  Geomagnetic storms play a critical role in space weather physics with the
potential for far reaching economic impacts including power grid outages, air
traffic rerouting, satellite damage and GPS disruption. The LFM-MIX is a
state-of-the-art coupled magnetospheric-ionospheric model capable of simulating
geomagnetic storms. Imbedded in this model are physical equations for turning
the magnetohydrodynamic state parameters into energy and flux of electrons
entering the ionosphere, involving a set of input parameters. The exact values
of these input parameters in the model are unknown, and we seek to quantify the
uncertainty about these parameters when model output is compared to
observations. The model is available at different fidelities: a lower fidelity
which is faster to run, and a higher fidelity but more computationally intense
version. Model output and observational data are large spatiotemporal systems;
the traditional design and analysis of computer experiments is unable to cope
with such large data sets that involve multiple fidelities of model output. We
develop an approach to this inverse problem for large spatiotemporal data sets
that incorporates two different versions of the physical model. After an
initial design, we propose a sequential design based on expected improvement.
For the LFM-MIX, the additional run suggested by expected improvement
diminishes posterior uncertainty by ruling out a posterior mode and shrinking
the width of the posterior distribution. We also illustrate our approach using
the Lorenz `96 system of equations for a simplified atmosphere, using known
input parameters. For the Lorenz `96 system, after performing sequential runs
based on expected improvement, the posterior mode converges to the true value
and the posterior variability is reduced.
