Adjoint-based marker-in-cell data assimilation for constraining thermal
and flow processes from Lagrangian particle records
Abstract
Geophysical problems often involve Lagrangian particles that follow
surrounding flows and record information about the system, such as the
pressure and temperature path recorded in metamorphic rocks. These
Lagrangian particles can be useful for constraining unknown parameters,
such as their sources and the thermal and flow processes of the
surrounding fluid. To use information about Lagrangian particles to
constrain unknown parameters about the surrounding fluid in an inverse
manner, we have developed a 4D-Var (four-dimensional variational) data
assimilation for thermal convection in a particle-grid coupled system.
Here we consider particles advected in a thermally convecting, highly
viscous fluid that mimics geochemical tracers in the Earth’s mantle, and
estimate time series of thermal and velocity fields only from the
particle records, focusing on their high traceability in the laminar
flow. We present preliminary 4D-Var results using a sufficient amount of
synthetic particle position and velocity data. The 4D-Var run achieves a
60-Myr time reversal of thermal convection with a horizontal wavelength
of 6,000 km, without using any temperature data. For smaller scale
convection, the cost function tends not to decrease well, but with a
shorter retrospective time domain or a large weight on early stage
information, the reconstruction improves. While this work focuses on
mantle dynamics, our framework has the potential to constrain thermal,
flow, and mixing processes in any other laminar flow containing
Lagrangian particles that record useful information.