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N ~ -.J ~, In the case of one variable depending on several others, stepwise multiple regression is a valuable tool. This analysis proceeds stepwise finding the least-squares relationship between the dependent variable and the others in order of their contribution or effect. This analysis indicates which variables are most important and should be included in an equation. This is needed in the model to preserve the relationships between stream gaging stations. The spatial variation of the residual components controls the relation- ship between high and low periods across basins, as well as among stations within a single basin. Thus, a basin may be above average on the whole, yet contain individual gaging stations with below- normal flows. Also, one basin may be above normal while adjacent basins are below normal. It should be clear that this type of spatial variation in the randomness of streamflow can have a substantial impact on the development, use, and management of the water resource system. To preserve the pattern of above- and below-normal relationships between stations and basins, extensive analysis of correlations between the random components was made. The residual series for several stations were first inspected by a simple correlation matrix. This matrix indicated the association between two stations by the correlation coefficient of each pair. For example, two stations which are concurrently above or below their normal flows might show a high degree of dependence as seen by a correlation coefficient on the order of 0.70 to perhaps 0.90. If two stations do not bekave similarly, their residuals will not tend to follow high and low values jointly. The correlation coefficient will be low (perhaps 0.00 to 0,30) and indicate the lack of dependence between them. It should be emphasized that this correlation study was performed on the residual values at each station after the mean, standard deviation, and serial dependence properties have been removed. A large portion of the correlation between total flow (the actual monthly value) is due to the fact that the flow series are periodic. The periodic structure of the time series representation used in the model preserves this dependence between flow stations before any correlation is explicitly investigated. By analyzing ;the relationship among the residual series we are able to quantify the degree of association between the abnormalities at neighboring stations. Stepwise multiple regression was used to quantify the dependence among stations. This analysis selects the most significant variables in a relationship between a dependent variable and several possible independent variables. It was decided to include a maximum of four independent variables for the equation used in estimating the residual values at each station. This equation is in the form of: 10