Tim Cullen: What a Wonderful Water World

Posted: December 24, 2012 by tallbloke in Analysis, atmosphere, climate, Clouds, general circulation, Ocean dynamics, sea ice, Uncertainty

While I was over in Spain I spent some time in the company of Tim ‘MalagaBay’ Cullen whose generous help and hospitality made my transport and accommodation arrangements a pleasure rather than a chore. We also got to spend a good amount of time brainstorming climate ideas and discussing this post, which I found very interesting and, as always with Tim’s work, thought provoking.

What a Wonderful Water World
Tim Cullen : December 2012


Having survived the End of the World [on Friday] and having started a new Mayan Long Count [on Saturday] it seems appropriate to celebrate our Wonderful Water World [on Sunday] by splashing a few ideas around for consideration [on Monday].

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”.



 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].



 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.



The results of the Earth’s Radiation Budget Experiment [ERBE] published in 1988 clearly demonstrate the dominant 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.


DiurnalRange 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.


DiurnalRange 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.

Click to access 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.


Use of thermal-inertia properties for material identification

Click to access 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. 


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 at least twice that of a smooth surface.



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.



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.

image10 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.


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.


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 VirginiaUniversity shows the Geothermal Gradient ranging from 15 to 55 degrees Celsius per kilometre of depth.

image11 http://www.geo.wvu.edu/~jtoro/petroleum/petroleum_figs/review1/thermal%20grad.gif

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

image12 ftp://ftp.dnr.state.oh.us/Geological_Survey/Geothermal/Maps/OHGRAD.pdf

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

image13 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.


 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

Click to access 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 some of 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 – J. H. Davies and D. R. Davies

Click to access se-1-5-2010.pdf



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


Geothermal Resources in Norway

Kirsti Midttømme, Inga Berre, Odleiv Olesen

Click to access 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 Wonderful Water World.

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.


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.


U.S. Standard Atmosphere


 Joining these two academic “dots” together provides a remarkably consistent holistic view of our Wonderful Water World.


Tim Cullen
MalagaBay – December 2012

  1. Max™‮‮ says:

    Now this: https://tallbloke.files.wordpress.com/2012/12/image191.jpeg is something which seems obvious after looking at it, yet I never really thought would line up like that.

  2. tallbloke says:

    Yeah, eye opener isn’t it? 🙂

    Coupled with Tim’s observation of the extent to which water penetrates the Earth’s crust, it makes a strong argument for the primacy of water as the controller of temperature from many kilometres below the surface, to many kilometres above it.

  3. tchannon says:

    I don’t expect a great effect on Earth but I suspect it is ground heat which is the real reason for the surface temperature of Venus which is well in excess of the maximum solar flux can reasonably give.

  4. oldbrew says:

    What might the surface temperature of earth be if its atmospheric pressure was 92 times greater i.e. like Venus?

  5. wayne says:

    oldbrew, “What might the surface temperature of earth be if its atmospheric pressure was 92 times greater i.e. like Venus?” Since the air species ratios are assumed the same, you just extend the pressure range using Poisson to get the potential temperature at the ELR:

    Φ = 216.77 * (92*101325/22700)^0.190259 or somewhat close to 681 K at the surface.

  6. wayne says:

    oldbrew, curiously with Venus’s orbit 0.723 that of Earth’s orbit and using instead Earth’s TOA alt and temp and Venus’s composition:

    Φ = 216.77*(1/√0.723) * (92*101325/22700)^0.1716 or 716 K. Not very far off between the two atmosheres. Off a mere 2.5%. Yes, it seems it must be TD at play in the troposphere and that seems the only simple and plausible explanation. An exponent of 0.176 instead of 0.172 brings it to the 735 K. Very curious!

    Big question is can that 2.5% be also explained some other way?

    Maybe the 216.77 K also needs a correction to allow for the 96.5% of GHG atmosphere on Venus.

  7. Max™‮‮ says:

    I can’t help but wonder what a global resurfacing event would do regarding heat flow into the atmosphere, also curious how much it would affect the mass of the atmosphere.

    I don’t think Venus needs to be treated as though it has been in this state for 4 billion years though, sometime in the past it underwent some rather… energetic events, to say the least.

  8. Richard says:

    Hmm. If you are talking about the Water planet we live on, surely the below ‘surface’ temps for the first few Kilometers should be for the deep Ocean, not on land. An even more interesting profile I believe ( a nearly vertical line with some wiggles in it?).

  9. Richard says:

    A standard Ocean profile will ‘kick’ the surface temps to the left for the first ~3-4Km down to <4C for instance.

  10. Tim Cullen says:

    Richard says: December 25, 2012 at 10:44 pm
    A standard Ocean profile will ‘kick’ the surface temps to the left for the first ~3-4Km down to <4C for instance.

    There seems to be a huge gap in our knowledge… well definitely in my knowledge.
    I haven’t encountered a study that attempts to join up the oceanic water temperatures “dot” with the oceanic crust temperatures “dot”.


    Perhaps the Challenger Deep gives us a clue:

    Potential temperature increased from 7500 db to the bottom at a constant rate of 0.9 m°C/1000 db.

    Deep CTD Casts in the Challenger Deep, Mariana Trench

    Click to access 61030447.pdf

  11. Tim Cullen says:

    PS: Submarine aquifers open up some interesting possibilities 🙂

    Left field: harvesting groundwater from the seabed

    But with large scale water projects off the agenda for now – harvesting Tasmanian water would cost perhaps $1 billion – the next idea is dubbed the Submarine Hydro Energy System (SHES). And it may have more chance of seeing the light of day because water is really the byproduct; the key potential, said Martin, is it could generate baseload, emissions-free energy at a paltry 3 cents per kilowatt hour.

    It relies on the fact that aquifers don’t only run under the land, they run under the seabed as well – and in some places the groundwater leaks out through seeps. The density difference between salt and freshwater means the fresh rises to the surface, a dynamic Docklands hopes to harness through “simple collection systems, power lines, switches and hydro-generators”.


    Slideshow: http://www.slideshare.net/docscipark/submarine-hydro-energy#btnNext

  12. Joe's World {Progressive Evolution} says:

    Very nice presentation…

    Salt seems to be the dominate mineral in ocean water. So where did the salt come from on the land?
    It is flammable so cannot possibly come from volcanic activity.
    The dating of it is based on the dry form.
    It is found in much higher elevations and some sea life have been captured into it.

    It used to be used to find oil deposits…
    Older volcanic activity has pressurized markings of being under immense pressure in the over billion year study.
    Why is our poles ice in ONLY the millions of years?

    Is not the evidence showing vastly more salt water?
    And why do meteors show they are virtually identical to our oceans composition?