The Inverse Poisson Functional for forecasting response time to environmental events and global climate change

A series of Poisson distributions are fit to sets of global cost-of-impact data representing large-scale accidents and anthropogenic catastrophes. The fits are used to build a function representing data means and are designated the Inverse Poisson Functional. Climate and environmental data have been used to develop a cost-frequency population distribution and to estimate the expected time between events. On a global scale, we show that expected wait- or reaction- times can be estimated using the Poisson density function. The functional is generated, representing the locus of means (peaks) from the individual Poisson distributions from different impact costs. Past (ex-post) forecasts relate to a range of natural and anthropogenic disasters; future (ex-ante) forecast presents global CO₂ emissions. This paper shows that a substantial reaction to global climate change (CO₂ emissions extremum) will occur in 55 to 120 years (95% CI) with a model prediction of 80 years.