Estimation of evaporation from the lake of the Aswan High Dam (Lake Nasser) based on measurements over the lake

Agricultural Meteorology, 23 (1981) 293--308

293

Elsevier Scientific Publishing Company, Amsterdam - - Printed in The Netherlands

ESTIMATION OF EVAPORATION FROM THE LAKE OF THE ASWAN HIGH DAM (LAKE NASSER) BASED ON MEASUREMENTS OVER THE LAKE M.H. OMAR and M.M. EL-BAKRY

Meteorological Authority, Cairo (Egypt) (Received March 24, 1979; revision accepted May 28, 1980)

ABSTRACT Omar, M.H. and EI-Bakry, M.M., 1981. Estimation of evaporation from the lake of the Aswan High D a m (Lake Nasser) based on measurements over the Lake. Agric. Meteorol., 23: 293--308. Monthly values of evaporation from the lake of the Aswan High D a m (Lake Nasser) were estimated by the heat budget and bulk aerodynamic methods, using average monthly estimates of different meteorological elements over the Lake based on measurements taken during survey trips over the Lake in different months of the period 1970--1971. Monthly evaporation was calculated as the average of estimates by both methods. Annual lake evaporation is about 7.4 m m day -z with m a x i m u m evaporation in June (10.9 m m day -I ) and m i n i m u m evaporation in January (3.8 m m day -I ). The annual evaporation is about 13% higher than the annual incoming net radiation. At the average Lake surface level of 175 m above mean sea level, the total water loss by evaporation should not be more than 14 × 109 m 3, which is about 1 1 % of the lake water content.

INTRODUCTION

The new lake behind the Aswan High Dam (Lake Nasser) is one of the largest artificial lakes in the world. The objective of this study is to determine, with reliable accuracy, the rate of water loss by evaporation from the Lake, which is an important factor for water management for irrigation and p o w e r supply purposes. The Lake lies between 21 and 24°N, with a length of a b o u t 500 kin, 350 km o f which lie in Egypt and 150 km lie in Sudan. The m a x i m u m width of the Lake is a b o u t 60 km and the average width is a b o u t 10 kin. The Lake has a surface area of a b o u t 5000 km 2 at the 175 m level (above sea level), including three large basins having a total area of a b o u t 3900 km 2 (Fig. 1). The m a x i m u m depth of the Lake is a b o u t 90 m and the average depth is a b o u t 25 m. The total capacity of the reservoir is 164 × 109 m 3. The Lake is surrounded by desert and hilly land. The Lake lies in a h o t and exizemely arid climate. The following information gives the main climatological factors at the meteorological station at

0002-1571/81/0000--0000/$02.50

© 1981 Elsevier Scientific Publishing Company

294

Fig. 1. Map of the lake of the Aswan High Dam (Lake Nasser).

Aswan Airport which lies about 3 km to the west of the High Dam. Mean maximum air temperature varies from 23.5°C in January to 41.8°C in June. Mean minimum air temperature varies from 8.1°C in January to 24.8°C in July. Mean relative humidity varies from 13% in May and June to 37% in December. Mean wind speed at 20m height varies from 7.8 kn (4 ms -1 ) in December to 9.3 kn (4.7ms -1 ) in April. The prevailing wind direction is northerly. A preliminary study of evaporation from Lake Nasser has been made (Omar and EI-Bakry, 1970). In this study average monthly evaporation was estimated by the bulk aerodynamic (Dalton), combination and evaporation pan approaches using climatological and pan evaporation data at Aswan station for the period 1962--1967, and water-surface temperatures at Aswan Reservoir for the period 1922--1945. An attempt was also made to estimate average annual values of air temperature, vapour pressure, wind speed at 2 m height over the Lake, and v~ater-surface temperature; evaporation was estimated by the bulk aerodynamic and combination approaches. I n the present study average monthly evaporation is estimated by the heat budget and bulk aerodynamic approaches, using average monthly estimations of different meteorological elements over the Lake based on measurements taken during survey trips on the Lake in different months in the period 1970--1971.

295

METHODS, MEASUREMENTSAND PROCEDURE Methods for calculating Lake evaporation Heat budget m e t h o d The heat budget method is considered to be suitable for application over periods of the order of a month or longer, as changes in the heat storage of the water can then be measured with adequate accuracy. The method is considered to be the most independent and absolute approach which can be used as a base to check other approaches. Lake evaporation (EH) estimated by the heat budget method is given by the following equation (see, for example, Hoy and Stephens, 1977)

EH

=

R n +A--G

L(1 +/3)(1 + r) + C(Te -- Ti)

(I)

where Rn is the incoming net radiation, A is the net heat advected to the lake by the net inflow of water, G is the net increase in heat storage in the lake water, L is the latent heat of evaporation of water,/3 is the Bowen ratio, r is a correction for the effect of fluctuating Bowen ratio on heat budget estimates of evaporation (Webb, 1960a, b, 1964; Hoy and Stephens, 1977), C is the specific heat of water, Te is the temperature of the evaporated water and can be taken as the surface temperature, and Ti is the temperature of water inflow which replaces the evaporated water. Bulk aerodynamic m e t h o d The following relation was obtained from investigations at Lake Hefner (U.S. Geological Survey, 1952), and supported by investigations at Lake Mead (Harbeck et al., 1958) and at Lake Eucumbene and other lakes in Australia (Webb, 1960a, b; Hoy and Stephens, 1977)

EB = 0.1296 U~(eo - - e 2 )

(2)

where U2 is wind speed at 2 m height ( m s -x ), e0 is saturation vapour pressure (rob) at the temperature of the water surface, and e2 is vapour pressure (nab) at 2 m height. For conversion for other latitudes and non-temperate regions the value of the coefficient should be modified inversely with the average absolute temperature (see, for example, Webb, 1965). Taking into consideration the values of average air temperature at Lake Hefner and Lake Nasser, it is found that the appropriate coefficient to be used for Lake Nasser is 0.126. Measuremen ts Measurements over the Lake During the period June 1970 to July 1971 survey trips were undertaken on Lake Nasser over a distance of 350 km from Aswan to Adendan near the southern Egyptian border, using boats belonging to the Lake Nasser Develop-

296 TABLE I Periods of measurement over Lake Nasser Month

Period of measurement

June 1970 July 1970 November 1970 February 1971 February 1971 March 1971 May 1971 July 1971

6--9 and 30 18--19 5--18" 2--3, 17--19 23--28* 1--4" 12--19" 6--17"

Temperature at different depths measured using Hydrolab II. m e n t Centre. During these trips meteorological measurements were made, including air temperature and humidity, wind speed at 2 m height over the water surface, and water-surface temperatures. Air temperature and humidity were measured using an aspirated Assmann psychrometer. Wind speeds were measured using a hand anemometer. Water surface temperature was measured by the bucket m e t h o d using a mercury-in-glass thermometer. Most of the observations during day-time were taken on an hourly basis, while during night-time they were taken at three-hour intervals. During day-time the observations were made in the main channel and large basins of the Lake and open khors {creeks), except during periods of strong winds when the boat should be kept on the shore. During night, time, measurements were made near the shores as the boats had to be there. Table I shows the periods of the trips in the different months during 1970--1971. In some of the trips (marked with an asterisk in the Table) Lake water temperature at different depths was measured using the new Hydrolab II. In addition to these measurements, the study makes use of similar water temperature measurements taken by the Limnological Group o f the Lake Nasser Development Centre during the periods 18, 26 and 27 August 1970, and 20--27 September 1970. M e a s u r e m e n t s at A s w a n land station

The m o n t h l y averages of air temperature, vapour pressure, wind speed and cloud a m o u n t at the meteorological station at Aswan Airport for the 10-year period 1965--1974 were used in the study. Dry and wet-bulb temperatures were measured in a Stevenson screen of Egyptian type. Wind speed was measured at 20 m height by a Dines anemograph. Global radiation was measured during the period 1972--1974 by a Robitzsch pyranometer which was calibrated using a similar instrument calibrated by an Eppley pyranometer at Cairo. The data for 1972 and 1974 only were used in the study as the 1973 data were not accurate.

297

Procedure The following procedure was followed for determination of the monthly vMues of the parameters used in computations of the heat budget and bulk aerodynamic methods: A i r temperature over the water surface For each day of measurement the hourly values of air temperature were plotted and a correction was made for night, time on-shore temperatures which were affected by conditions over land, based on the qualitatively known differences between over-water and over-land conditions. For every period of measurement, a smooth curve was obtained, representing average hourly conditions over the water surface. A temperature difference was obtained between average air temperature over the Lake and the corresponding average air temperature at Aswan station (on the same dates}. Values of the differences were drawn for the periods of measurement against the months of the year and a smooth curve round the differences provided an estimate of the monthly values of the differences. These monthly values were added to the average monthly values of air temperature at Aswan during the period 1965--1974, to give estimated monthly values of air temperature over the Lake, which are shown in Fig. 2 together with the mean monthly values of air temperature at Aswan. Water-surface temperature The average hourly values of water-surface temperatures during the days of measurement for each month were determined and plotted on a graph, and a correction was applied to the night on-shore values, taking into account the smaller diurnal variation of water temperature over the middle

Tas

34 32 oU 3C 28

,,'/.

2~

,\

S,;~

20 18

'72 .

.

.

.

.

.

.

.

.

.

w

12 10

F

M

A

M

J

J

A

S

0

N

D

MONTH

Fig. 2. Seasonal variation of air temperature at Aswan land station (10 year average), Tas, and the estimated values for the Lake of air temperature, Ta, water surface temperature, Ts, and water body temperature, Tw.

298

4z,~ . . . . . . . . . . . . . . . . . . . . t*O

~

es

~ 28

\.

o so

.......

12 . . . . .

~

8 J

)

e as

F

M

A

M

J MONTH

J

A

5

0

N

[]

Fig. 3. Seasonal variation o f v a p o u r pressure, eas, at A s w a n land s t a t i o n (10 year average), e s t i m a t e d v a p o u r pressure over t h e Lake , ea, and s a t u r a t i o n v a p o u r pressure at t h e Lake surface, e s (mb).

o f the Lake than near the shore. An average curve is thus obtained which is considered t o be appropriate t o the m o n t h concerned. The mean daily values o f water t e m p e r a t u r e f or every trip have been p l o t t e d on a graph against the different m o n t h s of the year and a s m o o t h best-fitting curve was drawn t o represent the seasonal variation of water-surface t em perat ure. The average m o n t h l y values were det er m i ned f r om this curve and axe shown in Fig. 2. Vapour pressure over the water surface F o r each day of m eas ur em e nt the hourl y values of vapour pressure were p l o t t e d and a cor r ect i on was made f o r night on-shore values affected by over-land conditions. T he difference between the last observation on the middle o f the Lake and the first observation on-shore was added to all values observed on-shore taking into consideration the difference in diurnal variation during day and night, using the trace of the diurnal variation of vapour pressure at Aswan as a guide. For every period of measurement, a s m o o t h curve was obtained, representing average hourl y conditions over the water surface. A vapour pressure difference was obtained between average vapour pressure over the Lake and the corresponding value at Aswan. The estimated m o n t h l y values of vapour pressure over the Lake were obtained as in case of air t e m p e r a t u r e over the Lake (see above) and the results are shown in Fig. 3. Wind speed over the Lake Th e ratio of the average value of wind speed over the Lake and the corresponding value, at the same time, of the average wind speed at Aswan was obtained f o r the different hours o f day-time and for the different months. There was n o definite diurnal variation of the ratio, and the average value of th e ratio f o r the different m o n t h s was a b o u t 0.90. It is assumed t h a t the ratio o f average wind speed over the Lake to the

299 TABLE II Monthly mean values for wind speed estimated over the Lake (m s -l ) Jan.

Feb.

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

3.9

4.1

4.1

4.4

4.2

4.1

3.8

3.8

3.9

3.7

3.8

3.8

average wind speed at Aswan during night-time is 0.90, as in case of day-time, so that the mean daily wind speed over the Lake is 0.90 of the mean daily wind speed at Aswan. The m o n t h l y values of estimated wind speed over the Lake are given in Table II.

N e t radiation The net radiation over Lake Nasser has been calculated as Rn

= R g (1 - - o0 - - I s

(3)

where Rn is net radiation, Rg is global radiation, Is is effective outgoing radiation, and c~ is water-surface albedo which was determined for each m o n t h according to Budyko (1956). In the present study it is assumed that average global radiation measured at Aswan is representative of the whole Lake. There is no appreciable difference between solar radiation with cloudless sky at Aswan and Wadi Halfa, as can be seen in table 1 of Omar a n d E1-Bakry (1970}. Also, the cloud a m o u n t is small in the area, as can be seen in table 3 of the same paper. Tables by B u d y k o (1956) also show t h a t there is no appreciable difference in global radiation in the two locations. The effective outgoing radiation, Is, has been calculated as in our previous work mentioned above, using the following equation (Omar and E1-Bakry, 1970) based on work by Swinbank (1963}, B u d y k o (1956) and Sellers (1965) Is = e(0.010 -- 0.195 O~k) (1 -- cn') + 4 e a T 3 (Tsk -- Tk)

(4)

where Is is in MJ m -2 , e is the water-surface emissivity taken as 0.97, o is the Stefan--Boltzman constant = 0.34 × 10 -11 MJ m -2 , Tk is absolute air temperature, Tsk is absolute water-surface temperature, c is a latitudinal cloud coefficient depending u p o n cloud type, and n' is the daily mean cloud a m o u n t in tenths, obtained from averages of cloud amounts at the principal times of observation at Aswan station. Global radiation, effective outgoing radiation and net radiation over the Lake are given in Table III.

B o w e n ratio and its correction factor (r) The Bowen ratio, which has been widely used as a measure of the ratio of sensible to latent heat flux over the water surface as a proportion of the energy utilized for evaporation, is expressed as

3OO TABLE III Monthly mean values of global radiation, Rg, effective outgoing radiation, Is, and net radiation, R n (MJ m -2 ) Month

Rg

Is

Rn

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

15.94 20.76 24.48 27.16 29.25 29.92 29.34 27.62 24.61 20.88 18.42 16.20

8.41 8.33 6.53 6.24 5.27 3.93 4.02 3.98 4.60 5.48 8.20 8.54

6.40 10.96 16.49 19.34 22.22 24.19 23.56 21.76 18.54 14.15 8.96 6.57

Mean

23.72

6.13

16.10

{J -= K P ( T s - - T a ) / ( e s - - e a )

(5)

w h e r e K is t h e B o w e n r a t i o c o e f f i c i e n t , t a k e n as 6.1 × 10 -4 °C -1 a c c o r d i n g t o the studies o f e v a p o r a t i o n f r o m L a k e M e a d ( H a r b e c k et al., 1 9 5 8 ) a n d L a k e E u c u m b e n e (Webb, 1 9 6 0 a ) ; P is t h e a t m o s p h e r i c pressure ( m b ) at the level o f t h e L a k e ( m o n t h l y values w e r e d e t e r m i n e d f r o m m e a s u r e m e n t s o f pressure at A s w a n S t a t i o n ) ; Ts is t h e L a k e w a t e r - s u r f a c e t e m p e r a t u r e ; Ta is t h e air t e m p e r a t u r e o v e r t h e L a k e ( m o n t h l y t e m p e r a t u r e values were obt a i n e d as p r e v i o u s l y e x p l a i n e d ) ; e s is t h e s a t u r a t i o n v a p o u r pressure ( m b ) ( m o n t h l y values w e r e d e t e r m i n e d as t h e s a t u r a t i o n v a p o u r pressures corresp o n d i n g t o t h e m o n t h l y values o f Ts); a n d e~ is t h e air v a p o u r pressure o v e r t h e L a k e w a t e r surface ( m o n t h l y values were o b t a i n e d as e x p l a i n e d previously). T h e B o w e n r a t i o f o r e v e r y m o n t h o f t h e y e a r was o b t a i n e d using t h e average m o n t h l y values o f t h e d i f f e r e n t e l e m e n t s on t h e r i g h t - h a n d side o f eq. 5. T h e m o n t h l y values o f ~ are given in T a b l e IV, Because t h e r e are n o regular h o u r l y o b s e r v a t i o n s o v e r L a k e Nasser which c o u l d be u s e d t o calculate t h e c o r r e c t i o n f a c t o r r f o r every m o n t h , m o n t h l y values f o r r w e r e d e t e r m i n e d b y t h e f o l l o w i n g m e t h o d . Values o f r a n d (1 + ~) w e r e given f o r several p e r i o d s f o r f o u r lakes in A u s t r a l i a b y H o y a n d S t e p h e n s ( 1 9 7 7 ) . I n s p e c t i o n o f t h e values s h o w e d a close r e l a t i o n b e t w e e n r a n d (1 + ~). T h e values o f r f o r t h e f o u r lakes w e r e s t u d i e d a n d a search was m a d e f o r t h e values o f r t h a t c o r r e s p o n d e d to values o f (1 + ~) a n d m e a n daily air t e m p e r a t u r e s similar t o t h o s e f o u n d f o r the d i f f e r e n t m o n t h s f o r L a k e Nasser. Values f o r L a k e E u c u m b e n e a n d L a k e M a n t o n w e r e f o u n d useful f o r o u r p u r p o s e . T h e result was t h a t r f o r L a k e

301 TABLE IV Bowen ratio, ~, for the different months Month

Jan. Feb. Mar. Apr. May

0.175 0.006 --0.041 --0.047 --0.064 --0.115 --0.095 --0.080 --0.068 --0.055 0.034 0.175

Jun.

Jul. Aug. Sep. Oct. Nov. Dec.

Nasser would be a b o u t --0.03 for both December and January and a b o u t --0.06 for April and October. Values of r for the other months were interpolated from a curve fitting the points for the four months. It was f o u n d that r was a b o u t --0.04 and --0.05 for February and March, respectively, --0.06 for May, --0.07 for the months June--September and --0.04 for November. Heat

advection

The advected heat term A in eq. 1 is defined as the net heat gained by a b o d y of water as a result of volumes of water entering or leaving the Lake during a heat budget period A

=

[cpVi(T

~ -- T b ) -- cpVo(Tso

-- Tb)]/Nt

(6)

where c is specific heat of water, p is density of water, Vi is volume of water inflow during a month, Vo is volume of water outflow during a m o n t h , Tsi is temperature of water inflow (°C), Tso is temperature of water outflow (°C), N is average surface area of the Lake, and t is number of days of the month. A is evaluated relative to the base temperature Tb which has been taken as 0°C (Hoy and Stephens, 1977). Specific heat and density of water were taken as unity. Rainfall over the Lake area is negligible; also seepage to or from the Lake has been assumed zero for the heat budget method, as its contribution to the heat budget of the Lake would be negligible. Therefore the net heat advected to Lake Nasser depends essentially u p o n surface inflow and outflow. The water inflow to the Aswan High Dam is estimated b y subtracting the following t w o items from the natural river discharge at Dongola, which lies at a b o u t 180 km south of the entrance of the Lake: (1) transmission losses

302 TABLE V Monthly values of the net heat advection, A, and the change in the Lake heat content, G (MJm -2 ) Month

Net heat advection (A)

Change in heat content (V)

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

-------

- 3.99 -- 1.65 0.41 5.97 0.91 -- 3.58 -- 1.01 14.92 13.08 -- 0.41 -- 6.93 -- 7.13

0.27 0.82 1.49 0.99 1.59 3.71 2.69 11.15 13.21 5.30 0.98 0.12

b e t w e e n D o n g o l a a n d A s w a n w h i c h w e r e a s s u m e d as 0.3% o f t h e n a t u r a l discharge; a n d (2) t h e a b s t r a c t i o n b y p u m p s a n d basins in this r e a c h o f t h e Kiver. T h e discharge d o w n s t r e a m at A s w a n r e p r e s e n t s t h e L a k e o u t f l o w . T h e w a t e r b u d g e t m e t h o d h a s b e e n a p p l i e d t o e s t i m a t e average m o n t h l y values o f e v a p o r a t i o n f r o m t h e L a k e f o r t h e p e r i o d 1 9 7 0 - - 1 9 7 5 . T h e estim a t e d values w e r e generally unreliable, w h i c h m a y be a t t r i b u t e d to i n a c c u r acies in e s t i m a t i n g t h e n a t u r a l river discharge at D o n g o l a , or in t h e p e r c e n t ages a l l o t t e d f o r t r a n s m i s s i o n losses a n d p u m p a b s t r a c t i o n . A c c o r d i n g l y , a preliminary estimate of evaporation for each month (determined by the heat b u d g e t m e t h o d using t h e e s t i m a t e d values o f inflow) was u s e d in t h e w a t e r budget equation to compute a corrected inflow. T h e t e m p e r a t u r e o f w a t e r i n f l o w was e s t i m a t e d using t h e t h e r m a l p r o f i l e d a t a o b t a i n e d t o t h e s o u t h o f t h e L a k e at A d e n d a n , a n d t h e w a t e r t e m p e r a t u r e o f t h e o u t f l o w was e s t i m a t e d using t h e t h e r m a l d a t a o f t h e u p p e r 30 m l a y e r o b t a i n e d t o t h e n o r t h o f t h e L a k e , n e a r t h e High D a m . T h e m o n t h l y values o f w a t e r t e m p e r a t u r e o f t h e surface i n f l o w a n d o u t f l o w w e r e interpolated f r o m the thermal data. T h e n e t a d v e c t e d h e a t was c a l c u l a t e d o n a m o n t h l y basis f r o m t h e m o n t h l y average o f t h e v o l u m e s o f w a t e r i n f l o w a n d o u t f l o w o v e r the p e r i o d 1 9 7 0 - - 1 9 7 5 , a n d t h e e s t i m a t e d m o n t h l y values o f w a t e r t e m p e r a t u r e s o f the i n f l o w a n d t h e o u t f l o w o v e r t h e p e r i o d 1 9 7 0 - - 1 9 7 1 . M o n t h l y values o f the n e t a d v e c t e d h e a t are given in T a b l e V. C h a n g e in h e a t c o n t e n t

T h e change in h e a t c o n t e n t in a l a k e is o n e o f t h e m o s t i m p o r t a n t t e r m s in t h e h e a t b u d g e t e q u a t i o n . I t c a n be given as G =

[cpY2(T 2

--

Tb)

-- cpV

1

(T 1 -- Tb)]/Nt

(7)

303

where V] is volume of water in the Lake at the beginning of the month, V2 is volume of water in the Lake at the end of the month, c is specific heat of water, p is density of water, Tb is the base temperature, 0°C, T1 is average temperature of the b o d y of water at the beginning of the month, T2 is average temperature of the b o d y of water at the end of the month, N is average surface area of the Lake, and t is number of days of the month. For Lake Nasser, G was calculated from the data of the thermal profiles o f the Lake taken during survey trips along the Lake (see section on measurements over the Lake), and the Lake volumes at the beginning of each month as an average for the period 1970--1975 which were supplied by the hydrological authorities of the Ministry of Irrigation. Monthly values of water temperature at every 1 0 m depth were interpolated from the data of the thermal profiles, and these values were assumed to be representative of a period of 5--10 years. Curves have been drawn for every 10 m depth to represent the seasonal variation of the water temperatures. These curves enabled us to determine the water temperatures at the beginning of each m o n t h at different levels, and the averages were considered to represent the corresponding water b o d y temperatures. The Lake heat content at the first day of each m o n t h of the average 6year period was c o m p u t e d t a n d their seasonal variation is shown in Fig. 4. Monthly values of the change in heat c o n t e n t are given in Table V. It is n o t e w o r t h y that the net increase in heat content is 10.6 MJ m -2 over the year. This should be very close to zero when using average data. This indicates that the few water temperature measurements taken during 1970-1971 were n o t sufficient to give a correct average seasonal variation of water temperature over the Lake.

Calculation of evaporation Monthly values of evaporation were calculated by applying the estimated monthly values of the different parameters in eqs. 1 and 2 for the heat budget and the bulk aerodynamic methods respectively. %10

~9 ~x 8 z Z

~5

W -r

.T

I

I

I

I

M

A

M

I

I

Y J MONTH

I

I

I

I

A

S

0

N

I

D

Fig. 4. S e a s o n a l v a r i a t i o n o f t h e L a k e heat content.

304

In the case of the heat budget method, Ti in eq. 1 has been taken as the average temperature of water inflow at every month. RESULTS AND DISCUSSION

Evaporation based on heat budget and bulk aerodynamic methods Table VI shows the mean daffy values of evaporation measured by the heat budget and bulk aerodynamic methods and their average E L for every month. It is surprising that the two methods gives the same annual value (7.35 mm day -1 ). It is well known that the energy budget m e t h o d is the most fundamental m e t h o d for evaporation measurements. The effects of errors in water-surface temperatures and vapour pressure on evaporation calculations are appreciably smaller when using the energy budget m e t h o d than the corresponding effect when the bulk aerodynamic m e t h o d is used. However, there is appreciable scatter in the values of both EH and EB so that the average values of evaporation by the two methods m a y give reasonably reliable results for the Lake evaporation. The monthly deviation of either EH or EB from E L is within 10% of EL except for three months where the deviation was within 14%. The deviations are n o t systematic which indicates that the monthly values of E L a r e probably reasonably reliable.

General features o f evaporation from Lake Nasser As shown in Table VI mean dally evaporation is maximum in June (about 10.9 mm day -1 ) and minimum in January (about 3.8 mm day -t ). The maxiTABLE VI Monthly evaporation values given by heat budget method, EH, bulk aerodynamic method, EB, and the monthly Lake evaporation, E L (ram day -l ) Month

EH

EB

EL

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

3.59 4.95 5.40 5.52 8.95 11.66 10.42 8.39 8.61 8.98 6.87 4.90

3.93 4.08 4.77 7.32 9.31 10.11 10.01 10.68 10.47 7.83 5.17 4.52

3.76 4.52 5.08 6.42 9.13 10.88 10.22 9.54 9.54 8.40 6.02 4.71

Mean

7.35

7.35

7.35

305

m u m evaporation in June should not be considered as t o o early in the year if it is taken into account that the average depth of the Lake is only 25 m. The mean daily value of evaporation for the year as a whole is 7.35 mm day -1 . Highest evaporation during a period of four consecutive months occurs between June and September where evaporation is 45% of the total yearly value. Lowest evaporation in four months occurs between December and March where the corresponding percentage is 20%. Evaporation in the period of highest evaporation from May to October amounts to a b o u t 65% of the total yearly value. The m o n t h l y total water losses by evaporation are proportional to the rate of evaporation and the Lake surface area, which is a maximum during the flooding season. Maximum losses occur from June to September. The total annual losses at the average Lake level of 175 m above mean sea level will be a b o u t 13.7 x 109 m 3 , i.e. a b o u t 11% of the Lake water content. Evaporation in relation to other heat budget terms Figure 5 shows the annual variation of the heat budget terms at the surface of the Lake. It can be noticed that evaporation is mainly determined by net radiation and sensible heat flux. However, maximum heat stored in the Lake (G) occurs during the months July to October, b u t its effect has been nearly cancelled b y the maximum net heat advected into the Lake (A) during the same period due to the flooding effect during that time, which is a special feature of Lake Nasser. The second increase in heat storage during April is due to the largest value of increase in water temperature during April, which is associated with the occurrence of highest increase in air temperature EL.

28 2~ 20

%. g~6

.s./"

\i

.

.

.

"

~

8

~

o -.z:,,,;_,.,.~,,..~....~..... ....,~ -,, -~,..~,...~

_

./

~

/

f

......

~ii'/i~ \ \ \ \\. ,,- .. //

-_ ~ _. ~_- - _: >,- ~ / '..

"'H-'"

2~ rn

\

"

N-8 w

-1- -1 2

J

i

I

I

F

M

A

I

1

I

I

I

I

i

M 5 ] A S 0 N D MONTH Fig. 5. A n n u a l variation o f the heat budget terms at the surface o f t h e Lake.

306 TABLE VII Comparison of some meteorological elements in the present and the 1970 studies of evaporation from Lake Nasser Study

U (m s-1 )

es--ea (rob)

Rn (MJ m -2 )

Ts - T a (°-C)

EL (mm day -1 )

1970 Present

4.2 4.0

15.5 15.8

18.04 16.07

-2.9 -- 1.1

7.9 7.4

d u r i n g M a r c h a n d April. This increase o f air t e m p e r a t u r e is a f e a t u r e o f t h e t r a n s i t i o n a l p e r i o d t h a t begins a f t e r t h e c o l d season a n d w h i c h is c h a r a c t e r ised b y a s u d d e n increase in air t e m p e r a t u r e a s s o c i a t e d w i t h K h a m s i n h e a t waves. O n average, e v a p o r a t i o n is a b o u t 13% higher t h a n n e t r a d i a t i o n . A b o u t 7% o f this d i f f e r e n c e is d u e t o sensible h e a t flux f r o m t h e w a r m e r air t o t h e u n d e r l y i n g relatively c o l d w a t e r surface a n d a b o u t 4% is due t o (A - - G ) .

Comparison with the results of the 1970 study T a b l e V I I s h o w s t h e m e a n daily values o f E , U, e s - - ea, Rn a n d Ts - - Ta, f o r t h e y e a r as a whole, resulting f r o m b o t h t h e 1 9 7 0 a n d p r e s e n t studies. T h e p r e v i o u s e s t i m a t i o n o f e v a p o r a t i o n f r o m L a k e Nasser is a b o u t 7% higher t h a n t h e c u r r e n t e s t i m a t i o n . I t c a n be seen t h a t U, e s - - e a a n d Rn in t h e curr e n t s t u d y are smaller t h a n t h e c o r r e s p o n d i n g 1 9 7 0 values, w h i c h w o u l d lead to a l o w e r value o f e v a p o r a t i o n in the c u r r e n t s t u d y t h a n in t h e p r e v i o u s one. I t is u n n e c e s s a r y to m e n t i o n t h a t the c u r r e n t values are t h e results o f m e a s u r e m e n t s o v e r the L a k e a n d t h e r e f o r e are m u c h m o r e reliable t h a n the previous values, w h i c h were m o s t l y b a s e d on e s t i m a t i o n s based on v e r y l i m i t e d d a t a at A s w a n s t a t i o n a n d A s w a n D a m , b e f o r e t h e f o r m a t i o n o f the L a k e .

Comparison of Lake evaporation with Class " A " pan and piche evaporation at Aswan T a k i n g i n t o a c c o u n t t h a t m e a n daily value of Class " A " p a n e v a p o r a t i o n f o r t h e y e a r as a w h o l e during t h e p e r i o d 1 9 6 4 - - 1 9 6 6 , was a b o u t 13.6 m m d a y -I ( O m a r a n d E1-Bakry, 1970), it can be c a l c u l a t e d t h a t t h e L a k e t o p a n c o e f f i c i e n t is a b o u t 0.54. In t h e L a k e M e a d s t u d y ( H a r b e c k et al., 1 9 5 8 ) it was f o u n d t h a t t h e r e p r e s e n t a t i v e L a k e t o p a n c o e f f i c i e n t was 0.60. T h e value 0.54 f o u n d at A s w a n is r e a s o n a b l e b e c a u s e o f t h e h o t t e r a n d drier c l i m a t e t h a n t h a t at L a k e Mead. A n n u a l e v a p o r a t i o n , as average e v a p o r a t i o n f r o m a large o p e n w a t e r surf a c e at A s w a n a n d Wadi Halfa, was e s t i m a t e d o n t h e basis o f an e m p i r i c a l f o r m u l a i n d i c a t i n g t h a t e v a p o r a t i o n f r o m a large o p e n w a t e r surface is e q u a l t o o n e h a l f o f Piche e v a p o r a t i o n ( H u r s t a n d Phillips, 1 9 3 1 ) . T h e e s t i m a t e d

307 T A B L E VIII C o m p a r i s o n o f s o m e m e t e o r o l o g i c a l e l e m e n t s in t h e studies o f e v a p o r a t i o n f r o m L a k e Nasser and Lake Mead Lake

EL (ram d a y -1 )

U ( m s -1 )

es - - ea (rob)

Rn (MJ m -2 )

Ts - - T a (°C)

Nasser Mead

7.4 6.0

4.0 3.3

14.8 12.7

16.07 12.51

- - 1.1 --0.6

value is a b o u t 4% higher than the average yearly evaporation given b y the present study.

Comparison with Lake Mead evaporation As far as the authors know, Lake Mead is the only lake in a warm arid climate in which evaporation has been studied (Harbeck et al., 1958). It m a y be of interest, therefore, to compare evaporation and other relevant elements at Lake Mead and Lake Nasser. Table VIII shows the mean daffy values of E, U, es -- ea, Rn, Ts -- Ta for the t w o lakes. Evaporation from Lake Nasser is 23% higher than that from Lake Mead. Values of U, es -- ea and Rn are larger for Lake Nasser than for Lake Mead, which would increase evaporation in the former lake relative to the latter. The effect of stability would lead to an opposite effect on evaporation for the two lakes. The larger values of U, es -- ea and Rn at Lake Nasser than at Lake Mead have the predominant effect leading to larger evaporation from the former lake. CONCLUSION

Average annual evaporation from the lake of Aswan High Dam (Lake Nasser) is a b o u t 7.4 mm day -~ . Despite the different estimations and approximations made it is felt that internal consistency is apparent, and so the results are probably reliable. It is planned to install a n u m b e r of floating stations along the Lake for measuring the meteorological elements used in the heat budget m e t h o d , in order to g e t more accurate results of evaporation and to derive the appropriate coefficients for the bulk aerodynamic m e t h o d applications. ACKNOWLEDGEMENTS

The authors wish to thank Dr. M.S. Harb, Chairman of the Board of Directors of the Egyptian Meteorological Authority for his kind encouragem e n t and permission to publish this paper. They are also thankful to Mr. A.A. Soliman, inspector of the Nile Control Department, for supplying some hydrological data used in the study. The authors are also indebted to L.P. Smith for valuable comments.

308 REFERENCES Budyko, M.I., 1956. The Heat Balance of the Earth's Surface. U.S. Dept. Commer., Off. Tech. Serv., Washington, DC, 259 pp. Harbeck, G.E., 1962. A Practical Field Technique for Measuring Reservoir Evaporation Utilizing Mass Transfer Theory. U.S. Geol. Surv. Prof. Paper, 272E. Harbeck, G.E., Kohler, M.A. and Koberg, G.E., 1958. Water-Loss Investigations: Lake Mead Studies. U.S. Geol. Surv. Prof. Pap., 298. Hoy, R.D. and Stephens, S.K., 1977. Field Study of Evaporation. Analysis of Data from Lakes Eu.cumbene, Cataract, Manton and Mundaring. Res. Proj. 68/5, Tech. Pap. No. 21, A.W.R.C., Canberra, A.C.T., 195 pp. Hurst, H.E. and Phillips, D., 1931. General description of the basin, meteorology, and topography of the White Nile basin. In: The Nile Basin, Vol. I. Government Press, Cairo, pp. 57--61. Omar, M.H. and EI-Bakry, M.M., 1970. Estimation of evaporation from Lake Nasser. Meteorol. Res. Bull.,Meteorol. Auth., Cairo, 2(1): 1--27. Sellers,W.D., 1965. Physical Climatology. Chicago University Press, Chicago, IL, 272 pp. Swinbank, W.C., 1963. Long-wave radiation from clear skies. Q. J. R. Meteorol. Soc., 89 : 339--348. Webb, E.K., 1960a. An Investigation of the Evaporation from Lake Eucumbene. C.S.I.R.O. Div. Meteorol. Phys., Tech. Pap., 10, 75 pp. Webb, E.K., 1960b. On estimating evaporation with fluctuating Bowen ratio. J. Geophys. Res., 65 : 3415--3417. Webb, E.K., 1965. Aerial microclimate. Meteorol. Monogr., 6(28): 27--58. U.S. Geological Survey, 1952. Water-loss investigations. Vol. 1. Lake Hefner Studies. U.S. Geol. Surv., Tech. Rep., 229.