A new method of parameter estimation in data scarce regions is valuable for bivariate hydrological extreme frequency analysis. This paper proposes a new method of parameter estimation (maximum entropy estimation, MEE) for both Gumbel and Gumbel-Hougaard copula in situations when insufficient data are available. MEE requires only the lower and upper bounds of two hydrological variables. To test our new method, two experiments to model the joint distribution of the maximum daily precipitation at two pairs of stations on the tributaries of Heihe and Jinghe River, respectively, were performed and compared with the method of moments, correlation index estimation, and maximum likelihood estimation, which require a large amount of data. Both experiments show that for the Ye Niugou and Qilian stations, the performance of MEE is nearly identical to those of the conventional methods. For the Xifeng and Huanxian stations, MEE can capture information indicating that the maximum daily precipitation at the Xifeng and Huanxian stations has an upper tail dependence, whereas the results generated by correlation index estimation and maximum likelihood estimation are unreasonable. Moreover, MEE is proved to be generally reliable and robust by many simulations under three different situations. The Gumbel-Hougaard copula with MEE can also be applied to the bivariate frequency analysis of other extreme events in data-scarce regions.
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The Yellow River is one of the rivers with the largest amount of sediment in the world. The amount of incoming sediment has an important impact on water resources management, sediment regulation schemes, and the construction of water conservancy projects. The Loess Plateau is the main source of sediment in the Yellow River Basin. Floods caused by extreme precipitation are the primary driving forces of soil erosion in the Loess Plateau. In this study, we constructed the extreme precipitation scenarios based on historical extreme precipitation records in the main sediment-yielding area in the middle reaches of the Yellow River. The amount of sediment yield under current land surface conditions was estimated according to the relationship between extreme precipitation and sediment yield observations in the historical period. The results showed that the extreme rainfall scenario of the study area reaches to 159.9 mm, corresponding to a recurrence period of 460 years. The corresponding annual sediment yield under the current land surface condition was range from 0.821 billion tons to 1.899 billion tons, and the median annual sediment yield is 1.355 billion tons, of which more than 91.9% of sediment yields come from the Hekouzhen to Longmen sectionand the Jinghe River basin. Therefore, even though the vegetation of the Loess Plateau has been greatly improved, and a large number of terraces and check dams have been built, the flood control and key project operation of the Yellow River still need to be prepared to deal with the large amount of sediment transport.
Simulating the hydrological processes of an inland river basin can help provide the scientific guidance to the policies of water allocation among different subbasins and water resource management groups within the subbasins. However, it is difficult to simulate the hydrological processes of an inland river basin with hydrological models due to the non-consistent hydrological characteristics of the entire basin. This study presents a solution to this problem with a case study about the hydrological process simulation in an inland river basin in China, Heihe River basin. It is divided into the upper, middle, and lower reaches based on the distinctive hydrological characteristics in the Heihe River basin, and three hydrological models are selected, applied, and tested to simulate the hydrological cycling processes for each reach. The upper reach is the contributing area with the complex runoff generation processes, therefore, the hydrological informatic modeling system (HIMS) is utilized due to its combined runoff generation mechanisms. The middle reach has strong impacts of intensive human activities on the interactions of surface and subsurface flows, so a conceptual water balance model is applied to simulate the water balance process. For the lower reach, as the dissipative area with groundwater dominating the hydrological process, a groundwater modeling system with the embedment of MODFLOW model is applied to simulate the groundwater dynamics. Statistical parameters and water balance analysis prove that the three models have excellent performances in simulating the hydrological process of the three reaches. Therefore, it is an effective way to simulate the hydrological process of inland river basin with multiple hydrological models according to the characteristics of each subbasin.
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