本文關(guān)鍵詞： 頻率分析 不完全降水序列 Copula函數(shù) 參數(shù)估計(jì) 關(guān)中地區(qū)　出處：《西北農(nóng)林科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：水文頻率分析以水文數(shù)據(jù)為基礎(chǔ)。在實(shí)際水文計(jì)算中,由于觀測(cè)條件限制,一些測(cè)站數(shù)據(jù)較短,難以滿足水文頻率分析計(jì)算條件,不能為工程規(guī)劃設(shè)計(jì)與管理提供合理的數(shù)據(jù)支撐。建立多維聯(lián)合分布模型,合理利用鄰近長(zhǎng)序列測(cè)站的特征信息,提高水文頻率分析精確度,是不完全水文序列頻率計(jì)算方法的一種新途徑。多變量分布模型在水文領(lǐng)域中的應(yīng)用已較為成熟。大量應(yīng)用研究表明,傳統(tǒng)多變量分布模型以變量間線性關(guān)系為基礎(chǔ),而Copula函數(shù)可刻畫變量間線性或者非線性關(guān)系,優(yōu)勢(shì)明顯。本文在吸收國(guó)內(nèi)外不完全水文頻率分析方法的基礎(chǔ)上,應(yīng)用Copula函數(shù)理論,探究基于Copula函數(shù)的不完全降水序列頻率計(jì)算方法。以陜西省關(guān)中地區(qū)年降水序列為研究對(duì)象,選取短序列測(cè)站為設(shè)計(jì)站,鄰近長(zhǎng)序列測(cè)站為參證站。首先,采用P-Ⅲ分布、Gamma分布和Gumbel分布對(duì)設(shè)計(jì)站及其參證站等時(shí)段長(zhǎng)度序列進(jìn)行單變量降水頻率分析,采用矩法、最大熵法、極大似然法和概率權(quán)重矩法4種參數(shù)估計(jì)方法計(jì)算3種線型分布參數(shù)值。用2種擬合優(yōu)度評(píng)價(jià)指標(biāo)對(duì)每一種線型下各參數(shù)估計(jì)值進(jìn)行擬合優(yōu)度檢驗(yàn),獲得設(shè)計(jì)站及其參證站等時(shí)段長(zhǎng)度序列聯(lián)合分布模型的邊緣分布。通過擬合檢驗(yàn),評(píng)判所選單變量概率分布模型的擬合效果。然后,計(jì)算設(shè)計(jì)站及其參證站等時(shí)段長(zhǎng)度序列秩相關(guān)系數(shù),在此基礎(chǔ)上,采用相關(guān)性指標(biāo)法和極大似然法計(jì)算Copula函數(shù)參數(shù)q的值,并選用均方根誤差法(RMSE)、赤池信息準(zhǔn)則(AIC)和貝葉斯信息準(zhǔn)則(BIC)作為擬合優(yōu)度評(píng)價(jià)標(biāo)準(zhǔn),選出各站擬合度較好的Copula函數(shù)。通過分析經(jīng)驗(yàn)頻率與理論頻率聯(lián)合擬合圖效果,并結(jié)合A-D檢驗(yàn),判定所選Copula函數(shù)的優(yōu)劣。最后,計(jì)算出基于Copula函數(shù)的不完全年降水序列參數(shù)估計(jì)值,并計(jì)算出設(shè)計(jì)站在該方法下年降水量設(shè)計(jì)值,并與單變量降水頻率分析下年降水量設(shè)計(jì)值進(jìn)行對(duì)比,探究基于Copula函數(shù)的不完全降水頻率分析,以期為工程水文提供理論依據(jù)。研究取得以下主要結(jié)論:(1)采用P-Ⅲ分布、Gamma分布和Gumbel分布對(duì)設(shè)計(jì)站及其參證站等時(shí)段長(zhǎng)度序列進(jìn)行單變量年降水頻率分析,擬合研究區(qū)年降水量值。擬合檢驗(yàn)結(jié)果表明:P-Ⅲ分布、Gamma分布和Gumbel分布對(duì)關(guān)中地區(qū)年降水序列擬合效果良好,可以用來進(jìn)行關(guān)中地區(qū)年降水量頻率分析;P-Ⅲ分布采用最大熵法估計(jì)參數(shù)值,更能符合年降水量取值要求。(2)用Gumbel-Hougaard(G-H)copula函數(shù)、Frank copula函數(shù)、Clayton copula函數(shù),構(gòu)建設(shè)計(jì)站及其參證站等時(shí)段長(zhǎng)度序列多變量概率分布模型。二維聯(lián)合分布擬合檢驗(yàn)結(jié)果表明:藍(lán)田站與長(zhǎng)安站、臨潼站與長(zhǎng)安站、臨潼站與咸陽站、旬邑站與彬縣站、岐山站與寶雞站、鳳翔站與寶雞站、鳳縣站與太白站選用Frank copula函數(shù),臨潼站與渭南站、華陰站與潼關(guān)站選用Clayton copula函數(shù),其余各組聯(lián)合分布選用G-H copula函數(shù),均能較好地反映實(shí)測(cè)點(diǎn)據(jù)的聯(lián)合分布,可用來對(duì)設(shè)計(jì)站及其參證站等時(shí)段長(zhǎng)度序列年降水量進(jìn)行多變量頻率分析。(3)在確立單變量分布模型和Copula聯(lián)合分布模型基礎(chǔ)上,計(jì)算出基于Copula函數(shù)的不完全降水序列參數(shù)估計(jì)值,并采用擬合標(biāo)準(zhǔn)差法(SEF)和最大相對(duì)誤差絕對(duì)值法(MARD)兩種擬合度評(píng)價(jià)方法進(jìn)行基于Copula函數(shù)的不完全降水頻率計(jì)算結(jié)果評(píng)價(jià)。Copula函數(shù)模擬結(jié)果和擬合度評(píng)價(jià)結(jié)果表明:基于Copula函數(shù)的不完全降水序列頻率計(jì)算方法合理可行,可為短序列測(cè)站降水頻率分析提供新的計(jì)算途徑。(4)根據(jù)基于Copula函數(shù)的不完全降水序列參數(shù)估計(jì)值,繪制設(shè)計(jì)站在新分布參數(shù)下的年降水量頻率曲線,并推算出不同頻率下的年降水量設(shè)計(jì)值。結(jié)果表明,新頻率曲線對(duì)實(shí)測(cè)數(shù)據(jù)的擬合效果較好,尤其在頻率曲線的中低部擬合效果好。(5)以Frank Copula為例,采用蒙特卡洛試驗(yàn)法探究基于Copula函數(shù)的不完全降水序列頻率計(jì)算方法統(tǒng)計(jì)性能。偏差和標(biāo)準(zhǔn)誤差值計(jì)算結(jié)果表明:基于Copula函數(shù)的不完全降水序列頻率計(jì)算方法不偏性與單變量降水頻率分析基本相同,有效性優(yōu)于單變量降水頻率分析方法。
[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.

【學(xué)位授予單位】：西北農(nóng)林科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P333

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本文編號(hào)：1533731