4.6.1: Basal Crop Coefficients

The crop coefficient system presented by Allen, et al. (1998) provides a comprehensive list of basal crop coefficients. The basal coefficients represent water use of a healthy, well-watered crop where the soil surface is dry. Allen’s basal crop coefficients are matched to the short reference crop used in this chapter. With this method the growing season is divided into four stages:

(1) initial stage: the period from planting through seedling growth when the soil is minimally shaded by the crop (ground shade < 10%).

(2) vegetative: the period from the initial stage to the time that the crop effectively shades the soil surface (ground shade ≅70 to 80%).

(3) midseason: period from full cover until the start of maturation when leaves begin to change color or senesce.

(4) maturing: the period from end of midseason until physiological maturity or harvest.

The progression of the basal crop coefficient during the season is illustrated in Figure 4.14 for field corn at an example site. The fraction of the growing season method developed by Stegman (1988) is used to normalize the time length of the crop growing season. The fraction of the growing season is defined as the ratio of the elapsed time since planting to the time between planting and harvest. During the initial stage, the primary water loss is due to evaporation from the soil. Since the basal curve represents dry soil surfaces, it has a constant value of 0.15 during this period. The initial value of the basal crop coefficient is denoted by K_ci.

Figure 4.14. Development of the basal crop coefficient throughout the growing season for field corn.

To compute the crop coefficient during other periods, four points need to be defined. The first point is the fraction of the growing season where canopy development begins (point 1 in Figure 4.14). At this point, the value of K_co = K_ci (usually equal to 0.15) is known. The second point occurs when the canopy has developed adequately to provide effective cover. This is when the basal crop coefficient reaches its peak value. Thus, for the second point (point 2 in Figure 4.14), both the peak value of the crop coefficient (K_cp′) and F_S2 are needed. The third point in Figure 4.14 is the time when the crop begins to mature (loses vitality). The only value needed for the third point is the time (F_S3) since the crop coefficient at that point equals the peak value. The fourth point in Figure 4.14 represents crops that senesce before harvest. To define this point, the value of the basal crop coefficient at harvest (K_cm′) must be known. If the crop is harvested before the plant begins to mature, the crop coefficient remains constant at the peak value until harvest. The five factors needed to compute the basal crop coefficient (F_S1, F_S2 F_S3, K_cp′, K_cm′) are labeled in Figure 4.14. The values presented in Figure 4.14 are F_S1 = 0.18, F_{S2 =} 0.41, F_S3 = 0.71, K_cp′ = 1.15 and K_cm′ = 0.15. Factors needed to compute basal crop coefficients for some crops are summarized in Table 4.3. Factors for crops not shown in Table 4.3 are reported by Allen, et al. (1998) or Doorenbos and Pruitt (1977). Locally developed crop coefficients can be used when available and reliable. Doorenbos and Pruitt (1977) stress that “crop coefficient values relate to ET of a disease free crop grown in large fields under optimum soil water and fertility conditions and achieving full production under the given growing environment.” Crops not meeting these provisions generally use less water unless raised in small fields where the effects of field boundaries can cause ET to be significantly different.

Table 4.3. Basal crop coefficient information for selected crops (adapted from Allen, et al. 1998).

Crops	Crops Coefficients Kci	Crop coefficients Kcp'	Crop coefficients Kcm′	Fraction of growing season FS1	Fraction of growing season FS2	Fraction of growing season FS3	Soil water stress threshold, frc ^[a]
Alfalfa, first cuttings	0.30	1.15	1.10	0.13	0.53	0.87	0.45
Alfalfa, later cuttings	0.30	1.15	1.10	0.11	0.56	0.78	0.45
Beans, dry	0.15	1.00	0.80	0.25	0.50	0.80	0.55
Beans, green	0.15	1.00	0.80	0.22	0.56	0.89	0.55
Carrot	0.15	0.95	0.85	0.17	0.42	0.83	0.65
Corn, field	0.15	1.15	0.15	0.18	0.41	0.71	0.45
Corn, sweet	0.15	1.10	1.00	0.30	0.60	0.90	0.50
Cotton	0.15	1.10	0.50	0.17	0.44	0.75	0.35
Cucumber	0.15	0.95	0.70	0.19	0.48	0.86	0.50
Grapes, table	0.15	0.80	0.40	0.10	0.34	0.71	0.65
Grapes, wine	0.15	0.65	0.40	0.10	0.34	0.71	0.55
Hay, Bermuda grass	0.50	0.95	0.80	0.07	0.19	0.74	0.45
Hay, rye grass	0.85	1.00	0.95	0.07	0.19	0.74	0.40
Lentil	0.15	1.05	0.20	0.15	0.35	0.76	0.50
Lettuce	0.15	0.90	0.90	0.29	0.67	0.90	0.70
Pepper, bell	0.15	1.00	0.80	0.14	0.33	0.86	0.70
Potato	0.15	1.10	0.55	0.27	0.45	0.88	0.65
Rice	1.00	1.15	0.55	0.20	0.40	0.80	0.80
Sorghum, grain	0.15	1.00	0.35	0.16	0.44	0.76	0.45
Soybeans	0.15	1.10	0.30	0.14	0.39	0.82	0.50
Sugar beet	0.15	1.15	0.90	0.28	0.50	0.78	0.45
Sunflower	0.15	1.10	0.25	0.19	0.46	0.81	0.55
Tomato	0.15	1.10	0.70	0.23	0.48	0.81	0.60
Watermelon	0.15	0.95	0.70	0.18	0.45	0.73	0.60
Wheat, spring	0.15	1.10	0.15	0.15	0.33	0.78	0.45
Wheat, winter [b]	0.15/0.50	1.10	0.15	0.48	0.70	0.93	0.45
Pasture, rotated grazing	0.30	0.90	0.80	0.05	0.15	1.00	0.40
Pasture, continuous grazing	0.30	0.70	0.70	0.05	0.15	1.00	0.40
Citrus, no ground cover
70% canopy	0.65	0.60	0.65	0.16	0.41	0.74	0.50
50% canopy	0.60	0.55	0.60	0.16	0.41	0.74	0.50
20% canopy	0.45	0.40	0.50	0.16	0.41	0.74	0.50
Citrus, with ground cover
70% canopy	0.75	0.70	0.75	0.16	0.41	0.74	0.50
50% canopy	0.75	0.75	0.75	0.16	0.41	0.74	0.50
20% canopy	0.80	0.80	0.85	0.16	0.41	0.74	0.50
Apples, cherries, pears
No ground cover, killing frost	0.35	0.90	0.13	0.13	0.33	0.88	0.50
No ground cover, no frost	0.50	0.90	0.13	0.13	0.33	0.88	0.50
Ground cover, killing frost	0.45	1.15	0.13	0.13	0.33	0.88	0.50
Ground cover, no frost	0.75	1.15	0.13	0.13	0.33	0.88	0.50

^[a] The critical fraction remaining (frc) is discussed in section 4.6.2.

^[b] Larger value for initial period is when fallow wheat provides full ground cover, but the soil is not frozen.

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The crop coefficient depends upon the prevailing climatic conditions. The ET of tall crops, such as trees, is affected more by wind than short crops such as grass. This effect is amplified in arid climates. Therefore, Allen, et al. (1998) recommended that the basal crop coefficient be adjusted based on wind speed and humidity. The basal crop coefficient is computed from the values listed in Table 4.3 plus the adjustment factor in Table 4.4. The initial value Kci is not modified; however, Kcp′ and Kcm′ are adjusted according to the following equations:

K_cp = K_cp′ + K_cf

and

K_cm = K_cm′ + K_cf

and where K_cp and K_cm are the adjusted coefficients, K_cp′ and K_cm′ are the tabular values of the coefficients (Table 4.3), and K_cf is the crop coefficient adjustment factor for crop height and wind speed (Table 4.4).

Table 4.4. Crop coefficient adjustment factor (K_cf) for wind speeds and relative humidity.

Wind Run(mi/d)	Average Minimum Relative Humidity (%) 20	Average Minimum Relative Humidity (%) 30	Average Minimum Relative Humidity (%) 40	Average Minimum Relative Humidity (%) 50	Average Minimum Relative Humidity (%) 60	Average Minimum Relative Humidity (%) 70	Average Minimum Relative Humidity (%) 80
Crop Height 2 ft
50	0.03	0.01	-0.02	-0.04	-0.06	-0.09	-0.11
100	0.06	0.03	0.01	-0.02	-0.05	-0.07	-0.09
150	0.08	0.05	0.03	0.00	-0.02	-0.05	-0.07
200	0.10	0.08	0.05	0.03	0.00	-0.02	-0.05
250	0.12	0.10	0.07	0.05	0.02	0.00	-0.03
300	0.15	0.12	0.10	0.07	0.05	0.02	0.00
350	0.17	0.144	0.12	0.09	0.07	0.04	0.02
crop height, 4 ft
50	0.04	0.01	-0.02	-0.05	-0.08	-0.11	-0.14
100	0.07	0.04	0.01	-0.02	-0.05	-0.08	-0.11
150	0.10	0.07	0.04	0.01	-0.02	-0.06	-0.09
200	0.12	0.09	0.06	0.03	0.00	-0.03	-0.06
250	0.15	0.12	0.09	0.06	0.03	0.00	-0.03
300	0.18	0.15	0.12	0.09	0.06	0.03	0.00
350	0.21	0.18	0.15	0.11	0.08	0.05	0.02
Crop height, 6 ft
50	0.05	0.01	-0.02	-0.06	-0.09	-0.12	-0.16
100	0.09	0.04	0.01	-0.02	-0.06	-0.09	-0.13
150	0.12	0.08	0.04	0.01	-0.03	-0.06	-0.10
200	0.15	0.11	0.07	0.04	0.00	-0.03	-0.07
250	0.19	0.14	0.10	0.07	0.03	0.00	-0.04
300	0.22	0.17	0.13	0.10	0.06	0.03	0.00
350	0.25	0.20	0.16	0.13	0.10	0.06	0.03
Crop Height, 8ft
50	0.05	0.01	-0.02	-0.06	-0.10	-0.14	-0.17
100	0.09	0.05	0.01	-0.03	-0.06	-0.10	-0.14
150	0.12	0.08	0.04	0.01	-0.03	-0.07	-0.11
200	0.15	0.12	0.08	0.04	0.00	-0.03	-0.07
250	0.19	0.15	0.11	0.07	0.04	0.00	-0.04
300	0.22	0.18	0.15	0.11	0.07	0.03	-0.01
350	0.25	0.22	0.18	0.14	0.10	0.07	0.03
Multiplier for Other Crop Heights (multiply times values for 6-ft crop)
Crop Height, ft		10	12	14	16	20	25
Multiplier		1.17	1.23	1.29	1.34	1.44	1.53

The climatic data used to adjust the crop coefficient are average values for the appropriate time of year for a specific region. Daily measured climatic conditions are not used to make the adjustment. The minimum relative humidity used in Table 4.4 can be computed by:

\(RH_{min} = 100\dfrac{e°(T_{dew})}{e°(T_{max})}\) (4.10)

Crop coefficient varies linearly with the fraction of the growing season during the vegetative and maturing growth stages. During the vegetative stage, the crop coefficient is computed with the following equation:

\(K_{co} = K_{ci}+\left(K_{cp}-K_{ci}\right)\left(\dfrac{F_S-F_{s1}}{F_{s2}-F_{s1}}\right) \) (4.11)

During the maturing stage, the crop coefficient is computed with:

\(K_{co} = K_{cp}-\left(K_{cp}-K_{cm}\right)\left(\dfrac{F_S-F_{s3}}{1-F_{s3}}\right) \) (4.12)

Example 4.2

Basal crop coefficients are fundamental to using ET in irrigation management. The procedure depends on the midseason and harvest values of the basal crop coefficient. Determine the peak and harvest values of the basal crop coefficient for corn at the site described below.

Given: Field corn with the following conditions:

Field corn conditions

Average Conditions	Midseason	Harvest
Maximum air temperature	90°F	50°F
Dew point temperature	65°F	40°F
Wind run	200 miles per day	150 miles per day

Solution

Corn will be about 8 ft tall.

From Table 4.3: K_cp′ = 1.15 and K_cm′ = 0.15

Determine minimum relative humidity using Equation 4.10 and Table 4.1:

at midseason:

\(RH_{min} = 100\left(\dfrac{e°(65)}{e°(90)}\right) = RH_{min} = 100\left(\dfrac{2.11 \text{kPa}}{4.81 \text{kPA}}\right) = 44\%\)

at harvest:*

\(RH_{min} = 100\left(\dfrac{e°(40)}{e°(50)}\right) = RH_{min} = 100\left(\dfrac{0.84 \text{kPa}}{1.23 \text{kPA}}\right) = 68\%\)

From Table 4.4 the adjustment factors are:

at midseason: K_cf is about 0.06

at harvest: K_cf is about –0.07.

The adjusted basal crop coefficients would then be:

K_cp = K_cp′ + K_cf = 1.15 + 0.06 = 1.21

K_cm = K_cm′ + K_cf = 0.15 – 0.07 = 0.08

Example 4.3

Ultimately computing crop ET depends on the value of the basal crop coefficient during the season. To illustrate the process compute the basal crop coefficient on the 15th of May, June, July, August and September for corn at the site in Example 4.2.

Given: Corn grown for grain planted on May 1 is harvested on September 30. Use the basal crop coefficients for K_cp and K_cm from Example 4.2.

Solution

Use the elapsed time since planting to describe canopy development. Determine the time from planting to harvest:

31 days in May + 30 in June + 31 in July + 31 in August + 30 in September

= 153 day growing season

Determine the fraction of the growing season for each date:

Corn growing season.

Date	Elapsed Time Since Planting	Fraction of the Growing Season
May 15	15	15 / 153 = 0.10
June 15	46	46 / 153 = 0.30
July 15	76	76 / 153 = 0.50
August 15	107	107 / 153 = 0.70
September 15	138	138 / 153 = 0.90

From Table 4.3: F_s1 = 0.18, F_s2 = 0.41, F_s3 = 0.71

From Example 4.2: K_cp = 1.21 and K_cm = 0.08

On May 15: F_s = 0.1, which is between 0 and F_s1, so K_co = K_ci = 0.15

On June 15: F_s = 0.30, which is between F_s1 and F_s2, so

\(K_{co} = 0.15+(K_{cp}-0.15)\left[\dfrac{F_S-F_{s1}}{F_{s2}-F_{s1}}\right] \) (Eq. 4.11)

\(K_{co} = 0.15+(1.21-0.15)\left[\dfrac{0.3-0.18}{0.41-0.18}\right] = 0.70\)

On July 15: F_s = 0.50, which is between F_s2 and F_s3, so K_co = K_cp = 1.21

On August 15: F_s = 0.70, which is between F_s2 and F_s3, so K_co = K_cp = 1.21

On September 15: F_s = 0.90, which is between F_s3 and 1.0, so:

\(K_{co} = 1.21-(1.21-0.08)\left[\dfrac{0.90-0.71}{1.00-0.71}\right] = 0.47\) (Eq. .12)