Abstract:
Delineation of Hydrologic Regions:
The initial step in delineating hydrologic regions was to develop a statewide regression equation through OLS (Ordinary Least-Squares) method. The response variable was the 50-year peak discharge, and the five most significant explanatory variables for the statewide equation were found to be drainage area, main-channel slope, basin storage, mean annual runoff, and water equivalent of snow cover.
Six hydrologic regions within New York were identified and delineated primarily through inspection of the areal distribution of the statewide regression residuals. Areas where the regression equation consistently overestimated or underestimated the peak-discharge response were delineated as discrete hydrologic regions, and separate GLS (Generalized Least-Squares) regression equations were developed to estimate peak-discharge frequencies for each region. Regional differences in geologic and physiographic conditions were also considered during the delineation; generally, the hydrologic-region boundaries were delineated to coincide with drainage-basin divides and are shown in U.S. Geological Survey Scientific Investigations Report 2006-5112.
The report also shows the distribution of regression residuals for each hydrologic region before and after regionalization. The box plots depict the clustering of residuals within the final six hydrologic regions before regionalization and also show the distribution of the final GLS regression residuals for the six hydrologic regions after regionalization. The 50-year peak-discharge was the response variable. Comparison of the two plots shows the regression residuals after regionalization to have a smaller range, as well as median values at or near zero.
A further evaluation of the hydrologic region delineations used statistical tests to compare residuals among the six regions; the results indicated a normal distribution of residuals within each of the six regions. Multiple comparison tests were then used to identify which regions’ means differed statistically from the other regions’ mean. The six regions sample sizes were unequal, ranging from 39 in Region 3 to 109 in Region 1; therefore, two simultaneous inference methods (SIM)-Fisher’s Least Significant Difference (LSD) test (t-tests) and Tukey’s multiple comparison test-were used. Both tests yielded the following comparisons of means of residuals among the six hydrologic regions:
for adjacent regions 1 = 2 < 3 > 4 < 5 > 6 < 1 > 4 = 6 < 1 < 3.
A few adjacent regions had mean residuals that did not differ statistically from each other (the regional residuals shown above that are statistically equal), but other factors, such as topography, geology, climate, and hydrologic judgment, indicate that delineation of these areas as separate hydrologic regions is justified.
Purpose:
Regionalization of Flood-Frequency Estimates:
Regression analysis provides a means of relating peak discharge to basin characteristics. Variability of the relation between peak discharge and basin characteristics among gaged sites can be reduced by regionalization, a process in which an area is divided into hydrologic regions to account for regional differences in peak-discharge response and in topographic and climatic variables that affect streamflow. Hydrologic regions refer to areas in which streamflow-gaging stations indicate a similarity of peak-discharge response that differs from the peak-discharge response in adjacent regions. These similarities and differences are defined by the regression residuals, which are the differences between the peak discharges calculated from station records (log-Pearson type III estimates) and the values computed through the regression equations.