Climate Dynamics

FAS course web page for EPS 231 (Spring 2013)

Instructor: Eli Tziperman,

TF: Alex Robel, robel at

Day, time: Monday 2:30-4:00, Thursday, 2:30-4;

Location: Geological Museum, 4th floor, room 418. 24 Oxford St, Cambridge.

Outline Textbooks Detailed Syllabus Bibliography Requirements

Announcements Last updated: February 22, 2013.
Feel free to write or call me with any questions:
Office hours: Eli: Tue 1:30-3, Thu 1-2; please write/ call before stopping by, if possible.

Detailed teaching notes and links to source materials, Matlab codes and more

Homework assignments and solutions may be downloaded here


The basics of climate dynamics, from the feedbacks that maintain the mean climate to phenomenology and mechanisms of climate variability. We will cover energy balance models, climate equilibria and stability with examples from equable (warm) climate to snowball earth. Examples of climate variability to be covered are El Nino (occurring roughly every 4 yrs), the thermohaline circulation and its multiple equilibria and variability (decadal and longer); thermohaline variability as a possible explanation for the medieval warm period and the little ice ate (hundreds of years); the Dansgaard-Oeschger warming events observed in the Greenland ice core (every 1500 yr), Heinrich events involving massive collapses of ice during glacial times (every 7-10,000yr), glacial-interglacial variability (100,000 yr), and equable climate dynamics (50 Myrs). In each case, we will discuss physical mechanisms and demonstrate them with a hierarchical modeling approach, from toy models to GCMs. Needed background in nonlinear dynamics will be covered.

Familiarity with some basic Geophysical Fluid Dynamics (the equivalent of MIT 12.800, or Harvard EPS 131, EPS 132 or EPS 232), or general fluid dynamics (e.g., engineering fluid courses at Harvard) will be assumed. The course may be taken as a sequel to Harvard's Physics of Climate (EPS 208), or MIT's Climate Physics and Chemistry (12.842), but can also be taken independently of these courses.

Course homepage:

First lecture (ppt),


Detailed syllabus

A detailed outline of the lectures, and a complete list of reference materials used in each lecture is available here.

  1. Outline and motivation.
  2. Basic climate feedbacks. Supporting material.
    1. energy balance
    2. small ice cap instability

  3. El Nino - Southern Oscillation (Cessi et al., 2001); supporting material.
    1. Phenomenology: basics: Gill atmosphere; reduced gravity models, equatorial ocean waves (Dijkstra, 2000), (Gill, 1982).
    2. Coupled ocean-atmosphere dynamics, demonstrated via the Cane-Zebiak model
    3. Delayed oscillator
    4. ENSO regimes: fast SST, fast wave, mixed; recharge oscillator:
    5. Irregularity: chaos
    6. Irregularity: stochastic forcing, non normal dynamics, optimal initial conditions and stochastic optimals (section 4, eqns 11-14, Tziperman and Ioannou, 2002).
    7. Westerly wind bursts
    8. Locking to seasonal cycle
    9. Atmospheric teleconnections, Rossby ray tracing

  4. Thermohaline circulation (Dijkstra, 2000); supporting material.
    1. Phenomenology, mixed boundary conditions, Stommel model
    2. Advective and convective feedbacks; flip flop and loop oscillations.
    3. Stability, bifurcations and multiple equilibria
    4. Stochastic forcing; linear vs nonlinear; non normal dynamics, noise induced transitions between steady states
    5. Thermohaline flushes (``deep decoupling'' relaxation oscillations)

  5. D/O and Heinrich events: supporting material.
    1. DO: THC flushes vs sea ice changes;
    2. Heinrich events: binge-purge oscillator, climatic effects, synchronous collapses

  6. Glacial cycles: supporting material.
    1. Phenomenology
    2. Milankovitch forcing
    3. Ice sheets: mass balance, geometry, parabolic profile.
    4. Glaciology basics: Glenn's law, basic solutions equilibrium profiles of ice sheets and ice shelves.
    5. Simple models of glacial cycles
    6. Phase locking to Milankovitch forcing
    7. CO and the ocean carbonate system

  7. Equable climate supporting material.
    • Equator to pole Hadley cell
    • Polar stratospheric clouds
    • Hurricane mixing of ocean
    • Convective cloud feedback


Homework assignments are 50% of final grade, and a final course project will constitute the remaining 50%. There is an option to take this course as a pass/fail with approval of instructor. If interested, you need to obtain this approval during the first three weeks of the course.



Cessi, P., Pierrehumbert, R., and Tziperman, E. (2001).
Lectures on enso, the thermohaline circulation, glacial cycles and climate basics.
In Balmforth, N. J., editor, Conceptual Models of the Climate. Woods Hole Oceanographic Institution.

Dijkstra, H. A. (2000).
Nonlinear physical oceanography.
Kluwer Academic Publishers.

Gill, A. E. (1982).
Atmosphere-Ocean Dynamics.
Academic Press, Inc, San Diego, CA, 662pp.

Hartmann, D. (1994).
Global Physical Climatology.
Academic press, San Diego.

Tziperman, E. and Ioannou, P. J. (2002).
Transient growth and optimal excitation of thermohaline variability.
J. Phys. Oceanogr., 32(12):3427-3435.