Uncertainty analysis of hydrological return period estimation, taking the upper Yangtze River as an example

Abstract. Return period estimation plays an important role in the engineering practices of water resources and disaster management, but uncertainties accompany the calculation process. Based on the daily discharge records at two gauging stations (Cuntan and Pingshan) on the upper Yangtze River, three sampling methods (SMs; (annual maximum, peak over threshold, and decadal peak over threshold), five distribution functions (DFs; gamma, Gumbel, lognormal, Pearson III, and general extreme value), and three parameterization methods (PMs; maximum likelihood, L-Moment, and method of moment) were applied to analyze the uncertainties in return period estimation. The estimated return levels based on the different approaches were found to differ considerably at each station. The range of discharge for a 20-year return period was 63,800.8–74,024.1 m³ s⁻¹ for Cuntan and 23,097.8–25,595.3 m³ s⁻¹ for Pingshan, when using the 45 combinations of SMs, DFs, and PMs. For a 1000-year event, the estimated discharge ranges increased to 74,492.5–125,658.0 and 27,339.2–41,718.1 m³ s⁻¹ for Cuntan and Pingshan, respectively. Application of the analysis of variance method showed that the total sum of the squares of the estimated return levels increased with the widening of the return periods, suggestive of increased uncertainties. However, the contributions of the different sources to the uncertainties were different. For Cuntan, where the discharge changed significantly, the SM appeared to be the largest source of uncertainty. For Pingshan, where the discharge series remained almost stable, the DF contributed most to the uncertainty. Therefore, multiple uncertainty sources in estimating return periods should be considered to meet the demands of different planning purposes. The research results also suggest that uncertainties of return level estimation could be reduced if an optimized DF were used, or if the decadal peak over threshold SM were used, which is capable of representing temporal changes of hydrological series.