The uncertainty of using carbon footprint as a predictor of overall environmental impacts: comparing linear, logarithmic and circular methods

The carbon footprint (CF) is widely used as a proxy indicator for the overall environmental impacts of entities such as countries, organizations, and products. However, since CF is by definition limited to greenhouse gas emissions, an important question arises: to what extent is CF a reliable predictor of other environmental impacts, including ozone layer depletion, acidification, eutrophication, and toxicity? This question has been examined in previous studies, yielding mixed results. In this paper, we argue that the analytical methods employed in earlier work may lead to misleading conclusions. We therefore propose the use of methods from directional statistics as an alternative approach. We analyze the correlation between life-cycle environmental impacts across approximately 4,000 products using a range of metrics, including linear, logarithmic, and rank-based regression, as well as directional statistics-based measures. Our findings are consistently negative: CF does not serve as a reliable predictor for any of the other environmental impact categories considered. Moreover, we show that traditional metrics used to assess such relationships can be misleading. Overall, relying on CF as a measure of total environmental burden is likely to introduce substantial uncertainty, even in cases where conventional correlation indicators suggest otherwise.