Linear selecting method in computing process of hydrological frequency

Abstract

The invention discloses a linear selecting method in the computing process of hydrological frequency, which includes: firstly, respectively selecting reasonable parameter prior distribution types, initial parameter samples and likelihood functions according to known regional prior information, performing parameter posterior distribution sampling by means of AM-MCMC (adaptive metropolis-markov chain monte carlo) to obtain parameter posterior distribution sampling results corresponding to each line type; analyzing and quantitatively describing probability distribution of the parameter posterior distribution sampling results by means of the POME (principle of maximum entropy) to obtain various parameter posterior distribution formulas in different line types, utilizing the method of approximate summation among application parameters to substitute for linear edge distribution integral process, solving bayes factor Bji of the hydrological line type Mj relative to the line type Mi according to the following formula; and finally selecting and comprehensively analyzing the hydrological line types on the basis of solving the bayes factor Bji. By the linear selecting method, uncertainty of the parameters analyzing and describing are analyzed reasonably, so that analyzed and computed results are improved evidently.

Description

[0001] technical field [0002] The invention relates to the fields of hydrology and water resources, in particular to a method for line type selection in the hydrological frequency calculation process. Background technique [0003] Two key issues are involved in the hydrological frequency calculation process: line type selection and parameter estimation. Due to the joint action and influence of many random and complex factors in the hydrological cycle (Liu Guangwen. Hydrological Analysis and Calculation. Beijing: Water Conservancy and Electric Power Press, 1989; Rui Xiaofang. Several issues in the study of watershed hydrological models. Advances in Water Science, 1997, 8(1): 94-98; Guo Shenglian. Design flood research progress and evaluation. Beijing: China Water Conservancy and Hydropower Press, 2005; Sang YF, Wang D, Wu JC, et al . The relation between periods' identification and noises in hydrologic series data. Journal of Hydrology, 2009, 368(1-4): 165-177), the hydrol...

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Problems solved by technology

This method has a sound theoretical basis, but there are two difficult problems in solving the Bayesian factor: the determination of the parameter prior distribution and the numerical integration of the linear marginal distribution

But when formula (1) is used to solve Bayesian factor, the parameter prior distribution π ( θ i ) is difficult to determine and select, and it is also difficult to integrate the linear marginal distribution

[0016] The BIC criterion (equation (5)) is a commonly used approximate processing method (Kass R E, Raftery A E. Bayes Factors. Journal of the American Statistical Association, 1995, 90(430): 773-795), but there are some defects : (1) Since its essence is to solve the Bayesian factor after optimizing the parameters by the maximum likelihood method, when the parameters in the P-III line type C s When >2, the maximum likelihood method has no solution (Jin Guangyan. Maximum likelihood method estimation τ Notes on distribution parameters. Water Resources Research, 2008, 29(2): 14-17), so this method has certain limitations; (2) There are also uncertainties in parameters in practice, and the essence and core of the BIC criterion is Parameter optimization does not analyze and describe the uncertainty of parameters

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