1. On the Mechanisms of the Late 20 th century sea-surface temperature trends in the Southern Ocean Sergey Kravtsov University of Wisconsin-Milwaukee Department of Mathematical Sciences Atmospheric Science Group Collaborators: I. Kamenkovich, University of Miami, USA; A. Hogg, Australian National University, Australia; and J. M. Peters, University of Wisconsin-Milwaukee, USA 6 th International Conference on Mathematical Modeling, Yakutsk, Russia July 3–8, 2011 http://www.uwm.edu/kravtsov/

2. Geophysical Fluid Dynamics Considers the motion of thin layers of fluid— the atmosphere and the ocean — on a rotating spherical Earth. Dominant motion — solid-body rotation; winds and currents we observe are, in general, small deviations from this motion; this smallness is measured by a dimensionless Rossby number Ro. These layers are stratified (light fluid is above the heavy fluid) and the local motion is quasi two-dimensional (vertical velocities are small).

3. The primary cause of the general circulation Unequal heating of the earth’s surface Temperature gradients — pressure gradients — winds

4. Coriolis Force

5. Dominant balances: Hydrostatic and geostrophic approximations The scale at which rotational effects become as important as buoyancy effects is called the Rossby radius Rd; typical values for midlatitude atmosphere — 1000km, ocean — 50km Eliminating pressure using equation of state results in thermal wind relation, which connects horizontal temperature gradients with vertical shear of horizontal wind u z, v z.

6. Typical map of sea-level pressure and winds (January) The response of the atmospheric jet over the Southern Ocean to anthropogenic forcing is to intensify and shift southward Midlatitude jets are largely eddy-driven Eddies are generated at the scale of Rd

8. Mid-latitude Jet Streams

9. Wind-driven (WDC) and thermohaline (THC) circulation WDC: Surface currents Both types of currents combine to define global 3-D circulation

10. Ocean’s “weather”: mesoscale eddy field

11. Summary thus far Differential heating by the sun induces equator-to- pole thermal contrasts that drive zonal atmospheric jets with vertical shear These jets are unstable and generate turbulent eddies at the Rd scale (~1000km for the atmo.); the eddies interact with the jet and produce eastward mid-latitude jets that reach the Earth’s surface The mid-latitude jet over the Southern Ocean drives the Antarctic Circumpolar Current (ACC) The instabilities of ACC current system lead to oceanic eddy field (50-km scale) not explicitly resolved by global climate models

12. Response of the Antarctic Circumpolat Current (ACC) to intensifying jet stream Hogg et al. (2008) demonstrated in an idealized, but eddy- resolving three-layer model that linearly increasing wind stress causes no change in the ACC transport!

13. Response of ACC to increasing wind-stress II: “eddy saturation” ACC transport does not change Instead, eddy field intensifies Enhanced eddy mixing modifies both surface and subsurface climate-change signatures, e.g., temperature trends These conjectures based on the idealized model simulations were confirmed using more complete eddy-resolving models and observations

14. Estimates of the eddy effects on SST in Hogg et al. (2008) model Typical eddy-driven SST trends forced by wind-stress trends similar to the observed (10% per decade) are 0.1–0.2 ºC per decade

15. SST trends over ACC: Observations and simulations by coarse-resolution global climate models SST trends match, but wind-stress trends don’t! (despite!)

16. Hypothesis to explain discrepancies: Global climate models make two compensating errors to achieve seemingly correct SST trends over the ACC: The wind-stress trends are much underestimated due, presumably, to incompleteness of anthropogenic forcing in many of the models comprising the present ensemble The models misrepresent eddies and cannot capture trends in eddy-induced lateral mixing

17. “Eddies” in coarse-resolution models: GM parameterization z-coordinates: Isopycnal coordinates: u* and w* — eddy-induced transports

18. Application of GM scheme in global climate models Resulted in solutions without climate drift, in part due to improvements in the ACC region The GM scheme needs to be turned off in the mixed layer, where the slopes of isopycnals are steep. Slope-limiting and/or taper functions were typically used Non-constant K(x, y, z, t) have been suggested. We argue that this is essential to model ACC changes forced by wind-stress trends in coarse- resolution models

19. SST response in a coarse-res. ocean model No change in wind Observed wind changes Linearly increasing K and K H (in mixed layer) The “eddy-induced” response magnitude consistent with that in idealized eddy- resolving model The SST trends due to various forcings combine linearly

20. Conclusions Correct simulation of surface response in the ACC region to various forcings has numerous implications for accurate climate prediction (coupled modes, CO 2 sinks etc.) The ACC operates in an eddy-saturated regime: increasing wind-stress forcing does not accelerate the time-mean current, but energizes eddy field The enhanced eddy mixing induces quantitatively important SST trends in the region This effect can be parameterized in coarse-grid climate models via variable GM and lateral diffusion coefficients. Such schemes are not implemented in many of these models... (or maybe it’s better to just resolve eddies!)