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DESCRIPTION OF THE MODEL 7 random variables. The probability distribution assigned to a random variable represents the best-fit distribution (one of 17 possible probability distributions) as deter- i mined using the Chi-square goodness-of-fit criteria. The addition of future measurements may modify selection of ', the probability distribution and associated statistics. ', 2. Measurement errors associated with random variables are second-order (less than 10 percent of the maximum) as compared to daily variability. Numerical simulation using random variables captures temporal variability thereby providing a realistic assessment of the effect reservoir operations have on streamflow quantity and quality in the Colorado River. ~, 4. The stability and convergence of a prediction variable is accurate to within 1 percent when using the Monte Carlo approach. Using the bootstrap approach (Werckman and ', others, 2001), the minimum number of simulations required to achieve this level of stability and convergence ', was determined to be about 1,500. Measurements Measurements used in developing the stochastic mixing ', model were obtained from various sources including the USGS's National Water Information System (NWIS) (Kiner- ney, 2001); State of Colorado, Division of Water Resources HydroBase (Colorado Division of Water Resources, 2002), and ', Colorado State University, Orchard Mesa database (Harold Larsen; personal commun., 2002). For example, streamflow and dissolved-solids measurements were retrieved from the USGS NWIS database for the Colorado River streamflow ' gaging stations near De Beque (09093700), Cameo (09095500), ' and below the Grand Valley diversion near Palisade (09106000); Plateau Creek near Cameo (09105000); and Dry ' Fork near De Beque, Colorado (09095400). Daily streamflow measurements were available fora 27-year period (1974- 2001), whereas values of the dissolved solids and associated instantaneous streamflow were available at an approximately ', monthly frequency and a fewer number of years: Because i streamflow is regulated by upstream reservoirs, streamflow in the Upper Colorado River Basin system is seasonally periodic, and correlation (dependency) between annual streamflow records generally exceeds 0.70. A matrix of correlation coeffi- dents between total annual streamflow (integrated on a daily '~ basis) time series for the Colorado station near Cameo I (09095500) is provided in table 1. Despite the persistent seasonal periodicities, correlations '', between annual streamflow records for different years are less '' than perfect (correlation coefficient less than 1.0) due to annual '~, variations in hydrologic conditions. Identifying the correspond-', ing hydrologic conditions is done by using a cumulative distri-. bution function (also called flow duration or exceedance curve) ', for annual flow (fig. 3). In the annual streamflow-exceedance curve, the 27-year period contains a range of hydrologic condi-'. lions that include 7 dry, 14 average, and 6 wet periods. The ' average hydrologic period is defined as that period where flow exceedances are in the 25 to 75 percent range, whereas the wet and dry hydrologic periods are defined as those respective annual flows that are in the 0 to 25 percent and 75 to 100 percent exceedance range. Discrete annual cumulative streamflow values, water year, rank, exceedance value, and corresponding hydrologic condi- tions are summarized by calendar year for the station near Cameo (09095500) in table 2. Based on information gathered at the time of this study, the annual streamflow of 657,210 ft3/s during 1977 was the minimum on record indicating a dry period, whereas streamflow of 2,859,690 ft3/s during 1984 was the maximum on record indicating a wet period. The 2002 drought resulted in a slightly smaller (about 8-percent) annual minimum streamflow record of 604,026 ft3/s compared to 1977. Selection of this streamflow record provided a wide variety and balanced number of hydrologic conditions so as to minimize any potential model bias. At time scales on the order of days or weeks, streamflow is highly variable and can be characterized by using probability distributions. Daily Colorado River diversion records for water years 1974 to 2001 were obtained for diverters downstream from De Beque and upstream from Palisade using the Colorado State HydroBase (Colorado Division of Water Resources, 2002). Pan evaporation measurements collected at the Orchard Mesa Research Station (about 15 mi west from the study area) were obtained from Harold Larsen (Colorado State University, writ- ten commun., 2002). Because evaporation measurements were limited to the growing season, a predictive equation was fit by using nonlinear regression so that the usefulness of these data could be extended to a full year. Because of the small number of salinity and evaporation measurements, these data also were fit to predictive equations by using nonlinear regression, and the probability distributions associated with residuals (difference between measurement and prediction) were used to generate random values for use in stochastic modeling. Nonlinear regres- sion also was used to fit functional relations for annual stream- flow exceedance probability and reservoir surface area as a function of reservoir volume. Instantaneous streamflow and salinity measurements were obtained from the USGS NWIS database for the Colorado River De Beque, Cameo, and Palisade and Plateau Creek stations, for Dry Fork and Upper Dry Fork stations near De Beque, and for a USGS National Water Quality Assessment (Spahr and others, 1996) site on the Dry Fork at Upper Station near De Beque. Hydrograph separation was performed on the Dry Fork dis- charge measurements using published USGS software (Rut- ledge, 1998). By using the computed baseflow (low-flow) hydrograph, the streamflow hydrograph was adjusted to obtain a unit runoff hydrograph that was applied to the Sulphur Gulch drainage. Two water samples also were collected from a site (391607108153500) at the mouth of the Sulphur Gulch water- shed and analyzed for salinity and selenium during the spring 2002 runoff. Instantaneous streamflow and basic parameters such as dissolved oxygen, alkalinity, pH, and temperature were measured concurrently with the sample collection.