基于Copula函数的不完全降水序列频率计算方法研究

发布时间：2018-02-25 08:43

本文关键词： 频率分析不完全降水序列 Copula函数参数估计关中地区　出处：《西北农林科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：水文频率分析以水文数据为基础。在实际水文计算中,由于观测条件限制,一些测站数据较短,难以满足水文频率分析计算条件,不能为工程规划设计与管理提供合理的数据支撑。建立多维联合分布模型,合理利用邻近长序列测站的特征信息,提高水文频率分析精确度,是不完全水文序列频率计算方法的一种新途径。多变量分布模型在水文领域中的应用已较为成熟。大量应用研究表明,传统多变量分布模型以变量间线性关系为基础,而Copula函数可刻画变量间线性或者非线性关系,优势明显。本文在吸收国内外不完全水文频率分析方法的基础上,应用Copula函数理论,探究基于Copula函数的不完全降水序列频率计算方法。以陕西省关中地区年降水序列为研究对象,选取短序列测站为设计站,邻近长序列测站为参证站。首先,采用P-Ⅲ分布、Gamma分布和Gumbel分布对设计站及其参证站等时段长度序列进行单变量降水频率分析,采用矩法、最大熵法、极大似然法和概率权重矩法4种参数估计方法计算3种线型分布参数值。用2种拟合优度评价指标对每一种线型下各参数估计值进行拟合优度检验,获得设计站及其参证站等时段长度序列联合分布模型的边缘分布。通过拟合检验,评判所选单变量概率分布模型的拟合效果。然后,计算设计站及其参证站等时段长度序列秩相关系数,在此基础上,采用相关性指标法和极大似然法计算Copula函数参数q的值,并选用均方根误差法(RMSE)、赤池信息准则(AIC)和贝叶斯信息准则(BIC)作为拟合优度评价标准,选出各站拟合度较好的Copula函数。通过分析经验频率与理论频率联合拟合图效果,并结合A-D检验,判定所选Copula函数的优劣。最后,计算出基于Copula函数的不完全年降水序列参数估计值,并计算出设计站在该方法下年降水量设计值,并与单变量降水频率分析下年降水量设计值进行对比,探究基于Copula函数的不完全降水频率分析,以期为工程水文提供理论依据。研究取得以下主要结论:(1)采用P-Ⅲ分布、Gamma分布和Gumbel分布对设计站及其参证站等时段长度序列进行单变量年降水频率分析,拟合研究区年降水量值。拟合检验结果表明:P-Ⅲ分布、Gamma分布和Gumbel分布对关中地区年降水序列拟合效果良好,可以用来进行关中地区年降水量频率分析;P-Ⅲ分布采用最大熵法估计参数值,更能符合年降水量取值要求。(2)用Gumbel-Hougaard(G-H)copula函数、Frank copula函数、Clayton copula函数,构建设计站及其参证站等时段长度序列多变量概率分布模型。二维联合分布拟合检验结果表明:蓝田站与长安站、临潼站与长安站、临潼站与咸阳站、旬邑站与彬县站、岐山站与宝鸡站、凤翔站与宝鸡站、凤县站与太白站选用Frank copula函数,临潼站与渭南站、华阴站与潼关站选用Clayton copula函数,其余各组联合分布选用G-H copula函数,均能较好地反映实测点据的联合分布,可用来对设计站及其参证站等时段长度序列年降水量进行多变量频率分析。(3)在确立单变量分布模型和Copula联合分布模型基础上,计算出基于Copula函数的不完全降水序列参数估计值,并采用拟合标准差法(SEF)和最大相对误差绝对值法(MARD)两种拟合度评价方法进行基于Copula函数的不完全降水频率计算结果评价。Copula函数模拟结果和拟合度评价结果表明:基于Copula函数的不完全降水序列频率计算方法合理可行,可为短序列测站降水频率分析提供新的计算途径。(4)根据基于Copula函数的不完全降水序列参数估计值,绘制设计站在新分布参数下的年降水量频率曲线,并推算出不同频率下的年降水量设计值。结果表明,新频率曲线对实测数据的拟合效果较好,尤其在频率曲线的中低部拟合效果好。(5)以Frank Copula为例,采用蒙特卡洛试验法探究基于Copula函数的不完全降水序列频率计算方法统计性能。偏差和标准误差值计算结果表明:基于Copula函数的不完全降水序列频率计算方法不偏性与单变量降水频率分析基本相同,有效性优于单变量降水频率分析方法。
[Abstract]:Hydrological frequency analysis in hydrological data base. In the calculation of the actual hydrological observation, because of conditions, some station data is short, it is difficult to meet the calculation condition of hydrological frequency analysis can provide reasonable data support for engineering design and management planning. Establish a multi-dimensional distribution model combined, rational use of long sequences adjacent feature information station the improvement of accuracy of hydrological frequency analysis is a new way of calculation method for incomplete hydrological sequence frequency. The application of multivariate distribution model in hydrology has been mature. A large number of application research shows that the traditional multivariate distribution model with variable linear relationship as the foundation, and the Copula function variables or linear the nonlinear relationship, the advantage is obvious. This paper analysis on the domestic and foreign incomplete hydrological frequency method based on the application of Copula function theory, inquiry function is not based on Copula Complete precipitation frequency method. The annual precipitation sequence in Guanzhong area of Shaanxi Province as the research object, select the short series of station design for the station, near the station for a long sequence of reference station. Firstly, using P- III distribution, analysis of single variable precipitation frequency design of station and reference station time length sequence Gamma distribution distribution and Gumbel, using the moment method, the maximum entropy method, estimated 3 linear distribution values of maximum likelihood method and probability weighted moment method. 4 kinds of parameter values of goodness of fit of each parameter for each linear estimation using 2 goodness evaluation index, design parameter and edge distribution station station time sequence length of joint distribution model. Through the test, the fitting effect of judge menu bivariate probability distribution model. Then, design and calculation of station and reference station time length sequence rank correlation coefficient, on this basis On the calculation of the Copula function parameter Q value using correlation index method and maximum likelihood method, and the root mean square error method (RMSE), Akaike information criterion (AIC) and the Bias information criterion (BIC) as the fitness evaluation standard, we choose the station well fitted Copula function. Through the analysis of the empirical frequency with the theory of frequency combination fitting effects, combined with the A-D test, to determine the pros and cons of the selected Copula function. Finally, calculate the estimated value of Copula function based on the incomplete precipitation parameters, and calculate the design in the method of precipitation design value, and analysis of annual precipitation design value are compared with a single variable frequency of precipitation, explore the analysis of incomplete precipitation frequency based on Copula function, in order to provide theoretical basis for engineering hydrology. The research obtained the following main conclusions: (1) the P- III distribution, Gamma distribution and Gumbel distribution of the station and its design Reference station time length sequence analysis of single variable annual precipitation frequency, annual precipitation in study area. The value of fitting fitting test results show that the P- III distribution, Gamma distribution and Gumbel distribution of good fitting effect of annual precipitation sequence in Guanzhong area, can be used for the annual precipitation frequency analysis in Guanzhong area; P- distribution by maximum entropy method to estimate the parameter values, more in line with the annual precipitation value. (2) with Gumbel-Hougaard (G-H) copula Frank copula function, Clayton function, Copula function, design and construction of station and reference station time sequence length multivariate probability distribution model. The two-dimensional joint distribution fitting test results show that: Lantian station and Changan station. Lintong Railway Station and Changan station, Lintong Railway Station and XianYang Railway Station, Xunyi station and Binxian County station, Qishan station and the Baoji Railway Station, Fengxiang Railway Station and Baoji Railway Station, Feng Xian Railway Station and TaiBai Railway Station using Frank copula function, the Lintong Railway Station and the WeiNan Railway Station, Huayin station and the Tongguan Railway Station with Clayton copula function, the other groups using G-H copula joint distribution function, which can reflect the joint distribution of the data observed, can be used to analyze multi variable frequency of precipitation station design and reference station time length sequence. (3) in the establishment of a single variable distribution model and Copula based on the distribution model, calculate the estimated value of incomplete precipitation parameters based on Copula function, and the fitting standard deviation method (SEF) and the maximum absolute value of relative error method (MARD) simulation results and evaluation of the.Copula function fitting of the evaluation results show that incomplete precipitation frequency two fitting degree evaluation method based on the Copula function: incomplete precipitation frequency based on Copula function calculation method is reasonable and feasible, for short sequence measurement provides a new computation method of precipitation station (4) according to the base frequency. The estimated value of incomplete precipitation parameters to the Copula function, drawing the design parameters of the new station in the distribution of annual precipitation frequency curve, and calculates the annual precipitation design under different frequency values. The results show that the better fitting effect of the new frequency curve of the measured data, especially the low frequency curve fitting results in good. (5) to Frank Copula as an example, using Monte Carlo method to explore the statistical performance test calculation method of incomplete precipitation frequency based on Copula function. The standard deviation and error calculation results show that the calculation method of Copula function is not completely reduced water sequence frequency deviation frequency and precipitation is basically the same based on univariate analysis, analysis method the effectiveness is better than the single variable frequency of precipitation.

【学位授予单位】：西北农林科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P333

【相似文献】