MATHEMATICS COLLOQUIUM
Speaker: Andrew J. Majda
Title: Multi-Scale Models for the Tropics: A Systematic Route
for Improving Theory, Computational, and Predictive Strategies
Affiliation: Courant Institute, New York University.
Date: Friday, January 26, 2007.
Place and Time: Room 101 - Love Building, 3:35-4:30 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.
Abstract.
One of the unexplained striking features of tropical convection is the
observed statistical self-similarity, in clusters, superclusters, and
intraseasonal oscillations through complex multi-scale processes ranging
from the mesoscales to the equatorial synoptic scales to the
intraseasonal/planetary scales. The intraseasonal planetary scale envelope
of these processes, called the Madden-Julian Oscillation (MJO),
profoundly influences long term midlatitude weather prediction, monsoon
development, and ENSO yet is not captured well by current computer models.
Thus, the accurate parameterization of moist convection presents a major
challenge for accurate prediction of weather and climate through numerical
models. After a brief survey of the observational record, this lecture
summarizes recent applied mathematical work giving insight into these
complex issues through the paradigm of modern applied mathematics done
by the lecturer with various collaborators. This part begins with new
multi-spatial scale, multi-time scale, simplified asymptotic models derived
systematically from the equatorial primitive equations on the range of scales
from mesoscale to equatorial synoptic to planetary/intraseasonal
(Majda 2006.) All these simplified models show systematically that the
main nonlinear interactions across scales are quasi-linear where eddy
flux divergences of momentum and temperature from nonlinear advection from
the smaller scale spatio-temporal flows as well as mean source effects
accumulate in time and drive the waves on the successively larger
spatio-temporal scales. Furthermore, these processes which transfer energy
to the next larger, longer, spatio-temporal scales are self-similar in a
suitable sense. The lecture continues with a brief summary of the multi-scale
MJO models (Biello-Majda) and recent multi-cloud models (Khouider-Majda)
for superclusters and their fidelity with key features of the observational
record.
Superparameterization is a promising recent alternative strategy for
including the effects of moist convection through explicit turbulent
fluxes calculated from a cloud resolving model. Basic scales for cloud
resolving modeling are the microscales of order 10km in space on time
scales of order fifteen minutes where vertical and horizontal motions are
comparable and moist processes are strongly nonlinear. Systematic
multi-scale asymptotic analysis (Majda 2006) is utilized to develop
simplified microscale mesoscale dynamic (MMD) models for interaction
between the microscales and spatio-temporal mesoscales on the order of
100km and 2.5 hours. The new MMD models lead to a systematic framework
for superparameterization for numerical weather prediction generalizing
the traditional column modeling framework.
Finally this lecture ends with a new use of the multi-scale cloud models
in the intraseasonal regime to produce realistic looking MJO analogue
waves with intermittently propagating smaller scale eastward convection
embedded in a planetary scale envelope moving at 5-7 ms-1 for flows above
the equator. In the model, there are accurate predictions of the phase
speed from linear theory and transitions from weak regular MJO analogues
to more realistic strong multi-scale MJO analogue waves as climatological
parameters vary. With all of this structure in a simplified context,
these models should be useful for MJO predictability issues in a
fashion akin to the Lorenz 96 model for predictability issues in the
midlatitude atmosphere. This last work is joint with the lecturer,
his Ph.D. student Sam Stechmann, and Boualem Khouider.
(Most of the papers in this research program can be found at
Majda's faculty website: http://www.math.nyu.edu/faculty/majda/)
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