378 Int. J. Global Warming, Vol. 1, Nos. 1/2/3, 2009
Copyright © 2009 Inderscience Enterprises Ltd.
Global energy accumulation and net heat emission
Bo Nordell* and Bruno Gervet
Department of Civil and Environmental Engineering
Luleå University of Technology
SE-97187 Luleå, Sweden
E-mail: bon@ltu.se
E-mail: brunogervet@hotmail.fr
*Corresponding author
Abstract: The increase in the global air temperature is an inadequate measure
of global warming, which should rather be considered in terms of energy. The
ongoing global warming means that heat has been accumulating since 1880 in
the air, ground and water. Before explaining this warming by external heat
sources, the net heat emissions on Earth must be considered. Such emissions
from, e.g., the global use of fossil fuels and nuclear power, must contribute to
global warming. The aim of this study is to compare globally accumulated and
emitted heat. The heat accumulated in the air corresponds to 6.6% of global
warming, while the remaining heat is stored in the ground (31.5%), melting of
ice (33.4%) and sea water (28.5%). It was found that the net heat emissions
from 1880–2000 correspond to 74% of the accumulated heat, i.e., global
warming, during the same period. The missing heat (26%) must have other
causes, e.g., the greenhouse effect, the natural variations in the climate and/or
the underestimation of net heat emissions. Most measures that have already
been taken to combat global warming are also beneficial for the current
explanation, though nuclear power is not a solution to (but part of) the problem.
Keywords: global warming; heat accumulation; heat emission; thermal
pollution.
Reference to this paper should be made as follows: Nordell, B. and Gervet, B.
(2009) ‘Global energy accumulation and net heat emission’, Int. J. Global
Warming, Vol. 1, Nos. 1/2/3, pp.378–391.
Biographical notes: Bo Nordell is a Professor of Water Resources Engineering
at the Luleå University of Technology (LTU) in Sweden. His expertise is in
seasonal thermal energy storage, in which he has worked for 30 years. He
heads LTU’s research group on renewable energy since 2000.
Bruno Gervet, from Chamonix in France, made his MSc thesis on global
warming at LTU, Sweden.
1 Introduction
Global mean temperatures have been compiled based on long-term air temperature
measurements (NCDC-NOAA, 2007). These temperatures (found in Figure 1) are
separated into a monthly Sea Surface Temperature (SST) and a monthly Land Area
Temperature (LAT). The global mean temperature is the area-weighted mean of LAT and
Global energy accumulation and net heat emission 37
9
SST. In 1880, SST was 15.9°C and LAT was 8.6°C, with a global mean of 13.6°C. Until
2000, SST had increased by 0.5°C and LAT, by 1.2°C. The corresponding global mean
temperature increase in 1880–2000 was 0.7°C. However, the global mean air temperature
increase is an inadequate measure of global warming and, independent of what causes
global warming, it should be considered in terms of energy (Pielke et al., 2004; Pielke,
2005). Here, global warming is considered the global energy accumulation in air, ground
and water since 1880.
Figure 1 The global LAT and SST from 1880–2000 (see online version for colours)
Source: NCDC-NOAA
Before explaining global warming by extraterrestrial heat sources, the net heat emissions
on Earth should be considered. Emissions such as heat dissipation from the global use of
fossil fuels and nuclear power must contribute to global warming. It is a common opinion
that the heat emitted by anthropogenic systems is insignificant because it is very small
compared to solar energy input. However, this solar energy input does not cause any
warming over the year as long as the planet is in thermal balance. Therefore, it is not
relevant to compare the net heat emissions with the flux of energy from the sun. What
really matters is the change in the energy balance and the occurring net heat emission
must, to some extent, contribute to global warming.
Another common idea is that the net heat emissions would be emitted to space. This
is partly true only in some rare cases when net heat is emitted at a high temperature. In
most cases, however, net heat emissions mean that low-temperature waste heat is dumped
into sea water or the atmosphere or heat leakage from buildings is transferred to the
surrounding air or ground. When this net heat is mixed with large recipients, it means that
it very soon will be at the ambient temperature.
In the current study, accumulated and emitted heat were estimated and compared.
2 Global heat accumulation
The methods used to calculate the temperature increase and the subsequent heat
accumulation in the ground and air are described in Appendix A. The performed
calculations include the period from 1880–2000.
380 B. Nordell and B. Gervet
2.1 Heat accumulation in the ground
As a result of the increased air temperature, the ground surface has also warmed up
and heat has been conducted into the ground. The performed calculations, which are
described in Appendix A, show that the ground heat accumulation rate was relatively
linear until 1960, when it began accelerating. Since the late 1990s, it has exceeded the
geothermal heat flow, indicating a net heat inflow from the surface into the ground. The
heat content of the ground increased by 23.4 kWh m
–2
from 1880 to 2000. This heat
conduction into the ground occurs neither in permafrost areas, defined as perennial
ground ice, nor on glacier ice or icings (National Snow and Ice Data Center – NSIDC,
2007a). Such areas, which are affected differently by global warming, are included
in the melting of ice and contributes to the rise in the sea level. The glaciated areas
(0.16
.
10
14
m
2
) (Singh and Singh, 2001) and permafrost areas in the world (0.30
.
10
14
m
2
)
thus reduce the total land area (1.5
.
10
14
m
2
) affected by heating to 1.02
.
10
14
m
2
. The total
ground heat accumulation since 1880 then becomes 23.9
.
10
14
kWh.
2.2 Heat accumulation in air
The heat accumulation in air (moist static energy) was estimated separately for sea and
land. Hence, different mean air temperatures over sea and land were considered. The total
heat accumulation in the air is 5.0
.
10
14
kWh, of which 44.6% is distributed over the land
area. The performed calculations are described in Appendix A.
2.3 Heat accumulation in water
The heat accumulation in ocean water was estimated from the Global Sea Level Rise
(GSLR), compiled by the Permanent Service for Mean Sea Level (PSMSL, 2007). The
GSLR is a result of various factors, e.g., the inflow of water from melting glaciers and the
thermal expansion of the warmer water, which are both a result of global warming,
i.e., indirect anthropogenic effects. Examples of direct anthropogenic effects (Harvey,
2000) since 1880 are the increasing water vapour content of the air, the permanent
removal of water from aquifers, deforestation and the loss of soil moisture, reduction in
the extent of wetlands, storage behind dams, deep infiltration behind dams, deep
infiltration of irrigation water and ocean sedimentation. An important factor might be the
ocean sedimentation rate, which increases with an increasing global mean temperature
(Broecker et al., 1958).
Measurements show that the GSLR has been relatively steady since 1880, rising
0.18 m until 2000 (PSMSL, 2007). Its constant increase indicates that it is not directly a
result of global energy consumption, which is far from linear (Figure 2). The values
based on the processes mostly responsible for the increase in GSLR mass, from melting
land ice and volume increase due to thermal expansion, give a considerably lower sea
level change (Miller and Douglas, 2006), suggesting that most of the rise is caused by
direct anthropogenic effects.
Global energy accumulation and net heat emission 381
Figure 2 The annual world consumption of commercial nonrenewable energy, 1880–2000
(see online version for colours)
Source: CDC (2007)
There are various data regarding the contribution of thermal expansion to the 20th
century sea level rise. The most commonly suggested thermal volume expansion rate is
presently 0.5 mm per year (Church et al., 2001; Antonov et al., 2002). Recent studies
show considerably lower values (Ishii et al., 2003) and it is reported that the ocean water
has been cooled for several years (Lyman et al., 2006). Satellite measurements show that
large-scale El Niño-like ocean temperature fluctuations occurred between 1955 and 1995
(Ishii et al., 2003).
Such fluctuations and the recently reported ocean temperature
decrease is a result of large-scale and long-cycled (~15 years) ocean circulation, leading
to the melting of sea ice and the subsequent cooling of the water. Based on the
temperature fluctuations between 1955 and 1995, with three maximum and two minimum
values during the period, a thermal expansion rate of 0.02 mm year
–1
was estimated (Ishii
et al., 2003). Since this expansion, i.e., 1 mm over the last 50 years, is a result of global
warming, the corresponding previous expansion until 1955 should be insignificant.
Assuming that this sea water heating occurred in the top 1000 m of the ocean with a
salinity of 35 ppm, this 1 mm thermal expansion corresponds to 21.6
.
10
14
kWh of heat.
Recent estimates of the total sea level rise due to the melting of small glaciers and
Greenland is about 60 mm. Here, this contribution is estimated to about 50 mm until
2000. The main uncertainty is whether the ice mass of Antarctica is decreasing or
increasing, i.e., causes the sea level to rise or not (Harvey, 2000). If the mass of ice on
Antarctica increases, the total melt heat will be correspondingly less. The energy required
to melt glaciers and permafrost, totalling a 50 mm sea level rise, is 16.8
.
10
14
kWh.
The total area of sea ice is 19.9
.
10
12
m
2
, of which 14.8
.
10
12
m
2
is floating
on the
northern hemisphere. The estimated annual melting in 1980–2000 was 0.38% ± 0.02%
on the northern hemisphere and 0.02% ± 0.48% (NSIDC, 2007b) on the southern
hemisphere. During the same period, the total thinning of the 3 m-thick ice was estimated
382 B. Nordell and B. Gervet
at 4% (Johannessen et al., 2003). Here, the values for the northern hemisphere are used,
while the very uncertain values for the southern hemisphere are disregarded. The
resulting annual melting of 258 km
3
of sea ice requires 0.22
.
10
14
kWh year
–1
during
1980–2000. The melted sea ice during the last 120 years is considered proportional to
the energy consumption during the same period (see Figure 2), resulting in the melting of
10
4
km
3
of sea ice and a corresponding heat absorption of 8.5
.
10
14
kWh. The melted sea
ice, which is often considered not to influence the sea level, will actually have a volume
that is 2.6% greater than that of the ice and contribute slightly to the sea level rise
(Noerdlinger and Brower, 2008). The total heat accumulation in ocean water during
1880–2000, i.e., by the heating of sea water and the melting of land and sea ice, then adds
up to 46.9
.
10
14
kWh.
The global heat accumulation in the air, ground and water during 1880–2000 is thus
75.8
.
10
14
kWh (27.3
.
10
21
J). This heat is distributed in the air (6.6%), ground (31.5%),
water (28.5%) and melting of land and sea ice (33.3%) according to Figure 3. It is
noticeable that the heat content in air only corresponds to 6.6% of global warming.
Figure 3 The total global warming, i.e., heat accumulation in air, ground and water/
ice since 1880 (see online version for colours)
Note: The total heat accumulation is 75.8
.
10
14
kWh (27.3
.
10
21
J).
3 Global net heat generation
The major natural heat source is geothermal heat flow, but heat is also generated by
volcanic eruptions, earthquakes and meteorites, among others. Non-natural heat sources
include the global use of fossil fuels, nuclear power and deforestation. Heat emissions
from nuclear bomb tests and conventional bombs also add to the net heat generation.
3.1 Geothermal heat flow
Global heat flow data are collected by the International Heat Flow Commission (IHFC,
2007). The compiled mean geothermal heat flow (Pollak et al., 1993) is 0.065 W m
–2
for
the continents and 0.101 W m
–2
for the oceans. Its variation is a result of the composition
and thickness of the upper part of the crust. The total geothermal heat flow during the last
120 years is 486
.
10
14
kWh (175
.
10
21
J). This energy is considerably greater than the
global energy consumption during the same period and is given as a reference value to
other net heat sources, though it does not contribute to global warming.
