The need for comprehensive preimpoundment studies of African man-made lakes has been clearly recognized (e.g., Adeniji et al., 1981). Despite this, relatively few have been carried out and those that have been tend to be descriptive accounts of the river system without making predictions about future conditions in the lake. A recent exception was Thornton's (1980) attempt to predict the trophic state of a proposed small Zimbabwean reservoir, using the Vollenweider model (see 4.3).
This paper is an attempt to improve the predictive capabilities of preimpoundment studies, with special emphasis on fish yields, and it relies heavily on empirical models based on a relatively limited data base. It is hoped that the results will show that meaningful predictions can be made from simple, easily obtained data, a consideration especially important in an era of limited manpower and financial resources.
The models described in this paper have not always been based on African data. Those that have been will be affected by the general inaccuracy of the original information, especially that regarding fish yields from African reservoirs. Nevertheless, if these limitations are borne in mind, the models may still be valuable and will have served their purpose if they stimulate others to use and improve them.
An aim of one widely-used type of empirical model in hydrobiology is to make possible the prediction of complex biological effects from simple environmental parameters. Rigler (1982) gives an eloquent outline of the aims, and justifications, of the empirical approach in limnology and fisheries.
One of the earliest empirical approaches (Rawson, 1952) demonstrated that it was possible to estimate fish yields for a particular set of lakes from a lake's mean depth. Ryder (1965) took this further by introducing the effect of lake fertility, indicated by total dissolved solids, and developed the now well-known morphoedaphic index (MEI). The MEI has since been expanded and reviewed by several other authors and is now an established empirical concept (see Schlesinger and Regier (1982) for the most recent review with a comprehensive bibliography).
Other workers have shown that factors such as primary production (Oglesby, 1977) or total phosphorus (Hanson and Legget, 1982) may be better predictors of fish yields than the MEI. Recent work on North American lakes has shown that surface area alone can be predictor of fish yield (Jenkins and Morais, 1971; Youngs and Heimbuch, 1982). A major contribution to understanding aquatic ecosystems was derived from analysis of the IBP data (LeCren and Lowe-McConnell, 1980); this modelled many aspects but was not used to estimate fish yields. (IBP = International Biological Programme.)
Despite these developments empirical models have not been widely-used in African waters, perhaps because of the general lack of accurate data. Fryer and Iles (1972) showed that fish yields were broadly related to mean depth, whilst Henderson and Welcomme (1974) showed that the MEI was applicable to African lakes and reservoirs and their fish yields. There are insufficient basic biological data which can be used to predict fish yields except for primary production which Melack (1976) found could predict yields more accurately than the MEI. Unfortunately it was not possible to predict primary production from the preimpoundment data used in this paper so this concept has not been discussed further.
There is bound to be concern about the accuracy and applicability of these models in African impoundments, especially when the data are known to be deficient. Fisheries statistics, in particular, may be inaccurate because of the difficulties associated with large, hetergenous waters and fish populations (Willoughby, 1979). For this reason, the models described in this paper should not be accepted uncritically. However, they are offered in an attempt to show that preimpoundment data can be used more effectively than it is at present, especially in regard to predicting fish yields. A mean of several predictions would appear to be the most useful in providing a reasonably realistic estimate (Marshall, in press). This is probably the most that can be expected with the present level of knowledge about African reservoirs, but it is to be hoped that increased interest in predictive techniques will lead to the collection of better information.
The following data have been selected because they can be used in the predictive models that will be discussed: the choice has been governed by the limitations that a worker in Africa is likely to experience and most of the data can be collected easily and without extensive field work.
Basic physical information should be available for most planned reservoirs because this is an essential engineering requirement. It is usually possible to estimate the following, if not already available, from maps or area/volume curves:
Altitude (full supply level elevation, m above sea level).
Latitude (to the nearest half-degree, N or S).
Morphometry at full supply level, especially
Shoreline length, Lo (km)
Surface area, Ao (km2)
Mean depth, z (m)
Volume, V (m3 × 106)
Catchment area, Ac, which must include the catchments of any upstream reservoirs.
This should be available before the reservoir is built. The seasonal pattern of the inflowing river is most important because, especially when rivers are highly seasonal, most nutrients are brought into lakes during flood periods.
An important hydrological concept is the hydraulic retention time (Tw) which can be calculated from the lake volume/mean annual outflow. In a preimpoundment study the annual outflow will be more or less equal to the annual river flow at the dam site and can be used to estimate Tw, if this is not already known from the engineering studies. It may also be necessary to introduce a correction for evaporation if the lake's surface : volume ratio is large and the climate arid.
These data are often difficult and time-consuming to obtain but sampling can be limited to a few major constituents such as phosphorus and nitrogen which have the greatest effect on lake productivity. If a river is highly seasonal adequate data may be obtained by sampling during the flood season only.
Chemical data on their own are often uninformative and it is recommended that attempts to estimate nutrients loading should be made since it has been shown that chemical processes in lakes are greatly influenced by the rate of nutrient supply and loss (e.g., Vollenweider and Kerekes, 1980). Understanding nutrient loading has made it possible to characterize the trophic status of lakes in Europe and North America and it should be applicable to African waters if the data are available. Nutrient loading has not been widely studied in African reservoirs, except for some in southern Africa where eutrophication has become a serious problem in a number of water bodies (e.g., Walmsley and Butty, 1980; Thornton and Walmsley, 1982). If basic chemical and hydrological data are available nutrient loading is relatively easy to calculate from the equation:
Lt = Q × c | |
| Q | = total annual water flow (m3) |
| c | = mean nutrient concentration (mg l-1) |
| Lt | = load. |
The accuracy of this will increase if samples are taken frequently, especially during periods of strong flow when nutrient loads are expected to be highest.
The loading rate can then be estimated by:
 | |
| Ln | = nutrient loading rate in g m-2 yr-1 |
| A | = surface area of impoundment in m-2 |
| Lt | = annual load in tonnes |
Loading rates are usually expressed in relation to the reservoir surface area (g m-2 yr-1) but in some cases may be volumentric (g m-3 yr-1). In this case lake volume is used instead of lake area in the preceeding equation.
In this paper phosphorus loading will be discussed in most detail since it is the major limiting nutrient in Africa, where most rivers drain geologically ancient rocks which yield few nutrients and are especially deficient in phosphorus (Viner et al., 1981).
The other important chemical parameter that will be discussed in this paper is conductivity, a measure of dissolved ions, since it is easy to measure and has been used in the MEI for African rivers and is usually lowest at peak flood (see Coche, 1974) which is, nevertheless, the period when most nutrients are brought into a lake. Very high values can be measured in the dry season when rivers may scarcely flow which can give a misleading picture. However, there are very few detailed studies of conductivity in African rivers and often only the range of values is available. In this paper the lowest value will be used as a measure of river conductivity (KR).
Some predictive models which can be used to give a general idea of an impoundment's characteristics will be discussed in this section. They are all based on data listed in the previous one; some are based on published work whilst others are presented for the first time. They include data from natural lakes, but, wherever possible, they have been based on information available from African reservoirs.
Temperature clearly affects biological processes in a lake and Schlesinger and Regier (1982) have used it, in conjunction with the MEI, to predict fish yields (see 5.2.2). It is a function of latitude and altitude and can be estimated from a general knowledge of the climate in the area of the new lake. In order to estimate temperatures more precisely, maximum and minimum surface temperatures from 20 African reservoirs were plotted against their “altitude factors”, AF (Fig. 1). The AF was calculated as follows:
AF = altitude (m) + (latitude × 49)
since according to Lewis (1973), one degree of latitude is equivalent in effect to 49 m of altitude.
From this information the following models were developed:
| Maximum temperature, Tmax = 34.581 - 0.004 AF | (1) |
| Minimum temperature, Tmin = 27.553 - 0.005 AF | (2) |
| Mean temperature may also be required, and in a preimpoundment study Tm = (Tmax + Tmin)/2, would probably be adequate | (3) |
This model gives a rather better prediction of minimum temperature because the two reservoirs with high AF (>3000) did not fit the maximum prediction very closely. The reasons for this are unclear. These models do not, of course, indicate the seasonal temperature cycle and reference should be made to Straskraba (1980) and Shuter et al. (1983) for a discussion on this. Clay (1976) was able to predict water temperatures from air temperatures for some African lakes, but this was not applicable generally and this is an aspect with requires further study.
Either conductivity or total dissolved solids (TDS) may be used to formulate the MEI and thus being able to predict one of these parameters is highly desirable, but it seems unlikely that this can be done with great precision. Two approaches have been adopted in this paper, however, in an attempt to do so.
The first is modified from Schindler's (1971) approach and is based on morphometric and hydrological data. A reservoir with a large catchment (Ac) might be expected to have a high conductivity (KL) because of the larger quantities of dissolved ions brought in from the catchment. On the other hand, this would be reduced if the lake volume (V) is large, and also if, as in most man-made lakes, retention time (Tw) is short because a short retention time implies a high loss of dissolved substances. The model was developed by plotting KL against (Ac/V) × Tw for 31 African reservoirs (Fig. 2). There was a high correlation and the regression equation was used as the predictive model:
| KL (μS cm-1) = 44.728 + 4.705 (Ac/V × Tw) | (4) |
Lake Kainji did not fit closely, possibly because it has a disproportionately large catchment area and very short retention time. Two precautions must be taken when using this model:
eutrophic or culturally-modified reservoirs must be excluded, e.g., McIlwaine, which has been enriched by sewage effluent (Marshall and Falconer, 1973); and
catchment areas must include those of any upstream reservoirs, e.g., Cahora Bassa's catchment includes Kariba's.
The second model was based on the premise that KL is related to conductivity of the main inflowing river (KR). The lack of information about conductivity of African rivers and its high variability has already been described and so the lowest available figure (on the grounds that this occurs during flood season) is used in the model, in which KL is plotted against KR for 23 African reservoirs (Fig. 3). The relationship is only for those reservoirs which have one major inflow, i.e., a single river contributing >70 percent of the total water supply.
The two parameters were strongly correlated and the following model was derived:
| Log KL = 0.754 + 0.734 log KR | (5) |
It generally predicts that KL will be from 1.0 – 2.0 times KR, an assumption that has already been used in some preimpoundment studies (Tanzania, 1981; Du Toit, 1982).
Some of the MEI models used TDS but this parameter is not estimated as frequently as conductivity in African waters. A relationship between the two parameters was demonstrated from three Zimbabwean reservoirs, in which:
| TDS = 24.629 + 0.506 KL | (6) |
where TDS = total dissolved solids (mg l-1) and KL = conductivity (μS cm-1) (Fig. 4). This might be a convenient relationship for converting conductivity into TDS but it is necessarily an oversimplification.
The trophic status of a new reservoir will be of interest, especially if sewage effluent is discharged into a river. Thornton (1980) attempted to predict the trophic status of a proposed reservoir in Zimbabwe using the Vollenweider model and it was later shown that Lake Kariba data fitted this model well (Marshall, 1984). The model (Vollenweider, 1976) plots phosphorus loading (as g P m-2yr-1) against mean depth divided by water retention time (z/Tw). Data were available for a number of southern African reservoirs (Thornton and Walmsley, 1982) and were used to fit the model (Fig. 5). Those lakes which were described as “eutrophic” or “oligotrophic” by the original investigators fitted it well but it is less clear for those described as “mesotrophic”, possibly because the term itself is imprecise. Nevertheless this appears to be a useful model for describing the general state of the lake and may have wider application in future.
Since phosphorus is such an important limiting factor it is highly desirable to be able to predict the steady state phosphorus concentration in the new reservoir. Thornton and Walmsley (1982) showed that this could be done in a number of southern African reservoirs if the phosphorus loading rate is known. They used Vollenweider's equation:
P = L/(z/Tw) (1 + Tw) | ||
| where | P | = lake phosphorus concentration (mg l-1), |
| L | = phosphorus loading rate (g P m-2 yr-1), | |
| z | = mean depth (m), | |
| Tw | = replacement time (years). |
Using this equation they were able to predict lake phosphorus with considerable accuracy (r = 0.62, n = 43) but they also found that the Dillion and Rigler (1974) model was better (r = 0.96, n = 37). Unfortunately it is unsuitable for a preimpoundment study as it requires a knowledge of phosphorus losses, which cannot be estimated before the dam is built.
An interesting and potentially useful approach is outlined by Westlake (1980) and his associates. If the input ortho-phosphate concentration (mg P m-3) and the exchange time (retention time can be used) are known then some biological characteristics can be predicted (Fig. 6). This first (Fig. 6a) is macrophyte penetration, the second (Fig. 6b) is phytoplankton concentration and the last (Fig. 6c) is zooplankton biomass. The author states that this model is oversimplified but that it is able to predict the general biological changes that might occur with eutrophication. It is difficult to test in most African lakes because adequate data are not available but it is hoped that this approach may eventually be valuable.
Predicting the fish yield is an important consideration of any preimpoundment study and a major objective of this paper is to suggest ways of making these predictions. The approach will be to review various models which would give an indication of maximum and minimum yields, whilst the mean would probably give a fairly reliable estimate.
A desirable objective is to be able to predict yields from simple, readily available morphometric data. Youngs and Heimbuch (1982) have shown that lake area alone is a powerful predictor of fish yield and their method was used for the 17 heavily-exploited water-bodies listed in Henderson and Welcomme (1974) (Fig. 7). From this a model to predict total yield from lake area can be derived as follows.
| Loge Y = 3.57 + 0.76 loge Ao | (7) |
where Y = total yield (t).
The correlation for African lakes (r = 0.858) was not as close as that for North American ones (r = 0.969) found by Youngs and Heimbuch but this may be a reflection of more accurate data for the latter. The slopes of the two relationships are close (0.76 for African lakes, 0.83 for American), but yield for the tropical African waters is at least an order of magnitude greater than for the temperate American ones. This phenomenon has been noted before with the MEI (Henderson and Welcomme, 1974) and extended to other climatic zones (cf. Schlesinger and Regier, 1982). The figure includes both natural lakes and reservoirs but there is some evidence that the former are less productive (see 5.2) which should be taken into account in using this model.
A second approach involves rather more detailed morphometry. The two concepts that form the basis of this model are that a dendritic reservoir would be more productive than a non-dendritic one, and a shallow reservoir more productive than a deep one. Lake shoreline development (DL) indicates how dendritic the shoreline is; it is calculated from shoreline length (Lo) and surface area (Ao) as follows:
Fish yields were then plotted against DL/z for 7 African reservoirs (Fig. 8). There was a good correlation for the 5 largest and the following model can be used:
| Y (kg ha-1) = 19.996 + 32.038 (DL/z) | (8) |
Two lakes, McIlwaine and Mwadingusha, did not fit this model. The former is enriched by sewage effluent (Marshall and Falconer, 1973) whilst the latter is very shallow (z = c. 2.5 m) which suggests that catchment and climatic influences will have a much greater effect on smaller lakes. For the present, therefore, this model (11) should only be applied to very large proposed lakes (> 1 000 km2). Smaller lakes may have a different relationship and it is to be hoped that sufficient data will eventually become available so that this can be studied.
This is one of the simplest and most widely-used empirical models for estimating fish yields. It may be calculated as either total dissolved solids (TDS) or conductivity divided by mean depth (z); the latter is more widely-used in Africa because conductivity estimates are usually readily available. A major disadvantage in using the MEI in a preimpoundment study is the difficulty in estimating conductivity which has already been discussed. In the following discussion all yields are expressed as kg ha-1 yr-1.
Henderson and Welcomme (1974) were the first to show a relationship between MEI and fish yield. They obtained the equation:
| Y = 14.3136 MEI0.4681 | (9) |
from a series of 17 intensively-fished (>1.5 fishermen per km2) lakes and reservoirs. This model was subsequently modified by Toews and Griffith (1979) who introduced lake area (Ao in km2) into the relationship to obtain the following equation:
| Log Y = 1.4071 + 0.3697 log MEI - 0.00004565 Ao | (10) |
Reservoirs appear to be more productive than natural lakes (Paugy, 1979; Bernacsek and Lopes, in press) and there are now enough data from them to enable this aspect to be investigated in greater detail. The relationship of fish yield to MEI were plotted for 11 African reservoirs, as well as for the 11 intensively-fished natural lakes listed by Henderson and Welcomme (1974) (Fig. 9). The reservoirs were more productive, except at very high MEI where they were likely to be about equal. The relationship for the reservoirs can then be used for preimpoundment estimates, i.e.:
| Y = 23.281 MEI0.447 | (11) |
One further MEI model which may be useful was calculated from a number of Sri Lankan reservoirs, the largest of which was 24.3 km2 (Wijeyaratne and Costa, 1981). Their relationship
| Y = 19.0677 MEI0.7950 | (12) |
gives the highest yield estimate but this may be most applicable to small reservoirs (< 25 km2). Unfortunately little is known about the production from small water-bodies in Africa although they appear to be potentially very productive (Kenmuir, 1981).
Schlesinger and Regier (1982) give 3 useful relationships based on tropical and temperate lakes, with the mean temperature (T-m) included as a parameter.
| Log Y = 0.061 T-m + 0.043 | (13) |
| Log Y = 0.050 T-m + 0.280 log MEI + 0.236 | (14) |
| Log Y = 0.044 T-m + 0.482 log MEI25 + 0.021 | (15) |
In model (15) the MEI was calculated with 25 m as the maximum for z; this is because mean depths >25 m have a limited effect on fish production (Rawson, 1952; Oglesby, 1977). If the proposed lake has z <25 m then (14) should be used, but if z > 25 m then it should be reduced to 25 m and applied to equation (18).
Few attempts, have been made to estimate fish yields in relation to limiting nutrients in African lakes which is almost certainly because of the lack of data. Some models relating fish yields to phosphorus have been constructed (e.g., Hanson and Leggett, 1982) but it is unlikely that they can be widely used at this stage. Lee and Jones (1981) showed that fish yields were related to phosphorus loading in a wide variety of water-bodies in North America (Fig. 10). This relationship might be a useful predictive model except that yield is expressed as dry weight and errors are likely to be introduced because conversion to wet weight is needed to make these predictions comparable to the others.
This paper has shown that a number of preimpoundment predictions can be made from relatively limited data. The objective has been to improve the quality of these predictions but it can only be a small step towards this. The aim will have succeeded if workers are stimulated into utilizing their physical and chemical data more effectively and, of course, to compare their predictions with reality. It is by doing this that these models can be improved.
I am grateful to J.M. Kapetsky and T. Petr for their assistance with this paper, and to G.M. Bernacsek for many stimulating ideas.
