Argonne National Laboratory

Can We Define Climate Using Information Theory?

TitleCan We Define Climate Using Information Theory?
Publication TypeConference Paper
Year of Publication2010
AuthorsLarson, JW
Conference NameEarth Environment Science 11
Date Published03/2010
PublisherIOP Conference Series
Other NumbersANL/MCS-P1738-0310

The standard definition of climate is, by convention, based on a thirty-year sample. But why? One way to define the sampling period for constructing climatologies is to ask: What is a sufficient sample to construct probability density functions (PDF) for key meteorological variables? One method for judging the sufficiency of a sample to construct a PDF is to use information theory. I propose a framework for evaluating climatic sampling periods based on level of detail and associated uncertainties in the estimated PDF, the Shannon entropy growth curve and its discrete derivative, and Klullback-Leibler divergence-based statistics for quantifying the information gain as the sampling period is expanded by a specified amount. I apply this approach to daily data from the Central England Temperature (CET) record spanning the period 1772-2006. PDF estimation is performed by using an optimal binning technique derived from Bayesian principles to determine a uniform binning strategy that maximizes the posterior probability given the data sample; this technique identifies the known heavy truncation of the CET data and yields insight into the PDF structure with estimated uncertainties for a sampling period spanning 1-235 years. Ensemble-generated statistics from windowed resampling and Monte Carlo calculations of neighboring estimated PDFs are computed, resulting in confidence intervals for all the structural quantities in the framework. I use these statistics to compare the relative confidence associated with a number of popular sampling periods.