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#25277 - 04/02/08 07:23 AM CRUSTAL HEATING
samwik Offline

Registered: 10/10/06
Posts: 1164
Loc: Colorado
This Crustal Heat Gain stuff was way off-topic... sorry,
so I'll just respond here with the Abstract and some quotes.

They don't have all the raw data in this "Letter," but they talk a bit about where their equation came from.
"We use an analytical representation derived from equations presented by Ingersoll et al. [1948] and Carslaw and Jaeger [1959] and employed by Lachenbruch et al. [1982]."

Originally Posted By: from GRL

Beltrami, H., J. E. Smerdon, H. N. Pollack, and S. Huang (2002), Continental heat gain in the global climate system, Geophysical Research Letters, 29(8), 1167.

Table 1. Mean Heat Flux into the Continental Lithosphere and the Corresponding Heat Gained in Fifty Year Intervals Over the Last Five Hundred Years

Time Interval Mean Heat Flux (mW m-2) Heat Gain (10^21 J)
19502000 39.1 9.1
19001950 29.1 6.8
18501900 18.0 4.2
18001850 14.2 3.3
17501800 10.0 2.3
17001750 7.6 1.8
16501700 4.9 1.1
16001650 3.5 0.8
15501600 1.9 0.4
15001550 1.0 0.2

Total 30.0 x10^21 J.

Recent estimates have shown the heat gained by the ocean, atmosphere, and cryosphere as 18.2 10^22 J, 6.6 10^21 J, and 8.1 10^21 J, respectively over the past half-century. However, the heat gain of the lithosphere via a heat flux across the solid surface of the continents (29% of the Earth's surface) has not been addressed. Here we calculate that component of Earth's changing energy budget, using ground-surface temperature reconstructions for the continents. In the last half-century there was an average flux of 39.1 mW m-2 across the land surface into the subsurface, leading to 9.1 10^21 J absorbed by the ground. The heat inputs during the last half-century into all the major components of the climate system atmosphere, ocean, cryosphere, lithosphere-reinforce the conclusion that the warming during the interval has been global.
We also recognize the possibility of additional uncertainty associated with the chosen value of average thermal conductivity that is required for this formulation. We have used the value 3.0 W m-1 K-1 which is very typical of a wide variety of common crustal rocks at near-surface temperatures [Cermak and Rybach, 1982]. A formal estimate of the uncertainty in the average thermal conductivity is difficult, but a 10% range would encompass most educated estimates. .... With specific attention to the 19502000 interval we calculate the mean value of the flux for the last half of the 20th century as 39.1 3.5 mW m-2. Integrated over the area of the continents for the fifty-year interval, this flux deposited 9.1 0.8 10^21 J into the continental crust. ....

.... The mean fluxes for each fifty year interval are also given in Table 1 along with the corresponding heat gained by the continental lithosphere during each period. The total energy deposited into the continental lithosphere over the last five centuries sums to 3.0 10^22 J. These fluxes indicate that 30% of the heat gained by the ground in the last five centuries was deposited during the last fifty years, and over half of the five-century heat gain occurred during the 20th century. However, the total energy gained by the continental lithosphere over the five-hundred year interval is less than the oceanic gain in the last fifty years.

.... Our conclusions about the heat gain of the lithosphere, the last major component of Earth's climate system, are consistent with those presented by Levitus et al. [2001]. While the estimates may eventually be refined, their fundamental implication remains clear: all major components of the Earth's climate system have warmed over the last half century. This further supports the conclusion that the observed warming of Earth during the last fifty years has been truly global and extends upward into the atmosphere as well as downward into the Earth's oceans, cryosphere and continental crust.

They have data from 616 boreholes, on six continents. Probably less than 100 are evenly (globally) distributed, and the rest are heavily concentrated in NW N. America, Europe, S. Africa, Mongolia, and Indonesia.

fyi, my interpretation of their equation #1...
Heat Flux, (in milliWatts/square meter), equals twice the thermal conductivity, divided by the square-root of [Pi times the thermal diffusivity (times the change in temperature/depth)]; and summed over the range of measurements multiplied by the "slope of a surface temperature ramp over a given uniform time interval, dt" (times the change in temperature/depth) (adjusted for the range of measurements).

Wow, who figured that out!

As you can see from the above table, it really has a dramatic rise, shaped a bit as a "hockey stick."
Right? confused

Now I can go ponder the significance of the LIA & MWP in relation to Beltrami's 500 year snapshot.
Pyrolysis creates reduced carbon! ...Time for the next step in our evolutionary symbiosis with fire.

#25322 - 04/05/08 09:26 AM Re: CRUSTAL HEATING [Re: samwik]
samwik Offline

Registered: 10/10/06
Posts: 1164
Loc: Colorado
Originally Posted By: from "Glaciers, Record Shrinkage"

Originally Posted By: ImranCan
Originally Posted By: samwik

"These fluxes indicate that 30% of the heat gained by the ground in the last five centuries was deposited during the last fifty years, and over half of the five-century heat gain occurred during the 20th century."

This is a definite "Hockey Stick" isn't it?

I think you have to be very careful with this kind of misleading statement. When you consider the possibility of natural variation over the last 500 years (eg. LIA) .... the statement is complete nonsense ... whats the point of making a view on the "percentage gain from the last century" out of the last 500 years if you don't look at the whole story ...

Originally Posted By: RicS
G'day ImranCan,

Which statement is misleading. I am a little confused with Samwik's comments. The comment "a hockey stick" normally refers to the very much fudged data used by Al Gore in an incomplete truth that was derived by a group of scientists that simply discarded any studies that gave a different result to their ideal of a hockey stick. That type of scientific methodology should be unacceptable to anyone and should be roundly condemned. That it wasn't by a great many shows just how bad this debate can get.

Both your posts, to me anyway, are ambigious. You indicate that there is a misleading statement but don't say what statement that is that is misleading. The research or the comment by Samwik? Samwik uses a reference to "Hockey Stick" that could mean that the study would produce a very neat hockey stick and thus would reinforce other studies or it could be in a derogatory way saying that this study too seems to be too good to be true.

This isn't a critiscm of any stance by either of you, only a request to make the comments less ambigious so we actually know what we are meant to be discussing.
...Oh, and I really don't like references to studies that are available only to members of the organisation that controls the website.

Originally Posted By: samwik
LOL, Richard. I hadn't thought of that interpretation; guess I'm not as cynical about Al's data (I thought it was just poorly "scaled").
Capitalizing the term probably made it sound like "the famous hockey stick," eh?

Thanks for asking for clarity on the comment; I too was wondering which was misleading or nonsense.
I think it's me that is misleading (and you were wondering!); and Beltrami, et al. that is "complete...."

Originally Posted By: ImranCan
I agree with your comments about the paper. But this paper just gives an example of a scenario where the global temperature has not been flat over the last centuries. We could equally well just call on anecdotal evidence from Europe regarding the LIA. My point was that in a scenario where global temperatures vary up and down (or down and up), a statement quoting 50 % of warming in the last 100 years from an overall period of 500 years might sound alarming but it doesn't mean much.

Originally Posted By: RicS
G'day Samwik and ImranCan,

Thanks for the clarifications. Makes more sense.

Actually to a lot of people, even with fluctuations, a substantial amount of warming occuring in a very compressed period (50% within a century, the other 50% over the previous 400 years) might still sound alarming. I'd like to see any data that suggests that there has been any overall warming over the period 1500 to 1900. That really doesn't match ANY data that I've seen, including all those that support global warming strongly. There was a bit of a warming in 1500 itself and certainly from 1870 or 1880 to 1900, and a fluctuation again in the late 1700's if I'm not mistaken but overall this period was a very cold period. I don't particularly like the term Little Ice Age because it is actually made up of three periods of cooling and all three might not have been world wide although two of the three appear to have been.

It may well be, just as 1880 seems always to be picked to show global warming, that picking 1500 or therabouts as a starting point does show a warming trend because you are cutting out one of the LIA components and some of the second, but overall I don't think anyone that has studied the various evidence that is available would say that the period wasn't basically colder than has been the norm this interglacial period. There is a great deal of argument about whether it was just a bit colder or very much colder but either way, where does this first 50% come from?

Another study that just looking at it briefly seems to demonstrate a failure to accord with basic evidence. I find the fact that these types of studies are published, peer reviewed, and not criticised extremely disheartening.

Regards, Richard

Okay, now that this is caught up....

Here's a link to a copy of the paper:

Charts and graphs, equations, etc.
Oh, and I see I was mistaken when I said "Indonesia." It should have been Australia.

Just a quick note to say I pondered your points, but after more research, I think this still does stand up.
The lack of any signature from the LIA is to be expected with a 50 year averaged reading.
There is some raw data out there with yearly readings. I'll look for it and see if some of the solar minima show up.

Also, I think the limited warming shown for the "first 50%" is entirely consistent with the course of the LIA.
It had reached its minimum by about 1550-1600; and so, has been rising (in general) since that time.

from: http://en.wikipedia.org/wiki/Little_Ice_Age

I'd say the average (from ~1500 on) of this picture matches Beltrami's "hockey stick."
Do you see what I mean?
Pyrolysis creates reduced carbon! ...Time for the next step in our evolutionary symbiosis with fire.


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