  A primary objective of the NASA Earth-Sun Exploration Technology Office is to
understand the observed Earth climate variability, thus enabling the
determination and prediction of the climate's response to both natural and
human-induced forcing. We are currently developing a suite of computational
tools that will allow researchers to calculate, from data, a variety of
information-theoretic quantities such as mutual information, which can be used
to identify relationships among climate variables, and transfer entropy, which
indicates the possibility of causal interactions. Our tools estimate these
quantities along with their associated error bars, the latter of which is
critical for describing the degree of uncertainty in the estimates. This work
is based upon optimal binning techniques that we have developed for
piecewise-constant, histogram-style models of the underlying density functions.
Two useful side benefits have already been discovered. The first allows a
researcher to determine whether there exist sufficient data to estimate the
underlying probability density. The second permits one to determine an
acceptable degree of round-off when compressing data for efficient transfer and
storage. We also demonstrate how mutual information and transfer entropy can be
applied so as to allow researchers not only to identify relations among climate
variables, but also to characterize and quantify their possible causal
interactions.
