The Dead Sea is a hypersaline terminal lake experiencing a water level drop of about 1 m/yr over the last decade. The existing estimations for the water balance of the lake are widely variable, reflecting the unknown subsurface water inflow, the rate of evaporation, and the rate of salt accumulation at the lake bottom. To estimate these we calculate the energy and mass balances for the Dead Sea utilizing measured meteorological and hydrographical data from 1996 to 2001, taking into account the impact of lowered surface water activity on the evaporation rate. Salt precipitation during this period was about 0.1 m/yr. The average annual inflow is 265–325 × 106 m3/yr, corresponding to an evaporation rate of 1.1–1.2 m/yr. Higher inflows, suggested in previous studies, call for increased evaporation rate and are therefore not in line with the energy balance.
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 Since the first half of the 20th century, the level of the lowest place on Earth, the Dead Sea, has declined by over 20 m [Gavrieli and Oren, 2004], and since 1996 the average rate of water level drop is about one m/year. The negative water balance of this unique terminal lake is due to diversion of freshwater from its drainage basin, mainly from water which in the past reached the lake through the lower Jordan River (Figure 1). Yet, despite the environmental impact associated with this decline and the regional and international discussions which aim to resolve and manage the Dead Sea, the water balance of the Dead Sea is not well constrained. The least known parameters in the balances are the evaporation rate and subsurface water inflow. This balance will be crucial for the feasibility study and planning of the proposed “Peace Conduit” project, which aims to convey seawater from the Red Sea to the Dead Sea thereby stabilizing its level [Gavrieli et al., 2005].
 Reliable determination of the water balance of hypersaline lakes in general and that of the Dead Sea in particular are more complicated than similar freshwater bodies due to two major factors.
 1. The first is difficulty in determining the amount of evaporated water due to reduced water activity and rate of evaporation: Evaporation from brine surface is less than that from a freshwater surface because the dissolved salts lower the free energy of the water molecules and hence the saturation vapor pressure above the brine. The activity coefficient of water (H2O) in the brine, β, represents the ratio between vapor pressure above a brine surface and vapor pressure above a freshwater surface at the same temperature [Stumm and Morgan, 1981]. The activity of freshwater is β = 1 by definition, while in hypersaline brines β < 1 (for the present Dead Sea composition, β ~ 0.67). Accordingly, the rate of evaporation from such water bodies is not equivalent to that from freshwater under similar conditions [Salhotra et al., 1985, 1987; Steinhorn, 1991].
 2. The second factor is difficulty in determining the net water deficit: The decline in the water level of a hypersaline chemically-saturated lake which precipitates salts does not represent the true change in the volume of the lake because the accumulation of the salts effectively raises its floor. The water deficit is therefore larger than it appears from simple level changes. In the Dead Sea, halite (NaCl) began to precipitate in 1979 [Steinhorn, 1983], and since then, continues to precipitate. The rate of accumulation has been estimated to be several centimeters per year, from chemical considerations [Gavrieli, 1997].
 To resolve the long-term evaporation rate and water balance of the Dead Sea, we adopt the energy budget method, which is considered the preferential technique for long-term monitoring [Winter et al., 2003]. A somewhat similar but simplified approach was applied to the Dead Sea by Stanhill  and Neumann  utilizing a limited data set. We first present a formulation for the simultaneous determination of the energy, water and salt balances for hypersaline lakes. This approach requires reliable meteorological and limnological data. Using detailed data that accumulated from a buoy in the center of the Dead Sea since 1992, we evaluate annual inflow, rate of evaporation and rate of salt precipitation. Figure 2 presents a flowchart for the methodological approach with reference to sections in this article, main equations, figures, and tables.
2. Hydrographical Setting of the Dead Sea
 The Dead Sea is a terminal hypersaline lake (salinity ~277 g/kg) with extremely high density (~1240 kg/m3 at 23°C). The present (2005) volume of the Dead Sea is ~132 km3, with surface area of ~625 km2, maximum depth of ~300 m and surface level at ~418 meters below mean sea level. It forms the lowest place on Earth, which currently is declining by ~1 m/yr. At the time of the first in-depth study of the properties of the Dead Seawater column, in 1959–1960, the lake was stratified (meromictic) with the shallow southern basin flooded (today it is the site of industrial evaporation ponds, Figure 1). Somewhat less saline upper water mass (epilimnion) floated over a denser lower water mass (hypolimnion) [Neev and Emery, 1967]. The lower water mass had been isolated for at least several centuries [Steinhorn et al., 1979; Stiller and Chung, 1984], was anoxic and contained H2S. It should also be noted that in the past 40 years, the solar radiation in the Dead Sea Rift Valley in general, and in the Dead Sea in particular, has declined by more than 10% [Stanhill and Cohen, 2001].
 In 1976, following the negative water budget and lake level drop, the very shallow southern Dead Sea dried out. With the increase in salinity of the epilimnion, its density increased and the stability of the upper layer that had existed during the meromictic state weakened. This finally led to a complete overturn and homogenization and oxidation of the entire water column in 1979 [Beyth, 1980; Steinhorn et al., 1979; Steinhorn and Gat, 1983]. Since then, the Dead Sea experiences mostly annual stratification and overturns (holomictic regime), while its salinity and temperature continuously rise at overturn and its water level declines [Anati and Stiller, 1991; Gertman and Hecht, 2002]. This trend was discontinued twice, following large freshwater inflow during the particularly rainy winters of 1979/1980 and 1991/1992. These inflows lead to the dilution of the surface water and to the development of a stabilizing halocline that maintained the stratification for 3–4 years [Anati and Stiller, 1991; Beyth et al., 1993]. During holomictic years, stratification develops in spring due to the warming of the upper water layer, or less commonly in late winter due to limited dilution of the water as a result of winter rain floods. During summer months, increased evaporation results in a salinity rise of the epilimnion and the development of a destabilizing halocline. However, stratification is maintained by the stabilizing thermocline (generally located between 25 and 30 m depth). Surface water temperatures reach up to 35°–36°C, while the temperature of the water mass below the thermocline remains stable in the range of 22–23°C. Overturn occurs following the autumn cooling of the upper water column and the consequent increase in its density. Figure 3a shows the surface water temperature interannual fluctuation during 1992–2001. The surface temperature in winters, when the lake is homogeneous, represents the temperature of the entire water column. During the holomictic years (1996–2001), this temperature increased from winter to winter by 0.2–0.3°C/yr [Hecht and Gertman, 2003]. This trend is compatible with the increase in the temperature of the deep water (deeper than 100 m, Figure 3b). Figure 3b also presents the change in the salinity of the deep water, given in quasi-salinity units (σ25). The latter was defined by Anati  as the deviation of the brine density at 25°C from density of freshwater. During the same holomictic period, the quasi-salinity of the deep water increased annually by about 0.3 kg/m3/yr [Gertman and Hecht, 2002], corresponding to a salinity increase of 0.24 g/kg/yr. The annual heating and increase in salinity are related to the negative water balance of the lake, as manifested by the annual water level drop during this period (Figure 3c).
 Natural water inflows to the Dead Sea during the first half of the 20th century were estimated to be in the range of 1600–2000 × 106 m3 per year [Klein, 1998; Neumann, 1958; Salameh and El-Naser, 1999]. The volume of water reaching the Dead Sea today is substantially lower, with estimates varying between <475 × 106 m3/yr (Table 1) and >1000 × 106 m3/yr [Salameh and El-Naser, 1999]. The difference (>500 × 106 m3/yr) is due to different estimations of the unobserved subsurface inflow. The higher inflow estimation is based on a higher estimation of evaporation rate (2 m/yr, from pan evaporation) [Salameh and El-Naser, 1999]. A much lower evaporation rate, 1.05 m/yr, was estimated for the Dead Sea based on an energy balance for the period of 1980s and 1990s [Stanhill, 1994]. Available standard pan evaporation measurements from Sedom in the southern Dead Sea basin (Figure 1), are difficult to use to resolve the evaporation rate from the Dead Sea for three reasons. (1) The lowered water activity in the Dead Sea brine [Salhotra et al., 1985]. (2) Reduced evaporation in an open lake compared to pan [Morton, 1983]. (3) According to Alpert et al. , the local conditions at Sedom are different than those in the northern basin, leading to enhanced evaporation. To resolve the evaporation from Dead Sea, we apply the energy balance method on a hydrometeorological data set measured in a buoy located in the middle of the Dead Sea (Figure 1).
Table 1. Estimated Annual Inflow Volumes to the Dead Sea During the Drought Years of 1996–2001
Western side of the Dead Sea (mainly En Fesh'ha, Kane, and Samar springs)
Israel Hydrological Service
Direct precipitation (70 mm/yr)
based on average rainfall of 70 mm/yr
Estimated flood water
 A water balance of the Dead Sea must also take into account the industrial activities in the Dead Sea chemical industries (DSCI, both Israeli and Jordanian). These pump brine from the Dead Sea into evaporation ponds which are located in the otherwise dry southern Dead Sea basin. Here salts precipitate and are harvested by the industry. The concentrated end brine is then returned to the lake with a net water loss of about 250 × 106 m3/yr [Gavrieli and Oren, 2004].
 Below we present a formulation for the mass and heat balances for salt lakes (section 3). We then apply this formulation to solve for the inflow, rate of evaporation and the rate of salt precipitation in the Dead Sea, based on recently measured meteorological and hydrographical data (section 4).
3. Formulation of the Mass and Heat Balances
3.1. Total Mass Balance
 Let us consider a saline lake with bulk density ρ and total volume Vt (see Figure 4a and notation section). The total mass of the brine, mt, is equal to the sum of mass of dissolved salts, ms, and the mass of fresh water, mw:
 With time, several processes change the mass balance (Figure 4b). Evaporation reduces the mass of water in the brine by Δme, whereas water enters the lake in the form of rivers, runoff, observed springs, and rain and subsea inflow, the total being Δmi. Salt precipitation reduces the mass of dissolved salts by Δms. In the case of the Dead Sea, additional uncommon factors need to be included in the balances: the DSCI pump Δmp of the Dead Sea brine into evaporation ponds, and reject Δmr of the evaporated end brine back to the lake. The change of the mass of the brine after a period Δt, is
As a result of the above processes, the new mass of the brine after a period Δt is
where Δρ is the change in density of the brine, ΔVs is the volume of salt precipitated on the sea bottom, and ΔVl is the volume loss as appears from water level drop. Substituting (1) and (2) into (3), and neglecting the second-order terms ΔρΔVl and ΔρΔVs (Δρ ≪ ρ, ΔVs ≪ Vt and ΔVl ≪ Vt), yields
 The equation of mass balance contains three unknowns: mass of water evaporated, Δme, mass of total water inflow, Δmi, and mass of salt precipitated, Δms. The total inflow is solved after the rate of precipitation is solved from salt balance considerations and the evaporation rate from energy balance considerations (sections 3.2 and 3.3, respectively).
3.2. Salt Mass Balance
 The salinity of the brine is the ratio between the mass of dissolved salts and the total mass of the brine:
After a given time (Δt), the new salinity (Sn = S + ΔS) is the ratio between the new mass of dissolved salts and the new total mass of the brine (mt − Δmt). The new mass of dissolved salts is the sum of masses of dissolved salts pumped from the Dead Sea (ΔmpS), end brines that return from the DSCI, (ΔmrSr), salts added by the inflow (ΔmiSi) and the mass of salt precipitated from the brine (Δms):
 After substitution of (3) in the denominator, substitution of ms = S · mt(5) in the numerator, using the relation ΔVs = Δms/ρs (volume of salt precipitated is the mass divided by density of the salt) and neglecting the second-order term ΔρΔVl, we get
 This equation can now be substituted into the total mass balance (4). The remaining unknown is then the amount of water evaporated, Δme, which is solved from energy balance considerations in section 3.3.
3.3. Energy (Heat) Balance
 The energy budget for water bodies is generally expressed as [Anderson, 1952]
 The energy flux terms (W/m2), shown in Figure 5, are QSN, net solar radiation incident into the water body; QLW, net energy lost through the exchange of long-wave radiation between the atmosphere and the body of water; Qe, evaporative heat flux; Qc, energy conducted to the atmosphere as sensible heat flux; QAD, net advected heat into the water body; Qn, net heat flux, which is the change in energy stored in the body of water. Below we present the different energy flux components in terms of measurable parameters.
3.3.1. Net Heat Flux Qn and the Net Advected Heat Flux QAD
 The net heat flux Qn, or the change in energy stored in the water body, is manifested by the change in the lake's temperature and mass after the considered period. The net annual energy change for a homogeneous water body, En, is related to the mass of the brine, mt, its surface temperature, Ts, temperature change, ΔT, and the change in the total mass of the brine, Δmt:
where cp is the specific heat capacity of the brine. The net energy is translated to heat flux, averaged for the Δt period over the area, A, of the lake:
 The second-order term, ΔT · Δmt, is negligible for ΔT ≪ T and Δmt ≪ mt. The first term is related to the change in mass, or the net advected heat flux, and the second term to other processes that change the temperature of the water body.
 The advected heat flux, QAD, is the net energy gained or lost by a body of water through the ingress or egress of water. Advected masses may result from surface inflow, evaporation and the other terms of equation (2).
 Using the definition of Δmt(2) and adding and subtracting Ts from every component in (11a), the advective heat flux is represented in the following form:
 Since we are interested in the calculation of the evaporative heat flux, we have to calculate the difference between the net heat flux (10) and the net advective heat flux (11b) rather than calculate them separately. Subtracting QAD from Qn yields
3.3.2. Net Solar Radiation QSN
 The net solar short-wave radiation penetrating into the water, QSN, is calculated from the solar radiation measured above the lake surface, QS:
 The net long-wave radiation is the difference between the upward infrared radiation emitted by the water body and the atmospheric radiation reaching the surface of the water body. Several bulk formulas for the net long-wave radiation at the sea surface exist [Bignami et al., 1995]:Brunt 
 In these equations, Ts and Ta are the sea surface and air temperature in °K, kb is the Boltzmann coefficient, η is the emissivity of the water body and C is cloud cover. The atmospheric vapor pressure, ea, is calculated from the measured relative humidity (RH) and the saturation vapor pressure (esat) at ambient air temperature:
where we use the Magnus-Tetens formula for the saturation vapor pressure:
 The heat flux of evaporation is proportional to the difference between saturation vapor pressure above the saline lake, ebrine, and the atmospheric vapor pressure, ea(15):
The vapor pressure of a brine, ebrine, is lower than that of freshwater, esat, by a factor β, which is the water activity [Salhotra et al., 1985]:
The wind function, f(w), accounts for the effect of air convection above the water surface on the rate of evaporation. This is the least known parameter in the energy balance, thus the Bowen's approach [Anderson, 1952; Bowen, 1926] is widely used to eliminate the wind function out of consideration, as described below.
3.3.5. Conductive (Sensible) Heat Flux QC
 Conductive heat flux, Qc, is driven by the temperature difference between the water surface and the atmosphere; it can be either a source or a sink of heat for the water body, depending on the difference between the temperatures:
and P is the atmospheric pressure. The conductive heat, Qc, is now expressed in terms of the evaporative heat, Qe. Substituting (20) into (8) enables expressing evaporation heat flux in terms of heat flux components:
This equation enables calculating the evaporative heat flux based on measurable meteorological and hydrological quantities without the need of the wind function.
3.3.6. Evaporation Rate Δhe
 The evaporative heat flux (22) is related to the rate of evaporation, Δhe (m/yr) through the latent heat of vaporization, Le:
Note that the density and the latent heat of vaporization refer to the brine. The mass of evaporated water is Δme = ΔheρwA.
 We now have a set of three equations (4, 7, 23) with three unknowns (Δmi, Δms, Δme) expressed through measurable data and physical properties of the brine and the atmosphere above it.
4. Application of the Model to the Dead Sea
 The solution of the mass and energy balances for the Dead Sea is based on the data set collected by Gertman and Hecht  at the hydrometeorological buoy which was anchored in the Dead Sea (station EG100, see Figure 1 for location) and operated from 1992 to 2001. The data set consists of meteorological and hydrographical measurements and includes air temperature (Ta), relative humidity (RH), incoming solar radiation (QS), atmospheric pressure (P), surface water temperature (Ts) and temperature profile down to 40 m below the sea surface. The data is averaged and recorded every 20 min. The balances are calculated for all data records (every 20 min) and then averaged over each year during the holomictic period 1996–2001. The Dead Sea level is measured on a monthly basis by the Israel Hydrological Service. Hydrographical profiles taken in intervals of two months at the deepest part of the Dead Sea, at site EG320 (water depth ~310 m, Figure 1), provide the vertical distribution of temperature, salinity and density and the annual change in surface temperature (ΔT), salinity (ΔS) and density (Δρ) of the bulk Dead Sea (Figure 3b).
 During the winters of 1996–2001, the Dead Sea water body was well mixed with homogeneous distribution of water temperature and composition. Therefore the measurements taken at the sampling station (EG-320) in consecutive winters represent the annual variations of the heat stored in the Dead Sea, the salinity of the brine and the total mass of the Dead Sea brine. Yearly balances are calculated based on the meteorological data for the holomictic period 1996–2001. The current situation of very low water inflow into the Dead Sea allows significant simplification of the balances. On an annual basis, the total inflow is less than 1% of the volume of the lake. The low inflow has negligible impact on the salt and heat balances, but is an important component in the water mass balance. The adjacent freshwater Lake Kinneret (Figure 1), which receives relatively large volume inflow, including saline springs, require a more complex solution of the balances as presented by Assouline .
 Below we calculate the balances of the Dead Sea and determine the water inflow, rate of evaporation and mass of precipitated salt for year 1999 (Table 2). The heat and mass balances for this year is the closest to the average annual balances calculated for each year during the holomictic period. The interannual variations of the balances during the holomictic years are discussed in section 4.4.
Table 2. Input Data, Physical Properties, and Some Results of the Balances of the Dead Sea, 1999a
4.1. Salt Accumulation at the Bottom of the Dead Sea
 The observed annual rise in the salinity of the Dead Sea brine (ΔS = 0.24 g/kg per year, Figure 3b) is lower than that expected from the negative water balance. This is attributed to the precipitation of salt (halite) from the saturated brine [Gavrieli, 1997]. Using the equation of salt balance (7) and the measured parameters, we solve for the mass of precipitated salts, Δms. It is useful to express Δms in units of volume per unit area. The surface area of the lake, A, is assumed to be constant during a year (ΔA ≪ A). This enables expressing the masses involved in the mass and salt balances in terms of volume per unit area and density:
 Substitution of (24) into the salt balance (7) yields
 The contribution of inflow to the salt balance is very low due to their relatively low volume and salinity (Si < 10 g/kg on average) and therefore the term ΔhiρiSi can be neglected. One can argue that the salinity is higher in the unobserved inflow. However, as will be shown below, the volume of unobserved inflow is no more than a few tens of 106 m3/yr. Substituting the measured data from Table 2 into the salt balance (25), the calculated rate of salt accumulation at the bottom of the Dead Sea is Δhs = 0.10 m/yr. Even if we assume Dead Sea salinity for the unobserved inflow, which is probably a wild overestimate, the contribution to the calculated salt layer is <0.02 m/yr. This would have a minor effect on the rest of the balances. The calculated salt precipitation is in the range of previous estimates based on changes in the composition of the brine [Gavrieli, 1997], measurements of samples collected from the bottom [Levy, 1992] and from sediment traps [Stiller et al., 1997].
 The evaporation rate from the Dead Sea surface is calculated from the energy balance (23). Figure 6 presents the calculated energy balance terms and shows that the largest component in the balance is the forcing solar radiation (QSN). The net long-wave radiation (QLW) is determined independently from equations (14). Table 2 presents these calculated QLW values for the Dead Sea in 1999, which span over the range of 68–108 W/m2. The minimum and maximum values of the evaporative flux (Qe) depend on the maximum and minimum QLW values, respectively (22), as shown in Figure 6. An additional, but relatively minor source of uncertainty in the calculated evaporation rate derives from the uncertainty in the reflected short-wave radiation (albedo). Under typical conditions of predominantly light winds and relatively smooth sea surface, the average value used for albedo is 6%, i.e., α = 0.94 [Payne, 1972; Rubin and Atkinson, 2001; Ryan and Harleman, 1973]. A deviation of 1% from the latter value changes the rate of evaporation by 0.02 m/yr. A similar uncertainty in the calculated evaporation derives from a 0.05°C/yr uncertainty in the measured annual temperature rise of the water. The uncertainty related to the Bowen ration approach cannot be estimated due to the lack of direct measurements, but, according to McNaughton and Laubach , “... using the Bowen ratio method to calculate surface energy fluxes will usually incur only minor errors.”
 When incorporating the range of calculated QLW values from equation (14) into (23), and temperature rise of 0.25°C/yr, the calculated annual evaporation rate varies between 0.83–1.21 m/yr (Figure 7a). However, as discussed below, estimated surface inflow constrain the lower range of the calculated Δhe to >1.1 m/yr. This range is close to the evaporation rates of 1.05 m/yr suggested by Stanhill  based on heat balance calculations, and 1.23 m/yr estimated by Yechieli et al. , but differs significantly from the rate of 2.0 m/yr based on pan evaporation by Salameh and El-Naser .
4.3. Water Inflow
 Annual water inflow to the Dead Sea are calculated from the mass balance (4) using the salt annual precipitation (25) and rate of evaporation (23). It is useful to reduce (4) using (24) into the following form:
Figure 7b presents the calculated total annual inflow for year 1999, as determined from the different formulations of QLW (equation (14) and Table 2) and the measured annual heating of 0.25°C/yr. The inflow range is 75–325 × 106 m3/yr (note that Δhi = ΔVi/A). Constraints on the minimum possible inflow derive from the minimum estimations of the observed surface inflow, which is 265 × 106 m3/yr (Table 1). Thus the more realistic estimate of inflow ranges from 265 × 106 m3/yr, estimated from observations, to 323 × 106 m3/yr, determined form the calculations. Since the inflow and evaporation are linked through equation (26), this also constrains the minimum evaporation rate to 1.10 m/yr (Figure 7a).
Figure 8 plots the correlation between the hypothetical annual temperature change of the Dead Sea, ΔT/Δt (representing the net heat flux (10)), and the hypothetical annual inflow (representing the mass balance (26)). The different correlations (the inclined lines) derive from the various formulations for the net long-wave radiation. Also included in Figure 8 is the measured annual heating (0.25 ± 0.05°C/yr, the horizontal rectangle). The observed annual inflow range (265–475, Table 2) is plotted as vertical lines. The gray area represents the possible total inflow into the Dead Sea in 1999. The maximum calculated total inflow, 323 × 106 m3/yr, is obtained when taking the lowest QLW value (the right inclined line) with an annual temperature rise of 0.25°C/yr. The uncertainty in the temperature rise (±0.05°C/yr) is translated to only ±8 × 106 m3/yr. Higher subsurface inflow is not possible as it requires a higher evaporation rate, for which there is no source of energy flux.
4.4. Interannual Variations
 The calculations presented above for year 1999 were repeated for the other holomictic years 1996–2001 as well. As noted above, the constraint for the minimal total inflow derives from the minimum observed inflow (265 × 106 m3/yr). The maximum calculated inflow for each year (Figure 9), is derived from the use of the formulation which yields the lowest long-wave radiation [Efimova, 1961] (see Table 2). The average interannual maximum inflow is 325 × 106 m3/yr ±10%. This variability is due to the interannual variation in the measured meteorological and hydrographical parameters over and in the Dead Sea. Accordingly, the average unobserved subsurface inflow for this period range from zero to a maximum of 60 × 106 m3/yr.
4.5. Dead Sea at High Water Levels (pre-1950)
 During the beginning of the 20th century, the Dead Seawater level was relatively stable and the lake extended also into the shallow southern basin. Here we analyze the Dead Sea balances during this period, assuming steady state conditions [Neumann, 1958]. A rough estimation of the rate of evaporation is given from water balance considerations. As a terminal lake under steady state conditions, evaporation equals inflow (Δmi = Δme), and the net heat flux is zero (ΔQn − ΔQAD = 0). The salt contribution entering with the enhanced freshwater inflow and the precipitating minerals were negligible (Δms = 0), and the industrial activity (Δmp, Δmr) was minimal. Applying the formulation described above ((4) and (23)) under the steady state conditions, it is possible to express the inflow (Δmi) as a function of surface temperature and meteorological parameters:
 Historical data for the Dead Sea during 1942–1946 are summarized by Neumann . The surface elevation at that time was ~392 m below sea level and the lake area (including the southern basin) was ~950 km2. At that time, the lake was still stratified with a relatively diluted epilimnion. The density of the surface water ranged between 1140–1190 kg/m3. The annual averages include Ta = 23.6–25.4°C; ea = 15.9–14.1 mbar and Ts = 24.7–25.3°C [Neumann, 1958]. On the basis of the chemical composition [Neev and Emery, 1967] for 1960, the water activity of the surface water was β ~ 0.73. In the beginning of the 20th century the salinity was even lower with estimated water activity of β ~ 0.8. The solar radiation in the Dead Sea rift valley was higher by more than 10% than the present radiation [Stanhill and Cohen, 2001]. Using the above ranges, the estimated inflow from energy balance calculations (27) falls in the range of 1550–1750 × 106 m3/yr. Accordingly, despite the lower average surface temperature, the evaporation rate was 1.6–1.85 m/yr, which is higher than present-day evaporation (1.1–1.2 m/yr). The above derived values for the beginning of the 20th century compare well with previous estimates of inflow (1580 × 106 m3/yr [Neumann, 1958]) and evaporation rates (1.57–1.98 m/yr [Stanhill, 1994]) for the same period.
 The higher solar radiation during the early 20th century has a significant impact on the calculated evaporation rate. Keeping the measured parameters for that period, and using the reduced present-day solar radiation, reduces evaporation rate to 1.35–1.6 m/yr. This means that for the historical inflow and present solar radiation, the surface level of the Dead Sea would be higher and the area would be larger than those of the early 20th century. Thus the increased evaporation rate during the early 20th century should be attributed not only to the higher surface water activity, but also to the higher solar radiation reaching the Dead Sea surface at that period.
5. Summary and Conclusions
 The existing estimations of the water balance of the Dead Sea are widely variable and reflect the unknown subsurface water inflow and rate of evaporation. The situation is further complicated by the continuous salt precipitation from the Dead Sea hypersaline brine which raises the Sea bottom, and the industrial activity in the southern Dead Sea basin. The industries pump brine from the Dead Sea into evaporation ponds and discharge the concentrated brines back to the Dead Sea.
 We presented here a framework for the calculations of the total inflow and rates of evaporation and salt accumulation in a hypersaline lake with application to the Dead Sea, using energy and mass balance considerations. The application of the formulation to the Dead Sea is simplified since, on an annual basis, the relatively low inflow has very small effect on the salt and energy balances. The annual inflow are much lower than the total volume of the Dead Sea (<1%), while the temperature difference between the inflowing water and the bulk lake is usually <10°C. The mass of salt carried in by such low inflow is negligible compared to the high total salt content of the Dead Sea.
 The terms of the energy budget are calculated using meteorological and hydrographical data collected by a buoy located in the middle of the Dead Sea. The data set for the holomictic years 1996–2001 is recorded every 20 min and is the most detailed record of the Dead Sea. The heat of evaporation is calculated using Bowen's approach that eliminates the poorly constrained wind function from the heat balance. Since we do not have a direct measurement of the net long-wave radiation, we apply existing formulations that rely on meteorological data.
 The total annual inflow into the Dead Sea is 265–335 × 106 m3/yr, corresponding to evaporation rates of 1.1–1.2 m/yr. The range of values derives mainly due to the variations between different formulations of the net long-wave radiation. A maximum subsurface inflow of 60 × 106 m3/yr is deduced from the maximal total inflow and minimal estimate of observed surface inflow (265 × 106 m3/yr). Higher subsurface inflow is impossible as it requires higher evaporation rate, for which there is no source of energy.
 Salt precipitation rate is 0.1 m/yr (per m2). The accumulation of a salt layer at the bottom of the Dead Sea implies that the net rate of decrease in the lake's volume (height) is even higher than may be deduced from water level decline. Accordingly, the water deficit of the lake is nearly 690 × 106 m3/yr. It should be noted that some 250 × 106 m3/yr of this deficit are due to the activity of the chemical industries in the southern basin of the Dead Sea, equivalent to water level drop of ~0.4 m/yr. Thus, without the current industrial activity, lake level drop would be ~0.6 m/yr.
 Higher evaporation rate during the early 20th century, when the Dead Sea level was stable at a higher position, is attributed not only to the lower salinity, but also to the higher solar radiation reaching the Dead Sea surface at that period.
 To reduce the uncertainties in the mass and energy balances, we intend to add to our meteorological buoy the measurements of the net long-wave radiation over the Dead Sea.
surface area of the Dead Sea.
annual change of the surface area.
specific heat capacity of the brine.
atmospheric vapor pressure.
saturation vapor pressure.
saturation vapor pressure above the saline lake.
annual energy change.
water level drop.
annual precipitation of salt.
annual freshwater inflow.
salt precipitation raises the floor of the lake.
latent heat of vaporization.
total mass of the brine.
mass of fresh water.
mass of dissolved salt.
mass of water evaporated.
mass of water inflow.
mass of pumped Dead Sea brine.
mass of rejected end brines.
mass of dissolved salts.
change of the total mass.
advective heat flux.
conductive heat flux.
evaporative heat flux.
net long-wave radiation.
net heat flux.
measured short-wave radiation.
net short-wave radiation.
salinity of the brine.
salinity of the inflow.
new salinity of the brine.
salinity of rejected end brines.
change in the salinity of the brine.
time period (year).
inflow water temperature.
reject end brine temperature
surface water temperature.
change in surface water temperature.
total volume of the brine.
volume loss as appears from the Dead Sea level drop.
volume of salt precipitated.
volume of rejected end brines.
fraction of Qs that penetrates into the water surface.
emissivity of water surface.
bulk density of the brine.
changes in the density of brine.
halite (solid) density.
rejected end brines density.
 Scott Wells, Nathan Paldor, Ilan Setter, Yitzhak Mahrer, Elad Shilo, and Stuart Wollman are acknowledged for fruitful discussions. Alon Rimmer is greatly acknowledged for detailed review with suggestions that significantly improved the paper. Two anonymous reviewers are acknowledged for their reviews. Marc Parlange, Editor in Chief, is greatly acknowledged for handling of the manuscript. This study was partly supported by the U.S. Agency for International Development, the Middle East Regional Cooperation program (MERC project TA-MOU-03-M23-024) granted to American Near East Refugee Aid (ANERA) for the benefit of FoEME, and the Israel Science Foundation (grant 902/05).