#
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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