2. Crop water requirement 2.1. General

Transcription

1 CHAPTER TWO 2. Crop water requirement 2.1. General Crop water requirement may be defined as the quantity of water, regardless of its source, required by crop or diversified pattern of crops in a given period of time for its normal growth under field conditions at a place. It includes the loss due to evapo-transpirtation (ET) or consumptive use (CU) plus the losses during the application of irrigation water and the quantity of water required for special operations such as land preparation, transplanting, leaching etc. it may those be formulated as: CWR=ET or CU + application losses +conveyance losses+ special needs. In other words crop water requirement can be defined as the total amount of water and the way in which a crop requires water from the time it is sown to the time it is harvested. It is clear that the water required will vary with the crop as well as the place. Different crops will have different water requirement and the same crops may have different water requirement at different place depending upon climate, type of soil method of cultivation and useful rainfall etc. Crop water requirement serves as the basis for the design of the capacity of reservoir and canal, irrigation scheduling and management. Crop period and base period Crop period: is a period elapsed from the instant of its sowing to the instant of harvesting. Base period: is the time between the first watering of a crop at the time of its sowing to its last water before harvesting. Crop period is slightly more than the base period but for all particular purpose, they are taken as one and the same thing, and generally expressed in days Duty and delta of a crop Duty (D) The duty of water is the relationship between the volume of water and the area of the crop it matures. This volume of water is generally expressed by a unit discharge flowing for a time equal to the base period of the crop called Base of Duty. Duty represents the irrigation capacity of a unit water (ha/m 3 /s). A D = ; Where A command area and Q continuous discharge required for the base period. Q If 3m 3 /s of water is required for a crop sown in area of 5100ha continuously, the duty of irrigation water will be 5100/3=1700ha/m 3 /s, and a discharge of 3m 3 /s is required throughout the base period. Duty is generally expressed by D. In a large canals irrigation system, the water from its source, first of all flows into the main canal, then it flows into primary canal; from the primary it flows into secondary canals and from secondary to 1

2 tertiary canals and finally in to the field. During the passage of water from those irrigation channels, the water is lost due to evaporation and percolation. Those losses are called transit loss or transmission or conveyance losses. Duty of water for a crop is the number of hectares of land which the water can irrigate. Therefore, if the water requirement of the crop is more, less amount of hectares of land it will irrigate. Hence, if water consumed is more, duty will be less. Therefore it s clear that the duty of water at the head of the water course will be less than the duty of water on the field; because when water flows from the head of the water course and reaches the field, some water is lost as transit losses. Duty of water, therefore, varies from one place to another and increases as we move downstream from the head of the main canal towards the head of branches or water courses. Delta ( ) Each crop requires certain amount of water depending up on the area to be cultivated. If the area to be cultivated is large, the amount of water required will be more; on the other hand if area is small the amount of water required will be less. The total quantity of water required by the crop for its full growth may be expresses in ha-m. Thus the total depth of water (in cm) required by a crop to come to maturity is called Delta. Suppose certain amount of water is applied to a crop from a time of sowing till the crop matures and if the applied water is not lost or used up by any means then there will be a thick layer of water standing all over the field. The depth or height of this water layer is known as delta for the crop. V = ; where V is total volume of water required for the base period and A is command area. A If rice required about 8cm depth of water at an average interval of about 12days, and the crop period for rice is 120days. Find out the delta of rice. 8cm of water at an average of 12 days Water requirement = 8cm/12days = cm/day For 120 days =120day*0.6667cm/day Delta ( ) =80cm The average values of delta for certain crops are shown below. Those values represent the total water requirement of the crop on the field, actually can be less depending upon the useful rainfall. Crop Delta on field cm Sugarcane 120 Rice 120 Tobacco 75 Garden fruit 60 Cotton 50 Vegetables 45 Wheat 40 Barly 30 Maize 25 Fodder 22.5 Peas 15 2

3 Relation between Duty and Delta Assume a crop of base period B in days, D duty of water in hectare per cubic meters per second and be the delta or depth of water for a crop in meter. From the definition of delta, duty and base period 1m 3 /s flowing continuously for B days mature D hectares of land under the crop or 1m 3 /s continuously for B days gives a depth, over D hectares of land. The total amount of water applied to this crop during B days. By definition of duty: 3 V = 1* 60*60 * 24 * B m ( ) 3 V = 86,400* Bm The depth of water applied on this land 1ha = 10 4 m 2 V 86400B 8. 46B = = m = m 4 A D *10 D Where: B in days, delta in m and D in ha/m 3 /s 2.3. Optimum utilization of irrigation water If a crop is sown under absolutely identical conditions, using different amounts of water depths, the resulting yield will not be the same. The yield increases with water and reaches a certain maximum value and then after falls down, see figure below. The quantity of water at which the yield is maximum, is called the optimum water depth. Max. Yield Yield kg Optimum Depth Water depth mm Fig Delta and yield relation Therefore, optimum utilization irrigation generally means, getting maximum yield with any amount of water. The supplies of water to the various crops should be adjusted in such a fashion, as to get optimum benefit ratio, not only for efficient use of available water of available water. You should be aware that more than the optimum depth or less than quantity reduces the yield. 3

4 2.4. Irrigation efficiency Efficiency is the ration of the water output to the water input, and is usually expressed as percentage. The design of the irrigation system, the degree of land preparation, and the skill and care of the irrigator is the principal factors influencing irrigation efficiency. Loss of irrigation water occurs in the conveyance and distribution system, non-uniform distribution of water over the field, percolation below crop root zone, and with sprinkler irrigation evaporation from the spray and retention of water on the foliage. Water is lost in irrigation during various processes and, therefore, there are different kinds of irrigation efficiencies as shown below: Conveyance efficiency (η c ): it is the ratio of the water delivered into the field from the outlet point of the channel, to the water pumped into the channel at the starting point. Application efficiency (η a ): it is the ratio of the quantity of water stored in to the root zone of the crops to the quantity of water actually delivered into the field. Water storage efficiency (η s ): is the ratio of water stored into the root zone during irrigation to the water needed in the root zone prior to irrigation (i.e field capacity existing moisture content). Water use efficiency (η u ): is the ratio of water beneficially used, including leaching water, to the quantity of water delivered. Ex 1. 15m 3 /s of water is delivered to 40ha field, for 5hrs. Soil probing after irrigation indicates that 0.5m of water has been stored in the root zone. Compute the water application efficiency. Ans (74.04%) Uniformity coefficient or distribution efficiency (η d ): represents the extent to which the water has pentrated to a uniform depth, through out the field. When the water has penetrated uniformly throughout the field, the deviation from the mean depth is zero and the water distribution efficiency is 100%. d η d = 1 D Where D d : mean depth of water stored during irrigation : average of absolute values of deviation from the mean 2.5. Crop water requirement (CWR) Crop water requirement may be defined as the quantity of water, regardless of its source, required by a crop or diversified pattern of crops in a given period of time for its normal growth under field condition. It includes the loss due to evapotranspiration (ET) or consumptive use (CU) plus the losses during the application and conveyance of irrigation water and the quantity of water required for special operation such as land preparation, leaching etc CWR = ET or CU + Application losses + Aonveyance loss + Special needs 4

5 Consumptive use of water (Evapotranspiration) (CU) Consumptive use for a particular crop may be defined as the total amount of water used by the plant in transpiration (building of plant tissues, etc) and evaporation from adjacent soils or from plant leaves in any specified time. The values of consumptive use (CU) may be different for different crops, and may be different for same crop at different time and places. The combination of two separate processes whereby water is lost on the one hand from the soil surface by evaporation and on the other hand from the crop by transpiration is referred to as evapotranspiration (ET). Values of monthly consumptive use over the entire crop period are then used to determine the irrigation requirement of the crop. Evaporation 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. Where the evaporating surface is the soil surface, the degree of shading of the crop canopy and the amount of water available at the evaporating surface are other factors that affect 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. The water, together with some nutrients, is taken up by the roots and transported through the plant. The vaporization occurs within the leaf, namely in the intercellular spaces, and the vapour exchange with the atmosphere is controlled by the stomatal aperture. 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. Evapotranspiration (ET) Evaporation and transpiration occur simultaneously and there is no easy way of distinguishing between the two processes. Apart from the water availability in the topsoil, the evaporation from a cropped soil is mainly determined by the fraction of the solar radiation reaching the soil surface. This fraction decreases over the growing period as the crop develops and the crop canopy shades more and more of the ground area. When the crop is small, water is predominately lost by soil evaporation, but 5

6 once the crop is well developed and completely covers the soil, transpiration becomes the main process. Fig. The partitioning of evapotranspiration into evaporation and transpiration over the growing period for an annual field crop The above figure shows partition of evapotranspiration into evaporation and transpiration in correspondence to leaf area per unit surface of soil below it. At sowing nearly 100% of ET comes from evaporation, while at full crop cover more than 90% of ET comes from transpiration. The evapotranspiration rate is normally expressed in millimetres (mm) per unit time. The time unit can be an hour, day, decade, month or even an entire growing period or year Factors affecting evapotranspiration Weather parameters, crop characteristics, management and environmental aspects are factors affecting evaporation and transpiration. 6

7 Fig. Factors affecting evapotranspiration with reference to related ET Weather parameters: The principal weather parameters affecting evapotranspiration are radiation, air temperature, humidity and wind speed. Crop factors: The crop type, variety and development stage should be considered when assessing the evapotranspiration from crops grown in large, well-managed fields. Differences in resistance to transpiration, crop height, crop roughness, reflection, ground cover and crop rooting characteristics result in different ET levels in different types of crops under identical environmental conditions. Management and environmental conditions: Factors such as soil salinity, poor land fertility, limited application of fertilizers, the presence of hard or impenetrable soil horizons, the absence of control of diseases and pests and poor soil management may limit the crop development and reduce the evapotranspiration. Other factors to be considered when assessing ET are ground cover, plant density and the soil water content Meteorological factors determining ETo Air Temperature The solar radiation absorbed by the atmosphere and the heat emitted by the earth increase the air temperature. The sensible heat of the surrounding air transfers energy to the crop and exerts as such a controlling influence on the rate of evapotranspiration. In sunny, warm weather the loss of water by evapotranspiration is greater than in cloudy and cool weather. The average daily maximum and minimum air temperatures in o c are required. Where only (average) mean daily temperatures are available, the calculations can still be executed but some underestimation of ETo will probably occur. Using mean air temperature instead of maximum and minimum air temperatures yields a lower saturation vapour pressure, e s, and hence a lower vapour pressure differences (es-ea), and a lower ETo estimate. The daily maximum air temperature (Tmax) and daily minimum air temperature (Tmin) are, respectively, the maximum and minimum air temperature observed during the 24-hr period, beginning at midnight, Tmax and Tmin for longer periods such as weeks, 10-days or months are obtained by dividing the sum of the respective daily values by the number of days in the period. Tmean for 24-hr periods is defined as the mean of the daily maximum (Tmax) and minimum temperatures (Tmin) rather than as the average of hourly temperature measurements. Air Humidity The water content of the air can be expressed as vapour pressure or relative humidity. Water vapour is a gas and its pressure contributes to the total atmospheric pressure. The amount of water in the air is related directly to the partial pressure exerted by the water vapour in the air and is therefore a direct measure of the air water content. When air is enclosed above an evaporating water surface, an equilibrium is reached between the water molecules escaping and returning to the water reservoir. At that moment, the air is said to be saturated since it cannot store any extra water molecules. The corresponding pressure is called the saturation vapour pressure (e o (T)). The number of molecules that can be stored in the air depends on the temperature (T). The higher the temperature, the higher the storage capcity, the higher its saturation 7

8 vapour pressure. The slope of the saturation vapour pressure curve,, is an important parameter in describing vaporization and is required in the equations for calculating ETo from climatic data. The actual vapour pressure (ea) is the vapour pressure exerted by water in the air. When the air is not saturated, the actual vapour will be lower than the saturation vapour pressure. The difference between the saturation and actual vapour pressure is called the vapour pressure deficit and is an accurate indicator of the actual evaporative capacity of the air. Relative Humidity The relative humidity (RH) expresses the degree of saturation of the air as a ratio of the actual(ea) to the saturation (e o (T)) vapour pressure at the same temperature (T): RH = ea/e o (T) Relative humidity is the ration between the amount of water the ambient air actually holds and the amount it could hold at the same temperature. It is dimensionless and is commonly expresses as a percentage. Although the actual vapour pressure might be relatively constant throughout the day, the relative humidity fluctuates between a maximum near sunrise and a minimum around early afternoon. The variation of the relative humidity is the result of the temperature changes during the day; the relative humidity also changes substantially. While the energy supply from the sun and surrounding air is the main driving force for the vaporization of water, the difference between the water vapour pressure at the evapotranspiring surface and the surrounding air is the determining factor for the vapour removal. In humid tropical regions, notwithstanding the high energy input, the high humidity of the air will reduce the evapotranspiration demand. In such an environment, the air is already close to saturation, so that less additional water can be stored and hence the evapotranspiration rate is lower than in arid regions. The (average) daily actual vapour pressure, ea (kpa) is required. The actual vapour pressure, where not available, can be derived from maximum and minimum relative humidity (%). Solar radiation The evapotranspiration process is determined by the amount of energy available to vaporize water. The potential amount of radiation that can reach the evaporating surface is determined by its location and time of the year. Due to differences in the position of the sun, the potential radiation differs at various latitudes and in different seasons. The average (daily) net radiation expressed in MJ/m 2 is required. These data are not commonly available but can be derived from the (average) shortwave radiation measured with a pyranometer, or from the (average) daily actual duration of bright sunshine (hours per day) measured with a (Campbell-Stokes) sunshine recorder. Wind Speed The process of vapour removal depends to a large extent on wind and air turbulence which transfers large quantities of air over the evaporating surface. When vaporizing water, the air above the evaporating surface becomes gradually saturated with water vapour. If this air is not continuously replaced with drier air, the driving force for water vapour removal and the evapotranspiration rate decreases. The (average) daily wind speed in m/s measured at 2 m above ground level is required. It is 8

9 important to verify the height at which wind speed is measured, as wind speeds measured at different heights above the soils surface differ. The evapotranspiration demand is high in hot dry weather due to the dryness of the air and the amount of energy available as direct solar radiation and latent heat. To adjust wind speed data obtained from instruments placed at elevations other than the standard height of 2 m, the following equation is used: 2.6. Reference Crop Evapotranspiration (ETo) To define unique evaporation parameters for each crop and stage of growth, the concept of a reference surface was introduced. Evapotranspiration rates of the various crops are related to the evapotranspiration rate from the reference surface (ETo) by means of crop coefficients. The reference surface closely resembles an extensive surface of green grass of uniform height, actively growing, completely shading the ground with adequate water. 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 and an albedo of 0.23, closely resembling the evaporation of an extensive surface of green grass of uniform height, actively growing and adequately watered, the FAO Panman-Monteith method was developed. The evaporation from a reference surface, not short of water, is called the reference crop evapotranspiration or reference evapotranspiration and is denoted as ETo. The only factors affecting ETo are climatic parameters. Consequently, ETo is a climatic parameter and can be computed from weather data. ETo expresses the evaporating power of the atmosphere at a specific location and time of the year and does not consider the crop characteristics and soil factors. The FAO Penman-Monteith method is recommended as the sole 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. Typical ranges for ETo values for different agroclimatic regions are given in Table below. These values are not intended for direct application. Table. Average ETo for different agroclimatic regions in mm/day Regions Mean daily temperature ( C) Cool ~10 C Moderate 20 C Warm > 30 C Tropics and subtropics - humid and sub-humid arid and semi-arid Temperate region - humid and sub-humid arid and semi-arid

10 \ Characteristics of the hypothetical reference crop Empirical methods of estimating ETo The FAO groups of scientists have screened 31 empirical formulae for predicting the ETo the following five methods will be discussed, which are used under different climatic conditions: 1. Pan evaporation 2. Blaney-criddle method 3. Hargreaves Method 4. Thornthwaite Method 5. Radiation method, and 6. Modified penman method 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. Three major steps involved in the estimation of ET of the crop: Estimation of reference evapotranspiration (ETo) Determination of the crop coefficient (kc), and Making appropriate adjustments to management condition and location specific crop environment. 10

11 1. Pan evaporation Evaporation pans provide a measurement of the combined effect of temperature, humidity, wind speed 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. Fig. Class A evaporation pan The principle of the evaporation pan is the following: 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 = Kpan * Epan With: ETo: reference crop evapotranspiration mm/day K pan: pan coefficient E pan: pan evaporation mm/day Determination of K pan When using the evaporation pan to estimate the ETo, in fact, a comparison is made between the evaporation from the water surface in the pan and the evapotranspiration of the standard grass. Of course the water in the pan and the grass do not react in exactly the same way to the climate. Note reflection of solar radiation from water in the shallow pan might be different from the assumed 23% for the grass reference surface. Storage of heat within the pan can be appreciable and may cause significant evaporation during the night while most crops transpire only during the daytime. There are also differences in turbulence, temperature and humidity of the air immediately above the respective surfaces. Heat transfer through the sides of the pan occurs and affects the energy balance. To relate pan evaporation to ETo, empirically derived pan coefficients are suggested to account for climate, type of pan and pan environment. Therefore a special coefficient is used (K pan) to relate one to the other. 11

12 The pan coefficient, K pan, depends on: The type of pan used The pan environment: if the pan is placed in a fallow or cropped area The climate: the humidity and wind speed For the Class A evaporation pan, the K pan varies between 0.35 and Average K pan = Normally details of the pan coefficient are usually provided by the supplier of the pan. The pan method it was suggested that calculations should be done for periods of ten days or longer. 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 has to be used. The most commonly used theoretical method is the modified Penman method which is described in detail in FAO Irrigation and Drainage Paper 24. This method, however, is rather complicated. The Blaney-Criddle method is simple, using measured data on temperature only. It should be noted, however, that this method is not very 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). ETo = P( 0.46* Tmean + 8) Where: ETo = Reference crop evapotranspiration (mm/day) as an average for a period of 1 month T mean = mean monthly temperature ( C) p = mean monthly percentage of annual daytime hours To determine the value of p. Table below is used. To be able to determine the p value it is essential to know the approximate latitude of the area: the number of degrees north or south of the equator Table: 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

13 3. Hargreaves Method: The Hargreaves (Hargreaves and Samani, 1985) method requires only maximum and minimum daily air temperature observations and it can be applied on daily, weekly, decadal or monthly time steps. 0.5 ( Tmax Tmin ) ( T mean 17. ) Ra ET = Where all temperatures are in 0 C and ET in mm/day. The mean temperature is calculated as 0.5(T max +T min ). R a is the extraterrestrial short wave radiation in mm/day. (If R a is given in MJm -2 d -1, then division by 2.45 yields the vale in mm/day). Unless unusual weather patterns exist, the Hargreaves method should agree within 15% of the Penman and Penman-Monteith calculations. The most important parameters in estimating ETo, are temperature and solar radiation. Although relative humidity is not explicitly contained in the equation, it is implicitly present in the difference in maximum and minimum temperature. The temperature difference (TD) is linearly related to relative humidity. 4. Thornthwaite Method: Thornthwaite developed an equation to predict monthly evapotranspiration from mean monthly temperature data. The small amount of data needed is attractive because often it needs to be predicted for sites where few weather data are available. M.E. Jensen et al. (1990) warn that Thornthwaite s method is generally only applicable to areas that have climates similar to that of central U.S, and it is not applicable to arid and semiarid regions. Thornthwaite found that evapotranspiration could be predicted from an equation of the form ET o 10T = 16 I a Where: ETo = Monthly reference crop evapotranspiration (mm/month) T = Mean monthly temperature ( C) a = is the location dependant coefficient I = is the annual heat index described below 12 T i 1 i= I = and the coefficient a is given by 2 a = I I I 5. Radiation Methods: Evapotranspiration is controlled by available energy and the availability of evaporated water to be transferred from the surface through turbulent transport. The transfer processes are a function of wind speed and amount of water vapour close to the surface. However, Priestley and Taylor (1972) showed that evapotranspiration is well described by net radiation, air temperature and pressure for large wellwatered surfaces. Radiation methods use solar radiation coupled with air temperature data to estimate the reference evapotranspiration ETo. 3 13

14 The Priestley-Taylor (1972) equation has the form Rn G ETo = α + γ λ Where α is usually taken as ET 0 is in mm/day, R n is the net radiation, G the soil heat flux in MJm -2 d -1, λ the latent heat of vaporization in MJkg -1 and and γ are as defined for the Penman equations (kpa 0 C -1 ). Shuttleworth (1993) recommends to take α=1.74 for arid climates, α=1.26 in humid climates. The Makkink (1957) method is commonly used in western Europe Rs ETo = γ 2.45 Where ET 0 is in mmd -1. R s is the incoming solar short wave radiation in MJm -2 d -1. Constant 2.45 is the latent heat of vaporization at about 20 o C 6. Modified penman method: In 1948, Penman combined the energy balance with the mass transfer method and derived an equation to compute the evaporation from an open water surface from standard climatological records of sunshine, temperature, humidity and wind speed. This so-called combination method was further developed by many researchers and extended to cropped surfaces by introducing resistance factors. The FAO Penman-Montheith equation is a close, simple representation of the physical and physiological factors governing the evapotranspiration processes. The FAO Penman-Monteith method to estimate ETo: ( Rn G) + γ U 2 ( es ea ) ET T 273 o = + + γ ( U 2 ) 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], :slope of vapour pressure curve [kpa C-1], γ :psychrometric constant [kpa C-1]. 14

15 Net Radiation Net radiation (Rn) is the balance of the shortwave and longwave radiation streams, such as Rsw and Rlw are the shortwave and longwave components and the arrows denote the direction of the flux, generally expressed in units of Watts per square meter (Wm-2). Thus, the Rn is the difference between total upward and downward radiation fluxes and is a measure of the energy available at the ground surface. Shortwave radiation Shortwave radiation from the Sun penetrates through space to the outer edge of the atmosphere unimpeded by the vacuum of outer space. If one places a surface oriented perpendicular to an incoming beam of light, 1.94 cal cm-2 min-1 of solar radiation will be received. This value is known as the solar constant but actually varies by a small amount as the Earth-Sun distance changes through the year. Once solar radiation begins to penetrate through the atmosphere this amount begins to decrease due to absorption and reflection. A portion of the incoming solar radiation is absorbed by the surface and a portion is also reflected away. The proportion of light reflected from a surface is the albedo (α). Albedo values range from 0 for no reflection to 1 for complete reflection of light striking the surface. Albedo can be expressed as a percentage (albedo multiplied by 100) that for some is easier to understand. For instance, grass has an albedo of about This means that of the incoming solar radiation that strikes the grass, 23% of it is reflected away. Net shortwave radiation is the difference between incoming and outgoing shortwave radiation expressed as: R ns = R R = 1 sw sw ( α ) R s Solar radiation Rs As the radiation penetrates the atmosphere, some of the radiation is scattered, reflected or absorbed by the atmospheric gases, clouds and dust. The amount of radiation reaching a horizontal plane is known as the solar radiation, Rs. For a cloudless day, Rs is roughly 75% of extraterrestrial radiation. On a cloudy day, the radiation is scattered in the atmosphere, but even with extremely dense cloud cover, about 25% of the extraterrestrial radiation may still reach the earth s surface. If the solar radiation, Rs, is not measured, it can be calculated as: Where Rs n N : solar radiation (MJ/m 2 day) : actual duration of sunshine (hour) : maximum possible duration of sunshine or daylight hours (hour) 15

16 n/n : relative sunshine duration (-) Ra : extraterrestrial radiation (MJ/m 2 day) a s, b s : regression constant, expressing the fraction of extraterrestrial radiation reaching the earth on overcast days (n=0) a s + b s : fraction of extraterrestrial radiation reaching the earth on clear days (n= N) Rs is expressed in the above equation in MJ/m 2 day. The corresponding equivalent evaporation in mm/day is obtained by multiplying Rs by When no actual solar radiation data are available (a s = 0.25 and b s = 0.50). The actual solar radiation reaching the evaporating surface depends on the turbidity of the atmosphere and the presence of clouds which reflect and absorb major parts of the radiation. Relative sunshine duration (n/n) The relative sunshine duration is another ratio that expresses the cloudiness of the atmosphere. It is the ratio of the actual duration of sunshine, n, to the maximum possible duration of sunshine or daylight hours N. In the absence of any clouds, the actual duration of sunshine is equal to the daylight hours (n = N) and the ratio is one, while on cloudy days n and consequently the ratio may be zero. In the absence of a direct measurement of Rs, the relative sunshine duration, n/n, is often used to derive solar radiation from extraterrestrial radiation. As with extraterrestrial radiation, the day length N depends on the position of the sun and is hence a function of latitude and date. Where ω s is the sunset hour angle in radians 16

17 Annual variation of the daylight hours (N) at the equator, 20 and 40 north and south Extraterrestrial Radiation (Ra) Solar radiation incident outside the earth's atmosphere is called extraterrestrial radiation. On average the extraterrestrial irradiance is 1367 Watts/meter2 (W/m2). This value varies by ±3% as the earth orbits the sun. The earth's closest approach to the sun occurs around January 4th and it is furthest from the sun around July 5th. The local intensity of radiation is, however, determined by the angle between the direction of the sun's rays and the normal to the surface of the atmosphere. This angle will change during the day and will be different at different latitudes and in different seasons. The solar radiation received at the top of the earth's atmosphere on a horizontal surface is called the extraterrestrial (solar) radiation, Ra. The extraterrestrial radiation, Ra, for each day of the year and for different latitudes can be estimated from the solar constant, the solar declination and the time of the year by: Where R a : extraterrestrial radiation [MJ m -2 day -1 ], G sc : solar constant = MJ m -2 min -1, d r : inverse relative distance Earth-Sun, ω s : sunset hour angle [rad], ϕ : latitude positive for the northern hemisphere and negative for the southern hemisphere [rad], δ : solar decimation [rad]. 17

18 Annual variation in extraterrestrial radiation (R a ) at the equator, 20 and 40 north and south Inverse relative distance Earth-Sun (dr) The earth revolves around the sun in an elliptical orbit with the sun at one of the foci. The amount of solar energy reaching the earth is inversely proportional to the square of its distance from the sun. The mean earth sun distance r o is called one astronomical unit 1AU = 1.496*10 6 km The minimum sun-earth distance is about AU approximately in 3 January and the maximum approximately 1.017AU approximately in 4 July. In long-term cycles, those distances are influenced, however slightly, by other heavenly bodies and the leap year cycle. However, the relative sun-earth distance d r for any day of the year is known with considerable accuracy. Where J is the number of the day in the year between 1 (1 January) and 365 or 366 (31 December). Solar decimation (δ) The declination angle, denoted by δ, varies seasonally due to the tilt of the Earth on its axis of rotation and the rotation of the Earth around the sun. If the Earth were not tilted on its axis of rotation, the declination would always be 0. However, the Earth is tilted by and the declination angle varies plus or minus this amount. Only at the spring and fall equinoxes is the declination angle equal to 0. The declination of the sun is the angle between the equator and a line drawn from the centre of the Earth to the centre of the sun. δ is angle between centers of the earth to center of sun to the equatorial plane J is the number of the day in the year Where J is the number of the day in the year between 1 (1 January) and 365 or 366 (31 December). Sunset hour angle (ω s ) Used to describe the earth's rotation about its polar axis. It is the angular distance between the meridian of the observer and the meridian whose plane contains the sun. ω s = arccos [-tan (ϕ) tan (δ)] Net longwave radiation (Rnl) The solar radiation absorbed by the earth is converted to heat energy. By several processes, the earths surface loss this energy. The earth, which is at a much lower temperature than the sun, emits radiative energy with wavelengths longer than those from the sun. Therefore, the terrestrial radiation is referred 18

19 to as longwave radiation. The gases of the atmosphere are relatively good absorbers of longwave radiation and thus absorb the energy emitted by the Earth's surface. The absorbed radiation is emitted downward toward the surface as longwave atmospheric counter-radiation (L ) keeping near surface temperatures warmer than they would be without this blanket of gases. This is known as the "greenhouse effect". The earth s surface both emits and receives longwave radiation. The difference between outgoing and incoming longwave radiation is called the net longwave radiation, Rnl. As the outgoing long wave radiation is almost always greater than the incoming long wave radiation, Rnl represents an energy loss. The difference between incoming and outgoing longwave radiation is net longwave radiation expressed as: R nl = Rlw Rlw The rate of longwave energy emission is proportional to the absolute temperature of the surface raised to the fourth power. Where Rnl : net outgoing longwave radiation (MJ/m 2 day) σ : Stefan-Boltmann constant (4.903*10-9 MJ/m 2 day) Tmax,k : maximum absolute temperature during the 24-hour period(k=0 C ) Tmin,k : minimum absolute temperature during the 24-hour period e a : actual vapour pressure (kpa) Rs/Rso : relative shortwave radiation ( 1.0) Rs : measured or calculated solar radiation (MJ/m 2 day) Rso : calculated clear-sky radiation (MJ/m 2 day) Clear-sky solar radiation (R so ) The calculation of the clear-sky radiation, Rso, when n = N, is required for computing net longwave radiation. For near sea level or when calibrated values for as and bs are available: R so = (a s +b s )R a where R so : clear-sky solar radiation [MJ m -2 day -1 ], a s +b s : fraction of extraterrestrial radiation reaching the earth on clear-sky days (n = N). W hen calibrated values for a s and b s are not available: R so = ( l0-5 Z)R a Where Z station elevation above sea level [m]. 19

20 Soil heat flux (G) The soil heat flux, G, is the energy that is utilized in heating the soil. Since the soil heat flux is small compared to Rn it may be ignored. Complex models are available to describe soil heat flux. Because soil heat flux is small compared to R n, particularly when the surface is covered by vegetation, As the magnitude of the day or ten-day soil heat flux beneath the grass reference surface is relatively small, it may be ignored and thus: G day = 0 For monthly periods: G month, i = 0.07 (T month, i+1 - T month, i-1 ) or, if T month, i+1 is unknown: G month, i = 0.14 (T month, i - T month, i-1 ) Where T month, i : mean air temperature of month i [ C], T month, i-1 : mean air temperature of previous month [ C], : mean air temperature of next month [ C]. T month, i+1 Air temperature (T) T max and T min for longer periods such as weeks, 10-day's or months are obtained by dividing the sum of the respective daily values by the number of days in the period. The mean daily air temperature (T mean ) is only employed in the FAO Penman-Monteith equation to calculate the slope of the saturation vapour pressure curves ( ) and the impact of mean air density (Pa) as the effect of temperature variations on the value of the climatic parameter is small in these cases. For standardization, T mean for 24-hour periods is defined as the mean of the daily maximum (T max ) and minimum temperatures (T min ) rather than as the average of hourly temperature measurements. In practice K = C Slope of saturation vapour pressure curve ( ) For the calculation of evapotranspiration, the slope of the relationship between saturation vapour pressure and temperature,, is required. The slope of the curve (Figure 11) at a given temperature is given by. Where 20

21 slope of saturation vapour pressure curve at air temperature T [kpa C-1], T air temperature [ C], Mean saturation vapour pressure (es) As saturation vapour pressure is related to air temperature, it can be calculated from the air temperature. The relationship is expressed by: Where e (T) saturation vapour pressure at the air temperature T [kpa], T air temperature [ C], Due to the non-linearity of the above equation, the mean saturation vapour pressure for a day, week, decade or month should be computed as the mean between the saturation vapour pressure at the mean daily maximum and minimum air temperatures for that period: Using mean air temperature instead of daily minimum and maximum temperatures results in lower estimates for the mean saturation vapour pressure. The corresponding vapour pressure deficit (a parameter expressing the evaporating power of the atmosphere) will also be smaller and the result will be some underestimation of the reference crop evapotranspiration. Actual vapour pressure (ea) The actual vapour pressure can also be calculated from the relative humidity. Depending on the availability of the humidity data, different equations should be used. where e a : actual vapour pressure [kpa], e (T min ) : saturation vapour pressure at daily minimum temperature [kpa], e (T max ) : saturation vapour pressure at daily maximum temperature [kpa], RH max : maximum relative humidity [%], RH min : minimum relative humidity [%]. For periods of a week, ten days or a month, RH max and RH min are obtained by dividing the sum of the daily values by the number of days in that period. In the absence of RH max and RH min, another equation can be used to estimate ea: 21

22 Where RH mean is the mean relative humidity, defined as the average between RH max and RH min. Vapour pressure deficit (e s - e a ) The vapour pressure deficit is the difference between the saturation (e s ) and actual vapour pressure (e a ) for a given time period. Psychrometric constant (γ) The psychrometric constant, γ, is given by: Where γ : psychrometric constant [kpa C -1 ], P : atmospheric pressure [kpa], λ : latent heat of vaporization, 2.45 [MJ kg -1 ], c p : specific heat at constant pressure, [MJ kg -1 C -1 ], ε : ratio molecular weight of water vapour/dry air = Energy required to change a unit mass of water from liquide water to water vapour in a constant pressure and temperature is called latent heat of vaporization. In other words, 2.45 MJ are needed to vaporize 1 kg or m3 of water. Atmospheric pressure (P) The atmospheric pressure, P, is the pressure exerted by the weight of the earth's atmosphere. Evaporation at high altitudes is promoted due to low atmospheric pressure as expressed in the psychrometric constant. The effect is, however, small and in the calculation procedures, the average value for a location is sufficient. Where P z : atmospheric pressure [kpa], : elevation above sea level [m], Wind speed (U2) Wind speeds measured at different heights above the soil surface are different. Surface friction tends to slow down wind passing over it. Wind speed is slowest at the surface and increases with height. For this reason anemometers are placed at a chosen standard height, i.e., 10 m in meteorology and 2 or 3 m in agrometeorology. For the calculation of evapotranspiration, wind speed measured at 2 m above the surface is required. To adjust wind speed data obtained from instruments placed at elevations other 22

23 than the standard height of 2m, a logarithmic wind speed profile may be used for measurements above a short grassed surface: U 2 = u z 4.87 ln(67.8z 5.42 Where U 2 U z Z : Wind speed at 2 m above ground surface (m/s) : measured wind speed at z m above ground surface(m/s) : height of measurement above ground surface (m) Adjusting wind speed data to standard height 23

24 2.7. Crop Evapotranspiration (ET C ) 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. Experimentally determined ratios of ETc/ETo, called crop coefficient (Kc) are used to relate ETc to ETo or ETc = Kc*ETo. Differences in leaf anatomy, stomatal characteristics, aerodynamic properties and even albedo cause the crop evapotranspiration to differ from the reference crop evapotranspiration under the same climatic conditions. ETc = Kc*ETo Where ETc Kc ETo crop evapotranspiration (mm/day) crop coefficient reference crop evapotranspiration (mm/day) Most of the effects of the various weather conditions are incorporated into the ETo estimate. The crop coefficient Kc represents an integration of the effects of four primary characteristics that distinguish the crop from reference grass: (1) Crop height, (2) Albedo (reflectance) of the crop-soil surface, (3) Canopy (stomatal) resistance, and (4) Evaporation from soil surface Factors determining the crop coefficient The crop coefficient integrates the effect of characteristics that distinguish a typical field crop from the grass reference, which has a constant appearance and a complete ground cover. Consequently, different crops will have different Kc coefficients. The changing characteristics of the crop over the growing season also affect the Kc coefficient. As evaporation is an integrated part of crop evapotranspiration, conditions affecting soil evaporation will also have an effect on Kc. i) Crop Type Due to differences in albedo, crop height aerodynamic properties and leaf and stomata properties, the evapotranspiration from full-grown, well-watered crops differs from ETo. The close spacings of plants and taller canopy height and roughness of many full grown agricultural crops cause these crops to have Kc factors that are larger than 1. The Kc factor is often 5-10% higher than the reference (where Kc = 1.0), and even 15-20% greater for some tall crops such as maize, sorghum or sugar cane. ii) Climate The Kc value in literature are typical values expected for average Kc under a standard climatic condition, which is defined as a sub-humid climate with average daytime minimum relative humidity of 45% and having a calm to moderate wind speeds averaging 2 m/s. Variation in wind after the aerodynamic resistance or the crops and hence their crop coefficients. Variations in wind alter the aerodynamic resistance of the crops and hence their crop coefficients, especially for those crops that are substantially taller than the hypothetical grass reference. More arid climates and conditions of greater wind speed will have higher values for Kc. More humid climates and conditions of lower wind speed will have lower values for Kc. 24

25 Typical K c for different types of full grown crops iii) Soil Evaporation Differences in soil evaporation and crop transpiration between field crops and the reference surface are integrated within the crop coefficient. The Kc for full-grown crops primarily reflects differences in transpiration, as the contribution of soil evaporation is relatively small. After rainfall or irrigation, the effect of evaporation is predominant when the crop is small and scarcely shades the ground. For such low-cover conditions, the Kc coefficient is determined largely by the frequency with which the soil surface is wetted. Where the soil is wet for most of the time from irrigation or rain, the evaporation from the soil surface will be considerable and Kc may exceed 1. On the other hand, where the soil surface is dry, evaporation is restricted and Kc will be small and might even drop to as low as 0.1 iv) Crop Growth Stages As the crop develops, the ground cover, crop height and the leaf area change. Due to differences in evapotranspiration during the various growth stages, the Kc for a given crop will vary over the growing period. The growing period can be divided into four distinct growth stages: initial, crop development, mid-season and the late season. 1. Initial stage: The initial stage runs from planting date to approximately10% ground cover. During the initial period, the leaf area is small, and evaporation is predominantly in the form of soil evaporation. Therefore, the Kc during the initial period (Kcin) is large when the soil is wet from irrigation or rainfall and low when the soil surface is dry. 2. Crop development stage: The crop development stage runs from 10% ground cover to effective full cover. Effective full cover for many crops is at the initiation of flowering. For row crops where rows commonly interlock leaves such as beans, sugar beats, potatoes and corn. Effective cover can be defined as the time when some 25

26 leaves of plants in adjacent rows begin to intermingle so that soil shading becomes nearly complete, or when plants reach nearly full size if no intermingling occurs. Another way to estimate the occurrence of effective full cover is when the leaf area index (LAI) reaches three. LAI is defined as the average total area of leaves (one side) per unit area of ground surface. As the crop develops and shades more and more of the ground, evaporation becomes more restricted and transpiration gradually becomes the major process. During the crop development stage, the Kc value corresponds to amounts of ground cover and plant development. 3. Mid-season stage: The mid-season stage runs from effective full cover to the start of maturity. The start of maturity is often indicated by the beginning of the ageing, yellowing or senescence of leaves, leaf drop, or the browning of fruit to the degree that the crop ET is reduced relative to the reference ETo. The midseason stage is the longest stage for perennials and for many annuals, but it may be relatively short for vegetable crops that are harvested fresh for their green vegetation. At the mid-season stage the Kc reaches its maximum value. The value of Kc (Kcmid) is relatively constant for most growing and cultural conditions. 4. Late season stage: The late season stage runs from the start of maturity to harvest or full senescence. The calculation for Kc and Etc is presumed to end when the crop is harvested, dries out naturally, reaches full senescence, or experiences leaf drop. The Kc value at the end of the late season stage (Kcend) reflects crop and water management practices. The Kcend value is high if the crop is frequently irrigated until harvested fresh. If the crop is allowed to senescence and to dry out in the field before harvest, the Kc end value will be small. The generalized crop coefficient curve is shown in Figure below. Shortly after the planting of annuals or shortly after the initiation of new leaves for perennials, the value for Kc is small, often less than 0.4. The Kc begins to increase from the initial Kc value, Kc ini, at the beginning of rapid plant development and reaches a maximum value, Kc mid, at the time of maximum or near maximum plant development. During the late season period, as leaves begin to age and senesce due to natural or cultural practices, the Kc begins to decrease until it reaches a lower value at the end of the growing period equal to Kc end. FIGURE. Generalized crop coefficient curve for the single crop coefficient approach 26