• The Ponzo Illusion

• But the bars are the same width. The upper bar seems wider because the brain judges it against the tracks and, unlike the lower bar, it straddles both rails.

• In the same way, some believe familiar foreground objects make a low-lying moon in the distance appear bigger.

• The Flattened Sky

• Alternatively, there is the flattened sky theory, although some believe this works in conjunction with Ponzo's illusion.

• The true size of the moon remains the same because it stays a constant distance from the eye as it rises into the sky.

The Flattened Sky

• But, it's suggested that the human brain perceives the sky to be a flattened dome rather than a true hemisphere.

• In doing so, it compensates for the supposed discrepancy, making the moon seem smaller than it is.

Maybe it's the shape of the sky. Humans perceive the sky as a flattened dome, with the zenith nearby and the horizon far away. It makes sense:

Birds flying overhead are closer than birds on the horizon. When the moon is near the horizon, your brain, trained by watching birds,

miscalculates the moon's true distance and size.

CROP WATER NEEDS

By: Dr Kassim BuhiranBSc(Hons) Malaysia 1976

MSc (Agr. Eng.) Cranfield Inst. Of Tech., England 1979PhD (Agr. Eng.) Tsukuba Uni., Japan 1987

Lecture for: International Short Course on Irrigation and Drainage Practices. 20 th Nov. 2007

International Commission on Irrigation and Drainage (ICID)

PRINCIPLES OF IRRIGATION WATER NEEDS

All field crops need soil, water, air and light (sunshine) to grow. The soil gives stability to the plants; it also stores the water and nutrients which the plants can take up through their roots. The sunlight provides the energy which is necessary for plant growth The air allows the plants to "breath".

Plants need soil, water, air and sunlight ...... The most well-known source of water for plant growth is

rain water. There are two important questions: What to do if there is too much rain water? What to do if there is too little

rain water?

If there is too much rain, the soil will be full of water and there will not be enough air. Excess water must be removed. The removal of excess water - either from the ground surface or from the root zone - is called drainage.

If there is too little rain, water must be supplied from other sources; irrigation is needed. The amount of irrigation water which is needed depends not only on the amount of water already available from rainfall, but also on the total amount of water needed by the various crops.

With respect to the need for irrigation water, a distinction can be made among three climatic situations: 1. Humid climates: more than 1200 mm of rain per year. The amount of rainfall is sufficient to cover the water needs of the various crops. Excess water may cause problems for plant growth and thus drainage is required. 2. Sub-humid and semi-arid climates: between 400 and 1200 mm of rain per year. The amount of rainfall is important but often not sufficient to cover the water needs of the crops. Crop production in the dry season is only possible with irrigation, while crop production in the rainy season may be possible but unreliable: yields will be less than optimal. 3. Semi-arid, arid and desert climates: less than 400 mm of rain per year. Reliable crop production based on rainfall is not possible; irrigation is thus essential.

The two major factors which determine the amount of irrigation water which is needed are: 1) the total water need of the various crops2) the amount of rain water which is available to the crops

In other words: the irrigation water need is the difference between the total water need of the crops and the amount of rainfall which is available to the crops.

Irrigation crops availablewater = water - rainfallneed need

In many countries it is already well known what the crop water needs and irrigation water needs can usually be obtained from the Extension Service, the Irrigation Department or Ministry of Agriculture. It is then not necessary to determine the crop and irrigation water need. However, there may be situations where it is not possible to obtain these data and it would thus be necessary to determine them on the spot.

CROP WATER NEEDS

The plant roots suck or extract water from the soil to live and grow. The main part of this water does not remain in the plant, but escapes to the atmosphere as vapour through the plant's leaves and stem. This process is called transpiration. Transpiration happens mainly during the day time. Water from an open water surface escapes as vapour to the atmosphere during the day. The same happens to water on the soil surface and to water on the leaves and stem of a plant. This process is called evaporation. The water need of a crop thus consists of transpiration plus evaporation. Therefore, the crop water need is also called "evapotranspiration".

Evapotranspiration

• The water need of a crop thus consists of transpiration plus evaporation. Therefore, the crop water need is also called evapotranspiration.

The crop water need (ET crop) is defined as the depth (or amount) of water needed to meet the water loss through evapotranspiration. In other

words, it is the amount of water needed by the various crops to grow optimally.

The crop water need always refers to a crop grown under optimal conditions, i.e. a uniform crop,

actively growing, completely shading the ground, free of diseases, and favourable soil conditions

(including fertility and water). The crop thus reaches its full production potential under the given

environment.

The water need of a crop is usually expressed in mm/day, mm/month or mm/season. Suppose the water need of a certain crop in a very hot, dry climate is 10 mm/day. This means that each day the crop needs a water layer of 10 mm over the whole area on which the crop is grown.

As an example above, the water need of a certain crop in a very hot, dry climate is 10 mm/day. It does not mean that this 10 mm has to indeed be supplied by rain or irrigation every day. It is still possible to supply, for example, 50 mm of irrigation water every 5 days. The irrigation water will then be stored in the root zone and gradually be used by the plants: every day 10 mm.

So the crop water need (ET crop) is defined as the depth (or amount) of water needed to meet the water loss through evapotranspiration. Although the values for crop evapotranspiration and crop water requirement are identical, crop water requirement refers to the amount of water that needs to be supplied, while crop evapotranspiration refers to the amount of water that is lost through evapotranspiration process by the various crops to grow optimally

So the crop water need always refers to a crop grown under optimal conditions, i.e. a uniform crop, actively growing, completely shading the ground, free of diseases, and favourable soil conditions (including fertility and water). The crop thus reaches its full production potential under the given environment.

The crop water need mainly depends on: · the climate:for example, in a sunny and hot climate crops need more water per day than in a cloudy and cool climate .· the crop type:crops like rice or sugarcane need more water than crops like beans and wheat .· the growth stage:grown crops need more water than crops that have just been planted .

Major climatic factors influencing crop water needs

apart from sunshine and temperature, humidity and the windspeed influence the crop water need.

The highest crop water needs are thus found in areas which are hot, dry, windy and sunny. The lowest values are found when it is cool, humid and cloudy with little or no wind.

Table 2 indicates the average daily water needs of this reference grass crop. The daily water needs of the grass depend on the climatic zone (rainfall regime) and daily temperatures.

Climatic zone Mean daily temperature low medium high

(less than 15°C) (15-25°C) (more than 25°C) Desert/arid 4-6 7-8 9-10 Semi arid 4-5 6-7 8-9 Sub-humid 3-4 5-6 7-8 Humid 1-2 3-4 5-6

From the above it is clear that one crop grown in different climatic zones will have different water needs. For example, a certain maize variety grown in a cool climate will need less water per day than the same maize variety grown in a hotter climate. It is difficults to determine every crop water needs for every climatic conditions.

It is therefore useful to take a certain standard crop or reference crop and determine how much water this crop needs per day in the various climatic regions. As a standard crop or reference crop: grass has been chosen.

So the daily water needs of the standard grass crop is also called "reference crop evapotranspiration“ .

What will be discussed next is "how do the water needs of the crops grown on, for an example, an irrigation scheme relate to the water need of the standard grass".

The influence of the crop type on the crop water need is important in two ways: 1. The crop type has an influence on the daily water needs of a fully grown crop; i.e. the peak daily water needs: a fully developed maize crop will need more water per day than a fully developed crop of onions. 2. The crop type has an influence on the duration of the total growing season of the crop. There are short duration crops, e.g. peas, with a duration of the total growing season of 90-100 days and longer duration crops, e.g. melons, with a duration of the total growing season of 120-160 days. And then there are, of course, the perennial crops that are in the field for many years, such as fruit trees.

CROP WATER NEEDS IN PEAK PERIOD OF VARIOUS FIELD CROPS AS COMPARED TO STANDARD GRASS

Column 1

Column 2

Column 3 Column 4 Column 5

-30% -10% same as standard grass + 10% +20%

citrus cucumber carrots barley paddy rice

olives radishes crucifers (cabbage, cauliflower, broccoli, etc.)

beans sugarcane

grapes squash lettuce maize banana

melons flax nuts & fruit trees with cover crop

onions small grains

peanuts cotton

peppers tomato

spinach eggplant

tea lentils

grass millet

cacao oats

coffee peas

clean cultivated nuts & fruit trees e.g. apples

potatoes

safflower

sorghum

soybeans

sugarbeet

sunflower

tobacco

wheat

When determining the influence of the crop type on the daily crop water needs, reference is always made to a fully grown crop; the plants have reached their maximum height; they optimally cover the ground; they possibly have started flowering or started grain setting. When the crops are fully grown their water need is the highest. It is the so-called "peak period" of their water needs.

EXAMPLE Suppose in a certain area the standard grass crop needs 5.5 mm of water per day.

Then, in that same area, maize will need 10% more water. Ten percent of 5.5 mm = 10/100 × 5.5 = 0.55 mm. Thus maize would need 5.5 + 0.55 = 6.05 or rounded 6.1 mm of water per day.

QUESTION

Estimate the water needs of citrus, bananas, onions, cucumber, clean cultivated apple trees and millet for an area where the water need of standard grass is 6.0 mm/day.

ANSWER

Citrus: -30% (compared to grass); thus the water need of citrus is 6.0 - 30% = 6.0 -1.8 = 4.2 mm/day

Bananas: +20%; thus the water need of bananas is 6.0 + 20% = 6.0 + 1.2 = 7.2 mm/day

Onions: same as grass; thus the water need of onions is 6.0 mm/day

Cucumber: -10%; thus the water need of onions is 6.0 - 10% =6.0-0.6 =5.4 mm/day

Apples (clean):

same as grass; thus the water need of clean cultivated apples is 6.0 mm/day

If the apples have a cover crop in between the trees, the water need would be 20% higher than grass and thus: 6.0 + 20% = 6.0+1.2 = 7.2 mm/day.

Millet: +10%; thus the water need of millet is 6.0 + 10% =6.0+0.6 = 6.6 mm/day

Influence of Crop Type on the Seasonal Crop Water NeedsThe crop type not only has an influence on the daily water need of a fully grown crop, i.e. the daily peak water need, but the crop type also has an influence on the duration of the total growing season of the crop, and thus on the seasonal water need for example, many rice varieties, some with a short growing cycle (e.g. 90 days) and others with a long growing cycle (e.g. 150 days). This has a strong influence on the seasonal rice water needs: a rice crop which is in the field for 150 days will need in total much more water than a rice crop which is only in the field for 90 days. Of course, for the two rice crops the daily peak water need may still be the same, but the 150 day crop will need this daily amount for a longer period.

INDICATIVE VALUES OF THE TOTAL GROWING PERIOD

Crop Total growing period (days) Crop Total growing period (days) Alfalfa 100-365 Millet 105-140

Banana 300-365 Onion green 70-95 Barley/Oats/Wheat 120-150 Onion dry 150-210

Bean green 75-90 Peanut/Groundnut 130-140 Bean dry 95-110 Pea 90-100

Cabbage 120-140 Pepper 120-210

Carrot 100-150 Potato 105-145

Citrus 240-365 Radish 35-45

Cotton 180-195 Rice 90-150

Cucumber 105-130 Sorghum 120-130

Eggplant 130-140 Soybean 135-150 Flax 150-220 Spinach 60-100

Grain/small 150-165. Squash 95-120

Lentil 150-170 Sugarbeet 160-230

Lettuce 75-140 Sugarcane 270-365

Maize sweet 80-110 Sunflower 125-130

Maize grain 125-180 Tobacco 130-160

Melon 120-160 Tomato 135-180

INFLUENCE OF THE GROWTH STAGE OF THE CROP ON CROP WATER NEEDSA fully grown maize crop will need more water than a maize crop which has just been planted. As has been discussed before, the crop water need or crop evapotranspiration consists of transpiration by the plant and evaporation from the soil and plant surface. When the plants are very small the evaporation will be more important than the transpiration. When the plants are fully grown the transpiration is more important than the evaporation.

Growth stages of a crop

At planting and during the initial stage, the crop water need is estimated at 50 percent of the crop water need during the mid - season stage, when the crop is fully developed. During the so-called crop development stage the crop water need gradually increases to the maximum crop water need. The maximum crop water need is reached at the end of the crop development stage which is the beginning of the mid-season stage. Fresh harvested crops: such as lettuce, cabbage, etc. the crop water need remains the same during the late season stage as it was during the mid-season stage. The crops are harvested fresh and thus need water up to the last moment. Dry harvested crops: such as cotton, maize (for grain production), sunflower, etc. During the late season stage these crops are allowed to dry out and sometimes even die. Thus their water needs during the late season stage are only some 25 percent of the crop water need during the mid-season or peak period. Of course, no irrigation is given to these crops during the late season stage.

EFFECTIVE RAINFALLApart from soil, air and sunlight, crops need water to grow. How much water the various crops need has been explained above. This water can be supplied to the crops by rainfall (also called precipitation), by irrigation or by a combination of rainfall and irrigation. If the rainfall is sufficient to cover the water needs of the crops, irrigation is not required. If there is no rainfall, all the water that the crops need has to be supplied by irrigation. If there is some rainfall, but not enough to cover the water needs of the crops, irrigation water has to supplement the rain water in such a way that the rain water and the irrigation water together cover the water needs of the crop. This is often called supplemental irrigation: the irrigation water supplements or adds to the rain water.

not all rain water which falls on the soil surface can indeed be used by the plants. Part of the rain water percolates below the root zone of the plants and part of the rain water flows away over the soil surface as run-off. This deep percolation water and run-off water cannot be used by the plants. In other words, part of the rainfall is not effective. The remaining part is stored in the root zone and can be used by the plants. This remaining part is the so-called effective rainfall. The factors which influence which part is effective and which part is not effective include the climate, the soil texture, the soil structure and the depth of the root zone.

Part of the rain water is lost through deep percolation and run-off

If the rainfall is high, a relatively large part of the water is lost through deep percolation and run-off. Deep percolation: If the soil is still wet when the next rain occurs, the soil will simply not be able to store more water, and the rain water will thus percolate below the root zone and eventually reach the groundwater. Heavy rainfall may cause the groundwater table to rise temporarily. Run-off: Especially in sloping areas, heavy rainfall will result in a large percentage of the rainwater being lost by surface run-off.

RAINFALL OR PRECIPITATION (P) AND EFFECTIVE RAINFALL OR EFFECTIVE PRECIPITATION (Pe) in mm/month

P (mm/month)

Pe (mm/month)

P (mm/month)

Pe (mm/month)

0 0 130 79

10 0 140 87

20 2 150 95

30 8 160 103

40 14 170 111

50 20 180 119

60 26 190 127

70 32 200 135

80 39 210 143

90 47 220 151

100 55 230 159

110 63 240 167

120 71 250 175

QUESTION Determine the effective rainfall for the following monthly rainfall: 65, 210, 175 and 5 mm.

ANSWER P (mm/month) Pe (mm/month)65 29210 143175 1155 0

IRRIGATION WATER NEEDSThe irrigation water need of a certain crop is the difference between the crop water need and that part of the rainfall which can be used by the crop (the effective rainfall). For each of the crops grown on an irrigation scheme the crop water need is determined, usually on a monthly basis; the crop water need is expressed in mm water layer per time unit, in this case mm/month.

the Irrigation water need for the tomatoes can be calculated on a monthly basis, as follows:

Feb Mar Apr May June Total

Crop water need (mm/month) 69 123 180 234 180 786

Effective rainfall: Pe (mm/month) 2 13 14 39 0 68

Irrigation water need (mm/month) 67 110 166 195 180 718

Evapotranspiration concepts

Evaporation is the process whereby liquid water is converted to water vapour (vaporization) and removed from the evaporating surface (vapour removal). Water evaporates from a variety of surfaces, such as lakes, rivers, pavements, soils and wet vegetation. Energy is required to change the state of the molecules of water from liquid to vapour. Direct solar radiation and, to a lesser extent, the ambient temperature of the air provide this energy.

The driving force to remove water vapour from the evaporating surface is the difference between the water vapour pressure at the evaporating surface and that of the surrounding atmosphere. As evaporation proceeds, the surrounding air becomes gradually saturated and the process will slow down and might stop if the wet air is not transferred to the atmosphere.

The replacement of the saturated air with drier air depends greatly on wind speed. Hence, solar radiation, air temperature, air humidity and wind speed are climatological parameters to consider when assessing the evaporation process.

Transpiration • Transpiration consists of the vaporization of liquid water contained in plant tissues and the vapour removal to the atmosphere. Crops predominately lose their water through stomata. These are small openings on the plant leaf through which gases and water vapour pass.

Nearly all water taken up is lost by transpiration and only a tiny fraction is used within the plant. Transpiration, like direct evaporation, depends on the energy supply, vapour pressure gradient and wind. Hence, radiation, air temperature, air humidity and wind terms should be considered when assessing transpiration. The soil water content and the ability of the soil to conduct water to the roots also determine the transpiration rate, as do waterlogging and soil water salinity.

Different kinds of plants may have different transpiration rates. Not only the type of crop, but also the crop development, environment

and management should be considered when assessing transpiration.

Evaporation and transpiration occur simultaneously and there is no easy way of distinguishing between the two processes. At sowing nearly 100% of ET comes from evaporation, while at full crop cover more than 90% of ET comes from transpiration.

Reference Crop Evapotranspiration (ETo).

• Evapotranspiration from the reference surface is called reference crop evapotranspiration or reference evapotranspiration, denoted as ETo. The reference surface is a hypothetical grass reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s m-1 and an albedo of 0.23. The reference surface closely resembles an extensive surface of green, well-watered grass of uniform height, actively growing and completely shading the ground. The fixed surface resistance of 70 s m-1 implies a moderately dry soil surface resulting from about a weekly irrigation frequency.

Major climatic factors

influencing evaporation and Transpiration.

• Sunshine, temperature, wind speed and humidity influence the crop water need

Typical presentation of the variation in the active (green) Leaf Area Index over the growing season for a maize crop

Illustration of the effect of wind speed on evapotranspiration in hot-dry and humid-warm weather conditions

The evapotranspiration rate from a reference surface, not short of water, is called the reference crop evapotranspiration or reference evapotranspiration and is denoted as ETo. The reference surface is a hypothetical grass reference crop with specific characteristics.

The concept of the reference evapotranspiration was introduced to study the evaporative demand of the atmosphere independently of crop type, crop development and management practices. As water is abundantly available at the reference evapotranspiring surface, soil factors do not affect ET. ETo values measured or calculated at different locations or in different seasons are comparable as they refer to the ET from the same reference surface.

The FAO Penman-Monteith method is recommended as the standard method for determining ETo. The method has been selected because it closely approximates grass ETo at the location evaluated, is physically based, and explicitly incorporates both physiological and aerodynamic parameters. Moreover, procedures have been developed for estimating missing climatic parameters.

The crop evapotranspiration under standard conditions, denoted as ETc, is the evapotranspiration from disease-free, well-fertilized crops, grown in large fields, under optimum soil water conditions, and achieving full production under the given climatic conditions. Crop evapotranspiration can be calculated from climatic data and by integrating directly the crop resistance, albedo and air resistance factors in the Penman-Monteith approach.

The crop evapotranspiration under non-standard conditions (ETc adj) is the evapotranspiration from crops grown under management and environmental conditions that differ from the standard conditions. When cultivating crops in fields, the real crop evapotranspiration may deviate from ETc due to non-optimal conditions such as the presence of pests and diseases, soil salinity, low soil fertility, water shortage or waterlogging.

Factors affecting evapotranspiration with reference to related ET concepts

Distinctions are made between reference crop evapotranspiration (ETo), crop evapotranspiration under standard conditions (ETc) and crop evapotranspiration under non-standard conditions (ETc adj).

Determining evapotranspiration (ET)

• Specific devices and accurate measurements of various physical parameters or the soil water balance in lysimeters are required to determine evapotranspiration. The methods are often expensive, demanding in terms of accuracy of measurement and can only be fully exploited by well-trained research personnel. Although the methods are inappropriate for routine measurements, they remain important for the evaluation of ET estimates obtained by more indirect methods.

1. Energy balance and microclimatological methods

• The evapotranspiration process is governed by energy exchange at the vegetation surface and is limited by the amount of energy available. Because of this limitation, it is possible to predict the evapotranspiration rate by applying the principle of energy conservation. The energy arriving at the surface must equal the energy leaving the surface for the same time period.

The equation for an evaporating surface can be written as:

Rn - G - λ ET - H = 0

• where Rn is the net radiation, H the sensible heat, G the soil heat flux and , l ET the latent heat flux. The various terms can be either positive or negative. Positive Rn supplies energy to the surface and positive G, λET and H remove energy from the surface.

Schematic presentation of the diurnal variation of the components of the energy balance above a well-watered transpiring surface on a cloudless day

2. Soil water balance

• If all fluxes including irrigation (I), rainfall (P), surface runoff (RO), deep percolation (DP) and capillary rise (CR) can be assessed, so the evapotranspiration can be deduced from the change in soil water content (∆SW) over the time period:

ET = I + P - RO - DP + CR ± ∆ SF ± ∆ SW

Soil water balance of the root zone.

3. Lysimeters

• In precision weighing lysimeters, where the water loss is directly measured by the change of mass, evapotranspiration can be obtained with an accuracy of a few hundredths of a millimetre, and small time periods such as an hour. As lysimeters are difficult and expensive to construct and their operation and maintenance require special care, their use is limited to specific research purposes.

4. ET estimated from pan evaporation

• Evaporation from an open water surface provides an index of the integrated effect of radiation, air temperature, air humidity and wind on evapotranspiration. However, differences in the water and cropped surface produce significant differences in the water loss from an open water surface and the crop. The pan has proved its practical value and has been used successfully to estimate reference evapotranspiration by observing the evaporation loss from a water surface and applying empirical coefficients to relate pan evaporation to ETo.

Pan Evaporation Method.ETo can be estimated from pan evaporation by observing the water loss from the pan and using empirical coefficients to relate pan evaporation to ETo. Evaporation pans provide a measurement of the combined effect of temperature, humidity, windspeed and sunshine on the reference crop evapotranspiration ETo. Many different types of evaporation pans are being used. The best known pans are the Class A evaporation pan (circular pan) and the Sunken

Colorado pan (square pan).

The principle of the evaporation pan is the following: - the pan is installed in the field - the pan is filled with a known quantity of water (the surface area of the pan is known and the water depth is measured) - the water is allowed to evaporate during a certain period of time (usually 24 hours). For example, each morning at 7 o'clock a measurement is taken. The rainfall, if any, is measured simultaneously - after 24 hours, the remaining quantity of water (i.e. water depth) is measured - the amount of evaporation per time unit (the difference between the two measured water depths) is calculated; this is the pan evaporation: E pan (in mm/24 hours) - the E pan is multiplied by a pan coefficient, K pan, to obtain the ETo. ETo = K pan × E panwith: ETo: reference crop evapotranspirationK pan: pan coefficientE pan: pan evaporation

Class A pan • The Class A Evaporation pan is circular,

120.7 cm in diameter and 25 cm deep. It is made of galvanized iron (22 gauge) or Monel metal (0.8 mm). The pan is mounted on a wooden open frame platform which is 15 cm above ground level. The soil is built up to within 5 cm of the bottom of the pan. The pan must be level. It is filled with water to 5 cm below the rim, and the water level should not be allowed to drop to more than 7.5 cm below the rim. The water should be regularly renewed, at least weekly, to eliminate extreme turbidity. The pan, if galvanized, is painted annually with aluminium paint. Pans should be protected by fences to keep animals from drinking.

• The site should preferably be under grass, 20 by 20 m, open on all sides to permit free circulation of the air. It is preferable that stations be located in the centre or on the leeward side of large cropped fields.

• Pan readings are taken daily in the early morning at the same time that precipitation is measured. Measurements are made in a stilling well that is situated in the pan near one edge. The stilling well is a metal cylinder of about 10 cm in diameter and some 20 cm deep with a small hole at the bottom.

Colorado sunken pan

• The Colorado sunken pan is 92 cm (3 ft) square and 46 cm (18 in) deep, made of 3 mm thick iron, placed in the ground with the rim 5 cm (2 in) above the soil level. Also, the dimensions 1 m square and 0.5 m deep are frequently used. The pan is painted with black tar paint. The water level is maintained at or slightly below ground level, i.e., 5-7.5 cm below the rim.

• Measurements are taken similarly to those for the Class A pan. Siting and environment requirements are also similar to those for the Class A pan.

• Sunken Colorado pans are sometimes preferred in crop water requirements studies, as these pans give a better direct estimation of the reference evapotranspiration than does the Class A pan. The disadvantage is that maintenance is more difficult and leaks are not visible.

If the water depth in the pan drops too much (due to lack of rain), water is added and the water depth is measured before and after the water is added. If the water level rises too much (due to rain) water is taken out of the pan and the water depths before and after are measured. For the Class A evaporation pan, the K pan varies between 0.35 and 0.85. Average K pan = 0.70. For the Sunken Colorado pan, the K pan varies between 0.45 and 1.10. Average K pan = 0.80.

Add water when the water depth in the pan drops too much

Take water out of the pan when the water depth rises too much

5. ET computed from meteorological data

• . A large number of empirical or semi-empirical equations have been developed for assessing crop or reference crop evapotranspiration from meteorological data. Some of the methods are only valid under specific climatic and agronomic conditions and cannot be applied under conditions different from those under which they were originally developed. The influence of the climate on crop water needs is given by the reference crop evapotranspiration (ETo). And crop evapotranspiration under standard conditions (ETc) refers to the evaporating demand from crops that are grown in large fields under optimum soil water, excellent management and environmental conditions, and achieve full production under the given climatic conditions.

There are several methods to determine the ETo . They are either: -experimental, using an evaporation pan-theoretical, using measured climatic data, e.g. the Blaney-Criddle method.-the FAO Penman-Monteith method is theoretical, using measured climatic data and now recommended as the standard method for the definition and computation of the reference evapotranspiration under all circumstances, even in the case of missing climatic data.

2. Blaney-Criddle Method• If no measured data on pan evaporation are available locally, a

theoretical method (e.g. the Blaney-Criddle method) to calculate the reference crop evapotranspiration ETo can be used. The Blaney-Criddle method is simple, using measured data on temperature only. It should be noted, however, that this method is not accurate; it provides a rough estimate or "order of magnitude" only. Especially under "extreme" climatic conditions the Blaney-Criddle method is inaccurate: in windy, dry, sunny areas, the ETo is underestimated (up to some 60 percent), while in calm, humid, clouded areas, the ETo is overestimated (up to some 40 percent).

• The Blaney-Criddle formula: ETo = p (0.46 T mean +8)• ETo = Reference crop evapotranspiration (mm/day) as an

average for a period of 1 monthT mean = mean daily temperature (°C)p = mean daily percentage of annual daytime hours

The Blaney-Criddle method

MEAN DAILY PERCENTAGE (p) OF ANNUAL DAYTIME HOURS FOR DIFFERENT LATITUDES

Latitude North Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

South July Aug Sept Oct Nov Dec Jan Feb Mar Apr May June

60° .15 .20 .26 .32 .38 .41 .40 .34 .28 .22 .17 .13

55 .17 .21 .26 .32 .36 .39 .38 .33 .28 .23 .18 .16

50 .19 .23 .27 .31 .34 .36 .35 .32 .28 .24 .20 .18

45 .20 .23 .27 .30 .34 .35 .34 .32 .28 .24 .21 .20

40 .22 .24 .27 .30 .32 .34 .33 .31 .28 .25 .22 .21

35 .23 .25 .27 .29 .31 .32 .32 .30 .28 .25 .23 .22

30 .24 .25 .27 .29 .31 .32 .31 .30 .28 .26 .24 .23

25 .24 .26 .27 .29 .30 .31 .31 .29 .28 .26 .25 .24

20 .25 .26 .27 .28 .29 .30 .30 .29 .28 .26 .25 .25

15 .26 .26 .27 .28 .29 .29 .29 .28 .28 .27 .26 .25

10 .26 .27 .27 .28 .28 .29 .29 .28 .28 .27 .26 .26

5 .27 .27 .27 .28 .28 .28 .28 .28 .28 .27 .27 .27

0 .27 .27 .27 .27 .27 .27 .27 .27 .27 .27 .27 .27

Sample to calculate ETo, using the formula: ETo = p (0.46 T mean + 8) For example, when p = 0.29 and T mean = 21.5°C the ETo is calculated as follows: ETo = 0.29 (0.46 × 21.5 + 8) = 0.29 (9.89 + 8) = 0.29 × 17.89 = 5.2 mm/day

Need for a standard ETo method

A large number of more or less empirical methods have been developed to estimate evapotranspiration from different climatic variables. Testing the accuracy of the methods under a new set of conditions is laborious, time-consuming and costly, and yet evapotranspiration data are frequently needed at short notice for project planning or irrigation scheduling design. To accommodate users with different data availability, several methods were presented to calculate the reference crop evapotranspiration (ETo): the Blaney-Criddle, radiation, modified Penman and pan evaporation methods. The modified Penman method was considered to offer the best results with minimum possible error in relation to a living grass reference crop. It was expected that the pan method would give acceptable estimates, depending on the location of the pan. The radiation method was suggested for areas where available climatic data include measured air temperature and sunshine, cloudiness or radiation, but not measured wind speed and air humidity. Finally, the proposed use of the Blaney-Criddle method for areas where available climatic data cover air temperature data only.

To evaluate the performance of these and other estimation procedures under different climatological conditions, a major study was undertaken and may be summarized as follows: The Penman methods may require local calibration of the wind function to achieve satisfactory results. The radiation methods show good results in humid climates where the aerodynamic term is relatively small, but performance in arid conditions is erratic and tends to underestimate evapotranspiration. Temperature methods remain empirical and require local calibration in order to achieve satisfactory results. A possible exception is the 1985 Hargreaves' method which has shown reasonable ETo results with a global validity. Pan evapotranspiration methods clearly reflect the shortcomings of predicting crop evapotranspiration from open water evaporation. The methods are susceptible to the microclimatic conditions under which the pans are operating and the rigour of station maintenance. Their performance proves erratic.

The analysis of the performance of the various calculation methods reveals the need for formulating a standard method for the computation of ETo. The FAO Penman-Monteith method is recommended as the standard method. It is a method with strong likelihood of correctly predicting ETo in a wide range of locations and climates and has provision for application in data-short situations. The use of older FAO or other reference ET methods is no longer encouraged.

3. FAO Penman-Monteith Method

The resistance nomenclature in this method distinguishes between aerodynamic resistance and surface resistance factors. The surface resistance parameters are often combined into one parameter, the 'bulk' surface resistance parameter which operates in series with the aerodynamic resistance. The surface resistance, rs, describes the resistance of vapour flow through stomata openings, total leaf area and soil surface. The aerodynamic resistance, ra, describes the resistance from the vegetation upward and involves friction from air flowing over vegetative surfaces. Although the exchange process in a vegetation layer is too complex to be fully described by the two resistance factors, good correlations can be obtained between measured and calculated evapotranspiration rates, especially for a uniform grass reference surface.

Simplified representation of the (bulk) surface and aerodynamic resistances for water vapour flow

The Penman-Monteith approach as formulated includes all parameters that govern energy exchange and corresponding latent heat flux (evapotranspiration) from uniform expanses of vegetation. Most of the parameters are measured or can be readily calculated from weather data. The panel of experts recommended the adoption of the Penman-Monteith combination method as a new standard for reference evapotranspiration and advised on procedures for calculation of the various parameters. By defining the reference crop as a hypothetical crop with an assumed height of 0.12 m having a surface resistance of 70 s m-1 and an albedo of 0.23, closely resembling the evaporation of an extension surface of green grass of uniform height, actively growing and adequately watered, the FAO Penman-Monteith method was developed. The method overcomes shortcomings of the previous FAO Penman method and provides values more consistent with actual crop water use data worldwide.

Characteristics of the hypothetical reference crop

From the original Penman-Monteith equation and the equations of the aerodynamic and surface resistance, the FAO Penman-Monteith method to estimate ETo can be derived :

where ETo reference evapotranspiration [mm day-1],Rn net radiation at the crop surface [MJ m-2 day-1],G soil heat flux density [MJ m-2 day-1],T mean daily air temperature at 2 m height [°C],u2 wind speed at 2 m height [m s-1],es saturation vapour pressure [kPa],ea actual vapour pressure [kPa],es - ea saturation vapour pressure deficit [kPa],D slope vapour pressure curve [kPa °C-1],g psychrometric constant [kPa °C-1].

The equation should uses standard climatological records of solar radiation (sunshine), air temperature, humidity and wind speed. To ensure the integrity of computations, the weather measurements should be made at 2 m (or converted to that height) above an extensive surface of green grass, shading the ground and not short of water. By using the FAO Penman-Monteith definition for ETo, one may calculate crop coefficients at research sites by relating the measured crop evapotranspiration (ETc) with the calculated ETo, i.e., Kc = ETc/ETo.

Calculation Procedure Penman-Monteith equation From the equations of the aerodynamic and canopy resistance, the FAO Penman-

Monteith equation is given:

where ETo reference evapotranspiration [mm day-1],

Rn net radiation at the crop surface [MJ m-2 day-1],G soil heat flux density [MJ m-2 day-1],T air temperature at 2 m height [°C],u2 wind speed at 2 m height [m s-1],es saturation vapour pressure [kPa],ea actual vapour pressure [kPa],es - ea saturation vapour pressure deficit [kPa],∆ slope vapour pressure curve [kPa °C-1],γ psychrometric constant [kPa °C-1].

Calculation sheet ETo can be estimated by means of the calculation sheet presented in Box 3.40. The calculation sheet refers to tables in Annex 3.40 for the determination of some of the climatic parameters. The calculation procedure consists of the following steps:

1. Derivation of some climatic parameters from the daily maximum (Tmax) and minimum (Tmin) air temperature, altitude (z) and mean wind speed (u2).

2. Calculation of the vapour pressure deficit (es - ea). The saturation vapour pressure (es) is derived from Tmax and Tmin, while the actual vapour pressure (ea) can be derived from the dewpoint temperature (Tdew), from maximum (RHmax) and minimum (RHmin) relative humidity, from the maximum (RHmax), or from mean relative humidity (RHmean).

3. Determination of the net radiation (Rn) as the difference between the net shortwave radiation (Rns) and the net longwave radiation (Rnl). In the calculation sheet, the effect of soil heat flux (G) is ignored for daily calculations as the magnitude of the flux in this case is relatively small. The net radiation, expressed in MJ m-2 day-1, is converted to mm/day (equivalent evaporation) in the FAO Penman-Monteith equation by using 0.408 as the conversion factor within the equation.

4. ETo is obtained by combining the results of the previous steps.

BOX 3.40. Calculation sheet for ETo (FAO Penman-Monteith) using meteorological tables of Annex 3.40

ParametersTmax °C

Tmin °C Tmean - (Tmax + Tmin)/2 °C

Tmean °C (Table 2.4) kPa/°C

Altitude m (Table 2.2) kPa/°C

u2 m/s (1 + 0.34 u2)

/[ + (1 + 0.34 u2)]

/[ + (1 + 0.34 u2)]

[900/(Tmean + 273)] u2

TABLE 2.2. Psychometric constant ( δ) for different altitudes (z)

z(m)

kPa/°C

z(m)

kPa/°C

z(m)

kPa/°C

z(m)

kPa/°C

0 0.067 1000 0.060 2000 0.053 3000 0.047

100 0.067 1100 0.059 2100 0.052 3100 0.046

200 0.066 1200 0.058 2200 0.052 3200 0.046

300 0.065 1300 0.058 2300 0.051 3300 0.045

400 0.064 1400 0.057 2400 0.051 3400 0.045

500 0.064 1500 0.056 2500 0.050 3500 0.044

600 0.063 1600 0.056 2600 0.049 3600 0.043

700 0.062 1700 0.055 2700 0.049 3700 0.043

800 0.061 1800 0.054 2800 0.048 3800 0.042

900 0.061 1900 0.054 2900 0.047 3900 0.042

1000 0.060 2000 0.053 3000 0.047 4000 0.041Based on = 2.45 MJ kg-1 at 20°C.

TABLE 2.4. Slope of vapour pressure curve () for different temperatures (T)

T°C

kPa/°C T°C

kPa/°C T°C

kPa/°C T°C

kPa/°C

1.0 0.047 13.0 0.098 25.0 0.189 37.0 0.342

1.5 0.049 13.5 0.101 25.5 0.194 37.5 0.350

2.0 0.050 14.0 0.104 26.0 0.199 38.0 0.358

2.5 0.052 14.5 0.107 26.5 0.204 38.5 0.367

3.0 0.054 15.0 0.110 27.0 0.209 39.0 0.375

3.5 0.055 15.5 0.113 27.5 0.215 39.5 0.384

4.0 0.057 16.0 0.116 28.0 0.220 40.0 0.393

4.5 0.059 16.5 0.119 28.5 0.226 40.5 0.402

5.0 0.061 17.0 0.123 29.0 0.231 41.0 0.412

5.5 0.063 17.5 0.126 29.5 0.237 41.5 0.421

6.0 0.065 18.0 0.130 30.0 0.243 42.0 0.431

Vapour pressure deficitTmax °C e°(Tmax) (Table 2.3) kPa

Tmin °C e°(Tmin) (Table 2.3) kPa

Saturation vapour pressure es = [(e°(Tmax) + e°(Tmin)]/2 kPa

ea derived from dewpoint temperature:

Tdew °C ea = e°(Tdew) (Table 2.3) kPa

OR ea derived from maximum and minimum relative humidity:

RHmax % e°(Tmin) RHmax/100 kPa

RHmin % e°(Tmax) RHmin/100 kPa

ea: (average) kPa

OR ea derived from maximum relative humidity: (recommended if there are errors in RHmin)

RHmax % ea = e°(Tmin) RHmax/100 kPa

OR ea derived from mean relative humidity: (less recommended due to non-linearities)

RHmean % ea = es RHmean/100 kPa

Vapour pressure deficit (es - ea) kPa

TABLE 2.3. Saturation vapour pressure (e°(T)) for different temperatures (T)

T°Ces

kPa T°Ce°(T)kPa T°C

e°(T)kPa T°C

es

kPa

1.0 0.657 13.0 1.498 25.0 3.168 37.0 6.275

1.5 0.681 13.5 1.547 25.5 3.263 37.5 6.448

2.0 0.706 14.0 1.599 26.0 3.361 38.0 6.625

2.5 0.731 14.5 1.651 26.5 3.462 38.5 6.806

3.0 0.758 15.0 1.705 27.0 3.565 39.0 6.991

3.5 0.785 15.5 1.761 27.5 3.671 39.5 7.181

4.0 0.813 16.0 1.818 28.0 3.780 40.0 7.376

4.5 0.842 16.5 1.877 28.5 3.891 40.5 7.574

5.0 0.872 17.0 1.938 29.0 4.006 41.0 7.778

RadiationLatitude °

Day Ra (Table 2.6) MJ m-2 d-1

Month N (Table 2.7) hours

n hours n/N

If no Rs data available: Rs = (0.25 + 0.50 n/N) Ra MJ m-2 d-1

Rso = [0.75 + 2 (Altitude)/100000] Ra MJ m-2 d-1

Rs / Rso

Rns = 0.77 Rs MJ m-2 d-1

Tmax (Table 2.8)

MJ m-2 d-1

Tmin (Table 2.8)

MJ m-2 d-1

MJ m-2 d-1

TABLE 2.6. Daily extraterrestrial radiation (Ra) for different latitudes for the 15th day of the month 1

(values in MJ m-2 day-1)2

TABLE 2.7. Mean daylight hours (N) for different latitudes for the 15th of the month1

TABLE 2.8.

(Stefan-Boltzmann law) at different temperatures (T) With = 4.903 10-9 MJ K-4 m-2 day-1 and TK = T[°C] + 273.16

T(°C) (MJ m-2 d-1)

T(°C) (MJ m-2 d-1)

T(°C) (MJ m-2 d-1)

1.0 27.70 17.0 34.75 33.0 43.08

1.5 27.90 17.5 34.99 33.5 43.36

2.0 28.11 18.0 35.24 34.0 43.64

2.5 28.31 18.5 35.48 34.5 43.93

3.0 28.52 19.0 35.72 35.0 44.21

3.5 28.72 19.5 35.97 35.5 44.50

4.0 28.93 20.0 36.21 36.0 44.79

4.5 29.14 20.5 36.46 36.5 45.08

5.0 29.35 21.0 36.71 37.0 45.37

5.5 29.56 21.5 36.96 37.5 45.67

ea kPa (0.34-0.14 ea)

Rs/Rso (1.35 Rs/Rso - 0.35)

Rn = Rns - Rnl

Tmonth °C Gday (assume) 0

Tmonth-1 °C Gmonth = 0.14 (Tmonth - Tmonth-1)

Rn - G MJ m-2 d-1

0.408 (Rn - G) mm/day

Grass reference evapotranspiration

mm/day

mm/day

mm/day

Computerized calculations Calculations of the reference crop evapotranspiration ETo are often computerized. The calculation procedures of all data required for the calculation of ETo by means of the FAO Penman-Monteith equation are presented. Typical sequences in which the calculations can be executed are given in the calculation sheets. Many software packages already use the FAO Penman-Monteith equation to assess the reference evapotranspiration. As an example, the output of CROPWAT and the FAO software for irrigation scheduling.