Two central issues in the predictability of geophysical flows are how to predict extreme events, and how to represent the collective effects of small-scale energetic processes. These grand themes are well illustrated by the tropical cyclone, a large-scale convective storm system in the tropical atmosphere that rotates counterclockwise in the northern hemisphere and draws its fuel principally from the evaporation of ocean water when the low-level winds attain sufficient strength. Intense tropical cyclones over the Atlantic are called hurricanes; similar storms in the North Pacific are called typhoons. Hurricanes and typhoons are among the fiercest storms conjured by nature, whose destructive power has become apparent to all over the last several years.
From the perspective of climate science the frequency and average intensity of tropical cyclones is also a question of great importance. The former requires an understanding of the mechanisms of cyclogenesis, a long standing and enigmatic problem in both tropical meteorology and geophysical fluid dynamics; the latter demands an understanding of how various physical processes interact to regulate intensity variations in storms. Both are questions at the forefront of contemporary research on the fluid dynamics and thermodynamics of tropical storms. Both are also challenging problems in moist vortex dynamics, the dry counterpart of which has a distinguished tradition within applied mathematics. A central issue in the cyclogenesis problem, for example, involves understanding how horizontally small-scale (order 10 km) hot towers (cumulonimbus clouds) create a self-sustaining large-scale vortex. The hot towers, and the coherent vortex wave structures they are embedded in, are believed to mediate the transfer of energy from the underlying ocean. These coherent structures are also believed to regulate intensification cycles in intense hurricanes/typhoons. The small-scale/large-scale interaction is an example of the parameterization problem, a leit motif of many problems in large-scale atmospheric dynamics, namely, how the large-scale adiabatic flow organizes and responds to small-scale diabatic forcing. Recent work examining how particle transport and mixing through the hurricane eyewall may regulate storm intensity has phrased these interactions in the language of combustion theory, an idea whose utility we will explore in this workshop.
Modern simulation methods being used to study hurricanes include fine-scale modeling of incipient storms, and hierarchical modeling of the entire system. Short-term predictions of tropical cyclone genesis and evolution requires accurate model initialization. This involves properly capturing both the nature of the underlying balanced flow, and the small scale features (cumulonimbus “hot” towers) it organizes—in ways which can be amplifying or not. The initialization problem proves to be a great challenge for modern data assimilation. Another theme of the workshop will thus be to explore techniques related to stochastic data assimilation, and information theory. On longer-time and larger-space scales, new techniques are being developed that involve normal (non-hierarchical) multi-scale methods. While bearing some resemblance to recent work in applied mathematics on hierarchical multi-scale methods, there are important differences (principally related to scale separation assumptions). The third element of the workshop will thus be to explore how to interpret the representation of tropical cyclones by such techniques, and the extent to which they provide a meaningful basis for predicting the intensity and frequency of hurricanes in other climates.
The goals of the workshop are four fold: (i) to re-introduce the mathematical community to modern problems in hurricane dynamics; (ii) to educate the atmospheric and oceanic sciences community about relevant developments in applied mathematics; (iii) to explore modern approaches in data assimilation, information theory, and multi-scale simulation in light of existing developments in applied math; (iv) to continue the training of a new generation of applied mathematicians and atmospheric scientists through inter-disciplinary workshops, thereby continuing an effort dating back to a previous IPAM workshop (February 2001), and IPAM summer school, and follow on recent events organized jointly by the Courant Institute, and the National Center for Atmospheric Research.
(University of California, Los Angeles (UCLA), Atmospheric Sciences)
Rupert Klein (Freie Universität Berlin, Department of Numerical Analysis and Modeling)
Andrew Majda (New York University, Courant Institute of Mathematical Sciences)
Michael Montgomery (Naval Postgraduate School)
Bjorn Stevens (University of California, Los Angeles (UCLA), Atmospheric Sciences)
Joseph Tribbia (National Center for Atmospheric Research)