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Posts Tagged ‘Probabilities’

Evidence Linking Global Warming and Extreme Weather

Thu ,08/05/2014

 “All weather events are affected by climate change because the environment in which they occur is warmer and moister than it used to be….  ”  – Trenberth


Kevin Trenberth, senior scientist at the National Center for Atmospheric Research, explains that asking for proof that global warming causes severe weather, is asking the wrong question. “All weather events are affected by climate change because the environment in which they occur is warmer and moister than it used to be. The main way climate change is perceived is through changes in extremes because those are outside the bounds of previous weather. The average anthropogenic climate change effect is not negligible, but nor is it large, although a small shift in the mean can lead to very large percentage changes in extremes. Anthropogenic global warming inherently has decadal time scales and can be readily masked by natural variability on short time scales.”

Scientists  have been very cautious about linking severe weather events to global warming, but the link is getting stronger each year. The Earth has warmed an average of 0.82 over the last century, which doesn’t sound like much, but it means that some places have warmed much more than in the past. Since the amount of moisture the air can hold depends on the temperature, the air can now hold about 6% more moisture. Before 2010, scientists would cautiously point out that higher temperatures lead to the likelihood of drought, and that more energy and moisture in the atmosphere was a recipe for severe weather. But how is it possible to establish that weather events were becoming more extreme?

There are many reports like the interim report by the Climate Council in Australia which found that, in the period between 1971 and 2008,  heatwaves in Australia were becoming more frequent, increasing in intensity and are lasting longer. The report said climate change was  having a key influence on a trend that has seen the number of hot days in Australia double and the duration and frequency of heatwaves increase. Reports like that were not good enough for the skeptics. By 2011 a good case was established that global warming was causing heat waves and droughts in the U.S., but the case was not strong enough to overcome the Skeptics objection, even when in 2012, a definite probability link  was established for  extreme temperatures and droughts. 

To understand whether a weather event is extreme, it must be compared to the norm. This can most easily be done for temperatures, as we have over a century of temperature records from almost all parts of the world.

Example of a Normal Distribution

Example of a Normal Distribution – Click to Enlarge

There is enough temperature data that normal distributions can be graphed, which allows us to quantify  the probability of a temperature event. In the example at the right, the maximum in the curve is the mean of the data. The probability of the occurrence of an event can be measured by the number of standard deviations, sigma(σ), a particular value is from the mean. The values within 2σ of the mean, blue, are considered to be in a mostly normal range. Those from 2 to 3σ, yellow, are considered to be exceptional events, and those beyond 3σ, red, are considered to be extreme. Those yearly events that fall in the yellow range are considered to be 100 year events while those that fall in the red are 1000 year event.

As an example, the normal distribution graph to the right is for the temperatures in Moscow since 1950.  The maximum in the curve is the average temperature, which is set to zero, and the temperature for other other year is described as a temperature anomaly, i.e., how far it is above or below the average value.Moscowjulytempanomaly2010 The curve approximates a normal distribution so the standard deviation of the temperature anomalies can be used to decide whether an event is extreme. The temperatures for 1972  and 2001 fall in the hundred year event range, while  that for 2010 would only be likely to occur only once in every hundred thousand years, unlikely, but still possible.

The Skeptics would still not be convinced, claiming that the link to global warming climate change causes severe weather was not proven, but proof is not necessary when probabilities for a large number of events are involved. For instance, you have only a 50% chance of calling a coin toss correctly, but you can likely guess the number of heads on 1000 flips with less than 1% error. Small differences in probabilities lead to big outcomes. The rules of blackjack give the house a 50.5% to 49.5% advantage, and though some players may win thousands on a lucky streak, considering all the bets placed, the house will make millions from that small difference in probability. And, probabilities are useful for predictions. A 0.270 hitter may get the game winning hit at his next bat while a 0.300 pinch hitter may strike out, but with the game on the line, the coach will likely pinch hit. If trying to predict the future, it is better to go with the probabilities. Though  it is not possible to prove that any one weather event is caused by global warming , scientists have observed a change in probabilities of severe weather events over long periods of time. With the thousands of weather events that occur on the Earth each year,  a small change in probability can cause an definite change in the number of severe weather events.  


An even more convincing argument can be made that global warming causes severe temperatures if the normal distribution is examined as a function of time. Research by James Hansen has established the link by showing that the normal distribution has changed since 1951. The curves show that beginning in about 1970, the mean begins to move to the right and the the curves flatten, showing that the probability of extreme temperatures increase greatly from 1950 to 2011.  His work shows that the probability of extreme temperatures is 10 times as great as for the 198o to 2010 years.

It should also be noted that the left side of the graph flattens, but that the probability of extremely cold temperatures is not zero. There is still a significant likelihood of cold temperatures -and a cold winter now and then does not disprove global warming.

The Skeptics are still claiming that is not proof enough, and that the data says nothing about droughts and wildfires.  There are still some Skeptics who argue that this does not mean  heat waves necessarily related to droughts or that the droughts are causing the increase in wildfires we have experienced, but their arguments seem to be improbable. It should be clear by now that no amount of evidence will convince Skeptics who wish to ignore probabilities.

(C) 2014  J.C. Moore



The Link between Global Warming and Extreme Weather

Wed ,22/08/2012

A large body of scientific evidence, going back to the middle of the 19th century, links the concentration of atmospheric carbon dioxide,  the temperature of the Earth, and the Earth’s climate. Those who study the Earth and its ecosystems have found ample evidence that the climate is changing. The USDA recently acknowledge that fact by shifting the plant hardiness zones for gardeners northward, acknowledging that frosts occur later in the fall and the last freeze in spring occurs earlier. However many people still doubt climate change and point to weather events as evidence.

Theory: Climate scientists would like to clearly establish the link between climate change and extreme weather events, but that is difficult because of the natural variability of the weather.  The link between global warming, heat waves and droughts would seem unquestionable, but it is difficult to prove. Global warming has increased the energy and moisture in the atmosphere, making conditions for severe storms and floods more likely.  In the last century, the Earth’s average temperature has increased by about 0.8°C, increasing the amount of water the air can hold by about 7%.  It is a reasonable conclusion that when it rains, it will rain more and when it snows, it will snow more. So strangely enough, global warming could actually lead to greater snowfall.  (1) However, it has been very difficult to prove, and certainly even more difficult to convince skeptics that that might be the case.

Climate Models: Another approach to linking extreme weather events to global warming has been through the use of climate models. The models take into account the factors that influence climate and weather, and are often used by meteorologists for “future casting” the weather for 10 day forecasts, which is about as long as normal weather patterns last. However, the models may also be used to examine the effect of global warming on the weather events. The models are used to compare the prediction for a weather event assuming that there is no global warming with a prediction of the weather event that includes global warming. In many cases, it can be shown that the weather and rainfall will be more extreme under the global warming conditions. The results are often challenged by climate Skeptics, who claim that the models do not accurately represent the data, or that the models are “falling apart”. The models were developed to fit a century’s worth of the weather and climate data, and there is little evidence to support the Skeptics claims. However climate scientists would like to show a definite link between global warming and weather events to silence those criticisms.

Statistical Evidence: A recent NOAA report, edited by Petersen, et al. (2) , examined 6 extreme weather events that occurred in 2011 and found that there was a link between climate change and the extreme weather event. One of the most interesting reports (3) ,  found that the 2011 heat wave and drought in Texas were 20 times more likely to happen than they would have been in the 1950’s. How did they arrive at that conclusion? A recent paper by Hansen et al.  (4), shows that extreme temperatures are much more likely to occur worldwide than in the 1950’s, and over 10 times as likely to occur as in 1980. As Hansen puts it, the extreme temperatures “which covered much less than 1% of Earth in 1950, now typically covers about 10% of the land area. It follows that we can state, with a high degree of confidence, that extreme anomalies such as those in Texas and Oklahoma in 2011 and Moscow in 2010 were a consequence of global warming because their likelihood in the absence of global warming was exceedingly small.”

Those two papers are important as they have been able to establish a quantitative link between the probabilities of weather events and global warming. More importantly, the link does not depend on theory or on climate models, and relies only on a straight forward statistical analysis of the data. The method depends on computing the normal distribution of the Earth’s temperature anomalies for each decade and then comparing how the distribution of extreme weather events change with time.

Normal distributions:  Before examining how the method works for weather events, it might be useful to examine how it works with something more familiar, like the height of American men. How could we show whether the number of extremely tall men was increasing as time went by?  This could be done by taking a representative sample of men and examining a graph of the normal distribution. We could find the average, μ , and then repeat the process every 10 years to see how the average changed with time. An increase in the average height might indicate that there would be more extremely tall men, but that is not the full story.

Another piece of information that needs to be considered is the variance, or how widely the height of men vary about the mean. The variance is usually measured by the standard deviation , σ, which can be easily calculated from the measurements done to compute the mean. A  graph of the normal distribution  is shown at the right.  “Normal” means that the data has been divided by the total number of men in sample, so that the area under the entire curve represents 100%. That feature is very useful for comparing heights, and it also allows us to associate an area under the curve with  probabilities.

The average height, μ on the graph, is 5’10”, and the standard deviation, σ, is 3 inches. About 95% of the sample falls within 2 standard deviations of the mean, which also says that the probability is 95% that a man selected at random would fall between 5’4″ and 6’4″. Those over 2σ  from the mean, or 6’4″, make up about 2% of the sample and are considered very tall. Finally, those over 3σ  from the mean , over 6’7″, are considered extremely tall and make up only 0.15 %. Michael Jordan and a host of other National Basketball Association players fall into that 3σ category.

How would it be possible to tell whether the incidence of extremely tall men is increasing? One way would be to take height data collected every 10 years, plot the normal distribution, and see how the area of the graphs out past 3σ change. We could not only tell whether there were more extremely tall men, but we could calculate how the probability of finding an extremely tall man changed, just by comparing areas on the graph.

Weather events. Enough data and computing power is now available to calculate normal distributions of temperature data every 10 years for many decades. Having the normal distribution of the temperature data by decade can be used to find whether the probability of extreme temperatures is increasing or decreasing. The Earth’s temperature was fairly stable from about 1950 to 1980, making it a convenient standard for comparing changes. Rather than using temperatures, the graph uses temperature anomalies, which measure how far a temperature reading was above or below average. 

The procedure is similar to the one described for examining the height of men. Hansen, et al. used the Earth’s temperature data to graph normal distributions of the Earth’s temperature anomalies by decade, from 1950 to the present. They found that the distribution of temperature anomalies approximate a normal distribution. 

The results of their work for the summer months show that beginning in about 1970, the mean begins to move to the right toward higher temperatures. It can also be seen that the variance of the data increased and shifted to the right, showing that the probability of extreme temperatures increase greatly from 1950 to 2011.  It can be seen that the number of extreme temperatures, those out past 3 ( meaning 3σ), almost nonexistent in the 1950s, have grown significantly larger in each decade after 1980. A similar graph, using  σ for the last 30 year period (not shown), found the probability of temperatures past 3 sigma is 10 times as great as for the 198o2 to 2010 years.

It should also be noted that the left side of the graph flattens, but that the probability of extremely cool temperatures is not zero. Though  hot temperatures became more probable, that there was still a significant likelihood of cooler temperatures.

Climate Skeptics often argue that an extremely cold weather event disproves global warming. The normal distributions by decade for the winter months is given at the right.  The graph shows the average winter temperatures have increased significantly during the last 30 years and the variance in the temperature has become greater as time progressed. However, the left side of the graph shows there is still a significant probability of extremely cold weather even though global warming is occurring. This means that the skeptics argument is baseless. It is also sometimes argued that extreme snowfalls disprove global warming, but that is also a baseless argument. Extremely cold air can hold little moisture, and it is warmer air, slightly below freezing, that produces the greatest amount of snow. The Inuit know that a warm spell brings a much greater chance of snow.

So there we have it. Climate physics predicts that global warming should cause higher incidences of extreme weather. Climate models find that global warming makes increased rainfall and storms more probable. A straightforward statistical analysis of temperature data not only shows that extreme temperatures are more likely, but has allow climate scientists to calculate how global warming affects the probability of extreme temperatures. A definite link between global warming and extreme weather has been established by the research.

 (1) http://jcmooreonline.com/2011/03/22/the-case-of-global-warming-and-extreme-weather/ 

(2) http://www1.ncdc.noaa.gov/pub/data/cmb/bams-sotc/2011-peterson-et-al.pdf 

(3) http://usnews.nbcnews.com/_news/2012/07/10/12665235-2011-texas-drought-was-20-times-more-likely-due-to-warming-study-says?

4) http://www.pnas.org/content/early/2012/07/30/1205276109.full.pdf+html

(C) 2012 J.C. Moore