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Why not use a clever mathematical trick?

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There is a clever mathematical trick for comparing different data sets, but it does not seem to be widely used. It is based on so-called empirical orthogonal functions (EOFs), which Edward Lorenz described in a Massachusetts Institute of Technology (MIT) scientific report from 1956. The EOFs are similar to principal component analysis (PCA). 

The EOFs and PCAs provide patterns of spatio-temporal covariance structure. Usually these techniques are applied to datasets with many parallel variables to show coherent patterns of variability. Myles Allen used to lecture on EOFs at Oxford University about twenty years ago and convinced me about their value. Many scientists do indeed use EOFs to analyse their data. 

It is not that there is little use of EOFs (they are widely used), but the question is how the EOFs are used and how the results are interpreted. I learned that EOFs can be used in many different ways from Doug Nychka, when I visited University Corporation for Atmospheric Research (UCAR) in 2011.

The clever trick is to apply these techniques to data compiled from more than one source of data. When used this way, the technique is labelled “common EOFs” or “common PCA”. There are some scientific studies that have made use of common EOFs or common PCA, such as Flurry (1988), Barnett (1999), Sengupta & Boyle (1993), Benestad (2001), and Gilett et al (2002). 

Nevertheless, a Scholar Google recent search with “common EOFs” only gave 101 hits (2020-03-05). I find this low interest for this technique a bit puzzling, since it in many ways has lots in common to machine learning and artificial intelligence (AI), both which are hot topics these days. 

Common EOFs are also particularly useful for quantifying local effects of global warming through a process known as empirical-statistical downscaling (ESD). It's pity that common EOFs aren't even mentioned in the recent textbook on ESD by Maraun and Widmann (2019)  (they are discussed in Benestad et al. (2008)).

Figure. Examples showing how common EOFs can be used to compare the annual cycle in T(2m) in the upper set of panels and precipitation (lower panels) simulated by global climate models from the CMIP5 experiment (red) and compared with the ERAINT reanalysis (black).

 

The take-home message from these common EOFs, eigenvalues and principal components, is that the models do reproduce the large-scale patterns in the mean annual cycle. For those interested, common EOFs can easily be calculated with the R-based tool: 

github.com/metno/esd.

References

  1. R.E. Benestad, "A comparison between two empirical downscaling strategies", International Journal of Climatology, vol. 21, pp. 1645-1668, 2001. http://dx.doi.org/10.1002/joc.703
  2. N.P. Gillett, F.W. Zwiers, A.J. Weaver, G.C. Hegerl, M.R. Allen, and P.A. Stott, "Detecting anthropogenic influence with a multi‐model ensemble", Geophysical Research Letters, vol. 29, 2002. http://dx.doi.org/10.1029/2002GL015836

Why are so many solar-climate papers flawed?

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The Zharkova et al paper that incorrectly purported to link solar-climate effects to movements of the Sun around the barycenter has been retracted.

This paper generated an enormous thread on @PubPeer where the authors continued to defend the indefensible and even added in new errors (such as a claim that the Earth’s seasonal cycles are due to variations in the Earth-Sun distance). Additionally, it seeded multiple nonsense newspaper articles in the UK and elsewhere (some of which were quietly deleted or corrected).

But the interesting thing is that this cycle of very public solar claim/counter-claim/claim/retraction was totally predictable.

[Read more…] about Why are so many solar-climate papers flawed?

References

  1. V.V. Zharkova, S.J. Shepherd, S.I. Zharkov, and E. Popova, "Retraction Note: Oscillations of the baseline of solar magnetic field and solar irradiance on a millennial timescale", Scientific Reports, vol. 10, 2020. http://dx.doi.org/10.1038/s41598-020-61020-3

Surprised by the shallows – again

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Guest commentary from Jim Acker (GSFC/Adnet)

Research on the ocean carbonate cycle published in 2019 supports results from the 1980s – in contrast to many papers published since then.

During my graduate school education and research program in the 1980s, conducted at the Department of Marine Science (now the College of Oceanography) of the University of South Florida in St. Petersburg, I participated in research on the production (biogenic calcification) and fate of calcium carbonate (CaCO3) in the open waters of the northern Pacific ocean. There were two primary aspects of this research: one, to measure the sinking flux of biogenic materials in the water column of the Pacific Ocean, and two, to measure the dissolution rates of aragonite, a CaCO3 crystal structure (polymorph) formed by pteropods, under in situ conditions of temperature, pressure, and seawater chemistry.

Figure 1. Drawings of pteropods from Cooke, A. H .; Shipley, A. E .; Reed, F. R. C. (1895) Molluscs, Cambridge Natural History, v.3, London: Macmillan and Co. A. Limacina retroversa australis syn. L. australis; B. Clio cuspidata syn. Cleodora cuspidata; C. Cuvierina columnella; D. “Crecia virgula“, E. Clio recurva syn. C. balantium. (Wikimedia Commons)
[Read more…] about Surprised by the shallows – again

BAU wow wow

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How should we discuss scenarios of future emissions? What is the range of scenarios we should explore? These are constant issues in climate modeling and policy discussions, and need to be reassessed every few years as knowledge improves.

I discussed some of this in a post on worst case scenarios a few months ago, but the issue has gained more prominence with a commentary by Zeke Hausfather and Glen Peters in Nature this week (which itself partially derives from ongoing twitter arguments which I won’t link to because there are only so many rabbit holes that you want to fall into).

My brief response to this is here though:

Mike Mann has a short discussion on this as well. But there are many different perspectives around – ranging from the merely posturing to the credible and constructive. The bigger questions are certainly worth discussing, but if the upshot of the current focus is that we just stop using the term ‘business-as-usual’ (as was suggested in the last IPCC report), then that is fine with me, but just not very substantive.

References

  1. Z. Hausfather, and G.P. Peters, "Emissions – the ‘business as usual’ story is misleading", Nature, vol. 577, pp. 618-620, 2020. http://dx.doi.org/10.1038/d41586-020-00177-3

Update day 2020!

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Following more than a decade of tradition (at least), I’ve now updated the model-observation comparison page to include observed data through to the end of 2019.

As we discussed a couple of weeks ago, 2019 was the second warmest year in the surface datasets (with the exception of HadCRUT4), and 1st, 2nd or 3rd in satellite datasets (depending on which one). Since this year was slightly above the linear trends up to 2018, it slightly increases the trends up to 2019. There is an increasing difference in trend among the surface datasets because of the polar region treatment. A slightly longer trend period additionally reduces the uncertainty in the linear trend in the climate models.

To summarize, the 1981 prediction from Hansen et al (1981) continues to underpredict the temperature trends due to an underestimate of the transient climate response. The projections in Hansen et al. (1988) bracket the actual changes, with the slight overestimate in scenario B due to the excessive anticipated growth rate of CFCs and CH4 which did not materialize. The CMIP3 simulations continue to be spot on (remarkably), with the trend in the multi-model ensemble mean effectively indistinguishable from the trends in the observations. Note that this doesn’t mean that CMIP3 ensemble means are perfect – far from it. For Arctic trends (incl. sea ice) they grossly underestimated the changes, and overestimated them in the tropics.

CMIP3 for the win!

The CMIP5 ensemble mean global surface temperature trends slightly overestimate the observed trend, mainly because of a short-term overestimate of solar and volcanic forcings that was built into the design of the simulations around 2009/2010 (see Schmidt et al (2014). This is also apparent in the MSU TMT trends, where the observed trends (which themselves have a large spread) are at the edge of the modeled histogram.

A number of people have remarked over time on the reduction of the spread in the model projections in CMIP5 compared to CMIP3 (by about 20%). This is due to a wider spread in forcings used in CMIP3 – models varied enormously on whether they included aerosol indirect effects, ozone depletion and what kind of land surface forcing they had. In CMIP5, most of these elements had been standardized. This reduced the spread, but at the cost of underestimating the uncertainty in the forcings. In CMIP6, there will be a more controlled exploration of the forcing uncertainty (but given the greater spread of the climate sensitivities, it might be a minor issue).

Over the years, the model-observations comparison page is regularly in the top ten of viewed pages on RealClimate, and so obviously fills a need. And so we’ll continue to keep it updated, and perhaps expand it over time. Please leave suggestions for changes in the comments below.

References

  1. J. Hansen, D. Johnson, A. Lacis, S. Lebedeff, P. Lee, D. Rind, and G. Russell, "Climate Impact of Increasing Atmospheric Carbon Dioxide", Science, vol. 213, pp. 957-966, 1981. http://dx.doi.org/10.1126/science.213.4511.957
  2. J. Hansen, I. Fung, A. Lacis, D. Rind, S. Lebedeff, R. Ruedy, G. Russell, and P. Stone, "Global climate changes as forecast by Goddard Institute for Space Studies three‐dimensional model", Journal of Geophysical Research: Atmospheres, vol. 93, pp. 9341-9364, 1988. http://dx.doi.org/10.1029/JD093iD08p09341
  3. G.A. Schmidt, D.T. Shindell, and K. Tsigaridis, "Reconciling warming trends", Nature Geoscience, vol. 7, pp. 158-160, 2014. http://dx.doi.org/10.1038/ngeo2105

One more data point

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The climate summaries for 2019 are all now out. None of this will be a surprise to anyone who’s been paying attention, but the results are stark.

  • 2019 was the second warmest year (in analyses from GISTEMP, NOAA NCEI, ERA5, JRA55, Berkeley Earth and Cowtan & Way, RSS TLT), it was third warmest in the standard HadCRUT4 product and in the UAH TLT. It was the warmest year in the AIRS Ts product.
  • For ocean heat content, it was the warmest year, though in terms of just the sea surface temperature (HadSST3), it was the third warmest.
  • The top 5 years in all surface temperature series, are the last five years. [Update: this isn’t true for the MSU TLT data which have 2010 (RSS) and 1998 (UAH) still in the mix].
  • The decade was the first with temperatures more than 1ºC above the late 19th C in almost all products.

This year there are two new additions to the discussion, notably the ERA5 Reanalyses product (1979-2019) which is independent of the surface weather stations, and the AIRS Ts product (2003-2019) which again, is totally independent of the surface data. Remarkably, they line up almost exactly. [Update: the ERA5 system assimilates the SYNOP reports from weather stations, which is not independent of the source data for the surface temperature products. However, the interpolation is based on the model physics and many other sources of observed data.]

The two MSU lowermost troposphere products are distinct from the surface record (showing notably more warming in the 1998, 2010 El Niño years – though it wasn’t as clear in 2016), but with similar trends. The biggest outlier is (as usual) the UAH record, indicating that the structural uncertainty in the MSU TLT trends remains significant.

One of the most interesting comparisons this year has been the coherence of the AIRS results which come from an IR sensor on board EOS Aqua and which has been producing surface temperature estimates from 2003 onwards. The rate and patterns of warming of this and GISTEMP for the overlap period are remarkably close, and where they differ, suggest potential issues in the weather station network.

The trends over that period in the global mean are very close (0.24ºC/dec vs. 0.25ºC/dec), with AIRS showing slightly more warming in the Arctic. Interestingly, AIRS 2019 slightly beats 2016 in their ranking.

I will be updating the model/observation comparisons over the next few days.

Unforced variations: Jan 2020

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The new open thread on climate science for a new year, and a new decade – perhaps the Soaring Twenties? What precisely will be soaring is yet to be decided though.

Two things will almost certainly go up – CO2 emissions and temperatures:

But maybe also ambition, determination, and changes that will lead to reduced emissions in future? Fingers crossed.