  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.
