EVAPORATION INVESTIGATIONS AT ELEPHANT BUTTE RESERVOIR

IN NEW MEXICO

Narendra N . G U N A J I (i)

ABSTRACT

The investigation reported in this paper describes studies of the water losses by evaporation at Elephant Butte Reservoir, near Truth or Consequences, in South Central New Mexico. This study represents the first phase of an evaporation suppres­sion research program which was initiated in the summer of 1963. Evaporation sup­pression investigations require the determination of evaporation as accurately as possible to evaluate the efficiencies of evaporation savings and the economic feasibility of suppression. Only after establishing certain experimental relationships and corre­lating the various parameters involved can full-scale evaporation reduction studies be performed. The determination of evaporation at this Rio Grande site is important not only for suppression studies to follow, but also for the growing problems involving interstate and international water rights and the reliabilities and assurances of domestic water delivery. The principal topics reported in this paper are: 1) to determine the water losses by evaporation from Elephant Butte Reservoir, utilizing the energy-budget technique; 2) to test the Cummings Radiation Integrator (CRI) as an effective means for measuring net incoming radiation for purposes of computing lake evaporation; 3) to determine the coefficient, N, in the quasi-empirical mass-transfer equation of evaporation, using the energy-budget method as a control ;4) to evaluate the coefficient, K, in the heat-transfer equation of energy convected to or from the reservoirs surface; and 5) to determine the significance of errors in data analysis in evaporation studies.

RÉSUMÉ

Des études ont été faites sur les pertes d'eau par evaporation dans le réservoir Elephant Butte, près de la ville de Truth or Consequences, au sud de la partie centrale de l'Etat du Nouveau-Mexique, aux États-Unis d'Amérique. Ces études, qui ont débuté au cours de l'été 1963, représentent la première étape d'un programme de recherche visant à réduire l'évaporation dans ce réservoir. Une détermination exacte de 1'evapo­ration doit être effectuée afin de pouvoir évaluer l'application économique de mesures tendant à la réduire, Avant de pouvoir tenter certains essais d'envergure pour réduire l'évaporation, il faut déterminer expérimentalement les relations pouvant exister entre certains facteurs. La connaissance du taux d'évaporation dans ce réservoir du Rio Grande est importante non seulement en vue des essais subséquents sur la réduc­tion de ce taux, mais également dans la considération des problèmes concernant le partage et la distribution de l'eau entre États limitrophes. Les principaux sujets traités sont : 1°, la mesure des pertes par evaporation dans le réservoir Elephant Butte par la technique du bilan de l'énergie; 2°, l'évaluation de l'intégrateur de radiations Cummings (CRI) comme moyen efficace pour mesurer l'irradiation totale qui permettra d'estimer l'évaporation; 3°, la détermination ducoefficient N, dans l'équation d'évapo­ration dite «quasi-empirical mass-transfer», par la méthode du bilan de l'énergie; 4°, la détermination ducoefficient K dans l'équation sur l'échange de l'énergier-chaleur par convection à la surface du réservoir; 5°, la détermination des erreurs significatives dans l'analyse des données sur l'évaporation.

INTRODUCTION

The increasing population of our Earth and the ever-increasing standards of living have precipitated a growing demand for water. In 1950, over 195 million acre feet of water were used in the United States. This figure jumped to 246 million acre feet in 1955.

(*) Professor of Civil Engineering and Associate Director, Engineering Experiment Station, New Mexico State University, Las Cruces, New Mexico, U.S.A.

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This was over a 20 percent increase in five years. It is estimated that by 1985, the demand for water in the United States will reach 672 million acre feet yearly, which is almost double the demand that exists today. Water losses by evaporation from reservoir surfaces in the 17 Western States have been estimated to be approximately 15 million acre feet annually. Naturally, it would be impossible ever to attempt to recover or prevent all these evaporation losses. Conservation of our diminishing water resources, however, can be achieved by learning to control and reduce evaporation through better understanding of the hydrologie cycle and the mechanics of the phenomenon of evapo­ration.

In the arid and repeatedly drought-stricken Southwest, where precipitation may yield less than 10 to 20 inches annually, evaporation exceeds 70 inches. Where over 27.5 million acres of irrigated crop land depends upon fresh water sources, one cannot afford to overlook this ever-growing problem. Several recent developments have made it necessary to take immediate steps to increase the conservation, improve the utilization, and expand the administration of our water resources. These developments are increases and shifts in population, shifts in industry, droughts, and pollution of our waters. In the vast areas of the arid West, where most of the economy depends upon adequate supplies of fresh water, industrial and economic expansion could be impeded because of inferior qualities and supplies of water.

The storage of stream flow from mountain watersheds and drainage basins in reservoirs has affected the development of the irrigated agriculture of the West. These reservoirs help to prevent floods, store water supplies that otherwise might be wasted, and make possible the production of power. However, these reservoirs expose large surfaces of water to the process of evaporation and become major sources of water losses. Since evaporation loss from reservoirs is a major item in the water budget of the Western states, reduction in evaporation losses would greatly benefit this region.

LOCATION AND GENERAL DESCRIPTION OF ELEPHANT BUTTE RESERVOIR

Elephant Butte Reservoir, located on the lower Rio Grande River in South Central New Mexico near Truth or Consequences, serves as a source of water for the lower Rio Grande Project of the Bureau of Reclamation. The Rio Grande Project serves over 615,000 people and about 235,000 acres of productive agricultural land on both sides of the river below Elephant Butte Dam. Waters of the Rio Grande are stored in Elephant Butte Reservoir, which has a capacity of 2,194,990 acre feet of water at a spillway elevation of 4407.0 feet. At this capacity, the surface area is approximately 36,580 acres, according to the 1961 hydrographie survey conducted by the Bureau of Reclamation. The reservoir is irregular along its shoreline and relatively long compared to its width. At full capacity its length extends 40 miles northward and its width varies from two to four miles. Presently, it is about 10 miles long and varies from approximately 1000 feet to a little over a mile wide in the middle and upper reaches. The storage capacity of the reservoir is continuously being decreased by silt influx which amounts to about one per cent of the total volumetric inflow. Water is released as needed to meet irrigation requirements from March to September at the rate of 600 to 1200 cubic feet per second for approximately 12 hours a day. This imposes a fluctuating water level condition, decreasing the reservoir level to a minimum in late August from summer draft and increasing its level to a maximum in March when the irrigation season begins. Annual fluctuations of 15 to 20 feet are common.

Elevations surrounding the reservoir range from approximately 4200 to 4500 feet above mean sea level. Vegetation grows quite sparingly in the vicinity. U. S. Weather Bureau records indicate average winter temperatures from 14 °F minimum to 70° maximum, and average summer temperatures from 63 °F to 103 °F. The average

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frost-free period of 203 days extends from April 9 to October 29. Winters are normally mild, and although mid-day summer temperatures of 95 °F are quite common, nights are cool. This diurnal fluctuation results from almost cloudless skies. The medium altitude and dry atmosphere serves to moderate the arid climate. Average annual rainfall is 8.9 inches, and more than half occurs in July, August, and September. Rainfall is not considered to be a major or consistent contributor to the flow in the Rio Grande above Elephant Butte. Records show that during the 34-year period from 1929 through 1962, there were only three years, 1929, 1941, and 1957, in which rainfall alone made major contributions to the flow of the river into Elephant Butte Reservoir. During the remaining 31 years, rainfall contributions ranged between negligible and moderate amounts. The bulk of the water supply that serves the area below Elephant Butte originates from snowmelt in mountains surrounding the San Luis Valley in South Central Colorado, and in the northern part of New Mexico. The greatest volume of runoff from snowmelt usually occurs during the months of May and June. During the remainder of the year, flow in the Rio Grande consists of water from mountain streams and drain return flow from the Middle Rio Grande area north of Elephant Butte. Low magnitude floods from rainstorms in various parts of the watershed may bring occasional inflow. Average annual wind velocities are approximately five to six miles per hour. In the spring, it is not uncommon to experience gusts of wind up to 60 miles per hour. Southwest winds are generally prevalent in the morning, switching to the west in the afternoon.

Instrumentation

The necessary meteorological data required for computing lake evaporation by the energy-budget and mass-transfer methods are:

Energy-Budget of Lake Mass Transfer CRI Energy Budget

1. Air temperature* 1. Air temperature* 1. Cummings Radiation 2. Relative humidity** 2. Relative humidity** Integrator (CRI) 3. Lake surface temperature*** 3. Lake surface tempera- 2. Air temperature* 4. Precipitation**** ture*** 3. Relative humidity** 5. Incoming short- and long- 4. Wind Speed 4. Water surface

wave radiation temperature 6. Inflow rate and temperature 5. Bulk watertemperature 7. Outflow rate and temperature 6. Precipitation**** 8. Lake temperature profile

(Factors indicated with asterisks represent parameters measured with the same instrument).

A centrally-located meteorological station was maintained at Long Point, four miles upstream from the dam. Station equipment included a thermocouple psychrometer, relative humidity sensing element, recording and non-recording rain gages, wind anemometer and direction vane, radiation instruments, and a Cummings Radiation Integrator. An air-conditioned house trailer accommodated the potentiometric multiple-channel and portable recorders and constant-power supply transformer, along with tools and spare parts. The trailer also served as a field workshop and routine equipment storage. The lake surface temperature was recorded at five different loca­tions on the reservoir by five anchored rafts. Mercury-in-steel pressure type probes were installed on the raft and were connected to the recorder. Wind speed over the lake was measured with 3-cup contact anemometers which were also installed on the rafts used for lake surface temperature measurement; anemometers were approximately two meters above the lake surface. Thermal profiles of the lake were taken every two

310

weeks at approximately 40 stations located throughout the, area of the lake. The temperatures were taken with an underwater thermometer, having a weighted thermistor bead probe.

DATA ANALYSES

Analyses of data, for the investigation period, embodying the various parameters of energy-budget, Cummings Radiation Integrator, and mass-transfer techniques were divided into 28 computation intervals. Each interval, or thermal survey period, as it is called, averages about 14 days.

THE HEAT-BUDGET EQUATION

Energy conservation requires that a balance of energy exist between the loss and gain of heat at the interface of water and air. The insolational energy absorbed at the water surface may be equated to the energy gained or lost from the surface by back radiation, reflection, conduction, convection, evaporation, and energy expended in raising or lowering the temperature of the body of water. Expressed as an equation in terms of energy flux units (energy per unit area per unit time),

Qs-Qr+Qa-Qbs-Qar + Qv-Qw-Qk-Qe = Qo U )

where Qs is incoming solar or short-wave radiation, Qr is reflected short-wave radiation ; Qa is incoming long-wave atmospheric radiation, Qfts is back-radiation emitted by the water surface to the atmosphere according to Stefan-Boltzmann's Law; Qar is reflected long-wave atmospheric radiation; Qv is net advected energy consumed or released by a volume of water in the form of inflow, draft, or precipitation; Qw is heat lost by advection of a mass of water resulting from evaporation; Qu is sensible heat, or heat lost or gained in thermal convection between the water surface and air; Qe is energy representing the quantity of heat required to change a liquid to a vapor state without a change in temperature, or latent heat of vaporization ; and Q0 is energy used in warming the body of water over a given time interval, or the net change in stored energy. Conduction of energy through the bottom, heating due to chemical and biological processes, and the transformation of kinetic energy into thermal energy are generally neglected because of their small magnitude. Equation 1 can be rewritten in the form

Qe+Qn + Q, = Qs-Qr+Qa-Qbs-Qar+Qv-Q0 (2) The energy used in evaporation can be expressed as

Qe = EQL (3)

Where E is volume of evaporated water (cubic centimeters), L is latent heat of vaporization at the water-surface temperature (calories g ram - 1 ) , and Q is mass density of evaporated water (gram cm - 3 ) . The sensible heat can be written as a function of latent heat, using Bowen's Ratio, R

Q„ = RQe = R(EQL) (4)

The advected energy of evaporation resulting from a loss of mass gKcan be expressed in the terms of the evaporated volume of water E as shown from equation

Q„ = Q VCp(T0 - Tb) = QCpE{T0 - Tb) (5)

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Substituting the expressions for Qe, Qu, and Qw into equation 2

E IQL(1+R) + CP Q(T0-TJ] = Qs-Qr+Qa-Qbs-Qar+Qv-Q0 (6)

Then

E = QS-Qr+Qa~Qar-QbS + Qv-Qo ( ? )

e [L( l + R) + Cp(T0-T6)]

When the energy terms in the numerator in equation 7 are expressed in terms of flux units (calories per square centimeter per day), .Ewill represent the volume of water, in cubic centimeters, evaporated over an area of one square centimeter per day. This can be defined as the depth (centimeters) evaporated in one day. If the energy terms in the numerator are total energies summed over the entire lake area for the thermal survey period (calories per period), the E will represent the volume of water, in cubic centi­meters, evaporated over the entire thermal survey period.

Proper selection of the base temperature can increase the accuracy of the computed evaporation from equation 7. Since seepage volumes are difficult to evaluate, the base temperature should be selected near the seepage temperature. This would altogether eliminate seepage energy from the equation. In general, the base temperature should be selected as the best temperature estimate of the largest unknown advected volume. A selection of Ti, = 0 °C greatly simplifies all calculations, and since the seepage energy has been shown to be a relatively small term in the energy budget, a reference tempe­rature of 0 °C will not materially affect the relative magnitude of this term. For a mass density, Q, and specific heat, Cp, both equal to unity and 7& equal to 0 °C, equation 7 be­comes

E = Qs-Qr+Qa~Qar-QhS + Qv-Qo ( g )

L(i + R) + T0

and now can be used to determine evaporation. When the terms in the numerator of equation 8 are in total energy units (calories) for each period, E represents the accumu­lated evaporation volume, in cubic centimeters, over the period. When the parameters in the numerator of equation 8 are defined in terms of energy flux (cal c m ' 2 day"1), the evaporation, E, represents the volume (cm3) of water evaporated over a unit area (cm2) per day. Figure 1 illustrates annual variation of important heat budget parameters by thermal survey periods measured at Elephant Butte Reservoir. Figure 2 shows annual variation of air and water surface températures experienced at Elephant Butte Lake during the investigation period. Figure 3 shows the annual variations of Bowen's Ratio computed during this study. Figure 5 shows the average daily evaporation rate in centimeters per day computed for Elephant Butte Lake by Heat Budget method.

CUMMINGS RADIATION INTEGRATOR

In 1926, at Fort Collins, Colorado, and Pasadena, California, Cummings and Richardson (1927) employed the energy-budget technique as a method for finding the difference between the incoming and outgoing radiation by means of observations on thermally-insulated pans. The studies were conducted to test the validity of the energy-budget equation, using two insulated pans in proximity and making use of the fact that the incoming radiation rate to both pans were equal. Cummings outlined a suggested design of an insulated pan or Cummings Radiation Integrator (CRI) to be constructed and operated as part of the Lake Hefner (1954) project. The purpose of its installation

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was to study its use as a possible replacement for the more expensive and complicated radiation instruments for measuring the net incoming sun and atmospheric radiation. Comparisons between the CRI and radiation instruments indicated in that study that the CRI measured the net radiation with a standard error of three per cent of the mean radiation instrument data. An error of this magnitude represented about a nine per cent error in evaporation, assuming that the radiation instruments were accurate. Lake Hefner results indicated that the CRI offers considerable promise as an instru­ment for measuring net incoming radiation. It was estimated in those studies that the error in computed weekly summer evaporation would be 10 to 15 per cent or less and five to ten per cent on a monthly basis.

THEORY OF CRI

The energy-budget for a water body can be expressed as

Qs-Q, + Qa-Qar-Qbs-Qi,-Qe-Q„+Qv = Qo (9) where the energy terms are expressed in calories per unit area per unit time. A CRI placed near the shore of a lake would also yield an energy budget which may be expres­sed as

Q's-Q'r+Q'a-Q'ar-QL-Q'h-Q'e-Q',+Q'v = Q'0 (10)

The symbols with primes refer to CRI. The basic assumption reflects that the net sum of sun and atmospheric radiation is

the same for the lake as for the CRI, or

Q's-Q'r + Q'a-Q'ar = Qs-Qr + Qa-Qar ( H )

It is probably not true that long-wave and short-wave incoming radiation (Qs + Qa) are the same over short periods of time, such as an hour, because of transient cloud effects. For longer periods, such as a day, week, or month, the assumption appears reasonable. Since the amount of reflected atmospheric radiation, Qar, is dependent only on the absorptivity of the water, there appears to be no reason to question the validity concerning this term, providing that lake water is used in the CRI and it does not be­come contaminated with substances that might affect its emissivity. Because the reflec­tion of solar energy is independent of wind effect and primarily dependent on sun altitude, the amount of reflected energy from the CRI should not materially differ from that on the lake. Equation 10 can be rewritten

Q's-Q'r+Q'a-Q'ar = Q'e + Q'„ + Q'w + QL ~ Q'v + Q'o (12)

Substituting QE' V for Q'e, R Q'e or R(QE'L') for Q'n, and Q CpE\T'0- Tb) for Q'w, where g is the mass density of lake water, E' is the observed CRI evaporation volume per unit area, V is the latent heat of evaporation, R is Bowen's Ratio, Cv is the specific heat of the lake water, T'0 is the average CRI surface temperature, and Tb is the base or reference temperature, taken as 0°C, equation 12 becomes

Q's-Q'r+Q'a-Q'ar = QE' [ L ' ( l + R') + Cp T0 '] + Q'bs~ Q'v+ Q'0 (13)

Equations 1 and 13 can be combined since the net incoming radiation terms of the CRI and lake are equal. Usingthe relations QEL for Qe, R(gEL) for Qn, QCpE{T0— TD) for

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Qw, Tb — 0°C, and the reasonable approximations, Q = 1 gram cm 3 and Cp = 1 cal­orie (gram °C)"x ,

E = E' ^'i1 + R) + r ° ] + {Q'b° ~ Q'"+ &> ~ ( 6 f a ~ Q»+ g ° } (14) L(l + K) + T0

In metric units, £ represents the estimated lake evaporation in cm3 c m - 2 or depth of evaporation in centimeters when L and L' are in cal gram"1 , T0 and T'0 are in °C, and (Q'bs^ Q'v+ Q'o) and (QbS— Qv+ Qo) are in cal cm" 2 . The lake evaporation indicated here represents the energy budget for the lake, utilizing the net radiation obtained from the CRI. The CRI pan evaporation, E', was computed from the difference in water surface stages between the beginning and end of each period, making corrections for the volume of make-up water added during each servicing, the amount of precipitation, and occasionally the stage differences resulting from any cleaningand refilling operations of the CRI. Figure 6 shows the average daily evaporation rate in centimeters per day for CRI at Elephant Butte Lake. The daily evaporation rate (cm day"1) was calculated by dividing the total period evaporation (cm3) by the number of days in each thermal survey period and the water surface area of the CRI (11433.3 cm2).

Mass and Heat-Transfer Data Analyses: It was shown that the semi-empirical mass-transfer equation

E=Nuz(e0-ea) (15)

can be used to determine evaporation on the reservoir, as suggested in the Lake Hefner (1954) study. In cgs units when the evaporation, E, is in cm day"1 , uz is average wind velocity at a height of two meters above the water surface, in miles per hour; e0 is vapor pressure of the air, in millibars, for actual conditions of humidity; JV is the ratio of the energy budget evaporation rate, E, for a stated period of time to the product "z (e0 — ea) for the same period. The ratio N = E/itz (eo — e») was calculated for each thermal survey period and averaged over the entire investigation period. The average wind velocity over the lake, at a height of two meters, was determined from the wind records on rafts 1, 2, 4, and 5. Continuous chart records were kept on all four rafts. Figure 4 shows the average annual variation of wind velocity. The simplified heat-transfer equation for sensible heat can be expressed as

Qh =KUZ{T0-Ta) (16)

in which K is an empirical coefficient containing Cp , g, Z, the height at which Ta and Uz

are measured and any variables other than Uz contained in eddy diffusivity. K now can be evaluated knowing water surface temperature, Te, and air temperature, Ta, average wind velocities, Uz , and Qh, making use of Bowen's Ratio R. Figure 7 shows variation of JVand AT for different thermal survey periods during this investigation.

SIGNIFICANCE OF ERRORS IN DATA ANALYSIS IN EVAPORATION STUDIES

Application of the energy-budget concept will yield the total of evaporative and convective heat losses in terms of the measured quantities through the following rela­tion:

(Qe + Qk + 6 J = Qo - Qs - Qa - Ô . + Qr + Qar + QbS ( " )

The measured quantities are all in the right-hand side of this expression. The sum of C e + Qw and Qh in the left-hand side must be separated by the use of the Bowen ratio

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to isolate the sum Qe+ Qw With a relationship of this type, an error in one of the quantities in the right-hand side will introduce an error of equal amount into the com­puted left-hand side. The two items which are difficult to evaluate are the Qv (adverted energy) and Q0 (energy storage). Conditions for a good evaluation of evaporation by energy-budget methods become unfavorable if inflow and outflow rates are large and temperatures are measured only at intervals. Energy storage is a large item and diffi­culties of evaluation make it desirable to conduct the thermal surveys at intervals of 7 to 10 days or longer. The Bowen ratio apparently works well if based on averages for periods of this length. It may be desirable to measure the reflected energy directly to avoid a possible error arising from estimates. Where a quantity in the energy budget is obtained by a direct measurement, a possible error can be assessed only by making a comparison measurement by some other devices. The flat-plate radiometer and the Cummings Radiation Integrator records might be used, for example, to obtain such a comparison

When the quantity is computed from observed data, it is possible to estimate the effect of observational error as suggested by Glover (1960). The back radiation, for example, is estimated by using an expression of this type: E = QJT4 (18) Where gi represents the Stefan-Boltzmann constant as modified by the absorptivity and T, the absolute temperature (0 "Kelvin). By differentiation, dE = 4giTsdT (19). This relation­ship can be used to evaluate the effect of an error AT in reading the surface tempera­ture T. Then,

AE = 4 e 1 T 3 AT (20)

This can be put in the form

A-* = *** (21) E T

At 300 "Kelvin, for example, an error of 1 °C in measuring the surface temperature would introduce an error of (4) (1.00)/300, a little over 1 percent. The advected energy is estimated from the inflow and outflow and the measured temperatures. The expression representing the energy carried into the lake by the inflow over the period T will be of the following type:

Atx

'ti

q9dt (22) o

An index error Ad in the instrument recording the temperature would produce an error

& - ^ (23) At1

where the total flow is

F = I ' qui (24)

An index drift can occur in some types of automatic recording devices. The practice of arranging the recorder to read a known resistance once each cycle has sometimes been adopted to detect and evaluate such a drift. Errors in the measurement of the flow rate q could be detected by making an independent measurement. A current meter is often used for this purpose where the quantities "q" are obtained from a rating curve.

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The heat storage Q in the lake is computed from the readings of a thermal survey by a process which may be expressed in the form

A H

0addh (25)

A is surface area, a is area at depth h, 6 is temperature. An index error leading to a systematic error of temperature evaluation would lead to an error:

AQt=^-A6 (26) A

where V represents the volume of the reservoir. An error in the areas a and A could be detected by making a new survey. The change in energy storage over a period t, is obtained from thermal surveys made at the beginning and end of the period. The errors of the determination Qt are carried over in this process and they may not be compen­sating. To minimize the effect of these errors, it is important to maintain a sufficiently long interval t, between thermal surveys. Experience seems to indicate that a week to 10 days is about a minimum. Table 1 below, summarizes estimated maximum errors in each energy budget term for Elephant Butte Evaporation Investigations.

TABLE 1

Estimated maximum errors in each energy budget term

Term Estimated Maximum Error

Qs ± 2 per cent Qr ± 1 0 per cent Qa ± 2 per cent Qar ± 1 per cent Qbs ± 1 per cent Qv ± 1 0 per cent Qw ± 6 per cent Qh ± 10 per cent Qo ± 8 per cent

The precision with which each term in the heat-budget equation can be determined is dependent on the inherent accuracy of the measuring equipment and completeness of the data. Statistically, if the errors are combined by adding individual variance, the estimated maximum error of computed evaporation for each thermal survey period can be evaluated. It should be kept in mind that the errors are estimated to be the maximum likely error, and the error in most thermal-survey periods is believed to be less than the values reported below. On a yearly basis, the error should be substantially less because the percentage of error in evaluating the change in energy storage in the lake decreases considerably as the length of the period increases. The maximum possible error in the heat-budget equation was computed by using the statistical equations for propagation of error. The maximum probable error likely to occur in evaporation determination by heat-budget equation for each thermal survey period is shown in table 2.

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TABLE 2

Maximum probable errors in Elephant Butte evaporation investigation

TSP No. Error in par cent TSP No. Error in per cent

1 2 3 4 5 6 7 8 9 10 11 12 13 14

12.6 11.5 7.2 6.2 8.1 10.1 12.1 10.8 14.7 16.9 17.4 21.2 27.8 15.5

15 16 17 18 19 20 21 22 23 24 25 26 27 28

13.0 11.9 8.1 9.2 5.4 4.6 7.8 6.6 4.4 5.3 6.1 6.8 6.3 7.7

The minimum value for probable error of evaporation loss estimates was 4.4 per cent and a maximum value of 27.8 per cent. The mean value of the probable error for the entire period of investigation reported here was found to be 10.5 per cent. In observations of the measurable parameters of the heat-budget equation, the accuracy of all instruments used should be the same. In any field experiment the instrument with the least accuracy controls the accuracy of the results; therefore, it should be kept in mind that the accuracy of all instruments used should be comparable. A thorough knowledge of the accuracy of the instruments,, and the number of significant figures that can be obtained from a measurement are essential for the reduction of heat-budget data. The use of measurements containing more figures than those which are significant will tend to lessen the total error in the final results. If this is done consistently throughout the investigation, the total error will be smaller than its true value and the validity of such results will be subject to question.

GENERAL CONCLUSIONS

Evaporation from Elephant Butte Reservoir was determined by the energy-budget technique and compared with that obtained using the CRI net radiation. The quasi-empirical mass-transfer equation coefficient, N, was determined by using the evapo­ration obtained from the energy-budget method. The accuracy with which each term in the energy-budget equation can be evaluated depends upon the inherent accuracy of the measuring equipment and the completeness of the record. Statistically, if the indicated energy-budget term errors are combined by adding the individual error variances, the estimated maximum error of computed annual evaporation is about 10 per cent. On the basis of error analysis, certain measurements should be made with a high degree of accuracy, while others need not be. For example, a two per cent error in measuring incoming long-wave radiation (Qa) may produce from

317

£>.6 co 0.4 £ < 0-2 o

CO

r0.2 AUG

F1G.3 80WEN S RATIOS FOR LAKE (SOLID)

AND CRi (DASHED)

1963 -*' 1964 _ " " " - " • SEPT[ } OÇ T t NOV t DEC p JAN , , fEB MAR . , APR | ; ft A Y | , JLIN[ < , JUL,,

FIG.4 AVERAGE WIND VELOCITY IN MPH

a, Q

2 S

FIG. 5 VARIATION OF EVAPORATION FROM LAKE IN CM. DAY

1963 19 6 4

.AUG, | .SEP . i ,qÇT. i . 3 9 y , i ,PEÇ. t . W . | ,FEB, , , , MAR , APR , , MA. Y , , , ^ > j . , ,J:UL.

-OOiOO

~oÔbiôo~

- 0 00400

- 0 00200

-0.00000

FIGURE 7. VARIATION OF IN AND IS BY THERMAL SURVEY PERIODS

N ^^NEAaiOQp6J i3_

N IS CALCULATED IN CM (DAY MPH MB)"'

K !S CALCULATED IN CALICM2 DAY MPH 'C)" '

~K

AUG. SEPT. OCT. NOV. DEC. JAN. FEB. MAR. APR. MAY JUN. JUL. ' • • • ' t 1 1 I I I I I 1 I I I I i I t i I t i i i i • I i . i t i t • . t i . 1 . i • • • 1 . , , • , I t • . . 1 • • • • ;

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3 to 15 per cent errors in monthly evaporation, or five per cent annual evaporation, while a 10 per cent error in determining reflected solar energy causes only a one to five per cent error in monthly evaporation or one per cent in annual evaporation. Sensible heat represents a small but necessary term in the energy-budget equation during short evaporation study periods such as two weeks, but over a year, the sensible heat conducted from the water surface balances that conducted to the water; for this reason, it may be neglected on an annual basis. When the net incoming radiation, in langleys per day, obtained from CRI, is compared with that measured with the flat-plate and pyrheliometer instruments, a least squares analysis yields the equation X = 0.0636 + 0.960 Y, where X, the dependent variable, is the net radiation flux obtained with the flat-plate and pyrheliometer instruments and Y, the independent variable, is the net radiation obtained from CRI. The standard error of estimate of Jfand y was found to be only 23 langleys per day, which represents but two per cent of the total incoming daily net radiation. The coefficient of correlation, which measures the degree of associ­ation of CRI to instrument radiation, is 0.994. The square of the correlation coefficient is 0.987, indicating that 98.7 per cent of the instrument radiation can be explained by using the Cummings Radiation Integrator. For 22 thermal survey periods, the weighted mean daily evaporation as determined using the CRI net radiation was 0.464 cm day ~1

or 3.5 per cent greater than the corresponding weighted mean energy-budget evapo­ration of 0.448 cm day"1 . The standard error of estimate was 0.084 cm, or 19 per cent of the weighted mean daily energy budget evaporation. For longer periods of time, such as a month or year, the error in evaporation from using the CRI net radiation would be expected to be much smaller. For instance, the 9'/2 month cumulative eva­poration on the lake, using CRI net radiation is 72.1 inches, while for the corresponding period, the energy-budget evaporation for the lake yields 69.4 inches, a four per cent difference. The Cummings Radiation Integrator may be used effectively as an instru­ment for measuring incoming net radiation. For purposes of computing evaporation within 10 to 15 per cent of the mean annual value, using the energy-budget technique, the instrument appears to be a satisfactory substitute for the flat-plate radiometer and pyrheliometer. Difficulty arises, however, during the winter when the CRI has to be taken out of service because of ice formation. Sensible heat was shown to be continu­ously conducted to the CRI since the average two-week air temperature, Ta, always exceeded the average water-surface temperature, T0. This phenomenon may be partly explained by the fact that instead of the incoming energy being used to heat the water within the CRI, it was utilized for evaporating larger quantities of water than observed on the lake. For example, average 9'/^ month evaporation at CRI was 100.4, while only about 70 inches evaporated from the lake over a corresponding period. The difference in evaporation between the integrator and lake may be attributed to (a) difference of stored energy in the lake and CRI, (b) convective currents over the CRI in the absence of wind, (c) difference in wave action on water surfaces, and (d) differences in mixing action between the reservoir and CRI. Bowen's Ratio varied on the reservoir from + 0.591 in January, 1964 to —0.129 in June, 1964; the annual average Bowen's Ratio was +0.064. Bowen's Ratio may be expected to lie between —0.242 and 0.370, 90 per cent of the time. Most sensible heat was conducted to the reservoir between June 6 and June 20, 1964, when it averaged 21 cal cm ~2 day - 1 ; most was conducted away between January 4 and January 17, 1964, when it was 41 cal cm ~2 day"1 . During most of the year, on a two-week basis, the conducted heat at Elephant Butte must be considered, while on an annual basis it may be neglected. Results of mass and heat transfer method indicated that use of an average annual TV-coefficient of 0.00633 in the quasi-empirical mass-transfer formula would produce a standard error of 0.00158, corresponding to a 25 per cent variation of N for short, two-week evaporation computations. For a confidence interval of 90 per cent, /Vlies between 0.00364 and 0.00902. This would mean that one would expect any two-week TV to vary 43 per cent, 90 per cent of the year, from

319

an annual average value of 0.00633. Statistically, a value of N based upon an annual average could produce semimonthly evaporation errors of 25 to 43 per cent from 68 to 90 per cent of the time, respectively. Although all four rafts which measured the wind velocity were found to measure the same annual mean wind at a 95 per cent confidence level, the standard error of the annual average wind velocity measured at the four individual rafts was about nine per cent. A±\ mb vapor-pressure error (±1.0°C error in water-surface temperature) at an annual mean water-surface temperature of 15.0°C is about eight per cent of the annual mean vapor pressure of 12 mb. This eight per cent, combined with the above nine per cent would produce an annual error in estimating evaporation from the mass-transfer equation of about 12%. However, if the value of N, determined from energy-budget evaporation, has an annual standard error of nine per cent, the maximum error expected in determining the evaporation from using the mass-transfer equation is approximately 15 per cent when the indi­vidual variances are combined. The annual weighted mean value of the heat-transfer coefficient, K, was determined to be 1.98. The standard error from the mean is 0.47. Thus a 24 per cent error in estimating semimonthly sensible heat could result when using an annual mean value of K in the heat-tranfer equation. The standard error in determining the annual sensible heat can be determined by combining the individual variances due to a ± ] .0°C error (approximately six per cent) in temperature measure­ment, wind velocity error of nine per cent, and a 10 per cent error in evaluating the sensible heat when determining K. Therefore, the maximum standard error expected in finding the annual sensible heat from using the heat-transfer equation is approximately 15 per cent. Evaporation, determined by use of the semi-empirical mass-transfer formula whose empirical coefficient, N, was derived on the basis of energy-budget data, cannot be expected to be greater than 95 per cent accurate on an annual basis, or greater than 75 per cent for any two-week period, assuming that the errors are normally distributed. The minimum value for probable error of evaporation loss estimates was 4.4 per cent and a maximum value of 27.8 per cent. The mean value was found to be 10.5 percent. The variation of errors in thermal survey period can be attributed to the fact that Elephant Butte Reservoir level fluctuates rather severely because of power and irrigation releases. The magnitude of error is maximum when evaporation is the least, particularly during winter months when ice formation takes place on the lake surface. During summer months evaporation is large and the magnitude of error decreases.

ACKNOWLEDGEMENTS

This investigation was supported by U.S. Bureau of Reclamation, Department of Interior, under Contract No. 14-06-D-5025. Sincere appreciation is expressed to Mr. R.E. Glover and Mr. H.D. Newkirk of the U.S. Bureau of Reclamation for their counsel, technical assistance, and suggestions in this investigation. Cooperation and contributions of the staff and students who have participated in this study are gratefully acknowledged.

REFERENCES

CUMMINGS, N.W., and RICHARDSON, Burt., Evaporation from Lakes, Physical Review, Vol. 30, pp. 527-535. October, 1927.

U. S. Geological Survey, Water Loss Investigations — Lake Hefner Studies, Technical Report: U.S.G.S. Professional Paper 269, 1954.

GLOVER, R.E., Unpublished technical memorandum, reference no. SI-13, U.S. Bureau of Reclamation, Denver, Colorado, 1960.

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DISCUSSION

1) Discussion by Prof., Dr. W.K. FRIEDRICH:

What is the reliability of suppressing evaporation from reservoirs and especially the costs of a saved cubic meter?

Discussion by C.G. KEYES, Jr.(*) and N .N. GUNAJI:

According to the method suggested by Harbeck and KobergC1), the monolayer does not effect the incoming short-wave radiation, the incoming long-wave radiation, the net advected energy in the body of water, the net change in energy stored, or the energy advected in the evaporated water. They also state that it markedly influences the remaining terms of the Energy Budget equation: (1) the long wave radiation emitted by the body, (2) the energy utilized by evaporation, and (3) the energy conducted from the body of water as sensible heat. For equilibrium conditions the net sum of these effects must be zero; therefore, the analysis yields the following equation:

(6L - 6 J + (Q'e - Qe) + (QH - QÙ = o (eq. l) The symbols with primes in equation 1 refer to the reservoir with a monolayer and the symbols without primes refer to the same reservoir without a monolayer. Using the relations in the Mass Transfer equation, equation 1 can be rewritten in the following form:

0.970 cr [(T^ + 273)4-(T0 + m)4l + [Q'e-Nu(e0-ea)-] + Ku(T0-Ta) =0 (eq. 2)

in which

a represents the Stefan—Boltzmann constant for black-body radiation; T'o represents water surface temperature in °C; To represents water surface temperature that would have been observed without the

monolayer; Q'erepresents observed heat energy utilized for evaporation; TV represents the empirical coefficient obtained during a pre-treatment period from the

quasi-empirical mass transfer equation ; K represents the empirical coefficient obtained during a pre-treatment period from the

heat transfer equation Q/,, = Ku (T0— Ta); u represents wind speed; e0 represents saturation vapor pressure at T0 in mb; ea represents vapor pressure of the air in mb.

(x) Application of the energy-budget concept will yield the total evaporative and convective heat losses in terms of the measured quantities through the following relation

(Qe+Qh+QJ = Qo-Q.-Q.-Qv + Qr+Q.r+Qb.

The measured quantities are all in the right-hand side of this expression. The sum of Qe+ Qw and Qu in the left-hand side must be separated by the use of the Bowen ratio to isolate the sum Qe + Qw- With a relationship of this type, an error in one of the quantities in the right-hand side will introduce an error of equal amount into the computed left-hand side. The energy-budget equation when applied to periods greater than 7 days, will result in a maximum accuracy approaching ± 5 % of the mean energy-budget evaporation according to the Lake Hefner studies provided all terms in the energy budget have been evaluated with the utmost accuracy.

(*) Assistant Professor, Civil Engineering Department, New Mexico State Univer­sity, Las Cruces, New Mexico.

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Koberg stated that there is a ± 5 percent uncertainty on the evaporation saving. His conclusion was based on the fact that the actual evaporation could only be deter­mined with an accuracy of 90 per cent.

Saving of evaporation may be stated as the volume of water saved, according to Frenkiel (2) as follows:

SV==Q£-Jk. (eq. 3) QL Q' L

in which Q,Q' represents the density of water; L,L' represents the latent heat of evaporation at T0 and T'0.

The ratio of water saved to the water that would have been lost in evaporation in the absence of a monolayer expressed as a percentage can be stated as follows:

P . = ^ x l 0 0 = Qe Q'e

_QL Q' L'.

100

QJQL

1 Q'eL

. Qe L'. 100 (eq. 4)

Substituting the values of Q'e obtained from the energy budget and heat transfer equation and Q'e from the mass transfer equation into equation 4, the following relation is obtained

Ps = l_iQ^Kutv-m L m (eq 5) Nu(e0-ea)Il

Equation 5 now can be used to determine possible sources of errors on the accuracy of Ps arising from the items on the right side of the equation. It can be assumed at first that K and N are precisely known. The quantities in the numerator of the fraction inside that bracket are known with an accuracy of ± 5 % . This conclusion can be drawn from the fact that the numerator indicates evaporation determined by the Energy Budget Method, which has maximum possible error of ± 5 % when all terms in the energy budget equation are carefully measured. The major error in the denominator is in the calculated value of e0-

The coefficients N and K have been assumed to be constant in the above analysis. This could be possibly true on a yearly basis, but Young (3) in 1967 found that evapo­rated depth did not vary as a linear function of (e0 — ea)- Therefore, equation 5 should be adjusted in such a way to conform with Young's recommendations.

A figure showing the amount of cost saved per cubic yard of film used has not been obtained at New Mexico State University. Figures comparing the net evaporation from an untreated water surface versus the net evaporation from a water surface treated with a film have been obtained by Heiler (4). The films used were oil-wax-surfactant mixture and hexadecanol.

Various investigators have quoted the cost of conservation of water from suppres­sion of evaporation by the use of monomolecular films. The table below gives the representative costs reported by the U.S. Bureau of Reclamation (5). It is anticipated that the saving of water by the application of monomolecular films on reservoirs may range from $20 to $35 per acre-foot once the technique and methodology is perfected. However, it should be realized that the above figure applies to those selected reservoirs which have proper size, shape, moderate winds and evaporation.

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COST OF EVAPORATION SUPPRESSION

Lake Test period Evaporation suppression

Cost/acre-ft. of water saved

Lake Hefner Oklahoma City Oklahoma, U.S.A. Sahuaro Lake Near Phoenix Arizona, U.S.A.

Lake Cachuma Near Santa Barbara, Calif. U.S.A. Pactola Reservoir Near Rapid City South Dakota, U.S.A,

July 7 9 ± 5%

Oct. 2, 1958 Oct. 1—Nov. 17 14 ± 5% 1960, Total Test Period, Oct. 19 Nov. 17, 1960 22 ± 5% Continuous Treatment July 31-Sept. 24, 1961 8 ± 5% Total Test Period Aug. 14-28, 1961 2nd Thermal Survey July 5-Sept. 1, 1962 14 ± 5% $69

It can be concluded that reduction in evaporation by means of monomolecular films may become a popular method of saving water in arid and semi-arid regions. A comparison with costs of alternate sources of water reported by Dr. Franzini (6) of Stanford University is shown in the table below. This table shows that the monomo­lecular film method is competitive.

COST OF RAW WATER

Dollars per acre-foot

Local Runoff Ground Water Imported Water Reclaimed Waste Water Sea Water Conversion Distillation Solar Stills Freezing Ion Exchange Electrolytic Action Ion-Permeable Membranes Evaporation Suppression

*Considerably lower for brackish water.

$3.00—$10.00 $3.00—$10.00 Variable $25.00—$40.00

$250.00—$600.00 $350.00 $700.00 $8,000.00* $500.00* $3,000.00* $20.00—$35.00

REFERENCES

C1) HARBECK, G.E. and KOBERG, G.E., A Method of Evaluating the Effect of Mono-molecular Film in Suppressing Reservoir Evaporation, Journal of Geophysical Research, 64, 83-93, 1959.

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(2) FRENKIEL, J., On the Accuracy of the Combined Energy-Budget and Mass Transfer Method, Journal of Geophysical Research, AGU Vol. 68, No. 17, Sept. 1963.

(3) YOUNG, W. L., " An Investigation of the Mass Transfer Technique for Determining Evaporation", Master of Science in Civil Engineering Thesis, New Mexico State University, Las Cruces, May 1967.

(4) HEILER, B.F., "Evaporation Suppression by Use of Surface Films: A Comparative Study between a Duplex Film and a Monomolecular Film", Master of Science in Civil Engineering Thesis, New Mexico State University, Las Cruces, May 1966.

(5) GARSTKA, W. U., The Bureau of Reclamation's Investigations Relating to Reservoir Evaporation Loss Reduction, Paper presented at Water Evaporation Symposium, Sponsored by UNESCO and NCL at Poona, India, Dec. 1962.

(6) FRANZINI, J. B., Evaporation Suppression Research, in two parts, Journal of Water and Sewage Works, May 1961-June 1963.

2) Discussion by P.O. WOLF:

P.O. Wolf suggested that the situation described so vividly by Prof. Gunaji seemed to lend itself particularly well to the economic application of refrigeration. If the water in the fresh-water pond is cooled, evaporation loss will be reduced and, in the limit, turned to a net gain of condensation from the atmosphere. At the other end of the refrigerator (or heat pump) would be the brine pond, which would be heated to boiling point if the concentration ratio of 1:25 mentioned by Prof. Gunaji was representative of this condition.

Discussion by C.G. KEYES, Jr. and N . N . GUNAJI:

In principle we agree with the method suggested by Prof. Wolf. It is, however, uneconomical to put such a system in operation. Also, we seldom find a storage reser­voir and a brine disposal pond located adjacent to one another to use the system suggested by Prof. Wolf.

3) Discussion by J. KEIJMAN:

What is measured by the method of the radio waves: The average humidity over the lake, or the vertical gradient of humidity ?

Discussion by C. Morales (*), C.G. Keyes, Jr. (**), and N .N. Guanji: The index of refraction of an electro-magnetic wave («) can be obtained by the

equation

n=* (1)

where v0 = velocity of the radio wave in a vacuum, and vm = velocity of the radio wave in a medium.

Now, if one is able to measure the velocity of a wave in a medium, the index of refrac­tion can be computed.

An electrotape is a precision electronic surveying instrument which is used for linear measurements. Basically, the instrument consists of a source for radio waves and a receiver or reflector. Its operation is simplified as follows: the source emits or trans­mits a radio-frequency signal which is received by the receiver or reflector some distance

324

away, which then transmits it back to the source. The source, upon receipt of the reflected signal, measures the time elapsed between original transmission and receipt of the returned signal. This measurement is normally in millimicroseconds. This time is then used to determine a linear distance based on a velocity of wave propagation.

One can work backwards to determine the velocity of the wave in the medium, if the exact distance between source and receiver is known. Once the velocity of the wave has been found the index of refraction can be computed by equation (1).

If a calibration exists relating index of refraction to water vapor in the path, then the water vapor content along the path can be computed. Measurement would only indicate an average water vapor content in the path between the source and the receiver.

(*) Doctoral Candidate, Civil Engineering Department, New Mexico State Univer­sity, Las Cruces, New Mexico, U.S.A.

(**) Assistant Professor, Civil Engineering Department, New Mexico State Uni­versity, Las Cruces, New Mexico, U.S.A.

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