Toshka Depression (TD), located about 250 km south west of the High Aswan Dam (HAD), consists of four deepcut basins connected by natural sills. It is required to assess the contribution of TD as a spillway, in enhancing the effectiveness of Lake Nasser in flood control and water availability. However, most related previous works are descriptive and use qualitative methods. In order to provide the required assessment quantitatively, we developed a numerical model which computes TD mass balance and interbasin water movements. The model computes the variation of water volume, surface area, and water level in each one of the four basins (subdepressions), thus depicting their filling sequence, for the past 130 years. This TD response to realistic time series of water inflow gains and evaporation losses is analyzed to compute the TD overflow time series. This response helps assess water availability for agricultural use and effectiveness in alleviating flood risks. Furthermore, the developed model compares between three TD configurations to help the decision maker and recommends (i) building a dam—height 10 m—at the end of the fourth subdepression near Kharga Oasis and/or (ii) incorporating the third subdepression into TD by digging a canal through the hill that blocks it from the first subdepression.
Lake Nasser is the huge lake formed after the construction of HAD for the purposes of flood control and water storage. To avoid flood damages, control imposed two requirements on Lake Nasser operation rules [
However, during the years 1996–2000, water levels in Lake Nasser reservoir reached high values: 178.54 m (in November 1996) and 181.19 m (in November 1998). Furthermore, studies predicted that a flow rate of more than 0.26 BCM/day may create serious degradation of the Nile bed [
Water was spilled to the TD to avoid releasing high discharges of water to the River Nile.
TD is located about 250 km south of HAD and consists of four deepcut basins or subdepressions, interconnected by natural sills. The High Dam Authority has labeled these basins 1, 2, 3, and 4. Satellite images of TD after floods showed the filling sequence between August 1998 and March 1999: basin 1 is filled first and then basin 2. However, the flood of years 1999–2002 filled basin (reservoir) 4 in addition to reservoirs 1 and 2 (see Figure
TD conditions during the flood period 1996–2002.
Flood year  Amount spilled to TD  Reservoir filled 

19961997  0.10 BCM  Reservoir 1 
19981999  12.6 BCM  Reservoir 1 and 2 
19992000  14.15 BCM  Reservoir 1, 2, and 4 
20002001  8.6 BCM  Reservoir 1, 2, and 4 
20012002  5.7 BCM  Reservoir 1, 2, and 4 
Toshka depression four subdepressions.
Therefore, TD proved to be a significant factor in alleviating these high floods since a total of 41.0 BCM were diverted into it.
However, satellite images showed these stored water in TD lakes was subject to considerable losses due to evaporation [
The sills between the subdepressions have changed in form and elevation due to water flushing from the Toshka canal to the first subdepression (Basin 1) and subsequently from it to the second and fourth subdepressions. These changeable sills’ elevations affected the filling sequence of the TD basins.
Therefore, these interbasin sill levels should be considered as design parameters to be selected by decision makers to achieve required performance criteria. Each subdepression lake has only one inflow source determined by the filling sequence shown in Figure
Schematic diagram for the filling sequence of TD.
B1, B2, B3, and B4 refer to the subdepressions of TD labeled according to the HAD authority. However, B5 and B6 refer to regions outside the current Toshka depression with B5 referring to the undesirable Oasis Kharga and B6 referring to the desirable extension of the third TD subdepression.
It is required to develop a numerical simulation model for TD to quantify TD contribution to two management goals: flood control measures and water availability for agricultural use. Previous works that deal with realtime flood control systems, other than the HAD system, include Unver and Mays [
Accordingly, the current Toshka depression simulation model (TDSM) is developed to provide detailed output numerical results that are essential for strategic decisions: (i) time series of overflow (excess water volumes that cannot be accommodated by TD) and (ii) time series of water levels and volumes in each one of the TD four subdepressions for quantitative assessment of water availability for agricultural use.
In Section
Because the geographic location of TD is in a hyperarid desert region, inflow gains due to rainfall may be neglected. Also, losses due to seepage or percolation may be neglected because the region bed is geologically composed of an impermeable 200 m thick layer of clayey rock.
In this section associated terms and notations are defined in order to distinguish between them.
Basinreservoirlake:
Basin refers to an empty subdepression.
Reservoir refers to a filled subdepression.
Lake refers to a partially filled subdepression.
Elevationleveldepth:
Elevation is the height above meansealevel of a basin location or a contour
Level is the height of water surface above meansealevel of the water surface in a lake
Depth is the height of water surface above the basin local bottom
Sillshills:
Sills are connections that allow overflow between the subdepressions. They are in the form of canals of small width (300–400 m). Their elevations are parameters.
Hills are connections that block overflow between the subdepressions,
The model is built to simulate water availability, surface area, and surface level in the four basins comprising TD as time series. The inputs of the model are monthly averaged time series of inflow from HAD to basin 1 of TD and time series of evaporation rates. Elevations of the sills between basins are given parameters while the height of the dam to be built at the end of basin 4 and initial volumes, surface areas, and water levels in the four subdepressions are initial conditions for the models. It consists of two linked models:
a levelareavolume model (LAVM),
a model of interreservoir water movements (MIWM),
Interactive structure of the simulation model.
The objective of this model is to transform the topographic data into digitized relationships for water surface level
Then a database is created for TD which contains water level, surface area, and water volume for each subdepression with water level increment of 10 cm.
For example when basins 1 and 2 work as one lake,
Figure
LAV output of basin capacities.
Basin  Area (km^{2})  Volume (BCM) 



B1  609  11.69  160  122 
B2  747  11.5  160  109.5 
B3  384.7  4.93  160  125.1 
B4  1259.8  38.01  160  100 
Topographic relation of water surface area versus water level.
Topographic relation of water volume versus water level.
The model is built to simulate water movement between the four basins comprising TD and the filling sequences. It consists of three submodels: volume conservation model (VCM), active lake model (ALM), and reservoir threshold model (RTM). The outputs of the model are time series of volumes and levels, maximum and average volumes and levels, and volumeduration tables.
The mass conservation equation for any of the TD subdepression lakes may be written in the following form, Zaki and Fassieh [
The volume inflow
inflow from lake Nasser to basin 1,
overflow from an adjacent reservoir basin.
Volume evaporation rate can be written as
The available data on
Since the time series of lake Nasser inflow and evaporation losses is given in 10 daily intervals, that is,
Equation (
Considering all quantities in (
Assuming quasisteady flow, the overflow from a filled lake to an empty adjacent basin may be considered as an allocation of the inflow. Hence
Now it is not correct to define lake as a partially filled subdepression because when two adjacent basins are filled, they act as one lake and are filled together under certain conditions. These possible lakes are ten as follows:
single subdepression lake:
twosubdepression lake:
threesubdepression lake:
foursubdepression lake:
index for the considered lake
index for the active lake
index for the evaporating lake
Water surface loses water to the atmosphere all the time. This loss occurs in all basins of TD all the days of the 130year period of investigation. The average decrease of a lake volume per time step of 10 days is obtained by
To avoid counting evaporation losses twice for a particular lake, we restrict calculations on the single subdepression lakes: that is,
This is accomplished by multiplying the evaporation loss term by kroneckerdelta:
When two lakes combine and start filling together, the evaporation losses from their combined surface are simply the superposition of their individual losses. Now the full operating equation for mass conservation is obtained by substituting (
The objective of this model is to determine the threshold elevation of each lake,
These are given below:
When two lakes reach the same water level and start to be filled together as one lake, we give it the double index name; that is,
The objective of this model is to determine the index
Each subdepression lake has only one inflow source determined by the sequence.
(1) A onebasin lake is active in the beginning of the
Its current water level is smaller than its threshold elevation
Its input lake source is filled; that is, it becomes a reservoir
(2) A Combined twobasin lake is active (lake
They reach a common level,
The common level exceeds their intersill elevation but is still smaller than the twobasin lake threshold,
Their inflow source becomes a reservoir
(3) A combined threebasin lake is active (lake
They reach a common water level,
The common water level exceeds their intersill elevation and is still smaller than the threebasin lake threshold elevation,
Their inflow source becomes a reservoir
(4) A combined fourbasin lake of the entire Toshka depression is filled together when three conditions are satisfied.
A virtual inflow time series is chosen to test the validity of SMTD predictive capability in simulating TD performance in both flood and drought situations. The model simulates the gradual water filling of each basin and the possible joining of two or more adjacent subdepressions as a function of time. The present state of sills after the three consecutive floods of 1996–2000 is considered:
Virtual inflow time series.
The filling sequence followed the expected pattern shown in Figure
The filling sequence for the test case.
Evaporative emptying is demonstrated and the validity of the developed model is asserted as shown in Figure
Water level time series for the validity test.
Data about the water arriving at Aswan is available from 1869, Suteliffe and Parks [
Realistic inflow time series.
This realistic inflow time series has three features:
two long flood periods 1873–1899 and 1955–1971,
two long drought periods 1890–1954 and 1977 to 1998,
three short flood periods 19101911, 19761977, and 19992000.
Different methods were used to estimate evaporation rates of Aswan High Dam lake and Toshka lakes, for example, Aly et al. [
Evaporation rates.
Month  Evaporation rate 

January  0.055 
February  0.05 
March  0.06 
April  0.065 
May  0.073 
June  0.076 
July  0.093 
August  0.1 
September  0.1 
October  0.09 
November  0.075 
December  0.065 
From Table
The appropriate flood management strategy depends on the local conditions and consists of a combination of measures. One of these measures is TD configuration, defined by interbasin sill elevations and a dam.
Specifically, TD configuration is defined by two parameters.
The elevations of interbasins connecting sills:
The Kharga Oasis dam whose height is
TD configurations A, B, and C.
Configuration  Dam 





A  Dam  160 m  152 m  151 m  142 m 
B  No Dam  150 m  152 m  151 m  142 m 
C  Dam  160 m  149 m  151 m  142 m 
The response of TD to each configuration is shown in two separate figures. The first figure depicts the time series of water levels in the four TD lakes while the second one depicts the time series of water overflow (the excess water volume that cannot be accommodated by TD).
This response is for the TD configuration A as shown in Figures
Water level time series for TD configuration A.
Overflow time series for TD configuration A.
In Figure
For both configurations B and C the water level time series in all basins are shown in charts (Figures
Water level time series for TD configuration B.
Overflow time series for TD configuration B.
Water level time series for TD configuration C.
Overflow time series for TD configuration C.
Results show that configuration C produces less overflow amounts and more water storage in TD when struck by floods. Hence, we can conclude that building a dam at the end of subdepression 4 near Kharga Oasis and lowering the hill that separates of subdepression 3 from subdepression 1 may be the best TD configuration.
One of the major outputs of this model is the simulation of the manner by which the flood water is accommodated by gradual (or sudden) filling of the separate subdepression. The filling sequence of TD depends not only on the inflow time series but also on the configuration of the TD.
Of particular interest is the TD filling sequence during the two major flood periods of the time series. These are the 6 crucial years of the first flood period (1872–1878) and the 12 crucial years of the second flood period (1955–1967). These are shown in Figures
Water levels during the first flood period.
Water levels during the second flood period.
In order to demonstrate the high time resolution of the simulation model of Toshka depression (SMTD), we zoom in to critical periods where changes in levels, volumes, and areas are drastic. These critical periods are the drought years 19751976 and the flood years 19992000. In Figures
Water level variations during the draught period.
Water level variations during the flood period.
Similar variations in lake volumes and surface areas may be shown for these or other critical periods. The user of SMTD can change the sill elevations and/or the dam height to investigate the response of a particular TD configuration. The flexibility of SMTD allows the user to investigate different scenarios for design and planning purposes.
The developed model computes the time variations of water levels, water surface areas, and water volumes in each one of the four basins of the TD. This time variation constitutes the detailed response of TD to realistic time series of both inflow gains and evaporation losses during the past 130year period.
The model provides detailed timedependent TD response which includes the monthly patterns of interbasin water movements and their filling sequence. This is essential for the decision maker to assess quantitatively water availability for the feasibility of agricultural use; water volumes with appropriate levels that may be stored for extended periods of time, in each one of the four TD subdepressions.
The model provides a tool to assess quantitatively the flood control effectiveness and limitations of TD. The output results show its strong time dependence on three alternative TD configurations (elevations of inner sills and outer boundary).
The model gives the time series of the overflow. These are the volumes that cannot be accommodated by the TD of a certain storage capacity. This capacity in turn is defined by the TD configuration. In addition to assessing TD limitations, this is important for developers and inhabitants of the regions close to TD, Oasis Kharga, for example.
The model quantifies the gains to flood control of two management decisions and hence recommends TD configuration C:
building a 10 m height dam at the 4th basin boundary (
digging a canal through the hill between 1st and 3rd basins (
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was sponsored by the Ministry of Water Resources and Irrigation. The authors were members of the COINS consultation team who developed and used this model to conduct the prefeasibility study documented in [