Frequency Analysis of the Nonstationary Annual Runoff Series Using the Mechanism-Based Reconstruction Method

Due to climate change and human activities, the statistical characteristics of annual runoff series of many rivers around the world exhibit complex nonstationary changes, which seriously impact the frequency analysis of annual runoff and are thus becoming a hotspot of research. A variety of nonstationary frequency analysis methods has been proposed by many scholars, but their reliability and accuracy in practical application are still controversial. The recently proposed Mechanism-based Reconstruction (Me-RS) method is a method to deal with nonstationary changes in hydrological series, which solves the frequency analysis problem of the nonstationary hydrological series by transforming nonstationary series into stationary Me-RS series. Based on the Me-RS method, a calculation method of design annual runoff under the nonstationary conditions is proposed in this paper and applied to the Jialu River Basin (JRB) in northern Shaanxi, China. From the aspects of rationality and uncertainty, the calculated design value of annual runoff is analyzed and evaluated. Then, compared with the design values calculated by traditional frequency analysis method regardless of whether the sample series is stationary, the correctness of the Me-RS theory and its application reliability is demonstrated. The results show that calculation of design annual runoff based on the Me-RS method is not only scientific in theory, but also the obtained design values are relatively consistent with the characteristics of the river basin, and the uncertainty is obviously smaller. Therefore, the Me-RS provides an effective tool for annual runoff frequency analysis under nonstationary conditions.

Reanalysis Product-Based Nonstationary Frequency Analysis for Estimating Extreme Design Rainfall

Nonstationarity is one major issue in hydrological models, especially in design rainfall analysis. Design rainfalls are typically estimated by annual maximum rainfalls (AMRs) of observations below 50 years in many parts of the world, including South Korea. However, due to the lack of data, the time-dependent nature may not be sufficiently identified by this classic approach. Here, this study aims to explore design rainfall with nonstationary condition using century-long reanalysis products that help one to go back to the early 20th century. Despite its useful representation of the past climate, the reanalysis products via observational data assimilation schemes and models have never been tested in representing the nonstationary behavior in extreme rainfall events. We used daily precipitations of two century-long reanalysis datasets as the ERA-20c by the European Centre for Medium-Range Weather Forecasts (ECMWF) and the 20th century reanalysis (20CR) by the National Oceanic and Atmospheric Administration (NOAA). The AMRs from 1900 to 2010 were derived from the grids over South Korea. The systematic errors were downgraded through quantile delta mapping (QDM), as well as conventional stationary quantile mapping (SQM). The evaluation result of the bias-corrected AMRs indicated the significant reduction of the errors. Furthermore, the AMRs present obvious increasing trends from 1900 to 2010. With the bias-corrected values, we carried out nonstationary frequency analysis based on the time-varying location parameters of generalized extreme value (GEV) distribution. Design rainfalls with certain return periods were estimated based on the expected number of exceedance (ENE) interpretation. Although there is a significant range of uncertainty, the design quantiles by the median parameters showed the significant relative difference, from −30.8% to 42.8% for QDM, compared with the quantiles by the multi-decadal observations. Even though the AMRs from the reanalysis products are challenged by various errors such as quantile mapping (QM) and systematic errors, the results from the current study imply that the proposed scheme with employing the reanalysis product might be beneficial to predict the future evolution of extreme precipitation and to estimate the design rainfall accordingly.

Uncertainty in nonstationary frequency analysis of South Korea's daily rainfall peak over threshold excesses associated with covariates

Several methods have been proposed to analyze the frequency of nonstationary anomalies. The applicability of the nonstationary frequency analysis has been mainly evaluated based on the agreement between the time series data and the applied probability distribution. However, since the uncertainty in the parameter estimate of the probability distribution is the main source of uncertainty in frequency analysis, the uncertainty in the correspondence between samples and probability distribution is inevitably large. In this study, an extreme rainfall frequency analysis is performed that fits the peak over threshold series to the covariate-based nonstationary generalized Pareto distribution. By quantitatively evaluating the uncertainty of daily rainfall quantile estimates at 13 sites of the Korea Meteorological Administration using the Bayesian approach, we tried to evaluate the applicability of the nonstationary frequency analysis with a focus on uncertainty. The results indicated that the inclusion of dew point temperature (DPT) or surface air temperature (SAT) generally improved the goodness of fit of the model for the observed samples. The uncertainty of the estimated rainfall quantiles was evaluated by the confidence interval of the ensemble generated by the Markov chain Monte Carlo. The results showed that the width of the confidence interval of quantiles could be greatly amplified due to extreme values of the covariate. In order to compensate for the weakness of the nonstationary model exposed by the uncertainty, a method of specifying a reference value of a covariate corresponding to a nonexceedance probability has been proposed. The results of the study revealed that the reference covariate plays an important role in the reliability of the nonstationary model. In addition, when the reference covariate was given, it was confirmed that the uncertainty reduction in quantile estimates for the increase in the sample size was more pronounced in the nonstationary model. Finally, it was discussed how information on a global temperature rise could be integrated with a DPT or SAT-based nonstationary frequency analysis. Thus, a method to quantify the uncertainty of the rate of change in future quantiles due to global warming, using rainfall quantile ensembles obtained in the uncertainty analysis process, has been formulated.