Werb, B. E., & Rudnick, D. L. (2023). Remarkable changes in the dominant modes of north Pacific sea surface temperature. Geophysical Research Letters, 50, e2022GL101078. https://doi.org/10.1029/2022GL101078

Climate science does love its indices. The SOI, ONI, PDO, NAO, IOD, DMI, TNI, PNA, NAM, SAM, EA, AO, AAO, EP, NP, WP, EATL, WRUS, SCAND, TNH, POLEUR, IPO, TAMG… the list goes on0. Some phenomena have multiple indices associated with them. ENSO – The El Niño Southern Oscillation – has the SOI and the ONI, a bunch of other SST indices (4, 3.4, 3, 1+2), as well as indices that distinguish between eastern Pacific, central Pacific (aka sometimes as El Niño Modoki) and coastal types of El Niño. These different types of ENSO are often referred to as flavours. Expert researchers have identified nine different flavours in data from 1950 to 2011, one flavour every seven years. I have heard tell of 13 different flavours, but after a few drinks, climate scientists will say anything.

Indices beguile. They take something messy and incomprehensible like the climate and reduce it to a one dimensional problem (or however many flavours you choose). You can give the resulting index a name and correlate it with other things, try and predict it, use it to predict other indices. They seem to be useful and it would be hard to argue that they are not – someone could wave several shelves of serious literature at you1 – but to me, they often seem to miss the point. The proliferation of flavours surely ends with assigning every El Niño and La Niña we ever observed its own flavour, though I suppose climate models could generate us a tantalising infinity of untasted Niños and ñas2. But, an index can’t capture the full range of behaviour which is generally messy and incomprehensible because the whole idea of indices is reductive. The seem like the kind of thing you need at first, as understanding is painstakingly built up, but can be done away with later. If one index doesn’t solve your problem, proliferation isn’t going to help.

Instead, what sometimes happens is that indices are granted something approaching independent existence, agency. Rather than being descriptive they become things that cause other things9. While this might make sense for something like ENSO whose persistence and global influence can make such statements useful, it makes much less sense to say that the NAO causes high winds over Europe (say). The NAO index might correlate with wind speed over the region, and indeed it’s directly related to the pressure gradient that does give rise to high winds, but it’s not causing them; it’s just that the thing causing them corresponds to a particular value of the NAO.

How to make an index

The recipe3 for creating an index is about as complex as you want to make it. A common and simple recipe is to grab an SST or MSLP data set, isolate an area, and do an EOF analysis. You then look at each EOF and pick the first one that’s interesting. With SST, the first EOF might be boringly identifiable with “large scale warming” (forgetting for a moment the caveat that EOFs are not physical) and so you would move to the second, usually some kind of dipole8. Once you have a dipole, you can calculate a simple index by choosing grid cells close to the centres of action, you can make composites of conditions associated with positive and negative values, correlate the index with other variables (and other indices) and so on and on.

To calculate EOFs, it’s typical to use a data set that is spatially complete within the chosen domain. Gaps in the data, which are common in observation-based data sets, mean you can’t use simple algorithms for calculating EOFs. There are methods for doing so, but it’s common to use a dataset where someone has helpfully filled the gaps for you already. For SST, that generally means something like HadISST, COBE-SST or ERSST. That these datasets are themselves constructed from EOFs is typically not mentioned. I’m not sure it matters that much, but it’s always been a vague worry of mine4. The alternative is to use a shorter satellite-based data set like the SST CCI L4 data set, but then…

What’s this got to do with that paper you mentioned?

Which long ramble (I apologise) brings me back to the paper I mentioned at the top of the page. In it, the authors revisit (very thoroughly) the calculation of the Pacific Decadal Oscillation, which is the first EOF of SST in a region of the north Pacific. The PDO has a better than usual claim to actually be something more than JAI5. They find that the shape of the relevant EOF changes if you include a longer period in the calculation. This is, in part, due to the “blob6,7“, an informal name given to a series of anomalous warm features/marine heatwaves in the northeast Pacific. The blob, being part of SST variability in the North Pacific, inevitably imprints itself on EOFs calculated from data that cover the blob period. From this they conclude that “the PDO and other EOF based metrics may not be as useful in the future as climate continues to change”. The paper is a neat illustration of the fact that the climate isn’t easily reducible to indices. Its statistical properties – including EOFs – change over time and probably don’t mean what you think they mean even if they don’t.


0 Many of the indices contain the word “oscillationa” which suggests, to any right-minded person, something alternating regularly between states. These climate oscillations are not like that. This serves to remind us that while scientists will argue endlessly over shades of meanings and precise definitions suggesting they possess and cherish an infinite sensitivity to nuance in language, they will often deploy words like an enraged chimpanzee flinging alphabetti-spaghetti (and other things) against a wall.

1 Assuming they had strong enough armsb.

2 I guess they mostly taste salty. In the old days, scientists used to taste things more often (though not always on purpose). I was delighted to discover this tradition continues amongst the more rugged disciplines.

3 I once wrote a paper-maker that quasi-automated this recipe. It selected a region of SST at random, calculated EOFs. I got to choose the most interesting EOF, then it correlated the PC series of that EOF with ENSO, made composites/correlations of conditions associated with high and low values of the index, converted the EOF pattern to a simple index calculated from point differences, smoothed the series to make a decadal-oscillation, and did a bunch of other things. I was writing an introduction to the output of the code for a particular region, when google scholar turned up a paper that had already done pretty much exactly the same for almost exactly the same region. Whereas my paper was intended as a joke, the paper I had found wasn’t. I got rather demoralised at that point and anyway, there was a far more constructive approach.

4 A statistical analysis of a statistical analysis of a statistical analysis of a… but also because an assumption of stationarity is built in. There are various things that mitigate against this – limited areas of effect, blending back in of observations, adding a local analysis etc… but if the data providers could calculate EOFs from incomplete data, so can anyone else. There are various techniques. The paleo community have a tonne of them. They can even work with observational uncertainty.

5 JAI: Just Another Index. I mean the PDO was implicated in the not-so-recent-anymore slowdown in warming, so it must be a thing, right. Right?

6 A reviewer once made me take the word “blob” out of an article I was writingc despite it’s use being enshrined in and sanctified by the literature. It even has a wikipedia page, which has this wonderful sentence “By September 2016, the Blob resurfaced and made itself known to meteorologists”. What did I say about attributing these things with agency? But also, did it wave?

7 If anything can oscillate, a blob can.

8 Tobler’s first law of geography says that “Everything is related to everything else. But near things are more related than distant things.” If we assume that means SST is spatially correlated with correlation decaying with distance, then we can model that statistically. Fields generated at random with this assumption generally have a first EOF which is quasi uniform (long-term warming) and a second and third which are dipoles (one of those is your index). If the second and third EOFs have a similar energy, then just make your domain wider in one direction.

9 Like gods from a particularly unimaginative pantheon, albeit one with inklings of a functional bureaucracy. ENSO, for example, is the liaison between the sky god and the ocean god with a special focus on the Pacific. They sit on a number of important committees.

a Which reminds me of one of the best jokes ever told: how do you titillate an ocelot? You oscillate its tit a lot. Not only is it very funny, but it’s immensely satisfying to say. Once heard, you will sometimes find that, such is the joy in merely uttering it, that you have started to tell the joke without giving proper consideration to how appropriate the punchline is for the situation in which you find yourself. In delivering said punchline – there is no way, once started, one can stop – you will realise with forensic precision exactly how much is packed into each of those five words and how transgressive is the whole when given due consideration, which is what it will receive in the long horrified moments of silence after the telling. The silence will be broken – eventually, carefully – by someone not heretofore given to thinking about that part of an ocelot (at least not in conjunction with titillation) and they will say, in tones suggesting they have tasted but not yet wholly embraced the wild and possibly exhilarating freedoms of a person who would tell this joke to a bible study group, “Don’t they have more than one?”

b and shelving, I suppose.

c My coauthors had already prevailed upon me to remove the word “wobblyd” as a description of the property that makes greenhouse gases greenhouse gases.

d Earlier research preferred this term to “floppy”. In recollecting this event, I searched my twitter timeline. It turns out that I use the words “wiggle”, “wiggly”, “waggle” and “wobbly” with a higher-than-average frequency.