I have 2 possible projects for this summer (2016):
1) Red-­‐noise-­‐based EEMD (Ensemble Empirical Mode DecomposiEon)
Fields: Numerical Analysis, MathemaEcal Modeling
Pre-­‐req: Basic numerical analysis / scienEfic compuEng, basic skill in
coding (we'll be working in Matlab), basic staEsEcs (preference for Eme
series analysis)
This is primarily a numerical analysis project with applicaEon to the
analysis of dynamical system simulaEons. Empirical Mode
DecomposiEon (EMD) is a relaEvely new Eme series analysis technique;
Ensemble EMD (EEMD) is a noise-­‐assisted variaEon which uses white
noise and averaging to address some of the short-­‐comings of regular
EMD. White noise is a random Eme series whose elements are
serially uncorrelated.
Recently, our applicaEon of EEMD to dynamical system simulaEons of
geophysical processes have resulted in unusual arEfacts in the analysis.
Geophysical systems are beGer characterized by red noise processes
than white noise (shi6 to longer Eme scale correlaEons -­‐ there's
memory in the noise.) The arEfacts might be ameliorated by the
replacement of white noise with red noise in the EEMD algorithm. This
project would implement this change to EEMD and study the
implicaEons of the change both from a theoreEcal perspecEve and from
a experimental one.
2. Analyzing a conceptual model for the Pleistocene glacial cycles.
Fields: Dynamical Systems, MathemaEcal Modeling, Paleoclimate
Pre-­‐reqs: Math 416, some understanding of staEsEcs and random
variables, basic programing skills (eg. Matlab)
There are many conceptual models (low complexity models) which
aGempt to explain the observed glacial cycles and their changes over
the last 2-­‐5 Myr (the Pliocene and the Pleistocene). The various models
are based on different hypotheses as to the suite of interacEng
underlying processes. The model results can be compared to data (called validaEon) to test such hypotheses.
There is a relaEvely new model, Paillard and Parrenin (2004), posiEng
that the fundamental relaEonship lies between atmospheric carbon
dioxide and the AntarcEc ice sheet. We will be implemenEng the model,
running simulaEons and analyzing them using EEMD (see above.) These
analyses will be compared to analyses already done of other models for
the same system.
Paillard, D. and F. Parrenin (2004); The AntarcEc ice sheet and the
triggering of deglaciaEons; Earth Planet Sci. LeG., 227, (263– 271)