Scientific Basis for Water Resources Management (Proceedings of the Jerusalem
Symposium, September 1985). 1AHS Publ. no. 153.
A daily simulation model for evaluation of future
Dead Sea levels
F. MERO & E. SIMON
TAHAL - Water Planning
11170, Tel Aviv 61111,
for Israel
Israel
Ltd,
PO Box
ABSTRACT
A daily simulation model for evaluation of
future Dead Sea levels is described. The model consists
of a two-layer system based on the principles of
continuity of the salinity and heat balances in both
layers. These balances are conditioned by the daily water
balances of inflows, diversions, direct rainfall and
evaporation, where the latter is calculated on the basis
of simulated energy and salt balances. Because of
insufficient data, a hydrometeorological rainfall-runoff
model was calibrated and later applied to simulate natural
inflows. For the same reason, various physical processes
were combined into simpler equivalent algorithms to
perform the salinity and heat balances. In spite of the
lack of a satisfactory physical explanation to some model
elements, it was concluded that the reasonably successful
simulation of the long-term records (lake levels) fully
justifies the use of the model for operational studies of
the Mediterranean-Dead Sea Project.
Modèle de simulation
a 1'échelle
1'évaluation
des futurs niveaux
journalière
pour
de la Mer Morte
RESUME
Un modèle déterministe pour simuler les futurs
niveaux de la Mer Morte, sous des conditions opérationnelles d'exploitation est présenté dans cette communication. Le modèle consiste en un système de deux couches
d'eau de différentes densités et temperatures. La partie
dynamique du modèle est basée sur les principes de la
continuité des changements au pas journaliers des éléments
des bilans d'eau, de la chaleur et de la salinité. Ces
bilans sont conditionnés par le bilan des débits entrant,
des dérivations à l'amont des rivières, la pluie direct?
et 1'evaporation ; 1'evaporation étant une fonction du
bilan thermique de l'énergie thermique influencée par la
salinité de la lame d'eau superficielle. Par suite du
manque de données observées, les débits journaliers
étaient simulées par le modèle hydrométéorologique,
préalablement calé et vérifié. Tandis que pour simuler
les phénomènes physiques relatifs aux bilans thermiques
et de la salinité, des hypothèses simplifiées étaient
adoptées, permettant d'appliques des algorithmes reliant
les phénomènes entre eux. Malgré le fait d'avoir appliqué
ces algorithmes qui n'ont pas d'explication physique et
qui étaient obtenus par des méthodes empiriques, on a
obtenu des résultats satisfaisants permettant leur
265
266 F.Mero
&
E.Simon
application avec succès dans le modèle pour les études des
opérations futures du projet reliant la Méditerranée à la
Mer Morte.
INTRODUCTION
The model presented in this paper is part of a larger simulation
system, dealing with future Dead Sea levels under various operational
conditions of the Mediterranean-Dead Sea Project.
The model consists of a two-layer system, based on the principles
of continuity of the salinity and heat balances in both layers.
These balances are conditioned by the daily water balances of inflows,
diversions, direct rainfall on the one hand, and evaporation based on
simulated energy and salt balances, on the other hand.
It is well known that the Jordan River was and still is the main
contributir of fresh water into the Dead Sea, despite the fact that
its water is increasingly being tapped by upstream users. The
present discharge of the Jordan River amounts to about 50% of its
historical flow, with most of the diversions occurring during the
summer months. The available gauged discharge data extend over the
period 1937-1963.
It should be emphasized that most of the difficulties in
calibrating the simulation system arise from an almost complete lack
of data concerning actual inflows into the Dead Sea, as well as
direct measurements of the actual evaporation, and other physical and
chemical data. Even energy and heat balance methods that were
developed, such as the methods of Neuman (1958) and others - are
presently insufficient for the operational studies of the
Mediterranean-Dead Sea Project.
More recently however, there has been an intensification of
direct observations of physical, chemical and hydrometeorological
phenomena in and around the Dead Sea. The new data together with the
prior data enabled the development of the model presented here which
combines, on a daily basis, the hydrometeorological model (providing
complete inflow series) with a simplified two-layered physical model
of the Dead Sea. For the model calibration process, a series of
monthly inflow values was calculated by a water balance method, which
was based on observed sea level data compiled by Klein (1961, 1981).
The model also enables a better estimation of the evaporation from
the Dead Sea.
In the following sections a description of this model is presented.
No description of the hydrometeorological model (daily rainfallrunoff simulation model) is included as it appears elsewhere (Mero,
1978; Simon & Mero, 1985).
BASIC CONSIDERATIONS
A detailed modelling of all the dynamic processes occurring in the
Dead Sea is impractical due to the extreme complexity of such a
model, and the lack of numerous data necessary to calibrate such a
model. Thus, it was decided to devise a much simpler simulation
model which avoids the use of explicit functions for describing all
the complex physical phenomena occurring in the Dead Sea, such as
Simulation
model for
Dead Sea levels
267
t u r b u l e n t h e a t t r a n s f e r , mixing of s a l t s between l a y e r s , caused by
wind d r i v e n f o r c e s a f f e c t i n g the motion ( s e i c h e s and i n t e r n a l waves)
and c i r c u l a t i o n of the v a r i o u s s t r a t i f i e d l a y e r s , and t h e r e s u l t i n g
w a t e r d e n s i t y and t e m p e r a t u r e d i s t r i b u t i o n .
I n s t e a d i t was assumed t h a t : (a) complete mixing occurs i n t h e
upper l a y e r between t h e incoming l i g h t e r w a t e r and the w a t e r i n t h e
l a k e , (b) exchange of s a l t s occurs by a f l u x between the upper and
the lower l a y e r s , (c) the e v a p o r a t i o n - d e n s i t y r e l a t i o n s h i p observed
i n e x p e r i m e n t a l ponds may r e p r e s e n t , a f t e r some m o d i f i c a t i o n , the
phenomena i n the l a k e .
Since a r e l a t i v e l y l o n g - t e r m w a t e r - l e v e l hydrograph e x i s t s (80
y e a r s of gauged l e v e l s ) , i t was b e l i e v e d t h a t a r e a s o n a b l e
c a l i b r a t i o n of the model could be achieved even with such a s i m p l i f i e d model, and t h a t such a model could s u b s e q u e n t l y be used for
o p e r a t i o n a l f o r e c a s t s . The b a s i c scheme of t h e model i s p r e s e n t e d i n
Fig.l.
I t s p r i n c i p a l components a r e d i s c u s s e d i n the following
sections.
INITIAL CONDITIONS, INPUTS READING
READING OF DAILY INFLOWS AND RAINFALL DATA
1'
CALCULATION OF DEAD SEA AREA AND
VOLUMES FROM SEA LEVELS
*
MODIFICATION OF CLIMATOLOGICAL INPUT DATA
ACCORDING TO RAINFALL INDEX
i
CALCULATION OF DENSITY IN THE TWO LAYERS
i
.
CALCULATION OF EVAPORATION
*
ENERGY-BALANCE AND TEMPERATURE DETERMINATION
'
SALT-BALANCE CALCULATIONS
'r
WATER-BALANCE CALCULATIONS
'
•
CALCULATION OF THE NEW DEAD SEA LEVEL
«,
Dead Sea simulation
•
FIG.l
model - generalized
scheme.
ELEVATI0N-AREA-V0LUME RELATI0NSHIP
For p r a c t i c a l a p p l i c a t i o n of the model, v a r i o u s mathematical formulae
have been developed. F i r s t , new e l e v a t i o n - a r e a - c a p a c i t y curves were
268 F.Mero S
E.Simon
e s t a b l i s h e d , based on t h e most u p - t o - d a t e b a t h y m e t r i c a l and
t o p o g r a p h i c a l maps, t o cover the f u l l range of e l e v a t i o n s between
-720 and -380 m (below m . s . l . ) . Though the a c t u a l bottom e l e v a t i o n
of the Dead Sea i s about -720 m. I t was found t h a t s e t t i n g an
a r b i t r a r y r e f e r e n c e datum a t -500 m would be e x p e d i e n t i n the
g e n e r a l i z e d f o r m u l a t i o n of t h e s e c u r v e s , duly accounting for the
volume below e l e v a t i o n -500 m.
Two e l e v a t i o n - a r e a r e l a t i o n s h i p s were c o n s i d e r e d :
(a) The h i s t o r i c a l s i t u a t i o n , i n which the n o r t h e r n and s o u t h e r n
p a r t s a r e l i n k e d when water l e v e l s are above - 4 0 3 . 5 m. Below t h i s
e l e v a t i o n the L i s s a n S t r a i g h t d r i e s up and the two p a r t s are
disconnected.
(b) The f u t u r e s i t u a t i o n , i n which the n o r t h e r n n a t u r a l deep l a k e
i s d i s c o n n e c t e d from the s o u t h e r n p a r t which i s p r a c t i c a l l y
surrounded w i t h dykes of the I s r a e l i and J o r d a n i a n p o t a s h works.
Brine supply for t h e p o t a s h works comes by pumpage from t h e deeper
l a y e r s of the n o r t h e r n p a r t where the t a i l i n g s w a t e r i s a l s o disposed.
Dead Sea w a t e r - s u r f a c e (AREA) and volume (VOLUME) as a f u n c t i o n of
e l e v a t i o n a r e d e s c r i b e d by t h e following e x p r e s s i o n s :
AREA = A(i) x e x p ( B ( i ) x DELEV) + DA
(1)
VOLUME = C ( i ) x e x p ( B ( i ) x DELEV) + E ( i + 1) - D(i)
(2)
where the c o e f f i c i e n t s A ( i ) , B ( i ) , C ( i ) , D ( i ) , E ( i ) and DA have been
determined for d i f f e r e n t e l e v a t i o n r a n g e s , as shown i n Tables 1 and 2,
and DELEV = 500.0 + ELEV (water s u r f a c e e l e v a t i o n ) .
PRELIMINARY WATER BALANCE AND INFLOWS
As mentioned above, d a i l y Dead Sea inflows have been s i m u l a t e d by a
h y d r o m e t e o r o l o g i c a l model (MM08), which was adopted t o r e p r e s e n t the
Dead Sea d r a i n a g e b a s i n by comparing i t s output with gauged r i v e r
flows and with the p r e l i m i n a r y water b a l a n c e of the Dead Sea for the
y e a r s 1937/1938-1951/1952. As an i n p u t t o the model, d a i l y r a i n f a l l
r e c o r d s for Nazareth ( f o r the n o r t h e r n s u b - b a s i n s ) and Jerusalem ( f o r
the s o u t h e r n s u b - b a s i n s ) were used, a f t e r adjustment by a p p r o p r i a t e
p r o p o r t i o n a l i t y f a c t o r s to account for the marked a r e a l v a r i a t i o n
of r a i n f a l l over the v a r i o u s s u b - b a s i n s . Accepted average évapot r a n s p i r a t i o n r a t e s for the v a r i o u s s u b - b a s i n s were a l s o used,
A d e s c r i p t i o n of the s i m u l a t i o n r e s u l t s i s given by Mero et al.
(1982) and Simon & Mero ( 1 9 8 5 ) .
In order t o c a l i b r a t e the MM08 model simple monthly w a t e r b a l a n c e s
were performed with the r e s u l t i n g b a s i c "measured" n a t u r a l and Dead
Sea inflow s e r i e s . Since e v a p o r a t i o n was the only o u t l e t from the
Dead Sea, the b a l a n c e e q u a t i o n could be w r i t t e n as f o l l o w s :
AELEV = (QIN - C0NS)/AREA + RF - EVPS
(3)
where AELEV i s the observed water l e v e l change (m); QIN i s the t o t a l
n a t u r a l inflow b e f o r e d i v e r s i o n f o r consumption (10 6 m 3 ); CONS i s the
upstream uses and d i v e r s i o n s (10 6 m 3 ); RF i s the d i r e c t r a i n f a l l over
the lake (m); EVPS i s the a c t u a l e v a p o r a t i o n from the Dead Sea (m);
Simulation
TABLE 1
i
1
2
3
4
5
6
7
Coefficients
Elevation
-380.0
-394.0
-398.5
-401.5
-402.0
-403.0
-410.0
Whole
range
-394.0
-398.5
-401.5
-402.0
-403.0
-410.0
-500.0
T
f
T
4v
T
v
range
*Also applied
TABLE 2
Elevation
1
2
3
4
5
6
7
-380.0
-394.0
-398.5
-401.5
-402.0
-403.0
-410.0
A(i)
B(i)*
387.8420
230.1097
59.0844
0.0178
0.0909
135.7230
514.9000
0.009
0.014
0.027
0.109
0.093
0.017
0.003
range
---~
-----
0.035
the volume-elevation
Coefficients
i
used in area-elevation
6.5967
for
-394.0
-398.5
-401.5
-402.0
-403.0
-410.0
-500.0
model for
function
25
18
57
86
31
94
12
92
Remarks
0
0
0
0
0
0
0
The
(for
7
165
928.865
232.343
143.069
0.162
0.974
804.660
032.051
coefficients
i = 1 to 7)
The
"historic"
conditions
are
valid
for the
combined
north-south
parts
514
9 North
part
only
function.
function
D(i)
C(i)
269
(1)
DA
used in the volume-elevation
41
16
2
Dead Sea levels
47
8
(2)
E(i)
2.6658
4.2159
15.1144
395.3841
524.3495
5.0236
0.5040
164
149
144
141
141
140
135
597
144
636
843
409
597
352
954
718
862
882
410
132
479
and AREA is the Dead Sea area (km ) .
QIN was then computed for the period 1937/1938-1951/1952, during
which no significant changes are known to have occurred, as far as
long-term water levels and salinities are concerned (levels
fluctuated around -395 m and densities remained near 1.2 g cm ) .
It could then be assumed, as a first approximation, that the salt
and heat balances of the Dead Sea remained relatively unchanged
during this period, and that the average evaporation rates did not
vary significantly. For the preliminary balance computation, evaporation values were obtained from estimates of potential evaporation
(as described later) and the findings from measurements in ponds with
different salinities which had been performed by the Dead Sea Works Co.
These evaporation estimates could not however be taken to
represent the changing conditions in the Dead Sea in the long term,
resulting from climatic fluctuations, diversions of water from its
drainage basin and the use of its water by the potash works. These
processes affect the salt concentrations of the various water bodies
in the more-or-less density-stratified lake. These changes have, in
turn, important effects on evaporation rates and on related
abstraction of energy from the heat storage in the various layers.
The following sections also describe the procedure which was
developed to deal with the above-mentioned changing conditions and
their influence on the actual evaporation.
270 F.Mero
&
E.Simon
THE SALT BALANCE
Observations in the Dead Sea suggest that the density stratification
is mainly controlled by the salt concentration and to a lesser degree
by the thermal distribution along a vertical column of water. Thus,
disregarding seiches and the associated internal waves, the movements
of the thermocline and the associated thermal distribution is almost
independent of the position of the pycnocline.
The salt concentrations and the related densities of the Dead Sea
water are closely related to its hydrometeorological water balance
over the ages. Under natural conditions, all salt accumulations in
their dissolved form are assumed to be the result of the concentration by evaporation of the relatively fresh water inflows. The
accumulated salts remained in a solute form, until they reached in
1979 a density of 1.235 g cm - 3 along the full vertical profile
(Steinhorn, 1980; Stiller et al.,
1980). This corresponds to a total
dissolved solids (TDS) concentration of about 344.5 g l - 1 at 25°C.
Excess salts above this limit tends to crystallize and settle on the
bottom of the Dead Sea.
Based on many hundreds of water samples collected and analysed,
and on in situ
measurements of temperatures and water densities, the
relations between Dead Sea water concentration, temperature and
density could be formulated as:
DENS = (1.0 - 10~ 5 x (TSURF - 4.0)
K 8 6 5
+ 0.0777 x exp(0.003 25 x TDS)
(4)
where DENS is the density of water (g c m - 3 ) ; TSURF is the average
water temperature (°C); and TDS is total dissolved solids (g l - 1 ) .
This relationship was found to be in good agreement over the whole
range of salinities and temperatures of water involved in this study.
The main factors governing the processes of mixing and stratification in the lake are wind forces horizontal currents, energy
exchange and diffusion. Several investigators (Blasberger & Elata,
1981; Vadaz & Weiner, 1980; Assaf, 1980) are currently developing
models of these processes in the Dead Sea. Numerical values for some
of the important parameters of these models are virtually nonexistent, and density-distribution data against which results from
various models can be checked, are very scarce. Therefore, it was
proposed to combine the various processes into an equivalent
mechanism of salt transfer between the layers, to maintain the mass
balance, and to obtain results in terms of water levels that could be
compared with the long-term historical records.
For the salt balance calculations the model was conceived as a
system of two layers, separated by an imaginary membrane at an
average depth equal to the historical position of the pycnocline
(about -420 m ) . This membrane acts as a boundary for volume changes,
but is open to salt fluxes between the two layers. Salt is added by
the water flowing into the upper layer, where evaporation causes a
gradual concentration of salts. This salinity may be augmented by an
influx from below - through the membrane - where almost constant
salinities and temperatures prevail.
The salt balance equations for the two layers have been
Simulation
model for
Dead Sea levels
271
formulated as:
s
1
^ TDSUj-i x VUP + CDUP t x VUP + TDSJ x VIN + TDSM x VMED
VUP + VIN + VOUT + VMED
and
TDSDi = TDSDJ.JL - (CDUP x VUP + T D S D ^ - L X ZMIF)/VBOT
(6)
where TDSU^ is the salt concentration in the upper layer of day "i";
TDSD^ is the same for the lower layer; VUP and VBOT are the volume of
water in the upper and lower layers; VIN and TDSJ are the net volume
and salt concentration of the inflowing fresh waters; VMED and TDSM
are the same for Mediterranean inflows; VOUT is the outflow
(evaporation minus direct rainfall) and ZMIF is the net amount
diverted from the bottom layer for potash production. CDUP i is the
daily rate of salt per unit volume transferred through the membrane
on day "i". CDUP^ is expressed as:
CDUPi ~
TCFD
x
ATDS i _ 1 /TDSD i _ 1
(7)
ATDS being the difference in TDS between the two layers and TCFD is
an empirical mixing parameter, involving coefficients obtained
through the calibration process. The notation (i - 1) defines
variables for the previous day.
THE ENERGY BALANCE AND EVAPORATION
It is a well known fact that the caloric energy balance is governed
mainly by three physical phenomena: the short and long wave radiation
balance, the internal heat balance and evaporation.
Long experience of such balances in deep fresh-water lakes and
oceans in various parts of the world, led to a fairly accurate
determination of evaporation from such water bodies. Similar
experience has been gained in Israel since the energy-balance
procedures based on micrometeorological observations were introduced
by Neuman (1954) for Lake Kinneret, and later applied to the Dead Sea
(Neuman, 1958) . However, the problems arising when applying this
method to the Dead Sea, are related to the physical properties of the
water, and actual micrometeorological processes over the Dead Sea and
its actual heat budget. The relatively few measurements available
can at best be used as indicators to these processes.
To overcome some of these difficulties, a semi-empirical approach
was attempted. It included a study of the temperature-bound
variation of vapour pressure of different concentrations of Dead Sea
brines, and the simultaneous evaporation observations, as compared to
evaporation from a standard class A pan. These observations were
made from November 1966 to July 1967 in the Sdom salt ponds, using
six tanks, each filled with a different but constant concentration of
Dead Sea brine. These data were used to establish a set of curves
relating evaporation to density and temperature (see Fig.2). This
relationship can be expressed by the formula:
EVPS = EVPDd.O - 138 x (exp(-2.035 x DENS) - 5) TSURF F R H 0 )
(8)
UJOO
1020
l.OiO
1,060
U)BO
1.100
1,120
l.HO
l.leo
DENSITY
1.160
1.200
1.220
1.210
1,260
1,260
1,300
1.310
(gr/tm3)
FIG.2
Relationship
between brine tanks
evaporation
as a function
of temperature
and class A pan
and
density,
where EVPS is the calculated evaporation rate from the Dead Sea
(mm day ); EVPD is the potential evaporation rate modified according
to cloud effects (mm day -1 ); DENS is the temperature-adjusted brine
density (discussed in the previous section); TSURF is the upper layer
temperature obtained from the energy balance (°C) and FRHO is the
temperature exponent which is equal to -151.5 x exp(-4.2 DENS).
In order to determine the temperature of the upper layer*, in the
absence of actual measurements, energy balance calculations were
performed, employing values of solar radiation (SUNRD), back
radiation (BRAD), energy consumed by evaporation (ENREV) and interlayer energy transfer (ENTRNS), which were computed from the abovementioned mass balances and from measured or adopted climatological
parameters.
The general energy balance equation used in the model is (all
terms of equation (9) are in cal cm _2 day -1 ) thus:
DENGY = SUNRD - BRAD - ENREV - ENTRNS
(9)
DENGY being the net increment of daily caloric energy balance along a
column of water mass (WCOL); SUNRD was calculated on the basis of
average values of meteorological data observed at Sdom, and adjusted
*Upper layer for the energy balance model.
As mentioned before
the
thermocline
and pycnocline
are almost independent
in their
positions.
U»0
Simulation
model
for
Dead Sea levels
273
by t h e d a i l y r a i n f a l l d a t a of J e r u s a l e m a s an i n d e x t o e s t i m a t e c l o u d
cover e f f e c t s .
The c a l c u l a t e d r a d i a t i o n v a l u e s w e r e found t o b e i n
good a g r e e m e n t w i t h m e a s u r e d v a l u e s a t t h e Lake K i n n e r e t m i c r o m e t e o r o l o g i c a l s t a t i o n ( e l e v a t i o n - 2 0 8 m b e l o w m . s . l . ) ; BRAD was c a l c u l a t e d
by t h e f o r m u l a :
BRAD = a x e ( T S K u
-
(0.52
+ 0.048
VPACT) x T A K 4 )
(10)
w h e r e 0 i s t h e S t e p h a n - B o l t z m a n c o n s t a n t = 1 . 1 7 3 6 x 1 0 - ? ( c a l cm 2 T~' t
d a y - ) ; e i s t h e e m i s s i v i t y c o n s t a n t = 0 . 8 9 ; TSK i s t h e u p p e r l a y e r
t e m p e r a t u r e ( K ) ; TAK i s t h e a i r t e m p e r a t u r e ( K ) ; VPACT i s t h e a c t u a l
v a p o u r p r e s s u r e ( s a t u r a t i o n v a p o u r p r e s s u r e m u l t i p l i e d by r e l a t i v e
h u m i d i t y ) ; ENREV was c a l c u l a t e d by t h e f o r m u l a :
ENREV = HLAT x EVPS
(11)
w h e r e HLAT = 5 9 . 7 - 0 . 0 5 6 x TAIR i s t h e a p p r o x i m a t e v a l u e of t h e
l a t e n t h e a t of v a p o r i z a t i o n , and TAIR i s a i r t e m p e r a t u r e i n °C;
ENTRNS± was c a l c u l a t e d by t h e f o r m u l a :
ENTRNS^^ = 0 . 0 1 x WE x W C 0 L l i _ 1 x (TSURF - BTEMP) x DENS/HCAP
(12)
w h e r e WE i s a c a l i b r a t i o n c o n s t a n t v a l u e d as 1 . 5 ; BTEMP i s t h e l o w e r
l a y e r t e m p e r a t u r e ( ° C ) ; HCAP i s t h e h e a t c a p a c i t y of t h e b r i n e i n t h e
u p p e r l a y e r w h i c h was f o u n d t o v a r y a p p r o x i m a t e l y as DENS - ; t h e t e r m
f o r WC0L1, t h e d e p t h i n m e t r e s of t h e t h e r m o c l i n e ( a n d of t h e u p p e r
layer) i s :
WCOL^ = W C 0 L l i _ 1 + WK x DENGY i _ 1 /ENGT0P i _ 1 /WEXP
(13)
w h e r e WK and WEXP a r e c a l i b r a t i o n c o e f f i c i e n t s , v a l u e d as 1.2 and 0 . 8
r e s p e c t i v e l y ; t h e r e f o r e t h e d e p t h of t h e l o w e r l a y e r i n m e t r e s c a n b e
c a l c u l a t e d by t h e f o l l o w i n g e q u a t i o n :
WC0L2 = 720 + ELEV - WC0L1
(14)
w h e r e ELEV i s t h e Dead S e a s u r f a c e e l e v a t i o n b e l o w m . s . l .
Thus t h e t o t a l e n e r g y c o n t e n t of t h e u p p e r l a y e r ENGT0P
c a l c m - 2 d a y - 1 ) can b e f o r m u l a t e d b y :
(in
ENGTOPi = ENGTOP^! + DENGYj^
(15)
a n d s i m i l a r l y t h e t o t a l e n e r g y c o n t e n t of t h e l o w e r l a y e r ENGB0T ( i n
c a l c m - 2 d a y - 1 ) i s c a l c u l a t e d by:
ENGB0T± = ENGBOTi.! + ENTRNSi
(16)
The c o r r e s p o n d i n g a v e r a g e w a t e r t e m p e r a t u r e s
then c a l c u l a t e d to be:
*i and i - 1 as befor
are the
day respectively.
A variable
current
day.
notation
without
f o r t h e two l a y e r s
for the
notation
current
relates
are
and
previous
to
the
274 F.Mero
&
E.Simon
TSURF = WT x ENGTOP/(HCAP x DENS x 100 x WC0L1)
(17)
BTEMP = ENGBOT/(HCAP x DENSB x 100 x WCOL2)
(18)
WT i n e q u a t i o n ( 1 7 ) i s a c a l i b r a t i o n c o e f f i c i e n t v a l u e d a s 1 . 2 ;
HCAPB i n e q u a t i o n ( 1 8 ) v a r i e s a p p r o x i m a t e l y a s DENSB - 2 ; DENSB i s
c a l c u l a t e d by e q u a t i o n ( 4 ) w i t h TDSD and BTEMP r e p l a c i n g TDS a n d
TSURF, r e s p e c t i v e l y .
CALCULATION OF WATER LEVELS AND VALIDATION OF THE MODEL
At this stage, when water abstraction by evaporation has already
been determined, a new daily water elevation in the lake is
calculated. A new cycle of computation is then initiated as
indicated in Fig.l.
Elevations of daily Dead Sea levels are calculated by equation
(19):
ELEVi = E L E V i . ! + (VIN + VMED - ZMIF)/AREA + (RF - E V P S ) / 1 0 0 0 ( 1 9 )
ANNUAL
^A_
•
•
•
*
*
'
•
'
,
/-\
\y
EVAPORATION
—.
*-y
\A-v
i i i i i i i ii
'
"
1111111
APPARENT DENSITY ON FIRST OCTOBER
/*w\
s> r
/ \
~
v v
\ , J^
V
/
/
,,,.,,,,
1.16
OBSERVED ANO CALCULATED DEAD SEA WATER LEVELS
^
' N\\,
l'\A[A "\ wî'f*. ,
, U
tytt
yvuM/^
V
\
^A
,.
i
^ J d ^A
LEGENO
v
OB! ERVEO WATER LEVEL
"\
\\
%
-103
,,,
' ''''''' '
-lOtl ' I I I 1 I I I I I I I I I I I I I 1 | I • I I I I I
1930/Î1
FIG.3
19tO/*1
Results
1950/51
of
,,
1980/61
, ,
1970/71 YEAR
the Dead Sea simulation
model.
Simulation
model
for
Dead Sea levels
275
fliere ELEVj IS the absolute Dead Sea level (m); VIN is the net inflow:
QIN - CONS in l o 6 m 3 d a y - l ; VMED Is the average daily additional
Mediterranean inflow, artificially discharged into the Dead Sea
(10 6 m 3 day~ 1 ); AREA is the water-elevation bound area of the Dead Sea,
which can be used optionally for historical or future conditions in
the model (km ) ; RF is the daily direct rainfall over the Dead Sea
area (mm day - ) ; EVPS is the daily evaporation rate (as described in
the above sections (mm day - ) .
The next step was the model calibration which was carried out by
matching the computed water levels (equation (19)) with the observed
hydrograph of Dead Sea levels in the years 1932/1933-1978/1979. The
results are shown in Fig.3 (together with calculated annual
evaporation rates and apparent* density of the upper layer).
In spite of the lack of a satisfactory physical explanation for
some of the model elements, it was concluded that the reasonable
successful simulation of the long-term records fully justifies the
use of the model for operational studies of the MediterraneanDead Sea Project. Using the model described here, rates of flow from
the Mediterranean to the Dead Sea could be determined, subject to the
Project's operation policy.
ACKNOWLEDGEMENT
The paper is based on material prepared and
included in a report to the Mediterranean-Dead Sea Company Ltd by
Mero et al. (1982). The permission by the Mediterranean-Dead Sea
Company Ltd to publish this paper is gratefully acknowledged.
REFERENCES
Assaf, G. (1980) The Dead Sea. I - energy balance and evaporation.
Unpublished paper, Solmat Systems Ltd, Jerusalem.
Blasberger, A. & Elata, C. (1981) A hydrometric model of the Dead Sea
(in Hebrew). First Year Report, The Ben Gurion University, Beer
Sheva.
Klein, C. (1961) On the fluctuations of the level of the Dead Sea
since the beginning of the 19th century. Israel
Ministry
of
Agriculture,
Hydrological
Service,
Hydrological
Paper no. 7.
Klein, C. (1981) Dead Sea level variations since the 12th century (in
Hebrew). Teva Va'arez
23 (5), 212-218.
Mero, F. (1978) The MM08 hydrometeorological simulation system.
Tahal, Water Planning for Israel
Ltd, Publ. no.
T/78/02.
Mero, F., Simon, E. & Last, Y. (1982) Estimation of Dead Sea
evaporation in various situations - Interim Report (in Hebrew).
Tahal Consulting
Engineers
Ltd, Publ. no.
04/82/06.
Neuman, J. (1954) Energy balance of and evaporation from sweet water
lakes of the Jordan rift. Israel
Ministry
of Transport
and
Communications,
Meteorological
Service,
Series
A,
Meteorological
Notes no. 10.
Neuman, J. (1958) Tentative energy and water balances for the Dead
Sea. Bull. Res. Counc. of Israel
7G, 137-163.
Simon, E. & Mero, F. (1985) The simulation of a 121-year series of
*"Apparent"
physically
means an average value instead
(but impossible
to be calculated)
of a point value
which
should have been
used.
276 F.Mero & E.Simon
natural Dead Sea i n f l o w s . In: Scientific
Basis for Water
Resources
Management (Proc. Jerusalem Symp., September 1985), 381-392.
IAHS Publ. no. 153.
Steinhorn, I. (1980) The density of Dead Sea water as a function of
temperature and s a l t concentration. Israel
J. Earth Sci. 29,
191-196.
S t i l l e r , M. , Steinhorn, I . , Karmi, I . , N i s h r i , A . & G a t , J. (1980)
A hydrographical follow-up and a research of seasonal v a r i a t i o n
of the "mixed" Dead Sea (in Hebrew). The Weizman Institute
at
Rehovot.
A report presented
to:
Israel
Ministry
of Energy and
Infrastructure.
Vadaz, P. & Weiner, D. (1980) A thermic simulation of the Dead Sea evaporation r a t e . Preliminary Report (in Hebrew). The
Israeli
Electric
Company Ltd Publ. no. R-592.