranspiration, abbreviated ET, is defined as the combined process by which water is converted from liquid or solid forms via evaporation from soil and wet plant surfaces and via evaporation of water from within plant tissue. The latter process is known as transpiration. ET can be expressed as the energy consumed as latent heat energy per unit area (and denoted as LE) or as the equivalent depth of evaporated water. Units for ET are typically mm t-1 where t denotes a time unit (hour, day, month, growing season, or year) and units for LE are typically W m-2 or MJ m-2 t-1.

The term reference evapotranspiration has been used as a standardized and repro-ducible index approximating the climatic demand for water vapor and is generally

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210 Chapter 8 Water Requirements

abbreviated ETref. Reference ET is the ET rate from an extensive surface of reference vegetation having a standardized uniform height and that is actively growing, com-pletely shading the ground, has a dry but healthy and dense leaf surface, and is not short of water. This definition is applied to the standardized reference crops of grass (ETo) and alfalfa (ETr).

The advantage of using the reference concept is that it enables the measurement and validation of estimated reference ET using living, standardized crops. In addition, because stomatal control of the alfalfa reference crop approximates that of most agri-cultural crops at full cover, ET from the reference crop is more like crop ET than is potential ET (Pereira et al., 1999).

Crop evapotranspiration, abbreviated ETc, is defined as the rate of ET from an ex-tensive surface of a specific crop. The ETc rate is influenced by crop growth stages, amount and frequency of wetting of the soil surface, environmental conditions, and crop management. Crop ET is usually less than about 1.3 ETo or 1.0 ETr when crop foliage does not completely shade the ground or when the crop has begun to mature and senesce.1 Crop ET may exceed ETo when the crop has substantially more leaf area, is taller, or has less stomatal control as compared to the clipped grass reference, or has a wet leaf or soil surface. Crop ET is normally expressed in units of mm h-1, mm d-1, mm month-1, or mm season-1, and is synonymous with the term consumptive use. ETc representing ET under any condition, ideal or nonideal, is termed “actual ETc” and is denoted as ETc act.

The “extensive surface” in the definition of ETc and calculation methodologies im-plies that the crop covers a large enough area that the energy exchange at the crop sur-face, and the wind speed, temperature and humidity profiles above the crop, are in equilibrium. Only when this equilibrium exists do energy-based flux-profile equations such as the Penman and Penman-Monteith equations attain the highest accuracy. The extensive surface condition applies to field sizes having dimensions greater than about 200 m (equivalent to 4 ha or 10 acres).

Landscape evapotranspiration, abbreviated ETL, is ET from residential and urban landscapes. Procedures for estimating ETL are similar to those for ETc, with two dis-tinctions: (1) landscape systems are nearly always comprised of a mixture of multiple types and species of vegetation, thereby complicating the estimation of the landscape coefficient and ET; and (2) typically, the objective of landscape irrigation is to pro-mote appearance rather than biomass production as is the case in agriculture. There-fore, target ET for landscape may include an intentional “stress” factor in the baseline value for ETc act. This adjustment can result in significant water conservation. A multi-component approach for estimating ETL is described that covers a wide range of land-scape vegetation and environmental conditions. This approach is similar to that adopted by the Irrigation Association (2003).

8.2.2 Effective Precipitation Effective precipitation, abbreviated Pe, was defined by Dastane (1974) in the con-

text of irrigation water management as precipitation that “is useful or usable in any phase of crop production.” This definition implies that precipitation must infiltrate and remain resident in the effective root zone of a cropped field long enough to be ex- 1 Senescence describes the natural aging process of leaves whereby leaves begin to yellow and die, and stomatal function and exchange of carbon dioxide and water vapor reduce. Senescence may be accelerated by environmental stresses such as disease and water shortage.

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Design and Operation of Farm Irrigation Systems 211

tracted by crop roots during the ET process or where evaporation from wet soil re-duces some transpiration demand. Effective precipitation is discussed further in Sec-tions 8.10 and 8.12, and in the context here includes evaporation from soil incidental to production agriculture and irrigation.

8.2.3 Irrigation Water Requirements The designer or operator of an irrigation system most frequently estimates irriga-

tion water requirements (IR) for short periods and on a seasonal basis. Short-term es-timates are needed for systems sizing and for day to day operations. Seasonal esti-mates are needed for allocation of water supplies and in water rights administration. The units for IR are often expressed as volume per unit area per unit time (for exam-ple, m3 ha-1 d-1) or as depth per unit time (for example, mm d-1). The “net” irrigation water requirement, abbreviated IRn, is defined as the depth of water needed to fulfill the ET requirement in excess of any effective precipitation for a disease-free crop growing in large fields under non-restricting soil and soil water conditions and under adequate fertility. In addition, IRn considers contributions of shallow ground water (GW) and change in stored soil water during the period of interest. In equation form:

secn zGWPETIR θΔ−−−= (8.1) where Pe = effective precipitation during the period of calculation

Δθ = change in soil water content in the root zone during the period of calculation

zs = depth of soil experiencing the change in water content. Units for all terms are the same. In essence, IRn is the beneficially consumed portion of an irrigation application.

The “gross” irrigation water requirement, abbreviated IR, includes the water re-quired for the IRn in addition to water for leaching salts and to satisfy delivery and field system losses. Delivery system losses include spillage and seepage. Field system losses include surface runoff and deep percolation. In equation form:

CFLR)

zGWPETCFLR

IRIR secn

−−−=

−=

1(Δ

)(1θ

(8.2)

where LR is the leaching requirement (a fraction) and CF is the consumed fraction of applied water, generally equivalent to the so-called “irrigation efficiency.” Usually, LR is considered only when irrigation uniformity is high. Under low to moderate uniform-ity, deep percolation incidental to irrigation is often sufficient to fulfill LR. Calculation of the leaching requirement is described in Chapter 7.

8.3 DIRECT MEASUREMENTS System designers and operators obtain ET data from either direct field measure-

ments or from estimates that are based on weather and crop data. Use of direct, real-time field measurements for ET in design and operation is rare due to the expense and operation and maintenance requirements of equipment. Direct measurements are pri-marily used to provide data for calibrating climatic and weather-based ET methods and for monitoring soil water conditions.

Although direct measurements are essential for ET equation development or validation, the user must exercise caution when using these systems, data collected by these systems, and also coefficients calibrated from such data. Errors involved can be subtle, yet large. For example, eddy covariance data are prone to under-measurement by up to 30% (Twine

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212 Chapter 8 Water Requirements

et al., 2000; Wilson et al., 2002). Bowen ratio (BR)-based estimates are prone to error and bias in net radiation and soil heat flux measurements (Payero et al., 2003). Both LE and BR estimates are sensitive to instrument siting relative to the roughness sublayer and evaporative footprint. Users should familiarize themselves with the problems as-sociated with design, installation, maintenance, and operation of direct ET measuring devices that may influence the values and integrity of direct ET measurement data.

One caution on measurement of ET is that measurements must represent conditions for which the data are applied. For irrigation systems design, measurements should be from or representative of ET from large expanses of vegetation where the ET process is essentially one-dimensional (upward). ET measurements should not be made from small groups of plants that are spatially isolated. Spatial isolation can increase transfer of heat and radiation energy from outside the measured group of plants to the plants, thereby increasing measured ET and making it unrepresentative of ET from large fields (Pruitt and Lourence, 1985; Meyer and Mateos, 1990; Pruitt, 1991; Allen et al., 1991b; Grebet and Cuenca, 1991).

The reader is referred to other literature sources for background and description of various measurement methods, including lysimeters: WMO (1966), Tanner (1967), Aboukhaled et al. (1982), Pruitt and Lourence (1985), Allen et al. (1991a), and Howell et al. (1991); eddy covariance: Swinback (1951), Businger et al. (1967), Brutsaert (1982), Campbell and Tanner (1985), Tanner (1988), Twine et al. (2000), Wilson et al. (2002), and Munger and Loescher (2004); and Bowen ratio: Sellers (1965), Tanner (1967), Blad and Rosenberg (1974), Dyer (1974), Sinclair et al. (1975), Brutsaert (1982), Pruitt et al. (1987), and Payero et al. (2003).

8.4 ESTIMATION OF REFERENCE ET Evaporation of water requires relatively large amounts of energy obtained either

from transfer of sensible heat from the air stream or from radiant energy. Therefore, the ET process is largely governed by energy exchange at the vegetation surface and is limited by the amount of energy available. Because of this limitation, it is possible to estimate the rate of ET based on a net balance of energy fluxes. This is the basis for the Penman and Penman-Monteith equations.

8.4.1 Reference Evapotranspiration Two types of reference crops have been widely applied. These are clipped, cool-

season grass, such as fescue and perennial ryegrass, and full-cover alfalfa. Reference ET for clipped grass is commonly denoted as ETo and reference ET for alfalfa is com-monly denoted as ETr.

8.4.2 Standardized Definitions and the Penman-Monteith Method Grass reference ETo was defined in FAO-24 (Doorenbos and Pruitt, 1977) as “the

rate of evapotranspiration from an extensive surface of 8 to 15 cm tall, green grass cover of uniform height, actively growing, completely shading the ground and not short of water.” It is generally accepted that the grass reference crop is a “cool-season,” C-3 type of grass with roughness, density, leaf area, and bulk surface resis-tance characteristics similar to perennial ryegrass (Lolium perenne L.) or Alta fescue (Festuca arundinacea Schreb. ‘Alta’).

Alfalfa reference ETr was defined by Wright and Jensen (1972) as: “... ET from well watered, actively growing alfalfa with 8 in. (20 cm) or more of growth ...” and by Wright (1982) as “... when the alfalfa crop was well watered, actively growing, and at

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Design and Operation of Farm Irrigation Systems 213

least 30 cm tall; so that measured ET was essentially at the maximum expected level for the existing climatic conditions.” The height of alfalfa (Medicago sativa L., v. Ranger) in the data set used to develop the 1982 Kimberly Penman (Wright, 1982) and used in developing resistance algorithms for the Penman-Monteith method (Allen et al., 1989) ranged from about 0.15 to 0.80 m in height and averaged 0.47 m (unpub-lished data from Wright, 1985).

Generally, ETr is about 1.1 to 1.4 times that of ETo due to the increased roughness and leaf area of alfalfa. The higher value (1.4) represents the ratio of ETr to ETo under extremely arid and windy conditions (minimum daytime relative humidity [RH] < 20% and wind speed > 5 m s-1 [11 mph]) and the lower value (1.1) represents the ratio of ETr to ETo under humid, calm conditions. Wright (referenced in Jensen et al. (1990), Table 6.9) has measured an average ratio of ETr to ETo at Kimberly, Idaho, equal to about 1.25. This value represents conditions common to the semiarid moun-tain states in the U.S.

Because of the challenges in growing and maintaining a living reference crop, the PM equation has been used by the Food and Agriculture Organization (FAO) (Smith et al., 1991, 1996; Allen et al., 1998) and ASCE-EWRI (2005) to represent a fixed definition for ETo. The FAO definition for ETo in terms of the PM equation is “the rate of evapotranspiration from a hypothetical reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s m-1 and an albedo of 0.23, closely resem-bling the evapotranspiration from an extensive surface of green grass of uniform height, actively growing, completely shading the ground and with adequate water” (Allen et al. 1998). ASCE-EWRI (2005) has adopted this same definition for stan-dardization of ETo, with the provision for lower surface resistance (50 s m-1), when calculating on hourly or shorter timesteps. This lower resistance for hourly calcula-tions has subsequently been adopted by FAO (Allen et al., 2006). ASCE-EWRI addi-tionally defined a standardized ETr for the alfalfa reference, also based on the PM, where the standardized height is 0.5 m.

The ASCE-EWRI (2005) standardized PM method has the form:

)1(

)(273

)(Δ408.0

2

2

uC

eeuT

CGRET

d

asn

n

ref ++

−+

+−=

γΔ

γ (8.3)

where ETref = standardized reference ET for short (ETos) or tall (ETrs) surfaces, mm d-1 for daily timesteps or mm h-1 for hourly timesteps

Rn = calculated net radiation at the crop surface, MJ m-2 d-1for daily timesteps or MJ m-2 h-1 for hourly timesteps

G = soil heat flux density at the soil surface, MJ m-2 d-1 for daily timesteps or MJ m-2 h-1 for hourly timesteps

T = mean daily or hourly air temperature at 1.5 to 2.5-m height, °C u2 = mean daily or hourly wind speed at 2-m height, m s-1 es = saturation vapor pressure at 1.5- to 2.5-m height, kPa, calculated for daily

timesteps as the average of saturation vapor pressure at maximum and minimum air temperature

ea = mean actual vapor pressure at 1.5 to 2.5-m height, kPa Δ = slope of the saturation vapor pressure-temperature curve, kPa °C-1 γ = the psychrometric constant, kPa °C-1

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214 Chapter 8 Water Requirements

Table 8.1. Values for Cn and Cd in Equation 8.3 (from ASCE-EWRI, 2005). Short Reference,

ETos (clipped grass)

Tall Reference, ETrs

(alfalfa) Calculation Timestep Cn Cd Cn Cd

Units forETos, ETrs

Units forRn, G

Daily 900 0.34 1600 0.38 mm d-1 MJ m-2 d-1

Hourly during daytime 37 0.24 66 0.25 mm h-1 MJ m-2 h-1

Hourly during nighttime 37 0.96 66 1.7 mm h-1 MJ m-2 h-1

Cn = a numerator constant that changes with reference type and calculation time

step, K mm s3 Mg-1 d-1 or K mm s3 Mg-1 h-1 Cd = a denominator constant that changes with reference type and calculation

timestep, s m-1. Table 8.1 provides values for Cn and Cd. The values for Cn consider the timestep

and aerodynamic roughness of the surface (i.e., reference type). The constant in the denominator, Cd, considers the timestep, bulk surface resistance, and aerodynamic roughness of the surface. Cn and Cd were derived by simplifying several terms within the ASCE PM equation of ASCE Manual 70 (Allen et al., 1989; Jensen et al., 1990) and rounding the result. Units for the 0.408 coefficient are m2 mm MJ-1. Daytime is defined as occurring when Rn during an hourly period is positive. The ASCE-EWRI definition uses smaller values for surface resistance for hourly or shorter calculation timesteps (during daytime) than for daily calculation timesteps. The FAO-PM (Allen et al., 1998) is equivalent to Equation 8.3, where Cn = 900 and Cd = 0.34. ASCE-EWRI (2005) and Allen et al. (2006) recommended applying the FAO-PM equation for ETo using the Cn and Cd coefficients for hourly and shorter calculation timesteps in Table 1. Daily ETref are obtained by summing ETref values from hourly or shorter peri-ods or by applying the ETref equations on a 24 h-timestep. Generally, summing hourly calculations is considered to be more accurate. ASCE-EWRI recommended applica-tion of ETos and ETrs for calculating reference evapotranspiration and development of new crop coefficients, and for facilitating transfer of crop coefficients.

8.4.3 The Classical Penman Equation

Besides the standardized Penman-Monteith equation that is now recommended by FAO (Allen et al., 1998) and by ASCE-EWRI (2005), some forms of the original Penman equation (Penman, 1948) are still in use that perform similarly to the ASCE PM. The classical form of the Penman equation is:

( ) ) ( ) + ( +

+ +

4080 = 2 eeubaKGR.ET aswwwnref −−γΔ

γγΔ

Δ (8.4)

where terms and definitions are the same as those used for the PM equation in Equa-tion 8.3. Parameter Kw is a units parameter, with Kw = 2.62 for ETref in mm d-1 and Kw = 0.109 for ETref in mm hour-1. The aw and bw terms are empirical wind coefficients that have often been locally or regionally calibrated. The values for aw and bw were 1.0 and 0.537, respectively, in the original Penman equation (Penman, 1948, 1963) for grass ETo, for wind speed in m s-1, (es – ea) in kPa and ETo in mm d-1. Generally, local calibration of the Penman method is neither required nor recommended and was often an artifact of earlier studies required to overcome biases or faulty measurements in

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Design and Operation of Farm Irrigation Systems 215

weather and ET data. Currently the commonly used Penman values for aw and bw are those for the hourly CIMIS Penman method for ETo and daily 1982 Kimberly Penman method for ETr.

8.4.3.1 CIMIS Penman equation for grass reference. Pruitt (Pruitt and Dooren-bos 1977a; Pruitt et al., 1984; Snyder and Pruitt, 1992) developed aw and bw for esti-mating grass ETo for hourly periods. These coefficients have been used since the 1980s for standard ETo estimation in the California Irrigation Management Informa-tion Service (CIMIS). The CIMIS Penman ETo equation uses aw = 0.29 and bw = 0.53 for Rn > 0, and aw = 1.14 and bw = 0.40 for Rn < 0, and is applied hourly, where in Equation 8.4, ETo = mm h-1, Rn = MJ m-2 h-1, and Kw = 0.109. Standard CIMIS calcula-tions assume G = 0. When applied hourly, ETo from the CIMIS Penman equation is summed over 24-h periods to obtain daily totals, similar to what is done using the PM method.

8.4.3.2 1982 Kimberly-Penman alfalfa reference. The 1982 Kimberly-Penman equation was developed from intensive studies of ET using precision weighing lysime-ters at Kimberly, Idaho (Wright and Jensen 1972; Wright, 1981, 1982, 1988) and is intended for application with 24-hour timesteps (Kw = 2.62 in Equation 8.4). The Kim-berly-Penman wind function is calibrated to estimate ET from full-cover alfalfa, where the aw and bw wind function coefficients vary with time of year (Jensen et al. 1990):

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

− J . + .aw 58173 exp4140 =

2 (8.5)

J . + .bw⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−80

243exp34506050 = 2

(8.6)

where J is the day of the year. For latitudes south of the equator, Equation 8.5 and 8.6 are applied using J' in place of J, where J' = (J – 182) for J ≥ 182 and J' = (J + 182) for J < 182. The (es – ea) term in the 1982 Kimberly Penman is computed the same as for the standardized PM equation (as the average of es computed at daily maximum and minimum temperatures; Equation 8.7).

8.4.4 Computation of Parameters for the Penman-Monteith and Penman Equations

It is recommended that standardized procedures and equations be used to calculate parameters in ETref equations. This insures agreement among independent calculations and simplifies calculation verification. Equations presented in this section follow pro-cedures standardized by FAO-56 and ASCE-EWRI (2005).

8.4.4.1 Saturation vapor pressure of the air. For 24-hour or longer calculation timesteps, es, the saturation vapor pressure of the air, is computed as:

2

)()( oo Te + Te = e minmaxs (8.7)

where Tmax and Tmin are daily maximum and minimum air temperature, °C, at the measurement height (1.5 to 2 m), and e° is the saturation vapor pressure function. For hourly applications, es is calculated as e°(T) where T is average hourly air temperature.

The saturation vapor pressure function is:

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216 Chapter 8 Water Requirements

⎟⎠⎞

⎜⎝⎛

237.317.27exp 0.6108)(oT+

T = Te (8.8)

where e°(T) is in kPa and T is in °C (Tetens, 1930). 8.4.4.2 Actual vapor pressure of the air. Actual vapor pressure of the air, ea, is

equivalent to saturation vapor pressure at the dew point, Td. For 24-h or longer timesteps, Td is taken as mean daily or early morning dewpoint temperature, °C. Hu-midity of the air can be measured using many different methods, including relative humidity sensors, dewpoint sensors, and wet bulb/dry bulb psychrometers, so that ea can be calculated using several ways. The recommended procedures, in order of what are considered to be the most reliable to the least reliable, are (ASCE-EWRI, 2005):

1. For 24-h periods, averaging ea measured or computed hourly over the 24-h pe-riod.

2. For 24-h periods, calculating ea from dewpoint, Td, that is measured or computed hourly over the 24-h period:

⎟⎟⎠

⎞⎜⎜⎝

⎛3237

2717exp 61080 = = o. + T

T . .)T(e ed

dda (8.9)

where ea is in kPa and Td is in °C. 3. Psychrometer measurements using dry and wet bulb thermometers, where

(Bosen, 1958):

( ) ( )wetdrypsyweta TTTee −−= γo (8.10)

where e°(Twet) is saturation vapor pressure at the wet bulb temperature in kPa (Equation 8.8), γpsy is the psychrometric constant for the psychrometer, in kPa °C-1, and Tdry – Twet is the wet bulb depression, where Tdry is dry bulb tempera-ture and Twet is the wet bulb temperature, both in °C. For 24-h periods, Tdry and Twet are preferably averaged over the 24-h period. Alternatively, once-per-day readings of Tdry and Twet can be used, for example, readings taken at 7 or 8 a.m. Tdry and Twet must be measured simultaneously.

The psychrometric constant for the psychrometer is:

Pa psypsy =γ (8.11)

where apsy is a coefficient depending on the type of ventilation of the wet bulb, in °C-1, and P is the mean atmospheric pressure, in kPa. The coefficient apsy de-pends primarily on the design of the psychrometer and on the rate of ventilation around the wet bulb. The following values are often used:

apsy = 0.000662 for ventilated (Asmann type) psychrometers having air move- ment between 2 and 10 m s-1 for Twet > 0 and 0.000594 for Twet < 0 = 0.000800 for naturally ventilated psychrometers having air movement of about 1 m s-1 = 0.001200 for non-ventilated psychrometers installed in glass or plastic greenhouses.

4. For 24-hour or longer timesteps, relative humidity (RH) measurements taken twice daily (early morning, corresponding to Tmin and early afternoon, corre-sponding to Tmax) can be combined to yield an approximation for 24-hour aver-age ea:

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Design and Operation of Farm Irrigation Systems 217

( ) ( )

2100100

oo minmax

maxmin

a

RHTeRHTee

+=

(8.12)

where RHmax is daily maximum relative humidity (%) (during early morning), and RHmin is daily minimum relative humidity (%) (during early afternoon, around 1400 hours).

For hourly calculations, ea is calculated from relative humidity as:

)(100

o TeRHea = (8.13)

where RH is mean relative humidity for the hourly or shorter period, %, and T is mean air temperature for the hourly or shorter period, °C.

5. From daily RHmax and Tmin:

( )

100o max

minaRH

Tee = (8.14)

6. From daily RHmin and Tmax:

( )

100o min

maxaRH

Tee = (8.15)

7. If daily humidity data are missing or are of questionable quality, ea can be ap-proximated for the reference environment assuming that Td is near Tmin:

omind KTT −= (8.16)

where Ko is approximately 2° to 4°C in dry seasons in semiarid and arid climates and Ko is approximately 0°C in humid to subhumid climates and the rainy sea-son in semi-arid climates (ASCE-EWRI, 2005).

8. In the absence of RHmax and RHmin data, but where daily mean RH data are avail-able, ea can be estimated as:

( )eanmmean

a Te RH

e o100

= (8.17)

where RHmean is mean daily relative humidity, generally defined as the average between RHmax and RHmin, and Tmean is mean daily air temperature. For daily or longer periods, Equation 8.17 is generally less desirable than methods 1-7 for calculating ea because the e°(T) relationship is nonlinear.

8.4.4.3 Psychrometric constant. The psychrometric constant (γ) in the Penman and PM equations is calculated as (Brunt, 1952): P000665.0 = γ (8.18)

where P has units of kPa and γ has units of kPa °C-1. 8.4.4.4 Atmospheric pressure. For purposes of ET estimation, mean atmospheric

pressure, P, can be based on elevation using an equation simplified from the universal gas law relationship (Burman et al., 1987, ASCE-EWRI, 2005):

( )z5-. = P 3400.0004062 5.26 (8.19)

where P has units of kPa and z is the weather site elevation (m) above mean sea level.

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218 Chapter 8 Water Requirements

8.4.4.5 Slope of the saturation vapor pressure-temperature curve. The slope of the saturation vapor pressure-temperature curve, Δ, is computed as:

( )2237.3

237.317.27exp2503

+T

+TT

= ⎟⎟⎠

⎞⎜⎜⎝

Δ (8.20)

where Δ has units of kPa °C-1 and T is daily or hourly mean air temperature in °C. 8.4.4.6 Wind speed at 2 meters. Wind speed varies with height above the ground

surface. For the calculation of standardized ETref, the wind speed measurement must be made equivalent to that 2 m above the surface. Therefore, wind measured at other heights is adjusted by:

)425867(ln

8742 .z.

.uuw

z −= (8.21)

where u2 = wind speed at 2 m above ground surface, m s-1 uz = measured wind speed at zw m above ground surface, m s-1 zw = height of wind measurement above the ground surface, m.

Equation 8.21 is used for measurements taken above a short grass (or similar) surface, based on the logarithmic wind speed profile equation. For wind measurements made above surfaces other than clipped grass, the user should apply a full logarithmic equa-tion that considers the influence of vegetation height and roughness on the shape of the wind profile. These alternative adjustments are described in Allen and Wright (1997) and ASCE-EWRI (2005). Wind speed data collected at heights above 2 m are acceptable to use in the standardized equations following adjustment to 2 m, and are preferred if vegetation adjacent to the weather station commonly exceeds 0.5 m. Measurement at a greater height, for example 3 m, reduces the influence of the taller vegetation surrounding the weather measurement site.

8.4.4.7 Net radiation. Net radiation, Rn, in the context of ET, is the net amount of radiant energy available at a vegetation or soil surface for evaporating water, heating the air, or heating the surface. Rn includes both short and long wave radiation compo-nents. Net radiation flux density can be measured directly using hemispherical net radiometers. However, measurement is difficult because net radiometers are problem-atic to maintain and calibrate, creating the likelihood of systematic biases. Therefore, Rn is often estimated from observed short wave (solar) radiation, vapor pressure, and air temperature. This estimation is routine and generally highly accurate for well de-fined vegetated surfaces. If Rn is measured, then care and attention must be given to the calibration of the radiometer, the surface over which it is located, maintenance of the sensor domes, and level of the instrument. The condition of the vegetation surface is as important as the sensor. For purposes of calculating reference ET, the measure-ment surface for Rn is generally assumed to be clipped grass or alfalfa at full cover.

When calculated, Rn is estimated from the short wave and long wave components: Rn = Rns – Rnl (8.22) where Rns is net short-wave radiation (in MJ m-2 d-1 or MJ m-2 h-1), defined as being positive downwards and negative upwards, and Rnl is net outgoing long-wave radiation (in MJ m-2 d-1 or MJ m-2 h-1), defined as being positive upwards and negative down-wards. Rns and Rnl are generally positive or zero in value.

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Design and Operation of Farm Irrigation Systems 219

Net short-wave radiation resulting from the balance between incoming and re-flected solar radiation is given by: sssns RRRR )1( αα −=−= (8.23)

where α is albedo, fixed in the ASCE-EWRI standardization at 0.23 for both daily and hourly timesteps (dimensionless), and Rs is incoming solar radiation (MJ m-2 d-1 or MJ m-2 h-1). Users may elect to use a different estimation for albedo; however, it is essen-tial to ascertain the validity and accuracy of an alternative method using good meas-urements of incoming and reflected solar radiation.

The standardized procedure of FAO-56 and ASCE-EWRI for estimating Rnl is based on the Brunt (1932, 1952) approach for estimating net emissivity. Users may choose to utilize a different approach for calculating Rnl; however, as with albedo it is essential to ascertain the validity and accuracy of the Rn method using net radiometers in excellent condition and that are calibrated to some dependable and recognized stan-dard. Rnl, net long-wave radiation, is the difference between upward long-wave radia-tion from the standardized surface (Rlu) and downward long-wave radiation from the sky (Rld), so that Rnl = Rlu – Rld. The ASCE-EWRI procedure for daily Rnl is:

daily ( )⎥⎥⎦

⎢⎢⎣

⎡ +−=

214.034.0

44minKmaxK

acdnlTT

efR σ (8.24)

and for hourly Rnl is: hourly ( ) 414.034.0 hrKacdnl TefR −= σ (8.25)

where Rnl = net outgoing long-wave radiation, MJ m-2 d-1or MJ m-2 h-1 σ = Stefan-Boltzmann constant, 4.901 × 10-9 MJ K-4 m-2 d-1 or 2.042 ×

10-10 MJ K-4 m-2 h-1 fcd = a cloudiness function (dimensionless) and limited to 0.05 < fcd < 1.0 (see

below) ea = actual vapor pressure , kPa TK max = maximum absolute temperature during the 24-hour period, K (recall

that K = °C + 273.15) TK min = minimum absolute temperature during the 24-hour period, K TK hr = mean absolute temperature during the hourly period, K.

The superscripts “4” in Equations 8.24 and 8.25 indicate the need to raise the air tem-perature, expressed in Kelvin units, to the power of 4.

For daily and monthly calculation timesteps, fcd is calculated as:

35.035.1 −=so

scd R

Rf (8.26)

Rs is measured or calculated solar radiation and Rso is calculated clear-sky radiation, both in MJ m-2 d-1. The relative solar radiation, Rs/Rso, represents relative cloudiness and is limited to 0.3 < Rs /Rso < 1.0 so that fcd has limits of 0.05 < fcd < 1.0.

For hourly periods during daytime when the sun is more than about 15° above the horizon, fcd is calculated using Equation 8.26 with the same limits applied. For hourly periods during nighttime, Rso, by definition, equals 0, and Equation 8.26 is undefined. Therefore, fcd during periods of low sun angle and during nighttime is defined using fcd

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220 Chapter 8 Water Requirements

from prior periods. When sun angle2 (β) above the horizon at the midpoint of the hourly or shorter time period is less than 0.3 radians (~17°), then: fcd = fcd β >0.3 (8.27) where fcd β >0.3 is the cloudiness function (dimensionless) for the time period prior to when sun angle β (in the afternoon or evening) falls below 0.3 radians.

If the calculation timestep is shorter than one hour, then fcd from several periods can be averaged into fcd β >0.3 to obtain a representative average value. In mountain valleys where the sun may set near or above 0.3 radians (~17°), the user should increase the sun angle at which fcd β >0.3 is computed and imposed. For example, for a location where mountain peaks are 20° above the horizon, a period should be selected for com-puting fcd β >0.3 where the sun angle at the end of the time period is 25° to 30° above the horizon. The same adjustment is necessary when deciding when to resume computa-tion of fcd during morning hours when mountains lie to the east.

Only one value for fcd β >0.3 is calculated per day for use during dusk, nighttime, and dawn periods. That value for fcd β >0.3 is then applied to the time period when β at the midpoint of the period first falls below 0.3 radians (~17°) and to all subsequent peri-ods until after sunrise when β again exceeds 0.3 radians.

Equations 8.26 and 8.27 will not apply at latitudes and times of the year when there are no hourly (or shorter) periods having sun angle of 0.3 radians or greater. These situations occur at latitudes of 50° for about one month per year (in winter), at lati-tudes of 60° for about five months per year, and at latitudes of 70° for about seven months per year (ASCE-EWRI, 2005). Under these conditions, the application can average fcd β> 0.3 from fewer time periods or, in the absence of any daylight, can assume a ratio of Rs/Rso ranging from 0.3 for complete cloud cover to 1.0 for no cloud cover. Under these extreme conditions, the estimation of Rn is only approximate.

The application of Equation 8.27 presumes that cloudiness during periods of low sun angle and nighttime is similar to that during late afternoon or early evening. This is generally a reasonable assumption and is commensurate with the relative simplicity and moderate accuracy of the procedure.

8.4.4.8 Clear-sky solar radiation (Rso). Clear-sky solar radiation (Rso) is used in the calculation of net radiation (Rn). Rso is defined as the amount of short-wave radia-tion that would be received at the weather measurement site under conditions of clear-sky (i.e., cloud-free). Daily Rso is a function of the time of year and latitude and is im-pacted by station elevation (affecting atmospheric thickness and transmissivity), the amount of precipitable water in the atmosphere (affecting the absorption of some short-wave radiation), and the amount of dust or aerosols in the air. Rso, for purposes of calculating Rn, can be computed as: Rso = (0.75 + 2 × 10-5 z) Ra (8.28) where z is station elevation above sea level in m. More complex estimates for Rso, which include impacts of turbidity and water vapor on radiation absorption, can be used for assessing integrity of solar radiation data and are described in Appendix D of ASCE-EWRI (2005). 2 The sun angle β is defined as the angle of a line from the measurement site to the center of the sun’s disk relative to a line from the measurement site to directly below the sun and tangent to the earth’s surface. This definition assumes a flat surface.

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Design and Operation of Farm Irrigation Systems 221

8.4.4.9 Exoatmospheric radiation. Exoatmospheric radiation, Ra, (also known as extraterrestrial radiation) is defined as the short-wave solar radiation in the absence of an atmosphere, and is a well-behaved function of the day of the year, time of day, and latitude. Ra is needed for calculating Rso, which is in turn used in calculating Rn. For daily (24-hour) periods, Ra is estimated from the solar constant, the solar declination, and the day of the year:

[ ])sin()cos()cos()sin()sin(24ssrsca dG

πR ωδϕδϕω += (8.29)

where Ra = exoatmospheric radiation, MJ m-2 d-1 Gsc = solar constant, 4.92 MJ m-2 h-1 dr = inverse relative distance factor (squared) for the earth-sun, unitless ωs = sunset hour angle, radians ϕ = station latitude, radians, positive for the northern hemisphere and negative

for the southern hemisphere δ = solar declination, radians.

Parameters dr and δ are calculated as:

⎟⎠⎞

⎜⎝⎛

+= Jdr 365π2cos033.01 (8.30)

⎟⎠⎞

⎜⎝⎛

−= 39.1365π2sin409.0 Jδ (8.31)

where J is the number of the day in the year between 1 (1 January) and 365 or 366 (31 December). The constant 365 in Equations 8.23 and 8.24 is held at 365 even during a leap year. J can be calculated as:

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ .YM

M9M + DJ M 9750 +

4)4 ,( Mod -

100 Int +

1 +3Int 2 + 275 Int 32 - = (8.32a)

where DM is the day of the month (1-31), M is the number of the month (1-12), and Y is the number of the year (for example 1996 or 96). The “Int” function in Equation 8.32 finds the integer number of the argument in parentheses by rounding downward. The “Mod(Y,4)” function finds the modulus (remainder) of the quotient Y/4.

For monthly periods, the day of the year at the middle of the month (Jmonth) is ap-proximately: )MJmonth 154.30Int( −= (8.32b)

The sunset hour angle, ωs, is given by:

[ ])(tan)(tanarccos δϕω −=s (8.33)

The “arccos” function is the arc-cosine function and represents the inverse of the co-sine. This function is not available in all computer languages, so that ωs can alterna-tively be computed using the arc-tangent (inverse tangent) function:

⎥⎦

⎤⎢⎣

⎡−−= 5.0

)tan()tan(arctan2π

Xs

δϕω (8.34)

where [ ] [ ]22 )(tan)(tan1 δϕ−=X (8.35)

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222 Chapter 8 Water Requirements

0if000010and ≤= X.X

For hourly time periods, the solar time angle at the beginning and end of the period serve as integration endpoints for calculating Ra:

( )[ ])sin()sin()cos()cos()sin()sin()(π

121212 ωωδϕδϕω −+−= ωdGR rsca (8.36)

where Ra = exoatmospheric radiation, MJ m-2 hour-1 Gsc = solar constant, 4.92 MJ m-2 h-1 ω1 = solar time angle at beginning of period, radians ω2 = solar time angle at end of period, radians.

ω1 and ω2 are given by 24π 1

1t

−= ωω (8.37)

24π 1

2t

+= ωω (8.38)

where ω is solar time angle at the midpoint of the period (radians), and tl is the length of the calculation period (hour): i.e., 1 for hourly periods or 0.5 for 30-minute periods. The solar time angle at the midpoint of the hourly or shorter period is:

}12])(06667.0{[12π

−+−+= cmz SLLtω (8.39)

where t = standard clock time at the midpoint of the period (hour) after correcting time for any daylight savings shift. For example, for a period between 1400 and 1500, t = 14.5 hours.

Lz = longitude of the center of the local time zone, expressed as positive degrees west of Greenwich, England. In the U.S., Lz = 75°, 90°, 105°, and 120° for the Eastern, Central, Rocky Mountain, and Pacific time zones, respectively, and Lz = 0° for Greenwich, 345° for Paris, France, and 255° for Bangkok, Thailand.

Lm = longitude of the solar radiation measurement site, expressed as positive degrees west of Greenwich, England

Sc = a seasonal correction for solar time, hours. Because ωs is the sunset hour angle and –ωs is the sunrise hour angle (noon has ω =

0), values of ω < –ωs or ω > ωs from Equation 8.39 indicate that the sun is below the horizon, so that, by definition, Ra and Rso are zero and their calculation has no mean-ing. When the values for ω1 and ω2 span the value for –ωs or for ωs, this indicates that sunrise or sunset occurs within the hourly (or shorter) period. In this case, the integration limits for applying Equation 8.36 should be correctly set using the following conditionals: If ω1 < –ωs then ω1 = –ωs

If ω2 < –ωs then ω2 = –ωs (8.40)

If ω1 > ωs then ω1 = ωs

If ω2 > ωs then ω2 = ωs

If ω1 > ω2 then ω1 = ω2

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Design and Operation of Farm Irrigation Systems 223

The above conditionals can be applied for all timesteps to insure numerical stability of the application of Equation 8.36 as well as correctly computing the theoretical quantity of solar radiation early and late in the day. Where there are hills or mountains, the hour angle when the sun first appears or disappears may increase for sunrise or decrease for sunset; however, generally, no corrections are necessary. The seasonal correction for solar time is: )sin(025.0)cos(1255.0)2sin(1645.0 bbbSc −−= (8.41)

364

)81(π2 −=

Jb (8.42)

where J is the number of the day in the year and b has units of radians. The user should confirm accurate setting of the datalogger clock. If clock times are

in error by more than 5–10 minutes, estimates of exoatmospheric and clear sky radia-tion may be significantly impacted. This can lead to errors in estimating Rn on an hourly or shorter basis, especially early and late in the day. A shift in “phase” between measured Rs and Rso estimated from Ra according to the data logger clock can indicate error in the reported time. Discussion is given in Appendix D of ASCE-EWRI (2005).

The angle of the sun above the horizon, β, at the midpoint of the hourly or shorter time period is computed as:

[ ])cos()cos()cos()sin()sin(arcsin ωδϕδϕβ += (8.43)

where β = angle of the sun above the horizon, radians ϕ = station latitude, radians δ = solar declination, radians ω = solar time angle at the midpoint of the period, radians.

The “arcsin” function is the arc-sine function and represents the inverse of the sine. This function is not available in all computer languages, but β can alternatively be computed using the arc tangent (inverse tangent) function:

( ) ⎥

⎥⎦

⎢⎢⎣

−= 5.021

arctanY

Yβ (8.44)

where )cos()cos()cos()sin()sin( ωδϕδϕ +=Y (8.45)

and all other parameters are as defined previously. 8.4.4.10 Soil heat flux. The magnitude of soil heat storage or release can be sig-

nificant in the surface energy balance over a period of a few hours, but is usually small day to day because heat stored early in the day as the soil warms is lost late in the day or at night when the soil cools. Since the magnitude of 24-hour average soil heat flux under a crop canopy over 10- to 30-day periods is relatively small, G normally can be neglected for daily and longer timesteps. The total G over a complete growing period, however, may be significant, especially for 30 days or longer. As defined here and by ASCE-EWRI (2005), G is positive when the soil is warming and negative when the soil is cooling.

For daily periods, the magnitude of G averaged over 24 hours beneath a fully vege-tated grass or alfalfa reference surface is relatively small in comparison with Rn. Therefore, it is ignored in the standardized ET calculations so that

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224 Chapter 8 Water Requirements

Gday = 0 (8.46) where Gday is the daily soil heat flux density, MJ m-2 d-1.

Over a monthly period, G for the soil profile can be significant, especially during spring and fall. Assuming a constant soil heat capacity of 2.0 MJ m-3 °C-1 and an ef-fectively warmed soil depth of 2 m, G for monthly periods in MJ m-2 d-1 is estimated from the change in mean monthly air temperature as: )(07.0 11 −+ −= i,monthi,monthi,month TTG (8.47)

or, if Tmonth,i+1 is unknown, )(14.0 1−−= i,monthi,monthi,month TTG (8.48)

where Tmonth,i is mean air temperature of month i, Tmonth,i-1 is mean air temperature of the previous month, and Tmonth,i+1 is the mean air temperature of the next month (all °C).

For application to short-periods, e.g., when hourly data for G are required, other approaches must be used. One method common to research uses heat flux plates in-stalled near the soil surface, usually at a depth of about 0.1 to 0.15 m. The total heat flux density is determined by performing a calorimetric balance of the soil layer above the plate. Because soil heat flux plates are not a common measurement at weather sta-tions, the reader is referred to other references (Tanner, 1960; Brutsaert, 1982; and Allen et al., 1996) for application descriptions.

For hourly or shorter time periods, G, in the standardized calculation is expressed as a function of net radiation for the two reference types. For the standardized short reference ETos : Ghr daytime = 0.1 Rn (8.49a)

Ghr nightime = 0.5 Rn (8.49b) where G and Rn have the same measurement units (MJ m-2 h-1 for hourly or shorter time periods). For the standardized tall reference ETrs : Ghr daytime = 0.04 Rn (8.50a)

Ghr nightime = 0.2 Rn (8.50b) For standardization, nighttime is defined as when measured or calculated hourly net

radiation Rn is < 0 (i.e., negative). The amount of energy consumed by G is subtracted from Rn when estimating ETos or ETrs. The coefficient 0.1 in Equation 8.49a represents the condition of only a small amount of dead thatch underneath the leaf canopy of the short (clipped grass) reference. Large amounts of thatch insulate the soil surface, re-ducing the daytime coefficient for grass to about 0.05. However, the 0.1 coefficient is part of the EWRI and FAO standardizations.

8.4.5 1985 Hargreaves Grass Reference Equation The Hargreaves equation (Hargreaves and Samani, 1982, 1985; Hargreaves et al.,

1985) is suggested as a means for estimating ETo in situations where weather data are limited and only maximum and minimum air temperature data are available. The form of the 1985 Hargreaves equation is: ETo = 0.0023 (Tmax – Tmin)0.5 (Tmean + 17.8) (Ra) (8.51) where Tmax and Tmin = maximum and minimum daily air temperature, °C,

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Design and Operation of Farm Irrigation Systems 225

Tmean = mean daily air temperature, (Tmax + Tmin)/2 Ra = average daily exoatmospheric radiation (Equation 8.29).

ETo in Equation 8.51 has the same units as Ra and can be converted from MJ m-2 d-1 to mm d-1 by dividing by λ = 2.45 MJ kg-1.

The Hargreaves equation was the highest-ranked temperature-based method in the ASCE Manual 70 analysis (Jensen et al., 1990). Droogers and Allen (2002) and Har-greaves and Allen (2003) reported Equation 8.51 to estimate well over a wide range of latitudes and climates for periods of 5 days or longer without significant error, pro-vided mean wind speeds averaged between 1 and 3 m s-1. Itenfisu et al. (2003) com-pared daily ETo by Equation 8.51 and that by the standardized ASCE PM method for 49 sites in 16 states in U.S. and found mean ratios of Hargreaves ETo to ASCE PM ETos to range from 1.43 to 0.79, with a mean of 1.06 and a standard deviation of 0.13. The Hargreaves equation tended to estimate higher than the ASCE PM method when mean daily ETo was low, and vice versa.

One advantage of an equation such as the Equation 8.51 relative to more complex equations such as the Penman or PM equation, which is often overlooked, is the re-duced data requirement and therefore reduced chance for data error. This is advanta-geous in regions where solar radiation, humidity, and wind data are lacking or are of low or questionable quality (Droogers and Allen, 2002). Generally, air temperature can be measured with less error, with less sophisticated equipment, and by less trained individuals than can the other three parameters required by combination equations. Equation 8.51 can be calibrated against the PM equation (Equation 8.3) when data are available to produce a regionally calibrated temperature equation. Examples of this type of calibration in Spain include Martinez-Cob and Tejero-Juste (2004), Vanderlin-den et al. (2004), and Gavilan et al. (2005). An alternative to using Equation 8.51 when data are lacking is to employ the PM equation using estimates for missing variables.

8.4.6 Effect of Timestep Size on Calculations The Penman and Penman-Monteith equations can be applied to hourly and 24-h

timesteps. The 24-h timesteps can use daily, weekly, 10-d, and monthly averages for weather data. Under many climatic conditions, calculating ETo or ETr using hourly timesteps and then summing over 24 hours provides estimates that closely equal ETo or ETr calculated using 24-h average data with 24-h calculation timesteps, especially when applying the standardized ASCE-EWRI PM method (Itenfisu et al., 2003; ASCE-EWRI, 2005). Generally, 24-h ETo and ETr have potential for higher accuracy when computed using hourly or shorter timesteps and then summed to 24-hour totals. Hourly calculation is better able to consider impacts of abrupt and gradual changes in weather parameters during the course of a day on ET (Irmak et al., 2005; Allen et al., 2006). Examples of this are high wind conditions during afternoons with low humid-ity, overpass of cloud fronts and rain events, wintertime, and nighttime calm.

8.4.7 Limited Data Availability Many historical weather data sets include only measurements of daily air tempera-

ture. When ETo estimates are desired, one of three approaches is recommended: 1. When approximate calculations of ETo are suitable, apply Equation 8.51. 2. When more accuracy is required, calibrate Equation 8.51 at a regional station or

stations that have Rs and u2 data. If Td or other humidity data are not available, Td can be estimated from Tmin as described in Equation 8.16. The desired stan-dard reference method can be used as the calibration basis (e.g., Equation 8.3) at

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226 Chapter 8 Water Requirements

the regional station. The calibration can be of the form:

ET

- aET b =

ETET

b = equation

ref

equation

ref or (8.52)

where ETref is the reference ET against which to calibrate and ETequation is ET es-timated by the equation being calibrated. Coefficients b and a are calibration factors that may vary by month. These coefficients can be determined by linear regression.

Reference ET is then calculated at locations with limited data as: ETref = b ETequation or ETref = a + b ETequation (8.53)

As an example of regional calibration, Allen et al. (1983) determined values for b by month for the state of Idaho when calibrating the FAO-Blaney-Criddle equation against ETr. The user is cautioned, however, that use of faulty regional weather data for calibration can create more error in the ET estimate than using an original equation.

3. The user may elect to use the Penman or PM equation, estimating Rs, Td, and/or u2. This is the approach recommended by FAO-56 for most situations. The bene-fit is that a physically correct equation for ETo is used, so that local or regional calibration should be unnecessary. The accuracy of the ETo estimate depends on how well missing data parameters are estimated. FAO-56 and ASCE-EWRI (2005) describe procedures for estimating Rs, Td and u2 , where Rs is estimated from Tmax, Tmin, and Ra, Td is estimated from Tmin, and u2 is estimated from re-gional averages or from some regional weather station. In some parts of the U.S., gridded estimates of weather data are available from weather forecast sys-tems such as by NCEP (McQueen et al., 2004). Allen and Robison (2007) ap-plied the ASCE PM method at 107 National Weather Service stations in Idaho where only daily maximum and minimum air temperature data were available for long historic periods. They estimated Rs using a procedure by Thornton and Running (1999) following regional calibration.

8.4.8 Weather Data Integrity ETo and ETr estimates are only as good as the weather data used in their estimation.

Weather data should be screened to insure integrity and representativeness. This is especially important with electronically collected data, since human oversight and maintenance may be limited. Solar radiation can be screened by plotting measure-ments against a clear sky Rso envelope provided by Equation 8.28, or a more accurate and complicated method in ASCE-EWRI (2005) Appendix D, illustrated in Allen (1996a). Humidity data (Td, RH, ea) can be evaluated by examining daily maximum RH (RHmax) or by comparing Td with Tmin. Under reference conditions, RHmax generally exceeds 80% during early morning and Td approaches Tmin (Allen 1996a; ASCE-EWRI, 2005).

Weather data should be representative of the reference condition. Data collected at or near airports can be negatively influenced by the local aridity, especially in arid and semiarid climates. Data from dry or urban settings may cause overestimation of ETo or ETr due to air temperature measurements that are too high and humidity measurements that are too low, relative to the reference condition. Allen et al. (1998) and ASCE-EWRI (2005) suggest simple adjustments for “nonreference” weather data to provide

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Design and Operation of Farm Irrigation Systems 227

data more reflective of well-watered settings. Allen and Gichuki (1989) and Ley et al. (1996) have suggested more sophisticated approaches.

Often, substituting Td = Tmin – Ko for measured Td, as suggested in Equation 8.16, can improve ETo estimates made with the combination equation when data are from a nonreference setting. Using the nonreference data in Equation 8.16 will overestimate the true Td and ea that would occur under reference conditions, since Tmin will be higher in the dry setting and, consequently, so will estimated Td. However, because es and ea in the nonreference setting are both inflated when calculated using Tmax, Tmin, and Td estimated from Equation 8.16, the es – ea difference in the combination equa-tion is often brought more in line with that expected for the reference condition and a more accurate estimate for ETref results.

8.5 ESTIMATING ET FOR CROPS The crop coefficient, Kc, has been developed over the past half-century to simplify

and standardize the calculation and estimation of crop water use. The Kc is defined as the ratio of ET from a specific surface to ETref. The specific surface can be comprised of bare soil, soil with partial vegetation cover, or full vegetation cover. The Kc repre-sents an integration of effects of crop height, crop-soil resistance, and surface albedo that distinguish the surface from the ETref definition. The value for Kc often changes during the growing season as plants grow and develop, as the fraction of ground cov-ered by vegetation changes, as the wetness of the underlying soil surface changes, and as plants age and mature.

The potential crop ET is calculated by multiplying ETref by the crop coefficient: ETc = Kc ETref (8.54) The reference crop corresponds to a living, agricultural crop (clipped grass or full-cover alfalfa) and it incorporates the majority of the effects of variable weather into the ETref estimate. Because ETref represents an index of climatic evaporative demand, the Kc varies predominately with specific crop characteristics and a small amount with climate in the case of ETo. This enables the transfer of standard values for Kc between locations and between climates. The transfer has led to the widespread acceptance and usefulness of the Kc-ETref approach. Values for Kc based on ETo tend to average 1.2 to 1.4 times Kc based on ETr due to differences in magnitudes between the two ETref types. For this reason, ASCE-EWRI (2005) has recommended differentiation between the two families of Kc by referring to ETo-based Kc as Kco and to ETr-based Kc as Kcr.

The Kc and ETc in Equation 8.54 represent ET under potential growing conditions with no stresses caused by shortage of soil water or salinity. These are the general conditions for agricultural production. Both water and salinity stress reduce transpira-tion and thus ET by causing plant canopies to reduce stomatal opening and water loss. When water or salinity-induced reductions are considered, ET is calculated as: ETc act = Kc act ETref (8.55) where ETc act and Kc act represent ET and associated Kc under actual field conditions that may include effects of environmental stresses.

8.5.1 Mean Kc and Dual Kc Methods Two approaches to Kc are described in this section. The first approach uses a mean

or “single” Kc where time-averaged effects of evaporation from the soil surface are averaged into the Kc value. The mean Kc represents, on any particular day, average evaporation fluxes from the soil and plant surfaces. The second Kc approach is the

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228 Chapter 8 Water Requirements

dual Kc method, where the Kc value is divided into a basal crop coefficient, Kcb, and a separate component, Ke, representing evaporation from the soil surface. The basal crop coefficient represents ET conditions when the soil surface is dry, but sufficient root zone moisture is present to support full transpiration. Generally, a daily calculation timestep is required to apply the dual Kc method, whereas the mean Kc method can be applied on daily, weekly, or monthly timesteps.

The mean (single) Kc approach is used for planning studies and irrigation systems design where averaged effects of soil wetting are appropriate. For typical irrigation management, this use is valid. The dual Kc approach, which requires more numerical calculations, is suited for irrigation scheduling, for soil water balance computations, and for research studies where specific effects of day-to-day variation in soil surface wetness and the resulting impacts on daily ETc, the soil water profile, and deep perco-lation fluxes are important.

The form of the equation for Kc act in the dual Kc approach is: Kc act = Ks Kcb

+ Ke (8.56) where Kact = actual crop coefficient that considers effects of moisture stressa stress reduction coefficient, 0 to 1

Ks = a stress reduction coefficient, 0 to 1 Kcb = basal crop coefficient, 0 to −1.4 for Kco and 0 to ~1.0 for Kcr Ke = soil water evaporation coefficient, 0 to −1.4 for Kco and 0 to ~1.0 for Kc r.

All three terms are dimensionless. Kcb is defined as the ratio of ETc to ETref when the soil surface layer is dry, but where the average soil water content of the root zone is adequate to sustain full plant transpiration. Ks reduces the value of Kcb when the aver-age soil water content of the root zone is not adequate to sustain full plant transpiration and is described later. Ke quantifies the evaporation component from wet soil in addi-tion to the evapotranspiration represented in Kcb.

The mean (single) Kc is a simplified, single coefficient that includes effects of time-averaged Ke: ecbc KKK += (8.57)

and csactc KKK = (8.58)

where Ke represents the time-averaged (i.e., multi-day) Ke. 8.5.2 The Crop Coefficient Curve

The crop coefficient curve represents the changes in Kc over the course of the growing season, depending on changes in vegetation cover and maturation. During the initial period, shortly after planting of annuals or shortly after the initiation of new leaves for perennials, the value of Kc is small, often less than 0.4. Figure 8.1 illustrates two general shapes of Kc curves as used by FAO (Doorenbos and Pruitt, 1977; Allen et al., 1998) and as used by Wright (1982). The curves by Wright exhibit a smoothed change in Kc with time, whereas Kc curves by FAO are constructed using linear line segments.

The simple, linear FAO Kc curve is widely used and generally provides sufficiently accurate description of linear crop growth and development and subsequently Kc, and is recommended for most applications. Definitions for three benchmark Kc values re-quired to construct the curve and associated definitions for growth stage periods and relative ground cover are illustrated in Figure 8.2.

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Design and Operation of Farm Irrigation Systems 229

Kc

0.00.20.40.60.81.01.21.4

May June July August

Kc WrightKc FAO

Figure 8.1. Typical crop coefficient curves from Wright (1982) and from FAO-24 and FAO-56.

Kc

KK

K

c ini

c mid

c end

initial crop development mid-season late season

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time (days)

Figure 8.2. FAO Kc curve with four crop stages and three Kc values relative to typical ground cover (from FAO-56).

Kc

initial crop development mid-season late season

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time (days)

K

cb

cb

K

Ke

= K + Kec

Figure 8.3. Generalized FAO Kc curve definitions showing the basal Kcb,

soil evaporation, Ke, and time-averaged mean Kc values.

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230 Chapter 8 Water Requirements

Typical shapes for the Kcb, Ke, and mean Kc curves are shown in Figure 8.3. The Kcb curve represents the minimum Kc for conditions of adequate soil moisture and dry soil surface. The Ke spikes represent increased evaporation following wetting of the soil surface by precipitation or irrigation. The spikes reach a maximum of about 1.2 for Kco and about 1.0 for Kcr. When summed, the values for Kcb and for Ke represent the total crop coefficient, Kc. The mean Kc curve shown as the dashed line illustrates the effect of averaging Ke over time and is displayed as a smoothed curve.

The mean Kc lies above the Kcb curve, with potentially large differences during the initial and development stages, depending on the frequency of soil wetting. During the midseason period when the crop is likely to be near full cover, the effects of soil wet-ness are less pronounced.

8.5.3 Construction of the FAO Kc Curve The linear FAO style Kc curve is constructed by the following steps. 1. Divide the growing period into four general growth stages describing crop

phenology and development (Figure 8.2). The four stages are: (1) initial period from planting or green-up until about 10% ground cover; (2) crop development period; (3) mid-season period from effective full cover to the beginning of the late season period; and (4) late-season period from the beginning of senescence until harvest, crop death, or full senescence.

2. Specify the three Kc values corresponding to Kc ini, Kc mid, and Kc end, where Kc ini represents the average Kc during the initial period, Kc mid represents the average Kc during the midseason period, and Kc end represents the Kc at the end of the late-season period.

3. Connect straight line segments through each of the four growth stage periods, with horizontal lines drawn through Kc ini during the initial period and through Kc mid during the midseason period. Diagonal lines are drawn from Kc ini to Kc mid within the domain of the development period and from Kc mid to Kc end within the domain of the late-season period.

In the case of basal Kcb, the same procedure for curve construction is followed. Kc

mid represents the mean maximum Kc expected during the midseason period, and does not necessarily represent the absolute peak Kc reached by the crop. This is illustrated in Figure 8.1, where the smoothed Kc curve, in this case for dry, edible beans devel-oped by Wright (1982; from Jensen et al. 1990), rises above the linearized curve dur-ing part of the midseason. As illustrated, the linearized FAO curve approximates the trends in Kc, and accurately estimates seasonal ET when the lengths of the growth stages and the value for Kc mid are properly selected.

Values for the grass-based Kco ini, Kco mid, and Kco end, and for Kcbo ini, Kcbo mid, and Kcbo end are listed in Table 8.2 for various agricultural crops (the o subscript indicates an ETo basis). The three Kco columns represent typical irrigation management and pre-cipitation frequencies. The Kc values are taken from FAO-56 (Allen et al., 1998) and are largely based on Doorenbos and Pruitt (1977) and Doorenbos and Kassam (1979). A primary departure made here is for trees and grapes where, rather than listing values for Kc and Kcb, values are instead given for Kcb full, Kc min and Kcb cover to be used in Equation 8.85 (with a density coefficient from Equation 8.80) introduced later. This modification provides flexibility in adjusting the value for Kc and Kcb according to the fraction of ground shaded by canopy, which is highly variable among orchards and cultures. Parameters are listed in footnotes for applying Equation 8.80 that reproduce

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Design and Operation of Farm Irrigation Systems 231

various Kc values reported in the literature. The Kco in Table 8.2 are applicable with grass reference ETo as defined by the standardized FAO/ASCE PM Equation (8.3) and are generally valid for use with other grass reference equations, provided these agree relatively closely with the standardized PM definition (ASCE-EWRI, 2005).

For several group types, only one value for Kc ini is listed for the group, since tabu-larized Kc ini are only approximate. Figures 8.5a-8.5c (in Section 8.5.3.4), from FAO-56, improve estimates for Kc ini by accounting for frequency of soil wetting and soil type.

8.5.3.1 The climatic basis of Table 8.2. The Kc mid values in Table 8.2 are typical values expected under a standard climatic condition defined in FAO-56 (Allen et al., 1998) as a subhumid climate having average daytime minimum relative humidity (RHmin) of 45 % and having calm to moderate wind speeds averaging 2 m s-1. More arid climates and conditions of greater wind speed have higher values for Kc and Kcb, especially for tall crops and more humid climates, and conditions of lower wind speed have lower values according to the relationship:

( ) ( )[ ]3.0

2 345004.0204.0 ⎟

⎠⎞

⎜⎝⎛

−−−+=hRHuKK mintablecc (8.59)

where Kc table is the Kc value (or Kcb value) from Table 8.2 for Kc mid (and for Kc end when Kc end > 0.45) and h is mean crop height in m. The Kc for crops 2 to 3 m in height can increase by as much as 40% when going from a calm, humid climate (for example, u2 = 1 m s-1 and RHmin = 70%) to an extremely windy, arid climate (for example, u2 = 5 m s-1 and RHmin = 15%). The increase in Kc is due to the influence of the larger aero-dynamic roughness of tall crops relative to grass on the transport of water vapor from the surface. The adjustments to Kc for climate are generally made using mean values for u2 and RHmin for the entire midseason period.

8.5.3.2 Lengths of crop growth stages. The four crop growth stages for the FAO Kco curves are characterized in terms of crop growth benchmarks as illustrated in Fig-ure 8.2. The crop development period is presumed to begin when approximately 10% of the ground is covered by vegetation and ends at attainment of effective full cover. Effective cover can be defined for row crops such as beans, sugar beets, potatoes, and corn as the time when some leaves of plants in adjacent rows begin to intermingle so that soil shading becomes nearly complete, or when plants reach nearly full size, if no intermingling occurs. For crops taller than 0.5 m, the average fraction of the ground surface covered by vegetation at the time of effective full cover is about 0.7 to 0.8 (Neale et al., 1989; Grattan et al., 1998). Effective full cover for many crops begins at the initiation of flowering. It is understood that the crop or plant can continue to grow in both height and leaf area after the attainment of effective full cover. Another way to estimate the occurrence of full cover is when the leaf area index (LAI) reaches about 3 (Ritchie, 1972; Wright, 1982; Ritchie and NeSmith, 1991).

The lengths of the initial and development periods are relatively short for decidu-ous trees and shrubs, depending on the amount of pruning, which develop new leaves in the spring at relatively fast rates. These two periods may thus be only a few days in length for trees and may include the flowering period. The Kc ini selected for trees and shrubs should reflect the ground condition prior to leaf emergence or initiation, since Kc ini is affected by the amount of grass or weed cover, soil wetness, tree density, and mulch density.

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232 Chapter 8 Water Requirements

Table 8.2. Mean crop coefficients, Kco, and basal crop coefficients, Kcbo, for well-managed crops in a subhumid climate, for use with ETos (following FAO-56*).

Crop Kc ini[1] Kc mid Kc end Kcb ini

Kcb mid Kcb end a. Small Vegetables 0.7 1.05 0.95 0.15 0.95 0.85 Broccoli 1.05 0.95 0.95 0.85 Brussels sprouts 1.05 0.95 0.95 0.85 Cabbage 1.05 0.95 0.95 0.85 Carrots 1.05 0.95 0.95 0.85 Cauliflower 1.05 0.95 0.95 0.85 Celery 1.05 1.00 0.95 0.90 Garlic 1.00 0.70 0.90 0.60 Lettuce 1.00 0.95 0.90 0.90 Onions, dry 1.05 0.75 0.95 0.65 green 1.00 1.00 0.90 0.90 seed 1.05 0.80 1.05 0.70 Spinach 1.00 0.95 0.90 0.85 Radish 0.90 0.85 0.85 0.75 b. Vegetables, Solanum

Family (Solanaceae) 0.6 1.15 0.80 0.15 1.10 0.70 Eggplant 1.05 0.90 1.00 0.80 Sweet peppers (bell) 1.05[2] 0.90 1.00[2] 0.80 Tomato 1.15[2] 0.70-0.90 1.10[2] 0.60-0.80c. Vegetables, Cucumber

Family (Cucurbitaceae) 0.5 1.00 0.80 0.15 0.95 0.70 Cantaloupe 0.5 0.85 0.60 0.75 0.50 Cucumber, fresh market 0.6 1.00[2] 0.75 0.95[2] 0.70 machine harvest 0.5 1.00 0.90 0.95 0.80 Pumpkin, winter squash 1.00 0.80 0.95 0.70 Squash, zucchini 0.95 0.75 0.90 0.70 Sweet melons 1.05 0.75 1.00 0.70 Watermelon 0.4 1.00 0.75 0.95 0.70 d. Roots and Tubers 0.5 1.10 0.95 0.15 1.00 0.85 Beets, table 1.05 0.95 0.95 0.85 Cassava, year 1 0.3 0.80[3] 0.30 0.70[3] 0.20 year 2 0.3 1.10 0.50 1.00 0.45 Parsnip 0.5 1.05 0.95 0.95 0.85 Potato 1.15 0.75[4] 1.10 0.65[4] Sweet potato 1.15 0.65 1.10 0.55 Turnip (and rutabaga) 1.10 0.95 1.00 0.85 Sugar beet 0.35 1.20 0.70[5] 1.15 0.50[5] * Primary sources of Table 8.2: FAO-56 (Allen et al., 1998), with Kc ini traceable to Doorenbos and Kassam (1979) and

Kc mid and Kc end traceable to Doorenbos and Pruitt (1977), Pruitt (1986), Wright (1981, 1982), and Snyder et al. (1989a,b). [1] These are general values for Kc ini under typical irrigation management and soil wetting. For frequent wettings such as

with high frequency sprinkle irrigation or daily rainfall, these values may increase substantially and may approach 1.0 to 1.2. Kc ini is a function of wetting interval and potential evaporation rate during the initial and development periodsand is more accurately estimated using Figure 8.5 or using the dual Kcb ini + Ke.

[2] Beans, peas, legumes, tomatoes, peppers and cucumbers are sometimes grown on stalks reaching 1.5 to 2 meters in height. In such cases, increased Kc values need to be taken. For green beans, peppers and cucumbers, 1.15 can be taken, and for tomatoes, dry beans and peas, 1.20. Under these conditions h should be increased also.

[3] The midseason values for cassava assume non-stressed conditions during or following the rainy season. The Kc end and Kcb end values account for dormancy during the dry season.

[4] The Kc end and Kcb end values for potatoes are about 0.40 and 0.35 for long season potatoes with vine kill. [5] This Kc end and Kcb end values are for no irrigation during the last month of the growing season. The Kc end and Kcb end

values for sugar beets are higher, up to 1.0 and 0.9, when irrigation or significant rain occurs during the last month. (continued)

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Design and Operation of Farm Irrigation Systems 233

Table 8.2 continued. Crop Kc ini

[1] Kc mid Kc end Kcb ini Kcb mid Kcb end

e. Legumes (Leguminosae) 0.4 1.15 0.55 0.15 1.10 0.50 Beans, green 0.5 1.05[2] 0.90 1.00[2] 0.80 Beans, dry, and pulses 0.4 1.15[2] 0.35 1.10[2] 0.25 Chick pea 1.00 0.35 0.95 0.25 Faba bean (broad bean), fresh 0.5 1.15[2] 1.10 1.10[2] 1.05 dry/seed 0.5 1.15[2] 0.30 1.10[2] 0.20 Garbanzo 0.4 1.15 0.35 1.05 0.25 Green gram and cowpeas 1.05 0.60-0.35[6] 1.00 0.55-0.25[6]

Groundnut (peanut) 1.15 0.60 1.10 0.50 Lentil 1.10 0.30 1.05 0.20 Peas, fresh 0.5 1.15[2] 1.10 1.10[2] 1.05 dry/seed 1.15 0.30 1.10 0.20 Soybeans 1.15 0.50 1.10 0.30

f. Perennial Vegetables (with winter dormancy and initially bare or mulched) 0.5 1.00 0.80

Artichokes 0.5 1.00 0.95 0.15 0.95 0.90 Asparagus 0.5 0.95[7] 0.30 0.15 0.90[7] 0.20 Mint 0.60 1.15 1.10 0.40 1.10 1.05 Strawberries 0.40 0.85 0.75 0.30 0.80 0.70

g. Fiber Crops 0.35 0.15 Cotton 1.15-1.20 0.70-0.50 1.10-1.15 0.50-0.40 Flax 1.10 0.25 1.05 0.20 Sisal[8] 0.4-0.7 0.4-0.7 0.4-0.7 0.4-0.7

h. Oil Crops 0.35 1.15 0.35 0.15 1.10 0.25 Castor bean (Ricinus) 1.15 0.55 1.10 0.45 Rapeseed, canola 1.0-1.15[9] 0.35 0.95-1.10[9] 0.25 Safflower 1.0-1.15[9] 0.25 0.95-1.10[9] 0.20 Sesame 1.10 0.25 1.05 0.20 Sunflower 1.0-1.15[9] 0.35 0.95-1.10[9] 0.25

i. Cereals 0.3 1.15 0.4 0.15 1.10 0.25 Barley, oats 1.15 0.25 1.10 0.15 Spring wheat 1.15 0.25-0.4[10] 1.10 0.15-0.3[10]

Winter wheat, frozen soils 0.4 1.15 0.25-0.4[10] 0.15-0.5[11] 1.10 0.15-0.3[10]

with non-frozen soils 0.7 1.15 0.25-0.4[10] Maize, field (grain corn) [12] 1.20 0.60,0.35 0.15 1.15 0.50,0.15 Maize, sweet (sweet corn) [12] 1.15 1.05[13] 1.10 1.00[13] Millet 1.00 0.30 0.95 0.20 Sorghum, grain 1.00-1.10 0.55 0.95-1.05 0.35 sweet 1.20 1.05 1.15 1.00 Rice 1.05 1.20 0.90-0.60 1.00 1.15 0.70-0.45

[6] The first Kc end is for harvested fresh. The second value is for harvested dry. [7] The Kc for asparagus usually remains at Kc ini during harvest of the spears, due to sparse ground cover. The Kc mid value

is for following regrowth of plant vegetation following termination of harvest of spears. [8] Kc for sisal depends on the planting density and water management (e.g., intentional moisture stress). [9] The lower values are for rainfed crops having less dense plant populations. [10] The higher value is for hand-harvested crops. [11] The two Kcb ini values for winter wheat are for less than 10% ground cover and for during the dormant, winter period, if

the vegetation fully covers the ground, but conditions are nonfrozen. [12] The Kc mid and Kcb mid values are for populations > 50,000 plants ha-1. For less dense populations or less uniform growth,

Kc mid and Kcb mid can be reduced by 0.10 to 0.2. The first Kc end value is for harvest at high grain moisture. The second Kc

end value is for harvest after complete field drying of the grain (to about 18% moisture, wet mass basis). [13] If harvested fresh for human consumption. Use Kc end for field maize if the sweet maize is allowed to mature and dry in the field. (continued)

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234 Chapter 8 Water Requirements

Table 8.2 continued. Crop Kc ini

[1] Kc mid Kc end Kcb ini Kcb mid Kcb end

j. Forages Alfalfa hay, ave.cutting effects 0.40 0.95[13] 0.90 individual cutting periods 0.40[14] 1.20[14] 1.15[14] 0.30[14] 1.15[14] 1.10[14] for seed 0.40 0.50 0.50 0.30 0.45 0.45 Bermuda hay, ave.cutting effects 0.55 1.00[13] 0.85 0.50 0.95[15] 0.80 spring crop for seed 0.35 0.90 0.65 0.15 0.85 0.60

Clover hay, berseem, averaged cutting effects 0.40 0.90[13] 0.85

individual cutting periods 0.40[14] 1.15[14] 1.10[14] 0.30[14] 1.10[14] 1.05[14] Ryegrass hay, ave. cuttings 0.95 1.05 1.00 0.85 1.00[15] 0.95

Sudan grass hay (annual), averaged cutting effects 0.50 0.90[13] 0.85

individual cutting periods 0.50[14] 1.15[14] 1.10[14] 0.30[14] 1.10[14] 1.05[14] Grazing pasture, rotated grazing 0.40 0.85-1.05 0.85 0.30 0.80-1.00 0.80 extensive grazing 0.30 0.75 0.75 0.30 0.70 0.70 Turf grass, cool season[16] 0.90 0.90 0.90 0.80 0.85 0.85 warm season[16] 0.85 0.90 0.90 0.75 0.80 0.80

k. Sugar Cane 0.40 1.25 0.75 0.15 1.20 0.70 l. Tropical Fruits and Trees Banana, 1st year 0.50 1.10 1.00 0.15 1.05 0.90 2nd year 1.00 1.20 1.10 0.60 1.10 1.05 Cacao 1.00 1.05 1.05 0.90 1.00 1.00 Coffee, bare ground cover 0.90 0.95 0.95 0.80 0.90 0.90 with weeds 1.05 1.10 1.10 1.00 1.05 1.05 Date palms 0.90 0.95 0.95 0.80 0.85 0.85 Palm trees 0.95 1.00 1.00 0.85 0.90 0.90 Pineapple,[17] bare soil 0.50 0.30 0.30 0.15 0.25 0.25 with grass cover 0.50 0.50 0.50 0.30 0.45 0.45 Rubber trees 0.95 1.00 1.00 0.85 0.90 0.90 Tea, non-shaded 0.95 1.00 1.00 0.90 0.95 0.90 shaded[18] 1.10 1.15 1.15 1.00 1.10 1.05

m. Berries and Hops Berries (bushes) 0.30 1.05 0.50 0.20 1.00 0.40 Hops 0.30 1.05 0.85 0.15 1.00 0.80

[13] This Kc mid for hay crops represents an averaged Kc for before and following cuttings. It is applied to the period follow-ing the first development period until the beginning of the last late season period of the growing season.

[14] These Kc coefficients for hay crops represent immediately following cutting; at full cover; and immediately beforecutting, respectively. The growing season is described as a series of individual cutting periods (Figure 8.4).

[15] This Kcb mid for bermuda and ryegrass hay crops represents an averaged Kcb mid for before and following cuttings. It is applied to the period following the first development period until the beginning of the last late season period.

[16] Cool season grass varieties include dense stands of bluegrass, ryegrass, and fescue. Warm season varieties include bermuda and St. Augustine. Values given are for potential conditions representing a 0.06- to 0.08-m mowing height. Turf, especially warm season varieties, can be stressed at moderate levels and still maintain appearance (see Section 8.6 and Table 8.13). Generally a value for the stress coefficient Ks of 0.9 for cool-season and 0.7 for warm-season varieties can be employed where careful water management is practiced and rapid growth is not required. Incorporating these Ks values into an “actual Kc” will yield Kc act values of about 0.8 for cool-season and 0.65 for warm-season turf.

[17] The pineapple plant has very low transpiration because it closes its stomates during the day and opens them during thenight. Therefore, the majority of ETc from pineapple is evaporation from the soil. The Kc mid < Kc ini since Kc mid occurs during full ground cover so that soil evaporation is less. Values assume that 50% of the ground surface is covered by black plastic mulch and that irrigation is by sprinkler. For drip irrigation beneath the plastic mulch, Kc values given can be reduced by 0.10.

[18] Includes the water requirements of the shade trees. (continued)

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Design and Operation of Farm Irrigation Systems 235

Table 8.2 continued. Crop Kc ini

[1] Kc mid Kc end Kcb ini Kcb mid Kcb end

n. Fruit Trees and Grapes Conifer trees[19] 1.00 1.00 1.00 0.95 0.95 0.95 Kiwi 0.40 1.05 1.05 0.20 1.00 1.00

The following, shaded, section for trees and grapes gives values for Kcb full used in Eq. 8.85. Kcb full

[20]

initial Kcb full

[20]

mid Kcb full

[20] end

Kc min[20] Kcb cover

[20]

initial Kcb cover

[20]

mid, end Almonds, no ground cover[21] 0.20 1.00 0.70[22] 0.15 ground cover 0.20 1.00 0.70[22] 0.15 0.75 0.80

Apples, cherries, pears; killing frost[23] 0.30 1.15 0.80[22] 0.15 0.40 0.80

no killing frost[23] 0.30 1.15 0.80[22] 0.15 0.75 0.80

Apricots, peaches, pears, plums, pecans;

killing frost[24] 0.30 1.20 0.80[22] 0.15 0.40 0.80 no killing frost[25] 0.30 1.20 0.80[22] 0.15 0.70 0.80 Avocado, no grnd cover[26] 0.30 1.00 0.90 0.15 ground cover 0.30 1.00 0.90 0.15 0.75 0.80 Citrus[27] 0.80 0.80 0.80 0.15 0.75 0.80 Mango, no ground cover[28] 0.25 0.85 0.70 0.15 Olives[29] 0.60 0.70 0.60 0.15 0.70 0.70 Pistachios 0.30 1.00 0.70 0.15 0.70 0.70 Walnut[30] 0.40 1.10 0.65 0.15 0.75 0.80 Grapes, table or raisin[31] 0.20 1.15 0.90 0.15 0.70 0.70 wine[32] 0.20 0.80 0.60 0.15 0.70 0.70

[19] Conifers exhibit substantial stomatal control due to soil water deficit. The Kc can easily reduce below the values pre-sented, which represent well-watered conditions for large forests.

[20] The first three columns for the orchard crops in the following rows are values for Kcb full for initial, mid- and end-season periods to be used in Eq. 8.85 along with the Kc min of column 4 to calculate Kcb for the initial, midseason and late-season periods, where the density coefficient, Kd, is calculated from Eq. 8.80 using effective fraction of cover fc eff and plant height, h, as noted in the following footnotes. The last two columns are Kcb cover for initial and for mid- and end-season periods to be used in Eq. 8.85 for when there is active ground cover. Generally the value for Kc ini is estimated as 0.10 + Kcb ini from Eq. 8.85 and Kc mid and Kc end are estimated as 0.05 + Kcb mid or Kcb end from Eq. 8.85.

[21] Apply Eq. 8.80 with fc eff = 0.4, ML = 1.5 and h = 4 m for Kd in Eq. 8.85 to derive Kcb values similar to FAO-56. [22] These Kc end values represent Kc prior to leaf drop. After leaf drop, Kc end ≈ 0.20 for bare, dry soil or dead ground cover

and Kc end ≈ 0.50 to 0.80 for actively growing ground cover. [23] Apply Eq. 8.80 with fc eff = 0.5, ML = 2 and h = 3 m for Kd in Eq. 8.85 to derive Kcb values similar to FAO-56. [24] Apply Eq. 8.80 with fc eff = 0.45, ML = 1.5 and h = 3 m for Kd in Eq. 8.85 to derive Kcb values similar to FAO-56. [25] Apply Eq. 8.80 with fc eff = 0.8, ML = 1.5 and h = 3 m for Kd in Eq. 8.85 to derive Kc values similar to Johnson et al.

(2005), with fc eff = 0.6, ML = 1.5, h = 3 m for Kc values similar to those derived from Girona et al. (2005), with fc eff = 0.45, ML = 1.5, h = 3 m for Kcb values similar to FAO-56, with fc eff = 0.29, ML = 1.5, h = 2.5 m for Kc values similar to Paço et al. (2006), and with any fc eff ≤ 0.7, ML = 1.5, h = 3 m to approximate Kc estimates by Ayars et al. (2003).

[26] Apply Eq. 8.80 with fc eff = 0.4, ML = 2 and h = 4 m for Kd in Eq. 8.85 to derive Kcb values similar to FAO-56. [27] Apply Eq. 8.80 with fc eff = 0.2, 0.5 and 0.7, ML = 1.5 and h = 2, 2.5 and 3 m for Kd in Eq. 8.85 to derive recommended

Kcb values that are about 15% higher than the values entered in FAO-56 for these same three levels of fc eff . [28] Apply Eq. 8.80 with fc eff = 0.7 to 0.85, ML = 1.5 and h = 5 m for Kd in Eq. 8.85 for Kcb values similar to those derived

from de Azevedo et al. (2003). [29] Apply Eq. 8.80 with fc eff = 0.7, ML = 1.5 and h = 4 m for Kd in Eq. 8.85 to derive Kcb values similar to FAO-56. Apply

with fc eff = 0.6, ML = 1.5, h = 4 m to derive Kc values similar to Pastor and Orgaz (1994), but with Kcb mid = 0.45. Apply with fc eff = 0.3 to 0.4, ML = 1.5, h = 4 m to derive Kcb values similar to Villalobos et al. (2000). Apply with fc eff = 0.05 and 0.25, ML = 1.5, h = 2 and 3 m to derive Kc values similar to Testi et al. (2004).

[30] Apply Eq. 8.80 with fc eff = 0.7, ML = 1.5 and h = 5 m for Kd in Eq. 8.85 to derive Kcb values similar to FAO-56. [31] Apply Eq. 8.80 with fc eff = 0.65, ML = 1.5 and h = 2 m for Kd in Eq. 8.85 to derive Kc values similar to Johnson.et al.

(2005). Apply with fc eff = 0.45, ML = 1.5, h = 2 m for Kcb values similar to FAO-56. [32] Apply Eq. 8.80 with fc eff = 0.5, ML = 1.5 and h = 2 m for Kd in Eq. 8.85 to derive Kcb values similar to FAO-56. (continued)

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236 Chapter 8 Water Requirements

Table 8.2 continued. Crop Kc ini

[1] Kc mid Kc end o. Wetlands, Temperate Climate Cattails, bulrushes, killing frost 0.30 1.20 0.30

Cattails, bulrushes, no frost 0.60 1.20 0.60 Short veg., no frost 1.05 1.10 1.10 Reed swamp, standing water 1.00 1.20 1.00 Reed swamp, moist soil 0.90 1.20 0.70

p. Special Open water, < 2 m depth or in subhumid climates or tropics 1.05 1.05

Open water, > 5 m depth, clear of turbidity, temperate climate 0.65[33] 1.25[33]

[33] These Kc values are for deep water in temperate latitudes where large temperature changes in the water body occurduring the year, and initial and peak period evaporation is low as radiation energy is absorbed into the deep water body.During fall and winter periods (Kc end), heat is released from the water body that increases the evaporation above that for grass. Therefore, Kc mid corresponds to the period when the water body is gaining thermal energy and Kc end when releas-ing thermal energy. These Kc values should be used with caution.

The start of maturity and beginning of decline in Kc is often signaled by the begin-

ning of aging, yellowing or senescence of leaves, leaf drop, or the browning of fruit so that ETc is reduced relative to ETo. Calculations for Kc and ETc are sometimes pre-sumed to end when the crop is harvested, dries out naturally, reaches full senescence, or experiences leaf drop. For some perennial vegetation in frost-free climates, crops may grow year round so that the date of termination is the same as the date of “plant-ing.” The length of the late season period may be relatively short (less than 10 days) for vegetation killed by frost (for example, maize at high elevations in latitudes > 40°N) or for agricultural crops that are harvested fresh (for example, table beets and small vegetables). The value for Kc end should reflect the condition of the soil surface (average water content and any mulch cover) and the condition of the vegetation fol-lowing harvest or after full senescence. Kc during nongrowing periods having little or no green ground cover can be estimated using the equation for Kc ini as described later.

FAO-56 provides general lengths of growth (development) stages for a wide vari-ety of crops under different climates and locations. This information is reproduced in Table 8.3. The lengths in Table 8.3 serve only to indicate typical proportions of grow-ing season lengths under a variety of climates. In all applications, local observations of the specific plant stage development should be made to account for local effects of plant variety, climate, and cultural practices. Local information can be obtained by interviewing farmers, ranchers, agricultural extension agents, and local researchers, by conducting local surveys, or by remote sensing (Neale et al., 1989; Tasumi et al., 2005).

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Design and Operation of Farm Irrigation Systems 237

Table 8.3. Lengths of crop development stages* for various planting periods and climatic regions (days) (from FAO-56).

Crop Init. (Lini)

Dev. (Ldev)

Mid (Lmid)

Late (Llate) Total Plant Date Region

a. Small Vegetables Broccoli 35 45 40 15 135 Sept Calif. desert, U.S. Cabbage 40 60 50 15 165 Sept Calif. desert, U.S.

Carrots 20 30 30

30 40 50

50/30 60 90

20 20 30

100 150 200

Oct/Jan Feb/Mar

Oct

arid climate Mediterranean

Calif. desert, U.S. Cauliflower 35 50 40 15 140 Sept Calif. desert, U.S.

Celery 25 25 30

40 40 55

95 45

105

20 15 20

180 125 210

Oct April Jan

(semi)arid Mediterranean

(semi)arid

Crucifers[1] 20 25 30

30 35 35

20 25 90

10 10 40

80 95

195

April February Oct/Nov

Mediterranean Mediterranean Mediterranean

Lettuce

20 30 25 35

30 40 35 50

15 25 30 45

10 10 10 10

75 105 100 140

April Nov/Jan Oct/Nov

Feb

Mediterranean Mediterranean

arid region Mediterranean

Onion, dry 15 20

25 35

70 110

40 45

150 210

April Oct; Jan.

Mediterranean arid region; Calif.

Onion, green

25 20 30

30 45 55

10 20 55

5 10 40

70 95

180

April/May October March

Mediterranean arid region Calif., U.S.

Onion, seed 20 45 165 45 275 Sept Calif. desert, U.S. Spinach 20

20 20 30

15/25 40

5 10

60/70 100

Apr; Sep/Oct November

Mediterranean arid region

Radish 5 10

10 10

15 15

5 5

35 40

Mar/Apr Winter

Medit.; Europe arid region

b. Vegetables, Solanum Family (Solanaceae) Egg plant 30

30 40 45

40 40

20 25

130 140

October May/June

arid region Mediterranean

Sweet peppers (bell)

25/3030

35 40

40 110

20 30

125 210

April/June October

Europe and Medit. arid region

Tomato

30 35 25 35 30

40 40 40 45 40

40 50 60 70 45

25 30 30 30 30

135 155 155 180 145

January Apr/May

Jan Oct/Nov

April/May

arid region Calif., U.S.

Calif. desert, U.S. arid region

Mediterranean c. Vegetables, Cucumber Family (Cucurbitaceae)

Cantaloupe 30 10

45 60

35 25

10 25

120 120

Jan Aug

Calif., U.S. Calif., U.S.

Cucumber 20 25

30 35

40 50

15 20

105 130

June/Aug Nov; Feb

arid region arid region

* Lengths of crop development stages provided in this table are indicative of general conditions, but may vary substantially from region to region, with climate and cropping conditions, and with crop variety.The user is strongly encouraged to obtain appropriate local information.

[1] Crucifers include cabbage, cauliflower, broccoli, and Brussels sprouts. (continued)

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238 Chapter 8 Water Requirements

Table 8.3 continued.

Crop Init. (Lini)

Dev. (Ldev)

Mid (Lmid)

Late (Llate) Total Plant Date Region

Pumpkin, winter squash

20 25

30 35

30 35

20 25

100 120

Mar, Aug June

Mediterranean Europe

Squash, zucchini

25 20

35 30

25 25

15 15

100 90

Apr; Dec. May/June

Medit.; arid reg. Medit.; Europe

Sweet melons

25 30 15 30

35 30 40 45

40 50 65 65

20 30 15 20

120 140 135 160

May March Aug

Dec/Jan

Mediterranean Calif., U.S.

Calif. desert, U.S. arid region

Watermelons 20 10

30 20

30 20

30 30

110 80

April Mat/Aug

Italy Near East (desert)

d. Roots and Tubers Beets, table 15

25 25 30

20 25

10 10

70 90

Apr/May Feb/Mar

Mediterranean Mediterranean, arid

Cassava, yr 1 yr 2

20 150

40 40

90 110

60 60

210 360

Rainy season tropical regions

Potato

25 25 30 45 30

30 30 35 30 35

30/45 45 50 70 50

30 30 30 20 25

115/130 130 145 165 140

Jan/Nov May April

Apr/May Dec

(semi)arid climate continental climate

Europe Idaho, U.S.

Calif. Desert, U.S. Sweet potato 20

15 30 30

60 50

40 30

150 125

April Rainy seas.

Mediterranean tropical regions

Sugar beet

30 25 25 50 25 45 35

45 30 65 40 35 75 60

90 90

100 50 50 80 70

15 10 65 40 50 30 40

180 155 255 180 160 230 205

March June Sept April May

November November

Calif., U.S. Calif., U.S.

Calif. desert, U.S. Idaho, U.S.

Mediterranean Mediterranean

arid regions e. Legumes (Leguminosae)

20 30 30 10 90 Feb/Mar Calif.,Mediterranean Beans, green 15 25 25 10 75 Aug/Sep Calif.,Egypt,Lebanon20 30 40 20 110 May/June continental climate15 25 35 20 95 June Pakistan, Calif.

Beans, dry

25 25 30 20 100 June Idaho, U.S. Faba bean

Broad bean Dry bean Green bean

15 20 90 90

25 30 45 45

35 35 40 40

15 15 60 0

90 100 235 175

May Mar/Apr

Nov Nov

Europe Mediterranean

Europe Europe

Green gram, cowpeas 20 30 30 20 110 March Mediterranean

Groundnut

25 35 35

35 35 45

45 35 35

25 35 25

130 140 140

Dry season May

May/June

West Africa high latitudes Mediterranean

Lentil 20 25

30 35

60 70

40 40

150 170

April Oct/Nov

Europe arid region

Peas

15 20 35

25 30 25

35 35 30

15 15 20

90 100 110

May Mar/Apr

April

Europe Mediterranean

Idaho, U.S. (continued)

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Design and Operation of Farm Irrigation Systems 239

Table 8.3 continued.

Crop Init. (Lini)

Dev. (Ldev)

Mid (Lmid)

Late (Llate) Total Plant Date Region

Soybeans

15 20 20

15 30/35

25

40 60 75

15 25 30

85 140 150

Dec May June

tropics central U.S.

Japan f. Perennial Vegetables (with winter dormancy and initially bare or mulched soil) Artichoke 40

20 40 25

250 250

30 30

360 325

Apr (1st yr) May (2nd yr)

California (cut in May)

Asparagus 50 90

30 30

100 200

50 45

230 365

Feb Feb

warm winter Mediterranean

g. Fiber Crops

Cotton

30 45 30 30

50 90 50 50

60 45 60 55

55 45 55 45

195 225 195 180

Mar-May Mar Sept April

Egypt,Pakistan,Cal.Calif. desert,U.S.

Yemen Texas

Flax 25 30

35 40

50 100

40 50

150 220

April October

Europe Arizona

h. Oil Crops Castorbeans 25

20 40 40

65 50

50 25

180 135

March Nov.

(semi)arid climate Indonesia

Safflower

20 25 35

35 35 55

45 55 60

25 30 40

125 145 190

April Mar

Oct/Nov

California, U.S. high latitudes

arid region Sesame 20 30 40 20 100 June China Sunflower 25 35 45 25 130 April/May Medit.; Calif. i. Cereals

Barley, oats, wheat

15 20 15 40 40 20

25 25 30 30 60 50

50 60 65 40 60 60

30 30 40 20 40 30

120 135 150 130 200 160

November March/Apr

July Apr Nov Dec

central India 35-45°L

East Africa

Calif. desert,U.S. Winter

wheat

20[2]

30 160

60[2] 140 75

70 40 75

30 30 25

180 240 335

December November October

California, U.S Mediterranean

Idaho, U.S. Grains

(small) 20 25

30 35

60 65

40 40

150 165

April Oct/Nov

Mediterranean Pakistan; arid reg.

Maize (grain)

30 25 20 20 30 30

50 40 35 35 40 40

60 45 40 40 50 50

40 30 30 30 30 50

180 140 125 125 150 170

April Dec/Jan

June October

April April

East Africa (alt.) arid climate

Nigeria (humid) India (dry, cool) Spain (spr,sum);Cal.

Idaho, U.S. [2] These periods for winter wheat will lengthen in frozen climates according to days having zero

growth potential and wheat dormancy. Under general conditions and in the absence of local data, fall planting of winter wheat can be presumed to occur in northern temperate climates when the 10-day running average of mean daily air temperature decreases to 17°C or December 1, whichever comes first. Planting of spring wheat can be presumed to occur when the 10-day running average of mean daily air temperature increases to 5°C. Spring planting of maize-grain can be presumed to occur when the 10-day running average of mean daily air temperature increases to 13°C.

(continued)

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240 Chapter 8 Water Requirements

Table 8.3 continued.

Crop Init. (Lini)

Dev. (Ldev)

Mid (Lmid)

Late (Llate) Total Plant Date Region

Maize (sweet)

20 20 20 30 20

20 25 30 30 40

30 25

50/30 30 70

10 10 10 10[3] 10

80 80 90

110 140

March May/June Oct/Dec

April Jan

Philippines Mediterranean

arid climate Idaho, U.S.

Calif. desert, U.S. Millet 15

20 25 30

40 55

25 35

105 140

June April

Pakistan central U.S.

Sorghum 20 20

35 35

40 45

30 30

130 140

May/June Mar/April

U.S., Pakis., Med. arid region

Rice 30 30

30 30

60 80

30 40

150 180

Dec; May May

tropics; Mediterr. tropics

j. Forages Alfalfa, total

season[4] 10 30 var. var. var. last –4°C in spring until first -4°C in fall

Alfalfa, 1st cutting cycle[4]

10 10

20 30

20 25

10 10

60 75

Jan Apr

(last –4°C)

Calif., U.S. Idaho, U.S.

Alfalfa, other cutting cycles[4]

5 5

10 20

10 10

5 10

30 45

Mar Jun

Calif., U.S. Idaho, U.S.

Bermuda for seed 10 25 35 35 105 March Calif. desert, U.S.

Bermuda for hay (several cuttings)

10 15 75 35 135 – Calif. desert, U.S.

Grass pasture[4] 10 20 – – –

7 days before last –4°C in spring

until 7 days after first –4°C in fall

Sudan, 1st cutting cycle 25 25 15 10 75 Apr Calif. desert, U.S.

Sudan, other cutting cycles 3 15 12 7 37 June Calif. desert, U.S.

k. Sugar Cane Sugar cane,

virgin

35 50 75

60 70

105

190 220 330

120 140 210

405 480 720

low latitudes tropics

Hawaii, U.S. Sugar cane,

ratoon

25 30 35

70 50

105

135 180 210

50 60 70

280 320 420

low latitudes tropics

Hawaii, U.S. l. Tropical Fruits and Trees Banana, 1st yr 120 90 120 60 390 Mar Mediterranean Banana, 2nd yr 120 60 180 5 365 Feb Mediterranean Pineapple 60 120 600 10 790 Hawaii, U.S.

[3] The late season for sweet maize will be about 35 days if the grain is allowed to mature and dry. [4] In climates having killing frosts, growing seasons can be estimated for alfalfa and grass as: alfalfa: last –4°C in spring until first –4°C in fall (Everson et al., 1978). grass: 7 days before last –4°C in spring and 7 days after last –4°C in fall (Kruse and Haise, 1974). (continued)

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Design and Operation of Farm Irrigation Systems 241

Table 8.3 continued.

Crop Init. (Lini)

Dev. (Ldev)

Mid (Lmid)

Late (Llate) Total Plant Date Region

m. Grapes and Berries

Grapes

20 20 20 30

40 50 50 60

120 75 90 40

60 60 20 80

240 205 180 210

April Mar May April

low latitudes Calif., U.S.

high latitudes mid-latitudes (wine)

Hops 25 40 80 10 155 April Idaho, U.S. n. Fruit Trees

Citrus 60 90 120 95 365 Jan Mediterranean Deciduous

orchard, little pruning

20 20 30

70 70 50

90 120 130

30 60 30

210 270 240

March March March

high latitudes low latitudes Calif., U.S.

Olives 30 90 60 90 270[5] March Mediterranean Pistachios 20 60 30 40 150 Feb Mediterranean Walnuts 20 10 130 30 190 April Utah, U.S.

o. Wetlands, Temperate Climate Wetlands

(cattails, bulrush)

10 180

30 60

80 90

20 35

140 365

May November

Utah, U.S.(killing frost)Florida, U.S.

Wetlands (short veg.) 180 60 90 35 365 November frost-free climate

[5] Olive trees gain new leaves in March and often have transpiration during winter, where the Kc continues outside of the “growing period” and total season length may be set to 365 days.

8.5.3.3 Kc curves for forage crops. Many crops grown for forage or hay receive multiple harvests during the growing season. Each harvest essentially terminates a sub-growing season and associated Kc curve and initiates a new sub-growing season and associated Kc curve. The resulting Kc curve for the entire growing season is the aggregation of a series of Kc curves associated with each sub-cycle. A Kc curve con-structed for alfalfa grown for hay in southern Idaho is illustrated in Figure 8.4. Cut-tings may create a ground surface with less than 10% vegetation cover. Cutting cycle 1 may have longer duration than cycles 2, 3, and 4 if low air and soil temperatures or short daylength during this period moderate the crop growth rate. Frosts terminate the growing season in southern Idaho sometime in the fall, usually in early to mid-October (day of year 280 to 300, see footnote 4 of Table 8.3). Magnitudes of Kc values during midseason periods for each cutting cycle change from cycle to cycle as a result of ad-justing Kc mid and Kc end for each period using Equation 8.59. Basal Kcb curves for for-age or hay crops can be constructed similar to Figure 8.4.

8.5.3.4 Mean Kc for the initial stage (annual crops). ET during the initial stage for annual crops is predominantly in the form of evaporation from soil. Accurate estimates for the time-averaged Kc ini for the mean Kc must consider the frequency that the soil surface is wetted. Kc mid and Kc end are less affected by wetting frequency since vegetation during these periods is generally near full ground cover so that effects of surface evapo-ration are smaller. Figures 8.5a-8.5c from FAO-56 estimate Kc ini as a function of ETo, soil type, and wetting frequency. Equations for these curves are given in Allen et al., (1998, 2005b). Figure 8.5a is used for all soil types when wetting events (precipitation and irrigation) are light (i.e., infiltrated depths average about 10 mm per wetting event), Figure 8.5b is used for “heavy” wetting events, where infiltrated depths are greater than

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242 Chapter 8 Water Requirements

90 120 150 180 210 240 270 3000.0

0.5

1.0

1.5

Kc

Alfalfa Hay Kimberly, Idaho

Cuttings

First CuttingCycle

Second Cutting Cycle

Third Cutting Cycle

Fourth Cutting Cycle

FrostLini LmidLdev Llate

Day of the Year

Figure 8.4. Crop coefficient curve for alfalfa hay crop in southern Idaho having four cuttings.

30 to 40 mm, on coarse-textured soils3 and Figure 8.5c is used for heavy wetting events on fine and medium-textured soils. In general, the mean time interval is estimated by counting all rainfall and irrigation events occurring during the initial period that are greater than a few mm. Wetting events occurring on adjacent days are typically counted as one event. When average infiltration depths are between 10 and 40 mm, the value for Kc ini can be interpolated between Figure 8.5a and Figure 8.5b or Figure 8.5c.

8.5.4 The Dual Kc Method: Incorporating Specific Wet Soil Effects The dual Kc method introduced in this section, based on FAO-56, is applicable to

both Kc based on ETo (Kco) and Kc based on ETr (Kcr), with differences only in the value for Kc max. The Ke component describes the evaporation component of ETc. Be-cause the dual Kc method incorporates the effects of specific wetting patterns and fre-quencies that may be unique to a single field, this method can provide more accurate estimates of evaporation components and total ET on an individual field basis.

When the soil surface layer is wet, following rain or irrigation, Ke is at a maximum, and when the soil surface layer is dry, Ke is small, even zero. When the soil is wet, evaporation occurs at some maximum rate and Kcb + Ke is limited by a maximum value Kc max: maxcewcbmaxcre KfKKKK ≤−= )( (8.60)

where Kc max is the maximum value of Kc following rain or irrigation, Kr is a dimen-sionless evaporation reduction coefficient (defined later) and is dependent on the cu-mulative depth of water depleted (evaporated), and few is the fraction of the soil that is both exposed to solar radiation and that is wetted. The evaporation rate is restricted by the estimated amount of energy available at the exposed soil fraction, i.e., Ke cannot exceed few Kc max. Kc max for the ETo basis (Kc max o) ranges from about 1.05 to 1.30:

[ ] { }⎟⎟⎠

⎜⎜

⎛+

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛

−−−+= 05.0,3

)45(004.0)2(04.02.13.0

2 ocbminomaxc KhRHumaxK (8.61a)

3 Coarse-textured soils include sands and loamy sand textured soils. Medium-textured soils include sandy loam, loam, silt loam, and silt textured soils. Fine-textured soils include silty clay loam, silty clay, and clay textured soils.

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Design and Operation of Farm Irrigation Systems 243

Table 8.4. Typical crop height, ranges of maximum effective rooting depth (Zr), and

soil water depletion fraction for no stress (p), for common crops (from FAO-56).

Crop Maximum CropHeight (h) (m)

Maximum Root Depth[1] (m)

Depletion Fraction[2] (p) for ETc = 5 mm d-1

a. Small Vegetables Broccoli 0.3 0.4-0.6 0.45 Brussels sprouts 0.4 0.4-0.6 0.45 Cabbage 0.4 0.5-0.8 0.45 Carrots 0.3 0.5-1.0 0.35 Cauliflower 0.4 0.4-0.7 0.45 Celery 0.6 0.3-0.5 0.20 Garlic 0.3 0.3-0.5 0.30 Lettuce 0.3 0.3-0.5 0.30 Onions, dry 0.4 0.3-0.6 0.30 green 0.3 0.3-0.6 0.30 seed 0.5 0.3-0.6 0.35 Spinach 0.3 0.3-0.5 0.20 Radishes 0.3 0.3-0.5 0.30

b. Vegetables, Solanum Family (Solanaceae) Eggplant 0.8 0.7-1.2 0.45 Sweet peppers (bell) 0.7 0.5-1.0 0.30 Tomato 0.6 0.7-1.5 0.40

c. Vegetables, Cucumber Family (Cucurbitaceae) Cantaloupe 0.3 0.9-1.5 0.45 Cucumber, fresh market 0.3 0.7-1.2 0.50 machine harvest 0.3 0.7-1.2 0.50 Pumpkin, winter squash 0.4 1.0-1.5 0.35 Squash, zucchini 0.3 0.6-1.0 0.50 Sweet melons 0.4 0.8-1.5 0.40 Watermelon 0.4 0.8-1.5 0.40

d. Roots and Tubers Beets, table 0.4 0.6-1.0 0.50 Cassava, year 1 1.0 0.5-0.8 0.35 year 2 1.5 0.7-1.0 0.40 Parsnip 0.4 0.5-1.0 0.40 Potato 0.6 0.4-0.6 0.35 Sweet potato 0.4 1.0-1.5 0.65 Turnip and rutabaga 0.6 0.5-1.0 0.50 Sugar beet 0.5 0.7-1.2 0.55[3]

[1] The larger values for Zr are for soils having no significant layering or other characteristics that can re-strict rooting depth. The smaller values for Zr may be used for irrigation scheduling and the larger values for modeling soil water stress or for rainfed conditions.

[2] The tabled values for p apply for ETc ≈ 5 mm/day. The value for p can be adjusted for different ETcaccording to p = pTable 8.4 + 0.04 (5 – ETc) where p is expressed as a fraction and ETc as mm/day.

[3] Sugar beets often experience late afternoon wilting in arid climates even at p < 0.55, with usually only minor impact on sugar yield.

(continued)

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244 Chapter 8 Water Requirements

Table 8.4 continued.

Crop

Maximum Crop Height (h) (m)

Maximum Root Depth[1] (m)

Depletion Fraction[2] (p)

for ETc = 5 mm d-1

e. Legumes (Leguminosae) Beans, green 0.4 0.5-0.7 0.45 Beans, dry and pulses 0.4 0.6-0.9 0.45 Beans, lima, large vines 0.4 0.8-1.2 0.45 Chick pea 0.4 0.6-1.0 0.50 Faba bean (broad bean), fresh 0.8 0.5-0.7 0.45 dry/seed 0.8 0.5-0.7 0.45 Garbanzo 0.8 0.6-1.0 0.45 Green gram and cowpeas 0.4 0.6-1.0 0.45 Groundnut (peanut) 0.4 0.5-1.0 0.50 Lentil 0.5 0.6-0.8 0.50 Peas, fresh 0.5 0.6-1.0 0.35 dry/seed 0.5 0.6-1.0 0.40 Soybeans 0.5-1.0 0.6-1.3 0.50 f. Perennial Vegetables (with winter dormancy and initially bare or mulched soil) Artichokes 0.7 0.6-0.9 0.45 Asparagus 0.2-0.8 1.2-1.8 0.45 Mint 0.6-0.8 0.4-0.8 0.40 Strawberries 0.2 0.2-0.3 0.20 g. Fiber Crops Cotton 1.2-1.5 1.0-1.7 0.65 Flax 1.2 1.0-1.5 0.50 Sisal 1.5 0.5-1.0 0.80 h. Oil Crops Castor bean (Ricinus) 0.3 1.0-2.0 0.50 Rapeseed, canola 0.6 1.0-1.5 0.60 Safflower 0.8 1.0-2.0 0.60 Sesame 1.0 1.0-1.5 0.60 Sunflower 2.0 0.8-1.5 0.45 i. Cereals Barley 1 1.0-1.5 0.55 Oats 1 1.0-1.5 0.55 Spring wheat 1 1.0-1.5 0.55

Winter wheat 1 1.5-1.8 0.55

Maize, field (grain) (field corn) 2 1.0-1.7 0.55 Maize, sweet (sweet corn) 1.5 0.8-1.2 0.50 Millet 1.5 1.0-2.0 0.55 Sorghum, grain 1-2 1.0-2.0 0.55 sweet 2-4 1.0-2.0 0.50 Rice 1 0.5-1.0 0.20[4] [4] The value for p for rice is 0.20 of saturation. (continued)

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Design and Operation of Farm Irrigation Systems 245

Table 8.4 continued.

Crop

Maximum Crop Height (h) (m)

Maximum Root Depth[1] (m)

Depletion Fraction[2] (p)

for ETc = 5 mm d-1

j. Forages Alfalfa, for hay 0.7 1.0-2.0 0.55 for seed 0.7 1.0-3.0 0.60 Bermuda, for hay 0.35 1.0-1.5 0.55 spring crop for seed 0.4 1.0-1.5 0.60 Clover hay, berseem 0.6 0.6-0.9 0.50 Ryegrass hay 0.3 0.6-1.0 0.60 Sudan grass hay (annual) 1.2 1.0-1.5 0.55 Grazing pasture - rotated grazing 0.15-0.30 0.5-1.5 0.60 extensive grazing 0.10 0.5-1.5 0.60 Turf grass, cool season[5] 0.10 0.5-1.0 0.40 warm season[5] 0.10 0.5-1.0 0.50

k. Sugar Cane 3 1.2-2.0 0.65 l. Tropical Fruits and Trees

Banana, 1st year 3 0.5-0.9 0.35 2nd year 4 0.5-0.9 0.35 Cacao 3 0.7-1.0 0.30 Coffee 2-3 0.9-1.5 0.40 Date palms 8 1.5-2.5 0.50 Palm trees 8 0.7-1.1 0.65 Pineapple 0.6-1.2 0.3-0.6 0.50 Rubber trees 10 1.0-1.5 0.40 Tea, non-shaded 1.5 0.9-1.5 0.40 shaded 2 0.9-1.5 0.45

m. Grapes and Berries Berries (bushes) 1.5 0.6-1.2 0.50 Grapes, table or raisin 2 1.0-2.0 0.35 wine 1.5-2 1.0-2.0 0.45 Hops 5 1.0-1.2 0.50

n. Fruit Trees Almonds 5 1.0-2.0 0.40 Apples, cherries, pears 4 1.0-2.0 0.50 Apricots, peaches, stone fruit 3 1.0-2.0 0.50 Avocado 3 0.5-1.0 0.70 Citrus 70% canopy 4 1.2-1.5 0.50 50% canopy 3 1.1-1.5 0.50 20% canopy 2 0.8-1.1 0.50 Conifer trees 10 1.0-1.5 0.70 Kiwi 3 0.7-1.3 0.35 Olives (40% to 60% ground

coverage by canopy) 3-5 1.2-1.7 0.65

Pistachios 3-5 1.0-1.5 0.40 Walnut orchard 4-5 1.7-2.4 0.50

[5] Cool season grass varieties include bluegrass, ryegrass, and fescue. Warm season varieties include ber-muda grass, buffalo grass, and St. Augustine grass. Grasses are variable in rooting depth. Some root be-low 1.2 m while others have shallow rooting depths. The deeper rooting depths for grasses represent conditions where careful water management is practiced with higher depletion between irrigations to encourage the deeper root exploration.

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246 Chapter 8 Water Requirements

(a)0 1 2 3 4 5 6 7 8 9 10 11 12

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Kc

ini

ET mm/dayo

1 day

2 day

4 day7 day

10 day20 day

small infiltration depths~ 10 mm

low moderate high very high

(b) 0 1 2 3 4 5 6 7 8 9 10 11 120.0

0.2

0.4

0.6

0.8

1.0

1.2

Kc

ini

ET mm/dayo

1 day

2 day

4 day

7 day10 day20 day

large infiltration depths> 40 mm

low moderate high very high

a. coarse textures

(c) 0 1 2 3 4 5 6 7 8 9 10 11 120.0

0.2

0.4

0.6

0.8

1.0

1.2

Kc

ini

ET mm/dayo

1 day

2 day

4 day

7 day10 day20 day

large infiltration depths > 40 mm

low moderate high very high

b. fine and medium textures

Figure 8.5. Average Kc ini for the initial crop development stage as related to the level of ETo and the interval between irrigations and/or significant rain during the initial period for (a) all soil types when wetting events are light (about 10 mm per event); (b) coarse-textured soils when wetting events are greater than about 40 mm; and (c) medium and fine-textured soils when wetting events are greater than about 40 mm (from FAO-56);

Equations for these curves are given in Allen et al. (2005b).

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Design and Operation of Farm Irrigation Systems 247

Table 8.5. Typical soil water characteristics for different soil types (from FAO-56). Depth of Water That Can

Be Depleted by Evaporation

Soil Water Characteristics

Soil Type (USDA Soil Texture Classifica-tion)

θFC m3 m-3

θWP m3 m-3

(θFC – θWP)m3 m-3

Stage 1 REW mm

Stages 1 and 2TEW[1]

(Ze = 0.10 m)mm

Stages 1 and 2TEW[1]

(Ze = 0.15 m) mm

Sand 0.07-0.17 0.02-0.07 0.05-0.11 2-7 612 9-13 Loamy sand 0.11-0.19 0.03-0.10 0.06-0.12 4-8 9-14 13-21 Sandy loam 0.18-0.28 0.06-0.16 0.11-0.15 6-10 15-20 22-30 Loam 0.20-0.30 0.07-0.17 0.13-0.18 8-10 16-22 24-33 Silt loam 0.22-0.36 0.09-0.21 0.13-0.19 8-11 18-25 27-37 Silt 0.28-0.36 0.12-0.22 0.16-0.20 8-11 22-26 33-39 Silt clay loam 0.30-0.37 0.17-0.24 0.13-0.18 8-11 22-27 33-40 Silty clay 0.30-0.42 0.17-0.29 0.13-0.19 8-12 22-28 33-42 Clay 0.32-0.40 0.20-0.24 0.12-0.20 8-12 22-29 33-43 [1] TEW = (θFC – 0.5 θWP) Ze

where h is the mean plant height (in m) during the period of calculation (initial, devel-opment, midseason, or late-season), and the max ( ) function indicates the selection of the maximum of values separated by the comma. Kc max for the tall reference ETr (Kc max r) does not require adjustment for climate, due to the greater roughness of the reference basis: Kc max r = max (1.0, {Kcbr + 0.05}) (8.61b) Kcbo and Kcbr are the basal Kc for the ETo and ETr bases. Equation 8.61 ensures that Kc max is always greater than or equal to the sum Kcb + 0.05, suggesting that wet soil increases the Kc value above Kcb by 0.05 following complete wetting of the soil sur-face, even during periods of full ground cover. Equation 8.56 and Equations 8.60 to 8.69 can be applied with both the straight-line Kcb curve style of FAO and with curvi-linear Kcb curves such as by Wright (1982), as illustrated later in this section.

The surface soil layer is presumed to dry to an air-dry water content approximated as halfway between wilting point, θ WP, and oven dry. The amount of water that can be removed by evaporation during a complete drying cycle is estimated as: eWPFC Z)θ.θ(TEW 501000 −= (8.62) where TEW (total evaporable water) is the maximum depth of water that can be evapo-rated from the surface soil layer when the layer has been initially completely wetted (in mm). Field capacity, θ FC, and θ WP are expressed in m3 m-3 and Ze is the effective depth (m) of the surface soil subject to drying to 0.5 θ WP by way of evaporation. Typi-cal values for θ FC, θ WP, and TEW are given in Table 8.5 for a range in soil types. Ze is an empirical value based on observation. Some evaporation or soil drying will be ob-served to occur below the Ze depth. FAO-56 recommended values for Ze of 0.10 to 0.15 m, with 0.1 m recommended for coarse soils and 0.15 m recommended for fine-textured soils.

The Kr coefficient of Equation (8.60) is calculated, assuming a 2-stage drying process: REW D K -1je,r ≤= for 0.1 (8.63a)

REW D REWTEWDTEW

K -1je,-1j,e

r >−

−= for (8.63b)

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248 Chapter 8 Water Requirements

where De,j-1 is cumulative depletion from the soil surface layer at the end of day j-1 (the previous day) (in mm), REW is the readily evaporable water that is evaporated during stage 1, and TEW and REW are in mm (REW < TEW). Evaporation from the soil beneath the crop canopy, occurring at a slower rate, is assumed included in the basal Kcb coefficient.

In the FAO-56 model, the term fw is defined as the fraction of the surface wetted by irrigation and/or precipitation. This term defines the potential spatial extent of evapo-ration. Common values for fw are listed in Table 8.6 and illustrated in Figure 8.6. When the soil surface is completely wetted, as by precipitation or sprinkler, few of Equation 8.60 is set equal to (1 – fc), where fc is the fraction of soil surface effectively covered by vegetation. For irrigation systems where only a fraction of the ground sur-face is wetted, few is limited to fw: ( )wcew f,ff −= 1min (8.64)

Both 1 – fc and fw, for numerical stability, have limits of 0.01 to 1. In the case of drip irrigation, Allen et al. (1998) suggest that where the majority of soil wetted by irrigation is beneath the crop canopy and is shaded, fw be reduced to about one-half to one-third of that given in Table 8.6. Their general recommendation for drip irrigation is to multiply fw by [1 – (2/3) fc]. Pruitt et al. (1984) and Bonachela et al. (2001) have described evaporation patterns and extent under drip irrigation.

The value for fc is limited to < 0.99 for numerical stability and is generally deter-mined by visual observation. For estimating few, fc can be estimated from Kcb as:

)5.01( h

mincmaxc

mincbcc KK

KKf

+

⎟⎟⎠

⎞⎜⎜⎝

−= (8.65)

where fc is limited to 0 to 0.99 and Kc min is the minimum Kc for dry bare soil with no ground cover and h is crop height in meters. The difference Kcb – Kc min is limited to > 0.01 for numerical stability. The value for fc will change daily as Kcb changes. Kc min ordinarily has the same value as Kcb ini used for annual crops under nearly bare soil conditions (i.e., Kc min ~ 0.15). However, Kc min is set to 0 or nearly zero under condi-tions with large time periods between wetting events, for example in applications with natural vegetation in deserts. The value for fc decreases during the late-season period in proportion to Kcb to account for local transport of sensible heat from senescing leaves to the soil surface.

Table 8.6. Common values for the fraction of soil surface wetted by irrigation or precipitation (after FAO-56).

Wetting Event fw Precipitation Sprinkler irrigation, field crops Sprinkler irrigation, orchards Basin irrigation Border irrigation Furrow irrigation (every furrow), narrow bed Furrow irrigation (every furrow), wide bed Furrow irrigation (alternated furrows) Microspray irrigation, orchards Trickle (drip) irrigation

1.0 1.0

0.7 to 1.0 1.0 1.0

0.6 to 1.0 0.4 to 0.6 0.3 to 0.5 0.5 to 0.8 0.3 to 0.4

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Design and Operation of Farm Irrigation Systems 249

initialcrop development

mid and late season

few = (1 - f c)

RainBasinBorder

SprinklerIrrigation

1 - f fc c

f = 1w f = 1w

1 - f fc c

few = f w few = (1 - f c)

few = 1.0 ... 0.3 f w

FurrowIrrigation

DripIrrigation

1 - fc 1 - fc

1 - fc 1 - fc fcfc

fc fc

fw fw

fwfw

Figure 8.6. Crop Determination of few (grayed areas) as a function of the fraction of

ground surface coverage (fc) and the fraction of the surface wetted (fw) (from FAO-56).

8.5.4.1 Water balance of the soil surface layer. Estimation of Ke requires a daily water balance for the few fraction of the surface soil layer. The daily soil water balance equation is:

je,j,eew

j

w

jjj-j,ej,e DPT

fE

+fI

ROPDD ++−−−= )(1 (8.66)

where De,j-1 and De,j = cumulative depletion depth at the ends of days j–1 and j, mm Pj = precipitation on day j, mm ROj = precipitation runoff from the soil surface on day j, mm Ij = irrigation depth on day j that infiltrates the soil, mm Ej = evaporation on day j (i.e., Ej = Ke ETref), mm Te, j = depth of transpiration from the exposed and wetted fraction of the soil

surface layer on day j, mm DPe j = deep percolation from the few fraction of the soil surface layer on day j

if soil water content exceeds field capacity, mm. Assuming that the surface layer is at field capacity following heavy rain or irrigation,

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250 Chapter 8 Water Requirements

the minimum value for De,j is zero. The limits imposed on De,j are consequently 0 < De,j < TEW. It is recognized that water content of the soil surface layer can exceed TEW for short periods of time while drainage is occurring. However, because the length of time that this occurs varies with soil texture, wetting depth, and tillage, De,j > 0 is assumed. Additionally, it is recognized that some drainage in soil occurs at very small rates at water contents below field capacity. To some extent, impacts of these simple assumptions can be compensated for, if needed, in setting the value for Ze or TEW. The irrigation depth Ij is divided by fw to approximate the infiltration depth to the fw portion of the soil surface. Similarly, Ej is divided by few because it is assumed that all Ej (other than residual evaporation implicit to the Kcb coefficient) is taken from the few fraction of the surface layer.

8.5.4.2 Transpiration from the surface layer. The amount of transpiration ex-tracted from the few fraction of the evaporating soil layer is generally a small fraction of total transpiration. However, for shallow-rooted annual crops where the depth of the maximum rooting is less than about 0.5 m, Te may have significant effect on the water balance of the surface layer and therefore on estimation of the evaporation component, especially for the period midway through the development period. The following ex-tension to FAO-56 by Allen et al. (2005a) estimates Te from the few fraction of the evaporation layer in proportion to the water content of that layer: refcbste ETKKKT = (8.67)

where Kt, having a range of 0 to 1, is the proportion of basal ET (= Kcb ETref) extracted as transpiration from the few fraction of the surface soil layer. Ks is the soil water stress factor computed for the root zone (range of 0 to 1). Kt is determined by comparing relative water availability in the Ze and Zr layers along with the presumed rooting dis-tribution. For the few fraction:

6.0

1

1⎟⎟⎠

⎞⎜⎜⎝

⎟⎟⎟⎟

⎜⎜⎜⎜

−=

r

er

e

t ZZ

TAWD

TEWD

K (8.68)

where the numerator and denominator of the first expression are limited to > 0.001 and the value for Kt is limited to < 1.0. TAW is the total available water (mm) in the root zone and Dr is the current depletion from the effective root zone.

In the simple water balance procedure of FAO-56, it is assumed that the soil water content is limited to < θ FC on the day of a complete wetting event. This is a reason-able assumption considering the shallowness of the surface layer. Downward drainage (percolation) of water from the surface layer is calculated as:

0)( ≥−+−= -1j,ew

jjjj e, D

fI

ROPDP (8.69)

8.5.4.3 Initialization of the water balance and order of calculation. To initiate the water balance for the evaporating layer, the user can assume that the soil surface layer is near θ FC following a heavy rain or irrigation so that De,j-1 = 0. Where a long period of time has elapsed since the last wetting, the user can assume that all evapor-able water has been depleted from the evaporation layer at the beginning of calcula-tions so that De, j-1 = TEW = 1000 (θ FC – 0.5 θWP) Ze. Calculations for the dual Kcb +

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Design and Operation of Farm Irrigation Systems 251

Ke procedure, for example when using a spreadsheet, proceed in the following order: Kcb, h, Kc max, fc, fw, few, Kr, Ke, E, DPe, De, I, Kc, and ETc.

8.5.4.4 Impacts of water stress. The Ks component in Equation 8.56 and 8.58 is the water stress coefficient used to reduce Kc or Kcb under conditions of water stress or salinity stress. FAO-56 describes the application of the salinity stress function for re-ducing ET. The water stress function is described here. Mean water content of the root zone is expressed as root zone depletion, Dr, defined as water shortage relative to field capacity. At field capacity, Dr = 0. The degree of stress is presumed to progressively increase as Dr increases past RAW, the depth of readily available water in the root zone. For Dr > RAW, Ks is:

TAWp1

DTAW=RAWTAW

DTAW=K rrs )( −

− (8.70)

where TAW is total available soil water in the root zone (mm), and p is the fraction of TAW that a crop can extract from the root zone without suffering water stress. When Dr < RAW, Ks = 1. Values for p are listed in Table 8.4. The total available water in the root zone is estimated as the difference between the water content at field capacity and wilting point: TAW = 1000 (θ FC – θ WP) Zr (8.71) where Zr is the effective rooting depth (m) and Zr contains Ze. RAW is estimated as: RAW = p TAW (8.72) where RAW has units of TAW (mm). Table 8.4 contains typical maximum values for Zr. FAO-56 describes several means to estimate the development (increase) in Zr with time for annual crops including in proportion to development of Kcb and in proportion to time. Other methods for Zr development include a sine function of time (Borg and Grimes, 1986), an exponential function of time dampened by soil temperature and soil moisture (Danuso et al., 1995) and a full root-growth simulation model by Jones et al. (1991).

8.5.5 Conditions for Maximum Transpiration The Kc values in Table 8.2 represent potential water consumption by healthy, rela-

tively disease-free, and densely planted stands of vegetation having adequate levels of soil water. When stand density, height, or leaf area are significantly less than that at-tained under ideal or normal (pristine) conditions, the value for Kc may be reduced. Low stand density, height, and leaf area are caused by disease, low soil fertility, high soil salinity, waterlogging or water shortage (moisture stress), or by poor stand estab-lishment. The reduction in the value for Kc during the midseason for poor crop stands can be as much as 0.3 to 0.5 for extremely poor crop stands and can be approximated according to the amount of effective (green) leaf area relative to that for healthy vegeta-tion having normal planting densities. Procedures for reducing Kc according to the re-duction in leaf area and the fraction of ground cover are given in Chapter 9 of FAO-56.

8.5.6 Application of the Basal Kcb Procedure over a Growing Season The first step in applying the basal Kcb approach is to construct the Kcb curve using

Kcb ini, Kcb mid, and Kcb end similar to constructing the Kc curve. Equations for computing Ke (and Ks if necessary) are applied on a daily calculation timestep where daily Kcb is interpolated from the constructed Kcb curve. Figure 8.7 is an illustration of applying the Kcb + Ke procedure for a snap bean crop harvested for dry seed. The measured ETc

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252 Chapter 8 Water Requirements

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Kcb

, Kc

0

50

100

150

200

250

300

Pre

cipi

tatio

n, n

et ir

rigat

ion,

mm

135 150 165 180 195 210 225 240 255

Day of Year, 1974

PP PP P PP

I

I

I I I II

Snap BeansFAO-56 PM EToFAO-56 KcboFAO-56 Ke

Basal Kcb Ks Kcb + Ke Kc from Lys. P = precipitation event I = irrigation

Figure 8.7. Measured (circles) and estimated (thin line) daily crop coefficients for a snap bean crop at Kimberly, Idaho. The basal crop curve (Kcb)

was derived from Kcb values given in Table 8.2. (Data from Wright, 1990.)

data are from a precision lysimeter system at Kimberly, Idaho (Wright, 1990; Vander-kimpen, 1991). The soil at Kimberly had a silt loam texture. Soil evaporation parame-ters were Ze = 0.15 m, TEW = 34 mm, and REW = 8 mm. Nearly all wetting events were from alternate-row furrow irrigation so that the value for fw was set to 0.5. Irriga-tion events occurred at about midday or during early afternoon. The agreement be-tween the estimated values for daily Kc from Equation 8.56 (thin, continuous line) and actual 24-hour measurements (symbols) is relatively good.

8.5.7 Alfalfa-Based Crop Coefficients Wright (1982, 1995) defined crop coefficients for crops common to higher eleva-

tions and latitudes of the western U.S. These coefficients, derived at Kimberly, Idaho, were initially based on the alfalfa reference ETr represented by the 1982 Kimberly Penman Equation (Equations 8.4–8.6). Wright developed both mean and basal Kc, denoted here as Kcr and Kcbr to distinguish them from the grass based Kc described earlier. These coefficients, if converted to an ETo basis by multiplying by the ratio of ETr to ETo and simplified to linear segment forms, agree closely with the Kco from Table 8.2 for similar crops. The Kimberly coefficients were converted from the 1982 Kimberly Penman ETr basis to the ASCE standardized Penman-Monteith ETrs basis by Allen and Wright (2006) and are listed in Tables 8.7 and 8.8. The Kc curves of Wright (1981, 1982) were changed little by the conversion due to the similarity in the two ETr references.

Coefficient curves by Wright are based on the relative time from planting to effec-tive full cover and on days after effective full cover. Effective full cover was defined by Wright (1982) as the time when leaves between row crops begin to interlock, at heading of grain, and flowering of peas. The Kc curves are constructed from the data in Tables 8.7 and 8.8 by using linear or curvilinear interpolation between adjacent columns or by fitting regression equations to the first half (planting to effective full cover) and to the second half (days after effective full cover) for each curve. Table 8.9 lists strategic dates of crop development recorded by Wright (1982).

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Design and Operation of Farm Irrigation Systems 253

Table 8.7. Alfalfa-based mean (single) crop coefficients (Kcr) by Wright (1981, 1995) converted for use with the ASCE standardized PM equation (Allen and Wright, 2006).

Percent Time from Planting to Effective Full Cover Date Crop 0 10 20 30 40 50 60 70 80 90 100 Spring grain[1] 0.20[2] 0.20 0.20 0.25 0.37 0.50 0.63 0.76 1.00 1.03 1.03 Peas 0.15 0.17 0.19 0.21 0.32 0.42 0.52 0.63 0.73 0.83 0.93 Sugar beets 0.26 0.26 0.26 0.26 0.26 0.28 0.30 0.38 0.55 0.74 1.03 Potatoes 0.20 0.20 0.20 0.22 0.30 0.41 0.53 0.67 0.73 0.77 0.8 Corn 0.20 0.20 0.20 0.20 0.24 0.34 0.44 0.58 0.72 0.90 1.00 Beans 0.20 0.20 0.22 0.26 0.35 0.45 0.55 0.68 0.83 0.95 0.97 Winter wheat 0.25 0.25 0.27 0.38 0.60 0.80 0.90 0.96 1.00 1.03 1.03 Days after Effective Full Cover Date Crop 0 10 20 30 40 50 60 70 80 90 100 Spring grain[1] 1.03 1.03 1.03 1.03 0.94 0.50 0.30 0.15 0.10 Peas 0.93 0.93 0.70 0.54 0.38 0.22 0.12 0.10 Sugar beets 1.03 1.03 1.03 1.00 0.97 0.92 0.82 0.74 0.65 0.61 0.56 Potatoes 0.80 0.80 0.76 0.72 0.68 0.63 0.58 0.50 0.38 0.20 0.15 Field corn 1.00 0.99 0.98 0.95 0.88 0.80 0.72 0.63 0.35 0.18 Sweet corn 1.00 0.97 0.94 0.90 0.84 0.70 0.55 0.35 0.20 0.10 Beans 0.97 0.97 0.94 0.64 0.32 0.15 0.10 0.05 Winter wheat 1.03 1.03 1.03 1.03 1.00 0.55 0.25 0.15 0.10

Alfalfa Hay: Percent Time from New Growth to Harvest and

from Harvest to Harvest Cycle 0 10 20 30 40 50 60 70 80 90 100 First[3] 0.50 0.62 0.73 0.83 0.88 0.94 1.00 1.00 1.00 0.98 0.96 Intermediate 0.30 0.40 0.55 0.80 0.94 0.97 1.00 1.00 1.00 0.97 0.94 Last 0.30 0.35 0.45 0.53 0.58 0.58 0.54 0.48 0.46 0.44 0.44 Alfalfa Hay and Ryegrass: Total Season (including all cutting effects) (days)Crop 0 20 40 60 80 100 120 140 160 180 200 Alfalfa[4] 0.45 0.69 0.87 0.88 0.70 0.75 0.88 0.81 0.88 0.71 0.65 Alfalfa[5] 0.44 0.77 0.82 0.86 0.90 0.88 0.85 0.82 0.78 0.66 0.50 Alfalfa, overall seasonal mean

0.85

Perennial ryegrass 0.55 0.66 0.77 0.8 0.8 0.8 0.78 0.76 0.72 0.68 0.55 [1] Spring grain includes wheat and barley. [2] The initial values 0.15 to 0.26 list for all crops are appropriate for relatively dry surface soil conditions

from planting until significant crop development. For moderately wet surface soil, as with pre-emergence irrigation(s) or some precipitation, use 0.35, and for very wet conditions use 0.50.

[3] First denotes first growth cycle. Intermediate growth cycles (following first cutting) may number one or more, depending on length of season. The last harvest terminates when crop becomes dormant in freez-ing weather. Alfalfa cultivar was Ranger.

[4] Each value represents the average Kc over the 20-day period at Kimberly, Idaho. The first value repre-sents from 0 to 10 days and the last value from 190 to 200 days.

[5] This is a seasonal curve for alfalfa cut periodically for hay where the values are from a smoothed, run-ning average of Kc.

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254 Chapter 8 Water Requirements

Table 8.8. Alfalfa-based basal crop coefficients (Kcbr) by Wright (1982, 1995), converted for application with the ASCE standardized PM equation (Allen and Wright, 2006).

Percent Time from Planting to Effective Full Cover Date Crop 0 10 20 30 40 50 60 70 80 90 100 Spring grain[1] 0.15 0.15 0.15 0.19 0.24 0.36 0.48 0.62 0.92 0.98 1.03 Peas 0.12 0.13 0.14 0.15 0.18 0.27 0.36 0.50 0.65 0.78 0.92 Sugar beets 0.15 0.15 0.15 0.15 0.15 0.16 0.17 0.21 0.40 0.66 1.03 Potatoes 0.15 0.15 0.15 0.15 0.15 0.20 0.34 0.49 0.64 0.72 0.77 Corn 0.15 0.15 0.15 0.16 0.17 0.20 0.27 0.41 0.55 0.80 0.96 Beans 0.15 0.15 0.17 0.19 0.23 0.35 0.46 0.60 0.78 0.93 0.95 Winter wheat 0.12 0.12 0.14 0.22 0.45 0.70 0.84 0.96 1.00 1.03 1.03 Days after Effective Full Cover Date Crop 0 10 20 30 40 50 60 70 80 90 100 Spring grain[1] 1.03 1.03 1.03 1.03 0.94 0.40 0.15 0.07 0.05 Peas 0.92 0.92 0.72 0.52 0.32 0.16 0.07 0.05 Sugar beets 1.03 1.03 1.02 0.98 0.93 0.86 0.78 0.72 0.66 0.60 0.54 Potatoes 0.77 0.77 0.73 0.68 0.64 0.59 0.54 0.47 0.20 0.08 0.08 Field corn 0.96 0.96 0.96 0.92 0.85 0.79 0.72 0.62 0.28 0.16 0.12 Sweet corn 0.96 0.95 0.93 0.88 0.80 0.65 0.47 0.23 0.12 Beans 0.95 0.95 0.88 0.64 0.30 0.09 0.05 Winter wheat 1.03 1.03 1.03 1.03 1.00 0.50 0.20 0.10 0.05 Alfalfa Hay: Percent Time from New Growth to Harvest and

from Harvest to Harvest Cycle 0 10 20 30 40 50 60 70 80 90 100 First[2] 0.35 0.45 0.56 0.72 0.82 0.90 1.00 1.00 1.00 0.98 0.96 Intermediate 0.25 0.30 0.42 0.72 0.90 0.95 1.00 1.00 0.98 0.96 0.94 Last 0.25 0.27 0.36 0.42 0.50 0.45 0.35 0.30 0.25 0.22 0.22 [1] Spring grain includes wheat and barley. [2] First denotes first growth cycle. Intermediate growth cycles (following first cutting) may number one or

more, depending on length of season. The last harvest terminates when crop becomes dormant in freez-ing weather. Alfalfa cultivar was Ranger.

Table 8.9. Dates (month/day) for crop growth stages at Kimberly, Idaho used in development of crop coefficient curves (after Wright, 1982).

Crop Planting Emergence

Rapid Growth

Full Cover

Head/ Bloom Ripening Harvest

Spring grain 4/01 4/15 5/10 6/10 6/10 7/20 8/10 Peas 4/05 4/25 5/10 6/05 6/15 7/05 7/25 Sugar beets 4/15 5/10 6/01 7/10 10/15 Potatoes 4/25 5/25 6/10 7/10 7/01 9/20 10/10 Field corn 5/05 5/25 6/10 7/15 7/30 9/10 9/20 Sweet corn 5/05 5/25 6/10 7/15 7/20 8/15 Beans 5/22 6/05 6/15 7/15 7/05 8/15 8/30 Winter wheat (2/15)[1] (3/01) [1] 3/20 6/05 6/05 7/15 8/10 Alfalfa First cutting 4/01 4/20 6/15 Second cutting 6/15 6/25 7/31 Third cutting 7/31 8/10 9/15 Fourth cutting 9/15 10/01 10/30 [1] For winter wheat, the first two dates are “effective dates” for green-up in the spring. Actual dates were

10/10 for planting and 10/25 for emergence, the previous year.

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Design and Operation of Farm Irrigation Systems 255

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Kcb

, Kc

0

50

100

150

200

250

300

Pre

cipi

tatio

n, n

et ir

rigat

ion,

mm

135 150 165 180 195 210 225 240

Day of Year, 1974

PP PP P PP

I

I

I I I II

Snap BeansASCE-PM ETrWright (1982) KcbrFAO-56 Ke

Basal Kcb Ks Kcb + Ke Kc from Lys. P = precipitation event I = irrigation

Figure 8.8. Measured (circles) and estimated (thin line) daily crop coefficients for a snap bean crop at Kimberly, Idaho. The basal crop curve (Kcb)

was derived from Kcbr values given in Table 8.8. (Data from Wright, 1990.)

8.5.8 Comparisons between FAO and Wright Kc Methods. Estimates of daily ETc by the linearized FAO-56 basal Kcb + Ke method and ETos

basis for a snap bean crop at Kimberly, Idaho, were shown in Figure 8.7 along with measured daily Kc. The same measurement data are plotted in Figure 8.8, but using the Wright (1982) curvilinear basal Kcb data from Table 8.8, instead, for snap beans, and ETrs by the ASCE PM ETr equation instead of ETos. Ke was calculated in both applica-tions using the FAO-56 method (Equations 8.60 to 8.68), with the only difference be-ing in the calculation for Kc max (Equation 8.61). The measured Kc values were calcu-lated for each day by dividing ET measured by the precision lysimeter system by ETo or ETr calculations. Stage lengths for the 1974 bean crop were 25/25/30/20 days for the FAO Kcb application and stage dates for constructing the curvilinear Kcb curve of Wright were taken from Table 8.9.

Both methods for constructing the daily Kcb + Ke curves fit observed Kc relatively well (Figures 8.7 and 8.8), where wet soil evaporation following precipitation and irrigation temporarily increased values for Kc act. The water-balance based FAO-56 Ke method estimated Kc act to remain above the Kcb curve throughout the midseason period for the bean crop due to the frequent irrigation and low, sustained rate of evaporation caused by the nearly full ground cover. The estimated Kc act followed measured Kc relatively closely during the initial period when reduction in Kcb and Es was simulated due to dryness of the surface soil layer, and during the late season period when soil water content of the root zone was estimated to be insufficient to sustain ET at poten-tial levels. These estimates were borne out by the lysimeter record.

Lysimeter-computed Kc act on about five days around day 190 (beginning of mid-season period) lay beneath both the FAO and Wright (1982) Kcb curves. The Wright Kcb curve (Figure 8.8) was constructed by Wright based on two years of data (only one is shown). The FAO-56 Kcb curve (Figure 8.7) was constructed to follow the same general shape as the Wright curve via the selection of stage lengths to provide for con-

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256 Chapter 8 Water Requirements

sistent comparisons between methods. The maximum estimated and measured Kc act for the FAO-56 ETo-based method averaged about 1.35 during the midseason period (Figure 8.7), whereas the estimated and measured Kc act for the Wright method averaged about 1.0 during the midseason period (Figure 8.8) due to the use of the alfalfa reference basis.

8.5.9 Soil Water Balance The calculation of Ks requires a daily water balance computation for the root zone.

Often, for purposes of estimating Kc, the water content of the root zone is expressed in terms of net depletion. This makes the adding and subtracting of losses and gains straightforward and various components of the soil water budget can be expressed in terms of water depth. Rainfall, irrigation, and capillary rise of groundwater add water to the root zone and decrease the root zone depletion. Soil evaporation, crop transpira-tion, and percolation losses remove water from the root zone and increase the deple-tion. A daily water balance, expressed in terms of depletion at the end of the day, is: ii,act ciii-1i,ri,r DP+ETCRIROPDD +−−−−= )( (8.73)

where Dr,i = root zone depletion at the end of day i, mm Dr,i-1 = water content in the root zone at the end of the previous day, i-1, mm Pi = precipitation on day i, mm ROi = runoff from the soil surface on day i, mm Ii = net irrigation depth on day i that infiltrates the soil, mm CRi = capillary rise from the groundwater table on day i, mm ETc act,i = actual crop evapotranspiration on day i, mm DPi = water flux out of the root zone by deep percolation on day i, mm.

Although following heavy rain or irrigation, soil water content might temporally exceed field capacity, in the above equation, the total amount of water exceeding field capacity is assumed to be lost the same day via deep percolation, following any ET for that day. This does permit the extraction of one day’s ET from this excess before per-colation. The root zone depletion will gradually increase as a result of ET. In the ab-sence of a wetting event, the root zone depletion will reach the value TAW defined from rooting depth, θ FC and θWP from Equation 8.71. At that moment no water is left for ET, and Ks becomes zero, from Equation 8.70. Limits imposed on Dr,i are: TAWD0 i,r ≤≤ (8.74)

8.5.9.1 Initial depletion. To initiate the water balance for the root zone, the initial depletion Dr,i-1 can be derived from measured soil water content by: riFC1-i,r ZD )(1000 1-θθ −= (8.75)

where θ i-1 is the average soil water content at the end of day i – 1 for the effective root zone. Following heavy rain or irrigation, the user can assume that the root zone is near field capacity, i.e., Dr,i-1 ≈ 0.

Pi is equivalent to daily precipitation. Daily precipitation in amounts less than about 0.2 ETref is normally entirely evaporated and can generally be ignored in depletion calculations. Ii is equivalent to the mean infiltrated irrigation depth expressed for the entire field surface. Runoff from the surface during precipitation can be estimated us-ing standard procedures from hydrological texts.

8.5.9.2 Capillary rise (CR). The amount of water transported upwards by capillary rise from the water table to the root zone depends on the soil type, the depth of the water table and the wetness of the root zone. Capillary rise can normally be assumed

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Design and Operation of Farm Irrigation Systems 257

to be zero when the water table is more than about 1 m below the bottom of the root zone. CR can be computed from parametric equations as a function of the water table depth, water content of the root zone, root density and soil characteristics (Liu et al., 2006). Some information on capillary rise is presented in Chapter 9.

8.5.9.3 Deep percolation from the root zone (DP). Following heavy rain or irriga-tion, the soil water content in the root zone may exceed field capacity. In applications of Equation 8.73, DP is assumed to occur within the same day of a wetting event, so that the depletion Dr, i in Equation 8.73 becomes zero. Therefore, 0)( , ≥−−+−= -1i,riciiii DETIROPDP (8.76)

As long as the soil water content in the root zone is below field capacity (i.e., Dr, i > 0), the soil will not drain and DPi = 0. The DPi term in Equations 8.73 and 8.76 is not to be confused with the DPe,i term used in Equations 8.66 and 8.69 for the evaporation layer. Both terms can be calculated at the same time, but are independent of one another.

8.5.9.4 Depth of root zone. The depth of the effective root zone can be estimated as:

growthroot

ini iminrmaxrminrir L

DoY DoYzzzz -

) -( + = (8.77)

for DoYi ≤ DoYini + Lroot growth where zr i = effective depth of the root zone on day i, mm

zr min = initial effective depth of the root zone (generally at DoY = DoYini) zr max = maximum effective depth of the root zone, m, reached Lroot growth days

following DoYini DoYi = day of the year (1–365) corresponding to day i DoYini = day of the year corresponding to the date of planting or initiation of

growth (or January 1 if a perennial is growing all of the year). When DoYi > DoYini + Lroot growth, zr = zr max. Other nonlinear schemes for root

growth such as that by Borg and Grimes (1986) can be applied, although these are often not very different from linear estimates.

8.5.10 ET During the Nongrowing Season During nongrowing periods, ET is dominated by evaporation, rather than transpira-

tion, especially if the nongrowing season is caused by killing frosts. Nongrowing sea-son ET is therefore generally best estimated using techniques that accurately estimate evaporation from the soil surface. Evaporation is a strong function of wetting fre-quency and reference ET rate and therefore, the Kc ini estimated from Figure 8.4 can be used as an estimate of Kc during the nongrowing season (Martin and Gilley 1993) with some adjustment for impacts of surface cover by dead vegetation, as described in Section 8.9.2. Alternatively, Kc during the nongrowing season can be estimated using the dual Kcb + Ke method with some adjustment to TEW and REW during cold periods (Allen et al., 2005a,b). The dual procedure was applied by Allen and Robison (2007) for complete calendar years including winter, with adjustments made during periods of snow cover. Snyder and Eching (2004, 2005) suggested a procedure for combining the Kc during the nongrowing season, estimated using a procedure similar to Figure 8.4, with the Kc curve for the growing season to create a continuous Kc for the entire calen-dar year. This was done by taking the maximum, for each day, of Kc ini as estimated from Figure 8.4 or similar curve and the Kc obtained from the growing season Kc ini curve.

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258 Chapter 8 Water Requirements

8.6 EVAPOTRANSPIRATION COEFFICIENTS FOR LANDSCAPES

Over the past several decades, the water requirements and water consumption by residential and urban landscapes have become increasingly important in terms of quantity and value of water consumed. Procedures similar to those from agriculture have been adapted to estimate ET from landscapes. However, two distinctions be-tween agriculture and landscapes exist regarding ET quantification: landscape systems are nearly always comprised of a mixture of multiple types and species of vegetation, thereby complicating the estimation of ET, and, typically, the objective of landscape irrigation is to promote appearance rather than biomass production, as is the case in agriculture. Therefore, target ET for landscapes may include an intentional “stress” factor in the baseline value for ETc act, where landscape plants are watered less than they would be if they were irrigated like a crop. They are watered enough to look good and to survive, but the plants are stressed and will not be at maximum productivity. This adjustment can result in significant water conservation. The magnitude of the stress factor depends on physiological and morphological requirements of the plants; the goal is to sustain health and appearance with minimal irrigation. For example, wa-ter conservation studies on turfgrasses have demonstrated that water savings of 30% for cool-season turfgrasses and 40% for warm-season turfgrasses may be attainable without significant loss of quality (Pittenger and Shaw, 2001). Many shrubs and groundcovers can be managed for even more stress-induced reduction in ET. Addi-tionally, few landscape sites meet the “extensive surface” requirement.

Because of the frequent inclusion of water stress in target ET values for landscape design and management, distinction must be made between these target ET values and actual ET values. Actual ET values may exceed target ET values if the landscape re-ceives more water than required by the target that includes intentional stress. Under these conditions, landscape vegetation may exploit the additional available water, sub-ject to some limit constrained by environmental energy for evaporation and leaf area. This limit, which follows behavior and principles used for agricultural crops, may ex-ceed the targeted ET rate for the particular landscape cover. Conversely, actual ET may be less than target ET values if actual stress levels to the landscape are greater than targeted. Therefore, two ET values for landscape are distinguished here. The first is the target landscape ET, referred to as ETL, that is based on minimum ET levels, relative to climate, necessary to sustain a healthy, attractive landscape. The second ET value is the actual landscape ET, ETL act, that is based on landscape type and on actual water availability.

The target ET for a landscape is calculated as ETL = KL ETo (8.78) where ETL is the target landscape ET (in mm d-1, mm month-1, or mm year-1), and ETo is the grass reference ET in the same units. KL is the target landscape coefficient, simi-lar to the crop coefficient used in agricultural applications.

There has been relatively limited experimental research on quantifying water needs of the diverse array of landscape plant types (Pittenger and Henry 2005). Much of the existing information is based largely on observation rather than on scientifically ob-tained data. Some of the leading work on landscape ET has been done in California, where water applied to landscapes in southern California is estimated to be 25% to

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Design and Operation of Farm Irrigation Systems 259

30% of all water used in the region (Pittenger and Shaw 2001). Pittenger and Shaw (2007, unpublished work from University of California Cooperative Extension) have produced a table of KL values for 35 landscape groundcovers and shrubs that provide acceptable landscape performance after establishment, but that cause a managed amount of moisture stress via limited water application. Costello et al. (2000) and IA (2005) described a recent procedure termed WUCOLS (water use classification of landscape species), where the KL has been decoupled into reproducible and visually apparent components representing the effects of three or fourfour factors that control the value for KL. The decoupling was done to provide for application to the wide di-versity of vegetation types and environments of landscape systems. Snyder and Eching (2004, 2005) have proposed a similar decoupled procedure for estimating a formulated KL, but which uses different ranges for the compoents. The Snyder and Eching (2004) procedure is described here, where KL = Kv Kd Kmc Ksm (8.79) where Kv is a vegetation species factor, Kd is a vegetation density factor, Kmc is a mi-croclimate factor, and Ksm is a managed stress factor. Kv can be considered to be the ratio of ETL to ETo for a specific single or mixture of plant species under full or nearly full ground cover and full soil water supply. Factors Kd, Kmc and Ksm modify Kv for less than effective full ground-cover, for impacts of shading or exposure to advective or reflective sources, and for intentional water stress. Each of these factors can be es-timated separate from the other, based on visual observation of the landscape (Kd and Kmc) and based on visual observation and grower experience (Ksm). Following the es-timation of the individual factors, KL is calculated using Eq. 8.79 and represents a rela-tively accurate and reproducible estimate of relative landscape ET. The procedure of Snyder and Eching (2004, 2005), used in the University of California-Davis LIMP software, differs from that of WUCOLS (Costello et al. 2000) in the ranges used to define Kd. In addition, the procedure of WUCOLS combines the values for Kv and Ksm into a “species” coefficient which can make the combined product difficult to esti-mate. The procedure and factor ranges of LIMP and Pittenger et al. (2001) may be more likely to produce more accurate and reproducible estimates of landscape ET.

8.6.1 Vegetation Coefficient The value for Kv for landscape vegetation represents the ratio of ETL to ETo for full

or nearly full cover (shading) of the ground and with full soil water supply and is used to estimate the maximum, potential rate of ratio of KL for the vegetation under ideal conditions. Costello and Jones (2000) have suggested values for a “species coeffi-cient,” Ksp, for hundreds of landscape species in California, however their values in-clude the Ksm factor and therefore should not be used with the LIMP procedure. Based on the definition for Kv used here, where Kv is fraction of ETo when the foliage is at near maximum density (Kd = 1) and full water availability (Ksm = 1), large numbers of landscape vegetation tend to have similar values for Kv due to similarity in total leaf area and stomatal response. Therefore, a condensed table of typical values for general species types can be used to provide general estimates for Kv for used in Equation 8.79, where Kv ranges from about 0.8 to 1.2. Historically the grass reference ETo has been used to estimate ET from landscapes, thus the upper limit for Kv can exceed 1.0 for some tall, leafy vegetation. Table 8.10 contains general values for Kv for general types of landscape vegetation.

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260 Chapter 8 Water Requirements

Table 8.10. Vegetation (species) factors (Kv) for general plant types. Vegetation Category[1] Kv Trees 1.15 Shrubs, desert species nondesert

0.7 0.8

Groundcover 1.0 Annuals (flowers) 0.9 Mixture of trees, shrubs,

and groundcover[2] 1.20 Cool season turfgrass[3] 0.9 Warm season turfgrass[4] 0.9 [1] The tree, shrub, and groundcover categories listed are for landscapes that are

composed solely or predominantly of one of these vegetation types. [2] Mixed plantings are composed of two or three vegetation types (i.e., where a

single vegetation type does not predominate). [3] Cool season grasses include Kentucky Blue grass, fescues, perennial ryegrass [4] Warm season grasses include Bermuda grass, St. Augustine grass, buffalo

grass, and blue grama.

The typical Kv values in Table 8.10 represent nearly full effective ground cover (fc > ~0.7) (see Section 8.5.3), and no water stress. The values in Table 8.10 are general and under most conditions, these values are not met due to the density factor being less than 1.0 and managed, intentional moisture stress. The Kv value for warm season grass is equal to that for cool season grass in Table 8.10 since both of these values represent ETL/ETo for nonstress conditions. Typically, warm season grasses can toler-ate more moisture stress than cool season grasses so that a lower managed stress factor can be applied to warm season grasses with less visual effect, as is illustrated later in Table 8.13. The Kv values for both cool season and warm season grasses are less than 1.0 in Table 8.10 due to the tendency for their mean height to be less than that of the standardized 0.12 m grass reference.

8.6.2 Density Factor Landscapes can vary considerably in vegetation density, due to wide variations in

plant spacing and maturity. Plant density factors, Kd, are listed in Table 8.11 for the pri-mary landscape vegetation types. Vegetation density refers to the collective leaf area of all plants in the unit landscape area. More densely growing vegetation has a higher Kd and will transpire and require more water. Immature and sparsely planted landscapes typically have less total leaf area per unit landscape area than mature landscapes and are assigned a Kd value in the low category. Often, landscapes have two and three tiers of vegetation including turf or groundcover, shrubs, and trees. Overlapping tiers are capable of more radiative and other energy exchange and tend to increase ET.

Allen et al. (1998) introduced a general equation for Kd that is based on the fraction of ground covered (or shaded at noon) by vegetation and mean plant height. This rela-tionship has the form:

⎟⎟⎟

⎜⎜⎜

⎛=

⎟⎠⎞

⎜⎝⎛

+heffeffcLd f,fMK 1

1

c,1min (8.80)

where fc eff is the effective fraction of ground covered or shaded by vegetation (0 to 1.0) near solar noon, h is the mean height of the vegetation in m, and ML is a multiplier on fc eff to impose an upper limit on relative transpiration per unit ground area as

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Design and Operation of Farm Irrigation Systems 261

Table 8.11. Density factor (Kd) for different vegetation heights, h, over a range of effective fraction of ground covered

or shaded by vegetation, fc eff, from Equation 8.80, where ML = 1.5. fc eff h = 0.1 m h = 0.4 m h = 1 m h = 4 m 0.0 0.00 0.00 0.00 0.00 0.1 0.12 0.15 0.15 0.15 0.2 0.23 0.30 0.30 0.30 0.3 0.33 0.42 0.45 0.45 0.4 0.43 0.52 0.60 0.60 0.5 0.53 0.61 0.71 0.87 0.6 0.63 0.69 0.77 0.90 0.7 0.72 0.78 0.84 0.93 0.8 0.82 0.85 0.89 0.96 0.9 0.91 0.93 0.95 0.98 1.0 1.00 1.00 1.00 1.00

represented by fc eff. Equation 8.80 estimates larger values for Kd as vegetation height increases. This accounts for the impact of larger aerodynamic roughness and generally more leaf area with taller vegetation, given the same fraction of ground covered or shaded. Allen et al. (1998) provided means to estimate values for fc eff as a function of time of year, latitude, vegetation height, canopy shape and, in the case of row vegeta-tion, row orientation. These relationships are provided in Equations 8.81 and 8.82 for randomly placed vegetation. For practical purposes, and due to the uncertainties asso-ciated with estimating fc for landscape vegetation, the value for fc eff can often be as-sumed to be the same as fc. The “min” function takes the smallest of the three values separated by commas. Parameter ML is expected to range from 1.5 to 2.0, depending on the canopy density and thickness and the value can be modified to fit the specific vegetation. The ML fc eff limit usually becomes invoked only for h greater than about 1 to 2 m.

For canopies such as trees or randomly planted vegetation, fc eff can be estimated as

1)sin(

≤=β

ceffc

ff (8.81)

where β is the mean angle of the sun above the horizon during the period of maximum ET (generally between 1100 and 1500 hours). β is calculated from Equation 8.43. Generally, fc eff can be calculated at solar noon when ω = 0 and Equation 8.43 becomes [ ])cos()cos()sin()sin(arcsin δϕδϕβ += (8.82)

Figure 8.9 shows Kd estimated by Equation 8.80 over a range of fraction of (effec-tive) ground cover and various mean heights for vegetation and compared to estimates for Kd from other sources for specific vegetation types. Hernandez-Suarez (1998) pro-duced estimates for Kd for low-growing vegetation and Fereres (1991) produced esti-mates for tree orchards. Snyder and Eching (2005) introduced an equation fitted to the Fereres (1991) data (Sammis et al., 2004). The Kd estimates by Hernandez-Suarez are similar to those by Equation 8.80 for h of 0.1 to 0.3 m and those by Fereres (1991) are simlar to those by Equation 8.80 for h = 5 m. These comparisons suggest that Equation 8.80 works well as a general estimate for Kd over a range of fc eff and h.

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262 Chapter 8 Water Requirements

0 0.2 0.4 0.6 0.8 1Fraction of Ground Cover

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Hernandez-Suarez (Vegetables)

Eq. 8.82, h = 0.1 m

h = 0.4 m

h = 1 m

h = 3 m

h = 5 m Fereres and Snyder and Eching (2005) (Orchards)

Kd

Figure 8.9. Density coefficient, Kd, estimated from Equation 8.80 with ML = 2 over a range

of fraction of ground cover and various plant heights, and compared with estimates by Fereres (1981) for orchards and Hernandez-Suarez (1988) for vegetables.

When two substantial tiers of vegetation are present, for example trees shading grass or flowers, the value for h can be approximated as a geometric mean of the heights of the vegetation or in proportion to the fc for each tier. The value for fc should be the total fc for the two vegetation tiers combined, accounting for any overlapped shading, i.e. using a weighted average.

It is important to note that the Kd factor estimated in this section from fc presumes that the fraction of ground surface not covered by vegetation (i.e., bare soil), is rela-tively dry and therefore does not contribute substantially to the ETL. In situations where the exposed soil surface is wet a majority of the time, the value for Kd should be increased by 10 to 20%, subject to Kd ≤ 1, to account for soil surface evaporation, es-pecially for trees and shrubs. Alternatively, a daily dual Kcb + Ke procedure, described previously, can be applied where Kcb is set equal to KL from Eq. 8.79 and Ke is esti-mated from wetting frequency.

8.6.3 Microclimate Factor Structures and paved areas typical of urban landscapes have pronounced effect on

the local energy balance and thus ET demand of adjacent vegetated areas due to the transfer of additional energy for evaporation. The environmental conditions of a land-scape may vary significantly across the landscape, for example, areas on the south side of a building vs. on the north side. The microclimate factor, Kmc, accounts for impacts of sun, shading, protected areas, hot or cool areas, reflected and emitted radiation from structures, wind, and transfer of heat energy from low ET surroundings on ET. Plant-ings adjacent to paved, open areas may have 50% higher ET demand than similar plantings among other vegetation due to the transfer of energy to the vegetation. Con-versely, plantings in shaded areas from sun and wind may have ET rates only one-half as high as those for open settings.

Values for Kmc are listed in Table 8.12 for the general classes of vegetation. In gen-eral, the “high” category (Kmc > 1) in Table 8.12 reflects harsh microclimate condi-tions such as planting in direct sunlight near a paved or other nonvegetated surface, planting near a reflecting window or heat-absorbing surfaces, or in exposed, windy conditions. The “low” category (Kmc < 1) reflects an environment where the planting is

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Design and Operation of Farm Irrigation Systems 263

Table 8.12. Microclimate factor, Kmc, for different plant types (from Irrigation Association, 2003).

Vegetation High

Average (reference condition) Low

Trees 1.4 1.0 0.5 Shrubs 1.3 1.0 0.5 Groundcover, flowers 1.2 1.0 0.5 Mixture of trees, shrubs, and

groundcover 1.4 1.0 0.5 Turfgrass 1.2 1.0 0.8

located in shade, shielded from wind, and away from dry, hot surfaces. The average or medium category (Kmc = 1) represents a reference condition similar to an open park setting, where conditions caused by buildings, pavement, shade, and reflection do not influence the ET by the landscape. The values given for Kmc are only approximate and local measurements are recommended to confirm or to derive local values.

The water manager should select the appropriate microclimate adjustment factor for each sector of a landscape or for each irrigation zone. For example, a turfgrass zone that thrives in sun may have an average Kmc of 1.0. The same zone in full shade of a building during midday may be assigned a Kmc of 0.8 or lower to better reflect the ac-tual plant water needs.

8.6.4 Managed Stress Factor As stated previously, the typical objective of landscape irrigation is to promote ap-

pearance rather than biomass production, as is the case in agriculture. Therefore, target ET for landscapes may include an intentional and managed “stress” factor in the base-line value for ETc act, where landscape plants are watered less than they would be if they were irrigated like a crop. This management is done by adjusting irrigation water schedules to apply less water than the vegetation will potentially transpire. The magni-tude of the stress factor depends on physiological and morphological requirements of the plants. For example, water conservation studies on turfgrasses have demonstrated that water savings of 30% for cool-season turfgrasses and 40% for warm-season turfgrasses may be attainable without significant loss of quality (Pittenger and Shaw, 2001). Many woody shrubs and groundcovers can be managed for even more stress-induced reduction in ET (Kjelgren et al., 2000).

Pittenger et al. (2001), Shaw and Pittenger (2004), and Pittenger and Shaw (2007) defined water needs of non-turf landscape plants as a percentage of ETo needed to maintain their appearance and intended function (e.g. shade, green foliage, screening element). In Equation 8.79, the landscape coefficient KL (equivalent to the crop coeffi-cient) is decoupled into components that describe the impacts of vegetation type, den-sity of vegetation, microclimatic effects, and managed stress factor. The managed stress factor, Ksm, represents the fraction of full ET rate targeted to obtain the func-tional and visual characteristics of the landscape vegetation. Parameter Ksm has a range of 0 to 1.0 where 1.0 represents conditions of no moisture stress (and no real water conservation) and 0 represents complete lapse of plant transpiration (i.e., probable plant death). High values for Ksm will sustain relatively more lush, high leaf-area vege-tation stands that tend to maximize ET and that may be necessary to sustain long-term plant health or appearance. Low values for Ksm represent substantial managed plant

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264 Chapter 8 Water Requirements

water stress and reduction in ET, generally at the cost of biomass accumulation and potentially visual effects (Richie and Pittenger, 2000).

Many landscape species can exercise significant stomatal control and can be “forced” to support relatively lower levels of ET. For instance, the low range for groundcover is 0.2, which is appropriate for a selected group of drought-tolerant groundcover species. This value may not be appropriate for some ornamental ground-covers, however, that require higher amounts of water (and less water stress) to main-tain health and appearance. It is recommended that one consult with local or regional sources to determine the appropriate managed stress factor (Ksm) to apply. Pettinger and Shaw (2007) suggested KL for more than 30 groundcovers and shrubs grown in southern California that contain low Ksm components and thus provide good water conservation. Many of the vegetation types listed by Pettinger and Shaw are native desert vegetation types that tolerate water stress. Other sources of KL information for specific species where the KL includes an implied Ksm < 1 include the WUCOLS pub-lication by Costello and Jones (1999).

8.6.5 Actual ET from Landscapes As discussed in the previous section, the vegetation coefficient KV represents a suf-

ficient water supply to support full ET from relatively dense vegetation having near maximum ground cover and open environmental exposure. However, the KL coeffi-cient may contain an implicit amount of managed stress for purposes of water conser-vation.. The degree of implied managed stress is quantified in Eq. 8.79 by the Ksm term. Therefore, the KL derived from Equation 8.79 using a recommended Ksm term may not represent actual conditions where actual stress deviates from the managed or target stress. Under these conditions, for purposes of water balance and determination of consumptive use from a landscaped or larger area, the “managed stress” coefficient in Equation 8.79 must be replaced by an “actual” stress coefficient, Ks, where Ks is computed from Equation 8.70 based on soil water depletion determined from a daily balance of root-zone soil water, for example usng Equation 8.73. Equation 8.79 there-fore assumes the form: KL act = Kv Kd Kmc Ks (8.83) where Ksm has been replaced by an actual stress coefficient Ks and where KL act is the actual ET anticipated from the landscape under actual water availability. Following

Table 8.13. Managed stress factors (Ksm) for general plant types and the general values of depletion fraction for no stress.

Vegetation Category High stress

Average managed

stress Low stress

Depletion fraction, p,

for no stress Trees 0.4 0.6 0.8 0.6 Shrubs, desert species nondesert

0.3 0.4

0.4 0.6

0.6 0.8

0.6 0.6

Groundcover 0.3 0.5 0.8 0.5 Annuals (flowers) 0.5 0.7 0.8 0.4 Mixture of trees, shrubs,

and groundcover[1] 0.4

0.6

0.8

0.6 Cool season turfgrass 0.7 0.8 0.9 0.4 Warm season turfgrass 0.6 0.7 0.8 0.5 [1] Mixed plantings are composed of two or three vegetation types and where a single vegetation type

does not predominate.

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Design and Operation of Farm Irrigation Systems 265

calculation of KL act, actual ET from the landscape under actual watering conditions is oactLactL ETKET = (8.84)

When Ks is estimated from Equation 8.70, the depletion fraction parameter p used to estimate RAW can be set to values listed in Table 8.13. However, it is recom-mended that one use specific values determined for specific species if these are avail-able. The effective depth of the root zone used to estimate TAW can be species or vari-ety specific and therefore information specific to the variety can be important.

8.7 ESTIMATING Kc FROM FRACTION OF COVER When a Kc value is needed for vegetation that is not similar to that listed in Tables

8.2, 8.3, or 8.5, or where a more specific value for KL (or the product KLKd ) is desired than provided by Table 8.10, the function of FAO-56 used to create the Kd density function and factor of Equation 8.80 can be applied.

The estimation of Kc for the initial growth stage of annuals, where the soil surface is mostly bare, can be determined from following Section 8.5.3.4 for the mean Kc (Kc

ini) where the crop coefficient in this stage is primarily determined by the frequency with which the soil is wetted. In the dual Kc approach, the Kcb for the initial period can be estimated as 0.1 to 0.15 for bare soil.

The Kc during the midseason and late season periods, if for a low fraction of ground cover, will be affected to a large extent by the frequency of precipitation and/or irriga-tion. Therefore, the basal Kcb + Ke approach is recommended, with Kcb estimated using the following Equation 8.85 based on the fraction of ground covered by vegetation during the particular period. For landscape crops, the impact of less than full ground shading on the ETL is incorporated by the Kd parameter in Equation 8.79 or 8.83 for KL. In the case of agricultural crops, Kd is used in a similar way: ( )mincfullcbdminccb KKKKK −+= (8.85a)

where Kcb = estimated basal Kcb (for example, during the midseason) when plant density and/or leaf area are at or lower than full cover

Kc min = the minimum Kcb representing bare soil Kcb full = the basal Kcb anticipated for the vegetation under full cover conditions

and corrected for climate Kd = the density factor from Equation 8.80.

Kc min ≈ 0.0 during long periods of no rain or irrigation and Kc min ≈ 0.15 to 0.20 during periods of rain or irrigation. For tree crops having grass or other ground cover, Equa-tion 8.85a can be re-expressed as: [ ]( )0,max covercbfullcbdcovercbcb KKKKK −+= (8.85b)

where Kcb cover is the Kcb of the ground cover in the absence of tree foliage. Kcb full for use with ETo can be approximated as a function of mean plant height and

adjusted for climate similar to the Kcb mid:

( ) [ ]3.0

2 3)45(004.0)2(04.020.1,1.00.1min ⎟

⎠⎞

⎜⎝⎛

−−−++=hRHuhK minfullcb (8.86a)

For use with alfalfa reference ETr, the climatic correction is not required for Kcb full because of the characteristics of the alfalfa reference crop. The equation is then: ( )0.1,1.08.0min hK fullcb += (8.86b)

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266 Chapter 8 Water Requirements

8.8 EFFECT OF IRRIGATION METHOD ON KC The type of irrigation system can affect the magnitude of ETc, principally in the

fraction of the field surface that is wetted during irrigation and in the irrigation inter-val. These two characteristics affect the average rate of evaporation from the soil sur-face and the frequency with which the soil surface is wetted. Other factors influencing ETc are the amounts of evaporation losses from droplets during sprinkle irrigation and evaporation of intercepted water from wet canopies following sprinkle irrigation.

All water evaporated from sprinkle droplets and from wet canopies consumes en-ergy, as liquid is changed to vapor. This energy is supplied from sensible heat con-tained in the lower atmosphere and from solar radiation. The evaporation process cools and humidifies the air. As a result, the ET demand placed on the vegetation can-opy itself (inside the leaf stomates) is generally moderated during the free water evaporation of water droplets. This effectively reduces the ETc demand from the soil profile estimated to occur in the absence of the free water evaporation. Therefore, the evaporation losses computed from free water surfaces during sprinkle irrigation cannot be directly added to the potential ETc demand as computed with Equation 8.56. As implied by Equation 8.61, an upper limit on the sum of free water evaporation from sprinkler irrigation and ETc exists. This sum approximately equals Kc max ETref. There-fore, Kc max ETref can be used to represent the maximum amount of evaporation and transpiration losses to be expected from an entire field during and immediately follow-ing irrigation for most types of irrigation systems.

8.9 EFFECTS OF SURFACE MULCHING ON KC Mulches are frequently used in vegetable production to reduce evaporation losses

from the soil surface, to accelerate crop development in cool climates by increasing soil temperature, to reduce erosion, or to assist in weed control. Mulches may be composed of organic plant materials or they may be synthetic mulches comprised of plastic sheets. Plastic mulches are the most common type of mulch used in vegetable production.

8.9.1 Plastic Mulches Plastic mulches (or covers) are generally comprised of thin sheets of polyethylene or

similar material placed over the ground surface and generally along plant rows. Holes are cut through the film at plant spacings to allow emergence of vegetation. Polyethylene covers are usually either clear or black. Effects on ETc by the two colors are generally similar (Haddadin and Ghawi, 1983; Battikhi and Hill, 1988a,b; and Safadi, 1991). Plas-tic mulches substantially reduce the evaporation of water from the soil surface, espe-cially under trickle irrigation systems. Associated with the reduction in evaporation is a general increase in transpiration from vegetation caused by transfer of both sensible and radiative heat from the surface of the plastic cover to adjacent vegetation. Usually, the ETc from mulched vegetables is about 5% to 30% lower than for vegetable production without a plastic mulch. A summary of observed reductions in Kc, evaporation, and in-creases in transpiration over growing seasons is given in Table 8.14 for five vegetable crops. Even though the transpiration rates under mulch may increase by an average of 10% to 30% over the season as compared to using no mulch, the Kc’s decrease by an aver-age of 10% to 30% due to the 50% to 80% reduction in evaporation from wet soil. Gener-ally, crop growth rates and vegetable yields are increased with the use of plastic mulches.

To consider the effects of plastic mulch on ETc, the values for mean Kc mid and Kc end for vegetables listed in tables can be reduced by 10% to 30%, depending on the fre-

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Design and Operation of Farm Irrigation Systems 267

Table 8.14. Approximate reductions in Kc, surface evaporation, and increases in transpiration for various vegetable crops under plastic mulch as compared

with no mulch using trickle irrigation (from Allen et al., 1998).

Crop

Reduction in Kc

[1] (%)

Reduction in Evaporation[1]

(%)

Increase in Transpiration[1]

(%) Squash 5-15 40-70 10-30 Cucumber 15-20 40-60 15-30 Cantaloupe 5-10 80 35 Watermelon 25-30 90 –10[2] Tomato 35 n/a n/a Average 10-30 50-80 10-30 [1] Relative to using no mulch. [2] A negative increase, i.e., a decrease in transpiration.

quency of irrigation; use the higher value for frequent trickle irrigation. The value for Kc ini is often as low as 0.10. When adjusting the basal Kcb for mulched production, less adjustment is needed, as compared to the mean Kc curve, being on the order of perhaps 5% to 15% reduction in Kcb, since the basal evaporation of water from the soil surface is less with a plastic mulch, but the transpiration is relatively more. Local calibration of Kcb (and Ke) is encouraged. When applying a basal approach with plastic mulch, fw should represent the relative equivalent fraction of the ground surface that contributes to evaporation through the vent holes in the plastic cover. This fraction can be substan-tially (at least 2 to 3 times) larger than the area of the vent holes to account for vapor transfer from under the sheet.

8.9.2 Organic Mulches Organic mulches are sometimes used with orchard production and row crops under

reduced-tillage operations. Organic mulches may be comprised of unincorporated plant residue or foreign material imported to the field. The depth of the organic mulch and the fraction of the soil surface covered can vary widely. These two parameters affect the amount of reduction in evaporation from the soil surface.

A general rule of thumb with a mulched surface is to reduce the amount of soil wa-ter evaporation by about 5% for each 10% of soil surface that is covered by the or-ganic mulch. For example, if 50% of the soil surface were covered by an organic crop-residue mulch, then the soil evaporation would be reduced by about 25%. To apply this to the Kc values in tables, one would reduce Kc ini values by about 25% and would reduce Kc mid values by 25% of the difference between Kc mid and Kcb mid.

When applying the basal approach with separate water balance of the surface soil layer, the magnitude of Esp can be reduced by about 5% for each 10% of soil surface covered by the organic mulch. These recommendations are approximate and attempt to account for the effects of partial reflection of solar radiation from residue, microad-vection of heat from residue into the soil, lateral movement of soil water from below residue to exposed soil, and the insulating effect of the organic cover. These parame-ters can vary widely, so that local research and measurement are encouraged.

8.10 PRECIPITATION RUNOFF Runoff during precipitation events is strongly influenced by land cover, soil tex-

ture, soil structure, sealing and crusting of the soil surface, land slope, local land form-ing (tillage and furrowing), antecedent moisture, and precipitation intensity and dura-

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268 Chapter 8 Water Requirements

tion. Therefore, estimation of runoff during precipitation is generally fraught with un-certainty. For general purposes, runoff can be estimated using the USDA-NRCS curve number approach. The NRCS curve number is simple to apply and is widely used within the hydrologic, soils, and water resources communities. Required data are daily precipitation depth and computation of a daily soil water balance by which to select the antecedent soil water condition.

8.10.1 The NRCS Curve Number The curve number (CN) represents the relative imperviousness of a soil-vegetation

complex and ranges from 0 for infinite perviousness and infiltration to 100 for com-plete imperviousness and total runoff (beyond abstraction). Generally the value for CN is selected from standard tables based on general crop and soil type and is adjusted for the soil water content prior to the wetting event. Examples of values for CN for vari-ous crop and soil combinations are given in Table 8.15. Parameter S in the CN proce-dure is the maximum depth of water that can be retained as infiltration and canopy interception during a single precipitation event (in mm). S is calculated as

⎟⎠⎞

⎜⎝⎛

−= 1100250CN

S (8.87)

and surface runoff is then calculated for P > 0.2 S as

( )SP

SPRO8.0

2.0 2

+−

= (8.88)

where RO is the depth of surface runoff during the event (mm), and P is the depth of rainfall during the event (mm). The 0.2S term is abstracted precipitation, i.e., that in-tercepted by canopy and soil surface before any runoff occurs. If P < 0.2 S, then RO = 0.0. In addition, RO ≤ P applies.

Table 8.15. Typical curve numbers for general crops for antecedent soil water condition (AWC) II from USDA-SCS (1972) and Allen (1988).

Soil Texture Crop Coarse Medium Fine Spring wheat 63 75 85 Winter wheat 65 75 85 Field corn 67 75 85 Potatoes 70 76 88 Sugar beets 67 74 86 Peas 63 70 82 Dry edible beans 67 75 85 Sorghum 67 73 82 Cotton 67 75 83 Paddy rice 50 60 70 Sugar cane, virgin 60 69 75 Sugar cane, ratoon 60 68 76 Fruit trees, bare soil 65 72 82 Fruit trees, ground cover 60 68 70 Small garden vegetables 72 80 88 Tomatoes 65 72 82 Alfalfa hay 60 68 77 Suggested defaults 65 72 82

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Design and Operation of Farm Irrigation Systems 269

The curve number is affected by the soil water content prior to the rainfall event, since soil water content affects the soil infiltration rate. Therefore, the CN is adjusted according to estimated soil water content prior to the rainfall event. This soil water content is termed the antecedent soil water condition or AWC. Adjustment ranges for CN were defined by SCS (1972) for dry (AWC I) and wet (AWC III) conditions. SCS defined AWC I as occurring when “watershed soils are dry enough for satisfactory plowing or cultivation to take place” and AWC III as when the “watershed is practi-cally saturated from antecedent rains” (USDA-SCS, 1972, p. 4.10). AWC II is defined as the “average condition” and represents values in Table 8.14.

Hawkins et al. (1985) expressed tabular relationships in USDA-SCS (1972) in the form of equations relating CN for AWC I and AWC III to CN for AWC II:

II

III CN ..

CNCN0128102812 −

= (8.89)

II

IIIII CN ..

CNCN0057304270 +

= (8.90)

where CNI is the curve number associated with AWC I (dry) [0 - 100], CNII is the curve number associated with AWC II (average condition) [0 - 100], and CNIII is the curve number associated with AWC III (wet) [0 - 100].

The soil surface layer water balance associated with the dual Kc procedure (Equa-tion 8.66) can be used to estimate the AWC condition. An approximation for the de-pletion of the soil surface layer at AWC III (wet) is when De = 0.5 REW, i.e., when the evaporation process is halfway through stage 1 drying. This point will normally be when approximately 5 mm or less have evaporated from the top 150 mm of soil since the time it was last completely wetted. Thus, the relationship: REW .5 D IIIAWC-e 0= (8.91)

where De-AWC III is the depletion of the evaporative layer at AWC III. AWC I can be estimated to occur when 15 to 20 mm of water have evaporated from the top 150 mm of soil from the time it was last completely wetted. This is equivalent to when the evaporation layer has dried to the point at which De exceeds 30% of the total evapor-able water in the surface layer beyond REW. This depletion amount is expressed as De = REW + 0.3(TEW – REW), where TEW is the total evaporable water in the surface layer. Therefore, TEW 0.3 REW .7 D I AWC-e += 0 (8.92)

where TEW is the cumulative evaporation from the surface soil layer at the end of stage 2 drying. When De is in between these two extremes, i.e., 0.5 REW < De < 0.7 REW + 0.3 TEW, then the AWC is in the AWC II condition and the CN value is line-arly interpolated between CNI and CNIII. In equation form: REW0.5DCNCN eIII ≤= for (8.93)

TEW0.3REWDforCNCN eI +≥= 7.0 (8.94) and, for 0.5 REW < De < REW + 0.3 (TEW – REW):

( ) ( )TEW0.3REW

CNDTEW0.3REWCNREWDCN IIIeIe+

−++−=

2.07.05.0 (8.95)

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270 Chapter 8 Water Requirements

Equation 8.95 produces CNII when De is halfway between the endpoints of CNI and CNIII due to the symmetry of CNI and CNIII relative to CNII.

8.10.2 Infiltrated Precipitation Once the surface runoff depth is estimated using the curve number procedure, the

depth of rainfall infiltrated is calculated as Pinf = P – RO (8.96) where Pinf = depth of infiltrated precipitation, mm

P = measured precipitation depth, mm RO = depth of surface runoff, mm.

If the soil will not hold the amount infiltrated, the remainder goes to deep percolation.

8.11 OTHER WATER REQUIREMENTS 8.11.1 Germination of Seeds

Seeds for many crops are planted within only a few cm of the soil surface where the soil dries quickly, as estimated in Section 8.5.4. Therefore, frequent irrigation during the week following planting may be required in dry environments to increase plant viability and health. Sprinkler irrigation is especially suited to seed germination be-cause small depths of water can be applied. Soil wetting by furrow irrigation is prac-ticed in many areas, but more water is required than with sprinklers since water re-quires more time to move horizontally from the furrow to the ridge where the seed may be planted. Furthermore, salt tends to concentrate in the ridge by evaporation when saline water is used.

Sprinkler systems for germination are normally solid set or center pivot systems that allow for daily or even more frequent wetting. Evapotranspiration requirements under conditions of high frequency irrigation are estimated using the Kc = Kcb + Ke procedure, where Kc typically approaches 1.2 to 1.3 for grass reference ETo and 1.0 for alfalfa reference ETr during the germination period. Evaporation from soil following irrigation reduces the warming of the soil, which may benefit seedling growth.

8.11.2 Climate Modification Irrigation can be used to both warm and cool the crop environment to increase

yields. Evaporation during irrigation and from wet soil following irrigation cools the air boundary layer and improves growing conditions during periods of high air tem-perature for sensitive crops of fresh vegetables and fruits including peas, tomatoes, cucumbers, muskmelons, strawberries, apples, and grapes (Burman et al., 1980). Cool-ing is accomplished by conversion of sensible heat of the air and soil into latent heat of vaporization.

All crops generally have foliar temperature thresholds above which photosynthesis is reduced due to stomatal closure or where a component of the carbon fixation proc-ess moves outside its kinetic window (Hatfield et al., 1987). For cool-season crops this occurs at temperatures in the neighborhood of 23° to 28° C and for warm-season crops at about 32° C (Hatfield et al., 1987; Keller and Bliesner, 1990). Foliar cooling re-quires high-intensity irrigation, where from two to six short applications are needed each hour. These intensities can only be practiced with automated fixed (solid set) sprinkler systems. Application rates are light, typically averaging 1 mm h-1 (Keller and Bliesner, 1990). Foliar cooling is of course more effective in arid climates where the low vapor pressure of the air and corresponding large vapor pressure deficit (es – ea) facilitates conversion of sensible heat into heat of vaporization. Misting to improve

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Design and Operation of Farm Irrigation Systems 271

greenhouse environments is a common practice. Wolfe et al. (1976) and Griffin (1976) explored the use of sprinkler irrigation systems

to cool orchard crops during early season warm periods in order to delay fruit bloom until later periods so as to reduce the risk of bloom freezing. Griffin (1976) and Griffin and Richardson (1979) developed mathematical models to estimate when irrigation bloom delay is effective. Their procedure was reviewed by Keller and Bliesner (1990).

8.11.3 Freeze Protection Both overhead and under-tree sprinkler systems are used for freeze protection. The

goal of irrigation for freeze protection is to convert enough liquid irrigation water to solid (ice) that the latent heat of fusion (approximately 335 kJ kg-1) released during the freezing of irrigation water is sufficient to maintain air temperature at 0°C. Normally fruit and vegetables will not freeze at 0°C due to the presence of sugars and other molecules in the biomass. Because irrigation for freeze protection is practiced when air temperatures and wind speeds are low and generally during nighttime, evaporation rates are low. Therefore, most irrigation water added infiltrates the soil or runs off following melting. Further information is provided by Snyder et al. (2005).

Design of sprinkler systems for frost control is covered in Keller and Bliesner (1990), Martin and Gilley (1993), and in Chapter 16. Minimum application rates are typically 2.5 to 3 mm h-1 (Keller and Bliesner, 1990). Larger applications are needed as the atmos-pheric dewpoint decreases below 0°C (Blanc et al., 1963; Keller and Bliesner, 1990).

8.11.4 Fertilizer Application Application of fertilizer by irrigation is often more economical than by other

means. Generally, irrigation for fertilizer, herbicide, or pesticide application is only initiated when there is sufficient water deficit in the root zone to retain the applied water. Otherwise, some of the applied chemical will leach below the root zone. There-fore, the evapotranspiration requirement for fertilizer application is considered to be essentially zero, unless it requires more frequent irrigation than required for soil water replacement only. This topic is described in detail in Chapter 19.

8.11.5 Soil Temperature Soil temperatures can be markedly affected by irrigation water, through cooling by

the water itself and by cooling during evaporation of water from wet soil following irrigation. Low irrigation water temperatures may depress soil temperatures and im-pede plant development. Soil cooling may be desirable under certain conditions, such as establishing seedling stands for head lettuce and during germination of grasses.

8.11.6 Dust Suppression Dust suppression, though not limited to agricultural fields, can be achieved using

sprinkler systems. Feedlot dust can be generated in hot, dry climates when cattle be-come active in early evening and the air boundary layer is stable, impeding mixing. Dust is common around construction sites and on unpaved roads. In all cases, dust can be suppressed by sprinkling. The evaporation component can be estimated using the dual Kc procedure in Section 8.5.4. A reasonable approximation can be made using Kc ini from Figure 8.4a (light wetting events) where the wetting frequency and ETo rate are used to estimate the average Kc during each wetting period.

8.11.7 Leaching Requirements Leaching of salts from the crop root zone is an essential component of irrigation

when the irrigation water carries salts. Generally, leaching of salts is accomplished

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272 Chapter 8 Water Requirements

during irrigation to replace ET losses so that the ET requirement is not increased by leaching. However, in some arid climates having heavy soils, special leaching irriga-tions are necessary. In these situations, the annual consumptive irrigation water re-quirement is increased by the evaporation from wet soil during and following each leaching irrigation. Chapter 7 describes the estimation of leaching requirements.

8.12 EFFECTIVE RAINFALL Estimation of effective rainfall is necessary in calculating net and gross irrigation

water requirements (Equations 8.1 and 8.2). In very arid climates, the majority of infil-trating rainfall is retained in the root zone and is consumed at some point as evapora-tion or transpiration. In more humid climates where rainfall totals are often greater than ET, portions of rainfall percolate below the root zone or runoff, thereby reducing the fraction that is effective in supplying crop ET. Evaporation of rainfall from wet soil is estimated using the Kcb + Ke procedure described in Section 8.5.4.

The depth of effective rainfall is estimated by subtracting runoff estimated using the curve number (Section 8.10.1) or other infiltration estimation approach and sub-tracting deep percolation from the root zone computed by Equation 8.76. The soil water balance for the root zone is updated each day using Equation 8.73 or similar equation.

Patwardhan et al. (1990) found that using a daily soil water balance equation (Equation 8.73) to estimate effectiveness of precipitation to be significantly more ac-curate than more simple and vague procedures such as the SCS monthly effective pre-cipitation method (NRCS, 1993; Dastane, 1974), especially for poorly drained soils. The effectiveness of rainfall is influenced by irrigation, since irrigation prior to a rain-fall event reduces the capacity of the soil to both infiltrate and retain the precipitation in the profile. The impact of irrigation on rainfall effectiveness is best determined by daily soil water balance. Application of the Kcb + Ke procedure provides an estimate of fraction of rainfall that evaporates with and without irrigation. The difference in DP and RO over the season with and without irrigation provides an indication of the rela-tive impact of irrigation on retained precipitation.

The daily soil water balance is the best method for estimating the carryover of win-ter precipitation into the growing period. However, the application is complicated by the impact of frozen soils on infiltration, by the estimation of crop coefficients and ETc during the dormant season, and by the challenge of estimating the energy and evapora-tion balance from any snow cover (Allen, 1996b; Wright, 1996). Chapter 11 of FAO-56 provides guidance on estimating ET during winter and dormant seasons.

There is some question on whether the evaporating compoenent of P (E from the soil surface) should be considered to be “effective.” This is especially true if estimat-ing accumulation of nongrowing season P in the root zone. In this case, only the por-tion of P that infiltrates and does not evaporate from the surface evaporation layer will accrue over time. Similar arguments can be made in estimating effective Pduring the growing season. If the dual Kcb + Ke method is ued to estimate ET, then the evapora-tive component of P is accounted for in the daily soil water balance and the estimation for effective precipitation is more accurate.

8.13 DESIGN REQUIREMENTS Design and operation of irrigation systems is affected by both the peak irrigation

water requirement and by the seasonal irrigation requirement. The seasonal irrigation water requirement dictates the annual operating time for the system and corresponding

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Design and Operation of Farm Irrigation Systems 273

costs for labor, water, and energy. The peak water requirement dictates the minimum capacity for supply pipes, pumps, and canals to sustain potential crop growth. It also governs the maximum land area that can be adequately supplied by a sprinkler irriga-tion lateral. The peak water requirement decreases as the allowable interval between irrigations increases as discussed in the next section.

8.13.1 Estimating Peak ET Using Climatic Records Because evapotranspiration is driven by weather parameters, ET can vary signifi-

cantly and randomly from day to day and from year to year. This is illustrated in Fig-ure 8.10 where daily alfalfa reference ETr estimated using the ASCE-EWRI standard-ized Penman-Monteith equation (Equation 8.3) is shown for a 20-year period at Kim-berly, Idaho. The variation in daily ETr is large. Overlain on the daily ETr are prob-ability lines for various levels of nonexceedence, based on a normal probability distri-bution. Nonexceedence is defined as the value of ET that is not expected to be ex-ceeded p% of the time, where p is the probability level.

A normal probability distribution presumes that the coefficient of skewness (CS) = 0, where CS is the ratio of skew to the population mean. Generally, with evapotranspi-ration, CS approaches 0, so that frequency estimates based on the normal distribution are generally valid (Allen and Wright, 1983; Allen et al., 1983). In the case of the normal distribution, an estimate for ET for a specific probability of nonexceedance is estimated as: s K + ET = ET PnmeanPn (8.97) where ETPn is the ET rate expected to be exceeded only 100% – p% of the time, KPn is a probability factor, and ETmean and s are the estimates for the mean and standard de-viation of the underlying ET population. Generally, ETmean, s, and ETPn are computed for a specific time period during the growing season, for example, for the peak 30-day period. The ETmean is calculated as:

nET

ET mean∑ = (8.98)

0 30 60 90 120 150 180 210 240 270 300 330 360

Day of year

0

2

4

6

8

10

12

14

Dai

ly E

Tr, m

m/d

ay

98% 95%90%70%

50%

30%

10%

5% 2%

Figure 8.10. Distribution of daily calculated alfalfa reference ETr at Kimberly, Idaho,

over a 20-year period and overlay of probability lines of nonexceedence.

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274 Chapter 8 Water Requirements

Table 8.16. Probability factors (KPn) for a normal distribution. Probability of non- exceedance, p (%) 2 5 10 25 50 75 80 90 95 98 Probability of exceedance (%) 98 95 90 75 50 25 20 10 5 2 Return period (years)

1.0 1.0 1.1 1.3 2 4 5 10 20 50

KPn –2.054 –1.645 –1.28 –0.675 0.0 0.675 0.841 1.28 1.645 2.054

where ET is the ET for each day of the period, over all years of record available for analysis, and n is the number of observations. Usually, a minimum of five years of records are required to obtain viable estimations for ETmean, s, and ETPn. ET is gener-ally estimated from weather records. The unbiased estimate for standard deviation is calculated as:

( ) ( )

⎥⎥⎦

⎢⎢⎣

⎡ ∑∑

⎥⎥⎦

⎢⎢⎣

⎡ −∑)n (n -

ET)ET(n)n -

ETET mean1

- = 1(

= s22 0.52 0.5

(8.99)

Table 8.16 lists KPn values for probabilities of interest in irrigation systems design and operation based on the normal distribution.

When the population of ET can not be considered to follow a normal distribution, for example, when the coefficient of skewness is less than about –0.5 or greater than about 0.5, then a Pearson Type III distribution can be used to estimate ETPn: ETPn = ETmean + KPPIII s (8.100) where KPPIII is the probability factor for the Pearson Type III distribution. For cases where –1.0 < CS < 1.0, an expression from Wilson and Hilferty (1931) and USGS (1981) can be used for KPPIII :

⎥⎥

⎢⎢

⎡⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ 11

662

3 - + CS CS - K

CS = K PnPPIII (8.101)

where KPn is from Table 8.16 for the normal distribution and CS is the coefficient of skewness:

( )

s n - n - n ET + ETET n - ET n=

s n - n -

ET - ETn = CS mean

3

3232

3

3

)2( )1(2)(3)(

)2( )1()(

∑∑∑∑

(8.102)

When CS exceeds the limits for Equation 8.100, values for KPPIII can be taken from tables given in USGS (1981) or other texts on frequency analysis. Martin and Gilley (1993) described the application of the Weibull probability distribution.

The length of the averaging period has substantial effect on the values for ETPn es-timated for a specific probability of nonexceedence. The length of averaging period in irrigation systems design and operation should normally be based on the allowable number of days between irrigation events. This time length, known as the irrigation interval, Iint, is estimated as:

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Design and Operation of Farm Irrigation Systems 275

ET

RAWIc

int = (8.103)

where RAW is the depth of water that can be depleted with no stress to the plant, from Equation 8.72 and ET c is the average ETc during the period:

I

ET

ETint

icdi

dic

∑2

1

=

= = (8.104)

where ETci is ETc on day i and d1 and d2 are beginning and ending days for the Iint av-eraging period, estimated as:

⎟⎠⎞

⎜⎝⎛ 60

2INT1 . + IJ - = d int (8.105)

⎟⎠⎞

⎜⎝⎛ 40

2INT2 . - IJ + = d int (8.106)

where INT( ) is the integer expression of the argument within the parentheses and J is the day of year number at the center of the period.

Figure 8.11 shows values for ETPn for the peak June 21–July 20 period at Kim-berly, Idaho between 1966 and 1985 as a function of the averaging period (i.e., irriga-tion interval). Alfalfa reference ETr is shown. ETPn is shown for both the normal and Pearson Type III frequency distributions, where differences between distributions are small. Coefficients of skewness for the data ranged from CS = –0.5 for Iint = 1 day to CS = –0.1 for Iint = 30 days. The comparison of ETPn computed by the two distributions in-dicates that the normal distribution is valid and representative for the Kimberly climate.

0 10 20 30Number of days in averaging period

0

2

4

6

8

10

12

Ave

rage

ETr

dur

ing

perio

d, m

m/d

ay

98%95%

90%75%50%

25%10% 5% 2%

Figure 8.11. Expected alfalfa reference ET rate at specified levels of nonexceedence as a

function of number of days in the averaging period for peak June 21–July 20 period, 1966–1985, at Kimberly, Idaho. Solid lines represent normal distributions

and grey lines represent log Pearson type III distributions.

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276 Chapter 8 Water Requirements

Figure 8.11 illustrates how ETPn decreases as the length of the averaging period (or irrigation interval) increases. For example, if an irrigation system design were based on probability of nonexceedance = 90% (10-year return period), the ETr used in design calculations at Kimberly would be 9.4 mm d-1 for crops having an irrigation interval of only 3 days. Design ETr would be 9.1 mm d-1 for crops having an irrigation interval of 7 days, and 8.6 mm d-1 for crops having an irrigation interval of 30 days. In other words, irrigation pipe, pump, and canal systems for the 30-day irrigation interval at Kimberly could be sized about 9% smaller than systems required for the 3-day irriga-tion interval (assuming that crop coefficients were the same). A 3-day interval would represent shallow rooted crops (Zr ~ 0.6 m) on coarse soils. The 30-day interval would represent deep-rooted crops (Zr ~ 2.5 m) on medium-textured soils.

8.13.2 General Design Curves Figure 8.11 illustrates the variation in ETPn with length of averaging period for the

southern Idaho climate, which is characterized as semiarid with relatively cloudless days during the peak monthly period. When climates have more variable cloudiness, the variation in day-to-day ET increases since solar radiation is a primary driver of evapotranspiration. Under variable cloudiness conditions, the likelihood of experienc-ing a period with cloud-free weather and corresponding high ET increases as the length of averaging period decreases. Therefore, the ratio of peak ET during short av-eraging periods relative to mean monthly ET increases as mean cloudiness of a loca-tion increases. This effect is illustrated in Figure 8.12 (adapted from Doorenbos and Pruitt, 1977), where the ratio of peak ET relative to mean monthly ET is shown to increase with increasing humidity and cloudiness. The peak ET estimated by Figure 8.12 is for the 75% probability level of nonexceedence (i.e., the ET level that is ex-ceeded in 2.5 years out of every 10). The curves in Figure 8.12 are expressed as a function of net application depth. Net application depth (Dn) is related to time length between irrigations, in days, as Dn = Iint ET c and where Dn is equivalent to the nu-merator in Equation 8.103.

1

43

2

0 40 80 120 160 200Net Application Depth, mm

1.0

1.1

1.2

1.3

1.4

Pea

k E

T (7

5% P

rob.

)

Mea

n M

onth

ly E

T

4 Mid-continental subhumid to humid climates with highly variable cloudiness during peak month. 3 Mid-continental climates with variable cloudiness and peak monthly ET = 8 mm/day.2 Mid-continental climates with variable cloudiness and peak monthly ET = 5 mm/day.1 Arid and semiarid climates with predominantly clear weather during peak month.

Figure 8.12. Expected ratio of peak design ET to mean monthly ET of the peak month for a 75% level of nonexceedence for four types of climates (after Doorenbos and Pruitt, 1977).

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Design and Operation of Farm Irrigation Systems 277

Figure 8.11 follows Curve 1 in Figure 8.12 relatively closely, where Curve 1 repre-sents arid and semiarid climates with predominantly clear weather. The four curves in Figure 8.12 can be reproduced mathematically by:

D N . + . = ETET

n N . - . -

clmonth

peak cl )0200370()20181( (8.107)

where Ncl is the number of the curve in Figure 8.12 [1 - 4] and Dn is the net application depth, mm. The standard error of estimate for the ratio estimated by Equation 8.107 is 0.012 relative to the original curves of Doorenbos and Pruitt (1977). Equation 8.107 should be applied with limits of Dn > 20 mm.

8.13.3 Population Statistics from ET Estimation Methods ET estimation equations, such as the Penman-Monteith, Penman, and Hargreaves

equations described in this chapter, may not reproduce the same variation in ET as is found in the actual, underlying ET population. In general, the more weather parame-ters contained in the ET equation, the larger will be the variation in ET estimates. Therefore, in applications where weather data are represented by long-term averages, for example wind speed, variation among ET estimates is reduced. Deviation in statis-tics from the underlying population, as represented by standard deviation, s, and coef-ficient of skewness, CS, will impact the estimation of ETPn or ETPPIII and subsequent irrigation design and operation. This behavior was discussed in more detail by Allen et al. (1983) and Allen and Wright (1983).

8.14 ANNUAL IRRIGATION WATER REQUIREMENTS Annual evapotranspiration requirements can be calculated by computing ETref on

daily, weekly, 10-day, or monthly timesteps and applying a crop coefficient over each period. When calculations are performed on a daily basis, the Kcb + Ke procedure can be utilized to improve accuracy. When weekly or longer timesteps are used, a time-averaged Kc is applied to ETref. Annual irrigation water requirements are estimated by summing the calculated ETc over the year and subtracting effective rainfall. Gross annual water requirements require division by a uniformity term (consumed fraction of applied water) and potentially a leaching factor (see Equation 8.2).

Ordinarily, ET and irrigation water requirements are needed for the growing season only. The soil water stored in the soil profile at the start of the season is estimated by operating the soil water balance over part or all of the winter period. In winter climates with frozen soils, this can be challenging. Often, in irrigated agriculture, the soil pro-file is recharged to near field capacity by the start of the growing season. In climates where the growing season is year-round, continuity between ending soil water content from one crop to the beginning soil water content of a subsequent crop should be con-sidered to adequately account for the total water requirement.

Acknowledgements The ASCE-EWRI, with support by the Irrigation Association, is commended for

the work on standardization of the calculation of reference evapotranspiration that provided the means for beginning the standardization of crop coefficients. Work by the Irrigation Association Water Management committee has helped shape the struc-ture for the landscape ET coefficients. The authors appreciate and acknowledge input and advice on agricultural crop coefficients and landscape coefficients by Dr. R. L. Snyder of the University of California, Davis.

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278 Chapter 8 Water Requirements

LIST OF SYMBOLS BR Bowen ratio Cd denominator coefficient for the ASCE standardized PM equation, s m-1 Cn numerator coefficient for the ASCE standardized PM equation; K mm s3 Mg-1 d-1, K mm s3 Mg-1 h-1 CF consumed fraction of applied water CN curve number CRi capillary rise from the groundwater table on day i, mm CS coefficient of skewness De,j-1 cumulative depletion from the soil surface layer at the end of day j – 1, mm DM day of month (1–31) Dr cumulative depletion from the root zone, including De, mm DoY day of year DPei,j deep percolation from the few fraction of the soil surface layer on day j, mm Ej evaporation on day j, mm ET evapotranspiration rate; mm d-1, mm h-1 ETc ET from a particular crop; mm d-1, mm h-1 ETc act actual evapotranspiration rate; mm d-1, mm h-1 ETL target ET from a particular landscape vegetation; mm d-1, mm h-1 ETmean mean ET of the underlying population; mm d-1 ETmonth mean ET during a month, mm d-1 ETo ET from a well-watered grass reference crop; mm d-1, mm h-1 ETpeak mean ET during peak ET period, mm d-1 ETr ET from a well-watered alfalfa reference crop; mm d-1, mm h-1 ETref reference evapotranspiration, general; mm d-1, mm h-1 G heat flux density to the ground; MJ m-2 d-1, MJ m-2 h-1, W m-2 Gsc solar constant, MJ m-2 h-1 GW contributions of shallow ground water; mm d-1, mm h-1 Ij irrigation depth on day j that infiltrates the soil, mm Iint irrigation interval, d J day of the year Jmonth day of the year for the middle of the month IR irrigation water requirement; mm d-1, mm season-1 Kc crop coefficient general Kc act crop coefficient under actual field conditions Kcb crop coefficient (basal), soil water not limiting transpiration, but the soil surface is visually dry Kcb adj basal Kcb (or Ksp pot) during the midseason when plant density and/or leaf area are at or lower than full cover Kcb full basal Kcb anticipated for vegetation under full cover conditions Kd vegetation density factor Ke evaporation coefficient Kc end Kc at the end of the late season period Kc ini average Kc during the initial period Kc m mean crop coefficient Kc max maximum value of Kc following rain or irrigation Kc mid average Kc during the midseason period

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Design and Operation of Farm Irrigation Systems 279

Kc min minimum Kc for dry bare soil with no ground cover Kco crop coefficient based on grass (ETo) reference Kcr crop coefficient based on alfalfa (ETr) reference Kd vegetation density coefficient KL target landscape coefficient KL act actual KL anticipated from the landscape under water availability Kmc microclimate factor Ko offset between mean daily Td and daily Tmin, °C KPn probability factor KPPIII probability factor for the Pearson Type III distribution Kr evaporation reduction coefficient Ks adjustment coefficient for water stress Ksm coefficient for managed water stress Kv vegetation species factor Ksp pot potential vegetation species factor under fully watered conditions Kt proportion of basal ET extracted as transpiration from surface soil layer Kw units parameter in the Penman equation; mm d-1kPa-1, mm h-1kPa-1 Ldev length of development period of crop growing season, d Lini length of initial period of crop growing season, d Lmid length of midseason period of crop growing season, d Llate length of late season period of crop growing season, d Lroot growth length of period of root growth, d Lm longitude of the solar radiation measurement site, degrees west of Greenwich Lz longitude of the center of the local time zone, degrees west of Greenwich LAI leaf area index LE latent heat energy (ET) per unit area; MJ m-2 d-1, MJ m-2 h-1, W m-2 LR leaching requirement M month number (1–12) P atmospheric pressure, kPa P precipitation, mm Pe effective precipitation (entering and remaining in the root zone), mm Pinf depth of infiltrated precipitation, mm Ra exoatmospheric solar radiation; MJ m-2 d-1, MJ m-2 h-1, W m-2 Rn net radiation; MJ m-2 d-1, MJ m-2 h-1, W m-2 Rnl net long-wave radiation; MJ m-2 d-1, MJ m-2 h-1, W m-2 Rns net solar radiation; MJ m-2 d-1, MJ m-2 h-1, W m-2 Rs solar radiation at the surface, MJ m-2 d-1, MJ m-2 h-1, W m-2 Rso solar radiation for cloudless sky; MJ m-2 d-1, MJ m-2 h-1, W m-2 RAW readily available water in the root zone, mm REW readily evaporable water from the surface soil layer, mm RH relative humidity, % RHmax maximum daily relative humidity, % RHmean mean daily or hourly relative humidity, % RHmin minimum daily relative humidity, % RO surface runoff, mm S maximum depth of water in CN procedure that can be retained as infiltra- tion, mm

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280 Chapter 8 Water Requirements

Sc seasonal correction for solar time, h T mean daily or hourly air temperature, °C Td dewpoint temperature of the air, °C Tdry dry bulb temperature of the air, °C Tei,j depth of transpiration from the few fraction of the soil surface on day j, mm TKmax maximum daily air temperature, K TKmin minimum daily air temperature, K Tmax maximum daily air temperature, °C Tmean mean daily or hourly temperature, °C Tmin minimum daily temperature, °C Twet wet bulb temperature of the air, °C TAW total available water in the root zone, mm TEW total evaporable water that can be evaporated from the surface soil layer, mm Y year (2007, for example) Ze effective depth of the surface soil subject to drying by way of evaporation, m Zr maximum effective rooting depth, m a, b constants; see usage apsy ventilation coefficient for psychrometric constant aw empirical coefficient in Penman wind function bw empirical coefficient in Penman wind function, s m-1 dr inverse relative distance factor (squared) for the earth-sun ea mean actual vapor pressure, kPa es saturation vapor pressure, kPa eo(T) saturation vapor pressure function at temperature T, kPa fc fraction of the soil surface covered by vegetation fcd cloudiness function fc eff effective fraction of the soil surface effectively covered by vegetation few fraction of the soil that is both exposed to solar radiation and that is wetted fw fraction of the soil surface wetted by irrigation and/or precipitation h height of vegetation, m n number of observations p soil water depletion fraction for no stress s standard deviation of the underlying ET population, mm d-1 t time, s, h, d tl time length of the calculation period, h uz horizontal wind speed at height z, m s-1

u2 horizontal wind speed at 2 m above the ground surface, m s-1

z elevation, m zs depth of soil experiencing the change in water content, mm, m zw height of anemometer above ground surface, m α shortwave reflectance coefficient or albedo β angle of the sun above the horizon, radians γ γ = 0.000665 P, Pa °C-1 γpsy psychrometric constant for psychrometers, kPa °C-1 Δ slope of the saturation vapor pressure-temperature curve, de/dT, kPa °C-1 Δθ change in soil water content in the root zone during period of calculation δ solar declination, radians

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Design and Operation of Farm Irrigation Systems 281

θ volumetric soil water content θFC volumetric soil water content at field capacity θWP volumetric soil water content at wilting point ϕ station latitude, radians Φ Stefan-Boltzmann constant, kJ m-2 h-1 K-4, MJ m-2 d-1 K-4 ω solar time angle at midpoint of hourly or shorter period, radians ωs sunset hour angle, radians ω1 solar hour angle at beginning of hourly or shorter period, radians ω2 solar hour angle at end of hourly or shorter period, radians

REFERENCES Aboukhaled, A., A. Alfaro, and M. Smith. 1982. Lysimeters. Irrigation and Drainage

Paper 39. Rome, Italy: FAO. Allen, R. G. 1988. IRRiSKED: Irrigation scheduling program for demand and rotation

scheduling: Logan, Utah: Dept. Biological and Irrigation Engineering, Utah State Univ. Allen, R. G. 1996a. Assessing integrity of weather data for use in reference evapotran-

spiration estimation. J. Irrig. Drain. Eng. 122(2):97-106. Allen, R.G. 1996b. Nongrowing season evaporation in Northern Utah. In Proc. North

American Water and Environment Congress, ASCE. Reston, Va.: American Soc. Civil Engineers.

Allen, R. G., C. E. Brockway, and J. L. Wright. 1983. Weather station siting and consump-tive use estimates. J. Water Resources Plan. and Man. Div., ASCE 109(2): 134-146.

Allen, R. G., A. J. Clemmens, C. M. Burt, K. Solomon, and T. O’Halloran. 2005. Pre-diction accuracy for project-wide evapotranspiration using crop coefficients and reference evapotranspiration. J. Irrig. Drain. Eng. 131(1): 24-36.

Allen, R. G., and F. N. Gichuki. 1989. Effects of projected CO2-induced climate changes on irrigation water requirements in the Great Plains states (Texas, Okla-homa, Kansas and Nebraska). In The Potential Effects of Global Climate Change on the United States: Appendix C-Agriculture. EPA-230-05-89-053. Washington, D.C.: U.S. Environmental Protection Agency, Office of Policy, Planning and Eval.

Allen, R. G., T. A. Howell, W. O. Pruitt, I. A. Walter, and M. E. Jensen, eds. 1991a. Lysimeters for Evapotranspiration and Environmental Measurements. New York, N.Y.: American Soc. Civil Engineers.

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Wright, J. L. 1995. Calibrating an ET procedure and deriving ET crop coefficients. In Proc. of the 1995 Specialty Seminar. Sponsored by the Water Res. Comm., Ameri-can Consulting Engin. Council of Colo. and the Colo. State Engineers Office.

Wright, J. L. 1996. Dormant Season Evaporation in Southern Idaho. Presentation at the North American Water and Environment Congress, ASCE.

Wright, J. L., and M. E. Jensen. 1972. Peak water requirements of crops in southern Idaho. J. Irrig. Drain. Div., ASCE 96(IR1): 193-201.