Recovery of the one and two dimensional windfields from chemical constituent observations using the constituent transport equation and an extended Kalman filter

Summary

The recovery of windfields from chemical constituents is a difficult, but potentially rewarding inverse problem. Advanced data assimilation methods, such as the extended Kalman filter, are theoretically capable of performing this task; but, at this time, little work has been undertaken. Daley (1994) constructed a one-dimensional extended Kalman filter (EKF) system to examine this problem. This work is extended here to include a more systematic examination of the one-dimensional case, together with experiments with non-divergent two-dimensional flow. The emphasis is on determining when wind recovery is likely to be successful or unsuccessful.

It was found that wind recovery is most successful with the EKF for constituent observations which are dense, frequent and accurate. Wind recovery is difficult or slow for the EKF (or any other procedure) when the true constituent time-tendency is small. This happens when the constituent spatial gradient is small, the true windspeeds are low or the stream-function and constituent fields are highly correlated. Wind recovery can also be difficult with constituent transport models which are highly damped, have significant phase errors or restrictive CFL criteria. Steady winds cannot be recovered inside data voids, although time-dependent winds may be recoverable. If constituent observations are too infrequent, estimates of the constituent time-tendency will be poor, and wind recovery (at least for the EKF) problematic.