In the 1960’s, MIT meteorologist Edward Lorenz was investigating the effects of nonlinearity on short-term weather prediction in a model of convection. In his ground-breaking paper “Deterministic Nonperiodic Flow,” Lorenz showed that numerical solutions of the model exhibit sensitive dependence on their initial position, leading virtually indistinguishable states to diverge quickly. This phenomenon, which became known as chaos, is a major contributor to inaccuracies in weather and climate forecasts.

The thermal convection loop is an experimental analog of Lorenz’s system in the form of a hula-hoop shaped tube, filled with fluid, and oriented vertically like a wheel. The bottom half of the tube is warmed uniformly by a bath of hot water and the top half is cooled. Under certain conditions, a steady state is never reached, and the fluid switches direction in an unpredictable pattern.

In the past few years, we have used Computational Fluid Dynamics (CFD) simulations of the loop as a testbed for data assimilation, ensemble forecasting, and model error experiments in weather and climate prediction. Our team is developing algorithms to improve forecasts and uncertainty quantification using this simple but realistic toy climate. Successful techniques are then implemented on more realistic weather and climate models.

Details:

K. D. Harris, E.-H. Ridouane, D. L. Hitt, C. M. Danforth. 2012. Predicting Flow Reversals in Chaotic Natural Convection using Data Assimilation. Tellus A, **64**, 17598. [pdf]

N. Allgaier, K. D. Harris, C. M. Danforth. 2012. Empirical Correction of a Toy Climate Model. Physical Review E. 85, 026201. [pdf]

R. Lieb-Lappen, C. M. Danforth. 2012. Aggressive Shadowing of a Low-Dimensional Model of Atmospheric Dynamics. Physica D. Volume 241, Issue 6, Pages 637–648. [pdf]

E.-H. Ridouane, C. M. Danforth, D. L. Hitt. 2009. A 2-D Numerical Study Of Chaotic Flow In A Natural Convection Loop. International Journal of Heat and Mass Transfer. [pdf]

and a lecture on the topic given by Danforth to the Applied Dynamics graduate course at UNC Chapel Hill:

Funding from the project comes from NASA and NSF through the Mathematics and Climate Research Network.