Similarities and differences of hydrologic frequency distribution models and their parameter estimation problems
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摘要: 回顾了20世纪50年代对水文频率分布模型异同性的认识,分析了分布模型在统计特征上的相异性与共通性。在分布的几何形态相同的条件下,目前所用的分布模型中,仅3个参数的模型基本上是相异的。通过观察与实例分析,初步发现,取4个参数,有可能使模型有统一的求解结果。用数学方法能得到参数的唯一解,但多数方法是先计算出不确定性较大的CS值,继而据此算得其它一个或两个参数,故这种结果是一种初值,有待通过合理性分析,才能得到最终取用值。Abstract: The consensus since 1950s on the similarities and differences of hydrologic frequency distribution models is reviewed.The similarities and differences of statistical characteristics in these models are analyzed.Under the condition of having the same distribution of geometric shapes,the currently used models with only 3 parameters are essentially different.Observations and real case studies reveal that a unique solution might be existed if a 4-parameter model is considered.We have obtained a unique solution in model parameter estimation using mathematic methods.However,as discussed in the paper,most others first calculate the parameter CS value that is subjected to larger uncertainty and the CS value is then used in the calculation of other one or two parameters,which also contain larger uncertainty.As such,the results can only be taken as the initial estimation of model parameters.The rational analysis must be used to finalize the model parameters.
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