Application of a new multiscale data assimilation: Estimation of local aerosol fluxes on a two-dimensional atmospheric boundary

Sequential data assimilations have been utilized in diverse scientific and engineering fields to retrieve model predictions via experimental measurements. However, their applications have been so far limited to single-scale problems, where model predictions at one scale were retrieved or calibrated only by measurements in that scale. For multiscale systems (e.g., atmospheric systems, complex biosystems, chemically reacting systems) for which microscopic observations are usually not available, it is expected to utilize measurements in macroscopic (e.g., coarse-grained, density-level, largely distanced from a boundary) scales to update or estimate microscopic (e.g., agent-based, particle-level, locally concentrated near a boundary) model quantities. This therefore requires techniques for multiscale data assimilation.

In this work, a newly proposed multiscale data assimilation technique [1] is used to estimate local aerosol fluxes emitted from a two-dimensional atmospheric boundary. Here the local aerosol fluxes near the boundary serve as the microscale state and their fluxes at a height above the boundary as the macroscale state. Model states in different scales, related through an interscale bridging model, are coupled to form an extended state. An advanced data assimilation method, the ensemble Kalman filter (EnKF) [2,3], is applied to update the extended model state, from which updated states in different scales can then be extracted. This data assimilation approach is appropriate for computationally multiscale systems where observables in different scales have the same dimension and can thus be coupled to form a meaningful extended state.

In this paper, we use Wilson's model to simulate intensities of vertical wind velocities, and use independent Brownian motions to simulate horizontal wind velocities. Macroscale aerosol fluxes can then be predicted from the microscale counterparts via this wind velocity field, thus forming an interscale bridging. The study shows that the Bayesian estimates of updated microscale aerosol fluxes close to macroscale measurement locations approach true values and their error variances have a tendency to decay. However, estimation of microscale fluxes in locations far from the macroscale measurements is poorly performed, which reminds importance of layout and quantities of macroscale measurements. This approach is also used in this study to estimate diffusion coefficients of Brownian motions of horizontal wind velocities.

[1] Y. Zou and R. Ghanem, 2004, SIAM Journal of Multiscale Modeling and Simulation, 3(1), 131-150. [2] G. Evensen, 1994, J. Geophys. Res., 99, 10143-10162. [3] R. Miller, M. Ghil and F. Gauthiez, 1994, J. Atmospheric Sci., 51, 1037-1056.