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基于交互熵原理的水文分布参数估计研究

ISSN号：1671-9387
期刊名称：《西北农林科技大学学报：自然科学版》
时间：0
分类：P333.9[天文地球—水文科学;水利工程—水文学及水资源;天文地球—地球物理学]
作者机构：西北农林科技大学水利与建筑工程学院,陕西杨凌712100
相关基金：国家自然科学基金项目（51179160,50879070,50579065）,高等学校博士学科点专项科研基金项目（201102041i0017）.

关键词：水文分布, 参数估计, 交互熵法, Gumbel分布, 分位数对约束, hydrological distribution, parameter estimation, cross entropy method, Gumbel distribu- tion, fractile-pair constraints

中文摘要：

【目的】研究交互熵法进行水文分布参数估计的普适性。【方法】应用最小交互熵原理研究Gumbel分布参数估计，在此基础上应用蒙特卡洛试验检验交互熵法统计性能，然后结合矩法和线性矩法等传统参数估计方法，以陕西省关中地区周至、武功、蒲城、礼泉、白水、潼关6个水文站年降水序列为例，计算年降水量设计值并拟合实测值序列，利用累积相对偏差平方和评价理论年降水量频率曲线对实测值序列的拟合效果。【结果】蒙特卡洛试验检验表明，交互熵法所求设计值的有效性指标估计量标准偏差（SE）和均方根误差（RMsE）小于矩法和线性矩法，偏差指标控制在7％以内；交互熵法估计周至、武功、蒲城、礼泉、白水、潼关6个水文站的累积相对偏差平方和分别为0.00001768，0.00006562，0.00001966，0.00006300，0.00001412和0.00001661，线性矩法估计上述6站的累积相对偏差平方和分别为0.00008762，0.00009355，0.00008652，0.00010139，0.00006515和0.00006905，矩法估计上述6站的累积相对偏差平方和分别为0.00010874，0.00012540，0.00009241，0.00012765，0.00008549和0.00009357。由此可知，交互熵法不仅具有较好的有效性与合理的不偏性，而且与实测序列的拟合效果也明显优于传统方法。【结论】交互熵法是一种可行的水文分布参数估计方法，能有效提高Gumbel分布参数的估计精度。

英文摘要：

[Objective] This paper studied the universal applicability of the cross entropy method in es- timation of hydrology frequency distribution parameters. [Method] Kullback minimum cross entropy prin- ciple was used to estimate the parameters of Gumbel distribution. Then, Monte Carlo experiments were performed to verify its statistical performance. Observed precipitations at 6 hydrologic stations, Zhouzhi, Wugong,Pucheng, Liquan, Baishui and Tongguan in Central Shaanxi, were compared with predictions and the fitting results were evaluated using cumulative square error. [Result] Monte Carlo experiments indica- ted that the SE and RMSE of cross entropy method were less than those of moments method and L-mo- ments method. The bias of cross entropy method was less than 7%. The cumulative of square errors of cross entropy method for the 6 hydrologic stations of Zhouzhi, Wugong, Pucheng, Liquan, Baishui, and Tongguan were 0. 000 017 68,0. 000 065 62,0. 000 019 66,0. 000 063 00,0. 000 014 12,and 0. 000 016 61, those of L-moments method were 0. 000 087 62,0. 000 093 55,0. 000 086 52,0. 000 101 39,0. 000 065 15, and 0. 000 069 05,while those of moments method were 0. 000 108 74,0. 000 125 40,0. 000 092 41, 0. 000 127 65,0. 000 085 49, and 0. 000 093 57, respectively. The cross entropy method not only possessed good effectiveness and reasonable non-biasedness,but also fitted better with the observed data series than traditional methods. [Conclusion] Cross entropy method is a feasible method for parameter estimation,and it can effectively improve the estimation precision of Gumbel distribution parameters.

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