Publisher Johns Hopkins Advanced Academic Programs

The Inverse Poisson Functional has been proposed by Dr. Zachary as a tool for forecasting response time to environmental events and global climate change.

Dr. Zachary has published a new method to determine ‘global reaction time’ in view of climate change. This approach is based on the Poisson distribution developed by Siméon Denis Poisson in the 1830s.

The model explores how long it will take for the international community (as a whole) to make substantial progress in curbing greenhouse gases. The model gives a pessimistic outlook for a quick climate solution.  The model shows that global emissions are expected to decrease (or at least level-off) in 55 to 120 years.

Scientific Reports of the Journal of Nature published this result in July 2018.


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.

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