5. DERIVATION OF NET BASIN SUPPLY TIME SERIES FOR THE EQUATORIAL
5.1 The Equatorial Lake Model
The water balance of a lake requires that the total inflow to the lake should be equal to the sum of the outflow and the change of storage. Assuming that subsurface inflow and seepage can be neglected (Kite, 1984), the water balance can be determined using Equation 5.1 where each component is expressed in millions of cubic metres. The lakes are taken to be in series.
I + R + P = O + E + ΔS (5.1) where: I = is the inflow from the upstream catchments,
R = is the runoff from the catchment of the lake excluding the catchment of the upstream lake,
P = is the rainfall over the lake surface,
O = is the outflow from the lake,
E = is the evaporation from the lake surface, and
ΔS = is the change in storage i.e. storage at the end of the time period minus the storage at the beginning.
The direct method of obtaining the Net Basin Supply (NBS) involves computation of the stream inflows to the lake, estimating the direct rainfall over the lake surface from rain gauges which, typically, are distributed around the shoreline and measurement of the lake evaporation as:
NBS = R + P – E (5.2)
There are many difficulties associated with determining the NBS directly for the equatorial lakes due to the lack of sufficiently long records of rainfall and evaporation. Tributary inflows to the lakes are also poorly estimated as many contributing catchments are un-gauged. These limitations have been discussed in detail above. Since concurrent records of lake levels and outflows of the lakes are available over longer periods than the meteorological data, it is therefore easier to estimate the net basin supply indirectly as follows:
NBS = ΔS + O – I (5.3)
Hence the net basin supply can be derived from change in storage, which can be obtained from the lake levels using the lake capacity curves and from the lake outflow (which is also inflow to the subsequent lake). Lake capacity curves or tables indicate the variation of lake level or elevation with volume.
A long term lake level – outflow discharge relationship is derived by plotting the mean monthly discharges against the mean lake levels. Such a curve is readily available for Lake Victoria i.e.
Agreed Curve. Under WMO (1977), similar relationships were established for Lake Kyoga and Albert, by plotting mean monthly discharges against the lake water levels and fitting up to 5th order polynomials to the data points. There was considerable scatter of points for lakes Kyoga and Albert. Owing to the large magnitudes of individual outflows from the Equatorial Lakes, inaccuracies in gaugings and water level – outflow relationships at key gauging stations along the Kyoga and Albert Nile, the simulation of levels at Lakes Kyoga and Albert are likely to be
number of studies have attempted to simulate the behaviour of the Equatorial Lakes by solving the water balance on either a monthly or annual timescale using either the observed or simulated net basin supplies (WMO, 1982; Kite, 1984; Kennedy & Donkin, 1996; Wardlaw et al., 2005).
In order to compute the net basin supply, a simulation model that had previously been set up for the Equatorial Lake system was used (Mott MacDonald, 1998). The model simulates each lake in turn in the sequence of Victoria, Kyoga and Albert and is very similar to the Lake Model component of the Hydrologic Model of the Upper Nile Equatorial Lake Basin. The Equatorial Lakes are represented in Figure 5.1 as a series of three individual reservoirs in series subject to inter-basin flows (Qi) and net basin supplies (Ni). The inter basin flows are conveyed along the Victoria Nile (Q1), Kyoga Nile (Q2) and Albert Nile (Q3).
Figure 5.1 Inter basin flows and net basin supplies at the Equatorial Lakes.
The modelling framework adopted in Figure 5.1 is largely motivated by the work of Sene (2000), who applied a similar approach to develop his theoretical model which was used to estimate the impacts of changes in Lake Victoria levels on river flows, lake levels and swamp areas in the White Nile basin. The basis of this simplified method is the consideration that there are no significant tributary inflows along the Victoria and Kyoga Nile (Sutcliffe & Parks, 1999). Only the major lakes (Victoria, Kyoga and Albert) are considered as they are linked by the connecting rivers through which the dominant flows are routed. All other inflows such as those arising through the Semliki River which drains Lakes Edward and George are accounted for through the net basin supply for each major lake.
To simulate the behaviour of the Equatorial Lakes or to simulate a regulation plan, recorded lake levels and outflows are converted to net basin supplies using the capacity curves. The long
Victoria Kyoga Albert
N1 N2 N3
Q1 Q2 Q3
term record of lake levels and outflows for Lake Victoria, Kyoga and Albert derived in Chapter 4 for the period 1899 – 2008 were utilised as the primary data input for the Equatorial Lake Model. The net basin supplies were then used as input to the regulation plan which estimates regulated lake levels and outflows. If natural conditions are specified as the regulation plan, for example the Agreed Curve, then the estimated lake levels and outflows should be equal to recorded lake levels and outflows.