A Guest Post “Some Back Of The Envelope Calculations About Energy” by Balázs M. Fekete

Today we have a guest post by Balázs M. Fekete.

“Some Back Of The Envelope Calculations About Energy” by Balázs M. Fekete

High energy use is often considered the most important sign of an unsustainable consumer economy. Increasing energy efficiency is viewed as the most important step in lowering carbon emission and mitigating climate change followed by the necessity to ensure that the remaining energy demand is satisfied in a sustainable manner using renewable resources. Perhaps a somewhat strict definition of renewable energy is to consider only energy that is driven by solar radiation.

What makes the following discussion about energy difficult is the plethora of units used in the literature. Some express energy in TOE (tons of oil equivalent), some use Wh or J (which often have an implicit annual dimension Wh/yr) just to list a few. In this blog, I will consistently use W, which seems to be the appropriate unit for discussing energy use.

People in developed world are often told that their addiction to energy has to be stopped, so as a first step it is worthwhile to see what energy addiction means and establish some sort of energy use baseline that  could be consider as the minimum for modern life. We often hear statements about the necessity to change our lifestyle. A good approach is to look at different countries and decide what would be a reasonable compromise. Table 1 shows the per capita energy use for a couple of countries from the CIA’s The World Factbook[1]. Contrasted with the ~100 W energy equivalent of a 2000 kCal/day diet, one can translate this table to the number of “servant” individuals need to make life more comfortable. People in Bangladesh rely on two servants as additional energy, while the residents of Qatar have almost 285 servants. Since these servants are fully dedicated to support their “master” and don’t take energy to maintain their own metabolism it is no surprise that the comfort of living far exceeds in many countries what kings used to enjoy centuries ago. In Table 1. Chile, Lebanon, and Romania are colored green, because the per capita energy consumption in these countries is around the 2200 W which is the global average.

Table 1. shows the per capita energy use for a couple of countries from the CIA’s The World Factbook[1].

Country W/capita
Bangladesh 214
Eritrea 265
Senegal 310
Brazil 1422
China 1516
Chile 2200
Lebanon 2264
Romania 2376
Cyprus 4370
Kazakhstan 4474
United States 10381
Luxemburg 12531
Iceland 15606



Figure 1: Energy use distribution as a function of population (black curve, left axis) and cumulative total (red curve, right axis)

Figure 1. shows the energy distribution by population and the cumulative total consumption. A striking characteristic is the non-even distribution of the global energy use. In a more just world, where everybody had access to 2200 W average energy (which is less than one fourth of the energy use in the United States) the red line would be a straight line from 0 to ~15 TW (which is the global energy use today, Figure 2.).

Only 26 % of the global population enjoys the luxury of access to >2200 W/capita energy, and the vast majority use much less. The majority of the world’s population lives in conditions not much different than Europe was in Medieval times. For instance, 1.4 billion people have no access to electricity (400 million in India alone). Anybody who thinks that is the living standards everybody should adopt is welcome to move to Bangladesh, Eritrea, or Senegal.

Figure 2: Total energy use in a more just world

Figure 2. shows the cumulative energy use in a more just world, where everybody has access to the current average (scenario 1). If people in the developed world did not reduce their energy use, while the 76 % living under the global average is allowed to 2200 W/capita (scenario 2) the global energy use would only grow by 40 %. A more generous allowance of doubled per capita energy use (4400 W/capita, scenario 3) would obviously mean that the global energy use would double. In Table 1. Cyprus and Kazakhstan are colored blue as examples of countries living at the level of twice the global per capita energy use level. Before rushing to the conclusion that the standard of living in Cyprus is probably a reasonable compromise, one has to realize that Cyprus is not known for much industry so their energy use is probably more driven by the energy use of individuals. At doubled per capita energy use level, the significance of the developed countries improving energy efficiency diminishes further making only a 10 % difference whether they reduce their energy use to the 4400 W/capita level or not (scenario 4). The little wedge between scenario 3 and 4 (since talking in wedges was popularized by Pacala and Socolow [2]) is where the developed world can make a difference by banning incandescent light bulbs.

Clearly, the driving force in growing energy use has to be the developing world catching up. Unless, over 5 billion people are denied the modern comfortable life which is far from the consumer economy of the Western world, energy use has to double regardless of changing our diet from beef to tofu or the number of Prius’ driven by academics. I overheard a dialog at the annual AGU conference in San Francisco a few years ago, when one participant expressed that driving a Toyota Prius was the excuse for not carpooling. If this is representative to the average thinking of academics, there is plenty of room for educating the level of energy efficiency needed for mitigating climate change.

Adding population growth will result in 9-12 billion people by 2050 (Figure 3 from Wikipedia[2]) therefore  the global energy use will have to triple or quadruple regardless of the energy efficiency improvement in the developed world.

Figure 3: Population projections

One might argue at this point that the core problem is overpopulation and introducing population control is the solution. Besides, the obvious conflict between population control and civil liberty, such an approach would likely lead to the conclusion that excessive population growth is the problem of the developing world and the population that needs to be controlled is the 76 % poor. Most of them are poorly educated illiterate, who do not participate in the global economy since the job they would qualify for are rapidly taken up by robots.

The developed world is actually already on the path of declining population. For instance, the fertility rate in Germany or Italy is 1.4 and 1.3 respectively, which is well below the 2.1 reproduction rate to maintain steady population. The only reason that the United States still has growing population is the continuous immigration. A quick note to those, who are proud of not having children and view themselves as savers of humanity, declining population also means less active people by the time they retire. The retirement systems are falling apart in many countries, which maintained generous retirement system for decades, when generations after generations paid less into the system than what the retirement system paid later. Such a system is only sustainable if the population grows steadily. Regardless of how savings of the retirees are managed (by the government or individuals investing in stocks or real estate), it is the next generation which ultimately pays retirement benefits (either caring for their parents, or through taxes or buying stocks and real estate from the elders).

Actually, climate change mitigation indirectly is leading to limiting the population growth of the poor. Denying people from accessing electricity leads to continued indoor air pollution, which is the primary source of many respiratory diseases in the developing world. Similarly, burning biomass as an energy source has already lead to growing food prices, which in turn already changed the previous trend of the steady decline of hunger and malnutrition as a result of the green revolution. The primary reason for the apparent collapse of the climate negotiation has nothing to do with conspiracy of the energy lobby, but clearly the developing countries (lead by Brazil, India, and China often referred as BRIC countries) realizing that the carbon emission targets on the table will severely limit their ability to catch up anywhere near to the living standard of the developed world. Hopefully, this discussion clearly illustrates that anybody who thinks climate change mitigation can be achieved primarily by improving energy efficiency either ignores 76 % of the global population who are extremely poor by any standard or did not do their homework. One would hope that those prominent climate scientists, who make these claims did a better job in their own science.

After establishing that tripling or quadrupling the global energy use is inevitable (which is not an energy demand forecast but a hopelessly idealistic assumption that the world is heading to a more just distribution of wealth) one needs to look at if this energy use can be satisfied from renewable resources. Strictly speaking, one needs to compare the amount of energy that the reaches the Earth’s surface (~89 PW) to the tripled energy consumption (45 TW). Since, 70 % of the Earth is covered by ocean, the available solar energy is only ~27 PW, assuming that solar panels or biomasses will be utilized dominantly on the continental land mass. This is still a comfortable 0.17 % energy consumption solar radiation ratio,  if 100 % of the solar insolation can be captured. Unfortunately, neither biofuels nor solar panels come close to that level of efficiency.

Interestingly, not much data is available on the land efficiency of producing biofuel. In a recent talk by Jose Marengo[3] at the Global Water Systems Project’s symposium in Bonn Germany, provided some interesting clues based on ethanol production from sugar cane. Brazil is planning to expand the amount of lands dedicated to grow sugar cane to 10-12 million ha to produce 48 billion l ethanol. Considering the energy content of the produced ethanol and the annual solar insolation of the sugar cane producing land, one can calculate a 0.3% efficiency without factoring in the energy investment needed to grow the plants and produce ethanol. Since, sugar cane ethanol so far is the most efficient form of producing biofuel, one has to realize satisfying the 45 TW energy demand would require dedicating all the land to energy production, which is obviously impossible.

A similar calculation can be carried out for solar panels. The most efficient photovoltaic solar panels have 10 % efficiency. Higher efficiency is achieved by concentrating solar insolation via a series of mirrors. It is unclear if the overall land use efficiency of such a configuration is improved. The solar panels are typically black, so wall-to-wall deployment would lower albedo and cause warming. To offset that, the panels need to have spaces in between them possibly with higher albedo surfaces, therefore a 5 % land efficiency is probably more realistic.  At that land efficiency, the land requirement would increase from 0.17 % (energy demand vs. solar energy ratio) to ~3 %, which is the equivalent of a current urban area. Putting solar panels on roof tops is clearly not enough, since roofs are the smaller portion of the urban area beside the competition for roof space. John Holden (President Obama’s science advisor) wants to paint them white (as a means to increase their albedo and combat global warming) others want to put grass as thermal insulation and to withhold precipitation for controlling storm runoff. If solar panels are installed in remote areas (preferably desert areas), additional energy transportation losses would mean that more land will be needed.

It is hard to judge the area requirement of wind power. Some might argue that it is minimal considering the actual footprint of a wind tower. Those unfortunate to live next to the hissing wind turbines might think otherwise. What is more informative is the ratio of the estimated potential wind power (370 TW[4]) and its commercially available portion (72 TW[5]), which is actually not much more than the 45 TW energy demand. Although, it is unclear how the total wind power was calculated particularly in the light of hydropower calculation bellow, but the high ratio of energy demand vs. available capacity is concerning since it would be hard to believe that the 45 TW level of utilization would not affect global circulation patterns.

The hydropower capacity reported in literature (6-10 TW) appears to be off by a factor of two to three. The computation is actually rather simple. The area integral of the elevation (in m above sea level) × runoff  (in kg/m2) product is the potential energy of the excess water on the land surface.  A simple way to make that calculation is to multiply the mean annual discharge to oceans (~40,000 km3/yr times density of water) by the runoff weighted elevation (275 m) which leads to 3.5 TW [1]. The discrepancy can come from two sources. The first is the runoff weighted elevation is obviously not identical to the global mean elevation (600 m). The second source is the misunderstanding of the reported built-in hydropower capacity 0.8 TW. The built-in capacity reported by IEA or other sources is not meant for 24/7 operation. Hydropower is often used to generate peak energy, since hydropower plants are the quickest to turn on (other power plants needs considerable amount of time to crank up). As a consequence, hydropower plants have a low utilization factor. IEA clams 40%, but it can be lower so the turbines sit idle most of the time. The 0.8 TW appears to be quite high even if the utilization factor is taken into account indicating the potential to increase that capacity further is rather limited. A growing number of hydropower plants are used to store energy. They might pump water during off peak hours to a reservoir at some higher elevation and release the water and generate electricity during peak hours. Unless, a better form of storing a massive amount of energy is found, the significance of hydropower is likely to remain for load balancing than its absolute contribution to the global energy source mix.

While satisfying energy needs from the Sun appears to be doable, such a transition will need substantial land dedicated to produce energy, when the available land is becoming increasingly a limiting factor for human development. A recent paper by Rockstörm et al. [3] introduces a series of planetary boundaries to express that our planet is finite. Perhaps, a more intuitive mean to realize the Earth’s limits is to consider population density.

Current population density over 133 million km2 continental land mass is 52 people/km2 or 1.96 ha/capita. Since half the global population lives in urban areas which is 3 % of the continental land mass the density in cities is 942 people/km2. One can argue that the total land that humans already appropriated is the sum of agricultural lands 10-17 % plus urban areas (a total 20 %), which would lead to 250 people/km2 over the human controlled lands. The “scientific narrative” is often to blame humans for destroying the Earth’s ecosystems, but it is hard to find any other species that can reach similar density beside the desert locust. The number of locusts in a swarm could be as high as 40-80 million, which is highly destructive and needs to keep moving. Factoring in the 2 g average weight of the locust, the human equivalent (at 75 kg/person) would be 1100 people/km2 (by the way, at this density, the locusts become cannibals, which is undeniably just a primitive form of waging wars). This density is similar to the population density of Bangladesh (1083 people/km2). Mankind’s only guilt is being populous and probably any other species at our density would be similarly destructive. At 250 people/km2 density, which is well below the destructive locust swarm level, there is still room for ecosystems to thrive, but satisfying our 22-44 energy “servants” for a growing population is clearly a challenge.

Sustainability can be ultimately posed as a land utilization question. The per capita land allowance is 1.96 ha (that will shrink as population grows). Three percent of that land is needed for cities that will double in the next 50 years as urban population is expected to double by 2050. Another 10-15 % is needed to grow food. Relying on ecosystem services (e.g., wetlands instead of sewage treatment plant) will also need more lands. Evidently not all lands are equal and the lands suitable to serve humans’ needs are likely in competition with natural ecosystems.

When discussing energy, one has to realize that the real challenge in utilizing renewable energies is not the energy source, but the energy storage and transportation. It is well known that the most efficient battery technology still has one quarter of the energy density by weight of the regular gasoline. It is telling that the putting a traditional combustion engine plus a gas tank into plugin hybrids like the GM Volt to extend the driving distance by 200 miles is more viable than adding more batteries to increase the 50 miles that the car can go on batteries. What is less realized is the efficiency of refueling. Jeremy Clarkson the arrogant host of BBC’s TopGear show demonstrated this when he introduced the fully electric Tesla supercar a few years ago that is popular amongst environmentally conscious celebrities like  George Clooney. The car uses the same lithium batteries that are common in laptop computers. While the car is significantly heavier than comparable cars with combustion engines, the batteries could last for 250 miles, which is significant compared to electric cars. The only drawback is that recharging on a regular 15 Amp outlet takes 16 hours, which is not surprising. One could come to the same conclusion by considering the energy content of a medium size 40 l gasoline tank (1368 MJ). To transfer that amount of energy in the usual 5 minute stop at the gas station is the equivalent of hooking up a car to a 4.5 MW powerline. Alternatively, refueling stations would need to replace the whole battery pack and charge them in warehouses. Electric vehicles may start to populate cities soon, but the good old combustion engine will have a bright future on the highways for a considerable time, which leads back to biofuels. Unless, engineers find efficient ways of producing synthetically, biofuels will be needed for transportation.

In summary, the technologies to transform our economy to renewables are far from ready and burning more fossil fuels will be inevitable for the 76 % of the Earth’s population, which is extremely poor. Elevating their living standard is a must not only in the spirit of equity, but as a means to control population growth humanly. Wealth and education (particularly women’s education) appears to be the best form of contraception. Putting the developing world on a rapid path to economic growth is the best means of ensuring that global population peaks around 9-10 billion instead of 12-15 billion (Figure 3). Denying them cheap energy (which are various forms of fossils fuels today) is not only immoral (and a crime against humanity) but will keep developing countries at the current level of population growth, which will lead to higher population size by the time they catch up. Someday, mankind will need to move to renewable energy sources (unless nuclear is widely endorsed), but that transition needs to be well planned. Acting in panic mode will probably do more damage than good.


1    Fekete, B. M.; D. Wisser, C. Kroeze, E. Mayorga, L. Bouwman, W. M. Wollheim and C. J. Vörösmarty: Millennium Ecosystem Assessment scenario drivers (1970-2050): climate and hydrological alterations, Global Biochemical Cycles, 24(GB0A12), 2010

2    Pacala, S. and R. Socolow: Stabilization Wedges: Solving the Climate Problem for the Next 50 Years with Current Technologies, Science, 305(13 August), 2004

3    Rockström, J.; W. Steffen, K. Noone, F. S. Chapin III, T. M. Lenton, M. Sheffer, C. Folke, H. J. Schellnhuber, B. Nykvist, C. A. de Wit, T. Hughes, S. van der Leeuw, H. Rodhe, S. Sörlin, P. K. Snyder, R. Costanza, U. Svedin, M. Falkenmark, L. Karlber, R. W. Corell, V. J. Fabry, J. Hansen, B. Walker, D. Liverman, K. Richardson, P. Crutzen and A. Foley: A safe operating space for humanity, Nature, 461, 2009 

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