GFDL - Geophysical Fluid Dynamics Laboratory

46. How can outgoing longwave flux increase as CO2 increases?

Posted on May 31st, 2014 in Isaac Held's Blog



















8 thoughts on “46. How can outgoing longwave flux increase as CO2 increases?”

  1. Isaac – That’s quite interesting. What happens, with either the “intuitive” or “counterintuitive” models, if after CO2 quadruples at 140 years, it stops rising and the models are allowed to run to radiative equilibrium? What will the equilibrium OLR, albedo, and temperature change (climate sensitivity) look like compared with what happens if CO2 is instantaneously quadrupled, dropping OLR by about 7 W/m2? Do you have any thoughts about which simulations are more realistic in either the short or long term? Does the historical record offer any clues?

    1. Fred, those are all interesting questions. I expect a run with instantaneous 4X CO2 to take on the character of the corresponding 1% run but it will take a while to build up the temperature change needed to potentially reverse the sign of the infrared perturbation. It should end up in about the same place in year 140 as the 1% run. As the model equilibrates when holding the CO2 fixed beyond year 140, the heat uptake efficiency drops to zero (the concept is not that useful in this limit) so if the same shortwave feedbacks operate as in the transient run the increase in outgoing OLR should end up even larger than in the 1% runs (but these feedbacks would presumably change somewhat). Someone who has actually looked at these things may need to correct me. As far as comparing to observations, it’s hard because of the short TOA flux records and the associated importance of internal variability and minor forcings. But L+S is constrained by the dynamics in ways that L and S separately are not, so maybe looking in the orthogonal direction (ie at L-S) might suggest something.

  2. Dear Isaac,

    This is an interesting perspective on the evolution of radiative fluxes in a transient scenario. As an extension to the post, I thought it might be interesting to explore what might happen to OLR if we subsequently reversed the CO2 scenario, i.e. 1%CO2 ramp-up, followed by a 1%CO2 ramp-down. I suppose this could be considered a hypothetical mitigation scenario. Mark Ringer and I used HadGEM2-ES to partly look at this in a recent paper (Andrews and Ringer, 2014, or here for an open-access pre-print, apologies for the different notation). We too observed that the OLR increased during the CO2 ramp up, but we were then surprised to find that it remained largely unchanged during the ramp-down (i.e. it plateaued), see Figure 1d and Figure 4 (actually we have plotted LW clear-sky, positive downward, rather than OLR).

    Your post inspired us to go back and look at this with the simple model to better understand what is going on. On the ramp up, the parameters of the simple model applied to HadGEM2-ES are: gamma ~ 0.5 Wm-2 K-1, beta_sw ~ -0.9 Wm-2 K-1. So the SW feedbacks are larger in magnitude than the ocean heat uptake efficiency and hence the LW flux to space reduces, as you have nicely discussed. On the return ramp-down, a simple linear model is also a good approximation, but only after a decade or so of curvature that comes about due to heat uptake affecting the evolution of the SST patterns, particularly in the East tropical pacific and Southern Ocean (which continue to warm for a decade or so despite the reversal in radiative forcing and global dT). The feedback parameters on the ramp-down are unchanged, but the climate resistance (rho=gamma+beta=F/dT) is larger. In other words, the forcing is symmetric about year 140 but surface temperatures do not come down as fast as they go up (rho ~1.2 Wm-2 k-1 on the ramp up, compared to ~1.6 Wm-2 K-1 on the ramp-down). So one way of interpreting this is that the ocean heat uptake efficiency, gamma, has changed, presumably due to the response of the deep-ocean. Perhaps surprisingly, gamma just so happens to be ~0.9 Wm-2 K-1 on the ramp down in our model, exactly the same in magnitude as the SW feedback parameter. Hence, the LW fluxes do not change despite large changes in CO2 concentration and surface temperatures. Another counterintuitive result perhaps?

    Best wishes,

    1. Tim, thanks for the reference. I’ll have to think more about the asymmetry in the TOA fluxes between the increasing and decreasing CO2 legs in your run after reading your paper. This seems like a nice standard case to probe how the simple picture in which everything is proportional to forcing breaks down in different models.

    2. Dear Tim, likewise thanks for the reference to your very interesting paper. I’ve only had a quick read of it as yet, but I have emulated your results by fitting a simple global 2-box model to them. I can obtain a pretty accurate fit for the whole 280 year period: a diffusion-upwelling model might give an even better fit. This seems to indicate that everything is remarkably linear and symmetrical overall between the ramp-up and ramp-down, notwithstanding the asymmetrical behaviour of individual TOA fluxes in HadGEM2-ES. There doesn’t seem to be any evidence of time-varying global climate sensitivity. The same model parameters suit both ramp-up and ramp-down.

      The asymmetry in global dT behaviour matches what would be expected as a result of the ocean below the mixed layer (ML) having warmed. One way of looking at this in the 2-box context is that there is ‘warming-in-the-pipeline’ of ~3.6 K after 140 years, of which ~1.4 K becomes realized during the next 140 years, however forcing evolves over that period. Since the down-ramp induces an equal and opposite transient response to the up-ramp, the surface temperature at year 280 just equals that part of the ‘warming-in-the-pipeline’ at year 140 that is realized during the down-ramp.

      Whilst heat uptake ‘efficiency’ γ is a useful concept for periods of a few decades, IMO it is not well suited for multidecadal periods over which the non-conservation of energy implicit in the concept leads to increasingly material inaccuracies, particularly when the time-evolution of forcing changes.

      I was surprised how well a linear 2-box model emulated HadGEM2-ES’s 1% p.a. CO2 change behaviour, in view of that model’s non-linear early behaviour shown in Figure 1 of Andrews, Gregory, Webb and Taylor (2012) in an abrupt 4x CO2 experiment (the first point is well away from the regression line). May I ask what thoughts you have on this difference in early behaviour? I don’t see why the forcing-adjustment vs feedback issue would cause non-linearity.

      FYI, I obtained the best 2-box fit to your results using an ERF for doubled CO2 of 3.2 Wm-2, in between the fixed SST ERF of 3.5 Wm-2 and the regression-based ERF of 2.9 Wm-2, with time constants of 9.32 and 386.3 years and response coefficients of 0.8188 K and 0.6156 K for boxes 1 and 2 respectively. With non-ocean heat sinks ignored, the corresponding effective ML and thermocline/deep ocean depths are 120 m and 1170 m (over the ocean area only). With an ECS of 4.59 K (and thus a climate feedback parameter 0.70 Wm-2K-1) these parameters produce a TCR of ~2.46 K, and surface temperature and heat uptake values close to those in your paper.

  3. Dear Isaac,

    Thank you for this interesting post, and indeed for many other excellent posts that I have read before but not commented on.

    I knew ESM2M was an unusual model, but I had not appreciated how large the differences in LW and SW behaviour were between it and other models. Your analysis makes sense to me, notwithstanding that I have reservations about the degree of approximation involved in use of heat uptake ‘efficiency’ (Jonathan Gregory’s ‘kappa’ method) over multidecadal timescales.

    I will make a separate comment in response to what Tim Andrews has written about HadGEM2-ES.

    1. Nic, thanks,

      i probably do overemphasize the “intermediate” regime with well-defined heat uptake efficiency — it’s of limited utility as you say — but i think it is the right idealization for understanding the qualitative behavior of L and S in these 1% simulations.

  4. This helps me understand much better the counterintuitive, surprising first impression of
    “Global warming due to increasing absorbed solar radiation”
    Kevin E. Trenberth and John T. Fasullo, DOI: 10.1029/2009GL037527

    Their plots in YottaJoules (the integral of the radiative energy imbalance) are numbers so huge that I missed an overall point: The radiative imbalance is so small, so much smaller than the forcing, that the subtle term (beta_S + gamma) can govern the size and even the sign of L, without necessarily implying that beta_S itself is huge or surprisingly large.

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