小样本观测资料条件下的耿贝尔极值水文频率分析模型

The prediction of hydrometeorological extreme elements is valuable for preventing natural disasters, controlling and reducing losses. However, the methods for analyzing hydrological frequency are based on a large amount of data, and the studies on hydrological frequency analysis cannot be made in data scarcity regions. This paper builds a Gumbel hydrological frequency analysis model in situations when insufficient data are available, and proposes a new method of parameter estimation (maximum entropy estimation, MEE) for Gumbel distribution. The maximum entropy estimation requires only the lower and upper bounds of hydrology variables. The main steps of the Gumbel hydrological frequency analysis model are as follows: Firstly, the entropy of Gumbel distribution is defined. Secondly, an optimization model is built to estimate the parameters of Gumbel distribution based on the maximum entropy principle. Finally, a K-S goodness of fit test is made for Gumbel distribution model. The experiments of the hydrological frequency analysis of the maximum daily precipitation at the Yellow River were performed to validate the effect of MEE. All the experiments showed that the performance of the maximum entropy estimation was nearly identical to those of the conventional methods of parameter estimation which requires a large amount of data. Furthermore, thirty-three simulations were performed to validate the reliability of MEE in situations when insufficient data were available. The simulations show that the MEE has the following potentials: The performance of three parameter estimation methods are almost identical when the sample size is greater than 25. However, the MEE performs the best and the maximum likelihood estimation performs worst where the sample size is less than 15. Moreover, the MEE is not sensitive to the accuracy of the minimum value but sensitive to that of the maximum value.