Research Interests and Potential Graduate Study

  Predictability theory and its applications

Lorenz showed many years ago that many dynamical systems relevant to climate and weather have a fundamental limitation to their predictability caused by the extreme sensitivity of long-range projections to the specification of initial conditions. This phenomenon is an example of chaotic behavior. In the case of weather this limit implies that detailed predictions beyond several weeks are impossible.  My research has concentrated on understanding the nature and dynamical evolution of predictability in a variety of different and complex dynamical systems. The work has resulted in a new perspective on why some predictions are better than others. It has also shown that the level of predictability is equal to the degree of statistical disequilibrium in a turbulent system. The work draws on mathematical methods from statistical physics and information theory. Applications include new and completely general methods for improving predictions by targetting observations of a system  as  well as  methods to  predict in advance the likely level of skill of any particular prediction.

 Stochastically forced dynamical systems

Many climate systems may be very successfully modeled using a stochastically forced dynamical system where the noise is taken to represent the day-to-day turbulent fluctuations known as weather. Such forcing has the potential to fundamentally limit the predictability of climatic phenomenon such as El Nino. My research has focused on developing the theoretical tools to understand this forcing. This has led to the introduction of the concept of  stochastic optimals which represents the spatially coherent part of noise most effective at perturbing the low frequency (or climate) behavior of the system.

This framework has been applied to El Nino where a new paradigm to explain the observed irregularity of this phenomenon has been proposed. This new framework has been very successful in explaining many observed aspects of the phenomenon. These include its time domain spectrum; its phase locking to the annual cycle and its susceptibility to change/disruption during the northern spring (the so-called "spring predictability barrier"). The stochastic optimals for El Nino resemble a tropical weather phenomenon known as the Madden Julian Oscillation (MJO) which suggests that this pattern may play a fundamental role in disrupting the El Nino climate system and hence limit our ability to make predictions beyond a year or so.

The above framework has been recently extended to model tropical moist convection. This phenomena exhibits coherent wave-like behavior and a ubiquitous red spectrum in both the temporal and spatial domain. These are all features of stochastically forced linear dynamical systems and ongoing research aims to better understand this relationship. This has important practical consequences since current generation numerical weather prediction models have limited skill in the deep tropics and also are poor at accurately simulating the observed coherent waves.

  Non-equilibrium statistical mechanics and information theory

The work above on predictability has led naturally to the study of disequilibrium in dynamical system. Information theory provides a powerful and general perspective on this unsolved problem in mathematical physics.  Research is concentrating on the problem of entropy generation and the connection with  information flow and stochastic modelling of turbulent systems.

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