I promised a list of what scares me (beyond spiders and ice climbing) when homogenizing temperature time series. As our focus is limited to temperatures, I will not worry with changes in variances, extremes, etc. The list:
1) Multiple changepoints
2) Seasonal features, especially those typically present in daily data
3) Autocorrelation
4) Missing and/or erroneous data
5) Mean misspecification, e.g., not accounting for a trend
6) Multiple reference series
Missing data is usually just a programming hassle, so maybe it shouldn't make this list. All of these issues have been tackled in the changepoint/homogenization literature to some degree, but I do not know of a reference where all issues are considered in tandem.
4 comments:
Robert, what do you mean with "scares me". Do you just want to say that the first 4 points are difficult scenarios that should be included in the benchmark? Or do you think that state-of-the-art homogenisation algorithms that were designed with the multiple breakpoint problem in mind (e.g. Prodige, MASH, ACMANT, USHCN), will produce biased results in such cases?
The benchmark dataset of the COST-HOME project had the first 4 features and the analysis did not show anything yet that scared me.
I have one problem that scares me: land-use change. Relative homogenisation is based on the principle that if we see a change to one station and not to the surrounding ones, this change is artificial. That is a reasonable assumption for large scale climate variability and climate change due to CO2. However, in case of land-use change we would remove a real signal. Thus whereas after homogenisation the data is better suited to study climate change due to CO2, the dataset is still not well suited to study the influence of land-use changes.
There is one thing about homogenisation that really scares me, and it's not the statistics:
We do not understand the causes of most errors, I mean, really the physics behind a break. We may not need to care about physics for detection of breaks, but for correction. This could be easily reflected in a benchmark data set (it may not be relveant as long as we are talking only about monthly means, but certainly when we go to dailies).
For instance, instruments may have errors that depend on radiation balance of the screen (and hence on the time of the day, season, cloud cover). A change of instrument or screen could lead to a step change with a distinct fingerprint. Or trends: There may be artificial trends due to growing trees in the station environment. Trees do not shrink, so the direction of the trend is not a free parameter. But if we do not understand whether growing trees near a station cause the temperature to increase or decrease, should we correct at all?
I fully agree with Stefan, that we need to understand the physical causes of inhomogeneities much better to be able to make a reliable correction of daily data or also to produce a daily benchmark dataset with realistic inhomogeneities. We need this to see which other meteorological parameters are covariates and to be able to introduce breaks with a realistic change in the distribution. (Sorry, for these statistical words, in the end our physical understanding will have to be converted again to statistical measures: we will not be able to understand the reason for every individual break in every station in the past.)
In the Cost Action Home we also produced a daily temperature benchmark to test daily correction methods. Producing the homogeneous surrogate daily data was easy, but introducing the inhomogeneities was not.
We exchanged the distribution of two nearby stations to simulate a moving station; that was realistic. However, all other inhomogeneities we had to simulate by perturbing the data with some equations to change, e.g., the standard deviation and skewness of the data. Someone who would know these equations would be able to homogenise this dataset very accurately with a method that may not perform well on real data.
Formulated in another way. If we introduce inhomogeneities by changing the moments, a method that corrects the moments would be good. If we introduce inhomogeneities by changing certain percentile classes, as method based on percentiles will perform well. Thus, the distribution should be realistic and we need to study the influence of known inhomogeneities (meta data) on the distribution.
Victor,
By scares, I'm referring to aspects that make the math in homogenizing temperature series more difficult....or at least more detailed. I'm not really up to speed on the methods behind all the acronyms you list. I would be very interested in a list of what features you have put into the COST benchmarks.
Somewhat aside: I am somewhat skeptical about the variance and percentile changepoints you all speak of. In temperature series, I don't see this feature too often. Granted, variance/autocovariance changepoints are the primary issue in speech recognition. I just worry that until mean misspecification and autocorrelation aspects are handled correctly, we are confounding (overparametrizing) issues by looking for variance changepoints. I'd appreciate a concrete data example of a temperature series where there is an obvious variance change with no accompanying mean shift structure.
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