Power Density

by Vaclav Smil

  Figure 6.2

  Ford Motor Company's River Rouge plant, aerial view. Ford Motor History (n.d.).

  Finally, I must stress that the 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 highthroughput enterprises. The best example is the 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, 1937) show that even in relatively high-yielding, irrigated fields in China, the rice harvest required the deployment of less than 7 GJ of animate metabolic energies, more than 95% of it in the form of the draft power of water buffaloes.

  When the power density of this traditional cropping is calculated by using actual time worked in the 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).

  In contrast, the direct energy investment in modern high-yield cropping is dominated by liquid fuels (diesel oil, gasoline) for machinery (used for plowing, planting, the 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 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). The overall fuel requirement will be no less than 65 L/ha (2.3 GJ/ha), which means that the 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.

  Fuel requirements can easily double in heavier soils and with irrigation drawing water from deep aquifers, and indirect energy needs (above all those to synthesize fertilizers, pesticides, and insecticides) may double that larger total. Attributing these indirect needs 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 the energy required to produce building materials and the energy embodied in furnishings, appliances, and other domestic items.

  Box 6.1

  Animate energies in traditional crop cultivation

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

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

  This brief retrospective makes several trends clear. The power densities of human metabolism rose by four, even five orders of magnitude as human societies advanced from small groups of foragers to inhabitants of large cities. Well into the early modern era, extrasomatic energies were dominated by the metabolic conversion of working animals and by biofuels. In cities, the rising use of wood and charcoal, and in a few countries also a higher reliance on coal, relegated all animate metabolism to a marginal role in energy supply. This trend became even more pronounced with advancing industrialization, which created numerous production sites (for metallurgy, refineries, chemical syntheses, intensive manufacturing) where energy uses proceed with power densities of 103 W/m2. The next section takes a revealing look at modern power densities of aggregate energy use by descending the spatial scale.

  Hierarchy of Modern Energy Uses

  I will move from global to local, presenting first large-scale power densities merely as interesting rates-some, as already noted, misleading, others actually quite revealing-before descending to scales that really matter, to the 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 attention; but in many instances the power densities involved in getting rid of heat are surprisingly high, in some cases reaching truly astonishing rates, and that is why I single them out for a closer look 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 a mean radius of 6,371 km, has a surface area of 510 Tm2, with oceans covering 361 Tm2, dry land 149 Tm2, and ice-free land about 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, the power density of primary energy use rose during the twentieth century by almost exactly an order of magnitude, from 0.0027 to 0.024 W/m2. The first 13 years of the twenty-first century saw (mainly thanks to Asia in general, and China in particular) a further rapid rise, to almost exactly 17 TW, and hence the power density of global energy use prorating to 0.033 W/m2 of the Earth's surface. But this rate can be actually observed at very few places on Earth as the distribution of global energy use remains highly uneven.

  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 under way, or where highly intermittent energy uses consist of a lone ship traversing some extreme latitudes or a jetliner on one of the least frequented routes. The simplest correction to 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 quadruples the global 2013 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 radiative forcing, largely resulting from the emissions of greenhouse gases, has already reached 2.3 (1.1-3.3) W/m2 since the beginning of the industrial era (IPCC 2013). Consequently, even another doubling of global energy use that would raise the mean continental heat dissipation to 0.25 W/m2 would still remain an order of magnitude below the current 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 resulting from 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 ice-free land have only a negligible, or exceedingly patchy, population presence, and fuels are also converted by shipping and intercontinental flights. 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 routes followed by container vessels from East Asia to North America and Europe) and are overflown by jetliners (particularly the northern Atlantic and the northern Pacific Ocean). 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.

  A more realistic expression of the 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. A critical assessment of these studies by Potere and colleagues (2009)-based mainly on a random sample of 10,000 validation sites an
alyzed in high resolution-found that Schneider, Friedl, and Potere (2009) offered the most accurate result, with 657,000 km2 of land where built structures covered more than 50% of the surface in the year 2001. Even if that total grew to about 800,000 km2 by 2013, it would still be just 0.6% of ice-free land.

  The first-order approximation would be to assume that at least 70% of all economic activity (and hence of all energy use) takes place in that relatively small area, which would result in a global power density of about 19 W/m2 for the year 2000 and 21 W/m2 for 2012. But using urban land is an imperfect correction as cities are quite heterogeneous: they include not only a large share of impervious surface areas (ISA, including all roofed and paved surfaces devoid of vegetation) but also the variable, and often extensive, grass and tree cover in residential districts, along city streets, highways, and railroads, and in parks. The best way to estimate the power densities of energy use on a global or national scale is to use the aggregates of ISA whose extent can be fairly satisfactorily estimated from satellite imagery. Elvidge and co-workers (2007) pieced together the first global account of ISA for the years 2000-2001. Their study found a global ISA total of about 580,000 km2, that is, just 0.43% of ice-free land, and an aggregate equivalent of Kenya or Madagascar.

  Adjusting the numerator can be done in two ways: by subtracting energy use outside urban energy use, and, in addition, by subtracting all transportation energies taken onboard in cities but used for intercity traffic. The first adjustment can be done by calculating the weighted mean based on the continental shares of urban populations. In Europe, the Americas, and Australia, as well as in Japan and South Korea, urban populations account for 75%-85% of the total population 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 account for about 45%-50% of the total and use about 55% of all energy. The weighted global mean is thus about 75% of energy used in urban or industrial regions, and that total (12.5 TW in 2012), prorated over 580,000 km2, results in a power density of about 22 W/m2.

  In the second case we have to subtract all energy for intercity shipping, aviation, and road and rail traffic. The global fuel demand for oceangoing vessels has recently been about 350 Mtoe/year and for aviation about 250 Mtoe/year. If we assume that 35%-40% of all road traffic is outside urban areas, that 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 (roughly 1.3 TW) and 75% of all other uses (or 10.1 TW) and, with an urban demand of 11.4 TW, the average power density of urban energy uses is just below 20 W/m2.

  Because of the great land cover and land-use disparities and the large economic differences between areas, continental averages of power densities are hardly more revealing than global means, and as long as we use entire national territories in numerators we do not get closer to truly informative rates even once we step down to the state level. The extremes of these unrepresentative power densities range from negligible rates for nearly all Sahelian countries, which generally have the world's lowest per capita energy use and large desert or and grassland territories. When USEIA data for 2010 are used the rates range from 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, high-energy economies: the Netherlands at about 3.4 W/m2, South Korea at 3.6 W/m2.

  Singapore, with a power density of nearly 140 W/m2, rates significantly higher, but the power density of this city-state is particularly misleading because most of the energy purchased and processed in the city is not for its own use but is fuel exported by its giant refineries and the fuel oil, diesel, and kerosene taken onboard ships and jetliners in one of the world's most important shipping and air travel hubs. Among larger, more populous nations, Japan (1.9 W/m2) and Germany (1.2 W/m2) stand out because of their relatively high power densities. In contrast, the mean for China, although it quadrupled between 1978 and 2008, is only 0.35 W/m2. And Canada's high per capita energy use cannot compensate for the country's large territory, and so the nationwide power density of energy use is just 0.045 W/m2, an order of magnitude below the US rate (0.33 W/m2, including Alaska and Hawaii).

  Urban Power Densities

  The power densities of energy use become meaningful only when the annual supply of fuels and electricity is prorated over those areas where most of it gets converted to final uses (or at least taken onboard), that is, when adjustments are made for energy use in a nation's urban areas. We now have at least four studies of the nationwide extent of urban areas or the ISA in the United States. The US Geological Survey put the first nationwide estimate of urban areas at 90,000 km2 (USGS 2000). The study that combined nighttime lights' radiance with LANDSAT imagery put the total extent of the US ISA at nearly 113,000 ± 13,000 km2, slightly less than the surface of Ohio (Elvidge et al. 2004). Elvidge and co-workers (2007) lowered the total to about 84,000 km2, close to the USGS study figures. Churkina, Brown, and Keoleian (2010) came up with a higher total of 141,000 ± 40,000 km2 for the year 2000, and they also calculated that grassy surfaces covered about 40% and treed surfaces extended over about 25% of America's urban areas.

  Correcting for these vegetated surfaces brings the mean total of the true US ISA to about 50,000 km2. For final energy uses I assume first that 80% of electricity is generated outside urban areas, and then I assume that 85% of all residential, 90% of all commercial, 75% of all industrial, and 50% of all transportation energy use take place in urban areas; their annual energy demand would have amounted to about 55% of the countrywide total of 3.25 TW in 2011, or nearly 1.8 TW. With the extremes of 84,000 km2 and 180,000 km2 in the denominator, this would translate to 10-21 W/m2. Excluding all vegetated surface and putting 50,000 km2 in the denominator raises the average US urban power density of energy conversions to about 35 W/m2. Power densities of 10-35 W/m2 are well supported by rates calculated by bottom-up sectoral aggregations for specific US cities, as well as for urban areas in an increasing number of other (mainly European and Asian) countries.

  Recent work on anthropogenic heat releases spans scales from global assessments to appraisals at national and city level and to microstudies of specific wards in large cities (Allen, Lindberg, and Grimmond 2010; Chen et al. 2012; Hsieh, Aramaki, and Hanaki 2007; Wong, Dai, and Paul 2012). There are also many studies of urban heat islands. Peng and colleagues (2011) quantified them for 419 of the world's big cities, but their results cannot be readily translated into the power density of specific urban energy use. And I should note that there is also a downward anthropogenic heat flux creating a subsurface urban heat island, but, naturally, its intensity is a tiny fraction of the surface counterpart. Menberg and co-workers (2013) actually calculated that in Karlsruhe, the average total heat flux into the city's shallow aquifer was about 760 ± 89 mW/m2 in 1977 and that by 2011 it had increased to nearly 830 ± 143 mW/m2.

  The power densities of urban energy dissipation have several common attributes. They display expected daily, weekly, and seasonal fluctuations (daily maxima between 11 AM and 6 PM local time; weekend lows; winter maxima in cold regions). Their annual means range between 10 and 100 W/m2, but the seasonal extremes for the smaller areas with the highest energy use go up to, and even above, 1,000 W/m2, exceeding the energy received in some locations even during the noontime peak. In the past, cities in cold climates had the highest pronounced winter peaks, but very high rates now prevail even in tropical climates with the emergence of high-rise-filled downtowns and ubiquitous air conditioning.

  Bottom-up approaches used to quantify the power densities of urban energy use rely on a wide range of relevant statistics (population densities, human metabolism, energy use by buildings and industries, the density of road transport, the specific energy demand of vehicles) incorporated into often detailed models. Quah and Roth (2012) presented more than two scores of annual (and also seasonal) power densit
ies published between 1952 and 2009 for cities in the United States, Canada, Europe, and Asia. The annual extremes in this set ranged from just 4-5 W/m2 for suburban areas of smaller cities (Swiss Basel and Polish L6dz) to 159 W/m2 for Manhattan in 1967. The modal range was between 11 and 30 W/m2, and Tokyo in 1989 had the hourly extremes (for both summer and winter) at, respectively, 908 W/m2 and 1,590 W/m2 (Ichinose, Shimodozono, and Hanaki 1999). Among notable recent bottom-up calculations are those of Hsieh, Aramaki, and Hanaki (2007) for Taipei; Iamarino, Beevers, and Grimmond (2012) for London; Quah and Roth (2012) for Singapore; and Howard and co-workers (2012) for New York City.

  A high-resolution (both in space and time) assessment for London shows that human metabolism contributed just 5% of the mean annual anthropogenic flux of 10.8 W/m2 for 2005-2008, that domestic and industrial sources were nearly equal (4.6 and 4.1 W/m2), and that road fuels contributed about 15% of the total (1.65 W/m2). As expected, the rates declined toward the outskirts of Greater London, and less than 3% of the city had values above 50 W/m2, with the City of London (highest density of high-rise buildings, 348,000 daily workers within 3.2 km2 in 1007) going up to 140 W/m2, with local peaks up to 210 W/m2. Sensible heat dominated the flux, latent heat carried away only about 7% of thermal energy, and heat transferred first to wastewater accounted for about 12% (lamarino, Beevers, and Grimmond 2012).

  In Singapore, 24-hour maxima reached 113 W/m2 in the commercial district, 17 W/m2 in high-density public housing, and 13 W/m2 in the lowdensity residential areas, with buildings (primarily due to cooling) being the largest source of dissipated heat, 49%-82% on weekdays and 46%-81% on weekends (Quah and Roth 2012). In Da-an ward of Taipei city, the daily heat rejection by air-conditioned buildings averaged 15 W/m2 for residential housing and 75 W/m2 for commercial establishments, with an overall mean of 34 W/m2 (Hsieh, Aramaki, and Hanaki 2007). The most informative of these studies of urban energy use is a citywide mapping on a block and lot level for New York (Howard et al. 2012).