During the past week we have had interesting discussions on this blog about a new paper that tries to filter the AMO signal out of the global temperature series. Several commenters thought that the paper contained serious flaws. Among them was Guido van der Werf, who is a scientist working at the Free University in Amsterdam. His research mainly focuses on forest fires and the effects they have on the carbon cycle. Guido is a friend and I greatly appreciate his efforts to replicate the results of the Zhou/Tung paper. He presents his finding in this guest post.

Guest post by Guido van der Werf

In a recent post Marcel Crok highlighted a new paper by Jiansong Zhou and Ka-Kit Tung in the Journal of the Atmospheric Sciences which halved recent anthropogenic warming and indicated no acceleration of anthropogenic warming over the past 100 years. If true, this is obviously a very important finding. The paper followed on two other papers by Lean and Rind (2008) and Foster and Rahmstorf (2011) aiming to disentangle anthropogenic and natural influences seen in the instrumental temperature record. Three different datasets of temperature are shown below.

To me, studies using the temperature record to study the relative importance of natural and anthropogenic factors are very interesting, for a part because they can be easily repeated and are based on the best data we have. The disadvantage is that they describe what happened in the past, and although this yields information to what may happen in the future it is not a substitute for climate models.

Just a little bit of background information: climate is obviously impacted by a large number of forcings occurring on different time scales. These are both anthropogenic and natural. For example, after the eruption of Mt.Pinatubo in the Philippines in 1991 the global temperature dropped for 2-3 years. And the year 1998 was much warmer than previous and following years because of a strong El Niño episode in 1997-1998. These two events are pointed out in the temperature graph above.

Over decadal time scales things become more complicated. There are at least two ocean oscillations that may impact climate on these time scales: the Pacific Decacal Oscillation (PDO) and the Atlantic Multidecadal Oscillation (AMO), plotted below with positive phases leading to warming and shown in red.

Now, what Zhou and Tung tried to do is subtract the influence of natural variations (AMO, sun, volcanoes, and the El Niño – southern oscillation or ENSO). In theory, what is left behind is the anthropogenic signal. The tool to do this is multiple linear regression (MLR), which basically gives a certain weight to each variable to best match the temperature record. Thanks to the well written paper I was able to reconstruct their results shown in their Figure 1a:

Original and replicated Figure 1a of Zhou and Tong showing the temperature record after the effect of the sun, volcanoes, and ENSO have been subtracted which yields a smoother curve than the “raw” temperature. It shows that there is still a cycle present which looks very similar to AMO. The novelty of the Zhou and Tung study over earlier studies is in that they tried to compensate for this. Basically you add AMO to the statistical method to filter out the natural signals. I was not able to fully replicate their data but came close:

Original and replicated Figure 1b of Zhou and Tong. The temperature record after the effect of the sun, volcanoes, ENSO, and AMO have been taken out. Suddenly the oscillation seen in Figure 1a is gone, and the trend is smaller. In my data I do find a small acceleration which was not seen in Zhou and Tung but the differences are small and may be due to their smoothing of the AMO data, but I am not sure.

To make these graphs they made one crucial assumption. Since none of the natural forcings or oscillation has a trend that can explain the temperature record one has to predefine the shape of the anthropogenic influence over time to be included in the MLR. Lean and Rind (2008) used the net effect of greenhouse gases (warming), changes in albedo (cooling), and aerosols (cooling) for this. Forster and Rahmstorf (2011) used a linear trend, but their study covered only the 1979 onwards period because they included the satellite temperature records which are only available since 1979. For that period the net effect may be rather linear, at least according to the data used by Lean and Rind (2008).

Zhou and Tong used a linear trend as well, but over the much longer time period. So basically they assumed that anthropogenic climate change in 1856 was of the same order of magnitude as in 2011. Below I will repeat their analysis but instead of a linear trend I use the time-evolution of the CO2 concentration, neglecting other greenhouse gases and aerosols which to some degree level out.

Original and replicated Figure 1b of Zhou and Tong with a pre-defined shape of CO2 concentration for the anthropogenic influence in the replicated data instead of a linear trend. The correlation coefficient between modeled and measured temperature is 0.95.

The difference with Zhou and Tong is clear: the acceleration of anthropogenic warming is stronger. Interesting is that in both approaches indicate no halting of anthropogenic warming after 2000; the prevalence of La Nina’s cancel out the anthropogenic forcing.

1940-1970 standstill
What is even more interesting is that the 32 and 50 year trend is still substantially lower than reported earlier. In other words, according to this simple analysis part of the 1970-2000 warming was due to the upswing of AMO. Similarly, the 1940-1970 flat temperature may have been the result of the downswing of AMO canceling the greenhouse gas warming. This provides in my opinion a more elegant explanation than the aerosol explanation most commonly used, but more research is needed to better pinpoint whether this is true.

If we were to convert the CO2 concentration to radiative forcing (RF) using the well established formula RF = 5.35 * ln(CO2 / CO2pre-industrial) and put this in the MLR, the slope for RF is 0.42 degree C warming per unit W/m2. A doubling of CO2 is 3.7 W / m2 so combining these numbers yields a transient climate sensitivity of 0.42 * 3.7 = ±1.5 degrees C. Clearly, these are not much more than back of the envelope calculations but still valuable.



  • It is important to include AMO in any regression analysis to deduce the warming trend as shown by Zhou and Tung
  • The outcome of this exercise is highly dependent on the assumed shape of the anthropogenic signal. If we assume that the anthropogenic influence is not linear then anthropogenic warming is accelerating
  • The climate sensitivity of the system seems lower than the usually assumed values, although this also depends on the time period covered in the MLR
  • Anthropogenic warming has not stopped in 2000 or so, this result is independent of the assumption on the shape of the anthropogenic influence in the MLR


Major uncertainties in this approach are related to:

  • The temperature record, which is in the 19th and first part of the 20th century based on a limited number of stations
  • The anthropogenic influence on AMO; we simply used the detrended values but accounting more precisely for the anthropogenic impact may give different results
  • And of course the shape of the anthropogenic influence. A linear influence seems unjustified, but the CO2 concentration as a proxy as I did is not perfect either
  • For the calculation of the transient climate sensitivity the relative role and time evolution of other greenhouse gases than CO2 and aerosols is crucial.
  • And anything else I overlooked, please respond!
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