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Adjoint-based marker-in-cell data assimilation for constraining thermal and flow processes from Lagrangian particle records
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  • Atsushi Nakao,
  • Tatsu Kuwatani,
  • Shin-ichi Ito,
  • Hiromichi Nagao
Atsushi Nakao
Akita University

Corresponding Author:[email protected]

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Tatsu Kuwatani
Japan Agency for Marine-Earth Science and Technology
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Shin-ichi Ito
The University of Tokyo
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Hiromichi Nagao
Earthquake Research Institute, The University of Tokyo
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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.
23 May 2024Submitted to ESS Open Archive
28 May 2024Published in ESS Open Archive