Power density

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Energy uses

Examinations of power densities of energy uses (a more accurate term than energy consumption) on scales ranging from global to local reveal quite a few unexpected (or at least unappreciated) realities. More importantly, historical perspectives illustrate one of the most important trends in the evolution of human societies, their quest for ever-higher power densities of energy use, be it on collective level or as individuals.

In this book’s preface I had already noted how land, a key concern of classical economics, became a decidedly secondary consideration in modern economies driven by concentrated labor and capital deployed in mass production. From the physically fundamental, that is the thermodynamic, perspective, this new pattern of economic organization is nothing but an expression of rising energy use, of deploying new energy conversions on unprecedented scales yet also with unprecedented intensities. This has resulted in a still continuing upward trend in typical power densities of energy uses. This has been an unmistakable but curiously unappreciated reality. Energy publications teem with data, comparisons and analyses of energy use per capita, per unit of gross domestic product, per unit of capital investment, more recently even per unit of energy (net energy return, or EROI, energy return on investment).

But energy use per unit of land is rarely investigated, and if so then in its most readily calculated, yet also the most misleading, form, as total annual energy use prorated over a nation’s territory. This quotient may be relevant for Monaco, but its utility breaks down even at Hong Kong’s level as even this circumscribed and densely populated (de facto) city-state contains relatively large areas of steep (and usually deforested) mountain slopes (about two-thirds of its territory) and swampland frequented only by hikers and birds. And calculating such rates for dozens of countries where virtually all population, agricultural and industrial activities are concentrated on a small share (<10%) of national territory is an exercise in deliberately introducing errors of one or more orders of magnitude. They are dozens of such nations, the largest ones including most countries of North Africa and the Middle East, but also Norway and Finland or Turkmenistan and Mongolia.

I will note these misleading rates in passing, as I follow spatial density of energy uses from the largest, planetary, scale to microprocessors, the smallest massively deployed energy-using products of modern civilization. Of course, I will do so by using the same rate that I used to quantify spatial claims of producing commercial flows of renewable and fossil energies and of electricity, power density measured as W/m2. But before starting a systematic appraisal of power densities of energy use I must make an important clarification. Observant readers may have noticed that I have not used the term energy consumption, only energy use: is this just an idiosyncratic preference or the proper way to address this matter?

Before I embarked on detailed reviews of power densities of energy sources and electricity generation I sorted out the key terms and provided their correct definitions. In energy studies this effort never ends, and I am not sure which pair of the terms is misused more often: talking or writing about energy when what is meant is power (and, of course, vice versa), or referring to energy consumption when what is meant is energy use. I try to be always correct about energy and power, but I, too, have been using the term energy consumption. According to the first law of thermodynamics that is an impossible feat: energy cannot be consumed, it remains conserved –- it can be converted to a different form, and all of the conversions eventually end in dissipated heat that provides feeble thermal backdrop of the known universe.

This is not verbal puritanism, this critical distinction has important implications for energy use in modern societies: too often people think about energy as truly consumed, gone, never to be of any use, or consequence, again. There are two important reasons why that is wrong. In the first place, even when we think that we are done with a particular energy conversion (that is once we conclude that we had derived all useful work in the form of chemical, thermal, electric, kinetic or electromagnetic energy) those energies have to be dissipated in the environment. This means that power densities of all of our final energy uses –- be it energy for crop cultivation, material extraction, industrial processes, transportation, heating, cooling, lighting –- are also power densities of heat rejection. Depending on the intensity and the scale of this heat rejection and on the heat-absorbing medium, such processes can cause significant temperature increases.

On one end of this heat release spectrum are microprocessors whose extraordinarily high operational power densities pose tremendous challenges for efficient heat dissipation. One of the most obvious objects much higher up along that size spectrum are giant cooling towers, the recipients of concentrated quantities of waste heat from the operation of large thermal electricity-generating plants. And at the spectrum’s other extreme are modern megacities and conurbations. Specific heat rejections (per person, per vehicle, per unit of GDP) within these areas may be small but their combined effect helps to create near-permanent urban heat islands that results in discernible changes in comfort, wind speed and even precipitation. And I will explain, by comparing anthropogenic and natural heat flows, how much further these environmental interventions can be carried, and if there should be any eventual concern about heat rejection on the global scale.

In the second place, there are still too many instances where the residual heat should not be left to dissipate, where it is unnecessarily wasted because we do not try hard enough to use it. I have already noted in the section on gas turbines how the combined-cycle generation takes advantage of the fact that hot gas discharged by turbines contains enough heat to vaporize water in a heat recovery steam generator and power an attached steam turbine, a combination that raises overall efficiency of fuel use to 60%, far above 35-40% that is standard for modern fossil fuel-fired steam turbogenerators or 40% that is the usual performance of self-standing gas turbines. Certainly the most common recent example of harnessing ‘’used’’ energy are hybrid vehicles whose regenerative braking can recover some of the energy that would be normally wasted in slowing a vehicle down by engaging an on-board electric motor as a temporary electricity generator that feeds a storage battery.

I will pay attention to both aspects of energy use: as final, controlled, deliberate conversions of fuels and electricity deployed to produce heat, motion and light –- and as unavoidable processes dissipating heat into the environment. This means that I will appraise power densities on the descending scale from megacities and transport corridors to specific industrial process and individual buildings all way to now so numerous indoor energy converters –- and that I will also look at power densities of heat rejection whenever they reach levels that pose either undesirable environmental problems or present great design challenges.

A brief historical perspective

I will open this segment with a brief look at power densities of human metabolism. No energy conversion is obviously more important for our survival than food digestion and as evolution of human societies led first to higher densities of sedentary farming populations and then to even higher concentration of anthropomass in cities, power densities of human metabolism have moved from negligible rates to surprisingly substantial, and in many places still rising, values. Calculation of population-wide metabolic rates is a complex task that must take into account age and sex structure of studied societies and then apply appropriate activity adjustments to age- and sex-specific basal metabolic rates (Smil 2008). But in order to get fairly representative rates it is much easier just to use data from metabolic models (Hall 2009) or from food intake surveys: they indicate that in affluent countries daily per capita means of food intake are mostly between 8.3-10 MJ (2,000-2,400 kcal/day).

These rates were considerably higher during the pre-modern eras when considerable physical exertions were necessary in all traditional agricultures in order to secure enough food and in all kinds of mining, transport, construction and artisanal manufacturing to provide shelter and some material comforts. Despite these exertions –- requiring commonly at least 15 MJ/day for such demanding work as digging, ploughing heavy soils, cutting down trees and sawing wood, extracting ores and carrying loads –- most people in pre-modern societies had barely adequate diets and owned little beyond often inadequate clothing and a small number of indispensable household items (Smil 2013a). On the other hand, smaller body sizes of most pre-industrial populations and common use of childhood labor tended to reduce average food requirements.

Population densities of foragers (hunters and gatherers) were as low as 1 person/10 km2 of exploited land in marginal (arid, Arctic) environments, and as high as 1/km2 in coastal ecosystems where most food came from the ocean. The latter rate translates, even with heavy exertions in fishing and boat-building (demanding up to 15 MJ/day for adult male work), to vanishingly low metabolic power density of 0.1 mW/m2. Shifting cultivation raised the population densities to 20-30/km2 (up to 4 mW/m2) and traditional farming had easily tripled or even quintupled those values, going from 100/km2 of arable land in dynastic Egypt to 150/km2 in medieval England and 400/km2 (metabolic power density of up to 45 mW/m2) in intensively cultivated China of the late 19th century (Smil 2013).

Even at the outset of the early modern era populations were overwhelmingly rural, as cities contained perhaps no more than 4% of all people in 1500 and just 5% a century later (Klein Goldewijk, Beusen and Janssen 2010). There were a few sizable cities in the antique as well as in the medieval world but they had high population densities within their often massive protective walls. In about 300 CE imperial Rome housed about one million people in an area of just 15 km2 enclosed by the Aurelian walls, population density of nearly 67,000 people/km2 (Smil 2010b) implying metabolic power density of 7 W/m2, a rate (as I will show) comparable to that of modern capitals.

Combination of post-1850 industrialization and rapid post-1950 population growth resulted in rapid urbanization: by 1900 15% of the global population lived in cities, by the year 2000 the share was about 47%. Using the historical estimates of the total built-up area occupied by cities –- 10,000 km2 in 1500, 47,000 km2 in 1900 and 538,000 km2 in the year 2000 (Klein Goldewijk, Beusen and Janssen 2010) –- results in the rise of average worldwide urban metabolic power densities from about 0.2 W/m2 in 1500 to 0.5 W/m2 in 1900 and to almost 0.6 W/m2 by the year 2000. The urban share of global population reached 50% in 2007 (with little change in metabolic power density) and by the middle of the 21st century it is expected to approach 70% (UN 2012).

Extrasomatic energies In preindustrial societies these energies came overwhelmingly from just two classes of ubiquitous conversions, from working animals and from combustion of biofuels. In the absence of any representative data on prevailing energy use we must make the best assumptions based on fragmentary historical evidence. My reconstruction of energy use in imperial Rome at the end of the third century of the common era ends up with about 100 MW of food energy (human metabolic power), less than 5 MW of feed energy (to sustain donkeys and horses engaged in urban transport), and at least 300 MW of wood and charcoal for cooking requirements, heating (including the capital’s numerous baths with hot water pools) and artisanal manufactures (Smil 2010b). This prorates to overall power density of energy use of at least 25 W/m2 within the Aurelian walls. This fairly high power density is the result of high density of Rome’s population during the later imperial era (with the human metabolism roughly a quarter of the total flux) and low efficiency of biofuel combustion (nearly three—quarters of all energy inputs).

Not surprisingly, as long as cities remained densely populated (confined by walls) and as long as human and animal metabolic energies and combustion of biofuels remained the only energy inputs the highest power densities of urban energy use remained very similar during the medieval era. Galloway, Keene and Murphy (1996) put London’s wood consumption at the beginning of the 14th century at about 25 GJ/capita, implying annual power of about 63 MW for the town’s 80,000 inhabitants; adding their metabolism and (relatively unimportant) feed for horses raises the total of less than 75 MW, and prorated over the area of some 1.8 km2 that yield overall power density of London’s energy use in 1300 at roughly 40 W/m2.

Industrialization brought first a counterintuitive shift of power densities of energy use: they began to decline even as the inputs of coal (for heating, cooking and industrial production, mainly to power steam engines) were rising in large European cities during the early and middle decades of the 19th century, and as coal-fired power plants (all originally situated in cities) created new large fuel demand starting in the early 1880s. This is easily explained by a rapid spatial growth of modern cities. For example, London’s area expanded more than tenfold during the 19th century, from about 24 to 280 km2 (Demographia 2013). Paris expanded at a slower rate, from 34 km2 in the early 18th century to just over 100 km2 two centuries later (with its population growing from 600,000 in 1700 to the maximum of 2.9 million in 1921) and a study by Kim and Barles (2012) makes it possible to follow the city’s rising, and changing, energy demand.

By 1800 the city’s average per capita demand for all extrasomatic energies was almost 30 GJ/capita, with wood dominant; coal began to supply more than half of the city’s energy demand by 1860 and while the population expanded nearly five-fold during the 19th century (from 550,000 to 2.7 million) average per capita energy use remained at about 25 GJ, reflecting higher efficiencies of modern conversions. These shifts translate to almost 500 MW of wood and charcoal in 1800 and 2.1 GW (mostly coal) in 1900, and prorate to power densities of nearly 15 and 20 W/m2, and the addition of metabolic energies would raise these rates to, respectively, 16 and 23 W/m2; obviously, rising fuel use in industrialized cities relegated somatic energies to totals lower than the inherent errors in estimating overall demand for extrasomatic energy inputs.

Fuels, and later also electricity, requirements for the most energy-intensive and spatially concentrated industrial processes have resulted in a similarly large increase of power densities. Contrast of the most advanced large-scale manufacturing enterprise of the early 19th century with the signature facility of the most important branch of the early 20th-century manufacturing offers an excellent example of rising power densities in industrial production. Merrimack Manufacturing Company was America’s first large and fully integrated clothing producer (mainly calico fabrics) to open in 1823 in Lowell, Massachusetts (Malone 2009). The plant occupied about 10 ha and it drew about 2 MW of water power from a large (10 m) drop of the Merrimack River, operating with power density of about 20 W/m2 when prorated over its entire area and about 50 W/m2 of its actual floor space.

Almost exactly a century later (in 1928) Henry Ford’s River Rouge plant began to produce cars on about 3.6 km2 of land west of Detroit in a completely integrated complex where all essential inputs (coke, steel, glass) and components (steel plates, forgings, engines) were made on-site; during its peak production the plant employed more than 100,000 people and produced a car every 50 seconds (The Henry Ford 2013). Primary energy inputs at the River Rouge –- dominated by coal for about 1.5 Mt coke/year and for generating electricity in a plant with installed capacity of 375 MWe –- amounted to nearly 3.5 GW resulting in power density in excess of 1,000 W/m2 when prorated over the entire site and about 2,500 W/m2 when using 1.42 Mm2 of floor space as the denominator. Consequently, signature establishments of textile and car production, the two great phases of modern industrialization set a century apart, saw roughly a 50-fold increase in their operating power density.

Operating power densities on the order of 103 W/m2 became common in large metallurgical enterprises as well as in expanding refineries producing a wider range of liquid fuels and gases with higher efficiency. Pennsylvania’s Homestead Steel Works –- bought in 1883 by Andrew Carnegie and expanded to become the largest component of his eponymous steel company –- are among the best illustrations of these high operating power densities. The complex required about 300 PJ of coke, coal and natural gas for some 6 Mt of finished steel products (Carnegie Steel Company 2012). The works occupied about 112 ha site on the southern bank of the Monongahela east of Pittsburgh and their operating power density of about 2,000 W/m2 remained characteristic of large iron and steel mills for most of the 20th century.

Finally, I have to stress the fact that power densities of agricultural operations have seen increases far higher than the rates in those industrial processes that moved from small-scale artisanal operations to large-scale high-throughput enterprises. The best example is by contrasting cultivation of grain crops used for food and feed. Traditional low-yield grain farming (wheat or rice yields no higher than 1.5 t/ha) was based solely on animate (human and draft animal) labor and on recycling organic wastes and rotations with leguminous crops (Smil 2008). Detailed accounts by Buck (1930 and 1937) show that even in relatively high-yielding, irrigated fields in China rice harvest required the deployment of less than 7 GJ of animate metabolic energies, more than 95% of it being draft power of water buffaloes used to plow and harrow heavy soils.

When power density of this traditional cropping is calculated by using actual time worked in fields (rather than the cropping period of about 150 days or, as in other power density calculations in this book, the entire year) human and animal exertion were deployed at rates lower than 1 W/m2 of arable land (Smil 2008).

Animate energies in traditional crop cultivation

Traditional rice cultivation in China: water buffalo, crop yield 1.4 t/ha

300 hours of human labor x 700 kJ/hour = 210 MJ/300 = ~ 200 W

250 hours of animal labor x 25 MJ/hour = 6.25 GJ/250 = ~ 7,000 W

7,200 W/10,000 m2 = 0.72 W/m2

Traditional wheat cultivation in the Netherlands: two horses, crop yield 2 t/ha

170 hours of human labor x 700 kJ/hour = 120 MJ/170 = ~ 195 W

120 hours of animal labor x 25 MJ/hour = 3 GJ/120 = ~ 6,900 W

6,900 W/10,000 m2 = 0.71 W/m2

In contrast, direct energy investment in modern high-yield cropping is dominated by liquid fuels (diesel oil, some gasoline) for powerful machinery used for all field operations (plowing, planting, application of agrochemicals, harvesting), and additional fuels or electricity are required for irrigation. Corn, America’s principal feed crop, now takes only about seven hours of labor (driving tractors, combines and trucks) per hectare to produce high (10-11 t/ha) yields in Iowa (Duffy 2013). Typical diesel fuel requirements are 17-20 L/ha for plowing, 10-15 L/ha for disking, 5 L/ha for planting, a similar amount of fuel for fertilizer application, and 15 L/ha for combining (Grisso et al. 2010).

Overall fuel requirement will be no less than 65 L/ha (2.3 GJ/ha) which means that power density of direct energy uses will be close to 10 W/m2 of cultivated land, an order of magnitude more than in traditional cropping. But fuel requirements can easily double in heavier soils and with irrigation drawing water from a deep aquifer, and indirect energy needs (above all those to synthesize fertilizers, pesticides and insecticides) may double that larger total, but attributing these indirect needs (energy used to produce inputs that are indispensable for modern cropping) would require a different definition of power densities of energy use, one that would have to consider (to give just one obvious example) not only fuels and electricity used by households but also energy required to produce building materials and energy embodied in furnishing, appliances and other domestic items.

This brief retrospective makes several trends clear. Power densities of human metabolism rose by four, or even five, orders of magnitude as human societies advanced from small groups of hunters and gatherers to inhabitants of large cities. Well into the early modern era (1500-1800) extrasomatic energies were dominated by metabolic conversion of working animals and by biofuels. In cities the rising use of wood and charcoal, and in a few countries also higher reliance on coal, relegated all animate (human and animal) metabolism to a marginal role in energy supply. This trend became even more pronounced with advancing industrialization which created numerous production sites (iron and steel works, non-ferrous metallurgical enterprises, refineries, chemical syntheses, intensive manufacturing) where highly concentrated fuel and electricity uses proceed with power densities of 103 W/m2. In the next section I will take a revealing look at modern power densities by descending the spatial scale.

Hierarchy of modern energy uses

In this segment I will move from global to local, presenting many large-scale power densities merely as theoretical rates –- some, as already noted, misleading, others actually quite revealing -– before descending to scales that really matter, to power densities of modern cities, some key industries, transportation corridors and individual buildings. In most of these instances heat rejection is just a different label for the process of energy use, the process simply takes place and it requires no specific comments, but in many instances power densities involved in getting rid of heat are surprisingly high, in some cases they reach truly astonishing rates and that is why I will single them out for closer looks in the next segment of this chapter.

Global scale The worldwide power density of human energy use is a perfect example of a misleading quantification. The Earth, with the mean radius of 6,371 km, has surface of 510 Tm2, with oceans covering 361 Tm2, dry land 149 Tm2, and ice-free land 133 Tm2. With global energy use rising from 1.38 TW in 1900 to 12.43 TW in 2000 this means that on the planetary level power density of primary energy use rose during the 20th century by almost exactly an order of magnitude, from 0.0027 to 0.024 W/m2. The first dozen years of the 21st century saw (mainly thanks to Asia in general and China in particular) a further rapid rise to 16.62 TW and hence he power density of global energy use rising to 0.032 W/m2 of the Earth's surface. But this easily calculated rate could be actually observed at very few places on the Earth as global energy use remains highly unevenly distributed.

Recent totals of global population, extent of economic activity and density of transportation links are all unprecedented, but vast areas of the ocean and large chunks of continental masses remain places where no continuous conversions of anthropogenic energy is underway, or where highly intermittent energy uses consist of a lone ship traversing some extreme latitudes or a jetliner on one of the least frequent routes. The simplest correction that would move the rate closer to its mean or modal value is to prorate the energy use over ice-free land where most fuels and electricity are produced and used. This will nearly quadruple the global 2012 power density to 0.125 W/m2 but the flux is still only a negligible fraction of the mean insolation received by the continents, just 0.066% of 188 W/m2.

Moreover, the total anthropogenic effective radiative forcing has already reached 2.3 (1.1-3.3) W/m2 since the beginning of the industrial era (largely due to the emissions of greenhouse gases), and in 2012 it was 44% higher than in 2005 (IPCC 2013). Consequently, even another doubling of global energy use that would double average continental heat dissipation to 0.13 W/m2 would still remain far below the increasing radiative impact of greenhouse gases; moreover, it would also remain much lower than the margin of error associated with quantifying such uncertain components of the Earth’s radiation balance as the tropospheric ozone and cloud albedo effect due to the presence of airborne aerosols.

In any case, prorating global energy solely over the continental area is an unsatisfactory correction as it ignores two obvious realities: parts of the ocean are traversed by relatively frequent and regular shipping routes (especially oil tanker routes from the Middle East to East Asia and Europe, and container vessels from East Asia to North America and Europe), and are overflown by even more frequent intercontinental flight connections, particularly the Northern Atlantic and the Northern Pacific; and parts of ice-free land have only negligible, or exceedingly patchy, population presence. Consequently, the best choice would be to calculate two rates, one with the denominator encompassing all of the relatively densely populated regions on land, the other one with the denominator aggregating shipping and air routes across the ocean. Only the first adjustment can be done with satisfactory accuracy.

The obvious choice to calculate a more realistic power density of continental energy use is to restrict the denominator to urban and industrial areas and their transportation corridors. Ten global assessments of urban (or urban-related) areas published between 1992 and 2009 and reviewed by Schneider, Friedl, and Potere (2009) resulted in aggregates ranging over an order of magnitude, with the lowest estimate at just 276,000 km2 (for areas defined as populated places based on digitized maps) to as much as 3.52 Tm2 for urban extent based on a combination of census data, maps and nighttime satellite images.

Critical assessment of these studies by Potere et al. (2009) –- based mainly on a random sample of 10,000 validation sites analyzed in high resolution –- found that a study using new MODIS 500-m data by Schneider, Friedl, and Potere (2009) offers the most accurate result with 657,000 km2 in the year 2001 (defined as land where built structures covered more than 50% of land, including all other anthropogenic constructs of more than 1 km2). Even if that total grew to about 800,000 km2 by 2013 it would be still just 0.6% of ice-free land, a very small land claim to accommodate (since 2007) half of all humanity.

A first-order approximations would be then to assume that at least 70% of all economic activity (and hence of all energy use) takes place in that relatively small area and that would result in global power density of about 19 W/m2 for the year 2000 and 21 W/m2 in 2012. But using urban land (with its diverse definitions) is an imperfect correction as land cover within these regions is rather heterogeneous: it includes not only a large share of impervious surface areas (ISA) –- that is roofed and paved surfaces (all residential, commercial and industrial buildings, all city streets, sidewalks, parking lots, highways, runways, ports) and above-ground storages of materials (fossil fuels, ores) –- that have no vegetation, but also variable, and often extensive, grassed and treed surfaces in residential districts and along city boulevards, as well as numerous (and often fairly large) groves in parks, adjacent to buildings and along transportation corridors.

The best practical choice of how to do this on global or national scale is to use the aggregates of ISA whose extent can be, far from precisely but fairly satisfactorily, estimated by using appropriate satellite imagery. Elvidge et al. (2007) pieced together the first global account of ISA for the years 2000-2001 from satellite observations of the brightness of night-time lights and from population counts, and calibrated their model by using 30-m resolution ISA of the USA from the U.S. Geological Survey. Their study found that the global total of constructed ISA was about 580,000 km2, that is just 0.43% of ice-free land and an aggregate equivalent of Kenya or Madagascar. Two choices are defensible for the numerator: a total adjusted for extra-urban energy use, and a total where, in addition, all energies used for intercity transportation are also subtracted.

In the first case we can simply argue that all but a small fraction of fuel used in intercity transportation (be it road, rail, or air) must be taken on-board in urban areas: clearly, its supply is an integral part of the overall urban energy demand, although most of that chemical energy will be converted to motion outside the cities and conurbations (the only notable exception is hydroelectricity used to power electric trains). The only adjustment is to subtract energy used outside urban/industrial areas, and that can be done by calculating weighted mean based on the continental shares of urban populations. In Europe, North and South America and Australia, as well as in Japan and South Korea, urban populations are 75-85% of the total and (because their per capita energy use is higher than a national average) use about 85% of all energy; in Africa and in Asia urban populations are 45-50% of the total, and use about 55% of all energy. Weighted global mean is thus about 75% of energy used in urban/industrial regions and that total (16.6 TW in 2012), prorated over 580,000 km2, results in power density of nearly 30 W/m2.

In the second case we have to subtract all extra-urban energy uses that take place on and above the ocean and between the cities, be it on land, water or in the air. In practice this means subtracting nearly all energy for shipping, aviation, and in intercity road and rail traffic. Global demand for ocean-going vessels has been recently at about 350 Mtoe/year, aviation demand at 250 Mtoe/year, and assuming that 35-40% of all road traffic is outside of urban areas leaves us with about 40% of all transportation fuel (roughly 1.25 TW out of the total of 3.2 TW) used in urban regions. The aggregate urban energy use is thus reduced to 40% of transportation energy (or 1.25 TW) and 75% of all other uses (or 10.1 TW) to about 11.4 TW and average power density of urban energy uses is just below 20 W/m2.

Given the great land cover/land use disparities and large economic differences, continental averages of power densities are hardly more revealing than global means, and we do not get closer to truly informative rates even once we step down to national levels that simply show total annual energy use prorated over the entire national territories. Extremes of these power densities range from negligible rates for nearly all Sahelian countries –- generally the world’s lowest per capita energy use combined with large desert or arid grassland territories, 0.0003 W/m2 for Mali and no more than 0.0005 W/m2 for Niger –- to values four orders of magnitude higher for small, densely populated nations with affluent (hence high-energy) economies: Netherlands at about 3.25 W/m2, Belgium at 2.95 W/m2.

Singapore with nearly 140 W/m2 rates significantly higher, but the power use density of this city state is are particularly misleading not only because of its tiny territories (just 710 km2) but because most of energy purchased and processed in the city is not for its own use but it is fuel exported by its refineries and fuel oil, diesel and kerosene taken onboard ships and fueling jetliners in one of the world’s most important shipping and air travel hubs. Among larger, more populous nations Japan (1.85 W/m2) and Germany (1.22 W/m2) stand out because of their relatively high densities. In contrast, Chinese mean, although it had quadrupled between 1978 and 2008, is only 0.28 W/m2 but the largest urban areas rate much higher, Shanghai about 15 W/m2 (Chen et al. 2012). And Canada’s high per capita energy use cannot compensate for the country’s small population and large territory and its rate is just 0.045 W/m2, an order of magnitude below the US (0.3 W/m2 including Alaska and Hawaii).

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