Wednesday, 12 December 2012

Zhou and Tung

In a recent posting I said I would be commenting on a paper by Zhou and Tung (Zhou, J., and K. Tung, 2012: Deducing Multi-decadal Anthropogenic Global Warming Trends Using Multiple Regression Analysis. J. Atmos. Sci.doi:10.1175/JAS-D-12-0208.1, in press.)

When I came across this paper I had mixed feelings. The paper says very similar things to those have I have been saying since January 2012: that the underlying rate of temperature increase is less than IPCC models assume, due to the influence of the Atlantic Multidecadal Oscillation (AMO). I was pleased to get further corroboration in a peer reviewed paper. On the other hand I was peeved as a paper I submitted earlier this year was not accepted.

Their approach is similar to that of Foster and Rahmstorf. See

Forster and Rahmstorf developed a multiple linear regression model using total solar radiation, aerosols, ENSO and a linear trend as independent variables and 5 alternate temperature records as the dependent variable. The period analysed was 1979 to 2010; the only period common to all 5 temperature series. They concluded that for that the period the underlying temperature trend was 0.014 to 0.18 °C per year. The paper was welcomed in many quarters as countering the claim that the rate of temperature increase had had been falling off or even stationary for the last decade or more of that period.

The Zhou and Tung paper adopts a similar approach but they have substituted the ENSO with the AMO. They conclude that the rate of temperature increase since the start of the 20th century, which they ascribe to anthropogenic effects, has been less that that estimated by Foster and Rahmstorf. They give 0.0068 °C for the 100 year trend, 0.0080 °C for the 75 year trend, 0.0083  °C for the 50 year trend and 0.0070  °C for the 25 year trend. These figures are about half of those of Foster and Rahmstorf.

They consider the suggestion of Booth et al that the AMO is anthropogenic and reject it.

My own equivalent figures are 0.0050 °C per year from 1856 to the present, 0.0067  °C for the 100 year rate and 0.011  for the 30 year rate. These values are similar to those of Zhou and Tung with one exception: I get an accelerating rate of increase which reflects the growing concentration of GHGs.

The conclusion of both their work and mine is the same: climate models, which simulate all the increase in temperature as anthropogenic and driven by GHGs, are overestimating the increase in temperature by a factor of two. A corollary to both sets of ideas is that if, as seems likely, the AMO is regular then it is likely to restrict temperature increase for the next few decades while the AMO is decreasing.

Thursday, 15 November 2012

AMO and anthropogenic aerosols

Anthropogenic Aerosols

It has been pointed out that the model I described in my earlier post (Climate and the Atlantic Multidecadal Oscillation) ignored anthropogenic aerosols. Here I look at the effect of adding these into the model.


The data used were downloaded from They were used in J. Hansen, et al. (2007) "Climate simulations for 1880-2003 with GISS model E", Clim Dyn, 29: 661-669 and J. Hansen, et al. (2011) "Earth's energy imbalance and implications, Atmos Chem Phys, 11, 13421-13449.

Figure 1 shows the individual components.

The individual components are:

WMGHGs – Well mixed greenhouse gases
O3 - Ozone
StrH2O – Stratospheric H­2O
ReflAer – Reflective Aerosols
AIE – Aerosol indirect effect
BC – Black carbon
SnowAlb – Snow albedo
StrAer – Stratospheric Aerosols (Volcanoes)
Solar – Solar irradiance
LandUse – Land Use.

To run a regression model with these 10 parameters plus the Atlantic Multidecadal Oscillation (AMO) would be nonsense. This would be particularly so since many of the components are highly correlated; the regression coefficient between WMGHGs and AIE is 0.98 for example. So I aggregated them into 4 groups. The first three (WMGHGs, O3 and StrH2O) I grouped as GHGs. Stratospheric aerosols and solar were treated separately. This gave 3 parameters which had exact equivalent in the original 4-parameter model. The fourth parameter was the sum of all the other components. The aggregated parameters are shown on Figure 2.

The fifth and final parameter was the AMO.

For temperature I used the HadCRUT3 global data set. I am aware that this has been superseded by the version 4 but for consistency with the earlier posting I am sticking to it.


The accuracy of the two models was almost identical. This can be seen on figure 3.

In terms of accuracy, the 4-parameter model (for the period 1880 to 2011) explained 89.3% of the variance and the 5-parameter model explained 89.5%, confirming the similar accuracy of the two models.


The comparison of observed and calculated temperatures does not describe how the values were actually calculated. Figure 4 shows the effect of each component on temperature.

In the above the use of ‘-5’ refers to 5 parameter model and ‘-4’ to the original 4 parameter model. The main differences between the models are:

  • The effect of GHGs is larger in the 5-parameter model, the difference being largely due to the effect of the anthropogenic factors.
  • Solar effects are slightly higher in the 5-parameter models.
  • The effect of volcanoes is minimal in both models.
  • The influence of the AMO is virtually identical in both models.
The coefficients for the 5 independent variables were:

Coefficient °C/W.m2
Standard error

Since the all parameters, except for AMO, are expressed as W/m2 and if the forcing sensitivity is close to the accepted value of 3.2 W/m2/°C then each coefficient should have the value 0.3125 °C/W/m2 (that is 1/3.2).  In this case the parameters for GHGs and solar irradiance are close to that value. That for volcanoes is much lower than expected. The parameter for combined anthropogenic effects is also lower than expected but has wide error bands so the ‘expected’ figure is within the 95% range.

Considering the critical period from 1976 to 2005, which had the largest increase, the observed temperature increases were as given in the table below.

5-parameter model
4-parameter model



Considering the period of rapid temperature rise, the original 4-parameter model suggested that 49% of the rise was due to GHGs, the equivalent figure for the 5-parameter model is 59%.

These findings are consistent with those reported in  Zhou, J., and K. Tung, 2012: Deducing Multi-decadal Anthropogenic Global Warming Trends Using Multiple Regression Analysis. J. Atmos. Sci. doi:10.1175/JAS-D-12-0208.1, in press. I will discuss this paper in another posting.


The conclusion remains as before. It is not clear whether the AMO is the ‘heart’ of the system and is driving global temperature or whether it is the ‘pulse’ and is an indicator another driver. What is clear that global temperatures reflect changes in the AMO but the AOGCMs used by the IPCC do not consider the AMO. In particular the AOGCMs simulated reasonably accurately the large temperature increase from 1976 to 2005 but attribute all the increase to GHGs. As a consequence, as pointed out in this and previous postings, and some recent peer-reviewed papers, temperature increases in the coming decades are likely to be lower than the IPCC projections.