The Extreme Minimum Distribution Of Stationary Hydrologic Time Series

The random hydrologic time series has rich statistical properties in the time domain and the frequency domain.Run theory,a basic analytical method of discrete random process,which can reflect the characteristics of time domain and frequency domain at the same time,has been widely used in the field of hydrological drought,wave groups and other research fields.However,most of the probability analysis of hydrologic time series based on run theory is aimed at the maximum value of hydrologic time series.The theoretical results are mostly used in flood and drought researches.In addition,the extreme value distribution of the random hydrologic time series implies more than these,and the minimum value of the run also has an important practical engineering significance.Therefore,this paper takes the stationary hydrologic time series as the research object,and analyzes the minimum value of the runs,which makes use of the first-order Markov chain to simplify the problem.And the theoretical method is applied to determine the construction water level of the inland river and other practical problems.The main research contents and conclusions are as follows:①This paper reviews the research results of the extreme value of the hydrologic time series,and verifies some basic theoretical formulas,and points out the shortcomings of the existing theoretical method for the hydrologic time series;②Based on the discussion of the shortcomings in the existing theory of the maximum value of run,an improved analysis theory for the extreme value of the run is put forward.The theory takes the relationship among the total run,the positive run and the negative run into account in the hydrologic time series.Taking the length of the total run and the length of the negative run as an example,the probability space is constructed by using the numerical relationship between them,and the probability calculation of the relevant variable is limited to the region;③Using the improved analysis theory,every important variable’s probability characteristics are re-deduced in the run extreme value analysis.At the same time,two approximate calculation methods of hydrologic time series of the maximum value of run are proposed.Taking the annual runoff of a river as an example,the two approximate methods are compared with the method in the literature.It shows that the results of theoretical methods are in good agreement with the literature.It means that,to a certain extent,the theoretical methods are valid in this case;④A study of the extreme minimum value of the run-length is carried out in this paper,and the approximate calculation method of the extreme minimum value of the hydrologic time series is obtained by using different ways.The above-mentioned run extreme theory is applied to determine the construction water level of the inland river channel waterway construction.The probability of each target corresponding to the three different construction water level schemes is calculated and compared,which infers a new method for the determination of construction water level.Based on the previous work on the maximum value of the two-state run,the probability characteristics of the extreme value of the stationary random hydrologic time series are further studied,which proposes the probability analysis theory of the minimum value of the run.And the theoretical method is applied to the practical problem,such as determining the construction water level of the island river.This theory enriches the practical application of the random hydrologic time series run analysis method in the hydraulic engineering.