Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100

Abstract

The necessary cumulative CO2 emissions reduction to reach the 1.5°C Global Warming limit in 2100 is 2,359,526 MtCO2. This may be done by decreasing the world's CO2 emissions per capita (CpC) annually by 17%. The necessary cumulative CO2 emissions reduction to reach the 1.7°C Global Warming limit in 2100 is 2,085,593 MtCO2. This may be done by decreasing the world's CO2 emissions per capita (CpC) annually by 7.85%. The necessary cumulative CO2 emissions reduction to reach the 2.0°C Global Warming limit in 2100 is 1,683,503 MtCO2. This may be done by decreasing the world's CO2 emissions per capita (CpC) annually by 4.46%.

Full text

Necessary Change in CO2 Emissions per Capita
to Reach 1.5°C-2.0°C Climate Change Limit in 2100
Joseph Nowarski, M.Sc., ME – Energy Conservation Expert
Version 1.1.1, 30 October 2022
DOI:10.5281/zenodo.7264419
all versions DOI:10.5281/zenodo.7264418
Abstract
The necessary cumulative CO2 emissions reduction to reach the 1.5°C Global
Warming limit in 2100 is 2,359,526 MtCO2. This may be done by decreasing the
world’s CO2 emissions per capita (CpC) annually by 17%.
The necessary cumulative CO2 emissions reduction to reach the 1.7°C Global
Warming limit in 2100 is 2,085,593 MtCO2. This may be done by decreasing the
world’s CO2 emissions per capita (CpC) annually by 7.85%.
The necessary cumulative CO2 emissions reduction to reach the 2.0°C Global
Warming limit in 2100 is 1,683,503 MtCO2. This may be done by decreasing the
world’s CO2 emissions per capita (CpC) annually by 4.46%.
Keywords: Climate Change, Global Warming, CO2 emissions, CO2 per capita, Global Warming forecast

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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Glossary
ΔCO2 CO2 emissions of the country above the world emissions per
capita in the period 1991-2020, tCO2
ΔCO2/y change in CO2 emissions per year
ΣΔCO2/y cumulative change in CO2 emissions per year in 2100 in the
mitigation program
ΣΣΔCO2/y sum of cumulative (2026-2100) change in CO2 emissions per year
in the mitigation program
Ave average
BAU Business as Usual
BL baseline
CCO2 global cumulative CO2 emissions according to publication [1] [2],
CO2 emissions produced from fossil fuels and cement production
only – land use change is not included, tCO2
CO2 emissions of Carbon Dioxide, CO2
CO2GW correlation between cumulative CO2 emissions and Global
Warming = 0.000745°C/GtCO2 [3]
CpC CO2 emissions per capita, tCO2/y,cap (ton CO2 per year, per
population of the country)
Global Warming global surface temperature change over land+ocean above
1850-1900 baseline (°C)
GtCO2 Giga-ton of CO2, 109 ton, 10^9 ton, 1,000,000,000 ton of CO2
MtCO2 Mega-ton CO2 = 106 ton, 10^6 ton, 1,000,000 ton CO2
OWID Our World in Data – Internet site [1] [2]
Ref reference
tCO2 ton CO2
tCO2/y,cap ton CO2 per year, per capita

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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Formula for Average Annual Change
Formula 1 - Average annual change of parameter X in the period 1990-2020
[%/year]
rX = (X2/X1)^(1/(y2-y1)) - 1
rX average annual change of parameter X in the period from y1 to y2,
%/year
X1 value of parameter X at the beginning of the period
X2 value of parameter X at the end of the period
y1 beginning of the period = 1990
y2 end of the period = 2020
Correlation between Cumulative CO2 Emissions and Global Warming
The correlation between cumulative CO2 emissions and Global Warming was
analyzed in the publication “Global Warming and Cumulative CO2” [3].
Formula 2 - Correlation between Cumulative CO2 Emissions and Global Warming
[3] [°C/GtCO2]
CO2GW = 0.000745°C/GtCO2
Dataset
Table 1 - CO2 emissions and population dataset [1] [2]
CO2 Population
emissions
Source of data OWID OWID
Reference [1] [2] [1] [2]
From year 1950 1750
To year 2020 2020
CO2 from fossil fuels Yes
CO2 from cement production Yes
CO2 from other sources No
Other GHG No
Land use change No
Units tCO2/y
Resolution 1 tCO2/y 1 Resident

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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The datasets are from publication [1] [2], CO2 emissions produced from fossil fuels
and cement production only – land use change is not included.
Cumulative Global CO2 Emissions
Total global CO2 emissions per year are from 1750 [1] [2]. This is also the first year of
calculations of the cumulative CO2 emissions of the world, which means that for
this parameter the baseline is 1749.
However, international transport CO2 emissions are from 1950 and the first year of
the cumulative CO2 emissions is 1950 [1] [2], which means that for this parameter
the baseline is 1949.
The datasets were converted to the 1875 baseline in publication [4].
Table 2 - Global cumulative CO2 emissions and international transport [4] [tCO2
above 1875 baseline]
1990 2020
Global cumulative CO2 emissions including
international transport tCO2 792,689,057,443 1,681,608,597,211
International transport cumulative CO2 emissions tCO2 16,042,804,984 43,700,803,946
Global cumulative CO2 emissions without
international transport tCO2 776,646,252,459 1,637,907,793,265

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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World CO2 Emissions per Capita 1990-2020
World CO2 Emissions per Capita 1990-2020 were analyzed in the publication “CO2
Emissions per Capita” [5]
Chart 1 - World averages of CO2 emissions per capita 1990-2020 [5] [tCO2 per
year, per capita]
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
Table 3 - World averages [1] [2]
1990 2020
CO2 emissions MtCO2/y 22,192 33,803
1990-2020 change %/year +1.41%
Population 5,327,529,078 7,794,798,725
1990-2020 change %/year +1.28%
CO2 per Capita tCO2/y,cap 4.1655 4.3366
1990-2020 change per period 4.1%
average annual change %/year +0.134%
The average annual change in the world CO2 emissions per capita in the period
1990-2020 was calculated using Formula 1.
The average change is +0.134% per year.

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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CO2 Emissions Forecast
The CO2 emissions forecast for 2020-2100 is from the publication “CO2 Emission per
Capita Forecast 2020-2100” [6].
Chart 2 - CO2 emissions per year without international transport BAU forecast for
2020-2100 [MtCO2/y] [6]
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
2020
2025
2030
2035
2040
2045
2050
2055
2060
2065
2070
2075
2080
2085
2090
2095
2100
The dataset of CO2 emissions forecast for 2020-2100 is available in the publication
[7].
World Population Forecast
The population forecast for 2020-2100 is from the publication “CO2 Emission per
Capita Forecast 2020-2100” [6].
The population forecast for 2020-2100 is based on the Excel chart parabolic
trendline formula of the actual world population in the period 1990-2020 [1] [2].

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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Table 4 - World population forecast [6]
World population 1990 5,327,529,078
World population 2020 7,794,798,725
Parabolic trendline chart formula:
y = 97038.960947752x2 + 78816017.1242695x + 5261771158.06877
World population 2020 according to the formula 7,798,322,130
Δ to actual 0.045%
World population in 2100 forecast 15,205,966,097
Chart 3 - World population forecast 2020-2100 [6] [7]
7,000,000,000
8,000,000,000
9,000,000,000
10,000,000,000
11,000,000,000
12,000,000,000
13,000,000,000
14,000,000,000
15,000,000,000
16,000,000,000
2020
2025
2030
2035
2040
2045
2050
2055
2060
2065
2070
2075
2080
2085
2090
2095
2100
The dataset of population forecast for 2020-2100 is available in the publication [7].
CO2 Emissions per Capita Forecast
CO2 emissions per capita (CpC) are calculated by dividing the CO2 emissions per
year by the population in the same year.
Table 5 - CO2 emissions per capita forecast
1990 2020 2100
CO2 emissions MtCO2/y 22,192 33,803
70,191
Population 5,327,529,078 7,794,798,725
15,205,966,097
CO2 per Capita (CpC) tCO2/y,cap 4.165 4.337
4.616
average annual change in CpC %/year 0.134%
0.078%

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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Chart 4 - CO2 emissions per capita 2020-2100 [tCO2/y,cap]
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
2020
2025
2030
2035
2040
2045
2050
2055
2060
2065
2070
2075
2080
2085
2090
2095
2100
Business as Usual Forecast for 2025
It is assumed in this work that the CO2 mitigation measures additional to BAU will
not start before the end of 2025.
Table 6 - BAU forecast for 2025 [4]
without International Transport Global
Year Population CpC CO2/y CCO2 International CCO2 GW
BL1875 Transport BL1875 BL1850-1900
tCO2/y,cap MtCO2/y MtCO2 MtCO2/y MtCO2 °C
2020 7,798,322,130 4.3347 33,803 1,613,287 1,004 1,656,988 1.235
2021 7,883,251,602 4.0586 31,995 1,645,282 1,024 1,690,007 1.260
2022 7,968,375,152 4.0716 32,444 1,677,726 1,044 1,723,495 1.285
2023 8,053,692,779 4.0843 32,894 1,710,619 1,065 1,757,454 1.310
2024 8,139,204,485 4.0968 33,345 1,743,964 1,086 1,791,885 1.336
2025 8,224,910,268 4.1091 33,797 1,777,761 1,108 1,826,789 1.362

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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Necessary Annual Change in CO2 Emissions per Capita to Reach 1.5°C Global
Warming Limit in 2100
Table 7 - Years to Global Warming 1.5°C
ΔCpC/y year ΔCO2/y ΔCO2/y ΣΔCO2/y ΣΣΔCO2/y GW in 2100
GW=1.5°C
2026 2026 2100 2026-2100 BL1850-1900
%/y %/y MtCO2/y MtCO2/y MtCO2/y °C
+0.0781%
2031 +1.123% 380
32,453
1,181,672 +4.136
-5.0000%
2032 -4.008% -1,355 -
32,464
-1,781,561 +1.927
-10.0000%
2034 -9.060% -3,062 -
33,774
-2,198,419 +1.616
-15.0000%
2040 -14.112% -4,770 -
33,797
-2,329,764 +1.518
-17.0000%
>2100 -16.133% -5,453 -
33,797
-2,359,526 +1.496
ΔCpC/y average annual change in CpC 2025-2100, %/y
year GW=1.5°C year when Global Warming will reach 1.5°C
ΔCO2/y 2026 change in CO2 emissions per year in 2026
ΣΔCO2/y cumulative change in CO2 emissions per year in 2100
ΣΣΔCO2/y sum of cumulative (2026-2100) change in CO2 emissions per
year
GW in 2100 Global Warming in 2100 above 1850-1900 baseline
Necessary Annual Change in CO2 Emissions per Capita to Reach 1.7°C Global
Warming Limit in 2100
Table 8 - Years to Global Warming 1.7°C
ΔCpC/y year Countries ΔCO2/y ΣΔCO2/y ΣΣΔCO2/y GW in 2100
GW=1.7°C
ΔCO2/y 2026 2100 2026-2100 BL1850-1900
%/y %/y MtCO2/y MtCO2/y MtCO2/y °C
+0.0781% 2038 +1.123% 380
32,453 1,181,672 +4.136
-5.00% 2046 -4.008% -1,355
-32,464 -1,781,561 +1.927
-6.00% 2049 -5.018% -1,696
-33,194 -1,920,388 +1.823
-7.00% 2057 -6.029% -2,038
-33,527 -2,020,702 +1.749
-7.85% 2097 -6.888% -2,328
-33,661 -2,085,593 +1.700
year GW=1.7°C year when Global Warming will reach 1.7°C

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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Necessary Annual Change in CO2 Emissions per Capita to Reach 2.0°C Global
Warming Limit in 2100
Table 9 - Years to Global Warming 2.0°C
ΔCpC/y year Countries ΔCO2/y ΣΔCO2/y ΣΣΔCO2/y GW in 2100
GW=2.0°C
ΔCO2/y 2026 2100 2026-2100 BL1850-1900
%/y %/y MtCO2/y MtCO2/y MtCO2/y °C
+0.0781% 2048 +1.123% 380
32,453 1,181,672 +4.136
-3.00% 2062 -1.987% -672
-27,434 -1,287,655 +2.295
-4.00% 2078 -2.997% -1,013
-30,872 -1,582,714 +2.075
-4.46% 2100 -3.462% -1,170
-31,757 -1,683,503 +2.000
year GW=2.0°C year when Global Warming will reach 2.0°C
Scenarios of Annual Change in CpC
Chart 5 - CO2 emissions per capita (CpC) [tCO2/y,cap]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
2025
2030
2035
2040
2045
2050
2055
2060
2065
2070
2075
2080
2085
2090
2095
2100
CO2
emissions per capita
1.5°C, -17%/y 1.7°C, -7.85%/y 2.0°C, -4.46%/y

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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Chart 6 - Cumulative CO2 emissions reduction per year in scenarios of average
annual change in CpC [MtCO2/y]
-40,000
-35,000
-30,000
-25,000
-20,000
-15,000
-10,000
-5,000
0
2025
2030
2035
2040
2045
2050
2055
2060
2065
2070
2075
2080
2085
2090
2095
2100
1.5°C, -17%/y 1.7°C, -7.85%/y 2.5°C, -4.46%/y
Chart 7 - Cumulative CO2 emissions reduction per period (2025-2100) in
scenarios of average annual change in CpC [MtCO2/period]
-2,500,000
-2,000,000
-1,500,000
-1,000,000
-500,000
0
2025
2030
2035
2040
2045
2050
2055
2060
2065
2070
2075
2080
2085
2090
2095
2100
1.5°C, -17%/y 1.7°C, -7.85%/y 2.5°C, -4.46%/y

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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Chart 8 - Global Warming in scenarios of annual change in CpC [°C]
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2025
2030
2035
2040
2045
2050
2055
2060
2065
2070
2075
2080
2085
2090
2095
2100
°C
1.5°C, -17%/y 1.7°C, -7.85%/y 2.0°C, -4.46%/y

Necessary Change in CO2 Emissions per Capita to Reach 1.5°C-2.0°C Climate Change Limit in 2100
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Table 10 - Maximum CO2 emissions per capita (CpC) to reach 1.5°C-2.0°C
Climate Change limit in 2100
target 2.0°C 1.7°C 1.5°C target 2.0°C 1.7°C 1.5°C
ΔCpC/y -4.46% -7.85% -17.00% ΔCpC/y -4.46% -7.85% -17.00%
%/y %/y %/y %/y %/y %/y
2020 4.335
4.335 4.335 2061 0.795
0.217
0.005
2021 4.059
4.059 4.059 2062 0.760
0.200
0.004
2022 4.072
4.072 4.072 2063 0.726
0.184
0.003
2023 4.084
4.084 4.084 2064 0.693
0.169
0.003
2024 4.097
4.097 4.097 2065 0.662
0.156
0.002
2025 4.109
4.109 4.109 2066 0.633
0.144
0.002
2026 3.926
3.787 3.411 2067 0.605
0.133
0.002
2027 3.751
3.489 2.831 2068 0.578
0.122
0.001
2028 3.583
3.215 2.350 2069 0.552 0.1
13
0.001
2029 3.424
2.963 1.950 2070 0.527
0.104
0.001
2030 3.271
2.730 1.619 2071 0.504
0.096
0.001
2031 3.125
2.516 1.343 2072 0.481
0.088
0.001
2032 2.986
2.319 1.115 2073 0.460
0.081
0.001
2033 2.853
2.137 0.925 2074 0.439
0.075
0.000
2034 2.725
1.969 0.768 2075 0.420
0.069
0.000
2035 2.604
1.814 0.638 2076 0.401
0.064
0.000
2036 2.488
1.672 0.529 2077 0.383
0.059
0.000
2037 2.377
1.541 0.439 2078 0.366
0.054
0.000
2038 2.271
1.420 0.365 2079 0.350
0.050
0.000
2039 2.169
1.308 0.303 2080 0.334
0.046
0.000
2040 2.073
1.206 0.251 2081 0.319
0.042
0.000
2041 1.980
1.111 0.208 2082 0.305
0.039
0.000
2042 1.892
1.024 0.173 2083 0.291
0.036
0.000
2043 1.808
0.943 0.144 2084 0.278
0.033
0.000
2044 1.727
0.869 0.119 2085 0.266 0.0
30
0.000
2045 1.650
0.801 0.099 2086 0.254
0.028
0.000
2046 1.576
0.738 0.082 2087 0.243
0.026
0.000
2047 1.506
0.680 0.068 2088 0.232
0.024
0.000
2048 1.439
0.627 0.057 2089 0.222
0.022
0.000
2049 1.375
0.578 0.047 2090 0.212
0.020
0.000
2050 1.313
0.532 0.039 2091 0.202
0.019
0.000
2051 1.255
0.490 0.032 2092 0.193
0.017
0.000
2052 1.199
0.452 0.027 2093 0.185
0.016
0.000
2053 1.145
0.417 0.022 2094 0.176
0.015
0.000
2054 1.094
0.384 0.018 2095 0.169
0.013
0.000
2055 1.045
0.354 0.015 2096 0.161
0.012
0.000
2056 0.999
0.326 0.013 2097 0.154
0.011
0.000
2057 0.954
0.300 0.011 2098 0.147
0.011
0.000
2058 0.912
0.277 0.009 2099 0.140
0.010
0.000
2059 0.871
0.255 0.007 2100 0.134
0.009
0.000
2060 0.832
0.235 0.006

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References
1. Hannah Ritchie, Max Roser, Edouard Mathieu, Bobbie Macdonald and
Pablo Rosado - Data on CO₂ and Greenhouse Gas Emissions by Our World
in Data
https://github.com/owid/co2-data#data-on-co2-and-greenhouse-gas-
emissions-by-our-world-in-data
2. Our World in Data, Cumulative CO2 emissions, 2020
https://ourworldindata.org/grapher/cumulative-co-emissions
3. Global Warming and Cumulative CO2 - Joseph Nowarski, DOI:
10.5281/zenodo.6619550
4. Dataset Global Warming Forecast using Acceleration Factors - Joseph
Nowarski, DOI:10.5281/zenodo.7151890
5. CO2 Emissions per Capita – Joseph Nowarski, DOI:10.5281/zenodo.7264405
6. CO2 Emission per Capita Forecast 2020-2100 – Joseph Nowarski,
DOI:10.5281/zenodo.7264407
7. Dataset CO2 Emission per Capita Forecast 2020-2100 – Joseph Nowarski,
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* * *