Evidence for super-exponentially accelerating atmospheric carbon dioxide   growth
  We analyze the growth rates of atmospheric carbon dioxide and human population, by comparing the relative merits of two benchmark models, the exponential law and the finite-time-singular (FTS) power law. The later results from positive feedbacks, either direct or mediated by other dynamical variables, as shown in our presentation of a simple endogenous macroeconomic dynamical growth model. Our empirical calibrations finds that the human population has decelerated from its previous super-exponential growth until 1960 to a slower-than-exponential growth associated with a decreasing growth rate. However, the past decade is found to be characterized by an almost stable growth rate approximately equal to r(2010) ~ 1% per year, suggesting that the population growth is stabilizing at "just" an exponential growth. As for atmospheric CO2 content, we find that it is at least exponentially increasing and most likely characterized by an accelerating growth rate as off 2009, consistent with an unsustainable FTS power law regime announcing a drastic change of regime. The coexistence of a quasi-exponential growth of human population with a super-exponential growth of carbon dioxide content in the atmosphere is a diagnostic that, until now, improvements in carbon efficiency per unit of production worldwide has been dramatically insufficient. 
Andreas D. H\"usler and Didier Sornette
physics.ao-ph cond-mat.other physics.soc-ph