Statistically interesting problems: correction methods in homogenization

This is the last post in a series on five statistically interesting problems in the homogenization of climate network data. This post will discuss two problems around the correction methods used in homogenization. Especially the correction of daily data is becoming an increasingly important problem because more and more climatologist work with daily climate data. The main added value of daily data is that you can study climatic changes in the probability distribution, which necessitates studying the non-climatic factors (inhomogeneities) as well. This is thus a pressing, but also a difficult task.

The five main statistical problems are:

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

Problem 4. Correction as model selection problem

The number of degrees of freedom (DOF) of the various correction methods varies widely. From just one degree of freedom for annual corrections of the means, to 12 degrees of freedom for monthly correction of the means, to 120 for decile corrections (for the higher order moment method (HOM) for daily data, Della-Marta & Wanner, 2006) applied to every month, to a large number of DOF for quantile or percentile matching.

What is the best correction method depends on the characteristics of the inhomogeneity. For a calibration problem just the annual mean would be sufficient, for a serious exposure problem (e.g. insolation of the instrument) a seasonal cycle in the monthly corrections may be expected and the full distribution of the daily temperatures may need to be adjusted.

The best correction method also depends on the reference. Whether the variables of a certain correction model can be reliably estimated depends on how well-correlated the neighboring reference stations are.

Currently climatologists choose their correction method mainly subjectively. For precipitation annual correction are typically applied and for temperature monthly correction are typical. The HOME benchmarking study showed these are good choices. For example, an experimental contribution correcting precipitation on a monthly scale had a larger error as the same method applied on the annual scale because the data did not allow for an accurate estimation of 12 monthly correction constants.

One correction method is typically applied to the entire regional network, while the optimal correction method will depend on the characteristics of each individual break and on the quality of the reference. These will vary from station to station and from break to break. Especially in global studies, the number of stations in a region and thus the signal to noise ratio varies widely and one fixed choice is likely suboptimal. Studying which correction method is optimal for every break is much work for manual methods, instead we should work on automatic correction methods that objectively select the optimal correction method, e.g., using an information criterion. As far as I know, no one works on this yet.

Problem 5. Deterministic or stochastic corrections?

Annual and monthly data is normally used to study trends and variability in the mean state of the atmosphere. Consequently, typically only the mean is adjusted by homogenization. Daily data, on the other hand is used to study climatic changes in weather variability, severe weather and extremes. Consequently, not only the mean should be corrected, but the full probability distribution describing the variability of the weather.

WUWT not interested in my slanted opinion

Today Watts Up With That has a guest post by Dr. Matt Ridley. In this post he seems to refer to a story that was debunked more than a year ago:

And this is even before you take into account the exaggeration that seemed to contaminate the surface temperature records in the latter part of the 20th century – because of urbanisation, selective closure of weather stations and unexplained “adjustments”. Two Greek scientists recently calculated that for 67 per cent of 181 globally distributed weather stations they examined, adjustments had raised the temperature trend, so they almost halved their estimate of the actual warming that happened in the later 20th century.

I tried to direct those WUWT readers that are interested in both sides of the conversation to an old post of mine about why these Greek scientist were wrong and mainly how their study was abused and exaggerated by WUWT.

Naturally, I did not formulate it that way, but in a perfectly neutral way suggested that people could find more information about the above quote as my blog. I see no way my comment could have gone against the WUWT commenting policy. Still the response was:

[sorry, but we aren't interested in your slanted opinion - mod]

Strange, people calling themselves skeptics that are not interested in hearing all sides. I see that some people from WUWT still find their way here to see what the moderator does not allow. Here it is:

Investigation of methods for hydroclimatic data homogenization

(I may remove this redirect in some days, as this post does not really provide any new information.)


UPDATE: Sou at Hotwhopper wrote a post, WUWT comes right out and says "We Aren't Interested" in facts , about his post. Thank you, Sou. So I guess I will have to keep this post up. And that also makes it worthwhile to add another gem to be found in the WUWT guest post of Dr. Matt Ridley.

Statistical problems: The multiple breakpoint problem in homogenization and remaining uncertainties

This is part two of a series on statistically interesting problems in the homogenization of climate data. The first part was about the inhomogeneous reference problem in relative homogenization. This part will be about two problems: the multiple breakpoint problem and about computing the remaining uncertainties in homogenized data.

I hope that this series can convince statisticians to become (more) active in homogenization of climate data, which provides many interesting problems.

The five main statistical problems are:

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

Problem 2. The multiple breakpoint problem

For temperature time series about one break per 15 to 20 years is typical. Thus most interesting stations will contain more than one break. Unfortunately, most statistical detection methods have been developed for one break. To use them on series with multiple breaks, one ad-hoc solution is to first split the series at the largest break (for example the standard normalized homogeneity test, SNHT) and investigate the subseries. Such a greedy algorithm does not always find the optimal solution.

Another solution is to detect breaks on short windows. The window should be short enough to contain only one break, which reduces power of detection considerably.

Multiple breakpoint methods can find an optimal solution and are nowadays numerically feasible. Especially using the optimization methods “dynamic programming”. For a certain number of breaks these methods find the break combination that minimize the internal variance, that is variance of the homogeneous subperiods, (or you could also state that the break combination maximizes the variance of the breaks). To find the optimal number of breaks, a penalty is added that increases with the number of breaks. Examples of such methods are PRODIGE (Caussinus & Mestre, 2004) or ACMANT (based on PRODIGE; Domonkos, 2011). In a similar line of research Lu et al. (2010) solved the multiple breakpoint problem using a minimum description length (MDL) based information criterion as penalty function.


This figure shows a screen shot of PRODIGE to homogenize Salzburg with its neighbors (click to enlarge). The neighbors are sorted based on their cross-correlation with Salzburg. The top panel is the difference time series of Salzburg with Kremsmünster, which has a standard deviation of 0.14°C. The middle panel is the difference between Salzburg and München (0.18°C). The lower panel is the difference of Salzburg and Innsbruck (0.29°C). Not having any experience with PRODIGE, I would read this graph as suggesting that Salzburg probably has breaks in 1902, 1938 and 1995. This fits to the station history. In 1903 the station was moved to another school. In 1939 it was relocated to the airport and in 1996 it was moved on the terrain of the airport. The other breaks are not consistently seen in multiple pairs and may thus well be in another station.

Five statistically interesting problems in homogenization. Part 1. The inhomogeneous reference problem

This is a series I have been wanting to write for a long time. The final push was last week's conference, the 12th International Meeting Statistical Climatology (IMSC), a very interesting meeting with an equal mix of statisticians and climatologists. (The next meeting in three years will be in the area of Vancouver, Canada, highly recommended.)

At the last meeting in Scotland, there were unfortunately no statisticians present in the parallel session on homogenization. This time it was a bit better. Still it seems as if homogenization is not seen as the interesting statistical problem it is. I hope that this post can convince some statisticians to become (more) active in homogenization of climate data, which provides many interesting problems.

As I see it, there are five problems for statisticians to work on. This post discusses the first one. The others will follow the coming days. UPDATE: they are now linked in the list below.

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

Problem 1. The inhomogeneous reference problem

Relative homogenization

Statisticians often work on absolute homogenization. In climatology relative homogenization methods, which utilize a reference time series, are almost exclusively used. Relative homogenization means comparing a candidate station with multiple neighboring stations (Conrad & Pollack, 1950).

There are two main reasons for using a reference. Firstly, as the weather at two nearby stations is strongly correlated, this can take out a lot of weather noise and make it much easier to see small inhomogeneities. Secondly, it takes out the complicated regional climate signal. Consequently, it becomes a good approximation to assume that the difference time series (candidate minus reference) of two homogeneous stations is just white noise. Any deviation from this can then be considered as inhomogeneity.

The example with three stations below shows that you can see breaks more clearly in a difference time series (it only shows the noise reduction as no nonlinear trend was added). You can see a break in the pairs B-A and in C-A, thus station A likely has the break. This is confirmed by there being no break in the difference time series of C and B. With more pairs such an inference can be made with more confidence. For more graphical examples, see the post Homogenization for Dummies.

Figure 1. The temperature of all three stations. Station A has a break in 1940.

Figure 2. The difference time series of all three pairs of stations.