Total Resource: Water, Wind and Waves

This is the fifth in our series on the physical limits of Earth's energy resources - previous entries covered chemical, fission , fusion and solar resources. Driven by the enormous solar input to the planet are a number of physical processes that channel and dissipate that incoming flow. Primary among these is evaporation of water in Earth's hydrologic cycle, and related processes result in Earth's weather patterns and the creation of winds and waves. 

The 40,000 TW of incoming solar energy that goes into evaporating water, primarily from the oceans, is in itself over 3000 times current world energy demand. Much of that energy flow may be very difficult for humans to harness, with dissipation throughout the atmosphere and especially over the oceans. One can get some idea of the challenges by looking at the distribution of instantaneous energy content in the world’s supply of water vapor and fresh water.

At any given time the atmosphere as a whole contains about 0.25%, by mass, water vapor. With an atmospheric mass of about 5x10^18 kg that puts 1.3x10^16 kg of H2O in the air. Water's latent heat is 2.27 MJ/kg, for a total energy content of close to 3x10^22 J, or 75 nominal years of present-day energy use. Since the water vapor energy used in a year is 3000 times human energy use, that gives us an average stay time for water vapor in the atmosphere of close to 9 days, over which time all the water condenses out and is replaced.

However, the bulk (about 2/3) of Earth’s fresh water is stored in massive ice sheets which themselves hold considerable gravitational potential energy due to their height above sea level. The total ice sheet mass is about 2.4x10^19 kg. With an average height on the order of 1 km above sea level that amounts to 2.4x10^23 J of gravitational potential energy, or 600 years worth of present energy use. One can imagine new hydroelectric technology to harness this vast store of energy as the ice melts in a warmer world.

The salinity difference between fresh and salt water is another potential source of energy - it is claimed that 1 MW can be derived from the osmotic pressure associated with bringing 1 m^3/sec of fresh water in contact with ocean water. That amounts to 1 kJ per kg of fresh water; the full store of fresh water on Earth, 3.4x10^19 kg, then yields 3.4x10^22 J or about 80 years of present energy demand just from the salinity differences between fresh and ocean water. Two thirds of this store of potential water energy is again in Earth’s ice sheets; if we just limit ourselves to fresh liquid water on the surface (lakes and rivers), only about 1 year’s worth of energy is on store at any given time.

Whether through expansion of traditional gravitational hydroelectric power, through some mechanism for harnessing the latent heat of water vapor, through salinity differences or some other mechanism, Earth's hydrologic cycle has enormous potential to power the world. It may face great technical challenges in meeting that potential, but the physical scale of the resource is very large.

Winds are powered from solar energy both directly through the differential heating of air, and indirectly with the release of water vapor’s latent heat as it condenses to form rain droplets in the atmosphere. If Earth's entire atmosphere moved at the low average wind speed of about 20 km/h (5.6 m/sec), the total kinetic energy, 1/2 m v^2 would amount to 8x10^19 J, or around one fifth of a year's worth of current energy demand.

On average winds around the planet dissipate power at a rate of at least 200 TW. Several studies(1) have shown several tens of TW could be practically extracted over or near land with near-current generations of wind turbines. So wind represents a resource a few times the present scale of world energy use - sufficient to power the world for a few decades at least.

Waves are largely driven by winds, and are estimated to capture and dissipate about 60 TW of the 200 TW of total wind power. With an average wave lifetime of about a day, that makes an accumulation of about 5x10^18 J in instantaneous wave energy around the world. Much of this energy flow is in waves above deep ocean basins, with only about 20 TW available from waves that break on shore. That leaves potential wave energy not much above current world demand.

(1) Cristina L. Archer and Mark Z. Jacobson, “Evaluation of global wind power”, J. Geophys. Res., 110, D12110 (2005), which estimates a global land wind resource of 72 TW at 80 m altitude.

Created: 2007-07-20 00:45:40 by Arthur Smith
Modified: 2007-07-20 00:57:32 by Arthur Smith