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Chapter 6 - ETc - Single crop coefficient (Kc)


Length of growth stages
Crop coefficients
Construction of the Kc curve
Calculating ETc
Alfalfa-based crop coefficients
Transferability of previous Kc values


This chapter deals with the calculation of crop evapotranspiration (ETc) under standard conditions. No limitations are placed on crop growth or evapotranspiration from soil water and salinity stress, crop density, pests and diseases, weed infestation or low fertility. ETc is determined by the crop coefficient approach whereby the effect of the various weather conditions are incorporated into ETo and the crop characteristics into the Kc coefficient:

ETc = Kc ETo (58)

The effect of both crop transpiration and soil evaporation are integrated into a single crop coefficient. The Kc coefficient incorporates crop characteristics and averaged effects of evaporation from the soil. For normal irrigation planning and management purposes, for the development of basic irrigation schedules, and for most hydrologic water balance studies, average crop coefficients are relevant and more convenient than the Kc computed on a daily time step using a separate crop and soil coefficient (Chapter 7). Only when values for Kc are needed on a daily basis for specific fields of crops and for specific years, must a separate transpiration and evaporation coefficient (Kcb + Ke) be considered.

The calculation procedure for crop evapotranspiration, ETc, consists of:

1. identifying the crop growth stages, determining their lengths, and selecting the corresponding Kc coefficients;

2. adjusting the selected Kc coefficients for frequency of wetting or climatic conditions during the stage;

3. constructing the crop coefficient curve (allowing one to determine Kc values for any period during the growing period); and

4. calculating ETc as the product of ETo and Kc.

Length of growth stages

FAO Irrigation and Drainage Paper No. 24 provides general lengths for the four distinct growth stages and the total growing period for various types of climates and locations. This information has been supplemented from other sources and is summarized in Table 11.

In some situations, the time of emergence of vegetation and the time of effective full cover can be predicted using cumulative degree-based regression equations or by more sophisticated plant growth models. These types of models should be verified or validated for the local area or for a specific crop variety using local observations.

TABLE 11. Lengths of crop development stages* for various planting periods and climatic regions (days)

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, USA

Cabbage

40

60

50

15

165

Sept

Calif. Desert, USA

Carrots

20

30

50/30

20

100

Oct/Jan

Arid climate

30

40

60

20

150

Feb/Mar

Mediterranean

30

50

90

30

200

Oct

Calif. Desert, USA

Cauliflower

35

50

40

15

140

Sept

Calif. Desert, USA

Celery

25

40

95

20

180

Oct

(Semi) Arid

25

40

45

15

125

April

Mediterranean

30

55

105

20

210

Jan

(Semi) Arid

Crucifers1

20

30

20

10

80

April

Mediterranean

25

35

25

10

95

February

Mediterranean

30

35

90

40

195

Oct/Nov

Mediterranean

Lettuce

20

30

15

10

75

April

Mediterranean

30

40

25

10

105

Nov/Jan

Mediterranean

25

35

30

10

100

Oct/Nov

Arid Region

35

50

45

10

140

Feb

Mediterranean

Onion (dry)

15

25

70

40

150

April

Mediterranean

20

35

110

45

210

Oct; Jan.

Arid Region; Calif.

Onion (green)

25

30

10

5

70

April/May

Mediterranean

20

45

20

10

95

October

Arid Region

30

55

55

40

180

March

Calif., USA

Onion (seed)

20

45

165

45

275

Sept

Calif. Desert, USA

Spinach

20

20

15/25

5

60/70

Apr; Sep/Oct

Mediterranean

20

30

40

10

100

November

Arid Region

Radish

5

10

15

5

35

Mar/Apr

Medit.; Europe

10

10

15

5

40

Winter

Arid Region

b. Vegetables - Solanum Family (Solanaceae)

Egg plant

30

40

40

20

130\1

October

Arid Region

30

45

40

25

40

May/June

Mediterranean

Sweet peppers (bell)

25/30

35

40

20

125

April/June

Europe and Medit.

30

40

110

30

210

October

Arid Region

Tomato

30

40

40

25

135

January

Arid Region

35

40

50

30

155

Apr/May

Calif., USA

25

40

60

30

155

Jan

Calif. Desert, USA

35

45

70

30

180

Oct/Nov

Arid Region

30

40

45

30

145

April/May

Mediterranean

c. Vegetables - Cucumber Family (Cucurbitaceae)

Cantaloupe

30

45

35

10

120

Jan

Calif., USA

10

60

25

25

120

Aug

Calif., USA

Cucumber

20

30

40

15

105

June/Aug

Arid Region

25

35

50

20

130

Nov; Feb

Arid Region

Pumpkin, Winter squash

20

30

30

20

100

Mar, Aug

Mediterranean

25

35

35

25

120

June

Europe

Squash, Zucchini

25

35

25

15

100

Apr; Dec.

Medit.; Arid Reg.

20

30

25

15

90

May/June

Medit.; Europe

Sweet melons

25

35

40

20

120

May

Mediterranean

30

30

50

30

140

March

Calif., USA

15

40

65

15

135

Aug

Calif. Desert, USA

30

45

65

20

160

Dec/Jan

Arid Region

Water melons

20

30

30

30

110

April

Italy

10

20

20

30

80

Mat/Aug

Near East (desert)

d. Roots and Tubers

Beets, table

15

25

20

10

70

Apr/May

Mediterranean

25

30

25

10

90

Feb/Mar

Mediterranean & Arid

Cassava: year 1

20

40

90

60

210

Rainy

Tropical regions

year 2

150

40

110

60

360

season


Potato

25

30

30/45

30

115/130

Jan/Nov

(Semi) Arid Climate

25

30

45

30

130

May

Continental Climate

30

35

50

30

145

April

Europe

45

30

70

20

165

Apr/May

Idaho, USA

30

35

50

25

140

Dec

Calif. Desert, USA

Sweet potato

20

30

60

40

150

April

Mediterranean

15

30

50

30

125

Rainy seas.

Tropical regions

Sugarbeet

30

45

90

15

180

March

Calif., USA

25

30

90

10

155

June

Calif., USA

25

65

100

65

255

Sept

Calif. Desert, USA

50

40

50

40

180

April

Idaho, USA

25

35

50

50

160

May

Mediterranean

45

75

80

30

230

November

Mediterranean

35

60

70

40

205

November

Arid Regions

e. Legumes (Leguminosae)

Beans (green)

20

30

30

10

90

Feb/Mar

Calif., Mediterranean

15

25

25

10

75

Aug/Sep

Calif., Egypt, Lebanon

Beans (dry)

20

30

40

20

110

May/June

Continental Climates

15

25

35

20

95

June

Pakistan, Calif.

25

25

30

20

100

June

Idaho, USA

Faba bean, broad bean

15

25

35

15

90

May

Europe

20

30

35

15

100

Mar/Apr

Mediterranean


- dry

90

45

40

60

235

Nov

Europe


- green

90

45

40

0

175

Nov

Europe

Green gram, cowpeas

20

30

30

20

110

March

Mediterranean

Groundnut

25

35

45

25

130

Dry

West Africa

35

35

35

35

140

season

High Latitudes

35

45

35

25

140

May May/June

Mediterranean

Lentil

20

30

60

40

150

April

Europe

25

35

70

40

170

Oct/Nov

Arid Region

Peas

15

25

35

15

90

May

Europe

20

30

35

15

100

Mar/Apr

Mediterranean

35

25

30

20

110

April

Idaho, USA

Soybeans

15

15

40

15

85

Dec

Tropics

20

30/35

60

25

140

May

Central USA

20

25

75

30

150

June

Japan

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

Artichoke

40

40

250

30

360

Apr (1st yr)

California

20

25

250

30

325

May (2nd yr)

(cut in May)

Asparagus

50

30

100

50

230

Feb

Warm Winter

90

30

200

45

365

Feb

Mediterranean

g. Fibre Crops

Cotton

30

50

60

55

195

Mar-May

Egypt; Pakistan; Calif.

45

90

45

45

225

Mar

Calif. Desert, USA

30

50

60

55

195

Sept

Yemen

30

50

55

45

180

April

Texas

Flax

25

35

50

40

150

April

Europe

30

40

100

50

220

October

Arizona

h. Oil Crops

Castor beans

25

40

65

50

180

March

(Semi) Arid Climates

20

40

50

25

135

Nov.

Indonesia

Safflower

20

35

45

25

125

April

California, USA

25

35

55

30

145

Mar

High Latitudes

35

55

60

40

190

Oct/Nov

Arid Region

Sesame

20

30

40

20

100

June

China

Sunflower

25

35

45

25

130

April/May

Medit.; California

i. Cereals

Barley/Oats/Wheat

15

25

50

30

120

November

Central India

20

25

60

30

135

March/Apr

35-45 °L

15

30

65

40

150

July

East Africa

40

30

40

20

130

Apr


40

60

60

40

200

Nov


20

50

60

30

160

Dec

Calif. Desert, USA

Winter Wheat

202

602

70

30

180

December

Calif., USA

30

140

40

30

240

November

Mediterranean

160

75

75

25

335

October

Idaho, USA

Grains (small)

20

30

60

40

150

April

Mediterranean

25

35

65

40

165

Oct/Nov

Pakistan; Arid Reg.

Maize (grain)

30

50

60

40

180

April

East Africa (alt.)

25

40

45

30

140

Dec/Jan

Arid Climate

20

35

40

30

125

June

Nigeria (humid)

20

35

40

30

125

October

India (dry, cool)

30

40

50

30

150

April

Spain (spr, sum.); Calif.

30

40

50

50

170

April

Idaho, USA

Maize (sweet)

20

20

30

10

80

March

Philippines

20

25

25

10

80

May/June

Mediterranean

20

30

50/30

10

90

Oct/Dec

Arid Climate

30

30

30

103

110

April

Idaho, USA

20

40

70

10

140

Jan

Calif. Desert, USA

Millet

15

25

40

25

105

June

Pakistan

20

30

55

35

140

April

Central USA

Sorghum

20

35

40

30

130

May/June

USA, Pakis., Med.

20

35

45

30

140

Mar/April

Arid Region

Rice

30

30

60

30

150

Dec; May

Tropics; Mediterranean

30

30.

80

40

180

May

Tropics

j. Forages

Alfalfa, total season 4

10

30

var.

var.

var.


last -4°C in spring until first -4°C in fall

Alfalfa 4 1st cutting cycle

10

20

20

10

60

Jan Apr (last - 4°C)

Calif., USA.

10

30

25

10

75


Idaho, USA.

Alfalfa 4, other cutting cycles

5

10

10

5

30

Mar

Calif., USA.

5

20

10

10

45

Jun

Idaho, USA.

Bermuda for seed

10

25

35

35

105

March

Calif. Desert, USA

Bermuda for hay (several cuttings)

10

15

75

35

135

---

Calif. Desert, USA

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, USA

Sudan, other cutting cycles

3

15

12

7

37

June

Calif. Desert, USA

k. Sugar Cane

Sugarcane, virgin

35

60

190

120

405


Low Latitudes

50

70

220

140

480


Tropics

75

105

330

210

720


Hawaii, USA

Sugarcane, ratoon

25

70

135

50

280


Low Latitudes

30

50

180

60

320


Tropics

35

105

210

70

420


Hawaii, USA

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, USA

m. Grapes and Berries

Grapes

20

40

120

60

240

April

Low Latitudes

20

50

75

60

205

Mar

Calif., USA

20

50

90

20

180

May

High Latitudes

30

60

40

80

210

April

Mid Latitudes (wine)

Hops

25

40

80

10

155

April

Idaho, USA

n. Fruit Trees

Citrus

60

90

120

95

365

Jan

Mediterranean

Deciduous Orchard

20

70

90

30

210

March

High Latitudes

20

70

120

60

270

March

Low Latitudes

30

50

130

30

240

March

Calif., USA

Olives

30

90

60

90

2705

March

Mediterranean

Pistachios

20

60

30

40

150

Feb

Mediterranean

Walnuts

20

10

130

30

190

April

Utah, USA

o. Wetlands - Temperate Climate

Wetlands (Cattails, Bulrush)

10

30

80

20

140

May

Utah, USA; killing frost

180

60

90

35

365

November

Florida, USA

Wetlands (short veg.)

180

60

90

35

365

November

frost-free climate

* 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 Brussel sprouts. The wide range in lengths of seasons is due to varietal and species differences.

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.

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, D. O., M. Faubion and D. E. Amos 1978. "Freezing temperatures and growing seasons in Idaho." Univ. Idaho Agric. Exp. station bulletin 494. 18 p.)

grass: 7 days before last -4° C in spring and 7 days after last -4° C in fall (Kruse E. G. and Haise, H. R. 1974. "Water use by native grasses in high altitude Colorado meadows." USDA Agric. Res. Service, Western Region report ARS-W-6-1974. 60 pages)

5 Olive trees gain new leaves in March. See footnote 24 of Table 12 for additional information, where the Kc continues outside of the "growing period".

Primary source: FAO Irrigation and Drainage Paper 24 (Doorenbos and Pruitt, 1977), Table 22.

The lengths of the initial and development periods may be relatively short for deciduous trees and shrubs that can develop new leaves in the spring at relatively fast rates (Figure 23).

The rate at which vegetation cover develops and the time at which it attains effective full cover are affected by weather conditions in general and by mean daily air temperature in particular. Therefore, the length of time between planting and effective full cover will vary with climate, latitude, elevation and planting date. It will also vary with cultivar (crop variety). Generally, once the effective full cover for a plant canopy has been reached, the rate of further phenological development (flowering, seed development, ripening, and senescence) is more dependent on plant genotype and less dependent on weather. As an example, Figure 28 presents the variation in length of the growing period for one cultivar of rice for one region and for various planting dates.

The end of the mid-season and beginning of the late season is usually marked by senescence of leaves, often beginning with the lower leaves of plants. 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).

High temperatures may accelerate the ripening and senescence of crops. Long duration of high air temperature (> 35°C) can cause some crops such as turf grass to go into dormancy. If severely high air temperatures are coupled with moisture stress, the dormancy of grass can be permanent for the remainder of the growing season. Moisture stress or other environmental stresses will usually accelerate the rate of crop maturation and can shorten the mid and late season growing periods.

The values in Table 11 are useful only as a general guide and for comparison purposes. The listed lengths of growth stages are average lengths for the regions and periods specified and are intended to serve only as examples. Local observations of the specific plant stage development should be used, wherever possible, to incorporate 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. When determining stage dates from local observations, the guidelines and visual descriptions may be helpful.

FIGURE 28. Variation in the length of the growing period of rice (cultivar: Jaya) sown during various months of the year at different locations along the Senegal River (Africa)

Crop coefficients


Tabulated Kc values
Crop coefficient for the initial stage (Kc ini)
Crop coefficient for the mid-season stage (Kc mid)
Crop coefficient for the end of the late season stage (Kc end)


Changes in vegetation and ground cover mean that the crop coefficient Kc varies during the growing period. The trends in Kc during the growing period are represented in the crop coefficient curve. Only three values for Kc are required to describe and construct the crop coefficient curve: those during the initial stage (Kc ini), the mid-season stage (Kc mid) and at the end of the late season stage (Kc end).

Tabulated Kc values

Table 12 lists typical values for Kc ini, Kc mid and Kc end for various agricultural crops. The coefficients presented are organized by group type (i.e., small vegetables, legumes, cereals, etc.) to assist in locating the crop in the table and to aid in comparing crops within the same group. There is usually close similarity in the coefficients among the members of the same crop group, as the plant height, leaf area, ground coverage and water management are normally similar.

The coefficients in Table 12 integrate the effects of both transpiration and evaporation over time. The effects of the integration over time represent an average wetting frequency for a 'standard' crop under typical growing conditions in an irrigated setting. The values for Kc during the initial and crop development stages are subject to the effects of large variations in wetting frequencies and therefore refinements to the value used for Kc ini should always be made. For frequent wettings such as with high frequency sprinkler irrigation or rainfall, the values for Kc ini may increase substantially.

TABLE 12. Single (time-averaged) crop coefficients, Kc, and mean maximum plant heights for non stressed, well-managed crops in subhumid climates (RHmin » 45%, u2 » 2 m/s) for use with the FAO Penman-Monteith ETo.

Crop

Kc mid

Kc end

Maximum Crop Height (h) (m)

a. Small Vegetables

0.7

1.05

0.95


Broccoli


1.05

0.95

0.3

Brussel Sprouts


1.05

0.95

0.4

Cabbage


1.05

0.95

0.4

Carrots


1.05

0.95

0.3

Cauliflower


1.05

0.95

0.4

Celery


1.05

1.00

0.6

Garlic


1.00

0.70

0.3

Lettuce


1.00

0.95

0.3

Onions






- dry


1.05

0.75

0.4


- green


1.00

1.00

0.3


- seed


1.05

0.80

0.5

Spinach


1.00

0.95

0.3

Radish


0.90

0.85

0.3

b. Vegetables - Solanum Family (Solanaceae)

0.6

1.15

0.80


Egg Plant


1.05

0.90

0.8

Sweet Peppers (bell)


1.052

0.90

0.7

Tomato


1.152

0.70-0.90

0.6

c. Vegetables - Cucumber Family (Cucurbitaceae)

0.5

1.00

0.80


Cantaloupe

0.5

0.85

0.60

0.3

Cucumber






- Fresh Market

0.6

1.002

0.75

0.3


- Machine harvest

0.5

1.00

0.90

0.3

Pumpkin, Winter Squash


1.00

0.80

0.4

Squash, Zucchini


0.95

0.75

0.3

Sweet Melons


1.05

0.75

0.4

Watermelon

0.4

1.00

0.75

0.4

d. Roots and Tubers

0.5

1.10

0.95


Beets, table


1.05

0.95

0.4

Cassava






- year 1

0.3

0.803

0.30

1.0


- year 2

0.3

1.10

0.50

1.5

Parsnip

0.5

1.05

0.95

0.4

Potato


1.15

0.754

0.6

Sweet Potato


1.15

0.65

0.4

Turnip (and Rutabaga)


1.10

0.95

0.6

Sugar Beet

0.35

1.20

0.705

0.5

e. Legumes (Leguminosae)

0.4

1.15

0.55


Beans, green

0.5

1.052

0.90

0.4

Beans, dry and Pulses

0.4

1.152

0.35

0.4

Chick pea


1.00

0.35

0.4

Fababean (broad bean)






- Fresh

0.5

1.152

1.10

0.8


- Dry/Seed

0.5

1.152

0.30

0.8

Grabanzo

0.4

1.15

0.35

0.8

Green Gram and Cowpeas


1.05

0.60-0.356

0.4

Groundnut (Peanut)


1.15

0.60

0.4

Lentil


1.10

0.30

0.5

Peas






- Fresh

0.5

1.152

1.10

0.5


- Dry/Seed


1.15

0.30

0.5

Soybeans


1.15

0.50

0.5-1.0

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

0.5

1.00

0.80


Artichokes

0.5

1.00

0.95

0.7

Asparagus

0.5

0.957

0.30

0.2-0.8

Mint

0.60

1.15

1.10

0.6-0.8

Strawberries

0.40

0.85

0.75

0.2

g. Fibre Crops

0.35




Cotton


1.15-1.20

0.70-0.50

1.2-1.5

Flax


1.10

0.25

1.2

Sisal 8


0.4-0.7

0.4-0.7

1.5

h. Oil Crops

0.35

1.15

0.35


Castorbean (Ricinus)


1.15

0.55

0.3

Rapeseed, Canola


1.0-1.159

0.35

0.6

Safflower


1.0-1.159

0.25

0.8

Sesame


1.10

0.25

1.0

Sunflower


1.0-1.159

0.35

2.0

i. Cereals

0.3

1.15

0.4


Barley


1.15

0.25

1

Oats


1.15

0.25

1

Spring Wheat


1.15

0.25-0.410

1

Winter Wheat






- with frozen soils

0.4

1.15

0.25-0.410

1


- with non-frozen soils

0.7

1.15

0.25-0.410


Maize, Field (grain) (field corn)


1.20

0.60-0.3511

2

Maize, Sweet (sweet corn)


1.15

1.0512

1.5

Millet


1.00

0.30

1.5

Sorghum






- grain


1.00-1.10

0.55

1-2


- sweet


1.20

1.05

2-4

Rice

1.05

1.20

0.90-0.60

1

j. Forages

Alfalfa Hay






- averaged cutting effects

0.40

0.9513

0.90

0.7


- individual cutting periods

0.4014

1.2014

1.1514

0.7


- for seed

0.40

0.50

0.50

0.7

Bermuda hay






- averaged cutting effects

0.55

1.0013

0.85

0.35


- Spring crop for seed

0.35

0.90

0.65

0.4

Clover hay, Berseem






- averaged cutting effects

0.40

0.9013

0.85

0.6


- individual cutting periods

0.4014

1.1514

1.1014

0.6

Rye Grass hay






- averaged cutting effects

0.95

1.05

1.00

0.3

Sudan Grass hay (annual)






- averaged cutting effects

0.50

0.9014

0.85

1.2


- individual cutting periods

0.5014

1.1514

1.1014

1.2

Grazing Pasture






- Rotated Grazing

0.40

0.85-1.05

0.85

0.15-0.30


- Extensive Grazing

0.30

0.75

0.75

0.10

Turf grass






- cool season 15

0.90

0.95

0.95

0.10


- warm season 15

0.80

0.85

0.85

0.10

k. Sugar Cane

0.40

1.25

0.75

3

l. Tropical Fruits and Trees

Banana






- 1st year

0.50

1.10

1.00

3


- 2nd year

1.00

1.20

1.10

4

Cacao

1.00

1.05

1.05

3

Coffee






- bare ground cover

0.90

0.95

0.95

2-3


- with weeds

1.05

1.10

1.10

2-3

Date Palms

0.90

0.95

0.95

8

Palm Trees

0.95

1.00

1.00

8

Pineapple 16






- bare soil

0.50

0.30

0.30

0.6-1.2


- with grass cover

0.50

0.50

0.50

0.6-1.2

Rubber Trees

0.95

1.00

1.00

10

Tea






- non-shaded

0.95

1.00

1.00

1.5


- shaded 17

1.10

1.15

1.15

2

m. Grapes and Berries

Berries (bushes)

0.30

1.05

0.50

1.5

Grapes






- Table or Raisin

0.30

0.85

0.45

2


- Wine

0.30

0.70

0.45

1.5-2

Hops

0.3

1.05

0.85

5

n. Fruit Trees

Almonds, no ground cover

0.40

0.90

0.6518

5

Apples, Cherries, Pears 19






- no ground cover, killing frost

0.45

0.95

0.7018

4


- no ground cover, no frosts

0.60

0.95

0.7518

4


- active ground cover, killing frost

0.50

1.20

0.9518

4


- active ground cover, no frosts

0.80

1.20

0.8518

4

Apricots, Peaches, Stone Fruit 19, 20






- no ground cover, killing frost

0.45

0.90

0.6518

3


- no ground cover, no frosts

0.55

0.90

0.6518

3


- active ground cover, killing frost

0.50

1.15

0.9018

3


- active ground cover, no frosts

0.80

1.15

0.8518

3

Avocado, no ground cover

0.60

0.85

0.75

3

Citrus, no ground cover 21






- 70% canopy

0.70

0.65

0.70

4


- 50% canopy

0.65

0.60

0.65

3


- 20% canopy

0.50

0.45

0.55

2

Citrus, with active ground cover or weeds 22






- 70% canopy

0.75

0.70

0.75

4


- 50% canopy

0.80

0.80

0.80

3


- 20% canopy

0.85

0.85

0.85

2

Conifer Trees 23

1.00

1.00

1.00

10

Kiwi

0.40

1.05

1.05

3

Olives (40 to 60% ground coverage by canopy) 24

0.65

0.70

0.70

3-5

Pistachios, no ground cover

0.40

1.10

0.45

3-5

Walnut Orchard 19

0.50

1.10

0.6518

4-5

o. Wetlands - temperate climate

Cattails, Bulrushes, killing frost

0.30

1.20

0.30

2

Cattails, Bulrushes, no frost

0.60

1.20

0.60

2

Short Veg., no frost

1.05

1.10

1.10

0.3

Reed Swamp, standing water

1.00

1.20

1.00

1-3

Reed Swamp, moist soil

0.90

1.20

0.70

1-3

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


0.6525

1.2525


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 periods and is more accurately estimated using Figures 29 and 30, or Equation 7-3 in Annex 7, 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 values account for dormancy during the dry season.

4 The Kc end value for potatoes is about 0.40 for long season potatoes with vine kill.

5 This Kc end value is for no irrigation during the last month of the growing season. The Kc end value for sugar beets is higher, up to 1.0, when irrigation or significant rain occurs during the last month.

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 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).

12 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.

13 This Kc mid coefficient for hay crops is an overall average Kc mid coefficient that averages Kc for both before and following cuttings. It is applied to the period following 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 before cutting, respectively. The growing season is described as a series of individual cutting periods (Figure 35).

15 Cool season grass varieties include dense stands of bluegrass, ryegrass, and fescue. Warm season varieties include bermuda grass and St. Augustine grass. The 0.95 values for cool season grass represent a 0.06 to 0.08 m mowing height under general turf conditions. Where careful water management is practiced and rapid growth is not required, Kc's for turf can be reduced by 0.10.

16 The pineapple plant has very low transpiration because it closes its stomates during the day and opens them during the night. 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 given 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's given can be reduced by 0.10.

17 Includes the water requirements of the shade trees.

18 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 (consult Chapter 11).

19 Refer to Eq. 94, 97 or 98 and footnotes 21 and 22 for estimating Kc for immature stands.

20 Stone fruit category applies to peaches, apricots, pears, plums and pecans.

21 These Kc values can be calculated from Eq. 98 for Kc min = 0.15 and Kc full = 0.75, 0.70 and 0.75 for the initial, mid season and end of season periods, and fc eff = fc where fc = fraction of ground covered by tree canopy (e.g., the sun is presumed to be directly overhead). The values listed correspond with those in Doorenbos and Pruitt (1977) and with more recent measurements. The midseason value is lower than initial and ending values due to the effects of stomatal closure during periods of peak ET. For humid and subhumid climates where there is less stomatal control by citrus, values for Kc ini, Kc mid, and Kc end can be increased by 0.1 - 0.2, following Rogers et al. (1983).

22 These Kc values can be calculated as Kc = fc Kc ngc + (1 - fc) Kc cover where Kc ngc is the Kc of citrus with no active ground cover (calculated as in footnote 21), Kc cover is the Kc, for the active ground cover (0.95), and fc is defined in footnote 21. The values listed correspond with those in Doorenbos and Pruitt (1977) and with more recent measurements. Alternatively, Kc for citrus with active ground cover can be estimated directly from Eq. 98 by setting Kc min = Kc cover. For humid and subhumid climates where there is less stomatal control by citrus, values for Kc ini, Kc mid, and Kc end can be increased by 0.1 - 0.2, following Rogers et al. (1983).

For non-active or only moderately active ground cover (active indicates green and growing ground cover with LAI > about 2 to 3), Kc should be weighted between Kc for no ground cover and Kc for active ground cover, with the weighting based on the "greenness" and approximate leaf area of the ground cover.

23 Confers exhibit substantial stomatal control due to reduced aerodynamic resistance. The Kc, can easily reduce below the values presented, which represent well-watered conditions for large forests.

24 These coefficients represent about 40 to 60% ground cover. Refer to Eq. 98 and footnotes 21 and 22 for estimating Kc for immature stands. In Spain, Pastor and Orgaz (1994) have found the following monthly Kc's for olive orchards having 60% ground cover: 0.50, 0.50, 0.65, 0.60, 0.55, 0.50, 0.45, 0.45, 0.55, 0.60, 0.65, 0.50 for months January through December. These coefficients can be invoked by using Kc ini = 0.65, Kc mid = 0.45, and Kc end = 0.65, with stage lengths = 30, 90, 60 and 90 days, respectively for initial, development, midseason and late season periods, and using Kc during the winter ("off season") in December to February = 0.50.

25 These Kc's are for deep water in temperate latitudes where large temperature changes in the water body occur during 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 releasing thermal energy. These Kc's should be used with caution.

Primary sources:

Kc ini: Doorenbos and Kassam (1979)
Kc mid and Kc end: Doorenbos and Pruitt (1977); Pruitt (1986); Wright (1981, 1982). Snyder et al., (1989)

The values for Kc mid and Kc end in Table 12 represent those for a sub-humid climate with an average daytime minimum relative humidity (RHmin) of about 45% and with calm to moderate wind speeds averaging 2 m/s. For more humid or arid conditions, or for more or less windy conditions, the Kc coefficients for the mid-season and end of late season stage should be modified as described in this chapter.

The values for Kc in Table 12 are values for non-stressed crops cultivated under excellent agronomic and water management conditions and achieving maximum crop yield (standard conditions). Where stand density, height or leaf area are less than that attained under such conditions, the value for Kc mid and, for most crops, for Kc end will need to be modified (Part C, Chapters 8, 9 and 10).

Crop coefficient for the initial stage (Kc ini)

Calculation procedure

The values for Kc ini in Table 12 are only approximations and should only be used for estimating ETc during preliminary or planning studies. For several group types only one value for Kc ini is listed and it is considered to be representative of the whole group for a typical irrigation water management. More accurate estimates of Kc ini can be obtained by considering:

Time interval between wetting events

Evapotranspiration during the initial stage for annual crops is predominately in the form of evaporation. Therefore, accurate estimates for Kc ini should consider the frequency with which the soil surface is wetted during the initial period. Where the soil is frequently wet from irrigation or rain, the evaporation from the soil surface can be considerable and Kc ini will be large. On the other hand, where the soil surface is dry, evaporation is restricted and the Kc ini will be small (Table 9).

Evaporation power of the atmosphere

The value of Kc ini is affected by the evaporating power of the atmosphere, i.e., ETo. The higher the evaporation power of the atmosphere, the quicker the soil will dry between water applications and the smaller the time-averaged Kc will be for any particular period.

Magnitude of the wetting event

As the amount of water available in the topsoil for evaporation and hence the time for the soil surface to dry is a function of the magnitude of the wetting event, Kc ini will be smaller for light wetting events than for large wettings.

Depending on the time interval between wetting events, the magnitude of the wetting event, and the evaporation power of the atmosphere, Kc ini can vary between 0.1 and 1.15. A numerical procedure to compute Kc ini is provided in Annex 7.

Time interval between wetting events

In general, the mean time interval between wetting events is estimated by counting all rainfall and irrigation events occurring during the initial period that are greater than a few millimetres. Wetting events occurring on adjacent days can be counted as one event. The mean wetting interval is estimated by dividing the length of the initial period by the number of events.

Where only monthly rainfall values are available without any information on the number of rainy days, the number of events within the month can be estimated by dividing the monthly rainfall depth by the depth of a typical rain event. The typical depth, if it exists, can vary widely from climate to climate, region to region and from season to season. Table 13 presents some information on the range of rainfall depths. After deciding what rainfall is typical for the region and time of the year, the number of rainy days and the mean wetting interval can be estimated.

TABLE 13. Classification of rainfall depths

rain event

depth

Very light (drizzle)

£ 3 mm

Light (light showers)

5 mm

Medium (showers)

³ 10 mm

Heavy (rainstorms)

³ 40 mm

Where rainfall is insufficient, irrigation is needed to keep the crop well watered. Even where irrigation is not yet developed, the mean interval between the future irrigations should be estimated to obtain the required frequency of wetting necessary to keep the crop stress free. The interval might be as small as a few days for small vegetables, but up to a week or longer for cereals depending on the climatic conditions. Where no estimate of the interval can be made, the user may refer to the values for Kc ini of Table 12.

EXAMPLE 23. Estimation of interval between wetting events

Estimate, from mean monthly rainfall data, the interval between rains during the rainy season for a station in a temperate climate (Paris, France: 50 mm/month), dry climate (Gafsa, Tunisia: 20 mm/month) and tropical climate (Calcutta, India: 300 mm/month).

Station

monthly rain (mm/month)

typical rainfall (mm)

number of rainy days

interval between rains

Paris

50

3

17

~ 2 days

Gafsa

20

5

4

weekly

Calcutta

300

20

15

~ 2 days

Determination of Kc ini

The crop coefficient for the initial growth stage can be derived from Figures 29 and 30 which provide estimates for Kc ini as a function of the average interval between wetting events, the evaporation power ETo, and the importance of the wetting event.

Light wetting events (infiltration depths of 10 mm or less): rainfall and high frequency irrigation systems

Figure 29 is used for all soil types when wetting events are light. When wetting during the initial period is only by precipitation, one will usually use Figure 29 to determine Kc ini. The graph can also be used when irrigation is by high frequency systems such as microirrigation and centre pivot and light applications of about 10 mm or less per wetting event are applied.

EXAMPLE 24. Graphical determination of Kc ini

A silt loam soil receives irrigation every two days during the initial growth stage via a centre pivot irrigation system. The average depth applied by the centre pivot system is about 12 mm per event and the average ETo during the initial stage is 4 mm/day. Estimate the crop evapotranspiration during that stage.

From Fig. 29 using the 2-day interval curve:

Kc ini =

0.85

-


ETc = Kc ETo = 0.85 (4.0) =

3.4

mm/day

The average crop evapotranspiration during the initial growth stage is 3.4 mm/day

Heavy wetting events (infiltration depths of 40 mm or more): surface and sprinkler irrigation

Figure 30 is used for heavy wetting events when infiltration depths are greater than 40 mm, such as for when wetting is primarily by periodic irrigation such as by sprinkler or surface irrigation. Following a wetting event, the amount of water available in the topsoil for evaporation is considerable, and the time for the soil surface to dry might be significantly increased. Consequently, the average Kc factor is larger than for light wetting events. As the time for the soil surface to dry is, apart from the evaporation power and the frequency of wetting, also determined by the water storage capacity of the topsoil, a distinction is made between soil types.

FIGURE 29. Average Kc ini as related to the level of ETo and the interval between irrigations and/or significant rain during the initial growth stage for all soil types when wetting events are light to medium (3-10 mm per event)

Figure 30a is used for coarse textured soils and Figure 30b is used for fine and medium textured soils. Coarse textured soils include sands and loamy sand textured soils. Medium textured soils include sandy loam, loam, silt loam and silt textured soils. Pine textured soils include silty clay loam, silty clay and clay textured soils.

Average wetting events (infiltration depths between 10 and 40 mm):

Where average infiltration depths are between 10 and 40 mm, the value for Kc ini can be estimated from Figures 29 and 30:

(59)

where

Kc ini (Fig.29) value for Kc ini from Figure 29,
Kc ini (Fig.30) value for Kc ini from Figure 30,
I average infiltration depth [mm].

The values 10 and 40 in Equation 59 are the average depths of infiltration (millimetres) upon which Figures 29 and 30 are based.

FIGURE 30. Average Kc ini as related to the level of ETo and the interval between irrigations greater than or equal to 40 mm per wetting event, during the initial growth stage for coarse textured soils

EXAMPLE 25. Interpolation between light and heavy wetting events

Small vegetables cultivated in a dry area on a coarse textured soil receive 20 mm of water twice a week by means of a sprinkler irrigation system. The average ETo during the initial stage is 5 mm/day. Estimate the crop evapotranspiration during that stage.

For:

7/2=

3.5

day interval

ETo = and a coarse textured soil

5

mm/day

From Fig. 29:

Kc ini (Fig. 29) »

0.55

-

From Fig. 30. a:

Kc ini (Fig. 30a) »

0.7

-

For:

I =

20

mm

From Eq. 59:

Kc ini = 0.55 + [(20 - 10)/(40 - 10)] (0.7 - 0.55) = 0.55 + 0.33(0.15) =

0.60


From Eq. 58:

ETc = 0.60 (5) =

3.0

mm/day

The average crop evapotranspiration during the initial growth stage for the small vegetables is 3.0 mm/day.

Adjustment for partial wetting by irrigation

Many types of irrigation systems wet only a fraction of the soil surface. For example, for a trickle irrigation system, the fraction of the surface wetted, fw, may be only 0.4. For furrow irrigation systems, the fraction of the surface wetted may range from 0.3 to 0.8. Common values for the fraction of the soil surface wetted by irrigation or precipitation are given in Table 20. When only a fraction of the soil surface is wetted, the value for Kc ini obtained from Table 12 or from Figures 29 or 30 should be multiplied by the fraction of the surface wetted to adjust for the partial wetting:

Kc ini = fw Kc ini (Tab, Fig) (60)

where

fw the fraction of surfaced wetted by irrigation or rain [0 - 1],
Kc ini (Tab Fig) the value for Kc ini from Table 12 or Figure 29 or 30.

In addition, in selecting which figure to use (i.e., Figure 29 or 30), the average infiltrated depth, expressed in millimetres over the entire field surface, should be divided by fw to represent the true infiltrated depth of water for the part of the surface that is wetted (Figure 31):

(61)

where

Iw irrigation depth for the part of the surface that is wetted [mm],
fw fraction of surface wetted by irrigation,
I the irrigation depth for the field [mm].

When irrigation of part of the soil surface and precipitation over the entire soil surface both occur during the initial period, fw should represent the average of fw for each type of wetting, weighted according to the total infiltration depth received by each type.

FIGURE 31. Partial wetting by irrigation

EXAMPLE 26. Determination of Kc ini for partial wetting of the soil surface

Determine the evapotranspiration of the crop in Example 24 if it had been irrigated using a trickle system every two days (with 12 mm each application expressed as an equivalent depth over the field area), and where the average fraction of surface wet was 0.4, and where little or no precipitation occurred during the initial period.

The average depth of infiltration per event in the wetted fraction of the surface:

From Eq. 61;

lw = I/fw = 12 mm/0.4 =

30

mm

Therefore, one can interpolate between Fig. 29 representing light wetting events (~10 mm per event) and Fig. 30.b representing medium textured soil and large wetting events (~40 mm per event).

For:

ETo = 4 mm/day

4

mm/day

and:

a 2 day wetting interval:

-

-

Fig. 29 produces:

Kc ini = 0.85

0.85

-

Fig. 30.b produces

Kc ini = 1.15

1.15

-

From Eq. 59:

Kc ini = 0.85 + [(30-10)/(40-10)] (1.15 - 0.85) =

1.05

-

Because the fraction of soil surface wetted by the trickle system is 0.4, the actual Kc ini for the trickle irrigation is calculated as:

From Eq. 60:

Kc ini = fw Kc ini Fig = 0.4 (1.05) =

0.42

-

This value (0.42) represents the Kc ini as applied over the entire field area.



-

ETc =Kc ini ETo = 0.42(4) =

1.7

mm/day

The average crop evapotranspiration during the initial growth stage for this trickle irrigated crop is 1.7 mm/day.

Kc ini for trees and shrubs

Kc ini for trees and shrubs should reflect the ground condition prior to leaf emergence or initiation in case of deciduous trees or shrubs, and the ground condition during the dormancy or low active period for evergreen trees and shrubs. The Kc ini depends upon the amount of grass or weed cover, frequency of soil wetting, tree density and mulch density. For a deciduous orchard in frost-free climates, the Kc ini can be as high as 0.8 or 0.9, where grass ground cover exists, and as low as 0.3 or 0.4 when the soil surface is kept bare and wetting is infrequent. The Kc ini for an evergreen orchard (having no concerted leaf drop) with a dormant period has less variation from Kc mid, as exemplified for citrus in Table 12, footnotes 21 and 22. For 50% canopy or less, the Kc ini also reflects ground cover conditions (bare soil, mulch or active grass or weed cover).

Kc ini for paddy rice

For rice growing in paddy fields with a water depth of 0.10-0.20 m, the ETc during the initial stage mainly consists of evaporation from the standing water. The Kc ini in Table 12 is 1.05 for a sub-humid climate with calm to moderate wind speeds. The Kc ini should be adjusted for the local climate as indicated in Table 14.

TABLE 14. Kc ini for rice for various climatic conditions

Humidity

Wind speed


light

moderate

strong

arid - semi-arid

1.10

1.15

1.20

sub-humid - humid

1.05

1.10

1.15

very humid

1.00

1.05

1.10

Crop coefficient for the mid-season stage (Kc mid)

Illustration of the climatic effect

Typical values for the crop coefficient for the mid-season growth stage, Kc mid, are listed in Table 12 for various agricultural crops.

As discussed in Chapter 5, the effect of the difference in aerodynamic properties between the grass reference surface and agricultural crops is not only crop specific but also varies with the climatic conditions and crop height (Figure 21). More arid climates and conditions of greater wind speed will have higher values for Kc mid. More humid climates and conditions of lower wind speed will have lower values for Kc mid.

The relative impact of climate on Kc mid is illustrated in Figure 32 where the adjustments to the values from Table 12 are shown for various types of climates, mean daily wind speeds and various crop heights. As an example, expected variations for Kc mid for tomatoes in response to regional climatic conditions are presented in Box 14.

Determination of Kc mid

For specific adjustment in climates where RHmin differs from 45% or where u2 is larger or smaller than 2.0 m/s, the Kc mid values from Table 12 are adjusted as:

(62)

where

Kc mid (Tab) value for Kc mid taken from Table 12,

u2 mean value for daily wind speed at 2 m height over grass during the mid-season growth stage [m s-1], for 1 m s-1 £ u2 £ 6 m s-1,

RHmin mean value for daily minimum relative humidity during the mid-season growth stage [%], for 20% £ RHmin £ 80%,

h mean plant height during the mid-season stage [m] for 0.1 m < h < 10 m.

FIGURE 32. Adjustment (additive) to the Kc mid values from Table 12 for different crop heights and mean daily wind speeds (u2) for different humidity conditions

The Kc mid values determined with equations 62 and 65 are average adjustments for the midseason and late season periods. The values for parameters u2 and RHmin should be accordingly taken as averages for these periods (see example, Annex 8). The limits expressed for parameters u2, RHmin and h should be observed.

BOX 14. Demonstration of effect of climate on Kc mid for wheat crop grown under field conditions

From Table 12 for wheat: Kc mid = 1.15 and h = 1.0 m

For semi-arid to arid conditions

- for strong wind (4 m/s)

Kc mid = 1.15 + 0.10 = 1.25

- for moderate wind (2 m/s)

Kc mid = 1.15 + 0.05 = 1.20

- for calm wind (1 m/s)

Kc mid = 1.15 + 0.00 = 1.17

For sub-humid conditions

- for strong wind (4 m/s)

Kc mid = 1.15 + 0.05 = 1.20

- for moderate wind (2 m/s)

Kc mid = 1.15 + 0.00 = 1.15

- for calm wind (1 m/s)

Kc mid = 1.15 - 0.05 = 1.12

For humid and very humid conditions

- for strong wind (4 m/s)

Kc mid = 1.15 - 0.05 = 1.10

- for moderate wind (2 m/s)

Kc mid = 1.15 - 0.10 = 1.05

- for calm wind (1 m/s)

Kc mid = 1.15 - 0.15 = 1.02

Depending on the aridity of the climate and the wind conditions, the crop coefficient for wheat during the mid-season stage ranges from 1.02 (humid and calm wind) to 1.25 (arid and strong wind).

Where the user does not have access to a calculator with an exponential function, the solution of the (h/3)0.3 expression can be approximated as [(h/3)0.5]0.5 where the square root key is used.

RHmin is used rather than RHmean because it is easier to approximate RHmin from Tmax where relative humidity data are unavailable. Moreover, under the common condition where Tmin approaches Tdew (i.e., RHmax » 100%), the vapour pressure deficit (es - ea), with es from Equation 12 and ea from Equation 17, becomes [(100 - RHmin)/200] e°(Tmax), where e°(Tmax) is saturation vapour pressure at maximum daily air temperature. This indicates that RHmin better reflects the impact of vapour pressure deficit on Kc than does RHmean.

RHmin is calculated on a daily or average monthly basis as:

(63)

where Tdew is mean dewpoint temperature and Tmax is mean daily maximum air temperature during the mid-season growth stage. Where dewpoint temperature or other hygrométrie data are not available or are of questionable quality, RHmin can be estimated by substituting mean daily minimum air temperature, Tmin, for Tdew1. Then:

(64)

1 In the case of arid and semi-arid climates, Tmin in equation (64) should be adjusted as indicated in Annex 6 (equation 6-6) by subtracting 2°C from the average value of Tmin to better approximate Tdew.

The values for u2 and RHmin need only be approximate for the mid-season growth stage. This is because Equation 62 is not strongly sensitive to these values, changing 0.04 per 1 m/s change in u2 and per 10% change in RHmin for a 3 m tall crop. Measurements, calculation, and estimation of missing wind and humidity data are provided in Chapter 3. Wind speed measured at other than 2 m height should be adjusted to reflect values for wind speed at 2 m over grass using Equation 47. Where no data on u2 or RHmin are available, the general classification for wind speed and humidity data given in Tables 15 and 16 can be used.

TABLE 15. Empirical estimates of monthly wind speed data

description

mean monthly wind speed at 2 m

light wind

...£ 1.0 m/s

light to moderate wind

2.0 m/s

moderate to strong wind

4.0 m/s

strong wind

... ³ 5.0 m/s

general global conditions

2 m/s

TABLE 16. Typical values for RHmin compared with RHmean for general climatic classifications

Climatic classification

RHmin (%)

RHmean (%)

Arid

20

45

Semi-arid

30

55

Sub-humid

45

70

Humid

70

85

Very humid

80

90

Equation 62 is valid for mean plant heights up to 10 m. For plant heights smaller than 0.1 m, vegetation will behave aerodynamically similar to grass reference and eq. 62 should not be applied. Example values for h are listed in Table 12 for various crops. However, the mean plant height will greatly vary with crop variety and with cultural practices. Therefore, wherever possible, h should be obtained from general field observations. However, the presence of the 0.3 exponent in Equation 62 makes these equations relatively insensitive to small errors in the value used for h. Generally, a single value for h is used to represent me mid-season period.

Adjustment for frequency of wetting

Kc mid is less affected by wetting frequency than is Kc ini, as vegetation during this stage is generally near full ground cover so that the effects of surface evaporation on Kc are smaller. For frequent irrigation of crops (more frequently than every 3 days) and where the Kc mid of Table 12 is less than 1.0, the value can be replaced by approximately 1.1-1.3 to account for the combined effects of continuously wet soil, evaporation due to interception (sprinkler irrigation) and roughness of the vegetation, especially where the irrigation system moistens an important fraction of the soil surface (fw > 0.3).

EXAMPLE 27. Determination of Kc mid

Calculate Kc mid for maize crops near Taipei, Taiwan and near Mocha, Yemen. The average mean daily wind speed (u2) during the mid-season stage at Taipei is about 1.3 m/s and the minimum relative humidity (RHmin) during this stage averages 75%. The average u2 during the mid-season near Mocha is 4.6 m/s and the RHmin during this stage averages 44%.

From Table 12, the value for Kc mid is 1.20 for maize. The value for h from Table 12 is 2 m. Using Eq. 62

For Taipei (humid climate):

For Mocha (arid climate):

The average crop coefficient predicted during the mid-season stage is 1.07 for Taipei and 1.30 for Mocha.

Crop coefficient for the end of the late season stage (Kc end)

Typical values for the crop coefficient at the end of the late season growth stage, Kc end, and listed in Table 12 for various agricultural crops. The values given for Kc end reflect crop and water management practices particular to those crops. If the crop is irrigated frequently until harvested fresh, the topsoil remains wet and the Kc end value will be relatively high. On the other hand, crops that are allowed to senesce and dry out in the field before harvest receive less frequent irrigation or no irrigation at all during the late season stage. Consequently, both the soil surface and vegetation are dry and the value for Kc end will be relatively small (Figure 33).

Where the local water management and harvest timing practices are known to deviate from the typical values presented in Table 12, then the user should make some adjustments to the values for Kc end. Some guidance on adjustment of Kc values for wetting frequency is provided in Chapter 7. For premature harvest, the user can construct a Kc curve using the Kc end value provided in Table 12 and a late season length typical of a normal harvest date; but can then terminate the application of the constructed curve early, corresponding to the time of the early harvest.

The Kc end values in Table 12 are typical values expected for average Kc end under the standard climatic conditions. More arid climates and conditions of greater wind speed will have higher values for Kc end. More humid climates and conditions of lower wind speed will have lower values for Kc end. For specific adjustment in climates where RHmin differs from 45% or where u2 is larger or smaller than 2.0 m/s, Equation 65 can be used:

(65)

where

Kc end (Tab) value for Kc end taken from Table 12,

u2 mean value for daily wind speed at 2 m height over grass during the late season growth stage [m s-1], for 1 m s-1 £ u2 £ 6 m s-1,

RHmin mean value for daily minimum relative humidity during the late season stage [%], for 20% £ RHmin £ 80%,

h mean plant height during the late season stage [m], for 0.1 m £ h £ 10 m.

FIGURE 33. Ranges expected for Kc end

FIGURE 34. Crop coefficient curve

Equation 65 is only applied when the tabulated values for Kc end exceed 0.45. The equation reduces the Kc end with increasing RHmin. This reduction in Kc end is characteristic of crops that are harvested 'green' or before becoming completely dead and dry (i.e., Kc end ³ 0.45).

No adjustment is made when Kc end (Table) < 0.45 (i.e., Kc end = Kc end (Tab)). When crops are allowed to senesce and dry in the field (as evidenced by Kc end < 0.45), u2 and RHmin have less effect on Kc end and no adjustment is necessary. In fact, Kc end may decrease with decreasing RHmin for crops that are ripe and dry at the time of harvest, as lower relative humidity accelerates the drying process.

Construction of the Kc curve


Annual crops
Kc curves for forage crops
Fruit trees


Annual crops

Only three point values for Kc are required to describe and to construct the Kc curve. The curve such as that shown in Figure 34 is constructed using the following three steps:

1. Divide the growing period into four general growth stages that describe crop phenology or development (initial, crop development, mid-season, and late season stage), determine the lengths of the growth stages, and identify the three Kc values that correspond to Kc ini, Kc mid and Kc end from Table 12.

2. Adjust the Kc values to the frequency of wetting and/or climatic conditions of the growth stages as outlined in the previous section.

3. Construct a curve by connecting straight line segments through each of the four growth stages. Horizontal lines are drawn through Kc ini in the initial stage and through Kc mid in the mid-season stage. Diagonal lines are drawn from Kc ini to Kc mid within the course of the crop development stage and from Kc mid to Kc end within the course of the late season stage.

Kc curves for forage crops

Many crops grown for forage or hay are harvested several times 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. Figure 35 presents a Kc curve for the entire growing season constructed for alfalfa grown for hay in southern Idaho.

FIGURE 35. Constructed curve for Kc for alfalfa hay in southern Idaho, the United States using values from Tables 11 and 12 and adjusted using Equations 62 and 65 (data from Wright, 1990)

In the southern Idaho climate, greenup (leaf initiation) begins in the spring on about day 90 of the year. The crop is usually harvested (cut) for hay three or four times during the growing season. Therefore, Figure 35 shows four Kc sub-cycles or cutting cycles: sub-cycle 1 follows greenup in the spring and the three additional Kc sub-cycles follow cuttings. Cuttings create a ground surface with less than 10% vegetation cover. Cutting cycle 1 is longer in duration than cycles 2, 3 and 4 due to lower air and soil temperatures during this period that reduce crop growth rates. The lengths for cutting cycle 1 were taken from the first entry for alfalfa (" 1st cutting cycle") in Table 11 for Idaho, the United States (10/30/25/10). The lengths for cutting cycles 2, 3 and 4 were taken from the entry for alfalfa in Table 11 for "individual cutting periods" for Idaho, the United States (5/20/10/10). These lengths were based on observations. In the southern Idaho climate, frosts terminate the growing season sometime in the fall, usually around day 280-290 of the year (early to mid-October).

The magnitudes of the Kc values during the mid-season periods of each cutting cycle shown in Figure 35 vary from cycle to cycle due to the effects of adjusting the values for Kc mid and Kc end for each cutting cycle period using Equations 62 and 65. In applying these two adjustment equations, the u2 and RHmin values were averages for the mid-season and late season stages within each cutting cycle. Basal Kcb curves similar to Figure 35 can be constructed for forage or hay crops, following procedures presented in Chapter 7.

Kc mid when effects of individual cutting periods are averaged

Under some conditions, the user may wish to average the effects of cuttings for a forage crop over the course of the growing season. When cutting effects are averaged, then only a single value for Kc mid and a only single Kc curve need to be employed for the whole growing season. When this is the case, a "normal" Kc curve is constructed as in Figure 25, where only one midseason period is shown for the forage crop. The Kc mid for this total midseason period must average the effects of occasional cuttings or harvesting. The value that is used for Kc mid is therefore an average of the Kc curve for the time period starting at the first attainment of full cover and ending at the beginning of the final late season period near dormancy or frost. The value used for Kc mid under these averaged conditions may be only about 80% of the Kc value that represents full ground cover. These averaged, full-season Kc mid values are listed in Table 12. For example, for alfalfa hay, the averaged, full-season Kc mid is 1.05, whereas, the Kc mid for an individual cutting period is 1.20.

Fruit trees

Values for the crop coefficient during the mid-season and end of late season stages are given in Table 12. As mentioned before, the Kc values listed are typical values for standard climatic conditions and need to be adjusted by using Equations 62 and 65 where RHmin or u2 differ. As the mid and late season stages of deciduous trees are quite long, the specific adjustment of Kc to RHmin and u2 should take into account the varying climatic conditions throughout the season. Therefore, several adjustments of Kc are often required if the mid and late seasons cover several climatic seasons, e.g., spring, summer and autumn or wet and dry seasons. The Kc ini and Kc end for evergreen non dormant trees and shrubs are often not different, where climatic conditions do not vary much, as happens in tropical climates. Under these conditions, seasonal adjustments for climate may therefore not be required since variations in ETc depend mostly on variations in ETo.

Calculating ETc


Graphical determination of Kc
Numerical determination of Kc


From the crop coefficient curve the Kc value for any period during the growing period can be graphically or numerically determined. Once the Kc values have been derived, the crop evapotranspiration, ETc, can be calculated by multiplying the Kc values by the corresponding ETo values.

Graphical determination of Kc

Weekly, ten-day or monthly values for Kc are necessary when ETc calculations are made on weekly, ten-day or monthly time steps. A general procedure is to construct the Kc curve, overlay the curve with the lengths of the weeks, decade or months, and to derive graphically from the curve the Kc value for the period under consideration (Figure 36). Assuming that all decades have a duration of 10 days facilitates the derivation of Kc and introduces little error into the calculation of ETc.

The constructed Kc curve in Box 15 was used to construct the curve in Figure 36. This curve has been overlaid with the lengths of the decades. Kc values of 0.15, 1.19 and 0.35 and the actual lengths for growth stages equal to 25, 25, 30 and 20 days were used. The crop was planted at the beginning of the last decade of May and was harvested 100 days later at the end of August.

For all decades the Kc values can be derived directly from the curve. The value at the middle of the decade is considered to be the average Kc of that 10 day period. Only the second decade of June, where the Kc value changes abruptly, requires some calculation.

BOX 15. Case study of a dry bean crop at Kimberly, Idaho, the United States (single crop coefficient)

An example application for using the Kc procedure under average soil wetness conditions is presented for a dry bean crop planted on 23 May 1974 at Kimberly, Idaho, the United States (latitude = 42.4°N). The initial, development, mid-season and late season stage lengths are taken from Table 11 for a continental climate as 20, 30, 40 and 20 days (the stage lengths listed for southern Idaho were not used in this example in order to demonstrate the only approximate accuracy of values provided in Table 11 when values for the specific location are not available). Initial values for Kc ini, Kc mid and Kc end are selected from Table 12 as 0.4, 1.15, and 0.35.

The mean RHmin and u2 during both the mid-season and late season growth stages were 30% and 2.2 m/s. The maximum height suggested in Table 12 for dry beans is 0.4 m. Therefore, Kc mid is adjusted using Eq. 62 as:

As Kc end = 0.35 is less than 0.45, no adjustment is made to Kc end. The value for Kc mid is not significantly different from that in Table 12 as u2 » 2 m/s, RHmin is just 15% lower than the 45% represented in Table 12, and the height of the beans is relatively short. The initial Kc curve for dry beans in Idaho can be drawn, for initial, planning purposes, as shown in the graph (dotted line), where Kc ini, Kc mid and Kc end are 0.4, 1.19 and 0.35 and the four lengths of growth stages are 20, 30, 40 and 20 days. Note that the Kc ini = 0.4 taken from Table 12 serves only as an initial, approximate estimate for Kc ini.

Constructed Kc curves using values from Tables 11 and 12 directly (dotted line) and modified using Kc ini from Fig. 29 and Lini = 25, Ldev = 25, Lmid = 30, and Llate = 20 days (heavy line) for dry beans at Kimberly, Idaho. Also shown are daily measured Kc (lysimeter data from Wright, 1990).

Kc ini can be more accurately estimated using the approach described in this chapter. ETo during the initial period at Kimberly (late May - early June, 1974) averaged 5.3 mm/day, and the wetting interval during this period was approximately 14 days (2 rainfall events occurred averaging 5 mm per event). Therefore, as the wetting events were light (< 10 mm each), Fig. 29 is used. The soil texture at Kimberly, Idaho is silt loam. From Fig. 29, Kc ini for the 14 day wetting interval and ETo = 5.3 mm/day is about 0.15. This value is substantially less than the general 0.4 value suggested by Table 12, and emphasizes the need to utilize local, actual precipitation and irrigation data when determining Kc ini.

Comparison of constructed curves with measurements

Because the ETc data for the dry bean crop at Kimberly, Idaho were measured using a precision lysimeter system during 1974 by Wright (1990), the actual Kc measurements can be compared with the constructed Kc curves, where actual Kc was calculated by dividing lysimeter measurements of ETc by daily ETo estimated using the FAO Penman-Monteith equation.

As illustrated in the graph, the mid-season length as taken from Table 11 for the general, continental climate overestimated the true mid-season length for dry beans in southern Idaho, which averaged only about 30 days rather than 40 days as suggested by Table 11. This illustrates the importance of using the local observation of 30 days for mid-season period length rather than the general value from Table 11.

The final, best estimate for the Kc curve for the dry bean crop in southern Idaho is plotted (lower curve in graph) using Kc values of 0.15, 1.19, and 0.35 and the actual observed lengths of growth stages equal to 25, 25, 30 and 20 days. Note the impact that the error in estimating mid-season length has on the area under the Kc curve. This supports the need to obtain local observations of growth stage dates and lengths.

The value calculated for Kc mid (1.19) appears to have underestimated the measured value for Kc during portions of the mid-season period at Kimberly. Some of this effect was due to effects of increased soil water evaporation following four irrigations during the 1974 mid-season which increased the effective Kc. This is illustrated in Box 16, where the basal Kcb + Ke approach is introduced and demonstrated for this same example.

The 0.15 value calculated for Kc ini using Fig. 29 agrees closely with measured Kc during the initial period. Measured Kc during the development period exceeded the final Kc curve during days on or following wetting events. The day to day variation in the lysimeter measured Kc is normal and is caused by day to day variations in weather, in wind direction, by errors in prediction of Rn and ETo, and by some random errors in the lysimeter measurements and weather measurements.

FIGURE 36. Kc curve and ten-day values for Kc and ETc derived from the graph for the dry bean crop example (Box 15)

first five days of that decade, Kc = 0.15, while during the second part of the decade Kc varies from 0.15 to 0.36 at the end of day 10. The Kc for that decade is consequently: 5/10 (0.15) + 5/10(0.15+0.36)/2 = 0.20.

Numerical determination of Kc

The Kc coefficient for any period of the growing season can be derived by considering that during the initial and mid-season stages Kc is constant and equal to the Kc value of the growth stage under consideration. During the crop development and late season stage, Kc varies linearly between the Kc at the end of the previous stage (Kc prev) and the Kc at the beginning of the next stage (Kc next), which is Kc end in the case of the late season stage:

(66)

where

i day number within the growing season [1.. length of the growing season],
Kc i crop coefficient on day i,
Lstage length of the stage under consideration [days],
S (Lprev) sum of the lengths of all previous stages [days].

Equation 66 applies to all four stages.

EXAMPLE 28. Numerical determination of Kc

Determine Kc at day 20, 40, 70 and 95 for the dry bean crop (Figure 36).

Crop growth stage

Length (days)

Kc

initial

25

Kc ini = 0.15

crop development

25

0.15... 1.19

mid-season

30

Kc mid = 1.19

late season

20

1.19 .. Kc end = 0.35

At i = 20:

initial stage, Kc = Kc ini =

0.15

-

At i = 40

Crop development stage,



For:

S (Lprev) = Lini =

25

days

and:

Lstage = Ldev =

25

days

From Eq. 66:

Kc = 0.15 + [(40 - 25)/25](1.19 - 0.15) =

0.77

-

At i = 70:

mid-season stage, Kc = Kc mid =

1.19

-

At i = 95

late season stage,



For:

S (Lprev) = Lini + Ldev + Lmid = (25 + 25 + 30) =

80

days

and:

Lstage = Llate =

20

days

From Eq. 66:

Kc = 1.19 + [(95-80)/20](0.35-1.19) =

0.56

-

The crop coefficients at day 20, 40, 70 and 95 for the dry bean crop are 0.15, 0.77, 1.19 and 0.56 respectively.

Alfalfa-based crop coefficients

As two reference crop definitions (grass and alfalfa) are in use in various parts of the world, two families of Kc curves for agricultural crops have been developed. These are the alfalfa-based Kc curves by Wright (1981; 1982) and grass-based curves by Pruitt (Doorenbos and Pruitt 1977; Jensen et al. 1990) and those reported in this paper. The user must exercise caution to avoid mixing grass-based Kc values with alfalfa reference ET and vice versa. Usually, a Kc based on the alfalfa reference can be 'converted' for use with a grass reference by multiplying by a factor ranging from about 1.0 to 1.3, depending on the climate (1.05 for humid, calm conditions, and 1.2 for semi-arid, moderately windy conditions, and 1.35 for arid, windy conditions):

Kc (grass) = Kratio Kc (alfalfa) (67)

where

Kc (grass) grass-based Kc (this handbook),
Kc (alfalfa) alfalfa-based Kc,
Kratio conversion factor (1.0... 1.3).

A reference conversion ratio can be established for any climate by using the Kc mid = 1.20 listed for alfalfa in Table 12 and then adjusting this Kc mid for the climate using Equation 62. For example, at Kimberly, Idaho, the United States, where RHmin = 30% and u2 = 2.2 m/s are average values during the summer months, a reference conversion ratio between alfalfa and grass references using Equation 62 is approximately:

(68)

where

h = 0.5 m is the standard height for the alfalfa reference.

Transferability of previous Kc values

The values for Kc mid and Kc end listed in Table 12 are for a large part based on the original values presented in FAO Irrigation and Drainage Papers No. 24 and 33 (FAO-24 and FAO-33), with some adjustment and revisions to reflect recent findings. Similarly adjustments in Kc mid to compensate for differences in aerodynamic roughness and leaf area, as introduced in Equation 62 are derived from the Kc values given for different wind and RHmin conditions in the concerned Kc table in FAO-24, with some upward adjustment to better reflect increased ETcrop values under high wind and low RHmin when applied with the FAO Penman-Monteith equation.

The Kc's from FAO-24 were based primarily on a living grass reference crop. The FAO Penman-Monteith equation presented in this publication similarly represents the same standardized grass reference. For that reason Kc values are in general not very different between these publications except under high wind and low RHmin.

The No. 24 modified Penman was found frequently to overestimate ETo even up to 25 % under high wind and low evaporative conditions and required often substantial local calibration (see chapter 2). Kc values derived from crop water use studies which used the FAO-24 Penman equation to compute grass reference crop evapotranspiration, can therefore not be used and need to be adjusted using ETo values estimated from the FAO Penman-Monteith equation. Similarly crop water requirement estimates based on the FAO-24 Modified Penman equation will need to be reassessed in view of the found differences between the FAO-24 Penman and the FAO Penman-Monteith reference equations.


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