A Fast Distributed Data-Assimilation Algorithm for Divergence-Free Advection
For researchers in data assimilation and atmospheric modeling, this work offers a computationally efficient method for large-scale advection problems, though it is limited to linear divergence-free cases.
The paper presents a fast distributed data assimilation algorithm for 2D linear advection with divergence-free coefficients, achieving linear scaling with the number of elements. It demonstrates effectiveness using both synthetic and real satellite data for cloud motion modeling.
In this paper, we introduce a new, fast data assimilation algorithm for a 2D linear advection equation with divergence-free coefficients. We first apply the nodal discontinuous Galerkin (DG) method to discretize the advection equation, and then employ a set of interconnected minimax state estimators (filters) which run in parallel on spatial elements possessing observations. The filters are interconnected by means of numerical Lax-Friedrichs fluxes. Each filter is discretised in time by a symplectic Mobius time integrator which preserves all quadratic invariants of the estimation error dynamics. The cost of the proposed algorithm scales linearly with the number of elements. Examples are presented using both synthetic and real data. In the latter case, satellite images are assimilated into a 2D model representing the motion of clouds across the surface of the Earth.