Abstract:This study employs the Bayesian Markov Chain Monte Carlo (MCMC) method with the Metropolis-Hastings algorithm and maximum likelihood estimation (MLE) using a quadratic approximation of the likelihood function for the evaluation of uncertainties in low flow frequency analysis using a two-parameter Weibull distribution. The two types of prior distributions, a non-data-based distribution and a data-based distribution using regional information collected from neighbouring stations, are used to establish a posterior distribution. Eight case studies using the synthetic data with a sample size of 100, generated from two-parameter Weibull distribution, are performed to compare with results of analysis using MLE and Bayesian MCMC. Also, Bayesian MCMC and MLE are applied to 36 years of gauged data to validate the efficiency of the developed scheme. These examples illustrate the advantages of Bayesian MCMC and the limitations of MLE based on a quadratic approximation. From the point of view of uncertainty analysis, Bayesian MCMC is more effective than MLE using a quadratic approximation when the sample size is small. In particular, Bayesian MCMC method is more attractive than MLE based on a quadratic approximation because the sample size of low flow at the site of interest is mostly not enough to perform the low flow frequency analysis.
Hydrological responses are being impacted by both climate change and human activities. In particular, climate change and regional human activities have accelerated significantly during the last three decades in South Korea. The variation in runoff due to the two types of factors should be quantitatively investigated to aid effective water resources' planning and management. In water resources' planning, analysis using various time scales is useful where rainfall is unevenly distributed. However, few studies analyzed the impacts of these two factors over different time scales. In this study, hydrologic model-based approach and hydrologic sensitivity were used to separate the relative impacts of these two factors at monthly, seasonal and annual time scales in the Soyang Dam upper basin and the Seom River basin in South Korea. After trend analysis using the Mann-Kendall nonparametric test to identify the causes of gradual change, three techniques, such as the double mass curve method, Pettitt's test and the BCP (Bayesian change point) analysis, were used to detect change points caused by abrupt changes in the collected observed runoff. Soil and Water Assessment Tool (SWAT) models calibrated from the natural periods were used to calculate the impacts of human activities. Additionally, six Budyko-based methods were used to verify the results obtained from the hydrological-based approach. The results show that impacts of climate change have been stronger than those of human activities in the Soyang Dam upper basin, while the impacts of human activities have been stronger than those of climate change in the Seom River basin. Additionally, the quantitative characteristics of relative impacts due to these two factors were identified at the monthly, seasonal and annual time scales. Finally, we suggest that the procedure used in this study can be used as a reference for regional water resources' planning and management.
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