Description of the water balance model

Introduction

The water balance model was developed according to the following steps:

• delineation of the river network and basins;
• soil water balance submodel to generate estimates of yearly water surplus (vertical component of the model);
• flow routing model (horizontal component of the model) to generate estimates of annual runoff at any point in the rivers.

The model is computed on a monthly basis and results are aggregated into yearly figures.

For the purpose of this study, water surplus has been defined as the part of the precipitation which does not evaporate and therefore contributes to the water resources (surface and groundwater flow). Based on a (vertical) soil water balance, the notion of surplus represents the contribution of all elementary areas to the overall water resources produced in a given river basin. Water surplus either infiltrates to recharge aquifers or runs off into rivers. As soon as water starts flowing, it is subject to losses by evaporation, resulting in a reduction of the available water resources.

These losses depend on a number of factors, particularly the size and the aridity of the river basin: the smaller and the more humid  the basin is, the closer the surplus will be to the actual water resources. The water balance results are therefore a reasonably good indicator of the water resources considered as the sum of the surplus of all grid cells within a basin.

The time distribution of the data used for the model may also induce an underestimation of the actual amount of surplus water, available for surface and groundwater. When rainfall is characterized by a few events scattered over the rainy season, the model, made on a monthly basis, cannot reproduce surplus issued from heavy rainfall. In humid areas, where rainfall is more evenly distributed, this underestimation of surplus is less significant.

Stream and river basin contour delineation

River basins and sub-basins have been delineated on the basis of the HYDRO1k DEM described in the "Data used" section. The drainage basins have been seeded following procedures articulated by O. Pfafstetter and adapted for use in the HYDRO1k dataset in which six levels are distinguished. For a detailed description of the methodology, reference is made to an article on this subject by Kristine L. Verdin.

The USGS has developed six levels of sub-basin delineation, from major continental basins (level 1) to a very detailed division of the land into sub-basins (level 6). For this study, the drainage basins up to level three only have been considered, leading to the delineation of 608 sub-basins for the whole of Africa. The basins from level four to six were generally considered to be too detailed for the purpose of a continental study.

The delineated drainage basins were compared with available digitized coverage of the rivers and the waterbodies (see "Data used" section). Anomalies in the delineation of basins appear in waterbodies, swamps and generally in the flat areas. They are inherent to the watershed delineation process, and result in watershed boundaries with straight lines across flat areas. In order to avoid these anomalies, flat areas were first identified from the DEM and treated as individual sub-basins. They include most lakes and large swamps.

Few additional adjustments were made to the level three delineated basins:

• In some cases the rivers from the hydrological network coverage crossed the delineated basin boundaries. In those cases where such a deviation was considered unacceptable, the DEM was modified to take into account these errors and the drainage basins were delineated again.
• The basins delineated at level three were considered to be too detailed in the Sahara. Runoff in the Sahara is so little that a detailed map of watersheds would not serve any goal for this project. Therefore only the major Saharan basins have been retained and individual level three sub-basins were merged into a few larger basins.
• In order to maintain a certain homogeneity in the sub-basin areas, more detailed sub-basins have been added when the automatic delineation resulted in a very large sub-basin, while very small sub-basins have been merged with neighbouring sub-basins.

Naming of the river basins

In order to facilitate the presentation of the water balance and comparison with other water resources estimates, the continent has been devided into major hydrological units or basin groups, as proposed in the FAO publication on Irrigation Potential in Africa (FAO, 1997). The division is based on four main categories and results in 22 units:

• eight major river basins, draining to the sea: Senegal River, Niger River, Nile, Shebelli-Juba, Congo/Zaire River, Zambezi, Limpopo and Orange;

• nine coastal regions grouping several small rivers, draining to the sea: Mediterranean, Northwest, West, West Central, Southwest, South Atlantic, Indian Ocean, East Central and Northeast;

• four regions grouping several endorheic drainage basins: Lake Chad, Rift Valley, South Interior and North Interior;

• one unit for the island of Madagascar.

A map of the major African river basins can be seen by clicking on .

All the sub-basins have been named after the major river or lake to which they pertain. For those rivers that flow through several successive sub-basins, a number has been associated to the name, the basin closest to the river mouth being ranked number 1.

A digital map with detailed information on these major basins, as well as their sub-basins, can be downloaded by clicking  .

This information consists of:

• the numerical code and name of the major basin (MAJ_BAS and MAJ_NAME);
• the area of the major basin in km² (MAJ_AREA);
• the numerical code and name of the sub-basin (SUB_BAS and SUB_NAME);
• the area of the sub-basin in km² (SUB_AREA);
• the numerical code of the sub-basin towards which each sub-basin flows (TO_SUBBAS) (the codes -888 and -999 have been assinged respectively to internal sub-basins and to sub-basins draining into the sea).

Soil water balance

Input data and computation of actual evapotranspiration

The soil water balance is calculated on a monthly basis with the following geographical datalayers as input parameters:

• precipitation (P);
• reference evapotranspiration (ETo);
• maximum soil moisture storage capacity (Smax);
• easily available soil moisture (Seav).

The spatial resolution of these datasets has been described in the section "Data used" (0.5 × 0.5 degree arc) for the climatic data, corresponding to 60 × 60 km approximately. In order to make the datasets compatible to the datasets as derived from DEM (1 × 1 km), they have been projected to a Lambert Azimuthal Equal Area Projection. The original climatic data layers cover only land areas; large water bodies are not covered. A simple linear interpolation has been applied over these areas in order to fill these spatial gaps in the dataset.

The Digital Soil Map of the World and Derived Soil Properties (DSMW) distinguishes the following classes regarding soil moisture:

In this study, the following values have been assigned to each class:

In the soil water balance, all wetlands have been treated as permanent open water areas. It is therefore assumed that evaporation is always equal to reference evapotranspiration over these areas.

If one considers the amount of water available in the soil at different suction pressures, the maximum soil moisture storage capacity (Smax) can be defined as the amount of water held in the soil between 0.05 and 15 bar suctions (pF 1.7 and pF 4.2 respectively). Easily available soil moisture (Seav) is defined as the amount of water held in the soil between 0.05 and 2 bar suctions (pF 1.7 and pF 3.3 respectively).

The amount of water available at pF 1.7 is the maximum amount of water that the soil can retain; this is the situation of field capacity. Above this limit, water cannot be retained by the soil and percolates. When the amount of water falls below pF 4.2, the vegetation is no longer able to extract water from the soil. This is called ‘wilting point’. Between pF 1.7 and pF 3.3, the vegetation can easily extract the moisture from the soil to satisfy its evapotranspiration needs. The available soil moisture at pF3.3 is called "reduction point"; when the suction pressure becomes higher than this limit, the evaporative capacity of plants is reduced and evapotranspiration is less than potential. The reduction in the evapotranspiration between the reduction point and the wilting point depends on the available soil moisture. In this model, the reduction in evapotranspiration was assumed to vary linearly with available soil moisture in the range between reduction point and wilting point (see Figure 1).

Figure 1: Reduction in evapotranspiration as a function of soil moisture

Description of the computation steps

The soil water balance computation described above has been applied to every pixel of the grid. For each pixel, the soil water balance model produces a monthly estimate of the water surplus, i.e. that part of the precipitation which does not evaporate and represents the pixel's contribution to the basin's water resources.

Two cases are considered for the computation of the water surplus:

• water balance over waterbodies (including lakes) and wetlands;
• soil water balance for land.

Water balance for waterbodies and wetlands

Waterbodies are assumed to be open waterbodies and the water surplus is calculated as the difference between precipitation and evaporation. It can either be positive or negative:

S(m)= P(m) - ETo(m)

where:

    S(m) = water surplus for the month m

    P(m) = precipitation for month m

    ETo(m) = reference evapotranspiration for month m.

With the assumption that water is always present in the water bodies, the actual evapotranspiration ETa(m) is equal to ETo(m):

    ETa(m) = ETo(m)

Soil water balance

The monthly computation is organised according to the following flowchart:

For each pixel, a monthly balance is computed by adding precipitation to the soil moisture content of the previous month and subtracting potential evapotranspiration. If this balance exceeds Smax, the excess is the monthly surplus.

If the balance is less than Smax, but still larger than the reduction point, there is no surplus and no reduction in evapotranspiration. When the balance falls below the reduction point, evapotranspiration is less than the potential.

The output of the model consists of the following data layers:

• monthly actual evapotranspiration;
• monthly surplus;
• available soil moisture at the end of each month.

Water routing in the streams, accumulation and losses

In ArcView, the DEM is processed to produce two guides: a "flow direction" grid and a "flow accumulation" grid, which are used to simulate the river network.

The surplus calculated monthly for each grid cell is routed in the streams by means of the flow direction grid layer derived from the DEM. The flowaccumulation gives the amount of runoff that flows through each cell. This can also be viewed as the amount of runoff produced in all the cells located upstream of the cell considered. In the model, the assumption is made that the losses in streams can occur only while the streams are flowing through open water or wetland areas. If the evaporation in these areas exceeds the precipitation, the difference is subtracted from the river flow.

Flow accumulation is computed on a monthly basis, but monthly results are not reliable because the model does not include time in the routing process. Therefore, only yearly totals are considered as valid results.

Current water use for agriculture

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