渭河流域主要河流水文干旱特性研究
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摘要
本文研究了渭河流域主要河流径流序列的变化特性和丰枯变化及遭遇情况。结合国内外水文干旱要素概率分布的研究成果,利用游程理论、极值理论及随机理论,探讨了不同分布水文序列的极限水文干旱要素概率分布和特征值;并应用解析法和模拟法进行了对比分析;借助Copula函数,建立了水文干旱双变量概率模型,并用泾河和北洛河的月径流资料对其做了检验。本研究取得如下主要结论:
(1)分析了渭河流域主要河流径流变化特性。渭河流域主要河流的径流长期变化趋势呈下降趋势;年径流序列有较强的自相依性和持续性;丰枯变化具有较高的同步性;径流序列年内分配不均匀,多集中在7、8月份。
(2)研究了渭河流域主要河流丰枯变化规律。渭河流域主要河流年径流序列有转枯的趋势,转枯概率大于转丰概率,对用水十分不利;连多连少概率分析表明,单独出现多水与单独出现少水相比,多水年平均为5.82次,少水年平均为5.27次,比多水年略少。但连续2年以上的少水年为5.81次,比连续2年以上的多水年4.91次高。相应游程概率连续2年多水略高于少水,分别为24%、22%,而3年连续多水概率为13%低于3年连续少水概率14%,连续4年,5年以及5年以上的概率也是少水大于多水,反映易出现少水事件;从游程平均连续年数看,多水集团游程连续年数为1.57~2.60,平均为2.16;少水集团游程连续年数为0.96~3.86,平均为2.83。游程平均强度多水集团为0.26~6.62,平均为2.40;少水集团为0.15~5.42,平均为1.88。渭河流域单独多(少)水年出现的概率比连续多(少)水年出现的概率大,单独多水年比单独少水年出现的概率高,而连续多(少)水年出现概率情况正好相反,连续多水年比连续少水年出现的概率低;表明该流域容易受到干旱的威胁,不足两年就可能有一年不利的状态出现。
(3)揭示了渭河流域主要河流丰枯遭遇规律。由丰枯遭遇分析可知,丰枯同步频率中,所研究的三种遭遇测站(林家村-千阳、黑峪口-鹦鸽、状头-张家山)较易发生同枯现象,在丰枯异步频率中,发生枯丰组合的频率较小。条件概率分析表明,枯水条件概率均大于丰水概率,即在前一个测站径流状况已知的情况下,后一测站的发生枯水的概率较大。
(4)研究了水文干旱变量概率分布特性,指出了其影响要素和随之变化规律。干旱历时和干旱烈度概率分布特性研究表明,负交互点数和长期干旱历时概率分布的计算公式具有较好的精度,只是由于资料长度的限制,在个别站出现了较大的偏差;解析法和模拟法得出的结果是一致的。干旱烈度的概率分布是径流序列均值、截取水平及偏差系数的函数;不同分布的水文序列,对数正态分布的极限干旱历时和干旱烈度的期望值均大于gamma分布和正态分布的期望值,利用这一特点可以在水文序列分布未知时,对其在一定时期内的极限干旱变量做出区间估计。一定时期内极限干旱变量期望值与序列一阶自相关系数,偏态系数(偏差系数)存在正相关系。应用于渭河流域不同时期内极限水文干旱分析表明,50年内,渭河流域出现极限干旱历时的期望值为5～9年,100年内渭河流域发生极限干旱历时期望值在6～12年之间变化。
(5)利用Copula函数建立了水文干旱双变量概率分布,并借助其尾部相关性分析,量化了风险。干旱历时与干旱烈度具有很高的相关性,两者边际分布很难全面反映真实干旱特性,而利用Copula函数建立干旱历时与干旱烈度双变量分布可以弥补边际分布这一不足,全面考虑了干旱历时与干旱烈度的相互组合及条件组合情况;通过对Copula函数的尾部相关性分析,管理者就可以根据尾部相关性,预测当干旱历时发生大幅度变化时干旱烈度发生大幅度变化的概率,这在风险管理中是很重要的。以状头站为例,当干旱历时超过q0 .95时,根据它与干旱烈度的尾部相关性,可以说,干旱烈度超过q0 .95的概率是34.48%。
The charateristics of runoff series of main rivers in Weihe River basin were studied in this paper, which involved runoff traits, high and low streamflow and encounter between high and low streamflow in different situations. Combination with the results of probability distribution of hydrologic drought variables which have been known and using run theory, extreme theory and stochastic theory, the probability distribution and charateristic value of critical hydrologic drought factors were analyzed, which the underlying hydrologic series were followed by different distributions. Meanwhile, Comparison between simulation and analytical methods was completed. Bivariate probability model of hydrologic drought was established by Copula function, which was tested through monthly streamflow series of Jinghe river and Beiluohe river. The main results are as follows:
(1) Runoff charateristics of main rivers in Weihe River basin were analyzed. Runoff of main rivers in Weihe River basin had a descend tendency. The annual runoff existed strong auto-correlation and persistence. Change between high and low flow exhibited good synchronization. The distribution of annual runoff in month was unequal, which concentrated in July and August.
(2) Transition between high and low flow of mai rivers in Weihe River basin was studied. The tendency of transition to low existed, the transitional probability of low flow was bigger than high flow, which was harm to water utilization. The probability analysis of several low or high flow showed that one-year high low occurred with the mean of 5.82 times, which was larger than one-year low flow with 5.27 times. More than 2-year low flow took place with the mean of 5.81 times which was higher than 4.91 times of more than 2-year high flow. The run probability analysis indicated that the probability of 2-year high flow was higher slightly than 2-year low flow, which were 24% and 22%,respectively. However, the probability of 3-year high flow with 13% was lower than 14% of 3-year low flow, which more than 3-year situation had the same results. The consecutive years of high flow group were between 1.57 and 2.60 years, the mean was 2.16 years. The consecutive years of low flow group were between 0.96 and 3.86 years, the mean was 2.83 years. The intensity of high flow group were from 0.26 to 6.62, the mean was 2.40. The intensity of low flow group were from 0.15 to 5.42, the mean was 1.88. In Weihe River basin, the probability of one-year high or low flow was higher than consecutive year high or low flow, the probability of one-year high flow was bigger than one-year low flow. Otherwise, the probability of consecutive year high flow was lower than consecutive year low flow, which showed that Weihe River basin was easy to threated by drought and there was a drought occurred in less than 2 years.
(3) Encounter of high flow and low flow of main rivers in Weihe River basin was considered. The results indicated that low flow state that three encounter stations which were Linjiacun-Qianyang, Heiyukou-Yingge and Zhuangtou-Zhangjiashan,were in the same year, was easy to happen, and low-high combination frequency was small. The analysis of conditional probability indicated that the conditional probability of low flow was bigger than high flow when the runoff state of foremore station was known.
(4) The probability distribution of hydrologic drought variables and its affected factors were analyzed. The results indicated that the formulations of negative acrossing and probability distribution of drought duration were accuracy except some errors in few stations due to the length of runoff series, the results from simulation and analytical method were coherent, the expected values of critical drought duration and severity of underlying hydrologic series with log-norm distribution were bigger than gamma distribution and norm distribution, which can be used to estimate the scope of critical drought variables in a certain period when the distribution of runoff series was unknown, the expected values of critical drought variable existed positive correlation with first-order auto-coefficient and skewed coefficient of runoff series. With application of above results in Weihe River basin, the results showed the expected values of critical drought duration in 50 years were from 5 years to 9 years, which were between 6 years and 12 years in 100 years.
(5) The probabilty distribution of bivariable hydrologic drought was developed by Copula function, and the drought risk was measured through tail-correlation of Copula function. There was a high correlation between drought duration and drought severity, which marginal distribution is difficult to reflect real drought characteristic. The bivariable hydrologic drought model by Copula function avioded the deficiency mentioned above, which included different combination of drought severity and drought duration. The supervisor can predict the probability of drought severity with a certain level when drought duration with the same level happened through tail correlation analysis, which was very important in risk management. For instance, it was said that the probability of drought severity more than 0.95 percentail was 34.48% when drought duration more than 0.95 percentail according to tail correlation analysis.
(1)分析了渭河流域主要河流径流变化特性。渭河流域主要河流的径流长期变化趋势呈下降趋势;年径流序列有较强的自相依性和持续性;丰枯变化具有较高的同步性;径流序列年内分配不均匀,多集中在7、8月份。
(2)研究了渭河流域主要河流丰枯变化规律。渭河流域主要河流年径流序列有转枯的趋势,转枯概率大于转丰概率,对用水十分不利;连多连少概率分析表明,单独出现多水与单独出现少水相比,多水年平均为5.82次,少水年平均为5.27次,比多水年略少。但连续2年以上的少水年为5.81次,比连续2年以上的多水年4.91次高。相应游程概率连续2年多水略高于少水,分别为24%、22%,而3年连续多水概率为13%低于3年连续少水概率14%,连续4年,5年以及5年以上的概率也是少水大于多水,反映易出现少水事件;从游程平均连续年数看,多水集团游程连续年数为1.57~2.60,平均为2.16;少水集团游程连续年数为0.96~3.86,平均为2.83。游程平均强度多水集团为0.26~6.62,平均为2.40;少水集团为0.15~5.42,平均为1.88。渭河流域单独多(少)水年出现的概率比连续多(少)水年出现的概率大,单独多水年比单独少水年出现的概率高,而连续多(少)水年出现概率情况正好相反,连续多水年比连续少水年出现的概率低;表明该流域容易受到干旱的威胁,不足两年就可能有一年不利的状态出现。
(3)揭示了渭河流域主要河流丰枯遭遇规律。由丰枯遭遇分析可知,丰枯同步频率中,所研究的三种遭遇测站(林家村-千阳、黑峪口-鹦鸽、状头-张家山)较易发生同枯现象,在丰枯异步频率中,发生枯丰组合的频率较小。条件概率分析表明,枯水条件概率均大于丰水概率,即在前一个测站径流状况已知的情况下,后一测站的发生枯水的概率较大。
(4)研究了水文干旱变量概率分布特性,指出了其影响要素和随之变化规律。干旱历时和干旱烈度概率分布特性研究表明,负交互点数和长期干旱历时概率分布的计算公式具有较好的精度,只是由于资料长度的限制,在个别站出现了较大的偏差;解析法和模拟法得出的结果是一致的。干旱烈度的概率分布是径流序列均值、截取水平及偏差系数的函数;不同分布的水文序列,对数正态分布的极限干旱历时和干旱烈度的期望值均大于gamma分布和正态分布的期望值,利用这一特点可以在水文序列分布未知时,对其在一定时期内的极限干旱变量做出区间估计。一定时期内极限干旱变量期望值与序列一阶自相关系数,偏态系数(偏差系数)存在正相关系。应用于渭河流域不同时期内极限水文干旱分析表明,50年内,渭河流域出现极限干旱历时的期望值为5～9年,100年内渭河流域发生极限干旱历时期望值在6～12年之间变化。
(5)利用Copula函数建立了水文干旱双变量概率分布,并借助其尾部相关性分析,量化了风险。干旱历时与干旱烈度具有很高的相关性,两者边际分布很难全面反映真实干旱特性,而利用Copula函数建立干旱历时与干旱烈度双变量分布可以弥补边际分布这一不足,全面考虑了干旱历时与干旱烈度的相互组合及条件组合情况;通过对Copula函数的尾部相关性分析,管理者就可以根据尾部相关性,预测当干旱历时发生大幅度变化时干旱烈度发生大幅度变化的概率,这在风险管理中是很重要的。以状头站为例,当干旱历时超过q0 .95时,根据它与干旱烈度的尾部相关性,可以说,干旱烈度超过q0 .95的概率是34.48%。
The charateristics of runoff series of main rivers in Weihe River basin were studied in this paper, which involved runoff traits, high and low streamflow and encounter between high and low streamflow in different situations. Combination with the results of probability distribution of hydrologic drought variables which have been known and using run theory, extreme theory and stochastic theory, the probability distribution and charateristic value of critical hydrologic drought factors were analyzed, which the underlying hydrologic series were followed by different distributions. Meanwhile, Comparison between simulation and analytical methods was completed. Bivariate probability model of hydrologic drought was established by Copula function, which was tested through monthly streamflow series of Jinghe river and Beiluohe river. The main results are as follows:
(1) Runoff charateristics of main rivers in Weihe River basin were analyzed. Runoff of main rivers in Weihe River basin had a descend tendency. The annual runoff existed strong auto-correlation and persistence. Change between high and low flow exhibited good synchronization. The distribution of annual runoff in month was unequal, which concentrated in July and August.
(2) Transition between high and low flow of mai rivers in Weihe River basin was studied. The tendency of transition to low existed, the transitional probability of low flow was bigger than high flow, which was harm to water utilization. The probability analysis of several low or high flow showed that one-year high low occurred with the mean of 5.82 times, which was larger than one-year low flow with 5.27 times. More than 2-year low flow took place with the mean of 5.81 times which was higher than 4.91 times of more than 2-year high flow. The run probability analysis indicated that the probability of 2-year high flow was higher slightly than 2-year low flow, which were 24% and 22%,respectively. However, the probability of 3-year high flow with 13% was lower than 14% of 3-year low flow, which more than 3-year situation had the same results. The consecutive years of high flow group were between 1.57 and 2.60 years, the mean was 2.16 years. The consecutive years of low flow group were between 0.96 and 3.86 years, the mean was 2.83 years. The intensity of high flow group were from 0.26 to 6.62, the mean was 2.40. The intensity of low flow group were from 0.15 to 5.42, the mean was 1.88. In Weihe River basin, the probability of one-year high or low flow was higher than consecutive year high or low flow, the probability of one-year high flow was bigger than one-year low flow. Otherwise, the probability of consecutive year high flow was lower than consecutive year low flow, which showed that Weihe River basin was easy to threated by drought and there was a drought occurred in less than 2 years.
(3) Encounter of high flow and low flow of main rivers in Weihe River basin was considered. The results indicated that low flow state that three encounter stations which were Linjiacun-Qianyang, Heiyukou-Yingge and Zhuangtou-Zhangjiashan,were in the same year, was easy to happen, and low-high combination frequency was small. The analysis of conditional probability indicated that the conditional probability of low flow was bigger than high flow when the runoff state of foremore station was known.
(4) The probability distribution of hydrologic drought variables and its affected factors were analyzed. The results indicated that the formulations of negative acrossing and probability distribution of drought duration were accuracy except some errors in few stations due to the length of runoff series, the results from simulation and analytical method were coherent, the expected values of critical drought duration and severity of underlying hydrologic series with log-norm distribution were bigger than gamma distribution and norm distribution, which can be used to estimate the scope of critical drought variables in a certain period when the distribution of runoff series was unknown, the expected values of critical drought variable existed positive correlation with first-order auto-coefficient and skewed coefficient of runoff series. With application of above results in Weihe River basin, the results showed the expected values of critical drought duration in 50 years were from 5 years to 9 years, which were between 6 years and 12 years in 100 years.
(5) The probabilty distribution of bivariable hydrologic drought was developed by Copula function, and the drought risk was measured through tail-correlation of Copula function. There was a high correlation between drought duration and drought severity, which marginal distribution is difficult to reflect real drought characteristic. The bivariable hydrologic drought model by Copula function avioded the deficiency mentioned above, which included different combination of drought severity and drought duration. The supervisor can predict the probability of drought severity with a certain level when drought duration with the same level happened through tail correlation analysis, which was very important in risk management. For instance, it was said that the probability of drought severity more than 0.95 percentail was 34.48% when drought duration more than 0.95 percentail according to tail correlation analysis.
引文
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