  A thermal convection loop is a circular chamber filled with water, heated on
the bottom half and cooled on the top half. With sufficiently large forcing of
heat, the direction of fluid flow in the loop oscillates chaotically, forming
an analog to the Earth's weather. As is the case for state-of-the-art weather
models, we only observe the statistics over a small region of state space,
making prediction difficult. To overcome this challenge, data assimilation
methods, and specifically ensemble methods, use the computational model itself
to estimate the uncertainty of the model to optimally combine these
observations into an initial condition for predicting the future state. First,
we build and verify four distinct DA methods. Then, a computational fluid
dynamics simulation of the loop and a reduced order model are both used by
these DA methods to predict flow reversals. The results contribute to a testbed
for algorithm development.
