I agree with most of what you said about heat accumulation and CO2. Over land, you are absolutely right about the effect of CO2, since the heat capacity of the land is quite small, and solar heating is mainly lost to radiative cooling in short order.

However over ocean, I think the situation is a little more complicated. It is true that the surface ocean temperature lags the solar seasons by about 80 days, at least outside the tropics. This does not mean that some of the heat from sunlight could not be lost to deeper layers. If the first several hundred meters of ocean have (on average) increased in temperature over the past 100 years, then this would represent a significant net accumulation of heat in the ocean. Perhaps measured increases in temperatures over a range of depths would help clarify how much heat has in fact been absorbed (though I do not know if these measurements exist). The temperature lapse rate for the ocean (often a 10C drop over the first 100 meters when the ocean has a relatively warm surface) suggests that slow heat loss to deeper water is likely, but I have no idea how it could be modeled accurately.

So probably the majority of radiative forcing from CO2 (and other greenhouse gases) is short term, but some undefined fraction is absorbed by the ocean, and so represents a lag in the global temperature response. The existing average ocean and land temperature data seem to support this; there has been significantly more increase in average temperature on land than in ocean surface water. This would be easy to add to your model by splitting the two portions, an immediate fraction (for example, 70% of the non-lagged CO2 concentration) and a long term trailing average portion (for example 30% of the lagged CO2 concentration).

Unfortunately, since the fit to the data is almost equally good for either immediate or trailing average CO2 concentrations, I don’t think it would be possible to tell from the model what the correct split would be.

I will think about this some more.

cheers.

I thought some more about the ocean lag and the lag/trailing average of CO2 impact and I think it is important that we think about how this could work in physics terms which would help with deciding which CO2 etc variables to use.

First, the greenhouse effect of CO2 operates at the speed of light. It is photons of light in the EM spectrum that we are talking about here. It is photons of light which are providing the energy here.

A photon comes in from the Sun, hits a rock on the beach in the morning and warms it up. Overnight, that rock cools off and gives back that photon in the IR spectrum upwards toward the atmosphere.

Half the time, that photon travels right through the atmosphere and goes right out into space. But now, there is slightly more CO2/GHGs in the atmosphere and that photon gets captured by one of the extra CO2 molecules.

An electron in the CO2 molecule moves to a higher energy state and in a picosecond, decides it is more comfortable at the lower energy state, and gives it back up in all directions.

That photon now skips around the atmosphere from Nitrogen molecule to Oxygen molecule back to a CO2 molecule and so on. The atmosphere is now slightly warmer – one photons worth that is. In a few days or less, that photon will be lost to space or be reflected back to the ground.

Here is where the warmer ocean comes in. That photon gets reflected by any one of the warmer atmosphere molecules toward the ocean surface.

The ocean is now just a fraction warmer than it was before, has a fraction more energy in its electrons than before, so it rejects the photon and reflects/gives back the photon to the atmosphere either right away or in a short time – where it happily skips around the atmosphere for a few more days or is reflected into space etc.

So, the now warmer ocean just allows more CO2 captured photons to stay in the atmosphere for some period of time whereas when they were cooler, the oceans would have captured some of those photons.

So, in effect, it is still the CO2 of today that we should be concerned with. It is just that a now warmer ocean (or a warmer land) is a variable in how much impact that CO2 will have.

CO2 of 30 years ago may have warmed the oceans but we are still operating at the speed of light here and it is today’s CO2 which provides the impact.

It may help to talk about some of the lags in the climate as well.

Land temperatures lag the equinox, the soltices by about 30 days. The hottest/coldest part of the year is 30 days after the summer/winter solstice.

The oceans lag the equinox/solstice by about 80 days. The oceans are at their warmest 80 days after the solstice (hurricane season peaks on September 12th, polar ice melt peaks on September 12th, the actual sea surface temperatures peak on September 12th.)

Overnight, 30% to 50% of the heating from the day is lost. If the Sun stopped working for two or three days, what would the temperature in your backyard be.

So, there are some lags in how much energy/photons can be stored for periods of time, but these are not really long.

The deep ocean warming does take much longer, 500 to 1,000 years but that just means the oceans will continue going on absorbing energy/photons for a long time, not that the CO2 of 30 years ago is impacting today.

If we add all that up, we have to use today’s CO2 in the model, it is just that the impact from each individual molecule will slowly rise as the land and sea surface and deep oceans warms. But then, each individual CO2 molecule itself, has less and less logarithmic impact as its concentration rises.

That was long, but I thought it was important to run this little thought experiment for the “warming in the ocean pipeline” explanation as well.

Don’t be so hard on yourself! If true, AGW will cause migraines! Barometric pressure changes are a common trigger: more storms and stronger storms means more barometric flux therefor more migraines. No fooling.

From Pamela Gray (20:11:26) :
Could it be that the equatorial chimney cooling theory has a cyclic pattern related to things like cosmic ray/ozone fluctuations?
-end quote

Don’t know how related this is to eq. chimneys ,but… From
http://www.ghgonline.org/otherstropozone.htm

Tropospheric ozone can act both as a direct greenhouse gas and as an indirect controller of greenhouse gas lifetimes. As a direct greenhouse gas, it is thought to have caused around one third of all the direct greenhouse gas induced warming seen since the industrial revolution.
[...]
The largest net source of tropospheric ozone is influx from the stratosphere.
-end quote

Would not lower solar output lead to less UV so less ozone formation? A direct solar driver of GHG. Could that get ‘levered up’ in some way?

After I wrote my last comment, I realized that it would be better to use the trailing average of the natural log of the CO2 concentration instead of the trailing average of the CO2 concentration itself. The trailing average of the log of the CO2 concentration is a more theoretically defensible parameter (Beer’s Law and all) than the trailing average of the CO2 concentration, when the objective is to combine past and present contributions to a long term oceanic temperature rise.

However, it looks like this makes very little difference; the model results (at least with the version of your model that I have) are pretty much the same, whether using trailing average of CO2 or trailing average of Ln(CO2). I would much appreciate if you could post a link to the current version of your model (Excel I assume), including the added southern ocean oscillation, since this seems to be a more accurate model than what I downloaded.

I hope you will forgive me Bill, but my comment on trailing averages of CO2 was in part a ruse to get your attention. The truth is that I believe other factors (like the solar cycle and the long term trend in solar cycles) are very important, and that if were it possible to identify and quantify other significant contributors to global temperature change, then CO2 and other greenhouse gases would become much less important in explaining the temperature trends of the last 125 years. “To the man who has only a hammer, most every problem resembles a nail.” When we attribute global warming to greenhouse gases alone, we limit ourselves to only one tool.

It seems to me preposterous to ignore the large and well documented natural temperature changes of the last several thousand years (yes, the Vikings really did grow crops in Greenland), and equally preposterous to offer no plausible explanation for these climate changes. Yet this is exactly what the IPCC climate models all do. The temperature changes and rates of temperature change of the last three thousand years are comparable in size and rate to those of the last 125 years, yet nobody in the IPCC seems to take note of this. (Or worse, they do their best to discredit the historical record in order to minimize the size and rate of past climate changes, ex post facto, so that they can be safely ignored in the greenhouse gas models.)

The IPCC models would actually be quite humorous, were it not that the predicted catastrophic increases in global temperature, sea level, storms, droughts, floods, hurricanes, tornadoes, general calamity, pestilence, and migraine headaches (OK, maybe not headaches) might motivate the public to accept draconian cuts in fossil fuel usage and rapid shifts to more expensive non-fossil energy sources. These solutions to the “global warming problem” will have serious negative economic consequences in the short to medium term, especially for the poorest of people. The existing climate models can do real harm to real people, and I predict that history will judge them and their purveyors very harshly.

But enough of my sermonizing.

What I think we need (‘we’ being all the rest of humanity, plus you and me) is a truly reasonable climate model; not just a model for the last 125 years, but for the last 5,000 years. Since human influence is clearly small before the last 150 years, any reasonable climate model must include solar forcing and perhaps other factors which can explain documented historical climate changes. The solar activity proxies (historical sunspot numbers, C14, Be10) would seem a reasonable starting point in any such model.

We need a climate model that lets us step back enough to see the forest, not just the trees… and the CO2 they consume.

Cheers.

Good stuff there. I tried out your idea of lagging CO2 by 30 years and it works just as good as anything I have done.

I wouldn’t worry about an R^2 that drops by 0.01. The F-statistic drops by a bigger relative margin but it is still a very significant number.

I will have to think about whether it is really valid to lag CO2 by 30 years (assuming that the oceans are absorbing some of the increase from the atmosphere to cause a net lag effect of 30 years.) (I’m just going to focus on 30 years rather than 10 since its effects are the greatest in terms of the warming conclusion.)

There is data that shows annual CO2 changes are closely related to changes in temperatures (annual CO2 changes are very closely correlated with changes in temperatures – lagged 5 months. CO2 is still increasing but the rate in effected 5 months after temperature changes. )

This suggests there is a relationship which is more immediate than 30 years although this relationship is one-way which is opposite to the one-way effect suggested by the 30 year CO2 lag. [I have to put this chart in since it is so wierd. I saw a similar chart on icecap today so I had to try it out my data going back to 1958.]

http://img339.imageshack.us/img339/879/co2lagkz2.png

I guess the other thing is the models are not really built with a 30 year lag in CO2 built into the assumptions. As you can see in this chart made from the IPCC Third Report (which means they had to adjust the warming line to include actual temperatures up to 2000 – I’m not going to give them that break), the warming levels in the models had temperatures starting to rise at an exponential rate by 1970 or so. (it does flatten out to a close to a linear line at a certain point and then it will flatten out in the future – but there is a pattern with the slopes of the line in this logarithmic CO2 impact.)

http://www.globalwarmingart.com/wiki/Image:Global_Warming_Predictions_png

Whereas the warming model based on a 30 year CO2 lag doesn’t start rising in an exponential sense until about 1985 or 1990 (I have slightly different numbers than you based on my newest model).

http://img376.imageshack.us/img376/940/co2lag30qv3.png

So I have to conclude this is not how it is supposed to work.

But, it is something to watch for sure. Watch the temperature response from the next big El Nino. Like I said before, there will have to be an uptick in temps in the next five years or the modelers will have to go back to the drawing board.

Good work. Made me go whoa when I saw the lag numbers were just as good.

I downloaded your spreadsheet and have given some additional thought to your model.

An implicit assumption in the model is that CO2 is a reasonable proxy for all greenhouse gases; that they have risen more or less proportionally over the last century. While this may not be completely correct, it is probably not too far off, since the sources for these gases (industrial activities, agriculture, transportation, and electricity production) have all increased pretty much in parallel over the last century.

The global circulation based climate modelers usually say that there is substantial (and unavoidable) warming on the way, even if CO2 were to be held at today’s level, due to the long time required to warm the oceans. Lags of 20 to 30 years up to a thousand years are often claimed, and this long lag is used to at least partly explain why the global average temperature has not already increased much more than it would have based on the assumed level of net radiative forcing from increased greenhouse gases.

This seems like a reasonable argument, since a quick estimate of the rate of temperature change in 1000 meters of ocean (not even considering any heat entering the deep ocean!), with about 2 watts per square meter of radiative forcing due to increases in CO2, NO2, and methane since the pre-industrial era (as currently assumed by the IPCC) gives an increase of only about 0.011 degree per year in ocean temperature. And as everyone seems to agree, the oceans rule the climate.

If the climate modelers are correct about the ocean driven lag in temperature rise, then it should be possible to improve the performance of your model by substituting a trailing average CO2 for the monthly values, to account for uptake of heat by the oceans. Incorporating a lag in the CO2 data should (of course) also increase the CO2 constant in the optimized model, perhaps more in line with the IPCC’s projected warming.

When I incorporated a trailing average CO2 in place of the monthly CO2, I found the following:

1. A 12 month trailing average CO2 value yields a very slight improvement in the scatter plot best fit (R^2 of 0.7829 versus 0.7828, slope of 0.9615 versus 0.9613, and the same slope of -0.005). The CO2 model constant increases from 2.7298 to 2.7560.

2. A 24 month trailing average yields exactly the same scatter plot values for R^2, slope, and intercept as the non-averaged monthly CO2 data, and the CO2 model constant increases to 2.782.

3. A 5 year trailing average yields a scatter plot R^2 of 0.7821, slope of 0.9601, intercept of -0.0057, and a CO2 constant of 2.861.

4. A 10 year trailing average yields R^2 of 0.7805, slope of 0.9577, intercept of 0.006, and a CO2 constant of 2.994.

5. A 20 year trailing average yields R^2 of 0.7746, slope of 0.9532, intercept of -0.0067, and a CO2 constant of 3.264.

6. A 30 year trailing average yields R^2 of 0.7713, slope of 0.9518, intercept of -0.0069, and a CO2 constant of 3.564.

The longer the averaging period, the poorer the fit, and the higher the CO2 constant, as expected. The things I find surprising in the above are:

a) A great deal of future warming “already in the pipeline” does not seem to be supported by the historic temperature and CO2 data, since the best fit is with a short (12 month) trailing average CO2 value. Reaching a CO2 constant of 4.7 (as suggested by IPCC models) would require extremely long ocean temperature lags, perhaps 50 years or so.

b) The change in R^2 values for different lengths of trailing average for CO2 is quite modest, while the change in the CO2 constant for the model is quite large.

So I guess we can say the most likely CO2 constant is a low one, but a model based on long trailing average CO2 concentration lag yields a much higher CO2 constant, and is not a lot different in R^2. I am not sure if a change in scatter plot R^2 from 0.7829 (12 months) to 0.7713 (30 years) is statistically significant, but perhaps you can comment on this. (In other words, I am not sure if we can confidently discount the possibility of a long ocean lag time based on the modest decrease in R^2.)

I think it would be interesting to freeze the model parameters (as you posted at http://img408.imageshack.us/img408/5993/finalhadcrut3modelbt5.png) and see how the model does in predicting temperatures over the next 10 years. It seems likely your model will put to shame the many models the IPCC relies on.

Amen! And this regularly kills stock traders who invent new trend following systems, and takes down ‘quant’ funds and… Every so often a new ‘hot hand’ with a new model will win a streak in the stock market, then when they go down in flames everyone is surprised. It always turns out to be the same thing. They ‘back tested’ and all was well, then reality kicked in. Data modeling is not proof of truth.

That’s part of why I’m a skeptic. I’ve seen this movie before too many times.

Yup! And don’t forget the Ca+ ions and …

And on the ocean skin issue: Having lived on a boat for a few years the notion that the surface of the ocean is at all stable is very broken. Wind, waves, ripples, currents, cyclones, mists, rain, evaporation, fish jumping, algae blooms, fog, plankton swarms, sea birds, poop, … It mixes down to the first thermocline and bits mix up into the air at least a few dozen (hundred?) feet. Ask any sailor why they have slickers…

Soooo chaotic…. Give it a skin in a model? Yeah, right… gonna need some better proof to swallow that one.

Bill, loved the model above! I think you have a winner.

I suspect that it is due to the perception, fostered IMHO by the AGW proponents, that being “green” is liberal while being pro-fossil fuels is being pro-business is being “conservative”. That being anti-AGW means you are a coal stooge or an oil lackey.

This is clearly false, but is the perception.

Above I noted there are repeating autocorrelation cycles in the residuals (after adjusting for the ocean indices influence) which are curiously close to the numbers one would expect to see with the solar cycle.

There is a slight 5.5 year, 9-11 year repeating cycle, 22 years, a really big one at 25 years, and the beginnings of a cycle at 44 years.

Above there is a link to a paper by Michael Mann (before he got into tree rings) where he found the same thing in the Hadcrut3 data. I found it as well in the Hadcrut3 data but also in my residuals.

If there was a solar cycle influence, with this analysis method you would expect to see some repeating cycles around the solar cycle numbers (actually NOT right at them but close to them), close to 5.5 years, close to 11 years, close to 22 years etc. The problem is the solar cycles are irregular so a cycle might appear for a time period and then not appear afterward.

Given the irregular nature of these signals (sometimes before and sometimes after the expected solar cycle timelines), the best place to actually search for them would be at the solar cycle timelines just where they are not supposed to appear (that is very hard to explain). This is where I found them (other than the 25 year signal) so it seems there is definitely a solar cycle influence in the numbers.

Given the irregular timing of the solar cycles, it would be really, really, really difficult to pull it out (in a practical way) and it wouldn’t help with a monthly temperature reconstruction or estimating the solar influence of today or last year or this year.

Given it is very difficult to even see a solar cycle, how would one adjust for an increase in solar irradiance over time.

I decided to trust Leif’s judgement and just assume there is a small solar influence which might be as high as +/-0.1C but it is not a focus of this model.

There was a recent paper, however, that indicated solar irradiance drove the AMO cycle down during the ice ages.

I note the AMO and the southern counterpart went down in the early 1900s when the solar cycle was low. They both go back up as the solar cycle revved up, up until about WWII. Both indices suddenly fall after WWII just as the solar influence was really peaking at 1950. etc. etc. So, I see some correlation but it is not consistent and I am looking for solid mathematical formulae to rely on, not conjecture.

The Sun plays a huge role in an El Nino, of course, its just that the Trade Winds and ocean currents/upwelling are the main drivers of this – causing the ocean surface in the Nino region to stall in place and be heated day after day by the Equatorial Sun. No Trades, no currents and there would be a permanent El Nino regardless of the solar cycle. Given the wild swings in the ENSO, I don’t see a changing Sun in the numbers, just natural variation in the Trades and currents.

What say Bill?

Have you done a model against satellite data?