Visualizing climate variability with time-dependent probability density functions, detecting it using information theory

A framework for visualizing and detecting climate variability and change based on time-dependent probability density functions (PDFs) is developed. A set of information-theoretic statistics based on the Shannon Entropy and the Kullback-Leibler Divergence (KLD) are defined to assess PDF complexity and temporal variability. The KLD-based measures quantify the representativeness of a thirty year sampling window of a larger climatic record, how well a long sample can predict a smaller sample's PDF, and how well one thirty year sample matches a similar sample shifted in time. These techniques are applied the the Central England Temperature record, the longest continuous meteorological observational record.