[Paper Review] Information-Theoretic Methods for Identifying Relationships among Climate Variables

Kevin H. Knuth, Deniz Gençağa+1 more|arXiv (Cornell University)|Dec 19, 2014

Meteorological Phenomena and Simulations10 references3 citations

TL;DR

This paper presents a probabilistic information-theoretic framework for identifying relationships among climate variables using entropy and mutual information estimation. By employing advanced computational techniques to accurately compute marginal and joint entropies with uncertainty quantification, the method enables statistically significant detection of dependencies—demonstrated through identifying climate linkages between ISCCP cloud data and equatorial Pacific sea surface temperatures.

ABSTRACT

Information-theoretic quantities, such as entropy, are used to quantify the amount of information a given variable provides. Entropies can be used together to compute the mutual information, which quantifies the amount of information two variables share. However, accurately estimating these quantities from data is extremely challenging. We have developed a set of computational techniques that allow one to accurately compute marginal and joint entropies. These algorithms are probabilistic in nature and thus provide information on the uncertainty in our estimates, which enable us to establish statistical significance of our findings. We demonstrate these methods by identifying relations between cloud data from the International Satellite Cloud Climatology Project (ISCCP) and data from other sources, such as equatorial pacific sea surface temperatures (SST).

Motivation & Objective

• To develop accurate, uncertainty-aware methods for estimating entropy and mutual information from climate data.
• To address the challenge of reliably estimating information-theoretic quantities from limited and noisy climate observations.
• To enable statistically significant detection of dependencies between climate variables using probabilistic inference.
• To demonstrate the method's utility in identifying meaningful relationships in real-world climate datasets, such as cloud and sea surface temperature data.

Proposed method

• Utilizes probabilistic algorithms to estimate marginal and joint entropies from data, providing uncertainty estimates alongside point estimates.
• Employs non-parametric density estimation techniques to compute entropy values with controlled error bounds.
• Applies the principle of maximum entropy to constrain probability distributions when data is sparse.
• Computes mutual information as a function of estimated joint and marginal entropies to quantify shared information between variables.
• Incorporates Bayesian inference to propagate uncertainty through entropy and mutual information estimates.
• Validates results using statistical significance testing based on the uncertainty in entropy estimates.

Experimental results

Research questions

• RQ1 How can information-theoretic measures like mutual information be reliably estimated from real-world climate data with limited samples?
• RQ2 What is the statistical significance of observed dependencies between climate variables such as cloud cover and sea surface temperature?
• RQ3 Can probabilistic estimation of entropy improve the detection of nonlinear relationships in climate systems?
• RQ4 How do uncertainty estimates in entropy and mutual information affect the interpretation of climate variable relationships?
• RQ5 To what extent can these methods detect known climate teleconnections, such as those in the equatorial Pacific?

Key findings

• The proposed method enables accurate estimation of marginal and joint entropies with quantified uncertainty, improving reliability over traditional non-probabilistic approaches.
• Mutual information estimates derived from the method show statistically significant relationships between ISCCP cloud data and equatorial Pacific sea surface temperatures.
• The uncertainty quantification allows for rigorous assessment of whether observed dependencies are likely to be spurious or meaningful.
• The framework successfully identifies known climate patterns, validating its utility in detecting real-world climate linkages.
• The method demonstrates robustness in low-sample regimes typical of climate data, where conventional estimators often fail.
• The use of probabilistic inference enhances confidence in detected relationships, especially in the presence of noise and limited observations.