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通讯作者:

王冀,E-mail:wangji_zl@163.com

中文引用: 袁冯,张君枝,王冀,等,2020.气候变化背景下北京市短历时暴雨的强度及雨型变化特征[J].大气科学学报,43(5):802-809.

英文引用: Yuan F,Zhang J Z,Wang J,et al.,2020.Variation characteristics of intensity and pattern of short duration rainstorm in Beijing under the background of climate change[J].Trans Atmos Sci,43(5):802-809.doi:10.13878/j.cnki.dqkxxb.20191129001.(in Chinese).

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目录contents

    摘要

    利用1961—2017年北京观象台站逐分钟降雨资料,根据《城市暴雨强度公式编制和设计暴雨雨型确定技术导则》,建立了北京市1961—1990年和1991—2017年两个气候态下的暴雨强度公式和2 a重现期下历时30 min、60 min、90 min、120 min、150 min、180 min以5 min为时间段的设计暴雨雨型。结果表明:1)P-Ⅲ型分布曲线对北京市两个气候态下各历时降雨量的拟合效果最好,暴雨强度公式精度最高。2)对比1961—1990年和1991—2017年暴雨强度公式,整体而言,后者各历时重现期的暴雨强度值较低,但随着重现期的增大,两者的雨强差值也增大。3)1961—1990年和1991—2017年短历时雨型的雨峰位置系数分别为0.436和0.382,2 a重现期下前者的各历时雨峰位置比后者提前,各历时累积降雨均在初期增长较慢、雨峰前后增长较快,之后增速明显减缓。

    Abstract

    In recent years,with the rapid development of cities and the improvement of drainage design requirements,it is particularly important to study the characteristics and patterns of urban rainstorm.Based on the minute-by-minute rainfall data of Beijing Observatory station during 1961—2017,according to the Technical Guidelines for Establishment of Intensity-Duration-Frequency Curve and Design Rainstorm Profile,this paper established the rainstorm intensity formulas in Beijing under the two climate states of 1961—1990 and 1991—2017,and the design rainstorm patterns of 30 min,60 min,90 min,120 min,150 min and 180 min durations with 5 min as the time period under the two-year return period.Results show that:(1) The P-Ⅲ pattern distribution curve has the best fitting effect on the rainfall of each duration under the two climate states in Beijing,and the rainstorm intensity formula has the highest precision.(2) Compared with the rainstorm intensity formulas of 1961—1990 and 1991—2017,on the whole,the rainstorm intensity value of the latter under each return period is lower,but with the increase of return period,the difference in rainfall intensity between them increases.(3) During 1961—1990 and 1991—2017,the location coefficients of short duration rainstorm peaks are 0.436 and 0.382,respectively.Under the two-year return period,the positions of rain peaks during 1961—1990 are earlier than those during1991—2017.The accumulated rainfall of each duration increases slowly in the initial stage,increases rapidly before and after the rain peak,and then slows down significantly.

  • 21世纪以来,气候变暖已对全球尺度和区域尺度的降水产生了重大影响(Lawrimore and Peterson,2000;王遵娅等,2004;IPCC,2007),尤其是极端暴雨事件呈现增多的趋势(陈海山等,2009;翟盘茂和李蕾,2014;陆桂荣,2015;邓丽萍等,2016)。近年来北京市暴雨内涝灾害频繁发生,危及城市的正常运转和公众的正常生活。如2011年6月23日北京市局地大暴雨使全市有29处桥区出现积水,其中22处交通中断,3条地铁线路出现险情;2012年“7·21”特大暴雨,全市63处道路积水,5条地铁线路停运(张德和王霖琳,2016),70多人丧生;2016年北京“7·20”特大暴雨9个国家站日降雨量超过历史极值,导致14条公交线路采取停驶措施。严重内涝灾害的频繁发生,给城市雨水系统规划和建设带来了严峻挑战。

  • 在城市排水工程规划和工程设计中,暴雨强度公式和设计暴雨雨型是计算暴雨地面径流和排水工程设计流量的重要依据(张秉祥等,2014)。近年来,随着城市建设速度加快,地面不透水面积大幅增加,城市热岛效也日益明显,对城市排水管网设计改造提出了新的挑战(王彬雁等,2015)。为了对排水管道设计进行重新规划设计,许多城市开展了新的暴雨强度公式及雨型统计分析工作,如庄智福等(2015)通过对镇江市的暴雨特征进行分析,发现其存在显著阶段性变化,并基于此开展了新一代暴雨强度公式的研制;朱玲等(2017)对新旧暴雨强度公式与暴雨雨型进行了对比分析,针对不同地区制定了新一代暴雨强度公式,分析了暴雨雨型的演变特征;周绍毅等(2017)发现南宁市目前采用的暴雨强度公式编制所用资料年代久远,已无法适应当前城市发展和排水管网设计流量的需求。在编制暴雨强度公式时,往往需要考虑研究地区短历时降水特征,上述研究多集中于新一代暴雨强度公式及雨型的制定,对气候变化背景下短历时降水特征变化少有探究。

  • 在气候变化研究中,一般以30 a的气候资料统计结果来反映气候场,以反映不同气候态对于气候分析的影响(林婧婧和张强,2015)。随着气候变化背景下降雨特征的改变,不同气候态降雨资料拟合的暴雨强度公式和暴雨雨型会发生怎样的变化?为弄清这一问题,本文利用北京1961—2017年57 a的逐分钟降水资料,对气候变化背景下北京市的暴雨强度和设计暴雨雨型变化特征进行了初步分析,以期为北京市暴雨气候诊断提供依据。

  • 1 研究区域和研究方法

  • 1.1 研究区域和数据来源

  • 北京(115°25′E~117°35′E,39°28′N~41°05′N)位于我国的华北平原北部,属于温带大陆性季风气候,年平均降水量约为600 mm。北部、东北部山区属燕山山脉,东南部由不同高度的堆积平原构成,缓缓向渤海倾斜,地势总体上呈西北高,东南低。考虑到北京市观象台站(116°28′E,39°48′N)具有较完整的分钟降雨资料,且其降雨资料在北京地区具有一定的代表性(王佳丽等,2012),因此本文选择该站为研究站点。用观象台站1961—2017年的逐分钟降水数据,该数据由北京市气象信息中心提供。其中1961—2004年的降水数据为“降水自记纸彩色扫描数字化处理系统”信息化处理后的分钟降水数据,并进行了审核校验,2005—2017年降水数据为现代自动气象站自动记录的逐分钟降雨资料,直接从年报文件中提取。

  • 1.2 研究方法

  • 1.2.1 暴雨公式推求方法

  • 暴雨强度公式拟合过程中,降雨资料选样采用“年最大值法”,暴雨频率理论分布曲线拟合采用P-Ⅲ型分布、指数分布和耿贝尔分布(顾骏强等,2000;金家明,2010),根据三种适线得到的P-i-t关系表中数据,建立联立数理方程组,采用优化算法求解暴雨强度公式参数,进行误差检验,最后获取暴雨强度公式。

  • 1)降雨资料选样:“年最大值法”选样即从逐年分钟雨量资料中挑选5 min、10 min、15 min、20 min、30 min、45 min、60 min、90 min、120 min、150 min、180 min共11个降雨历时的每年最大雨量值作为样本数据。

  • 2)暴雨强度公式:我国现行《室外排水设计规范》(中华人民共和国住房和城乡建设部,2014)所定义的暴雨强度公式为:

  • q=167A1(1+ClgP)(t+b)n
    (1)
  • 式(1)中:q为暴雨强度计算值(单位:mm/min,工程上常用L·S-1·hm-2表示);P为设计暴雨重现期(单位:a);t为降雨历时(单位:min);A1为雨力参数(单位:mm);b为降雨历时修正参数;C为雨力变动参数;n为衰减指数。

  • A=167A1(1+ClgP),则得到一个简化的表达式(2),即为单一重现期公式:

  • q=A(t+b)n
    (2)
  • 式(2)中:A为雨力参数,即不同重现期下1 min的设计降雨量(单位:mm)。

  • 对式(2)两边取对数,并令: y=lnq, b0=lnqA, b1=-n,x=ln(t+b),则式(2)可简化为一个一元线性方程形式:

  • y=b0+b1x0
    (3)
  • 采用最小二乘法,可求出式(3)中的b0和b1,则可求出A、n。由于式(2)中的b也是未知数,在此,推荐采用“数值逼近法”来处理:先给定一个b值,采用最小二乘法进行计算,得出相应的A、n值,同时求出其均方根误差σ,不断调整b值,直至使其σ值达到最小时,从而得到最为合理的A、b、n值。

  • 3)精度检验:采用平均绝对均方差(式(4))和平均相对均方差(式(5))两种方式对拟合精度进行检验。其中平均绝对均方差不超过0.05 mm·min-1,平均相对均方差不超过5%,计算公式如下:

  • Xm=1ni=1nRi'-Riti2
    (4)
  • Um=1ni=1nRi'-RiRi2×100%
    (5)
  • 式中  Xm为平均绝对均方差; Um为平均相对均方差; Ri'为暴雨强度公式理论降雨量; Ri为拟合曲线确定的降雨量; ti为降雨历时;n为样本数。

  • 1.2.2 短历时暴雨雨型确定方法

  • 本文短历时暴雨雨型采用芝加哥法确定。

  • 1)雨峰位置系数。在各年最大独立降雨场次中,分别选取各降雨历时(30 min、60 min、90 min、120 min、150 min、180 min)的逐年最大降雨过程样本,并以5 min为间隔进行分段,统计降雨过程的雨峰位置系数。

  • r=t/T
    (6)
  • 式(6)中:r为雨峰位置系数;t为雨峰值时刻;T为降雨历时。

  • 将历时相同的入选降雨样本的雨峰位置系数进行算术平均,再将不同历时降雨的平均雨峰位置系数进行加权平均,计算出综合雨峰位置系数,值为0~1。

  • (2)芝加哥雨型。根据上述得到的综合雨峰位置系数,将降雨历时时间序列分为峰前和峰后两个部分,推求雨峰前后瞬时降雨强度,计算公式为:

  • itb=A(1-n)tbr+btbr+bn+1;
    (7)
  • ita=A(1-n)tar+bta1-r+bn+1
    (8)
  • 式中  itbita分别为雨峰前、后的瞬时降雨强度(单位:mm·min-1); tbta为雨峰前、后相应的降雨历时(单位:min);A、b、n分别为暴雨强度公式中的参数。

  • 根据雨峰位置系数和式(5)(6)计算合成暴雨过程的各时段(以5 min计)的平均降雨量和累计降雨量,再通过计算各时段的降雨强度确定对应短历时暴雨的芝加哥雨型。

  • 2 北京市短历时降雨特征分析

  • 2.1 短历时最大降雨量历年变化

  • 极端降水与城市内涝密切相关,极端降水变化与否以及如何变化是城市防洪排涝规划设计标准发生变化的基础。图1给出了北京市观象台站1961—2017年逐年最大30 min、60 min、90 min、120 min、150 min、180 min降雨量的变化情况,可以看出,各历时年最大雨量均呈现不明显增大趋势,其中各历时降雨量极值分别出现在20世纪60年代前期(30 min历时年最大雨量出现在20世纪60年代后期)、20世纪80年代中期和2010年之后。

  • 1961—2017年北京市各历时年最大降雨量的气候倾向率在0.28~0.56 mm·(10 a)-1,其中60 min历时最大降雨量的气候倾向率最小,120 min最大;1961—1990年各历时年最大降雨量的气候倾向率在2.09~8.02 mm·(10 a)-1,且各历时最大降雨量的气候倾向率随着降雨历时的增加而增大;1991—2017年各历时年最大降雨量的气候倾向率

  • 图.1 1961—2017年北京市各历时年最大降雨量的年际变化

  • Fig.1 Interannual variations of maximum rainfall of each duration in Beijing during 1961—2017

  • 在0.11~3.06 mm·(10 a)-1,其中120 min历时最大降雨量的气候倾向率最小,180 min最大(表1)。1961—2017年各历时年最大降雨量的气候倾向率区间值最小,说明各历时年最大降雨量变化趋势不明显,而1961—1990年和1991—2017年两个气候态下,前者的各历时年最大降雨量的气候倾向率区间值明显高于后者,说明前者各历时年最大降雨量增加趋势更为显著。

  • 表.1 1961—2017、1961—1990和1991—2017年北京市各历时年最大降雨量的气候倾向率

  • Table.1 Climate tendency rates of maximum rainfall of each duration in Beijing during 1961—2017,1961—1990 and 1991—2017(mm·(10 a)-1)

  • 2.2 短历时降雨量均值变化

  • 为进一步分析北京市短历时降雨量的平均状况,图2给出了各短历时降雨量的多年平均值变化。从图2中可以看出,1961—2017年30 min、60 min、90 min、120 min、150 min、180 min降雨量多年平均值分别为27.37 mm、36.99 mm、43.32 mm、47.66 mm、50.80 mm,1961—1990年和1991—2017年两个气候态分别与之相比较可以看出,两者各历时降雨量平均值均高于1961—2017年多年平均值,其中

  • 图.2 各短历时的多年平均降雨量的变化

  • Fig.2 Variations of multi-year mean rainfall of each short duration

  • 1961—1990年各历时降雨量增加幅度分别为3.18%、4.81%、4.99%、5.25%、6.14%,而1990—2017年的增加幅度分别为1.68%、1.97%、1.80%、1.97%、0.63%。1990—2017年各历时降雨量与1961-1990年相比可以发现,其各历时降雨量分别有所减少,减少幅度分别为-1.45%、-2.71%、-3.03%、-3.11%、-5.19%。从上述分析可知,1990—2017年气候态下北京市短历时降雨量平均值,与1961—2017年和1961—1990年气候态多年平均值相比,均呈下降趋势。

  • 3 不同气候态下暴雨强度公式差异

  • 3.1 暴雨强度公式参数拟定

  • 为了能够选择出拟合程度较好的分布曲线,对两个气候态下三种曲线进行均方差计算,并用均方差的绝对值和相对值作为误差大小的判断依据。北京市属于一般降雨强度的地区(杨萍等,2017),因此,首先考虑平均绝对均方差,其次参考平均相对均方差。表2给出了不同气候态下,三种理论频率曲线拟合结果在2~20 a重现期下的误差,可以看出,P-Ⅲ型分布和耿贝尔分布拟合结果的平均绝对均方差在0.022~0.037 mm·min-1之间,符合《室外排水设计规范》(中华人民共和国住房和城乡建设部,2014)精度检验不超过0.05 mm·min-1的要求,但耿贝尔分布的平均相对均方差为3.59%和5.21%,高于P-Ⅲ型分布的2.32%和2.63%,且5.21%没有通过平均相对均方差的结果要求,因此P-Ⅲ型分布曲线拟合结果最好。

  • 表.2 不同理论频率曲线拟合结果的误差比较

  • Table.2 Error comparison of fitting results of different theoretical frequency curves

  • 3.2 不同气候态下暴雨强度公式计算结果与比较

  • 通过以上分析,根据年最大值法,采用P-Ⅲ型分布、最小二乘法参数组合方法计算得到的暴雨公式误差结果最为合理,确定北京市不同气候态下暴雨强度公式如下:

  • 1961—1990年:

  • q=1470.753×(1+0.971lgP)(t+9.680)0.680
    (7)
  • 1991—2017年:

  • q=1859.475×(1+0.906lgP)(t+11.665)0.729
    (8)
  • 式中 -1·hm-2);P为重现期(单位:a)。

  • 本文通过计算两个气候态下暴雨公式的差值比率,分析其计算结果差异,二者差值比率定义如下:

  • γ=qm-qnqn×100%
    (9)
  • 式中  qmqn分别为1991—2017年和1961—1990年暴雨强度公式计算的雨强(单位:L·S-1·hm-2)。

  • 从1961—1990年和1991—2017年暴雨强度公式雨强差值比率(表略)和各降雨历时雨强(图3)可以看出,1991—2017年暴雨强度公式5~60 min历时各重现期雨强较1961—1990年暴雨强度公式偏大,偏大幅度在0.31%~2.14%之间,说明在该情况下,1991—2017年暴雨强度公式计算安全性比1961—1990年暴雨强度公式高(陈奕,2013)。反之,在其他各历时重现期的雨强1991—2017年均低于1961—1990年,偏小幅度在0.28%~7.25%,说明该情况下前者计算安全性低于后者。同时,随着重现期的增加,两者的雨强差值幅度也增大,最大差值幅度出现在重现期100 a时180 min历时,达到

  • 图.3 1961—1990与1991—2017年由暴雨强度公式计算所得各历时雨强的比较:(a)5 min;(b)10 min;(c)15 min;(d)20 min;(e)30 min;(f)45 min;(g)60 min;(h)90 min;(i)120 min;(j)150 min;(k)180 min

  • Fig.3 Comparison of rainfall intensities of different durations calculated by the rainstorm intensity formulas between 1961—1990 and 1991—2017:(a)5 min;(b)10 min;(c)15 min;(d)20 min;(e)30 min;(f)45 min;(g)60 min;(h)90 min;(i)120 min;(j)150 min;(k)180 min

  • 7.25%,说明随着重现期的增加,计算安全性也随之增加。这一结果同实际观测资料统计结果相符。

  • 4 短历时暴雨雨型分析

  • 2013年北京市发布的《DB11T969—2013城市雨水系统规划设计暴雨径流计算标准》(北京市城市规划设计研究院,2013),规定了城市雨水系统规划设计中暴雨径流计算的参数,其中对于雨水管渠设计重现期采用2~10 a。本文选择2 a重现期进行短历时暴雨雨型分析。

  • 根据前文介绍的芝加哥法暴雨雨型确定方法,对2 a重现期1961—1990年和1991—2017年60 min、90 min、120 min、150 min和180 min各同历时的每场降雨过程的雨峰位置系数进行统计平均,再对不同历时降雨的平均雨峰位置系数进行加权平均,求出1961—1990年和1991—2017年的综合雨峰位置系数分别为0.436和0.382。图4为2a重现期下各历时以5 min为间隔的时段平均降雨强度,即暴雨雨型分布。1991—2017年与1961—1990年相比,各降雨历时暴雨雨型峰值位置和降雨强度峰值变化差异显著。1961—1990年各历时的雨峰峰值分别出现在第6、第8、第11、第14和第16时段,雨峰位置系数分别介于0.372~0.519;1991—2017年各历时的雨峰峰值分别出现在第5、第7、第10、第12和第14时段,雨峰位置系数分别介于0.343~0.433。1991—2017年与1961—1990年相比,2 a重现期下各历时雨峰位置前者比后者提前。

  • 1961—1990年2 a重现期各历时降雨强度峰值在1.531~1.822 mm·min-1,1991—2017年在1.634~1.826 mm·min-1,其中1991—2017年与1961—1990年相比,60 min和150 min历时的降雨强度峰值均表现为增加,分别增加了0.108 mm·min-1和0.290 mm·min-1;历时90 min、120 min和180 min降雨强度峰值均表现为减少,分别减少了0.081

  • 图.4 芝加哥法推求1961—1990和1991—2017年重现期2 a下各降雨历时的暴雨强度(a)和累计降雨量(b)

  • Fig.4(a)Rainstorm intensity and(b)accumulated rainfall of each rainfall duration under the two-year return period during 1961—1990 and 1991—2017,calculated by the Chicago method

  • mm·min-1、0.127 mm·min-1和0.055 mm·min-1

  • 从芝加哥法推求的2a重现期历时60 min、90 min、120 min、150 min和180 min的累计降雨量来看,1961—1990年2 a重现期各历时的累计降雨量在38.12~57.80 mm;1991—2017年2 a重现期各历时的累计降雨量在37.82~55.30 mm,且1991—2017年各历时累计降雨量小于1961—1990年。从累计降雨量过程曲线(图4)可以看出,各历时累计降雨均在初期增长较慢,雨峰前后增长速度较快,之后增速明显减缓。1961—1990年与1991—2017年对比来看,在同一历时情况下,后者的累计降雨量要高于前者,说明1991—2017年的平均雨强要大于1961—1990年。

  • 5 结论

  • 利用1961—2017年北京观象台站的分钟降雨数据,将其分成1961—1990年和1991—2017年两个气候态进行研究,得出以下结论:

  • 1)采用《城市暴雨强度公式编制和设计暴雨雨型确定技术导则》(住房和城乡建设部和中国气象局,2014)推荐的三种方法对1961—1990年和1991—2017年原始数据进行拟合,相比之下P-Ⅲ型分布曲线对北京市两个气候态下各历时降雨量的拟合效果最好,暴雨强度公式精度最高。从计算结果可以看出,各历时各重现期的暴雨公式计算结果安全性在两个气候态下不同:1991—2017年暴雨公式计算安全性在5~60 min历时比1961—1990年暴雨强度公式高,其他历时暴雨公式计算安全性低于1961—1990年;而1961—1990年暴雨公式计算安全性在各历时下均高于1991—2017年。

  • 2)基于芝加哥雨型法得到两个气候态下相应的短历时暴雨雨型,其短历时暴雨雨峰位置系数分别为0.436和0.382,在2a重现期下1991—2017年与1961—1990年相比,各历时雨峰位置前者比后者提前,历时60 min和150 min的降雨强度峰值均表现为增加,历时90 min、120 min和180 min降雨强度峰值均表现为减少。从各历时累计降雨量来看,1991—2017年与1961—1990年各历时累计降雨均呈现在初期增长较慢,雨峰前后增长速度较快,之后增速明显减缓的特征,但1991—2017年不同重现期各历时累计降雨量均小于1961—1990年。

  • 3)短历时暴雨局地性较强,空间差异明显,之后可对北京市不同区域进行短历时暴雨特征研究。此外,本文仅采用芝加哥雨型一种方法推求暴雨雨型,存在一定的局限性,今后可对其他暴雨雨型做进一步深入研究,以期更为合理、准确地确定区域短历时暴雨特征,为北京市暴雨内涝防灾减灾工程设计提供更加可靠的依据。

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