Standardised UK rainfall data, putting winter 2013/2014 into context
This is a major work started during January. Results for the 17 Met Office areal time series from 1910 are presented standardised and ranked.
The only region of the 17 with remarkable rainfall was the data combination South East and Central Southern England with a Z-score of +3.2 based on de-annualised.
The primary plots and presentation is in PDF format where zoom can be used. Here is the file (2MB)
The objective was if possible Standardising the data with the intention of
- revealing any data structure
- allowing better regional comparison
- producing a statistical measure for both dry and wet periods in spite of the wet/dry process being effectively non-linear, it does not rain dryness
The result is successful. A noise signal with no obvious structure appears. In common language it is called weather.
A calculation of Return Period for the most affected 2013 / 2014 area via GEV software gives a figure of 33 years. GEV is a huge subject where results need a contextual interpretation. See ref2
The exact geographic areas used by the Met Office is not clear.
England and Wales
England East and Northeast
England Northwest and North Wales
England Southwest and South Wales
England Southeast and Central Southern
- Remove annual signal
- Normalise data
- Adjust skewness and kurtosis to zero
- Renormalise data (skewness and kurtosis are unaltered)
I decided to keep the processing simple, hence the the use of skewness and kurtosis as measures of normality. See ref1 for detail of the functional adjustment, which was computer optimised. (there are 17 datasets)
All the processing is well within the capability of a simple datasheet except for the method used to remove the annual cycle.
Experimentation showed an excessive leakage of the annual cycle post processing. Going on a hunch from specialist knowledge I tried harmonic removal. This gave better results. An explanation is beyond this text, briefly it is to do with Nyquist artefacts and noise from least squares methods, essentially how normal meteorological mathematics operates. The difference is fairly small.
Timeseries plot no comment needed.
Probability Plot (ref3) is a common and simple technique intended primarily for viewing as part of data appraisal. It is simply formed
- sort the Standardised data low to high forming it’s CDF
- create a standard curve, CDF of Standard.
- XY plot
There is no useful measure of goodness, r2 in this case is circa 0.999 and RMSD means little to humans. I’ve provide a difference plot, which better shows the error from Normal.
Annual cycle, see comment about method in previous section.
Function law plot is a manual stimulation of the optimised setting used for this particular dataset. Re normalisation takes place afterwards so zero etc. is irrelevant. Possibly this is the only technically interesting part of the work, the use of hyperbolic, in this case sinh and asinh. It is very simple. Notably R.A. Fisher used hyperbolic on rainfall data to do with his work at the Rothampstead Agricultural Research Station during the 1920s.
On the data
The Met Office data here is sums of months at an unpublished and changing network of station, taken together with equipment changes and station environmental changes some degree of caution is wise.
A surprising source of caution is OFCOM as a spin-off from due diligence work they carried out on the robustness of microwave links , heavily affected by tropical downpours, one of the lauded effects of AGW. In their opinion the Scottish data is not usable prior to 1990. (Ref4)
I’m inclined to agree with this view based on data showing abnormal features, inconsistent and on the sparse nature of historic Scottish stations.
A major concern is UK data containing Scottish data.
Precipitation at an individual site seems to follow a different law from the en-mass amalgamated station data. Perhaps 1/f law but when many are averaged data tends more to Gaussian, a large and involved subject with many opinions. Note with the result here, UK data is more regular than regional, tending to confirm the effect.
In addition when it rains it one thing but the volume of water is more related to individual sites. The simple parallel is rainfall on a long rising mountain slope where even for the same clouds the volume will vary greatly.
Localised extreme rainfall is common at the same time as rare for a particular site. An excellent example is contain in the Met Office Wick data. One extreme storm. Less localised but nevertheless an outlier can be seem in the subject of this work: Region East Anglia, Z-score 4.17 August 1912. A web search will produce reports. It is also mentioned in the excellent Booty site
> August 1912 was EXCEPTIONALLY WET with 193 mm of RAIN, the wettest such-named month in the EWP series. Severe FLOODING occurred across many parts of east & central England. (EWP)
Winter 2013 / 2014
This was only notable in intensity in part of the UK. The duration which is another factor some have suggested as unusual does not in my opinion rate as outstanding.
This did occur at the wettest time of the year for that area, an effect I have deliberately excluded, we know it rains a lot at that time of the year. It does nevertheless show as exceptional.
I know the area. I’ve seen similar water amounts in the past, the early 1960s for example which was not so much intensity as duration. There was a great deal of minor flooding.
Here in the small town where I live there was minor flooding where I have seen it before, in some ways less. On investigating the variety of local history books I have here I found a copyright photograph from the late 1800s of flooding just like recently or the 1960s. The photograph was posed, a man is standing in the street up to his ankles in flood-water, he is carrying a child piggyback. A elderly woman resident is looking on from the front door of her house. One of the buildings close by is identical today.
Also recorded is the town bridge being swept away twice by floods, 1500s, 1700s and was finally rebuilt as a more solid structure in the 1800s, as it is today except the outer arches are now in filled.
Another series of reports writes of severe floods elsewhere during the late 1800s and led to a complete rebuilding of the drains.
Biometrika 01/2009; 96(4). DOI:10.1093/biomet/asp053
ABSTRACT Jones & Pewsey (2009) introduce the ‘sinh-arcsinh’ transformation and use it to define the sinh-arcsinh family of distributions. When the generating distribution is standard normal, the ‘normal sinh-arcsinh’ (NSAS) class of distributions is obtained. The four-parameter location-scale extension of this class contains sym-metric as well as asymmetric members and allows for tailweights that are heavier or lighter than those of the normal distribution. As will be shown, the NSAS class is highly tractable and has many appealing properties.
This is not a Box-Cox variant.
Ref2 GEV (Generalised Extreme Value)
The value quoted was produced by execution of the Windows program CumFreq on raw England SE and Central S data.
As a land and watermanagement specialist at the International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands, I have worked since 1965 in almost 30 countries in Asia, Africa and Latin America, giving training courses, participating in research programs and providing project advice as a consultant. In 2002, I left ILRI to be independent.
When I went to pick up a good link for the Scottish problem I failed to find the earlier work, so here is the final report, which does not discuss the pre-1990 Scottish problem. If I am wrong this will be amended on request.