Monday 2 December 2013

On the importance of changes in weather variability for changes in extremes

This is part 2 of the series on weather variability.

A more extreme climate is often interpreted in terms of weather variability. In the media weather variability and extreme weather are typically even used as synonyms. However, extremes may also change due to changes in the mean state of the atmosphere (Rhines and Huybers, 2013) and it is in general difficult to decipher the true cause.

Katz and Brown theorem

Changes in mean and variability are dislike quantities. Thus comparing them is like comparing apples and oranges. Still Katz and Brown (1992) found one interesting general result: the more extreme the event, the more important a change in the variability is relative to the mean (Figure 1). Thus if there is a change in variability, it is most important for the most extreme events. If the change is small, these extreme events may have to be extremely extreme.

Given this importance of variability they state:
"[Changes in the variability of climate] need to be addressed before impact assessments for greenhouse gas-induced climate change can be expected to gain much credibility."

The relative sensitivity of an extreme to changes in the mean (dashed line) and in the standard deviation (solid line) for a certain temperature threshold (x-axis). The relative sensitivity of the mean (standard deviation) is the change in probability of an extreme event to a change in the mean (or standard deviation) divided by its probability. From Katz and Brown (1992).
It is common in the climatological literature to also denote events that happen relatively regularly with the term extreme. For example, the 90 and 99 percentiles are often called extremes even if such exceedances will occur a few times a month or year. Following the common parlance, we will denote such distribution descriptions as moderate extremes, to distinguish them from extreme extremes. (Also the terms soft and hard extremes are used.) Based on the theory of Katz and Brown, the rest of this section will be ordered from moderate to extreme extremes.

Examples from scientific literature

We start with the variance, which is a direct measure of variability and strongly related to the bulk of the distribution. Della-Marta et al. (2007) studied trends in station data over the last century of the daily summer maximum temperature (DSMT). They found that the increase in DSMT variance over Western Europe and central Western Europe is, respectively, responsible for approximately 25% and 40% of the increase in hot days in these regions.

They also studied trends in the 90th, 95th and 98th percentiles. For these trends variability was found to be important: If only changes in the mean had been taken into account these estimates would have been between 14 and 60% lower.

Also in climate projections for Europe, variability is considered to be important. Fischer and Schär (2009) found in the PRUDENCE dataset (a European downscaling project) that for the coming century the strongest increases in the 95th percentile are in regions where variability increases most (France) and not in regions where the mean warming is largest (Iberian Peninsula).

The 2003 heat wave is a clear example of an extreme extreme, where one would thus expect that variability is important. Schär et al. (2004) indeed report that the 2003 heat wave is extremely unlikely given a change in the mean only. They show that a recent increase in variability would be able to explain the heat wave. An alternative explanation could also be that the temperature does not follow the normal distribution.


I could not find much literature on this question and have also likely not found everything yet. The studies I could find suggest that the intensity of heat waves is very sensitive to changes in temperature variability (Schär et al., 2004; Fischer and Schär, 2009; Clark et al., 2006; Della-Marta et al., 2007). This limited evidence fits to the Katz and Brown theorem in that the most extreme example, the European heat wave of 2003, small-scale weather variability seems to be very important.

There are also some studies that suggest that the changes in the mean temperature are most important for explaining changes the frequency and duration of heat waves (Barnett et al., 2006; Ballester et al., 2010). These difference illustrate the importance of methodological choices and scales considered.

I would argue that the IPCC (2012) special report on extremes rightly concludes that in projecting future changes in extremes we need to consider changes in the variability and the shape of the probability distribution. Variability is especially important for short-duration precipitation and temperatures in the mid- and high-latitudes.

In the next two posts in this series we will review which changes in weather variability have been found in observations and modelling.

Other posts in this series

1. Introduction to series on weather variability and extreme events
The introduction to this series on weather variability.
2. On the importance of changes in weather variability for changes in extremes
This post.
3. Modelled climatic changes in weather variability
On model results on changes in variability and the validation of the model results.

Related posts

A real paper on the variability of the climate
A post on the beautiful paper by Reinhard Böhm on the variability of monthly data from the Greater Alpine Region.
What is a change in extreme weather?
Two possible definitions, one for impact studies, one for understanding.
Series on five statistically interesting problems in homogenization
First part of a series aiming to entice more statisticians to work on homogenization of climate data.
Future research in homogenisation of climate data – EMS 2012 in Poland
A discussion on homogenisation at a Side Meeting at EMS2012.
HUME: Homogenisation, Uncertainty Measures and Extreme weather
Proposal for future research in homogenisation of climate network data.
Homogenization of monthly and annual data from surface stations
A short description of the causes of inhomogeneities in climate data (non-climatic variability) and how to remove it using the relative homogenization approach.
New article: Benchmarking homogenization algorithms for monthly data
Raw climate records contain changes due to non-climatic factors, such as relocations of stations or changes in instrumentation. This post introduces an article that tested how well such non-climatic factors can be removed.


Ballester, J., F. Giorgi, and X. Rodo, 2010: Changes in European temperature extremes can be predicted from changes in PDF central statistics. Clim. Change, 98, pp. 277-284, doi: 10.1007/s10584-009-9758-0.

Barnett, D.N., S.J. Brown, J.M. Murphy, D.M.H. Sexton, and M.J. Webb, 2006: Quantifying uncertainty in changes in extreme event frequency in response to doubled CO2 using a large ensemble of GCM simulations. Clim. Dynamics, 26, pp. 489-511, doi: 10.1007/s00382-005-0097-1.

Clarke, R.T., S.J. Brown, and J.M. Murphy, 2006: Modeling northern hemisphere summer heat extreme changes and their uncertainties using a physics ensemble of climate sensitivity experiments. J. Clim., 19, pp 4418-4435, doi: 10.1175/JCLI3877.1.

Della-Marta, P.M., J. Luterbacher, H.V. Weissenfluh, E. Xoplaki, M. Brunet, H. Wanner, 2007: Doubled length of Western European summer heat waves since 1880. J. Geophys. Res., 112, doi: 10.1029/2007JD008510.

Fischer , E.M. and C. Schär, 2009: Future changes in daily summer temperature variability: driving processes and role for temperature extremes. Clim. Dyn., 33, pp. 917-935, doi: 10.1007/s00382-008-0473-8.

IPCC, 2012: Managing the risks of extreme events and disasters to advance climate change adaptation. A special report of Working Groups I and II of the Intergovernmental Panel on Climate Change [Field, C.B., V. Barros, T.F. Stocker, D. Qin, D.J. Dokken, K.L. Ebi, M.D. Mastrandrea, K.J. Mach, G.-K. Plattner, S.K. Allen, M. Tignor, and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, UK, and New York, NY, USA, 582 pp, ISBN 978-1-107-60780-4.

Katz, R.W. And B.G. Brown, 1992: Extreme events in a changing climate: variability is more important than averages. Clim. Change, 21, pp. 289–302, doi: 10.1007/BF00139728.

Rhines, A. and P. Huybers, 2013: Frequent summer temperature extremes reflect changes in the mean, not the variance. Proc. Natl Acad. Sci. USA, 110, E546, doi: 10.1073/pnas.1218748110.

Schär, C., P.L. Vidale, D. Lüthi, C. Frei, C. Häberli, M.A. Liniger and C. Appenzeller, 2004: The role of increasing temperature variability in European summer heatwaves. Nature, 427, pp. 332–336, doi: 10.1038/nature02300.


  1. So are we seeing more extreme weather than we used to? This is on my mind at the moment because I've just been arguing with someone on Wotty's blog about it.

  2. For changes in extremes, I would refer to the SREX report, linked above. They are much more knowledgeable as I am. There you can find a lot of information that heat waves are increasing and will become even stronger and that severe precipitation is generally increasing, but not everywhere. Other severe weather phenomena are a separate field of study for domain experts.

    This post was about another question, whether changes in the mean or changes in the weather variability are most important for changes in extreme weather.

  3. Maybe this is a question more appropriate for future posts but, how is the variability measured in those studies?
    A while ago Tamino wrote this post that made me wary of this kind of papers. He looks at work by Hansen that seems to show an increase in temperature variability in the US and finds that what the found probably was not an increase in variability in the same location over time but of spacial variability. That is, since different areas warm at different rates, their pooled temperature distribution will widen over time even if each individual area doesn't show an increase in temperature variability.

    Maybe other studies are more careful but it seems to me that is an easy mistake to make but that is bot subtle and important.

  4. Hansen even explicitly stated that his paper was not about changes in variability. Although the main figure in his paper surely suggested this, he also did not write it in the paper.

    The funny thing is that the spatial variability is actually decreasing. High latitudes are warming more than the low latitudes. That showed up as a broader distribution in the Hansen et al. paper, which suggested more variability.

    So yes you should be very careful is such analysis. For example if the annual cycle is decreasing and you analyse the data after subtracting the average annual cycle, you would find that the variability at time scales of less than a year is increasing. But that would just be the annual cycle, which becomes visible in years where the average annual cycle is not appropriate.

    I will discuss a little of such problems in the future posts. Such problems also make it difficult to compare the papers with each other, because everyone makes somewhat different choices in their analysis, which may be important.

    The importance of such details also mean that just reading the abstract or just the newspaper headlines is not sufficient. Variability is a tricky topic and most natural scientists have only been trained in linear methods focussing on the means.


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