The joint effect of changes in urbanization and climate on trends in floods: A comparison of panel and single-station quantile regression approaches

Estimates of annual maximum (peak) flow quantiles are needed for basins undergoing changes in both urbanization and climate. Most previous work on the effect of urbanization on peak flows has considered urbanization alone and only the spatial variation in flood quantiles or its mean temporal effect, and most work on the effect of nonstationarity in climate has focused on single-station analyses, which give uncertain results for extreme quantiles. To address these gaps, three approaches to the statistical estimation of the joint effects of changes in impervious cover and climate on the estimation of peak-flow quantiles were compared: single-station quantile regression; a fixed effect panel-quantile regression (pQR) method using a location (mean) shift to homogenize the panel; and a location-scale panel regression model (pQRmom), which accounts for both scale (variance) and location effects. The different approaches were applied to a dataset consisting of instantaneous annual peak flows from 127 minimally nested basins in the midwestern United States with at least 4 % change in imperviousness. The annual maximum daily discharge from a water-balance model was selected as the primary climate predictor; in addition, to provide a comparison of climate predictors, precipitation was also considered. The coefficients from single-station regressions were usually sufficiently certain to determine the effects of climate variation but usually too uncertain to estimate the effects of urbanization. The panel-quantile regression approaches give much more certain results, but their estimates of quantile dependence differ: although both indicate urbanization effects decreasing with decreasing annual exceedance probability (AEP), the pQRmom urbanization coefficients are insignificantly different from zero for AEPs less than 0.10, whereas the pQR coefficients remain positive and are significant except for AEP = 0.01, the smallest AEP value considered. Although the location-scale structure of the pQRmom approach has less flexible quantile dependence than the pQR approach, the pQRmom approach has somewhat lower overall error, and it is found that by subsetting the dataset to homogenize the scale effects, the pQR and pQRmom results become similar, indicating the insignificant urbanization coefficients for small AEPs of the pQRmom results are likely correct for the study dataset.