## Marotzke & Forster Respond to Nic Lewis

#### Posted on 13 February 2015 by Guest Author

This is a re-post from Climate Lab Book

In a recent post on Climate Audit, Nic Lewis criticised Marotzke & Forster (2015, Nature) for applying circular logic to their arguments about forcing, feedbacks & global temperature trends. This is a guest post by Jochem Marotzke & Piers Forster replying to those criticisms.

### No circularity

It has been alleged that in Marotzke & Forster (2015) we applied circular logic. This allegation is incorrect. The important point is to recognise that, physically, radiative forcing is the root cause of changes in the climate system, and our approach takes that into account. Because radiative forcing over the historical period cannot be directly diagnosed from the model simulations, it had to be reconstructed from the available top-of-atmosphere radiative imbalance in Forster et al. (2013) by applying a correction term that involves the change in surface temperature. This correction removed, rather than introduced, from the top-of-atmosphere imbalance the very contribution that would cause circularity. We stand by the main conclusions of our paper: Differences between simulations and observations are dominated by internal variability for 15-year trends and by spread in radiative forcing for 62-year trends.

### Specifics

Our paper relies on one piece of explicit (deterministic) physics, namely energy balance (conservation). We maintain that the best way to represent this deterministic physics during a period of warming caused by radiative forcing F is through the model properties α and κ (see final paragraph below), in addition to F. This well-established tenet leads us to formulate the Earth’s energy balance in the form:

ΔT = ΔF / (α + κ) (1)

where ΔT and ΔF are (linear) trends over a specified period of global-mean surface temperature and radiative forcing, respectively. We reason in our paper why equation (1) motivates the linear regression that quantifies the contributions of *across-ensemble variations of* ΔF, α, κ, and furthermore of internal variability, to ΔT in the CMIP5 ensemble. Internal variability is represented as an additional error term in (1). Our linear regression motivated by (1) and applied to all possible trends during the historical period is a major methodological innovation of our paper, irrespective of how the numbers on the right-hand side are obtained.

The issue that was brought up relates to how we obtained the time series of simulated radiative forcing F from which to calculate the trends ΔF. Unfortunately, radiative forcing for the historical period is not straightforward to diagnose from a model. However, the top-of-atmosphere radiative imbalance N (downward minus upward radiation) is available for many models. This radiative imbalance arises originally from the radiative forcing from increasing greenhouse gas concentrations and other influences. But N and F are not equal, because the surface warms (say, by an amount T), and more radiation is emitted back to space. This amount of radiation is usually expressed as ΔT, such that we have:

N = F – αT (2)

Because N is readily available but F is not, Forster et al. (2013), from where the time series of F were taken, used the pre-determined model property α to obtain F by:

F = N + αT (3)

using the N and T that they diagnosed from simulations of the 20th century. This is a correction that needs to be applied to N so that one obtains the radiative forcing. On the right-hand side of (3), the two terms are of comparable magnitude over multi-decadal timescales, and the first term dominates over 15 years. *Not*correcting for the increased back radiation would, on physical grounds, imply using N, which contains the very contribution from the surface response T that we must eliminate in our estimate of F.

Of course one could legitimately ask how accurate this correction is, and we would hope that in future generations of coordinated model simulations a better direct diagnostic of F is possible. But for the CMIP5 models used in our study and in Forster et al. (2013), applying equation (3) has been the only approach possible. Forster et al. (2013) performed a number of tests of their procedure and found it to be adequate to produce time series of radiative forcing. However, it is possible that owing to an imperfect correction, our attribution of temperature trends to either forcing trend or feedback contains some ambiguity. This ambiguity is not new. In fact there is no unambiguous way of splitting forcing and feedback, and this remains a problem that the climate research community has grappled with for some time (e.g., Hansen et al. 2005, Myhre et al. 2013).

For understanding the results and limitations of our paper, it is crucial to appreciate that this ambiguity only refers to the contributions by the different elements of deterministic physics that we identify, and not to the total of deterministic (regression) contributions. In particular, our conclusion about the magnitude of internal variability in surface-temperature trends (dominant for 15-year trends, substantial for 62-year trends) is insensitive to the ambiguity.

As we have shown in our paper, our novel estimates of internal variability in the CMIP5 ensembles are consistent with completely different approaches, for both 15-year and 62-year trends.

We note that the order of magnitude of our diagnosed α contributions to spread in 62-year temperature trend are consistent with what is expected from equation (3) in Marotzke and Forster (2015). We notice further that from equation (1) here, it is obvious that ΔT varies proportionally with ΔF whereas ΔT varies less than proportionally with either α or κ (unless κ becomes very small, close to a new equilibrium, in which case ΔT varies inversely proportionally with α); this provides ready explanation for a lesser role of ensemble spread in α or κ over the historical period, compared to ensemble spread of radiative forcing. This counters the spurious argument outlined by Lewis for rejecting a small role for α on purely physical grounds.

Additionally, Lewis claims that the values for climate feedback parameter α and ocean heat uptake efficiency κ are so uncertain as to render them useless. But the α and κ values we use were diagnosed previously using established methods, relying on strongly forced, idealized model simulations (Andrews et al. 2012, Kuhlbrodt & Gregory 2012; Vial et al. 2013, Flato et al. 2013). These approaches and simulations are defined such that α and κ can be viewed as being model properties. By contrast, Lewis used historical simulations in trying to diagnose α and κ.

At the 2014 AGU Fall Meeting it was shown independently by Kyle Armour (MIT), Drew Shindell (Duke University), and Piers Forster that over the historical period these quantities change over time. Hence, their diagnosis from historical simulations is highly uncertain. This also supports the physical explanation as to why α and κ have a small role in determining model spread that Lewis did not understand. The small spread supports the reasoning that unique values of α and κ do not well characterise 20th century trends.

### Contact

Professor Jochem Marotzke

Max Planck Institute for Meteorology

Tel.: +49 40 41173 311 (Kornelia Müller)

E-Mail: jochem.marotzke@mpimet.mpg.de

Professor Piers Forster

School of Earth and Environment

University of Leeds

Tel.: +44(0) 113 34 36476

E-Mail: p.m.forster@leeds.ac.uk

### References

Andrews, T., J. M. Gregory, M. J. Webb, and K. E. Taylor, 2012: Forcing, feedbacks and climate sensitivity in CMIP5 coupled atmosphere-ocean climate models. Geophys. Res. Lett., 39, L09712, doi: 09710.01029/02012GL051607.

Flato, G., and Coauthors, 2013: Evaluation of Climate Models. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, T. F. Stocker, and Coauthors, Eds., Cambridge University Press, 741-866.

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, 1-12, doi: 10.1002/jgrd.50174.

Hansen, J., and Coauthors, 2005: Efficacy of climate forcings. Journal of Geophysical Research: Atmospheres, 110, D18104.

Kuhlbrodt, T., and J. M. Gregory, 2012: Ocean heat uptake and its consequences for the magnitude of sea level rise and climate change. Geophys. Res. Lett., 39.

Marotzke, J., and P. M. Forster, 2015: Forcing, feedback and internal variability in global temperature trends. Nature, 517, 565-570.

Myhre, G., and Coauthors, 2013: Anthropogenic and Natural Radiative Forcing. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, T. F. Stocker, and Coauthors, Eds., Cambridge University Press, , 659-740.

Vial, J., J.-L. Dufresne, and S. Bony, 2013: On the interpretation of inter-model spread in CMIP5 climate sensitivity estimates. Clim. Dyn., 41, 3339-3362.

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