The Cooling Earth

The Hitchhiker’s Guide to the Galaxy considers the Earth to be “mostly harmless” whilst satellite observations reveal the Earth’s surface to be “mostly water”.

Iceberg_with_hole_near_sanderson_hope_2007-07-28_2

http://en.wikipedia.org/wiki/Water

Saline water covers about 71 percent of the Earth’s surface according to Wikipedia. Frozen water, in the form of ice sheets, seems to cover about 3% of Earth’s surface.
With an allowance for ice caps, lakes, rivers, and swamps it appears that water covers approximately 75 percent of the Earth’s surface [in one form or another].

Earths_Water_Distribution
http://en.wikipedia.org/wiki/Water

However, if we make an allowance for groundwater [and it “is likely that much of the Earth’s subsurface contains some water” according to Wikipedia] then it is arguable that the Earth’s climate system conforms to the “80–20 rule” [the Pareto principle] and that water [in one form or another] controls 80 percent of Earth’s climate system.

Earth_elevation_histogram
http://en.wikipedia.org/wiki/Elevation

The results of the Earth’s Radiation Budget Experiment [ERBE] published in 1988 clearly demonstrate the dominate role of water. The presence of water, ice and surface moisture clearly limits the clear-sky diurnal range [in long wave radiation] to less than 30 watts per square metre over most of the globe. The higher clear-sky diurnal ranges [to about 70 watts per square metre] are primarily associated with arid land surfaces.

Diurnal Range - Clear Skies - April 1985
Diurnal Range of clear-sky LWRE for April 1985

However, the presence of atmospheric water [clouds] clearly limits the average diurnal range in many arid areas whilst enhancing heat loss over wetter regions.

1988 First estimates of the diurnal variation of longwave radiation
Diurnal Range of LWRE from ERBE for April 1985

Harrison, Edwin F., David R. Brooks, Patrick Minnis, Bruce A. Wielicki, W. Frank Staylor, Gary G. Gibson, David F. Young, Frederick M. Denn, and the ERBE Science Team, 1988: First estimates of the diurnal variation of longwave radiation from the multiple-satellite Earth Radiation Budget Experiment (ERBE).
Bull. Amer. Meteor. Soc., 69, 1144-1151.
http://www-pm.larc.nasa.gov/manuscripts/pdffiles/Harrison.etal.BAMS.88.PDF

Having [hopefully] clearly demonstrated that water [as traditionally represented in climate science] is very significant it’s now time to revisit the “poor orphan” of climate science: Geothermal energy.

The satellite images from the 1980s indicate that regions with dry surfaces had high diurnal ranges in long wave radiation and this is typical for desert environments which experience surface heating during the day [via insolation] followed by night time cooling [via long wave radiation].

Interestingly, a 1978 study in the Nevada Desert indicated that the solar energy absorbed by the surface during the day had been totally radiated away by 03:15 in the morning and that [therefore] geothermal energy was radiating away from the surface for at least 3 hours each day.

Goldfield NV - Soil Temperature_Anotated
Use of thermal-inertia properties for material identification
http://dana.ess.washington.edu/Publications/Use%20of%20thermal-inertia%20properties%20for%20material%20identification.pdf

Wikipedia indicates that the continental crust supports a very modest mean heat flow of around 65 milliwatts per square metre and it is probable that this heat flow is effectively radiated away, in arid regions, during the early hours of the morning.

Heat flows constantly from its sources within the Earth to the surface. Total heat loss from the Earth is estimated at 44.2 TW (4.42 × 1013 watts).
Mean heat flow is 65 mW/m2 over continental crust and 101 mW/m2 over oceanic crust. This is 0.087 watt/square meter on average (0.3 percent of solar power absorbed by the Earth ), but is much more concentrated in areas where thermal energy is transported toward the crust by convection such as along mid-ocean ridges and mantle plumes.

http://en.wikipedia.org/wiki/Geothermal_gradient

Arid regions clearly support the view that geothermal energy is a very trivial energy input to the Earth’s climate system.

However, there is a complication that needs to be considered: topology.

The Earth does not have a smooth surface.

Therefore, the surface area that can absorb solar radiation during the day and radiate away long wave radiation during the day depends upon the Earth’s topology.

Arguably, the Earth’s surface area is a fractal quantity which varies depending upon the granularity of your measurements [very much like the measurement of coastline].

Unfortunately, I haven’t stumbled across any estimates for the actual surface area of the Earth. However, it doesn’t take a lot of imagination to envisage an actual surface area for the continental crust that is twice that of a smooth surface.

Topographic profile
http://www.searchanddiscovery.com/documents/2009/40414bonow/images/fig04.htm

The Earth’s topography, therefore, does introduce some very interesting challenges when considering the Earth’s energy budget:

1) How should we calculate the insolation received [per square metre] for the Earth?
2) How should we calculate the geothermal radiation [per square metre] for the Earth?
3) Can satellites accurately measure Earth’s radiation output from inclined surfaces?

These problems also apply [to a lesser degree] to the Earth’s watery surfaces which are [as any mariner will confirm] notoriously treacherous.

Unfortunately, these issues appear to be ignored in the typical “flat-earth” energy budget diagram.

Pacific_Waves
http://en.wikipedia.org/wiki/Wind_wave

However, the role of geothermal energy becomes far more interesting when we remember that the Earth’s contains groundwater because these repositories of water slowly extract geothermal energy from the Earth’s surface before re-emerging as surface water.

Groundwater_flow
http://en.wikipedia.org/wiki/Groundwater

The extent of ground water reserves beneath the continental and oceanic crust [and their hydrothermal profiles] are not know precisely but some structures, such as the Great Artesian Basin in Australia, are known to be sources of hydrothermal energy with water temperatures ranging from 30 to 100 degrees Celsius.

The Great Artesian Basin provides the only reliable source of freshwater through much of inland Australia. The basin is the largest and deepest artesian basin in the world, stretching over a total of 1,711,000 square kilometres (661,000 sq mi), with measured temperatures ranging from 30°C to 100°C.

It underlies 23% of the continent, including most of Queensland, the south-east corner of the Northern Territory, the north-east part of South Australia, and northern New South Wales. The basin is 3,000 metres (9,800 ft) deep in places and is estimated to contain 64,900 cubic kilometres (15,600 cu mi) of groundwater.

http://en.wikipedia.org/wiki/Great_Artesian_Basin

Although many known surface features [such as springs and geysers] are easily associated with groundwater emissions it is far harder to quantify the overall background level of hydrothermal emissions which directly support vegetation and contribute to the local surface water resources.

Additionally, the overall level of hydrothermal activity in the oceanic crust has yet to be fully explored [and quantified] but we do know that hot hydrothermal features also exist on the ocean floor.

Another aspect of geothermal cooling [of the Earth] is the Geothermal Gradient which Wikipedia indicates is 25 degrees Celsius per kilometre of depth.

Geothermal gradient is the rate of increasing temperature with respect to increasing depth in the Earth’s interior. Away from tectonic plate boundaries, it is about 25°C per km of depth (1°F per 70 feet of depth) in most of the world.

http://en.wikipedia.org/wiki/Geothermal_gradient

Unfortunately, the source used by Wikipedia [for the Geothermal Gradient] is the International Geothermal Association which aims “to encourage research, the development and utilization of geothermal resources worldwide”.

However, the following Petroleum Geology diagram produced by the West Virginia University shows the Geothermal Gradient ranging from 15 to 55 degrees Celsius per kilometre of depth.

Geothermal Gradient - Oil Window

Whilst the Geological Survey of Ohio indicates the Geothermal Gradient dips below 10 degrees Celsius per kilometre of depth.

Geothermal Gradient in Ohio

ftp://ftp.dnr.state.oh.us/Geological_Survey/Geothermal/Maps/OHGRAD.pdf

Clearly, the Geothermal Gradient is more complex than Wikipedia suggests.

Geothermal Gradient in Coso
Idealized equilibrium thermal gradient profiles for 24 shallow boreholes at the Coso geothermal area. In general, boreholes with high thermal gradients are located in the immediate vicinity of the Devil’s Kitchen and Sugarloaf Mountain thermal manifestations.

http://publishing.cdlib.org/ucpressebooks/view?docId=ft6v19p151&chunk.id=d0e10705&toc.id=d0e10705&brand=ucpress

The oceanic Geothermal Gradients and deduced heat flows appear to be far more speculative:

Despite its conceptual simplicity, the process of deducing heat flow from a measured gradient and conductivity values has surprising complexity.

However, the process of penetrating the surface to measure the temperatures disturbs the thermal structure. For marine measurements, thrusting a probe into the sediments to depths of about 5 m results in frictional heating, which takes from 5 to 30 minutes to dissipate depending mostly on the probe diameter. Prior to 1975 most heat flow values were based on single measurements, which were typically spaced about 200 km apart. Subsequently, digital instrumentation has resulted in both better temperature determinations and the capability to make closely-spaced seafloor (“pogo”) penetrations more rapidly than before. Hence, local variations in the heat flux can be better identified and their cause determined.

Heat Flow of the Earth – Carol A. Stein – 1995
http://www.unicamp.br/fea/ortega/extensao/Stein.pdf

Although there are many imponderables when considering geothermal heat [in a climate context] there are a few diagrams that suggest hydrothermal emissions may not be quite so trivial after all.

The 2010 research by Davies and Davies indicates that the global heat flux from the Earth’s interior ranges from 23 to 450 milliwatts per square metre – although these numbers still understate the actual total emissions associated with the topographic surface area of the Earth.

Interestingly, the largest oceanic hot-spot is under the south-eastern Pacific Ocean and it is not beyond the realm of possibility that this hot-spot provides the energy that drives the El Nino phenomenon.

Paradoxically, the largest continental hot-spots are under the ice sheets of Greenland and Antarctica. This may indicate that the Earth’s ice sheets provide a level of geothermal insulation by inhibiting cooling via long-wave radiation. If this is the case then the continental geothermal heat flux may have been significantly underestimated.

Earth’s surface heat flux
Earth’s surface heat flux – J. H. Davies and D. R. Davies
http://www.solid-earth.net/1/5/2010/se-1-5-2010.pdf

Enso_el_nino
http://en.wikipedia.org/wiki/El_Ni%C3%B1o%E2%80%93Southern_Oscillation

Interestingly, more sophisticated heat flow studies are beginning to report higher heat flow rates when corrections for climate and topography are introduced.

Heat flow map Scandinavia 2011
Geothermal Resources in Norway
Kirsti Midttømme, Inga Berre, Odleiv Olesen
http://www.geoelec.eu/wp-content/uploads/2012/01/Geothermal-Resources-in-Norway.pdf

Overall, it appears that we still have a lot to learn about the geothermal heat flux and hydrothermal emissions.

However, in conclusion, I will simply join up a couple of academic “dots” to reveal a truly remarkable perspective on our Cooling Earth.

The first “dot” is the table of thermal properties for the continental upper mantle that is tucked away in the appendices of the Physics of the Earth textbook written by Frank D Stacey and Paul M Davis.

Thermal Properties of the Continental Upper Manle
Physics of the Earth – Fourth edition
Frank D Stacey – CSIRO Exploration and Mining, Brisbane, Australia
Paul M Davis – Department of Earth and Space Sciences, University of California, USA

The second “dot” is the Wikipedia graphic of the U.S. Standard Atmosphere.

US_standard_atmosphere
U.S. Standard Atmosphere
http://en.wikipedia.org/wiki/U.S._Standard_Atmosphere

Joining these two academic “dots” together provides a remarkably consistent holistic view of the Cooling Earth.

The Cooling Earth

UPDATE
Standard Atmosphere Supplements 1966

See: https://malagabay.wordpress.com/2014/08/04/us-standard-atmosphere-supplements-1966/

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