Climate Audit

Ian Castles

Re #2. True. In fact the GISS observations (“Table of global-mean monthly, annual and seasonal land-ocean temperature index”) show mean temperature in the first seven months of 2006 as 0.10° C lower than in the corresponding months of 2005. That’s a big decrease – half the size of the cells in the vertical grid in Figs. 1 & 2.

Phil B.

Recently, on the Discovery Channel here in the states, there was a program with Tom Brokaw called “What you need to know about Climate Change”. Tom interviewed Jim Hansen and during that interview, Hansen essentially stated without any caveats that the (his team?) modeling predicted that half the world’s species would be extinct by the turn of the century. Tom nodded knowingly and said nothing. I didn’t tape the show, so I am paraphrasing what Hansen said, but it appears that Jim has “moved on” in his modeling.

joshua corning

Just for good due dillegance purposes what is the HADCRUT3 and why did you choose it?

Willis Eschenbach

Re #5, Phil, thanks for the posting, wherein you note that:

Hansen essentially stated without any caveats that the (his team?) modeling predicted that half the world’s species would be extinct by the turn of the century.

These predictions of extinctions are among the most bogus forecasts arising out of the models, although they originally came, not from the models, but from estimates of tropical deforestation.

I wrote a paper on this subject which is available here. I found when researching the subject that there have been very few bird or mammal extinctions on the continents “¢’‚¬? only nine in the last 500 years, six birds and three mammals. This was a great surprise to me, with all of the hype I expected many more.

In any case, my paper shows that there has been no increase in extinctions … have a read, it’s an interesting paper.

w.

MarkR

Re#10 The graphic you show still appears to have observed temperatures starting higher than model temperatures by about 0.1C, enough to bring the smoothed line of the observable temperature to below the zero emissions plot.

Dan Hughes

The observed and calculated initial values will be the same only if the calculated value equals the observed value. Clearly this is not the case. Additionally, the calculated initial values for the Global Average Temperature (GAT) anomalies could be determined in at least two different ways. The first would be the difference between the calculated ensemble-average (GAT)ea at the end of the control runs and the individual (GAT)cj values; these would all be different The second would be the difference between the individual model/code (GAT)cj values at the end of the control runs and its (GAT)cj; and so would be 0.0.

One of many questions is should the initial values on the graph be shifted so as to correspond? If it is shifted then the graph does not represent the actual results of the calculations. And if the calculations had used the value corresponding to the shifted value the calculated response would have been different.

Whatever the case, it seems to me that only the very, very rough trends of the calculations are the same as the observations; a very long-term increase. And even that doesn’t look so hot to me. The variability shown in the observations is not at all captured, even over periods of a decade. What then are the effects of this clearly evident lack of agreement on the calculated responses of local environmental, social, and health issues such as biomass, long-range weather, ice, ocean temperatures, etc.

Finally, someone has noted that some (GAT) calculations are done with the sea surface temperatures fixed. Given the recent observations on the changes in the energy content of the oceans, this does not seem to be a good assumption.

David Smith

What would a plot, of A,B,C, HADCRUT3 and GISS, zeroed in 1988 as noted, look like?

It would be nice to understand why the two sets of observations (GISS and HADCRUT3) differ.

Tim Lambert

HADCRUT3 measures the anomaly from the 1961-1990 mean, while Hansen’s scenarios used the anomaly from the 1951-1980 mean. The 1961-1990 mean is higher than the 1951-1980 mean. Furthermore, Willis has not plotted HADCRUT3 accurately – all his numbers are too low by about 0.05 degrees.

When you compare apples with apples and not Willis’s oranges, Hansen’s model has been eerily correct.

David Smith

An interesting chart would be to average each data set over, say, five-year periods, and, using 1959-63 as the zero point, see what a combined plot looks like.

I would do this but I cannot read the data points on the graphs very well.

The data groups would be updated GISS, HADCRUT3, scenarioA, scenarioB and scenarioC.

I tried this for 1985-89 and 2000-2004 and got actuals running a bit below scenarioC (the no-CO2-growth scenario). But, again it is hard to read the points.

per

I have plotted out giss, hadcrut and crutem, and the difference between giss and the two hadley datasets. There is a bigger difference opening up between giss and hadcrut, presumably because giss and crutem are just over land, whereas hadcrut includes sea temperatures.
I have posted the graphic on to steve if he wants to incorporate it.
yours
per

Willis Eschenbach

Re # 17, Tim, thanks for your contribution. You say:

HADCRUT3 measures the anomaly from the 1961-1990 mean, while Hansen’s scenarios used the anomaly from the 1951-1980 mean. The 1961-1990 mean is higher than the 1951-1980 mean. Furthermore, Willis has not plotted HADCRUT3 accurately – all his numbers are too low by about 0.05 degrees.

When you compare apples with apples and not Willis’s oranges, Hansen’s model has been eerily correct.

As I stated very clearly, I have not plotted the HadCRUT3 data inaccurately. Instead, I have started the observational data at the same place the scenarios start. You could say this puts the HadCRUT data too low … or you could say that puts the scenarios too low … but if you want to compare them, you have to start everyone off at the same place.

Otherwise, you could just pick your offset to suit your purposes, as Hansen has done. To compare apples with apples means that we start everyone out at the same temperature, and see where the observations and the scenarios go from there. That is what I have done.

Remember, these are anomalies, not actual temperatures. The starting point is arbitrary. We are interested in comparing the trends, not the absolute values, and to do that, we need to start all of them from the same point.

This is implicitly shown by the fact that all three scenarios start from the same identical temperature. If your analysis were correct, Tim, they would all start from different temperatures. Hansen is the one comparing apples and oranges, by starting off from a much warmer temperature than the scenarios.

w.

Willis Eschenbach

Re #11, per, you say:

if the prediction was published in 1988,it is woth noting that the temperatures for the three scenarios and the giss data seem to be quite close in 1988.

No, it means nothing, because the model is tuned to reproduce that data.

w.

per

No, it means nothing, because the model is tuned to reproduce that data

I do not know how Hansen zeroed his predictions, and the giss data set. If there are facts here, I welcome them. What I was suggesting was that Hansen set the zero and the models to be very close in 1988, which is when the prediction was made. I am not suggesting that “means anything”, merely this is what his zeroing convention might be.

yours
per

Roger Pielke, Jr.

All- We discussed this over on our blog a few months ago. Hansen himself has admitted that his 1988 predictions of climate forcings overshot, hence so too did his temperature predictions. This is obvious from Figures 5A and B in this publication by Hansen et al.:

Click to access 1998_Hansen_etal_1.pdf

Hansen reissued his 1988 preditions in the 1999 paper, because they overshot (otherwise why resissue them!). As well it looks like (to date at least) that his 1999 updated predictions have also overshot in terms of predicted change in aggregate forcings, though it is very early for such judgments.

When evaluating predictions it is not enough to look only at the predicted temperature change, but also predictions for changes in various components of climate forcings that enter into the prediction. A good prediction will get the right answer and for the right reasons.

John A

Hansen reissued his 1988 preditions in the 1999 paper, because they overshot (otherwise why resissue them!). As well it looks like (to date at least) that his 1999 updated predictions have also overshot in terms of predicted change in aggregate forcings, though it is very early for such judgments.

Will we have to wait until 2009 before Hansen admits that he’s been flat wrong for all of this time?

Willis Eschenbach

Per, thanks for the observation where you say:

I do not know how Hansen zeroed his predictions, and the giss data set. If there are facts here, I welcome them. What I was suggesting was that Hansen set the zero and the models to be very close in 1988, which is when the prediction was made. I am not suggesting that “means anything”, merely this is what his zeroing convention might be.

However, examination of the chart shows that the three scenarios are far apart in 1988, and are the same in 1958. This agrees with the reference given by Roger Pielke Jr. above, which shows that Hansens’ forcings start out together in 1958, and diverge from there.

Thus, we need to start our comparison with observations in 1958.

w.

Steve McIntyre

Here is

John Creighton

#135 I bet time series work better then computer models because we have a better grasp of what the confidence intervals are for the predictions and we are less likely to make a coding error.

Kenneth Blumenfeld

I have glanced at (and I mean that literally,

Kenneth Blumenfeld

Willis,

If the temperature baseline is from a climate normals period, then there is no reason that the delta-T for the first observation should be zero. It would simply be the difference between the observed value and the climate normals value (in the case of 1958, it is positive).

Your methodology only makes sense if the delta-t is with respect to 1958. Note that I am not saying that it is or is not. All I am saying is before you go changing a graph, you should be absolutely certain that you understand the context of it. I am admitting I do not; do you?

Tim Ball

#22 Willis
You quote me but it is not anything I said in #17.

Willis Eschenbach

I got to thinking about the Hansen scenarios, and I thought I’d compare their statistics to the actual observations.

One of the comparisons we can make regards the year-to-year change in temperature. The climate models are supposed to reproduce the basic climate metrics, and the average year-to-year change in temperature is an important one. Here are the results:

These are “boxplots”. The dark horizontal line is the median, the notches represent the 95% confidence intervals on the medians, the box heights show the interquartile ranges, the whiskers show the data extent, and the circles are outliers.

It is obvious that the “Scenarios” do a very poor job at reproducing the year-to-year changes of the real world. Whether or not they can reproduce the trend (they don’t, but that’s a separate question), they do not reproduce the basic changes of the climate system. They should be disqualified on that basis alone.

w.

Willis Eschenbach

Re 43, David Smith, I appreciate your contributions. You ask:

Besides all of that, I have wondered how the models were able to predict a multi-year dip in temperatures around 1964 which came true. That is remarkable. Perhaps it is just chance.

The answer, of course, is that up until 1988 the models were tuned to the reality. It is only for the post-1988 period that they are actually forecasting rather than hindcasting.

I just noted another oddity about the scenarios versus the data. The lag-1 autocorrelation of the scenarios is incredibly high:

GISTEMP       0.79
HadCRUT3       0.82

Scenario A       0.98
Scenario B        0.96
Scenario Càƒ‚⠠     0.94

I remind everyone that the modeler’s claim is that they don’t need to reproduce the actual decadal swings, that it is enough to reproduce the statistical parameters of the climate system. To quote again from Alan Thorpe:

However the key is that climate predictions only require the average and statistics of the weather states to be described correctly and not their particular sequencing.

In this case, they’ve done a very poor job at describing the average and statistics …

w.

Michael Jankowski

Re#10-Here’s one I found some time ago – C or B I’d say.

and Re#21 –

Re #20 To me, the chart presented by Hansen, taken at a glance, indicates that temperature rises are running at about a scenario B rate, indicating the models have it “about right”.

So you are picking the “correct” model scenario(s) based on the results? That’s inappropriate. The “correct” scenario is the one which meets the scenario assumption criteria, not the one that most closely matches the observed results. One has to take the scenario A, B, or C which has occurred and compare those model results with the observed temperature.

So the questions is…which greenhouse growth scenario has most closely occurred since 1988 – A, B, or C? That’s the ONLY scenario that should be compared to the observations.
RE#14-

If the model runs start in 1958?, then the observed temperature data trend should start at 0 in 1958 and so should the models.

However, it is possible that the model runs actually start earlier than 1958 (where the temperature trend started at 0 initially as well) but Hansen did not show the earlier than 1958 simulations and observations.

I’m curious how the pre-1988 results look.

Other posters here have argued for/zeroes observed values to match the model predictions of 1988, and I think that’s valid – especially since the y-axis is not T but delta T.

jae

Bender and others ragged me so much about overfitting that I think I finally understand it. And it looks to me like these models are just a very complex type of overfitting. If you have to change a model every few years to reflect reality, then it seems to me that you definitely are engaging in overfitting. If the model stands the test of time, then maybe you are on to something.

Gerhard W.

One question:
How do the contributions of Thomas R. Karl and Patrick J. Michaels from the 2002 U.S. National Climate Change Assessment: “Do the Climate Models Project a Useful Picture of Regional Climate?” fit into this picture? The link to the hearing was recently posted here, but there were no comments…
~ghw

Francois Ouellette

#54 Willis, the r^2 is a bit unfair. B gets low r^2 because it’s in antiphase with observations, but it still the closest to obs. The problem is that observations include stuff such as the Pinatubo eruption and the anomalous 1998 ElNino that cannot be predicted by the models (maybe eventually ElNino, but not volcanic eruptions). Wouldn’t a better comparison use the linear trends from the 3 scenarios r-squared with observations? What is typically used as a measure of model skill?

#51 you make an interesting point. If the models are changed all the time, then we can never really know if they are “better” than the previous versions. The skill of the model is in predicting the unknown, not reproducing the known. One could then argue that we never know if we are “improving” the models or not. That’s a kind of fundamental philosophical argument against models, similar to what Hank Tennekes did, following Karl Popper.

Does anyone know how many parameters are needed to “tune” the model? An ideal model would have no free parameter. Can we evaluate the skill of a model by how few free parameters it has?

Willis Eschenbach

RE 55, you ask, “how many parameters are needed to “tune” the model? An ideal model would have no free parameter.”

I am reminded of Freeman Dyson’s story of taking his results to Enrico Fermi for evaluation:

. . .[Fermi] delivered his verdict in a quiet, even voice: “There are two ways of doing calculations in theoretical physics”, he said. “One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither.”

. . .”To reach your calculated results, you had to introduce arbitrary cut-off procedures that are not based either on solid physics or on solid mathematics.” In desperation, I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. “How many arbitrary parameters did you use for your calculations?” I thought for a moment about our cut-off procedures and said “Four.” He said “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” With that, the conversation was over.

So yes, the models can reproduce the past, and the elephant can wiggle his trunk …

w.

Willis Eschenbach

Re 56, Francois, thanks for your questions. You say:

Willis, the r^2 is a bit unfair. B gets low r^2 because it’s in antiphase with observations, but it still the closest to obs. The problem is that observations include stuff such as the Pinatubo eruption and the anomalous 1998 ElNino that cannot be predicted by the models (maybe eventually ElNino, but not volcanic eruptions). Wouldn’t a better comparison use the linear trends from the 3 scenarios r-squared with observations? What is typically used as a measure of model skill?

Actually, the scenarios include random volcanic eruption, but you are right regarding the general effect of unpredictable future events. As a full-service thread, I will show the results, but I don’t put too much stock in them. Why? Because:

1) the models are supposed to do better than just a straight-line trend … otherwise, why have models? and

2) it’s quite possible, especially when we reduce a complex situation (climate changes) to one single number (trend per decade), to get the right answer for the wrong reasons. I have already shown that the models are far from lifelike, in that their year-to-year changes in temperature are much smaller than reality. They are very poor at modeling the statistics of the climate.

Given all that, here’s the trends and the RMS error:

The RMS errors are:

Scenario A RMS = 1.05°C
Scenario A RMS = 0.44°C
Scenario A RMS = 0.56°C
Extended 1979-1988 trend: RMS = 0.48°C

Note that despite the claim by Hansen that the scenarios should give the range of possibilities, the trend line of the observations is below the trend line of all of the scenarios.

w.

Steve McIntyre

Willis, can you post up some of the digital series for these models so that people can do simple time series work on them. Also what the url is for the source of the digital version. Thx

Willis Eschenbach

Re 61, Steve M., here’s the data. There’s no URL, these guys rarely publish their results, it is digitized from the Hansen graph. It was then checked by using Excel to generate graphs of the digitized data, then overlaying those graphs on the original Hansen graph to make sure there are no errors. I’ve done this data comma delimited, to make it easy to import into Excel or R. The GISTEMP and HadCRUT3 data has been aligned at the start with the three scenarios.

Year,GISTEMP,HadCRUT3,Scenario A,Scenario B,Scenario C
1958,-0.030,-0.030,-0.030,-0.030,-0.030
1959,-0.050,-0.090,-0.005,-0.065,-0.065
1960,-0.120,-0.140,-0.020,0.075,0.075
1961,-0.030,-0.040,-0.005,0.030,0.030
1962,-0.070,-0.040,-0.005,0.010,0.010
1963,-0.030,-0.020,-0.090,-0.085,-0.085
1964,-0.320,-0.320,-0.165,-0.165,-0.165
1965,-0.220,-0.240,-0.110,-0.165,-0.165
1966,-0.140,-0.170,-0.045,-0.130,-0.130
1967,-0.110,-0.170,-0.035,-0.095,-0.095
1968,-0.150,-0.180,0.000,-0.070,-0.070
1969,-0.030,-0.030,-0.090,-0.105,-0.105
1970,-0.080,-0.090,0.045,0.040,0.040
1971,-0.210,-0.210,0.050,-0.035,-0.035
1972,-0.110,-0.080,0.125,0.060,0.060
1973,0.030,0.060,0.175,0.200,0.200
1974,-0.190,-0.230,0.217,0.130,0.130
1975,-0.160,-0.190,0.075,0.075,0.075
1976,-0.270,-0.270,0.213,0.100,0.100
1977,0.020,0.000,0.140,0.120,0.120
1978,-0.090,-0.080,0.209,0.070,0.070
1979,-0.020,0.030,0.250,0.110,0.110
1980,0.070,0.060,0.320,0.150,0.065
1981,0.160,0.100,0.380,0.140,0.105
1982,-0.060,-0.010,0.320,0.090,0.085
1983,0.150,0.160,0.105,-0.055,-0.145
1984,-0.020,-0.040,0.065,0.045,-0.005
1985,-0.050,-0.060,0.215,0.175,0.060
1986,0.020,0.010,0.275,0.270,0.120
1987,0.160,0.160,0.400,0.280,0.125
1988,0.200,0.160,0.440,0.345,0.221
1989,0.080,0.080,0.425,0.390,0.325
1990,0.270,0.230,0.495,0.435,0.325
1991,0.240,0.190,0.495,0.400,0.355
1992,0.020,0.040,0.505,0.455,0.350
1993,0.030,0.090,0.640,0.440,0.335
1994,0.130,0.150,0.680,0.445,0.305
1995,0.270,0.250,0.710,0.405,0.335
1996,0.190,0.120,0.860,0.275,0.213
1997,0.290,0.330,0.860,0.305,0.365
1998,0.460,0.530,0.925,0.395,0.410
1999,0.210,0.280,0.915,0.525,0.435
2000,0.220,0.250,0.820,0.560,0.515
2001,0.370,0.390,0.855,0.645,0.515
2002,0.450,0.440,0.940,0.610,0.540
2003,0.440,0.450,0.905,0.675,0.555
2004,0.380,0.420,0.955,0.725,0.510
2005,0.520,0.450,1.025,0.695,0.630

My best to everyone, have fun,

w.

Paul Penrose

Remember the old saw “All models are wrong; some models are useful”. But that begs the question “Useful for what?” I think for pure research, to try to ferret out all the complexities of the physics of climate and weather, the GCMs (and the coupled versions) are interesting and probably useful. For the purpose of trying to say something meaningful about the future state of the climate, either locally or globally, they are pretty much useless.

Just think about the initial conditions problem: these models compute the flow of heat (flux) through the different layers of a gas (or liquid for the oceans) and try to account for the mixing of the different layers, etc. They do this by breaking up the surface of the planet into cells, and the newest ones slice these cells vertically as well. Now before they can start a model run they need to seed all the cells with data, but how do they know what the right values are for any particular starting point in time? There’s a lot of data for each cell, and most of it must be in the form of a vector – for example it’s not good enough to just know how much heat is in a cell, you have to keep track of which direction it is flowing in. As complex as these models are it would seem to me that even small changes in the initial conditions could change the outcome drastically.

The flux adjustment issue is a whole other can of worms. Some modelers believe that the drift they are seeing in the outputs are caused by fundimental erros in the models, with improper cloud modeling at the top of the suspect list. Others think that the model resolution is just too low and the drift is a consequence of subtle data-losses that accumulate over simulation time. Newer, faster computers will solve the problem they think. Either way, this problem introduces unknown, and maybe unknowable errors into the results.

I won’t even go into the Linearity Assumption and whether it can even be proven; the known problems with the models already show why the results should not be quoted outside the lab.

Finally, Jae is right. Comparing these model outputs to observation is a massive exercise in overfitting.

Mark T.

Proving a climate model even with a 0.6 Celsius error that accumulated in four decades requires a really skillful scientist.

Proving even the 0.6 C is problematic when your error is +/- 1.0 C at best.

Mark

bender

That is a great quote, and I was going to mention it in the “overfitting”” discussion with jae … along with another one by a French mathematician (who escapes my memory): “give me enough parameters and I will give you a universe”. Unfortunately, that’s a paraphrase. I couldn’t track down the original.

Bob K

re #60
Pat,
To my knowledge uncertainty in values isn’t quantified by them. They do say they have three values available for use with each of their 34 parameters. I got the impression they have low, medium and high values for each. Sort of like an electric stove. These parameters don’t even cover the external forcings. I don’t know how they handle them.

Had a discussion in a previous thread with a fellow named Carl that works for CP.net. Found here. http://www.climateaudit.org/?p=635#comments
Starting around comment #174. He wasn’t at all helpful in answering questions. Although he did post a link to this letter they had in Nature.

Click to access nature_first_results.pdf

I’m not the sharpest tack in the box, since my formal education ended with HS in the mid 60’s. But I critiqued it and found it to be extremely biased in their selection of model runs to discard. Essentially almost all that showed negative temps in the training period.

John Creighton

I think the parameters in the model should not be identified by using the computer model to find the best fit as the computer model are far too complex. Things like cloud feed back can be estimated from satellite and instrumental data. I assume other experiments could be done to describe the various energy exchanges between phases of mater. As for fitting the initial conditions I would recommend using Bayesian probability. We have some prior idea of the probability of the initial states p(a) based on principles like maximum entropy. We have a set of measurements b we want to find the expectation of a given the distribution p(a,b)=p(b|a)p(a).

bender

In financial forecasting, there is always a reckoning when the out-of-sample validation test data come in. A judgement day, if you will. The pain on that day is palpable. In climate modeling science, do you know what they do to avoid that judgement day? They “move on“.

Willis Eschenbach

Re # 70, Francois, because the models are tuned (not to mention overfitted) to the past trends, how well they do in replicating the past trends is meaningless.

However, there are a number of other measures that we can use to determine how well the models are doing, measures to which they are not tuned. See for example my post #45 in this thread, which examined the models perfomance regarding ‘ˆ’€ T, the monthly change in temperature. That analysis made it clear that Hansen’s model did not hindcast anywhere near the natural range of temperatures.

Other valuable measures include the skew, kurtosis, normality, autocorrelation, and second derivatives (‘ˆ’€ ‘ˆ’€ T) of the temperature datasets. Natural temperatures tend to have negative kurtosis (they are “fat tailed”, for example. Let me go calculate the Hansen data … I’m going out on a limb with this prediction, I haven’t done the calculations before on this …OK, here it is. From the detrended datasets, we find the kurtosis to be:

GISTEMP , -0.85
HadCRUT3 , -0.50
Scenario A , 0.68
Scenario B , 0.15
Scenario C , 1.14

You see what I mean, that although the models are tuned to duplicate the trend, they do not replicate the actual characteristics of the natural world. In this case, unlike natural data, the scenarios all exhibit positive kurtosis.

Re the comment that a “30 year trend” should be used instead of lining up the starting points … why 30 years? Why not 10, or 35? Each one will give you a different answer. It seems to me that the answer we are looking for is “where will we be in X years from date Y?” To find that out, we have to line up starting points at date Y.

But first, we’d have to have models that I call “lifelike”, that is to say, models whose results stand and move and turn like the real data does, they match observations in kurtosis, and average and standard deviation of ‘ˆ’€ T, and a bunch of other measures. Then we need models that don’t have parameters and flux adjustments to keep them in line.

At that point, we can talk about starting points and thirty year averages. Until then, the models are only valuable in the lab in limited situations.

w.

Jeff Norman

Just an observation. Willis quoted the original article as saying:

Scenarios B and C also included occasional large volcanic eruptions, while scenario A did not.

If I recall correctly, since Pinatubo in 1991 there haven’t been any large volcanic eruptions. This suggests again that perhaps the AGW forcing is overstated in the model(s).

Pat Frank

#65 — another can of worms to add to your list, Paul, is that the data calls in the GCMs, while running a simulation, can act like a periodicity in climate and end up accelerating some momenta artifactually. I remember reading a paper warning about this a while back.

#71 — Thanks for your thoughts, Bob. I recall Carl from ClimatePrediction. Calling him ‘non-helpful’ is granting him far too much grace. As I recall, Willis critiqued the CP Nature paper here in CA. After that crushing expose’, it was easy to see the paper was worthless. It then became more easy to conceptualize something that had been bothering me in a visceral sort of way, namely that Nature isn’t really a science journal. It’s an editorializing magazine specializing in science and its more expert imitators.

Robert G. Brown

Very interesting thread — I’ve been studying the global warming issue some time as something of a hobby and am continually struck by the utter lack of appreciation for the essential variability of global climate as best as we can determine it from paleontological records over very long time scales. Ice ages. Drought and desert. Humans not present at all for most of it.

The data presented above is of course a snapshot of the merest flicker of time. It correlates well with almost any upwardly trended number (with suitable one or two parameter adjustment) — the rate of growth in the GDP, for example. However, correlation is not causality is a standard adage of statistics.

Correlation can make one think of causality, however. The most plausible explanation I have seen for climate variations over time periods of centuries has to be that given here:

http://www.john-daly.com/solar/solar.htm

There is lovely and (I think) compelling correlation between various direct and proxy measures of solar activity stretching back over at least 1000 years and historical records of temperature including the medieval optimum. To me the most interesting thing about it (and the reason that I bring it up now) is that it is pretty much the only single predictor that very clearly reproduces the “bobble” in temperatures that occurred in the 50’s through the 70’s, that provoked doom-and-gloom warnings at that time not of global warming but of the impending Ice Age!

Figure 3 is a pretty picture of the trend through the late 80’s — I don’t know of anyone that has extended the result out through the present although that would clearly be a useful thing to do. Plots like this, either lagged 3-5 years or otherwise smoothed, exhibit correlations in the 0.9 and up range, including all the significant variations. I have no idea what goes into the multiparameter fits like Hansen’s, but a one parameter fit that beats them hands down over a far longer time scale is obviously a much better candidate for a causal connection.

Beyond the statistics, I have to say (as a physicist) that I find solar dynamics to be an appealing dynamical mechanism for climate variation as well. To begin with, I’m far from convinced that the physics of the greenhouse effect for CO_2 supports a linear relationship between CO_2 concentration and heat trapping. Is an actual greenhouse with thick glass panes better at trapping radiation than one with thin ones? I think not, and that isn’t even considering the quantum mechanics (where the efficiency of CO_2 as a greenhouse gas actually drops with as the mean temperature of the blackbody radiator rises and shifts the curve peak away from the relevant resonances, as I understand it).

Then there is the monotonic increase of CO_2 over hundreds of years but the clearly visible and significant variations in temperature with no observed fluctuation correlations with this trend. Clearly CO_2 can be no more than
a factor in global temperature, and equally clearly solar irradiance variations must be another. Of course that leaves one requiring a two or more parameter fit, and one can either make CO_2 dominant (and explain the fluctuations with solar irradiance) or make solar irradiance dominant (and throw the CO_2 contribution out all together). Occam would prefer the latter, but the former could be right, if one looks at only 200 years of data.

If you look all the way back one to two thousand years, however, then things like accurate estimations of global temperature become paramount. CO_2 from human sources (at least — there are many sources of CO_2 and it isn’t clear that the dynamics of CO_2 itself in the ecosystem is well understood or entirely predictable) was clearly negligible over most of this time, yet historically there appear to have been periods when the temperature was as high as it is today if not higher.

Finally there is the nastiness of politics. I’ve just finished reading the papers that absolutely shred the statistical analysis behind the “approved” view of global warming with its “hockey stick” end and shoddy (and dare I say ignorant) statistical methodology. This isn’t science — this is about money, getting votes, saving rain forests, pursuing secondary agendas. Science is an open process, and one that doesn’t tailor results and ignore (or worse, hide in a mistreatment of a dizzying array of numbers) “inconvenient” truths — like the fact that an unbiased examination of global temperatures over long time scales suggests that our current climate is “nothing special”

Dino

Would you care to comment on this?

http://tinyurl.com/rrbdt

Someone seems to think you are doctoring the data.

KevinUK

#83 RB

Can I ask how and where you started your research on AGW and what caused you to look into it in the first place? It sounds like you’ve had a similar experience to me. In my case Tim Lambert’s dissing of someone who I respect caused me to wonder whether there was something not quite right and sure enough (as you’ve seen for yourself) it isn’t. Like me, I hope you have lots of friends who are also scientists and engineers. Are any of them also waking up to the poor science that underpins the AGW myth?

KevinUK

jae

Another example of the models not reflecting past reality.

Willis Eschenbach

Re #89, Eli, thank you for your posting. Among other points which I will answer when time permits, you say:

Finally, per has a good point. HadCrut3 includes sea surface temperatures, GISSTEMP does not. The 1988 Hansen graph is for “Annual mean global surface air temperatures from the model compared with the Hansen and Lebedeff GISSTEMP series. By the way it is contructed, the latter does not cover most of the ocean. Therefore comparing HadCrut3 with the 1988 calculations is comparing ducks with geese, even if all of the sets were properly zeroed. If you are going to use a Hadley Center product Crutem3 is a much better choice. It is quite clear from looking at the data that HadCrut3 has much less variability that Crutem3 which, of course, is no big surprise.

Eli, I fear you are in error about the GISTEMP datasets. GISTEMP has two datasets, one of which includes SST, and one of which does not. The 1988 Hansen graph uses the dataset which includes the SST, which is why it correlates well with the HadCRUT3 dataset. In short, the HadCRUT3 dataset is the proper one for comparison.

I have used both the GISTEMP + SST and the HadCRUT3 datasets in my analysis, since they are quite similar, and which one you choose doesn’t make much difference to the outomes or the statistics.

w.

John Creighton

Oh, gosh and somehow I messed up my html twice in a row:

John Creighton

Here is an idea of how good the above fit is:

The fit uses an AR (4,4) model for each input. The standard deviation of the residual y-Ax-S shows how close the fit is with the estimated noise, while the standard deviation of residual y-Ax shows how good the deterministic part of the fit is.

In this case the estimation of the noise did not effect the deterministic fit much because there were enough measurements for the noise and the deterministic output to be nearly orthogonal. We see that around 60% of the standard deviation is due to noise with an AR(4,4) fit. Looking at the above plot for a standard regression fit AR(1,0) we see that there is much more noise then signal. I suspect the same results with a standard regression fit for AR(4,4) because in the algorithm I used the first iteration only fits a small part of the noise and thus should not significantly effect the regression parameters. If I had of used less measurements though I would expect a difference between my algorithm and the standard regression fit. I’ll compare that later.

Robert G. Brown

Which, by the way, agrees qualitatively with John’s observation that he can fit the recent data decently by a multiparameter model with significant “noise” that can be interpreted as “missing dynamics in the model. Indeed, it extends it as some of the source of noise could have very long timescales compared to 500 or so years.

I do have a question about the fit. Some of the sources of noise one might expect to be driven by global temperatures and hence possess some covariance with model parameters. If (say) cloud coverage was related to CO_2 concentrations via the possibly multi-timescale lagged effect of the former on temperature and hence oceanic evaporation, there are opportunities galore for chaotic (nonlinear) mesoscale fluctuations. Ditto, by the way, if (say) solar dynamics drives temperature drives CO_2 concentrations which feeds back onto temperature which feeds back onto cloud coverage which affects the temperature and maybe the rate of CO_2 being scrubbed into e.g. the oceanic reservoir… one would expect a highly non-Markovian description of the actual true energy dynamics.

Would your model account for any portion of that sort of dependent covariance, or would it only account for effects with a straightforward (e.g. linear or near linear) non-delayed effect on temperature? Outside of the noise, I mean.

The entire existence of ice ages seems to suggest that either the Sun has serious long period variability (sufficient to significantly lower global temperatures for hundreds of thousands of years stably) or there exist multiple attractors in a chaotic model driven by a more uniform heat source, with transitions that are perhaps initiated by fluctuations of one sort or another to different stable modes. I know there are people looking at this, but I don’t know that they’ve gotten good answers. A chaotic model might well exhibit “interesting” behavior on a whole spectrum of time scales, though, as various parts of the dynamic cycle undergo epicyclic oscillations.

rgb

rgb

Francois Ouellette

#98 since the original model prediction work was done in 1988, he presumably did a 30 year run on the models, thus the 1958 start.

TAC

#97 Robert, you might want to google Demetris Koutsoyiannis (or look )here) on long-memory (LTP) processes and climate. Koutsoyiannis has given a lot of thought to this problem.

TAC

#96 and #102 Robert and JohnA: I share your pessimism about climate modeling (poor data; uncertain physics; shoddy mathematical and statistical methods; etc.). Yet, I’m not sure I would disparage models that reduce “climate down to one variable.” Doesn’t it depend on what you’re trying to accomplish? For example, imagine a model for temperature combining some kind of (log)linear deterministic (physically based — get the physicists involved) predictor related to CO2 (if that is what we are interested in testing) with a realistic stochastic component for natural variability (I would look to the statisticians or Koutsoyiannis for this). No more than 3 fitted parameters altogether. Such parsimonious models are hard to build and easily “falsified” (everyone knows “all models are wrong,” and with small-dimension models you can easily see it), but they are much easier to interpret and understand. Though naive, such models might provide real insight. Alternatively, they might demonstrate that, given the complexity of background variability, we aren’t going to be able to say much. That would be interesting, too.

Whatever. Just an early-morning thought; likely it has already been tried…

Steve McIntyre

#103. TAC – I agree entirely. I’d love to see some more articulated 1D and 2D models. While I can’t prove it mathematically, my entire instinct is that, if the metric is NH (or global) average temperature, there is a latent 1D model that approximates the 3D model to negligible difference.

The 1D “explanations” of AGW are interesting and I wish that more effort was spent in explaining and expanding them. The only exposition of how AGW works in all three (four) IPCC reports is a short section in IPCC 2AR responding to skeptic Jack Barrett, arguing that increased CO2 will lead to absorption and re-radiation in weak lines at higher (colder) altitudes.

This is the line of reasoning in radiative-convective models (which would be interesting to consider from a calculus of variations approach for someone with requisite skills). Some of Ramanathan’s articles from the 1970s and 1980s are quite illuminating and, if I ever get to it, I should post up some comments on them. Many of them are now online at AMS Journal of Climate.

Robert G. Brown

To TAC #97, you are absolutely correct. The preprint linked to this site was a pleasure to read, and contained absolutely precisely the figures I was visualizing and most of the relevant remarks I sought to make, but with full detail. To bring it back to this thread (and indeed this entire site): Figures 1 and 4 of this preprint say it all. They should be required viewing for anybody who wants to even THINK of building a predictive model for this problem. Figure 4, in particular, is relevant to the M&M debate vs Mann, which in turn is ABSOLUTELY relevant to the Hansen graph even if one assumes that the “global temperatures” portrayed therein and being fit are actually meaningful instead of the method-error laden, biased garbage that they almost certainly are.

Fitting in any short “window” onto the geologic time-temperature series leaves one absolutely, cosmically blind to underlying functional behavior of longer time scales. The only way one has even a hope of extracting meaningful longer-time behavior from such a fit is one knows PRECISELY what the actual underlying functional form is that one must fit to, and only then if that form possesses certain useful properties, like projective orthogonality. Without wanting to review all of functional analysis or fourier transforms or the like to prove this — it should be obvious or else you shouldn’t be participating in this debate.

However there are some very simple statistical measures one can use to at least characterize things, positing a state of utter ignorance about the functional behavior and viewing the entire temperature series as “just a bunch of data”. For example, all the statistical moments (cumulants) — mean, variance, skew, kurtosis. Thus the importance of M&M vs Mann et al. If the temperature around the 1300’s was in fact as warm as it is today, the scientific debate about “global warming” as anything but speculative fiction is over. Period. It relies on the temperatures we observe being “unusual”. In a purely statistical sense, according to my good friend the central limit theorem, that means “unlikely to be observed in a random iid sample drawn from the distribution” where in turn “unlikely” is a matter of taste — a p-value of 0.05 might suffice for some, even though of course it occurs one year in 20, others might want it to be less than 0.01 (although that happens too).

However, if two extensive excursions, lasting decades or more, of warm weather like we are currently experiencing, are observed in a mere seven hundred year sample, I don’t even need to do a computation to know that the this isn’t a 0.01 event on a millenial-plus scale. More like a 0.1 or 0.2 event. It also utterly, cosmically confounds attempts to fit human-generated CO_2 as THE primary controlling variable in temperature excursions from the mean, as human generated CO_2 is surely a monotonic function on the entire interval of human history.

The sun, however, remains not only a plausible causal agent as the primary determinant in the observed variation (given that it IS, after all, the most significant source of free energy for the planet, dwarfing all other sources except possibly tidal heating due to the moon and radioactive heating of the earth’s core, and MAYBE cosmic rays (don’t know what the total power flux is due to cosmic rays but I’ll guess that it equals or exceeds the release of non-solar free energy sources by humans by a few orders of magnitude), averaged over the entire 4\pi solid angle…

Besides, a number of measures of solar activity are strongly correlated with global temperature over at least a couple of thousand years, as best as proxies (including plain old history books) can tell us. Here the problem is complicated tremendously by the silliness of what one expects out of the fits and the massaging of the data that everybody does to perform them (effectively ignoring the stochastic richness of our ignorance of all causes and delayed differential effects).

First of all, one needs to make it clear that we Do Not Understand Mr. Sun. We are working on it, sure, but in addition to considerable ignorance concerning the actual magnetohydrodynamics models being proposed (that all have to be validated with horribly incomplete information about interior state — initial conditions, if you will — from observations primarily of exterior state, where it is KNOWN that there are very long time scales to consider — as in a major fluctuation that arrives at the surface to significantly alter solar irradiance and this and that might have actually occurred a rather long time ago). Then we don’t understand all aspects of how the sun transmits energy to the planet or affects the rate and ways energy is absorbed or retained except via ordinary E&M radiation, maybe. Tidal heating, magnetic heating, cosmic rays and charge particles affecting cloud formation which in turn alters the Earth’s mean albedo (in a way many orders of magnitude more significant than CO_2 — clouds are a hell of a greenhouse “gas”).

We do know that the Sun orbits the center of mass of the solar system, and that its orbit is highly irregular. We do know that there appears to be a transfer effect between orbital angular momentum and the sun’s visible spin, and that altering the latter is a process involving truly stupendous amounts of energy with the consequent release of heat. We know that the Sun does all sorts of strange magnetic things as it proceeds through these irregularly spaced (but predictable) orbital events. We know that they are correlated with, but not absolutely predictive of, things like sunspot count and interval. And we know that these things are correlated very strongly with events in the Earth’s global temperature series, not just over the last 200 years where we have something approximating temperature readings but over the entire range of times where we can deduce temperatures via any sort of proxies.

It is equally obvious that it is one of MANY parametric inputs (the obviously dominant one, in my opinion) and that our ignorance of many of a near infinity of these inputs (fine grained, they go down to that damnable butterfly in Brazil, after all) requires that a HALFWAY believably model be something like a langevin equation (solved via a fokker-plank equation approach, maybe), if not a full-blown non-Markovian, stochastic, integrodifferential equation. Quasi-linear parametric models (“if CO_2 goes up, global temperatures go up”) are a joke, not serious science.

But don’t mind me, this is just one of the things I “do” in other contexts where results are easily falsifiable and where we actually have a handle on the microscopic dynamics.

One other thing I do is neural networks, which in the context of problems like this can be viewed as generalized nonlinear function approximators. The result of building a neural network is of course anathema to most model builders, who want to trumpet things like “This parameter is causing this output to happen the way that it is”. A neural network utterly obscures the true functional relationships it discovers. It also can handle input covariance transparently, and is perfectly happy in a high dimensional multivariate problem describing non-separable input relationships (ones that cannot be expressed as an outer product of independent functions of those variables, ones that e.g. encode an exclusive or or more complex relationship for example).

They are, however, useful in two ways to the unbiased, even for addressing problems like this. For example, it would be interesting to try training a NN to predict “this year’s mean temperature” from (say) the last twenty-five years’ sunspot data, the last twenty-five years global temperature data (to give it a mechanism for doing the integro-differential non-markovian part of the solution) and with an input for some measure of the total volcanic activity for the last twenty five years. Nothing else. Train it over selected subsets of the last 250 years’ data (it needs to include examples of the bounded variance of the inputs and outputs. Then apply it and see how it does.

One can then compare the performance of such a network to one built e.g. only with sunspots as input (no non-Markovian inputs). Only with volcanos. With sunspots and volcanos. Only with CO_2. With CO_2 and temperature. Etc. Abstracting information from this process is tedious, but it does not depend on any particular assumptions concerning functional dependence of the inputs. If they are useful, the network will use them. If not, it will ignore them. If they are strongly covariant with other inputs, it won’t matter. Even so, one can sometimes obtain very interesting information about the underlying process dependencies. Oh, and one will likely end up with a quantitative model that is more accurate a predictor than ANY existing model is today by far, but that is besides the point. In fact, if the markovian model proved accurate (and I’ll bet it would:-) one could use the network recursively with simulated inputs drawn from the expected distribution of e.g. sunspots and get an actual prediction of global future temperatures some years in the future that might even accurately describe the hidden feedback stabilization mechanisms that are obviously absent from quasi-linear (monotonic and non-delayed) models.

To John A — I also completely agree, especially about the wishful thinking aspect of things. The above is the merest outline of how one might actually attack the problem in a way that didn’t necessary beg all sorts of questions. It still leaves one with the very substantial problem of the base data one attempts to fit — the temperature series one tries to fit is a patchwork of changing methodologies, technologies, locations, and worse with urbanization alone providing systematic errors that are corrected for more or less arbitrarily (so that what one measures depends on who is doing the correcting). The patches don’t even fit together well where they overlap — there are weather stations all over the planet that show no statistically significant global warming EVEN in the last decade and current measures of global temperature are either being “renormalized” by individuals with a stake in the discussion or are being based with extraordinary weight given to parts of the world where there IS NO reliable data that covers hundreds of years to which current measurements can be compared (and where it is easy to argue to the current data itself isn’t terribly reliable).

GIGO. The very first problem one has to address, unless/until one agrees to use only satellite data and radiosonde data and dump surface measurements altogether as the load of crap they probably are. That still leaves one with accurately normalizing to the scale of the RELIABLE measurements we do have that stretch back over 250 years, but that is a more manageable problem.

In the meantime, I find it overwhelmingly amusing, in a sick sort of way, that Time Magazine published in one month a cover story on the sun that clearly describes the immense complexity of solar dynamics, discusses the high probability that things like its irradiance and magnetic field and solar wind are significant contributers to things like earthbound weather and how important it is to understand them, and then JUST A MONTH OR THREE LATER publishes a cover story on global warming that utterly ignores the sun! No mention of Maunder minima, no glimpse of the Medieval Optimum, no look at temperature varation on a truly geological time scale — just “it is now a known and accepted scientific FACT that human generated CO_2 is about to destroy the planet as we know it”.

The greatest tragedy associated with this is that the people betting on this horse had damn well be right. If (for example) the current sunspot minimum is in fact the edge of another Maunder minimum (as the solar theories seem to suggest and we’re about to enter a downturn that lasts some thirty years, it will (rightfully) damage the credibility of all scientists, everywhere, for the next fifty years. Chicken Little on a grand scale. As a scientist, I find the sheer probability of this very disturbing, as most ordinary citizens are utterly incapable of differentiating a scientist being enthusiastic about a pet theory from Darwin or Newton, where the “pet theory” is falsifiable and so overwhelming validated by observation that nobody sane expects it to ever be proven false.

rgb

bender

Re #107:
On the utility/futility of neural networks.

The result of building a neural network is of course anathema to most model builders, who want to trumpet things like “This parameter is causing this output to happen the way that it is”.

Now why do you think that people would like to understand the relationship between input and output?

A neural network utterly obscures the true functional relationships it discovers. It also can handle input covariance transparently, and is perfectly happy in a high dimensional multivariate problem describing non-separable input relationships (ones that cannot be expressed as an outer product of independent functions of those variables, ones that e.g. encode an exclusive or or more complex relationship for example).

This sounds like a research proposal. Are you sure you’re being objective here?

one will likely end up with a quantitative model that is more accurate a predictor than ANY existing model is today by far, but that is besides the point

Neural network models are overfit models. They are as likely to fail in an out-of-sample validation test as any other overfit model. No?

charles

Bender,

“This sounds like a research proposal. Are you sure you’re being objective here?” talking about Dr. Brown’s post.

If true this puts Brown into the same position as all the grant funded climate scientist. Bloom/Dano are constantly telling us we should trust grant funded scientist because they are objective – receive no FF monies.

bender

Re #111
He’s criticizing the traditional approach to climate modeling. I want to know what kind of weapons he’s packing. Could be interesting. I say ‘leave the trolls out of this’.

John Creighton

There has been some discussion here how averaging effects the model fit. Averaging can be corrected for in a limited way. For instance in audio systems speakers use sin(x)/x compensation to compensate for the distortion as a result of the sampling process. In the case of temperature averaging cause a more serious problem because the total power dissipated from the earth is proportional to the forth power of the temperature yet we average temperature and not the forth power of the temperature. To compensate for this fact I suggest that one of the forcing terms be -^(1/4).

The regression coefficient for this term should be roughly proportional to the third power of temperature and we expect close agreement with the equations for black body radiation. I also suggest that we try to quantity other forcing terms like thermal transfer of energy though convection and evaporation. I wonder if any of these forcing components can be estimated though satellite data.

bender

Re: #101
Anyone interested in red noise processes and scaling of uncertainty should read papers on 1/f noise as well.

srp

Bender: I read Baum’s book What is Thought? and he describes a theorem by Vapnik and somebody else (whose name regrettably slips my mind) that precisely describes the fitting/overfitting behavior of NNs in a binary classification context. The basic idea, loosely, seems to be that if a) the data generating process is stationary and b) the NN is trained on historical samples, then c) the NN’s predictive power is inversely related to the number of free parameters the training has searched over. This is all defined in a precise mathematical way, but that’s the gist of it–if you find a good fit with one or two parameters, then it’s likely to work out of sample, but if you splined the data, there’s no reason to think your fit is going to be good on the next instance.

That said, I also recall reading that NNs are no panacea in that training and convergence are often painfully slow and ineffective if the problem structure isn’t “friendly” to the NN’s architecture. It’s probably worth a try, though.

John Creighton

#119 I doubt that the Neural Networks predictive power is always inversely proportional to the number of free parameters. There should be an optimal number of parameters. I’ve tried doing noise removal before in speech with a predictive MA filter and what I found was that the number of parameters that you need it had to be sufficient long enough to describe at least one or two cycles of the vowel frequency.

Steve McIntyre

#120. Francois, esnips.com (used by jae) has free storage that would be a good place to upload papers. I’m thinking of using it for pdf storage.

John Creighton

I’m looking at the instrumental temperature record from 1600 to 2000 and I’m looking at the C14 over that same period and I can’t help but think that the C14 which is an indicated of cosmic rays, fits the temperature data much better then solar, greenhouse gases and volcanic eruptions. I wonder if the other drivers are significant at all. Unfortunately the C14 does not explain the high frequency data so I am still left to wonder what cause this.

Perhaps the high frequency data has to do with when the clouds were formed. If the clouds were formed evenly throughout the year there would be less cooling I think then if it was concentrated within a shorter period of time. Or perhaps it has something to do with the global distribution of cloud cover. More clouds at the equator would have a greater cooling effect then at the poles I think. There is also the altitude distribution of clouds. I confess I haven’t read the paper yet.

James Lane

Re #107

Could someone refer me to the preprint that rgb is discussing?

TAC

#127 I think the preprint you refer to is of one of Koutsoyiannis’s latest papers (here). It was cited in #101. I (and/or RGB) will likely be sending SteveM a post on it.

John Finn

Just a comment on the Hansen graph

In his article Hansen writes

Scenarios B and C also included occasional large volcanic eruptions

This would suggest that the plots of B and C are ‘lower’ than they might have been (without volcanos). The last major eruption was in 1991 (Pinatubo) which according to NASA was responsible for a temperature drop of up to 0.5 deg C and affected global temps for up to 3 years.

If Hansen were to re-run his model with just the 1991 volcanic eruption the observed temperatures would be running well below both scenarios B & C.

On the discrepancies between GISS and HADCRUT. Tim lambert is correct about the different anomaly periods, but the ‘discrepancy’ seems to be growing (it should be reasonably constant). I think it may be due to the way the ocean temperatures are measured.

Robert G. Brown

OK, I should, of course, be doing something like actual work but this is more fun so I’ll see what I can do about the questions/suggestions above.

Lessee…

a) Currently I am completely unfunded by federal money, and while I have been so funded in the past, the agency (ARO) that funded me could give a rodent’s furry behind for the entire weather debate one way or the other. In fact, I’d say that is true for pretty much all physics funding. Physics has its own problems with politicization of the funding process, but thankfully they are vastly smaller than Climate. So ain’t nobody holding a gun to my head here, I have no vested economic interest in this discussion, and although I have no way of “proving” this I am an ethical person — an ex-boy scout, a university professor and student advisor, a beowulf computing guy, open source fanatic, husband, father, and have hardly ever been accused of crimes major or minor over the years. I did get caught driving with an expired registration once, if that counts. So: “Everything I state in this discussion is my actual, unpaid for opinion based on doing half-assed web-based research and applying whatever I have learned for better or worse in 30 years or so of doing and teaching theoretical physics, advanced computation, statistical mechanical simulation, and in the course of starting up a company that does predictive modelling with neural networks (currently defunct, so no that is not a vested interest either).” Good enough disclaimer?

b) Re: Neural networks. I have fairly extensive experience with neural networks (having written a very advanced one that uses a whole bunch of stuff derived from physics/stat mech to accelerate the optimization process for problems of very high input dimensionality). As I said, one of the best ways of viewing a NN is as a generalized multivariate nonlinear function approximator. In commercial predictive modelling, the multivariate nonlinear function one is attempting to model is the probability distribution function, usually used as a binary classification tool (will he/won’t he e.g. purchase the following product if an offer is made, based on demographic inputs). However, NNs can equally well be trained to just plain model nonlinear complex (in the Santa Fe Institute sense, not complex number sense though of course they can do that as well) functions presented with noisy training data pulled from that function, not necessarily in an iid sense since the support of a 100 dimensional function may well live in a teeny weeny subvolume and there isn’t enough time in the universe to actually meaningfully sample it (even with only binary inputs, let alone real number inputs).

For very high dimensional functions with unknown analytic structure, I personally think that NNs are pretty much the only game in town. To use anything else (except possibly Parzen-Bayes networks or various projective trees for certain classes of problems) restricts the result to preordained projective subspaces of the actual problem space. The process of projection, especially onto separable/orthogonal multivariate bases, can completely erase the significant multivariate features in the data, hiding key relationships and costing you accuracy.

NNs have a variety of “interesting” properties (in the sense of the chinese curse:-). For one, constructing one with a “canned” program (even a commercial canned program) is likely to fail immediately for a novice user leaving them with the impression that they don’t work. Building a successful NN for a difficult problem (with that really DOES have high dimensionality and nontrivial internal correlations between input degrees of freedom and the output desired) is as much art as it is science, simply because the construction process involves solving an NP complete optimization problem and one needs to bring heavy guns to bear on it to have good success. Training takes as long as days or weeks, not minutes, and may require trying several different structures of network to succeed, facts that elude a lot of casual appliers of canned NNs. Having the source to the NN in question is even an excellent idea, because one may need to actually use human intuition, insight, and a devilishly deep understanding of “how it all works” to rebuild the NN on the spot at the source code level to manage certain problems.

NNs also have a built in “heisenberg”-like process that resembles in some ways the quantum physics one (which is based on vector identities in a functional linear vector space or the properties of the fourier transform that links position and momentum descriptions as you prefer). If one builds a network with “too much power”, a NN overfits the data, effectively “memorizing specific instances” from the training set and using its internal structure to identify them, but then it does a poor job of interpolating or extrapolating. If one builds a network with too little “power” (too few hidden layer neurons, basically) then the network cannot encode all of the nonlinear structures that actually contribute to the solution and it again fails to reach is extrapolatory/interpolatory optimum. So in addition to building a NN (solving a rather large optimization problem in and of itself) one has to also optimize the structure of the NN itself in terms of number of hidden layer neurons, precisely what inputs to use from a potentially huge set of input variables (building a NN with more than order 100 inputs starts to get very sketchy even with a cluster, even with NN’s significant scaling advantage in searching/sampling the available space, even for my program), and then there are a number of other control variables and possibilities for customized structure to optimize on top of that for truly difficult problems. Finally, NNs perform well for certain mappings of the input numbers into “neural form” and perform absolutely terribly for other encodings of the same input data. One has to actually understand how NNs work and what the data represents to present inputs to the network in a way that makes it relatively “easy” to find a halfway decent optimum (noting that the system is nearly ALWAYS sufficiently complex that you won’t find THE optimum, just one that is better than (say) 99.999999% of the local optima one might find by naive monte carlo sampling followed by e.g. a conjugate gradient or worse, a simple regression fit).

Oops! I forgot to mention the entire problem of selecting an adequate training set! This problem is coupled to a number of the others above — for example, finding the right resolving power for the network — and above all, is related to the problem of being able to extrapolate any model beyond the range of the functional data used to build the model. This problem is discussed in a separate section below, so I won’t say more about it now, but at that time you will see that NNs aren’t any more or less capable of solving this problem in the strict sense of Jaynes (the world’s best description of axiomatic probability, in my humble opinion) and maximum likelihood, Polya’s urn, entropy etc for people who know what they are. Extrapolation necessarily involves making assumptions about the underlying functional form (even if they are only “it is an analytic function and hence smoothly extensible” and one can always find or define an infinite number (literally) of possible exceptions where the assumption breaks down. This leads to some pretty heavy stuff, mathematically speaking, concerning the dimensionality of the actual underlying function, the way that dimensionality projects into the actual dimensions you are fitting which may be non-orthogonal curvilinear transforms of the true dimensions or worse, and the log of the missing information — the information lost in the process of projection. WAY more than we want to cover here, way more than I CAN cover here — read Jaynes and prosper.

From this you may imagine that I don’t think much of published conclusions concerning NNs — they tend to be based on simple feed forward/back propagation networks applied to simple problems or naively applied to problems that they cannot possibly solve, although there are exceptions. The exceptions are worth a lot of money, though, so people who work out truly notable exceptions do not necessarily publish at all.

With regard to the specific problem at hand — building NNs to model a nonlinear function “T(i)” (temperature as a function of some given vector of “presumed climatological variables that might be either causal agent descriptors or functions of causal agent descriptions”) — the problem itself is actually simple enough that I think that NNs would do fairly well, subject to several constraints. The most important constraint is that the network needs to be trained on valid data. NNs aren’t “magical” any more than human brains are — they suffer from GIGO as much as any program on earth. They are simply far, far better at searching high dimensional spaces in a mostly UNSTRUCTURED way that makes the fewest possible assumptions about the underlying form of the function being fit, in comparison to using a power series, a fourier representation, a (yuk!) multivariate logistic representation, or fitting anything with a quasi-linear few-variable form that effectively separates contributions from the different dimensions into a simple product of monotonic forms (assumptions that are absolutely not justified in the current problem, by the way).

As previously noted, this leads us back to the M&M vs Mann result, and the lovely papers with links provided by TAC. I don’t really see how to uplink and embed jpgs grabbed from the figures in these papers and I have to teach graduate E&M in a couple of hours (which does require some prep:-) so I’ll try to summarize the basic idea in (my own) general terms. I STRONGLY urge people to at least skim the actual papers by following the links TAC provided as they use simpler (although perhaps less precise) language than that below and besides, have simply LOVELY figures that say it all.

c) Suppose you have a completely deterministic function (equation of motion) with (say) 10^whatever degrees of freedom, where whatever is “large”, 10^whatever is “very large” and numbers like 10^whatever! are “good friends with infinity, who lives just past the end of their street” (the latter number figures prominently in various computations of probability in this sort of system). OK, so we cannot think about actually solving such a system, so we go from the actual equation of motion to its Generalized Master Equation. The way this works is that one selects a subset of the degrees of freedom or a functional transform thereof and performs a projection from the actual degrees of freedom to the new ones. To do this one has to embrace a statistical description of the underlying process and average over the neglected degrees of freedom. This results in the appearance of new, coarse grained degrees of freedom (like “temperature”, which is a proxy as it were for the average internal energy per degree of freedom in a multiparticle physical system at equilibrium, but there may be many others as well) and a new equation of motion for the quantities that remain in your microscopic description. See in particular links on the master equation page for Chapman-Kolmogorov and Fokker-Planck and Langevin.

Note well that at the CK level, solutions on the projective subspace are most generally going to be the result of solving non-Markovian integrodifferential equations with a kernel that makes the time derivative of the quantities of interest at the current time (say, the joint probability distribution for global temperatures at all the measurement stations around the planet as a function of time) a function of not only the current values of those states and other input variables describing the current values of projective (coarse grained averaged) quantities, but the values of those variables at a continuum of times into the past that has to be integrated over. The system has a “memory”, and the dynamics are no longer local in time. Note well that the MICROSCOPIC dynamics IS time-local, but in the process of projection and coarse-grain averaging the new variables “forget” critical information from earlier times that would have been encoded on the degrees of freedom averaged over, and that is still at least weakly encoded on previous-time values of those average degrees of freedom. This sort of evolution is a generalized master equation, and alas wikipedia doesn’t yet have a reference for it but they are in use in physics in a number of places in e.g. the quantum optics of open systems.

Sorry, I don’t know of any easier way of describing this, as this is the actual bare bones underlying mathematical structure of the actual physical problem one is trying to solve. One CAN (and obviously most people DO) just naively say “hey, global temperature (however that is defined) might be a smooth function of CO_2 concentration (however that is defined) with the following (presumed) parametric form and here is the best parametric fit to that form in comparison to the data” without even thinking about those hidden degrees of freedom and non-Markovian effects, but that is, really, a pretty silly thing to do WITHOUT even explicitly acknowledging the limitations on the likely meaning of the result.

The point is that there are many physical systems where the local dynamics depends on the particular history of how one arrived at the current state, not just the values of its variables at that state. Pretty much any non-equilibrium, open system in statistical mechanics, for example.

This gives you the merest glimpse at the true complexity of the problem at hand. The neglected degrees of freedom of the coarse grained variables are responsible for the colored stochastic noise that appears in the actual distribution one is trying to time-evolve or state-evolve, the state evolution is generally non-Markovian so that making a Markov approximation and time evolving it only on the basis of current state is itself an additional source of error and erases the POSSIBILITY of certain kinds of dynamics in the result, etc.

Now, again for the specific problem at hand, the data being fit is a coarse-grained average of temperature measurements. Those measurements were recorded over hundreds of years and in a very, very inhomogeneous distribution of locations. Those measurements themselves (as measurements always are) are subject to errors both systematic and random — the former become what amounts to an unknown functional transformation of the results from each measurement apparatus and the latter appears as noise of one sort or another.

The number of locations, the site of the locations, the unknown transformation of the measurements from these locations, all themselves have varied in ways both known and unknown over time. Finally, the results from those locations are THEMSELVES transformed in a specific way into the single number we are calling (e.g.) “global average temperature for the year 1853” (or 2004, or 1932). Note that different transforms are required for all of those years simply because of HUGE differences in the profile of the contributing sites over decadal timescales. Note also that there are those that accuse the transform itself being used of significant bias, at least in recent years. I cannot address this — it really isn’t necessary. The point is that there is an UNCERTAINTY in T(t) for any given year, and that the deviation is almost certainly not going to be a standard normal error but rather an unknown systematic bias with a superimposed variance that is not normal. Curve fitting without an error estimate on the points is already an interesting exercise that we will not now examine, especially when that error estimate is not presumed normal — suffice it to say that this unknown error SHOULD cause us to reduce the confidence we place in the resulting fit.

This, then, is the data that is extended by proxies by Mann et. al. to produce a temperature estimate back roughly 1000 years, T(t) for t in the general range of 1000-200* CE. Let us call this curve T_mea(t) (for Mann et. al.). MEA used tree rings as proxies, and as I’m sure everybody who is reading this site is aware, used a statistical weighting mechanism while effectively normalizing the T(t) for the last couple of hundred years to current tree rings that de facto gave a huge weight to just two species of tree in their sample, both with highly questionable growth ring patterns in modern times that may or may not be related to temperature at all and that are not CONSISTENT with patterns observed in the growth rings of hundreds of other neighboring species over the same interval. By doing what amounted to a terrible job with the actual process of proxy extrapolation, they completely erased a warm period back in the 1300-1400’s that is well-documented historically and by all the OTHER tree ring proxies they claimed to use.

All of this computation was hidden, of course. M&M, by means of some brilliant detective work and bulldog-like dedication to task, had to DEDUCE that this was what had been done by attempting to reproduce their result and by means of limited private communications with MEA who as of the last M&M paper I read still have not disclosed all of their actual code.

Steve, it would actually be lovely if you would drop A copy of the basic figure from one of your papers in here — one with and one without the hockey stick form (or if you like, one with and one without bristlecone pines being anomalously weighted).

Two more remarks and then I have to go teach, sorry — maybe I’ll get back to this if there is still interest in people hearing more.

First, at the VERY least this means that there is YET ANOTHER layer of systematic error AND stochastic noise on top of the projection of T(t) back over 1000 years via proxies. In my opinion, having read M&M and understanding what they are talking about, at least one source of systematic error has been uncovered by them and can be resolved by simply shifting from T_mea(t) to T_mm(t), which shows that temperatures a mere 700 years ago were as warm or warmer than they are today, in the complete absence of anything LIKE the anthropogenic CO_2 that everybody is worried about today.

Second, an interval 200 years long, or 1000 years long, is still tiny on a geological scale and we KNOW that there are significant geological scale variations in global temperature. Forget possible causes — remember the process of projection and coarse graining/averaging that is implicit in any such description. Think instead about the TAC-referenced papers. We could well be in the position of the ant, living on the side of Mount Everest, who is trying to decide how to climb to the top of the world. To figure out which way to go, he wanders around a bit in his immediate neighborhood, and seems a few grains of sand, a gum wrapper, and — look! An acorn sitting just downhill of him! The shortsided ant climbs to the top of the acorn and proclaims himself king of the world.

Right.

BEFORE talking about causes, curves, fits, ALL of the above has to be understood and the data itself has to be reliable. Error estimates have to be attached to the data being fit, and those estimates have to include the effects of convolving the measurement process with the actual values both systematic and random. Finally, NO method for fitting the data to ANY control parameters will succeed if the data has significant variation on timescales larger than the window being fit that are not represented in the basis of the fit.

Sigh. Have to go. Perhaps I’ll return later to the actual point, which was NNs vs the data span and their likely ability to predict. In an acorn-shell, if the training data spans the REAL range of data in the periods of interest, it should be as good at capturing internal multivariate projective variation as anything. Nothing can extrapolate without assumptions, there is no way to validate those assumptions without still more data. Period.

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KevinUK

#133, RGB

Hard going but fascinating stuff. Slight off thread but keep it up.

Kevin

Robert G. Brown

Whew! I just reread what I wrote and it is far too much, sorry.

Let me wrap up (since I have a couple of minutes before I have to do my next daily chore) with the following. This isn’t my field, and I have no idea where to get actual data sets, e.g. T_mm(t), T_mea(t), CCO_2(t). I did find sunspots on the web from 1755 on, or so it appears, which unfortunately doesn’t extend back to 1300. There are solar dynamics theories that try to extend patterns back that far and there may even be comparable data of some sort as sunspots were observed a LONG time ago by this culture or that, but I don’t know where to get that data if it does.

If anybody can direct me at the data, I’d be happy to build a genetically optimized NN (with bells and whistles added as needed) to see it can do with various inputs to predict e.g. T(t,i) where i are the input vectors and where t may or may not be explicitly included (probably not, actually).

What this can do is give one a reason to believe that a nonlinear functional mapping exists between the inputs used and the target in the different cases. It will not tell one what that relationship is, or whether the relationship is direct or indirect, only that with a certain set of inputs one “can” build a good network and without them one “cannot”, all things being equal. It will not be able to address, in all probability, whether or not e.g. CO_2 or sunspots or the cost of futures in orange juice is “the” best or worst variable to use as an input if, as is not unreasonable, it is discovered that all three are correlated in their variation to T() (quite possibly as effect, not cause, in some cases). But it might be fun just to see what one can see.

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John Creighton

Well here is the data Michael Man used. I got it from the nature website.
http://www.geocities.com/s243a/warm/code/m_fig7_solar.txt
http://www.geocities.com/s243a/warm/code/m_fig7_volcanic.txt
http://www.geocities.com/s243a/warm/code/nhmean.txt
http://www.geocities.com/s243a/warm/code/fig7_co2.txt

Sometime I am coning to try to find the data in a more raw form and rebuild it but not today.

John Creighton

I also found some length of day data which I posted here:
http://www.climateaudit.org/?p=692#comment-43941

P.S. I would of put this all in one post but the spam filter doesn’t seem to like me putting a lot of links in one post.

Martin Ringo

A FYI and follow-up on earlier posts about trends versus model scenarios

Because there was am early discussion in this thread of the relative merits of a simple time trend versus the Hansen Scenarios, I thought it would be interest to run a Diebold-Mariano predictive accuracy test.
This test allows testing for different objective values — absolute value difference, squared differences, weighted, etc. — and accounts for the autocorrelations and heteroskedasticity of forecast errors (predicted minus actual values): characteristic missing in most common tests of forecast efficiency. The tests a “forecast” comparison of the Scenarios versus both a simple linear trend and a quadratic trend with an ARMA(3,3) structure, and were run for both absolute value and squared differences from the actual anomalies with both the GISS and Hadley series of anomalies. All series centered on the 1958-1988, common data set, means. Out of the 24 comparison there were 12 rejections of the “no statistical difference” between the forecasts, and each case the time series trend forecast was closer to the actuals.

The results shown below [how does one post a table into a comment?] should not be interpreted as saying that a simple time series forecast is really superior. Rather, it should more modestly be considered to say that the Hansen scenarios offer no more predictive accuracy over what can be seen from a naàƒÆ’à‚⮶e or semi-semi extrapolation of the series.

ABSOLUTE VALUE OF DIFFERENCES FROM ACTUAL
Scenario Trend Data ……Rejection.. t-stat . % Prob
A Linear GISS………………..Yes…….-3.52………0.16%
B Linear GISS…………………No………0.42……..33.92%
C Linear GISS…………………No………1.42……….8.84%
A ARMA+quadratic GISS..Yes…….-5.55………0.00%
B ARMA+quadratic GISS..Yes……-2.34……….1.67%
C ARMA+quadratic GISS…No…….0.14………44.71%

Scenario Trend Data ….Rejection.. t-stat . % Prob
A Linear HADLEY…………….Yes……-7.44……..0.00%
B Linear HADLEY……………..No……..0.35…….36.46%
C Linear HADLEY……………..No……..1.26…….11.27%
A ARMA+quadratic HAD….Yes…….-8.06……..0.00%
B ARMA+quadratic HAD….Yes……-2.75……….0.74%
C ARMA+quadratic HAD…..No…….0.90……..19.09%

SQUARED DIFFERENCES FROM ACTUAL
Scenario Trend Data ……Rejection.. t-stat . % Prob
A Linear GISS……………….Yes…….-3.57………0.14%
B Linear GISS………………..No………0.39……..35.09%
C Linear GISS………………..No………1.28……..10.96%
A ARMA+quadratic GISS.Yes…….-6.44………0.00%
B ARMA+quadratic GISS.Yes……-2.70……….0.82%
C ARMA+quadratic GISS..No…….-0.72………24.13%

Scenario Trend Data .. …Rejection. t-stat . % Prob
A Linear HADLEY…………….Yes….-9.61………0.00%
B Linear HADLEY……………..No……0.73……..23.86%
C Linear HADLEY……………..No……1.47……….8.12%
A ARMA+quadratic HAD….Yes……-5.64………0.00%
B ARMA+quadratic HAD…Yes……-2.10……….2.64%
C ARMA+quadratic HAD….No…….0.27………29.42%

John Creighton

Speaking of C14 has anyone heard about the Suess effect? Apparently galactic cosmic rays are not the only thing the effects the c14 concentration. Also the burning of c14 depleted fossil fuels. I’m curious though, wouldn’t it be c14 rich fuels that should effect the c14 concentration the most. I wonder how difficult it would be to correct the c14 concentration for fossil fuel burnings so we could isolate the solar effects. I also wonder if frost fires effect the c14 concentration at all.

Robert G. Brown

Re #144

I just don’t worry about the statistical properties of NNs — I view them as “practical” predictive agents, not as formal statistical fits. In fact, I feel the same way about modelling in general in cases where the underlying model is effectively completely unknown, so one gets no help from Bayes and no help from a knowledge of functional forms.

I’m working currently on a major random number testing program (GPL) called “dieharder”, that incorporates all of the old diehard RNG tests AND will (eventually) incorporate all the STS/NIST tests, some of the Knuth tests, and more as I think of things or find them in the literature. A truly universal RNG testing shell with a fairly flexible scheme for running RNG tests.

In this context, I can speak precisely about statistical properties. Random number testing works by taking a distribution of some sort that one can generate from random numbers and that has some known property (ideally one that is e.g. normally distributed with known mean and variance). One generates the distribution, evaluates the statistic, and compares the mean result to the expected mean, computes e.g. chisq, transform to a p-value for the null hypothesis and I can then state “the probability of getting THIS result” from a PERFECT RNG is 0.001″ or whatever.

Now, just how can one do that when one is pulling samples from an unknown distribution, with unknown mean, variance, kurtosis, skew, and other statistical moments, where the long time scale, short time scale, intermediate time scale behavior is not known, and where we KNOW that the underlying system is chaotic, with a high dimensionality to the primary causally correlated variables and clear mechanisms for nonlinear feedback? The answer is, we can’t. The basic point is that nobody can make a statement about p-value associated with any of the fits being discussed, which is why using them in public policy discussions is absurd.

What we CAN do by simple inspection of the data is note that if the data range over 1000 years contains two warm excursions like the one we are just finishing this year, a simple maximum entropy assignment of probability (a la polya’s urn) for such excursions occurring in any give century is something like 10% to 20%, or in any given 100 year interval it is not unlikely to find at least one or two decades of similarly warm weather. To make statement beyond that requires accurate and similarly normalized data that stretches back over a longer time, and we observe (when we attempt to do so via proxies) long term temperature variability that vastly exceeds any of that observed in the tiny fraction of geological time since the invention of thermometer.

So when I build NNs for this problem, it will not be so that I can “succeed” and build one that is highly predictive with some set of inputs and they say “Aha, now we understand the problem” or “Clearly these are the important inputs”. That’s impossible, given that there are lots of inputs and that their EFFECT is clearly all mixed up by feedback mechanisms so that they are all covariant in various ways. For example, there are clear long term variations in CO_2 (evident in e.g. ice core) that seem to occur with temperature. Is this cause? Effect? Both (via positive feedback through any of several positive mechanisms)?

There are many worthwhile questions for science in all of this, but it is absolutely essential to separate out the real science, which SHOULD have a healthy amount of self-doubt and a strong requirement for validation and falsifiability (and hence for challenge from those that respectfully disagree) from the politics and public policy. Performing statistical studies is by far the least “meaningful” of all approaches to science, because correlation is not causality. It is easy in so many problems to show correlation. Most introductory stats books (at the college level) contain whole chapters with admonitory examples of how one can falsely claim that smoking causes premarital sex and other nonsense from observing correlations in the populations.

Alas, people who become politicians, nay, who become presidents of the united states, may well be “C-” students in general and have never taken a singe stats course (let alone an advanced one), and besides, one of the lovely thing about misusing statistics is that is a fabulous vehicle for politicians and con artists both to make their pitches. “Help prevent teen pregnancy! Don’t let your daughter smoke!”

I personally view statistical surveys and models of the sort being bandied about in this entire debate as being PRELIMINARY work one would do in the process of building a real science — exploring the correlations, trying to determine what needs to be explained and what CAN be MAYBE explained, and eventually connecting this back to “theoretical models” in the scientific sense. However, the PHYSICS of current models is so overwhelmingly underdone that I just think that it is absurd that anyone thinks that they can make any sort of statement at all about what causes what. The models contain parameters that are at best estimated and where the estimates can be off by a factor of two or more! They are missing entire physical mechanisms, or include them only by weak proxies (e.g. “solar activity” measures instead of “solar magnetic field” measures instead of “flux of cosmic rays”, where all of the above may vary in related ways, but with noise and quite possibly with additional significant functional variation from other systematic, neglected, mechanism).

So seriously, the NN is “just for fun” and to see if one can read the tea leaves it produces for some insight, not to be able to make a statement with some degree of actual confidence (in the statistical sense). Sorry about your C++ experience — I actually don’t like C++ either as you can see from my website, where I have the “fake interview” on C++ that is pretty funny, if you are (like me) a C person…;-)

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Martin Ringo

Re # 147
I’m all for reading the tea leaves with a hope of insight. When I look at the various ARMA estimates I have made of annual or even monthly data, I don’t see any common structure to the patterns. I contrast this with daily and hourly temperature data which has been pretty consistent, at least for the data sets I have seen in the US. So maybe NNs catch a pattern which gives an insight which … And maybe the Laplacian efforts to model climate may come to fruition.

If you have it, could you post the exact location of the “interview” regarding C++. I can’t really claim to be a C person — I haven’t written a line of C in over 10 years — but I still think K&R is, if not the greatest, then the cleanest book written on programming. But then the language is pretty clean also.

John Creighton

With regards to sunspot number I plotted the sunspot number and I looked at Mann’s graph of solar activity (Okay I forget what he called it) Anyway, Mann’s graph looked like the sunspot number put though a low pas filter. In the paper Mann referenced the figure was constructed from many solar indicators.

So say Mann’s graph is an indication of solar flux while the sunspot number (with the mean subtracted) better correlates with solar magnetism and clouds. So a Neural network with suitably chosen nonlinearities may be able to extract a good deal of information from sun spot number alone. Additionally sunspot number extends though most of the years that Mann did his figure 7 correlations for.

John Creighton

I was thinking about the orthogonally of the proxies and my first thought was it is probably a precipitation index. Precipitation indexes can be related to cloud cover which play a big part in warming. Of course low clouds cause cooling and high clouds cause warming so precipitation is not directly related to warming. I then recall one of Robert’s posts,

“I pulled just a couple of proxies (e.g. some african lake data, chinese river data) and they show beyond any question an extended warm spell in the 1100-1300 range that was clearly global in scope. I thought that this was visible in nearly all the tree ring data on the planet “¢’‚¬? but I see that now I can look for myself (if I can figure out how “¢’‚¬? there is a LOT of tree ring data, and of course (sigh) tree growth is itself multivariate and not a trivial or even a monotonic function of temperature).”
http://www.climateaudit.org/?p=796#comment-44086

and I then wonder if maybe Mann took care to select the worst of the tree proxies. I am not sure if Robert was saying the MWP and LIA was in most tree data or not. Interestingly enough tree proxies supposedly best for high frequency information so if low frequency proxies are first used to identify the low frequency model and then if the low frequency part of the signal is removed by an inverse filter (similar to differencing) then maybe trees will provide a more robust method of identifying the high frequency part of the signal.

Anyway, we may be able to use trees to get low frequency information but we have better ways of doing it. I think tree proxies should only be used were they are supposedly suppose to excel.

Steve McIntyre

GISS has SST back to the 1870s for 0.5N 159E in the Hansen PNAS study, while HadCRU has virtually no values around 1900 – so someething else must be oging on as well

Willis Eschenbach

I’ve been having a bit of a discussion with a rather “in-your-face” gentleman called Eli Rabett on another blog not to be named, about the changes in CO2 in Hansen’s different forcing scenarios. Eli’s claim is that there is “not a tit’s worth” of difference in CO2 in Scenarios B and C until the year 2000. In support of this, he provided the following chart:

He does not say where the data for the chart comes from … or how he did the calculations … or anything. He just claims that’s the truth. But it can’t be, because if the difference were only a few parts per million between the observations and all three scenarios, why are the scenarios so different from each other and from the observations?

(And in a bizarre twise, he has the Scenario C levels flattening out in 2000, whereas Hansen states that “Slow growth [Scenario C] assumes that the annual increment of airborne CO2 will average 1.6 ppm until 2025, after which it will decline linearly to zero in 2100.”

Now, I’ve been putting off actually doing the exercise of figuring out the CO2 levels in Hansen’s scenarios, because it’s somewhat complex. The problem comes from Hansen’s specification of the inputs to the models, which are as follows:

Scenario A
CO2 3% annual emissions increase in developing countries, 1% in developed.

Scenario B
CO2 2% annual emissions increase in developing countries, 0% in developed.

Scenario C
CO2 1.6 ppm annual atmospheric increase until 2025, and decreasing linearly to zero by 2100.

(He also specifies changes in methane and nitrous oxide, but as he says, “Comparable assumptions are made for the minor greenhouse
gases. These have little effect on the results.”)

As you can see, the CO2 inputs are in different units, with A and B given as emission changes, and C given as a change in atmospheric ppmv. That’s the difficulty.

However, I am nothing if not persistent, so I tackled the problem.

I got the historical carbon emission data by country from the CDIAC for 1958, the start of the run. I divided it into developed and developing countries. It breaks down like this (in gigatonnes of carbon emitted:

World : 2.33 gTC
Developed : 1.90 gTC
Developing : 0.43 gTC

That was the laborious part, splitting out the emission data. Next, the atmospheric data. Not all of the CO2 that is emitted stays in the atmosphere. To account for this, I had to calculate the percentage that remained in the atmosphere each year. This varies from year to year. To compute this, I took the Mauna Loa data for the change in CO2 year by year. Knowing the atmospheric concentration and the amount emitted, I then calculated the amount retained by the atmosphere. Over the period, this varied in the range of 80% to 40%.

I was then ready to do the calcuations. For Scenarios A and B, I calculated each succeeding year’s increased emissions, multiplied that by the percentage retained in the atmosphere, and then used that to calculate the new atmospheric concentration. Scenario C was much easier, it was a straight 1.6 ppmv increase annually.

Here are the final results:

A couple things of note. First, Scenarios A, B and C are fairly indistinguishable until about 1980. This is also visible in the model results, where those scenarios do not diverge significantly until 1980.

Second, all of the scenarios assume a higher rate of CO2 growth than actually occurred.

Finally, since these scenarios were designed by Hansen to encompass the range of high and low possibilites, this sure doesn’t say much for the scenarios …

w.

MarkR

From Steve Milloy Junkscince.com

Check the link out for maths of exagerated warming trend forecast.

“Real-world measures suggest moderate to strong negative feedback, currently unnamed and un-quantified, mitigates the Earth’s thermal response to additional radiative forcing from both human activity and natural variation. Justification for amplification factors >2.5 for unmitigated positive feedback mechanisms is not evident in empirical measures. It is not clear whether any amplification factor should be applied or even what sign any such factor should be. Nor is there evidence to support such large ? values in GCMs. Division of real-world measures continue to exhibit the same surface thermal response derived by Idso for contemporary local, regional and global climate, for ancient climate under a younger, weaker sun and for Earth’s celestial neighbors, Mars and Venus.

In the absence of support for amplification factors and in view of their erroneously large ? values it is apparent that the wiggle fitting so far achieved with climate model output is accidental or that these models contain equally large opposing errors in other portions of their calculations such that a comedy of errors produce seemingly plausible results in the short-term. In either case no confidence is inspired.

On balance of available evidence then the current model-estimated range of warming from a doubling of atmospheric carbon dioxide should probably be reduced from 1.4 – 5.8 °C to about 0.4 °C to suit observations or ËÅ”
0.8 °C to accommodate theoretical warming — and that’s including ?F of
3.7 Wm-2 from a doubling of pre-Industrial Revolution atmospheric carbon dioxide levels, a figure we suspect is also inflated.

The bottom line is that climate models are programmed to overstate potential warming response to enhanced greenhouse forcing by a huge margin. The median estimate 3.0 °C warming cited by the IPCC for a doubling of atmospheric carbon dioxide is physically implausible.”

“We do not know why modelers persist in using their 2.5 times amplification factor when empirical measure repeatedly demonstrates 0.5 to be the correct ratio. We would like to think competition for a share of the multi-billion-dollar global warming research largesse had nothing to do with it but we can see how difficult it would be to get published in such a frenetic field with results reflecting trivial response. With such a large cash cow to roast we expect heat settings to remain on “high” for the foreseeable future.”

Link

Willis Eschenbach

Thanks, UC, for the clarification.

My understanding, open to correction, is that “stationary and “iid” are different things. All iid means is that they are not autocorrelated, and that they have the same distribution (gaussian, poisson, etc.). These data points might or might not contain a trend. Adding a linear trend to gaussian data merely produces a new distributition, let me call it “trended gaussian”. As long as all of the data points are “trended gaussian” in distribution, are they not “identically distributed”?

Also, you say:

Yes, in autocorrelated case, sample standard deviation from small sample will usually underestimate the process standard deviation.

This is true regardless of the size of the sample.

w.

bender

“identical” means the distribution doesn’t change. If there is a trend, then a key parameter of the distribution – the mean – is changing.

“non-autocorrelated” and “independent” are synonymous.

“stationary” typically means first order *and* second order moments (mean, variance) do not change.

bender

UC, if x1 is dependent on x2, and so on, then xi is, by definition, autocorrelated. Now, the ability to infer autocorrelation based on a sample autocorrelation statistic, that’s an issue. It’s nigh impossible if the series is very short. The dependency among xi needs to be somewhat persistent before the sample autocorrelation coefficient becomes significantly different from zero. The dependency may exist, but not be detectable via a (small) sample autocorrelation coefficient.

Similarly, if the autocorrelation relationship varies from one (or some) xi to the next, then a dependency is always there, but it will not yield a significant autocorrelation coefficient, because it is not one, homogeneous dependency. This illustrates your point.

But then I ask you: how would you characterize this moving dependency? You can’t. Therefore you have the same problem with the term “dependence” as you do with “autocorrelation” – whether the series is short, or whether the dependency varies.

Sure, the terms can mean different things; but they are synonymous in the context you and Willis were using them.

Willis Eschenbach

Man, I love this blog. I learn more here in one day than I can even process. Thanks, guys.

My original post that led to this discussion was originally intended for a less mathematically knowledgeable blog, so I tried to simplify the math, describing the standard deviation as the “average size” of the residuals, which is not strictly true, etc.

w.

bender

#168 is consistent with #165.

Of course, the nature of w(k) matters. The correlation in x(k) will degrade as the variance in w(k) increases. That does not mean x(k) is not autocorrelated. It means the autocorrelation coefficient is a weak model for describing the autoregressive effect of alpha.

Your caution about definitions, I imagine, stemmed from this line in #158:

A scorching hot month is not usually followed by a freezing month, for example. This type of dependence on the previous data point is called “autocorrelation“.

If you “agree with Willis” on this point, then why raise the issue about definitions, particularly the distinction between of “dependence” and “autocorrelation”?

His statement is accurate enough for a blog and accurate enough to make his case. If he wanted to be more accurate he might have said:

This type of dependence on the previous data point is callled what leads to “autocorrelation”.

But then we’re splitting hairs here. And I just don’t think it’s necessary. Last post.

lucia

Out of curiosity, have Hansen et al 2006 ever provided a source for the values in their charts? I’d like to see the number in the graph.

FWIW, I think the difficulty with lining everything up in 1958 is that the initial conditions (IC) for the runs were probably midnight, Dec. 31, 1957. Hansen et al. doesn’t say this, but one must provide initial conditions to a run, and setting the IC to match that particular time is the only thing that makes any real sense.

The Annual Average temperatures in 1958 did rise, and however the initialized the model didn’t.

It does make complete sense to put HADCRUT and GISS on the same basis time basis, so what willis does makes sense there. You need to normalize everything to the same year.

I’m actually not sure quite what is correct to do about matching or not matching start points.

I could be wrong, but it seems to me there are challenges revolving around with setting initial conditions. You can’t set them for a full average year, you must set them for a precise time. How well can any modeler know everything in Dec. 31, 1957? Whatever choices are made have some effects on climate. Some choices — for example individual storms– may have short term effects on predicted climate; others’ long term effects on predicted climate. (Anomolously high or low amounts of stored heat in the oceans could have a quite long term effect.)

The sensitivity to these initial conditions is not discussed in the 1988 papers, I don’t run these models, so I don’t know.

But… anyway, did anyone ever find the data for the Hansen graph on line? I’m hankerin’ for the unshifted stuff, and I’d like 2006 and 2007!

John M

FWIW, here is my crude (sorry, I had to use Paint) update of the Hansen plot. For the sake of argument, I have done it on the “apples to apples” basis supported by Peter Hearnden in #10. I have estimated the GISS anomaly for 2007 to be +0.74, based on the J-N data and the fact that it looks like Dec will about the same or cooler than Nov.