In the last post I graphed the average temperature for 2015 *so far* with the annual averages prior to that. It’s certainly not the clearest way to show things, and someone who doesn’t read the text and pay close attention could get the wrong impression. It was also pointed out that there may be seasonal differences in the way temperature has changed; maybe January through April has behaved differently than other times of the year. Finally, the inherent scatter in a 4-month average is bound to be higher than that in an annual average.

In an attempt to present things more clearly, here are a few more views of where we are. We’ll begin with year-long averages for all the data points, but to include the most recent data let’s end each year with April. Here is the average temperature for each May-through-April period since 1880:

Another popular choice, and in my opinion a very good one, is to plot 12-month *moving averages*. In those terms here is where we are:

Let’s also take a look at the seasonality issue. I took the data since 1970 for each month separately, and fit a smooth (modified lowess) to get some clue about how different times of the year may have differed. Here are the smooths themselves, one for each month, and for one of the months I have highlighted the result, plotting it in red and with a thicker line:

The one in red, which looks distinctly different from the others, is the month of February.

As I have often emphasized, fitting a smooth isn’t the same as testing for a genuine change in the trend. But it is suggestive, so let’s isolate February data and try to fit an alternative model other than a straight line. I fit a piece-wise linear function to imitate the behavior of change-point analysis, and the best fit was for a change in 2000:

Considered as an isolated statistical test, this would pass statistical significance and demonstrate that the February trend has not been constant. But when one takes into account all the possible start years one can try, as well as the twelve different months that one could choose, it turns out that the result is not significant.

So, we can’t really claim to have demonstrated a trend change in February. That doesn’t mean there hasn’t been one, just that there’s not yet enough evidence to say so definitively.

What this means is that although it is certainly the case that February temperature has shown a different short-term pattern than the other months, the difference hasn’t yet been great enough or long-lasting enough to rise to the level of *trend*. While it certainly does *look like* its trend has changed, with so many places to look it was likely all along that we would find one which looked that much like a trend change.

I will also mention that this conclusion is based on studying *only* global temperature data in isolation.

Well Tamino, we went from a frigid Feb-April to a summer in May where I am. I’d say there’s an El Nino in progress.

Hi Tamino,

Interesting post. Do you know if the variation in response to El Nino affects some months more than others?

perhaps of interest (I’m assuming it’s published or will be; this is all ‘oogle found for me)

http://climdyn.usc.edu/Publications_files/skewness_rev_v2.pdf

PALEOCEANOGRAPHY, VOL. Z, XXXX, DOI:10.1029/THIS IS A DRAFT, JUNE 2014

Inferring climate variability from nonlinear proxies.

Application to paleo-ENSO studies.

Julien Emile-Geay

Department of Earth Sciences, University of Southern California, Los Angeles, CA

Martin Tingley

Departments of Statistics & Meteorology, Pennsylvania State University, State College, PA

Underlying most paleoclimate studies is the frequently violated assumption of a linear relationship between the proxy and the climate variable of interest. Inspired by tropical runoff proxies, we simulate an idealized proxy characterized by a nonlinear, thresholded relationship with surface temperature, and demonstrate the pitfalls of ignoring nonlinearities in the

proxy-climate relationship. We explore three approaches to using this idealized proxy to infer past climate: (i) methods commonly used in the paleoclimate literature, without consideration of nonlinearities; (ii) the same methods, after empirically transforming the data to normality to account for nonlinearities; (iii) using a Bayesian model to invert the mechanistic

relationship between the climate and the proxy. We find that neglecting nonlinearity often exaggerates changes in climate variability between different time intervals, and leads to reconstructions with poorly quantified uncertainties. In contrast, explicit recognition of the nonlinear relationship, using either a mechanistic model or an empirical transform, yields signif-

icantly better estimates of past climate variations, with more accurate uncertainty quantification. We apply these insights to two paleoclimate settings. Accounting for nonlinearities in the classical sedimentary record from Laguna Pallcacocha leads to quantitative departures from the results of the original study, and markedly affects the detection of variance changes over time. A comparison with the Lake Challa record, also a nonlinear proxy for El Ni ̃no-Southern Oscillation, illustrates how inter-proxy comparisons may be altered when accounting for nonlinearity. Our results hold implications for how nonlinear proxy records are interpreted, compared to other proxy records, and incorporated into multiproxy reconstructions.

I’ve looked at seasonal ENSO impact on temperatures in some detail for UAH (which has a stronger reaction to ENSO then surface temps) and the peak impact is roughly Dec to Apr, with a distinct peak in January. The February result is not so surprising considering that we’ve had stronger La Nina events since 1999 and particularly since 2008. Surprising that it shows up only in February though, and that the kind of warm ENSO years 2002 to 2007 don’t seem to push the Feb temps up as high in comparison to the 30 year straight line trend.

Given that any change in trend will almost certainly be gradual, are there other ways to test whether the trend (trajectory) for Feb (or any other single month) is different from the overall mean trend, without assuming that either is linear or piecewise linear? Something like a latent trajectory model?

It certainly does look different…is it a similar pattern in both hemispheres?

What I find interesting is that even though your previous post compares the first months of 2015 to yearly averages from the years before – those few months of 2015 actually include the february temp reading that has the reduction change you show above. Which then gives the “cooling” of february fewer months to average out on in your previous graph, but still reaches sky high, a clear warming signal in other words. To me it looks like 2015 El Nino will blow the 1998 temps completely out of the water even if its a moderate one.

Thanks. This is great, and very interesting. I still feel that there are indications that the seasonal cycle has changed detectably, and perhaps there are other ways of showing this … I’ll look into it.

One question: Your previous post was on May 14. On May 15, GISS issued an updated version of the land/ocean temperature data, due to some stations having been inadvertently omitted from the May 13 version. Are the figures in this new post based on the updated April value, or the original? Just curious.

Thanks for this update that compares like with like. Your previous report (comparing Jan-Apr with previous whole years) looked like something akin to cherry picking. I figured it was actually just a ‘quick first look’ that needed refining. Now with a ‘2nd look’, the same pattern emerges: the Earth’s surface is getting warmer, and recent months continue the trend. (No surprise here, of course.) For full disclosure, I wonder what the graph of only ‘Jan-Apr’ anomaly data from 1880 to 2015 looks like. (We know where the last point lies from the previous post.)

Also — the first two graphs in this post are an improvement over the original, because they are comparing 12-month averages to 12-month averages, i.e. apples to apples.

But … let’s say one is interested in the question of what the final, annual average will be for 2015. Will it set a new record? (No this isn’t very meaningful, but people seem to enjoy making a big deal about these records, so bear with me…)

One approach is to just assume the annual average will be similar to the four-month average, in which case 2015 would be 0.775, about four sigma above the previous record of 0.681.

Another approach is to figure out what the expected difference is between the four-month mean and the 12-month mean. Since 1975, those differences have averaged -0.02733, meaning that 2015 would probably end up around 0.748, slightly lower than its current mean of 0.775.

But that assumes that the difference is constant, and that there’s no regression to the mean over the course of the year. In general, years that start out “hot” or “cold” both tend to end up reverting a bit. Regressing the annual mean on the first four months’ mean suggests that 2015 would end up at 0.730, again a bit lower than its current 0.775.

That could be further improved by calculating the uncertainty around that predicted value and improved further by accounting for temporal autocorrelation (yes, we all learn stuff from reading this blog) in that estimate of uncertainty. If I did this rightly, the 95% confidence interval for the annual mean would include values that are lower than 2014 and several previous years, so it’s by no means certain than a new record will be set, but our expected value would be a new record.

But … this all neglects to consider all the “ancillary” information we have about what’s happening with the climate in 2015, specifically ENSO. This would seem to at least partially counter the normal expectation that the annual mean would end up cooler than the first four months. I guess one could build a model to predict the end-of-year average based on the end-of-April average plus some representation of ENSO … but maybe I’m getting carried away here.

Is there a local or regional pattern or fingerprint in the February temperatures that would give a clue to the physical basis for the apparent shift in trend in February ?

Perhaps the Feb shift is a N Atlantic influenced drop because of the N Atlantic cold-spot and jet-stream loops?!

I think Hansen said something like only the winter in NH shows a slowdown of the temperature increase.

As an experimentalist, what this screams is to go look at February data since about 2000. and look what changed there.

Tamino, you state that February isn’t statistically significant. Of course, by this you mean at the standard 95% level, or two standard deviations, ignoring the redness of the noise that is due to autocorrelation. Out of curiosity, though, what is the statistical significance?

I note Dr. Jeff Master’s WunderBlog includes “April 2015’s warmth makes the year-to-date period (January – April) the warmest such period on record.” Therefore, whatever the graph of Jan-Apr anomaly data from 1880 through 2015 looks like, the latest data point will be on top as well.

Does the noise — error band — uncertainty around any given data point grow and shrink along with changes in anything like, say, el nino/la nina? Just wondering if looking at the year-after-year zigzag needs an error range around the line, and what affects the size of that error range if anything.

I can see the WUWT headline now, “Tamino admits possible global cooling”

In line with past behavior patterns, February 2015 would have already taken the major negative hit expected this year. So it seems to me that the already towering gap between NASA GISS 2014 and 2015 will, more likely than not, get larger!

Would it be possible to make a credible estimate of where we’ll be by the end of the year by combining the already recorded first four+ months data with projections to 2015 for each of the remaining months (i.e. extend each of the black lines in the monthly graph by one year)?

BTW, The way you do your graphics with a red double-circle, it looks to me like Times Square will have company next New Year’s Eve in the rising ball department.