Guest post by Dr. Roger Pielke Senior
As discussed in the post
the global annual average surface temperature trend has become the icon of communicating climate change to the policymakers and even within the climate science community.
However, as I have written previously; e.g. see
The Terms “Global Warming” And “Climate Change” – What Do They Mean?
Pielke Sr., R.A., 2003: Heat storage within the Earth system. Bull. Amer. Meteor. Soc., 84, 331-335
and as presented elsewhere; e.g. see
An Important Weblog Post On “The Air Vent”
Misconception #2: The global average annual temperature average is an appropriate metric to diagnose global warming.
Global warming, of course, is just a subset of climate variability and long-term change [see], which I will discuss further in a later post.
A change in heat (e.g. global warming) is defined in Joules [not degrees Celsius by itself) and can be written for the climate system as
ΔH = MA * [CA * ΔT + L Δq] for the atmosphere + MO* [CO* ΔT ] for the ocean + ML* [C L* ΔT + heat from phase changes of soil water] for land + MI* [CI * ΔT + heat from phase changes of ice] for continental glaciers and sea ice
where H is heat in Joules, M, C and ΔT represents the mass, the heat capacity and the temperature change for the respective components of the climate system, respectively. L is the latent heat of vaporization and q is the specific humidity.
As clearly overviewed in the excellent post on the Air Vent
Global Temperatures and Incomplete Rationale of My Own Skepticism
where a figure from that weblog is reproduced below
the ocean is a much larger reservoir of heat changes. A similar plot for land, and the continental glacier and sea ice would show a similar very large disparity between the oceans and the other reservoirs.
Where does the global annual average surface temperature trend fit into this framework? I present four reasons below that document why this temperature fails to accurately diagnose global warming. Other reasons are discussed in several of our research papers; e. g. see
Pielke Sr., R.A., C. Davey, D. Niyogi, S. Fall, J. Steinweg-Woods, K. Hubbard, X. Lin, M. Cai, Y.-K. Lim, H. Li, J. Nielsen-Gammon, K. Gallo, R. Hale, R. Mahmood, S. Foster, R.T. McNider, and P. Blanken, 2007: Unresolved issues with the assessment of multi-decadal global land surface temperature trends. J. Geophys. Res., 112, D24S08, doi:10.1029/2006JD008229.
First, as seen in the above figure from the Air Vent the absolute value [MA * [CA * ΔT + L Δq] for the atmosphere] << absolute value [MO* [CO* ΔT ] for the ocean]
Thus we can define that
Global Warming is an increase in the heat (in Joules) contained within the climate system. The majority of this accumulation of heat occurs in the upper 700m of the oceans.
Global Cooling is a decrease in the heat (in Joules) contained within the climate system. The majority of this accumulation of heat occurs in the upper 700m of the oceans.
Even over the ocean, the surface air temperature (marine air) is only a small part of this heat accumulation, and then only if it is well correlated with temperatures over at least a few meters of depth.
Second, over land, there is another issue, heat is not only contained in the temperature but also the moisture content of the air. The moist enthalpy [CA * ΔT + L Δq] is the appropriate measure of atmospheric heat content; e.g. see
Pielke Sr., R.A., C. Davey, and J. Morgan, 2004: Assessing “global warming” with surface heat content. Eos, 85, No. 21, 210-211.
Thus, in using the global annual average surface air temperature trend to diagnose global warming and co0ling, the contribution to heat changes of the air by concurrent water vapor changes [L Δq], an important fraction of the heating/cooling is missed.
Third, there is issue of the height at the air temperature measured? As we have shown in
Steeneveld, G.J., A.A.M. Holtslag, R.T. McNider, and R.A Pielke Sr, 2011: Screen level temperature increase due to higher atmospheric carbon dioxide in calm and windy nights revisited. J. Geophys. Res., 116, D02122, doi:10.1029/2010JD014612.
Lin, X., R.A. Pielke Sr., K.G. Hubbard, K.C. Crawford, M. A. Shafer, and T. Matsui, 2007: An examination of 1997-2007 surface layer temperature trends at two heights in Oklahoma. Geophys. Res. Letts., 34, L24705, doi:10.1029/2007GL031652. [see correction also]
air temperature trends are a function of height above the surface.
Fourth is the complex spatial and temporal heterogeneity of surface air temperatures. The assumption that a single trend value can characterize the heating and cooling of the climate system is based on an oversimplistic assumption based on an object with a uniform mass and temperature change (such as a metal sphere of a few centimeters in size). I discuss this issue in my post
The Computation Of A Global Average Surface Temperature Anomaly
Below are the latest anomaly plots (for February 2011) from http://earthobservatory.nasa.gov/GlobalMaps/view.php?d1=MOD_LSTAD_M&d2=AMSRE_SSTAn_M#
Not being someone of a scientifically sound mind and body, but someone who likes colors (especially blue and red), it seems to me that, in general, water anomalies are higher near land anomalies that are lower and visa versa. Can someone give a reason for this or is it just a coincidence of the maps.
It may not be the correct measure, but it has changed by a whole 0.01C. That’s gotta be significant, surely!
/sarc off
Thanks Dr. Pielke!
The “thing” itself remains unmeasured, its cause unknown, but some would squelch civilization to stop the “thing”. The “thing” is man-made global warming, a fire-breathing dragon in the sky!
Every shred of evidence points to global warming and cooling to be natural, cyclical trends.
CO2 has nothing to do with it, see http://www.oarval.org/ThermoAtmos.htm
When showing the land and sea anomalies, the maps should have the same color scale [they don’t].
Thank you for your feedback.
Leif – Good point and I agree. However, that is how NASA presents them. I have contacted them to see if they can present using the same scales.
Tom in Florida – The land did show quite a few areas that were cooler than average in Feb 2011.
Dr Pielke:
You say;
“Clearly, to use a single value (the global average annual average surface temperature trend) to characterize global warming is a naive approach and is misleading policymakers on the actual complexity of the climate system.”
I strongly agree with you that to use a single value” of anything “is a naive approach and is misleading policymakers on the actual complexity of the climate system”.
However, I disagree with much of your views because I dispute that the concept of Mean Global Temperature (MGT) is valid.
(If you want explanation of this then see my submission to the UK Parliamentary Inquiry into ‘climategate’: it explains how a paper of which I was lead author was prevented publication by frequent changes to the MGT data sets. That paper assessed MGT according to two different understandings; viz.
(i) MGT is a physical parameter that – at least in principle – can be measured;
or
(ii) MGT is a ‘statistic’; i.e. an indicator derived from physical measurements.
And it concludes that none of the MGT data sets is valid according to either of these understandings).
But I write to thank you for the above brief and clear post. It is elegant. Thankyou.
Richard
Joules seem correct. Is there any such accounting that would indicate trends over the past decades? In other words, is it possible to compute heat content of the oceans, land mass, and atmosphere based on the existing temperature record and other proxies? If so, has anyone done a credible job in that respect?
Leif,
There is no intrinsic reason that the temperature scales need to be the same for the land and the oceans. Using the same scales would certainly be one way to do it.
OTOH, the graph posted above (which incidentally should be titled “Heat Capacity Atmosphere vs Ocean” ) shows that the heat capacities are vastly different. If a 5C change in ocean temps is similar to a change of 12 C for land in terms of energy change, then using the two scales would be a better comparison of energy.
It is nice to see the enthalpy of humid air mentioned. Anyone that ‘averages’ temperatures between the extremely dry polar tropospheric air and the very humid equatorial tropospheric air is displaying abject ignorance.
Please tell me what will happen to this calculation if I succeed in transforming Earth’s vast tropical-to-temperate deserts into highly productive green land. This would involve a huge increase in water vapor over those areas.
Over the past month or so, David M. Hoffer and I have been exchanging emails and kicking around how something like trends of the heat content of the Earth System could be calculated (or at least estimated).
How about this? The satelite record measures W/m^2 emissions of Oxygen, I believe, for cloud-free areas of both ocean and land surfaces, or at least of the lower Atmosphere adjacent to these good storage masses for heat energy. Is there a way to use these W/m^2 values as a proxy for the underlying ocean or land mass heat content, or to use them to calculate the same?
Conversely, the temperature record over the past century from land and shipboard thermometers could be converted from Kelvins to W/m^2 (using Stefan Boltzmann) and those data, from each equal area patch of ocean and land surface, could be averaged to provide what may be an estimate of the heat content, and trends of change in heat content, for the whole Earth System.
David pointed out to me that, based on Stefan Boltzmann, W/m^2 varies to the fourth power of temperature in Kelvins. Therefore, it is mathematically wrong to average temperature anomalies for equal area patches in the Polar and Tropical regions with those in the Temperate region, because a given temperature difference represents a different change in W/m^2 depending upon the base temparature in Kelvins.
If what I suggest was done, how might it correlate (or not) with the GISS, Hadcrut and UAH global mean temperature plots?
Lief Svalgaard says:
“When showing the land and sea anomalies, the maps should have the same color scale [they don’t].”
How about proportional to C? If +/- 5 for SST then about four to one or +/- 20 for air.
By the way, Dr Svalgaard, when I found your website at: http://www.leif.org/research/ I bacame a frequent visitor. Thank you.
Tim Folkerts says:
April 14, 2011 at 10:38 am
There is no intrinsic reason that the temperature scales need to be the same for the land and the oceans.
OTOH, the graph posted above (which incidentally should be titled “Heat Capacity Atmosphere vs Ocean” )
They are presumably for public consumption and that very precise name [and still not correct as the heat capacity is measured in J/kg K and not in degrees] may not be generally understood. But, I agree this is a bit thorny.
Richard – Thank you for your comments. I also conclude that the concept of a of Mean Global Temperature (MGT) is flawed. I emphasize that in the two posts
Climate Science Myths And Misconceptions – Post #2 On The Metric Of Global Warming. http://pielkeclimatesci.wordpress.com/2011/04/14/climate-science-myths-and-misconceptions-%e2%80%93-post-2-on-the-metric-of-global-warming/
Climate Science Myths And Misconceptions – Post #1 On The Global Annual Average Surface Temperature Trend
http://pielkeclimatesci.wordpress.com/2011/04/11/climate-science-myths-and-misconceptions-post-1-on-the-global-annual-average-surface-temperature-trend/
Ira – Excellent question. Heat content change estimates are available for the oceans with the data since about 2004 being quite robust, particularly for the upper ocean; e.g. see
Preliminary Upper Ocean Heat Data Analysis By Josh Willis – “An Unpublished Update”
http://pielkeclimatesci.wordpress.com/2011/02/07/where-is-the-missing-argo-upper-ocean-heat-data/
Update Of Preliminary Upper Ocean Heat Data Analysis By Josh Willis – “An Unpublished Update”
http://pielkeclimatesci.wordpress.com/2011/02/13/update-of-preliminary-upper-ocean-heat-data-analysis-by-josh-willis-%e2%80%93-%e2%80%9can-unpublished-update%e2%80%9d/
Lief, not to be TOO nit-picky, but for typical use of the terms:
* “heat capacity” is indeed measured in J/K as listed on the vertical axis
* “specific heat capacity” (or often just “specific heat”) is measured in J/kg*K
You are right that there is always a tough balance between being correct and being simple. Sometimes, trying to be too precise leads to people getting lost in the details. OTOH, often people oversimplify and then end up creating even bigger misunderstandings.
For example, for some purposes, a single “average global temperature” is all that some people will care to know. For other purposes, this is indeed too simple to describe a complex system that changes in time and in location.
There is a saying attributed to Einstein that fits perfectly:
— “Everything should be made as simple as possible, but no simpler.”
Any school children that studied what means the word Science could say that it is impossible to measure world temperature with necessary precision for 0.x degrees.
For over-educated people that has the arrogance and vanity of think that everything can be explained and everything have a meaning of course there are no impossible things.
They after all have to justify to their selfs the investment they have made.
And it ended with over-education for Witchcraft.
Dr. Pielke, thank you for all that you do to make sense of global warming. You are very good at laying out the references and cites plus keeping major points simple. I have often wondered why Climatologists did not use Heat and Material balances to measure climate changes. With the ocean surface (700 m) temperatures dropping, the Troposphere temperatures dropping and as evidenced by new 100+ year cold records being broken the last two winters the land temperatures are dropping, it seems obvious that the earth has lost heat.
If the moderator will oblige me, I have a question about Figure 1 in your 2003 Forum paper you cited in your essay above. In Figure 1, you left water out of your list of High Mean Radiative Forcings of the climate system. I believe that water produced from no or slow to recharge aquifers i.e. fossil water, should be included in the earth’s heat balance. My calculations show that in the six decades since 1950, the heat added to the earth from produced fossil water has been 1.85 e22 J per decade. While not necessarily humongous, it is 8% of the heat added from decadal radiative forcing you show in your Forum paper.
When first produced, the fossil water is not in equilibrium with the earth’s surface water, since it may have been deposited in the aquifers up to many millions of years before. Plus the fact that it is no or slow to recharge is evidence that the pathways to the earth surface have closed off or have become very tortuous. The potential energy in the produced water is changed into kinetic energy at constant temperature by the latent heats involved in evapotranspiration. The water vapor rised in the Troposphere and is converted back into potential energy by giving up specific heat when it re-condenses as rainfall. The condensed water will results in the ocean levels rising by 2.6 mm per year. The specific heat heats the Troposphere at an elevation that depends on the saturated adiabatic lapse rate. My calculations are based on a fossil water production of 900 cubic kilometers per year in 2000. About 92% of the produced fossil water eventually winds up in the oceans.
Although a smaller amount (7% of the fossil water), I also believe that the water chemically produced when oxygen is combined with hydrogen in a fossil fuel combustion process, should be added to the earth’s heat balance.
Unlike carbon dioxide, fossil water and fossil fuel water, will not accumulate in the atmosphere, so will be effective only as long as production continues.
Dear Dr. Pielke: Given, that an increase or decrease in the amount of heat in the climate system is a better way to determine global warming or cooling, what are your thoughts on the discrepancies between March 2011 GISTemp, 0.57C global temperature anomaly and -0.26C for RSS and -.1C for UAH. The fact is, that when AGW proponents make their case to the public, legislators, and regulators, GISTemp is the figure they point to.
I just stumbled on this:
Was that really that cool for Feb (summer) in Australia? And does that have anything to do w/the heavy rains there this past summer?
Of course, there could in principle, be global warming without any accumulation of energy in the climate system. The energy can be redistributed in space and time. For example, some change might result in accumulation during the day, leading to higher daytime temperatures, and higher radiation or other dissipation during the night. Energy coming into the system might flow differently and be in different places at different times while on its way out (at the same rate).
The climate system obviously does have massive spacial and temporal non-uniformities. Could these not shift to produce higher near surface temperatures without energy accumulation?
Of course, this is not what the warmists are claiming or what is being modeled. But if we’re after a better definition of “global warming” shouldn’t we be careful before simply equating this with energy accumulation in the climate system?
Interesting seeing how many regions in the Earth Observatory maps have +ve SST anomalies next to -ve land anomalies and vice versa.
Peter George:
At April 14, 2011 at 3:01 pm you suggest:
“The climate system obviously does have massive spacial and temporal non-uniformities. Could these not shift to produce higher near surface temperatures without energy accumulation?”
Oh, YES!
All the energy emitted from the planet is radiated from the top of the atmosphere and gets there from below. But the energy of the radiated IR is proportional to the fourth power of the temperature of each unit area of the radiating surface(s); i.e. the radiated energy is proportional to T^4.
The tropics are hot and receive much solar heating while the polar regions are relatively cold and obtain very little solar heating (indeed, polar regions obtain no solar heating in their winter months).
Also, the tropics are net absorbers of radiation while the polar regions are net emitters of radiation. And this is because heat is transferred from the ‘hot’ tropics (that get much solar heating) to the ‘cold’ polar regions (that get very little solar heating). But most of the emitted radiation is from the tropics.
Reduce the temperature of the tropics by e.g. one degree and the energy of the emitted radiation reduces. A similar area near the poles would need to warm by more than one degree if the total radiated energy from the Earth were to remain constant (because the radiated energy is proportional to T^4).
So,
(a) if the thermal input and output of the planet were constant
but
(b) the surface temperature of the tropics fell
then
(c) the average surface temperature of the planet would be higher
because
(d) the average surface temperature of cooler regions would rise by more than the fall of surface temperature of the tropics.
And energy is transferred from the tropics to the polar regions so it is reasonable to suppose that the average global surface temperature does vary by some amount as a result of this effect. Any variation of heat transfer from the tropics would induce the effect, and ocean currents are not completely constant.
I have tried to quantify the effect but it requires so many assumptions that a realistic value is not possible of estimation.
Richard
Ira and many physicist do not understand the use of the Stefan-Boltzman equation. By definition a blackbody has a surface. The equation can not be used for the absorption of radiant energy without some modifications and understand of the context of application ie other processes (eg convection and phase change ) which may occur at the same time. Further, by definition a blackbody absorbs and emits radiation over the full electrmagnetic spectra. Blackbodies do not exist and that includes the sun although some objects (with a surface) may come close. My post here http://jennifermarohasy.com/blog/2011/02/a-note-on-the-stefan-boltzman-equation/ maybe useful to get some better understanding.
There is a temperature that is not (to my knowledge at least) being measured:
Rock.
Only 50 feet into any rock formation you will find a near-constant temperature. It varies according to latitude. It is the base temperature of the crust near the surface.
That it remains so stable in temperature summer vs winter I find remarkable.
Does this light any bulbs out there?
“Fourth is the complex spatial and temporal heterogeneity of surface air temperatures.”
Tsk, tsk. Leif Svalgaard has made clear to all that this is “spatiotemporal cult” “mumbo-jumbo”. Thanks for the laugh Leif!
[ See here: http://wattsupwiththat.com/2011/04/10/solar-terrestrial-lunisolar-components-of-rate-of-change-of-length-of-day/ .]
Paul Vaughan says:
April 14, 2011 at 8:35 pm
“Fourth is the complex spatial and temporal heterogeneity of surface air temperatures.”
Tsk, tsk. Leif Svalgaard has made clear to all that this is “spatiotemporal cult” “mumbo-jumbo”. Thanks for the laugh Leif!
Indeed it is when you could simply say that the temperature varies with location and time. There is one little difference: a cult member would have said ‘spatiotemporal’ instead of ‘spatial and temporal’.
“All the energy emitted from the planet is radiated from the top of the atmosphere and gets there from below. But the energy of the radiated IR is proportional to the fourth power of the temperature of each unit area of the radiating surface(s); i.e. the radiated energy is proportional to T^4.”
Doesn’t the average energy the earth receives from the sun equal the energy radiated from the TOA or the earth would not be in equilibrium? In other words, temperature ^ 4 is proportional to the energy received from the sun.
ferd berple:
At April 14, 2011 at 10:51 pm you quote from my post at April 14, 2011 at 4:43 pm where I wrote:
“All the energy emitted from the planet is radiated from the top of the atmosphere and gets there from below. But the energy of the radiated IR is proportional to the fourth power of the temperature of each unit area of the radiating surface(s); i.e. the radiated energy is proportional to T^4.”
Then you ask and say;
“Doesn’t the average energy the earth receives from the sun equal the energy radiated from the TOA or the earth would not be in equilibrium? In other words, temperature ^ 4 is proportional to the energy received from the sun.”
The answer to your question is, yes.
And the response to your statement is, no.
My post tried to explain this, but I will illustrate it with an analogy that I hope will make the matter clear.
1.
Consider a laboratory experiment that establishes two surfaces each of unit area
where
2.
one of the surfaces is heated by a radiant input and the other is not heated
but
3.
there is a connection that permits heat to flow from the heated surface to the unheated one
so
4.
both surfaces lose heat by radiation
and
5.
the described system is in thermal equilibrium such that the radiated heat into the surface(s) equals the radiated heat out of the surfaces.
The described apparatus is a crude analogy to a unit area of the tropics (heated by the Sun) and a unit area of a polar region (that gets almost no solar heating) with the thermal connection between them being ocean currents.
Now let the temperatures of the two surfaces be
40 deg. C (i.e. 313 K = Th)
and
10 deg. C (i.e. 283 K = Tc).
The average temperature of the two surfaces of equal area is 25 deg. C.
The total radiated energy (e) is a constant and is proportional to the fourth power of the surface temperature(s). Therefore, the radiation from the surfaces is in the ratio
Th^4 : Tc^4 = 313^4 : 283^4
Now, drop the value of Th by one degree, so Th1 = 312 K
but the total radiated energy (e) remains constant, so
Th^4 : Tc^4 = 313^4 / 283^4 = Th1^4 : Tc1^4 = 312^4 / Tc1^4
i.e.
Tc1^4 = 312^4 / (313^4 / 283^4) = 8567625486
So, Tc = 304.2 K which rounds to 304 K
Thus, a fall of one degree in the temperature of the ‘hot’ surface causes the temperature of the ‘cold’ surface to rise by (304 – 283) = 21 K
So the average temperature of the two surfaces increases from 25 deg. C to over 35 deg.C.
The change in average temperature is because an effect of a fourth power is to amplify small changes.
Richard
ferd berple at 10.51PM, the earth is never in equilibrium. The oceans have a huge heat capacity. 0.1K change has has a very large effect on temperature of the lower atmosphere- look at the graph in the post. Further, having an average temperature over all the surface for one year makes provides no information about climate or weather in any part of the world. I am sure Dr Pielke has put that in refereed articles.
“Does this light any bulbs out there?”
Also interesting is the fact that the direction of the temperature gradient in the rock/soil deeper than that point of constant temperature (no influence of diurnal and seasonal changes) is inwards. That means the direction of the net heat flux is outwards.
So, the net heat flux in the deeper ground is outwards. The earth is transfering heat from the depth to the surface.
I think this “geothermal” heat flux is actually a net (total) flux at the respective depth. You can not calculate it and compare it to solar heat flux and say it’s neglibile compared to the solar flux. The solar flux is already in the equation.
ferd berple says:
April 14, 2011 at 10:51 pm
Doesn’t the average energy the earth receives from the sun equal the energy radiated from the TOA or the earth would not be in equilibrium? In other words, temperature ^ 4 is proportional to the energy received from the sun.
Yes, on average. But not at every instant, e.g. the temperature doesn’t instantly fall to zero at night.
Dr Pielke:
One small suggestion; Great post. I enjoy all of your series posts. My only helpful advice would be to include more quotes in your running text whenever you site outside source material, such as journal publications.
Thanks and keep up the great work.
Gary
Chuck L. – Your question is an excellent one. Our interpretation (which we have published on) is that their is a systematic warm bias in the land surface portion of the surface temperature trend data; e.g. see
Klotzbach, P.J., R.A. Pielke Sr., R.A. Pielke Jr., J.R. Christy, and R.T. McNider, 2009: An alternative explanation for differential temperature trends at the surface and in the lower troposphere. J. Geophys. Res., 114, D21102, doi:10.1029/2009JD011841. http://pielkeclimatesci.wordpress.com/files/2009/11/r-345.pdf
Klotzbach, P.J., R.A. Pielke Sr., R.A. Pielke Jr., J.R. Christy, and R.T. McNider, 2010: Correction to: “An alternative explanation for differential temperature trends at the surface and in the lower troposphere. J. Geophys. Res., 114, D21102, doi:10.1029/2009JD011841”, J. Geophys. Res., 115, D1, doi:10.1029/2009JD013655.
http://pielkeclimatesci.wordpress.com/files/2010/03/r-345a.pdf
Christy, J.R., B. Herman, R. Pielke, Sr., P. Klotzbach, R.T. McNider, J.J. Hnilo, R.W. Spencer, T. Chase and D. Douglass, 2010: What do observational datasets say about modeled tropospheric temperature trends since 1979? Remote Sensing, 2(9), 2148-2169.
http://pielkeclimatesci.files.wordpress.com/2010/09/r-358.pdf
Richard S Courtney says:
“Thus, a fall of one degree in the temperature of the ‘hot’ surface causes the temperature of the ‘cold’ surface to rise by (304 – 283) = 21 K”
Not even close! The TOTAL stays the same, not some ratio.
If the hot surface cooled from 40C to 39C, the cool surface would warm from 10C to 11.33 C. The average temperature will indeed rise, but only to 25.17C
Thus, a fall of one degree in the temperature of the ‘hot’ surface causes the temperature of the ‘cold’ surface to rise by 1.3 C
The average rises by ~ 0.17 K
Even if both were the same temp, both would be ~ 26.15 C, an average rise of only ~ 1.15 C.
There IS a change in the average when radiation is held constant.
The change IS due to the T^4 nature of the radiation.
The difference IS significant.
But it is nowhere near 10 K!
Tim Folkerts:
With respect, your comment at April 15, 2011 at 10:39 am is mistaken.
You state the source of the error when you say;
“There IS a change in the average when radiation is held constant.”
But the radiation is NOT held constant. The total energy flux of the radiation is held constant.
Your failure to understand this point is explicitly stated by you when you wrote:
“Even if both were the same temp, both would be ~ 26.15 C, an average rise of only ~ 1.15 C.”
But the illustration specifically stipulated that the two surfaces were at very different temperatures and then the temperature of the hotter one was reduced slightly. It is hard to equate that stipulation with “Even if both were the same temp”.
Anyway, this is an ‘angels on a pin’ argument.
1.
I said the average temperature would rise if the hotter temperature were reduced and I tried to explain why by using what I stated is an unrealistic simplification.
2.
You agree that the average temperature of that simplification would rise but not by the amount of my estimation.
3.
So what? If you are right and I am wrong then you have agreed my point: viz. the average temperature would rise.
Indeed, the temperatures of my simplistic illustration were 40 deg.C and 10 deg.C but the real world has a larger range of temperatures, and I only changed the hotter temperature by one deg.C, but temperature usually varies by more than that over 24 hours at every real location. And your figure for the change to the average is ~0.2 deg.C so your calculation would support my case if it were right.
Richard
“
Ira says:
April 14, 2011 at 11:33 am
‘The satelite record measures W/m^2 emissions of Oxygen, I believe, for cloud-free areas of both ocean and land surfaces, or at least of the lower Atmosphere adjacent to these good storage masses for heat energy. Is there a way to use these W/m^2 values as a proxy for the underlying ocean or land mass heat content, or to use them to calculate the same? ”
Not really. The radiative intensity of any gas in the atmopshere depends not only upon the the heat content of the underlying ocean/land, but upon the local atmospheric pressure, temperature, and moisture, i.e., its enthalpy. Although the units are the same, it is not an energy-conserving measure of thermal flux from the surface.
Leif Svalgaard wrote,
“[…] ‘spatiotemporal’ instead of ‘spatial and temporal’.”
‘Spatial’ & ‘temporal’ are adjectives describing marginal distributions, whereas ‘spatiotemporal’ is an adjective describing a joint distribution — conceptually different things and the distinction is NOT trivial.