Crop evapotranspiration - Guidelines for computing crop water requirements - FAO Irrigation and drainage paper 56

 

Preface

This publication presents an updated procedure for calculating reference and crop evapotranspiration from meteorological data and crop coefficients. The procedure, first presented in the FAO Irrigation and Drainage Paper No. 24 'Crop Water Requirements', is termed the 'K_c ET_o' approach, whereby the effect of the climate on crop water requirements is given by the reference evapotranspiration ET_o and the effect of the crop by the crop coefficient K_c. Other procedures developed in FAO Irrigation and Drainage Paper No. 24 such as the estimation of dependable and effective rainfall, the calculation of irrigation requirements and the design of irrigation schedules are not presented in this publication but will be the subject of later papers in the series.

Since the publication of FAO Irrigation and Drainage Paper No. 24 in 1977, advances in research and more accurate assessment of crop water use have revealed the need to update the FAO methodologies for calculating ET_o. The FAO Penman method was found to frequently overestimate ET_o while the other FAO recommended equations, namely the radiation, the Blaney-Criddle, and the pan evaporation methods, showed variable adherence to the grass reference crop evapotranspiration.

In May 1990, FAO organized a consultation of experts and researchers in collaboration with the International Commission for Irrigation and Drainage and with the World Meteorological Organization, to review the FAO methodologies on crop water requirements and to advise on the revision and update of procedures.

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 calculating the various parameters. The FAO Penman-Monteith method was developed by defining the reference crop as a hypothetical crop with an assumed height of 0.12 m, with a surface resistance of 70 s m^-1 and an albedo of 0.23, closely resembling the evaporation from an extensive surface of green grass of uniform height, actively growing and adequately watered. The method overcomes the shortcomings of the previous FAO Penman method and provides values that are more consistent with actual crop water use data worldwide. Furthermore, recommendations have been developed using the FAO Penman-Monteith method with limited climatic data, thereby largely eliminating the need for any other reference evapotranspiration methods and creating a consistent and transparent basis for a globally valid standard for crop water requirement calculations.

The FAO Penman-Monteith method uses standard climatic data that can be easily measured or derived from commonly measured data. All calculation procedures have been standardized according to the available weather data and the time scale of computation. The calculation methods, as well as the procedures for estimating missing climatic data, are presented in this publication.

In the 'K_c-ET_o' approach, differences in the crop canopy and aerodynamic resistance relative to the reference crop are accounted for within the crop coefficient. The K_c coefficient serves as an aggregation of the physical and physiological differences between crops. Two calculation methods to derive crop evapotranspiration from ET_o are presented. The first approach integrates the relationships between evapotranspiration of the crop and the reference surface into a single K_c coefficient. In the second approach, K_c is split into two factors that separately describe the evaporation (K_e) and transpiration (K_cb) components. The selection of the K_c approach depends on the purpose of the calculation and the time step on which the calculations are to be executed.

The final chapters present procedures that can be used to make adjustments to crop coefficients to account for deviations from standard conditions, such as water and salinity stress, low plant density, environmental factors and management practices.

Examples demonstrate the various calculation procedures throughout the publication. Most of the computations, namely all those required for the reference evapotranspiration and the single crop coefficient approach, can be performed using a pocket calculator, calculation sheets and the numerous tables given in the publication. The user may also build computer algorithms, either using a spreadsheet or any programming language.

These guidelines are intended to provide guidance to project managers, consultants, irrigation engineers, hydrologists, agronomists, meteorologists and students for the calculation of reference and crop evapotranspiration. They can be used for computing crop water requirements for both. irrigated and rainfed agriculture, and for computing water consumption by agricultural and natural vegetation.

Chapter 1 - Introduction to evapotranspiration

A.    Evapotranspiration process

B.    Units

C.    Factors affecting evapotranspiration

D.    Evapotranspiration concepts

E.       Determining evapotranspiration

This chapter explains the concepts of and the differences between reference crop evapotranspiration (ETo) and crop evapotranspiration under standard conditions (ETc) and various management and environmental conditions (ETc adj). It also examines the factors that affect evapotranspiration, the units in which it is normally expressed and the way in which it can be determined.

A. Evapotranspiration process

    1.  Evaporation

    2.  Transpiration

    3.  Evapotranspiration (ET)

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).

1.   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. Frequent rains, irrigation and water transported upwards in a soil from a shallow water table wet the soil surface. Where the soil is able to supply water fast enough to satisfy the evaporation demand, the evaporation from the soil is determined only by the meteorological conditions. However, where the interval between rains and irrigation becomes large and the ability of the soil to conduct moisture to pear the surface is small, the water content in the topsoil drops and the soil surface dries out. Under these circumstances the limited availability of water exerts a controlling influence on soil evaporation. In the absence of any supply of water to the soil surface, evaporation decreases rapidly and may cease almost completely within a few days.

2.   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 (Figure 1). 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. 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. The transpiration rate is also influenced by crop characteristics, environmental aspects and cultivation practices. 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.

3.   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 once the crop is well developed and completely covers the soil, transpiration becomes the main process. In Figure 2 the partitioning of evapotranspiration into evaporation and transpiration is plotted 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.

B.      Units

The evapotranspiration rate is normally expressed in millimetres (mm) per unit time. The rate expresses the amount of water lost from a cropped surface in units of water depth. The time unit can be an hour, day, decade, month or even an entire growing period or year.

As one hectare has a surface of 10000 m2 and 1 mm is equal to 0.001 m, a loss of 1 mm of water corresponds to a loss of 10 m3 of water per hectare. In other words, 1 mm day-1 is equivalent to 10 m3 ha-1 day-l.

Water depths can also be expressed in terms of energy received per unit area. The energy refers to the energy or heat required to vaporize free water. This energy, known as the latent heat of vaporization (l), is a function of the water temperature. For example, at 20°C, l is about 2.45 MJ kg-1. In other words, 2.45 MJ are needed to vaporize 1 kg or 0.001 m3 of water. Hence, an energy input of 2.45 MJ per m2 is able to vaporize 0.001 m or 1 mm of water, and therefore 1 mm of water is equivalent to 2.45 MJ m-2. The evapotranspiration rate expressed in units of MJ m-2 day-1 is represented by l ET, the latent heat flux.

Table 1 summarizes the units used to express the evapotranspiration rate and the conversion factors.

TABLE 1. Conversion factors for evapotranspiration

* For water with a density of 1000 kg m-3 and at 20°C.

  Figure 1: Factors affecting evapotranspiration with reference to related ET concepts

 

C. Factors affecting evapotranspiration

    1.  Weather parametes

    2.  Crop factors

    3.  Management and environmental conditions

Weather parameters, crop characteristics, management and environmental aspects are factors affecting evaporation and transpiration. The related ET concepts presented in Figure 3 are discussed in the section on evapotranspiration concepts.

1.   Weather parameters

The principal weather parameters affecting evapotranspiration are radiation, air temperature, humidity and wind speed. Several procedures have been developed to assess the evaporation rate from these parameters. The evaporation power of the atmosphere is expressed by the reference crop evapotranspiration (ETo). The reference crop evapotranspiration represents the evapotranspiration from a standardized vegetated surface. The ETo is described in detail later in this Chapter and in Chapters 2 and 4.

2.   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. 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.

3.   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. The effect of soil water content on ET is conditioned primarily by the magnitude of the water deficit and the type of soil. On the other hand, too much water will result in waterlogging which might damage the root and limit root water uptake by inhibiting respiration.

When assessing the ET rate, additional consideration should be given to the range of management practices that act on the climatic and crop factors affecting the ET process. Cultivation practices and the type of irrigation method can alter the microclimate, affect the crop characteristics or affect the wetting of the soil and crop surface. A windbreak reduces wind velocities and decreases the ET rate of the field directly beyond the barrier. The effect can be significant especially in windy, warm and dry conditions although evapotranspiration from the trees themselves may offset any reduction in the field. Soil evaporation in a young orchard, where trees are widely spaced, can be reduced by using a well-designed drip or trickle irrigation system. The drippers apply water directly to the soil near trees, thereby leaving the major part of the soil surface dry, and limiting the evaporation losses. The use of mulches, especially when the crop is small, is another way of substantially reducing soil evaporation. Anti-transpirants, such as stomata-closing, film-forming or reflecting material, reduce the water losses from the crop and hence the transpiration rate.

FIGURE 2: Reference (ETo), crop evapotranspiration under standard (ETc) and non-standard conditions (ETc adj)

Where field conditions differ from the standard conditions, correction factors are required to adjust ETc. The adjustment reflects the effect on crop evapotranspiration of the environmental and management conditions in the field.

D. Evapotranspiration concepts

    1.  Reference crop evapotranspiration (ETo)

    2.  Crop evapotranspiration under standard conditions (ETc)

    3.  Crop evapotranspiration under non-standard conditions (ETc adj)

Distinctions are made (Figure 4) between reference crop evapotranspiration (ETo), crop evapotranspiration under standard conditions (ETc) and crop evapotranspiration under non-standard conditions (ETc adj). ETo is a climatic parameter expressing the evaporation power of the atmosphere. ETc refers to the evapotranspiration from excellently managed, large, well-watered fields that achieve full production under the given climatic conditions. Due to sub-optimal crop management and environmental constraints that affect crop growth and limit evapotranspiration, ETc under non-standard conditions generally requires a correction.

1.   Reference crop evapotranspiration (ETo)

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 use of other denominations such as potential ET is strongly discouraged due to ambiguities in their definitions.

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. Relating ET to a specific surface provides a reference to which ET from other surfaces can be related. It obviates the need to define a separate ET level for each crop and stage of growth. 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 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. Moreover, procedures have been developed for estimating missing climatic parameters.

Typical ranges for ETo values for different agroclimatic regions are given in Table 2. These values are intended to familiarize inexperienced users with typical ranges, and are not intended for direct application. The calculation of the reference crop evapotranspiration is discussed in Part A of this handbook.

2.   Crop evapotranspiration under standard conditions (ETc)

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.

TABLE 2. Average ETo for different agroclimatic regions in mm/day

The amount of water required to compensate the evapotranspiration loss from the cropped field is defined as crop water requirement. 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. The irrigation water requirement basically represents the difference between the crop water requirement and effective precipitation. The irrigation water requirement also includes additional water for leaching of salts and to compensate for non-uniformity of water application. Calculation of the irrigation water requirement is not covered in this publication, but will be the topic of a future Irrigation and Drainage Paper.

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. As there is still a considerable lack of information for different crops, the Penman-Monteith method is used for the estimation of the standard reference crop to determine its evapotranspiration rate, i.e., ETo. Experimentally determined ratios of ETc/ETo, called crop coefficients (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. Due to variations in the crop characteristics throughout its growing season, Kc for a given crop changes from sowing till harvest. The calculation of crop evapotranspiration under standard conditions (ETc) is discussed in Part B of this handbook (Box 2).

3.   Crop evapotranspiration under non-standard conditions (ETc adj)

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. This may result in scanty plant growth, low plant density and may reduce the evapotranspiration rate below ETc.

The crop evapotranspiration under non-standard conditions is calculated by using a water stress coefficient Ks and/or by adjusting Kc for all kinds of other stresses and environmental constraints on crop evapotranspiration. The adjustment to ETc for water stress, management and environmental constraints is discussed in Part C of this handbook .

E. Determining evapotranspiration

    1.  ET measurement

    2.  ET computed from meteorological data

    3.  ET estimated from pan evaporation

1.   ET measurement

Evapotranspiration is not easy to measure. 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.

Energy balance and microclimatological methods

Evaporation of water requires relatively large amounts of energy, either in the form of sensible heat or radiant energy. Therefore 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.

All fluxes of energy should be considered when deriving an energy balance equation. The equation for an evaporating surface can be written as:

Rn - G - l ET - H = 0 (1)

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, l ET and H remove energy from the surface (Figure 5).

In Equation 1 only vertical fluxes are considered and the net rate at which energy is being transferred horizontally, by advection, is ignored. Therefore the equation is to be applied to large, extensive surfaces of homogeneous vegetation only. The equation is restricted to the four components: Rn, l ET, H and G. Other energy terms, such as heat stored or released in the plant, or the energy used in metabolic activities, are not considered These terms account for only a small fraction of the daily net radiation and can be considered negligible when compared with the other four components.

The latent heat flux (l ET) representing the evapotranspiration fraction can be derived from the energy balance equation if all other components are known. Net radiation (Rn) and soil heat fluxes (G) can be measured or estimated from climatic parameters. Measurements of the sensible heat (H) are however complex and cannot be easily obtained. H requires accurate measurement of temperature gradients above the surface.

Another method of estimating evapotranspiration is the mass transfer method. This approach considers the vertical movement of small parcels of air (eddies) above a large homogeneous surface. The eddies transport material (water vapour) and energy (heat, momentum) from and towards the evaporating surface. By assuming steady state conditions and that the eddy transfer coefficients for water vapour are proportional to those for heat and momentum, the evapotranspiration rate can be computed from the vertical gradients of air temperature and water vapour via the Bowen ratio. Other direct measurement methods use gradients of wind speed and water vapour. These methods and other methods such as eddy covariance, require accurate measurement of vapour pressure, and air temperature or wind speed at different levels above the surface. Therefore, their application is restricted to primarily research situations.

Soil water balance

Evapotranspiration can also be determined by measuring the various components of the soil water balance. The method consists of assessing the incoming and outgoing water flux into the crop root zone over some time period (Figure 6). Irrigation (I) and rainfall (P) add water to the root zone. Part of I and P might be lost by surface runoff (RO) and by deep percolation (DP) that will eventually recharge the water table. Water might also be transported upward by capillary rise (CR) from a shallow water table towards the root zone or even transferred horizontally by subsurface flow in (SFin) or out of (SFout) the root zone. In many situations, however, except under conditions with large slopes, SFin and SFout are minor and can be ignored. Soil evaporation and crop transpiration deplete water from the root zone. If all fluxes other than evapotranspiration (ET) can be assessed, the evapotranspiration can be deduced from the change in soil water content (D SW) over the time period:

ET = I + P - RO - DP + CR ± D SF ± D SW (2)

Some fluxes such as subsurface flow, deep percolation and capillary rise from a water table are difficult to assess and short time periods cannot be considered. The soil water balance method can usually only give ET estimates over long time periods of the order of week-long or ten-day periods.

FIGURE 3: Soil water balance of the root zone

 

 

Lysimeters

By isolating the crop root zone from its environment and controlling the processes that are difficult to measure, the different terms in the soil water balance equation can be determined with greater accuracy. This is done in lysimeters where the crop grows in isolated tanks filled with either disturbed or undisturbed soil. 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 can be considered. In non-weighing lysimeters the evapotranspiration for a given time period is determined by deducting the drainage water, collected at the bottom of the lysimeters, from the total water input.

A requirement of lysimeters is that the vegetation both inside and immediately outside of the lysimeter be perfectly matched (same height and leaf area index). This requirement has historically not been closely adhered to in a majority of lysimeter studies and has resulted in severely erroneous and unrepresentative ETc and Kc data.

As lysimeters are difficult and expensive to construct and as their operation and maintenance require special care, their use is limited to specific research purposes.

2.   ET computed from meteorological data

Owing to the difficulty of obtaining accurate field measurements, ET is commonly computed from weather 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.

Numerous researchers have analysed the performance of the various calculation methods for different locations. As a result of an Expert Consultation held in May 1990, the FAO Penman-Monteith method is now recommended as the standard method for the definition and computation of the reference evapotranspiration, ETo. The ET from crop surfaces under standard conditions is determined by crop coefficients (Kc) that relate ETc to ETo. The ET from crop surfaces under non-standard conditions is adjusted by a water stress coefficient (Ks) and/or by modifying the crop coefficient.

3.   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.

Chapter 2 - FAO Penman-Monteith equation

A.  Need for a standard ETo method

B.  Formulation of the Penman-Monteith equation

C.  Reference surface

D.  FAO Penman-Monteith equation

This chapter introduces the user to the need to standardize one method to compute reference evapotranspiration (ETo) from meteorological data. The FAO Penman-Monteith method is recommended as the sole ETo method for determining reference evapotranspiration. The method, its derivation, the required meteorological data and the corresponding definition of the reference surface are described in this chapter.

A. Need for a standard ETo method

A large number of more or less empirical methods have been developed over the last 50 years by numerous scientists and specialists worldwide to estimate evapotranspiration from different climatic variables. Relationships were often subject to rigorous local calibrations and proved to have limited global validity. 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 meet this need, guidelines were developed and published in the FAO Irrigation and Drainage Paper No. 24 'Crop water requirements'. To accommodate users with different data availability, four 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 publication proposed the use of the Blaney-Criddle method for areas where available climatic data cover air temperature data only.

These climatic methods to calculate ETo were all calibrated for ten-day or monthly calculations, not for daily or hourly calculations. The Blaney-Criddle method was recommended for periods of one month or longer. For the pan method it was suggested that calculations should be done for periods of ten days or longer. Users have not always respected these conditions and calculations have often been done on daily time steps.

Advances in research and the more accurate assessment of crop water use have revealed weaknesses in the methodologies. Numerous researchers analysed the performance of the four methods for different locations. Although the results of such analyses could have been influenced by site or measurement conditions or by bias in weather data collection, it became evident that the proposed methods do not behave the same way in different locations around the world. Deviations from computed to observed values were often found to exceed ranges indicated by FAO. The modified Penman was frequently found to overestimate ETo, even by up to 20% for low evaporative conditions. The other FAO recommended equations showed variable adherence to the reference crop evapotranspiration standard of grass.

To evaluate the performance of these and other estimation procedures under different climatological conditions, a major study was undertaken under the auspices of the Committee on Irrigation Water Requirements of the American Society of Civil Engineers (ASCE). The ASCE study analysed the performance of 20 different methods, using detailed procedures to assess the validity of the methods compared to a set of carefully screened lysimeter data from 11 locations with variable climatic conditions. The study proved very revealing and showed the widely varying performance of the methods under different climatic conditions. In a parallel study commissioned by the European Community, a consortium of European research institutes evaluated the performance of various evapotranspiration methods using data from different lysimeter studies in Europe.

The studies confirm the overestimation of the modified Penman introduced in FAO Irrigation and Drainage Paper No. 24, and the variable performance of the different methods depending on their adaptation to local conditions. The comparative studies 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 relatively accurate and consistent performance of the Penman-Monteith approach in both arid and humid climates has been indicated in both the ASCE and European studies.

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 sole 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.

B.  Formulation of the Penman-Monteith equation

    1.  Penman-Monteith equation

    2.  Aerodynamic resistance (ra)

    3.  (Bulk) surface resistance (rs)

1.   Penman-Monteith equation

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 resistance nomenclature distinguishes between aerodynamic resistance and surface resistance factors (Figure 7). 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.

 

FIGURE 4: Simplified representation of the (bulk) surface and aerodynamic resistances for water vapour flow

The Penman-Monteith form of the combination equation is:

  (3)

where Rn is the net radiation, G is the soil heat flux, (es - ea) represents the vapour pressure deficit of the air, r a is the mean air density at constant pressure, cp is the specific heat of the air, D represents the slope of the saturation vapour pressure temperature relationship, g is the psychrometric constant, and rs and ra are the (bulk) surface and aerodynamic resistances. The parameters of the equation are defined in Chapter 3.

The Penman-Monteith approach as formulated above 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 equation can be utilized for the direct calculation of any crop evapotranspiration as the surface and aerodynamic resistances are crop specific.

2.   Aerodynamic resistance (ra)

The transfer of heat and water vapour from the evaporating surface into the air above the canopy is determined by the aerodynamic resistance:

  (4)

where

ra aerodynamic resistance [s m-1],
zm height of wind measurements [m],
zh height of humidity measurements [m],
d zero plane displacement height [m],
zom roughness length governing momentum transfer [m],
zoh roughness length governing transfer of heat and vapour [m],
k von Karman's constant, 0.41 [-],
uz wind speed at height z [m s-1].

The equation is restricted for neutral stability conditions, i.e., where temperature, atmospheric pressure, and wind velocity distributions follow nearly adiabatic conditions (no heat exchange). The application of the equation for short time periods (hourly or less) may require the inclusion of corrections for stability. However, when predicting ETo in the well-watered reference surface, heat exchanged is small, and therefore stability correction is normally not required.

Many studies have explored the nature of the wind regime in plant canopies. Zero displacement heights and roughness lengths have to be considered when the surface is covered by vegetation. The factors depend upon the crop height and architecture. Several empirical equations for the estimate of d, zom and zoh have been developed. The derivation of the aerodynamic resistance for the grass reference surface is presented in Box 4.

3.   (Bulk) surface resistance (rs)

The 'bulk' surface resistance describes the resistance of vapour flow through the transpiring crop and evaporating soil surface. Where the vegetation does not completely cover the soil, the resistance factor should indeed include the effects of the evaporation from the soil surface. If the crop is not transpiring at a potential rate, the resistance depends also on the water status of the vegetation. An acceptable approximation to a much more complex relation of the surface resistance of dense full cover vegetation is:

   (5)

where

rs (bulk) surface resistance [s m-1],
rl bulk stomatal resistance of the well-illuminated leaf [s m-1],
LAIactive active (sunlit) leaf area index [m2 (leaf area) m-2 (soil surface)].

The Leaf Area Index (LAI), a dimensionless quantity, is the leaf area (upper side only) per unit area of soil below it. It is expressed as m2 leaf area per m2 ground area. The active LAI is the index of the leaf area that actively contributes to the surface heat and vapour transfer. It is generally the upper, sunlit portion of a dense canopy. The LAI values for various crops differ widely but values of 3-5 are common for many mature crops. For a given crop, green LAI changes throughout the season and normally reaches its maximum before or at flowering (Figure 8). LAI further depends on the plant density and the crop variety.

The bulk stomatal resistance, rl, is the average resistance of an individual leaf. This resistance is crop specific and differs among crop varieties and crop management. It usually increases as the crop ages and begins to ripen. There is, however, a lack of consolidated information on changes in rl over time for the different crops. The information available in the literature on stomatal conductance or resistance is often oriented toward physiological or ecophysiological studies.

The stomatal resistance, rl, is influenced by climate and by water availability. However, influences vary from one crop to another and different varieties can be affected differently. The resistance increases when the crop is water stressed and the soil water availability limits crop evapotranspiration. Some studies indicate that stomatal resistance is influenced to some extent by radiation intensity, temperature, and vapour pressure deficit.

C.  Reference surface

To obviate the need 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.

In the past, an open water surface has been proposed as a reference surface. However, the differences in aerodynamic, vegetation control and radiation characteristics present a strong challenge in relating ET to measurements of free water evaporation. Relating ETo to a specific crop has the advantage of incorporating the biological and physical processes involved in ET from cropped surfaces.

Grass, together with alfalfa, is a well-studied crop regarding its aerodynamic and surface characteristics and is accepted worldwide as a reference surface. Because the resistance to diffusion of vapour strongly depends on crop height, ground cover, LAI and soil moisture conditions, the characteristics of the reference crop should be well defined and fixed. Changes in crop height result in variations in the roughness and LAI. Consequently, the associated canopy and aerodynamic resistances will vary appreciably with time. Moreover, water stress and the degree of ground cover have an effect on the resistances and also on the albedo.

To avoid problems of local calibration which would require demanding and expensive studies, a hypothetical grass reference has been selected. Difficulties with a living grass reference result from the fact that the grass variety and morphology can significantly affect the evapotranspiration rate, especially during peak water use. Large differences may exist between warm-season and cool-season grass types. Cool-season grasses have a lower degree of stomatal control and hence higher rates of evapotranspiration. It may be difficult to grow cool-season grasses in some arid, tropical climates.

The FAO Expert Consultation on Revision of FAO Methodologies for Crop Water Requirements accepted the following unambiguous definition for the reference surface:

"A hypothetical 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 grass of uniform height, actively growing, completely shading the ground and with adequate water. The requirements that the grass surface should be extensive and uniform result from the assumption that all fluxes are one-dimensional upwards.

The FAO Penman-Monteith method is selected as the method by which the evapotranspiration of this reference surface (ETo) can be unambiguously determined, and as the method which provides consistent ETo values in all regions and climates.

D.  FAO Penman-Monteith equation

    1.  Equation

    2.  Data

    3.  Missing climatic data

1.   Equation

A consultation of experts and researchers was organized by FAO in May 1990, in collaboration with the International Commission for Irrigation and Drainage and with the World Meteorological Organization, to review the FAO methodologies on crop water requirements and to advise on the revision and update of procedures.

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.

From the original Penman-Monteith equation (Equation 3) and the equations of the aerodynamic (Equation 4) and surface resistance (Equation 5), the FAO Penman-Monteith method to estimate ETo can be derived:

    (6)

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 reference evapotranspiration, ETo, provides a standard to which:

· evapotranspiration at different periods of the year or in other regions can be compared;
· evapotranspiration of other crops can be related.

The equation 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.

No weather-based evapotranspiration equation can be expected to predict evapotranspiration perfectly under every climatic situation due to simplification in formulation and errors in data measurement. It is probable that precision instruments under excellent environmental and biological management conditions will show the FAO Penman-Monteith equation to deviate at times from true measurements of grass ETo. However, the Expert Consultation agreed to use the hypothetical reference definition of the FAO Penman-Monteith equation as the definition for grass ETo when deriving and expressing crop coefficients.

It is important, when comparing the FAO Penman-Monteith equation to ETo measurements, that the full Penman-Monteith equation (Equation 3) and associated equations for ra and rs (Equations 4 and 5) be used to enable accounting for variation in ET due to variation in height of the grass measured. Variations in measurement height can significantly change LAI, d and zom and the corresponding ETo measurement and predicted value. When evaluating results, it should be noted that local environmental and management factors, such as watering frequency, also affect ETo observations.

The FAO Penman-Monteith equation is a close, simple representation of the physical and physiological factors governing the evapotranspiration process. 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. In the crop coefficient approach, differences in the crop canopy and aerodynamic resistance relative to the hypothetical reference crop are accounted for within the crop coefficient. The Kc factor serves as an aggregation of the physical and physiological differences between crops and the reference definition.

2.   Data

Apart from the site location, the FAO Penman-Monteith equation requires air temperature, humidity, radiation and wind speed data for daily, weekly, ten-day or monthly calculations. The computation of all data required for the calculation of the reference evapotranspiration is given in Chapter 3. It is important to verify the units in which the weather data are reported. Factors to convert common units to the standard unit are presented in Annex I.

Location

Altitude above sea level (m) and latitude (degrees north or south) of the location should be specified. These data are needed to adjust some weather parameters for the local average value of atmospheric pressure (a function of the site elevation above mean sea level) and to compute extraterrestrial radiation (Ra) and, in some cases, daylight hours (N). In the calculation procedures for Ra and N, the latitude is expressed in radian (i.e., decimal degrees times p /180).

Temperature

The (average) daily maximum and minimum air temperatures in degrees Celsius (°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 due to the non-linearity of the saturation vapour pressure - temperature relationship (Figure 11). Using mean air temperature instead of maximum and minimum air temperatures yields a lower saturation vapour pressure es, and hence a lower vapour pressure difference (es - ea), and a lower reference evapotranspiration estimate.

Humidity

The (average) daily actual vapour pressure, ea, in kilopascals (kPa) is required. The actual vapour pressure, where not available, can be derived from maximum and minimum relative humidity (%), psychrometric data (dry and wet bulb temperatures in °C) or dewpoint temperature (°C) according to the procedures outlined in Chapter 3.

Radiation

The (average) daily net radiation expressed in megajoules per square metre per day (MJ m-2 day-1) 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. The calculation procedures are outlined in Chapter 3.

Wind speed

The (average) daily wind speed in metres per second (m s-1) measured at 2 m above the ground level is required. It is important to verify the height at which wind speed is measured, as wind speeds measured at different heights above the soil surface differ. The calculation procedure to adjust wind speed to the standard height of 2 m is presented in Chapter 3.

3.   Missing climatic data

Situations might occur where data for some weather variables are missing. The use of an alternative ETo calculation procedure, requiring only limited meteorological parameters, should generally be avoided. It is recommended that one calculate ETo using the standard FAO Penman-Monteith method after resolving the specific problem of the missing data. Procedures for estimating missing climatic data are outlined in Chapter 3. Differences between ETo values obtained with the FAO Penman-Monteith equation with, on the one hand, a limited data set and, on the other hand, a full data set, are expected to be smaller than or of similar magnitude to the differences resulting from the use of an alternative ETo equation.

Even where the data set contains only maximum and minimum air temperature it is still possible to obtain reasonable estimates of ten-day or monthly ETo with the FAO Penman-Monteith equation. As outlined in Chapter 3, radiation data can be derived from the air temperature difference, or, along with wind speed and humidity data, can be imported from a nearby weather station. Humidity data can also be estimated from daily minimum air temperature. After evaluating the validity of the use of data from another station, ten-day or monthly estimates of ETo can be calculated.

The procedures for estimating missing data should be validated at the regional level. This can be done for weather stations with full data sets by comparing ETo calculated with full and with limited data sets. The ratio should be close to one. Where the ratio deviates significantly from one, the ratio can be used as a correction factor for estimates made with the limited data set. Where the standard error of estimate exceeds 20% of the mean ETo, a sensitivity analysis should be performed to determine causes (and limits) for the method utilized to import the missing data. A validation should be completed for each month and variable, for the monthly as well as for the daily estimates.

Chapter 3 - Meteorological data

A.                       Meteorological factors determining ET

B.                       Atmospheric parameters

C.                       Air temperature

D.                       Air humidity

E.                        Radiation

F.                        Wind speed

G.                       Climatic data acquisition

H.                        Estimating missing climatic data

I.                           Minimum data requirements

The methods for calculating evapotranspiration from meteorological data require various climatological and physical parameters. Some of the data are measured directly in weather stations. Other parameters are related to commonly measured data and can be derived with the help of a direct or empirical relationship. This chapter discusses the source, measurement and computation of all data required for the calculation of the reference evapotranspiration by means of the FAO Penman-Monteith method. Different examples illustrate the various calculation procedures. Appropriate procedures for estimating missing data are also provided.

Meteorological data can be expressed in several units. Conversion factors between various units and standard S. I. units are given in Annex 1. Climatic parameters, calculated by means of the equations presented in this chapter are tabulated and displayed for different meteorological conditions in Annex 2. Only the standardized relationships are presented in this chapter. The background of certain relationships and more information about certain procedures are given in Annex 3. Annexes 4, 5 and 6 list procedures for the statistical analysis, assessment, correction and completion of partial or missing weather data.

A.  Meteorological factors determining ET

    1.  Solar radiation

    2.  Air temperature

    3.  Air humidity

    4.  Wind speed

The meteorological factors determining evapotranspiration are weather parameters which provide energy for vaporization and remove water vapour from the evaporating surface. The principal weather parameters to consider are presented below.

1.     Solar radiation

The evapotranspiration process is determined by the amount of energy available to vaporize water. Solar radiation is the largest energy source and is able to change large quantities of liquid water into water vapour. 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 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. When assessing the effect of solar radiation on evapotranspiration, one should also bear in mind that not all available energy is used to vaporize water. Part of the solar energy is used to heat up the atmosphere and the soil profile.

2.     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.

3.     Air humidity

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. Well-watered fields in hot dry arid regions consume large amounts of water due to the abundance of energy and the desiccating power of the atmosphere. 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.

4.     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 combined effect of climatic factors affecting evapotranspiration is illustrated in Figure 10 for two different climatic conditions. 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. Under these circumstances, much water vapour can be stored in the air while wind may promote the transport of water allowing more water vapour to be taken up. On the other hand, under humid weather conditions, the high humidity of the air and the presence of clouds cause the evapotranspiration rate to be lower. The effect on evapotranspiration of increasing wind speeds for the two different climatic conditions is illustrated by the slope of the curves in Figure 10. The drier the atmosphere, the larger the effect on ET and the greater the slope of the curve. For humid conditions, the wind can only replace saturated air with slightly less saturated air and remove heat energy. Consequently, the wind speed affects the evapotranspiration rate to a far lesser extent than under arid conditions where small variations in wind speed may result in larger variations in the evapotranspiration rate.

B.  Atmospheric parameters

    1.      Atmospheric pressure (P)

    2.      Latent heat of vaporization (l)

    3.      Psychrometric constant (g)

Several relationships are available to express climatic parameters. The effect of the principal weather parameters on evapotranspiration can be assessed with the help of these equations. Some of the relationships require parameters which express a specific characteristic of the atmosphere. Before studying the four principal weather parameters, some atmospheric parameters will be discussed.

1.     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. A simplification of the ideal gas law, assuming 20°C for a standard atmosphere, can be employed to calculate P:

   (7)

where

P atmospheric pressure [kPa],
z elevation above sea level [m],

Values for atmospheric pressure as a function of altitude are given in Annex 2 

2.   Latent heat of vaporization (l)

The latent heat of vaporization, l, expresses the energy required to change a unit mass of water from liquid to water vapour in a constant pressure and constant temperature process. The value of the latent heat varies as a function of temperature. At a high temperature, less energy will be required than at lower temperatures. As l varies only slightly over normal temperature ranges a single value of 2.45 MJ kg-1 is taken in the simplification of the FAO Penman-Monteith equation. This is the latent heat for an air temperature of about 20°C.

3.   Psychrometric constant (g)

The psychrometric constant, g, is given by:

   (8)

where

g psychrometric constant [kPa °C-1],
P atmospheric pressure [kPa],
l latent heat of vaporization, 2.45 [MJ kg-1],
cp specific heat at constant pressure, 1.013 10-3 [MJ kg-1 °C-1],
e ratio molecular weight of water vapour/dry air = 0.622.

The specific heat at constant pressure is the amount of energy required to increase the temperature of a unit mass of air by one degree at constant pressure. Its value depends on the composition of the air, i.e., on its humidity. For average atmospheric conditions a value cp = 1.013 10-3 MJ kg-1 °C-1 can be used. As an average atmospheric pressure is used for each location (Equation 7), the psychrometric constant is kept constant for each location. Values for the psychrometric constant as a function of altitude are given in Annex 2

C.  Air temperature

Agrometeorology is concerned with the air temperature near the level of the crop canopy. In traditional and modem automatic weather stations the air temperature is measured inside shelters (Stevenson screens or ventilated radiation shields) placed in line with World Meteorological Organization (WMO) standards at 2 m above the ground. The shelters are designed to protect the instruments from direct exposure to solar heating. The louvered construction allows free air movement around the instruments. Air temperature is measured with thermometers, thermistors or thermocouples mounted in the shelter. Minimum and maximum thermometers record the minimum and maximum air temperature over a 24-hour period. Thermographs plot the instantaneous temperature over a day or week. Electronic weather stations often sample air temperature each minute and report hourly averages in addition to 24-hour maximum and minimum values.

Due to the non-linearity of humidity data required in the FAO Penman-Monteith equation, the vapour pressure for a certain period should be computed as the mean between the vapour pressure at the daily maximum and minimum air temperatures of that period. The daily maximum air temperature (Tmax) and daily minimum air temperature (Tmin) are, respectively, the maximum and minimum air temperature observed during the 24-hour period, beginning at midnight. Tmax and Tmin 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 (Tmean) is only employed in the FAO Penman-Monteith equation to calculate the slope of the saturation vapour pressure curves (D) 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, Tmean for 24-hour periods is defined as the mean of the daily maximum (Tmax) and minimum temperatures (Tmin) rather than as the average of hourly temperature measurements.

   (9)

The temperature is given in degrees Celsius (°C) or Fahrenheit (°F). The conversion table is given in Annex 1. In some calculation procedures, temperature is required in Kelvin (K), which can be obtained by adding 273.16 to the temperature expressed in degrees Celsius (in practice K = °C + 273.16). The Kelvin and Celsius scale have the same scale interval.

D.  Air humidity

    1.  Concepts

    2.  Measurement

    3.  Calculation procedures

1.     Concepts

The water content of the air can be expressed in several ways. In agrometeorology, vapour pressure, dewpoint temperature and relative humidity are common expressions to indicate air humidity.

Vapour pressure

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.

In standard S. I. units, pressure is no longer expressed in centimetre of water, millimetre of mercury, bars, atmosphere, etc., but in pascals (Pa). Conversion factors between various units and Pa are given in Annex 1. As a pascal refers to a relatively small force (1 newton) applied on a relatively large surface (1 m2), multiples of the basic unit are often used. In this handbook, vapour pressure is expressed in kilopascals (kPa = 1000 Pa).

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°(T)). The number of water molecules that can be stored in the air depends on the temperature (T). The higher the air temperature, the higher the storage capacity, the higher its saturation vapour pressure (Figure 11).

As can be seen from Figure 11, the slope of the curve changes exponentially with temperature. At low temperatures, the slope is small and varies only slightly as the temperature rises. At high temperatures, the slope is large and small changes in T result in large changes in slope. The slope of the saturation vapour pressure curve, D, is an important parameter in describing vaporization and is required in the equations for calculating ETo from climatic data.

FIGURE 11. Saturation vapour pressure shown as a function of temperature: e°(T) curve

FIGURE 12. Variation of the relative humidity over 24 hours for a constant actual vapour pressure of 2.4 kPa

The actual vapour pressure (ea) is the vapour pressure exerted by the water in the air. When the air is not saturated, the actual vapour pressure will be lower than the saturation vapour pressure. The difference between the saturation and actual vapour pressure is called the vapour pressure deficit or saturation deficit and is an accurate indicator of the actual evaporative capacity of the air.

Dewpoint temperature

The dewpoint temperature is the temperature to which the air needs to be cooled to make the air saturated. The actual vapour pressure of the air is the saturation vapour pressure at the dewpoint temperature, The drier the air, the larger the difference between the air temperature and dewpoint temperature.

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°(T)) vapour pressure at the same temperature (T):

   (10)

Relative humidity is the ratio 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 given 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 (Figure 12). The variation of the relative humidity is the result of the fact that the saturation vapour pressure is determined by the air temperature. As the temperature changes during the day, the relative humidity also changes substantially.

2.     Measurement

It is not possible to directly measure the actual vapour pressure. The vapour pressure is commonly derived from relative humidity or dewpoint temperature.

Relative humidity is measured directly with hygrometers. The measurement is based on the nature of some material such as hair, which changes its length in response to changes in air humidity, or using a capacitance plate, where the electric capacitance changes with RH. Vapour pressure can be measured indirectly with psychrometers which measure the temperature difference between two thermometers, the so-called dry and wet bulb thermometers. The dry bulb thermometer measures the temperature of the air. The bulb of the wet bulb thermometer is covered with a constantly saturated wick. Evaporation of water from the wick, requiring energy, lowers the temperature of the thermometer. The drier the air, the larger the evaporative cooling and the larger the temperature drop. The difference between the dry and wet bulb temperatures is called the wet bulb depression and is a measure of the air humidity.

The dewpoint temperature is measured with dewpoint meters. The underlying principle of some types of apparatus is the cooling of the ambient air until dew formation occurs. The corresponding temperature is the dewpoint temperature.

Relative humidity and dewpoint temperature data are notoriously plagued by measurement errors. Measurement error is common for both older hygrothermograph types of instruments and for the more modem electronic instruments. These instruments are described in Annex 5. Great care should be made to assess the accuracy and integrity of RH and dewpoint data. The user is encouraged to always compare computed dewpoint temperatures to daily minimum air temperatures, as described at the end of this chapter and in Annexes 5 and 6. Frequently, it is better to utilize a dewpoint temperature that is predicted from daily minimum air temperature, rather than to use unreliable relative humidity measurements. The user is encouraged to utilize good judgement in this area.

3.     Calculation procedures

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:

   (11)

where

e°(T) saturation vapour pressure at the air temperature T [kPa],
T air temperature [°C],
exp[..] 2.7183 (base of natural logarithm) raised to the power [..].

Values of saturation vapour pressure as a function of air temperature are given in Annex 2 (Table 2.3). 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:

   (12)

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. Therefore, the mean saturation vapour pressure should be calculated as the mean between the saturation vapour pressure at both the daily maximum and minimum air temperature.

Slope of saturation vapour pressure curve (D )

For the calculation of evapotranspiration, the slope of the relationship between saturation vapour pressure and temperature, D, is required. The slope of the curve (Figure 11) at a given temperature is given by.

   (13)

where

D slope of saturation vapour pressure curve at air temperature T [kPa °C-1],
T air temperature [°C],
exp[..] 2.7183 (base of natural logarithm) raised to the power [..].

Values of slope D for different air temperatures are given in Annex 2 (Table 2.4). In the FAO Penman-Monteith equation, where D occurs in the numerator and denominator, the slope of the vapour pressure curve is calculated using mean air temperature (Equation 9).

Actual vapour pressure (ea) derived from dewpoint temperature

As the dewpoint temperature is the temperature to which the air needs to be cooled to make the air saturated, the actual vapour pressure (ea) is the saturation vapour pressure at the dewpoint temperature (Tdew) [°C], or:

   (14)

Actual vapour pressure (ea) derived from psychrometric data

The actual vapour pressure can be determined from the difference between the dry and wet bulb temperatures, the so-called wet bulb depression. The relationship is expressed by the following equation:

e_a = e° (T_wet) - g _psy (T_dry - T_wet)   (15)

where

ea actual vapour pressure [kPa],
e°(Twet) saturation vapour pressure at wet bulb temperature [kPa],
g psy psychrometric constant of the instrument [kPa °C-1],
Tdry-Twet wet bulb depression, with Tdry the dry bulb and Twet the wet bulb temperature [°C].

The psychrometric constant of the instrument is given by:

g psy = apsy P (16)

where apsy is a coefficient depending on the type of ventilation of the wet bulb [°C-1], and P is the atmospheric pressure [kPa]. The coefficient apsy depends mainly on the design of the psychrometer and rate of ventilation around the wet bulb. The following values are used:

Actual vapour pressure (ea) derived from relative humidity data

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.

· For RHmax and RHmin:

 

   (17)

 

where

ea actual vapour pressure [kPa],
e°(Tmin) saturation vapour pressure at daily minimum temperature [kPa],
e°(Tmax) saturation vapour pressure at daily maximum temperature [kPa],
RHmax maximum relative humidity [%],
RHmin minimum relative humidity [%].

For periods of a week, ten days or a month, RHmax and RHmin are obtained by dividing the sum of the daily values by the number of days in that period.

· For RHmax:

When using equipment where errors in estimating RHmin can be large, or when RH data integrity are in doubt, then one should use only RHmax:

 

   (18)

 

· For RHmean:

In the absence of RHmax and RHmin, another equation can be used to estimate ea:

 

   (19)

 

where RHmean is the mean relative humidity, defined as the average between RHmax and RHmin. However, Equation 19 is less desirable than are Equations 17 or 18.

Vapour pressure deficit (e_s - e_a)

The vapour pressure deficit is the difference between the saturation (es) and actual vapour pressure (ea) for a given time period. For time periods such as a week, ten days or a month es is computed from Equation 12 using the Tmax and Tmin averaged over the time period and similarly the ea is computed with one of the equations 4 to 19, using average measurements over the period. As stated above, using mean air temperature and not Tmax and Tmin in Equation 12 results in a lower estimate of es, thus in a lower vapour pressure deficit and hence an underestimation of the ETo (see Box 7). When desired, es and ea for long time periods cal also be calculated as averages of values computed for each day of the period.

E.  Radiation

    1.  Cincepts

    2.  Units

    3.  Measurements

    4.  Calculation procedures

1.     Concepts

Extraterrestrial radiation (R_a)

The radiation striking a surface perpendicular to the sun's rays at the top of the earth's atmosphere, called the solar constant, is about 0.082 MJ m-2 min-1. 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.

Solar or shortwave 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. Because the sun emits energy by means of electromagnetic waves characterized by short wavelengths, solar radiation is also referred to as shortwave radiation.

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 mainly as diffuse sky radiation. Solar radiation is also known as global radiation, meaning that it is the sum of direct shortwave radiation from the sun and diffuse sky radiation from all upward angles.

Relative shortwave radiation (R_s/R_so)

The relative shortwave radiation is the ratio of the solar radiation (Rs) to the clear-sky solar radiation (Rso). Rs is the solar radiation that actually reaches the earth's surface in a given period, while Rso is the solar radiation that would reach the same surface during the same period but under cloudless conditions.

The relative shortwave radiation is a way to express the cloudiness of the atmosphere; the cloudier the sky the smaller the ratio. The ratio varies between about 0.33 (dense cloud cover) and 1 (clear sky). In the absence of a direct measurement of Rn, the relative shortwave radiation is used in the computation of the net longwave 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.

Albedo (a) and net solar radiation (R_ns)

A considerable amount of solar radiation reaching the earth's surface is reflected. The fraction, a, of the solar radiation reflected by the surface is known as the albedo. The albedo is highly variable for different surfaces and for the angle of incidence or slope of the ground surface. It may be as large as 0.95 for freshly fallen snow and as small as 0.05 for a wet bare soil. A green vegetation cover has an albedo of about 0.20-0.25. For the green grass reference crop, a is assumed to have a value of 0.23.

The net solar radiation, Rns, is the fraction of the solar radiation Rs that is not reflected from the surface. Its value is (1-a)Rs.

Net longwave radiation (R_nl)

The solar radiation absorbed by the earth is converted to heat energy. By several processes, including emission of radiation, the earth loses 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 to as longwave radiation. The emitted longwave radiation (Rl, up) is absorbed by the atmosphere or is lost into space. The longwave radiation received by the atmosphere (Rl, down) increases its temperature and, as a consequence, the atmosphere radiates energy of its own, as illustrated in Figure 15. Part of the radiation finds it way back to the earth's surface. Consequently, 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 longwave radiation is almost always greater than me incoming longwave radiation, Rnl represents an energy loss.

Net radiation (R_n)

The net radiation, Rn, is the difference between incoming and outgoing radiation of both short and long wavelengths. It is the balance between the energy absorbed, reflected and emitted by the earth's surface or the difference between the incoming net shortwave (Rns) and the net outgoing longwave (Rnl) radiation (Figure 15). Rn is normally positive during the daytime and negative during the nighttime. The total daily value for Rn is almost always positive over a period of 24 hours, except in extreme conditions at high latitudes.

Soil heat flux (G)

In making estimates of evapotranspiration, all terms of the energy balance (Equation 1) should be considered. The soil heat flux, G, is the energy that is utilized in heating the soil. G is positive when the soil is warming and negative when the soil is cooling. Although the soil heat flux is small compared to Rn and may often be ignored, the amount of energy gained or lost by the soil in this process should theoretically be subtracted or added to Rn when estimating evapotranspiration.

2.     Measurement

Solar radiation can be measured with pyranometers, radiometers or solarimeters. The instruments contain a sensor installed on a horizontal surface that measures the intensity of the total solar radiation, i.e., both direct and diffuse radiation from cloudy conditions. The sensor is often protected and kept in a dry atmosphere by a glass dome that should be regularly wiped clean.

Net longwave and net shortwave radiation can be measured by recording the difference in output between sensors facing upward and downward. In a net radiometer, the glass domes are replaced by polyethylene domes that have a transmission range for both shortwave and longwave radiation.

Where pyranometers are not available, solar radiation is usually estimated from the duration of bright sunshine. The actual duration of sunshine, n, is measured with a Campbell-Stokes sunshine recorder. This instrument records periods of bright sunshine by using a glass globe that acts as a lens. The sun rays are concentrated at a focal point that burns a hole in a specially treated card mounted concentrically with the sphere. The movement of the sun changes the focal point throughout the day and a trace is drawn on the card. If the sun is obscured, the trace is interrupted. The hours of bright sunshine are indicated by the lengths of the line segments.

The quantity of heat conducted into the soil, G, can be measured with systems of soil heat flux plates and thermocouples or thermisters.

3.     Calculation procedures

Extraterrestrial radiation for daily periods (R_a)

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:

 

   (21)

 

where

R_a extraterrestrial radiation [MJ m^-2 day^-1],
G_sc solar constant = 0.0820 MJ m^-2 min^-1,
d_r inverse relative distance Earth-Sun (Equation 23),
w _s sunset hour angle (Equation 25 or 26) [rad],
j latitude [rad] (Equation 22),
d solar decimation (Equation 24) [rad].

R_a is expressed in the above equation in MJ m^-2 day^-1. The corresponding equivalent evaporation in mm day^-1 is obtained by multiplying R_a by 0.408 (Equation 20). The latitude, j, expressed in radians is positive for the northern hemisphere and negative for the southern hemisphere (Example 7). The conversion from decimal degrees to radians is given by:

 

   (22)

 

The inverse relative distance Earth-Sun, d_r, and the solar declination, d, are given by:

 

   (23)

 

   (24)

 

where J is the number of the day in the year between 1 (1 January) and 365 or 366 (31 December). Values for J for all days of the year and an equation for estimating J are given in Annex 2 (Table 2.5).

The sunset hour angle, w _s, is given by:

w _s = arccos [-tan (j) tan (d)] (25)

As the arccos function is not available in all computer languages, the sunset hour angle can also be computed using the arctan function:

 

   (26)

 

where

X = 1 - [tan(j)]² [tan(d)]² (27)
and X = 0.00001 if X £ 0

Values for R_a for different latitudes are given in Annex 2 (Table 2.6). These values represent R_a on the 15^th day of each month. These values deviate from values that are averaged over each day of the month by less than 1% for all latitudes during non-frozen periods and are included for simplicity of calculation. These values deviate slightly from the values in the Smithsonian Tables. For the winter months in latitudes greater than 55° (N or S), the equations for R_a have limited validity. Reference should be made to the Smithsonian Tables to assess possible deviations.

Extraterrestrial radiation for hourly or shorter periods (R_a)

For hourly or shorter periods the solar time angle at the beginning and end of the period should be considered when calculating R_a:

 

   (28)

 

where

R_a extraterrestrial radiation in the hour (or shorter) period [MJ m^-2 hour^-1],
G_sc solar constant = 0.0820 MJ m^-2 min^-1,
d_r inverse relative distance Earth-Sun (Equation 23),
d solar declination [rad] (Equation 24),
j latitude [rad] (Equation 22),
w ₁ solar time angle at beginning of period [rad] (Equation 29),
w ₂ solar time angle at end of period [rad] (Equation 30).

The solar time angles at the beginning and end of the period are given by:

 

   (29)

 

   (30)

 

where

w solar time angle at midpoint of hourly or shorter period [rad],
t₁ length of the calculation period [hour]: i.e., 1 for hourly period or 0.5 for a 30-minute period.

The solar time angle at midpoint of the period is:

 

   (31)

 

where

t standard clock time at the midpoint of the period [hour]. For example for a period between 14.00 and 15.00 hours, t = 14.5,

L_z longitude of the centre of the local time zone [degrees west of Greenwich]. For example, L_z = 75, 90, 105 and 120° for the Eastern, Central, Rocky Mountain and Pacific time zones (United States) and L_z = 0° for Greenwich, 330° for Cairo (Egypt), and 255° for Bangkok (Thailand),

L_m longitude of the measurement site [degrees west of Greenwich],

S_c seasonal correction for solar time [hour].

Of course, w < -w _s or w > w _s from Equation 31 indicates that the sun is below the horizon so that, by definition, R_a is zero.

The seasonal correction for solar time is:

S_c = 0.1645 sin(2 b) - 0.1255 cos(b) - 0.025 sin(b)    (32)

 

   (33)

 

where J is the number of the day in the year.

Daylight hours (N)

The daylight hours, N, are given by:

 

   (34)

 

where w _s is the sunset hour angle in radians given by Equation 25 or 26. Mean values for N (15^th day of each month) for different latitudes are given in Annex 2, Table 2.7.

Solar radiation (R_s)

If the solar radiation, R_s, is not measured, it can be calculated with the Angstrom formula which relates solar radiation to extraterrestrial radiation and relative sunshine duration:

 

   (35)

 

where

R_s solar or shortwave radiation [MJ m^-2 day^-1],

n actual duration of sunshine [hour],

N maximum possible duration of sunshine or daylight hours [hour],

n/N relative sunshine duration [-],

R_a extraterrestrial radiation [MJ m^-2 day^-1],

a_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).

R_s is expressed in the above equation in MJ m^-2 day^-1. The corresponding equivalent evaporation in mm day^-1 is obtained by multiplying R_s by 0.408 (Equation 20). Depending on atmospheric conditions (humidity, dust) and solar declination (latitude and month), the Angstrom values a_s and b_s will vary. Where no actual solar radiation data are available and no calibration has been carried out for improved a_s and b_s parameters, the values a_s = 0.25 and b_s = 0.50 are recommended.

The extraterrestrial radiation, R_a, and the daylight hours or maximum possible duration of sunshine, N, are given by Equations 21 and 34. Values for R_a and N for different latitudes are also listed in Annex 2 (Tables 2.6 and 2.7). The actual duration of sunshine, n, is recorded with a Campbell Stokes sunshine recorder.

Clear-sky solar radiation (R_so)

The calculation of the clear-sky radiation, R_so, when n = N, is required for computing net longwave radiation.

· For near sea level or when calibrated values for a_s and b_s are available:

R_so = (a_s+b_s)R_a (36)

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).

· When calibrated values for a_s and b_s are not available:

R_so = (0.75 + 2 l0^-5z)R_a (37)

where

z station elevation above sea level [m].

Other more complex estimates for R_so, which include turbidity and water vapour effects, are discussed in Annex 3 (Equations 3.14 to 20).

Net solar or net shortwave radiation (R_ns)

The net shortwave radiation resulting from the balance between incoming and reflected solar radiation is given by:

R_ns = (1-a)R_s (38)

where

R_ns net solar or shortwave radiation [MJ m^-2 day^-1],

a albedo or canopy reflection coefficient, which is 0.23 for the hypothetical grass reference crop [dimensionless],

R_s the incoming solar radiation [MJ m^-2 day^-1].

R_ns is expressed in the above equation in MJ m^-2 day^-1.

Net longwave radiation (R_nl)

The rate of longwave energy emission is proportional to the absolute temperature of the surface raised to the fourth power. This relation is expressed quantitatively by the Stefan-Boltzmann law. The net energy flux leaving the earth's surface is, however, less than that emitted and given by the Stefan-Boltzmann law due to the absorption and downward radiation from the sky. Water vapour, clouds, carbon dioxide and dust are absorbers and emitters of longwave radiation. Their concentrations should be known when assessing the net outgoing flux. As humidity and cloudiness play an important role, the Stefan-Boltzmann law is corrected by these two factors when estimating - the net outgoing flux of longwave radiation. It is thereby assumed that the concentrations of the other absorbers are constant:

 

   (39)

 

where

R_nl net outgoing longwave radiation [MJ m^-2 day^-1],
s Stefan-Boltzmann constant [4.903 10^-9 MJ K^-4 m^-2 day^-1],
T_{max, K} maximum absolute temperature during the 24-hour period [K = °C + 273.16],
T_{min, K} minimum absolute temperature during the 24-hour period [K = °C + 273.16],
e_a actual vapour pressure [kPa],
R_s/R_so relative shortwave radiation (limited to £ 1.0),
R_s measured or calculated. (Equation 35) solar radiation [MJ m^-2 day^-1],
R_so calculated (Equation 36 or 37) clear-sky radiation [MJ m^-2 day^-1].

An average of the maximum air temperature to the fourth power and the minimum air temperature to the fourth power is commonly used in the Stefan-Boltzmann equation for 24-hour time steps. The term (0.34-0.14Ö e_a) expresses the correction for air humidity, and will be smaller if the humidity increases. The effect of cloudiness is expressed by (1.35 R_s/R_so - 0.35). The term becomes smaller if the cloudiness increases and hence R_s decreases. The smaller the correction terms, the smaller the net outgoing flux of longwave radiation. Note that the R_s/R_so term in Equation 39 must be limited so that R_s/R_so £ 1.0.

Where measurements of incoming and outgoing short and longwave radiation during bright sunny and overcast hours are available, calibration of the coefficients in Equation 39 can be carried out.

Net radiation (R_n)

The net radiation (R_n) is the difference between the incoming net shortwave radiation (R_ns) and the outgoing net longwave radiation (R_nl):

R_n = R_ns - R_nl (40)

Soil heat flux (G)

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 and calculation time steps are 24 hours or longer, a simple calculation procedure is presented here for long time steps, based on the idea that the soil temperature follows air temperature:

 

   (41)

 

where

G soil heat flux [MJ m^-2 day^-1],
c_s soil heat capacity [MJ m^-3 °C^-1],
T_i air temperature at time i [°C],
T_i-1 air temperature at time i-1 [°C],
D t length of time interval [day],
D z effective soil depth [m].

As the soil temperature lags air temperature, the average temperature for a period should be considered when assessing me daily soil heat flux, i.e., D t should exceed one day. The depth of penetration of the temperature wave is determined by the length of the time interval. The effective soil depth, D z, is only 0.10-0.20 m for a time interval of one or a few days but might be 2 m or more for monthly periods. The soil heat capacity is related to its mineral composition and water content.

· For day and ten-day periods:

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 (42)

· For monthly periods:

When assuming a constant soil heat capacity of 2.1 MJ m^-3 °C^-1 and an appropriate soil depth, Equation 41 can be used to derive G for monthly periods:

G_{month, i} = 0.07 (T_{month, i+1} - T_{month, i-1}) (43)

or, if T_{month, i+1} is unknown:

G_{month, i} = 0.14 (T_{month, i} - T_{month, i-1}) (44)

where

T_{month, i} mean air temperature of month i [°C],
T_{month, i-1} mean air temperature of previous month [°C],
T_{month, i+1} mean air temperature of next month [°C].

· For hourly or shorter periods:

For hourly (or shorter) calculations, G beneath a dense cover of grass does not correlate well with air temperature. Hourly G can be approximated during daylight periods as:

G_hr = 0.1 R_n (45)

and during nighttime periods as:

G_hr = 0.5 R_n (46)

Where the soil is warming, the soil heat flux G is positive. The amount of energy required for this process is subtracted from R_n when estimating evapotranspiration.

F.  Wind speed

    1.  Measurement

    2.  Wind profile relationship

1.     Measurement

Wind is characterized by its direction and velocity. Wind direction refers to the direction from which the wind is blowing. For the computation of evapotranspiration, wind speed is the relevant variable. As wind speed at a given location varies with time, it is necessary to express it as an average over a given time interval. Wind speed is given in metres per second (m s^-1) or kilometres per day (km day^-1).

Wind speed is measured with anemometers. The anemometers commonly used in weather stations are composed of cups or propellers which are turned by the force of the wind. By counting the number of revolutions over a given time period, the average wind speed over the measuring period is computed.

2.     Wind profile relationship

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 than the standard height of 2m, a logarithmic wind speed profile may be used for measurements above a short grassed surface:

 

   (47)

 

where

u2 wind speed at 2 m above ground surface [m s-1],
uz measured wind speed at z m above ground surface [m s-1],
z height of measurement above ground surface [m].

G.  Climatic data acquisition

    1.  Weather stations

    2.  Agroclimatic monthly databases

1.     Weather stations

Meteorological data are recorded at various types of weather stations. Agrometeorological stations are sited in cropped areas where instruments are exposed to atmospheric conditions similar to those for the surrounding crops. In these stations, air temperature and humidity, wind speed and sunshine duration are typically measured at 2 m above an extensive surface of grass or short crop. Where needed and feasible, the cover of the station is irrigated. Guidelines for the establishment and maintenance of agrometeorological stations are given in the FAO Irrigation and Drainage Paper No. 27. This handbook also describes the different types of instruments, their installation and reliability.

Data collected at stations other than agrometeorological stations require a careful analysis of their validity before their use. For example, in aeronautic stations, data relevant for aviation are measured. As airports are often situated near urban conditions, temperatures may be higher than those found in rural agricultural areas. Wind speed is commonly measured at 10 m height above the ground surface.

The country's national meteorological service should be contacted for information on the climatic data collected at various types of weather stations in the country. National services commonly publish meteorological bulletins listing processed climatic data from the various stations.

The annexes list procedures for the statistical analysis, assessment, correction and completion of partial or missing weather data:

2.     Agroclimatic monthly databases

CLIMWAT for CROPWAT (FAO Irrigation and Drainage Paper No. 46) contains monthly data from 3 262 climatic stations contained on five separate diskettes. The stations are grouped by country and by continent. Monthly averages of maximum and minimum temperatures, mean relative humidity, wind speed, sunshine hours, radiation data as well as rainfall and ETo calculated with the FAO Penman-Monteith method are listed on the diskettes for mean long-term conditions.

FAOCLIM provides a user friendly interface on compact disc to the agroclimatic database of the Agrometeorology Group in FAO. The data presented are an extension of the previously published FAO Plant Production and Protection Series and the number of stations has been increased from 2300 to about 19000, with an improved world wide coverage. However, values for all principal weather parameters are not available for all stations. Many contain air temperature and precipitation only.

These databases can be consulted in order to verify the consistency of the actual database or to estimate missing climatic parameters. However, they should only be used for preliminary studies as they contain mean monthly data only. FAOCLIM provides monthly time series for only a few stations. The information in these databases should never replace actual data.

Other electronic databases for portions of the globe have been published by the International Water Management Institute (IWMI). These databases include daily and monthly air temperature, precipitation and ETo predicted using the Hargreaves ETo equation that is based on differences between daily maximum and minimum air temperature.

H.  Estimating missing climatic data

    1.  Estimating missing humidity data

    2.  Estimating missing radiation data

    3.  Missing wind speed data

The assessment of the reference evapotranspiration ETo with the Penman-Monteith method is developed in Chapter 4. The calculation requires mean daily, ten-day or monthly maximum and minimum air temperature (Tmax and Tmin), actual vapour pressure (ea), net radiation (Rn) and wind speed measured at 2 m (u2). If some of the required weather data are missing or cannot be calculated, it is strongly recommended that the user estimate the missing climatic data with one of the following procedures and use the FAO Penman-Monteith method for the calculation of ETo. The use of an alternative ETo calculation procedure, requiring only limited meteorological parameters, is less recommended. Procedures to estimate missing humidity, radiation and wind speed data are given in this section.

1.     Estimating missing humidity data

Where humidity data are lacking or are of questionable quality, an estimate of actual vapour pressure, ea, can be obtained by assuming that dewpoint temperature (Tdew) is near the daily minimum temperature (Tmin). This statement implicitly assumes that at sunrise, when the air temperature is close to Tmin, that the air is nearly saturated with water vapour and the relative humidity is nearly 100%. If Tmin is used to represent Tdew then:

 

   (48)

 

The relationship Tdew » Tmin holds for locations where the cover crop of the station is well watered. However, particularly for arid regions, the air might not be saturated when its temperature is at its minimum. Hence, Tmin might be greater than Tdew and a further calibration may be required to estimate dewpoint temperatures. In these situations, "Tmin" in the above equation may be better approximated by subtracting 2-3 °C from Tmin. Appropriate correction procedures are given in Annex 6. In humid and subhumid climates, Tmin and Tdew measured in early morning may be less than Tdew measured during the daytime because of condensation of dew during the night. After sunrise, evaporation of the dew will once again humidify the air and will increase the value measured for Tdew during the daytime. This phenomenon is demonstrated in Figure 5.4 of Annex 5. However, it is standard practice in 24-hour calculations of ETo to use Tdew measured or calculated during early morning.

The estimate for ea from Tmin should be checked. When the prediction by Equation 48 is validated for a region, it can be used for daily estimates of ea.

2.     Estimating missing radiation data

Net radiation measuring devices, requiring professional control, have rarely been installed in agrometeorological stations. In the absence of a direct measurement, longwave and net radiation can be derived from more commonly observed weather parameters, i.e., solar radiation or sunshine hours, air temperature and vapour pressure. Where solar radiation is not measured, it can perhaps be estimated from measured hours of bright sunshine. However, where daily sunshine hours (n) are not available, solar radiation data cannot be computed with the calculation procedures previously presented. This section presents various methods to estimate solar radiation data with an alternative methodology.

Solar Radiation data from a nearby weather station

This method relies on the fact that for the same month and often for the same day, the variables affecting incoming solar radiation, Rs, and sunshine duration, n, are similar throughout a given region. This implies that: (i) the size of the region is small; (ii) the air masses governing rainfall and cloudiness are nearly identical within parts of the region; and (iii) the physiography of the region is almost homogenous. Differences in relief should be negligible as they strongly influence the movement of air masses. Under such conditions, radiation data observed at nearby stations can be used.

Caution should be used when applying this method to mountainous and coastal areas where differences in exposure and altitude could be important or where rainfall is variable due to convective conditions. Moreover, data from a station located nearby but situated on the other side of a mountain may not be transferable as conditions governing radiation are different. The user should observe climatic conditions in both locations and obtain information from local persons concerning general differences in cloud cover and type.

Where the north-south distance to a weather station within the same homogeneous region exceeds 50 km so that the value for Ra changes, the Rs measurement should be adjusted using the ratio of the solar to extraterrestrial radiation, Rs/Ra:

 

   (49)

 

where

R_{s, reg} solar radiation at the regional location [MJ m^-2 day^-1],
R_{a, reg} extraterrestrial radiation at the regional location [MJ m^-2 day^-1].

Once the solar radiation has been derived from the radiation data of a nearby station, the net longwave radiation (Equation 39) and the net radiation (Equation 40) can be calculated.

The estimation method of Equation 49 is recommended for monthly calculations of ET_o. If using the method for daily estimates of ET_o, a more careful analysis of weather data in the importing and exporting meteorological stations has to be performed to verify whether both stations are in the same homogeneous climatic region and are close enough to experience similar conditions within the same day. The analysis should include the comparison of daily weather data from both stations, particularly the maximum and minimum air temperature and humidity. In fact, similar cloudiness and sunshine durations are related to similarities in temperature and humidity trends.

Generally, daily calculations of ET_o with estimated radiation data are justified when utilized as a sum or an average over a several-day period. This is the case for the computation of the mean evapotranspiration demand between successive irrigations or when planning irrigation schedules. Under these conditions, the relative error for one day often counterbalances the error for another day of the averaging period. Daily estimates should not be utilized as true daily estimates but only in averages over the period under consideration.

Solar Radiation data derived from air temperature differences

The difference between the maximum and minimum air temperature is related to the degree of cloud cover in a location. Clear-sky conditions result in high temperatures during the day (T_max,) because the atmosphere is transparent to the incoming solar radiation and in low temperatures during the night (T_min) because less outgoing longwave radiation is absorbed by the atmosphere. On the other hand, in overcast conditions, T_max is relatively smaller because a significant part of the incoming solar radiation never reaches the earth's surface and is absorbed and reflected by the clouds. Similarly, T_min will be relatively higher as the cloud cover acts as a blanket and decreases the net outgoing longwave radiation. Therefore, the difference between the maximum and minimum air temperature (T_max - T_min) can be used as an indicator of the fraction of extraterrestrial radiation that reaches the earth's surface. This principle has been utilized by Hargreaves and Samani to develop estimates of ET_o using only air temperature data.

The Hargreaves' radiation formula, adjusted and validated at several weather stations in a variety of climate conditions, becomes:

 

   (50)

 

where

R_a extraterrestrial radiation [MJ m^-2 d^-1],
T_max maximum air temperature [°C],
T_min minimum air temperature [°C],
k_Rs adjustment coefficient (0.16.. 0.19) [°C^-0.5].

The square root of the temperature difference is closely related to the existing daily solar radiation in a given location. The adjustment coefficient k_Rs is empirical and differs for 'interior' or 'coastal' regions:

· for 'interior' locations, where land mass dominates and air masses are not strongly influenced by a large water body, k_Rs