Global Warming Acceleration v1.2.1

Abstract

This publication analyzes changes in 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 to forecast 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 1.2.1, 6 June 2022
DOI:10.5281/zenodo.6616928
all versions (also future versions) DOI:10.5281/zenodo.6386217
Keywords: Climate Change
Global Warming
Global Warming Rate
velocity of global warming
Global Warming Acceleration
acceleration of global warming
surface temperature
global temperature
global temperature forecast
Abstract
This publication analyzes changes in 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 to forecast 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
Ave average
BL Global Warming baseline 1850-1900
dGWA annual change in Global Warming Acceleration, GWA, in the
trendline period, °C/y3 (°C/y2 per year) (°C y−3)

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GW Global Warming, global surface temperature above the 1850-1900
baseline, °C
GWA Global Warming Acceleration, change of the velocity of the Global
Warming in time, the annual change in Global Warming Rate in the
trendline period, °C/y2 (Centigrade per year per year) (°C y−2)
GWR Global Warming Rate, the velocity of the Global Warming, change of
Global Warming in time, annual change in global surface
temperature in the trendline period, °C/y ([8] Formula 1)
Ref reference
TL trendline
Units
The temperature change is in °C above the 1850-1900 baseline.
Global Warming Rate, GWR, annual change in the global surface temperature in
the trendline period, is in °C/y.
Global Warming Acceleration, GWA, annual change in the global warming rate in
the trendline period, is in °C/y2 (Centigrade per year per year).
The annual change in the global warming acceleration in the trendline period,
dGWA, is in °C/y3 (°C/y2 per year).

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Trendlines
Global surface temperature 61 years linear trendlines are applied every 10 years
starting from 1850 (1880 for ocean only).
Table 1 - Trendlines
Trendline
Trendline period Trendline
i ID Center
from to years
Symbol
TL(i) CenterTL Δy
Formula Formula 6
Formula 5
Units year year years year years
1 TL1 1850 1910 61 1880
2 TL2 1860 1920 61 1890 10
3 TL3 1870 1930 61 1900 10
4 TL4 1880 1940 61 1910 10
5 TL5 1890 1950 61 1920 10
6 TL6 1900 1960 61 1930 10
7 TL7 1910 1970 61 1940 10
8 TL8 1920 1980 61 1950 10
9 TL9 1930 1990 61 1960 10
10 TL10 1940 2000 61 1970 10
11 TL11 1950 2010 61 1980 10
12 TL12 1960 2020 61 1990 10
13 TL13 1961 2021 61 1991 1
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
1961-2021 n=1960
a, b parameters related to the linear function displayed on the Excel
trendline chart
Formula 2 - Global Warming Rate, GWR
GWR = a [°C/y]
Formula 3 - Global Warming Acceleration, GWA
GWA = Δa / Δy [°C/y2]

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Formula 4 - Δa
Δa = a(i) - a(i-1)
a(i) annual change in global surface temperature in trendline period “i”,
equals to parameter “a” of trendline “i” (from Excel chart formula),
°C/y
a(i-1) annual change in global surface temperature in trendline period “i-
1”, equals to parameter “a” of trendline “i-1” (from Excel chart
formula), °C/y
Formula 5 - Δy
Δy = CenterTL(i) - CenterTL(i-1)
CenterTL(i) center of trendline “i”, year
CenterTL(i-1) center of trendline “i-1”, year
Formula 6 - CenterTL
CenterTL(i) = average year between start year and end year of trendline TL(i))
Formula 7 - dGWA – annual change in Global Warming Acceleration
dGWA = a(GWA) / Δy [°C/y3]
dGWA annual change in Global Warming Acceleration, °C/y3
a(GWA) parameter “a” in the Global Warming Acceleration linear trendline,
°C/y2
Δy time difference between trendlines on the chart = 10 years
Databases Applied
 NASA [1] [2]
 NOAA [3]
 Berkeley Earth (LBL) [4] [5] [6] [7]

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Global Warming
Global Warming, GW, is defined in this work as the global surface temperature
above the 1850-1900 baseline, °C.
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 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”.
Global Warming Rate, GWR, is defined in this work as the velocity of the Global
Warming, GW, change of Global Warming in time, annual change in the global
surface temperature in the trendline period, °C/y ([8] Formula 1)
Publication [8] includes 61 years trendlines and the Global Warming Rate values in
each trendline period.
Global Warming Acceleration
Global Warming Acceleration, GWA, is the change in the velocity of the Global
Warming in time. The velocity of the Global Warming is in this work Global Warming
Rate, GWR, and is determined for each trendline. As the trendlines are for every 10
years, the GWA is calculated as the difference between the current GWR and the
GWR in the previous trendline, divided by 10 years.

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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]
Chart 2 - Last trendline TL13 (1961-2021), land+ocean, 1850-1900
baseline [8] [°C]
T = 0.017436347611 x + 0.140372131148
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1961
1971
1981
1991
2001
2011
2021
The above trendline (TL13) is from 1961 to 2021, having a center in the year 1991.
The formula of this trendline is:
T = 0.017436347611x + 0.140372131148

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a = +0.017436347611
b = +0.140372131148
The slope of the above trendline is parameter “a” in the trendline formula
displayed on the chart. The trendline slope (parameter “a”) is the Global Warming
Rate in the period of the trendline and equals +0.017 °C/y.
Table 2 - Global Warming Rate (GWR) and Global Warming Acceleration
(GWA), land+ocean
Trendline
Trendline period Trendline
Global GWR Global
i ID Center Warming Change Warming
from to years Rate per Δy Acceleration
Symbol
TL(i) CenterTL Δy GWR ΔGWR GWA
Formula Formula 6
Formula 5
Formula 1 Formula 4 ΔGWR/Δy
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 1960 2020 61
1990
10 +0.017213 +0.003851 +0.000385
13 TL13 1961 2021 61
1991
1 +0.017436 +0.000223 +0.000223
Chart 3 - 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 4 - 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
Since 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 in GWR.
Chart 5 - Trendline of Global Warming Acceleration, land+ocean
[°C/y3/10years]
TL(GWA) = 0.000032352964 x - 0.000041422880
-0.0002
-0.0001
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
2020
Axis x is the end of the 61 years trendline period
Table 3 - dGWA, change in Global Warming Acceleration
Global Warming Acceleration GWA Trendline formula:
TL(GWA) = 0.000032352964x - 0.000041422880
Parameter "a" in GWA trendline
formula a(GWA) +0.000032352964 °C/y2/10y
Parameter "b" in GWA trendline
formula b(GWA) -0.000041422880 °C/y2/10y
Time difference between
trendlines on the chart Δy 10 years
Annual Change in Global
Warming Acceleration dGWA Formula 7: a(GWA)/Δy °C/y3
Change in Global Warming
Acceleration dGWA +0.000003235296 °C/y3

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Change in Global Warming Acceleration (dGWA) is determined in this work as a
slope of the Global Warming Acceleration trendline. The slope is indicated in the
chart trendline formula as parameter “a”.
The value of the chart slope is per 10 years, therefore the “a” parameter is divided
by 10 to receive the dGWA.
Table 4 - Starting values for the forecast
Starting
TL TL GW(BL) GWR GWA dGWA
year a b TL
°C °C/y °C/y2 °C/y3
2020 +0.017213 +0.132767 +1.183 +0.017213 +0.000385 +0.0000032

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Global Surface Temperature Changes over Land
Chart 6 - 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 5 - 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 7 - 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 8 - 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 9 - 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 TL4
Table 6 - 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 10 - 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 11 - 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 12 - 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 13 - 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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Application of Global Warming Acceleration for Forecast of Global Warming
In the fallowing example it is assumed that the current year is 2010, attempting to
estimate global warming for land+ocean for the 2010-2020 decade.
The calculations are based on TL11 (1950-2010).
Table 7 - Starting point for the forecast
Trendline Starting GW GWR GWA dGWA
from to a b year TL
°C °C/y °C/y2 °C/y3
1950 2010 +0.013362 +0.109975 2010 +0.925 +0.013362 +0.000562 +0.0000032
Table 8 - Forecast of next decade Global Warming Rate using GWA for
land+ocean
dGWA GWA GWR GW GW Δ Δ
TL actual
°C/y3 °C/y2 °C/y °C °C °C %
2010 +0.0000032 +0.000562 +0.013362 +0.925 +1.040 +0.115
2011 +0.0000032 +0.000565 +0.013927 +0.939 +0.916 -0.023
2012 +0.0000032 +0.000568 +0.014495 +0.953 +0.953 -0.000
2013 +0.0000032 +0.000572 +0.015067 +0.969 +0.982 +0.014
2014 +0.0000032 +0.000575 +0.015642 +0.984 +1.053 +0.069
2015 +0.0000032 +0.000578 +0.016220 +1.000 +1.217 +0.217
2016 +0.0000032 +0.000581 +0.016801 +1.017 +1.323 +0.306
2017 +0.0000032 +0.000584 +0.017385 +1.035 +1.232 +0.197
2018 +0.0000032 +0.000588 +0.017973 +1.053 +1.154 +0.101
2019 +0.0000032 +0.000591 +0.018564 +1.071 +1.287 +0.216
2020 +0.0000032 +0.000594 +0.019158 +1.090 +1.319 +0.229
Ave +1.003 +1.134 +0.131 11.5%
The procedure recommended in this work results in an underestimation of the
actual Global Warming by 11.5%, which means that the actual Global Warming
exceeded the estimation based on previous decade data by 11.5%.

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Chart 14 - Forecast and actual Global Warming 2010-2020 [°C]
0.9
1.0
1.1
1.2
1.3
1.4
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
Forec ast Ac t ual
Changes in this Version
 addition of parameter “Annual Change in Global Warming
Acceleration” (dGWA) based on GWA trendline slope
 replacement of the 1961-2021 trendline by the 1960-2020 trendline for
some calculations
 editorial changes
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.

Global Warming Acceleration v1.2.1 - Joseph Nowarski
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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
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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