1. Quantifying rapid adjustments using radiative kernels
Chris Smith, Gunnar Myhre, Ryan Kramer, Piers Forster, Bjørn Samset, Toshi Takemura + PDRMIP authors

2. Effective radiative forcing
We define IRF at the top of the atmosphere even for GHGs, for consistency with ERF definition
Adapted from IPCC AR5 WG1, Ch. 8, p. 669

3. Then, ERF = IRF + adjustments Formally: 𝐸=𝐼+ 𝐴 𝑇 + 𝐴 𝑞 + 𝐴 𝛼 + 𝐴 𝑐 +𝑟
Rapid adjustments
Aim for a clean separation of GMST-driven feedbacks from forcing-driven rapid adjustments
Then, ERF = IRF + adjustments
Formally:
𝐸=𝐼+ 𝐴 𝑇 + 𝐴 𝑞 + 𝐴 𝛼 + 𝐴 𝑐 +𝑟
temperature
albedo
residual
humidity
clouds

4. Non-cloud adjustments
Assume TOA radiative fluxes R change linearly w.r.t. small perturbations in T, q and α
Then 𝐴 𝑥 = 𝜕𝑅 𝜕𝑥 ∆𝑥 for x in {T, q, α}
Δx represents change in state between perturbed and base climate. Separate T into stratosphere, troposphere and surface
𝜕𝑅 𝜕𝑥 is the radiative kernel (month[, height], lat, lon). Make clear sky and all sky kernels using the SOCRATES (HadGEM) radiation code from one year of piControl run.

5. Change in vertical profiles
Fixed SST experiment atmospheric temperature change in HadGEM2

6. HadGEM2 non-cloud kernels

7. Non-cloud adjustments

8. Estimated as a residual; assumes either
Clouds (one method)
Estimated as a residual; assumes either
IRF all-sky and IRF clear-sky are known, and r is calculated from IRF clear-sky; or
IRF all-sky is known and r is assumed to be zero
Previous work used IRF from double-call 4×CO2 or assumed it from SRES A1B
Need more direct approach for PDRMIP
𝐸=𝐼+ 𝐴 𝑇 + 𝐴 𝑞 + 𝐴 𝛼 + 𝐴 𝑐 +𝑟
𝐸 0 = 𝐼 0 + 𝐴 𝑇,0 + 𝐴 𝑞,0 + 𝐴 𝛼,0 +𝑟

9. Full analysis limited to models where double-call IRFs exist
Clouds and IRF
Therefore we need estimates of IRF from double-call simulations from PDRMIP models
2% solar is easy
CO2 and CH4 experiments could substitute global values into SOCRATES radiation code
Aerosols are too spatially variable to do this
Full analysis limited to models where double-call IRFs exist
HadGEM2, CAM4 and MIROC-SPRINTARS

10. ERF and adjustments Large residual for 2×CO2
2×CO2 TOA IRF is too low in SOCRATES Hansen et al. (1997) says 2.62 W m-2

11. Comparison of kernels
Both the differences in kernel climatology and the kernel truncation height can affect the results.
Note different scale

12. Comparison of kernels
The upper truncation level of the kernel has a significant effect on the stratospheric adjustment to CO2.
This is the other cause, other than low IRF, of the large residual for CO2 forcing.

13. Another method for cloud adjustments
ISCCP simulator kernel can be used if model has ISCCP diagnostics
Based on what satellites see from TOA
I ran in HadGEM2
Zelinka et al., 2012, J. Clim., /JCLI-D

14. ISCCP simulator cloud adjustments
Net TOA cloud adjustments show reasonable agreement between residual and ISCCP simulator
LW and SW individual values can disagree substantially

16. Estimates of clear-sky IRF, assuming r=0
Good agreement between residual and double-call IRF for all experiments except 2×CO2
Evidence of why IRF cannot be assumed except for solar
Concentration based: dark shading
Emissions-based: light shading
GISS is an outlier for 5×SO4

17. Add in more kernels into the kernel intercomparison
Things to do
Add in more kernels into the kernel intercomparison
Determine a better value of TOA IRF for 2×CO2
Use partial radiative perturbation in each model in a different radiative transfer code?

18. A request to modelling groups
IRFs from fixed-SST experiments would be really useful
both all-sky and clear-sky for all fixed-SST forcing experiments + base run
Cloud diagnostics calculated from the ISCCP simulator would be desirable too

19. Conclusions
Rapid adjustments are model-specific especially due to cloud adjustments
Tropospheric adjustments are significant even for GHGs
Knowing IRF is critical to assessing model responses
Kernels lead to small residuals except for CO2 but reasons for deficiencies are known
Clouds dominate the uncertainty