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

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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 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 +0.559 GtCCO2/y in the last 31 years and the acceleration of change in cumulative CO2 emissions, ACCO2, is +0.011 GtCCO2/y 2 in the last 31 years.
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Global Warming:
Velocity and Acceleration of
Change in Cumulative CO2 Emissions
Joseph Nowarski, M.Sc., ME – Energy Conservation Expert
Version 1.1.1, 27 April 2022
DOI:10.5281/zenodo.6497321
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 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 +0.559 GtCCO2/y
in the last 31 years and the acceleration of change in cumulative CO2 emissions,
ACCO2, is +0.011 GtCCO2/y2 in the last 31 years.
Velocity and Acceleration of Change in Cumulative CO2 Emissions - Joseph Nowarski
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Glossary
a = VCCO2 = velocity of change in cumulative CO2 emissions,
parameter “a” in linear trendline:
dCO2(y) = (y-n) * a + b, average change in cumulative CO2 emissions
per year in the trendline period, tCO2/y
ACCO2 Acceleration of change in cumulative CO2 emissions, tCO2/y2 (ton
CO2 per year per year)
Ave average
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
CO2 emissions of Carbon Dioxide, CO2
dCO2 Change in global cumulative CO2 emissions (CCO2), tCO2/y (ton
CO2 per year)
GtCO2 Giga-ton of CO2, 109 ton, 10^9 ton, 1,000,000,000 ton of CO2
GWA Global Warming Acceleration, yearly 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 = a = Velocity of change in cumulative CO2 emissions, tCO2/y
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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.
Formulas
Formula 1 - Linear trendline
dCO2(y) = (y-n) * a + b
dCO2(y) change in global cumulative CO2 emissions in year y [tCO2/y]
n the year before the trendline start point, i.e., for trendline in period
1950-1980 n=1949
a, b parameters related to the linear function displayed on the Excel
trendline chart
Formula 2 - Velocity of change in cumulative CO2 emissions, VCCO2 [tCO2/y]
VCCO2 = a [tCO2/y]
Formula 3 - Acceleration of change in cumulative CO2 emissions, ACCO2
[tCO2/y2]
ACCO2 = Δa / Δy [tCO2/y2]
Formula 4 - Δa
Δa = a(i+1) – a(i)
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a(i+1) average change in cumulative CO2 emissions per year in trendline
“i+1” period = parameter “a” of trendline “i+1” (from Excel chart
formula) [GtCO2/y]
a(i) average change in cumulative CO2 emissions per year in trendline “i”
period = parameter “a” of trendline “i” (from Excel chart formula)
[GtCO2/y]
Formula 5 - Δy
Δy = CenterTL(i+1) – CenterTL(i)
CenterTL(i+1) center of trendline “i+1” [year]
CenterTL(i) center of trendline “i” [year]
Formula 6 - CenterTL
CenterTL(i) = Average(start year of trendline TL(i), end year of trendline TL(i))
Period Applied for Calculations of Trendlines
The period applied in this work for calculations of trendlines is 31 years. The starting
points of the trendlines are every 10 years from 1750.
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Change in Cumulative Amount of CO2
Chart 1 - Annual change 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.
Velocity of Change in Cumulative CO2 Emissions
In this work, the velocity of change in the cumulative CO2 emissions is determined
as the slope of the 31 years trendline, as indicated on the trendline chart in the
specific period.
Following is an example of a trendline in the period 1990-2020, trendline ID=TL25.
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Chart 2 - 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
dCO2 Linear (dCO2)
The trendline formula for this period (TL25) is:
y = 0.559047036232x + 20.463928521193
a = 0.559047036232
b = 20.463928521193
The average change in cumulative CO2 emissions in the period 1990-2020 is 0.559
GtCO2/y (=a), which is the slope of the linear trendline in this period (1990-2020).
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Table 2 - Velocity of change in cumulative CO2 Emissions
Trendline Trendline period Trendline
Velocity Acceleration
i ID Center of change of change
from to years VCCO2
Symbol TL(i) CenterTL Δy a Δa ACCO2
Formula Formula
6
Formula
5 Formula 1 Formula 4 Formula 3
Units year year years year years GtCO2/y GtCO2/y GtCO2/y2
1 TL1 1750 1780 31 1765 0.000220
2 TL2 1760 1790 31 1775 10 0.000311 +0.000091 +0.000009
3 TL3 1770 1800 31 1785 10 0.000453 +0.000142 +0.000014
4 TL4 1780 1810 31 1795 10 0.000776 +0.000323 +0.000032
5 TL5 1790 1820 31 1805 10 0.001066 +0.000290 +0.000029
6 TL6 1800 1830 31 1815 10 0.001443 +0.000377 +0.000038
7 TL7 1810 1840 31 1825 10 0.002604 +0.001162 +0.000116
8 TL8 1820 1850 31 1835 10 0.004615 +0.002010 +0.000201
9 TL9 1830 1860 31 1845 10 0.007932 +0.003317 +0.000332
10 TL10 1840 1870 31 1855 10 0.013843 +0.005911 +0.000591
11 TL11 1850 1880 31 1865 10 0.020686 +0.006843 +0.000684
12 TL12 1860 1890 31 1875 10 0.030357 +0.009671 +0.000967
13 TL13 1870 1900 31 1885 10 0.043131 +0.012773 +0.001277
14 TL14 1880 1910 31 1895 10 0.071491 +0.028360 +0.002836
15 TL15 1890 1920 31 1905 10 0.084017 +0.012526 +0.001253
16 TL16 1900 1930 31 1915 10 0.063628 -0.020389 -0.002039
17 TL17 1910 1940 31 1925 10 0.039970 -0.023658 -0.002366
18 TL18 1920 1950 31 1935 10 0.071128 +0.031158 +0.003116
19 TL19 1930 1960 31 1945 10 0.179048 +0.107920 +0.010792
20 TL20 1940 1970 31 1955 10 0.322026 +0.142978 +0.014298
21 TL21 1950 1980 31 1965 10 0.491742 +0.169716 +0.016972
22 TL22 1960 1990 31 1975 10 0.452316 -0.039426 -0.003943
23 TL23 1970 2000 31 1985 10 0.316548 -0.135768 -0.013577
24 TL24 1980 2010 31 1995 10 0.448283 +0.131735 +0.013174
25 TL25 1990 2020 31 2005 10 0.559047 +0.110764 +0.011076
Velocity and Acceleration of Change in Cumulative CO2 Emissions - Joseph Nowarski
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Chart 3 - Velocity of change in cumulative CO2 emissions a=VCCO2 [GtCO2/y]
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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Chart 4 - Acceleration of change in cumulative CO2 emissions, ACCO2
[GtCO2/y2], [Giga-ton CO2 per year per year]
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
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)
Negative acceleration in the years 1915-1925 and the year 1985 means a
decrease in velocity of change in the cumulative amount of CO2. In the period of
trendline 1985, from 1970 to 2000, the velocity changed from 0.45 GtCO2/y to 0.32
GtCO2/y, -0.13 GtCO2/y.
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References
1. Hannah Ritchie, Max Roser, Edouard Mathieu, Bobbie Macdonald and
Pablo Rosado - Data on CO 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 CO emissions, 2020
https://ourworldindata.org/grapher/cumulative-co-emissions
3. Global Warming Acceleration - Joseph Nowarski, DOI:
10.5281/zenodo.6393436
* * *
ResearchGate has not been able to resolve any citations for this publication.
Bobbie Macdonald and Pablo Rosado -Data on CO₂ and Greenhouse Gas Emissions by Our World in Data
  • Hannah Ritchie
  • Max Roser
  • Edouard Mathieu
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-gasemissions-by-our-world-in-data