Towards Temporal Scaling Laws for the Risk Analysis of Rare Flood Events

Extreme flood events are rare but catastrophic and have tremendous adverse impacts on human lives and the economy. The frequency and magnitude of such events have increased globally and are likely to worsen in the future. Traditional flood risk methods estimate the extreme quantiles based on the assumption that historical data recorded at gauge stations contain a spectrum of extreme flood magnitudes. However, the available gauge station record lengths are small for several gauge stations, and these records are less likely to capture the full range of likely flood magnitudes. Hence, it is necessary to develop methods to extrapolate better the dynamics of large and rare events from historical data containing only small but frequent fluctuations. This study aims to use the scaling relation of return intervals, which is invariant for various thresholds in long-term correlated historical records and accurately estimate the risk associated with rare events. The analysis is carried out on 212 daily streamflow series across the major river basins in peninsular India. Persistence in the streamflow series is examined by estimating the Hurst coefficient with a Detrended Fluctuation Analysis. Return level distribution parameters are then estimated using the analytic equations between parameters and the Hurst coefficient. The threshold-invariant scaling of the probability of return intervals and the ratio of return levels to mean return levels allows the formulation of hazard functions, which are, in turn, used to estimate the risk of rare events. This work provides an approach for obtaining flood event sets that may contain  a wider range of magnitudes than present in the historical data. The present study contributes towards improving the at-site frequency analysis of floods using the temporal scaling law of return levels. Simultaneous occurrence of different extremes may alter the return levels of rare events such as, for example, flooding in coastal areas caused by the compound effect of storm surge and streamflow. This work can be extended to understand the effect of long-term memory and the cross-correlation of causal factors on risk estimation of compound extremes.