Impact of Forest Service Activities on Stream Flow

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Troendle/Nankervis/Ponth Page22 5/22/2003 The final step in the process was to model the relationship between cumulative stream flow (y) and either cumulative snow pack (X) or cumulative precipitation (X). Since we are primarily interested in the comparison of the pre 1997 data with post 1997 data, a typical way to analyze the data is through ana.lysis of covariance. Unfortunately, when working with cumulative data, as in this case, the data are correlated and analysis of covaziance is not the best method. We prefer to present the data in cumulative form because the double-mass plots provide a very simple and comprehensive way to examine the relationship between two parameters and the technique is very sensitive to even the most minor changes in the relationship. Location of Precipitation Gages with >SOyrs Record 'vn Relation to remaining Streatngages and Snowcourses a? ? ? .? cO ? Longitude Figure 19. Relative location of the stream gauges, precipitation gauges, and snow courses selected as reference sites for further analysis. We modeled the cumula.tive relationship between measured seasonal stream flow (Y) and either April 1 snow pack accuimulation (X) oY- annual precipitation (X) :for data pairs up through 1997 using simple lineaz regression. For the most part, data were normal and had homogeneous variance, with the few e;xceptions that are addressed in Appendix C. However, the data were correlated, as noted above, because we made them as such in order to generate the double-mass plots. In order to address this correla.tion we modeled the residuals (from the simple lineaz regression) as an AR (111. This then pravides us with a valid mean squared enor (MSE) that we can use to develop predi.ction intervals :Por our simple lineaz regression models. A projection of the fitted line will be ad(ied to the data i.'or any years beyond 1997 with 95% prediction intervals. This allows the user to easily visualize 1:he magnitude of change that would need to occur in any one year in order to detect a possible change in the watershed as subsequent post 1997 data pairs become available. If anty post 1997 p:)int or points were to plot outside of these prediction intervals this would then be a flag signifying the user must go back and perform a standard analysis of covariance o:n the original data to determine if there has been a significant change in the watershed response since 1997. An example of the lineaz regression model, confidence bands, and the inclusion of post 1997 data pair is shown for Encampment River above Hog Park plotted over Wyoming P'recipitatiorn gauge 7990 (Figure 20). In this case, the data appear to drift in that stream flow appf;ars to be decre;asing relative to precipitation in recent yeazs. The post -111 -110 -109 -108 -107 -106 -105 -104