Document Type


Publication Date

January 1979


Rising water surface elevations in perennial terminal lakes threaten major damages to shoreline industrial plants, transportation routs, and wetlands. Falling elevations increase pumping costs for industries extracting minerals from the lake water and reduce the quality of shoreline recreation. The managers of these properties need information on future lake level probabilities for planning, and public agencies need information on both probabilities and damages to determine whether lake level control is justified. Standard methods for estimating flood frequency and damages in riverine areas do not work well for terminal lakes because of the interdependency in annual peaks and the long advanced warning and duration of flood events. For this reasons, the methods of operational hydrology were use to simulate lake level and shoreline damage sequences for the Great Salt Lake. Both ARMA (1,0) and ARMS (1,1) models were tried in generating multivariate sequences of precipitation, evaporation, and three river flows for 1937-1977. The multivariate Markov model was the only one able to preserve historical sequences, but recommendations for improved parameter solution techniques for the ARMA (1,) model are made to help future users take better advantages of its theoretically greater ability to preserve hydrologic persistence. The Markov model was used to generate 100 and 125 year lake sequences as inputs to a lake water balance model which used them to generate 125 year lake stage sequences. The generated sequences showed lake level probabilities for current land and water use conditions the tributary area to be affected by known present conditions for about 35 years after which they stabilize in a normal distribution of mean 4196.42 and standard deviation of 4.56. The one-percent high event has a value of 4207.0, and the one-percent low event is 4191.5, and the amount by which these values exceed the forecast stages is indicative of the long term downward trend in lake stage caused by increasing upstream water use. The model developed with the capability of estimating low future lake level probabilities would be affected by upstream water development and by pumping water from the lake during high stages into the western desert. Data on damages to 21 cost centers were collected, and a damage simulation model was developed to use them to estimate average annual damages under current conditions and benefits from lake level control efforts. Averages annual damages to the mineral industry, railroads, highways, wetlands, and other properties were estimated to be currently $1,550,000. The computer programs for multivariate stochastic flow generation, lake water level simulation, and damage estimation are reproduced and documented in the appendices. The models will be available for future use in re-estimating probabilities and damages as initial lake stages and lake use conditions change, additional years of input data are collected, and the state of the art stochastic flow generation is refined.