Here, F is the average per-capita ecological footprint in Earths/person/year and Fmin is the minimum ecological footprint. Points on the graph represent a value of global footprint (Fe = P * F, where P is population), separated in each simulation by a difference of 0.01 Earths/year. Simulations and the result all start at year 10000 B.C.E., when P = 1E+06 people and f0 = F0 / Fmin = 7.97E-01.
The simulations are calculated as follows:
Simulation 1 |
f1 = f0
P1 = Fe / (f1 * Fmin)
Maximum Limits:
f1 |
(Felow / Fmin) / P1 - 2 |
P1 |
(Felow / Fmin) / (f1 + 2) |
Fe |
Fehigh |
|
Simulation 2 |
f2 = (Fe / P2) / Fmin
P2 = P0
Maximum Limits:
f2 |
(Felow / Fmin) / P2 - 2 |
P2 |
(Felow / Fmin) / (f2 + 2) |
Fe |
Fehigh |
|
Simulation 3 |
f3 = f0
P3 = Fe / (f3 * Fmin)
Maximum Limits:
f3 |
(Fhigh / Fmin) / P3 - 2 |
P3 |
(Fhigh / Fmin) / (f3 + 2) |
Fe |
Fehigh |
|
Simulation 4 |
f4 = (Fe / P2) / Fmin
P4 = P0
Maximum Limits:
f4 |
(Fhigh / Fmin) / P4 - 2 |
P4 |
(Fhigh / Fmin) / (f4 + 2) |
Fe |
Fehigh |
|
The result is calculated using two equations:
Presult = (a1 * P1 + a2 * P2 + a3 * P3 + a4 * P4) * (fresult > 1)
+ (a1 * P1 + a2 * P2 + a3 * P3 + a4 * P4) * fresult * (fresult <= 1)
fresult = a1 * f1 + a2 * f2 + a3 * f3 + a4 * f4
The weights ( an ) and maximum global footprints (Felow and Fehigh) are chosen to best fit the result to historical data:
a1 = 1.66546503E-01
a2 = 7.14484E-04
a3 = 8.32732517E-01
a4 = 6.49531E-06
Felow = 2.5E-01
Fehigh = 2.972069653
The resulting values of f , P, and Fe are shown below along with historical data and includes a futurecast with no global warming: |