Assessment of trends in hydrological extremes using regional magnification factors

Detection and attribution of trends in individual at-site series of hydrological extremes is routinely undertaken using simple linear regression-based models. However, the available records are often too short to allow a consistent assessment of trends across different stations in a region. The theoretical developments presented in this paper propose a new method for estimating a regional regression slope parameter across a region, or pooling group, of catchment considered hydrologically similar, and where annual maximum events at different sites are cross-correlated. Assuming annual maximum events to follow a two-parameter log-normal distribution, a series of Monte Carlo simulations demonstrate the ability of the new framework to accurately identify the regional slope, and provide estimates with a reduced sampling variability as compared to the equivalent at-site estimates, thereby enhancing the statistical power of the trend test. This regionally-based trend estimates would allow for a clear characterization of changes across several stations in a region. Finally, the new method is applied to national dataset of annual maximum series of peak flow from 662 gauging sites located across the United Kingdom. The results show that the regional slope estimates are significantly positive (p < 0.05) consistently in the west and north of the country, while mostly not significant in the east and south. This translate into a corresponding increase in design flood (as measured by regional magnification factors) of up-to 50% for time horizon of 50-years into the future.