Introduction to series on weather variability and extreme events

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.

Upcoming posts

In this series, I will first discuss the relationship between changes in extremes and changes in the mean and in the variability; see figure below. Especially changes in extreme extremes are connected to changes in the variability; this can be shown using extreme value theory and is reflected in the literature on climatic changes in extremes.

Figure is taken from Real Climate, which took it from IPCC (2001).

The next two posts will be on changes in variability from modelling studies and observations. These posts will present many results, which are, or seem to be, conflicting. One reason for this is probably the strong dependence on methodological choices given the complexities mentioned above. There does seem to be a pattern emerging: the temperature variability on inter-annual time scales is decreasing, while it is increasing on intra-seasonal time scales (important for for example heat waves). The variability of precipitation seems to increase: The increasing trends in median precipitation amounts are weaker than the trends in severe precipitation.

An important reason for conflicting findings is likely the quality of the observations, this will also be the topic of a post. Inhomogeneities caused by changes in climate monitoring practices are already important for studying changes in the mean. Our basic understanding of the changes in observational methods and first empirical studies indicate that taking inhomogeneities into account is likely even more essential for studying changes in the variability. Empirical evidence comes from the results of new statistical homogenization methods for daily data and from parallel measurements with historical and modern measurement set-ups.

Long time series are needed in order to distinguish natural (multi-decadal) changes in variability from long-term changes and large international datasets are needed to corroborate the results of regional studies and to put them into a larger perspective. Such efforts have, however, to bear in mind that up to now continental and global collections are not homogenized because of the immense – usually unappreciated - labour required. Currently, only smaller homogenized daily temperature datasets are available.

There will also be a post on the research needed to understand changes in weather variability better. I see three main topics for future research on weather variability.

1. The quality of the observations.
2. The suitability of climate models.
3. The analyses of changes in weather variability.

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.

(This article is a repost from Variable Variability.)

Climate changes in weather variability

Scientific summary, Priority research program (DFG-SPP) proposal

This SPP will study changes in the variability of the weather using daily climate data. An important reason to study variability is that changes in extremes can be caused by changes in the mean and in the variability. Variability is more important for extreme extremes and the mean is more important for moderate extremes. It is thus not clear whether results for moderate extremes, which are most studied, extrapolate to true extremes, which are important for many climate change impacts. Furthermore, the mean state has been studied in much more detail and is thus likely more reliable. Also for modelling nonlinear processes in climate models, variability is important.

In the first three-year period the SPP will study weather variability with a focus on the quality of observational data and on the performance of the modelling and analysis tools. This phase will concentrate on Europe, which has the longest and best observations available. In the second phase, the focus will be on understanding the mechanisms that cause these changes. Such studies need to be performed on the global scale.

First phase

1. Weather variability needs to be analysed in a range of difference climatic variables and phenomena at various temporal time scales and spatial ranges, as well as for different measures of variability, seasons and regions and their relations with climate modes. To learn most from these studies, they should be performed in a way that eases intercomparisons.

2. We will improve the analysis methods to study changes in the spatial and temporal dependence of variability over a range of spatio-temporal scales. Important for the comparability of studies is that the range of spatio-temporal scales is well defined. These methods will analyse the full probability distribution or multiple variability measures and not just one or a few.

3. Non-climatic changes due to changes in monitoring practices are especially important when it comes to changes in variability. We will thus develop quality control and (stochastic) homogenization methods for the probability distribution of daily data and estimate uncertainties due to remaining data problems.

4. We will investigate the properties of inhomogeneities in the essential climatic variables in various climate regions. Two methods for this are 1) using parallel measurements with historical and modern set-ups and 2) by studying the adjustments made by homogenisation methods.

5. An attractive alternative to creating homogenized datasets is the development of analysis methods that use data from homogeneous subperiods (similar to what the Berkeley project (BEST) has done for the mean temperature).

6. We will validate climate models with respect to variability at various temporal and spatial scales. Because of the differing spatial averaging scales, this includes the study of the downscaling or gridding methods.

Second phase

7. The methods developed in the first phase will have to be made robust to be applied to large global datasets to be able to study changes in weather variability for all climate regions of the Earth.

8. We will validate climate models globally, for various climate regions, with respect to variability at various temporal and spatial scales.

9. The mechanisms that determine natural and man-made changes in variability will be studied in global models and datasets.

Climatologists, statisticians and time series analysts working on extreme weather, quality control, homogenization, model validation or downscaling likely have the skills to participate in this SPP.

The SPP is focused on our understanding of the climate system. While impact studies will strongly benefit from the results, they are not part of this SPP. Studies on changes in extremes are welcome if they analyse the extremes together with other variability measures. Research on long-term (climatic) changes in the mean does not fit in this SPP on weather variability.

Five statistically interesting problems in homogenization

For many the term homogenization is associated with dusty archives. Surely good metadata on station histories is important for achieving best results, but homogenization is much more, it is especially a very exiting statistical problem. It provides a number of problem that are of fundamental statistical interest.

Most of the work in homogenization has been focussed on improving the monthly and annual means, for example to allow for accurate computations of changes in global mean temperature. The recent research focus on extreme and server weather and on weather variability, has made the homogenization of daily data and its probability distribution necessary. Much recent work goes in this direction.

As I see it, there are five problems for statisticians to work on. The first problems are of general climatological interest and thus also for the study of weather variability. The latter ones are more and more important for the study of weather variability.

Problem 1. The inhomogeneous reference problem

Neighboring stations are typically used as reference. Homogenization methods should take into account that this reference is also inhomogeneous

Problem 2. The multiple breakpoint problem

A longer climate series will typically contain more than one break. Methods designed to take this into account are more accurate as ad-hoc solutions based single breakpoint methods

Problem 3. Computing uncertainties

We do know about the remaining uncertainties of homogenized data in general, but need methods to estimate the uncertainties for a specific dataset or station

Problem 4. Correction as model selection problem

We need objective selection methods for the best correction model to be used

Problem 5. Deterministic or stochastic corrections?

Current correction methods are deterministic. A stochastic approach would be more elegant

A real paper on the variability of the climate

(Reposted from Variable Variability)

I am searching for papers on the variability of climate and its natural variability and possible changes due to climate change. They are hard to find.

The New Climate Dice

This weekend I was reading a potential one: the controversial paper by James Hansen et al. (2012) popularly described as "The New Climate Dice". Its results suggest that variability is increasing. After an op-ed in the Washington Post, this article attracted much attention with multiple reviews on Open Mind (1, 2, 3), Sceptical Science and Real Climate. A Google search finds more than 60 thousand webpages, including rants by the climate ostriches.

While I was reading this paper the Berkeley Earth Surface Temperature group send out a newsletter announcing that they have also written two memos about Hansen et al.: one by Wickenburg and one by Hausfather. At the end of the Hausfather memo there is a personal communication by James Hansen that states that the paper did not intend to study variability. That is a pity, but at least saves me the time trying to understand the last figure.

Reinhard Böhm

That means that the best study I know on changes in variability is a beautiful paper by Reinhard Böhm (2012), who unfortunately recently passed away, an enormous loss. His paper is called "changes of regional climate variability in central Europe during the past 250 years". It analyses the high-quality HISTALP dataset. This dataset for the greater Alpine region contains many long time series; many of the earliest observations were performed in this region. Furthermore, this dataset has been very carefully homogenized.

Reinhard Böhm finds no change in variability, not for pressure, not for temperature and not for precipitation. His main conclusions are:

• The first result of the study is the clear evidence that there has been no increase of variability during the past 250 years in the region.
• We can show that also this recent anthropogenic normal period [1981-2010, red.] shows no widening of the PDF (probability density function) compared to preceding ones.
• It shows that interannual variability changes show a clear centennial oscillating structure for all three climatic elements [pressure, temperature and precipitation, red.] in the region.
• For the time of being we have no explanation for this empirical evidence.