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Staged Meteorological Drought Index Based on Boltzmann Function
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摘要: 基于逐日气象干旱指数，构建了可以反映某一时段内气象旱涝强度的标准化阶段气象旱涝强度指数 (staged meteorological drought intensity index, ISD) 和阶段气象旱涝时间分布状态的标准化阶段气象旱涝空间分布差异指数 (staged meteorological drought discrepancy index, ISDD)。以构建昆明月尺度的ISD和ISDD为例说明了阶段气象旱涝指数的构建方法，通过对不同时段降水距平百分率、ISD, ISDD和标准降水指数 (standardized precipitation index, ISP) 的对比分析，结合降水及逐日气象干旱指数 (multi-scale standardized precipitation index, IMSP) 的演变，验证了ISD和ISDD的有效性。对于任一站点的不同时间尺度，两个指数可以在日尺度到年尺度乃至更大的时间尺度上进行计算，通过Boltzmann函数来构建ISD和ISDD的方法具有很好的拓展应用性，其他气象干旱指数也可以采用该方法来构建阶段干旱指数。
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关键词:
- 气象干旱指数;
- Boltzmann函数;
- 标准化
Abstract: In the practical research and business, it's often needed to evaluate the overall meteorological drought degree of a site within a certain period of time. Based on the daily meteorological drought index, the accumulative probability distribution of the number of days for different drought and flood degrees at a time scale can be obtained, and through solving the accumulative probability distribution by Boltzmann function, the standardized staged meteorological drought intensity index (ISD) and staged meteorological drought discrepancy index (ISDD) is designed.ISD and ISDD of Kunming Station at the monthly scale are constructed as an example. Through comparing and analyzing the precipitation anomaly percentage, ISD, standardized precipitation index (ISP) and ISDD in the different periods, and combined with the day by day evolution of the rainfall and multi-scale standardized precipitation index (IMSP), the effectiveness of ISD and ISDD index are verified. A basic principle is that the rainfall at a certain moment could affect the drought and flood states after that moment, but has no impact on the drought and flood states before.ISD makes full use of daily meteorological drought index which contains prophase precipitation information to synthesize drought and flood characteristics of a certain period of time. The bigger ISD is, the more serious the drought is, and vice versa. The larger (smaller) ISDD means the drought or the flood is more concentrated (scattered). Moreover, these two indices can be calculated in different time scales for any site, and in the practical application, the other meteorological drought index also can be used by a forementioned method to build ISD and ISDD. A theoretical algorithm to get ISD and ISDD on any time scale is proposed, but the most applicable time scale should be 10 days, month and season, and on the inter-annual and inter-decadal scale, the proposed approach and other methods such as precipitation anomaly percentage and ISP can also be used.In view of the complexity of drought, no single index can fully express its intensity, harm and the potential impact, so the drought index is still being continuously explored and improved. -
图 1 2009年7月与2008年7月昆明站各等级气象旱涝日数平均发生概率分布
Fig. 1 The average probability distribution of the number of days for different drought and flood degrees in July 2009 and July 2008 at Kunming Station
图 2 2009年7月与2008年7月昆明站不同等级气象旱涝日数平均发生概率的累计概率分布
Fig. 2 The average accumulative probability distribution of the number of days for different drought and flood degrees in July 2009 and July 2008 at Kunming Station
图 3 1981—2010年7月昆明站不同等级气象旱涝日数平均发生概率的累计概率分布
Fig. 3 The average accumulative probability distribution of the number of days for different drought and flood degrees in July from 1981 to 2010 at Kunming Station
图 4 昆明站4个时段的逐日降水量演变
(a)2006年7—8月，(b)2006年8—9月，(c)2010年2—3月，(d)2010年3—4月
Fig. 4 The daily variation of precipitation in four periods at Kunming Station
(a) from July to August in 2006, (b) from August to September in 2006, (c) from February to March in 2010, (d) from March to April in 2010
图 5 昆明站4个月份IMSP演变 (a)2006年8月，(b)2006年9月，(c)2010年3月，(d)2010年4月
Fig. 5 The daily variation of IMSP in four months at Kunming Station (a) August 2006, (b) September 2006, (c) March 2010, (d) April 2010
图 6 昆明站4个月份各个等级气象旱涝日数的平均发生概率及其累计概率分布
(a)2006年8月，(b)2006年9月，(c)2010年3月，(d)2010年4月
Fig. 6 The probability distribution of the number of days for different drought and flood degrees at Kunming Station
(a) August 2006, (b) September 2006, (c) March 2010, (d) April 2010
表 1 昆明站4个时段降水距平百分率、ISD，ISDD和ISP对比
Table 1 The contrast of precipitation anomaly percentage, ISD, ISDD and ISP in four periods at Kunming Station
时间 降水距平百分率/% ISD ISDD ISP 2006-08 -42.2 -0.15 -0.87 -1.14 2006-09 -49.7 0.32 -0.40 -1.25 2010-03 38.4 0.67 -0.48 0.78 2010-04 22.6 -0.02 -0.87 0.67 
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