A stochastic method for the predetermination of the probable fluctuations in service duration of hill reservoirs in Tunisia
A stochastic rainfall generator and a model for calculating the erosivity index of the Universal Soil Loss Equation (USLE) are coupled. The first one operates on a 30 min time step and it is calibrated on a 15 year historical pluviographic database for central Tunisia. The second model works like an automatic calculator, where the rain erosivity index can be averaged or summed. These two models are applied to simulate the annual siltation of hill reservoirs in arid and semi-arid areas of Tunisia. The catchment is considered as a "black-box" where mostly climatic aggressivity is varying (some extreme rainfall events cause most of the erosion) and the other erosion parameters are considered to remain constant over the lifetime of the reservoir. We know that the WISCHMEIER rain erosion index has no upper limit. When all the other factors are maintained constant, erosion is proportional to it. This climatic index is calculated for each rain event, but we can also calculate the annual average or sum it over many years. Soil losses (or solid transport) during a period are proportional to the value of this index summed over the same period. We demonstrate on three representative catchments lying from north to south (from 500 mm to 250 mm annual average rainfall) that the annual rain erosion index distribution can be considered comparable to the solid transport distribution (Galton distributions with equal statistical parameters). For the OUED EL HISSIANE catchment (15.9 km2), the annual extreme value of erosion is proportional to the annual extreme value of the rain erosion index. Only spring and autumn storms need be considered to calculate the annual sediment loss. On gauged small catchments like those of hill reservoirs, the rainfall generator can provide an erosivity rainfall record. Considering that the other erosion parameters are constant, this model allows one to calculate the confidence intervals of a reservoir's predicted durations. We equate the annual erosivity index distribution to the annual solid supplies distribution, and we generate and sum over several consecutive years many series of "solid supplies" to simulate the progressive silting up of the reservoirs (represented by the chosen period : sum over T=5 years, 10 years, 15 years ...). In the context of setting up hill reservoirs, this study concerns the potential duration and possible services of hydraulic structures (including the risk of rapid silting up of the reservoirs). This generator can be computed over many years and avoids the limitation due to the short observed time series. The methodological benefit of such an approach is therefore to avoid the difficulty of limited observed samples. It enlarges the data analysis of the series dispersal and residuals. This approach, based on observations and a statistical method, supports experimental analysis. It gives a clear idea of the rate of siltation, according to climatic hazards. A sensitivity analysis, where we modify the rainfall generator parameters (number of episodes and quantity of rain, peak and duration of storm...), is used to validate the methodology. A regional analysis shows a very low fluctuation considering the whole arid and semi-arid area of Tunisia. These two results led us to set up a regional abacus. This abacus reports the forecasts of the fluctuations of the time length service for hilly and small dams, including the probable average of their service duration. It allow a predetermination of the small dams' life time together with a confidence interval, and it can be used for small dam construction, planning and management. It improves the first feasibility study and can be included in economic calculations.