1. Climatic impacts of stochastic fluctuations in air–sea fluxes Paul Williams Department of Meteorology, University of Reading, UK

2. Outline Motivation Air–sea fluxes vary partly on scales that are too small or fast to be resolved explicitly by global climate models Conjectured mechanism Rapid fluxes will systematically deepen the ocean mixed layer, even though the mean fluctuation is zero, because of an asymmetry in mixed-layer physics Demonstration in a coupled GCM The mixed layer deepens, and the mean climate and the ENSO variability are significantly changed

3. Motivation (1) The atmosphere and ocean are coupled by fluxes of energy, momentum, and matter across the air–sea interface (Peixóto and Oort, 1984) The fluxes vary partly on scales that are too small or fast to be resolved explicitly by global climate models (Sun et al., 1996). For example: sub-grid fluctuations in precipitation and short-wave solar radiation may occur because of convective clouds sub-grid fluctuations in evaporation, latent heat, and momentum may occur because of turbulence in the surface wind stress These fluctuations may play an important role in climate, despite their high frequencies and short spatial scales (Bernie et al., 2005)

4. Sub-grid air–sea flux variability appears to be a good candidate for stochastic modelling, which is increasingly used in climate science (e.g. Kuhlbrodt and Monahan, 2003; Palmer and Williams, 2008; Penland 2011) The effects of stochasticity have so far been studied mainly in conceptual (“toy”) models with only a few degrees of freedom, because analytic progress is possible Various effects are seen, including changes to the time- mean state (via noise-induced rectification) and changes to the variability But to what extent are these simple noise-induced phenomena relevant in comprehensive general circulation models with O(10 7 ) degrees of freedom? Motivation (2)

5. ● = fast molecule ● = slow molecule Maxwell’s demon Conjectured mechanism

6. ● = dense perturbation ● = buoyant perturbation atmosphere ocean Stommel’s demon Conjectured mechanism

7. In a statically stable water column in the ocean mixed layer, dense anomalies at the surface (created by evaporation or cooling) can destabilize the water column, initiate convection and vertical mixing, and deepen the mixed layer. In contrast, buoyant anomalies at the surface (created by precipitation or heating) simply further stabilize the water column and cannot shoal the mixed layer. In short, positive buoyancy fluctuations cannot undo the vertical mixing caused by negative buoyancy fluctuations of equal magnitude. Therefore, rapid fluctuations to the air–sea fluxes will systematically deepen the mixed layer, even though the mean fluctuation is zero.

8. mean state without noise mean state with noise “noise-induced rectification” Conjectured mechanism

9. Run three integrations: –CTL: control experiment –WAT: stochastically perturb the air–sea water flux –HEA: stochastically perturb the air–sea heat flux –use uncorrelated multiplicative noise drawn from ~U(0.5,1.5) SINTEX-G coupled GCM: –atmosphere is ECHAM4.6 @ T30L19 –ocean is ORCA2 (OPA8.2) @ 2° x 0.5-2° x 31 levels –sea-ice is LIM –coupler is OASIS2.4 with flux exchange every 3 hours 100-year integrations initiated from the Levitus (1982) ocean observations Demonstration in a coupled GCM

10. Effects on the time-mean climate equator~30°N 3) Hadley cell weakens (e.g. Bjerkness 1966) tropo- sphere mixed layer ocean interior 1) mixed layer deepens 2) surface ocean cools 4) reduced precipitation in the ITCZ 5) increased precipitation in the subtropics i.e. the net upward water flux is rectified

11. Net upward water flux (mm/day)

12. Strength of ENSO variability (  C)

13. Air-sea buoyancy fluxes contain rapid fluctuations that are too fast or small to be explicitly resolved by global climate models There is a physical mechanism by which these fluctuations may affect the time-mean mixed-layer depth The mechanism has been demonstrated in a coupled general circulation model. It modifies the sea-surface temperature, the atmospheric Hadley circulation, and the net upward water flux ENSO variability is enhanced by the noise Therefore, we conclude that missing sub-grid variability in the air–sea fluxes may contribute to some of the biases exhibited by contemporary climate models Summary

14. PD Williams (2012) Climatic impacts of stochastic fluctuations in air–sea fluxes Geophysical Research Letters, 39, L10705 www.met.reading.ac.uk/~williams p.d.williams@reading.ac.uk Reference

15. www.met.reading.ac.uk/~williams