Estimating the Wind Field from Chemical Constituent Observations: Experiments with a One-Dimensional Extended Kalman Filter

Modern data assimilation algorithms such as the four-dimensional variational algorithm or the extended Kalman filter (EKF) can, in theory, estimate the wind field from chemical constituent observations. This seems to be possible because of the wind-constituent coupling in the chemical transport equation. This paper examines this possibility by applying an EKF to the one-dimensional constituent transport equation and to a prognostic, linear wind model. Generally, both transport and wind models are assumed to be perfect. Tangent linear (TLM) and adjoint models for the chemical transport model are developed and examined. A set of preliminary experiments was performed assuming perfect winds and examining the propagation of constituent errors. For this case, it was shown that the analysis of the constituent in zones of strong convergence can only be determined from nearby observations inside the zone; but the situation is much more favorable in divergent zones. This was shown to be consistent with observability theory. Experiments with imperfect wind fields focused on the validity of the TLM and on wind and constituent error propagation. EKF experiments with constituent observations only showed that the wind field can indeed be recovered from these observations provided there is sufficient structure in the constituent field, the observations are sufficiently frequent and accurate (particularly for low constituent concentrations), and data voids are small.