you can produce a map that looks different by using another baseline. If it was 1985 you could show the world was getting colder by comparing 1890-1950 to 1972-1985.

and you can change the maps you see in the pics by using yet another baseline and then asking what happens each season.

be straighforward. lets compare one 60 year period to another, one 60 years of low co2 to one of high and growing co2

try 1890-1950 and compare to 1950 to 2006.

the results are here

http://www.flickr.com/photos/23668657@N07/

not only is there no “Global” warming within error, there isnt even any summer artic warming. “Warming” is in the artic in the winter a a little in the spring, and certainly a bit above 45 degrees latitude. It appears that global warming is really people using their furnaces to keep warm, and the number of people is growing.

And its very hard to understand radiative forcings and global temperature change models when they use a global temp and not the actual seasonally recorded spatially accurate temp.

C02 is not the same all over the earth either. it varies a lot. it varies a real lot by season and by hemispher.

how do you make a climate model with 2 “global” averaged “variables”?

you cant.

Perhaps i should add “never mind!” to the top of my post.

Heh! I’ve written posts like that.

but with respect to this:

how can one say with any certainty one way or the other whether the difference between the integral of emission one gets using the actual temperatures across the globe vs the integral one gets get using the global average temperature is significant (at least to better than +- 15%)

No one is trying to say the error is 15%. That’s not the purpose of this sort of analysis.
If you ask the issue is: Have we determined the precise magnitude of the effect from this analysis?
I think the answer is,

My final conclusion from all this is that I don’t think one can settle this particular issue based on simple approximations.

Well, then you, Dr. Pielke and I are likely in violent agreement. The purpose of this sort of analysis is not to put something to rest. It’s the opposite.

Just so it is clear: My comment about the 12.5% error above was not the difference I found between the surface integral of emission performed with the two methods (using varying temperatures across the surface and using the global mean temp).

I actually found that the two integrals came out within about 4% of one another. That does not change.

But my conclusion that they actually are that close was faulty, since the two sigma error associated with the surface integral of emission for the temperature function I was using is at least 12.5% (probably greater, since my sinusoidal graph does not match up perfectly). So, the 4% difference I got might be wrong. But then again, it might not be. I can’t say for sure.

That simply cannot be answered with the analysis i used. All I can say is that if there is that the difference is probably within 20% or so (presuming my temperature vs latitude graph is accurate!) which is not particularly useful if one is trying to determine whether two quantities (in this case surface integrals) do not differ significantly (are within 10% of one another, say).

Again, so much for the simple analysis.

Perhaps i should add “never mind!” to the top of my post.

Perhaps, but the real issue is “how much”?

If the uncertainty associated with a crude calculation (one like I did) is of the order of 15% or so (which I now believe mine is), then how can one say with any certainty one way or the other whether the difference between the integral of emission one gets using the actual temperatures across the globe vs the integral one gets get using the global average temperature is significant (at least to better than +- 15%)?

“b) Roger Sr.’s simple algebraic estimate was more or less correct. (It is. He was comparing poles heat to equator heats, so his numbers are twice ours”

I don’t debate that the difference in radiative emission from the pole to the equator is quite significant (I made that clear in my post). But, unless I completely off base here, the real issue is the integral across the globe.

Finally, when I said above that “what puzzles me most about all this is this: I find it very hard to believe that someone has not actually done this analysis with the actual temperature data across the globe, since the GCM’s use such data to do their radiative emission calculations.”, what I really meant is this:

It could be true, but i find it very unlikely, quite frankly, considering that someone could probably do the necessary comparison in a matter of seconds (since the GCMs apparently already do this kind of stuff and the global energy imbalance is based on detauiled temperature information across the globe)

For all i know, some scientist HAS (I would guess probably has) done this and if they have, it is very possible that they have already put the issue to rest — ie, concluded that it does not make a significant difference, at least not when it comes to making assessments about whether we should keep the change in global mean temp under 2K or some such value.

My final conclusion from all this is that I don’t think one can settle this particular issue based on simple approximations.

Finally, the thing that puzzles me most about all this is this: I find it very hard to believe that someone has not actually done this analysis with the actual temperature data across the globe, since the GCM’s use such data to do their radiative emission calculations.

I’m sort of surprised it isn’t previously quantified because it’s the sort of thing one wants to know when using the IPCC equation to estimate the magnitude of other things. Also, the equations I derived are a 1 page homework problem!

While it’s true that sometimes even those who know this effect might overlook errors of this magnitude in certain cases, it’s still useful to know they exists. I’m also a bit surprised by the venom in comments at ‘another blog’ at the whole idea this effect might even exist.

This uncertainty is similar in magnitude to others that exist. It’s an uncertainty. We should be aware of it.

Why does this unsettle some quite so much?

I think, in contrast, your error came about due to taking short cuts with notation, forgetting which variables were already averaged and which were not. But to be honest, I had a bit of difficulty reading what you intended because you didn’t break down and insert real integrals etc. (Plus, your format won’t let me spread out the page. I wear bi-focals, and when I blow up the text, I see very less on the screen than you likely to.)

I totally agree that my temperature bands are cruder that yours! I used those because it’s the easiest way to do a back of the envelope calculation that way. Exact instantaneous data over the entire surface of the earth, are required to do this absolutely. I don’t plan to do that.

My really crude bands were chosen for an order of magnitude estimate; order of magnitude estimates are always necessarily crude. So, yes, my answer is different from yours. But in either case, this is large enough people should be aware of it.

FWIW: At the time I wrote this, my main goal was to show that
a) The terms do matter (as Roger Sr. says.

b) Roger Sr.’s simple algebraic estimate was more or less correct. (It is. He was comparing poles heat to equator heats, so his numbers are twice ours and

c)and to illustrate what went wrong in Eli’s series analysis. As you can see, Eli made an undergraduate level conceptual error. (It was particularly amazing in light of the fact that he went on to cast aspersions on Dr. Pielke Sr., Dr. Pielke Jr, making various snide remarks.)

I’m glad to see you are finding my mathematical terms are matching. I’m always worried I may have made mistakes (and make them often). So it’s nice to see you are getting the same result.

let me clarify: that’s the error in the integral of radiative emission across the surface associated with the particular 2-sigma error for “temperature as a function of latitude” that i used to estimate that surface integral.

I also assumed emissivity was the same across the surface (I ignored it in the anlysis). That is NOT what i am referring to above.

My primary mistake (as i see it, at least) was in not taking into account the error associated with the temperature as a function of latitude that i used to estimate the surface integral of radiative emission from.

The error is of order +- 12.5% (perhaps larger if one takes into account variation of temperature with latitude).

I now believe that a simple model really can’t decide the answer to this issue to better than 15% or so, which is the order of the difference you seem to be indicating above.

Your simplified estimate suffers from the same problems as mine: associated with not doing the full surface integral with actual temperatures. In fact, your estimates of temperature based on a few “bands” seems to be even cruder than the one I used.

Finally, the thing that puzzles me most about all this is this: I find it very hard to believe that someone has not actually done this analysis with the actual temperature data across the globe, since the GCM’s use such data to do their radiative emission calculations.

The terms extra terms in equation (1) here turn out to work amazingly well. (I’m doing this with emissivity of 1 for the earth’s surface, as emissivity if dirt/trees/ ice is not the issue in this particular dispute.)

I’ll be explaining which of your errors I think was most important. However, I need to proofread my equations, as I like to be able to read them myself.

To settle the question, one needs to do the integral with actual temperatures from across the globe

Thanks for the math lesson, by the way!

I’ll admit I still make those myself from time to time. So far, I’ve caught my mistakes before my readers do, but that’s because my blog is boring and no one reads it!

“UPDATE 2/6/08: As pointed out in the comments Eli screwed this up

[T^4 - (T+T')^4] = T^4-T^4*(1 + 4 T’/T) = T^4* 4 T’/T = 4T’*T^3

good thing no one reads this blog. The change in emission depends on T^3
for a constant change T’. OTOH for the 250-350 K interval this is also
pretty well approximated by a linear function in T.”

In fact there are three errors in the above!
1. First = should be ~, approx =
2. After the second and third = there should be a minus sign (I’ll be generous and count these two errors as just one)
3. T^3 cannot be well approximated by a linear function in T, because the slope changes by almost a factor of 2 over that interval, as anyone who has done any calculus should know.

Why does anyone take this innumerate blogger seriously?

If it wasn’t so obvious and sad, it would almost be funny.