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。知识产权的优点一个长期的传统链接的建模和分析降雨极端Gumbel？的极值（EV）理论（和最近皮肯斯？极端过剩或EE理论）。这包括使用年最大降雨量和超过阈值的峰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，可以证明，无论是EV或EE理论适用。这不仅适用于长期降雨的平均值d，也适用于长期降雨的平均值d。其基本原因是年最大值取决于远低于上尾的边缘分布范围。为了分析下尺度不变降雨过程的年最大值，人们必须使用概率的另一个分支，称为大偏差（LD）理论。当应用LD理论时，人们发现，对于较短的平均持续时间，年最大值的分布总是EV 2型，与EV和EE理论预测的不同。在d是有限的非常重要的情况下，精确的年最大值分布不是任何EV类型，但可以精确地近似为EV 2分布。这就解释了经常观察到的年度最大值更好地拟合EV 2模型也当Gumbel？的理论预测的EV 1渐近分布。我们建议开发一种新的方法，降雨极值，包括渐近的情况下（例如）和非渐近条件，并将新的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都假设极端降水遵循Gumbel？的极端理论。我们建议从根本上改变这种模式。新的框架在概念上更合适，源于概率理论的一个领域，随机水文学到目前为止已经被忽视。拟议中的研究将对我们概念化极端降雨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数据库进行测试。将使用简单的建模假设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。更广泛的影响该项目将支持一名博士后（为期5个月）和2名研究生（第一年一名学生）的研究。将寻求本科研究人员的参与，并努力吸引妇女和代表性不足的少数民族，符合麻省理工学院的政策。为了更好地在研究，教学和实践社区中传播成果，我们打算出版一本综合性专著，除了使用传统的学术传播渠道外，还包括水文极端新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.