Collaborative Research: Quantifying Predictability in Nonlinear Multiscale Systems with Applications to Tropical Cyclone Prediction

量化动态可预测性是动力系统中的一个基本问题，具有巨大的社会和经济意义。这项任务在涉及大范围相互作用的时空尺度的非线性多尺度系统中尤其具有挑战性。多尺度现象的突出例子包括停电、地震、海啸和热带气旋(TCS)。尤其是TCS，仅在美国每年就造成数十亿美元的损失。为了考虑初始条件中不可避免的不确定性的增长和/或计算模式公式中的不确定性，集合预报已经发展并得到了重要的应用，特别是在天气和气候预报中，包括TC预报。目前，对于简单的模型，人们会选择尽可能多的合奏，每个合奏包含大量成员。然而，当预报模型变得越来越复杂时，人们只能负担得起少量的集合，每个集合的成员数量有限，从而牺牲了预测的估计精度。系综技术的一个更严重的限制是，当模型方程不可用时，它根本不能应用，这在实践中经常是这样的。这个项目的主要目标是开发一种新的理论框架和实用技术，称为伪系综？为了量化动态可预测性，可以从根本上提高对集合预报的理解，可以显著提高从天气到气候尺度的预报精度，并可以极大地减少预报中的计算复杂性和数据存储。这些应通过将集合预报中使用的统计、动力学和不同信息理论处理的方法统一起来实现。伪合唱团？该技术尤其适用于有观测数据但精确的动力学模型方程未知的重要情况。因此，这将允许确定重要天气和气候系统的实际可预报性，包括洪水、TCS、冬季风暴和季风。该计划将从少数族裔和女性群体中招收学生。该提议的更广泛影响包括与台湾国家台风与洪水研究中心(NCTFR)建立国际合作关系。该项目将直接培养研究生和本科生。研究成果将通过各种渠道传播，包括普渡气候变化研究中心和美国国家科学基金会TeraGrid。

Quantifying dynamical predictability is a fundamental problem in dynamical systems, having enormous social and economic implications. The task is especially challenging in nonlinear multiscale systems involving a vast-range of interacting spatial-temporal scales. Outstanding examples of multiscale phenomena include electrical power outages, earthquakes, tsunamis, and tropical cyclones (TCs). TCs in particular, are responsible for billions of dollars of damage annually in the United States alone. To take into account the growth of inevitable uncertainties in the initial conditions and/or the uncertainties in the computational model formulation, ensemble forecasting has been developed and found important applications, especially in weather and climate forecasting, including TC forecasting. Currently, with simple models, one would choose as many ensembles as possible, with each ensemble containing a large number of members. When the forecast models become increasingly complicated, however, one would only be able to afford a small number of ensembles, each with limited number of members, thus sacrificing estimation accuracy of the forecasts. An even more serious limitation with the ensemble technique is that it cannot be applied at all, when the model equations are not available, which is often the case in practice. The major objective of this project is to develop a new theoretical framework and a practical technique, called ?pseudo-ensemble? technique, for quantifying dynamical predictability, so that understanding of ensemble forecasting can be fundamentally advanced, forecast accuracy from weather to climate scales can be drastically improved, and computational complexity and data storage in forecasting can be tremendously reduced. These shall be achieved by unifying statistical, dynamical, and different information theoretic approached used in ensemble forecasting. The ?pseudo-ensemble? technique in particular, shall be applicable to the important situation that observational data are available but the exact dynamical model equations are unknown. This thus shall allow determination of practical predictability of important weather and climate systems including floods, TCs, winter storms, and monsoons. The PI will recruit students from underrepresented minority and women groups.The broader impacts of the proposal include establishment of an international collaboration with the National Center for Typhoon and Flooding Research (NCTFR) in Taiwan. The project will directly train both graduate and undergraduate students. The research results will be disseminated through various channels including the Purdue Climate Change Research Center and the NSF TeraGrid.