I am still working on my junior Climate Audit merit badge. In this post I continue bashing on Tamino because he is a Left wing scientist who believes we can legislate climate and is willing to write anything to see that we give it our best shot. Also, he still won’t let me comment on his blog. (Not many dissenters there I’ve noticed!)
In my other post Tamino’s Folly – Temperatures did Drop I demonstrated that we know temperature trend to a higher degree than Tamino has asserted. Several readers made the claim that Tamino was arguing that we don’t know the temps dropped due to weather noise, however that was not part of the post I was addressing.
I repeatedly stated that I agreed with Tamino’s analysis of trends indicating that the recent drop could easily be part of a longer term warming and in fact I had replicated it. However, I didn’t explain the rest of the story. His link is here
There is a serious problem with his argument which goes unsaid, not that his demonstration is terribly wrong just that the assumptions are designed with a predetermined conclusion. It happens right in the first paragraph.
In the last post we discussed MA (moving average) noise processes, and even combined them with AR (autoregressive) noise processes to define ARMA (autoregressive moving average) processes. I mentioned that global average temperature behaves approximately as a trend plus ARMA(1,1) noise, i.e., a 1st-order AR, 1st-order MA process.
Let’s put some of this to practical use; let’s create some artificial data, the sum of a steady trend at a rate of 0.018 deg.C/yr (about the rate of global average temperature), and pure ARMA(1,1) noise with AR parameter
, MA parameter
, and white-noise standard deviation
. With these parameters, it’ll have just about the same structure as GISS monthly temperature data since 1975.
He assumes that the trend is only known to be perfectly linear upward and the rest of the data is noise. By making this assumption he automatically assigned anything except a linear uprise as noise. He modeled the level of his “noise” and got the a similar result as we see in current temperatures. He then measured a slope in the noise and demonstrated that the measured slope is not outside the 95% confidence of the rest of the slopes. Really it’s more of an exercise in math than an exercise in global warming. I found the series to be quite interesting as I haven’t ever needed to create fake data to make a point in my own work. I prefer the real stuff.
Since that time he has made increasingly bold statements about our knowledge of temperature even stepping way over the bounds of reality, claiming we don’t know temps have dropped in his latest post on this topic (a completely unrelated issue). He slammed Bjorn Lomborg for saying temps have dropped or flattened in the last decade stating that we don’t really know. This is a pile.
Well, I wanted to see what happens when we modify the initial assumption that we only know a linear trend in the data. Below is a plot of the GISS data. The top plot is the data, the second plot is a 21 year gauss filter using the CA algorithm and the third plot is what I call Jeff’s weather noise. I say that because we know the actual temperatures with high precision but low accuracy from my previous post (there are major problems in overall measurement ). See accuracy and precision HERE.
The top graph is actual giss monthly data, the 21 year gauss record is the filtered top graph using a function by CA, the bottom graph is the difference. This is the noise level with long term signal removed rather than using an artificial linear slope.
I also modeled Tamino ARMA noise from the values given at his site. My GISS data minus 21 year filtered trend from above is the top graph in the figure below. Tamino’s ARMA values were used for the third and fourth graph in the figure. It looks pretty reasonable as a match between the first and third plots but look closely at the scale of the filtered second and fourth plots. The actual data after low frequencies (21 year filter) are removed has a variation from about -0.4 to 0.4 while Tamino’s graph goes from -0.1 to 0.1. Since all I did was remove the long term trend, Tamino’s estimate of variance is quite high.
Well what can we do with a correct variance?
The standard deviation of the above GISS data is
GISS SD = 0.131
Sigma Tamino using ARMA sigma 0.11 results in SD- 0.144
SD looks slightly high but reasonable yet the max-min filtered values Tamino VS GISS above have a variation of 2.5 times over the real data!!
I used an ARMA 1,1 process fitted in R to create my own noise series. See below.
My SD was 0.134. ARMA 1,1 regression seems to overestimate longer term trends, you can see my actual signal in pane 3 of the above plot is quite similar to pane 1. Pane 4 which is the 11 yr filtered curve has a slightly larger distribution -0,5 to 0.5 than the actual data pane 2 -0.4 to 0.4. This means that despite all of my work ARMA isn’t a trusted replacement for actual data. That doesn’t mean it can’t have some value but conclusions must be kept within reason. Tamino lost it there for sure.
Well the real reason for this analysis is to look at trends and the probability of certain trends occurring in temperature data. I fitted ten year slopes to the above series in a sliding window for each ten year group of months and just for you plotted some histograms. (what do you do with your free time?)
This is flat trend data so the mean is always averaged to zero over long term, the series are the same length as GISS data so there is distortion in the Gaussian shape.
Well great, my histogram is lopsided. I ran it a bunch of times and found that the shape changes right and left of center even sometimes sitting in the middle. The basic meaning is that I didn’t have enough data to resolve an accurate bell curve. Tamino’s distribution is substantially wider though above than GISS or my weather data so his ARMA values resolved to a better bell.
Keep in mind that I could have presented a normal shaped distribution just by re-running a couple of times and made no mention but I hope my site is more honest than that. A longer series would average to a normal bell curve centered distribution as guaranteed by ARMA math, so please be assured nobody is tricking you here.
Well graphs are cool for sure, but what do the numbers really say about the distributions. What is the standard deviation of the slopes?
I calculated the SD of the slope values for the ARIMA noise. Jeff Id and GISS weather variation in this section includes the removal of the 21 year filtered trend as shown above where annotated.
TEN YEAR SLOPES STANDARD DEVIATION
GISS Actual Data – +/-0.014 Deg C/Yr
GISS 21 Year Values Removed – +/-0.0081 Deg C/Yr
Jeff Id 21 Year filtered GISS trend removed ARMA 1,1- +/-0.0089 Deg C/Yr
Tamino linear 0.018 year slope trend removed ARMA 1,1- +/-0.0146 Deg C/Yr
So inserting the Tamino calculated SD value of 0.11 in an R based ARMA calculation results in an SD of 0.14, this is quite a bit larger than the intended SD of 0.11.
Anyway it really doesn’t matter much, the SD of the slopes of the lines are determined by the assumptions rather than the data. If I make the assumption that all 10 year variations are well known and not “noise”, I filter by a 10 or less years and those trends get copied into the “trend” curve while the “noise” curve contains the designated spurious information. The assumption guarantees the conclusion!!!
Below I looked at the probability of certain 10 yr slopes occurring after removal of gaussian 21 year variation.
What does the SD of the 10 year slopes in the above curves mean when compared to an overall annual rise of 0.018 Deg C/Yr. Two sigma ~95% values. The values below were generated in annotated cases to be after the 21 year filtered curves were removed from the data.
GISS Actual Data SD 0.014 Deg C/Yr = 0.018 Tamino assumed C/yr +/-0.028 2 sig distribution = 0.046/-.01 Deg C/yr
GISS 21 Year Values Removed 0.0081 Deg C/Yr = 0.018 Tamino ass. +/- 0.0162 2 sig dist.= 0.034/0.002 Deg C/yr
Jeff Id 21 Year filtered GISS trend removed ARMA 1,1 0.0089 Deg C/Yr = 0.018 +/- 0.018 2 sig dist = 0.036/0.000 Deg C/yr
Tamino linear 0.018 year slope trend removed ARMA 1,1 0.0146 Deg C/Yr = 0.018 +/-0.028 2 sig dist = 0.046/-0.010 Deg C/yr
Ok, sorry about the pile of numbers. What it means is that Tamino’s ARMA slopes with the International Panel on Climate Change’s number 0.018 deg C/year of guaranteed temp rise added in have an amazingly wide range of “weather noise” slopes. As a non-climatologist using Tamino’s values, pretty much everything except for a huge meteor strike will be within IPCC slope predicitons (95% or 2 sigma confidence interval of 0.046/-0.010 Deg C/yr).
The standard deviation of the ARMA noise values presented by Tamino includes a few of these short term standard deviation expanding “major events” as stated by Lucia in the thread.
I don’t think the probability of a downturn or flat periods since 2001 is properly estimated by fitting the ARMA(1,1) process to a period where the major plunges are due to Pinatubo, Fuego, and El Chicon rather than weather processes like El Nino, La Nina, the PDO, AMO or other oscillations.
She isn’t exactly hammering the concept I am describing in her replies but is respectfully commenting on an overestimation of the SD values. I made no effort here to correct for these real issues.
Well what happens when we include 11 year gauss trend as actual fluctuations in climate rather than weather noise.
Now we have the middle pane above. These values are measured with high precision so we know they are real. What we don’t know well is the actual slope due to the massive corrections in GISS. We also don’t know the actual value with the same accuracy as the relative value. I hate using GISS numbers but it is what I have available. Someday I will show the huge corrections made to GISS temps which are nearly as big as the entire signal, something which should worry any real scientist yet somehow is regularly overlooked by our brilliant AGW friends.
Well I calculated a sliding ten year slope analysis on the signal above for comparison to previous values and calculated SD values.
Two SD of 10 year slopes is 0.0104. In an IPCC upslope of 0.018 +/- 0.0104 = 0.0284/0.0076 DegC/yr
Ten year trends outside of these 95% confidence and both positive 0.0284/0.0076 values in the weather noise are unusual because my assumption was that ten year trends are not noise. We know from my previous post that we can measure 10 year trends with high accuracy so they are quite real. While my first 21 year GISS trend is a reasonable counter for Tamino’s result (except for Lucia’s point about major volcanic influences) \. This example is not very meaningful as I have made the assumption that 11 year trends are not noise and then looked for 10 year trends in the noise data. Unlike much of the AGW community I’m being honest about my calculation.
In Tamino’s post, he says anything shorter than 130 years in trend is noise and then finds the noise shorter than 130 years in the data. It is completely circular reasoning.
That is the difference between my blog and Tamino’s. It would be simple to distort my comments and make a bunch of points against the AGW guys, that is not my intent. I simply want to show that some AGW guys are selling us a bunch of statistical rubbish as though it were proof. Tamino used this example to state that we can’t say if the recent downtrend is real. This is a false conclusion, and in my opinion it is deliberately and with intent, misleading. Unfortunately he got a bunch of smart people to buy into it.
We do know the 10 year trends are real, we can measure them. We don’t know if the down or up trends will continue, this type of analysis doesn’t change that. Many of us are suspicious that we have been in a long ‘ natural’ uptrend for the last 150 ish years (starting before industrialization) but the corrections to the GISS data make it impossible to trust. Most proxy based temperature reconstructions have serious flaws which leaves honest scientists with little to conclude.
Looking at the second pane of the last graph above if you were to bet your life, could you put it on a definite increase in the next 10 years or would you bet on a continued downslope? (ignoring the fact that politically biased scintists controll the GISS data) I’m going with – don’t know.
Conclusions
— Taminos linear + ARMA model overestimates typical 10 year slope variation by about 2 times. (His magnitude of the -0.035DegC/Yr downslope in his own examples)
— My non-linear + ARMA estimates using 21 year trend removal show that assuming a 0.018 linear upslope, a 10 year trend less than 0 deg C/yr is outside of the 95% significance interval.
— Both estimates are skewed to a wider range by major events such as volcanoes and El Nino’s etc.
— Changing the assumptions to be more reasonable demonstrates that out current downtrend known to a high probability to be outside of Tamino’s definition of weather noise yet conclusions about the future trend are still not warranted.
— Tamino used circular reasoning by first assuming that any variation less than a 130ish year linear trend is noise, modeling the noise and then finding trends in the data assigned to be noise. This is more of a political point than a useful demonstration. He is correct that if the AGW assumed uptrend is real short term downtrends are also possible, he overestimated the confidence interval and conveniently fails to mention that our current trend may also continue downward.
It was suggested on one of my other threads that if I could demonstrate that a trend was outside of the 95% confidence including weather noise I would have something. What we need to understand is that this type of analysis is not useful for making conclusions about the significance of a trend as the significance is defined by the assumption of what is or is not noise, nothing more.
the Air Vent 
Jeff,
Why use 21 years instead of the accepted 30-years-is-climate?
Wouldn’t volcano’s explain your lopsided bell curve?
Raven,
I used an arbitrary 21 years and also redid it at 11 simply because we know temps better than that. The lopsided bell curve is created from ARMA data only so no volcanoes, each time I run it it shifts a bit. Sometimes it looks near perfect.
As a non-statistician (ie I don’t understand some of your post) I asked a question on Tamino’s blog that seems very relevant here:
===My question on “open mind”====
I have a question that doesn’t seem raised here (implied maybe?). I have followed a few discussions in this blog for a little while only, so if it has been covered elsewhere, please feel free to point me to that resource.
Clearly you can’t take two end points and say that the trend is up or down.
But how do you determine what statistical analysis to apply to a given period? And how do you determine what period is significant?
To someone as uninformed as me, it seems to go to the heart of the problem. I’m not a statistician so bear with me. Doesn’t calling variation noise imply that you know what the signal is?
I’m looking at a graph of global temperatures from 1860 to present, that someone has thoughtfully added a 5-yr average to. It’s an arbritrary choice I’m sure but it makes the swings from year to year disappear. To say that climate is measured over 30-years is again an arbitrary choice. If we put a 30-yr average over the graph, would the cooling from 1940 – 1970 appear to be “noise” until it was over? Or even disappear as noise if you put the right time period of averaging onto it?
So this is what I’m missing. Do you need to have a climate model to determine the right period? Without a climate model is any period as good as any other, with the only proviso that longer is better? And if that’s the case, how do you ever know that you have picked a long enough time period?
======response from Tamino=========
[Response: It’s immensely difficult to know what the “signal” looks like when the noise level is so high. Over a period as brief as a decade, it’s not even possible to demonstrate that there’s a signal at all — it could be just noise. But as the time span gets longer, the signal level increases while the noise level (presumably) stays the same, so the signal-to-noise level gets high enough that it finally becomes possible to demonstrate there really is a signal there.
Then one has to identify the shape of the signal. This can’t be done with certainty, we can only approximate it, but the right thing to do is to find the *simplest* description which “explains” the variation in the sense that what’s left over (the “residuals”) aren’t unambiguously different from noise. The data since 1975, for example, are well modeled by a linear increase plus noise. The linear increase is the simplest pattern to explain the signal, and the residuals are indistinguishable from noise.
Often you can get valuable clues about the signal shape by smoothing the data — the 5-year averages do exactly that. There’s still noise there, but it’s less than in the 1-yr averages or the monthly averages. Meanwhile the signal is undiminished, at least that part of the signal on a time scale of about 5 years or longer! Fluctuations on shorter time scales are lost; for example we lose the seasonal changes with 5-yr averages. But we’re not really interested in the seasonal changes anyway — if we didn’t get rid of them by averaging we’d want to get rid of them some other way — so that’s OK. But there could be other changes on short time scales that would be “smoothed out” by smoothing on a longer time scale.
The main thing to keep in mind is that all we get from statistical analysis, in the end, is an approximation. The last 30 years are indistinguishable from a linear increase plus noise, but that doesn’t mean the increase is truly linear; it almost certainly isn’t. But we can establish for certain that over that time span it’s more than just noise. And over the entire span of available data, it’s clearly not just a linear increase.
I realize this is an incomplete answer — a complete one would take volumes.]
======end of response=============
It seemed like the answer didn’t really answer my question – but that might be me missing the point. I felt as though the post “Bjorn Lomborg: How did you get those numbers” did kind of assume the answer to prove the answer. But as a non-statistican, I might be way off base. Anyone here have any comments?
Now you got me thinking. Congrats.
JeffID–
I’ll be discussing a similar idea, but taking a different approach. 🙂
Jeff you say “What we need to understand is that this type of analysis is not useful for making conclusions about the significance of a trend as the significance is defined by the assumption of what is or is not noise, nothing more.” Along those lines, as developed by the IPCC, could you not replace “trend” with signal. I once engaged in such a discussion at RC about how the signal of AGW was determined. I got verbal hammering, but your point about noise is what I was asking. But what I really asked was how was this AGW signal determined. The conversation centered around the findings of the IPCC and not the assumptions that led to those assumptions. The basic answer was the IPCC claim that they looked everywhere and only an AGW-CO2 signal could produce the result. So my question to you is can you replace the word “trend” with “signal”?
Hi Jeff,
Will you kindly send me an e-mail. I can’t find your address anywhere around here.
Thanks,
Dan
I have to apologize to everyone for a lack of reply. I am in China this week on business and am being censored a bit. Logging on to make a comment here took more than 10 minutes but was eventually accepted once the people in charge realized this is not an anti-china blog.
Steve,
I think you asked the right question. The underlying theme to his argument is that the trend is not discernible from linear. When I read Tamino’s answer to you it makes no sense. He puts far too much weight on his circular argument.
The point that the longer term trend might be up even after this downward movement is correct but the claim that we don’t know it exists is well….. odd. Especially for a self proclaimed statistician. Our instruments are better than that. When he claims we don’t know if the trend is not linear you can refer to hundreds of peer reviewed papers which show shape in measured temp. It seems to me that he is intentionally confusing the issue. I’m just an engineer but I know the difference between instruments and conjecture.
John,
It is a confusing issue to refer to data as signal or trend and the rest as noise. My first thought is you can say trend or signal interchangeably. It is an artificial nomenclature in this case because the quality of the measurement is good between multiple techniques (despite numerous questionable corrections). i.e. GISS, UAH, and RSS.
We therefore know the real temp much better than the “weather noise” as designated arbitrarily by the AGW guys. It is the height of convenience in my mind to claim that “climate” signal or trend is basically linear and it cannot be resolved by anything to date. It’s even more suspect when when Mann uses 30 year filtered data to present the RED non-linear curve on the blade of the HS.
This same linear assumption is used in the Santer 08 paper to (falsely) verify weather models are accurate. (Without any shyness by the authors). Lucia and CA pretty well kicked the CR.. out of that one though.
I guess it is a matter of convenience for the AGW guys. The same group of people uses the data both ways.
Thanks Jeff. I hope you enjoy your stay in China.
The way AGW proponents use the term signal reflects their point of veiw about climate sensitivity to CO2. I have always thought it interesting if one asks himself just how do you separate this signal from the noise. As an engineer, I know how I do it. It depends on the physical system that I am dealing with. So I ask myself how do they get the signal from such a physical system. I did not find the conversation at RC enlightening. Just because the temperature response of CO2 is assumed linear; and you assume a linear response because of that, this is still a circular argument. That is why I was curious as to whether they could show that they had a signal. To me, without a physical reason a trend is simply an artifact. It is as incorrect to talk of noise, or of trend, without a physical reasoning.
I got a load of childish abuse too from Tamino for saying that forcing a linear fit in a non-linear system makes no sense and that a spline would be more common/suitable. He just repeated similar rubbish – that the simplest fit is the best and that using a spline would be to commit the “crime of over-fitting”. A more rational person would realize that fitting a straight line is a rather larger crime because it leads to over-confident extrapolations. Of course the climate clan must surely know that it all depends on initial bias. Hence the abuse and censorship.
The bottom line is simply that they see a rising trend, they think they know the underlying mechanism and they think it’ll continue. We’ve all seen that type of naive overconfidence many times – and especially lately. However it is an attitude that is incredibly prevalent and hard-to-shift among intellectuals.