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Stage 3

Page history last edited by Stubborn Mule 14 years, 7 months ago

Diagnosing the regression to see what's wrong and what's right.

 

We can use the fairly innovative GLVMA statistic from Peña and Slate (2006) to assess the model with a linear and non-linear response.  Rather unsurprisingly they both come out with some problems, most notbly that there are linearities involved.  For the model using co2:

 

 gvlma(x = my.model)

                     Value   p-value                   Decision

Global Stat        33.3035 1.035e-06 Assumptions NOT satisfied!

Skewness            2.7901 9.485e-02    Assumptions acceptable.

Kurtosis            4.6877 3.038e-02 Assumptions NOT satisfied!

Link Function      25.3560 4.767e-07 Assumptions NOT satisfied!

Heteroscedasticity  0.4698 4.931e-01    Assumptions acceptable.

And using log co2 difference:

 

Global Stat        3.065e+02 0.000e+00 Assumptions NOT satisfied!

Skewness           8.434e-03 9.268e-01    Assumptions acceptable.

Kurtosis           1.391e+02 0.000e+00 Assumptions NOT satisfied!

Link Function      9.804e+01 0.000e+00 Assumptions NOT satisfied!

Heteroscedasticity 6.931e+01 1.110e-16 Assumptions NOT satisfied!

 

Interpreting this is a bit of a black art, but it seems to me that the linear model is less invalid than the non-linear one.  I think at least in the linear model, the skewness and kurtosis are significant because of dependence on the link function (testing for overall linearity of the model).  Whereas with larger, and more significant significant terms for the non-linear model, there are other problems.

 

This doesn't really matter any way, as we can look at the diagnostic graphs produced by the gvlma package which are straightforward.  It's certainly very difficult to envisage any other reason other than increasing greenhouse gas concentration for the rising temperatures observed.

 

The graphs show clearly that volcanic doesn't do a very good job of predicting anomaly, solar is rather better, and co2 is lock step.  Anomaly versus time sequence for directional stat 4 does a very good job of nixing the asertion that the earth has started cooling.  What we're really seeing there is evidence for an  interesting trend for warming followed by an abrupt temperature drop (with a minimum higher than the minimum of the last period) followed by a further rise.  There's certainly no evidence to suggest that "global warming has stopped", which is one of the most idiotic assertions of the climate skeptic brigade.

 

 

 

Peña, E. A., & Slate, E. H. (2006). Global Validation of Linear Model Assumptions. Journal of the American Statistical Association, 101(473), 341-354. doi: 10.1198/016214505000000637

 

Next up, regression diagnostics over a thousand or so years here: Solar ...

 

Here's an similar graph from Lean, J., Beer, J. and Bradley, R. 1995. Reconstruction of solar irradiance since 1610: Implications for climate change. Geophysical Research Letters 22: 3195-3198:

 

 

 

Truncating the data.

 

climate.summary.end <- subset(climate.summary, climate$Year > 1979)

> summary(my.short.model)

Call:

lm(formula = ANOMALY ~ SOLAR + co2_mean, data = climate.summary.end)

Residuals:

     Min       1Q   Median       3Q      Max

-0.19938 -0.05220  0.03270  0.06071  0.09708

Coefficients:

             Estimate Std. Error t value Pr(>|t|)  

(Intercept) -2.366450   0.794575  -2.978  0.00806 **

SOLAR        0.688377   0.348307   1.976  0.06364 .

co2_mean     0.007756   0.002140   3.625  0.00194 **

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.09009 on 18 degrees of freedom

  (8 observations deleted due to missingness)

Multiple R-squared: 0.4563,    Adjusted R-squared: 0.3959

F-statistic: 7.553 on 2 and 18 DF,  p-value: 0.004153

> gvlma(my.short.model)

Call:

lm(formula = ANOMALY ~ SOLAR + co2_mean, data = climate.summary.end)

Coefficients:

(Intercept)        SOLAR     co2_mean 

  -2.366450     0.688377     0.007756 

ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS

USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:

Level of Significance =  0.05

Call:

 gvlma(x = my.short.model)

                     Value p-value                   Decision

Global Stat        8.16221 0.08581    Assumptions acceptable.

Skewness           3.35623 0.06695    Assumptions acceptable.

Kurtosis           0.01176 0.91363    Assumptions acceptable.

Link Function      4.28587 0.03843 Assumptions NOT satisfied!

Heteroscedasticity 0.50834 0.47586    Assumptions acceptable.

plot.gvlma(gvlma(my.short.model))

 

 

So you see some cyclical change in variability.  Is this solar or is it ENSO or is it something else?

 

Scaling the same model is also useful:

 

lm(formula = scale(ANOMALY) ~ scale(SOLAR) + scale(co2_mean), data = climate.summary.end)

Call:

lm(formula = scale(ANOMALY) ~ scale(SOLAR) + scale(co2_mean),     data = climate.summary.end)

Coefficients:

    (Intercept)     scale(SOLAR)  scale(co2_mean) 

         0.4280           0.3665           0.9426 

 

which shows that co2 is 3 times more important than solar in the prediction of anomaly.  With the whole model explaining 76% of the variance you can do the maths on the relative contributions.

Comments (111)

kenlambert said

at 11:34 pm on Jul 24, 2009

Kdkd

What forcings are you now using. The aerosol cooling, water vapour, pre-1750 co2 (natural warming) and a natural cooling forcing should be included to account for the pre-1750 balances, the LIA and MWP.

kenlambert said

at 11:53 pm on Jul 24, 2009

It is not surpiising that you would get co2 as the main forcing correlating with temperature anomaly. It is running at approx 1.6W/sq.m compared with solar at 0.3-0.5 W/sq.m. in 2005.

The only problem is comparing apples with apples. The solar and volcanic forcings are made or reconstructed from direct measurement.

As far as I know there is no way of directly measuring co2 forcing. The eqan; Forcing (co2) = 5.35 ln (CO2a/CO2b) is a theoretical construct which I have not investigated. The value of 'K' = 5.35 W/sq.m may be derived from a curve fit with other forcings undefined. Since the IPCC Fig 2.4 quoted solar at 0.12 W/sq.m. when its absolute value is up to 0.5W/sq.m, I would like to see other sources of co2 forcing evaluation.

Where did you get your data set for aerosols (direct and cloud albedo) which add up to about -1.2 W/sq.m. Other GHG are also important adding up to about 1.0 W/sq.m

The full equatinn should be:

Delta T (anomaly) = function (F.co2 + F.ghg + F.ozone + F.surfalbedo + F.diraerosol + F.cloudaerosol + F.solar)

kenlambert said

at 11:55 pm on Jul 24, 2009

Maybe a F.watervapour forcing term should also be added to above equation as wv is supposed to be the main GHG - much more important that co2.

kenlambert said

at 12:00 am on Jul 25, 2009

Another thought - you could cut off your 900 - 2005AD correlation at say 1900, 1930, 1950, 1980 in order to see what the measured Temp Anomaly is explained by for each increment. Given that theoretical Co2 forcing passes solar at some time between 1930 and 1950, if might be possible to partition the proportions attributable to each in this way.

kenlambert said

at 12:04 am on Jul 25, 2009

Another thought:

If you ran analysis from 900AD - 1750AD you might also discover what is the main forcing of the MWP and the LIA

Kieren Diment said

at 9:31 am on Jul 25, 2009

I don't have any direct data for aerosols etc, that's your job.

"If you ran analysis from 900AD - 1750AD you might also discover what is the main forcing of the MWP and the LIA"

Yes, I was thinking of doing this. I want to understand the drivers of the present change work together, which means understanding what the partial regression plots mean.

And we do understand that water vapour is a feedback mechanism to other forcings, not a driver in itself. But if you can get data then I'll chuck it in despite my theoretical misgivings.

kenlambert said

at 2:36 pm on Jul 25, 2009

kdkd

I will go looking for data sets on the other forcings - IPCC AR4 would be a start.

Don't think I am being negative - I can understand that the stuff you are playing with can be fun, addictive - even orgasmic

Ken

Kieren Diment said

at 3:46 pm on Jul 25, 2009

Water vapour should show roughly equal dependence on each forcing parameter. This will conclusively demonstrate that it's a follower of rather than a cause of warming.

Kieren Diment said

at 7:41 pm on Jul 25, 2009

The comments in this thread (http://www.realclimate.org/index.php/archives/2009/07/friday-round-up-3/) are instructive as to how climate data is used and abused.

I want to get rid of Co2 log forcing, and just use plain co2 levels , as 1. the co2 anomaly relationship is apparently linear (according to the data), and 2. the goodness of fit is indistinguishable betwen log co2 diff and co2.mean. On the other hand, it's easier to see the effect of co2 concentration on anomaly when using untransformed units.

kenlambert said

at 11:11 pm on Jul 25, 2009

kdkd Which data set are you using for temperture anomaly?

Don't know about getting rid of the F.logdiffco2. It places the dimensions of the co2 term as W/sq.m which are the same as those of solar, volcanic, and other forcings. You can run co2 concentration as a separate variable if you like.

Kieren Diment said

at 11:26 pm on Jul 25, 2009

All the data comes from ftp://ftp.ncdc.noaa.gov/pub/data/paleo/ipcc2007/fig613ipcc2007-unsmoothed.txt as requested with the exception of CO2 data which is a combination of data from http://cdiac.ornl.gov/ftp/trends/co2/maunaloa.co2 and http://cdiac.ornl.gov/ftp/trends/co2/lawdome.combined.dat

Ordinarily in a linear regression (which is what this stuff is), one would transform non-linear terms into linear ones, via various techniques - antilog, ploynomial transformation, fourier analysis or whatever, so using co2 is the correct thing to do. Non linear regression proceeds by transforming data to linear data before proceeding so that the assumptions of the linear model still apply. In this case you also need to perform an appropriate transformation at the end to ensure the regression coefficients make sense in the final predicted figures is the correct way to proceed.

I'll try to get around to presenting the regression diagnostics this weekend as promised ...

An interesting thing in this dataset is that r2 is very high compared to what I'm used to (in social sciences r2 of between .3 and .5 are realistically what we can achieve, so examination of the individual regression coefficients is generally quite hand-wavy and qualitative.). Because Volcanic, Solar and CO2 explain over 90% of the variance of the anomaly though it means that we can look at how each predictor works - what it explains, and what it doesn't - in much more detail than I'm used to.

Kieren Diment said

at 11:53 pm on Jul 25, 2009

Duh, silly me. If you look at the correlation matrix chart, you see the co2/co2.log.diff versus ANOMALY charts, you see an aproximately linear relationship with both, slightly more so with the log figures, but not really enough to make a material difference with the final regression result.

kenlambert said

at 9:40 pm on Jul 26, 2009

Am working on the F.cloudalbedo and F.direct albedo and F.other GHG (mainly methane) and not having much success finding the components in a data.txt format. These represent -1.2 and 1.0 W/sq.m. so are major components compared with CO2 at 1.6 W/sq.m. (IPCC AR4 Fig 2.4) so must be included in the forcing terms.

Kieren Diment said

at 9:48 pm on Jul 26, 2009

To be honest new forcing terms won't make extra sense of what the strong predictors are, but they will help even out the distribution of the residuals (error terms) a bit.

kenlambert said

at 11:52 pm on Jul 26, 2009

kdkd

Don't forget that Solar and Co2 showed a strong correlation, which also can provide a logical mechanism for CO2 and other GHG trapping more heat.

Eliminating volcanic as a strong 'external' force leaves Solar as the only 'external' driver of the Earth's climate.

Greenhouse effect warming and Cloud albedo cooling are really absorbers and reflectors of Solar irradiance energy(constant)(TSI), which is commonly quoted as 1366 W/sq.m at the top of the atmosphere.

We are talking about 1.6 and 0.5 and -1.2 and 1.0 W/sq.m for the variances in forcings of a heat source running at 1366 W/sq.m - so that gives a little perspective as to the magnitudes involved in this LOSU heat source.

By the way, the latest TIM radiometers (4) fromthe SORCE experiment Ref :(http://lasp.colorado.edu/sorce/data/tsi_data.htm) has an absolute accuracy of 0.48W/sq.m.

As of 2005 quote:

"There remains an unresolved 4.5W/sq.m difference between the TIM and other space-borne radiometers, and this difference is being studied by the TSI and radiometry communities" end quote (last updated 13DEC2005)

The 4 TIM' are reading about 1361.5 W/sq.m.

I have not found any further update on the net or the SORCE website.

If you divide this 4.5 W/sq.m. 'error' by 4 to get the distribution over the surface of the Earth (area of the sphere divided by the area of the circular disc exposed to the sun) you get an average of 341 W/sq.m. over the whole surface and the TIM difference of 4.5 W/sq.m divided by 4 gives 1.12 W/sq.m - which is in the ballpark of the forcings from Co2 etc.

So much for Solar Irradiance being 'low' LOSU. My point being that if Solar Irradiance is driving everything including the GHG absorbers and cloud reflectors then they must also have a 'low' LOSU.

Kieren Diment said

at 9:32 am on Jul 27, 2009

Ken,

You're either overstating the importance of solar, or your point is obscure. If we look at the correlations, there are three that are of interest - the correlation between solar and anomaly (0.68), co2 and anomaly - (0.9), and solar and co2 (0.77). If you look at solar over time for the period under analysis, we see solar output increasing in recent years, so there's some time-dependent effect which is likely to be the cause of the correlation between solar and co2. This is in fact likely one of the sources of violation of assumptions (probably your albedo/aerosols effect).

I don't see any way that it challenges the significance of co2 emissions though, and likely strengthens it.

Kieren Diment said

at 11:28 am on Jul 27, 2009

It seems to me that the solar/co2 time dependency is a result of the enhanced greenhouse effect. i.e. as co2 increases, it allows solar to have an increased effect. That would certainly explain the significance of the link function in the regression validataion.

Ken, are you arguing that the sun is responsible for the warming anomaly? It would seem to me that co2 is responsible for enhancing the effect of the sun to drive the warming anomaly. You might have to do some algebra to transform this into a linear model for me to test.

kenlambert said

at 12:45 am on Jul 28, 2009

kdkd

If volcanic is excluded, the Sun is the only external source of heat for the Earth's biosphere (atmosphere, land surface and oceans). If the solar energy reaching Earth (by more output or orbital proximity) is increased you would expect more energy to be available for GHG (CO2 & Methane etc) absorption.

I need to know more about the energy budget of he system because the TSI is 1366 W/sq.m. and spread out over the Earth's surface that is about 341 W/sq.m which is a much bigger number than the small 0.5 - 1.6 W/sq.m 'forcing' imbalances we are playing with in the analysis. I am intrigued by the 4.5 W/sq.m low reading by the latest and supposedly most accurate TIM radiometers though.

The other issue is one of thermal lags in the system. The oceans have about 1000 times the heat capacity of the atmosphere so even if you take the top 200-300 meters of the oceans, you still have 80 times the heat capacity. I don't know how to translate this into months or years or decades of lag on effects. An interesting point made was that with CO2 increase lagging temperature by 7-800 years in the last 400-600000 years of interglacials from ice core data, we could be seeing a component increase in CO2 from the warming in the MWP. Sounds crazy, but why would this cycle not be happening in the background?

Kieren Diment said

at 9:10 am on Jul 28, 2009

Ken,

I finally worked out why I'm having trouble following you. You don't have a hypothesis. Re-state what you're trying to say in terms of one, two or three hypotheses.

By contrast, I already achieved what I set out to. My hypothesis is that the main determinant of the current global temperature anomaly is CO2. I've showed this as conclusively as it is possible with the limited time I have available to devote to this, and with my existing skill base. I've also postulated a convincing looking link that CO2 also enhances the effect of solar forcing, but would need some help with algebra to actually demonstrate this via a model.

Along the way I have also provided very very strong evidence that Volcanic activity is essentially irellevant to current long term trend in temperature nomaly.

So this is achieved via the principle of parsimony (the least information that can explain the most stuff), and a single equation. The data looks convincing enough to me that there's really no need to debate the cause of the current warming at all. On the other hand I would like to substitute out the anomaly data with some of the climate skeptic's data sources, as I'm 99.9% sure that they won't show the least discernable difference to long term trend.

My next ought to be to demonstrate that we should be very worried about the observed magnitude of warming.

So, Ken, in summary, I'm not clear what you're trying to do here. Put it in terms of a hypothesis or two, and then I might be able to follow you.

kenlambert said

at 10:14 pm on Jul 28, 2009

The UAH Temperature Anomaly data (courtesy of Tamas' search) for the lower troposphere can be found at:
http://vortex.nsstc.uah.edu/public/msu/t2lt/tltglhmam_5.2

kenlambert said

at 10:38 pm on Jul 28, 2009

kdkd:

kdkd Only forcing data on aerosols I could find is from NASA/GISS (Hansen et al) Graph (b) 1850 - 2000AD

http://data.giss.nasa.gov/modelforce/trop.aer/

kenlambert said

at 11:21 pm on Jul 28, 2009

kdkd: Analysis so far: "the correlation between solar and anomaly (0.68), co2 and anomaly - (0.9), and solar and co2 (0.77)."

Can you determine from this, the relative effects of Solar vs CO2 over time? eg between say 1750 to 1900, 1900 - 1930, 1930-1950, 1950 - 1980, 1980-2005. This would tend to separate out the effects of both in 20-30 year blocks which you claim are the minimum for significance.

I would suggest a few hypotheticals:

1) Analysis between 900AD and 1750AD would identify Solar forcings as the main driver of the MWP and LIA.
2) That the Temperature anomaly in the MWP was of similar magnitude to the last 25-50 years of the 20th century.
3) That Solar forcing since 1750 plays a much greater part in the observed warming than that implied by the IPCC in Fig 2.4 ie 0.12W/sq.m compared with 1.6W/sq.m for AG forcings.
4) That CO2 and GHG warming forcings may correlate with Cloud Albedo and Direct Albedo cooling forcings producing a natural balancing mechanism going forward.
5) That Solar will have contributed a portion of the warming currently attributed to CO2 over the last 25-50 years, rendering the alarmist predictions of catastrophic temperature increase exaggerated.
6) If your conclusion is that Temperature anomaly is linear with CO2 concentration, then we can look forward to less than 1 degC increase at double the CO2 concentration (560ppmv), which gives us plenty of time to implement Ken Lambert’s 10 point plan.

Kieren Diment said

at 8:18 am on Jul 29, 2009

1. Yes, I suppose if fit is better than the present day, it would be pretty good proof that solar is the driver of the mwp etc. I need solar input figures, not solar forcing for this to be reliable.

3. What's the model that you propose to test this?

4. Again, give me a model. Sounds spurious to me - wishful thinking as it were. You always seem to want to ignore the positive feedback loops - decrease in ice albedo, methane production from melting permafrost, peat bog oxidation, all of which are observed, while playing up the possibility of enhanced negative feedback.

5. You need to provide me with estimates of solar input, not solar forcing for this one. I can't test it otherwise.

6. Again your bias is being exposed. We're not accounting for lags in co2 at all, so my model significantly underestimates anomaly caused by co2, so your assumption here is not tenable. We certainly can't extrapolate beyond the current co2 levels reliably with this model.

Summary: Let's find better figures for solar, in terms of absolute input from the cosmos - I suggest that the solar figures presented by the IPCC are solar input from the atmosphere (looking at solar over time - I see something that appears to look like the enhanced greenhouse effect at the end of the graph - I'm sure that solar actvity is not at historic highs at the moment).

kenlambert said

at 11:42 pm on Jul 29, 2009

Don’t ruin a useful exercise with baseless assertion and snide accusation of bias.

Why didn't you answer #2. The Temp anomaly looked suspiciously like a 'similar’ level at the start (MWP) and the end (late 20th century) of the record? (Ref Stage 1)

#3 Your model paleface. That is why you should partition it into time blocks and see what the block correlations are.

#4 You have that raw data on aerosols: "Only forcing data on aerosols I could find is from NASA/GISS (Hansen et al) Graph (b) 1850 - 2000AD”

viz; http://data.giss.nasa.gov/modelforce/trop.aer/"

#5 Don't think you understand that the Solar forcing *IS* the *variation* in INCOMING Solar Radiation which averages out at about 341 W/sq.m. (see my JUL26 and JUL28 posts).

(Remember that INCOMING Solar Radiation is TIS divided by 4 (1366/4 = 341.5 W/sq.m).)

The overall forcing balance equation for the Earth is:

(F.incoming solar at about 341W/sq.m) = (F.reflected by cloud and surface albedo at about 102 W/sq.m) + (F. outgoing longwave radiation at about 239 W/sq.m): Eqan 1

The imbalance forcings which are supposed to be heating the Earth can be taken from the above three broad terms. (Which we have postulated before ie:

Delta T (anomaly) = function (F.co2 + F.ghg + F.ozone + F.surfalbedo + F.diraerosol + F.cloudaerosol + F.solar) where these are the *VARIATIONS* in these forcing values.)

See a short explanation for the above by Kevin E. Trenberth viz:

http://www.aps.org/units/fps/newsletters/200904/trenberth.cfm

#6 kdkd "I suggest that the solar figures presented by the IPCC are solar input from the atmosphere" - this does not make sense. Go and read Trenberth and understand.

kenlambert said

at 11:47 pm on Jul 29, 2009

Suggest you refrain from accusations of bias against me and use the UAH Temperature anomaly, the aerosols data (which is a big part of Eqan 1), and run these variables in concert with your existing variables if possible to see what happens.

As far as CO2 concentration is concerned, the heating (forcing) effect is supposed to be the log function ie. F.CO2 = K ln(Co2a/CO2b). It only makes sense to compare forcings (W/sq.m) in the valiables relating to all the heating and cooling terms.

Kieren Diment said

at 11:09 am on Jul 30, 2009

Sorry, I did answer #2, deleted the comment to put in an edited version and then forgot to paste the edited version.

Anyway, we can answer most of your questions by looking at the residuals of the model including only solar in the analysis. It's fairly technical, but a quick precis (I will post the whole thing later on) is that the residuals from a ANOMALY = f(SOLAR) model conclusively demonstrate that the predictive ability of SOLAR during the mwp is quite different to the present day.

If you want your "complete" model tested (i.e.:

Delta T (anomaly) = function (F.co2 + F.ghg + F.ozone + F.surfalbedo + F.diraerosol + F.cloudaerosol + F.solar)

Then you need to provide data for every single one of those things. Otherwise we have to continue down the path of inference with incomplete data that I've been doing.

Kieren Diment said

at 9:30 pm on Jul 30, 2009

I don't actually understand the purpose of this complete model. It looks like an excercise in climate natural history rather than trying to test any actual hypothesis about the cause and magnitude of climate change.

The job I've done at the new page http://climatekaraoke.pbworks.com/Solar does the same job as partitioning it into blocks in that it shows where the predictability of anomaly and solar forcing breaks down more than elsewhere. I don't see what additional benefit a partitioned model would bring.

kenlambert said

at 11:27 pm on Jul 30, 2009

No time to make other than brief comment (running two companies to pay enough tax to support the Uni of Kiera View),
but I would like you to assign the above forcing components to the three major terms in the Earth's forcing balance equation (Eqan 1) to see if you really understand the Trenberth story.

Kieren Diment said

at 9:17 pm on Jul 31, 2009

No, I really don't know what the need is to have this complete model. We've shown that solar and co2 combined explain 90% of the variance of anomaly already. That only leaves 10% of the variance left to explain. If extra variables were the source of negative feedback phenomena, then we would expect to see positive residuals at the end of the time series (i.e. the model over-estimating temperature). However we see no positive residuals and lots of negative residuals (i.e. co2 and solar underestimating anomaly). Therefore there is no evidence for negative feedback, and some evidence for positive feedback in these results.

So remind me why you need a model that provides a complete description of "reality" again? It seems like busy work for no particular purpose to me. I've left the goalposts as wide as possible for you, yet you still can't point to a shred of evidence that co2 is not a major concern.

kenlambert said

at 12:13 am on Aug 1, 2009

Unless of course the Temperature anomaly data is wrong.

kenlambert said

at 12:19 am on Aug 1, 2009

If you are so confident that CO2 and Solar explain 90% of the Temperature anomaly - can you estimate the proportions of the contributions of each?

Kieren Diment said

at 10:05 am on Aug 1, 2009

Well the temperature anomaly data is the average from multiple sources (from the IPCC data you provided). So it would take a rather large systematic error for it to be simulultaneously wrong from so many places.

As for the contribution of solar and CO2 ...

Probably the easiest way to do this is to run the regression on standardised scores and look at the coefficient. Now for every standard deviation that co2_mean increases, anomaly increases by 0.86 standard deviations. For every standard deviation that solar increases, anomaly increases by 0.66 standard deviations. So the effect of co2 between 1830 and the start of the 21st century is 23% greater than that of solar forcing.

kenlambert said

at 12:27 am on Aug 2, 2009

Ok that is a starting point whthe proportions of the planet has estimated. I don't know why you picked 1830 as the base year - 1750 would have aligned with the IPCC AR4.

So if the effect on Temp Anomaly is *linear* then CO2:Solar is 1.23:1. 55% C02 and 45% Solar.

*Linear* sensitivity might be a big ask with ocean lags, ice melt latent heat (phase change at no temp increase) and complex atmospheric interactions - but it is a start.

If the global temp increase since 1830 is about 0.8 degC then CO2 is responsible for 0.44 degC and Solar 0.36 degC.

That sounds feasible. Certainly a lot different from the IPCC's AR4 Fig 2.4 ratio of forcings which placed CO2:Solar at 13.8:1.

How about a run for the period 900AD to 1750AD and 1750AD to 1978AD, and a run on the 30 years of the UAH data only 1979-2008AD?

kenlambert said

at 12:39 am on Aug 2, 2009

"Ok that is a starting point whthe proportions of the planet has estimated" Stuffed up the first line - it should read:

*Ok that is a starting point which no other reference on AGW on the planet has estimated*

By the way note my points on the satellite data on that page. The temp anomaly I supplied (Graph (d) Fig 613) is for the NH only. The UAH data for both hemispheres shows a decadal temp anomaly trend of 0.19 NH and 0.058 SH - NH is 3.27 times the SH trend.

Averaging NH and SH gives global at 0.124, with Global:NH at 0.124:0.190 or 65% of NH.

It might be worth looking at using 65% of the NH Temp Anomaly and see if C02 + Solar still underestimate the Temp.

Kieren Diment said

at 8:48 am on Aug 2, 2009

1830 is the base year as that's the first year I have co2 data available for. I'm happy if you can find me more.

Kieren Diment said

at 5:26 pm on Aug 3, 2009

"If the global temp increase since 1830 is about 0.8 degC then CO2 is responsible for 0.44 degC and Solar 0.36 degC."

but the way that the IPCC calculate solar forcing, it is dependent on CO2. You can see this if you look at actual solar output which is not increasing, http://www.ngdc.noaa.gov/stp/SOLAR/IRRADIANCE/irrad.html while the IPCC's solar forcing figure is (correlation 0.77 from memory, wheras irradiance and co2 are uncorrelated)

kenlambert said

at 10:57 pm on Aug 3, 2009

Did you also arithmetically average the 5 or 6 Solar Irradiance Forcing sets making up Graph (b)? These are reconstructions by various methods going back in time.

http://www.ngdc.noaa.gov/stp/SOLAR/IRRADIANCE/irrad.html - These are TOA satellite measurements of TSI which going back to 1978 are reflecting the Solar 11 year cycle (plus overlays of longer cycles which stretch out to 100,000 years). Is there txt data for these TSI graphs?




Kieren Diment said

at 12:44 am on Aug 4, 2009

Yes, I just take the mean of anything with multiple observations.

I'm pretty reluctant to use datasets of less than about a century to answer the question "is CO2 causing global warming at a level to be of serious concern". The evidence so far, particularly some of the residuals at the end of the time series, really strongly suggests a resounding yes. You can't really observe this pattern without a decent series of baseline observations, otherwise you won't catch the apparent non-linear positive feedback suggested by the residuals.

Remember we can see that residual analysis is useful here as we can catch other anomalous phenomenon over the last milleneum with the same method, and the current warming trend is of significantly larger magnitude over a shorter time scale.

The next question to ask as far as I can see is "What level of CO2/temperature rise would be of serious concern".

Kieren Diment said

at 12:48 am on Aug 4, 2009

Check out the "Response Variable versus tiime sequence" plot in the graph on this stage (second row RHS). Something fishy there. There are two steep gradients and one precipitous drop, that indicates that we're starting to observe a simultaneous increase in the rate of warming with a simultaneous (cyclical) increase in the variability of anomaly. There's another 20 or 30 years to go before this trend is fully confirmed though (although it could probably be done spatially, but that's beyond my knowledge).

kenlambert said

at 11:08 pm on Aug 4, 2009

Don't understand what this means.

If you run the analysis 900AD to 1978AD you might discern the relative magnitudes of the pre-satellite temp anomaly with the MWP and late 20th century and get a pointer to the relativities of the warmings.

Kieren Diment said

at 8:26 am on Aug 5, 2009

Look at the end of the graph "Response variable versus time sequence" (second row RHS) over the past centry or so and describe what you see. Then compare it to the standardised residual versus time sequence (bottom row RHS) over the same period, and you will see that this (post-industrial) model consistently under-estimates temperature.

This is decent evidence for some kind of positive feedback mechanism occuring in the present day.

Pre-industrial, solar plus volcaninc accounts for 55% of the variance of anomaly, both of roughly equal importance to the goodness of fit of the model. This is consistent with their relative importance in the present day. However it's not a satisfactory linear model (all but one assumption violated), but the constant variance across data range assumption is satisfied, unlike when CO2 is introduced when we see non-random distribution of error (which indicates CO2 is associated with feedback mechanisms), but that solar and volcanic are not.

kenlambert said

at 10:31 pm on Aug 5, 2009

kdkd

Here is an interesting report and exchange regarding CO2 levels in the early Holocene - follow it right through to the reply by F. Wagner. You might have an opinion on the statistical analysis mentioned therein. Viz

Early Holocene Atmospheric CO2 Concentrations:

http://www.sciencemag.org/cgi/content/full/286/5446/1815a

More Solar data and discussion from:

http://www.ngdc.noaa.gov/stp/SOLAR/solarda3.html

Interestingly enough the authors claim that between 1980 and 1986 Solar forcing was 0.24W/sq.m, and CO2 GHG effect was 0.25W/sq.m which is roughly 50/50.

Not far from your 45/55 correlation.

Regarding your above discussion: Are we seeing a roughly 11 year cycle overlayed by the solar maximum around 1950AD?

kenlambert said

at 10:42 pm on Aug 5, 2009

You might like to correlate Sea surface temperatures wiith the NH Anomaly used in your Stage 1 analysis

Data here:


ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/GLOBAL_CHANGE/sea_sfc_temp_anomalies.txt

Kieren Diment said

at 2:37 pm on Aug 6, 2009

The SST/NIH stuff won't work very well. One is 1886 to 1995, the other is 1978 to 2004. So that's under 20 years of global means. This means the correlation is necessarily uncertain. However it is non-zero and positive (0.58) with the 95% confidence interval between 0.12 and 0.84.

Don't know about the 11 year solar cycle. You'd have to find me a century or more of tabular data estimating that to be able to control for it. This would also provide a reasonably definitive answer.

Also Recall that solar forcing seems to be related to CO2 in the present day. I guess this is due to the way that the IPCC guys calculate it. Also remember that in the present day solar forcing consistently under-estimates anomaly. For negative feedback mechanisms to be starting to kick in we'd want our model to consistently over-estimate anomaly.

kenlambert said

at 10:55 pm on Aug 6, 2009

You should be able to use the SST 1886 to 1995 - this is more than 100 years. This is all we have in terms of direct measurement I think. Hope you are not avoiding SST data – it might give us some indication of thermal lags compared with the NH Temp data.

Have a look at the Satellite page for comment on your persistent claim that CO2 + Solar underestimate the Temp Anomaly. I assume that my suggestion of a Global T: NH T ratio of 0.65 was treated as a constant. This was derived from a ratio of the trends; which is a ratio of rates of increase. I assume that you have discounted this as a constant which does not affect the rate of increase – just the absolute values. Ratioing the SH and NH rates of increase produces a new rate of increase between the two. With the Antarctica ice factor – I would suggest that this global T anomaly is non-linear and well below your NH T anomaly, and the SST data might shed light on this.

Check out this abstract: You might conclude that the other kiddies playing in this sandpit are just getting their act together in 2006.

http://geology.geoscienceworld.org/cgi/content/abstract/33/1/73

Re: 11 year Solar cycle:

You should have been able to pick up the 11 year cycle from the Solar Forcing data back to 1000AD used in Stage 1. The TSI variation is supposed to be about 0.1% over the 11 year cycle - which at TOA for the TSI is 0.1% of 1366 W/sq.m which is about 1.4 W/sq.m. Applied to the whole Earth surface - divide by 4, which is 0.35 W/sq.m from peak to trough.


Kieren Diment said

at 11:18 pm on Aug 6, 2009

I added a solar v year plot in the main body of the page above so that you can see the 11 year cycle is undetectable, and the solar forcing figure is dependent on some factor(s) other than the sun.

I'll write up the SST versus CO2/solar regression over the weekend. The short story is: 70% of the variance explained, and a more linear model than the atmospheric one. The effect of co2 is less marked than for atmospheric temp(buffer effect). The model still underestimates temperature consistently (slightly less so) at the end of the time series, thus supporting evidence for the operation of some kind of positive feedback mechanism.

kenlambert said

at 12:51 am on Aug 8, 2009

"The model still underestimates temperature consistently (slightly less so) at the end of the time series, thus supporting evidence for the operation of some kind of positive feedback mechanism."

Or over-measurement of the SST anomaly. Remember that the Argobuoys are measuring lower SST's but you are discounting them as only 5 years in operation.

kenlambert said

at 1:17 am on Aug 8, 2009

"Kieren Diment writes: I take Tamas Calderwood’s graph (yesterday, comments) from a single source of data and raise is with a plot of temperature anomaly using the multi-source 1100 year data set published by the IPCC. This data encompasses the little ice age and the medieval warm period. From this graph we see we’re warmer than the medieval warming period in the present day, and the degree of change is greater than that during the little ice age.

If you do the gory statistics you’ll see that the only thing that predicts the increase in temperature between 1800 and 2000 properly is the CO2 concentration in the atmosphere. Worse, there’s evidence from the same statistics that we’re now starting to see positive feedback effects. Don’t believe me? Look at the data yourself.

I’ve looked at Tamas favourite NIH satellite data, and there is something odd about it — I can’t quite put my finger on it. However, it does broadly agree with the trend in the attached graph, and does not invalidate the anthropogenic global warming theory in the least."

What kdkd did not say was that he was jointly researching the AGW data with Ken Lambert, and that is ongoing, with neither party agreeing to go off and publish results outside the PB worksheets.

Kieren Diment said

at 1:24 am on Aug 8, 2009

We certainly haven't shown anything contrary to the conventional wisdom at this stage. Although we have demonstrated some interesting bits of the data.

And Tamas has demonstrated his astonishing levels of imbecility yet again.

And this site is on the world wide web. Feel free to take a private discussion to the inside of your own mind.

kenlambert said

at 1:38 pm on Aug 8, 2009

That is all the more reason to restrain yourself from using 'idiot' and 'imbecile' in the PB workspace. This is supposed to be Nobel prize winning research isn't it?

You should confine yourself to these terms of abuse in the Crikey Cage Match or the Corrections & Cockups etc, but don't be surprised if Tamas calls you:

'twenty-something Maoist social researcher from a second rate regional University - Uni of Kieren View isn't it?"

Kieren Diment said

at 1:42 pm on Aug 8, 2009

Glad I look so young then :)

There's really no excuse for the kind of Dishonesty that Tamas is peddling with that gibberish. The fact that it's even considered makes me quite angry.

kenlambert said

at 2:30 pm on Aug 8, 2009

Back to the analysis:

Intriguing that the Solar 11 year cycle is not showing up in the historical Solar forcing data. Seems to be a strong 100-120 year cycle though?

Suggest you look at: http://www.agu.org/pubs/crossref/1995/95GL03093.shtml

Its about time you summarized what correlation runs you have done;

I have not seen any graphical plots of the UAH data, SST data and Aerosols data, 900-1750 run, 1750-1978 run, 1978-2008 run, or any attempt to use a truly Global Temp Anomaly data set.

And on the contrary, you might have correlated a NH Temp Anomaly hockeystick with a CO2 hockeystick; but the putative finding that the CO2 to Solar contributons to the current warming are roughly 55% to 45% has major implications. viz.

1) It shows with the IPCC's own data that the IPCC has vastly understated the Solar contribution; which is a natural factor Earthlings can do nothing to stop, and;

2) The atmosphere of moral panic created by AGW alarmists that CO2 was doing all the damage; is shown to be an exaggeration which subtle sceptics like myself suspected all along, and;

3) There is a much greater window of time to devise sensible precautionary CO2 emissions reduction measures such as replacement of major coal fired emitters with nuclear (Swedish and Chinese style).

4) With the Solar Irradiance predicted to decline to a low in 2040, we could see removal of roughly half the Solar forcing and the CO2 half may prevent the Earth cooling or at lease flatten or slow the warming.

Is it the glass half full or the glass half empty Kieren?

Kieren Diment said

at 3:29 pm on Aug 8, 2009

Are you trying to claim that there's no association between the temperature anomaly is not dependent on the co2 concentration? In that case you'll have to find solar irradiance data rather than forcing. And find some other factor that's strongly associated but independent of co2

"I have not seen any graphical plots of the UAH data, SST data and Aerosols data, 900-1750 run, 1750-1978 run, 1978-2008 run, or any attempt to use a truly Global Temp Anomaly data set."

The UAH data I've looked at. From a statistical point of view it's on a much shorter timeframe than the IPCC data, so we can't tell that much from it. We're unable to demonstrate a statistically significant difference in trend that's meaningfully different from the IPCC data. In fact, SOLAR is not a significant predictor for the NIH model, while CO2 is. I think I may have mistakenly refered to it as NIH data before. And the same negative residuals at the last five years of the time series.

You need to clearly point to where all these measures can be found in one place. It's not my job to find the data, it's yours.

The partitioned year runs are pointless extra busy work. The residuals analysis and time-series analysis (such as it is) are good enough, and in many cases better than this. Also it doesn't rely on subjective assumptions (i.e. the time periods to partition). So I've already done the equivalent of this. Look at the graphs.

Kieren Diment said

at 3:30 pm on Aug 8, 2009

Now for your four points:

1. No. For that we need about 100 years of raw solar irradiance figures to replace solar forcing in the model. At present co2 and our forcing figure are dependent. It would be better to have prediction variables that were independent of each other.

2. You have nothing here that demonstrates this at all. This is a bare faced assertion with no evidence.

3. See 2. Certainly not if there are positive feedback mechanisms kicking in. The residual analysis of the time series suggests that there are. This part of the analysis is very important, and you appear determined to overlook it.

4. This ought to be demonstrable with the existing data set, if you can find raw irradiance (not forcing) figures. This effect would be more marked in the absence of positive feedback loops. We could probably look at that with the raw irradiance data if you can find it anywhere.

I'm concerned about your rather torturous rationalisation of the data analysis to date. If you don't lift your game, I'm going to lose patience again.

kenlambert said

at 11:54 pm on Aug 8, 2009

kenlambert said

at 12:01 am on Aug 9, 2009

Can't find a tabular dataset for the TSI going back 100 years, but it would not be too hard for you to take 10 decadal data points. 1900-2000. As you know satellite measurement has only been available since 1978, and the historical prior to that are reconstructions from sunspots, etc.

kenlambert said

at 12:06 am on Aug 9, 2009

Check out this paper:

Phenomenological solar contribution to the 1900–2000 global surface warming

Phenomenological solar contribution to the 1900–2000 global surface warming
N. Scafetta

Physics Department, Duke University, Durham, North Carolina, USA

B. J. West

Physics Department, Duke University, Durham, North Carolina, USA

Mathematical and Information Science Directorate, U.S. Army Research Office, Research Triangle Park, North Carolina, USA

We study the role of solar forcing on global surface temperature during four periods of the industrial era (1900–2000, 1900–1950, 1950–2000 and 1980–2000) by using a sun-climate coupling model based on four scale-dependent empirical climate sensitive parameters to solar variations. We use two alternative total solar irradiance satellite composites, ACRIM and PMOD, and a total solar irradiance proxy reconstruction. We estimate that the sun contributed as much as 45–50% of the 1900–2000 global warming, and 25–35% of the 1980–2000 global warming. These results, while confirming that anthropogenic-added climate forcing might have progressively played a dominant role in climate change during the last century, also suggest that the solar impact on climate change during the same period is significantly stronger than what some theoretical models have predicted.

Received 19 December 2005; accepted 30 January 2006; published 9 March 2006.

Citation: Scafetta, N., and B. J. West (2006), Phenomenological solar contribution to the 1900–2000 global surface warming, Geophys. Res. Lett., 33, L05708, doi:10.1029/2005GL025539.

kenlambert said

at 12:48 am on Aug 9, 2009

Quote from above: "We use two alternative total solar irradiance satellite composites, ACRIM and PMOD, and a total solar irradiance proxy reconstruction. We estimate that the sun contributed as much as 45–50% of the 1900–2000 global warming, and 25–35% of the 1980–2000 global warming."

Your naive analysis comes up with 45% for Solar from a completely different data source.

You still don't seem to 'get' the difference between *Solar forcing* and TSI (total solar irradiance) variation.

TSI is measured at the top of the Earth's atmosphere by satellite radiometers at around 1366-1367 W/sq.m. The variation in this is quoted as 0.1% by IPCC, which is about 1.4 W/sq.m.

TSI is divided by 4 to get the incoming solar irradiance distributed on the surface because the irradiated area is the circular disc of the Earth as seen by a point source of heat (the sun) from 93 million miles away, and the surface area of the spinning earth is 4 times the area of the circular disc facing the sun. (check out the surface area of a sphere is
4 x pi x R2, and a circle is pi x R2).

The *variation* in TSI is also divided by 4 which gives a "solar forcing" of 1.4W/sq.m / 4 = 0.35W/sq.m.at the surface.

Other references argue that the 0.1% variation in TSI is underestimated and could be 0.2% or more.

These variations are cyclical with Suess, Geissberg cycles at 11 years, 80-120 years etc and might be roughly sinusoidal, which might play havoc with your liking for linearized relationships.

Anyhow, I stand by my 4 points - which I predict will prove correct.

kenlambert said

at 1:05 am on Aug 9, 2009

What was done
Scafetta and West developed "two distinct TSI [total solar irradiance] reconstructions made by merging in 1980 the annual mean TSI proxy reconstruction of Lean et al. (1995) for the period 1900-1980 and two alternative TSI satellite composites, ACRIM (Wilson and Mordvinov, 2003), and PMOD (Frolich and Lean, 1998), for the period 1980-2000," after which they used what they deemed to be appropriate climate sensitivity transfer functions to transform the TSI histories they developed into 20th-century temperature histories.

What was learned
The two researchers determined that the sun contributed some 46-49% of the 1900-2000 global warming of the earth; and considering that there may have been uncertainties of 20-30% in their sensitivity parameters, they suggest that the sun may possibly have been responsible for as much as 60% of the 20th-century temperature increase.

What it means
The role of the sun in 20th-century global warming, according to Scafetta and West, has been vastly underestimated by the climate modeling community, with various energy balance models producing estimates of solar-induced warming over this period that are "two to ten times lower" than what they found.. Why is this so? The two researchers say "the models might be inadequate because of the difficulty of modeling climate in general and a lack of knowledge of climate sensitivity to solar variations in particular." They also note that "theoretical models usually acknowledge as solar forcing only the direct TSI forcing," thereby ignoring "possible additional climate effects linked to solar magnetic field, UV radiation, solar flares and cosmic ray intensity modulations." In this regard, we additionally note that some of these phenomena may to some degree be independent of, and thereby add to, the simple TSI forcing Scafetta and West employed, which suggests that the totality of solar activity effects on climate may be even greater than what they calculated.

kenlambert said

at 1:06 am on Aug 9, 2009

Could not fit all the references into 2000 characters above:

References
Frohlich, C. and Lean, J. 1998. The Sun's total irradiance: Cycles, trends and related climate change uncertainties since 1976. Geophysical Research Letters 25: 4377-4380.

Lean, J., Beer, J. and Bradley, R. 1995. Reconstruction of solar irradiance since 1610: Implications for climate change. Geophysical Research Letters 22: 3195-3198.

Wilson, R.C. and Mordvinov, A.V. 2003. Secular total solar irradiance trend during solar cycles 21-23. Geophysical Research Letters 30: 10.1029/2002GL016038.

Reviewed 14 June 2006

Kieren Diment said

at 9:14 am on Aug 9, 2009

Unless you want to sit down with a ruler and a print out of one of the graphs, we're not going to get good tabluar annual data on TSI. To be honest it doesn't matter that much unless you want to continue to obsess on solar issues - what we have is good enough. There's some climate skeptic stuff among the papers you've posted above that attempts to (and fails) to discount the role of CO2.

Here's a particularly egregious example:

"The two researchers determined that the sun contributed some 46-49% of the 1900-2000 global warming of the earth; and considering that there may have been uncertainties of 20-30% in their sensitivity parameters, they suggest that the sun may possibly have been responsible for as much as 60% of the 20th-century temperature increase."

What's being reported here is information about the confidence interval of the estimate. But it's done in a very very bad way. If you report confidence levels, you report both sides. You don't selectively report the most "optimistic" side of the CI as it demonstrates researcher bias. This comment should therefore be dismissed out of hand.

Examining the error of prediction is much more reliable, and less subjective. We see that at the end of the time series, our predicted anomaly is always under-estimated using either IPCC or UAH data sources. My hypothesis is that this is due to the start of one or more positive feedback mechanism (e.g. decreased arctic albedo, increased methane emissions). Do you have some other hypothesis that could account for the consistent under-estimate of anomaly at the end of our time series - because like it or not, this is the crux of our discussion.

You're over-preoccupied with historical data at the expense of what we're observing in the present.

Kieren Diment said

at 9:15 am on Aug 9, 2009

Interestingly this comment also supports my hypotheis that we're seeing the start of positive feedback:

"We estimate that the sun contributed as much as 45–50% of the 1900–2000 global warming, and 25–35% of the 1980–2000 global warming."

It's nice to be independently validated :)

kenlambert said

at 10:54 am on Aug 9, 2009

I noted that too - and quoted the Scafetta and West abstract verbatim.

So after your little Maoist rant against the commentary on the S&W paper, you now find that it is worth quoting as *nice to be independently validated*

Ya can't have the 25-35% without the 45-50% Kieren.

Why don't you test the 1980 - 2008 data by doing a run then, as I have been urging?

kenlambert said

at 10:57 am on Aug 9, 2009

Geophysical Research Letters is a subscription service with no indication of raw datasets being available. You have not read the full paper - nor have I. We are relying on the abstract, which I have no reason to doubt.

Kieren Diment said

at 11:39 am on Aug 9, 2009

Happy now? I've done the truncated analysis above. It's not particularly informative about the overall warming trend, although some underlying cycle is detectable in the residuals versus time series. This doesn't affect my earlier conclusions at all though.

kenlambert said

at 11:49 am on Aug 9, 2009

If you are doing a 1980 (or 1978) - 2008 run you should add in all the possible factors which we have much more extensive data - Satellite Temps, Solar UV, Cosmic Ray Influences, Methane levels, Cloudiness etc.

kenlambert said

at 12:05 pm on Aug 9, 2009

I will happily admit that I have only a middle aged undregraduate understanding of your regression analysis variables and how you interpret residuals etc.

I assume that you mean that if the two variables in an X-Y plot do not follow a reasonably linear path (defined by the R value or some like), then the divergences from the linear trend line are examined for a pattern - be it chaotic, cyclic etc?

If you are finding anything cyclical or sinusoidal, - it would have to point strongly to similar underlying forcings would it not??

You would have to admit though, that you did not expect the Solar forcing or TSI (same thing effectively) to be 45% of the last 100 years warming.

Note that I never claimed that CO2 played no role - I have a mantra which says that (until our perfect union of analytical prowess was unleashed) we don't know what portion of the post 1750AD warming was contributed by 'natural' factors and what proportion was AGW.

It seems that we have made progress in zeroing in on those proportions which is finding independent support from some 'expert' sources.

Kieren Diment said

at 12:58 pm on Aug 9, 2009

There's no point in doing a short time range of analysis of everything as the sample size is too small. We can already see that at a short term time range all of the short-term variability masks the long-term variability.

Kieren Diment said

at 2:00 pm on Aug 9, 2009

You're right, non-linearities and cycles will manifest themselves as systematic changes in prediction accuracy. The random distribution of error variance is a strong assumption in linear regression, so examining the residuals is a prime activity for diagnosing the data.

Kieren Diment said

at 2:22 pm on Aug 9, 2009

Here's a recorded interview with an australian paleoclimate specialist who is stressing the importance of the global warming problem, and the need for urgent, immediate action http://www.radioaustralia.net.au/connectasia/stories/200907/s2634156.htm

Kieren Diment said

at 8:26 pm on Aug 9, 2009

Ken:

With respect to "So after your little Maoist rant against the commentary on the S&W paper, you now find that it is worth quoting as *nice to be independently validated* Ya can't have the 25-35% without the 45-50% Kieren."

I was specifically being critical of the 60% figure being thrown about. It seems to expose the authors bias rather unnecessarily. Nothing Marxist about it though - it's just an example of bad practice. They still independently validate my findings though.

kenlambert said

at 10:25 pm on Aug 9, 2009

The commentary on the S&W paper was from a different source than the paper which I found directly on the web. I agree that the commentator should not have mentioned the 60% without also quoting the lower limit (whatever that was). A minor indiscretion compared to the IPCC claims which places CO2 forcing at 92% and Solar forcing at 8% relative to 1750AD in AR4 Fig 2.4. Agree??

Moving on to the important bits:

Your short 1978 - 2008? run shows some intriguing results and cyclical patterns:


1) For the 76% explained by CO2 and Solar; ratio of CO2:Solar is 2.57:1 which is 72%CO2 and 28% Solar. Plumb in the range of 25%-35% Solar for the 1980-2000 period from the S&W paper. Kieren you are amazing!!

What are the odds of Scafetta and West being in agreement with you on both paleface??


2) The T vs Co2 mean, T vs Time Stat 4, and Resdiuals vs Time Stat 4 all show a cyclical pattern. Is the Time Stat 4 scale in years? If so it seems to match a roughly 11 year cycle - a Solar cycle.

I seem to remember Solar and CO2 showing a strong correlation from the Stage 1 Analysis.

I thought ENSO was a SH phenomenon - are you still using the NH Temp Anomaly set?

Otherwise cyclical CO2 and Temp can only mean Temp is rising AND falling with a continually rising CO2 - could this indicate that a CO2 saturation effect is occuring? The Co2 greenhouse gas absorber is not a one way window. It can gain Temp (heat) and lose Temp (heat) while steadily rising in concentration.

If the Time Stat axis is years - the 11 year Solar cycle is the likely culprit.

Kieren Diment said

at 10:39 pm on Aug 9, 2009

I don't actually understand the "IPCC claims which places CO2 forcing at 92% and Solar forcing at 8% relative to 1750AD in AR4 Fig 2.4" at all well, so I couldn't possibly have an opinon on who's right, you or the IPCC. I think if you start taking partial correlations, you might see something like the IPCC figures (i.e. solar forcing with the effect of co2 removed), but I'd have to remember where I put the figures.

ENSO affects weather globally. Obviously any honest analysis at the same time frame with similar data will come to the same conclusion, so it's not surprising that what I've done is in agreement with others.

"Otherwise cyclical CO2 and Temp can only mean Temp is rising AND falling with a continually rising CO2 - could this indicate that a CO2 saturation effect is occuring? The Co2 greenhouse gas absorber is not a one way window. It can gain Temp (heat) and lose Temp (heat) while steadily rising in concentration."

This comment has two problems. One is that it doesn't make much sense. Two, the long term trend is clearly rapid rise in temperature, as seen on the http://climatekaraoke.pbworks.com/Idiot page (second graph is much clearer) of greater magnitude than anything else over the past thousand years.

Finally need to acknowledge the potential positive feedback that we're seeing evidence for at the end of the time series. Failing to do so is being very selective with the results that you want to consider, and it's not good for your credibility.

kenlambert said

at 11:05 pm on Aug 9, 2009

This is from Summary for Policy Makers IPCC AR4:

Note that the FIG 2.4. from the Main Report has been re-named SPM2 in the Summary for Policymakers)

"The understanding of anthropogenic warming and
cooling infl uences on climate has improved since
the TAR, leading to very high confi dence7 that the
global average net effect of human activities since
1750 has been one of warming, with a radiative
forcing of +1.6 [+0.6 to +2.4] W m–2 (see Figure
SPM.2). {2.3., 6.5, 2.9}"

AND

• Changes in solar irradiance since 1750 are estimated
to cause a radiative forcing of +0.12 [+0.06 to +0.30]
W m–2, which is less than half the estimate given in the
TAR. {2.7}


Ref: http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_SPM.pdf

kenlambert said

at 11:07 pm on Aug 9, 2009

This is what PM Rudd and Minsiter Wong read before bedtime.

kenlambert said

at 11:51 pm on Aug 10, 2009

http://climate.envsci.rutgers.edu/pdf/StottEtAl.pdf

"Nevertheless, our main conclusion, that models underestimate
the climatic response to solar forcing, is
supported by two other detection studies that used diagnostics
tailored for the 11-yr solar cycle. Hill et al.
(2001) showed that models underestimate the tropospheric
temperature response to solar forcing by a factor
of 2 to 3 and North and Wu (2001) found an underestimate
of about 2 for near-surface temperatures.
These results indicate that climatic processes, not
present in the model, have acted to alter the magnitude
of the large-scale spatial and temporal near-surface temperature
response. Our methodology is not designed to
identify missing processes that alter small-scale details
of the response. Although our study indicates that there
could be an enhanced global-scale temperature response
to solar forcing, convincing evidence for a mechanism
remains elusive. Potentially the largest amplification of
solar forcing could result from modulation of stratospheric
ozone by variations in solar ultraviolet, which
could influence the troposphere via modulation of planetary
waves (Shindell et al. 1999b) or modulation of
the Hadley circulation (Haigh 1996), although none of
the published studies indicate that ozone feedback could
enhance solar radiative forcing by more than a factor
of one-half (J. D. Haigh 2003, personal communication).

...next half....

kenlambert said

at 11:52 pm on Aug 10, 2009

Alternatively, solar effects on climate could be mediated
by cosmic rays, the intensity of which has declined at
the earth as the interplanetary magnetic field increased
during the twentieth century. It has been speculated that
cosmic rays could modulate global temperature by
changing clouds (Marsh and Svensmark 2000; Yu 2002)
or by altering the global electric circuit (Harrison 2002).
The results presented here suggest that climate models
underestimate the sensitivity of the climate system to
changes in solar irradiance, but a conclusive demonstration
of an enhanced role for solar forcing requires
an understanding of the physical mechanisms underlying
such an effect.*

kenlambert said

at 11:58 pm on Aug 10, 2009

The above reference spun from your Wiki 'Solar' reference.

It splits the last 100 years into 1900 -1949 and 1950-1999 - gets Solar:GHG 53%/47% in the first half century and Solar at 16-36% in the secong half, but higher in the last 30 years?? Lots of regression analysis for you to compare.

Kieren Diment said

at 7:50 am on Aug 11, 2009

Apparently the cosmic ray theory is a furphy: http://en.wikipedia.org/wiki/Global_warming#Solar_variation

Kieren Diment said

at 7:51 am on Aug 11, 2009

Ken,

You still haven't touched my positive feedback theory. This is just about the most important and most relevant thing in this set of analysis, so I'm a bit shocked that you're totally ignoring it.

kenlambert said

at 10:09 pm on Aug 11, 2009

kdkd

I'm all ears Kieren. Fill us in on your feedback theory - show some references and describe a mechanism.

I note you have ignored my conclusive points about the misleading nature of IPCC AR4 'Radiative Forcings' - even you now can see that the contribution of Solar forcings has been very significant - up to 45% of the last 100 years warming, and 25-30% of the warming since approx 1980 using the IPCC's own source data.

Which puts us back into the cage fight and Crikey comments where I made the consistent point that the panic is all about the last 25-30 years of temperature data - the last 10 of which have flattened or cooled since the 1998 ENSO high peak and aftermath.

Here is what you say about doing a comprehensive forcing 1980-2008 run on AUG9:

*There's no point in doing a short time range of analysis of everything as the sample size is too small. We can already see that at a short term time range all of the short-term variability masks the long-term variability.*

You don't seem too keen on thououghly analysing the last 25-30 years - not enough data points - yet happy enough to accept the results when they appear to favour a CO2 answer.

See next post for an interesting comparison of the GISS and UAH data.

Kieren Diment said

at 10:42 pm on Aug 11, 2009

Ken: well the fact that these solar forcings are a. not independent of CO2 (as we see from the link function statistic), and b. this dependence has reduced in the past 20-odd years since CO2 has taken over as the main driver of temperature change "up to" (weasel words?) 45% reducing to 25-30%? There's evidence for a mechanism already.

The residual analysis clearly points to the existence of a positive feedback. Albedo, and methane production from melting tundra are both possible candidates.

If 1980-2008 data broadly suports existing conclusions, then there's no controversy (this is what we see for the most part, but with a lower signal to noise ratio). If it's in sharp contradiction to other data then we have a situation where we can make new hypothesis. Unfortunately for you, the meager inconsistencies with the rest of the data point to a positive feedback mechanism, not a negative feedback mechainsm.

kenlambert said

at 11:54 pm on Aug 11, 2009

I know it hurts to have that 45% Solar mentioned, but that is what your analysis produced paleface!! I won't use 'up to'........ just 'at'!

Check out the differences between UAH and GISS Temp Data here:

http://wattsupwiththat.com/2009/06/24/a-comphrehensive-comparison-of-giss-and-uah-global-temperature-data/

Check out Dutch alternative data sets here:

http://climexp.knmi.nl/selectfield_obs2.cgi?someone@somewhere

Show us some data for the Methane and Tundra Albedo effects and why the (Solar 11 year?) cyclical nature of these feedbacks which I assume comes from the signature of the residuals.

Kieren Diment said

at 7:51 am on Aug 12, 2009

Ken

There's a lot of wishful thinking going on in your commentary. Firstly the wattsup with that data doesn't support your conclusions unless you squint and ignore the statistical evidence.

It's not my job to find data, it's yours. You asked for a hypothesis, I gave you wan. You want proof, you find the data.

And the tempreature anomaly data at http://climexp.knmi.nl/selectfield_obs2.cgi seems quite consistent with the IPCC data. There is a lot of data there though, that's probably worth exploring. However, it's going to be a lot of work for you to corral it together in a coherent way for further analysis.

kenlambert said

at 12:21 am on Aug 13, 2009

I have proposed 6 Hypotheticals on JUL28 and 4 Propositions on AUG8. Are you going to find data for those?

I don't agree that the UAH Temp data is statistically consistent with the GISS data. I stick with the comments in the cage fight. The 1997-98 ENSO is a disruptive spike which has displaced a two relatively flat trends - and a linear trend line for the whole 30 year period is misleading.

Your consistent line that the CO2 + Solar underestimate Temp is still based on the IPCC-GISS Northern Hemisphere data. You ignored my points about SH being 65% of NH *trend* and probably less than linear. A global set of data should be used.

The variation in the sun's TSI is a combination of output and orbital proximity - not CO2 related.

You seem to still be unclear that Solar forcing is the variation in incoming radiation - not the portion absorbed by CO2 and other GHG (greenhouse effect variations in forcing).

The sun does not know that CO2 on Earth is increasing; so if the Solar forcing variation and CO2 forcing (log diff relationship) are cyclically related, it cannot be CO2 driven - it can only be Solar driven, can't it?? Any other explanation?

Kieren Diment said

at 12:34 am on Aug 13, 2009

Ken,

Disagree all about the consistency of UAH / GISS all you like. But your disagreement belongs in the faculty of making data up - it's not supported by the data.

Kieren Diment said

at 7:03 am on Aug 13, 2009

Ken

Or to be more clear about it. If you have specific objections to my interpretation of the UAH data cf the GISS data, which the statistics clearly and quantitatively show are comparable to each other, and statistically consistent, then you have to explain that objection clearly and quantitiatively. In my objective (in that the analysis is done without any reference to my preconceptions) quantitative analysis versus your qualitative analysis, my quantitative analysis wins every time.

Oh yeah. I don't have masses of time to deal with this stuff. If you want complex data analyzed, provide me with the tables.

kenlambert said

at 11:59 pm on Aug 13, 2009

I get an hour or two at night to indulge in saving the planet with you Kieren. The rest of the time I devote to my family and employing people, designing and exporting things.

I found and lost a website with a global set of Temp Anomaly data. Will keep looking for a realllycomprehensive set.

Meanwhile the UAH data seems to be 'flat' according to one of your "Idiot" associates. I am rather a fan of areas under curves and integrals as meaningful in measuring means and trends.

I would punt that by this method there are two flatish trend lines 1979-1996, and 1998-2009 split by a sharp spike of the 97-98 ENSO. Will see if we can look at Tamas' UAH excel data match on a site somewhere.

Meanwhile we need to look forward to the debate over whether the warming is likely to 'run-away' or is nothing we can do much about.

If you subscribe to the significance of the CO2 log diff forcing as the main driver of warming in the last 25-30 years, you should have a look at this paper;

http://wattsupwiththat.com/2009/08/08/how-sensitive-is-the-earth%e2%80%99s-climate/

This guy has thought about the issues of hindcasting before forecasting - and come up with a novel proof test.

Interestingly - he has assumed lower Solar forcing content than we have seen form the raw IPCC data sets, and placed most of the correlation on the CO2 log diff formula.

The conclusions are very interesting. The difference between 'do nothing', 'do sensible' and 'do crazy' are not very much out to 2060. Pretty much what I recommend - 'do sensible' and watch.

Kieren Diment said

at 8:48 am on Aug 14, 2009

The UAH data is not flat. It shows a positive trend. No amount of bending the truth can alter this. Wattsupwiththat has some difficulty with this as he asserts the trend since 2001 is flat, while it's just that month-to-month variability is greater than year-to-year variablity. Another decade or two of data would be required to debunk warming, and the model we've come back to here (with the consistent underestimate of temp anomaly at the end of the time series). The IPCC projections appear to take limited account of this, while Watt's projections don't. Therefore the conclusion is erroneous as it doesn't account for prediction error. QED.

kenlambert said

at 10:35 pm on Aug 17, 2009

Attached is the UAH Excel data kindly sent to me by Tamas. The trend since 2001 is clearly cooler.

Kieren Diment said

at 6:57 am on Aug 18, 2009

Ken,

It's not a trend, it's noise within a larger signal. You have to be particularly biased to interpret it otherwise.

The UAH data from 2001 is not a random walk either according to the PP test. But on the other hand, there is no statistically significant trend, using smothed data or otherwise, using the correct time series approach. Trying to measure a trend using unsmothed time-series data like this is dodgy anyway, as you need to correct for seasonal trends in order to ensure the "signal" is greater than the "noise". Internal seasonal trends over a short time series will mask all of the real trend without smothing.

You're clutching at straws. Better to get back to what you're good at.

Kieren Diment said

at 6:59 am on Aug 18, 2009

I dare say you could find many instances in the unsmoothed IPCC data over the past century where the trend has appeared to have stopped for a number of years. It doesn't affect the trend as a whole. In this case, the trend has (almost certainly temporarily) stopped at the end of the time series. The correct response isn't to claim that it's stopped, it's to await the arrival of more data.

kenlambert said

at 12:05 am on Aug 19, 2009

Well, let's wait for 10-15 years then - in the meantime do a sensible program like Ken Lambert's 10 point plan and watch what happens.

By the way you still have not explained the cyclical pattern in the Temp-CO2 residuals plot. Stubborn has pointed out that the time series variables are not iid. If that is the case, why would any of the forcing variables be iid?

Kieren Diment said

at 7:23 am on Aug 19, 2009

Well given that the uncertainty is not as great as you claim it is, and current observations of the consequences of warming sugggest that the uncertainty is positive (i.e. the consequences of warming are more serious than we thought Tamas' delusions notwithstanding), then waiting 10-15 years would be dangerous and stupid.

The cyclical pattern in the temp-co2 residuals plot is still much smaller than the pattern of overall warming (the association between co2 and warming), so that would be just an academic exercise.

Although the forcing variable generally increase over time, their measures of central tendancy (mean, standard deviation and standard error) are meaningful. The problem with the time series specifically is that the mean and standard deviation of time is not meaningful. Having an informative mean and SD are essentially the cornerstone of these kinds of inferrential statistics.

On a side note, if you treat time as a proxy for co2 level, and thus treat time as a rank, the iid problems disappear by statistical slight of hand, although you are then answering a different question.

Stubborn Mule said

at 8:35 am on Aug 19, 2009

Without the data, it's hard to test, but could the pattern be related to the aerosol CFC albedo effect?

Stubborn Mule said

at 8:39 am on Aug 19, 2009

I should add, that while the individual variables may not be iid, that doesn't mean you can't go a long way with relationships between the variables. With a model along the lines of

temp = function(forcings) + residuals

you could well have a situation where neither temp nor forcings were iid, but the residuals, in which case there is a lot you can say about the statistical confidence of the model. Looking at temp ~ CO2, the residuals clearly still have a pattern there, so while a significant percentage of the variance is accounted for in the regression, there's still something there in the residuals, which is not really surprising at all (and does not undermine the thesis that CO2 is pushing temperatures up).

Kieren Diment said

at 9:39 pm on Aug 19, 2009

And the proportion of the variance explained in the residuals is really quite small. And because we have a strong theoretical understanding of why co2 would cause the temperature to increase (the rather unassailable theory of chemical bonds), any significant co-dependent variables are likely modulated by co2. And because the residuals at the higher co2 concentrations are all negative (i.e. the model underestimates temperature), that's extremely strong evidence that the co-dependent variables are causing temperature to increase, not decrease - i.e. positive, not negative feedback.

Hence, not much point at looking at more variables in this forum, as it's a bit of an academic exercise, and while between stubborn and myself we have significant statistical (and some limited scientific) expertise, we lack the domain knowledge elsewhere.

But logical inference based on statistical theory will still get you a long way there.

Kieren Diment said

at 9:41 pm on Aug 19, 2009

Ken,

The non random distribution of the residuals at the higher co2 concentrations (which is also the end of the time series) is very very significant from a practical point of view, and we can use this information to draw strong conclusions. The fact that they also oscillate at this point is interesting, but much less significant, due to the reasons given above.

Stubborn Mule said

at 9:49 pm on Aug 19, 2009

Kieran: agree completely. Digging into the stats is interesting and revealing up to a certain point, but it is not done in a vacuum. It should be informed by the science as well and I would like to improve my own understanding of that science.

Kieren Diment said

at 9:54 pm on Aug 19, 2009

Stubborn, do you agree with me about the residuals as well? (just want an explicit conformation or denial, as Ken seems to be trying to ignore that particular bit of evidence).

kenlambert said

at 10:14 pm on Aug 19, 2009

Stubborn - here is a bit of info from the Satellite page: Might explain NH and SH Temp variations:

Ken Lambert at 11:02 pm on Aug 4, 2009


#2

With 90% of the Earth's ice in Antarctica, I would expect that the temperature response of the SH would be less linear than the NH. This is due to the roughly linear response of air and water with a constant specific heat ie. Delta F (Forcing) x Time = Delta T x Mass x Sh (specific heat constant) ....Eqan 2

ie; Delta T = Delta F x Time /Mass x Sh - a linear relationship for constant mass, time, Sh.

In the SH, ice is involved in significant quantity - it undergoes a phase change (melts) without increase in temperature – a very non-linear response........

Delta F x time = Mass x S.lat (latent heat of fusion of ice) ….Eqan 3

S.lat = 334 kJ/kG of ice. Sh water = 4.2kJ/kG-degC and Sh ice = 2.1kJ/kG-degC

Melting 1 kG of ice absorbs the same energy as raising the temperature of 1 kG of water by 79.5 degC or 1 kG of ice (below zero) by 159 degC.

So melting ice absorbs about 80 times the energy as raising the temp of water by 1 degC .

kenlambert said

at 10:28 pm on Aug 19, 2009

AND:

"Only forcing data on aerosols I could find is from NASA/GISS (Hansen et al) Graph (b) 1850 - 2000AD”

viz; http://data.giss.nasa.gov/modelforce/trop.aer/"

#5 Don't think you understand that the Solar forcing *IS* the *variation* in INCOMING Solar Radiation which averages out at about 341 W/sq.m. (see my JUL26 and JUL28 posts).

(Remember that INCOMING Solar Radiation is TIS divided by 4 (1366/4 = 341.5 W/sq.m).)

The overall forcing balance equation for the Earth is:

(F.incoming solar at about 341W/sq.m) = (F.reflected by cloud and surface albedo at about 102 W/sq.m) + (F. outgoing longwave radiation at about 239 W/sq.m): Eqan 1

The imbalance forcings which are supposed to be heating the Earth can be taken from the above three broad terms. (Which we have postulated before ie:

Delta T (anomaly) = function (F.co2 + F.ghg + F.ozone + F.surfalbedo + F.diraerosol + F.cloudaerosol + F.solar) where these are the *VARIATIONS* in these forcing values.)

See a short explanation for the above by Kevin E. Trenberth viz:

http://www.aps.org/units/fps/newsletters/200904/trenberth.cfm

#6 kdkd "I suggest that the solar figures presented by the IPCC are solar input from the atmosphere" - this does not make sense. Go and read Trenberth and understand.

kenlambert said

at 10:31 pm on Aug 19, 2009

Stubborn:

Tis might help your understanding of "Forcings":

The overall forcing balance equation for the Earth is:

(F.incoming solar at about 341W/sq.m) = (F.reflected by cloud and surface albedo at about 102 W/sq.m) + (F. outgoing longwave radiation at about 239 W/sq.m): Eqan 1

The imbalance forcings which are supposed to be heating the Earth can be taken from the above three broad terms. (Which we have postulated before ie:

Delta T (anomaly) = function (F.co2 + F.ghg + F.ozone + F.surfalbedo + F.diraerosol + F.cloudaerosol + F.solar) where these are the *VARIATIONS* in these forcing values.)

kenlambert said

at 10:40 pm on Aug 19, 2009

Kieren - if you want to get a truly global set of data these are the Hadley Sea surface Temps 1850-2008.

http://hadobs.metoffice.com/hadsst2/

AND

These are the combined Land and Sea set:

http://hadobs.metoffice.com/hadcrut3/index.html

Best run these in preference to your NH set only.

Kieren Diment said

at 10:48 pm on Aug 19, 2009

Ken, OK, you're not avoiding the karaoke. I'll grab that data and look at it as time allows. Busy reshaping the health industry to be more efficient and meet end-user's needs this week, so my time is rather limited.

Kieren Diment said

at 10:55 pm on Aug 19, 2009

Ken, re your magical "complete model". We already know that co2 is explaining the majority of the variance in the system, and that there are extremely theoretically sound reasons for this. Therefore all other factors are of limited relevance, and given that their variation is much less sytematic, will not be driving the clear increase in the anomaly. So of course it's academically interesting, but it's highly unlikely to alter the outcome of the to-everybody-except-you-and-tamas settled debate about the role of co2 and the warming projections.

Again you're ignoring the negative residuals at the highest co2 concentrations. These are extremely important and must not be ignored, otherwise you can't understand the model properly. Positive feedback, not negative feedback. I'll try to check to see if the hadley data supports this.

kenlambert said

at 11:01 pm on Aug 19, 2009

"Ken,

The non random distribution of the residuals at the higher co2 concentrations (which is also the end of the time series) is very very significant from a practical point of view, and we can use this information to draw strong conclusions. The fact that they also oscillate at this point is interesting, but much less significant, due to the reasons given above."

The residuals are negative cyclical Yes?

The negative could be explained by the fact that you have used only NH Temperatures with steeper trend (3.27 times steeper than the SH trend - and the non-linear ice factor.

The cyclical roughly follows the 11 year Solar cycle which is supposed to deliver approx 0.35W/sq.m (0.1% variation of 341W/sq.m incoming Solar Insolation over the surface of the Earth).


VIZ: (F.incoming solar at about 341W/sq.m) = (F.reflected by cloud and surface albedo at about 102 W/sq.m) + (F. outgoing longwave radiation at about 239 W/sq.m): Eqan 1

Any of the above three broad terms of the Earth's energy balance Eqan can have variations which will produce a net heating or cooling.

"F.outgoing" is longwave radiation is where CO2 and other GHG plays the absorbing role. We know about "F.incoming" Solar variation as above, and your modelling has not considered "F.reflected" - by aerosols (cloud ) and surface albedo.

Now tell me which of the three broad terms would have cyclical variations on an 11 year cycle? Could be all three?

Kieren Diment said

at 11:06 pm on Aug 19, 2009

Yes, there's a fair bit of code to write to make that data into something amenable to this type of analysis, but it's doable, but it'll take me a week or so to get around to it ...

kenlambert said

at 11:07 pm on Aug 19, 2009

If you are going to say "CO2 feedbacks" then explain why Temp goes up AND down against the steadily rising CO2 - positive feedbacks would reinforce an UP direction in Temp only - YES? (ignoring seasonal variation of course)

Kieren Diment said

at 7:35 am on Aug 20, 2009

Ken, you're right, temperature is always variable, it has short term variation as well as the long term trend. But when we PREDICT temperature from co2 and other factors, the residual (what's left over, the error) is always negative - that is the model is consistently UNDERESTIMATING temperature at the highest co2 concentrations. So this is indeed strong evidence that "positive feedbacks would reinforce an UP direction in Temp only".

You can't eliminate the noise from any system, you have to live with it, so it's unreasonable to expect zero random error. Here we see significant random error, but we also see substantial systematic error as well, and it's the latter that allows us to draw conclusions.

Kieren Diment said

at 7:38 am on Aug 20, 2009

So the cyclical nature of the residuals are a separate thing from them being smaller. But they still don't alter the fact that they're persistently underestimating anomaly.

I would expect this tendency to be damped in the southern hemisphere. I suppose once I can beat the hadley data into shape we can look at this, but it will take a bit of time to do.

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