One of the programmes of FAO's Land and Water Development Division (AGL) for the biennium 1998 - 1999 is the development of  Land and Water Information Systems (LWIS). The programme includes activities for the development of LWIS at global, regional, national and sub-national levels. At global level the objectives of the programme are to develop a capability to asses the state of land and water resources to help predicting the potential for future agricultural production world wide. Part of the programme is dedicated to the development of a methodology for assessment and presentation of water resources. The methodology currently under development combines the capacity of geographical information systems and water balance models to produce maps showing spatial distribution of water resources over large areas. As part of this exercise, the present article gives an overview of the methodology used to create a simple water balance model, including river flow and main water use, for the Aral Sea basin (a general description of the current hydrological situation of this basin is given in Water Report 15:" Irrigation in the countries of the former Soviet Union in Figures", page 22 to 28: The Aral Sea Basin (FAO, 1997)) . The method as described is applicable, with minor adjustments, on other large river basins.

 
Watersheds

The first step involved in the creation of a small scale surface water model for the whole Aral Sea basin is the delineation of sub-basins within the Aral Sea basin. The method used to delineate the basins is described by  Maidment et al (1997). The basis upon which the sub-basins are delineated is a digital elevation model (DEM) with a resolution of 30 arc-seconds longitude and latitude (approximately one square kilometre) developed by the United States' Geological Survey (USGS). This DEM covers the whole world and is freely available on the Internet. Part of this DEM covering the Aral Sea basin is shown in Figure 1.

Delineation of watersheds from a digital elevation model has been done in the GRID-package of the Geographical Information System (GIS) software Arc-INFO:

• The digital elevation model is checked for the occurrence of fictious "pits" due to minor errors in the DEM;
• the depressions which are regarded as mistakes are filled to a corrected digital elevation model (filled DEM);
• from this filled DEM the flow direction of each cell of the model is identified;
• given the flow direction of each cell, flow accumulation is calculated, it indicates for each cell how many cells are situated upstream of this cell;
• whenever the flow accumulation of a certain cell exceeds a user defined threshold value, the cell is regarded as part of a stream, the threshold value in this study has been chosen to be 5000 square kilometres; this means that the automatically delineated watersheds are generally larger than 5000 square kilometres;

Precipitation

After delineation of watersheds the precipitation on the watersheds is calculated. There are two global data sets available with precipitation figures in grid format with cells of 0.5 degree longitude by 0.5 degree latitude. These data sets are the  Legates-Willmott data set and the Leemans-Cramer data set. The Legates-Willmott data set covers the whole world, while the Leemans-Cramer set only covers the land surface of the whole world (excluding oceans and small islands). In order to decide which data set is most suitable for this study, the average yearly precipitation of each country of the world has been calculated and compared. The differences between the values per country are significant. On average, annual precipitation in the Legates Willmott data set is 95 mm higher per country than the Leemans Cramer data set.

To calculate reference precipitation per watershed, it was decided to use the Leemans Cramer data base as there are more stations included and the interpolation method between the stations is 3 dimensional, while Legates Willmott used a 2 dimensional interpolation method. The 3-D method should provide better results in mountainous areas. However, the Leemans - Cramer database does not include data on large water areas such as the Aral Sea. Precipitation data on the Aral Sea were obtained by interpolating the surrounding values.

In order to calculate mean precipitation per watershed, the projection of the gridded data is transformed from a geographic projection to an equal area Alberts projection. To lose as little as possible from the original shape of the geographic grid cells, the resolution of the cells (approx. 50 * 50 km) was densified to a grid with cells of 5 * 5 km during the projection.  The resulting figures on precipitation per watershed are presented in Figure 3.
 

Runoff

In general runoff can be calculated by several ways, one of these ways is by means of a soil water balance, another one is by means of runoff coefficients. Calculating runoff by means of a soil water balance is a conceptual way of calculating runoff while runoff coefficients are obtained by comparing river discharges with precipitation statistics. For a basic soil water balance, it is necessary to have information on the following parameters:

• precipitation on a monthly basis or preferably at shorter intervals;
• actual evapotranspiration on the same time intervals as precipitation;
• soil water storage capacity.

• seepage from / to the groundwater in the saturated zone;
• land use;
• advanced soil characteristics (e.g. soil conductivity and soil moisture content at different pressure heads), necessary to calculate the water balance of the unsaturated zone.

Q_runoff     =     r * P                                                                                               (1)

with:
Q_runoff           =     runoff discharge
r                     =     runoff coefficient
P                    =     precipitation

Runoff coefficients have been mapped for the whole world and are published on a scale of 1 : 20,000,000 in the Atlas of World Water Balance (1974, 1977). Unfortunately data in this atlas have not been digitised, so this has been done for the Aral Sea region. In order to cover the whole study area the lines with runoff coefficients were interpolated in the Triangular Interpolation Network (TIN)-package of Arc-INFO. This TIN was converted to a point coverage to be able to make an interpolation of the points resulting in a grid (Figure 4). Average runoff coefficients per watershed were calculated according to equation (2):

r_watershed = (S(r_grid-cell* P_grid-cell ))_watershed  / (S P_grid-cell)_watershed                                     (2)

Applying these runoff coefficients to precipitation figures according to equation 1 yielded the mean annual runoff per watershed, presented in Figure 5.
 

Open water evaporation

One of the disadvantages related to the use of the runoff coefficient for the calculation is that evaporation and evapotranspiration are not taken into account explicitly. For terrestrial areas this is not much of a problem as it is taken into account implicitly by the use of the runoff coefficient. In open water areas however the water accumulates and evaporates. To calculate the total runoff of a watershed, the figure for accumulated runoff should be corrected by the evaporation of open water areas. For the Aral Sea basin the evaporation of open water bodies has been calculated with a global data set with values for Penman Monteith reference evapotranspiration on a grid with cells of 0.5 degree longitude by 0.5 degree latitude (Fischer, IIASA in prep.). Just as the grid with precipitation, the evapotranspiration grid has been densified to a grid with cells of 5 * 5 kilometre. Penman Monteith reference evapotranspiration calculated per watershed for the whole Aral Sea basin, is presented in Figure 6.

Open water evaporation per year has been calculated with equation (3):

E_ow     =     k_w * ET₀                                                                                                 (3)

with:
E_ow                         =     Open water evaporation
ET ₀                        =     Penman Monteith reference evapotranspiration
k_w                           =     correction factor for open water evaporation

The correction factor used for open water evapotranspiration is 1.3. The relation between open water evaporation and crop evapotranspiration is very complex (Smith, 1990). The value of 1.3, therefore, is an arbitrary value valid only under average circumstances. The water bodies for which open water evaporation has been taken into account have been subtracted from the Arc World 1 : 3 million digital map. Evaporation through rivers was not taken into account as the rivers were digitised as line elements and therefore do not have an area. Open water evaporation from a river has been taken into account only in the case where the rivers have such a width that they were digitised as polygons.
 

Irrigation

In natural circumstances rivers cannot cross the borders of watersheds. However, in some watersheds water is not only flowing in natural direction but is also artificially redirected through canals towards other areas where it can be used for irrigation, domestic use, industrial use etc. This situation often occurs in the Aral Sea basin. Therefore it was decided to allow two outlets per watershed; one as natural outlet and another one as artificial outlet. The natural outlet always directs the water to the nearest watershed downstream of the concerned watershed. Canals can redirect water upstream from the concerned watershed.

In the Aral Sea basin, irrigation is consuming the bulk of the available water. Figures concerning irrigation were derived from the AQUASTAT database. For all countries in the Aral Sea basin, irrigated areas are known per province. These figures per province have been assigned to the basins within the province. This assignment of irrigated area per province to watersheds has been done arbitrarily on the basis of available information. If there was no information at all, the irrigated area per watershed was calculated as the area weighted mean of the total irrigated area per province. In very large provinces with watersheds along surface waters as well as watersheds in dry parts of the province, the irrigated areas were assigned to the watersheds along the surface water. Figure 7 shows the irrigated area as percentage of the total area of the watersheds in the Aral Sea basin.

Figures concerning the amount of water used in the irrigated areas, as well as figures of drainage discharges resulting in return flow to the rivers, are, to some extent, available in AQUASTAT. The figures on return flow are not available for all countries. If the figures are available they have been used to calculate a consumptive use coefficient with equation (4):

U     =     1 - D / I                                                                                                   (4)

with:
U               =     consumptive use coefficient
D               =     drainage resulting in return flow
I                =      irrigation

Calculating consumptive use with AQUASTAT data yields a wide range of figures varying from 43 percent in Uzbekistan to 82 percent in the Kyrgyz Republic with a mean value of 70 percent for the region. It was not possible to explain the differences between the figures by differences in natural circumstances. For this reason, and in absence of more detailed information, it was decided to use, as a first approximation, a consumptive use coefficient of 70 % for the whole Aral Sea basin. As soon as more information is available a different figure for every watershed can be applied.
 

Water balance

An annual water balance per watershed has been calculated with equation 5:

Q_in,up+ Q_in,irr + Q_runoff     =  Q_out + Q_out,drain + E_ow + I * U                              (5)

with:
Q_in,up        =     Discharge entering the watershed from upstream watersheds
Q_in,irr         =     Discharge entering the watershed through irrigation canals
Q_runoff       =     Runoff generated from precipitation falling on the watershed
Q_out,main    =     Discharge at the main outlet of the watershed
Q_out,drain     =     Discharge leaving the natural outlet of the watershed through drainage of irrigated fields
E_ow             =     Open water evaporation
I                  =     Water withdrawal for irrigation
U                =     Consumptive use coefficient

The water balance is calculated for each basin with the help of a FORTRAN program. First the water balance of the most upstream watersheds (which do not receive any water from other watersheds) is calculated. For these watersheds the term Q_in,up+ Q_in,irr of equation 3 is zero. A value is obtained for Q_{out, main} , this value is equal to Q_in,up of the watershed immediately downstream of these upstream watersheds.
 
The program can handle two outlets per watershed; one for natural flow and one for irrigation canals. The discharge entering the watershed through the natural flow pattern is calculated by the program, the discharge entering the watershed through irrigation canals has to be given. The discharge leaving the watershed through drainage of irrigated fields is calculated only if the natural outlet of the watershed differs from the main outlet (in the case of redirection of flow through irrigation canals). In this case discharge caused by drainage will follow the natural flow path while the calculated Q_out,main flows through the given stream network. Discharge leaving the watershed through drainage is calculated with equation (6):

Q_out,drain = (1- U) * I                                                                                         (6)

The program can simulate the water balance of a natural situation as well as the water balance with irrigation. Figure 8 and Figure 9 show the water balance of the Aral Sea basin, respectively in the natural situation and in the situation with irrigation. The figures present the results of the water balance model without any calibration.
 

Comparison with measured data

For the two main rivers flowing into the Aral Sea, Amu Darya and Syr Darya, the calculated discharges have been compared with measured values available from the Global Runoff Data Centre (GRDC). In Figure 10 measured discharges of both rivers in two downstream gauging stations are presented.
 
In order to make a valid comparison between measured and calculated data under average, stationary circumstances, one would need a long period with measured data. However, the area under irrigation in the watersheds of both rivers has increased steadily since the 1950’s. In Figure 10 can be seen that a fitted trend line of the discharges in both rivers are more or less horizontal in the years before 1955. After 1955, with increased irrigated area, the trend lines show a clear downward tendency. The circumstances under natural flow, therefore, can be compared only with data measured before 1955. To make such a comparison, all data of the rivers of the Aral Sea basin available from GRDC were checked, and a selection was made to compare them with calculated figures. Criteria upon which the selection was made are the following:

• the percentual difference between the catchment area as given by GRDC and the catchment area as calculated by the model should not exceed 20%;
• the catchment area as given by GRDC should be larger than 10000 km²;
• the location of the station in the river should be easy to find on either a digital or a conventional map.

table 1: Comparison of GRDC-data with data calculated by the model under natural circumstances
 

River	measured natural annual runoff   (km3 / year)	calculated natural   annual runoff   (km3 / year)	difference as percentage of      measured runoff
Syr-Darya	24	31	29
Chirchik	7.0	3.9	-44
Naryn	13	9.5	-27
Amu-Darya	49	69	41
Zaravchan	5.0	3.7	-26
Gunt	3.4	4.5	32
Bartang	1.4	2.8	100
Vakhsh	10	16	60

 

After calculation of natural runoff, mean annual runoff was calculated taking irrigation into account. The results were compared only with the stations in the Syr Darya and in the Amu Darya because only in these cases the catchment areas are large enough to get a good impression of the impact of irrigation.

The data series in Figure 10 stops at 1973 for the Amu Darya but the trend lines for both rivers are more or less parallel. Therefore it has been decided to compare the flow with irrigation included with the flow predicted by the trend line in 1984 for both rivers. The results of this comparison is presented in table 2:

table 2: Comparison of measured annual runoff and runoff calculated by the model, taking irrigation into account.
 

River	measured natural annual runoff   (km3 / year)	calculated annual runoff  (with irrigation)  (km3 / year)	difference as percentage of      measured runoff
Syr Darya	4	8	100
Amu Darya	28	20	-29

 

Table 1 and 2 show that the model leads to a relatively large inaccuracy in the results. This is not surprising in view of the simplicity of the model and of the scarce information available on the different elements of the water balance (i.e. distribution of irrigation, consumptive use of irrigation water, areas with open water evapotranspiration, etc.) However, the model gives a fair estimate of the magnitude of the discharges in the rivers of the Aral Sea basin. Therefore the program can be used also as a large scale model to predict the effect of changes in the water management. Once again it should be stated that the purpose of the study is to develop a robust and simple water balance model which could be used for global application. It should thus not be expected from this model that it reproduces the hydrology of the Aral Sea basin with great accuracy. The absence of calibration of the model should also be considered in evaluating the quality of the results.

Until now the model has not been calibrated yet. The water balance under natural circumstances can be calculated with the use of precipitation figures, runoff coefficients, and open water evaporation. Of these parameters the figures on precipitation are probably the most accurate, because these figures can be checked easily with measured data. The figures on open water evapotranspiration are less accurate as they have to be calculated from several other parameters. In the water balance as presented, however, open water evapotranspiration is not a major post on the water balance, in most watersheds there is no open water at all. The runoff coefficient is a variable which is very difficult to parameterise because of all the complex processes which have to be included. In this study, the runoff coefficients used originate from a map available only on a very small scale ( 1 : 20 000 000 ). It is therefore expected that the model would yield much better best results if a better estimate of the  runoff coefficient would have been available.
 

Conclusions 

The data used in this study are available for the whole world. The method is scale independent and can be applied also on a more detailed scale provided that there are reliable data. If necessary, several components of the method can be replaced by more sophisticated models, provided that the information needed for such models is available. Application of the runoff coefficient, for example, can be replaced by applying a monthly soil water balance which can result in a more detailed water balance both in time and in space.

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