This is the introduction to a series on

**changes in the daily weather and extreme weather**. The series discusses how much we know about whether and to what extent the climate system experiences changes in the variability of the weather. Variability here denotes the the changes of the shape of probability distribution around the mean. The most basic variable to denote variability would be the

variance, but many other measures could be used.

## Dimensions of variability

Studying weather variability adds more dimensions to our apprehension of climate change and also complexities. This series is mainly aimed at other scientists, but I hope it will be clear enough for everyone interested. If not, just complain and I will try to explain it better. At least if that is possible, we do not have much solid results on changes in the weather variability yet.

**The quantification of weather variability requires the specification of the length of periods and the size of regions considered** (extent, the scope or domain of the data). Different from studying averages is that the consideration of

**variability adds the dimension of the spatial and temporal averaging scale** (grain, the minimum spatial resolution of the data); thus variability requires the definition of an upper and lower

scale. This is important in climate and weather as specific climatic mechanisms may influence variability at certain scale ranges. For instance, observations suggest that near-surface temperature variability is decreasing in the range between 1 year and decades, while its variability in the range of days to months is likely increasing.

Similar to extremes, which can be studied on a range from moderate (soft) extremes to extreme (hard) extremes,

**variability can be analysed by measures which range from describing the bulk of the probability distribution to ones that focus more on the tails.** Considering the complete probability distribution adds another dimension to anthropogenic climate change. Such a soft measure of variability could be the variance, or the

interquartile range. A harder measure of variability could be the

kurtosis (4th moment) or the distance between the first and the 99th

percentile. A hard variability measure would be the difference between the maximum and minimum 10-year

return periods.

Another complexity to the problem is added by the data:

**climate models and observations typically have very different averaging scales.** Thus any comparisons require upscaling (averaging) or

downscaling, which in turn needs a thorough understanding of variability at all involved scales.

A final complexity is added by the

**need to distinguish between the variability of the weather and the variability added due to measurement and modelling uncertainties, sampling and errors.** This can even affect trend estimates of the observed weather variability because improvements in climate observations have likely caused apparent, but non-climatic, reductions in the weather variability. As a consequence, data

homogenization is central in the analysis of observed changes in weather variability.