Adjusting annual maximum peak discharges at selected stations in northeastern Illinois for changes in land-use conditions

The effects of urbanization on annual maximum peak discharges in northeastern Illinois and nearby areas from 1945 to 2009 were analyzed with a two-step longitudinal-quantile linear regression approach. The peak discharges were then adjusted to 2010 land-use conditions. The explanatory variables used were daily precipitation at the time of the peak discharge event and a housing density-based measure of developed land use. The effect of the implementation of stormwater detention was assessed indirectly. Peak discharge records affected by the construction of large reservoirs that affect channel routing were identified and were split into segments at the time of completion of the reservoir. Longitudinal regressions of the peak discharge records on linear and logarithmic transformations of the selected measures of urbanization and precipitation were tested, and the best fitting model was selected for quantile regression and adjustment of the peak discharges.

Because the uncertainties of streamgage-by-streamgage regressions of peak discharges as a function of urbanization are so large, a regional urbanization response was computed. Streamgages used in this study fit the following two criteria: (1) drainage area is at most 200 square miles and, (2) at least 10 consecutive years of peak discharge record are available. In the first step of the regression analysis, linear longitudinal regression models with fixed intercepts estimated for each segment of the peak discharge records were computed. The segment intercepts were then subtracted from the discharge records to homogenize the discharge dataset across the segments in preparation for the quantile regression analysis. From the quantile regression analysis, the effect of urbanization on peak discharge varies strongly with the exceedance probability of the peak discharge event; coefficients monotonically increase from 0.340 to 0.969 over exceedance probabilities from 0.002 to 0.99. The regression analyses yield estimates of the population-wide effect of the explanatory variables on the dependent variables as a function of exceedance probability. These estimates are similar to the coefficients of the regional regression relations in USGS regional flood-frequency studies such as those implemented in the Web application StreamStats; although in the longitudinal analysis used in this study, it is the temporal not the spatial (between-streamgage) variations that are taken into account.

The observed and adjusted values for each streamgage are tabulated. To illustrate the overall effect of the adjustments, differences in the mean, standard deviation, and skewness of the log-transformed observed and urbanization-adjusted peak discharge series by streamgage are computed. For almost every streamgage where an adjustment was applied (no increase in urbanization was reported for a few streamgages), the mean increased and the standard deviation decreased; the effect on skewness values was more variable but usually they increased. Significant positive peak discharge trends were common in the observed values, occurring at 27.3 percent of streamgages at a p-value of 0.05 according to a Kendall’s tau correlation test; in the adjusted values, the incidence of such trends was reduced to 7.0 percent.