1. Investigating Dansgaard-Oeschger events via a 2-D ocean model
Kevin Lewis
California Institute of Technology

2. Climate change cycles Orbital Frequencies – 20-100 kyr
Major climate shifts also recorded on kyr timescales
Dansgaard et al., 1993

3. Dansgaard-Oeschger Events
Characterized by rapid warming in the N. Atlantic, followed by slower cooling
Quasi-Periodic, with a timescale of ~1400 years
Recorded by diverse climate proxies
Evidence for global climatic effects
(Data From ftp://ftp.ngdc.noaa.gov/paleo/icecore/greenland/summit/grip/isotopes/gripd18o.txt)

4. Other Evidence of D-O events
Sediment cores from the Santa Barbara Basin (Hendy and Kennet, 1999)

5. Other Evidence of D-O events
Stalagmites from Eastern China (Wang et al., 2001)

6. Global Map of D-O records

7. Global Thermohaline Circulation

8. Atlantic Circulation
Deep water formation
Deep Water is formed at the Northern and Southern extents of the Atlantic Ocean
This deep circulation has an overturning timescale of ~103 years
Surface currents strongly influence climate in many areas, as in the N. Atlantic
Plane of 2-D model
(Source: Ge101 lecture notes)
Deep water formation

9. Previous Work (Briefly)
D-O events have been studied by many others using models of all complexities
Many of these models require specific additional assumptions
(Ganopolski and Rahmstorf, 2001)

10. Goals
Study changes in the overturning circulation using a model of intermediate complexity (between box models and full 3-D climate models)
Investigate the possibility of thermobaric energy release in connection to changes in circulation
Look for a self-sustaining oscillatory mode intrinsic to the ocean, with no time-dependent parameters
Introduce only the minimum number of parameters/assumptions necessary

11. Thermobaric Potential Energy
The effect of temperature on density increases with pressure
Cold, fresh water can be stable above or below warm, salty water
Warm, Salty water
Cold, Fresh water

12. Equations Variables: Equations: Streamfunction, ψ Density, ρ
Salinity, S
Temperature, θ
Equations:
Model Assumptions:
Boussinesq
Mixed boundary conditions for S,θ
No flux, no-slip sides/bottom (u=0)
stress-free top surface (ζ=0), with freshwater and salinity flux

13. Model Parameters N-S symmetric, time independent fluxes
Constant horizontal and vertical diffusivities
Linear equation of state

14. Observed Stable Modes Thermal Stratification Salt Stratification
Heating of deep water from surface
Rapid sinking of Cold, Fresh surface reservoir
Strong surface current, transporting salt to one pole
Temperature (oC)
Temperature (oC)
Method: Find the balance point between these modes

15. Results
Centennial-scale oscillations can be sustained for >10^4 years
Transitions between two separate modes occur quasi-periodically
Timescale is diffusion controlled
Trigger is a thermobaric PE reservoir at the surface (Cold, Fresh water)
Solution is symmetric

16. Results

17. Stability Diagram for viscosities
Below 5000 m^2/s vertical diffusivity, no oscillations have been observed
A small transition region is present, where irregular oscillations are observed

18. Effect of Thermobaricity
Without the thermobaric term for density, oscillations are impossible

19. Effect of Geothermal Heating
Deep ocean must be warmed to create a thermobaric instability
Geothermal has not been observed to affect outcome
Temperature (oC)
Heating From Above
Heating from below

20. Future work Explore parameters governing oscillations
Horizontal and Vertical diffusivities
Heat and Salinity Fluxes
Investigate the effects of model assumptions, e.g.:
Mixed boundary conditions
No Convective Adjustment

21. Conclusions
Centennial-Scale oscillations have been observed for a given range of parameters
Presence of oscillations is largely limited by vertical diffusion
Warming of deep ocean from surface is able to create a thermobaric instability

23. Misc. Parameters Relaxation time – 23 days Dt – 2 hours
Write Out time – 4 years
Vert. Diffusion – 5e-3 m^2/s
Horiz. Diffusion – 5e3 m^2/s
Alpha1 = 8e-5, Alpha2 = 3e-12, Beta = 9e-4

24. Possible Improvements
Variable diffusivities with depth, ν = ν(z)
Convective adjustment
Geothermal Heating
Sea Ice parameterization
In general, additional parameters should only be added when necessary