Abstract
Stationarity in the mean and standard deviation of annual peak discharge were examined at 34 USGS streamflow-gaging stations. All stations were determined to be free of significant upstream regulation, diversion, land-use change, or urbanization effects and were representative of California’s varying hydrologic regions. Data from the last 60 years (1947-2006 water years) were used for all sites, and the records were split into two equal blocks (1947-1976 and 1977-2006) so that changes in means and standard deviations (moments) of the logs of annual peak flows could be detected using nonparametric statistical tests. The Mann-Whitney Rank Sum Test and the Brown-Forsythe test were used to determine if differences in the mean and standard deviation, respectively, between the two 30-year periods were significant. A change in mean or standard deviation was considered to be statistically significant if the p-value of the two-sided test statistic was less than or equal to 0.10 (10% level of significance). The Shapiro-Wilk test for normality of annual peak flow data also was used for the entire 60 years of record to ascertain if the data were normally distributed. The logs of the annual peak flow data were considered to not be normally distributed if the p-value of the w test statistic was less than 0.05 (5% level of significance). A second method for visualizing trends in the mean and standard deviation over the entire 60-year test period was applied using Locally Weighted Scatterplot Smooth (LOWESS) curves. Two sites showed a significant decrease in the means of annual peak discharge, and five sites showed a significant change in standard deviation-- three sites showed a significant increase, while two sites showed a significant decrease. Overall, the test results indicate that differences in the means are not significantly different from zero and can thus be considered stationary over the 60-year (1947-2006) period. However, the test results for differences in standard deviation of annual peak discharge were not definitive. While five sites showed a statistically significant change over the 60-year period, about 10 percent of the 34 test sites, or 3-4 sites, could be expected to show a significant change by chance alone. Interestingly, the three sites with a significant increase in standard deviation are in the northern part of California, while the two sites with a significant decrease are in the northern Sierra-Nevada Range and southern California. Average annual temperature and precipitation are the most likely explanatory variables that account for significant changes in the standard deviation of the annual peak discharge throughout the 60 years. Additional statistical parametric t and f tests were performed on the mean and standard deviation, respectively, for both the average annual temperature and precipitation for those climate divisions in which the 34 gage-sites are located. All climate divisions tested showed a statistically significant increase in average annual temperature, while all but the central California coastline showed a statistically significant increase in the standard deviation of average annual precipitation. Pearson sample correlation tests were run among annual peak discharge, average annual precipitation and the Multivariate ENSO Index (MEI) to identify any relationships between the three time series. High correlations were not only found among concurrent annual peak discharges within climate divisions, but between the annual peak discharges and average annual precipitation. No correlation was found between peak discharge and MEI, but sites in central and southern California showed the highest correlation between average annual precipitation and MEI. While some correlations were found among the three time series, no definitive relationship was found that would relate any changes in standard deviation in annual peak discharge to longer-lived climate patterns such as ENSO.