Digital simulation of inorganic water quality of Tahoe-Truckee system, Nevada-California

Abstract

A digital inorganic water-quality model was developed for Tahoe-Truckee System, Nevada-California. The system consists of mainstem and tributaries of Truckee River between Tahoe City, California and Nixon, Nevada (near Pyramid Lake). Flows and inorganic quality of surface waters are influenced by impoundments behind lakes and dams, diversions for and returns from municipal, industrial, and agricultural uses; and inflow of ground water including from thermal springs. The model is based on the principle of mass-flux-balance and presumes than: 1) inorganic constituents are conservative, 2) complete mixing occurs within each reach, and 3) flows can be recapitulated accurately at the defunct gaging station near Truckee, California. The model was developed from three years of water-quality data collected monthly at approximately 40 sites along the mainstem and on tributaries. Constituents modeled were bicarbonate, chloride, sulfate, sodium, potassium, calcium, magnesium, silica, and total dissolved solids (less silica). The model simulates concentrations of inorganic constituents at selected points on the mainstem and in tributaries near their confluences with the mainstem. Chemical quality of dispersed flows is also simulated. Dispersed components are treated as point sources. Quality of individual inputs is predicted as either concentration or flux. Fluxes and flows are added in a downstream direction and concentrations at points on the mainstem are calculated by dividing flux by flow. In gaged, unregulated streams, concentrations are predicted by a regression equation describing the exponential relationship with flow plus a component to reflect annual-cyclical behavior of differences between regression estimates and observed concentrations. Concentrations in reservoir releases are estimated using multiple regression equations which reflect mixing processes and short circuiting and physical characteristics of the impoundments. Concentrations of dissolved constituents in outflows from Lake Tahoe and Donner Lake have either low amplitude annual-cyclical behavior or are nearly constant with respect to time. Because other data are insufficient for prediction of these concentrations, average monthly concentration or average of all observations is used for estimation as appropriate for time-systematic or constant behavior. Concentrations in dispersed flows in reaches above Farad and in Wadsworth-Nixon reach are estimated from exponential concentration-flow regression equations. Quality of dispersed flow in other reaches is estimated from fourth-order polynomials fit to plots of net flux versus flow. A stochastic component is added to all predictive, equations to account for unexplained variance in estimates. Comparisons between simulated concentrations and data developed in the course of this research showed that simulation was achieved with minimal bias in upper river reaches. Changing patterns in water use in Truckee Meadows resulted in biased estimates in downstream reaches. Comparisons with U.S.G.S. water-quality records near Farad for a period preceding the data base of the model indicates simulation has minimal bias and higher intensity of association between simulated and observed data than is obtainable from flow-concentration regression estimates at that site on the mainstem. The historical water-quality record was simulated for water years 1964 through 1971. Cumulative frequency distributions were fit to mean monthly simulated chloride, sulfate, and total dissolved solids concentrations at sites on the main- stem. Concentrations were normally (Gaussian) distributed or near normally distributed at most sites. Frequency distributions showed sulfate simulations in upper river reaches were occasionally unstable.