1. a. . . .1. a \LI 1 $005.1 . "ml... 594...: f. fifiwmp . ). t . I. “70.“. , r1 ...: ‘I . ‘ ~ 5.2. . 3‘.£.I:\th. . w. J I I-‘h‘ I'llxulv-v- 9.. 1L t; o .- Surnllu. ; 3:7! riff.”- .)..~.!?Pv. 7 L.» J an “3. .1 I . .5 3- . so) . :t! V. . . u \r. h P. .1 3’. I V 1' I? 1.1; i “J; B a) ..\ v... :A 3!. .2. ’5'! ,4. . r.l.. p. . .lo). Mw‘ésbl UNI IVERSITY LIBRARlES 11111111111111111111111 31 1293 00609 116 11 LIBRARY Michigan State University This is to certify that the thesis entitled Evaluating Daily Evapotranspiration Estimation Methods: A Comparison of Potential Evapotranspiration Equations and Irrigation Scheduling Models with Weighing Lysimeter Measurement presented by Thomas Russell Olmsted has been accepted towards fulfillment of the requirements for M.S. . A.T.M.. degree 1n ajor ofessor Acting Chairperson Damm— 0—7639 MS U is an Affirmative Action/Equal Opportunity Institution PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or baton date due. DATE DUE DATE DUE DATE DUE M M FEB251W ‘ MSU Is An Affirmative ActiorVEqual Opportunity Institution EVALUATING DAILY EVAPOTRANSPIRATION ESTIMATION METHODS: A COMPARISON OF POTENTIAL EVAPOTRANSPIRATION EQUATIONS AND IRRIGATION SCHEDULING MODELS WITH WEIGHING LYSIMETER MEASUREMENT BY Thomas Russell Olmsted A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1990 0054772 ABSTRACT EVALUATING DAILY EVAPOTRANSPIRATION ESTIMATION METHODS: A COMPARISON OF POTENTIAL EVAPOTRANSPIRATION EQUATIONS AND IRRIGATION SCHEDULING MODELS WITH WEIGHING LYSIMETER MEASUREMENT BY Thomas Russell Olmsted Four popular methods of calculating a potential evapotranspiration (ET) rate were evaluated. The calculated rates were compared to measured ET of alfalfa from a large weighing lysimeter. The affect of climatic data collected from two differently exposed weather stations at the same geographical location was also evaluated. The comparison incorporated various methods of calculating the vapor pressure deficit term in the "combination" potential ET equations. Crop ET from two irrigation scheduling programs and the CERES-Maize crop model were compared to actual ET rates of maize from a large weighing lysimeter. The FAO modified Penman equation performed well at estimating daily potential ET. The CERES-Maize model estimated daily crop ET of corn well, while the irrigation scheduling programs had limitations in their method of predicting the crop physiological maturity which affected the estimated crop ET rate late in the growing season. To my loving wife and best friend, Sylvia. iii ACKNOWLEDGMENTS I would like to gratefully acknowledge the assistance of my guidance committee chairperson, Dr. Ted Loudon, whose extensive support and trust has made this research possible. Special appreciation goes to Dr. Joe Ritchie and Dr. Fred Nurnberger for being members on my guidance committee and whose valuable suggestions helped to shape this research topic. Special thanks goes to John Gorentz whose computer programs simplified extraction of data needed for this research and to all the people at the Kellogg Biological Station for their support during various stages of the research. I extend warm appreciation to my parents, Donald and Lillian Olmsted, for supporting the paths I have chosen and having faith that someday they will lead somewhere. Finally, I would like to especially thank my wife, Sylvia. Without her encouragement, patience, love, and support this achievement could not have been a reality. Because she was the basic motivation behind this work, I dedicate this work to her. iv TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . LIST OF FIGURES . . . . . . . . . I. INTRODUCTION . . . . . . . . Background . . . . . . . . Objectives . . . . . . . . II. LITERATURE REVIEW . . . . . . Crop Water Requirements Soil Factors . . . Plant Factors . . Moisture Stress . . Measuring Evaporation . . Water Balance Measurements Sampling Soil Profile Moistur Lysimeters . . . . . Micrometeorological Measurements Wind Profile . . . . . . Energy Balance. . . . . . Eddy Correlation . . . . . Estimating Potential and Reference Evapotranspiration . . . . . Empirical Methods . . . . Crop ET and Crop Coefficients. Temperature Correlation Methods Evaporation Pan Correlations . Radiation Correlation Methods Combination Methods . . . . Penman Formula . . van Bavel Modification FAG-24 Modification . Resistance Model . . . Equilibrium Evaporation Ritchie Model . . . . III. METHODS . . . . . . . . . . Research Method - Objective 1 Statistical Analysis . . Research Method - Objective 2 Statistical Analysis . . Research Method - Objective 3 Statistical Analysis . . vii ix bid 60 60 64 65 70 71 72 IV. RESULTS . . . . . . . . . . . . . . Climatic Data . . . . . . . . . . . Net Radiation . . . . . . . . . . Vapor Pressure Deficit . . . . . . . Potential Evapotranspiration Estimation . . Penman Formula . . . . . . . . FAO Modified Penman Formula . . . . . . Priestley-Taylor Equilibrium Formula . . . CERES-Maize Potential Equation Formula . . Irrigation Scheduling . . . . . . . . V. CONCLUSION AND RECOMMENDATIONS . . . . . . Climatic Data Research Findings . . Potential Evapotranspiration Research Findings Irrigation Scheduling Research Findings . . Limitations of this Research . . . . . . Recommendations for Future Research . . . LIST OF REFERENCES . . . . . . . . . . . . vi 74 74 100 106 112 114 122 129 135 138 154 154 155 156 156 158 159 Table 10. 11. 12. 13. 14. 15. 16. Statistics Statistics (%). Statistics Statistics Results of Results of humidity. Results of Results of radiation. Ranking by LIST OF TABLES of daily temperature comparison (°C). of daily relative humidity comparison of wind speed comparison (m/s). of solar radiation comparison (MJ/m’). calculation methods Ranking by calculation methods Ranking by mean comparison tests - temperature. mean comparison tests - relative mean comparison tests - wind speed. mean comparison tests - solar means of 1986 vapor pressure deficit (kPa) (n = 82). means of 1987 vapor pressure deficit (kPa) (n = 142). means of 1988 vapor pressure deficit (kPa) (n = 118). calculation methods Vapor pressure deficit equations compared. Summary statistics from the days used ET equation comparison. Correlation and regression statistics in potential of measured ET versus potential ET estimated from Penman equation (mm). Correlation and regression statistics ET versus potential ET estimated from equation (mm). of measured FAG-Penman Correlation and regression statistics of measured ET versus potential ET estimated from FAG-Penman equation with not-recommended vapor pressure deficit methods (mm). vii Page 75 76 77 78 79 80 81 82 107 108 109 111 113 116 124 127 17. 18. 19. Correlation and regression statistics of measured ET versus potential ET estimated from Priestley- Taylor method (mm). 134 Correlation and regression statistics of measured ET versus potential ET estimated from CERES-Maize equilibrium ET equation (mm). 139 Correlation and regression statistics of ET calculated from models and measured lysimeter ET (mm) (n=79). 143 viii 10. 11. 12. 13. 14. 15. 16. LIST OF FIGURES Example of crop curve. Lysimeter location (Kellogg 1986 daily mean temperature temperature during daylight (LYS station). 1987 daily mean temperature temperature during daylight (LYS station). 1988 daily mean temperature temperature during daylight (LYS station). 1986 relative humidity daily comparison between stations. 1987 relative humidity daily comparison between stations. 1988 relative humidity daily comparison between stations. 1986 relative humidity daily between stations. 1987 relative humidity daily comparison between stations. 1988 relative humidity daily comparison between stations. 1986 relative humidity daily comparison between stations. 1987 relative humidity daily comparison between stations. 1988 relative humidity daily comparison between stations. 1986 wind speed daily mean ( between stations. 1987 wind speed daily mean ( between stations. ix Biological Station). (TEMP24) and mean hours (TEMPDAY) (TEMP24) and mean hours (TEMPDAY) (TEMP24) and mean hours (TEMPDAY) mean (RH24) mean (RH24) mean (RH24) maximum (RHMAX) maximum (RHMAX) maximum (RHMAX) minimum (RHMIN) minimum (RHMIN) minimum (RHMIN) WINDZ4) comparison WINDZ4) comparison Page 34 61 83 84 85 86 87 88 89 90 91 92 93 94 95 96 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 1988 wind speed daily mean (WINDZ4) comparison between stations. 1986 total solar between stations 1988 total solar between stations Regression of net SOLRAD) radiation Regression of net SOLRAD) radiation and net and net over a radiation (SOLRAD) comparison radiation. radiation (SOLRAD) comparison radiation. radiation on total solar (LYS corn crop (1986). radiation on total solar (LYS over alfalfa (1988). Means of vapor pressure deficits from different methods calculation (see 1987 1988 1987 1988 1987 FAO equation 1988 FAO equation 1987 FAO equation 1988 FAO equation 1987 FAO equation 1988 FAO equation Penman Penman Penman Penman potential ET potential ET potential ET potential ET modified Penman #7. modified Penman #7. non-recommended #6. non-recommended #6. non-recommended #3. non-recommended #3. Table 12). #2. #2. #6. #6. equation equation equation equation potential ET potential ET VPD potential ET VPD potential ET VPD potential ET VPD potential ET 1987 Priestley-Taylor potential ET equation #4. 1988 Priestley-Taylor potential ET equation #4. 1987 CERES-Maize potential ET equation. 1988 CERES-Maize potential ET equation. MSU-CBS "spreadsheet" irrigation scheduling program ET. 97 101 102 104 105 110 118 119 120 121 125 126 130 131 132 133 136 137 140 141 144 38. 39. 40. 41. 42. 43. 44. 45. MSU-CES "spreadsheet" daily ET comparison with lysimeter ET. MSU-CES "spreadsheet" scheduling program ET and lysimeter ET daily accumulations (n=79). MSU-SCS "Scheduler" irrigation scheduling program ET. MSU-SCS "Scheduler" program daily ET comparison with lysimeter ET. MSU-SCS "Scheduler" program and lysimeter daily ET accumulations (n=79). CERES-Maize model ET. CERES-Maize model daily ET comparison with lysimeter ET. CERES-Maize model and lysimeter ET daily accumulations (n=88). xi 145 146 147 148 150 151 152 153 I. INTRODUCTION Background A good understanding of the water usage of agricultural crops benefits the farm manager who irrigates. Applying less than the needs of the crop may cause plant water stress with the possibility of reducing harvest yields. Excess application wastes energy and can lead to rapid leaching of nutrients into the ground water. In the Lake States, irrigation is considered supplemental. Natural precipitation supplies the majority of the moisture used by growing crops in most years with irrigation being used when rainfall is not adequate or reliable particularly during the crop’s critical growth stage. The need for supplemental irrigation is more pronounced on coarse textured soils because of their lower water holding capacity. Irrigation scheduling has been developed as a tool to address the management issues of irrigation timing, water application amounts, and impacts of irrigation on groundwater quality given uncertain weather conditions. The various means to schedule irrigations include monitoring the soil water status in the soil profile with tensiometers or other devices, determining plant water stress using infrared thermometry to measure canopy temperature, and the use of models that compute a soil water balance based on the calculation of crop evapotranspiration (ET) from climatic data. Personal computers have made scheduling with the models practical. Most irrigation scheduling computer programs contain a function which calculates a reference ET rate based on measured local climatic data. From the calculated reference ET rate, the water evaporative demand for a specific crop is determined by multiplying the reference ET rate by a crop coefficient which is dependent on the stage of growth and crop characteristics. Based on the water holding capacity of the soil and the depth of root zone, a water balance is calculated to find the amount of soil water available for crop use. Usually, if the amount present in the soil is 50% of available soil water or less a decision is made to irrigate. Various methods have been developed to calculate the ET rate differing mainly in the variables used and the theoretical and physical principles for including those variables. Many are sensitive to the type of climate where they are used. Obtaining the required climatological data in a timely manner and in the form needed for an ET equation in an irrigation scheduling program has not always been easy or simple. With the development of micro-dataloggers, there has been an increase in the number of automated weather stations available in irrigated areas to download the necessary climatological data into irrigation scheduling computer programs. This means, where in the past ET equations relied on empirical functions to estimate certain weather variables, they can now be measured directly. Also, there is more flexibility in the time interval over which a variable is integrated. Since early plant water loss studies by Briggs and Shantz (1913, 1914 and 1916), various means have been proposed for the measurement of ET. Currently, actual field crop ET can be computed from measurements of temperature and vapor gradients with very sensitive temperature and humidity sensors above the crOp and measured with very accurate weighing lysimeters. Weighing lysimeters consist of an isolated block of soil in a field with a large area of the same crop surrounding it as growing on it. The mass change of the soil block is accurately measured, usually by an electronic load cell and recorded by a micro-datalogger. The high construction and management costs of weighing lysimeters make them impractical to be used for irrigation scheduling in farm fields. Large weighing lysimeters have been constructed at many agricultural field stations. These research lysimeters are used to calibrate certain ET equations incorporated in the irrigation scheduling programs and to compare different methods of calculating an ET rate to actual ET rates of various crops in different climatic areas. Objectives The overall goal of this research is to determine how variables from weather stations of different exposures and various vapor pressure deficit terms affect the estimation of potential ET calculated using different equations and how accurately irrigation scheduling programs estimate crop ET of corn on a weighing lysimeter in Michigan. The specific objectives of this research are: 1. To determine significant difference and variance of climatic variables measured at a weather station in an irrigated area and a non-irrigated area in the same geographical location. To evaluate daily potential ET rates from various potential ET equations and comparing the calculated ET to actual measured weighing lysimeter ET under "potential" evaporating conditions. To compare estimated daily crop ET rates from irrigation scheduling computer programs and a crop growth model with actual weighing lysimeter ET. II. LITERATURE REVIEW Crop water Requirements Evapotranspiration (ET) is the evaporation of water from soil and plant surfaces (transpiration) of vegetated land areas. In dry climates, it is possible for plants to consume hundreds of metric tons of water for each metric ton of vegetative growth. This insatiable thirst for water is not a consequence of an essential plant physiological process, but a function of the evaporative cooling demand of the climate in which the plants live (Hillel, 1982). Essentially, ET involves the net upward flux of water vapor, from the liquid-air interfaces of plant and soil surfaces to bulk air by molecular diffusion and turbulent eddy movement. This transfer initially begins as molecular diffusion across a thin boundary layer surrounding the plant and soil surface. Further out from the boundary layer, turbulent eddy transport is the primary mechanism for water vapor transport. Soil Factors Soil water available for ET is a function of soil texture, structure and organic matter with soil texture being the dominate influence at any one soil moisture tension. The higher the clay content of a soil the greater the moisture holding capacity it has due to the more uniform distribution of micropores compared to a sandy soil. 6 The water available to plants is generally expressed as the water content in the soil between field capacity and permanent wilting point. Field capacity has been used to describe the upper moisture content of a soil which has been saturated and all free drainage has ceased. Even though field capacity is thought of as a "constant" (-33 kPa matric potential) describing a dynamic situation, using it allows categorizing of the soil water content in a reproducible manner (Slatyer, 1967). The permanent wilting point is based upon the wilting coefficient of Briggs and Shantz (1912) and has been referred to as the lower limit of moisture available to plants. Usually this "constant" (-1500 kPa matric potential) is determined in the laboratory by sealing the soil of growing plants and allowing the plants to deplete the soil moisture until a threshold is reached where the plants will not recover turgidity after being placed in a humid environment. Available water is then defined as the soil water content between -33 and -1500 kPa. Problems of space-time relationships arise when using an exact physical description of the available soil water because root depths and densities change with time and there is no experimental method to measure microscopic variation of moisture gradients and fluxes of water in the immediate vicinity of the roots (Slatyer, 1967). However, the concept has been useful when water content limits need to be set. 7 The concept of extractable water (Ritchie, 1974) attempts to eliminate some of the problems associated with the available water definition. Extractable water is defined as the difference between the highest measured volumetric water content in the field after free drainage and the lowest measured water content when well developed plants are either dead or dormant (Ritchie, 1981). Thus, the available water content is weighted by the root distribution when the lower limit is measured in the field. Plant Factors Only about 1% of the water consumed by plants is used in metabolic processes. The rest is lost as water vapor through transpiration. The amount that is used by the plant for metabolic processes provides hydrogen atoms for the reduction of carbon dioxide in photosynthesis and is used as the solvent and conveyor of transportable ions and compounds within and out of the plant. It also is the structural component of plants, constituting about 90% of the living mass (Hillel, 1982). Water movement from the soil through the plant and into the atmosphere can be regarded as occurring along a gradient of decreasing water potential. The various resistances to be overcome by the water flow can be thought of as coming from the soil matrix, roots, xylem in plant stems, stomata and the aerial boundary layer. Under steady-state conditions, flow through each segment is equal 8 and the potential gradients and resistances are related as follows (Blad, 1983): qw=———=————=——— 111 where qw is the water flow; P P P1, and Pa are the s’ r’ water potentials of soil, root, leaf, and air, respectively: rm is the resistance through the soil to the root surface; rr is the resistance across the root: rx is the xylem resistance; r is the stomatal resistance; and r s a is the aerial boundary layer resistance. This analogy fails if resistances change in response to flow rate. The greatest resistance encountered in this dynamic process is the flow into the vapor phase (Cowen and Milthorpe, 1968). Regulating the flow of vapor when wind is high and boundary layer resistance is low (usual field conditions), comes from the stomatal resistance. Under similar environmental conditions, stomatal resistances differ among species. Alfalfa seems to exert very little canopy resistance to ET when it is well supplied with water (van Bavel, 1967), whereas, sorghum has been shown to use less water perhaps signifying greater stomatal resistance (van Bavel and Ehrler, 1968; Teare g; al;+ 1973). Moisture Stress Typical crops well supplied with water and nutrients will experience only small diurnal water deficits. Under 9 drying soil conditions where higher (more negative) soil matric potential has increased the resistance to moisture movement, stomatal closure will retard transpiration causing an increase in leaf temperature and photosynthesis will probably decrease due to a reduction in CO2 exchange. Further stress will result in the reduction of cell enlargement causing a decrease in plant growth rates. As the soil moisture decreases to the permanent wilting point, tugor pressure will approach zero and plant desiccation will increase until the water supply is renewed or until the death of the plant occurs. Research with corn has shown that moisture stress during the reproductive stage (silking) will have the greatest negative affect on yields (Robins and Domingo, 1953; Denmead and Shaw, 1960). Measuring Evapotranspiration Methods used to estimate the ET rate under field conditions generally fall into the categories of water balance measurements, micrometeorological measurements, and empirical based measurements. The first two methods are based on rationale and physical principles whereas empirical methods are based on model estimates that need to be calibrated by relating the empirical ET to actual ET measurements if reasonable confidence is to be obtained (Tanner, 1967). The methods included in the water balance measurements 10 include soil profile moisture sampling and the use of non- weighing and weighing lysimeters. The micrometeorological methods include the partitioning of the energy balance and the mass transfer methods of eddy correlation and aerodynamic profile measurements. The empirical methods may use a combination of energy balance and mass transfer or may rely on totally empirical relationships between ET and one or more meteorological variables. Water Balance Measurements The water balance involves tracking the changes of the soil moisture over time. By recording the moisture inputs and outputs into and out of a root zone, a water balance equation can be solved for ET: ET = R + I - D - R0 1 68M [2] where ET is the evapotranspiration; R is the rainfall; I is any irrigation; D is the deep percolation or drainage; R0 is the surface runoff; and SSM is the change in soil moisture. By assuming surface runoff (R0) is negligible under field conditions, then with accurate measurements of R, I, D and 63M, ET can be estimated. Over long periods, such as the entire growing season, the change in water content of the root zone is likely to be small in relation to the total water balance, so the sum of rainfall and any irrigation is approximately equal to 11 the sum of ET and drainage. Under shorter periods of time, the change in soil moisture may be large and would need to be measured to obtain accurate estimations of ET. Sampling Soil-Profile Moisture One method to obtain soil-moisture measurements has been to employ the gravimetric sampling method. However, it is laborious, time consuming, and involves destructive sampling of different locations, since the same area cannot be sampled more than once. Recently, soil-moisture sampling using neutron scattering has become the more preferred method (Hillel, 1980). Some advantages of the neutron method are: less experimental error because the same soil is non- destructively sampled each time and the larger volumes of soil sampled in the sphere of influence generally yield in better estimates of soil-moisture than small samples obtained with gravimetric sampling (Nixon and Lawless, 1960). Shortcomings of the neutron method occur when sampling near the soil surface where neutrons escape into the air and are not deflected back to the counter as would be the case when the sphere of influence is completely underneath the surface. Also, wetting fronts are difficult to detect due to the sphere of influence taking an average reading of soil-moisture within the soil volume being measured. Since D is not directly measured, the error in ET is 12 directly proportional to the amount of the drainage error. During the dry season Nixon and Lawless (1960) have found significant downward drainage below the root zone in unsaturated conditions. Robins et a1; (1954) found considerable drainage from a one meter root zone in a fine sandy loam for eight days following irrigation. In some cases, the drainage may account for a tenth or more of the total water balance (Hillel, 1980). Sampling the soil-profile moisture will only give valid results for long periods due to the small amount of soil moisture lost to ET compared with the total amount of moisture held in the soil (Deacon gt gig, 1958). Lysimeters According to Kohnke et a1. (1940) the first lysimeter studies began in Paris in 1688 by De La Hire who was searching for the answer of how groundwater springs were formed. However, Dalton is commonly credited with being the first to install lysimeters back in 1795. The early lysimeters were used primarily to study the amount of percolate. Later, chemical changes of the percolate were studied beginning with Way in 1850. In 1870, Lawes and Gilbert constructed three "drain-gauges" each containing an undisturbed soil profile at Rothamsted, England. The first undisturbed profile, or monolith lysimeter, installed in the United States, which was the weighing type, was constructed and installed at Coshocton, Ohio by the U.S. 13 Soil Conservation Service in 1937. Usually, lysimeters provide confinement of a volume of soil with the purpose of preventing lateral moisture exchange and collecting any percolate for precise measurement (van Bavel, 1961). The soil within a lysimeter can be classified as either filled-in representing a disturbed soil profile or soil block monolith representing an undisturbed soil profile. The filled-in type usually consists of repacked soil which has been excavated according to textural or structural likeness and being replaced into the container to duplicate the density and structure of the existing natural conditions as closely as possible. Reports of disturbed profiles returning to field bulk densities have occurred in as little as one growing season (Ritchie and Burnett, 1968 and Howell g; 31‘, 1985). The monolith lysimeter or undisturbed profile is the most desirable type because it can better represent field conditions. It consists of taking an undisturbed block of soil in situ and isolating it from the rest of the field usually with a steel container. The monolith is taken from a representative part of the field where the lysimeter will be installed and is usually transported to an excavated site for final placement. The lysimeter can also be classified as non-weighing or weighing. The non-weighing lysimeter is unable to measure evaporative flux for short periods, however, it has 14 been used to estimate the ET rate over long periods (Kohnke g; a1., 1940). Van Bavel and Myers (1962) listed five purposes of a weighing lysimeter: (a) To provide direct measurement of evaporation and transpiration from soil surfaces on which plants are growing to permit studies of factors affecting these processes. (b) To provide an absolute and accurate measurement of evaporative flux as a primary process in research on the physics of atmosphere close to the ground. (c) To serve as a standard of comparison for evaluating indirect methods of measuring or predicting ET. (d) To accurately measure loss of water from bare soil in studies of upward movement of water in soil as a result of surface drying. (e) To serve as an accurate standard of comparison in evaluating instruments designed to measure precipitation in the form of rain or dew. In all cases, a lysimeter should be a representative sample of the larger environment. This includes the soil in the lysimeter having the same thermal, moisture, and mechanical properties as the environment and the vegetation on the lysimeter having the same height, density, and physiological well-being as the environment (Tanner, 1967). It is important the representative area around the lysimeter be large, especially in arid areas where advective conditions are common (Aboukhaled at all, 1982). The management and application of inputs (gig; fertilizer and irrigation) to the lysimeter should be the same as what is applied to the larger environment if the lysimeter is to estimate the ET rate of the larger area. 15 In a disturbed profile lysimeter, percolation, moisture retention, and root distribution are most likely to be different than the original soil profile. In cases where the maximum ET rate is to be determined, these are not critical factors where root growth is normal. However, in cases where the actual ET rate is to be measured, the consequences of the different soil conditions in the lysimeter compared to the surrounding field could include more soil moisture available for ET and a larger root zone (Pelton, 1961). Because of upward extended lips of most lysimeter soil containers, runoff is prevented from leaving or entering except under the most intense precipitation events. Due to its construction, a lysimeter prevents normal vertical flow because the bottom results in a moisture tension profile different than in the surrounding environment. To duplicate the moisture tension of a normal profile, an artificial tension may need to be maintained in the bottom of the lysimeter. Where lysimeters are deep enough to allow normal root development, tension should not be needed (van Bavel, 1961). Determination of ET with non-weighing lysimeters usually involves tracking the change in soil moisture with a neutron soil moisture probe and collecting the drainage amount for a specified length of time to solve for ET in the water balance equation. Weekly estimations of ET have been made with reasonable accuracy when the neutron l6 moisture meter is used to measure changes in soil moisture in non-weighing lysimeters (Tanner, 1967 and McGuinness gt git, 1961). Weighing lysimeters are the best method for giving unbiased information on the time rate loss of water from a surface over short periods of time (van Bavel and Reginato, 1965). They differ from non-weighing lysimeters in that the mass change of the soil and soil moisture is precisely measured, usually electronically, at different time intervals. This allows accurate short period estimates of ET. The soil container is usually placed inside a second container which retains the surrounding soil and allows some kind of weighing mechanism to be placed underneath. Weighing lysimeters differ in their mode of weighing with the most common being the mechanical balance (Ritchie and Burnett, 1968; van Bavel and Myers, 1962; Pruitt and Angus, 1960: Harold and Dreibelbis, 1958; Howell gt alt, 1985; Armijo gt alt, 1972; and Bhardwaj and Sastry, 1979). Another less common mode of weighing is the use of hydraulic load cells (Black gt B11. 1968 and Hanks and Shawcroft, 1965). A potential problem among weighing lysimeters has been the gap between the soil container wall and the outer container wall. This non-homogeneity in the soil surface can set up small scale advection and is important that it is kept small in relation to the total area of the lysimeter soil surface (Aboukhaled gt alt, 1982). l7 Describing the effective area of the lysimeter which the total volume of water loss is divided by to obtain the equivalent ET depth takes into account the type of11 vegetation on the lysimeter and the shape of the soil container. The lysimeter area must be large compared to the scale of non-homogeneity in the vegetation. For spatially homogeneous crops, such as forages, the area can be smaller than when the non-homogeneity of crop cover is large as with row crops (Tanner, 1967). In row crop studies it is important that the lysimeter be rectangular with the width dimension equal to a multiple of the field row width (Ritchie and Burnett, 1968). Another difficulty in assessing the effective area is caused by the overlap between internal and external vegetation which can effect the interception and channeling of precipitation at the lysimeter perimeter (Denmead and McIlroy, 1970). Micrometeorological Measurements Micrometeorological methods provide a measurement of the flux density of water vapor in the boundary layer of the atmosphere. The micrometeorological methods in greatest use are wind profile, energy balance, and eddy correlation. Wind Profile A means by which the vertical flux of water vapor due to turbulent diffusion can be estimated is the use of the 18 wind profile aerodynamic method. Vertical flux of mass (water vapor) near the earth’s surface is driven by turbulence that is produced by the frictional retardation of horizontal wind moving across the ground. The flux can be considered a continuous absorption of momentum (mass x velocity) from the horizontal wind, suggesting a continuous downward flux of momentum from the air flow to the surface. The size of the momentum flux in relation to wind speed and surface roughness determines the effectiveness of turbulence in transporting water vapor and also other properties, such as carbon dioxide and heat. At the surface, the horizontal momentum is zero and increases with height proportional to the velocity. The vertical flux of momentum, also called the shearing stress is given by: t = p KM (6U/62) 131 where t is the horizontal momentum transferred to the surface per unit area per unit time; p is density of air; KM is the eddy transfer coefficient for momentum; u is wind speed; and z is height above the ground. If it is assumed that momentum is carried by the same eddies as water vapor then KM = KW and if sufficient fetch of a continuous surface allowing reliable wind profile measurements under neutral atmospheric stability conditions exists, then the shearing stress can be represented by: 19 t=r>w112 [41 where u*2 is the friction velocity derived from the shape of the wind profile. In a well developed boundary layer, the eddy transfer coefficient of momentum is proportional to height and wind velocity as: KM = ku*z [5] where k is the dimensionless von Karman's constant (0.4). The shape of an adiabatic profile is given by: 6u/6z = u*/kz [6] and since u* is constant at any instant, integration yields u = (u*/k) 1n (2/20) [7] where 20 is the roughness length and z is the height in a logarithmic profile under neutral conditions at which the wind would be zero. The effectiveness of turbulent transfer is then directly related to the degree of roughness, as specified by 2 which is generally an order 0 of magnitude smaller than the actual height of the roughness elements (Priestley, 1959). In the case where a crop extends the surface above the ground, it is necessary to subtract from 2 the height, d, 20 into the crop where the zero-wind reference surface is displaced. Then under conditions of neutral atmospheric stability (adiabatic conditions) and under uniform rough surface conditions such as crop vegetation, wind is represented by: u(z) = (u*/k) 1n[(z - d)/zol [8] where d is called the zero plane displacement and can be considered to indicate the mean level at which momentum is absorbed by individual elements in the plant community. The zero plane displacement can be found by plotting u(z) against 1n (2 - d') where values are substituted for d'. The value of d' that results in a straight line is the value of d required. Usually d turns out to be 0.6h to 0.8h where h is the actual height of the vegetation (Monteith, 1973). The surface roughness 20 is then found as the y-intercept of this line, where u(z) is zero. The measurement of the wind profile data should occur under neutral atmospheric stability when estimating the parameters, 20 and d. Likewise, adequate upwind fetch is essential so that the boundary layer developed is equilibrated with the surface of interest. Several empirical approximations have been developed to determine d and z Monteith (1973) suggests using: 0. d = 0.63 h and 20 = 0.13 h [9]. 21 Szeicz gt £11 (1969) developed the regression equation: 1n 20 = 1n h - 0.98 [10]. For maize, Jacobs and Boxel (1988) found: d = 0.84 h - 0.14 and 20 = 0.25(h - d) [11]. Munro and Oke (1973) compared several empirical formulae and found d could be estimated well by the methods presented, but zo was less easily predicted. The use of empirical expressions are useful as checks for the order of magnitude of 20 and d, but as yet they cannot be applied universally or substituted generally for direct field determinations (Rosenberg, 1974). In non-neutral atmospheric conditions the shape of the wind profile deviates from the logarithmic ideal. Under stable conditions, turbulence is damped. In unstable conditions turbulence is increased because of buoyancy effects and can be expressed by parameters that depend on the relation between the production of energy by buoyancy forces and the dissipation of energy by mechanical turbulence (Monteith, 1973). The two most established parameters are the Richardson number Ri and the and the Monin-Obukhov length. The Richardson number Ri, can be calculated directly from gradients of temperature and wind speed as: 22 R1 = g(66/62)/T(6U/6z)2 [12] where g is the acceleration due to gravity; (66/6z) and (6U/62) are the vertical gradients of mean potential temperature and mean horizontal wind speed: and T is the mean absolute temperature. The Monin-Obukhov length L, is a function of the corresponding fluxes of heat and momentum: L = - p cp T u*3/k g H [13] where p is the density of the air; C is the specific heat P of air; T is the absolute temperature; u* is the frictional velocity; k is the von Karman constant; 9 is acceleration due to gravity; and H is the sensible heat flux. The diffusivity coefficients of momentum Km' sensible heat Kh’ and water vapor Kw' may be assumed to be identical when the atmosphere is at or near neutral stability and the determination of one allows the estimation of any of the appropriate fluxes. Webb (1970) has shown when the Monin- Obukhov stability parameter z/L, is between -0.003 and 1.0 (unstable to very stable) the diffusivity coefficient of momentum can be expressed as: 1 Km = ku*z (1 - nz/L)’ [14] where n is a number to be determined empirically. 23 From the logarithmic profile, Thornthwaite and Holzman (1939) derived the expression: _ 2 2 E - k P (ql ‘ qz) (02 - U1) /[ln (22 / 21) ] [15] where E is evaporation; k is the von Karman’s constant; q1 is the moisture concentration (specific humidity) at the lower level; q2 is the moisture concentration at the higher level; u is the wind velocity at the higher level: u1 is 2 the wind velocity at the lower level: 22 is the height of the upper instruments; and 21 is the height of the lower instruments. The formula has been found correct in adiabatic conditions, but will underestimate E in unstable atmospheric conditions and overestimate E in stable atmospheric conditions (Priestley, 1959). Pasquill (1949) simplified the expression with sufficient accuracy using a gradient of vapor pressure (e — e2) to: 1 [16] where B = kzM/RT (1 - ul/uz) / (ln 22 /21)2 [17] and M is the molecular weight of water; R is the gas constant; T is the absolute temperature of the air: and e1 and e2 are the vapor pressures at two heights. Sutton 24 (1953) reported a modification applicable for rough surfaces as: E = pk2 (u2 - u111q1 - q21/11n [(22 - di/(z1 - d1112 1181. Penman and Long (1960) applied the equation: E = u2 (el - e21/11n [(22 - d1/20112 [191 to wind profiles over wheat and after comparing the results to observed evaporation concluded that the preciseness needed in the data exceeded what the instrumentation could provide. The necessity for stringently accurate observations of wind speed and either specific humidity or vapor pressure at a number of heights, as well as temperature measurements to permit stability corrections to be made, makes the aerodynamic profile method impractical for routine use in the estimation of ET for irrigation scheduling (Rosenberg gt 31., 1983). Energy Balance Solar energy from the sun is the driving force that changes liquid water from the plant and soil surfaces into water vapor. The energy available for evaporation is termed the net radiation, Rn' the difference between the incoming and outgoing short and long-wave solar radiation fluxes and may be stated as: 25 Rn = Rs (1 - r) + R1 [20] where R8 is the net short-wave flux; r being the shortwave reflection or albedo: and R1 is the net long-wave flux. The net radiation can be partitioned into the energy consuming processes 2 Rn = LE + H + G + Ps + M [21] where LE is the latent heat flux of evaporation; H is the sensible heat exchange with the air; G is the soil heat flux; P8 is the energy for photosynthesis; and M is the term for any miscellaneous energy exchanges. The amount of energy consumed by PS and M usually amounts to less than 2% of the total Rn (Slatyer, 1967), so equation [21] can be simplified to: R = LE + H + c [22] Over periods of 24 hours, the net flux of G is usually negligible (the inward flux by day balancing the outward flux at night) and is generally disregarded when looking at daily values. The remaining terms LE and H represent the net exchanges of latent and sensible heat between the plant community and the atmosphere. Both exchanges are affected primarily by turbulent eddy diffusion in the lower atmosphere. The eddy diffusion equations are: 26 LE = -L€Kw (6e/62) [23] H = -pcpKh (6T/6z) [24] where L is the latent heat of vaporization; e is the ratio of the molecular weight of water to dry air at same temperature and pressure (0.622); p is the density of moist air; Cp is the specific heat of air at constant pressure; (Se/62) is the vertical specific humidity gradient; and (ST/62) is the vertical temperature gradient. Kw and Kh are the eddy transfer coefficients for water vapor and heat transport, respectively. The net flux outward from the earth’s surface is represented by the negative sign. Bowen (1926) introduced a relationship between LE and H known as the Bowen ratio, 8. It is defined as: B = H/LE = (PCp/L6)(Kh/Kw)[(6T/6z)/(69/62)] = r(Kh/Kw)t(6T/621/(6e/6211 [251 where P is the atmospheric pressure and r is the psychrometric constant. The relationship is usually simplified by assuming Kw = Kh and the ratio of the temperature and humidity gradients being replaced by the ratio of the differences measured over the same height interval. The relation now becomes: a z 1 (GT/6e) [26]. 27 From equation [25] H = 3 LE [27] and substituting into [22] and solving for LE results in LE = (Rn - G)/(1 + B) [28]. Errors may be introduced from the application of the Bowen ratio if there are horizontal gradients of temperature or humidity. Likewise, if there is non- homogeneity of vapor and heat sources and sinks, such as in row crops, there will be differences between Kw and Rh and they cannot be assumed equal. Also, the relative error in E is proportional to a relative error in B only when 8 = -0.5 (half the heat in E is derived from sensible heat transferred to the surface) (Tanner, 1967). When 8 > -0.5 the error in E is less than the error in 8. Conversely, when B < -0.5 and approaching -1.0 the error in E is greater than that in B and ET cannot be determined with suitable accuracy. These periods usually occur around sunrise and sunset. This contrasts to the aerodynamic profile method which has errors directly proportional to errors arising from incorrect assumptions concerning the eddy diffusion coefficients and to instrumental errors in the gradient measurements. Another advantage of the energy balance 28 method is that the measurement of net radiation and soil heat flux at the surface places reasonable limits on the magnitude of sensible and latent heat flux, especially during periods of temperature lapse (Tanner, 1960). Eddy Correlation The vertical transport of water vapor can be estimated from the measurement of the water vapor concentration gradient and the vertical mass air movement, or eddies, above the canopy surface. Two types of eddies exist above a surface, buoyant (free convective) eddies that are generated by vertical temperature gradients and frictionally generated eddies which, if over a uniform and level ground, results in a simple variation in mean wind speed with height (Thom, 1975). The mean vertical flux is given by: F = p ws + p w's' [29] where F is the mean vertical flux; p is the air density; w is the vertical velocity; and s is a measure per unit mass of air. The prime symbols denote instantaneous departures from the mean and the overbar represents the average value during a time period of suitable length. The first term on the right-hand side represents flux due to the mean vertical flow or mass transfer. The second term represents the flux due to eddying motion. Since the total quantity 29 of ascending air is approximately equal to the quantity of descending air over a sufficiently long period of time and a horizontally uniform surface, the mean value of vertical velocity will be negligible and the mean vertical flux reduces to: F = p w’s' [30]. Swinbank (1951) used the following expression for the measurement of water vapor flux: E = -(Mw P/Ma) p w’e’ [31] where E is the water vapor flux; M is the molecular weight w of water; P is atmospheric pressure; M3 is the molecular weight of dry air; and e’ is the vapor pressure flhctuations about the mean. The instrumentation Swinbank used to record the fluctuations were sensitive hot wire anemometers for measuring vertical wind movement and wet- bulb thermocouples for measuring the vapor-pressure fluctuations. Eddy correlation methods ultimately should prove to be the most accurate of the micrometeorological methods and least dependent on surface conditions (Tanner, 1967). The constraints of the method have included the need for very sensitive instrumentation to detect simultaneous changes in the fluctuations of w and e and the capability to record 30 and process the large quantity of data produced by the sensors. With continuing improvement in instrumentation, data acquisition equipment, and computing systems, eddy correlation as a method to estimate ET is becoming more practical. Estimating Potential or Reference Evapotranspiration Since the expense of constructing and managing weighing lysimeters make them mainly a research instrument and because of the complicated instrumentation and fetch requirements needed for the eddy flux and wind profile methods a simplified method for estimating ET was needed that used existing meteorological data. Some methods such as Penman’s formula are based on the physical principles of evaporation while others develop an empirical relationship between ET and one or more meteorological measurements usually calibrated to a given location. Empirical Methods Empirical methods are usually based upon determining the maximum evaporative flux from plant-soil surfaces for given meteorological conditions. Thornthwaite (1944) made a distinction between potential or maximum and actual ET. He defined the potential ET (ETp) as "the water-loss which will occur if at no time there is a deficiency of water in the soil for the use of vegetation." From his experiments over grass, Penman (1956a) was more specific and defined 31 the potential ET rate as the amount of water transpired from a short green crop, completely shading the ground of uniform height and never deficient in water. Under irrigated agriculture, when it became important to determine the ET rate of various crops under different climatic conditions, but impractical to measure actual ET for all the different crops and sites, the concept of reference ET (ETr) became important. By applying empirical coefficients or crOp coefficients, crop ET could be estimated with a reference crop ET equation using local meteorological data. In agriculture, especially irrigated agriculture under advective conditions, ET is influenced by the aerodynamic roughness of the crop, so water use referenced to an agricultural crop more representative of the aerodynamic characteristics of crops was adopted by water scientists of the western United States. Alfalfa was chosen as the reference crop because it develops crop cover early and has an extensive root system that minimizes the effects of decreasing soil water. It also provides a dense crop cover with low stomatal resistance which results in relatively high ET rates under arid conditions, except for a time after harvesting (Wright and Jensen, 1978). Similar to Penman’s definition of potential ET, Doorenbos and Pruitt (1977) used grass as the reference crop in their development of ET models for world wide application and defined it as "the rate of ET from an 32 extensive surface of 8 to 15 cm tall, green grass cover of uniform height, actively growing, completely shading the ground and not short of water." Crop ET and Crop Coefficients The use of empirically derived crop coefficients (KC) allow crop ET (ETC) for a particular crop to be estimated from measurements or estimates of potential or reference ET as: ETC = KC ETp or ET C = Kc ETr [32]. The crop coefficients reflect the physiology of the crop, the degree of ground cover, and resistance to water movement from soil and plant surfaces. These were first proposed in concept by Van Wijk and De Vries (1954). Crop coefficients are crop specific as well as reference crop and reference equation specific since they are derived as dimensionless empirical ratios of actual ET to the calculated reference ET as: K = Et/Etr or K = Et/E [33]. c tp The ideal method for calculating Kc is with well representative and sensitive weighing lysimeters where daily actual ET and reference ET can be measured simultaneously (Jensen, 1968). 33 The distribution of crOp coefficients over the growth cycle of the crop is known as a crop curve (Figure 1). The curve begins low at planting, illustrating primarily the relatively large diffusive resistance of the soil. The resistance decreases during rapid leaf development and the crop coefficient can approach unity when alfalfa is used as the reference crop. As the crop matures, the diffusive resistance increases and there is a decrease in the crop coefficient value. Crop coefficient curves represent an "average" of the effects of rainfall and irrigation, cropping procedures, and crop characteristics and depend largely on the planting date, rate of crop development, length of growing season, and climatic conditions (Doorenbos and Pruitt, 1977). Modified forms of crop coefficients have been used in irrigation scheduling models to account for the varying soil wetness. Jensen gt git (1971) calculated the crop coefficient as: K=K K+K [34] where Kco is a mean crop coefficient based on experimental data where soil moisture is not limiting; Re is a coefficient whose value is relative to the available soil moisture; and Ks is a coefficient to adjust for the increased evaporation occurring when the soil surface is partially or completely wetted by irrigation or rains. 34 so. .9236 no.8 a Co 29:86. ._ ennui common wastes» «coupon _.o N! 0 figs To 0.0 cd 5.0 1. Q.o cm on an. on an av an om @— ll:kll!J;1 _ q _ _ a _ d 14 \1 \\ 1 ,, \\ / \ 1 \\ / / .\\ \\x\\ \\ / \ / 1 is 0! ad E— N. — 35 When available soil water does not limit plant growth and soil evaporation is minimal, then Ka = 1 and KS = 0. Temperature Correlation Methods Since temperature is the most widely and easily measured weather variable, many relationships to estimate potential ET using temperature have been developed. They have mainly been used for monthly and growing season estimates due to temperature varying very little on a day to day basis, while radiation and the potential ET may be quite variable. A common temperature method used widely in the western United States, originally published by Blaney and Morin (1942), related monthly ET to mean monthly temperature and relative humidity, monthly percent of annual daytime hours, and an empirical consumptive-use crop coefficient. The method was modified by the U.S. Soil Conservation Service (1970) to obtain monthly ET as: ET = 25.4 k kc f [35] t where ET is monthly ET (mm); k is the monthly consumptive- c use crop coefficient obtained from SCS Technical Release #21; and k is a climate coefficient related to the mean t air temperature as: kt = 0.0311 T + 0.240 [36] 36 where T is the mean monthly temperature (°C) and f is a factor of temperature and monthly percentage of daylight hours determined by: f = (1.8 T + 32) p /100 [37] where p is the monthly percentage of daylight hours in the year. Doorenbos and Pruitt (1977) made a modification to the Blaney-Griddle method that incorporates the use of reference ET and grass related crop coefficients. The modified equation is: ETr = c [ p (0.46 T + 8)] [38] where ETr is the monthly mean reference ET(mm); T is the monthly mean temperature (°C); p is the daily percentage of annual sunshine; and c is an adjustment factor based on minimum relative humidity, sunshine hours, and daytime wind. Thornthwaite (1948) developed an expression relating mean temperature to potential ET that includes a daylength term and a "station" constant based on long-term mean monthly temperatures. The empirical formula is: a ETp = 1.6 Ld (10 T/I) [39] 37 where ETp is a monthly estimate of potential ET (cm); Ld are daytime hours in units of 12: T is the mean monthly temperature (°C); I is a heat index for the station based on long-term mean monthly temperatures: and a is an exponent dependent on I and can be found in tables along with I in Thornthwaite and Mather (1955). Evaporation Pan Correlations One of the earliest approaches to estimate evaporation from water bodies and potential ET from soils and vegetation has been through correlations with measured evaporation from pans. When care is taken to standardize the environment where the pan is maintained, and where advective wind conditions are rare, monthly potential ET. should be predictable within 1 10% or better from the use of pan evaporation (Jensen, 1974). Potential or reference ET are determined from pan evaporation through the use of pan coefficients as: ET =k E [40] where kp are the pan coefficients found in Doorenbos and Pruitt (1977) and E is the daily pan evaporation. It is P recommended that the use of pan evaporation to predict crop water requirements be over an interval of 10 days or longer. 38 The most common pan used in the United States is the USWB Class-A standard pan, 121 cm in diameter, 25.5 cm deep and is usually mounted on a wooden platform 15 cm above the ground. Another pan in common use for crop water requirement studies is the Sunken Colorado pan. Since these pans have a water level 5 cm below the pan rim and even with soil surface elevation, they are able to give a better direct prediction of potential ET of grass than the Class-A pan (Doorenbos and Pruitt, 1977). Christiansen (1968) developed a formula which could estimate Class A pan evaporation from climatic data. The formula could also be applied to calculate actual or potential crop ET through the use of crop coefficients. Pan evaporation can be estimated from: Ep = 0.473 R cT cw cH cS CE cM [41] where R is the extraterrestrial radiation and CT’ CW’ CH' C CE and CM represent coefficients for temperature, wind, SI humidity, sunshine percentage, elevation, and a monthly function. Radiation Correlation Methods The high correlation between solar radiation and ET was shown early by Briggs and Shantz (1916). The ratio of ET to solar radiation changes with temperature (Stanhill, 1961), so some models based on radiation include 39 a temperature term either directly or indirectly as the slope of the saturation vapor pressure curve. If solar radiation is not measured, estimates from percent of sunshine or cloud cover are used. Makkink (1957) proposed the following relationship: ETp = Rs [6/(6 + 1)] + 0.12 [42] where ETp is the potential ET; R5 is solar radiation in equivalent millimeters of water; 6 is the slope of the saturation vapor pressure vs. temperature curve: and r is the psychrometric constant. A method was develOped by Jensen and Raise (1963) from 35 years of ET data collected from irrigated areas in the western United States and estimates of solar radiation. They formulated: ETr = cT (T - TX) Rs [43] where ETr is alfalfa referenced ET: CT is an air temperature coefficient which is constant for a given area: T is the mean daily air temperature: Tx is a constant for a given area and is the linear equation intercept on the temperature axis; and RS is the solar radiation (Jensen gt B11, 1970). Equation [43] provides estimates of potential ET for a 5 day to one month period (Jensen, 1974). If measurements of solar radiation, Rs are not I 40 available, estimations may be made from: RS = [a + b(n/N)] Ra [44] where a and b are empirical coefficients which vary with latitude and time of year (found in Penman, 1948: Fritz and MacDonald, 1949: Black gt git, 1954; Linacre, 1967; and Doorenbos and Pruitt, 1977): n/N is a ratio representing the actual duration of bright sunshine as a fraction of the maximum possible for a cloudless sky; and Ra is the extraterrestrial radiation theoretically reaching the earth in the absence of an atmosphere and found in tables, such as List (1968). Net radiation There is even a closer relationship between net radiation and potential or reference ET. In humid regions, Tanner (1960) found there is little vertical transfer of sensible heat to the surface, so under "potential" conditions, ET will approximate the daily net radiation. In Central Texas, when soil water was not limiting and canopy cover was at least 45 % of the ground surface, daily ET was approximately within i 10 % of the net radiation (Ritchie, 1971). Regression relationships between ET and net radiation are not common because measurements of net radiation are rare and the highly empirical nature of the coefficients would make them location specific and preclude 41 their general use. However, the high correlation between net radiation and solar radiation has resulted in another method to estimate net radiation for ET models that require net radiation as the energy term. Shaw (1956) reported correlation coefficients of 0.98 on clear days and 0.97 on cloudy days over clipped grass between net and solar radiation. Numerous site specific linear regression relationships have been developed with regression coefficients for many areas around the world (Jensen, 1974). The linear regression equation is in the form of: Rn = a R5 + b [45] or with known albedo: Rn = a (l-a) RS + b [46] where Rn is the estimated net radiation: a and b are the regression coefficients: a is the albedo: and R8 is the measured solar radiation. Fritschen (1967) that found net radiation is a linear function of solar radiation when measured over an actively transpiring field crop and that the inclusion of the albedo term does not improve the estimate of net radiation. 42 Combination Methods Penman Formula Early evaporation studies by Dalton led him to what is now Dalton's law of partial pressures, which stated that the space above a water surface could contain only a limited amount of water vapor and that the maximum partial pressure exerted by water vapor is dependent on temperature and independent of the pressures of other gases. He showed experimentally that where the partial pressure was less than the maximum value at a water surface, evaporation would take place at a rate directly proportional to the partial pressure difference with a constant in the relation increasing with increasing wind speed. The relation took the form of: E = (eS - ed) f(u) [47] where E is the evaporative flux: es is the saturation water vapor pressure at the water surface temperature: ed is the saturation water vapor pressure at the dew point temperature: and f(u) is a derived wind function from horizontal wind velocity. Rohwer (1931), from experiments with open water of area 0.19 m2 derived: E = 0.40 (eS - ed) (1 + 0.27 uo) [48] where uo is the wind velocity at the surface. 43 Penman (1948) developed an expression for estimating evaporation over open water by combining an energy balance and wind function plus eliminating the difficult to measure es term from the saturation vapor pressure deficit. He began with the Bowen ratio neglecting the soil heat flux, G, E = Rn /(1 + B) = Rn /[1 + r(Ts - Ta)/(es - ed)] [49] and letting ( e - e )/6 = (Ts - T [50] s a a) where ea is the saturation vapor pressure of the bulk air at Ta and 6 is the slope of the saturation vapor pressure vs. temperature curve (Se/6T) at temperature Ta. Then from R=E+H [51] where sensible heat, H, is replaced by r f(u)(Ts - Ta) yields Rn = E + r f(u)(Ts - Ta) [52] and substituting equation [50] gives: Rn = E + (1/6) f(u)(es - ea) [53]. 44 Us1ng the 1dent1ty (eS - ea) = (eS - ed) - (ea - ed) results in the equation: Rn = E + (1/6) f(u) [(eS - ed) - (ea - ed)] [54]. From the Dalton form of E and a new parameter Ea introduced by Penman (1948) as: E = (e a - ed) f(u) [55] a which represents what he calls the sink strength (later referred to as the "drying power of the air" or aerodynamic term) and substituting, results in: Rn = E + (1/5) E + (1/6) Ea [56]. Solving for E gives evaporation for open water surfaces: E = (6 Rn + 1 Ea)/(6 + r) [57] where Rn is the net radiation with an albedo of a water surface. He proposed estimating net radiation as: Rn = (1 - r) Ra(0.18 + 0.55 n/N) -a Ta4 (0.56 - 0.092 ed5)(0.10 + 0.90 n/N) [58] 45 where r is the upward reflection coefficient or albedo: Ra is the extraterrestrial radiation: n/N is the ratio of actual to possible bright sunshine: 0 is the Stefan- Boltzman constant: Ta is the mean air temperature: and ed is the saturation vapor pressure at the dew point temperature. The empirical wind function, f(u), which Penman (1948) derived over open water from experiments at Rothamsted, England is: f(u) = 0.35 (1 + 0.0062 u [59] 2) where u2 is the horizontal wind in km/day measured at a height of 2 meters. The empirical wind function of the Penman equation, while a good generalization, shows weakness when applied to areas of large roughness (Stiger, 1980). An aerodynamic term proposed by Thom and Oliver (1977) in a modified expression is applicable over a range of surface roughnesses. Another way of dealing with the generalized wind function of Penman is to calibrate it to local conditions (Jensen, 1974). To do so requires measurements of actual ET and consistency in the vapor pressure deficit used (Cuenca and Nicholson, 1982). A calibration by Wright (1982) uses a polynomial expression based on the day of the year. Merva and Fernandez (1985), found the Penman equation is not sensitive to changes in wind speed in humid 46 areas with the higher ambient vapor pressures. They suggested a simplification where low, average and high wind speeds can be selected based on long-term averages. By combining the Bowen energy balance with the aerodynamic wind function, Penman's equation includes the two requirements needed for evaporation, that is, energy to provide the latent heat of vaporization and a mechanism for removing the water vapor from a saturated surface. From the practical standpoint, the equation requires measurements at one level for mean air temperature, mean dewpoint temperature, mean wind velocity and mean daily duration of sunshine. Penman (1948) related the evaporation from open water to soil and grass by the use of empirical constants found by: f = Eb/Eo and f = Et/Eo [60] where f is the empirical constant: Eb is the evaporation from bare soil: Et is the evaporation from short grass: and E0 is the evaporation from open water. The evaporation rate from wet bare soil was found to be 0.9 times Eo under the same weather conditions. The evaporation rate for grass well watered varied from 0.6 to 0.8 of Eo for southeast England throughout the year. To find a theoretical explanation for f being less than unity, Penman and Schofield (1951) reasoned that lower evaporation in vegetation is influenced by the resistance to vapor 47 diffusion located in the stomata, by stomata closure at night and that vegetation reflects a larger part of the incoming radiation than does a water surface. Crop ET can then be realized without reference to open water evaporation as: Et = (6 Rn + r Ea)/(6 + r/SD) [61] where S is a stomatal factor and D is a daylength factor. The expression was not offered as a working equation due to the complication of determining S and D, but allowed Penman to generalize that transpiration from a short green cover cannot exceed the evaporation from an open water surface exposed to the same weather. Working from wind profile and lysimeter observations, Businger (1956) was able to develop more scientifically a value of l/SD equal to 0.92 and estimated potential transpiration as: Et = (6 Rn + 1 Ea)/(6 + 0.92 r) [62]. Other early work (De Vries and Van Duin, 1953: and Makkink, 1957) at verifying Penman's equation found discrepancies when it was applied to crops of different roughness than what the equation was originally developed. Potential ET estimates of alfalfa using Penman’s equation showed it underestimating measured ET (Tanner and Pelton, 1960) on a daily basis. The error was attributed to the 48 wind function not taking into account the surface roughness. Vapor pressure deficit Penman (1948) did not specify how he calculated the vapor pressure deficit term (ea - ed) in his Rothamsted experiment, but implied ea was found as the saturation vapor pressure with a mean air temperature calculated from the daily minimum and maximum temperature and ed was found as the saturation vapor pressure at mean dewpoint temperature. Only one value of the dewpoint temperature was obtained and it was a weighted value based on dewpoint temperatures estimated at six hour intervals from a different location. Since the result of the vapor pressure deficit calculation determines the weight given to the wind function, using different methods than what the function was calibrated for may affect the reliability of ET estimation (Cuenca and Nicholson, 1982). Another problem has been obtaining estimates of mean dewpoint temperature. Since relative humidity is the ratio of actual vapor pressure to saturation vapor pressure and relative humidity is measured widely, it has been used to obtain the vapor pressure deficit as: ed = ea RH/lOO [63]. 49 Another method, but still using mean dewpoint temperature (Jensen, 1974), is an average of the saturation vapor pressure found at maximum and minimum temperatures and calculating the actual vapor pressure as the saturation vapor pressure at mean dewpoint temperature. The formula is: (ea - ed) = [(emax + emin)/2] - ed [64]. Using the night time minimum temperature as a substitute for dew point temperature in the vapor pressure deficit term of Penman’s formula has been done in humid climates where dew occurs since the absolute vapor pressure density in the air does not vary appreciably (Merva and Fernandez, 1985). Van Bavel Modification Van Bavel (1966) developed a combination equation along the lines of Businger (1956) that eliminates the empirical coefficients in the wind function term of Penman. The equation for daily potential ET rate is: ETp = [6/(6 + 1)] Rn + [1/(5 + 7)] p e k2/P uz/[ln'(z/zo)]2 d2 [65] where ETp is the potential ET: 6 is the slope of the vapor pressure temperature curve: 1 is the psychrometric 50 constant: Rn is the net radiation: p is the density of air: 6 is the water-air molecular weight ratio: R is the Von Karman constant: P is the ambient pressure: 112 is the wind speed at height 2: z is the roughness parameter: and d2 is o the vapor pressure deficit at height 2. The equation is only valid for adiabatic conditions in the wind profile. The value for 20 was determined from wind profile data over alfalfa in two of the three years studied. In the third year, z was estimated from height 0 and appearance of the crop, based on the previous years experience. With 20 estimated as 1 cm and net radiation measured, very good agreement was obtained for potential ET over alfalfa when compared to lysimetric measurements. The error from estimating 20 is magnified under high wind conditions and high vapor pressure deficits (van Bavel 1966). Rosenberg (1969) found the van Bavel equation underestimated potential ET on calm days and over estimated it on windy days. Reicosky gt 311 (1983) found good agreement of potential ET with lysimeter measured ET on an hourly basis. Tanner and Pelton (1960) suggested that an ET equation with a wind function with a rational basis, indicates that there is no need for wind functions with empirical coefficients. FAD-24 Mbdification Doorenbos and Pruitt (1977), wanting to avoid the necessary local calibration of the wind function f(u) in 51 the Penman formula, arrived at a single wind function for all locations. They found the differences in wind functions between various locations are in a large part due to the method which the vapor pressure deficit and net radiation are calculated. Their wind function for all locations is: f (u) = 0.27(l + U/lOO) [66] where U is the mean wind speed in km/day. From a practical standpoint they felt it was necessary to determine net radiation on relationships which need not be locally determined, but are more universally applicable. Net shortwave radiation is determined as: Rns = (1 - a)(a + b n/N) Ra [67] where a is the crop albedo: a and b are coefficients 0.25 and 0.50: n/N is the ratio of actual to maximum possible sunshine hours: and Ra is the extra-terrestrial radiation. Net longwave radiation is determined as: _ 4 5 Rn1 — 6 T (0.34 - 0.044 ed )(0.1 + 0.9 n/N ) [68] where 6 is the Stefan-Boltzman constant: T is the mean daily temperature (absolute scale): and ed is the saturation vapor pressure at mean dewpoint temperature. 52 Net radiation is then the difference between the net shortwave radiation and net longwave radiation. The vapor pressure deficit can be calculated three ways depending on the air humidity measurements. If humidity is measured as relative humidity then: (ea - ed) = ea (1 - RH/lOO) [69]. If wet and dry bulb temperatures are available then: [70] where eawa is the vapor pressure determined at the wet bulb temperature. Finally, if dew point temperature is available then: (ea - ed) - ea - eapo [71] where eapo is the vapor pressure determined at the dew point temperature. The reason only one wind function applies to all locations for the FAO modified Penman is due to the reference ET rate being multiplied by a correction factor which takes into account daytime and night time weather conditions. The factor developed from different climates, takes into account relative humidity plus day and night wind speed conditions. Solar radiation is included in the 53 correction factor as an adjustment to different daylengths as suggested by Penman and Schofield (1951). The correction factor can be determined from a table in the Doorenbos and Pruitt reference or from a multiple regression equation (Frevert gt alt, 1983). Resistance Model Monteith (1965) approached the estimation of ET as a combination equation incorporating diffusive resistances of leaves and plant communities. The Penman equation assumes a surface at saturation vapor pressure, but is not valid when a surface is less than the saturation vapor pressure, such as, when water in a leaf evaporates at the surfaces of cell walls surrounding sub-stomatal cavities, and reaches the outer surface of the leaf by molecular diffusion through stomata and through the cuticle. Actual ET can be determined from the following equation derived by Monteith when the resistances are known or can be estimated: E (e = [6 (Rn - G) + p C - ea)/ ra]/[6 + 1(1 + rs/ra] [72] t s P where Et is the actual ET: 6 is the slope of the saturation vapor pressure curve: Rn is net radiation flux: G is the soil heat flux: p is the air density: C is the specific P heat of air: es is the saturation vapor pressure: ea is the 54 ambient vapor pressure: ra is the aerodynamic resistance: r is the psychrometric constant: and rS is the surface resistance. The aerodynamic resistance, r is found from the wind al profile above the surface under neutral conditions as: 2 2 r8 = {1n [(2 - d)/zo]} / [k u(z)] [73] where z is the measurement height above the ground surface: d is the zero plane displacement: z is the vegetation o roughness length: k is the von Karman constant: and u(z) is the wind speed. In unstable atmospheric conditions, ra is overestimated, conversely when the air is stable, ra is underestimated. The crop surface resistance, rs, from a uniform surface can be estimated from profiles of temperature, humidity and wind speed above the vegetation and measurements of evaporation as: rs = p Cp [(es(To) - eo)/LE]/T [74] where p is the air density: C is the specific heat of air: P es(To) is the saturation vapor pressure at mean leaf temperature: eo is the vapor pressure outside the leaf: LE is the latent heat of evaporation: and r is the psychrometric constant. The practical application of equation [74] has been 55 limited due to the difficulty of obtaining representative values of ra and rs. Monteith (1963) obtained representative surface values of vapor pressure and of temperature by extrapolating straight lines drawn through plots of e(z) and T(z) versus u(z) to u=0, to furnish the values of eo and To. The surface resistance can also be calculated from stomatal dimensions and populations (Milthorpe and Penman, 1967) or measured by porometers (Szeicz gt alt, 1973), but there is the difficulty of arriving at a representative model of a crop based on information from single leaves (Szeicz gt git, 1969). Different methods for determining the surface resistances of agricultural crops in different locations were reviewed by Szeicz and Long (1969). Equilibrium Evaporation McIlroy (Slatyer and McIlroy, 1961) defined potential ET from a freely transpiring or wet surface as: ETp = [6/(6 + 1)] (Rn - c) + c p h 02 [75] P where RD and G are the net radiation and soil heat flux respectively: C is the specific heat of air: p is the air P density: h is an empirical turbulent transfer coefficient: and D2 is the wet bulb depression at a height above the surface. As an unsaturated air mass moves across a large enough irrigated or wet surface the humidity gradient 56 increases in the boundary layer and the temperature gradient decreases to where Dz can be assumed to be zero resulting in a minimum potential ET rate defined as equilibrium evaporation: ETeq = [6/(6 + 7)] (Rn ~ G) [76]. Thus, the proportion of net radiation used in evaporation will increase with temperature due to variation in [6/(6 + 1)] and the evaporation into the saturated surface layer is independent of the aerodynamic roughness of the vegetation and the wind speed. Priestley and Taylor (1972) showed that potential ET is directly proportional to the equilibrium evaporation as: ETp = a[6/(6 + 1)] (Rn - c) [77] where a is an empirical coefficient and was determined to have a mean of 1.26. Davies and Allen (1973) confirmed the use of the equilibrium model for potential ET over cropped surfaces when temperatures are between 15 and 30°C and derived a similar value for a of 1.27. Ritchie (1974), from lower standard deviations of potential ET calculated from the Priestley-Taylor model compared to the Penman formula containing the wind function, found that for regions with no large scale advection, the Priestley-Taylor 57 model has the advantages of slightly greater accuracy and it requires fewer atmospheric parameters. A radiation method similar to the Priestley-Taylor model was presented by Doorenbos and Pruitt (1977) where solar radiation is substituted for the net radiation and soil heat fluxes: ETr = c [6/(6 + 1)] Rs [78] where ETr is the reference ET: c is an empirical function of daytime wind movement and mean daily relative humidity found in tables of the reference or can be calculated from a multiple regression equation (Frevert gt alt, 1983): and RS is the solar radiation. Ritchie Model Calculating the evaporation rate of the soil separately from the transpiration rate of a crop was formulated in a model by Ritchie (1972). The soil evaporation rate, 35' was described in two stages, the constant rate stage where the evaporation of a wet soil surface is limited only by the supply of energy reaching the surface and the falling rate stage where the surface soil water has decreased so evaporation at the surface is dependent on the hydraulic properties of the soil. During stage one, the soil is wet enough for the soil water to be transported to the surface at a rate at least equal to the 58 energy available at the soil surface for evaporation which can be approximated from the net radiation as: Rns = Rn exp(-0.4 Lai) [79] where Rns is the net radiation reaching the soil surface: Rn is the net radiation above the canopy: and Lai is the leaf area index. Soil evaporation under a full canopy where wind speed and vapor pressure deficit are lowered is equal to potential evaporation calculated as: Eso = U [6/(6 + 1)] Rns [80] where Eso is the potential soil evaporation and U is an empirical coefficient replacing the wind speed and vapor pressure deficit terms. When the canopy is not full, U is calculated as (Ritchie, 1974): U = 0.92 + 0.4 Rns/Rn [81]. Stage one evaporation continues until a soil dependent upper limit, a, is reached. In stage two, soil evaporation becomes a declining function of time calculated as: ZESZ = a t5 [82] where EES is the accumulation of stage two evaporation, a 2 59 is an upper limit of soil surface evaporation dependent on the hydraulic properties of the soil and t is the time in days after stage two evaporation has begun. Es for a given day is obtained by subtracting the 2E5 for all the 2 previous days from 2E5 through the current day. 2 An equation for estimating plant transpiration of a growing crop was developed as a function of Lai (Ritchie and Burnett, 1971). For cotton and sorghum they found a minimum threshold canopy Lai of about 2.7 which was necessary to obtain 90% of potential evaporation. Plant transpiration when soil water is not limited for 0.1 S Lai S 2.7 is: _ _ *2 Ep — E0 ( 0.21 + 0.70 Lai ) [83] where Ep is the plant transpiration: E is the potential 0 ET rate calculated by an equilibrium ET equation method similar to the Priestley-Taylor method: and Lai is the leaf area index. When the Lai is greater than 2.7, Ep is independent of Lai and E = E [84]. If Ep + ES 15 greater then Eo then E = E - E [85]. I I I . METHODS The review of literature has shown there are many methods and procedures available for estimating ET. However, the effect of equation variables calculated in different ways and measured under different exposures on estimated ET for certain equations has not been evaluated closely. More accurate estimates of ET will improve how well irrigation scheduling programs estimate crop water use and help irrigators manage their resources. Research Method - Objective 1 Climatic data were obtained from two weather stations located at the Michigan State University Kellogg Biological Station (KBS), Hickory Corners, Michigan (42° 24' N latitude, 85° 23’ W longitude, 288 m elevation). One station (LYS) is located in an irrigated field next to a weighing lysimeter (Figure 2) and the other (PL) which is known as the pond lab station is over cut grass with natural rainfed conditions. The crops in the irrigated field were corn (King 5574) in 1986 and alfalfa (WL 316) in 1987 and 1988. The sensors at both stations include Li-Cor LIZOOS solar pyranometers, Campbell Scientific 201 temperature and relative humidity probes, Met-One 014A anemometers and 024A wind direction sensors, and Weathertronics 6010 or Sierra Misco 2500 tipping bucket rain gauge. In addition, the LYS station has a Fritschen 60 61 Figure 2. l I) weighing lysimeter and 1 l S weather station _ I z 0 V I 1 a \b D ' ; k-tSw l f ; l l {I x} d alley I i .._/ .. 1 s W, . :- lL - _ .__.[ j I-—— l/oo... 'I‘ 400». Q:? E: road : Ejg Lysimeter location (Kellogg Biological Station). 62 type miniature net radiometer. Both stations are equipped with Campbell Scientific dataloggers which have their data automatically downloaded to a Digital Equipment Corporation VAX 11/780 at the K88 computer center via phone lines and modems. To evaluate the ET estimated by different potential ET equations with variables integrated over different time intervals and between stations, it was first necessary to determine if significant differences in mean and variance exist between the variables calculated differently and the same variable from the two weather stations. Comparisons were made for temperature, relative humidity, wind speed and solar radiation variables of years 1986 through 1988. Certain variables were averaged only during the daylight hours as determined when the pyranometer measured solar radiation greater than zero. In addition, different methods of calculating the vapor pressure deficit were evaluated and compared. The temperature variables compared were: TEMP24 - daily mean of 24 hourly temperature means. TEMPAVG - average of daily minimum and maximum temperatures. TEMPDAY - mean of hourly temperature means occurring during daylight hours. TEMPMAX - maximum daily temperature. TEMPMIN - minimum daily temperature. The relative humidity variables compared were: RH24 - daily mean of 24 hourly relative humidity means. RHAVG - average of daily minimum and maximum relative humidities. RHDAY - mean of hourly relative humidity means 63 occurring during daylight hours. RHMAX - maximum daily relative humidity. RHMIN - minimum daily relative humidity. The wind speed variables compared were: WINDZ4 - daily mean of 24 hourly wind speed means. WINDDAY - mean of hourly wind speed means occurring during daylight hours. WINDPM - mean of hourly wind speed means occurring after dusk the preceding day and ending at sunrise. WINDRATIO - ratio of WINDDAY over WINDPM (used in FAO modified Penman equation correction coefficient). The solar radiation variable compared was: SOLRAD - daily summation of 24 hourly total solar radiation means of radiation flux. The various methods of calculating the vapor pressure deficit that were compared are: LYS VPDEF - daily mean of 24 hourly vapor pressure deficit means. VPDEF = SVP (1 - LYSRH/IOO). PL VPDEF - daily mean of 24 hourly vapor pressure deficit means. VPDEF = SVP (1 - PLRH/lOO). LYS VPDAVG - calculated from daily means of temperature for saturation vapor pressure and the average of minimum and maximum relative humidity for vapor pressure. VPDAVG = SVP24(1 - (LYSRHMIN + LYSRHMAX)/200). PL VPDAVG - calculated from daily means of temperature for saturation vapor pressure and the average of minimum and maximum relative humidity for vapor pressure. PLVPDAVG = SVP24(1 -(PLRHMIN + PLRHMAX)/200). LYS VP024 - calculated from 24 hourly means of temperature and relative humidity. VPD24 = SVP24 (1 - LYSRH24/100). PL VPD24 - calculated from 24 hourly means of temperature and relative humidity. VPD24 = SVP24 (1 - PLRH24/100). LYS VPDDAY - average of the hourly vapor pressure deficit values during daylight. VPDDAY = SVP(1 - LYSRH/IOO). PL VPDDAY - average of the hourly vapor pressure deficit values during daylight. VPDDAY = SVP(1 - PLRH/IOO). 64 LYS VPDDRHD - temperature and relative humidity averaged during the daylight hours. VPDDRHD SVPDAY (l - LYSRHDAY/lOO). PL VPDDRHD - temperature and relative humidity averaged during the daylight hours. VPDDRHD SVPDAY (1 - PLRHDAY/lOO). VPDTEMP - average saturation vapor pressure from minimum and maximum temperature and substituting minimum temperature for dew point temperature. VPDTEMP = (SVPTEMPMAX + SVPTEMPMIN)/2 - SVPTEMPMIN. VPDZ4MTP -using daily mean temperature for SVPRES and substituting the daily minimum temperature for dew point temperature. VPD24MTP = SVP24 - SVPTEMPMIN. The saturation vapor pressures were calculated from the expression (Bosen, 1960): SVP = 33.8639 ((0.00738 TEMP + 0.8072)8 - 0.000019 [1.8 TEMP + 48| + 0.001316) [86] where TEMP is mean daily temperature: temperature during daylight hours: maximum temperature: or minimum temperature as required by the vapor pressure deficit calculation method used. Statistical Analysis Mean comparisons were made between the same variables from the two different stations within the same year and between variables averaged or integrated over different time intervals. Significant mean differences were determined using Student's t criteria at the 5% and 1% significance levels. The same dates from both stations were used in the analysis with a missing observation from 65 one station causing both stations not to be analyzed for that date. Sensor failure or power loss at the dataloggers were responsible for most of the missing values. The variances were tested for homogeneity. If the null hypothesis of equal varianCe was rejected as determined by a significant F calculated from the two variances, then the procedure for mean comparison with unequal variance was followed (Steel and Torrie, 1980). The various methods of calculating the vapor pressure deficit were ranked according to the means for both weather stations in each year. Research Method - Objective 2 Various methods of calculating potential ET were compared against measured ET rates from a large weighing lysimeter located at the Kellogg Biological Station. The weighing lysimeter is the undisturbed soil profile type with internal dimensions at the surface of 3.04 m (10 ft) wide by 1.92 m (6.3 ft) long. A boarder separating the internal soil tank wall from the outer tank is approximately 4.45 cm (1.75 in) wide. The effective area used was 6.05 m2 (64.7 ftz). The depth of the lysimeter is 1.52 m (5 ft) with natural drainage occurring through dense fired clay bricks laid in the bottom and covered over with a porous fiber mat. The drainage was collected to one point beneath the lysimeter where a tipping bucket rain gauge connected to the datalogger recorded the amount of 66 deep percolation in an equivalent depth of water over the surface area. This amount was later added back into the daily total scale mass change so the net mass decrease due to ET could be determined. The change in mass of the soil block was measured by an electronic load cell and kept in range by a counter balance arm and weight as described by Ritchie and Burnett (1968). The recording of the mass change was done by the datalogger which then calculated the net change for each day. Planting of the lysimeter was done by hand. In 1986, corn was planted in 4 rows with 11 plants in each row resulting in a density of 7.27 plants/m2. For 1987 and 1988 alfalfa was hand planted at the rate of 19 kg/ha to achieve a crown density on the lysimeter of about 340 crowns/m2. Accepted cultural practices were performed on the lysimeter as on the surrounding field so lack of nutrients or infestation of pests would not be factors limiting ET. Two years (1987 and 1988) of alfalfa under potential evaporating conditions (water not limiting) and at full cover were used in the comparison. If rainfall occurred during the day, that day was not used due to the possibility of rainfall mass cancelling out small losses from ET during the datalogger averaging period. The equations evaluated were Penman, FAO modified Penman, Priestley-Taylor, and an equilibrium ET equation 67 used in CERES-Maize. The Penman (1948) equation is in the form: ETp = [6/(6+1)] Rn + [r/(6+r)] 2.63(1 + 0.537 U2) (ea - ed) [87] where: ET = potential ET (mm/day): 6 g slope of the saturation vapor pressure-temperature curve (kPa/'K): r = the psychrometric constant (kPa/°K): Rn = net long-wave and short-wave radiation (mm/day equivalent): 2.63 = a constant of proportionality (mm/day kPa): Ug = mean wind speed at 2 m (m/s): and ( a-ed) = vapor pressure deficit (kPa). The slope of the saturation vapor pressure vs. temperature curve was approximated from an expression adapted from Bosen (1960) as: 6 = 0.200(0.00738 T + 0.8072)7 - 0.00116 [88] where T is the daily mean temperature (C). The psychrometric constant was found using: 1 = cp P / 0.622 L [89] where: C = specific heat of water (kJ/kg C): Pp= station atmospheric pressure (kPa): and L = the latent heat of vaporization (kJ/kg C). Net and solar radiation data from 1986 and 1988 were used to develop a linear function to estimate net radiation 68 from solar radiation. The resulting linear regression equation was used for empirically determining net radiation from solar radiation measured at the PL station. Daily average wind speed was measured at a 2m height. For the PL station, wind speed was measured at 3m and was corrected to 2m using the logarithmic wind profile: 02 = 02 (2/2) 0'2 [90] where U2 is the wind speed measurement (m/s) taken at height 2. Twelve different forms of the Penman equation were compared using wind speeds from the two weather stations and six different methods of calculating the vapor pressure deficit. The Penman equation modified by Doorenbos and Pruitt (1977) for various climatic conditions worldwide is: 6/(6+1)] Rn + [T/(6+1)] 2.03(1 + 0.537 U2) (e - ET = C e [31] {1 P d1} where: ET = potential ET (mm/day) and C 2 an adjustment factor to compensate for the effect of day and night weather conditions, calculated with a multiple regression expression by Frevert at £11 (1983) as: C = 0.6817006 + 0.0027864 X1 + 0.0181768 X -0.0682501 x3 + 0.0126514 x + 0.0097297 x5 + 0.43025E-4 X6 -0.92118E-7 x7 4 [921 69 where: x1 = maximum relative humidity (%): x2 = solar radiation (mm/day): x3 = daytime wind speed (m/s): x4 = day/night wind ratio: x5 = x3 * x4: x6 = x1 * x2 * x3: x7 = x1 * x2 * x4: 6 = slope of the saturation vapor pressure vs. temperature curve (kPa/°K): r = the psychrometric constant (kPa/°K): Rn = net long-wave and short-wave radiation (mm/day equivalent): 2.03 = a constant of proportionality (mm/day kPa): U = mean wind speed at 2 m (m/s): and (3a - ed) = vapor pressure deficit (kPa) The FAG-Penman was evaluated with the vapor pressure deficit calculations suggested by Doorenbos and Pruitt in FAO Irrigation and Drainage Paper No. 24 and also ones not suggested, but which were used in the Penman equation comparison. The equilibrium ET equation of Priestley-Taylor (1972) that was compared is: ETp = 1.26 [6/(6+r)] Rn [93] where: = potential ET (mm/day): ET 6 B slope of the saturation vapor pressure-temperature curve (kPa/°K): r = the psychrometric constant (kPa/°K): and Rn = net long-wave and short-wave radiation (mm/day equivalent). A comparison was also made with an equilibrium ET function used in CERES-Maize (Jones and Kiniry, 1986): ET = 1.1 [( R (4.88E-3 - 4.37E-3 ALB) p (0.6 MXTP + 0.4 MNTP + 29)] [94] 70 where: ET = potential ET (mm/day): 2 R p: total solar radiation (MJ/m ): AEB = crop albedo: MXTP daily maximum temperature (C): and MNTP daily minimum temperature (C). The crop albedo is calculated as a function in the model as: ALB = 0.23 -(0.23 - SALE) e(’°°75 LAI) [95] where: SALB = soil albedo (0.13 for Kalamazoo loam) and LAI = leaf area index For this analysis, the maximum value of 0.23 was used for the crop albedo since the comparisons were done using alfalfa only at full cover. Statistical Analysis Linear regression analysis was applied to evaluate the agreement and variation of calculated potential ET estimates with actual ET from the weighing lysimeter. The regression model evaluated was in the form: ETp = a + b ET1 [96] where: ET = equation estimated potential ET: a 3nd b = intercept and regression coefficients: and ET1 = lysimeter measured ET. The factors evaluated from comparisons made on a daily basis were the regression coefficient (b), 1121 slope, the 71 intercept (a), the standard error of estimate (SEE), and the coefficient of determination (R2). In addition, the accumulation of daily ET estimated from the equation was compared to the actual lysimeter accumulation used in the comparison. A regression equation with a slope of 1.0 and zero intercept would be a perfect fit of calculated or model potential ET vs. lysimeter ET. If the intercept was not zero, it was tested for being significantly different than zero. The square of the standard error of estimate, 1121 standard deviation of the residuals, is an unbiased estimate of the true variance about regression (Steel and Torrie, 1980). The coefficient of determination is a measure of the proportion of the total variation in ETp accounted for by the regression of calculated potential ET on lysimeter ET. Research Method - Objective 3 The estimated daily ET rates from two irrigation scheduling programs were compared along with the ET rate estimated from a crop growth model. The irrigation scheduling programs are: 1) the Michigan State University- Cooperative Extension Service 120 day version spreadsheet program written by M. Vitosh, and 2) Michigan State University-Soil Conservation Service "Scheduler" version 1.10 program developed by Shayya and Bralts (1988). The crop growth model is CERES-Maize version 2.1, originally developed at the USDA-Agricultural Research Service, 72 Temple, Texas (Jones and Kiniry, 1986). The two irrigation scheduling programs and the crop growth model were developed for different objectives. The MSU-CES spreadsheet program is useful where minimum climatic data are available since it requires only temperature and precipitation. Its objective is to estimate ET over longer intervals using crop coefficients. The MSU-SCS "Scheduler" program requires more climatic data and has been developed for use all over the country with appropriate crop curves developed locally. The larger data requirement allows the ET rate to be estimated on a daily basis. The usual function of the CERES-Maize crop growth model is not as an irrigation scheduling program but as a research model to compare different crop management practices. It simulates the growth of the crop and has as one of its outputs the daily evaporation from the plant and soil. The lysimeter data are from the 1986 season when the lysimeter was in corn. The soil moisture condition on the well watered weighing lysimeter was assumed to be non- limiting to plant growth and all the actual rainfall and applied irrigation amounts were entered into the programs and model. Statistical Analysis Linear regression analysis was applied to evaluate the 73 agreement and variation of ET estimates from the irrigation scheduling models and the growth model with the actual ET from the weighing lysimeter. The regression model was the same as in objective 2 in the form: ETm = a + b ETl [97] where: ET = model estimated ET: a and b = intercept and regression coefficients: and ET1 = lysimeter measured ET. The factors evaluated from comparisons made on a daily basis were: the regression coefficient (b) or slope, the intercept (a), the standard error of estimate (SEE), and the coefficient of determination (R2). The accumulation of daily ET estimated from the models was compared to the actual total lysimeter ET over the days in the comparison. IV. RESULTS AND DISCUSSION Climatic Data Comparison of the mean difference of measured climatic variables at the two weather stations was performed using the Student’s t test of two means with equal n. The variable statistics of temperature, relative humidity, wind speed, and solar radiation from both weather stations and for years 1986 - 1988 are in Tables 1 through 4. The results of the mean comparison tests with the null hypothesis of no difference are in Tables 5 through 8. The mean daily temperature and temperature averaged only during the daylight hours from the LYS station for all three years are shown graphically in Figures 3 through 5. The daily mean, maximum, and minimum relative humidities from both stations for the three years are compared in Figures 6 through 14. The mean daily wind speeds are shown graphically in Figures 15 through 17. The mean, maximum, and minimum temperature variables were found to be not significantly different between the weather stations. There was also no significant difference between how the daily mean was determined. In this comparison, finding a daily average from the daily minimum and maximum temperature gave the same result as averaging 24 hourly means. Temperature averaged only during daylight periods was significantly different than an average of 24 hourly means which was expected (continued on p. 98). 74 75 Table 1. Statistics of daily temperature comparison (°C). urinals LXLstatign ELstatian 1986 (n = 87) mean SD 91131 mean 80 91(1). TEMP24 19.0 3.86 20.4 19.4 3.89 20.0 TEMPAVG 19.2 3.92 20.4 19.5 4.00 20.4 TEMPMIN 13.1 4.58 34.9 13.9 4.51 32.5 TEMPMAX 25.3 3.94 15.6 25.1 4.0 16.0 TEMPDAY 21.5 3.76 17.5 not calculated 1987 (n TEMP24 19.3 4.64 24.1 19.9 4.80 24.1 TEMPAVG 19.2 4.72 24.6 20.1 4.94 24.6 TEMPMIN 13.6 4.86 35.6 14.3 5.14 36.0 TEMPMAX 24.8 5.23 21.1 26.0 5.36 20.6 TEMPDAY 21.2 4.83 22.7 not calculated 1988 (n TEMP24 19.8 4.68 23.6 20.6 4.82 23.4 TEMPAVG 19.8 4.84 24.4 20.6 5.01 24.4 TEMPMIN 13.0 5.27 40.6 13.7 5.25 38.4 TEMPMAX 26.7 5.09 19.1 27.5 5.46 19.9 TEMPDAY 21.8 4.85 22.3 not calculated 76 Table 2. Statistics of daily relative humidity comparison mean 512an SEC—viii 1986 (n = 76) RH24 78.57 9.53 12.1 72.89 4.80 6.6 RHAVG 77.12 9.01 11.7 70.19 5.27 7.5 RHMIN 58.76 13.97 23.8 56.58 10.93 19.3 RHMAX 95.47 6.91 7.2 83.78 1.31 1.6 RHDAY 71.27 11.56 16.2 68.00 7.66 11.3 1987 (n = 119) RH24 73.78 11.39 15.4 62.92 11.39 18.1 RHAVG 71.84 10.43 14.5 61.20 9.73 15.9 RHMIN 55.60 17.31 31.1 45.76 15.68 34.3 RHMAX 88.07 6.96 7.9 76.64 6.49 8.5 RHDAY 68.97 13.22 19.2 58.53 12.84 21.9 1988 (n = 94) RH24 71.65 13.38 18.7 64.60 13.90 21.5 RHAVG 71.13 11.55 16.2 64.05 12.20 19.1 RHMIN 51.13 16.93 33.1 43.69 17.31 39.6 RHMAX 91.14 9.53 10.5 84.41 9.66 11.5 RHDAY 67.14 14.45 21.5 59.19 15.31 25.9 Table 3. xariahle 1986 (n = 83) WIND24 WINDDAY WINDPM WINDRATIO 1987 (n = 142) WIND24 WINDDAY WINDPM WINDRATIO 1988 (n = 113) WINDZ4 WINDDAY WINDPM WINDRATIO 37.6 38.1 64.8 48.6 31.1 30.3 45.6 44.5 34.1 32.7 59.2 47.7 Statistics of wind speed comparison (m/s). SD 92131 0.66 32.8 0.69 29.7 0.84 55.2 0.90 48.3 0.62 29.4 0.71 28.8 0.67 43.7 0.81 43.8 0.74 34.1 0.82 31.7 0.93 65.7 1.31 54.1 78 Table 4. Statistics of solar radiation comparison (MJ/mz). xariahle Lx&_etatien PL_etatien mean SD 92121 mean 60 92111 1986 (n = 83) SOLRAD 18.2 6.69 36.9 20.0 6.99 35.1 1987 '(n = 136) SOLRAD 20.2 6.83 33.8 20.8 6.87 33.1 1988 (n = 113) SOLRAD 23.2 6.63 28.6 24.1 6.93 28.7 79 Table 5. Results of mean comparison tests - temperature. 1986 1987 1988 Comparison mean variance mean variance mean variance LYS temp24 vs. PL temp24 ns ns ns ns ns ns LYS tempavg vs. PL tempavg ns ns ns ns ns ns LYS temp24 vs. LYS tempday ** ns ** ns ** ns LYS temp24 vs. LYS tempavg ns ns ns ns ns ns PL temp24 vs. PL tempavg ns ns ns ns ns ns LYS tempmax vs. PL tempmax ns ns ns ns ns ns LYS tempmin vs. PL tempmin ns ns ns ns ns ns Legend: LYS - LYS weather station PL - PL weather station * - significant at the 0.05 level ** - significant at the 0.01 level ns - not significant 80 Table 6. Results of mean comparison tests - relative humidity. 1986 1987 1988 Compar1son mean variance mean variance mean variance LYS rh24 vs. PL rh24 ** ** ** ns ** ns LYS rhavg vs. PL rhavg ** ** ** ns ** ns LYS rhmin vs. PL rhmin ns * ** ns ** ns LYS rhmax vs. PL rhmax ** ** ** ns ** ns LYS rh24 vs. LYS rhday ** ns * ns * ns PL rh24 vs. PL rhday ** * ** ns ** ns LYS rhday vs. PL rhday * * ** ns ** ns LYS rh24 vs. LYS rhavg ns ns ns ns ns ns PL rh24 vs. PL rhavg ** ns ns ns ns ns Legend: LYS - LYS weather station PL - PL weather station * - significant at the 0.05 level ** — significant at the 0.01 level ns - not significant 81 Table 7. Results of mean comparison tests - wind speed. 1986 1987 1988 Comparison mean variance mean variance mean variance LYS wind24 vs. PL wind24 ** ns ** ns ns ns LYS windday vs. PL windday * ns ** ns ns ns LYS wind24 vs. LYS windday ** ns ** ns ** ns PL wind24 vs. PL windday ** ns ** ns ** ns LYS windpm vs. PL windpm * ns ns ns ns ns LYS windratio vs. PL windratio * ns ns ns ns ns Legend: LYS - LYS weather station PL - PL weather station * - significant at the 0.05 level ** - significant at the 0.01 level ns - not significant 82 Table 8. Results of mean comparison tests - solar radiation. 1986 1987 1988 Comparison mean variance mean variance mean variance LYS solrad vs. PL solrad ns ns ns ns ns ns Legend: LYS - LYS weather station PL - PL weather station * - significant at the 0.05 level ** - significant at the 0.01 level ns - not significant 83 .2268 was 2.565: 2:2. 26:86 9:26 9333.2: :62: new :49...th otsamtoasoa cmoE 230 one? .0 052“. can... 2.2320! ago... 2.66 ..... mwxh Omxh hxh wao pwxo Oxa ouxo rmxm mwxw mxm o Qza 33433441311344.4441 a +1.13 411—14131344+ 33111131441341 4 or 4. ~42 . no. 4 ~. . — ~ - a . .. . . . . ~ . .o u . s . c . ea . .v \ . . . . 2 . 4 . . e .. .\. . .. .. 4. . 1 . \ OF - 6 s a . a a . L . . . o . . . . . . . a 4 . . . m c g - ea s y a . . s . x 2 .a e 4 . . . a .11 . . . .4 . I \ . . 4 . . . . .. . s . s - . . 6 u . . s . . . . , . .. .. s ’ .. . 2 a . . . .. \ o . . s 11 ON . s e: a . . s n. \ . . 2 .. I. e e .s . . s . . a . a . p e 0‘ ) u a . \ ; 2 . . .. .- 2 . .2 . o a . e s a 4 s . . a I . r o I . o. C 4 . . . II. C a s o a g a. o . o o o s . ‘ am e a o o e — . .. . . . 1 UN . . g . . . . . x I. 1 . on 3. 23anth 84 .2653... ma: £3..sz 9:6: 29.52. acts—o anaemia—EB :on cam Avwmzmt .v 0.53m 2.582355 5.65 3:26 .23— :so:. .2220 ..... 535 $32.23. a} a} an}. 2}. {a an} s}. as as 3}“ ER in _ _ _ _ _ _ _ _ r _ _ :22.22:23:21:22:Z::11.32.—1:12.231:_2:22:22:._:._1::::::j_2222121222:.2212: c 1 m. as 0 ~..-.- 4 @— -----.- _ I 63 engages“; on on 85 .2653. $3 :31sz 9:6; 202.26 war—:.. 0:530:53 C005 0:0 Amy—Em: 9.3000553 :005 A330 3:: .m PEEL :09: 3:... ..... :00:~a:u:A0v s}. on} 2}.“ ”\n an} :3 an} E? a}. on}. mi... _\s is 31413231331334.4321;3233?:35332251273333713:2.512533112331333o -- a o. a. 5.:.. on ..... ... ...... an on 8v 0.~3s._0a._.0._. 86 .mcozwam 200.50: 55:09:50 2.33: :005 .33. 36:55 2538 £2 .0 95»: :osfim .E II 532m m: ..... :3 a; on} SE SE _ _ _ _ NS 5}. ab. on? u —:___fifi4_04__fiq~:_____d_:_~fi_ m). 1+-34-3..3-T344444Tfl311111344141113: on 5. Lee 1 co ALE".---. -- Q- -----. ..- cc an. as ea at 3.35:: 2:23. cc— 87 m\m um\c 0:030? :00.50n 503000500 3&sz :00:— 516 938:: 2532 $2 x 95»: 553.. .E I :23,» m5 ..... a} on}. SE a? a} _ b _ _ p _ _ . :‘IZAaddeAIZ_H4:22.—2::2232__::::::_22:23—24:444:__fi ‘ o .“ ‘ 3} min in. 34444:.-szij cu - on 1 2. L an .. 2. E + a: 2: at 3.28:: 3:23. 88 .9520? :00>50n cantan—Eoo Avmzmv :00:— xzac .3625: «532 9:: .c 0.5”?— Efifm 2 ll :22; m5 ..... ”\m 5.3 on}. on}. on? 23 a}. ”in min a} 13133313341+13431A3j4j4+133j+33441jj4qj+4413j1 on I. on ow on so cm. -cc ca 2: :3 3.25:: 2:20: .mcoSSm c0950: 55:09:00 322.3: 55:3me 3:2. 325:; «>522 2:: .a Sam: :23? .E I .3330 m>4 ..... N_\a cm}. 2}“ 2? ”>0 ab. .5. on}. an}. _ _ _ _ r _ _ -- . 3_____2__.______2_2_2._afi__432_fi23242244__q«qa_3~_q3_3_._a4_____ch .. cm. so 9 8 -. E. -. an ,..o.. n s... ...... ..s ... UL. ca o~c ... .. .. ... ... \ \ ... ... H. s. .. ... H. ' :.. N. ‘ go ' ks - b. n N\ a! L. a . .4, . p) u a? s $6“ :5 3.28:: 2:23. 9O .mCOSSm c0930: :OmZaQEoo 322:5 :25:me 3:6 32:5: 332...... $2 .3 95.0.2 53% .E I .833» m: ..... 5}. an? a} cm}. 2:. mm}. 2}. SE SE :\n _\ 1133+j§3+§i43jjifi 31: 73433-: 3.333 r 3.33:, r 31 a 3-31: 3.3 31313 :2 Q; 3:252. 3:52 m :7 cc an an an ac— 91 .mcoSSm .5930: 500200500 322:5 53:62:: 3:6 3:28.... 2522 32 .2 2:0: 553m .5 I :233 m: ..... SE 3.2 {a 3K... Eb. an}. 2}. a). 53 1.13. +3444l|3441fifi+j4j111+4j 3 3?. 2?. NS -1 jjjilfiqj-1_j-_-_jlfillfiffijji 33.334Tjjj A E. 1 an cc cm. as 33 .- Q; 325:: 3:23. cc— :3 0:03.30 c0250: 500:0an0 A2353: £23558 3:3 3:222. 2522 2:: .3 3:2... 92 :23; E I :23» m5 ..... {a an} BE 2? NE Sb. 3... an} an _ _ _ _ _ 2:22__22_~___~_________2_4_______444__+fi4_ _ _ 84-]_4_____fi___fi.__fi_1421121 .- ““ -c OI: o: 03 <5 32:3: 2528. cc— 93 6:23am :00353 55mean A2345: 8352:: EEC 32:55: 2,553.. $2: .2. 0.53,.— cossn .E II 553.». m: ..... cm}. 2}. 5). a}. on} min (a a} S? a? o ..+_.3|3313.l-_ 413.3 ._-jj_rfl3§fil4j§.:q _+4._43433-_13ji13 3.; 3.3- 244.3 +3.: 3 4-344- 4 3. 313% :1 9‘--. -¢----- .--¢‘.“- 0- 9-- .- ‘~ cm. 0--------.’ . OO-Cuvv- _ cc an. “"-'--‘—-v - 1 cc oo— §. 3.25:: 2:2»: 94 .mcofigm .3953; 5535950 A2253: Bah—$25 :26 93:5: 3:22 2:: .3 2%: :22; .2 I :23; m: ..... ”\a 5% on} on} 3.9 SE a? 5R 2}. a}. c 44...].44433334T44: _ _ . _ w q _ _ ‘4‘: _ T _ _ _ 2 _ _A-_4jjqfifi+3jflfi3+4-fifl34nfija \‘1 cc .U‘r' an. -~----C-.----o-C--w n- g---ga-C"'- “'5 cc -.- on: C5 5215:: 3:23— 9S . .3230: EN 3 cmaomtoov mcofiwam cmubzmn :Omiwaaoo Avmnziv 55:. 53v .525 6:; one .9 95m; 535% .E I :csfim m: ..... on? 2 \o {a .3} v _ \c a} an} 5}. a} on} an? §%.Tj§¢3i-3-juflfil-lajjfijal Iii; «1.2;2231 o 4 a... a}... 32$ 3:: 9v 96 .Gsmmmn EN 3 9:02.53 mGOSSm Gumtree; :OmCmano :Naz;: cams: >556 cavam 653 2:3 .2 95%: :33? ,E l. 533$. m: ..... 53 a} an} S? {a nab. a? 5.3 c\c an} 2}. --_ .~-“ . .. Q . _\ ..aqarjddqagfiqfiggjjrajqflqfii;j a: 331—731: I _ 2:344:3«1 gqarjflgl . 334224. .L-.--_.-j..-.-.- ...-.. m. Am\c:v vvoam ..:E c n. C O») 9N 97 .CswE: EN 3 .Vmaomugoov mcofism 55250: :omtaaaoo Avmoz_3v :88 :23 .52; Ex: 25. .2 2%: :23.» m: ..... {a an}. IE m\ 55% .E II n n c in 2}. an? :E on} 23 a} on? 2D 31: 531221313.33%323l2332$33.3}13513...:33233133213 33:31:: :1 -4— N J o .r a.” g min Am)»: 102—m 1:; 98 More variance was recorded in the relative humidity measurements. From Table 2, it can be seen that the coefficient of variation of the variables from the PL station in 1986 were substantially less than half of the values in 1987 and 1988. Year to year variation is expected, but this appears to show problems with the measurement of relative humidity at the PL station in 1986. The higher means at the LYS station are likely due to the RH sensor being in the adjusted boundary layer of irrigated corn in 1986 and irrigated alfalfa in 1987 and 1988. The thickness of the fully adjusted boundary layer was approximated using the relationship by Munro and Oke (1975): 6(x) = 0.1x°'8 200'2 [98] where 6(x) is the thickness of the fully adjusted boundary layer; x is the distance downwind from the leading edge of the field; and 20 is the roughness length of the crop surface. It was determined that the LYS station RH- temperature sensor was within the adjusted boundary layer given the fetch around the station for all three years. The no significant difference of minimum relative humidity in 1986 between stations may have been the result of the PL station sensor recording incorrect minimum values. This in turn would have an effect on the average RH calculated from the minimum and maximum values and is 99 evident by the comparison with the daily mean of 24 hourly means from the PL station being very significant (a=0.01). The comparison of the two calculated means from the LYS station in 1986, in contrast, was not significant. In 1987 and 1988, the comparisons of the two calculated means from the same station were not significantly different. In general, there is no significant difference between determining a daily mean of relative humidity from 24 hourly means or from the daily minimum and maximum values. Due to different heights of the wind speed sensors above the ground at the two stations, a correction was applied to the higher PL station values using the logarithmic profile. The significant differences of the wind speed variables between the two weather stations in 1986 are most likely due to the higher canopy of the corn since an in season correction was not made to the wind measurement as the corn canopy grew in height. The 1987 and 1988 comparison of the night wind speed and the day- night ratio were not significantly different probably due to measured wind speed being close to the sensor threshold at night and alfalfa being more similar in height to grass than corn. The daily wind speed (24 hour average) and average during the daylight between stations were found significantly different in 1986 and 1987, but not 1988. The mean wind speed at the LYS station was found to be higher than the PL station in 1987. Since both 1987 and 1988 were over alfalfa, a possible explanation for the very 100 significant difference (a=0.01) in 1987 is the greater number of observations (142 compared to 113). In 1987, more measurements were made over a lower alfalfa crop height due to the crop being first year alfalfa and wind still being measured after last cutting resulting in less resistance in the wind profile. Another possible factor may be due to roughness elements around the PL station, such as: weeds and brush not mowed and buildings up wind of the weather station. Statistically, the solar radiation between stations agreed well with the means from the PL station being higher than those from the LYS station. In 1987, an incorrect sensor multiplier was entered in the datalogger program at the LYS station, but with a new pyranometer installed in 1988, the old sensor was recalibrated and a back calculation was performed to correct the 1987 data. Except for the mean comparisons, the 1987 radiation data from the LYS station were not used in the equation calculations. The total solar radiation from the two stations are compared with net radiation for the years 1986 and 1988 in Figures 18 and 19. Net Radiation The measured net radiation from 1986 and 1988 were used to develop a relationship with total solar radiation. The net radiometer was not functioning reliably in 1987, so no regression with total solar radiation was performed in 101 .flofloflvau god and 3333.. nookaoa 5339300 33303 5383 .38 33 88 ..: 23:. so. .3 II and II. .33- mra ..... 3} 2} {a on} 3). 3). s}. a}. §\s 3}. a}. on). a} _ — _ _ _ _ P _ _ _ _ _ a:—_—_—aqq4_::_—:_A—_q~d_4_4qq::—_:_::d—::_____:dqa—_4_d__:_uq_fi—A_____: Anus-v suntan: gang—.0 fin 102 dead?!" «on was 3333.. Quebec.— aonidmaoo Andy—.38 83.5.3 .38 33 82 .2 cans 38.—ml «all .3895 ..... 3). a}. a}. «\o «a? 2}. a}. 8} 2}. {a an}. «in «\u _ _ _ _ _ _ _ p _ _ _ _ :Aqule—I:2.31:2:12:..—...::—_:::=:::::::_::::=:=::__:..—2::—:::::::::: O #— Agv defiance->0 ado—.3390 103 that year. Data were from the LYS station where the miniature net radiometer and pyranometer were mounted on the same tower. The two sets of data were analyzed in the linear regression model: y = a + b x [99] where y is the measured net radiation; x is the total solar radiation: b is the regression coefficient: and a is the y- intercept. The 1986 data set consisted of 88 days from mid-June to mid-September and was measured over a corn crop. The regression equation for the 1986 data is: y = 0.45753 + 0.51035 x [100] which is shown graphically in Figure 20. An R2 of 0.91 was obtained and the intercept coefficient was found to be significantly different than zero. In 1988, a data set of 151 observations over second year alfalfa from May through September was used resulting in the relationship: y = 0.04182 + 0.486127 X [101] which is shown graphically in Figure 21. The R2 was 0.91 and in this case the y-intercept was determined to be not 104 vn an «a an .33: no.8 500 a no; 2338 mic 83.5.3 .38 33 8 55.5.: «on we nomunouuom .om car— ?)55 83:8: 38 189 S a a s o o 8 a u a a on H a . S... u mm am 3n... + cafe fl 0325 J 2555 53.3 «oz 8.3-8: 105 *— .Acoa—v can? hobo 353cm mac sons—:..— uflou 33 :0 Q8333.— aofl no 5:80.53— .uN 0.:qu finial—av floflI—vlfl How 38. an an an an o c b o o v n N n c _ _ _ u _ _ _ d 1 _ _ _ — I II I I l I II I I I l I I I II II II .1 II . .u . . . .. . .. I I I I I II I I I III I I. .1 . .1... r I ._. ...a. I II I I. II I . . Gan: . Sauna! mm mean: + «3.6 fl 010:3 :35: nos-:..: 82 e888: 106 significantly different than zero. Forcing the regression through the origin resulted in: y = 0.49038 x [102]. For this study, the following expression was used to calculate net radiation when that variable was required in a potential ET equation: ncalc = 0.5 Rs [103] where R is the calculated net radiation and RS is the ncalc total solar radiation measured at the PL station. Vapor Pressure Deficit Various methods of calculating the vapor pressure deficit using different equations and variables from the two stations were compared and ranked by means (Tables 9 through 11) and shown graphically in Figure 22. The equations used in the different methods are listed in Table 12. The methods with the higher deficit values are calculated as hourly vapor pressure deficit values averaged during the daylight hours and the calculation using temperature and relative humidity averaged during the daylight hours. The daylight hours are determined when the pyranometer sensor was recording greater than zero. Table 9. Rank Station 1 LYS 2 LYS 3 LYS 4 PL 5 PL 6 PL 7 8 LYS 9 PL 10 PL 11 12 LYS 107 calculation methods (kPa) (n = 82). Variable VPDl (VPD24) VPD2 (VPDAVG) VPD3 (VPDEF) VPD4 (VP024) VPDS (VPDAVG) VPDG (VPDEF) VPD? (VPD24MTP) VPD8 (VPDDRHD) VPD9 (VPDDRHD) VPDlO (VPDDAY) VPDll (VPDTEMP) VPDlZ (VPDDAY) X 0.510 0.540 0.584 0.595 0.655 0.668 0.673 0.780 0.818 0.857 0.858 0.885 SD 0.210 0.199 0.220 0.162 0.178 0.189 0.203 0.272 0.243 0.267 0.258 0.304 Ranking by means of 1986 vapor pressure deficit CV(%) 41.1 36.8 37.6 27.2 27.1 28.3 30.1 34.8 29.6 31.2 30.1 34.4 108 Table 10. Ranking by means of 1987 vapor pressure deficit calculation methods (kPa) (n = 142). Rank Station Variable i SD CV(%) 1 LYS VPD1 (VPD24) 0.657 0.381 58.0 2 VPD? (VPD24MTP) 0.683 0.288 42.1 3 LYS VPDZ (VPDAVG) 0.714 0.355 49.7 4 LYS VPD3 (VPDEF) 0.737 0.419 56.9 5 VPDll (VPDTEMP) 0.814 0.333 40.3 6 PL VPD4 (VPD24) 0.848 0.386 45.5 7 LYS VPDB (VPDDRHD) 0.879 0.485 55.2 8 PL VPDS (VPDAVG) 0.892 0.365 40.9 9 PL VP06 (VPDEF) 0.935 0.437 446.7 10 LYS VPDlZ (VPDDAY) 0.950 0.526 55.4 11 PL VPD9 (VPDDRHD) 1.084 0.503 46.4 12 PL VPDlO (VPDDAY) 1.151 0.546 47.4 109 Table 11. Ranking by means of 1988 vapor pressure deficit calculation methods (kPa) (n = 118). Rank Station Variable Q SD CV(%) 1 LYS VPDl (VP024) 0.723 0.380 52.6 2 LYS VPD2 (VPDAVG) 0.738 0.352 47.7 3 LYS VPD3 (VPDEF) 0.829 0.434 52.4 4 VPD? (VPD24MTP) 0.832 0.324 38.9 5 PL VPD4 (VPD24) 0.900 0.493 54.8 6 LYS VPDB (VPDDRHD) 0.963 0.518 53.7 7 PL VPDS (VPDAVG) 0.965 0.539 55.8 8 VPDll (VPDTEMP) 1.037 0.383 36.9 9 PL VPD6 (VPDEF) 1.038 0.539 51.9 10 LYS VPDlZ (VPDDAY) 1.081 0.548 50.7 11 PL VPD9 (VPDDRHD) 1.182 0.619 52.4 12 PL VPDlO (VPDDAY) 1.299 0.690 53.1 Vapor Pressure (kPa) 110 m1“ !\ WW ' ' ' m T; |\\ .V‘r._\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\I I .& \IIIIIIIIIIIIIIIIIIIIIIIIIL l\\\\ \ \\\\\ \\\\\\\ \ ‘ i\\\\ \‘l‘l‘ VPD] VPD2 VPDS VPD4 VPD5 VPD6 VPD? VPD8 VPD9 VPDlO VPDIl VPDIZ 118) CI] 1988 (n 142) % 1937 (n - 1986 (n=82) Figure 22. Means of vapor pressure deficits from different methods of calculation (see Table 12). 111 Table 12. Vapor pressure deficit equations compared. VPDl (LYS vpd24) = SVp24 (1 - LYSrh24/100) VPDZ (LYS vpdavg) = sva4 (1 - (LYSrhmin + LYSrhmax)/200) VPDB (LYS vpdef) = svp (1 - LYSrh/lOO) [hourly vapor pressure deficit values averaged over 24 hours] VPD4 (PL vpd24) = sva4 (1 - PLrh24/100) VPDS (PL vpdavg) = sva4 (1 - (PLrhmin + PLrhmax)/200) VPDG (PL vpdef) = svp (1 - PLrh/lOO) [hourly vapor pressure deficit values averaged over 24 hours] VPD? (vpd24mtp) = svp24 - svptempmin VP08 (LYS vpddrhd) = svpday (1 - LYSrhday/IOO) VPDQ (PL vpddrhd) svpday (1 - PLrhday/lOO) VPDlO (PL vpdday) = SVp (1 - PLrh/lOO) [hourly vapor pressure deficit values averaged during daylight] VPDll (vpdtemp) = (svptempmax + svptempmin)/2 - svptempmin VPDlZ (LYS vpdday) = svp (1 - LYSrh/lOO) [hourly vapor pressure deficit values averaged during daylight] where: svp = hourly saturation vapor pressure calculated with hourly mean temperature sva4 = satuation vapor pressure from daily mean temperature svpday = saturation vapor pressure calculated with temperature averaged during daylight hours svptempmax = saturation vapor pressure calculated from maximum daily temperature svptempmin = saturation vapor pressure calculated from minimum daily temperature rh = hourly mean of relative humidity rh24 = daily mean relative humidity from 24 hourly values rhmin = daily minimum relative humidity rhmax daily maximum relative humidity relative humidity averaged during the daylight hours rhday 112 Since the LYS station was over an irrigated crop it, generally, had a lower mean vapor pressure deficit than the values from the non-irrigated PL station. All the vapor pressure deficit values except VPDTEMP and VPDZ4MTP used a relative humidity term in their calculation of vapor pressure. Daily minimum temperature was substituted for dew point temperature in VPDTEMP and VPDZ4MTP. Since there was no significant difference detected in the minimum temperature between the two different stations, the minimum temperature from the PL station was used. Potential Evapotranspiration Estimation The two years of alfalfa on the weighing lysimeter provided an excellent opportunity to compare how well various equations estimate potential ET. Days before the first cutting in the first year were not included in the analysis and thereafter only the days when the alfalfa was at full cover were used. Water was assumed to be non- limiting to plant growth and days with precipitation during the daytime were deleted from the analysis. A total of 28 days in 1987 and 54 in 1988 were used in the analysis. The lysimeter ET totaled over the 28 and 54 days was 122.7 and 310.7 mm, respectively. Table 13 is a summary of the climatic statistics of the days included in the potential ET equation analysis. 113 Table 13. Summary statistics from the days used in potential ET equation comparison. --1987 1988 Crop alfalfa alfalfa Number of full cover days with no daytime precipitation (potential evapotranspiration conditions) 28 54 Range of dates in comparison 7/28-9/10 5/2-9/1 Mean lysimeter evapotranspiration (mm/d) 4.4 5.8 Accumulated evapotranspiration (mm) 122.7 310.7 Mean temperature (LYS station) (°C) 20.6 19.2 Mean temperature (PL station) (°C) 21.6 20.1 Mean relative humidity (LYS station) (%) 75.1 67.5 Mean relative humidity (PL station) (%) 64.3 61.0 Mean wind speed (LYS station) (m/s) 2.0 2.1 Mean wind speed (PL station) (m/s) 1.8 2.2 Mean solar radiation (LYS station) (MJ/mz) 20.7 24.6 Mean solar radiation (PL station) (MJ/mz) 21.4 25.6 114 Penman Formula Twelve different forms of the Penman "combination" formula were calculated differing mainly in the weather station from which the wind speed was obtained and which method was used to calculate the vapor pressure deficit. With the Penman equation in the form of: ET = P the variables EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ 6/(6+1) Rn + 1/(6+1) 2.63(1 + 0.537 U2) VPD [104] used in the various equations were: 1 - 0.5 2 - 0.5 3 - 0.5 4 - 0.5 5 - 0.5 6 - 0.5 7 - 0.5 8 - 0.5 9 - 0.5 10 - 0.5 11 - 0.5 12 - 0.5 (PL (PL (PL (PL (PL (PL (PL (PL (PL (PL (PL (PL RS) Rs) Rs) RS) RS) Rs) Rs) Rs) RS) Rs) RS) Rs) The regression statistics LYS wind PL wind LYS wind PL wind LYS wind PL wind LYS wind PL wind LYS wind PL wind LYS wind PL wind VPD LYS vpdef PL vpdef LYS vpdday PL vpdday vpdtemp vpdtemp vpd24mtp vpd24mtp LYS vpdavg PL vpdavg LYS vpddrhd PL vpddrhd for both years are contained 115 in Table 14 with the various equations ranked according to the total ET estimated over the days in the analysis. Within each year, the range between the various equations was considerable. In 1987, the range was 116.4 mm to 138.9 mm compared to the lysimeter recording a total of 122.7 mm. In 1988, the range was 259.9 mm to 315.6 mm with the lysimeter recording 310.7 mm. The year 1988 was unseasonably hot and dry during most of the growing season resulting in most of the equations underestimating the ET from the irrigated alfalfa. No equation estimated daily potential ET particularly well when slope, intercept, and R2 are considered. Two equations that performed reasonably in both years were #2 and #6 and their fit with the lysimeter ET is shown in Figures 23 through 26. Both contained the wind speed from the PL station with the vapor pressure deficit in #2 calculated as a daily mean from hourly vapor pressure deficit values calculated as: PL vpdef = SVPRES (1 - PL RH/lOO) [105]. The vapor pressure deficit in equation #6 was calculated as: Vpdtemp = (SVPMAXTP + SVPMINTP)/2 - SVPMINTP [106]. 116 Table 14. Correlation and regression statistics of measured ET versus potential ET estimated from Penman Equation (mm). 1987 (n = 28) E0 2 ET slope intercept SEE R2 MEAN "1'" '11??? '5??? "63337;" $337 3363' "23" 9 117.6 0.727 1.006 ** 0.216 0.870 4.2 8 118.8 0.801 0.726 * 0.286 0.823 4.2 7 120.3 0.810 0.741 * 0.289 0.823 4.3 11 124.3 0.782 1.000 ** 0.202 0.899 4.4 6 125.1 0.804 0.957 ** 0.281 0.828 4.5 10 126.3 0.837 0.848 ** 0.268 0.852 4.5 5 126.8 0.807 0.995 ** 0.287 0.908 4.5 2 127.4 0.848 0.842 ** 0.260 0.863 4.6 3 127.5 0.796 1.064 ** 0.215 0.891 4.6 12 135.9 0.857 1.106 ** 0.264 0.862 4.9 4 138.9 0.848 1.239 ** 0.266 0.857 5.0 * - intercept significantly different than zero at the 5% eve ** - intercept significantly different than zero at the 1% level 117 Table 14 (cont'd). 1988 (n = 54) EQ 2 ET slope intercept SEE R2 MEAN "3'" '35:? "3233' "131371" ”3311" '32??? "I3" 7 267.1 0.534 1.878 ** 0.692 0.539 4.9 8 268.5 0.536 1.889 ** 0.686 0.544 5.0 1 270.7 0.619 1.449 ** 0.840 0.516 5.0 10 275.4 0.690 1.129 * 0.789 0.560 5.4 5 283.9 0.556 2.054 ** 0.729 0.533 5.3 11 284.1 0.647 1.538 ** 0.906 0.500 5.3 6 285.6 0.564 2.046 ** 0.725 0.543 5.3 2 288.1 0.736 1.104 * 0.910 0.562 5.3 3 294.6 0.659 1.655 ** 0.962 0.479 5.5 12 305.0 0.782 1.150 * 0.971 0.560 5.6 4 315.6 0.817 1.143 * 1.053 0.542 5.8 * - intercept significantly different than zero at the 5% eve ** - intercept significantly different than zero at the 1% level 118 .N* combo—ice PM 33:32— amficom .25— .nm 953..— .: Ii .5 55.5.5 52:55 ._ :(EE. :oSahA—nsabogerm 532593 ad ad. v min 9 Wm N n; _ 0.: o in, i L _ a a _ _ A . nil. _ _ \ 1 \\ . and H mm 1 . ..:. $66 + as; n PE 1 ..\.\.il.. - :.\EE. cotahaa:cbcaa>m €30.53”.— ad a; mum mun 0.9 an 119 .31 :23:on E 3:688 565:. $2 3 23: L: E ~335qu saga—om .. :(EEV :oSahaE—cboou>u 33.593 _: E a a a c n v m m _ c I s L _ _ s s _ _ s s .\ \\\\\\ I \\ I \ I I I I I L I. - I I I I I J \.\.\ \ 8.6 u mm 1 -.\ :.m once + 2:4 u PE -. :.\:25 .8323933 933— toga—Sam c— .— 120 e on m n... 6* .3331; ,5 63:33 588.1 .82 .mm 2:9... L: i .5 :oflcsvm season lol :{EEV somaabaasgaoagm Logos—L83 v nd a 9N N n; L 06 o L a L L L 1-1L L L mod N. NE .5 39¢ + $56 n 5m 1 :w\EEV comauhomcabomofi coda-5:5 n6 n6 If) we tn 121 LL 6* science .5 LmLLCoLoAL amazon— mca— .om osswLfiL L; III .5 5.33:5 can—ES . Lo\EEL :oLLauEuccbon—gm Loam—=33 CL 5 a b c n v n N L o \ 36 H mm 75 86.6 + 625. u ALE Lv\EEL :oLLcuLa—mcaboaakm @355me 0L LL 122 FAQ Modified Penman Formula The FAO modified Penman was better at estimating the potential ET at the lysimeter. Four equations were compared in 1987 using calculated net radiation. Actual measured net radiation was added to the equations in 1988 making a total of eight. With the modified FAG-Penman equation in the form of: ETp = c [ 6/(6+1) Rn + 1/(6+r) 2.03 (1 + 0.537 U2) VPD ] [101] the variables used in the various equations were: C Rn U2 VPD E0 1 - (LYS) actual LYS wind LYS vpdavg E0 2 - (LYS) actual LYS wind vpd24mtp EQ 3 - (LYS) 0.5 (PL Rs) LYS wind LYS vpdavg EQ 4 - (LYS) 0.5 (PL RS) LYS wind Vpd24mtp EQ 5 - (PL) actual PL wind PL vpdavg E0 6 - (PL) actual PL wind vpd24mtp EQ 7 - (PL) 0.5 (PL Rs) PL wind PL vpdavg EQ 8 - (PL) 0.5 (PL RS) PL wind vpd24mtp Equations 3, 4, 7 and 8 were the ones used in 1987. The methods of calculating the vapor pressure deficits are the ones recommended in the FAO Irrigation and Drainage Paper 24. Table 15 lists the regression statistics and ranking 123 of equations by total ET estimated. All the intercept terms were tested as not being significantly different than zero. Equation #7 did stand out as estimating accumulated potential ET closest to the actual lysimeter ET total, underestimating 0.8 mm (-0.65%) in 1987 and 10.5 mm (-3.38%) in 1988 and is shown in Figures 27 and 28. Its variables were: calculated net radiation, wind speed from PL station, and the vapor pressure deficit calculated as: PL vpdavg = SVPRES (1 - (PL MINRH + PL MAXRH)/200 ) [108]. Other vapor pressure deficit methods which are not recommended by Doorenbos and Pruitt (1977), but used in the Penman equations were compared in the FAO modified Penman with the corresponding regression results and ranking listed in Table 16. The variables used in these equations were: C Rn U2 VPD EQ 1 - (LYS) 0.5 (PL RS) LYS Wind LYS vpdef E0 2 - (PL) 0.5 (PL Rs) PL wind PL vpdef E0 3 - (LYS) 0.5 (PL Rs) LYS wind LYS vpdday EQ 4 - (PL) 0.5 (PL Rs) PL wind PL vpdday EQ 5 - (LYS) 0.5 (PL Rs) LYS wind vpdtemp EQ 6 - (PL) 0.5 (PL RS) PL wind vpdtemp EQ 7 - (LYS) 0.5 (PL Rs) LYS wind LYS vpd24 EQ 8 - (PL) 0.5 (PL R ) PL wind PL vpd24 124 Table 15. Correlation and regression statistics of measured ET versus potential ET estimated from FAD-Penman. 1987 (n = 28) EQ 2 ET slope intercept SEE R2 MEAN "3"" '11:? 3323' 'STBEE'QQ' 7333' ".731" "31'1" 3 115.5 0.892 0.212 ns .323 .819 4.1 4 117.6 0.970 -.060 ns .356 .815 4.2 7 121.9 0.990 0.027 us .376 .804 4.4 1988 (n = 54) EQ 2 ET slope intercept SEE R2 MEAN "1"" "53?? "6313' 331233;" "BT33? "EYES?" "3T3" 2 279.0 0.762 0.779 ns 0.941 0.563 5.2 3 281.9 0.767 0.813 ns 0.861 0.609 5.2 6 283.5 0.716 1.132 ns 1.079 0.464 5.2 4 288.2 0.713 1.244 ns 0.883 0.561 5.3 5 290.4 0.863 0.415 ns 1.105 0.544 5.4 8 293.3 0.664 1.616 * 1.056 0.437 5.4 7 300.2 0.805 0.929 ns 1.087 0.519 5.6 ns - intercept not significantly different than zero level **— level intercept significantly different than zero at the 5% intercept significantly different than zero at the 1% 125 5% noise—Loo Em LwLLGoLoQ ceases 66:62: 92 .82 .5. Es»; 3 II E .8333. 3... IT Lp\EEL coLLouLmnscSooI>m ..36533 n m6 v ad a 0N N nL L 06 o . and H mm L L L L L L L1 L L L :.m med + Sod u 95 GEE»: :oLLauLsmseboA—akm LeoLcELme 9L 0N min 06 on 126 LL cL i1..-!- L..i-!-.l ELL :oLLasLoo .5 Lose—32L Season LooLLLLooE OLE 35L .LLN manna 3 II E 5:35 2; IT Lv\EEL COLLILLALBLPSOASLM .LBQELPS mod .I. Nm .1 LEM. Goad + mmmd H abm -1 Lv\EEL :oL_Lm.~LALm:oLLon—a>m @325me L: LL 127 Table 16. Correlation and regression statistics of measured ET versus potential ET estimated from FAD-Penman with not-recommended vapor pressure deficit methods (mm). 1987 (n = 28) EQ 2 ET slope intercept SEE R2 MEAN 8 109.6 0.900 -.040 ns 0.346 0.800 3.9 7 111.3 0.929 -.093 ns 0.325 0.828 4.0 1 114.4 0.937 -.024 ns 0.340 0.818 4.1 6 120.3 0.954 0.114 ns 0.368 0.799 4.3 5 123.0 0.977 0.112 ns 0.355 0.817 4.4 3 123.9 0.961 0.210 ns 0.377 0.793 4.4 4 132.0 1.015 0.274 ns 0.440 0.759 4.7 2 132.4 1.286 -.905 ns 0.450 0.829 4.7 ns - intercept not significantly different than zero * - intercept signicantly different than zero at the 5% level ** - intercept signicantly different than zero at the 1% level 128 Table 16 (cont'd) 1988 (n = 54) EQ 2 ET slope intercept SEE R2 MEAN ""7"" "2333" "3321" "373532;" "6335" "3:333" "3'3"" 1 292.4 0.795 0.846 ns 0.968 0.569 5.4 8 300.9 0.814 0.888 ns 1.108 0.514 5.6 5 304.2 0.741 1.366 * 0.915 0.563 5.6 6 309.8 0.691 1.763 ** 1.084 0.443 5.7 2 312.8 0.850 0.905 ns 1.230 0.483 5.8 3 315.2 0.845 0.967 ns 1.097 0.538 5.8 4 339.8 0.942 0.874 ns 1.367 0.482 6.3 ns- level **- level intercept not significantly different than zero intercept signicantly different than zero at the 5% intercept signicantly different than zero at the 1% 129 Interestingly, but not surprising, equation #6, one of the equations estimating ET better than the others, contained the same variables as Penman equation #6, which was also better at estimating the lysimeter ET in the Penman equation comparison. Its fit with lysimeter ET is shown in Figures 29 and 30. Another equation doing well in both years was equation #3 which contained wind speed from the LYS station and the vapor pressure deficit as the mean of hourly vapor pressure deficits calculated as: LYS vpdday = SVPRES (1 - LYS RH/100) [109] and averaged over the daylight hours. Its regression is represented in Figures 31 and 32. This is the only equation in the potential ET equation comparison that used relative humidity from the LYS station and had a variable averaged during the daylight hours. Priestley-Taylor Equilibrium Formula The variables changed in the equilibrium ET equation of Priestley-Taylor were the time interval and station from which the temperature in the 6/(6+1) term was obtained and net radiation being the actual measured in 1988. The regression results and ranking for both years are contained in Table 17. With the Priestley-Taylor method in the form of: ETP = 1.26 6/(6+1) Rn [110] 130 1 111114 L L L L n L L T L L |\I. cs E .8333 so 35:33 9; cooLLoEEoooLlso: om voLIELme mic AWL G1 9N w. 0') 0.9 n6 133 .QL :ofiwsvw 9m LaLacmLoa 02> cavemEEoomulco: OLE one .Nm 9.sz E 1.. ,5 532......— ofi IT L v\EEL :oSaaEIcaboggm £52593 LL CL a a m. c n v n N L c I I \\\x\ \ \\\ 1 \\\\\ II I \ I I l 1 . I I I I I I I II I I I I I I I II I III _ I I I I I U L II I II I I I I .1 I I I \ #0 O H NM 1 \\\ \1\ 75 Sad + $3. n 95 Rm 1 I Sing—L :cSahamcabonSfi @325me u: L: LL 134 Table 17. Correlation and regression statistics of measured ET versus potential ET estimated from Priestley-Taylor method (mm). 1987 (n = 28) EQ 2 ET slope intercept SEE R2 MEAN "2’" "16;? 3333' 33332;" "572;? 3322’ "373" 4 111.9 0.852 0.265 ns 0.309 0.818 4.0 1988 (n = 54) EQ 2 ET slope intercept SEE R2 MEAN "1"" "333?? '33? "33321;" "6333' ‘63? "2'3" 3 238.5 0.596 0.983 * 0.816 0.512 4.4 2 241.6 0.515 1.514 ** 0.666 0.540 4.5 4 250.2 0.530 1.585 ** 0.701 0.529 4.6 ns - intercept not significantly different than zero * — intercept significantly different than zero at the 5% level ** - intercept significantly different than zero at the 1% level 135 where the temperature and net radiation variables in the various forms were: 6/(6+1) Rn EQ 1 - PL TEMP24 actual EQ 2 - PL TEMP24 0.5 (PL RS) EQ 3 - LYS TEMPDAY actual EQ 4 LYS TEMPDAY 0.5 (PL Rs) Using the coefficient of 1.26, the Priestley-Taylor method underestimated potential ET in all forms. The form using temperature from the LYS station averaged during the daylight hours underestimated lysimeter ET by 10.8 mm (-8.80%) in 1987 and 60.5 mm (-19.47%) in 1988. Its regression with lysimeter ET is shown in Figures 33 and 34. CERES-Maize Potential Evapotranspiration Equation Formula One form of the ET method in CERES-Maize was analyzed in both years. Since there are not many variables required in the equation and the ones used are specific to the equation, no variable substitution was performed. An albedo value of 0.23 was used since the total analysis was done over a full cover crop of alfalfa where no soil was exposed. The form of the CERES-Maize EEQ equation and the 136 4% :oLLosLom Hm LoLLGoLoQ LAVLhmhlmmLLmoLum 2:: .mm 95th 3 .II E 532.5 .7; IT Lo\EEL :oLLIuLA—InaboAELML 53653.3 ad 9 9v v ad 9 Wm N mL L ad 6 ‘ L . 1, I L11---I.IIL.-.i!|I.IALbIIi fl L L 11:43:25. .14-- 1311;41:11111L1liamwxu ‘1 7E «and + moms n at. Ami-=5. :oSELAm:I.52La>m poses—3mm u: c' O! 1.7 O u“ \C‘ v O L? to 137 L.» :ofiozvo Hm LwLacoLod 8:513:82; 32 .2“ 95»: LHL ll: Pm cofiozvm .L.InL III Lo\EEL :oSauLAIcaboagm swam-Em} LL 2 a o m. c n v n N L c -3114“ L L J m L L L L L \X mod H mm .5 Sad + 3...; n Em K a l.ul.l|\ll‘ll| 1" Lv\:=5 :oLVLouEmssboagm Logos—3mm I». OL LL 138 variables used were: ETp = 1.1 [(R5 (4.88E-3 - 4.37E-3 ALB)(0.6 MXTP + 0.4 MNTP + 29)] [111] where: R5 = PL total solar radiation: ALB = albedo (0.23): MXTP PL maximum temperature; and MNTP PL minimum temperature. The equation overestimated lysimeter ET by 11 mm (+8.96%) in 1987 and underestimated it by 12.7 mm (-4.09%) in 1988. The regression results are shown in Table 18 and graphically in Figures 35 and 36. Irrigation Scheduling Crop ET of corn estimated from two irrigation scheduling computer programs and a crop growth model were compared using weighing lysimeter data of 1986. All the programs were run with actual rainfall and irrigation. A total of 79 days were used in the comparison. When a day from the lysimeter data was missing that day was also deleted from the program results before the analysis was done. Total lysimeter ET for the 79 days was 337.5 mm. The results of the statistical analyses for all programs are presented in Table 19. The fit of the regression analysis for the MSU-CES 139 Table 18. Correlation and regression statistics of measured ET versus potential ET estimated from CERES-Maize equilibrium ET equation (mm). 1987 (n = 28) 2 ET slope intercept SEE R2 MEAN 133.7 1.107 -.079 ns 0.374 0.838 4.8 1988 (n = 54) 2 ET slope intercept SEE R2 MEAN 298.0 0.678 1.617 ** 0.844 0.559 5.5 ns - intercept not significantly different than zero ** - intercept significantly different than zero at the 1% level I» 140 .coLLosao Hm 33:30.. oNLm—lemmmo 53L .mm 2:3: LL III- Hm :oLLosLum mmmmo III Lv\_=EL :oSahoE—obodflrm Loam—:63 co m ad. a m... L. ad a 0N N mL L ad a .,L I. L - iIllL. III A a L L L L I---- !L- L L Load H mm— .E S: + SSS- ” PE .1 3 \ .l Lv\E._.L :oLL showcaboofirm voLaELme 141 .GoLLasLoo 9m 35:33 SLaLL-mmmmo 2x: .8 25»: L; I E .8335 mammo I LL.\EEL :oLLoLLALmL—Iboogm ..32593 LL 3 LL N. LL 9 v n N L c --I-. 1IL L L L L L L L L by NJ. \\\\\ \- I I \\\ L I I-\-I I - I I I“ I I \\i\ I I I II 1 SS H mm \ a LE cued + .23 n .LL-m K.- LL.\EEL =oLLaLLaIcoboao>m LooLIELme 01 a CL LL 142 spreadsheet program is shown graphically in Figure 37. On a daily basis in 1986, the scheduling program did not estimate ET of the corn crop very well, but over the length of the analysis, the totals came to about the same, 337.5 mm for the lysimeter and 333.7 mm or -1.26% for the program. The worst deviations from lysimeter ET occurred at the end of the season. The large underestimation of ET may be the result of the program predicting crop physiological maturity before it actually occurred since length to maturity is entered into the program as calendar days. In this case the potential ET value is being multiplied by a lower crop coefficient sooner resulting in the lower crop ET estimated by the program. Figures 38 and 39 show the daily comparisons and accumulations. Running the MSU-SOS SCHEDULER 1.10 computer program for the 1986 corn data produced the regression line in Figure 40. Over the period of analysis, the program did underestimate the lysimeter ET (315.3 mm compared to 337.5 mm or -6.58%), but on a daily basis estimated the lysimeter ET quite well (r2 = 0.705). Near the end of the season the scheduling program estimated a lowering of ET while the lysimeter indicated otherwise which can be seen in Figure 41. Again, this may be the result of crop maturity being predicted too soon by the program. This would be expected to occur if early in the growing season the temperatures were below average for the particular time period. The mean monthly temperatures for May through September 1986 143 Table 19. Correlation and regression statistics of ET calculated from models and measured lysimeter ET (mm) (n=79). MSU-CES Spreadsheet Irrigation Scheduling Program 2 ET slope intercept R CERES-Maize Crop Growth Model 2 ET slope intercept R ns - intercept not significantly different than zero ** - intercept significantly different than zero at the 1% level 144 ..L.m 59393 9.23558 ..Emnmcamam: mmonzmz .3 2:”: Lv\.LLcLL :oLLILLomcoL-Loafifi 256.593 L. o n L. n LLL I L L L L L Pm. E Sue-i L. :.o n :3 fed + awed“ H mm ohm I LL.\EEL :oLLILLsmcabonoLLmL @343:me ‘5'? LL 14S ..L.ML .LoLoSmeL a; :OILLILLSoo hm hLLaLL ..Lumficamam: mmouomz .3 2.6L... :oLLIuLLLL .Lo 56.. I E Luann-Lab 9m 5959:— I 58 .- 8.: «L; a} 5). on}. 23 2}. a). L}. on} em}. a}. a}. La} meo L L L L LL I I L I O“ I. L L. L L I N . L L. L L o c .O o a O L L LL L L L L L L LL L L L L L L L. L L L .L . L .. L.. L" L. . L. . L a L L L“ L L LL . L L, \L L L L L LL — s o a c a o . \a d L L L L L. L L L L L L LL L L L L L L L. L . . L L L L L L L L L L L L.. t L . L L L. L L L .L L . L L L L L L .L L . L . L L L L L L L . L L L L L L . L .L L c ..L. L. L L. L L. L L L L L L L L L. L a TI. LL L a LL .L L f L o o L L LL L ‘ll v LL L L L LL L L L L L L L L L L .L L L. L L .L L . L . L L L L L L L L. L. L \ L L L L L L L L L L I L L LL L L L L o o L .\ L L L L L L L LL - L . L L L L L L. L L \L L L L L L L LL L L L L L \ L L L L L L L L L J L LL L L L s L . L L I L L L L L L L L L L . L L L L I. . L L L L L L L L L . .. L . . .L L L L . L. L L L . . L L L L L L I L \ I L L L. L a s L L L L LL L L \ L L L L. L \ L L L LL . _ L L I. L L L L L. L L L L L L. L . L . L L. L on I L . . . : - . -- o L L L L L L IL L L LL L LL L L L L L. L L L LL L. LL. L LL LL I L L L. L I L L c .L L LL LL LL L. .L L. cv I .L. a oL ALL-EL :oLLILLLLLoOLnL Lad—L :oLLILLLLILLLL-LLOLLSLH 146 c .Ambncv mcoLLLLLLLELLoom 3me ...m .LmLoELmb LLLLLL em Eagwoua mczsnmnom ..Loozmcamam: mmouamz .an 2%: 58:32 «(a {a 5} an? 2% GE {a in on} 85.. a}. a} an? a? _ JLLJTL:L.LLLZTLLLLJL11LLLLLTL:LTLLLLLLLLLTLL:TLLLLLVLLLILLLLij co Go— cm— can can can .5 .8355»..— ..... .E 55.50...— AEEL ,5 fives—35:93 147 Fm Ewuucua mam—352% :oLwaLLLL ..mmgzomzom: momuzm: 9:: .3 2%: GEES. LLQLLLLLEmELLLcL—LLLLW $52593 L; c n v n C‘J 0.0 O L: III L L L L L L L \ Pm ”Lassa—20m Isl \ GEMS :...o H mm L TE bond + oomd H ohm— :L\EEL :oSaLEmLLaLL oLLLLLLm @325me N u‘) a 148 mic .hm £52592 5MB :Ommuaaaoo am .236 Efiuoa ..mfiaammum: momusm: .3. 2:6: 5:33P: .3 5a.. I E .3353: ..... 9m 5939:— ll Eco I acc— n—\o b\c —\c oN\b cxa Ln} an} 2 a a»). a}. a}. .5} Lm\c . c . i N L... 1 .. . . 1 L. S. r ..L. -, e en a. 335 553.2095 3:5 :oflafiagaboagm 149 were: 15, 19, 23, 19, and 18 °C, respectively. The 30 year averages at KBS for the same months were: 15, 20, 22, 21, and 17 'C, respectively. While a more useful figure would be the accumulated degree days, it was not part of the research. The length to maturity for the corn hybrid is also entered into the "Scheduler" program in calendar days. The daily accumulations of program ET and lysimeter ET are shown in Figure 42. The crop ET from the crop model CERES-Maize 2.10 was compared to the lysimeter ET and over the period of 79 days overestimated the actual lysimeter ET (359.2 mm to 337.5 mm or +6.43%). The model estimates the daily variation in lysimeter ET very well (r2 = 0.830) with a slope of 0.9 and an intercept of 0.697 (Figure 43). A larger data set (n=88) in Figure 44 shows the model estimated the crop ET up to the physiological maturity, which the model predicted would occur on September 28. The daily accumulations of daily and lysimeter ET for the 88 days is shown in Figure 45. Since the model is driven by thermal time in its "growth" of the crop, it is more sensitive to the temperature affecting the time to maturity of the corn plant. 150 NL\o o\a Ln)» c on 9: end can con .Lasué mcoSmLLLSSooo km. .356 c.3259».— .05... 529:; ..mmLLEmLLom: 8.0.15: .3 29w: 5.8 n 32 _. _ P _ _ _ _ _ L L.—____L__L__L___L_—_____L—E_L___q_fi.__.__~_AL__LJAL_L_L~_ 9m Logos—Lam.— -- - .5 35.395 is: an} 2} 23 {a (a cub. on). a} Q... S}. La}. L L L -m LLLLLLLLLLLZLj4xj \ \ \ A55. .5 pogo—38:84.4 151 a ._ -4 é-:..Lil}-l|liqx»1:i[Ii « L L ‘I‘ .5— 373; mat—mo l¢l .R ..L.H._ L25:— oNLmZImazzu .mv 0.53.. :‘.\:::L :oSchamcaboaa>m cocoa—3.3 : m. c c. u. n N _ c an. N Z wad H m: :2 sad + Bocd H 9:. :.\::_: :c..m......:..:c.3o._a>m :32:me I» = 152 ..wm poems—max: 5; nomionaoo E :3. L258 SLazummmmo .3 2:5 concur—h .3 Ea.— ' .5 53083». an Even. I 58 .. 8.: , 2} «(a ck. Ln}. 3}. a. o 2}. a}. L). on}. 8 s a}. a} 3). Lu? c #4. C 2 :.-. _ . L m L . _.. L. on I L . . . o 2. r . a on - 8 2 3:5 533.98... 3:5 cofluhqmcobongm 153 an ac— on. com onN can can 9:. Among mcoSoLzssooo 33p .5— coaoELmb L28 .25.: mNLaznmmLLmo .2 85w: 58 I 2:: a} on} mic 23 a} L). on? on}. LS. L L L L L L L SE NLS a}. L L a}. an} L L Lu). km $356.3 ..... L L L AaZfi—LLLL:LLLLqu—fifiLLLLLfiZLLLqu::ija4:__:4::4LL:LLLLL—LLLLLLLLLLLLL— ..\ .5 Love: I}! v ABEL ...m voaaL=E=OQ< V. CONCLUSIONS AND RECOMMENDATIONS Climatic Data Research Findings Climatic data have been compared using different methods of averaging and when measured from two different weather station environments. Mean temperature and relative humidity, for the purpose of irrigation scheduling programs which require those values, may be calculated from only the daily minimum and maximum values with no loss in accuracy. The environment around a weather station is an important factor when variables collected from the station are used in irrigation scheduling programs. Irrigation of the area has been shown to have an affect on the values for mean relative humidity. The higher measured relative humidity from a weather station in an irrigated area, which if used in the calculation of the vapor pressure, will result in lower vapor pressure deficit terms with possible underestimation of ET occurring. The calculation of net radiation needed for various potential ET equations is made simpler by estimating it from total solar radiation as in the following relationship: net radiation = 0.5 * solar radiation . The relationship is valid for southern lower Michigan. 154 155 Potential Evapotranspiration Research Findings The various "combination" potential ET equations have been evaluated with vapor pressure deficits calculated using different methods and with the variables from weather stations of different exposures. The equations have also been evaluated with the wind speed variable measured from the two weather stations in different exposures. The comparison to the weighing lysimeter ET was done among the "combination" equations and between two equations estimating the "equilibrium" ET. The best fit of potential ET to the lysimeter ET occurred when mean relative humidity from the non-irrigated station is used in the vapor pressure deficit term. The wind speed variable measured over cut grass, likewise, produced the best fit of estimated potential ET to lysimeter ET. In cases where the dew point temperature or relative humidity is not measured then the minimum temperature can be substituted for the dew point temperature in the calculation of the vapor pressure deficit in areas where dew occurs. The FAO modified Penman equation using a vapor pressure deficit term calculated from minimum and maximum relative humidity is an excellent method to estimate potential ET of alfalfa in the Lake States climate. The ET equation contained in CERES-Maize provides a good alternative to using a combination equation for the 156 calculation of potential ET without the need for climatic data to calculate a vapor pressure deficit term and a wind function. Irrigation Scheduling Research Findings The MSU-CBS spreadsheet program should be used when minimum climatic data are available since it requires only temperature and precipitation. The MSU-SCS "Scheduler" program incorporates the FAO modified Penman equation and estimates daily ET of corn very well except at the end of the season where it appears the program determined crop maturity, but the corn on the lysimeter continued to use water. The corn growth model, CERES-Maize produced the best estimates of daily ET. It requires extensive initial conditions and presently is used only as a research tool and not an irrigation scheduling program. Limitations of this Research A limitation of this research has been the limited number of years of good weighing lysimeter data available for comparing with the scheduling programs. The scheduling programs calculate a reference ET rate which is multiplied by a crop coefficient to obtain the crop ET rate. Since the crop coefficients are empirically derived and represent an average of many years it can be expected that in any one year there will be deviations from that average reflected 157 in the calculated crop ET. The scheduling programs compared with the one year of corn lysimeter data can give a good comparison among programs in that one year, but cannot be expected to follow the same behavior given data sets from other years. This is due to the crop coefficients being applied in stages based on a percentage of the total growing season in calendar days which is input at the beginning of the season as days from emergence to crop maturity. Depending on the temperature during the growing season, the maturity of the crop may be delayed or advanced around the maturity date given in the scheduling programs. CERES-Maize does not have this limitation since it "grows" a new plant every year based on thermal time and not calendar days. The lack of measured wet bulb temperature at the Kellogg Biological Station has meant that the vapor pressure could only be estimated from relative humidity or substituting minimum temperature for dew point temperature. It is felt that systematic errors were introduced from the relative humidity sensor using a resistive chip. While the various methods of calculating the vapor pressure deficit produced a range of results, they could not be compared to one calibrated with the actual vapor pressure determined from wet bulb temperature. 158 Recommendations for Future Research A comparison of the relative humidity calculated from measured wet bulb temperature should be performed on the relative humidities estimated from the resistive type sensor probes. A method by which the irrigation scheduling programs can better determine crop maturity based on accumulated heat units and adjust the crop coefficients accordingly, should be developed. The feasibility of developing the CERES-Maize crop growth model into an irrigation scheduling program which would model the crop growth up to the scheduling date and predict ET for small intervals in the future after that, should be investigated. A nitrate leaching function to incorporate into irrigation scheduling programs and allow the programs to schedule irrigations not only on plant requirements but on the movement of nitrates below the crop root zone should be developed. Using the CERES-Maize model, develop nitrogen application strategies which would minimize nitrate leaching, but have the crop well supplied with water and nutrients. LIST OF REFERENCES Aboukhaled A., A. Alfaro and M. Smith. 1982. Lysimeters. FAO irrigation and drainage paper no. 39. Rome: FAO. Armijo, J.D., G.A. Twitchell, R.D. Burman and J.R. Nunn. 1972. A large undisturbed, weighing lysimeter for grassland studies. Trans. ASAE. 15: 827-830. Bhardwaj, S.P. and G. Sastry. 1979. Development and installation of a simple mechanical weighing type lysimeter. Trans. ASAE. 24: 797-802. Black, J.N., C.W. Bonython and J.A. Prescott. 1954. Solar radiation and duration of sunshine. Proc. Roy. Meteorol. Soc. 80: 231-235. Black, T.A., G.W. Thurtell and C.B. Tanner. 1968. Hydraulic load-cell lysimeter, construction, calibration and tests. Soil Sci. Soc. Am. Proc. 32: 623-629. Blad, B.L. 1983. Atmospheric demand for water. In: 1.0. Teare and M.M. Peet, ed. Crop-water relations. New York: John Wiley and Sons. pp. 1-44. Blaney, H.F. and K.V. Morin. 1942. Evaporation and consumptive use of water empirical formulas. Trans. Am. Geophys. Union. 23: 76-83. Bowen, 1.3. 1926. The ratio of heat losses by conduction and by evaporation from any water surface. Phys. Rev. 27: 779-787. Briggs, L.J. and H.L. Shantz. 1912. The wilting coefficient for different plants and its direct determination. USDA Bur. Plant. Ind. Bulletin 230. Briggs, L.J. and H.L. Shantz. 1913. The water requirements of plants. I. Investigations in the Great Plains in 1910 and 1911. U.S.D.A. Bur. Plant Ind. Bull. Briggs, L.J. and H.L. Shantz. 1914. Relative water requirements of plants. J. Agr. Res. 3: 1-64. Briggs, L.J. and H.L. Shantz. 1916. Daily transpiration during normal growth period and its correlation with the weather. J. Agr. Res. 7: 155-212. 159 160 Burman, R.D., R.H. Cuenca and A. Weiss. 1983. Techniques for estimating Irrigation water requirements. In: D. Hillel ed. Advances in irrigation. New York: Academic Press. 1:335-394. Burman, R.D., P.R. Nixon, J.L. Wright and W.C. Pruitt. 1983. Water requirements. In: M.E. Jensen, ed. Design and operation of farm irrigation systems. St. Joseph, MI: American Society of Agricultural Engineers. pp. 189-232. Businger, J.A. 1956. Some remarks on Penman's equations for the evapotranspiration. Neth. J. Agr. Sci. 4: 77-80. Christiansen, J.E. 1968. Pan evaporation and evapotranspiration from climatic data. J. Irri. Drain. Div. ASCE. 94: 243-265. Cowen, I.R. and F.L. Milthorpe. 1968. Plant factors influencing the water status of plant tissues. In: T.T. Kozlowski, ed. Water deficits and plant growth, Vol. 1. New York: Academic Press. pp. 137-193. Cuenca, R.H. and M.T. Nicholson. 1982. Application of Penman wind function. J. Irrig. Drain Div. ASCE. 108: 13-23. Davis, J.A. and C.D. Allen. 1973. Equilibrium, potential and actual evaporation from cropped surfaces in southern Ontario. J. Appl. Climatology. 12: 649- 657. Deacon, E.L., C.B.B. Priestley and W.C. Swinbank. 1958. Evaporation and the water balance. Climatology: Reviews of Research. UNESCO. Arid Zone Research. 10: 9-34. Denmead, 0.T. and R.H. Shaw. 1960. The effects of soil moisture stress at different stages of growth on the development and yield of corn. Agron. J. 52: 272- 274. Denmead, 0.T. and I.C. McIlroy. 1970. Measurement of non- potential evaporation from wheat. Agric. Meteorol. 7: 285-302. Doorenbos, J. and W.C. Pruitt. 1977. Crop water requirements. FAO Irrigation and Drainage Paper No. 24. Rome. De Vries, D.A. and R.H.A. van Duin. 1953. Some considerations on the diurnal variation of transpiration. Neth. J. Agr. Sci. 1: 27-34. 161 Ferguson, J. 1952. The rate of natural evaporation from shallow ponds. Aust. J. Sci. Res. 5: 315-330. Frevert, D.K., R.W. Hill and B.C. Braaten. 1983. Estimation of FAO evapotranspiration coefficients. J. Irrig. Drain. Engr. ASCE. 109: 265-270. Fritz, S. and J.H. MacDonald. 1949. Average solar radiation in the United States. Heating and Ventilating. 46: 61-64. Fritschen, L.J. 1967. Net and solar radiation relations over irrigated field crops. Agric. Meteorol. 4: 55- 62. Hanks, R.J. and R.W. Shawcroft. 1965. An economical lysimeter for evapotranspiration studies. Agron. J. 57: 634-636. Harrold, L.L. and P.R. Dreibelbis. 1958. Evaluation of agricultural hydrology by monolith lysimeters (1944- 1955). USDA Tech. Bull. No. 1179. Washington DC. Hillel D. 1982. Introduction to soil physics. New York: Academic Press. Hillel D. 1980. Applications of soil physics. New York: Academic Press. Howell, T.A., R.L. McCormick and C.J. Phene. 1985. Design and installation of large weighing lysimeters. Trans. ASAE. : 106-117. Jacobs, A.F.G. and J.H. van Boxel. 1988. Changes of the displacement height and roughness length of maize during a growing season. Agric. and Forest Meteor. 42: 53-62. Jensen, M.E. 1968. Water consumption by agricultural plants. In: T.T. Kozlowski, ed. Water deficits and plant growth. New York: Academic Press. Vol. II: 1-22. Jensen, M.E., ed. 1974. Consumptive use of water and irrigation water requirements. New York: American Society of Civil Engineers. Jensen, M.E. and H.R. Haise. 1963. Estimating evapotranspiration from solar radiation. J. Irri. Drain. Div. ASCE. 89: 15-41. Jensen, M.E., D.C.N. Robb and C.E Franzoy. 1970. Scheduling irrigations using climate-crop-soil data. J. Irrig. Drain. Div. ASCE. 96: 25-38. 162 Jensen, M.E., J.L. Wright and B.J. Pratt. 1971. Estimating soil moisture depletion from climate, crop and soil data. Trans. ASAE. 14: 954-959. Jones, C.A. and J.R. Kiniry, ed. 1986. CERES-Maize: A simulation model of maize growth and development. College Station: Texas A & M University Press. Kohnke, J., F.R. Dreibelbis and J.M. Davidson. 1940. A survey and discussion of lysimeters and a bibliography on their construction and performance. USDA Misc. Publ. No. 374. Washington DC. Lettau, H. 1969. Note on aerodynamic roughness-parameter estimation on the basis of roughness-element description. J. Appl. Meteor. 8: 828-832. Linacre, E.T. 1967. Climate and the evaporation from crops. J. Irrig. Drain. Div., ASCE. 93: 61-79. List, R.J. 1968. Smithsonian meteorological tables. Washington DC: Smithsonian Institution Press. Makkink, G.F. 1957. Testing the Penman formula by means of lysimeters. Inst. Water Engr. 11: 277-288. McGuinness, J.L., F.R. Dreibelbis and L.L. Harold. 1961. Soil moisture measurements with the neutron method supplement weighing lysimeters. Soil Sci. Soc. Am. Proc. 25: 339-342. McIlroy, I.C. and D.E. Angus. 1963. Grass, water and soil evaporation at Aspendale. Agric. Meteorol. 1: 201- 224. Merva, G. and A. Fernandez. 1985. Simplified application of Penman’s equation for humid regions. Trans. ASAE. 28: 819-825. Milthorpe, F.L. and H.L. Penman 1967. The duffusive conductivity of the stomata of wheat leaves. J. Exp. Bot. 18: 422-456. Monteith, J.L. 1959. The reflection of short-wave radiation by vegetation. Quart. J. Roy. Meteor. Soc. 85: 386-392. . 1963. Gas exchange in plant communities. In: L.T. Evans, ed. Environmental control of plant growth. pp. 95-111. . 1965. Evaporation and environment. Symposia of the Society for Experimental Biology. 19: 205-234. 163 . 1973. Principles of environmental physics. New York: American Elsevier Publishing Co. Munro, D.S. and T.R. Oke. 1973. Estimating wind profile parameters for tall dense crops. Agric. Meteorol. 11: 223-228. Nixon, P.R. and G.P. Lawless. 1960. Translocation of moisture with time in unsaturated soil profiles. J. Geophys. Res. 65: 655-661. Pasquill, F. 1949. Some estimates of the amount and diurnal variation of evaporation from a clayland pasture in fair spring weather. Quart. J. Roy. Meteorol. Soc. 75: 249-256. Pelton, W.L. 1961. The use of lysimetric methods to measure evapotranspiration. Proc. Hydrol. Symp., Nat. Res. Council, Canada. 2: 106-122. Penman, H.L. 1948. Natural evaporation from open water, bare soil and grass. Proc. Roy. Soc. London. 193: 120-145. Serial A. . 1963. Vegetation and Hydrology. Commonwealth Bureau of Soils. Technical Communication 53. Penman, H.L. and R.K. Schofield. 1951. Some physical aspects of assimilation and transpiration. Symposia SOC. Exptl. Biol. 5: 115-129. Penman, H.L. and I.F. Long. 1960. Weather in wheat: An essay in micro-meteorology. Quart. J. Roy. Meteor. Soc. 86: 16-50. Penman, H.L., D.E. Angus and C.H.M. van Bavel. 1967. Microclimatic factors affecting evaporation and transpiration. In: R.H. Hagan, H.R. Haise and T.W. Edminster, ed. Irrigation of Agricultural Lands. Madison, WI: American Society of Agronomy, Monograph 11. pp. 433-505. Priestley, C.H.B. 1959. Turbulent transfer in the lower atmosphere. Chicago: University of Chicago Press. Priestley, C.H.B. and R.J. Taylor. 1972. On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly Weather Review. 100: 81-92. Pruitt, W.0. and D.E. Angus. 1960. Large weighing lysimeter for measuring evapotranspiration. Trans. ASAE. 3: 13-18. 164 Reicosky, D.C., Sharratt, B.S., Ljungkull, J.E. and D.G. Baker. 1983. Comparison of alfalfa evapotranspiration measured by a weighing lysimeter and a portable chamber. Agric. Meteorol. 28: 205- 211. Ritchie, J.T. 1971. Dryland evaporative flux in a subhumid climate: I. Micrometeorological influences. Agron. J. 63: 51-55. . 1972. Model for predicting evaporation from a row crop with incomplete cover. Water Resour. Res. 8: 1204-1213. . 1974. Evaluating irrigation needs for southeastern U.S.A. In: Contribution of irrigation and drainage to world food supply. ASCE. pp. 262-279. . 1981. Water dynamics in the soil-plant- atmosphere system. In: J. Monteith and C. Webb, ed. Soil water and nitrogen in Mediterranean-type environments. The Hague: Martinus Nijhoff. pp. 81-96. Ritchie, J.T. and E. Burnett. 1968. A precision weighing lysimeter for row crop water use studies. Agron. J. 60: 545-549. Ritchie, J.T., E.D. Rhoades and C.W. Richardson. 1976. Calculating evaporation from native grassland watersheds. Trans. ASAE. 19: 1098-1103. Robins, J.S. and C.E. Domingo. 1953. Some effects of severe soil moisture deficits at specific growth stages in corn. Agron. J. 45: 618-621. Robins, J.S., W.0. Pruitt and W.H. Gardner. 1954. Unsaturated flow of water in field soils and its effect on soil moisture investigations. Soil Sci. SOC. Am. Proc. 18: 344-348.7 Rohwer, C.S. 1931. Evaporation from water surfaces. U.S. Dept. Agr. Tech. Bull. 271. Rosenberg, N.J. 1969. Seasonal patterns in evapotranspiration by irrigated alfalfa in the Central Great Plains. Agron. J. 61: 879-886. Rosenberg, N.J. 1974. Microclimate: The Biological Environment. New York: John Wiley and Sons. Rosenberg, N.J., B.L. Blad and 8.8. Verma. 1983. Microclimate: The Biological Environment. New York: John Wiley and Sons. 165 Sharma, H.L. 1985. Estimating evapotranspiration. In: D. Hillel ed. Advances in irrigation. New York: Academic Press. 3: 213-281. Shaw, R.H. 1956. A comparison of solar radiation and net radiation. Bull. Am. Meteorol. Soc. 37: 205-206. Shayya, W.H. and V.F. Bralts. 1988. Guide to microcomputer irrigation scheduler. Michigan State University, Dept. of Agricultural Engineering. Slatyer, R.O. 1967. Plant-water relationships. New York: Academic Press. Slatyer, R.O. and I.C. McIlroy. 1961. Practical microclimatology. CSIRO. UNESCO. Stanhill, G. 1961. The accuracy of meteorological estimates of evapotranspiration in arid climates. J. Inst. Water Eng. 15: 477-482. Steel, R.G.D. and J.H. Torrie. 1980. Principles and Procedures of Statistics: A Biometrical Approach. New York: McGraw-Hill. Stiger, C.J. 1980. Assessment of the quality of generalized wind functions in Penman's equations. J. Hydrol. 45: 321-331. Sutton, 0.6. 1953. Micrometeorology. New York: McGraw- Hill. Swinbank, W.C. 1951. The measurement of vertical transfer of heat and water vapor by eddies in the lower atmosphere. J. Meteor. 8: 135-145. Szeicz, G. and I.F. Long. 1969. Surface resistance of crop canopies. Water Resources Research. 5: 622-634. Szeicz, G., G. EndrOdi and S. Tajchman. 1969. Aerodynamic and surface factors in evaporation. Water Resour. Res. 5: 380-394. Szeicz, G., van Bavel, C.H.M. and S. Takami. 1973. Stomatal factor in the water use and dry matter production by sorghum. Agric. Meteor. 12: 361-389. Tanner, C.B. 1960. Energy balance approach to evapotranspiration from crops. Soil Sci. Proc. 24: 1-9. 166 . 1967. Measurement of evapotranspiration. In: R.H. Hagan, H.R. Haise and T.W. Edminster, ed. Irrigation of Agricultural Lands. Madison, WI: American Society of Agronomy, Monograph 11: pp. 534- 574. Tanner, C.B. and W.L. Pelton. 1960. Potential Evapotrans- piration Estimates by the Approximate Energy Balance Method of Penman. J. of Geophy. Res. 65: 3391-3413. Teare, I.D., E.T. Kanemasu, W.L. Powers, and H.S. Jacobs. 1973. Water use efficiency and its relation to crop canopy area, stomatal regulation and root distribution. Agron. J. 65: 207-211. Thom, A.S. 1975. Momentum, mass and heat exchange of plant communities. In: J.L. Monteith, ed. Vegetation and the atmosphere. London: Academic Press. pp. 57- 109. Thom, A.S. and H.R. Oliver. 1977. On Penman’s equation for estimating regional evaporation. Quart. J. Roy. Meteorol. Soc. 103: 345-357. Thornthwaite, C.W. 1944. Report of the committee on transpiration and evaporation. Trans. Amer. Geophy. Union. 25: 686-693. Thornthwaite, C.W. 1948. An approach toward a rational classification of climate. Geogr. Rev. 38: 55-94. Thornthwaite, C.W. and B. Holzman. 1939. The determination of evaporation from land and water surfaces. Mon. Weather Rev. 67: 4-11. Thornthwaite, C.W. and B. Holzman. 1942. Measurement of evaporation from land and water surfaces. USDA Tech. Bull. No. 817. Thornthwaite, C.W. and J.R. Mather. 1955. The water budget and its use in irrigation. Yearbook Agr. U.S. Dept. Agr. pp. 346-357. United States Department of Agriculture. 1970. Irrigation water requirements. Technical Release No. 21. Soil Consevation Service Engineering Division. van Bavel, C.H.M. 1961. Lysimetric measurements of evapotranspiration in the eastern United States. Soil Sci. Proc. 25: 138-141. . 1966. Potential Evapotranspiration: The Combination Concept and Its Experimental Verification. Water Resour. Res. 2: 455-467. 167 . 1967. Changes in canopy resistance to water loss from alfalfa induced by soil water depletion. Agric. Meteor. 4: 165-176. van Bavel, C.H.M. and W.L. Ehrler. 1968. Water loss from a sorghum field and stomatal control. Agron. J. 60: 84-86. van Bavel, C.H.M. and L.E. Myers. 1962. An automatic weighing lysimeter. Agr. Engr. 43: 580-588. van Bavel, C.H.M. and R.J. Reginato. 1965. Precision lysimetry for direct measurement of evaporative flux. In: F.E. Eckardt, ed. Methodology of plant eco- physiology. Proc. Montpellier Symposium. UNESCO. Arid Zone Research. 25: 129-135. van Wijk, W.R. and D.A. De Vries. 1954. Evapotranspiration. Neth. J. Agr. Sci. 2: 105-118. Vitosh, H.L. Irrigation scheduling by water balance - A spreadsheet program for microcomputers. Michigan State University, Dept. of Crop and Soil Sciences. Webb, E.K. 1970. Profile relationships: The log-linear range, and extension to strong stability. Q. J. Roy. Meteor. Soc. 96: 67-90. Wright, J.L. 1982. New evapotranspiration crop coefficients. J. Irrig. Drain. Div. ASCE. 108: 57- 74. Wright, J.L. and M.E. Jensen. 1972. Peak water requirements of crops in southern Idaho. J. Irrig. Drain. Div. ASCE. 98: 193-201. . 1978. Development and evaluation of evapotranspiration models for irrigation scheduling. Trans. ASAE. 21: 88-96. "ITllllflljllllflllllfllfllll“