Thursday, 8 May 2014

Modelled climatic changes in weather variability

This is part 3 of a series on what we know about changes in weather variability on climatic time scales. This series is more technical as most posts on this blog and more directed at the scientific community. The introduction gives some background on the topic. If you did not read this post back in November, you might want to do that now before continuing. Variability is not as trivial as some may think.

The second part of the series explains why weather variability is important for extremes weather and especially for the most extreme extremes.

The logical next step would have been to have a look at how weather variability is changing in reality. However, this will take more than one post, thus I will start in this post with what we know from dynamical climate models and how good the models are able to reproduce weather variability.


A number of recent model simulation studies address changes in the temperature variability in the past and future. Fitting to what we will next see in the next post on observations, the year to year variability typically decreases, while increases are found at daily time-scales.

Huntingford et al. (2013) computed the year to year (interannual) temperature variability by subtracting a running mean from the simulated global annual mean temperature. Their analysis of this variability in 17 CMIP5 simulations (the main intercomparison project for global climate models) does not show large variability decreases up to the present time; but their study does predict (RCP8.5 scenario) that globally the variability is expected to decrease in the coming century (Figure 1).

Figure 1. The global standard deviation of the annual temperature derived for two window sizes to compute the anomalies: 11 years (top) and 31 years (bottom). The black line shows the average, the blue area the spread of the ensemble of 17 climate models with historical-plus-RCP8.5-scenario simulations in the CMIP5 database. From Huntingford et al. (2013).

A more detailed study on the temperature variability of a 10-member multi-model RCM ensemble (a large number of runs from regional climate models) produced by the PRUDENCE project for Europe shows increases for the summer temperature variability at various temporal scales from daily to inter-seasonal (the variability in summer means from year to year). The increases are seen in the average variability over all of Europe, but are especially strong in what they call the Transitional Climate Zone (TCZ), the region between the Mediterranean and the Nordic countries (Fischer and Schär, 2009). In this zone, soil moisture is very important in the summer. More to the South, in the Mediterranean countries, the soil is typically dry in summer. More to the North soil moisture is also plentiful in summer.

Figure 2. Simulated change in total daily temperature variability (K) in the period 2071–2100 with respect to the current climate (control run). Figure 2b of Fischer and Schär (2009)

Also Beniston (2004) finds an increase in variability: the daily maximum temperatures averaged over the summer in the PRUDENCE dataset increases by "only" 5°C in the South-West of France at the end of this century, whereas the upper extremes increase more: about 6 to 8°C.

The striking differences between the above mentioned results, decreasing variability (Huntingford et al.) and increasing variability (Fischer & Schär and Beniston) is most likely due to the difference in the temporal extend (annual vs. summer), but could also be due to the area considered (global vs. Europe). The relatively small methodological differences are probably not the reason.

The importance of methodology, however, is seen by comparing Fischer and Schär (2009) with the study on the same PRUDENCE dataset by Ballester et al. (2010). They analyse daily temperature data, but instead of one season (summer) they take the full year. On this dataset they study the importance of the first three moments (mean, standard deviation and skewness). Since they keep the annual cycle, the calculated standard deviation is dominated by the annual cycle, whereas in Fischer and Schär the variability was to a large part day to day variability. This may explain the findings of Ballester et al., which indicate that the changes in the warm percentiles are mainly determined by the mean temperature, not by the standard deviation or skewness. Ballester et al. (2010) do find the variance and skewness to be important to explain changes in the cold tail of the temperature distribution.


An increase in short- and long-duration extreme precipitation is projected in the PRUDENCE ensemble for most of Europe, even for regions in Central Europe where mean precipitation is projected to decrease (Christensen and Christensen, 2003; Fowler et al., 2007). This indicates that the variability of precipitation will increase as expected by Trenberth (1999).

In a recent study Maraun (2013) studied trends in the season maximum of daily precipitation in ENSEMBLE projections using a Generalised Extreme Value (GEV) distribution. He found that both the location (related to the mean value of the extremes) and the scale parameter (related to the width of the distribution of the extremes) of the GEV needed to have a trend component. Otherwise trend in the seasonal maxima would be underestimated. This indicates that changes in variability are important for extreme precipitation.


Also the variability of air pressure may change as suggested by many studies on changes in (winter) storms. Zahn and Von Storch (2010) showed that the frequency of North Atlantic polar lows is projected to decline in response to future climate warming. Chen and Von Storch (2013) studied the climatology of North Pacific Polar Lows in downscaled reanalysis data. This climatology is consistent with the limited observational evidence and exhibits strong year-to-year variability, but weak decadal variability and a small positive trend.

Model variability validation

The scientific literature shows substation deviations between modelled and observed variability for many variables and temporal scales. Some examples are summarized below; a much too limited number to draw firm conclusions. If these deviations are due to model deficiencies (and not the observations) this is not only problematic for studies on extreme weather, but also for accurate climate model simulations of the mean model state. Climate models contain many nonlinear processes (such as radiative transfer and precipitation production) and threshold-like processes (such as phase transitions and wilting of plants). To model such nonlinear processes the variability is paramount.

Temperature variability of the European PRUDENCE ensemble was validated with ECA&D station data and a gridded ENSEMBLES observational dataset by Fischer and Schär (2009). They found that the models typically strongly overestimate the total daily summer variability and the interannual variability, by up to a factor 2. The models that overestimate the current intraseasonal variability tend to be the ones that showed larger increases in the period 2071-2100.

Lovejoy et al. (2013) validate the temperature fluctuations of GCM runs against observations, reanalysis data and multi-proxy reconstructions. They do not study the absolute amount of variability, but how the variability changes as a function of temporal scale across several orders of magnitude. Whereas at small scales the relationships are relatively good, at larger scales they can even have the wrong sign. They attribute this to missing long-term processes in the models, but errors in the empirical datasets can also not be excluded and the paper compares unforced simulations with empirical datasets that include anthropogenic global warming.


Schindler et al. (2012) validate the seasonal cycle of extreme precipitation in the UK in the ENSEMBLE dataset. The strong seasonal cycle in North-West Scotland is well reproduced, but only few models are able to reproduce the strong seasonal cycles in East-Anglia. Furthermore, they found that in general spring and fall have the lowest biases, whereas extreme precipitation in winter is too strong and in summer is too low.

For the Alpine region (Frei et al., 2006) found that RCM model biases for extreme precipitation are comparable to or even smaller than those for wet day intensity and mean precipitation. The model differences are well explained by differences in the precipitation frequency and intensity process (Frei et al., 2006).

Volosciuk et al. (submitted, 2013) study the influence of the horizontal and vertical model resolution for ECHAM5 on extreme value statistics. They compare the differences at a common coarse grid and find that return level generally decrease with coarser model resolution. Also regional patterns change, for instance a coarse vertical resolution results in a shift in extreme precipitation toward the equator. In contrast to these results for extreme precipitation, the impact on average precipitation of vertical resolution is less pronounced, whereas the impact of the horizontal resolution is negligible. This suggests that the mentioned result for the extremes are due to the precipitation variability.


This is unfortunately just a blog post and not a review article (if anyone want to help write one, please say so). I have probably still not read a considerable part of the literature. Still the results suggest that the models show similar changes on climatic scales as the measurements: Less variability in temperature from year to year, more variability on daily scales. And on daily scales the variability of precipitation is increasing and will further increase.

The authors of validation papers tend to focus on what does not work well yet. Still if the sample above is representative, the modelling of variability still shows considerable deficiencies. Surprisingly temperature seems to be as difficult as precipitation, in as far as one can compare two dislike variables, whereas for the means precipitation is seen as a difficult variable.

My impression about the model deficiencies is at least shared by one reviewer. A research proposal of mine on weather variability was just rejected with as reason that the models are not able to model variability sufficiently well. I would argue that should have been the reason for acceptance. If we cannot do weather variability, we also cannot do extreme weather. And many people are working on that. Shouldn't they know?

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
The more extreme the extremes are the more important are changes in weather variability relative to changes in the mean.
3. Modelled changes in variability
This post.

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.

Beniston, M., 2004: The 2003 heat wave in Europe: A shape of things to come? An analysis based on Swiss climatological data and model simulations. Geophys. Res. Lett., 31, doi: 10.1029/2003GL018857.

Chen, F. and H. von Storch, 2013: Trends and variability of North Pacific Polar Lows. Advances in Meteorology, ID 170387, doi: 10.1155/2013/170387.

Christensen, J.H. and O.B. Christensen, 2003: Climate modelling: Severe summertime flooding in Europe. Nature, 421, no. 6925, pp. 805–806, doi: 10.1038/421805a.

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.

Fowler, H.J., M. Ekström, S. Blenkinsop, and A.P. Smith, 2007: Estimating change in extreme European precipitation using a multimodel ensemble. J. Geophys. Res., 112, D18104, doi: 10.1029/2007JD008619.

Frei, C., R. Schöll, S. Fukutome, J. Schmidli, and P.L. Vidale, 2006: Future change of precipitation extremes in Europe: Intercomparison of scenarios from regional climate models. J. Geophys. Res., 111, D06105, doi: 10.1029/2005JD005965.

Huntingford, C. P.D. Jones, V.N. Livina, T.M. Lenton, and P.M. Cox, 2013: No increase in global temperature variability despite changing regional patterns. Nature, published online, doi: 10.1038/nature12310.

Lovejoy, S., D. Schertzer, and D. Varon, 2013: Do GCM's predict the climate or macroweather? Earth Syst. Dynam. Discuss., 4, pp. 439-454, doi: 10.5194/esd-4-439-2013.

Maraun, D. 2013: When will trends in European mean and heavy daily precipitation emerge? Env. Res. Lett., no. 8014004.

Schindler, A., D. Maraun, and J. Luterbacher, 2012: Validation of the present day annual cycle in heavy precipitation over the British Islands simulated by 14 RCMs. J. Geophys. Res., 117, doi: 10.1029/2012JD017828.

Trenberth, K.E., 1999: Conceptual framework for changes of extremes of the hydrological cycle with climate change. Climate Change, 42, pp. 327-339.

Volosciuk, C., D. Maraun, V.A. Semenov, and W. Park, 2013: Extreme precipitation in an atmosphere general circulation model: Impact of horizontal and vertical model resolution. Submitted.

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