Updated 10/5/2015

Cumulative carbon emissions from fossil fuels (the total amount in the atmosphere) varies linearly with global footprint (Fe), as shown in the following graph. The global temperature change since preindustrial times (the "temperature anomaly") for land and sea varies linearly with emissions, as shown in the graph after that.


Cumulative total emissions since 1750, plotted for the years 1950-2008 using global ecological footprint values derived for the Half-Earth Hypothesis. Emissions data source: Source: Tom Boden Gregg Marland and Bob Andres (Oak Ridge National Laboratory).


Emissions vs. Temp

Temperature data source: Global Annual Temperature Anomalies (Land + Ocean), 1880-2014; R. Ruedy, M. Sato, K. Lo.

The error statistics for 1950-2008 data are:

Variable Mean Standard Deviation
Cumulative Emissions (Mtonnes Carbon) -0.6 21257.1
Temperature Anomaly (degrees C) 0.00 0.12

Emissions and temperature are calculated as follows:

Variable Conditions/Description
EmissionsFe = 265148.056540627 * Fe - 85892.0702666212
  • EmissionsFe = cumulative emissions due to Fe
  • Fe = global footprint = Population * Footprint


If  EmissionsFe is less than the value in the previous year, then it is set equal to the value in the previous year.

EmissionsRdrop = 265148.056540627 * Rdrop - 85892.0702666212
  • EmissionsRdrop= cumulative emissions related to resource drop
  • Rdrop = FeTotalyear-1 - FeTotalyear
  • FeTotalyear-1 > FeTotalyear
  • FeTotal = total resources
EmissionsRdrop = 0
  • FeTotalyear-1 <= FeTotalyear
Temperature = 0.0000025293492405247 * Emissions - 0.264407394625994
  • Temperature = temperature anomaly
  • Emissions = EmissionsFe+ EmissionsRdrop

The following summary, based on the limit-seeking case, shows the highest resource depletion rate that can be adapted to, with no casualties until beyond 2200. Unfortunately, population is doomed to crash (fall to zero) at some point if the resources continue to decline, since the footprint will be forced below the minimum needed to survive.

In the graph below the summary, the corresponding temperature anomaly is shown (red) along with a linear extrapolation (dotted blue line) from historical values (1950-2014).

Min Safe Temp Increase
No Casualties Temperature


If the historical temperature extrapolation is assumed for future temperatures, then global warming will begin affecting total resources in 2019. The result is summarized below, where default behavior (population and consumption limit-seeking) is applied. Temperature and casualties are displayed in the following two graphs.

Note the values for maximum temperature anomaly (2.5 degrees Celsius, currently 0.7 degrees) and cumulative emissions (1.1 teratonnes of carbon, currently 0.4 teratonnes) in this updated version of the summary. The emissions reported include the amount due to consumption and the effective amount contributed to resource decline.

Resource-matched Temperature Increase Summary


The following graph compares the population trajectories for the default case and the global warming case above.


Population Comparison


The following summary and graphs show that the population crash can only be delayed four years, by having no progress in population or consumption.

Adaptation Summary
© Copyright 2015 Bradley Jarvis. All rights reserved.