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~ ~ .J ~1 addition to the normal, the log-normal and gamma distribution func- tions are used to match the sample distribution. Another is a func- tion which results from relating values from the normal distribution to the observed data values by a polynominal-type equation. Each of these functions is applied to the residual series and measured to see how well it fits. This permits selection of the best distri- bution function to represent the characteristics of the sample residuals. Experience has shown the polynomial relationship adequately defines the data we have studied. The shape of the distribution function in conjunction with the other properties of the time series is assumed to represent all the variation and patterns that comprise the structure of the original data set. 2.2 Streamflow Simulation The analysis of hydrologic data by inspecting the various components has two uses. One is to inspect raw data to detect inconsistencies, changes over time such as a trend, missing data, alteration of the flow due to manmade structures, or other properties useful to the hydrologist who might use historic streamflow records. The second use is for synthesizing hydrologic traces. The structure of the time series and the values which quantify each property can be used to generate an unlimited number of traces. This is done by going through the steps of the data analysis in reverse order and building up the various components instead of trying to separate them. The simulation of streamflow data may be correctly thought of as the inverse of the analysis of streamflow data. Basically, a random number generated from a computer function is taken as the starting value. This number is processed through the appro- priate mathematical equations to give it a value to reflect the particular distribution function for the station. The correlations with other stations and values from the past are then used to modify it. The specific values for the mean and standard deviation for the month are then incorporated with the linear dependent random number to produce the actual streamflow. Specific steps will now be described in slightly more detail. The first step in the data generation procedure is to produce a random uniformly distributed number. The uniformly distributed number is then transformed into a normally distributed number. The normally distributed number is transformed by means of a polynomial into the desired distribution for the independent stochastic component. Spatial dependences between the various time series are now included. Follow- ing the inclusion of the spatial dependence, serial dependence is taken into account. Summarizing using equations, if e(l) is the independent stochastic component, the value for the spatially depend- ent,serially independent stochastic component is given by: 12