by In a BBC radio interview on Tuesday 9 December, Geoff Jenkins of the Hadley Centre informed listeners that his organization had identified a significant trend in UK storminess over the past half-century or so. He explained this in terms of storm tracks in the Atlantic region and insisted that it could not be explained other than via man-made climate change. My ears pricked up at this as I recalled a salutary tale about time series and trends by Sir John Mason, at the time Director General of the Met Office, which also concerned UK wind storms. He first showed a pillar-graph of storm frequency by decade (starting, I think, from the 1950s). This revealed a very clear upward trend within the span of the diagram. He then added the data from the previous decade which entirely quashed that original impression. At that time (early 1980s I guess), the meteorological establishment was sceptical about man-made global warming, 180 degrees away from their current stance. So I was motivated to follow up on these new data. A bit of digging led to the conference of the parties (COP9) in Milan and a report for it prepared by the Met Office (you can read it at www.met-office.gov.uk/research/hadleycentre/pubs/brochures/2003/global.pdf .) The relevant diagrams and text make it clear that the pronouncements about trend and attribution were not based on wind data (too many disturbances) but on a storm index derived from changes in 3-hour air pressure data from 28 UK locations. Details of the construction of the index are not provided. However the key phrase is "the average number of storms (per station) shows a significant increase in the United Kingdom winter period" and this, coupled with the positive attribution to man’s activities in causing a shift in storm tracks, was also the take-home message from the interview. The diagrams in the COP9 report reveal very noisy time series with a positive skewness (upward spikes taller than downward). An upward trend is indeed discernible, assisted by the addition of trend and smoothing lines. What interested me was the significance of the trend especially as the passage from storminess index to wind speed will inject further scatter. So I digitised the graphs to obtain the annual time series. In what follows I tended to stick to the Jan-Mar data as I couldn’t be sure which winter the Oct-Dec data referred to (lagged correlations were higher than current-year correlation). The initial analysis was a regression of storminess index on year number. The regression coefficient implies a 17% increase in storminess index per decade. At nearly 2.4 times its own standard error of estimate, this appears highly significant and remains so even after allowing for a null hypothesis that doesn’t predetermine the sign of the trend (something which is frequently forgotten by researchers eager to establish the existence of upward trends). This conclusion is also not altered by transforming the data to eliminate the asymmetry between upward and downward spikes. Of course this does not exhaust the scope for inflating the significance through selection of season, base time period, and spatial boundaries, but a large reduction in the number of degrees of freedom would be required to bring a multiple of 2.4 out of the range of statistical significance. Establishing a trend is of course not the same as establishing attribution. Specifically it does not examine the possible influence of natural fluctuations that are known to operate on the decadal time period. In climatological studies for the UK area, they are frequently represented by the North Atlantic Oscillation (NAO) index which is itself based on the meridional air pressure gradient in the North Atlantic. The Met Office’s COP9 report in fact does discuss the possible relevance of the NAO as a natural contributor to the trend but dismisses it as being of secondary importance. It was noticeable though that this dismissal was rather uncharacteristically hedged with several small provisos so one sensed that the issue might not be as clear cut as the bold take-home message implied. This prompted a more detailed analysis of the time series adding in NAO data as an explanatory variable (NAO monthly data are available on the Climatic Research Unit website at http://www.cru.uea.ac.uk/ftpdata/nao.dat). The first calculation was to compare the simple pairwise correlations between the variables. It transpired from this that the variance in storminess index explained by the NAO was considerably greater that that explained by the trend term (over 25% for NAO versus less than 10% for year number) a finding which is itself at variance with the implication of the statement in the report for COP9 that "although there is a similar upward trend in the NAO, there is quite a poor correlation between this figure and the storm rate ….". However, because of interactions between them, pairwise comparisons are insufficient to separate the variance explained by two contending variables. This can be done using a linear regression between the storminess index as dependent variable and year number and NAO as independent variables. The analysis confirmed the initial finding based on the pairwise correlations in that the burden of explained variance fell on the NAO term. In fact the regression coefficient of the secular trend term dropped from 2.4 to 1.4 times its standard error which takes it out of the range of acceptable significance; as many as one trend-free sample in five could throw up a positive or negative trend of this size. The weakness of the secular trend is illustrated in the above graph which shows the time trend (or lack of) in the storminess index once the effect of NAO is removed. There is a hint of a quadratic term visible on the diagram and adding such a term in an analysis of variance shows the linear and quadratic terms to be of approximate equal "power", though neither are significant. I suspect that "Still Waiting for the Greenhouse" readers will not need a moral to this tale – secular trend disappears once one allows for non-stationary fluctuations operating in the background - it is all too common in global change science to find little or nothing of substance once one takes the time and effort to dig behind the headlines. |

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