Equilibrium Climate Sensitivity

There has been much media interest  about “climate sensitivity”, following a recent paper (Otto et al.) which showed lower values than previous IPCC estimates. Climate sensitivity essentially measures  how earth’s  climate reacts to a sudden kick (volcano, meteor, CO2). The new lower result is mainly  due to the stalling in observed global temperatures since 1998 despite rising CO2 levels. One measure of climate sensitivity is called Transient Climate Response (TCR) which is the instantaneous  temperature rise once CO2 levels reach twice  pre-industrial levels (560 ppm). The eventual rise in temperature with full energy balance (perhaps decades later)  is the second measure –  Equilibrium Climate Sensitivity (ECS).  The difference between them is  due to the time lag heat inertia within oceans.  In this post I focus on ECS and simply assume that GCM models are a correct description of climate. I  then use HADCRUT4 temperature data to try to pin down ECS.  Unlike the Otto et al. paper I will avoid using OHC data and simply assume an e-folding ocean heat capacity  delay of 15 years (also based on models) to reach equilibrium.  The result shows  that ECS due to the CO2 GHG effect is unlikely to be more than  3 deg.C. Recent temperatures instead imply a lower  estimate of ECS ~  2C.

The dashed curve is the transient CO2 temperature dependence assuming a feedback factor equivalent to an ECS = 2.0. The red and blue curves are predictions for different ECS values  using CMIP5 model forcings up to 2005. Calculated model temperatures assume an ocean relaxation time of 15 years (see text). The data points are the latest HADCRUT4 values

Background

In the end the whole climate debate boils down to just one thing – climate sensitivity. So what is it and how can we measure it ? Climate sensitivity is the temperature response to an increment in forcing.

In the  case of no “feedbacks”    due to the Stefan Boltzman stabilization term   with  T=288K. The climate reacts to any increase or decrease in “forcing” by radiating a little more or a little less energy from the surface. Temperature changes are slight because radiation varies a the 4th power of T.

Confusingly however the term “Climate Sensitivity” is usually defined as the change in temperature after a doubling of CO2. So for the no feedback case this results in a “climate sensitivity” ~ 1.1C.  This is no big deal because even if mankind continued to burn all available fossil fuels so that CO2 levels reached up to 1000ppm  global temperatures would only increase by at most  2C, which some argue might actually be beneficial to life on Earth.

The global warming scare then is all about “positive feedbacks” to CO2 forcing. However these positive feedbacks must not be too large, because otherwise temperatures would explode – just like the feedback you get when  a microphone gets too close to its speakers.  Suppose then the net feedback gain is f so that a temperature rise DT gets enhanced by  (1+f)DT, but now we have a second amplification f(fDT) or f^2DT to add on and so on. The climate system would soon  run out of control if the feedback gain approaches 1 as follows.

Figure 1 shows the temperature response to a doubling of CO2 for different feedback factors f.

Fig 1: Positive feedbacks can soon blow up “climate sensitivity”. Negative feedbacks are stable always stable.

So if the feedback gain approaches 1 the climate simply runs away with itself. So this is the problem that global warming alarmists face. They need to demonstrate that “run away” warming  might occur unless civilization “de-carbonizes” and/or abandons growth. This means that feedbacks must be positive so that warming becomes scary but  can’t be too strongly positive because otherwise the climate would have run away eons ago, and we wouldn’t be here. The earth’s climate has seen huge swings in CO2 levels in the past, survived meteor impacts, supernovae and a 30% increase in solar output. During all this time (4 billion years) liquid oceans have existed on Earth and life has prospered, which implies that feedbacks must be small or even negative. Figure 1 shows the range of estimates for climate sensitivity from the IPCC 2007 AR4 report ranging from 2C- 5C.

A  recent paper (Otto et al.) has measured climate sensitivity based on Hadcrut4 temperature data, OHC (Levitus et al.) and model forcing data. They used the relationships for “equilibrium climate sensitivity (ECS)” and ” transient climate response (TCR)” as follows.

TCR is the based on the immediate temperature response to a change in forcing DF, ignoring any temperature inertia of the oceans, where as ECS is the final temperature response once the oceans have stabilized. This equilibrium value is calculated by including the transient heat uptake by the oceans with the surface temperature value. is the forcing due to a doubling of CO2 (~ 3.7 W/m2).  When they include the flat period 2000-2012 they  find the most likely value of ECS to be now 2C – which is significantly lower than 2007 IPCC estimates. The main reason for the updated estimates is the inclusion of temperature data up to 2009(12).

We can do the same analysis without OHC data if we assume  a climate inertia time delay as described here. For this work I use the average forcings derived  from CMIP5 generation climate models (Forster et al.) which have been digitized by Willis Eschenbach  – see his post here. Note here that these model forcings have been tuned to fit the hindcast of temperature data since 1850. I find this backward retrofitting to be fairly suspect because they assume the models describe nature. The variable forcings  include  known volcanic eruptions,  man made aerosols and “natural variability”. We can see just how quickly these  forcings change  in Figure 2 where the CMIP5 spectrum is compared to an absolute CO2 forcing calculated   . The CO2 values are taken from seasonally averaged Mauna Loa data extrapolated back to 1750.

Fig2: Comparison of a pure CO2 GHG forcing and the CMIP5 avergaed forcings used to hindcast past temperature dependency since 1850.

It is clear that the model forcings are moving up and down rapidly in order to match the measured temperature anomalies from Hadcrut4. It is not just simple man-made or natural aerosols, but also to follow “natural variations”. Despite this let’s now use these CMIP5 forcings together with the Hadcrut4 data to measure the resultant climate sensitivity.

        where  is the transient temperature response and is the equilibrium temperature response.

and then taking Stefan Boltzman to derive the IR energy balance

or in terms of feedbacks

and for equilibrium climate sensitivity for a doubling of CO2

Figure 3 shows the temperature response calculated from the model forcings for given values of ECS.

Figure 3: Comparison of CMIP5 models with Hadcrut4 data for different ECS.

Until 2005 the CMIP5 models give ECS = 3 deg.C. Extending the data till 2012 reduces the apparent value to 2.5C. However, the model forcing data are not available post 2005. Although the models are driven by CO2 forcing, and climate feedbacks, it is clear that they have a natural forcing component that is adjusted so as to agree with the temperature data. How well does the CO2 forcing alone do in matching the Hadcrut4 data?

To calculate the CO2 forcing  I take a yearly increment of

 ,     where  C and C₀ are the values before and after the yearly pulse. All values are calculated from seasonally averaged Mauna Loa data smoothed back to an initial concentration of 280ppm in 1750.

Each pulse is tracked through time and integrated into the overall transient temperature change using:

was calculated based on an assumed ECS of 2.0C.  The results are compared to the observed HADCRUT4 anomaly measurements in Figure 4.

Fig 4: The dashed curve is the transient CO2 temperature dependence assuming a feedback factor equivalent to an ECS = 2.0

Willis Eschenbach fitted the model forcing/temperature response of CMIP5  model data to an e-folding factor of just  2.9y, and then showed that the measured data fails to reproduce volcanic cooling. He then makes a compelling argument that the models fail to match such volcanic forcing in the measured data.  This argument is less strong however if the ocean heat capacity  results in an e-folding time of ~ 15 years as shown in figure 4. This washes out the volcanic signals.

A  CO2 signal for ECS gives a value ~ 2.0 deg.C agrees to match the overall trend of recent temperature data.  Superimposed on this trend is an apparent regular 60y  oscillation. This has been noted by many others and been  identified  and fitted previously.   These results for a lower ECS than reported in AR4 are in line with those of Otto et al. This analysis assumes a slow climate inertia time e-folding scale of 15 years. If In suspect temperatures remain flat for another 5-10 years then ECS will reduce further and we can then worry about something else.

References

Otto, A. et al. (2013): Energy budget constraints on climate response. Nature Geoscience,doi:10.1038/ngeo1836

Forster, P. M., T. Andrews, P. Good, J. M. Gregory, L. S. Jackson, and M. Zelinka (2013): Evaluating adjusted forcing and model spread for historical and future scenarios in the CMIP5 generation of climate models, J. Geophys. Res. Atmos., 118, doi:10.1002/jgrd.50174

Christopher Colose, An analysis of Radiative Equilibrium, Forcings and Feedbacks