Global Warming: Velocity and Acceleration of Change in Cumulative CO2 Emissions

Abstract

This publication introduces two parameters related to cumulative CO2 emissions. The first parameter is "Velocity of Change in Cumulative CO2 Emissions", VCCO2. This parameter represents an average annual change in cumulative CO2 emissions and is expressed in ton of CO2 per year. The second parameter is "Acceleration of Change in Cumulative CO2 Emissions, ACCO2, and is expressed in ton of CO2 per year, per year (tCCO2/y 2). These two parameters are in addition to the parameter "Global Warming Rate", GWR [°C/y], and "Global Warming Acceleration", GWA [°C/y 2 ], described in the previous publication. The velocity of change in cumulative CO2 emissions, VCCO2, is +35.33 GtCCO2/y in the last 11 years, and the acceleration of change in cumulative CO2 emissions, ACCO2, is +0.559 GtCCO2/y 2 in the last 31 years.

Full text

Global Warming:
Velocity and Acceleration of
Change in Cumulative CO2 Emissions
Joseph Nowarski, M.Sc., ME – Energy Conservation Expert
Version 2.2.1, 6 June 2022
DOI:10.5281/zenodo.6617814
all versions (also future versions) DOI:10.5281/zenodo.6497320
Keywords: Climate Change
Global Warming
CO2 emissions
cumulative CO2
velocity of CO2 emissions
acceleration of CO2 emissions
global warming forecast
Abstract
This publication introduces two parameters related to cumulative CO2 emissions.
The first parameter is “Velocity of Change in Cumulative CO2 Emissions”, VCCO2.
This parameter represents an average annual change in cumulative CO2
emissions and is expressed in ton of CO2 per year.
The second parameter is “Acceleration of Change in Cumulative CO2 Emissions,
ACCO2, and is expressed in ton of CO2 per year, per year (tCCO2/y2).
These two parameters are in addition to the parameter “Global Warming Rate”,
GWR [°C/y], and “Global Warming Acceleration”, GWA [°C/y2], described in the
previous publication.
The velocity of change in cumulative CO2 emissions, VCCO2, is +35.33 GtCCO2/y
in the last 11 years, and the acceleration of change in cumulative CO2 emissions,
ACCO2, is +0.559 GtCCO2/y2 in the last 31 years.

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Glossary
ΔCCO2 actual annual changes in cumulative CO2 emissions, tCO2/y
ACCO2 Acceleration of Change in Cumulative CO2 Emissions, annual
changes in Velocity of Change in Cumulative CO2 Emissions, VCCO2,
determined as 31 years trendline slope of the annual changes in the
cumulative CO2 emissions, tCO2/y2 (ton CO2 per year per year)
Ave average
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
GtCO2 Giga-ton of CO2, 109 ton, 10^9 ton, 1,000,000,000 ton of CO2
GWA Global Warming Acceleration, the annual change in the global
warming rate, °C/y2 [3]
GWR Global Warming Rate – average change in global surface
temperature per year in the trendline period, °C/y [3]
OWID Our World in Data – Internet site [1] [2]
Ref reference
tCO2 ton CO2
TL trendline
VCCO2 Velocity of Change in Cumulative CO2 Emissions, 11 years average of
annual changes in cumulative CO2 emissions, tCO2/y

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Periods Applied for the Calculations
For determination of VCCO2, 11 years periods are applied every 10 years for
averages of the actual annual changes in cumulative CO2 emissions.
For determination of ACCO2, 31 years periods are applied every 10 years for
trendlines of the actual annual changes in cumulative CO2 emissions.
Formula
Formula 1 - Velocity of change in cumulative CO2 emissions, VCCO2
[GtCO2/y]
VCCO2 = Ave(ΔCCO2) [GtCO2/y]
The velocity of change, VCCO2, is determined in this version as an 11 years
average of the actual annual changes in cumulative CO2 emissions.
Database of Global Cumulative Amount of CO2
Table 1 - Database of global cumulative amount of CO2
Source of data OWID
Reference [1] [2]
Baseline year 1749
From year 1750
To year 2020
Period, years 271
CO2 from fossil fuels Yes
CO2 from cement production Yes
CO2 from other sources No
Other GHG No
Land use change No
Units ton CO2
Resolution 1 ton CO2/y
The database is from publication [1] [2], CO2 emissions produced from fossil fuels
and cement production only – land use change is not included.

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Cumulative CO2 Emissions
Chart 1 - Cumulative CO2 emission [1] [2] [GtCO2]
0
200
400
600
800
1,000
1,200
1,400
1,600
1,800
1750
1770
1790
1810
1830
1850
1870
1890
1910
1930
1950
1970
1990
2010
Chart 2 - Annual changes in the cumulative amount of CO2 [GtCO2/y]
0
5
10
15
20
25
30
35
40
1750
1770
1790
1810
1830
1850
1870
1890
1910
1930
1950
1970
1990
2010
The change in 2019 was +36.70 GtCO2/y and in 2020 +34.81 GtCO2/y.

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Velocity of Change in Cumulative CO2 Emissions
The velocity of change is determined in this version as 11 years average of annual
changes in cumulative CO2 emissions.
Table 2 - Velocity of Change in Cumulative CO2 Emissions [GtCO2/y]
from to years
Center
VCCO2
year year years
year GtCO2/y
1750 1760
11 1755 0.01
1760 1770
11 1765 0.01
1770 1780
11 1775 0.01
1780 1790
11 1785 0.02
1790 1800
11 1795 0.02
1800 1810
11 1805 0.03
1810 1820
11 1815 0.04
1820 1830
11 1825 0.06
1830 1840
11 1835 0.10
1840 1850
11 1845 0.15
1850 1860
11 1855 0.26
1860 1870
11 1865 0.43
1870 1880
11 1875 0.67
1880 1890
11 1885 1.04
1890 1900
11 1895 1.54
1900 1910
11 1905 2.47
1910 1920
11 1915 3.28
1920 1930
11 1925 3.69
1930 1940
11 1935 3.95
1940 1950
11 1945 5.05
1950 1960
11 1955 7.50
1960 1970
11 1965 11.51
1970 1980
11 1975 17.49
1980 1990
11 1985 20.50
1990 2000
11 1995 23.65
2000 2010
11 2005 29.22
2010 2020
11 2015 35.33
Chart 3 - Velocity of Change in Cumulative CO2 Emissions [GtCO2/y]
0
5
10
15
20
25
30
35
40
1755
1765
1775
1785
1795
1805
1815
1825
1835
1845
1855
1865
1875
1885
1895
1905
1915
1925
1935
1945
1955
1965
1975
1985
1995
2005
2015
Axis x is the center of the 11 years period applied for the calculation

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Acceleration of Change in Cumulative CO2 Emissions
The Acceleration of Change in Cumulative CO2 Emissions is determined in this
version as the 31 years trendline slope of the annual changes in the cumulative
CO2 emissions.
The trendlines period applied in this version is 31 years and the starting points of the
trendlines are every 10 years from 1750.
Table 3 - 31 years trendlines
Trendline
Trendline period Trendline
i ID Center
from to years
Symbol
TL(i) CenterTL Δy
Units year year years year years
1 TL1 1750 1780
31 1765
2 TL2 1760 1790
31 1775 10
3 TL3 1770 1800
31 1785 10
4 TL4 1780 1810
31 1795 10
5 TL5 1790 1820
31 1805 10
6 TL6 1800 1830
31 1815 10
7 TL7 1810 1840
31 1825 10
8 TL8 1820 1850
31 1835 10
9 TL9 1830 1860
31 1845 10
10 TL10 1840 1870
31 1855 10
11 TL11 1850 1880
31 1865 10
12 TL12 1860 1890
31 1875 10
13 TL13 1870 1900
31 1885 10
14 TL14 1880 1910
31 1895 10
15 TL15 1890 1920
31 1905 10
16 TL16 1900 1930
31 1915 10
17 TL17 1910 1940
31 1925 10
18 TL18 1920 1950
31 1935 10
19 TL19 1930 1960
31 1945 10
20 TL20 1940 1970
31 1955 10
21 TL21 1950 1980
31 1965 10
22 TL22 1960 1990
31 1975 10
23 TL23 1970 2000
31 1985 10
24 TL24 1980 2010
31 1995 10
25 TL25 1990 2020
31 2005 10
Following is an example of a trendline in the period 1990-2020, trendline ID=TL25.

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Chart 4 - Annual change in cumulative CO2 emissions in period 1990-
2020, TL25 [GtCO2/y]
y = 0.559047036232x + 20.
463928521193
20
22
24
26
28
30
32
34
36
38
40
1990
2000
2010
2020
ΔCO2 Linear (ΔCO2)
The trendline formula for this period (TL25) is:
y = 0.559047036232x + 20.463928521193
a = 0.559047036232
The average acceleration of the change in cumulative CO2 emissions in the
period 1990-2020 is 0.559 GtCO2/y2 (=a), which is the slope of the linear trendline in
this period (1990-2020).

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Table 4 - Acceleration of Change in Cumulative CO2 Emissions
[GtCO2/y2]
Trendline Trendline period Trendline
Acceleration Change
ID Center of change ΔACCO2/y
from to ACCO2
TL(i) CenterTL a
year year year GtCO2/y2 %/y
TL1 1750 1780 1765 0.00022
TL2 1760 1790 1775 0.00031 4.1%
TL3 1770 1800 1785 0.00045 4.6%
TL4 1780 1810 1795 0.00078 7.1%
TL5 1790 1820 1805 0.00107 3.7%
TL6 1800 1830 1815 0.00144 3.5%
TL7 1810 1840 1825 0.00260 8.1%
TL8 1820 1850 1835 0.00461 7.7%
TL9 1830 1860 1845 0.00793 7.2%
TL10 1840 1870 1855 0.01384 7.5%
TL11 1850 1880 1865 0.02069 4.9%
TL12 1860 1890 1875 0.03036 4.7%
TL13 1870 1900 1885 0.04313 4.2%
TL14 1880 1910 1895 0.07149 6.6%
TL15 1890 1920 1905 0.08402 1.8%
TL16 1900 1930 1915 0.06363 -2.4%
TL17 1910 1940 1925 0.03997 -3.7%
TL18 1920 1950 1935 0.07113 7.8%
TL19 1930 1960 1945 0.17905 15.2%
TL20 1940 1970 1955 0.32203 8.0%
TL21 1950 1980 1965 0.49174 5.3%
TL22 1960 1990 1975 0.45232 -0.8%
TL23 1970 2000 1985 0.31655 -3.0%
TL24 1980 2010 1995 0.44828 4.2%
TL25 1990 2020 2005 0.55905 2.5%
Ave 4.5%
since 1900 3.3%
last 3 1.2%
Chart 5 - Acceleration of Change in Cumulative CO2 Emissions, ACCO2,
[GtCO2/y2]
y = 0.020664973607x - 0.139577412972
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
1765
1775
1785
1795
1805
1815
1825
1835
1845
1855
1865
1875
1885
1895
1905
1915
1925
1935
1945
1955
1965
1975
1985
1995
2005
Axis x is the center of the trendline period (2005 is the center of the 1990-2020 trendline period)

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Change in Acceleration
Change in acceleration, dACCO2, is the slope of the ACCO2 trendline. The
ACCO2 trendline formula is:
y = 0.020664973607x - 0.139577412972
The trendline slope is 0.0207 GtCO2/y2/10y = 0.00207 GtCO2/y3 (GtCO2/y2 per
year).
Table 5 - Annual change in Acceleration of Cumulative CO2 Emissions,
dACCO2 [GtCO2/y3]
ACCO2 Linear Trendline Formula y = 0.020664973607x - 0.139577412972
Δy 10 y
TL a
0.020664974
dACCO2 0.002066497 GtCO2/y3
Forecast of Cumulative CO2 Emissions using Velocity and Acceleration
In the following example, it is assumed that the current year is 2010, attempting to
estimate cumulative CO2 emissions for the 2010-2020 decade.
The calculations are based on TL24 (1980-2010).
Table 6 - Starting point for the forecast
Trendline Starting CCO2 VCCO2 ACCO2 dACCO2
from to year
GtCO2 GtCO2/y GtCO2/y2 GtCO2/y3
1980 2010 2010 1,341 29.22 +0.4482834 +0.0020665

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Table 7 - Forecast of cumulative CO2 emissions
dACCO2 ACCO2 VCCO2 CCO2 CCO2 Δ Δ
TL actual
GtCO2/y3 GtCO2/y2 GtCO2/y GtCO2 GtCO2 GtCO2 %
2010 +0.00207 +0.44828 +29.22 1,341 1,341 +0.000
2011 +0.00207 +0.45035 +29.67 1,371 1,376 +4.798
2012 +0.00207 +0.45242 +30.12 1,401 1,411 +9.650
2013 +0.00207 +0.45448 +30.58 1,432 1,446 +14.356
2014 +0.00207 +0.45655 +31.03 1,463 1,481 +18.856
2015 +0.00207 +0.45862 +31.49 1,494 1,517 +22.860
2016 +0.00207 +0.46068 +31.95 1,526 1,552 +26.360
2017 +0.00207 +0.46275 +32.42 1,558 1,588 +29.870
2018 +0.00207 +0.46482 +32.88 1,591 1,625 +33.636
2019 +0.00207 +0.46688 +33.35 1,625 1,662 +36.991
2020 +0.00207 +0.46895 +33.82 1,659 1,697 +37.982
Ave 1,496 1,518 +21.396 +1.4%
The procedure recommended in this work results in underestimation of the actual
cumulative CO2 emissions by 1.4%, which means that the actual cumulative CO2
emissions exceeded the estimation based on previous decade data by 1.4%.
Chart 6 - Forecast and actual cumulative CO2 emissions for years 2010-
2020 [GtCO2/y2]
1,300
1,350
1,400
1,450
1,500
1,550
1,600
1,650
1,700
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
Forecast Actual

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Current Situation
Table 8 - Most recent data (June 2022) regarding cumulative CO2
emissions
Trendline Starting CCO2 VCCO2 ACCO2 dACCO2
from to year
GtCO2 GtCO2/y GtCO2/y2 GtCO2/y3
1990 2020 2020 1,697 35.33 +0.5590470 +0.0020665
Changes in This Version
 Addition of change in acceleration of annual changes in cumulative
CO2 emissions, dACCO2
 Addition of example of estimation of cumulative CO2 emissions in the
last decade
 Editorial changes

Velocity and Acceleration of Change in Cumulative CO2 Emissions v2.2.1 - Joseph Nowarski
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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 Acceleration - Joseph Nowarski, DOI:
10.5281/zenodo.6616928
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