Many natural phenomena ranging from climate through to biology are
described by complex dynamical systems. Getting information about
these phenomena involves filtering noisy data and prediction based
on incomplete information (complicated by the sheer number of
parameters involved), and often we need to do this in real time,
for example for weather forecasting or pollution control. All this
is further complicated by the sheer number of parameters involved
leading to further problems associated with the 'curse of
dimensionality' and the 'curse of small ensemble size'. The authors
develop, for the first time in book form, a systematic perspective
on all these issues from the standpoint of applied mathematics. The
book contains enough background material from filtering, turbulence
theory and numerical analysis to make the presentation
self-contained and suitable for graduate courses as well as for
researchers in a range of disciplines where applied mathematics is
required to enlighten observations and models.
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