ESDEarth System DynamicsESDEarth Syst. Dynam.2190-4987Copernicus GmbHGöttingen, Germany10.5194/esd-6-689-2015Resource acquisition, distribution and end-use efficiencies and the growth of industrial societyJarvisA. J.a.jarvis@lancs.ac.ukJarvisS. J.HewittC. N.Lancaster Environment Centre, Lancaster University, Lancaster, UKOffice of Gas and Electricity Markets, London, UKA. J. Jarvis (a.jarvis@lancs.ac.uk)13October2015626897024December201429January20157September201515September2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://esd.copernicus.org/articles/6/689/2015/esd-6-689-2015.htmlThe full text article is available as a PDF file from https://esd.copernicus.org/articles/6/689/2015/esd-6-689-2015.pdf
A key feature of the growth of industrial society is the acquisition of
increasing quantities of resources from the environment and their
distribution for end-use. With respect to energy, the growth of industrial
society appears to have been near-exponential for the last 160 years. We
provide evidence that indicates that the global distribution of resources
that underpins this growth may be facilitated by the continual development
and expansion of near-optimal directed networks (roads, railways, flight
paths, pipelines, cables etc.). However, despite this continual striving for
optimisation, the distribution efficiencies of these networks must decline
over time as they expand due to path lengths becoming longer and more
tortuous. Therefore, to maintain long-term exponential growth the physical
limits placed on the distribution networks appear to be counteracted by
innovations deployed elsewhere in the system, namely at the points of
acquisition and end-use of resources. We postulate that the maintenance of
the growth of industrial society, as measured by global energy use, at the
observed rate of ∼ 2.4 % yr-1 stems from
an implicit desire to optimise patterns of energy use over human working lifetimes.
Introduction
The growth of industrial society since the Industrial Revolution has
required the continual exploitation of a diverse range of
environmentally derived resources. Because resources are seldom consumed at
the point of extraction, this in turn has required the construction of
ever-expanding distribution networks. These networks can be seen to form
part of a global Resource Acquisition, Distribution and End-use (RADE)
system linking environmental resources with points of end-use. In many
respects these man-made networks resemble those seen in natural systems,
both in terms of form and function. Here we attempt to apply theoretical
insights from research into the evolution of natural systems to the man-made
system that constitutes global industrial society, with a particular focus on energy.
This paper builds on a long tradition of attempting to understand
socio-economic systems through the application of insights from the natural
sciences. Initially these insights were largely metaphoric, but increasingly
the application of evolutionary (Nelson and Wilson, 1982), metabolic
(Fischer-Kowalski and Huttler, 1998) and thermodynamic (Garrett, 2011, 2012)
theories has become much more direct in this area. The fundamental physical
constraints that underpin the development of distribution networks have
previously been used to try and explain the behaviour of biological systems
(West et al., 1997), river basins (Rodríguez-Iturbe and Rinaldo, 1997),
electricity grids, water distribution systems, road networks (Dalgaard and
Strulik, 2011; Pauliuka et al., 2014; Bettencourt et al., 2007), and even
cities (Bettencourt, 2013), but have not previously been applied to the
behaviour and growth of global industrial society itself.
Here we explore the possibility that the growth of industrial society is in
part regulated by the behaviour of the distribution networks within a global
RADE system. The resources moved by man-made distribution networks include
energy and the other materials from which industrial society is constructed.
In the following analysis we focus specifically on the energy used in
acquisition, distribution and end-use. We do this because the performance of
RADE networks is determined by their energy efficiency (i.e. the proportion
of energy lost in transporting mass across networks) and because energy use
is one of the best observed metrics of global economic activity.
Furthermore, because all aspects of industrial society use energy, and are
themselves constructed using energy, a potentially self-reinforcing feedback
exists between energy use and the growth of industrial society.
Our analysis suggests that:
By definition, resource distribution networks must fill the space occupied
by industrial society. These networks appear to behave near-optimally with
respect to minimising energy losses if the space being filled is three-dimensional.
Whether optimal or not, the distribution efficiency of the global RADE
system declines over time, apparently due to the increasing distribution costs
associated with growth-induced network expansion.
This declining distribution efficiency appears to be offset by increasing
acquisition and end-use efficiencies. This is evidenced by the observed near-constant relative growth rate in energy use that has been maintained at the global scale
despite declining distribution efficiencies.
The maintenance of growth in energy use at the global scale, specifically
at the observed long-term average of ∼ 2.4 % yr-1, may be
explained by the minimisation of energy losses over a timescale characteristic
of human working lifetimes.
The paper is structured as follows. Section 2 introduces the distribution
network theory that underpins the work. This is then used in Sect. 3 to
specify and test a predicted scaling relationship between energy flows at
the point of acquisition (global primary energy) and those arriving at the
points of end-use (global final energy). Section 4 is a discussion on the
geometry of the space being filled by the RADE system. Section 5 extends the
analysis to consider behaviour at the country scale and how this aggregates
to give the observed global-scale behaviour. Section 6 then explores how the
observed global trends (at least with respect to primary energy) may extend
back to at least 1850. In so doing we focus on one of the specific
mechanisms that appears to mediate the evolution of the RADE system, namely
the dematerialisation of resource flows. Section 7 offers a simple model of
the full RADE system that accounts for the exponential growth in global
energy use observed. This model yields constant relative growth in energy
use despite the decreasing returns to scale associated with the expansion of
the RADE distribution network(s). Section 8 uses this simple model to
attempt to account for the specific observed long-term relative growth rate
in global primary energy use of ∼ 2.4 % yr-1. This is
done by exploring an optimisation of average personal energy use over
specific integration timescales. Finally, Sect. 9 offers some concluding
remarks concerning the growth of industrial society in general and some
thoughts on further work.
Energy and resource distribution networks
Resource distribution networks are ubiquitous in nature. Specifically, in
biology these networks, such as cardiovascular systems in mammals and
vascular systems in higher plants, distribute resources from points of
acquisition to the end-use tissues and cells which require these resources
to function. Because this form of spatial distribution must itself consume a
significant proportion of the acquired energy resources, this has provided
strong selective pressure for the evolution of optimal forms of network
architecture and operation, with branched directed networks becoming
ubiquitous in nature (Savage et al., 2004). Furthermore, biological systems
are frequently comprised of complex networks of networks. These networks
often co-evolve together as parts of an overall system that both collects
and distributes resources, e.g. lungs, blood, lymph and nerves in animals.
This means that the networks can be configured both many-to-one (i.e. points
of acquisition to collection point) and one-to-many (i.e. distribution point
to points of end-use) within the same organism. Interestingly, these
integrated systems still appear to follow the same theoretical laws, and
thus exhibit the same scaling behaviour, as single directed networks (Savage et al., 2004).
We believe it is self-evident that the growth of industrial society has also
required the construction of ever-expanding resource distribution networks.
These networks include a wide range of infrastructures such as pipes,
cables, footpaths, roads, railways, shipping lanes and flight paths. The
resources being distributed through these networks are also diverse,
including energy, raw materials, manufactured goods, waste, people etc. Here
we focus largely on flows of energy. These flows originate from the
acquisition of environmentally derived resources which pass through
distribution networks to points of end-use. These terminal points of the
networks can be thought of as units of energy consumption distributed in the
space occupied by industrial society. Taken as a whole, we view this entire
process as a RADE system.
RADE networks are optimised by minimising energy distribution losses whilst
facilitating resource use (West et al., 1997; Banavar et al., 2010). For
energy flows we can define the distribution efficiency of such networks by
the ratio of the energy entering the network (primary energy, x) to that
arriving at the points of end-use (final energy, x*). Networks can be thought
of as optimal if, under the constraint of having to satisfy particular
end-use demand, the distribution losses, x-x*, are minimised for any given x and
hence the distribution efficiency can be defined as x*/x. Maximisation of this
distribution efficiency (x*/x) can be achieved by both minimising total path
lengths and maximising unit path length efficiencies.
One of the most effective means of minimising path lengths is to optimise
the structure of the system by co-locating points of end-use at optimal
locations within RADE networks. Such behaviour is ubiquitous in industrial
society expressed through the process of urbanisation. As for unit path
length efficiencies, these can be affected by the method of distribution and
the nature of the resource being distributed. Two examples are the
increasing use of more fuel efficient vehicles and the liquefaction of
natural gas for transportation. It is also important to appreciate that path
lengths and their efficiencies are not only determined by infrastructural
modes of distribution and the geographies of points of end-use but also by
decisions that people make when choosing between the pathways available to
them. For example, there may be many routes between two locations, but
quicker and less arduous routes are generally preferred.
In summary, our conceptual model of the distribution element of the global
RADE system is one of a space-filling network linking points of
environmental resource acquisition to points of societal end-use. To explore
the possibility that the distribution element of the global RADE system
behaves in this way we now investigate the relationship between global
primary energy use, x, and global final energy use, x*. We refrain from
looking at the architectures of specific networks because, as stated
previously, our analysis is largely dependent on flows of energy at the
global scale. As such, we believe it is the emergent behaviour of the
network of networks that comprise the global RADE system that is relevant.
This suggests that the behaviour of individual network elements must be
considered within the context of the other network elements they operate alongside.
Primary and final energy flows at the global scale
As discussed previously, one definition of an optimal network is where
distributional energy losses are minimised. West et al. (1997) employed an
optimal model of a fractal space-filling network to demonstrate how
distribution networks in nature can give rise to observed scaling patterns.
Banavaar et al. (2010) showed that these patterns were not restricted to
fractal networks. Although not articulated in these papers, both of these
analyses allude to a theoretical upper limit of the distribution efficiency
x*/x for any given space being occupied by a distribution network. If L is the
linear size of the network then the size of the space being filled by the
network is given by LD where D is the dimension of the space being filled
by the network. Independent of the specific modelling assumptions considered
by either West or Banavaar, to be consistent with their modelling results,
optimal network efficiency has to scale with network size according to
x*/x∝L-D/(D+1). This even holds as L tends to
zero because D must also tend to zero in the limit, so the efficiency of the
network has a theoretical unity upper limit even as L→ 0.
The scaling relationship between x*/x and L suggests that the relationship
between the energy arriving at the points of final use, x*, and the primary
energy flow entering the network, x, should scale as x*∝xD/(D+1).
This is the same scaling relationship proposed
by Dalgaard and Strulik (2011), building on Banavar et al. (2010), when
attempting to account for the energy distribution losses in the US
electricity grid. The reason for sub-unity scaling between x* and x is simply
because as the size of the system increases so does its average path length
between points of acquisition and end-use, L. This increase in path length
causes the distribution efficiency, x*/x, to fall. However, rather than the
efficiency falling in proportion to increases in network size, LD, it
falls in proportion to LD/(D+1) , i.e. at a rate slower
than one would predict from geometric considerations alone. This is because
of the optimisation of the distribution links within the RADE network as
discussed earlier.
We define global primary energy use, x, as the annual energy flow from nature
to society in the form of wood, coal, oil, gas, nuclear, renewables and
food. Primary energy is generally treated as the combustible energy
equivalent of these sources. This does introduce some complexity when
handling non-combustible sources (e.g. wood used for construction), but
given that these are such a small fraction of the total this is not believed to
significantly affect the quality of the aggregate global primary energy data
(Macknick, 2009). Total food use was estimated by assuming global per capita
consumption of 3 × 109 J yr-1 (United Nations, 2002), although
presently this represents less than 1 % of the total.
We define x* (final energy use) as the energy available to industrial society
once distribution losses have been accounted for. The International Energy
Agency (IEA) provides estimates of energy lost through its acquisition,
processing and delivery to end users. However, these data do not account for
energy losses associated with either the acquisition of non-energy resources
and agriculture or the transport of all mass through industrial society. In
an effort to account for these losses to obtain x* we have subtracted the IEA
estimates of energy used in quarrying, mining, agriculture, forestry and, in
particular, transport, from the IEA final energy consumption data.
Considering transport as a distributional loss raises an important
conceptual issue. Currently approximately 50 % of transport energy use
is associated with passenger movements. Traditionally these are seen as
end-use energy services enjoyed by people. However, here we treat them as
necessary distributional losses required to get energy consumers to spatial
nodes where they can contribute to the continued growth of the RADE system.
In other words, we view the flow of people like the flow of any other mass
in the RADE system. Hence we view nodes of final consumption as static
locations where final energy is consumed, albeit with human agency applied
to the purpose of consumption. Importantly, this means that nodes are best
viewed as more than just passive recipients of resource. Instead final
consumption nodes must in turn facilitate the further acquisition of
resources through extending the interface between industrial society and the
environment (Garrett, 2011, 2012). Taking this approach essentially means
that all components of the RADE system that are mobile are distributional
and all static components are either acquiring resources or consuming
resources for end-use. Although this framing may be contrary to more
traditional views of humans as “energy consumers” we believe it is at least
internally consistent with our view of the RADE system and the role of humans in it.
It should be noted that our estimates of x* do not adequately account for the
distribution energy losses occurring between the point of sale and the point
of end-use of energy (e.g. in the case of electricity, losses occurring
between the meter and the plug). However, we assume these to be relatively
small relative to all upstream losses associated with acquiring and
distributing all resources. The small underestimate of distributional loss
implied by our estimate of final energy using the IEA data should be
partially offset by the fact that our revision of the IEA final energy use
will also include some non-distributional energy uses (e.g. end-use energy
in agriculture) due to the way the IEA data are compiled.
We define the space associated with unit final energy consumption (referred
to as a “control volume” by Dalgaard and Strulik, 2011) as being that
where the consumption of useful energy in that space is significantly
greater than the transfer of useful energy from that space to other regions
of the network. These spaces are complex entities and not easy to identify,
because in a global mean sense they are comprised of broad portfolios of
energy uses. That said, examples of end-use processes might include reading
this article on a computer, cooking, constructing or demolishing a
residential building etc.
As for energy losses due to energy transformations that occur between
primary and final energy, these are far more significant. One way of
reconciling these transformations within the current framework is that they
are deployed to reduce mass flows in critical parts of the system (e.g. by
generating electricity from coal). Here the substantial energy losses
incurred by these transformations are presumably offset by the downstream
savings they facilitate (in this example, by reducing the amount of coal
distributed to individual households). This point will be explored in
greater detail in Sect. 4.
(a) The relationship between global primary
energy use, x, and global final energy, x*. Two definitions of final energy
are shown; (o) are the IEA estimates, (•) are the IEA estimates
adjusted for energy used for transport, agriculture, forestry, mining and
quarrying. (b) The relationship between global primary energy use,
x, and primary to final network efficiency, defined as the ratio x*/x(⚫).
Also shown are the estimated variations in end-use
efficiency assuming a total system efficiency 10 % (+). The IEA
definition of primary to final energy efficiencies (o) are also shown for
reference. (c) The relationship between global primary energy use,
x, and global anthropogenic CO2 emissions, y, for the data shown in
Fig. 3. (d) The relationship between global primary energy use,
x, and the carbon intensity of global primary energy, x/y again for the data shown in Fig. 3. The bands for all
plots represent 5th to 95th uncertainty ranges from the linear
regressions. See text for all data sources and compilation.
Figure 1a shows the relationship between x and x* for the available IEA data (IEA, 2012).
We find that x*∝xc (c= 0.75 ± 0.02)
Scaling
exponents have been estimated using ordinary least squares of the linear
model ln(x*) =θ1ln(x)+θ2. Parameter uncertainties are
reported at 95 % confidence. 1σ uncertainties in the data were
assumed to be 5 % (Macknick, 2009). All results were also
cross-checked using nonlinear least squares of the untransformed data.
,
i.e. the scaling exponent c is statistically indistinguishable from three
quarters. For reference, using the IEA definition of final energy gives
c= 0.84 ± 0.01 with practically all of the difference between these two
estimates attributable to the inclusion of transport in our specification of
final energy. Figure 1b shows the equivalent relationship between the
distribution efficiency, x*/x, and primary energy, x. It confirms that, as
predicted, the overall efficiency of the network has progressively fallen
over time as x has increased and is now below 50 %, i.e. more than half
of all primary energy is now used simply to move all the materials and
resources required by industrial society (e.g. environmentally derived
materials, mobile system infrastructure and people) to final nodes of end-use.
What space does society inhabit?
The fact that we observe scaling between x* and x that is statistically
indistinguishable from three quarters suggests D= 3 in the framework set
out above. Although the relative dimensions are far from equal, it is
self-evident that the networks moving mass through global industrial society
occupy a three-dimensional space. However, since the horizontal dimensions
of this space are approximately 3 orders of magnitude greater than the
vertical dimension (delineated by, for example, the distance between the
deepest mines and the height at which aircraft fly), it is appropriate to
ask whether this space is more appropriately approximated by a two-dimensional surface rather than a three-dimensional volume. This question
cannot be answered conclusively here but we offer the following lines of
evidence to suggest that D= 3 does indeed provide a plausible description
of the space filled by the global RADE system.
Firstly, the effect of gravity obviously imposes disproportionately higher
distribution costs on movement in the vertical dimension than in the
horizontal. We conjecture that these differences in cost are between 1 and
2 orders of magnitude. This could rise significantly above 3 orders of
magnitude when the engineering difficulties of exploring the vertical
dimension below ground are considered. Whether this is sufficient to result
in D= 3 in the global RADE networks is unclear although we note that we
invariably treat the atmosphere as a three-dimensional object even though it
too has a severely diminished vertical dimension. Secondly, the scaling
behaviour of urban centres suggests that people occupy a three-dimensional
space at the city scale, despite the fact that the vertical dimension is
again very much attenuated (Nordbeck, 1971). Even silicon chips, which have
a trivial vertical dimension, exhibit scaling of the order of D= 2.5 (Deng
and Maly, 2004) suggesting that even a highly attenuated vertical dimension
with no disproportional losses can result in non-trivial scaling effects.
Finally, although the Earth's surface can, by definition, be considered a
two-dimensional object, the curvature of this surface at the global scale
may be sufficient to introduce three-dimensional effects in the links
between network nodes.
An alternative explanation to our observed scaling behaviour of the global
energy system is that D< 3 and that the system operates
supra-optimally, which appears infeasible. Equally, the observed exponent of
three quarters may have arisen by chance and the systemic explanation
explored here is incorrect. This proposition cannot be rejected, but then
neither can the proposition that D= 3. It also seems somewhat anomalous
that we would observe a scaling exponent that is indistinguishable from
three quarters if the system was two-dimensional.
If the global RADE network has the dimensions of D= 3, then the scaling
observed between x and x* suggests that, at the global scale, the distribution
networks that underpin the RADE system are, in aggregate, optimised with
respect to energy losses, despite filling a highly irregular three-dimensional space. That the RADE networks created within industrial society
should be near-optimal does not seem unreasonable given the pressures to
seek out performance improvements in a competitive global market system.
As a result of the framework set out above we identify three related
mechanisms through which distribution efficiency gains, and hence the
optimisation of this element of the global RADE system, could be realised.
The efficiency of network infrastructure is progressively improved over
time (e.g. by the use of more aerodynamic vehicles, more efficient combustion
processes).
The flows are themselves persistently dematerialised over time (e.g. by
introduction of lighter vehicles, shifting the primary fuel mix from wood to
coal to oil to gas or turning coal into electricity – see later).
The structure of and practices on the network are modified over time to
reduce average path lengths, L (e.g. by building a new road, introducing car
navigation systems, by the reorganisation of the points of acquisition and
end-use during urbanisation).
The first two of these are primarily concerned with maximising unit path
length efficiencies, whilst the third is primarily concerned with minimising
total path lengths. It may also be that processes like urbanisation offer
additional benefits in that the increased social interactions that result
from the clustering of people stimulate the innovations required to discover
and realise the three efficiency mechanisms mentioned above (Bettencourt,
2013). These innovations have to be continuously discovered, developed and
implemented in order to accommodate the growth of the RADE system. We shall
return to the subject of resource flow dematerialisation in more detail in Sect. 6.
What happens at the regional scale?
Thus far our analysis has been focused at the global scale, yet this global
behaviour must emerge from regional-scale dynamics. Each region, i, uses
primary energy, xi, and final energy, xi*, where ∑xi=x
and ∑xi*=x*. As we have already discussed, networks tend to
become less efficient as they expand due to the size-related penalties of
growth. It appears that this behaviour is observed at the global scale with
x*/x decreasing as x increases (Fig. 1b). In the absence of further
innovation and all else remaining equal, we would anticipate the same
behaviour at the regional scale. This means that in portions of the system
with higher energy use densities (i.e. higher energy use per unit space) we
would expect lower regional distribution network efficiencies,
xi*/xi. Conversely, in portions of the system with lower energy use
densities (i.e. lower energy use per unit space) we would anticipate higher
regional distribution network efficiencies. However, if this divergence in
distribution efficiencies between regions, due to differing energy use
densities, actually arose at any given point in time it would presumably
cause the global system to be sub-optimal because global final energy use
could be increased for the same global primary energy use simply by shifting
resource distribution from the less efficient to the more efficient portions
of the system.
This sub-optimality is not what we observe at the global scale. Instead, as
discussed above, the observed approximate three quarter scaling between x and
x* indicates that the global RADE system is operating near-optimally with
respect to distribution if D= 3. Because it appears that the system could be
near-optimal at the global scale, we would expect distribution efficiency
gains to be persistently sought out. In other words, if optimal, the RADE
system would evolve such that it seeks to exhaust all potential improvements
with respect to energy use. As a result, we hypothesise that, at any
particular point in time, all countries of the world should have similar
network efficiencies and these should be independent of their energy use
densities (i.e. their xi per unit space). In order to achieve this,
countries located in more energy-dense (i.e. more developed) portions of the
system presumably innovate more aggressively on distribution efficiency to
overcome the size-related penalties of growth than do those in less energy-dense (i.e. less developed) portions of the system. Once again, examples of
these innovations might be the enhanced efficiency of mass transport,
enhanced urbanisation and the enhanced use of gas or electricity.
We test this hypothesis using IEA data for 140 countries for the period 1971–2010.
Figure 2 shows the relationship between primary and final energy
use (xi and xi*) for these data. In the absence of a measure of the
effective volume being filled by society, we have normalised energy use by
country land area in order to attempt to reflect the space-filling aspect of
the system. Because this assumes uniform average vertical dimensions between
countries and is applied to both xi and xi* this only changes the
relative positions of countries, not their individual efficiencies.
The relationship between country-specific primary energy
use, xi, and final energy use, xi* for the period 1971–2010.
Individual countries are marked with different colours, N= 140. The data
for all countries for 2010 are marked separately (o). All country-specific
energy data are normalised using the surface area of the country. The
surface area is an imperfect proxy for the space occupied by each country if
the global system is filling a three-dimensional volume. In the absence of
data, we assume that the magnitude of the vertical dimension is constant
across all 140 countries. Note that the higher per unit area energy
consumers have per unit area energy flows that are a significant proportion
of the solar constant. The inset figure shows both the exponential scaling
coefficient estimated from the annual relationship between xi and
xi* (values near 1) along with the primary-to-final energy efficiency
xi*/xi plotted for each year 1970 to 2010. The bands
represent 5th to 95th uncertainty range for the estimates. See
text for data sources and compilation.
As predicted, Fig. 2 shows that at any given point in time
xi*/xi is largely independent of xi (xi*∝xic;
c= 0.97 ± 0.03 for all 40 years). This appears
to hold across all 140 countries sampled, which have a range of 105 in
energy use per unit area. For example, currently the UK has a similar
distribution efficiency, x*/x, to that of Bolivia (0.473 vs. 0.466), despite
having > 102 greater energy use density. A significant
contributor to the variation in xi* and xi is probably the less
reliable IEA energy data for less-developed countries. We note that the
variation created by these uncertainties is not systematically above or
below the central trend. Moreover, we would expect the relationship to be
even clearer if we were able to normalise the data by the appropriate
volume, rather than area, occupied by society in each country.
Because of the apparent invariance of distribution network efficiency with
energy use density it would appear that regional networks are not scaled
versions of the global system, i.e. the global RADE network appears to be
scale dependent rather than scale free. This implies that you cannot simply
look at isolated sub-components of the global RADE network (e.g. individual
countries) in order to infer the behaviour of the global system.
Long-run growth and decarbonisation of global energy use
Thus far we have focused on data on primary and final energy use covering
the last 40 years. However, there are data on primary energy use going back
much further than this. As mentioned earlier, global primary energy use,
x, is taken here to be the annual energy flow from the environment to society
in the form of wood, coal, oil, gas, nuclear, renewables and food. In order
to construct a consistent time series for x since 1850, following Jarvis et
al. (2012), the global primary energy use data for the period 1850 to 1964
are taken from Grübler (2003) and for the period from 1965 to 2010 from
BP (2011). We note that compiling long-term historic series for virtually
any relevant measure of economic activity is challenging due to the paucity
of available data and increasing uncertainties the further back one goes.
Data on energy use are not exempt from these limitations. For example, the
Grübler data we use do not appear to capture the full portfolio of
renewables in use in the 1800s (e.g. wind and water power). However, we also
note that the energy data used here still represents one of the best
observed metrics of global economic activity. Also on the specific issue of
renewables post-1850, evidence suggests that they constituted a negligible
part of the global energy portfolio during this period (O'Connor and
Cleveland, 2014; Fouquet, 2014).
We opt to use the BP data in order to attempt to have some limited
independence from the IEA data used to explore the relationship between x and
x*. To produce a homogeneous record for 1850 to 2010 the mean difference
between the two series for the period 1965 to 1995 (which is largely due to
lack of wood fuel use in the BP data set) was added to the BP data. The data
were converted from tonnes of oil equivalent (toe) to Joules, assuming
1018 J = 2.38 × 107 toe (Sims et al., 2007).
Figure 3 shows the primary energy use data, x, for the period 1850–2010.
These suggest that, in the long term, x has grown near exponentially since at
least 1850, with a long-term relative growth rate of 2.4 (±0.08) yr-1
(Jarvis et al., 2012).
Relative growth rates have been
estimated using ordinary least squares of the general linear model
ln(x)=θ(t-t1). Parameter uncertainties are reported at 95 %
confidence. The model residuals, which were significantly autocorrelated,
have been de-correlated assuming a first-order autoregressive noise model to
minimise any bias in the estimates of θ. 1σ uncertainties in
the data were assumed to be 5 % in energy use and fossils fuel
emissions (Macknick, 2009); and 20 % in land-based emissions (C. Le
Quéré, personal communication, 2013).
Using global Gross Domestic Product (GDP) data as a
proxy for global energy use, Garrett (2014) suggests that the relative
growth rate of global primary energy has increased significantly over this
period. The data and analysis in Fig. 3 would indicate otherwise, although
clearly there are significant uncertainties over actual global primary
energy measures both now and more significantly pre-1900. For example it is
unclear what contribution wind makes through shipping over this period. That
said, that the long-run growth in primary energy use observed over the last
40 years actually appears to extend back at least 160 years suggests that
the processes and trends that have underpinned the development of the global
RADE system may have actually been operating for considerably longer than
the IEA data provide evidence for. If this is the case we would predict that
the optimisation mechanisms identified earlier would also have been at work
over the same period. In particular, we would expect that these optimisation
mechanisms would be sought out and implemented at a rate that matches the
growth-induced declines in distribution efficiency experienced by the global
RADE system revealed in Fig. 1b.
(i) Annual global primary energy use [11, 12, 13]
with regression line given by lnx=a(t-t1); a= 0.0238 ± 0.0008 yr-1;
t1= 1775 ± 3.5 CE. (ii) Annual global
anthropogenic CO2 emissions [15, 16, 17] with regression line given by
lny=b(t-t1); b= 0.0179 ± 0.0006 yr-1;
t1= AD 1883 ± 1.7. (iii) Carbon intensity of global primary energy
determined by the ratio y/x. See text for data sources and compilation.
To explore this proposition we focus on the dematerialisation of resource
flows. The primary energy carrier for industrial society is carbon, and in
fact some estimates suggest that carbon currently accounts for as much as
50 % of the total amount of materials moved by industrial society through
its RADE networks (Dittrich and Bringezu, 2010). This material flow
ultimately leads to the emissions of carbon dioxide as carbon-based energy
carriers are consumed. Hence the emission rates of carbon dioxide can be
seen as giving a measure of the flow of carbon-based energy carriers through
the RADE system. In the context of the distribution costs of resources,
decarbonisation can therefore be viewed as merely one, albeit important,
component of a general systemic dematerialisation of resource flows
(Ausubel, 1989) through the RADE system. Here dematerialisation is taken as
the removal of “unnecessary” mass from resource flows through innovation.
This systemic dematerialisation is almost certainly not unique to carbon and
may indeed be a necessary response to the increasing distribution costs
inherent in any expanding network.
To estimate the amount of carbon flowing through the RADE system we use
global carbon emissions data from Houghten (2010), Boden et al. (2010) and
Peters et al. (2012).
As in Jarvis et al. (2012), we have included
land use change in the measurement of carbon emissions because our
definition of x necessarily includes wood use. However, although
deforestation dominates the land use change emissions estimates, not all
deforestation emissions are associated directly with the production and
distribution of wood as a fuel, as they include significant contributions
from slash-and-burn land clearance activities for food production.
Furthermore, carbon-neutral biomass production is not accommodated by net
anthropogenic CO2 emissions inventories. Between 1850 and 1900 wood
fuel use constituted a significant proportion of global primary energy use
(Grubler, 2003) but beyond 1900 their contribution to global carbon use
quickly become dominated by fossil fuels.
Figure 3 shows that global
carbon emissions, y, have also grown near-exponentially since at least 1850
at the long-term rate of 1.8 (±0.06) % yr-1 (Jarvis et al.,
2012). The difference between this growth rate and the growth rate of
primary energy indicates that the global primary energy portfolio has been
systematically decarbonised at a rate of ∼ 0.6 % yr-1
since at least 1850 (Jarvis et al., 2012). This decarbonisation is normally
viewed as being the result of societal preferences for cleaner, more
convenient, energy carriers (Grübler and Nakienovic, 1996). It has also
been partially attributed to improvements in the efficiency of converting
solid, liquid and gaseous fuels to electricity (Nakienovic, 1993). Both
these explanations seem unsatisfactory given the constant long-run nature of
the decline in carbon intensity. Furthermore, conversion efficiency affects
the distribution efficiency, x*/x, and hence x*. It does not directly affect
the primary portfolio comprising x. Instead, it is more appropriate to
consider innovations on energy transformations as co-evolving with the
portfolio of global primary energy. More specifically, it appears to us that
the pattern of decarbonisation of the global energy portfolio is in line
with, and a necessary response to, the declining distribution efficiency of
the global RADE network, x*/x.
The long-term exponential growth in both x and y set out above suggests that
global primary energy use and carbon flows share a common exponential
scaling relationship, y∝xb/a, where a and b are the relative
growth rates of x and y, respectively. Figure 1c shows the scaling relationship
between x and y since 1850. From these data we see that the exponential
scaling between x and y is not only a property of the 160 year average
behaviour, but also holds remarkably well on intervening timescales. This
relationship has a scaling exponent of b/a= 0.76 (±0.05). Calculating
this exponent using the long-term (160 year) exponents for x and y gives
b/a= 0.75 (±0.06). As with the primary-to-final scaling identified
earlier, this too is statistically indistinguishable from three quarters.
The scaling observed between x* and x and between y and x therefore leads to
direct proportionality between carbon intensity and network distribution
efficiency (y/x∝xcx*/x; c=-0.006 ± 0.043, hence
xc≈ 1; see Fig. 2c and d). As predicted then, the
implementation of dematerialisation appears to occur at a rate that is
proportional to the growth-induced declines in distribution efficiency
experienced by the global RADE system. This would appear to further
corroborate our view of the role of the distribution networks that make up
the global RADE system. Interestingly, the result of the scaling between
x, x* and y also indicates that total global anthropogenic CO2 emissions
grow in proportion to the consumption of final energy, x*, not primary
energy, x.
To place our interpretation of the role of decarbonisation of the primary
fuel mix in context, the historic trend in primary energy use from wood to
coal to oil to gas and renewables has occurred because it has allowed less
mass to be transported through the RADE network per unit of energy used
(Ausubel, 1989). Fundamentally this represents an innovation on the
distribution efficiency, x*/x.
A schematic 1-D representation of the global RADE system.
Here units of primary energy, x, are linked to those of final energy, x*, via
a distribution network. The black outlined system represents the initial
stage of the systems evolution. The red outlined system represents the
subsequent addition of units of final energy use and hence primary energy
use and hence the expansion of the network linking the two.
The recent shift towards the use of gas globally (ExxonMobil, 2013)
represents a particularly interesting continuation of this trend. Gas has a
lower unit volume energy density than other fossil fuel sources (i.e. coal
or oil). Lower energy density carriers like gas suffer from higher long-distance transportation costs, which is presumably why a smaller proportion
of gas is traded internationally than oil or coal (ExxonMobil, 2013).
However, gas also incurs lower energetic costs when being distributed though
the more tortuous finer terminal parts of the distribution network (Banavar et al., 2010).
To illustrate this point it is useful to consider the paths that make up the
global distribution network as passing through three stages: the gathering
together of resources from their extraction points in the environment; the
intermediate transportation of resources from regions of extraction to
regions of end-use; and lastly the distribution of resources to the nodes of
final end-use (see Fig. 4). As the global distribution network develops,
the relative importance of these three network elements in controlling
overall distribution costs should change. This is because, although the long-distance intermediate costs increase as the network expands, the final
distribution costs increase faster (Banavar et al., 2010). This concept is
already well established in transportation and telecommunications networks
as “the last mile problem”. So as the RADE system as a whole grows, low
carbon energy carriers such as gas are increasingly preferred, and this
preference is most keenly felt in the final distribution elements of the
RADE system. This seems intuitive when one imagines the vastly increased
distributional costs that an advanced (i.e. energy dense) country like
Germany would incur if it tried to meet its energy demands for heating and
cooking solely through distributing coal to individual end users, instead of
by the increasing use of gas.
This demand for low-carbon energy carriers in the terminal parts of the RADE
system may also stimulate innovations such as the liquefaction of natural
gas (LNG) because LNG reduces the costs of moving gas long distances during
intermediate transportation. Similarly, innovations in hydraulic fracturing
can allow the exploitation of gas resources near to the final point of use,
removing some of the need for long-distance transport. Lastly,
electrification is currently the primary means of dematerialising energy
flows through transformation and, just as with gas, the lower energetic
costs of transmitting electricity are most effectively deployed in the final
distribution parts of the network, e.g. in developed, urbanised areas. This
would explain why decarbonisation is sometimes associated with energy
transformation efficiencies given that both would co-evolve as distribution
networks expand. However, we would argue that it is misleading to implicate
conversion efficiency as a driver for the decarbonisation of energy
portfolios. It is interesting to note from Fig. 3 that the recent increase
in global coal use, which tends to counter the long-term trend of
decarbonisation, has been largely offset at the global scale by the
increased use of gas, renewables and decreases in land-based emissions.
Furthermore, the vast majority of this coal is not distributed to final
points of end-use as it was a century ago. Instead it is used to generate
electricity which is then distributed to end users, which is consistent with
the process of dematerialisation discussed above.
Total energy efficiency and growth – a model
If industrial society does indeed experience declining network distribution
efficiency, as indicated by Fig. 2b, then, all else remaining equal,
global industrial society should experience size-related limits to growth in
x, just as growth is self-limiting in most biological systems (West et al.,
2001). It is possible that the observed long-term exponential growth in x
could reflect the early stages of what is otherwise logistic size-restricted
growth. If this is the case then ultimately the growth of the global RADE
system would be self-limiting, even though primary energy use has risen
exponentially and by ∼ 50-fold since 1850. This in and of
itself is a fascinating prospect.
However, we argue that global industrial society is continually innovating
to overcome the increasing size-related penalties associated with growth.
This seems consistent with the apparent growth imperative of industrial
society and the fact that the observed declines in distribution efficiency
shown in Fig. 1b have been countered in order to maintain the near-constant relative growth rate of ∼ 2.4 % yr-1 shown in
Fig. 3. We illustrate this point with the following simple endogenous
growth model in which we treat global industrial society as a homogeneous unit.
As global society grows, it acquires additional primary energy flows to
support additional end uses, the two being linked by extensions to existing
networks. Therefore, we can conceptualise the growth of industrial society
both as its expansion into new environmental resources, and hence space, and
the establishment of new points of end-use. Although the space occupied by
industrial society is complex, if D= 3, then it is appropriate to consider
society as occupying an (irregular) volume, V. If the end-use control volumes
are considered as being within V then, from a network perspective, it is also
reasonable to assume the in-use environmental resources are also within V,
i.e. industrial society grows into its resources (Garrett, 2011). If so,
then we assume in the simplest case that the flow of resource into
industrial society is proportional to the volume of resources subsumed and
hence V.
We note that Garrett (2014) assumes environmental
resources flow to industrial society across an environment–society interface
(surface) and hence speculates that this flow is proportional to V1/3 on
theoretical grounds.
Therefore, in the absence of any storage, the supply
and consumption of primary energy resources might simply be described by
x=kAV,
where the proportionality kA is the resource acquisition efficiency and
is the product of the energy potential between the environmentally derived
energy resources and society and the efficiency with which these resources
can be assimilated into the RADE system and hence into industrial society.
Assuming networks distribute captured resources optimally within the volume,
V, then the final energy flow arriving at points of end-use, x*, is given by
x*=gxD/(D+1),
where g is a scaling constant (Dalgaard and Strulik, 2011). Once at the
points of end-use, and after subtracting the end-use inefficiencies
(i.e. the costs of transforming final energy into useful work), the remaining
portion of x* provides work which is used to increase the size of industrial
society (Garrett, 2011, 2012). This in turn expands V and allows the
co-option of further resources. Because it requires work to expand V, the
size of industrial society can also be viewed as the accumulation of this
work, X, occupying the space, V. The balance of this accumulated work can be
seen as the difference between work done and the decay of the stock of
accumulated work,
dXdt=kEx*-kDX,
where kE is the end-use efficiency of final energy conversion to useful
work and kD is the aggregate decay rate of X.
The system diagram representation of the endogenous
growth model set out in Eqs. (1)–(5). Numbers in boxes denote which
equations apply. s in the “construction” transfer function is the derivative
operator, d/dt.
Equations (1)–(3) are exponential in x, in line with the observations in
Fig. 3, if X∝V, i.e. work operates uniformly in space. Because the
mean energy density of industrial society is unknown we assume X=V for
simplicity given this has no bearing on our analysis. Equations (1)–(3) now give
dxdt=kAkEgx-1/4-kDx=ax,
where a is the relative growth rate of global primary energy, or
∼ 2.4 % yr-1. From Eq. (4) we see that a∝x-1/4
(West et al., 2001), i.e. as the system grows the relative growth rate
should fall. Therefore, in order to maintain exponential growth in x, the
acquisition efficiency, kA, and/or the end-use efficiency, kE, must
be increased and/or the decay rate, kD, must be decreased to compensate
for the declining capacity of primary energy to support growth.
We assume that both kA and kE are dynamically adjusted by society in
order to maintain growth, whilst kD remains fixed. The assumption of a
fixed decay rate is supported by the observation that the mean lifetime of
technologies (Grübler et al., 1999), including large energy projects
(Davis et al., 2010) has remained fairly constant at
∼ 40 years, or (∼ 2.4 % yr-1)-1, i.e. technologies
decay at the same rate as the relative growth of industrial society
(kD=a). One way of understanding such a link is that physical capital
is turned over at about the same rate as the system evolves, thereby
allowing the appropriate rate of adoption of the innovations required to
preserve growth at the rate a.
In the absence of any change in the acquisition and end-use efficiencies,
a∝x-1/4. Therefore for a to remain constant requires
kAkE=hx1/4,
where again h is a scaling constant. This now gives exponential growth in x as
dxdt=hg-kDx=ax
and hg= 2a if kD=a as discussed above. Within this framework, if
kD=a, the energy that is available to grow X and hence V, xG, is
given by
xG=kA-1hgx=εx,
where ε is the overall primary to end-use energy efficiency of
the RADE system (see also Garrett, 2011). The observed near-constancy of the
long-term relative growth rate in global primary energy use strongly
suggests that ε has remained more or less constant over at
least the last 160 years. Using IEA data, Nakicenovic et al. (1996) have
estimated ε to be ∼ 30 %, although this figure
is highly uncertain because their analysis could not accurately account for
the end-use efficiency of final energy in productive work. Ayres (1989)
attempted a similar analysis for the US attempting to account for so-called
useful work (or exergy) effects and derived an estimate of 2.5 % for
ε. In addition to the declining network distribution efficiency
x*/x, Fig. 1b also shows an illustration of the simultaneous increases in
end-use efficiencies, kE, required to keep ε at a
hypothetical value of 10 %, assuming kA is constant.
Here
10 % is simply taken as an illustrative value for ε given its
true value remains highly uncertain. This only affects the level of the
relationship between xG/x* and x, not its scaling. Having
assumed this value we can also specify a fixed value for kA from
Eq. (7) of 2a/0.1 = 0.5 yr-1 for the case of X=V.
Figure 5
shows the model described above in block diagram form.
Growth optimisation and working lifetimes
Thus far we have sought to illustrate how the growth of industrial society,
as determined by its energy use, could be controlled by the optimisation of
the RADE network. In part this optimisation is facilitated by reducing
material flows including decarbonisation of the primary energy portfolio. We
have also attempted to show that, despite this optimisation, RADE network
efficiency necessarily falls. We have therefore set out how an observed near-constant relative growth rate is maintained through continuous but measured
implementation of innovations on both energy acquisition and end-use
efficiencies. An important question that remains is, if growth is desirable,
why does industrial society only compensate for falling distribution network
efficiency, and not overcompensate to allow super-exponential growth? Or,
put another way, why is constant relative growth good? This cannot be due to
the lack of innovative capacity because there appears to be a surplus of
this available to enhance acquisition and end-use efficiencies in the global
RADE system. This suggests that industrial society is somehow self-regulated
such that the relative growth rates of, for example, energy use, are held
near-constant in the long run.
If there is a tendency in industrial society to implicitly regulate growth
in things such as energy use, insights into this could be obtained from
considering the ∼ 2.4 % yr-1 long-term growth rate on
which industrial society appears to settle. At this point, we note that a
relative growth rate of a= 2.4 % yr-1 corresponds to a growth
timescale of a-1= 42 years. It would therefore appear sensible to
attempt to understand growth in the context of this timescale.
To explore the possible relationships between a and the timescale a-1 we
start by assuming that the optimisation of the distribution component of the
RADE network, combined with the increasing acquisition and end-use
efficiencies to control growth (as implied by the control in Eq. 5),
point to energy efficiency being an important systemic consideration. Energy
efficiency improvements of any kind amount to actions taken to reduce waste
and hence increase energy available for specific end uses. Although end-use
is notoriously difficult to specify, in the highly reduced description of
the global energy system offered above, this end-use can be summarised
simply as the work done to expand the size of industrial society. As a
result, we refer to the energy not used directly in this work as
“supportive” energy use, xS, i.e. energy supporting, but not directly
used, in growth. System-wide optimal energy efficiency improvements imply that
xS is minimised in order to liberate as much energy for growth as
necessary. Examples of supportive energy might be the energy expended on
exploring, acquiring and distributing resources, personal transport, waste
heat and light, etc. Examples of energy directly used for growth, xG,
would be energy used to construct, replace and repair the physical
components of industrial society such as buildings, oil wells, pipelines,
power stations, electricity grids, roads, railways etc.
We can express this supportive energy simply as
xS=x-xG=(1-ε)x.
This definition of supportive energy may, at first, appear counter-intuitive
because a significant proportion of xS (such as personal transport) may
be thought of as being useful to society. However, in the spatial context
considered here, the components of xS simply represent expenditures of
energy necessary to facilitate the useful work of actually expanding the
size of industrial society.
If industrial society does indeed attempt to minimise supportive energy use
then we should be able to identify a value of a that minimises xS over a
given timescale, T. Noting that Eq. (6) resolves to x=eat, and
combining within Eq. (8) gives
XS=a-1(1-ε)eaT,
where XS is supportive energy accumulated over the integration timescale T.
We can now differentiate Eq. (9) with respect to a to find the value
of a that minimises XS and, by implication, maximises growth over this
timescale. Hence,
dXSda=(1-ε)TeaTa-(1-ε)eaTa2
which, for dXS/da= 0, has a minimum in XS at T=a-1.
Therefore, the growth rate of such a system is fundamentally linked to the
timescale over which the system behaviour is optimised with respect to xS.
Figure 6 shows the relationship between a and XS predicted by
Eq. (9). The minimum in XS with respect to a can be understood in that, for
any given integration timescale T, if a is below its optimum then the system
experiences disproportionate short-term increases in xS and hence in
XS (Eq. 8). However, if a is above its optimum the system
experiences disproportionate long-term increases in XS because of the
effects of enhanced growth (Eq. 6).
Having established a possible connection between the long-run relative
growth in global primary energy use, a≈ 2.4 % yr-1, and the
associated timescale, a-1= 42 yr, the question remains, why does
growth proceed on this timescale? As pointed out above, both technologies in
general (Grübler et al., 1999) and large power schemes in particular
(Davis et al., 2010) have average lifetimes of ∼ 40 years.
However, as also noted above, these may simply be manifestations of
the need to evolve the global energy portfolio in line with its growth rate
in order to allow for the required rate of uptake of innovations. Therefore,
we look to an alternative explanation of the underlying driver for growth
organised at this ∼ 40 year timescale.
The relationship between the relative growth rate on
global primary energy, a, and the total energy not directly used in growth,
XS. Two scenarios are presented, one with an integration timescale of
T= 42 years (–) and one with an integration timescale of T= 84 years (–).
Thus far, we have largely avoided discussing the role of the now 7
billion agents involved in making the decisions that lead to the observed
emergent behaviour we have attempted to describe above. We note that where
observations are available, ∼ 40 years is the average working
lifetime of people in industrial societies and that this has been a
relatively constant property of industrial societies (Ausbel and
Grübler, 1995; Conover, 2011) despite the very significant improvements
in overall life expectancy in most countries. In addition to the empirical
observation that working lifetimes have been stable at around 40 years for a
long time, the reason we might implicate working lifetimes as a possible
factor on which growth might be organised is that it is only during this
timeframe that people can exert influence over the decisions governing the
evolution of industrial society. Prior to working, or during retirement,
although people are using resources, they are not directly able to influence
the evolution of the system. If during their working lifetimes the objective
is to seek out near-optimal energy efficiency improvements and hence, by
implication, to maximise work done, then this should be sufficient to result
in a∼T-1∼ 2.4 % yr-1.
Figure 6 also shows that the objective function (Eq. 9) is more
sensitive to changes in a below the optimum than above it. If this is true it
would explain why periods of below optimum growth are more acutely
experienced by industrial societies than are periods of above optimum growth.
In many respects this is linked to the concept of business
cycle asymmetries; or what Keynes (1936) referred to as “the phenomenon of
the crisis” – the fact that the substitution of a downward for an upward
tendency often takes place suddenly and violently, whereas there is, as a
rule, no such sharp turning-point when an upward is substituted for a
downward tendency.
Figure 6 also shows the effects of doubling the
integration timescale T. As T is increased the optimal growth rate falls
because the effects of the long-run growth on supportive energy (Eq. 6)
weigh more than those of short-term losses (Eq. 8). This is equivalent
to an inter-generational view of sustainability in that, by extending the
integration interval beyond an individualistic working lifetime, growth is moderated.
Concluding remarks
In this paper we offer a novel analysis of the behaviour of industrial
society based on the physical behaviour of distribution networks.
Specifically, we have used global energy use data to explore our hypothesis
that industrial society progressively fills space as it grows and that
innovations are continually used to overcome the increasing size-related
penalties of this growth.
In order for industrial society to grow, the Resource Acquisition,
Distribution and End-use (RADE) system must be adaptive because the optimal
portfolio of resources and end-uses and the appropriate networks linking the
two cannot be known a priori. Solving this problem under conditions of relatively
deep uncertainty would require forms of dynamic optimisation. As a result,
it is not surprising that we see quite rich dynamic behaviour in the growth
rate of global primary energy use about its long-run value of
∼ 2.4 % yr-1 (Jarvis and Hewitt, 2014). Such behaviour
is clearly not planned centrally, but emerges through the free exchange of
information afforded by globalised market mechanisms.
We have identified three distinct points at which we believe the innovations
necessary for adaptation occur: at the point of acquisition of resources
from the environment; during their distribution; and during their conversion
at points of end-use. Without such adaptive capacity both resource
availability and their associated distribution costs should limit growth.
Within the framework we have set out, growth in global primary energy use is
fundamentally controlled by the optimisation of the RADE system. We have
speculated that this optimisation is driven by the inherent desire of people
in industrial societies to minimise energy losses and hence maximise work.
Since people are only able to significantly influence such decisions during
their working lifetimes it may not be surprising that the growth in
industrial society appears to be regulated on this timescale.
We acknowledge there are many contentious points in our discussion that
challenge conventional views about how industrial society behaves. If it
could be stated with confidence that the behaviour of industrial society is
largely known, then our attempts to offer an alternative perspective could
be considered foolish. However, industrial society must rank as one of the
most complex objects in the known universe and our understanding of its
behaviour remains poor, to say the least. Utilising theoretical insights
from other fields in order to explore this behaviour appears a reasonable
strategy. The same can be said for exploiting long-run global energy use
data given that changes in energy use are obviously coupled with the
evolution of global industrial society. However, significant further work is
required to substantiate or refute our arguments. This is ongoing.
Acknowledgements
We thank Piers Forster for suggesting the use of the IEA data and helping
define final energy as used in this paper and Bron Szerszynski for valuable
discussions. We also would like to acknowledge the now 15 reviewers to date
who have offered comments on versions of the manuscript, and in particular
Tim Garrett and Mike Raupach. Finally we thank Yan Peng Nie and Stephanie Edeoghon
for collating the IEA data. This work was supported by the UK
Engineering and Physical Sciences Research Council (EP/I014721/1) and
Lancaster University.
The views expressed in this paper are those of the authors and do not
necessarily represent the views of, and should not be attributed to, Ofgem
or the Gas and Electricity Markets Authority.
Edited by: J. Annan
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