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FINES will be charged if book is returned after the date stamped below. vmgma, a .17 .:- EU" 131'“: C17 A STUDY OF EVAPORATION IDSSES FROM SANDY 10AM AND SANDY CLAY 10AM SCI"; by You-tsai Hung A THESIS mmitted to Michigan State University in partial fulfillrrent of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 196k ABSTRACT The objective of this preliminary study using a closed chamber to control temperature, relative humidity, wind velocity and using a ten- sion table to control soil moisture to determine evaporation losses from -sandy clay loam and sandy loam soil was intended to find the effects of soil moisture and soil type on evaporation. The equations derived from this laboratory test chamber study were fairly adaptable to the physi- cal characteristics of the variables. The formulas were not assumed to be used in practical problems. However, they showed that both soil mois- ture factor and soil type factor would exert significant effects on eva- poration and play an important role in the process of evaporation. Two equations of evaporation from soil in terms of air tempera- ture, wind velocity vapor pressure deficit and soil moisture and two equations of evaporation from soil in terms of air temperature, wind velocity, vapor pressure deficit and soil tension for sandy clay loan and sandy loam soil were derived from the results of this experiment. The equations based on soil moisture for sandy clay loam and sandy loam soil were: (1). For sandy clay loam soil; E=thchCncCsc (1) where E is the evaporation from the soil in inches per day ii th = 0.209 - 0.00h T + 0.000033 T2; th is the subcoefficient of air temperature, T is the temperature of the overrunning air in OF cwc = 0.559 + 0.th3 W'+ 0.000805 we; ch is the subcoefficient of wind, w is the velocity of overrunning air in feet per second Che = 0.8233 - 0.1029(eS - e) + 1.706(eS - e)2; Che is the sub- coefficient of vapor pressure deficit, (es - e)2; Chc is the vapor8pressure deficit at a given overrunning air tempera- ture in pound per square inch csc : 2.2791 - 0.2395 s + 0.00666 32; 03c is the subcoefficient of soil moisture, S is moisture in the soil expressed by percentage of moisture on oven-dry basis. {2). For sandy loan soil; E = Cts Cws Chs Css . . . . . . . . . . . . . . . . . . . .(2) where E is the evaporation from the soil in imhes per day = 0.133 - 0.00226 T + 0.00003h9 T2 Cts cwS = 0.599 + 0.0809‘w8- 0.00297‘w2 Chs CSS 0.726 + 1.3t01(es - e) + O.h700(e5 - 3)? 1.013 - 0.06t7 s + 0.00371 32 : Except the second subcript "s" of the subcoefficient was used to distinguish sandy loam from sandy clay loam, the other symbols had the same explanation as used in equation(l). The equations based on soil tension for sandy clay loam and sandy iii loam soils were; (3). For sandy clay loam soil; EzctCCWCChCCTco-oooooo../..........(3) where E is the evaporation from the soil in inches per day Cm, Cm and the are equivalent to the values of cm, ch and she in equation( 1) 2 cient of tension, Ten is tension in centimeters. (11). For sandy loam soil; E=CtsCWSChSGrsooooooooooooooooooooO-J) where E is the evaporation from the soil in inches per day Cts: Cws and Chs are equivalent to the values of 0’05: Cws and Ghs in equation(2) CTs = 1-515 ‘ 0002658 Ten + 0.000225 Tenz; 3:3 is tension in , 7 A Approved by ;%%Z Z centimters. w iv The author wishes to express his sincere appreciation to Professor L11 rnest H. Kidder of the Agricultural Engineering Department under whose guidance, supervision, and unfailing interest this work was done. The author is especially indebted to the Agency For International Development for the graduate research and financial aid that made this research possible. The author also wishes to eXpress his sincere gratitude to Dr.Fre- derick H. Buelow, Mr. Clarence M. Hansen and Mr. R. Z. Wheaten of the Agricultural Engineering Departnent for their criticisms and comments. Grateful acknowledgement is also extended to Dr. A. Earl Erickson and Mr. Curtis D. Piper of the Soil Science Department for their fre- quent assistance. Appreciation is extended to Mbssrs. James B. Cawood and all other friends who provided valuable aid during the investigation. The author also is indebted to his wife, Yueh-chin who has been taking care of their two children in Taiwan and encouraged him to esta- blish his research work. Section IN'I’FKDDUCTIC-N REVIEW OF LITERATURE DESIGN OF EXPERII8’ENT APPARATUS EXPERIMENTAL PROCEDNRE DISCUSSION OF RESULTS C ONC LUS IO N S LIT rJRAT'JRE C ITED A PPENDIX TA ZELIE OF CONTENTS Page 10 13 21 23 35 37 39 LIST OF FIGURES Figure Page 1. Schematic diagram of test apparatus . . . . . . . . . . . . . lb 2. Soil samples . . . . . . . . . . . . . . . . . . . . . . . . 16 3. Soil moisture control system . . . . . . . . . . . . . . . . 16 h. Humidity control systen . . . . . . . . . . . . . . . . . . . 17 5. Air speed control system . . . . . . . . . . . . . . . . . . l9 6. Temperature sontrol system . . . . . . . . . . . . . . . . . 19 7. Temperaturevs.evaporation ................. 25 E. The ratios of Ec/th and Es/Cts vs. 1.11;}? tr+ . . . . . 26 9. The ratios of 130/thch and Es/Ctscws vs. vapor pressure deficit . . . . . . . . . . . . . . . . . . . . . . . . . . 28 10. The ratios of ec/ctccwcchc and Es/ctscwsohs vs. soil moisture. 30 1:. The ratios of Ec/thcwcchc and Es/ctscwschs vs. tension . . . 32 vii INTRODUCTION The consumption of heat frontthe sun in the evaporation of mois- ture from land and water surfaces and in the transpiration of soil mois- ture by vegetation is the process by which precipitated water is return- ed again to the earth's atmosphere as vapor to perpetuate the hydr010gic cycle. Evaporation is the process by which water is changed from the li- quid or the solid state into the gaseous state through the transfer of heat energy. The study of evaporation from soil has important applications in the field of irrigation. The complex nature of the relating factors of temperature, vapor pressure deficit, wind velocity, solar radiation, type of soil ani soil moisture produces a very difficult problem. In particular the variation of soil moisture and the soil type are phases of this study which seems to have been wholly neglected by previous re- searchers. Most researchers are concerned with the evaporation from the free water surface. Therefore it was not possible to find a formula which included soil moisture and soil type factors which must be taken into consideration. Since it was apparent that work had not been done on the effects of soil moisture and type of soil on soil moisture loss, a study to in- vestigate these factors was pr0posed.'This study had the following ob- jectives: 1. Construct a suitable test chamber which would enable control of air temperature, relative humidity and wind velocity. 2. Construct two tension tables for naintenance of tensions which would make possible the control of the moisture content in soil samples. 3. Determine suitable equations from eXperimental results to predict evaporation from soil on the basis of soil moisture, soil tension and soil type in addition to the factors previously studied. It was known from previous studies that the factors affecting eva- poration had linear combination, therefore the expected equations based on soil moisture and soil tension for these factors were assumed to be: Exctcwchcs......................(1) E=CthChC~p......................(2) where [‘1 *J m '8 evaporation in inches per day Ct is the subcoefficient of air temperature Cw is the subcoefficient of wind velocity Ch is the subcoefficient of vapor pressure deficit, which is expressed by (e3 - e) es is the saturated vapor pressure at a given temperature e is the actual vapor pressure at the given temperature Cs is the suhcoefficient of soil moisture CT is the subcoefficient of soil tension. ."VIEW OF LITERATURE Reparts on evaporation and evaportranspiration in the literature are extensive. Robinson and Johnson's compilation of the literature for the periOd 1800 to 1958 was published by U.S. Geological Survey in 1961. Christiansen and Lauritizen(l963) compiled a bibliography of 22S publi- cations with emphasis on recent publications. The methods used in investigating evaporation from lakes or reser- voirs fall into four categories: 1. The "water budget determinations of evaporation". This approach is simple in theory, but application rarely produces reliable results since all errors in measuring outflow, inflow, and change in storage are reflected directly in the computed evaporation. 2. The "energy-budget determination of evaporation". This approach like the water budget, employs a continuity equation and solves for evapo- ration as the residual required to maintain a balance. Application of the energy budget has been attempted by numerous investigators, with cases selected so as to minimize the effect of terns that could not be evaluated. The principal limitation of this approach is the lack of su- fficient climatological measurements in most localities. Only a few cli- matological stations record the needed solar energy data. The fornula, even though quite reliable, has serious practical limitations. 3. The "mass-transfer determinations of evaporation"; The theoretical develop- ment of turbulent-tranSport equations has followed two basic approaches, the discontinous, or mixing length and continots tixing concepts. The 3 derived formulas are according to the differences of wind and vapor pre- ssure at two levels near the surface. This method is simpler and can utilize readily available climatological data. Thornthwaite(1955) theo- rized that temperature was a good index to energy in a zone of essential equilibrium. In essence, the procedure developed by Thornthwaite has the same limitations regarding areas of application as energy buiget, It applies quite well to humid, well-vegetated areas. Increased errors are observed in arid, low-humidity regions. b. The "estimation of evaporation from pan evaporation and related meteorological data"; The pan is the most widely used evaporation instrument today. Its application in hydro- logic design and Operation is of long standing. Several authors have developed pan coefficients to transform pan evaporation to lake evapo- ration. Mann(187l) concluded that evaporation from a free water surface depends almost wholly on three factors; 1. The area of the water surface, 2. The tenperature of the water at its surface, 3. Vapor pressure of water in the air above the water. Fortier(l907} .12ted that the factors having the greatest influence on evaporation from soils are the quantity of water in the top soil, the temperature of the soil and air movement. Fukuda(1955, 1956) studied the effect of wind on soil. he reported that the soil depth to which air can penetrate as a result of wind gustiness is very slight. Even in sandy soils the particles of which have a mean diameter of 0.5 - 0.25 mm, the wind penetrates only about 5 mm below the surface. Staple(l9§6) suggested that computation of evaporation must be stepwise process involving the calculation, in short time intervals, of both the changing moisture profiles in the drying soil and the resulting evaporation at the surface. Cnchukov(l957) concluded that evaporation should not occur below 25 cm but that extensive evaporation occurs within S cm of the soil surface. Richards et al.(1956) reported that vapor transfer was agriculturally insignificant below the 15 cm depth. Peter- son(l959) found that maximal evaporation occurred at a depth l/2 to 1 inch below the soil surface. Evaporation formulas The fundamental law of evaporation from a free water surface was enunciated by Dalton in 1882. He stated that if the actual vapor pre- ssure of the air above the water is less than that at the water surface, then evaporation will occur. Several empirical equations to estimate evaporation are based on Dalton's law. It may be written as: E 2 (e0 - ea) NJ) where E is the evaporation in a unit of time eo is the vapor pressure of the evaporating surface ea is the vapor pressure in the atmosphere f(U) is a function of the wind velocity that can be of the form - a + b u, or c un where a, b, c and n are constants. Meyer 19L2) suggested a formula for estimating evaporation from a lake which can be expressed by the equation: v E=C(es - ea)(l+ 7‘ where H L is evaporation in inches per day eS is the vapor pressure of the water surface(in. of Fg) is the vapor pressure of the overrunning air(in. of Hg) v is the wind Speed (mph) about 25 ft above the surface c is the coefficient (about 0.36 when the formula is applied to daily data for an ordinary lake}. Edney(l957) eXpressed it as: E = we - pa) where E is the rate of evaporation K is a proportionality "constant" P0 is the partial pressure of water vapor in air saturated at temperature of the surface P8 is the partial pressure of water vapor in air a short dis- tance away from the surface. Rohwer(l931) working at Fort Collins, Colorado, proposed an equa- tion of the form: E = (l.h65 - 0.0186 B)(0.Lh + 0.318 W)(eo - ea) where B is the barometric pressure in inches of mercury at 32°F w is the wind velocity near the ground in miles per hour. Penman(l9h8) prOposed a formula in England: -1 £0 = O.35(l + 9.8 x 10 ’ U2)(eo - ea) E0 is the evaporation in millimeters per day U2 is the wind velocity in miles per day measured 2 meters above the surface. In investigating evaporation from shallow lakes near Ogden, Utah, Christiansen(l960) derived a formula, which can be eXpressed by the equa- tion: where where E = KTC R E is the evaporation (or evapotranspiration) K is the dimensionless constant R is the extraterrestrial radiation that is received at the outer surface of the atmsphere eXpressed as an equivalent depth of evaporation in the same units of E C is a diuensionless coefficient that is the product of se- veral subcoefficients, each one a function of climatic and related factors that affect evaporation. The value of the coefficient C in the above equation is: Cw Cs Cu CE CL 0M C3CT CT is OH is CS is Ch is CE is CL is CM is the the the the the the the subcoefficient subcoefficient Subcoefficient subcoefficient subcoefficient subcoefficient subcoefficient Linear equations were found of tenperature of wind of sunshine percentage of huvidity of elevation of latitude of month for the subcoefficients CT, Cw, Cs, Cg and Lean values were found for the monthly coefficient CM. A further study in determining the subcoefficients was conducted by thhison(l963) in Utah. He used data from LO weather stations scatter- ed throughout the weatern United States and pr0posed a formula for com- puting evaporation from a Standard weather Bureau Class A pan: where E = Co CT Cw 041‘ Cs CE E is the evaporation in inches per month Cc = 03 Ccos(L - D)CM CR is the coefficient of radiation, where CR = 0.20 R + 0.015 R23 R is radiation in inches water Ccos(L _ D) is the cosine of the latitude minus the declina- tion coefficient, where Ccos(L - D) = 1.16 + 0.b2 cos(L - D) - 0.7 c052(L - e} in which L and n are the latitude and the declination CM is the monthly coefficient, where CM== l + 0.00155(L - D) cos(N + 1) in which N is the number of month CT 2 - 0.26 + 0.03h25 T - 0.000075 T2, where T is air tempera- ture cw.= 0.8 + 0.0035 w - 0.0000027 we, where w is wind velocity in miles per day da = 0.bs + 9.6 x io'harz - 2.76 x io'ZATh, where AT is the difference in average maximum and minimum temperature for the month 08 = 0.622 + 0.005875 3 - 0.000011 52, where s is the sunshine percentage .CE = 0.967 + 0.35 E - 0.00156 E2, where E is the elevation in .thousands of feet. Pan evaporation The U.S.'Weather Bureau Class A evaporation pan is widely used in the United States. Records were published for 350 stations in 1956. Pan coefficient is defined as a ratio of lake evaporation to pan evapora- tion. Mean annual USWB Class A pan coefficients range from 0.81 at Lake Okeechobee to 0.60 at Lake Mead(Linsley, Ray K. Jr. and Max A. Kohler and Joseph L. H. Paulhus, 1958). The subcommittee on evaporation of the Special committee on Irrigation Hydraulics of the American Society of Civil Engineers, adopted 0.70 as a ratio of the annual evaporation from a USWB Class A pan to that from a reservoir. This value would result in a maxium difference of 12 percent from 0.81 at Lake Okeechobee. Ybung(19b2) reported that Lake Elsinore has an average annual coefficient of 0.77 for the Class A pan, but the monthly coefficient varied fro-{0.63 in Fe- bruary to 0.97 in November. A sunmary of pan coefficients (Lake-to-pan ratios) has been published(Linsley, Ray K. Jr. and max A. Kohler and Jo- seph L. H. Paulhus, 1958). DESIGN OF EXPERIMENT In order to meet the objectives of this study, it was necessary to evaluate the factors of temperature, relative humidity, wind velocity: and soil moisture in a closed chamber. The factors of elevation and la- titude were kept constant since all tests were conducted in the same place. Since the test chamber was closed, the factors of radiation or sunshine and monthly variations were eliminated. From the literature survey it was concluded that the factors in- fluencing evaporation from soil, except soil moisture, were limiting only within a thin tap soil layer. In order to eliminate the nonuniform verti- cal distribution of soil moisture it was decided to use a thin layer of soil and conduct an eXperiment in which the soil moisture and soil type factors were taken into consideration. The only factors consedered in this eJcperiment were temperature, relative himidity, wind velocity, soil moisture and soil type. Each of the variables was controlled separately in order to obtain various combinations of treatments. Environmental variables The tenperature levels consisted of three average values of 60°F, 75°F and 95°F. The relative humidity ranged from about 20 to 95 percent. Three wind velocities of 0, 8 and 16 feet per second were used. Soil mois- ture was varied to three levels by soil tensions of 0, 27.5 and b5 on. Two soil types were used. 10 The treatments of these variables were arranged so as to have all possible combinations of factors. The combinations of the treatments are listed in Table 1. Table l. Combinations of treatments Temperature Relative ‘Wind velocity Soil moisture Types of soil < 0 F ) h??? (ft/sec) $3233.52: 33$; 60 20 0 Sandy clay loam 75 60 8 95 95 16 Sandy loam From Table 1, it was apparent that 162 combinations of the treat- ments must be evaluated. Each combination had three replications. A total of h86 observations were made. Soil samples In order to compare the effects of two soil types and to eliminate the errors due to the effects of different operating conditions, it was decided to run the two soil types at the same Operating conditions during the test. The moisture content of the two soil types was controlled by tension tables. The soils were taken from locations on the Pflchigan State Universi- ty farm. Mechanical composition was determined by the hydrometer method. Mechanical composition, bulk densities and saturated moisture are listed in Table 2. Table 2. Properties of two soil samples Mechanical composition Sand Silt (z) (z) Sandy loam 66 19 Sandy clay h8 28 10am Cla (as), 15 2h 12 Bulk density 1.t12 1.31h Saturated moisture ( % ) 23.27 35.87 APPARATUS Test chamber In order toicontrol the factors affecting evaporation from soils, a closed test.chamber was constructed in the Land DevelOpment Laboratory in the Department of the Agricultural Engineering, Michigan State Univer- sity. The chamber was 8 feet high, 8 feet wide and 3 feet deep(Fig. l). The walls of chamber consisted of l/L inch plywood inside and outside with 2 inches of glass wool insulation in between. Four doors were set in the front face of the chamber to handle and check the salt solution, heat exchanger and soil samples. Soil samples Two sample boxes 1 foot long, 6 inches wide and 2 inches deep were constructed of 3/8 inch plastic. Two samples were placed side by side with the greatest dimension parallel to the direction of air flow A at the top portion of the chamber(Fig. l and Fig. 2). The required ten- sion was established prior to filling the sample box. The box had a l/L inch hole in the middle of the bottom and was connected by a l/h inch tube to a glass bottle (Fig. 3). The box was cleaned with soap and dis- tilled water. The next step was to fill the box and the plastic tube with distilled water. The tube was clamped. A mesh screen h inches long, 2 in- ches wide was put in the middle bottom of the box, then three layers of blotting paper'were placed on the screen. In order to prevent air from 13 egg on: no «Inna: canal-A8 « 6.: E 3- uoaol 0:03.". a“ a A h?! 3 é . .. \\\§ \.—. IIIHuIIIIMWuIIIIMIuIII u «33 .34 llama" .3 3...... / m.mn »2 a b . ...-ion» .34 H _ a anon A . golfing \ so»... no? 3, «advance on .:.\.n h: ‘Osg. 5O 83m 3 {a . .....wL. a 3.335 (I Agzdogn a2: a." k \Ifil/ua .8 «38:2. €3.3— \.\. 83 33m\ 83 “can! no: 0.0 15 coming in at the edges of the paper, four plastic strips were used to press down these edges. The box was raised above the glass bottle about one foot, then the clamp was loosened to drain the water until it reach- ed one foot of tension. This unit was observed for at least 6 hours to determine whether the tension would hold. The disturbed soil sample was uniformly placed on the blotting paper up to the top of the box. Soil moisture control The moisture content of the soil samples was controlled by different tensions. The tensions were measured by the difference of water heads be- tween the soil and the free water surfaces which were controlled by a glass bottle mounted on the front face of the chamber(Fig. 3). The bottle was filled with distilled water and a M. inch diameter tube was connect- ed to the bottom of the sample. In order to maintain constant water level in the bottle it was necessary to have an automatic water surface control device. A one foot long, one inch diameter cylinder with its tap sealed with a rubber plug was used for this function. A l/h inch dia'aeter glass tube with both ends open was inserted from the rubber plug to one inch from the bottom of the cylinder. The t0p end was exposed to atmosphere and the lower end was immersed in the water in the cylinder. A second l/h inch plastic tube was connected from the bottom of the cylinder to the glass bottle in order to keep water supply continuous. The cylinder was movable so that the lower end of the glass tube could be adjusted at the same level as the water surface in the glass bottle. Since there were two soil samples, two sets of the above equipment were prepared. Graduations of 1/5 c.c. were placed on the side of the cylinder. W ' a It.“ - -~. «mafia were” ... 4.4 2. refine-... n8. 2 3011 m8 Fig. 3 Soil moisture control system 3 E- 3' s E E a: .97 ha 18 The water lost from two samples was measured hang. The moisture contents in the soil samples for various tension le- vels were measured by taking small samples from the soils. fiumidity control Three saturated salt solutions were prepared to control the humi- dity in the chamber. Lithium chloride, magnesium nitrate and potassium nitrate were used to supply low, medium and high humidity reapectively. Saddle porcelain of 3/1; inch size was used for a contact area bottleen the salt solution and the air coming in from the air blower in order to obtain the desired himidity. A container 2 feet long, 2 feet wide and 1 foot deep having a screen at its bottom was placed in the left central side of the chamber. This container was filled with saddle porcelain(Fig. l). A tank 3 feet long, 2.5 feet wide and 6 inches deep was placed under the container to catch the salt solution. The solution was circulated by a pump equipped with a 1/2 hp electric motor through a one inch rubber hose and sprayed by four nozzles onto the saddle porcelain(Fig. l and Fig. h). An automatic recording hygroneter was placed below the soil sam- p183. Air speed c ontro_l_ The air flow passing over the soil samples was controlled by an air blower. It was placed at the right hand side of the chamber. An 8 inch diameter pipe covered with glass wool insulation connected the blo- wer to the tap and to the bottom of the chamber to circulate the air( Fig. 1 and Fig. 5). The blower speed was regulated to control the air Fig. 6 Temperature control system Fig. 5 Air speed central system 20 Speed. A pitot tube was inserted from the top center of the chamber near the surface of the samples to measure air velocity over the soil samples (Fig. l). ' Temperature control A tank filled.with water and a heat exchanger were prepared to control the temperature in the chamber. The temperature in the tank was adjusted by putting ice, running cool or hot water through the water in the tank. The heat exchanger was placed 2 feet away from the outlet of the air blower. It was connected to the pump and tank by'a one inch pipe (Fig. 6). The air temperature in the chamber was measured with a glass bulb thermometer inserted from the top of the chamber and close to the sur- face of the two soil samples(Fig. 1). It was checked by the above men- tioned recording hygrometer. The soil samples were so small that the temperature of the soil was essentially controlled by the temperature of the chamber. EXPERI DEN TA L PROC EDURE The first variable to be controlled in the chamber was humidity. Three levels of soil tensions were set to correspond to the controlled humidity. Temperatures and air velocities were changed and set so as to meet the. required combinations of the treatments. While humidity was changed, the same procedure for tension, temperature and air velocity was repeated. During the test, while tension was changed, the time needed for the tension to reach equilibrium was about 21; hours. It was also nece- ssary to run the whole system of the chamber for two hours to obtain the desired conditions for each day's test. All test runs were for 30 mi- nutes. The readings for 3 replications were taken when each combination of the treatments was being conducted. Evaporation losses from the two soil samples were measured by the water lost in cubic centimeters from the cylinders which were mounted on the front face of the chamber(Fig. 3). The loss readings were con- verted into inches per day. The correction of the error of the lost wa- ter volume due to the glass tube in the cylinder was also made. The temperatures of the air overrunning the samples were measured by the glass bub thermometer. The temperatures in the samples were also measured at the end of every treatment. It was found that the tempera- tures in the soils were the same as in the air. Wind velocities passing over the samples were measured by the pitot 21 22 tube in feet per second. Three wind velocities of O, 8 and 16 feet per second were controlled by the air blower. Relative humidities were measured by hygrometer and were converted into vapor pressure deficit in pound per square inch by using Psychro- metric Charts prepared by the American Society of Agricultural Engineers. Since there was some chamber leakage, it was difficult to control the low and the high humidities. The saturated lithium chloride solution on- 17 brought the humidity down to 27 percent of relative humidity. The hi- ghest relative humidity varied a small amount during the test. The sa- turated lithium chloride solution lost its ability to control the humi- dity while the tests at zero tension were being conducted. The relative humidity for the experiment on zero tension controlled.by the saturated lithium chloride solution was found to be around hO - 50 percent. The moisture content of the soil samples was controlled by various tensions. The soil moisture for each tension was determined by taking small soil samples from the soils. It was expressed by percentage on oven-dry basis. DISC USSION OF RESULTS Presentation of data Each value of evaporation for 81 combinations was obtained by tak- ing the average value of three replications. The mean low, medium and high temperatures of 61.9°F, 76.0°F ani 95.80? of .over all observations “were found. Three values of wind velocities(0, 8 and 16 feet per second) were obtained. Since the humidities found from the experiment were so scattered, it was almost impossible to get three average values close to the designed values. Five average values of 0.638, 0.151., 0.252, 0.3142 and a“. 08 pound per square inch of vapor pressure deficit for the ranges 0.035 - 0.09, 0.10 - 0.19, 0.20 - 0.29, 0.30 - 0.39 and o.t0 - 0.57 were found and the method of least squares was used to find the best-fit- curves and the equations of the subcoefficient of vapor pressure defi- cit. Soil moistures obtained from three tensions were fairly stable. The average values of moisture content for 0, 27.5 and 115 cm of tension were 35.87, 27.22 and 11.61 percent for sandy clay loam and 23.27, 16.1.9 and 9.71 percent for sandy loam soil respectively. Procedure to find the coefficients For determination of the formula presented here, 81 average va- lues of evaporation for both sanch' clay loam and sandy loam soils, three average values of temperature, three average values of wind velocity, five average values of vapor pressure deficit, three average values of moisture for both sandy clay loam and sandy loam soil and three tensions 23 234 were used to plot the curves and to find the equations of the subcoe- ffic ient. 1. Temperature coefficient: The first coefficient found was th and Cm. All data of evapora- tion were grouped in 3 lots of 27 according to low, medium and high tem- peratures(6l.9°F, 76.0°F and 95.801?) to find average values. The equa- tions for the curves were found to be(Fig. 7): - 0.209 - 0.00h r + 0.000033 T2 8'0 I - 0.133 - 0.00226 T + 0.00003h9 T2 o d- to I where cm is the subcoefficient of air temperature for sandy clay loam soil Cts is the subcoefficient of air temperature for saniv loam soil T is the temperature of overrunning air in 0F. From Fig. 7, it was obvious that the effect of air temperature on evaporation for the sandy loam soil was greater than that for the sandy clay loam soil. As the temperature of the air increased, more rapid in- crease of evaporation occurred in the sandy loam soil. It was also found that the effect of temperature on evaporation from the sancb' clay loam soil was less if the temperature of air was less than 75°F. The next step was to divide values of E (evaporation) of each of 81 average values by calculated values of th and Cts respectively to eliminate the effect of air temperature. 2. Wind velocity coefficient: 25 8." 333232- ..» 0.3.933 N . .3.— .no ...—.3388... can on on 2. a _ _ . — . _ ... 3 bed. he! not 0 .. glad he“. nah O \.\\.\ _ J91 we 2908.0 + a menace .. n26 ... 3e me 2886 ... a :86 u mead .. 2o 0.0 .10 «.0 n6 :6 um Morn-roan 26 532:.» e5» 3» 3o? e8 3o? no 33... an. m .3.— 84: .383.» Be. 9.. w w _ _ _ as 3. a... .3.— . Scenes-non o \ - Rmood n .— 88.0 + $.90 ... .J «a .8886 + a $36 + mama .- use 0.0 m6 0.A m..— 0.N "all 1",. "all 27 The second step was to arrange all data according to wind velo- cities(0, 8 and 16 feet per second) into 3 lots of 27 to find average values of Ec/th and EsflCbs for each lot. The values of 3 points for sandy clay'loammand sandy loam soils were plotted and equations for the curves were found(Fig. 8): cm = Etc/Cw 0.558 + 0.1.1.3 w + 0.000805 w2 cws = 25/0t5 = 0.599 + 0.0809 w + 0.00297 "2 where ch is the subcoefficient of wind for sandy clay loam soil Cws is the subcoefficient of wind for sandy loam soil ‘w is the wind velocity near the surface of the soil Fig. 8 showed that the effect of wind on evaporation for the sandy loam was greater than that for the sandy clay loam when the wind velo- city was less than 10 feet per second, but the reverse phenomenon was found when the wind velocity was greater than 10 feet per second. Values of Ec/th and Es/Cts were divided by 0Wc and cW8 reSpective- ly in order to take out the effect of wind. 3. Vapor pressure deficit coefficient: The third step was to arrange all data of vapor pressure deficit in increasing order and to group the data in 5 lots according to S in- tervals of vapor pressure deficit. The average value of vapor pressure deficit and the corresponding average value of Ec/thcwc and Es/btscws for each lot was found. The values of these 5 points for each soil sam- ple were plotted and equations for the best-fit curves found by the me- thod of least squares were(Fig. 9):' 28 m6 3.38 28.23 «.8»... 26.6} e3 26.6? 3... .6 m a: «5}: .333. ......8e .88» me :6 To «.0 10 _ _ _ q a '3 bone .35. .3.— 0 ice hund- uoh O a? .. £3026 .. A. .. .33an + mane .. 3o m? 2.58»... ... A. .. ..me26 .. nmmmé .. 3o 0.0 m6 0..n m2" 0.~ ”‘0"0/1 pm “0940/3 29 ~ 0.8233 - 0.1029(es - e) + 1.706(es - e)2 O {3‘ O I ~ 0.726 + 1.3h01(eS - e) + 0.u706(eS - e)2 o :7 In t where Chc is the subcoefficient of vapor pressure deficit for sandy Chs is the subcoefficient of vapor pressure deficit for sanchr loam soil (es - e) is vapor pressure deficit; where as is the saturated vapor pressure at a given temperature, e is the actual vapor pressure at the given temperature. Fig. 9 showed that when vapor pressure deficit was greater than 0.060 pound per square inch, the effect of vapor pressure deficit on evaporation for sandy loam seemed greater than that for sandy clay loam. 'vmen vapor pressure deficit was less than 0.06, the effects of vapor pressure on evaporation for both sandy clay loam soil and sandy loam soil seemed similar. Values of Egg/C1130,“3 and Efl/Ct'scws were divided by Chc and Chs res- pectively to take out the effect of vapor pressure deficit. 11. Soil moisture coefficient: The final step was to determine the average value of Ec/thchChc and Es/ctscwschs for the lot corresponding to each of three various ten- sions(0, 27.5 and ’45 cm). Each tension had its average value of mois- ture content for each soil sample. The values of these 3 points for each sample were plotted and equations for the curves were(Fig. 10): 2.2791 - 0.2395 s + 0.00666 32 CSC cSS 1.013 - 0.061.? s + 0.00371 32 mm 33.3.. :8 a» 30.330? new 962630} no 333 2S S .3.— on mm 9580A 3.2530... .38 cm 2 S m _ _ 33 3.3 had: .3.— O .33 henna you O _ _ _ _ Nu ”Rood o a $8.0 .. MS.” a :0 mm $80.0 + m mmmmd .. $5..“ ... one 0.0 or” m.” o.~ “Ho-wash: 1m Wowmo/a 31 where C50 is the subcoefficient of soil moisture for sandy clay loam soil CSS is the subcoefficient of soil moisture for sandy loam soil Another relations were found by expressing soil tension vs. ‘ Ec/btccwcchc and Es/Ctscwschs. The data used for finding C80 and 088 were used here, and were plotted vs. tensions. The equations for the curves were found(Fig. 11): — 2.281 - 0.0803 Ten + 0.0008Sb Ten? 0 *3 a I CT, = 1.515 - 0.02658 Ten + 0.000225 Tenz where CTc is the subcoefficient of tension for sandy clay loam soil 3T8 is the subcoefficient of tension for sandy loam soil Ten is the soil tension in cm. ' Two interesting results from Fig. 10 were found. At the same soil moisture percentage, evaporation from the sandy loam was greater than that from the sandy clay loam. The other.fact showed that the higher saturated soil moisture resulted in higher evaporation. It was apparent that the sandy loam had lower saturated soil moisture and the sandy clay had a higher saturated soil moisture. From the aspect of tension, higher tension applied to sandy clay loam resulted in less effect on evaporation. When tension was reduced to 18 cm or less, the effect of tension in the sandy loam on evaporation was less than the sandy clay loam. 315» .3 ago-3.16? e3 Beaded? me .633 Ba 3 .3.— 50 Jon. mom. on o: OM OM OH _ _ _ _ _ .33 hoao henna mom O .33 henna nah 0 «new mmwoood e 8» $80.0 .. mam.” « 3.0 ~89 smwoood ... 89 mowed .. Sent. .. one o ..3 . mt— o.~ 3‘10““0'30/0: 1m WOWOQO/E Final equations The formulas derived for sandy clay loam and sandy loam soils from the eXperimental results are: (1). where (2). For sandy clay loam based on soil moisture; E=th%0hccsceeeeeeeeeeeeeeeeoeeee(1) E th is the evaporation from the soil in inches per day = 0.209 - 0.00L r + 0.000033 T2; ctc is the subcoefficient of overrunning air temperature, T is the temperature of overrunning air in 0? one = 0.558 + 0.hb3 w + 0.000805 wz; c“,c is the subcoefficient of wind, W is the velocity of overrunning air in feet per second. = 0.8233 - 0°1029(°s - e) + 1.706(es - e)2; Che is the sub- coefficient of vapor pressure deficit, (es - e) is the vapor pressure deficit at a given overrunning air temperature in pound per square inch = 2.2791 - 0.2395 s + 0.00666 82; Cs. is the subcoefficient of soil moisture, S is moisture in the soil eXpressed by percentage of moisture on oven-dry basis. For sandy loam soil based on soil moisture: E=ctscwschscssoeeeeeeeeeeeeeeeeeee(2) E Cts is the evaporation from the soil in inches per day = 0.133 - 0.00226 T + 0.00003h9 T? 3h N cws 0.599 + 0.0809 w - 0.00297 w2 Chs Css = 1.013 - 0.06h7 S + 0.00371 S 0.726 + 1.3h01(eS - e) + 0.h706(63 - e)2 2 Except the second subscript "s" of the subcoefficient was used to distinguish sandy clay loam soil, the other symbols had the same nota- tion as used in equation(l). (3). For sandy clay loam soil based on moisture tension: E=ctccwc0thTc..eeeeeeeeeeeeeeeeee(3) where E is the evaporation from the soil in inches per day Cm, cwc and Chc were equivalent to the values of Cm, ch and Chc in equation(l) cTc = 2.281 - 0.0803 Ten + 0.000225 ren?; CTc is the subcoeffi- cient of tension, Ten is tension in centimeters. (h). For sandy loam soil based on moisture tension: E:Ctsc"s%sCTsoeeeeeeeeeeeeeeeeeee where E is the evaporation from the soil in inches per day Cts2 Cws and Chs were equivalent to the values of Cts: Gus and Chg in equation(2) CT, = 1.515 - 0.02658 Ten + 0.000225 ten?; CT, is the subcoeffi- cient of tension, Ten is tension in centimeters. 1. 3. 7. 0‘ "'Y"Q‘ "’1‘ r,» D‘J “Jul L L‘J The use of the tension table to control soil moisture in the thin layer of soil gave a very stable moisture content and uniform mois- ture distribution. Soil tension was a good index of soil moisture. The moisture content of the soil depended on the tension appliedh The moisture in the soil was inversely proportional to the soil tension. Increasing air temperature produced more evaporation in the soil of coarser particles than in the soil of finer particles. The effect of wind on evaporation in the soil depended on wind velo- city and the particle size of the soil. More evaporation occurred in the soil of coarser particles when the wind velocity was low, but the reverse phenomenon was observed when the wind velocity was higher. thimum constant wind effect on evaporation was observed from the sandy loam soil. Evaporation does not depend on the moisture content of the different soils, however it does depend on the moisture content of the parti- cular soil. More evaporation occurs in a Specified soil when its moisture content is higher. In comparing the evaporation from di- fferent soils, the type of soil as well as the moisture content of soil has to be taken into account. Maximum evaporation occurring in the saturated soil depends on the maximum capillary capacity of the soil. The soil of the finer par- 35 8. 36 ticles has more capillary capacity than that of the coarser parti- cles. Therefore in the close saturated conditions, the evaporation occurring in the soil of the finer particles is greater than that of the coarser particles. When soil is unsaturated, the rate of evaporation depends on the size of the particles in the soil. The soil of the coarser parti— cles has more evaporation than that of the finer particles although the moisture contents are the same in these different soils. LITERATURE CITED Christiansen, J. E. and Nella W. Lauritzen(l963), A bibliography on eva- poration and evapotranSpiration. Utah State University, Logan, Utah. March 1, 1963. Christiansen, J. E.(l960), water requirement for waterfowl areas near the Great Salt Lake. Progress Rpt. Utah State Univ. Jan 1960. Edney, E.(l957), The water relations of terrestrial Arthropods. cambridge Eng., Cambridge Univ. Press, 1957. Fortier, S.(l907), Evaporation losses in irrigation and water require- ment of crops. U.S. Dept. Agr. Bul. 177. 1907. Fukuda, H.(l9SS), Air and vapor mevement in soil due to wind gustiness. Soil Sci. 79: 2&9 - 256. 1955. Fukuda, H.(l9S6), Diffusion of water vapor and its exchange between con- densation and evaporation in soil. Soil Sci. 81 - 9S. 1956. Kenneth Jose Mathison(l963). The use of climatological and related fac- tors for estimating evaporation. Utah State Univ. M.S. thesis. 1963. Linsley, Ray K. Jr. and Max A. KOhler and Joseph L. H. paulhus,(l958), Hydrolggy;for engineers. NEGRAW-HIIL.BOOK COMPANY, INC., New York Toronto London 1958. Mann, R. J.(1371), 0n evaporation, rainfall, and elastic force of vapor. Brit. Met. Soc. Proc. 5: 285-297. 1871. Meyer,‘Adolph F.(l9h2), Evaporation from lakes and reservoirs. Minn. Resources Comm. St. Paul, Minn. June l9h2. 3? 38 Onchukov, D. N.(1957), The phenomenon of heat and moisture transmission in soils and subsoils. Moskov. Technol. Inst. Pishch. Promush. Trudy, p. 55 - 63. 1957. _ Penman, H. L.(19h8), Natural evaporation from open water, bare soil and grass. Proc. of the Royal Society, Series A. l9h8. Perterson, H. B.(l959). Personal communication. 1959. Richards, et a1.(l956), Physical processes determining water loss from soil. Soil Sci. Soc. Amer. Proc. 20: 310 - 31h. 1956. Rohwer, Carl. (1931), Evaporation from free water surfaces. USDA and Colo. Agr. mp, Sta. Tech. Bul. 271: 1 - 97. Dec. 1931. ' Spiegel, Nhrray'R.(l96l), The theory and problems of STATISTICS. Schaum Publishing Co. New York. 1961. Staple, w. J.(l956), Evaporation from soil and.vegetation. Netherlands Jour. Agr. Sci. h: 39 - h2. 1956. Thornthuaite, c. w. and J. R. Mather(1955), The water balance. Publ. in ClimatolOgy, Vol. VIII, No. l, Drexel Institute Laboratory of Cli- matology, Centerton, N. J., 1955. YOung, A. A. and H. F. Blaner.(l9h2), Use of water by native vegetation. Calif. Div. of'water Resources Bull. 50. l9h2. APPENDIX Procedure for finding the constants of the best-fit parabola equa- tion may be stated as follows: 1. For determining the constants of the parabola equation of the co- efficients Ct, C", C8 and CT; Three points on the curve were given by the results of the ex- periment. The assured parabola equation was Y=ao+a1x+a2x2 where a0, a1 and a2 were three constants to be determined. Three sets of (X, I) were substituted in the equation and three simutaneous equations were obtained; Y1=a°+alxl+a2 112 Y2=ao+a1X2 +a2 X22 r3=ao+a113+a2x32 Then, solved the equations to obtain a0, a1 and a2. 2. For determining the constants of the parabola equation of the co- efficient Ch; . It was necessary to use the least square method to obtain the best -fit equation for the coefficient of Oh. The least square parabola approximating the set of 5 points (X1, Y1), (X2, Y2), (X3, Y3), (Xh, Yh) and (X5, Y5‘ obtained from the results: at»? the experiment ha? the equation 39 ho (Spiegel, Murray R, 1961); Y'= so + a1 X + a2 X2 where a0, a1 and a2 were determined by solving simultaneously equa- tions: ‘ZY=a°N+a12x+a22x2 ZXY=ao£X+a12X2+a22X3 2x2Y=ao£X2+a12.'1{3'l-a2.§:Xh where N is number of set. In this experiment, N equals 5. HICHIGQN STFITE UNIV. LIBRRRIES 1| l1 “HI “WIN I ||1| |1||| 1 "IN 312932010 8136