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No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise.Applications for such permission, with a statement of the purpose and extent of the reproduction, should be addressed to the Director, Information Division, Food and Agriculture Organization of the United Nations, Viale delle Terme di Caracalla, 00100 Rome, Italy.Even if the quality of digitalisation is high, the FAO declines all responsibility for any discrepancies that may exist between the present document and its original printed version. Martin Smith Martin Smith This person is not on ResearchGate, or hasn't claimed this research yet.The procedure, first presented in the FAO Irrigation and Drainage Paper No. 24 'Crop Water Requirem ents', is term ed the 'K c ET o ' approach, whereby the effect of the climate on crop water requirements is giv en 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 estim ation 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 rev ealed the need to update the FAO methodologies for calculating ET o. The FAO Penman method was found to frequently overestimate ET o while the o ther FAO r ecommended equatio ns, namely t he radiation, the Blaney- Criddle, and the pan evaporation methods, showed variable adherence to the grass reference crop evapotranspiration.

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In May 1990, FAO organized a consultation of experts and researchers in collaboration with the International Commission for I rrigation and Drainage and with the World Meteorological Organization, to review the FAO methodologies on crop water requirements and to adv ise on the revision and update of procedures. The pan el of exp erts re commended t he adopt ion of t he Penman-Monteith combination m ethod as a new standard for reference evapotranspiration and advised on procedures for calculating the various parameters. The FAO Penman-Monteith m ethod was developed by defining the reference crop as a hypothetical crop with an assumed height of 0.12 m, with a surface resistance o f 70 s m -1 and an albedo of 0.23, closely re sembling the evaporation from an ext ensive surface of green g rass of uniform height, actively g rowing and adequately watered. The method overcomes the shortcomings of the previous FAO Penman m ethod and provides values that are more consistent with actual crop water use data worldwide. Furthermore, recommendations have been developed using the FAO Penman-Monteith m ethod with limited climatic data, thereby larg ely e limin ating 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 clim atic data that can be easily measured or derived from comm only measured data. All calculation procedures have been standardized according to the available weather data and the time scale of com putation. The calculation methods, as well as the procedures for estimating missing clim atic data, are presented in this publication. In the 'K c -ET o ' approach, differences in the crop canopy and aerody nam ic resi stance relativ e to t he reference crop are accounted for within the crop coefficient.

The K c coefficient serves as an aggregati on of th e physica l and phys iologic al dif ferenc es between crops. Two calculation methods 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 manag ement 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, irrig ation engineers, hydrologists, agronomists, meteorolog ists 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 consum ption by agric ultural and n atural vegetation. The consultation was organized to review the then current FAO guidelines to determine Crop Water Requirements, published in 1977 as FAO Irrigation and Drainage paper No. 24 (FAO-24) and authored by J. Doorenbos and W. Pruitt.

The conceptual framework for the revised methodolog ies introduced in this publication came fort h out of the advice of the group of eminent experts congregated in the 1990 meeting s and who have importantly contributed to the development of the further studies conducted in the fram ework of the publication. Members of the 1990 FAO expert consultation included Dr P. Fleming of Australia, Dr A. Perrier of France, Drs L. Cavazza and L. Tom besi from I taly, Drs R. Fed des an d J. Doorenbos of the Netherlands, Dr L.S. Pereira of Portugal, Drs J.L. Monteith and H. Gunston from the United Kingdom, Drs R. Allen, M. Jensen and W.O. P ruitt of USA, Dr D. Rijks from the World Meteorological Organization and various staff of FAO. Many other experts and persons from different organizations and institutes have provided, in varying degrees and at different stages, important advice and contributions. Special acknowledgements for this are due in particular to Prof. W.O. Pruitt (retired) of the U niversity of California, Davis and J. Doorenbos of FAO (retired) who set the standard and tem plate for this work in the predecessor FAO-24, and to Prof. J.L. Monteith whose unique work set the scientific basis for the ET o review. Prof. Pruitt, despite his emeritus status, has consistently contributed in making essential data available and in adv ising on critical concepts. Dr James L. Wright of the USDA, Kimberly, Idaho, further contributed in providing data from the precision lysimeter for several crops. Further important contributions or reviews at critical stages of the publication were received from Drs M. Jensen, G. Hargreaves and C. Stockle of USA, D r B. Itier of France, and various members of technical working groups of the International Comm ission on Irrigation and Drainage (ICID ) and the American Societies of Civil and Agricultural Eng neers.

The authors thank their respective institutions, Utah State University, Instituto Superior de Agronomia of Lisbon, Katholieke Universiteit L euven and FA O for the gener ous s upport of faculty time and staff services during the developm ent of this publication. The authors wish to express their gratitude to Mr H. Wolter, Director of the Land and Water Development Division for his encouragement in the preparation of the guidelines and to FA O colleagues and others who have reviewed the document and m ade valuable comments. Special thanks are due to Ms Chrissi Redfern for her patience and valuable assistance in the preparation and formatting of the text. Mr Julian Plummer further contributed in editing the final document. ET C DURING NON - GROWING PERIODS 207 Types of surface conditions 207 Bare soil 207 Surface covered with dead vegetation 207 Surface covered with live vegetation 208 Frozen or snow covered surfaces 209 Illustration of the effect of wind speed on evapotranspiration in hot-dry and hum id- warm weather conditions 30 11. Various components of radiation 44 16. Conversion factor to convert wind speed measured at a certain height abov e ground level to wind speed at the standard height (2 m) 56 17. Two cases of evaporation pan siting and their environment 79 20. Typical K c for different types of full grown crops 92 21. Extreme ranges expected in K c for full grown crops as climate and weather change 92 22. The effect of evaporation on K c. The horizontal line represents K c when the soil surface is kept continuously wet. The curved line corresponds to K c when the soil surface is kept dry but the crop receives sufficient water to sustain full transpiration 94 23. Crop growth stages for different types of crops 94 Typical ranges expected in K c for the four growth stages 97 25. Generalized crop coefficient curve for the single crop coefficient approach 100 26. General procedure for calculating ET c 102 28.

Variation in the length of the growing period of rice (cultivar: Jaya) sown during various months of the year at different locations along the Seneg al River (Africa) 109 29. Average K c ini as related to the level of ET o and the interval between irrigations greater than or equal to 40 mm per wetting event, during the initial growth stage for: a) coarse textured soils; b) medium and fine textured soils 118 31. Partial wetting by irrigation120 32. Adjustment (additive) to the K c mid values from Table 12 for different crop heights and mean daily wind speeds (u 2 ) for different hum idity conditions 122 33. Ranges expected for K c end 126 34. Crop coefficient curve 126 35. Constructed curve for K c for alfalfa hay in southern Idaho, the United States using values from Tables 11 and 12 and adjusted using Equations 62 and 65 128 36. K c curve and ten-day values for K c and ET c derived from the g raph for the dry bean crop example (Box 15) 132 37. Constructed basal crop coefficient (K cb ) curve for a dry bean crop (Example 28) using growth stage lengths of 25, 25, 30 and 20 days 142 38. Soil evaporation reduction coefficient, K r 145 39. Determination of variable f ew as a function of the fraction of ground surface coverage (f c ) and the fraction of the surface wetted (f w ) 148 40. Water balance of the topsoil layer 152 41. Depletion factor for different levels of crop evapotranspiration 166 42. Water stress coefficient, K s 167 43. Water balance of the root zone 169 44. The effect of soil salinity on the water stress coefficient K s 181 45. Different situations of intercropping 198 46. Mean evapotranspiration during non-growing, winter periods at Kim berly, Idaho, measured using precision weighing ly simeters 210 Lengths of crop development stages for v arious planting periods and climatic regions 104 12. Classification of rainfall depths 115 14. K c ini for rice for various climatic conditions 121 15. Empirical estimates of monthly wind speed data 124 16.

Typical values for RH min compared with RH mean for general clim atic classifications 124 17. General guidelines to derive K cb from the K c values listed in Table 12 141 19. Typical soil water characteristics for different soil types 144 20. Common values of fraction f w of soil surface wetted by irrig ation or precipitation 149 21. Common values of fractions covered by vegetation (f c ) and exposed to sunlight (1- f c ) 149 22. Ranges of maximum effective rooting depth (Z r ), and soil water depletion fraction for no stress (p), for common crops 163 23. Salt tolerance of common agricultural crops as a function of the electrical conductivity of the soil saturation extract at the threshold when crop yield first reduces below the full yield potential (EC e, threshold ) and when crop yields becomes zero (EC e, no yield ).Calculation sheet for net radiation (R n ) 53 11. Calculation sheet for ET o (FAO Penman-Monteith equation) 67 12. Description of Class A pan 84 13. Description of Colorado sunken pan 85 14. Demonstration of effect of climate on K c mid for tomato crop g rown in field 123 15. Case study of a dry bean crop at Kimberly, Id aho, the United States (single crop coefficient) 130 16. Case study of dry bean crop at Kimberly, Id aho, the United States (dual crop coefficient) 158 17. Measuring and estimating LAI 186 18. Measuring and estimating f c eff 187 Determination of solar radiation from measured duration of sunshine 50 11. Determination of net longwave radiation 52 12. Determination of net radiation 53 13. Determination of soil heat flux for monthly periods 55 14. Adjusting wind speed data to standard height 56 15. Determination of solar radiation from temperature data 61 16. Determination of net radiation in the absence of radiation data 62 17. Determination of ET o with mean monthly data 70 18. Determination of ET o with daily data 72 19. Determination of ET o with hourly data 75 20. Determination of ET o with missing data 77 21.
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Determination of ET o from pan evaporation using tables 83 22. Determination of ET o from pan evaporation using equations 86 23. Estimation of interval between wetting ev ents 116 24. Graphical determination of K c ini 116 25. Interpolation between light and heavy w etting events 119 26. Determination of K c ini for partial wetting of the soil surface 120 27. Determination of K c mid 125 28. Numerical determination of K c 133 29. Selection and adjustment of basal crop coefficients, K cb 136 30. Determination of daily values for K cb 141 Determination of the evapotranspiration from a bare soil 146 32. Estimation of crop evapotranspiration with the dual crop coefficient approach 154 36. Determination of readily available soil water for various crops and soil ty pes 166 37. Effect of water stress on crop evapotranspiration 168 38. Irrigation scheduling to avoid crop water stress 172 39. Effect of soil salinity on crop evapotranspiration 182 40. First approximation of the crop coefficient for the mid-season stag e for sparse vegetation 185 41. Estimation of mid-season crop coefficient 190 42. Estimation of mid-season crop coefficient for reduced ground cov er 191 43. Estimation of K cb mid from ground cov er with reduction for stomatal control 192 44.Effects of surface mulch 197 46. Intercropped maize and beans 200 47. Overlapping vegetation 201 Relative humidity (RH) 35 11. Saturation vapour pressure (e s ) 36 13. Actual vapour pressure derived from psychrom etric data (e a ) 37 16. Psychrometric constant of the (psychrometric) instrum ent (.Actual vapour pressure derived from RH max (e a ) 39 19. Actual vapour pressure derived from RH mean (e a ) 39 20. Conversion form energy to equivalent ev aporation 44 21. Extraterrestrial radiation for daily periods (R a ) 46 22. Conversion from decimal degrees to radians 46 23. Inverse relative distance Earth-Sun (d r ) 46 24. Solar declination ( ? ) 46 25. Sunset hour angle - arccos function ( ? s ) 46 26.

Sunset hour angle - arctan function ( ? s ) 47 27. Parameter X of Equation 26 47 28. Extraterrestrial radiation for hourly or shorter periods (R a ) 47 29. Solar time angle at the beginning of the period ( ? 1 ) 48 Solar time angle at the end of the period ( ? 2 ) 48 31. Solar time angle at midpoint of the period ( ? ) 48 32. Seasonal correction for solar time (S c ) 48 33. Parameter b of Equation 32 48 34. Daylight hours (N) 48 35. Solar radiation (R s ) 50 36. Clear-sky radiation near sea level (R so ) 51 37. Clear-sky radiation at higher elev ations (R so ) 51 38. Net solar or net shortwave radiation (R ns ) 51 39. Net longwave radiation (R nl ) 52 40. Net radiation (R n ) 53 41. Soil heat flux (G) 54 42. Soil heat flux for day and ten-day periods (G day ) 54 43. Soil heat flux for monthly periods (G month ) 54 44. Soil heat flux for hourly or shorter periods during daytime (G hr ) 55 46. Soil heat flux for hourly or shorter periods during nighttime (G hr ) 55 47. Adjustment of wind speed to standard height (u 2 ) 56 48. Estimating actual vapour pressure from T min (e a ) 58 49. Importing solar radiation from a nearby weather station (R s ) 59 50. Estimating solar radiation from tem perature differences (Hargreaves’ formula) 60 51. Estimating solar radiation for island locations (R s ) 62 52. 1985 Hargreaves reference evapotranspiration equation 64 53. FAO Penman-Monteith equation for hourly time step 74 54. Actual vapour pressure for hourly time step 74 55. Deriving ET o from pan evaporation 79 56. Crop evapotranspiration (ET c ) 90 57. Dual crop coefficient 98 58. Crop evapotranspiration - single crop coefficient (ET c ) 103 59. Interpolation for infiltration depths between 10 and 40 mm 117 60. Adjustment of K c ini for partial wetting by irrigation 119 61. Irrigation depth for the part of the surface that is wetted (I w ) 119 62. Climatic adjustment for K c mid 121 Interpolation of K c for crop development stage and late season stag e 132 67.

Relation between grass-based and alfalfa-based crop coefficients 133 68. Ratio between grass-based and alfalfa-based K c for Kimberly, I daho 134 69. Crop evapotranspiration - dual crop coefficient (ET c ) 135 70. Climatic adjustment for K cb 136 71. Soil evaporation coefficient (K e ) 142 72. Upper limit on evaporation and transpiration from any cropped surface (K c max ) 143 73. Maximum depth of water that can be evaporated from the topsoil (TEW) 144 74. Evaporation reduction coefficient (K r ) 146 75. Exposed and wetted soil fraction (f ew ) 147 76. Effective fraction of soil surface that is covered by vegetation (f c ) 149 77. Daily soil water balance for the exposed and wetted soil fraction 152 78. Limits on soil water depletion by evaporation (D e ) 153 79. Drainage out of topsoil (DP e ) 156 80. Crop evapotranspiration adjusted for water stress - dual crop coefficient 161 81. Crop evapotranspiration adjusted for water stress - single crop coefficient 161 82. Total available soil water in the root zone (TAW) 162 83. Readily available soil water in the root zone (RAW) 162 84. Water stress coefficient (K s ) 169 85. Water balance of the root zone 170 86. Limits on root zone depletion by evapotranspiration (D r ) 170 87. Initial depletion (D r,i-1 ) 170 88. Deep percolation (DP) 171 89. Yield response to water function (FAO Irrigation and Drainage Paper No. 33) 176 91. Water stress coefficient (K s ) under saline conditions 177 92. Water stress coefficient (K s ) under saline and water stress conditions 177 93. Soil salinity (EC e ) predicted from leaching fraction (LF) and irrigation w ater quality (EC iw ) 180 94. K c adj for reduced plant coverage 184 Adjustment coefficient (from LAI) 185 96. Adjustment coefficient (from f c ) 185 97. K (cb mid) adj from Leaf Area Index 186 98. K (cb mid) adj from effective ground cover 187 99. K cb full for agricultural crops 189 100. K cb full for natural vegetation 189 101. K cb h for full cover vegetation 189 102.

Adjustment for stomatal control (F r ) 191 103. Water stress coefficient (K s ) estimated from yield response to water function 194 104. Crop coefficient estimate for intercropped field (K c field ) 199 105. Crop coefficient estimate for windbreaks (K c ) 203 It al so examines the factors that affect evapo transpiration, th e units in which it is no rmally expresse d and the way in which it can be determined. E VAPOTRANSPIRATION PROCESS The combination of two separate processes whereby water is lost on t he one hand from the soil surface by evaporation and on the other hand from the crop by transpirat ion is referred to as evapotranspiration (ET). Evaporation Evaporation is the process whereby liquid water is converted to water vapour (vaporizati on) and removed from the evaporating surface (vapour removal). Water evaporates from a vari ety of surfaces, such as lakes, rivers, pavements, soils and wet vegetati on. 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 am bient temperature of the air provide this energy. The driving force to remove water vapour from the evaporating surface is t he 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 s low down and might sto p if the wet air is no t 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 cl imatological 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 evaporat ing surface are other factors that affect the evaporation process.

Frequent rains, irrigati on and water transported upwards in a soil from a shallow water table wet t he soil surface. Where the soil is able to suppl y water fast enough to satisfy the evaporation demand, the evaporati on from the soil is determined only by the meteorological conditions. However, where the int erval between rains and irrigation becomes large and the ability of the soil to conduct moisture to near the surface is small, the water content in the t opsoil 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, evaporat ion decreases rapidly and may cease almost completely w ithin a few days. Crops predominately lose their water t hrough 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 root s and transported through the plant. The vaporization occurs within t he leaf, namely in the intercell ular spaces, and the vapour exchange with the atmosphere is controlled by the stomatal aperture. Nearly all water taken up is lost by transpira tion and only a tiny f raction is used within the plant. Transpiration, like direct evaporation, depends on t he energy supply, vapour pressure gradient and wind. Hence, radiation, air temperature, air humidity and wind t erms should be considered whe n assessing transpiration. T he soil water con tent and the ability of the soil to conduct water to the roots also determine the t ranspiration rate, as do waterlogging and soil water salinity. Th e transpiration rate is also influ enced by crop characteristic s, environmen tal aspects and c ultivation practic es. Differe nt kinds of plants may ha ve different trans piration rates.

Not only the type of crop, but also the crop development, environment and management should be considered when assessing transpiration. Evapotranspiration (ET) Evaporation and transpiration occur simultaneously and there is no easy way of disti nguishing between the two pro cesses. Apa rt from the water av ailability in the topso il, the evaporation from a cropped soil is mainly determined by t he fraction of the solar radiation reaching the soil surface. This fraction decreases over the growing period as the crop develops and t he 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 i s well developed and completely covers the soil, transp iration becomes the main proces s. In Figure 2 the partitioning of evapotranspiration into evaporation and transpi ration 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 cov er more than 90 of E T comes from trans piration. U NITS The evapotran spiration rate is n ormally express ed 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 10 000 m 2 and 1 mm is equal to 0.001 m, a loss of 1 mm of water corresponds to a loss of 10 m 3 of water per hectare. In other words, 1 mm day -1 is equivalent to 10 m 3 ha -1 day -1. 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 ( ? ), is a function of the wat er temperature. ET, the latent hea t flux. If 80 of the energy is used to vaporize water, how large could the depth of evaporation be.

The relat ed ET concepts presented in Figure 3 are discussed in the section on evapotranspiration concept s. Weather parameters The principal weather parameters affecting evapotranspiration are radi ation, air temperature, humidity and wind speed. Several procedures have been developed t o assess the evaporation rate from these parameters. The evaporation power of the atm osphere is expressed by the reference crop evapotranspiration (ET o ). The reference crop evapotranspiration represents the evapotranspiration from a standardized vegetated surface. The ET o is described in detail later in this Chapter an d in Chapters 2 an d 4. Crop factors The crop type, variety and development stage should be considered when assessing the evapotranspiration from crops grown in large, well-managed fi elds. Differences in resist ance to transpiration, crop height, crop roughness, reflecti on, ground cover and crop root ing characteristics result in different ET l evels in different types of crops under identical environmental conditions. Crop evapotranspiration under standard conditions (ET c ) refers to the evaporating demand from crops that are grown in large fields under optimum soil water, excellent management and environmental conditions, and achi eve full production under the given climatic conditions. Management and environmental conditions Factors such as soil s alinity, poor land fertility, limited application of fertilizers, the presence of hard or impenetrable soil horizons, the absence of control of di seases and pests and poor soil management may limit the crop development and reduce the evapotranspirat ion. 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 a nd the type of so il.

On the other han d, 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 considerati on should be given to the range of management practices that act on the cl imatic 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 th e field. Soil evaporation in a young orchard, where trees are widely spaced, can be reduced by using a well-designed drip or trickle irrigatio n system. T he drippers apply water dir ectly to the soil ne ar trees, ther eby leaving the major part of the soil surface dry, and limiting the evaporation losses. The use of mulches, espe cially when the cro p is small, is ano ther way of subs tantially reducing soil evaporation. Anti-transpirants, such as stom ata-closing, film-forming or reflecting materi al, reduce the water losses from the crop and hence the transpirat ion rate. The adjustment reflect s the effect on crop evapotranspirati on of the environmental and management conditions in the fiel d. E VAPOTRANSPIRATION CONCEPTS Distinctions are made (Figure 4) between reference crop evapotranspiration (ET o ), crop evapotranspiration under standard conditions (ET c ) and crop evapotranspiration under non- standard conditions (ET c adj ). ET o is a climatic parameter expr essing the eva poration power o f the atmosphere. ET c refers to the evapotranspiration from excellently managed, large, well- watered fields that achieve full production under the given climatic conditions.