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In this text, modern applied mathematics and physical insight are
used to construct the simplest and first nonlinear dynamical model
for the Madden-Julian oscillation (MJO), i.e. the stochastic
skeleton model. This model captures the fundamental features of the
MJO and offers a theoretical prediction of its structure, leading
to new detailed methods to identify it in observational data. The
text contributes to understanding and predicting intraseasonal
variability, which remains a challenging task in contemporary
climate, atmospheric, and oceanic science. In the tropics, the
Madden-Julian oscillation (MJO) is the dominant component of
intraseasonal variability. One of the strengths of this text is
demonstrating how a blend of modern applied mathematical tools,
including linear and nonlinear partial differential equations
(PDEs), simple stochastic modeling, and numerical algorithms, have
been used in conjunction with physical insight to create the model.
These tools are also applied in developing several extensions of
the model in order to capture additional features of the MJO,
including its refined vertical structure and its interactions with
the extratropics. This book is of interest to graduate students,
postdocs, and senior researchers in pure and applied mathematics,
physics, engineering, and climate, atmospheric, and oceanic science
interested in turbulent dynamical systems as well as other complex
systems.
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