Can We Define Climate Using Information Theory?

The standard definition of climate is, by convention, based on at 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? I propose an information-theoretic 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 the Kullback-Leibler divergence. I compute these quantities for 235 years of daily data from the Central England Temperature record and use these statistics to compare popular sampling periods and discuss the feasibility of determining an optimal sampling period.