Mathematical Representation of Elevation-Area-Capacity Curves for Indian Reservoirs

Abstract

Elevation-Area-Capacity (EAC) curves of a storage reservoir are among the primary requirements for various kind of reservoir analysis such as reservoir flood routing, reservoir operation analysis, reservoir classification, and reservoir sediment distribution. A river basin may contain a large number of reservoirs/hydraulic structures. Though some of the general details like MDDL, FRL, and storage capacity/reservoir area at FRL and MDDL may be available from various sources (say, web site of India WRIS), it may be difficult to gather EAC tables for various reservoirs. In this study, an effort has been made to characterize the elevation-area and elevationcapacity curves for Indian reservoirs. The elevation-area-capacity tables of 84 Indian reservoirs have been used to develop such relationships. Depending on the availability of type and range of original and revised EAC tables for different reservoirs, the reservoirs have been classified into four types: Gorge, Hill, Flood plain – foothill, and Lake. Dimensionless plots (relative depth vs. relative area or relative capacity) in the live storage zone of reservoirs in normal and Log scales have been prepared for each reservoir. Such plots have been clubbed for all the reservoirs for deriving representative unique mathematical equations for the area and capacity curves. The methodology has been programmed in MS-EXCEL. From the available plots, average dimensionless curves have been plotted and generalized mathematical equations have been derived which can be used to approximate the elevationarea and elevation-capacity curves within the live storage zone of a reservoir. In the study, the developed mathematical relationships (within the live storage zone) and the method proposed by J. Mohammadzadeh-Habili et. al (2009) have been used to investigate their applicability for Indian reservoirs. A number of reservoirs, for which the data requirements of the two methods could be met, have been selected and comparative plots of areas and capacities from the two methods have been prepared in conjunction with the original curves. It is seen that the two methods approximate the intermediate areas and capacities quite close to the observed values. However, the mathematical relationships developed in this study are applicable only in the live storage zone of a reservoir and do not take into account the type of reservoir under consideration. Since average relationships have been worked out, the mathematical relationships may over or under-estimate the intermediate area and capacity values for some reservoirs depending on the location of their dimensionless area and capacity curves with respect to the average curve. On the other hand, method proposed by J. Mohammadzadeh- Habili et. al (2009) provides area and capacity estimates in the full range of the reservoir and also accounts for the characteristics of a reservoir in terms of reservoir coefficient. The developed equations only approximate the intermediate area and capacity curves of a reservoir. For those analyses which are highly sensitive to the accurate specification of reservoir areas and capacities at intermediate elevations, observed elevation-area-capacity tables may be used.