Global Warming Acceleration

Abstract

This publication analyzes changes of global warming rates (GWR) expressed in Centigrade per year (°C/y) and introduces a parameter “global warming acceleration” (GWA) expressed in Centigrade per year per year (°C/y2).
GWA may be applied for prediction of the GWR for the next decade. If the current decrease of GWA will continue for the next 11 years, Global Warming Rate will increase from the current +0.017 °C/y to +0.019 °C/y, for land+ocean.

Full text

Global Warming Acceleration
Joseph Nowarski, M.Sc., ME – Energy Conservation Expert
Version 1.1.1, 25 March 2022
DOI:10.5281/zenodo.6386218
Abstract
This publication analyzes changes of global warming rates (GWR) expressed in
Centigrade per year (°C/y) and introduces a parameter “global warming
acceleration” (GWA) expressed in Centigrade per year per year (°C/y2).
GWA may be applied for prediction of the GWR for the next decade. If the current
decrease of GWA will continue for the next 11 years, Global Warming Rate will
increase from the current +0.017 °C/y to +0.019 °C/y, for land+ocean.
Glossary
a = GWR = global warming rate, parameter “a” in linear trendline:
T(y) = (y-n) * a + b, average change of global surface temperature
per year in the trendline period, °C/y ([8] Formula 1)
Ave average
GWA Global Warming Acceleration, °C/y2 ([Centigrade per year per year]
[°C y−2])
GWR = a = Global Warming Rate – average change of global surface
temperature per year in the trendline period, °C/y
Ref reference
TL trendline

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Units
The temperature change unit is °C.
Global warming rate, average change of global surface temperature per year in
the trendline period is in °C/y.
The global warming acceleration (yearly change of the global warming rate) is in
°C/y2 [Centigrade per year per year].
Global Warming Rate
According to IPCC [9] “Since 1970 the global average temperature has been
rising at a rate of 1.7°C per century”.
According to NASA [10] “The majority of the warming has occurred since 1975, at
a rate of roughly 0.15 to 0.20°C per decade”.
According to NOAA's 2020 Annual Climate Report [11] “the combined land and
ocean temperature has increased at an average rate of 0.13 degrees Fahrenheit (
0.08 degrees Celsius) per decade since 1880; however, the average rate of
increase since 1981 (0.18°C / 0.32°F) has been more than twice that rate”.
Publication [8] includes 61 years trendlines and the average global warming rate
per year in the trendline period.
Formulas
Formula 1 - Linear trendline
T(y) = (y-n) * a + b
T(y) global surface temperature above 1850-1900 baseline in year y [°C]
n the year before the trendline start point, i.e., for trendline in period
1961-2022 n=1960

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a, b parameters related to the linear function displayed on Excel trendline
chart
Formula 2 - Global Warming Rate, GWR
GWR = a [°C/y]
Formula 3 - Global Warming Acceleration, GWA
GWA = Δa / Δy [°C/y2]
Formula 4 - Δa
Δa = a(i+1) – a(i)
a(i+1) average change of global surface temperature per year in trendline
“i+1” period = parameter “a” of trendline “i+1” (from Excel chart
formula) [°C/y]
a(i) average change of global surface temperature per year in trendline
“i” period = parameter “a” of trendline “i” (from Excel chart formula)
[°C/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 of trendline TL(i))
Period Applied for Calculations of Trendlines
The period applied in [8] for calculations of trendlines is 61 years. This is also the
trendlines period applied in the current work. The starting points of the trendlines
are every 10 years from 1850 (1880 for ocean only).

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Databases Applied
 NASA [1] [2]
 NOAA [3]
 Berkeley Earth (LBL) [4] [5] [6] [7]
Global Surface Temperature Changes over Land and Ocean
Chart 1 - Trendlines, land+ocean, 1850-1900 baseline [8] [°C]
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
2020
Ave TL1 TL2 TL3 TL4
Ave average of all databases [°C]

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Table 1 - Global Warming Rate (GWR), land+ocean
Trendline Trendline period Trendline Global
i ID Center GWR Warming
from to years Acceleration
Symbol TL(i) CenterTL Δy a Δa GWA
Formula Formula 6 Formula 5 Formula 1 Formula 4 Formula 3
Units year year years year years °C/y °C/y °C/y2
1 TL1 1850 1910 61 1880 +0.000417
2 TL2 1860 1920 61 1890 10 -0.000865 -0.001282 -0.000128
3 TL3 1870 1930 61 1900 10 -0.000578 +0.000287 +0.000029
4 TL4 1880 1940 61 1910 10 +0.002629 +0.003207 +0.000321
5 TL5 1890 1950 61 1920 10 +0.006173 +0.003544 +0.000354
6 TL6 1900 1960 61 1930 10 +0.007406 +0.001233 +0.000123
7 TL7 1910 1970 61 1940 10 +0.006335 -0.001071 -0.000107
8 TL8 1920 1980 61 1950 10 +0.004676 -0.001659 -0.000166
9 TL9 1930 1990 61 1960 10 +0.005681 +0.001005 +0.000101
10 TL10 1940 2000 61 1970 10 +0.007744 +0.002063 +0.000206
11 TL11 1950 2010 61 1980 10 +0.013362 +0.005618 +0.000562
12 TL12 1961 2021 61 1991 11 +0.017436 +0.004074 +0.000370
Chart 2 - GWR – Global Warming Rate, land+ocean [°C/y]
-0.005
0.000
0.005
0.010
0.015
0.020
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1991
Axis x is the center of the 61 years trendline period

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Chart 3 - GWA - Global Warming Acceleration, land+ocean [°C/y2]
-0.0003
-0.0002
-0.0001
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1991
Axis x is the center of the 61 years trendline period
From 1960 the GWA is above zero, which means the Global Warming Rate (GWR)
[°C/y] is increasing. The negative slope of GWA between 1980 and 1991 means a
slower increase of GWR.

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Global Surface Temperature Changes over Land
Chart 4 - Trendlines, land only, 1850-1900 baseline [8] [°C]
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1750
1760
1770
1780
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
2020
Ave TL1 TL2 TL3 TL4 TL5 TL6
Table 2 - Global Warming Rate (GWR), land only
Trendline Trendline period Trendline Global
i ID Center GWR Warming
from to years Acceleration
Symbol TL(i) CenterTL Δy a Δa GWA
Formula Formula 6 Formula 5 Formula 1 Formula 4 Formula 3
Units year year years year years °C/y °C/y °C/y2
1 TL1 1850 1910 61 1880 +0.005583
2 TL2 1860 1920 61 1890 10 +0.004718 -0.000865 -0.000087
3 TL3 1870 1930 61 1900 10 +0.005764 +0.001046 +0.000105
4 TL4 1880 1940 61 1910 10 +0.009694 +0.003930 +0.000393
5 TL5 1890 1950 61 1920 10 +0.008613 -0.001081 -0.000108
6 TL6 1900 1960 61 1930 10 +0.006541 -0.002072 -0.000207
7 TL7 1910 1970 61 1940 10 +0.005145 -0.001396 -0.000140
8 TL8 1920 1980 61 1950 10 +0.002857 -0.002288 -0.000229
9 TL9 1930 1990 61 1960 10 +0.005129 +0.002272 +0.000227
10 TL10 1940 2000 61 1970 10 +0.010380 +0.005251 +0.000525
11 TL11 1950 2010 61 1980 10 +0.019618 +0.009238 +0.000924
12 TL12 1961 2021 61 1991 11 +0.025828 +0.006210 +0.000565

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Chart 5 - GWR – Global Warming Rate, land only [°C/y]
0.000
0.005
0.010
0.015
0.020
0.025
0.030
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1991
Axis x is the center of the 61 years trendline period
Chart 6 - GWA - Global Warming Acceleration, land only [°C/y2]
-0.0004
-0.0002
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1991
Axis x is the center of the 61 years trendline period

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Global Surface Temperature Changes over the Ocean
Chart 7 - Trendlines, ocean only, 1850-1900 baseline [8] [°C]
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
2020
NASA TL1 TL2 TL3 T L4
Table 3 - Global Warming Rate (GWR), ocean only
Trendline Trendline period Trendline Global
i ID Center GWR Warming
from to years Acceleration
Symbol TL(i) CenterTL Δy a Δa GWA
Formula Formula 6 Formula 5 Formula 1 Formula 4 Formula 3
Units year year years year years °C/y °C/y °C/y2
1 TL1 1880 1940 61 1910 -0.001397
2 TL2 1890 1950 61 1920 10 +0.003850 +0.005246 +0.000525
3 TL3 1900 1960 61 1930 10 +0.006790 +0.002940 +0.000294
4 TL4 1910 1970 61 1940 10 +0.006577 -0.000213 -0.000021
5 TL5 1920 1980 61 1950 10 +0.005600 -0.000978 -0.000098
6 TL6 1930 1990 61 1960 10 +0.005928 +0.000328 +0.000033
7 TL7 1940 2000 61 1970 10 +0.005895 -0.000032 -0.000003
8 TL8 1950 2010 61 1980 10 +0.009489 +0.003593 +0.000359
9 TL9 1961 2021 61 1991 11 +0.011652 +0.002163 +0.000197

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Chart 8 - GWR – Global Warming Rate, ocean only [°C/y]
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
1910 1920 1930 1940 1950 1960 1970 1980 1991
Axis x is the center of the 61 years trendline period
Chart 9 - GWA - Global Warming Acceleration, ocean only [°C/y2]
-0.0002
-0.0001
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
1910 1920 1930 1940 1950 1960 1970 1980 1991
Axis x is the center of the 61 years trendline period

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All Global Warming Rates and Acceleration
Chart 10 - All GWR – Global Warming Rate [°C/y]
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
0.030
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1991
Land+Ocean Land Ocean
Axis x is the center of the 61 years trendline period
Chart 11 - All GWA - Global Warming Acceleration [°C/y2]
-0.0004
-0.0002
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1991
Land+Ocean Land Ocean
Axis x is the center of the 61 years trendline period

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Prediction of Next Decade Global Warming Rate Using GWA
Table 4 - Prediction of next decade Global Warming Rate using GWA for
land+ocean
Trendline period Trendline Global
Center GWR Warming
from to years Acceleration
CenterTL Δy a Δa GWA ΔGWA
Formula 6 Formula 5 Formula 1 Formula 4 Formula 3
year year years year years °C/y °C/y °C/y2 °C/y2
1950 2010 61 1980 10 +0.013362 +0.013362 +0.000562
1961 2021 61 1991 11 +0.017436 +0.004074 +0.000370 -0.000191
1972 2032 61 2002 11 +0.019405 +0.001969 +0.000179 -0.000191
Currently, the Global Warming Acceleration (GWA) is decreasing -0.000191°C/y2. If
this decrease will continue for the next 11 years, the GWA for the 1972-2032 (center
2002) trendline will be +0.000179°C/y2, which will result in the Global Warming Rate
+0.019405°C/y, for land+ocean.
Chart 12 - Prediction of Global Warming Acceleration - GWA for the next
decade, land+ocean [°C/y2]
-0.0003
-0.0002
-0.0001
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1991 2002
Axis x is the center of the 61 years trendline period

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Chart 13 - Prediction of Global Warming Rate - GWR for the next decade,
land+ocean [°C/y2]
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1991 2002
Axis x is the center of the 61 years trendline period

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References
1. GISTEMP Team, 2022: GISS Surface Temperature Analysis (GISTEMP), version
4. NASA Goddard Institute for Space Studies. Dataset accessed 2022-02-05
at https://data.giss.nasa.gov/gistemp
2. Lenssen, N., G. Schmidt, J. Hansen, M. Menne, A. Persin, R. Ruedy, and D.
Zyss, 2019: Improvements in the GISTEMP uncertainty model. J. Geophys.
Res. Atmos., 124, no. 12, 6307-6326, doi:10.1029/2018JD029522.
3. NOAA National Centers for Environmental information, Climate at a Glance:
Global Time Series, published February 2022, retrieved on March 9, 2022
from https://www.ncdc.noaa.gov/cag/
4. Berkeley Earth - Global Temperature Report for 2021
http://berkeleyearth.org/global-temperature-report-for-2021/
5. Rohde, R. A. and Hausfather, Z.: The Berkeley Earth Land/Ocean
Temperature Record, Earth Syst. Sci. Data, 12, 3469-3479,
https://doi.org/10.5194/essd-12-3469-2020, 2020.
6. Berkeley Earth - Time Series Data, Land Only (1750 – Recent), Monthly
Average Temperature (annual summary)
http://berkeleyearth.org/data/
7. Global Surface Temperature Changes over Land Dataset - Joseph Nowarski.
DOI:10.5281/zenodo.6373255
8. Global Warming Datasets Converted to 1850-1900 Baseline - Joseph
Nowarski. DOI:10.5281/zenodo.6386179

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9. IPCC: SPECIAL REPORT: GLOBAL WARMING OF 1.5 ºC, p7
https://www.ipcc.ch/sr15/chapter/chapter-1/
10. NASA, Earth Observatory, World of Change: Global Temperatures
https://earthobservatory.nasa.gov/world-of-change/global-
temperatures?src=eoa-features
11. Climate Change: Global Temperature
https://www.climate.gov/news-features/understanding-climate/climate-
change-global-temperature
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