KWRRI Research Reports


Recent studies indicated the need for development of surface water supplies in Kentucky. Rising resource costs make economically efficient reservoir designs increasingly important. This study was undertaken to provide methods in water supply reservoir design that increase system benefits.

Two major factors influencing reservoir design were studied: estimated future streamflow into the reservoir and demands placed on the reservoir. Standard reservoir sizing methods rely on historical streamflow data. This data is frequently limited and uncertainty in required storage estimates may result. To assess the reliability of a design, the use of mathematical models in simulation studies was proposed. Existing stochastic and parametric models of streamflow were reviewed and their limitations discussed. Parameters for the stochastic models must be estimated from historical streamflow data, and limited data produces unreliable estimates of the true values for these parameters. A streamflow record extended by a parametric model through simulation may provide more reliable estimates of the parameters in the stochastic streamflow model than the short historical record. A methodology was presented to evaluate the ability of a parametric model to improve the stochastic model parameter estimates in this manner. It was found that the parameter estimates of a stochastic model might be significantly improved by this process. A long historical record of rainfall may not be available to provide the necessary inputs to a parametric model. One method for providing these inputs is to model the daily rainfall process at the potential site. A modified Markov Chain model was proposed which used continuous distributions, rather than discrete transition probabilities, to represent the process when rainfall actually occurred. A two-parameter gamma distribution fit the Kentucky data. The model provided a good representation of the daily point rainfall process. 15-20 years of historical daily rainfall data were required to produce stable estimates of model parameters.

The role of the demand function in reservoir design was examined. Projected demand is commonly assumed not to depend on the concurrent water rates. Data on rural residential water demand in Kentucky has indicated that a price-demand relationship does exist for this sector. The second part of the study was undertaken to see if benefits to a hypothetical community from water supply could be increased by utilizing price-demand information in reservoir design studies. Three pricing policies were examined and their effect on reservoir design determined. The first policy assumed no price-demand relationship, and demand was based on existing community usage with a low water rate. A price-demand relationship was assumed in the second policy, and the water rate was constant. The third policy assumed the price-demand relationship, and the price charged for water during each billing period was a non-linear function which increased as the amount of water in storage at the beginning of the period decreased.

It was found that the use of the conservation pricing policies substantially reduced storage requirements while providing increased, demonstrable net benefits to the community. The conservation pricing policies substantially lowered the average price paid for water. The effect of uncertainty in consumer response to changes in price was studied by using a probabilitistic price-demand relationship. This uncertainty did not significantly reduce the effectiveness of the conservation policy. It was concluded that demand management by the use of a proper pricing policy could significantly increase water supply benefits to a community.

Publication Date


Report Number


Digital Object Identifier (DOI)

Funding Information

The project was supported in part by funds provided by the United States Department of Interior to the University of Kentucky Water Resources Institute as authorized by the Water Resources Act of 1964, Public Law 88-379, and the Office of Water Research and Technology Project A-052-KY. Partial funding was also provided by the Kentucky Agricultural Experiment Station as a contribution to Southern Regional Research Project S-53 "Factors Affecting Water Yields from Small Watersheds and Shallow Ground Aquifers".