First some background for our readers that may not be familiar with the term “random walk”
See: http://en.wikipedia.org/wiki/Random_walk
New Paper “Random Walk Lengths Of About 30 Years In Global Climate” By Bye Et Al 2011
There is a new paper [h/t to Ryan Maue and Anthony Watts] titled
Bye, J., K. Fraedrich, E. Kirk, S. Schubert, and X. Zhu (2011), Random walk lengths of about 30 years in global climate, Geophys. Res. Lett., doi:10.1029/2010GL046333, in press. (accepted 7 February 2011)
The abstract reads [highlight added]
“We have applied the relation for the mean of the expected values of the maximum excursion in a bounded random walk to estimate the random walk length from time series of eight independent global mean quantities (temperature maximum, summer lag, temperature minimum and winter lag over the land and in the ocean) derived from the NCEP twentieth century reanalysis (V2) (1871-2008) and the ECHAM5 IPCC AR4 twentieth century run for 1860-2100, and also the Millenium 3100 yr control run mil01, which was segmented into records of specified period. The results for NCEP, ECHAM5 and mil01 (mean of thirty 100 yr segments) are very similar and indicate a random walk length on land of 24 yr and over the ocean of 20 yr. Using three 1000 yr segments from mil01, the random walk lengths increased to 37 yr on land and 33 yr over the ocean. This result indicates that the shorter records may not totally capture the random variability of climate relevant on the time scale of civilizations, for which the random walk length is likely to be about 30 years. For this random walk length, the observed standard deviations of maximum temperature and minimum temperature yield respective expected maximum excursions on land of 1.4 and 0.5 C and over the ocean of 2.3 and 0.7 C, which are substantial fractions of the global warming signal.”
The text starts with
“The annual cycle is the largest climate signal, however its variability has often been overlooked as a climate diagnostic, even though global climate has received intensive study in recent times, e.g. IPCC (2007), with a primary aim of accurate prediction under global warming.”
We agree with the authors of the paper on this statement. This is one of the reasons we completed the paper
Herman, B.M. M.A. Brunke, R.A. Pielke Sr., J.R. Christy, and R.T. McNider, 2010: Global and hemispheric lower tropospheric temperature trends. Remote Sensing, 2, 2561-2570; doi:10.3390/rs2112561
where our abstract reads
“Previous analyses of the Earth’s annual cycle and its trends have utilized surface temperature data sets. Here we introduce a new analysis of the global and hemispheric annual cycle using a satellite remote sensing derived data set during the period 1979–2009, as determined from the lower tropospheric (LT) channel of the MSU satellite. While the surface annual cycle is tied directly to the heating and cooling of the land areas, the tropospheric annual cycle involves additionally the gain or loss of heat between the surface and atmosphere. The peak in the global tropospheric temperature in the 30 year period occurs on 10 July and the minimum on 9 February in response to the larger land mass in the Northern Hemisphere. The actual dates of the hemispheric maxima and minima are a complex function of many variables which can change from year to year thereby altering these dates.
Here we examine the time of occurrence of the global and hemispheric maxima and minima lower tropospheric temperatures, the values of the annual maxima and minima, and the slopes and significance of the changes in these metrics. The statistically significant trends are all relatively small. The values of the global annual maximum and minimum showed a small, but significant trend. Northern and Southern Hemisphere maxima and minima show a slight trend toward occurring later in the year. Most recent analyses of trends in the global annual cycle using observed surface data have indicated a trend toward earlier maxima and minima.”
The 2011 Bye et al GRL paper conclusion reads
“In 1935, the International Meteorological Organisation confirmed that ‘climate is the average weather’ and adopted the years 1901-1930 as the ‘climate normal period’. Subsequently a period of thirty years has been retained as the classical period of averaging (IPCC 2007). Our analysis suggests that this administrative decision was an inspired guess. Random walks of length about 30 years within natural variability are an ‘inconvenient truth’ which must be taken into account in the global warming debate. This is particularly true when the causes of trends in the temperature record are under consideration.”
This paper is yet another significant contribution that raises further issues on the use of multi-decadal linear surface temperature trends to diagnose climate change.
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
For a walk to be truly random the size and direction of each step must be independent of those of its predecessors.
But we know the “walk” in this case is not random. It is driven by features too complicated for us to determine though. From our point of view this might be taken to be the same thing.
However that over a 30 year period climate has the features of a random walk strongly suggests that there is no single driving “forcing” (CO2).
The issue with the CO2 warmists is that they think they can actually model the world’s climate with some degree of realism. That a simple random walk model works just as well suggests that they are wrong, not that the climate is actually random.
Dave Springer says:
February 14, 2011 at 10:42 am
Perhaps you could illuminate your waffle with a couple of well-chosen examples?
Brian H says: “[Drunkard’s] walks are often staggering. By definition.” 😉
I find them rather pedestrian, myself.
rbateman says: February 14, 2011 at 11:17 am
‘climate is the average weather’ For you C++ fans out there, weather is an instance of the class climate.
An alternate is to consider multiple instances of Class Weather with Climate being a container within which they reside. Climate may then be averaged on a sensible basis, regardless of chaotic behaviour within the individual Weather objects…
“…eight independent global mean quantities (temperature maximum, summer lag, temperature minimum and winter lag over the land and in the ocean)…”
How are these independent? Mins and Maxes should rise and fall with temperature trends, summer and winter lag should be related to how warm or cold it is. I cannot see that these are truly independent quantities.
And, if you account for known forcings (http://tamino.wordpress.com/2011/01/20/how-fast-is-earth-warming/, http://tamino.wordpress.com/2011/01/06/sharper-focus/ – yearly cycle, volcanic activity, solar activity, ENSO, etc.) the actual variability of these quantities is much smaller than what seems to have been used to compute these excursions.
I do not believe this amount of random walk excursion is justified by the data, given actual observed variability of these rather interdependent values after accounting for known perturbations.
art johnson says:
February 14, 2011 at 10:06 am
reliapundit says:
“how about they select any period which helps them prove their case against industrialism and helps them advocate socialism?”
Of course everyone’s entitled to their point of view. My point of view is that I really dislike this sort of comment. The notion that alarmist scientists are somehow all conspiring to destroy capitalism is just hogwash. More importantly, it feeds into certain stereotypes that do the skeptics no good. I wish people would stick to the science, or lack thereof.
_________________________
Out of curiosity, how do you characterize the behavior of the alarmist scientists?
As a group they are advocating a position that would require unprecedented controls by governments around the world to have any chance of lowering CO2 emissions. They advocate this based on flawed science.
What is their motivation?
rbateman says:
February 14, 2011 at 11:17 am
‘climate is the average weather’
For you C++ fans out there, weather is an instance of the class climate.
You will need many climates to make up the next class. Then there is the added complexity of regions, which can and do act independently and oppositely of neighboring regions, as well as sympathetically.
###
Climate is a factory that returns type “weather” :b
DesertYote says:
Your comment is awaiting moderation.
February 14, 2011 at 12:17 pm
rbateman says:
February 14, 2011 at 11:17 am
#####
OOPs, make that “…returns an instance of type weather”.
Yup, despite the best computerised prognostications,
the Climate just Keeps on a’Doin’ Whatta Climate’s Gotta Do…….
Ross McKitrick,
I have a hard time believing that any natural process on the planet has a unit root time series. Everything is bounded eventually because the planet has a finite size. If it’s bounded, it cannot have a root identical to one, although it can be very close to one. The classic example is a tank of water to which you randomly add or remove a bucket of water at fixed time intervals. That will behave like a unit root process until the tank overflows or empties. Then there’s the problem that the tank actually leaks. That also makes pure unit root behavior impossible in the long term (I think). Fractional integration, which amounts to long term persistence, makes more sense to me. However, it’s not at all clear that, given spatio-temporal chaos, any statistical process is valid.
KR says: “How are these independent? Mins and Maxes should rise and fall with temperature trends, summer and winter lag should be related to how warm or cold it is. I cannot see that these are truly independent quantities.”
Have you plotted and analysed them for the full term of GISS LOTI or HADCRUT or the NCDC’s merged land plus sea surface temperature data or are you simply expressing a belief?
[snip. You need to provide a short explanation, not just a stand-alone link. ~dbs, mod.]
the actual variability of these quantities is much smaller than what seems to have been used to compute these excursions.
In time series random walk tends to manifest itself in small undetectable errors at each measurement at time t(i). The forcing values may seem small at each measurement but if they are part of a random walk process then, over a series of measurements they show up generating a large error. Each time a drunk takes an apparently random step, some of his error is white noise and cancels out, but some is RW and he subsequently wanders hither and yon even though each step is small.
KR says: “And, if you account for known forcings (…yearly cycle, volcanic activity, solar activity, ENSO, etc.) the actual variability of these quantities is much smaller than what seems to have been used to compute these excursions.”
The seasonal component in global temperature anomaly data and ENSO are not forcings!
Also Tamino’s finding of a solar component with a lag of a few months in the global temperature data is questionable. It’s likely due to his limiting his analysis to the past few decades and possibly due to the ENSO residuals he’s left in the adjusted data. Solar lag is a function of the thermal inertia of the oceans, and if memory serves me well, estimates of the lag vary from 5-7 years at the low end to a couple of decades at the high.
Mr. Watts,
What is needed is an unbiased third party. They some how get the data on all the people from both sides of this dispute who have recived grants, money by others that might bend their opinions. That third party would need to match that to the posters here in such a way that only the third party knows who took money from who.
Then a number/ranking would come up beside each posters nick to show how much they recived on which ever side. You and the blog would not have that data, just the off site third party.
[snip]
[reply] can’t post unverified info – sorry RT-mod
Bob Tisdale – “Have you plotted and analysed them for the full term of GISS LOTI or HADCRUT or the NCDC’s merged land plus sea surface temperature data or are you simply expressing a belief?”
Given the warming trend, we’re seeing more record highs than record lows (http://www2.ucar.edu/news/1036/record-high-temperatures-far-outpace-record-lows-across-us), which means that they are correlated to temperature and inversely correlated to each other.
Northern hemisphere annual snow extent is declining (http://web.unbc.ca/%7Esdery/publicationfiles/2007GL031474.pdf), which affects both winter and spring lag dates – again, not independent variables.
So no, I’m not just expressing a belief, I’m looking at the data, and considering the causal links between these various values.
Bob Tisdale – “The seasonal component in global temperature anomaly data and ENSO are not forcings!”
You are correct, Bob, bad terminology on my part, my apologies. They are components of expected variations in temperatures based upon seasonal and oceanic cycles. And accounting for (correcting for) these cyclic variations reduces the underlying variability of the observed temperature data.
Solar lag is (to me) the most questionable part of Tamino’s analysis, but that may be a limitation of my knowledge. I will note that he’s perhaps one of the most skilled time series analysts I know of – if he says that there is a good correlation than I believe that’s what he’s seeing in the data.
I believe he’s finding the transient response to solar variations, not any long-term response – just the upper 100 meters of well-mixed ocean.
Uncanny! Last week I wrote a short random walk program to make 30 step walks which I graphed in EXCEL just for kicks. I gave it 3 options in each iteration, same,up,down and graphed them all out to compare with the new 30 year UAH baseline.
It’s pretty hard to tell blind which is the real and which is made up. I found it a pretty interesting exercise. I’m not a programmer, so in BASIC (don’t laugh!) I used a FOR NEXT loop with 2 random number generators and 2 IF THEN statements. Pretty simple fun which demonstrates how many “trends” can appear in spite of the purely random set. It doesn’t tell me much about the real world, but it does tell me something about assuming a trend means anything.
here’s my random walk code for anyone who wants to make their own data and knows even less about code than me!
20 FOR T=1 TO 30
30 S= RND (2)
32 IF S=2 THEN GOTO 60
40 V= RND (6)
60 PRINT V
70 NEXT T
VS’s first entry at Bart Verhengeen’ s blog said this
“# VS Says:
March 4, 2010 at 13:54
Hi Bart,
Actually, statistically speaking, there is no clear ‘trend’ here, and the Ordinary Least Squares (OLS) trend you estimated up there is simply non-sensical, and has nothing to do with statistics.
Here is a series of Augmented Dickey-Fuller tests performed on temperature series (lag selection on basis of a standard enthropy measure, the SIC), designed to distinguish between deterministic and stochastic trends. This is the first and most essential step in any time series analysis, see for starters Granger’s work at http://nobelprize.org/nobel_prizes/economics/laureates/2003/
Test resutls:
** CRUTEM3, global mean, 1850-2008:
Level series, ADF test statistic (p-value<):
-0.329923 (0.9164)
First difference series, ADF test statistic (p-value<):
-13.06345 (0.0000)
Conclusion: I(1)
** GISSTEMP, global mean, 1881-2008:
Level series, ADF test statistic (p-value<):
-0.168613 (0.6234)
First difference series, ADF test statistic (p-value<):
-11.53925 (0.0000)
Conclusion: I(1)
** GISSTEMP, global mean, combined, 1881-2008:
Level series, ADF test statistic (p-value<): -0.301710 (0.5752)
First difference series, ADF test statistic (p-value): -10.84587 (0.0000)
Conclusion: I(1)
** HADCRUT, global mean, 1850-2008
Level series, ADF test statistic (p-value<):
-1.061592 (0.2597)
First difference series, ADF test statistic (p-value<):
-11.45482 (0.0000)
Conclusion: I(1)
These results are furthermore in line with the literature on the topic. See the following:
** Woodward and Grey (1995)
– reject I(0), don’t test for I(1)
** Kaufmann and Stern (1999)
– confirm I(1) for all series
** Kaufmann and Stern (2000)
– ADF and KPSS tests indicate I(1) for NHEM, SHEM and GLOB
– PP annd SP tests indicate I(0) for NHEM, SHEM and GLOB
** Kaufmann and Stern (2002)
– confirm I(1) for NHEM
– find I(0) for SHEM (weak rejection of H0)
** Beenstock and Reingewertz (2009)
– confirm I(1)
In other words, global temperature contains a stochastic rather than deterministic trend, and is statistically speaking, a random walk. Simply calculating OLS trends and claiming that there is a 'clear increase' is non-sense (non-science). According to what we observe therefore, temperatures might either increase or decrease in the following year (so no 'trend').
There is more. Take a look at Beenstock and Reingewertz (2009). They apply proper econometric techniques (as opposed to e.g. Kaufmann, who performs mathematically/statistically incorrect analyses) for the analysis of such series together with greenhouse forcings, solar irradiance and the like (i.e. the GHG forcings are I(2) and temperatures are I(1) so they cannot be cointegrated, as this makes them asymptotically independent. They, therefore have to be related via more general methods such as polynomial cointegration).
Any long term relationship between CO2 and global temperatures is rejected. This amounts, at the very least, to a huge red flag.
Claims of the type you made here are typical of 'climate science'. You guys apparently believe that you need not pay attention to any already established scientific field (here, statistics). In this context, much of McIntyre's criticism is valid, however much you guys experience it as 'obstructionism'.
It would do your discipline well to develop a proper methodology first, and open up all of your methods to external scrutiny by other scientists, before diving head first into global policy consulting.
PS. Also, even if the temperature series contained a deterministic trend (which it doesn't), your 'interpretation' of the 95% confidence interval is inprecise and misleading, at best. I suggest you brush up on your statistics."
This entry provoked an almost record 2184 blog entries by such eminent writers as Tamino, Dhogaza and many others. Not surprising really when VS questioned the CO2/Global Temperature relationship and dismissed Temperature over time as statistically equivalent to a random walk
This is why I can neither “believe” nor “disbelieve” in AGW. I consider myself relatively sharp, educated, and well-read, but the title of this article conveys absolutely nothing tangible to my mind, and it just gets worse from there. It might as well be written in Lojban. When I contemplate the effort that would be needed to comprehend it, never mind evaluate it for truth, I make the affirmative decision that I can and should and ought to have nothing to say about the issue.
Brian H says: February 14, 2011 at 10:06 am
“Oops, meant to say “drunkards’ walks”. Oh, well.
Is there, btw, a “technical” distinction between “random” and “drunkards’”, anyone? Inebriated minds want to know.”
A drunk still has some goal in their walk … the randomness has a general direction … given time it will become obvious they are heading somewhere.
A random walk is by definition completely random. At any time all directions are equally probable – they arrive somewhere by chance alone.
Climate is much closer to a drunken walk than a random walk – but in short term simulations it is difficult to ascertain the difference.
Gary Pearse said “…A year or so ago in a comment on major floooding of the Red River of the North on WUWT, I used permutation analysis of the flood record going back 150 years (I believe) to show that the frequency of new records in flooding (assuming that year 1 was a record) roughly equalled the function ln(n) where n is the number of years considered (150). Ln 150 = 5, which, if flooding is a random event there will be 4 new records established after years one. … ”
I’m pretty sure that your analysis makes assumptions about the statistical character of the record that is not warranted. Actual weather/climate/hydrological records have very high autocorrelation. Also sometimes described as being pink or red rather than white noise.
So the frequency of new records in a real life climate/weather/hydrological time series will not be space as far apart as you would expect in very long time series.
You might find it interesting to apply your analysis to the longest known hydrological record, the flow measurements on the Nile river.
I’ve found the website by D KOUTSOYIANNIS to be very useful, with
http://itia.ntua.gr/en/docinfo/511/ being a good starting point.
Headpost says ” …..and indicate a random walk length on land of 24 yr and over the ocean of 20 yr. Using three 1000 yr segments from mil01, the random walk lengths increased to 37 yr on land and 33 yr over the ocean. ”
It appears that the three 1000 year segments were from models, not actual (or reconstructed) data. Various studies have shown that the statistical characteristics of various model outputs have less variability than real life records, so it is likely that the random walk length for 1000 year segments is significantly longer than 37 years.
At least that is my belief. Does anybody have knowledge of what the true rescaling factors are for real life temperature records, such as the long Central England Temperature record?
“”””” rbateman says:
February 14, 2011 at 11:17 am
‘climate is the average weather’ “””””
Well not exactly; and that is the root of Trenberth’s problem. I would agree if weather/climate were linear; but they are not; certainly the T^4 and T^5 aspects off BB radiation total emittance, and spectral peak emittance respectively are anything but linear.
So it is more correct to say that climate is the integral of weather; NOT the average of weather. Climate rests on the real time value of EVERYTHING weatherwise, that has previously happened. Mother Gaia does NOT do averages.