## Extreme Events Increase With Global Warming

#### Posted on 11 November 2011 by Rob Painting

For a more basic version of this post, see here

That continued warming of the Earth will cause more frequent and intense heatwaves is hardly surprising, and has long been an anticipated outcome of global warming. Indeed the 1990 Intergovernmental Panel on Climate Change (IPCC) Policymakers Summary stated that:

"with an increase in the mean temperature, episodes of high temperatures will most likely become more frequent in the future, and cold episodes less frequent."

One such "high temperature episode" was the monster summer heatwave centred near Moscow, Russia in 2010, where temperatures rocketed well above their normal summertime maximum and were so record-shattering they may have been the warmest in almost 1000 years.

Rahmstorf and Coumou (2011) developed a statistical model and found that record-breaking extremes depend on the ratio of trend (warming or cooling) to the year-to-year variability in the record of observations. They tested this model by analysing global temperatures and found that warming increased the odds of record-breaking. When applied to the July 2010 temperatures in Moscow, they estimated a 80% probability that the heat record would not have occurred without climate warming.

*Figure 1 - Probability of July average temperature anomalies in Moscow, Russia since 1950. This image shows that the average temperature in Moscow for July 2010 was significantly hotter than in any year since 1950. Credit: Claudia Tebaldi and Remik Ziemlinski. From ClimateCentral.org*

### Some statistical background

Earlier statistical work on record-breaking events has shown that for any time series that is stationary (i.e. no trend), the probability of record-breaking falls with each subsequent observation. This is known as the 1/*n* rule, where* n* equals the previous number of data in the series. For example, the first observation has a 1-in-1 chance of being the record extreme (100%), the second has a 1-in-2 chance (50%), the third a 1-in-3 chance, and so on.

For climate heat records, the stationarity rule is not apparent, as one might expect in a warming world. Previous work in this area has shown that the slowly warming mean (average) temperature is responsible for this nonstationarity.

### Monte Carlo

Following on from this earlier work, Rahmstorf and Coumou (2011) sought to disentagle the two effects of the mean change in temperature (climate warming), from the random fluctuations of weather, so as to find out the contribution of each to record-breaking. To do this, the study authors turned to Monte Carlo simulations. These are computer-generated calculations which use random numbers to obtain robust statistics. A useful analogy here is rolling a dice. Rolling once tells us nothing about the probability of a six turning up, but roll the dice 100,000 (as in this experiment) and you can calculate the odds of rolling a six.

From the simulations the authors obtain 100 values which represent a 100 year period. Figure 2(A) - 2(C) are the "synthetic" time series, and 2(D), 2(E) are respectively, the 'synthetic' global mean and Moscow July temperature. In all panels the data have been put into a common reference frame (nomalized) for comparison. (See figure 1 for an example of a Gaussian or normal distribution. Noise represents the year-to-year variability).

*Figure 2 - examples of 100 year time series of temperature, with unprecedented hot and cold extremes marked in red and blue. A) uncorrelated Gaussian noise of unit standard deviation. B) Gaussian noise with added linear trend of 0.078 per year. C) Gaussian noise with non-linear trend added (smooth of GISS global temp data) D) GISS annual global temp for 1911-2010 with its non-linear trend E) July temp at Moscow for 1911-2010 with non-lnear trend. Temperatures are normailzed with the standard deviation of their short-term variability (i.e. put into a common frame of reference). Note: For the Moscow July temperature (2E) the long-term warming appears to be small, but this is only because the series has been normalized with the standard deviation of that records short-term variability. In other words it simply appears that way because of the statistical scaling approach - the large year-to-year variability in Moscow July temperatures makes the large long-term increase (1.8°C) look small when both are scaled. Adapted from Rahmstorf & Coumou (2011)*

### Follow steps one.....

Initially, the authors ran the Monte Carlo simulations under 3 different scenarios, the first is for no trend (2[A]), with a linear trend (2[B]) and a nonlinear trend (2[C]). The record-breaking trends agree with previous statistical studies of record-breaking namely that: with no trend the probability of record-breaking falls with each observation (the 1/*n* rule), and with a linear trend the probability of record-breaking gradually reduces until it too exhibits a linear trend. With a non-linear trend (2[C]), the simulations show behaviour characteristic of the no-trend and linear trend distibutions. Figures 2(D) and 2(E) are the actual GISS global and Moscow July temperatures respectively.

### .....two.....

Next, the authors then looked at both the GISS global and Moscow July temperature series to see whether they exhibited a gaussian-like distribution (as in the 'lump' in figure 1). They did, so this supports earlier studies indicating that temperature deviations are fluctuating about, and shifting with a slowly moving mean (as in the warming climate). See figure 3 below.

*Figure 3 -Histogram of the deviations of temperatures of the past 100 years from the nonlinear climate trend lines shown in Fig. 2(D) and (E) together with the Gaussian distributions with the same variance and integral. a) Global annual mean temperatures from NASA GISS, with a standard deviation of 0.088 ºC. (b) July mean temperature at Moscow station, with a standard deviation of 1.71 ºC. From Rahmstorf & Coumou (2011)*

### .....and three.

Although the authors calculate probabilities for a linear trend, the actual trend for both the global, and Moscow July temperature series is nonlinear. Therefore they separated out the long-term climate signal, and the weather-related annual temperature fluctuation, which gave them a climate 'template' on which to run Monte Carlo simulations with 'noise' of the same standard deviation (spread of annual variability from the average, or mean). This is a bit like giving the Earth the chance to roll the 'weather dice' over and over again.

From the simulations with, and without the long-term trend, the authors could then observe how many times a record-breaking extreme occurred.

*Figure 4 -Expected number of unprecedented july heat extremes in Moscow for the past 10 decades. Red is the expectation based on Monte Carlo simulations using the observed climate trend shown in Figure 2(E). Blue is the number expected in a stationary climate (1/n law). Warming in the 1920's and 1930's and again in the last two decades increases the expectation of extremes during those decades. From Rahmstorf and Coumou (2011)*

### Large year-to-year variability reduces probability of new records

A key finding of the paper was that if there are large year-to-year non-uniform fluctuations in a set of observations with a long-term trend, rather than increasing the odds of a record-breaking event, they act to reduce it because the new record is calculated by dividing the trend by the standard deviation The larger the standard deviation the smaller the probability of a new extreme record.

This can be seen by comparing the standard deviation of the NASA GISS, and Moscow July temperature records (figure 3), plus figure 2(D) and [E]). As the GISS global temperature record has a smaller standard deviation (0.088°C) due to the smaller year-to-year fluctuations in temperature, you will note in figure 2(D) that it has a greater number of record-breaking extremes than the Moscow July temperature record over the same period (2[E]). So, although the long-term temperature trend for Moscow in July is larger (100 year trend=1.8°C), so too is the annual fluctuation in temperature (standard deviation=1.7°C), which results in lower probability of record-breaking warm events.

Interestingly it's now plain to see why the MSU satellite temperature record, which has a large annual variability (large standard deviation, possibly from being overly sensitive to La Niña & El Niño atmospheric water vapor fluctuations) still has 1998 as it warmest year, whereas GISS has 2005 as it's warmest year (2010 was tied with 2005, so is not a *new* record). Even though the trends are similar in both records, the standard deviation is larger in the satellite data and therefore the probability of record-breaking is smaller.

### That other Russian heatwave paper

The results of this paper directly contradict the findings of Dole (2011) who discounted a global warming connection with the 2010 Russian heatwave. Rahmstorf & Coumou (2011) demonstrate that the warming trend from 1980 onwards (figure 4) greatly increased the odds of a new record-breaking warm extreme, and in fact should have been anticipated.

It turns out that Dole (2011) failed to account for a quirk in the GISS Moscow station data which had wrongly applied the annual urban heat island (UHI) adjustment for the monthly July temperatures, when UHI is a winter phenomenon in Moscow. This meant that the large warming trend evident there in July had been erroneously removed. This was confirmed by looking at Remote Sensing Systems (RSS) satellite data over the last 30 years, which shows a strong warming trend in Moscow July temperatures. See Real Climate post "The Moscow Warming Hole" for detail, and note Figure 5 below.

*Figure 5 - Comparison of temperatues anomalies from RSS satellite data (in red) over the Moscow region versus Moscow station data (in blue). Solid lines shows the average July value for year, whereas the dashed lines show the linear trend for 1979-2009. Satellite data have a trend of 0.45°C per decade, as compared to 0.72°C per decade for the Moscow station data*.

### Whatchoo talkin' bout Willis?

Using the GISS data from 1911-2010 (a nonlinear trend), the authors calculate a 88% probability the extreme Russian heatwave (a record in the last decade of the series) was due to the warming trend. Clearly the summer temperatures for July 2010 in Moscow were a massive departure from normal, and including them would create bias, so the study authors exclude 2010 from their analysis, and re-calculate for 1910-2009. They found a 78% probability the freak heatwave was due to warming, and extending their analysis back to include the entire GISS temperature observations (1880 -2009), they found an 80% probability.

So to sum up:

- Rahmstorf and Coumou (2011) is a statistical/analytical study, which does not look at the physical causes of the 2010 Russian heatwave. Instead they assess the likelihood of record-breaking extremes.
- Based on earlier work, and confirmed by the Monte Carlo simulations; in a climate with no trend (no long-term warming or cooling), the probability of record-breaking extremes falls over time (perhaps contrary to popular belief).
- With a warming (linear) trend, the number of record-breaking warm extremes reduce until they eventually increase in a linear manner.
- With a nonlinear trend (warm/stagnation intervals) the probability of record-breaking is a combination of the no trend/linear trend scenarios.
- Larger annual fluctuations (larger standard deviation) reduce the number of records, whereas smaller fluctuations increase the number of record- breaking extremes.
- This helps explain why the satellite temperature record (large annual fluctuation) has 1998 as it warm record, whereas GISS (small annual fluctuation) has 2005 - GISS has a greater likelihood of seeing record-breaking.
- By seperating out the random (weather) component and the long-term (warming) component, the authors established there is a 80% probability that the 2010 July temperature record in Moscow would not have happened without climate warming from 1880-2009.
- The record-breaking extreme should have been anticipated, which contradicts earlier work on the Russian heatwave (Dole [2011]).
- In a warming world expect to see more record-breaking warm temperatures.

Rob Paintingat 14:08 PM on 17 November, 2011So once again:In a stationary climate (no warming trend) the probability of record-breaking falls (the 1/nrule). This doesn't mean that natural variability alone cannot break records, just that the odds decrease with each subsequent observation. In a warming climate the probability of record-breaking warm extremes increase. This assumes of course, that the standard deviation follows a gaussian distribution - which it does in the case of the GISS global and Moscow July temperatures. As Tom Curtis has already pointed out to you, arguing probability on the basis of a singular event is an illogical premise.Normanat 14:09 PM on 17 November, 2011Rob Paintingat 14:24 PM on 17 November, 2011"It was also the coldest February recorded in the US. It has the record number of consecutive days below zero in the lower 48th (41 days).Yes, hardly a surprise given this occurred early in the observational record. This asymmetry of warm vs cold records is discussed in Rahmstorf & Coumou, although I don't deal with it in the blog post. I you take a gander at Figure 1 in the post above, that's a gaussian (or normal) distribution. Keep moving that distribution to the right (climate warming trend) and the cold extremes (to the left) gradually diminish. In other words the frequency of record-breaking cold extremes decrease - as observed in figure 2 in both the GISS data and the Monte Carlo simulations.skywatcherat 14:31 PM on 17 November, 2011anypast individual event change anything about the increasing probability of extremes in a warming world? Your #50 is irrelevant - all it shows is that in the map for 1936 a la Hansen et al 2011, North Dakota would have experienced a >= 3-sigma event and been coloured brown. Otto would have had a hot summer had he been in the town named after him. You're still avoiding the focus of everyone's issues with you: thatnobody here doubts that large extremes happened in the past. But the data here (Hansen and R & C) provide strong evidence for the frequency of heatwaves increasing - the Gaussian distribution flattening slightly and shifting to the right, and each year, a greater proportion of the Earth's surface experiences extremes. Without being pejorative, I do wonder if you get what probability is all about?Normanat 14:42 PM on 17 November, 2011Response:[DB]

"Not enough to really affect the 2010 Moscow anomaly either way or make it more likely."Based on what citation do you state this so authoritatively?

"The research I have done on the topic still indicates that blocking patterns caused this heat wave and the pattern would have taken place regardless of warming."Then feel free to submit that research for publication in a reputable journal. In the meantime, you continue to prosecute your agenda of selective cherry-picking & disregarding all evidence that doesn't conform to your preset view of things.

Shorter response: you continue to waste the time of others here. For now. This will not last, however...

Tom Curtisat 14:45 PM on 17 November, 2011monthlyaverage. That means while, assuming a normal distribution and no global warming, the probability of a Moscow 2010 heat wave is only 1 in 66,667 in a given year, the probability of a Bismarck maximum under the same assumptions, and using your data is only one in every 32,258 years. Of course, temperature records are not normally distributed. Accounting for that, and for global warming, Tamino shows that the average return interval of a Moscow style heat wave is 260 years given the current level of global warming, or close to 1 in every 1000 years without global warming. (Note that that makes the event 4 times more likely based on global warming, an independent confirmation of Rahmstorf and Comou.) The correct estimate of the temperature record for Bismarck requires a similar detailed analysis to that provided by Tamino, using more than a single months data. One thing we can be sure of, however, is that the result will (once again) show the event to be significantly more probable than the Moscow event. Finally, you still appear to be arguing that because you can role a '12' on a pair of standard dice, that shows you will not role '12's more frequently if you use a standard die, and a second die numbered '2' to '7'. Such an argument is a game effort in denialism, but is doomed to failure for anyone prepared to look at the data logically.muoncounterat 14:47 PM on 17 November, 2011global. Increasing the global - or even hemispheric - average temperature by 'a few degrees' is alotof warming. But your fascination for individual location, short term records is more of the same 'I can't see it, so its not happening.' How does one month in Bismarck, ND equate to all of Europe showing a significant increase in the number of summer days much warmer than a 30 year average? The graphs here include your 1936 heat wave. At that time, approx 40% of the NH land area saw summers classified as 'hot' and very little area was classed as 'extremely hot.' Now we see approx 80% 'hot' and nearly 20% 'extremely hot.' What happened in Bismarck this past summer is just a tiny spot out of that land area. How can you continue to miss this point?muoncounterat 14:54 PM on 17 November, 2011skywatcherat 15:03 PM on 17 November, 2011Tom Curtisat 15:38 PM on 17 November, 2011First, nobody is denying that meteorological, and major climactic events have the dominant role in day to day weather. There is a drought in Texas because of a La Nina event. There was a heat wave in Moscow because of a blocking event. Trivially, the probability of exactly identical heatwaves of blocking events occurring at exactly the same time without greenhouse gas forcing is almost zero (butterfly effect); but almost as trivially and far more importantly, La Nina's and blocking events would have occurred at very similar frequencies in the absence of GHG forcings.What is being claimed is that global warming influences the events that occur so that very high temperatures become more common than they once where.Second, you can approximate to the effect of global warming by simply adding the monthly value of the trend in global warming to the monthly or daily temperatures. This is a very crude approximation, but it does not lead you totally astray. Based on that, for example, John Nielsen-Gammon (state climatologist for Texas) argues that: I would quibble that the drought was partly the result of the heat, so that some of the "drought contribution" is a secondary effect of global warming. But Neilsen=Gammon's position is perfectly reasonable. You could alsoas a crude modelsimply add the regional global warming anomaly to the Russian heatwave and say that that was the contribution of global warming.That contribution is not 0.8 degrees C, ie, the global anomaly, but closer to 1.8 degrees C (four decades of the decadal trend) for the Moscow region). But using the correct figures, the approach is not unreasonable. Using that approach, you would say that global warming added 1.8 C to the 6.67 degree C July 2010 Moscow anomaly, or 27%. However,leaving the analysis there seriously underestimates the effect of global warming on the return frequency of extreme events. For example, even a 0.8 degree C increase in mean temperatures represents a significant fraction of a Standard Deviation. For high Standard Deviation events such as those in the US in 1936 or Moscow in 2010, even a small increase in temperature can greatly increase the return interval. As an example of this, your state SD of the Bismarck record was 5, whereas, the actual value was 4.89. That 0.11 difference in SD increases the return intervalby more than 70%. That is, a 0.67 degree C increase in temperature can increase the return inverval from 32,000 years to 56,000 years assuming normal distribution. For actual values found such as the Moscow event, the return interval can be increased from 1 in 260 year events to 1 in 1000 year events just by that small difference in temperature. Hence, using this crude model,the only logical conclusion is that global warming significantly reduces the return period of extreme temperature events.Finally, and briefly, it is not at all clear that the crude model is in fact warranted. There is evidence that global warming is changing the frequency and intensity of ENSO episodes (although the evidence is not conclusive). There are good logical reason to expect a non-stationary climate, ie, one significantly warming over time, to not be as well behaved as a stationary climate. These are areas around which there is legitimate debate. But without venturing into those areas, the conclusion you are arguing against follows directly from your own premises. And a final note about your 52, despite the many records set in the state, the map you show (as also the one from GISS) shows the highly localized nature of the very extreme heat. Further, I'll see your 17 states from 1936 and raise you 19 national records from 2010.Response:[DB] Fixed html issues.

Normanat 15:39 PM on 17 November, 2011skywatcherat 15:52 PM on 17 November, 2011muoncounterat 15:57 PM on 17 November, 2011The researchers observed the frequency of blocked weather events in the North Atlantic ... over the entire twentieth century and compared it to the evolution of ocean surface temperatures for the same area. They thenNothing there about global warming - by design. Your 'Abstract describes':removed the effect that global warming has on water temperatures, and found that decades with more frequent, recurring blocking events in the North Atlantic corresponded to those decades when the North Atlantic Ocean was warmer than usual, as it is now.Winters with clusters of more frequent blocking between Greenland and western Europe correspond to a warmer, more saline subpolar ocean.It's not clear from that whether blocking causes warming or warming causes blocking.scaddenpat 06:31 AM on 18 November, 2011John Hartzat 10:57 AM on 18 November, 2011John Hartzat 11:00 AM on 18 November, 2011Normanat 15:40 PM on 19 November, 2011muoncounterat 02:14 AM on 20 November, 2011Blocking events occur when one of the jet streams ... pinches off large masses of air from the normal wind flow for an extended period. These kinks in the jet streamAgreed, then, that 'a blocking event' causes stalled weather patterns; but this is apparently a short-term phenomenom. Do you associate a year-long mega-drought with events that last days to weeks? From Mendes et al 2008, Table 2 shows that Atlantic blocking events are most frequent in May and Sept (at a whopping 6% or 2 days per month); blocking in the Pacific southwest peaks in July/Aug at 27% (8 days per month) and Oceania peaks in July (25% or 8 days per month). From Barriopedro et al 2004:typically last at least five days but can persist for weeks. They can cause weather patterns to stall over one area and fuel floods, droughts, and other extreme weather events.The long-term analysis in blocking frequencies has shown a downward (upward) trend in blocking days over ATL and EUR (WPA) sectors. ... These results suggest that those observational trends could be partially explained by--emphasis added This paper also discussed blocking duration, producing a graph (their Fig 10) with the most commonly observed duration on the order of 7 days. If blocking frequency and duration are modulated by surface temperatures, it would be incorrect to conclude on the basis of superficial evidence that 'blocking causes warming.' If blocking formation responds to 'forcing factors,' then it is those forcings that must be investigated. Croci-Maspoli and Davies 2009, studying the European winter of 2005/6:simultaneous changes in the forcing factors responsible for blocking formation (ATL and WPA) and maintenance (EUR), respectively. ... regional modes have shown to modulate blocking occurrence through the anomalous TCP-associated temperature distributions.Thus, recent trends in surface temperature could be partially responsible for the observed trends in blocking occurrence.... the occurrence of the blocks was sensitive to, and significantly influenced by, the warm surface temperature anomalies upstream over the western Atlantic Ocean and North America.So the question appears to be: What's causing warm surface temperature anomalies?John Hartzat 03:18 AM on 20 November, 2011John Hartzat 04:41 AM on 20 November, 2011Rob Paintingat 06:17 AM on 20 November, 2011John Hartzat 08:41 AM on 20 November, 2011Normanat 13:47 PM on 20 November, 2011Bibliovermisat 14:38 PM on 20 November, 2011Bibliovermisat 15:05 PM on 20 November, 2011muoncounterat 15:09 PM on 20 November, 2011The presence of high pressure centers for long times, therefore, provides a primer for drought occurrence, but they cannot explain why dry periods survive much longer than the anti-cyclone from which they originate."a detailed explanation of what caused the current drought in Texas." Your 'drought explanation' is actually more of that anecdotal evidence you seem to prefer:... our 12-month running total will be at about half the previous record low for any comparable period since rainfall records have been kept. ... The early 1950s drought lasted much longer than our current drought has existed so far, but the past year was worse than any single year during that five-year drought-of-record. ... We have already had highs of over 100 for 73 days this summer, with highs of 110 the past few days. The live oaks across the ranch are mostly leafless, and the post oaks, blackjack oaks, and Texas red oaks are brown and look like winter.Yep, that's extreme; it certainly debunks your 'this is nothing unusual' from prior threads. BTW, the author is a professor of biology. What was the point of that reference? No, the key question remains unanswered: What's causing warm surface temperature anomalies? Do you deny that has anything to do with global warming?Normanat 16:26 PM on 20 November, 2011Normanat 17:41 PM on 20 November, 2011Rob Paintingat 18:09 PM on 20 November, 2011"The reason I am questioning the use of a Gaussian distribution is because I am not sure extreme temperatures fall under the concept of random variables"Rahmstorf and Coumou (2011) demonstrate that both global temperatures and Moscow July temperatures follow a Gaussian distribution. That comes about by doing the math, not by repeated handwaving. If you have some scientific literature that supports your notion, then post it here, otherwise your continued handwaving is tantamount to trolling.Tom Curtisat 20:24 PM on 20 November, 2011assuming global warming, and close to 1/1000 without it. In other words, Tamino has clearly taken into account Norman's concern, and shown that global warming has made such events significantly more probable. Even this must be taken with a grain of salt, however. Because no event even close to Moscow 2010 is on record (in Moscow), we do not have statistical evidence showing that the divergence which makes warm events more common than the normal distribution will predict is not reversed at even higher levels. Indeed, we know it must be. Any standard statistical distribution will have an infinite tail, indicating that though 3,000 C days are very rare, they are possible. Cearly that is just as much nonsense as an expectation of rolling 19 on three six sided dice. So very extreme events such as Moscow 2010 may be even rarer than Tamino indicates, but are unlikely to be more common. Further, even if the distribution is not gaussian, shifting the temperature to the right will significantly increase the probabilities of warmer eventsunless the probability distribution is constant with increasing temperature. That is very clearly not the case - 50 degree C days are not as common as 40 degree C days in any part of the world. Norman ignores the significance of global warming on probability distribution, therefore, on no basis at all.Normanat 22:48 PM on 20 November, 2011Response:[DB] Since others have already touched upon this there is no need to rehash the whole thing...but it must be reiterated:

As such your comment then simply amounted to further wasting the time of others, so it was moderated out.

michael sweetat 23:37 PM on 20 November, 2011muoncounterat 02:13 AM on 21 November, 20111936: 0.134, 2010: 0.497, 2011: 0.477. Perhaps a bigger question is this: If you do not understand something, do you automatically

assumeit isn't true?muoncounterat 02:30 AM on 21 November, 2011... the bottom line is thatThat post is well worth some study for anyone struggling with the notion of increased probability of extreme events.every degree Celsius increase in mean July temperature in Moscow, roughly doubles the chances of any given extreme heat wave. In fact Moscow temperature has increased as much as 3 deg.C since the early 20th century, and according to the extreme-value approximation model I computed, this makes a given extreme 8 times more likely than before. Without global warming, Moscow’s July 2010 would have been one for the history books. As global warming drives average temperatures even higher, present citizens of Moscow are likely to see multiple such events in a single lifetime. Which is scary.muoncounterat 03:06 AM on 21 November, 2011The Hot Summer of 2010: Redrawing the Temperature Record Map of Europe.Increasing greenhouse gas concentrations are expected to amplify the variability of summer temperatures in Europe. Along with mean warming, enhanced variability results in more frequent, persistent, and intense heatwaves.They also note that despite increasing overall probability of additional heatwave, the 2010 heatwave wasso extremeit is not very likely to be repeated in the near term. I suppose some will translate that observation into yet another 'what global warming?' headline: Forecast: Smaller chances of record-breaking heatwaves!Normanat 06:06 AM on 21 November, 2011Normanat 06:40 AM on 21 November, 2011michael sweetat 07:04 AM on 21 November, 2011anomalyand then you conclude "I still do not see an area twice as large for extremely hot in 2011 summer as compared to 1936 summer". Extremely hot is a designation of a variation ofstandard deviation. It is impossible to look at a graph of anomaly and reach an understanding of standard deviation. It has been pointed out to you previously on this thread that anomalies and standard deviations are different. If you cannot read the graph, accept that Hansen did it correctly and in 2011 there was twice as much "expremely hot" as there was in 1936. The hot areas were hotter in 2011 than 1936 (although they were similar in extent), the data proves you are wrong. If I look at a table of watermellons and I conclude that all oranges are the same, how far have I advnaced the discussion? You must understand statistical arguments to argue statistics.Albatrossat 09:57 AM on 21 November, 2011"I reviewed your prior posts and I am going to remove myself from this discussion. I see no point in discussing data with someone who does not know how to look at data."You are not the only one Michael. Rightly or wrongly, I gave up trying to discuss the science and statistics with Norman a long time ago.Tom Curtisat 10:26 AM on 21 November, 2011muoncounterat 11:22 AM on 21 November, 2011John Hartzat 11:25 AM on 21 November, 2011Normanat 12:12 PM on 21 November, 2011Normanat 12:34 PM on 21 November, 2011Normanat 12:53 PM on 21 November, 2011Tom Curtisat 13:34 PM on 21 November, 2011it follows that a simple comparison of anomalies cannot test Hansen's claim in any way. Indeed, that fact makes it more likely that Hansen's claim is correct. That is, to the extent you are showing anything, you are confirming rather than contradicting Hansen. c) Whatever confirmation exists is minimal, however, because neither an anomaly nor a record is a variation measured as a standard deviation. Absent evidence of the standard deviation of temperatures of the various sites, the anomaly informationcannotcontradict or confirm Hansen's claim. Finally, d) the maps you have shown have all employed a mercartor projection which exagerates the size of northern states relative to southern states. It is absurd, therefore, to think a simple eyeball comparison can tell you which area is larger if they are at all close. So, although you claim to know the difference between an anomaly and a standard deviation, you act as though you don't. Either you do not understand what you think you know, or you are being deliberately deceitful.skywatcherat 13:37 PM on 21 November, 2011globalanalysis by Hansen et al which empirically shows you to be wrong on the increase in extreme events. You haven't produced the statistics to support your assertions about the US, which in this case would need to cover all the US, giving # standard deviations from the mean. That's pretty poor, really.Tom Curtisat 13:41 PM on 21 November, 2011skywatcherat 13:42 PM on 21 November, 2011muoncounterat 13:59 PM on 21 November, 2011