The influence of data gaps and outliers on resilience indicators

TL;DR

This paper analyzes how data gaps and outliers affect the reliability of resilience indicators based on variance and autocorrelation, crucial for early warning signals of regime shifts.

Contribution

It provides a rigorous mathematical framework revealing dependencies between resilience indicators and demonstrates the impact of data issues on their accuracy.

Findings

Missing data weakens indicator agreement

Outliers cause systematic bias and overestimation of resilience

Initial data point heavily influences indicator agreement

Abstract

The resilience, or stability, of major Earth system components is increasingly threatened by anthropogenic pressures, demanding reliable early warning signals for abrupt and irreversible regime shifts. Widely used data-driven resilience indicators based on variance and autocorrelation detect `critical slowing down', a signature of decreasing stability. However, the interpretation of these indicators is hampered by poorly understood interdependencies and their susceptibility to common data issues such as missing values and outliers. Here, we establish a rigorous mathematical analysis of the statistical dependency between variance- and autocorrelation-based resilience indicators, revealing that their agreement is fundamentally driven by the time series' initial data point. Using synthetic and empirical data, we demonstrate that missing values substantially weaken indicator agreement, while outliers introduce systematic biases that lead to overestimation of resilience based on temporal autocorrelation. Our results provide a necessary and rigorous foundation for preprocessing strategies and accuracy assessments across the growing number of disciplines that use real-world data to infer changes in system resilience.