NEW THEORY AND METHODS FOR RAINFALL EXTREMES

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)资助的。长期以来，学术界一直将降雨极值的建模和分析与甘贝尔、S的极值理论(以及最近的皮克兹？极端过剩或EE理论)。这包括使用年最大降雨量和峰值超过阈值降雨量信息的方法。然而，对于现实的尺度不变的降雨模型，人们可以证明EV和EE理论都不适用。这不仅适用于长时段的平均降雨量d，也适用于低于d的平均降雨量。基本原因是，年最大值依赖于远低于上尾部的一系列边际分布。要分析尺度不变降雨过程的年最大值，必须使用概率的另一个分支，即大偏差(LD)理论。当应用LD理论时，人们发现，在短平均持续时间内，年最大值的分布总是EV2型的，与EV和EE理论预测的不同。在最重要的情况下，当d是有限时，准确的年最大值分布不是任何EV类型，但可以用EV2分布精确地近似。这解释了当Gumbel-S理论预测EV1渐近分布时，EV2模型也能更好地拟合年最大值的常见观察结果。我们建议发展一种新的方法来计算降雨极值，它涵盖了这两种渐近情况(例如)。和非渐近条件，并将新方法转化为实际程序。几十年来，水文学教科书和风险分析实践一直假设极端降水遵循甘贝尔·S的极值理论。我们建议从根本上改变这一范式。新的框架在概念上更合适，源于随机水文学到目前为止一直忽视的概率理论领域。这项拟议的研究将对我们对极端降雨量的概念和评估水文风险的方式产生深远的影响。新方法将使用国家降雨量数据库进行测试。简单的建模假设将用于将平均最大降雨量与洪水联系起来，并评估气候变化对极端降雨量的潜在影响。更广泛的影响这个项目将支持一名博士后(为期5个月)和两名研究生(一名第一年的学生)的研究。将寻求本科生研究人员的参与，并将努力吸引女性和代表不足的少数族裔，以符合麻省理工学院的政策。为了更好地在研究、教学和实践界传播研究成果，除了使用传统的学术传播渠道外，我们还打算出版一本全面的专著，涵盖新的水文极端理论和相关的实施方法。

ABSTRACTThis award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Intellectual MeritA long tradition links the modeling and analysis of rainfall extremes to Gumbel?s extreme-value (EV) theory (and more recently Pickands? extreme-excess or EE theory). This includes methods that use annual-maximum and peak-over-threshold rainfall information. However, for realistic scale-invariant rainfall models one can show that neither EV nor EE theory applies. This is true not just for rainfall averages over long durations d but also under . The basic reason is that the annual maxima depend on a range of the marginal distribution much below the upper tail. To analyze the annual maxima of scale-invariant rainfall processes under , one must use another branch of probability known as large deviation (LD) theory. When LD theory is applied, one finds that for short averaging durations the distribution of the annual maximum is always of the EV2 type and is different from what EV and EE theories predict. In the all-important case when d is finite, the exact annual-maximum distribution is not of any EV type, but can be accurately approximated by an EV2 distribution. This explains the frequent observation that annual maxima are better fitted by EV2 models also when Gumbel?s theory predicts an EV1 asymptotic distribution.We propose to develop a new approach to rainfall extremes that covers both asymptotic cases (e.g. ) and non-asymptotic conditions and to translate the new approach into practical procedures. For decades, hydrology textbooks and risk analysis practice have assumed that extreme precipitation follows Gumbel?s theory of extremes. We propose a fundamental change to this paradigm. The new framework is conceptually more appropriate and stems from an area of probability theory that stochastic hydrology has up to now ignored. The proposed research will have far-reaching consequences on the way we conceptualize rainfall extremes and assess hydrologic risks.The new approach will be tested using national rainfall databases. Simple modeling assumptions will be used to relate average rainfall maxima to floods and to evaluate the potential effects of climatic changes on rainfall extremes. Broader ImpactsThis project will support the research of one post-doc (for 5 months) and 2 graduate students (one student during the first year). Involvement of undergraduate researchers will be sought and efforts will be made to attract women and under-represented minorities, in conformance with MIT policies. To better disseminate the results among the research, teaching and practicing communities, we intend to publish a comprehensive monograph covering the new theory of hydrologic extremes and related implementation methodologies, in addition to using traditional scholarly dissemination channels.