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This chapter outlines the crop coefficient approach for calculating the crop evapotranspiration under standard conditions (ETc). The standard conditions refer to crops grown in large fields under excellent agronomic and soil water conditions. The crop evapotranspiration differs distinctly from the reference evapotranspiration (ETo) as the ground cover, canopy properties and aerodynamic resistance of the crop are different from grass. The effects of characteristics that distinguish field crops from grass are integrated into the crop coefficient (Kc). In the crop coefficient approach, crop evapotranspiration is calculated by multiplying ETo by Kc.Differences in evaporation and transpiration between field crops and the reference grass surface can be integrated in a single crop coefficient (Kc) or separated into two coefficients: a basal crop (Kcb) and a soil evaporation coefficient (Ke), i.e., Kc = Kcb + Ke. The approach to follow should be selected as a function of the purpose of the calculation, the accuracy required and the data available.Calculation procedures Direct calculation

Crop coefficient approach

The crop coefficient integrates the effect of characteristics that distinguish a typical field crop from the grass reference, which has a constant appearance and a complete ground cover. Consequently, different crops will have different Kc coefficients. The changing characteristics of the crop over the growing season also affect the Kc coefficient. Finally, as evaporation is an integrated part of crop evapotranspiration, conditions affecting soil evaporation will also have an effect on Kc.Crop typeDue to differences in albedo, crop height, aerodynamic properties, and leaf and stomata properties, the evapotranspiration from full grown, well-watered crops differs from ETo.The close spacings of plants and taller canopy height and roughness of many full grown agricultural crops cause these crops to have Kc factors that are larger than 1. The Kc factor is often 5-10% higher than the reference (where Kc = 1.0), and even 15-20% greater for some tall crops such as maize, sorghum or sugar cane (Figure 20). Typical values for the crop coefficient for full grown crops (Kc mid) are listed in Table 12.Crops such as pineapples, that close their stomata during the day, have very small crop coefficients. In most species, however, the stomata open as irradiance increases. In addition to the stomatal response to environment, the position and number of the stomata and the resistance of the cuticula to vapour transfer determine the water loss from the crop. Species with stomata on only the lower side of the leaf and/or large leaf resistances will have relatively smaller Kc values. This is the case for citrus and most deciduous fruit trees. Transpiration control and spacing of the trees, providing only 70% ground cover for mature trees, may cause the Kc of those trees, if cultivated without a ground cover crop, to be smaller than one (Figure 20).ClimateThe Kc values of Table 12 are typical values expected for average Kc under a standard climatic condition, which is defined as a sub-humid climate with average daytime minimum relative humidity (RHmin) 45% and having calm to moderate wind speeds averaging 2 m/s.Variations in wind alter the aerodynamic resistance of the crops and hence their crop coefficients, especially for those crops that are substantially taller than the hypothetical grass reference. The effect of the difference in aerodynamic properties between the grass reference surface and agricultural crops is not only crop specific. It also varies with the climatic conditions and crop height. Because aerodynamic properties are greater for many agricultural crops as compared to the grass reference, the ratio of ETc to ETo (i.e., Kc) for many crops increases as wind speed increases and as relative humidity decreases. More arid climates and conditions of greater wind speed will have higher values for Kc. More humid climates and conditions of lower wind speed will have lower values for Kc.FIGURE 20. Typical Kc for different types of full grown cropsFIGURE 21. Extreme ranges expected in Kc for full grown crops as climate and weather changeThe relative impact of the climate on Kc for full grown crops is illustrated in Figure 21. The upper bounds represent extremely arid and windy conditions, while the lower bounds are valid under very humid and calm weather conditions. The ranges expected in Kc as climate and weather conditions change are quite small for short crops but are large for tall crops. Guidelines for the adjustment of Kc to the climatic conditions as a function of crop height are given in Chapter 6.Under humid and calm wind conditions, Kc becomes less dependent on the differences between the aerodynamic components of ETc and ETo and the Kc values for 'full-cover' agricultural crops do not exceed 1.0 by more than about 0.05. This is because full-cover agricultural crops and the reference crop of clipped grass both provide for nearly maximum absorption of shortwave radiation, which is the primary energy source for evaporation under humid and calm conditions. Generally, the albedos, a, are similar over a wide range of full-cover agricultural crops, including the reference crop. Because the vapour pressure deficit (es - ea) is small under humid conditions, differences in ET caused by differences in aerodynamic resistance, ra, between the agricultural crop and the reference crop are also small, especially with low to moderate wind speed.Under arid conditions, the effect of differences in ra between the agricultural crop and the grass reference crop on ETc become more pronounced because the (es - ea) term may be relatively large. The larger magnitudes of (es - ea) amplify differences in the aerodynamic term in the numerator of the Penman-Monteith equation (Equation 3) for both the crop and the reference crop. Hence, Kc will be larger under arid conditions when the agricultural crop has a leaf area and roughness height that are greater than that of the grass reference.Because the 1/ra term in the numerator of the Penman-Monteith equation (Equation 3) is multiplied by the vapour pressure deficit (es - ea), the ET from tall crops increases proportionately more relative to ETo than does ET from short crops when relative humidity is low. The Kc for tall crops, such as those 2-3 m in height, can be as much as 30% higher in a windy, arid climate as compared with a calm, humid climate. The increase in Kc is due to the influence of the larger aerodynamic roughness of the tall crop relative to grass on the transport of water vapour from the surface.Soil evaporationDifferences in soil evaporation and crop transpiration between field crops and the reference surface are integrated within the crop coefficient. The Kc coefficient for full-cover crops primarily reflects differences in transpiration as the contribution of soil evaporation is relatively small. After rainfall or irrigation, the effect of evaporation is predominant when the crop is small and scarcely shades the ground. For such low-cover conditions, the Kc coefficient is determined largely by the frequency with which the soil surface is wetted. Where the soil is wet for most of the time from irrigation or rain, the evaporation from the soil surface will be considerable and Kc may exceed 1. On the other hand, where the soil surface is dry, evaporation is restricted and Kc will be small and might even drop to as low as 0.1 (Figure 22).Differences in soil evaporation between the field crop and the reference surface can be forecast more precisely by using a dual crop coefficient.FIGURE 22. The effect of evaporation on Kc. The horizontal line represents Kc when the soil surface is kept continuously wet. The curved line corresponds to Kc when the soil surface is kept dry but the crop receives sufficient water to sustain full transpirationFIGURE 23. Crop growth stages for different types of cropsCrop growth stagesAs the crop develops, the ground cover, crop height and the leaf area change. Due to differences in evapotranspiration during the various growth stages, the Kc for a given crop will vary over the growing period. The growing period can be divided into four distinct growth stages: initial, crop development, mid-season and late season. Figure 23 illustrates the general sequence and proportion of these stages for different types of crops.Initial stageThe initial stage runs from planting date to approximately 10% ground cover. The length of the initial period is highly dependent on the crop, the crop variety, the planting date and the climate. The end of the initial period is determined as the time when approximately 10% of the ground surface is covered by green vegetation. For perennial crops, the planting date is replaced by the 'greenup' date, i.e., the time when the initiation of new leaves occurs.During the initial period, the leaf area is small, and evapotranspiration is predominately in the form of soil evaporation. Therefore, the Kc during the initial period (Kc ini) is large when the soil is wet from irrigation and rainfall and is low when the soil surface is dry. The time for the soil surface to dry is determined by the time interval between wetting events, the evaporation power of the atmosphere (ETo) and the importance of the wetting event. General estimates for Kc ini as a function of the frequency of wetting and ETo are given in Table 9. The data assume a medium textured soil. The procedure for estimating Kc ini is presented in Chapter 6.TABLE 9. Approximate values for Kc ini for medium wetting events (10-40 mm) and a medium textured soilwetting intervalevaporating power of the atmosphere (ETo)

low 1-3 mm/daymoderate 3-5 mm/dayhigh 5-7 mm/dayvery high > 7 mm/dayless than weekly1.2-0.81.1-0.61.0-0.40.9-0.3weekly0.80.60.40.3longer than once per week0.7 - 0.40.4 - 0.2*0.3 - 0.2*0.2*- 0.1*Values derived from Figures 29 and 30

(*) Note that irrigation intervals may be too large to sustain full transpiration for some young annual crops.Crop development stageThe crop development stage runs from 10% ground cover to effective full cover. Effective full cover for many crops occurs at the initiation of flowering. For row crops where rows commonly interlock leaves such as beans, sugar beets, potatoes and corn, effective cover can be defined 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 some crops, especially those taller than 0.5 m, the average fraction of the ground surface covered by vegetation (fc) at the start of effective full cover is about 0.7-0.8. Fractions of sunlit and shaded soil and leaves do not change significantly with further growth of the crop beyond fc 0.7 to 0.8. It is understood that the crop or plant can continue to grow in both height and leaf area after the time of effective full cover. Because it is difficult to visually determine when densely sown vegetation such as winter and spring cereals and some grasses reach effective full cover, the more easily detectable stage of heading (flowering) is generally used for these types of crops.For dense grasses, effective full cover may occur at about 0.10-0.15 m height. For thin stands of grass (dry rangeland), grass height may approach 0.3-0.5 m before effective full cover is reached. Densely planted forages such as alfalfa and clover reach effective full cover at about 0.3-0.4 m.Another way to estimate the occurrence of effective full cover is when the leaf area index (LAI) reaches three. LAI is defined as the average total area of leaves (one side) per unit area of ground surface.As the crop develops and shades more and more of the ground, evaporation becomes more restricted and transpiration gradually becomes the major process. During the crop development stage, the Kc value corresponds to amounts of ground cover and plant development. Typically, if the soil surface is dry, Kc = 0.5 corresponds to about 25-40% of the ground surface covered by vegetation due to the effects of shading and due to microscale transport of sensible heat from the soil into the vegetation. A Kc = 0.7 often corresponds to about 40-60% ground cover. These values will vary, depending on the crop, frequency of wetting and whether the crop uses more water than the reference crop at full ground cover (e.g., depending on its canopy architecture and crop height relative to clipped grass).Mid-season stageThe mid-season stage runs from effective full cover to the start of maturity. The start of maturity is often indicated by the beginning of the ageing, yellowing or senescence of leaves, leaf drop, or the browning of fruit to the degree that the crop evapotranspiration is reduced relative to the reference ETo. The mid-season stage is the longest stage for perennials and for many annuals, but it may be relatively short for vegetable crops that are harvested fresh for their green vegetation.At the mid-season stage the Kc reaches its maximum value. The value for Kc (Kc mid) is relatively constant for most growing and cultural conditions. Deviation of the Kc mid from the reference value '1' is primarily due to differences in crop height and resistance between the grass reference surface and the agricultural crop and weather conditions.Late season stageThe late season stage runs from the start of maturity to harvest or full senescence. The calculation for Kc and ETc is presumed 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 may be taken as the same as the date of 'planting'.FIGURE 24. Typical ranges expected in Kc for the four growth stagesThe Kc value at the end of the late season stage (Kc end) reflects crop and water management practices. The Kc end value is high if the crop is frequently irrigated until harvested fresh. If the crop is allowed to senesce and to dry out in the field before harvest, the Kc end value will be small. Senescence is usually associated with less efficient stomatal conductance of leaf surfaces due to the effects of ageing, thereby causing a reduction in Kc.Figure 24 illustrates the variation in Kc for different crops as influenced by weather factors and crop development.Crop evapotranspiration (ETc) Single and dual crop coefficient approaches