What Period Should We Use to Compare Uncertainty Bands?
There have been concerns that the uncertainty intervals based on linear regression of seven years data are too small and not correctly account for the full range of “weather noise”. Generally speaking, counter examples of historic variability used to justify larger effects of “weather noise” than appear in my uncertainty intervals have all estimated “weather noise” using periods affected by major eruptions of stratospheric volcanos.
The most recent period is one in which stratospheric volcanos have been calm. For this reason, I think it is very important to based historic estimates on periods when major eruptions were not superimposed on what might otherwise be called “non-volcanic weather noise”.
In pursuing this answer to “what are the correct uncertainty intervals” am looking at three major things:
- identifying the “correct” historic period that we might be able to agree is a period with “no volcanic activity” (as the present appears to be).
- estimating the variability in computed trends during that period. This is straight-forward.
- communicating with Martin Ringo about econometric methods to estimate the uncertainty intervals when Cochrane-Orcutt applies. Martin has suggested a standard method to improve my uncertainty intervals. It makes sense, and I’m implementing it.
For today’s post, I’m going to discuss how I am identifying periods of time that are not affected by stratospheric volcanos. The choice of time periods can affect the final outcome of any analysis. As I am certain many of us will differ the precise period we think is “volcano dust free”, I think it’s worth discussing our reasons for focusing on any particular years before doing too much analysis.
I’m obviously not going to do computations with every conceivable choice of “volcano dust free” period, but I think it’s worth posting my thoughts before discussing result. (Or even finishing them my analyses. FWIW, the information about uncertainties from Martin Ringo is very useful, and I’ll be incorporating it in my future uncertainty bars and the upcoming discussions.)
So, on to the question for the day!
When did the effects of stratospheric volcanic eruptions veil the earth?
One might think the question “When did the effects of stratospheric volcanic eruptions veil the earth?” would be easy to answer. In fact, it is not– or at least the answer is not entirely obvious to me. (Possibly, after this discussion, others will provide links to references that help clarify the answer, but for now, I will show what I considered when identifying the period when volcanic dust us known not to veiled the earth.)
It happens, that I have posted graphs showing estimates of stratospheric volcanic eruptoins veiling of the earth and causing cooling. In one post, I included a graph from Robok showing veiling as estimated by Mitchel, in another I showed a graph showing the forcings as used by NASA GISS.
To permit easy comparison, I’ve merged the two graphs below.
The brown curve in the top graph in the figure above represents the forcing as used by NASA GISS when running model hindcasts. The light green curve represents the sum of all forcings used.
It is easy to see that stratospheric volcanic activity is thought to cause extremely large deviations in the overall forcing on the earth’s climate. So, one would likely expect the variability in temperature and temperature trends associated with periods containing this sort of volcanic activity would differ from periods with no effects of stratospheric volcanos. We are in such a calm period currently.
To identify a similar calm period based on the NASA data, I rather arbitrarily decided that I would exclude all 7 year averages whose computation is affected by a year in which stratospheric aerosols were resulting in an anomalous forcing less than -0.25 W/m^2. This is sketched by hand on the Excel graph above.
Having done this I found a stretch of years that appears unaffected by volcanic activity. At this point, I found no suitably long spans– unless I ignored one month in 1929 which had a deviation of -0.253 W/m^2, and which was surrounded by similar levels of “masking”. Ignoring that month resulted in a nice span of roughly 40 years , illustrated by the blue line at the top of the NASA figure. If this span were unimpeachable, I would then have analyzed all 7 year trend centered on years in the smaller regions shown with the purple line. The neighboring edge years are would be excluded, owning to the fact that to calculate the 7 year trend centered on 1921, I would need to include 3.5 years prior to 1921, there by including 7 year trends whose computation is affected by years with a volcanic eruption.
The Mitchell Graph
My intention in doing this analysis is to find a period of time that source of volcanic masking suggests is affected by volcanic eruptions. After identifying the span of “no eruptions” based on the NASA data, I turned to the Mitchell graph to see whether any of the years included in my span might be excluded on the basis of other estimates of veiling due to volcanic activity; this graph is shown in the figure above– just below the graphs based on the NASA values.
Because NASA chose to use a source other than Mitchell, I investigated to see if it is still used by anyone. As recently as May 2000 in Reviews of Geophysics, Robok discussed the Mitchell and Lamb DVI indices for volcanism in a index paper discussing the effects of volcanism on climate. So, one might presume the Mitchell DVI information is not totally discounted. If I am to lean in the direction of exclusing absolutely all years when stratospheric volcanos erupted, I would need to consider the Mitchell data.
I noted that, based on Mitchell, I would need to some years from the record, owing to the eruption of Hekla, in Iceland on March 27, 1947. (Hekla is far to the north. However, though this eruption is not included in the Sato charts of optical depth, the temperature did drop after Hekla. That said, the temperature was already dropping. So, we could, and likely will, argue.)
Excluding the years after the eruption of Hekla left the range of years illustrated by the horizontal red line, with arrows indicated, shown above the Mitchell graph. As described previously, I then computed the 7 year trends centered on years inside this band, excluding those on the edge whose computation involved even 1 month outside the “volcano free” region.
The set of months deemed free of the effects of stratospheric volcanic activity on the basis described ran from February 1921 to February 1947. The period that permits computation of 7 year trends goes from July 1924- Sept. 1943.
Open questions.
- I selected -0.253 W/m^2 as the criteria for “volcano free” with NASA GISS data. Any votes for -0.3 W/m^3? -0.5 W/m^2? (My inclination is to make absolutely sure volcanos are not affecting are not affecting the calculation of 7 year trends.
- I am taking the information from Mitchell seriously; this is because my inclination is to be absolutely sure volcanos are not affecting the calculation of 7 year trends. I will be doing all computations assuming Mitchell is correct initially. Given what the temperature data look like, it is certain some others will wish to ignore Mitchell, and include the mid-40s in the “volcano dust free” period. I’ll be happy to repeat the computations including the late mid-late forties afterwards.
- Are there other issues I haven’t thought of?
As a closing note: This is taking a bit of time because I am digesting a bit of information from various places. However, the preliminary results suggest that using the time period I suggest and the uncertainty in determining the trend using 84 months of data collected when there are no stratospheric volcanos erupting is approximately 1-sigma ~1.3-1.5C/century if the measurement uncertainty were as large as it between the 20s and the early 50s. However the uncertainty is a bit lower now, owing to improved measurement techniques. That siad, my new uncertainties will be larger than the 1.0 C/century to 1.1 C/century I used in previous hypothesis tests.
All these numbers are provisional based on implementing the information Martin Ringo communicated and checking my spread sheet for blunders.
References
“Internally and Externally Caused Climate Change” by Robock (1978).
Comments
Arthur Smith (Comment#2982) May 21st, 2008 at 8:57 pm
It occurs to me from looking at those graphs that the true situation we have is one of quite frequent (but irregular) stratospheric volcanic eruptions, and one ought to include some average frequency/magnitude of the things when looking at trends anyway. After all, if volcanoes regularly cool the atmosphere every few years, then a period with no volcanoes for a while will gradually get warmer (a contributing factor in the warmth of the early 1940’s perhaps?)
I realize you’re trying to compare the most recent 7 year period with earlier ones here so it’s perfectly legit to ignore the volcano years, but I just wanted to point out there may be something more complicated to think about in the analysis…
Also - while a volcano year does drop the average temperature of a seven-year period, it doesn’t necessarily affect the trend (or does it? Time-constant issues again I guess!) - as long as the volcano year was roughly in the middle where its lower temperature wouldn’t have much weight on the trend calculation… so it might make sense to include some time-spans with volcano years as well. If you wanted more comparable data that is…
rex (Comment#2985) May 22nd, 2008 at 2:14 am
http://wattsupwiththat.wordpress.com/
I put it to you that GISS should no longer be quoted as a reliable mean global temperature source due to these various errors quoted and found by various statisticians
Julian Flood (Comment#2986) May 22nd, 2008 at 4:37 am
Re Arthur Smith May 21st, 2008 at 8:57 pm
a
period with no volcanoes for a while will gradually get warmer (a contributing factor in the warmth of the early 1940’s perhaps?)
I’d not describe that as a gradual warming — a jump by .4 deg in less than two years if you judge by the (non-corrected portion of) the SST graph at:
http://www.climateaudit.org/in.....ct3b44e627
I’d still like to see the stats on a linear warming from 1910 to 2010 at a rate of .14 deg/decade vs uncorrected hadcrut, NH and SH, with the period 40 to 50 replaced by a straight line. It stands out in all the graphs like a (insert testicular metaphor here). Alas, my maths isn’t up to it.
JF
lucia (Comment#2987) May 22nd, 2008 at 6:45 am
Arthur–
I agree with everything you say. I’m looking at the “no volcano” period only to estimate uncertainty intervals for calculating the current trend based on the specific period of time from 2001-now.
The fact of volcanos does not put the determination of the trend over the century in any doubt. The upward trend from the 50s is near certain.
I’ve calculated for 1979-now. The variability about the mean trend, as measured by the residuals to the fit, is larger than currently. However, uncertainty intervals for the trend are very small, because even with volcanos, the way 30 years gives you both a larger number of data points and a larger span in time. (Both matter: All things being equal, the uncertainty in the trend goes roughly as ~N-0.5, where N is the number of data points. So, if you have 4 times as many data points, the uncertainty bands on a calculation of the mean trend are cut in half. But with linear regression y=mx+b, we also have the standard deviation of all measured “x”s and all measured “y”s in the denominator of the calculation for the standard error in the trend, “m”. So, “N” data points spread out over a 20 years gets smaller uncertainties for the trend “m”, than the same number of data points over 5 years. )
Using Cochrane Orcutt for 1979-now based on the merged data I used way back in January, I get a warming trend of 1.5 C/century ±0.2C/century for that period — that’s 1 sigma. (With OLS, correcting uncertainty intervals I get 1.6 C/century ± 0.2C/century uncertainty bars — once again 1-sigma.)
I observed this way back in February — just before the first “falsification”. My uncertainty intervals weren’t so “controversial” when I did that post.
Anyway, the volcanos don’t put the measured trend since the late 70s in any doubt. It’s definitely there.
The question I’ve been asking is: Are the AR4 predictions this has increased to 2C/century correct? The answers I’m getting suggest no. But, John’s made a point about the uncertainty intervals– and it does look like mine might be a bit too small. (Reasons to be explored. . . )
But, if we look at volcano-free periods, they only look a bit too small. On the other hand, other places look way too big for the current period.
So.. now I better post what I get for the uncertainty during that period.
lucia (Comment#2988) May 22nd, 2008 at 6:50 am
rex–
I think there are problems with all measurements, everywhere. (I don’t just mean ones used in climate change. )
But, we have to use something.
In any case, even those most suspicious of GISS measurements would be unlikely to suggest they intentionally perverted the ’20s-50’s record with the intention of making the weather look more variable just to screw up my analysis of a “no volcano” period in the future! To do that, the group would need to be both malicious and psychic!
If the climatologists at GISS were psychic, we wouldn’t need GCM’s.
Phil. (Comment#2990) May 22nd, 2008 at 10:29 am
I put it to you that GISS should no longer be quoted as a reliable mean global temperature source due to these various errors quoted and found by various statisticians
Which errors and which statisticians?
Would you adopt the same procedure with UAH and RSS because of the various errors found in them?
Alan S. Blue (Comment#2991) May 22nd, 2008 at 11:10 am
If you use the daily data instead of the monthly data, you end up with 30x the amount of trend data. Then you’ll end up with extremely tight error bars for the observed trend.
The issue about the tight error bars come back to the question: What are you measuring exactly? There’s a difference between the climatic trend, the weather trend, and the best-fit trend. And the definitions of two of those are too flexible - they’re coupled.
Getting a tight set of error bars around the current trend would be nice. And getting a tight set of error bars around the other volcano-free periods will also be nice. But even perfect knowledge of the one true ‘measurement trend’ through either (or both) of the available periods doesn’t seem like a step down the path towards discerning whether this is a climate trend or a weather trend. Both of those trends could reasonably be outside the error bars of the measurement trend!
Postulate a simplistic monotonic 1C/C ± 0.001C/C trend for the entire ‘climatic trend’ across 1800-now. Postulate ‘all deviations from the climatic trend are weather and measurement’. (C + W + E -> O) Now look at our recent trends. The Climate trend would be 1C/C (by assumption). The “weather trend” for 2000-2008 would be more variable, but around negative 1C/C or so. The Observed trend would be around 0C/C. All three will “falsify” one another.
Disentangling ‘climate’ and ‘weather’ isn’t a trivial problem. The recent Nature article boils down to “Ok, ENSO is a stronger weather trend than we thought, but the underlying climate trend will be unchanged.” That’s a concession that the error bars on ‘weather’ are a lot larger than previously thought. Perfect knowledge of both the climate trend and the observed trend would still be fundamentally difficult to falsify - definitionally. Any discrepancy can be attributed to weather. With ever-widening error bars.
Variability of 7 years trends during a “volcano dust-free” period | The Blackboard (Pingback#2992) May 22nd, 2008 at 11:47 am
[...] Comments: What Period Should We … [...]
lucia (Comment#2993) May 22nd, 2008 at 12:01 pm
Alan–
Daily data would be help a lot if the weather weren’t so strongly autocorrelated in time. So, switching to daily isn’t going to solve any major arguments.
Estimating the amount of energy in “weather noise” is precisely the issue here. JohnV suggested I look at variability during periods with no volcanic activity. This doesn’t get us a precise answer, but it’s a shot at the problem.
I’ve been mentioning in comments that it would be interesting to do the following:
1) Get GISS Model E realizations for cases with solar only.
2) Find the spectral characteristics.
3) Do the calculation to find out how the uncertainty bands you get when estimating over 7 years means differs from the ones you get over 20 years (and or forever.)
I’m pretty sure that if I have 1&2, I know how to do 3. For example– in the articles on “nearly spherical Enso”, we looked at the error in the regression due missing a periodic temperature variation with a known period and known phase shift.
If we know the spectral distribution of temperature variation, we can use that sort of analysis, but integrate over the full probability distribution function of frequency and phase, we can estimate the uncertainty in an OLS fit due to having a shortened time period. (I admit, I don’t think anyone understands what I’m talking about, but at some point, I’ll write a post.)
Of course, if my idea works, the answer would be for “model data”, but at least that would give an estimate. In my opinion, estimates are always better than just saying “It can’t be done!”
Hans Erren (Comment#2981) May 21st, 2008 at 3:47 pm
Here is another independent estimate of the Volcanic aerosol optical thicknesses using lunar eclipses
Dust veil index derived from Lunar eclipse darkness
http://www.volcano.si.edu/repo.....#bgvn_2605
http://www.volcano.si.edu/repo.....05_25s.png