Computing and interpreting Fisher Information as a metric of sustainability: regime changes in the United States air quality

As a key tool in information theory, Fisher Information has been used to explore the observable behavior of a variety of systems. In particular, recent work has demonstrated its ability to assess the dynamic order of real and model systems. However, in order to solidify the use of this metric for measuring sustainability, it is pertinent that Fisher Information be understood both conceptually and practically. As such, this document has been developed as a guide for interpreting Fisher Information as sustainability metric. Moreover, this study provides details on an analytical and numerical approach to estimating Fisher information based on the evaluation of changes in the system’s trajectory for determining stable and unstable regimes in real systems, which might represent sustainable or unsustainable systems. Using this novel approach, the sustainability of US air quality characterized by criteria pollutants (i.e., lead, carbon monoxide, ozone, nitrogen dioxide, and sulfur dioxide) was assessed from 1980 to 2009. Further, the precision of Fisher Information computations was examined, thereby establishing an alternative procedure for evaluating real systems characterized by noisy and sparse datasets. Throughout this article, the reader is led through the analysis of Fisher Information results with the goal of both providing guidance on the interpretation of Fisher Information and giving a more tactile understanding of the results applied to sustainability assessment.