Our new method for data assimilation consistently hybridizes the two outstanding classes of algorithms used in the weather forecasting community today:
(i) The Ensemble Kalman Filter (EnKF) quantifies the uncertainty of the estimate in a tractable fashion by comparing the spread of a set of "ensemble members" (that is, parallel disturbed computations of the high-dimensional state model). This method comes in many closely-related variations.
(ii) The Space/Time Variational (4Dvar) method repeatedly reconciles the current state estimate with a batch of recent observations (that is, not just updating the state estimate sequentially, one measurement at a time, as do Kalman-based approaches), thereby revisiting past measurements in light of new data, which is a very beneficial thing to do in nonlinear systems with nongaussian uncertainty.
Our team has developed a consistent, high-performance method for hybridizing these two existing classes of approaches, dubbed the Hybrid Ensemble Smoother (HEnS), which performs much better in numerical tests than either the EnKF or the 4Dvar approach used on its own, while inheriting the numeric tractability for large-scale problems that both the EnKF and 4Dvar approaches exhibit.
The HEnS approach is also naturally parallelizable. It is being tested on a range of model problems, extending all the way to the
parking-lot smoke plume tests
recently performed at UCSD.
Our present problem of data assimilation for the smoke movement in the parking lot is quite similar to the standard weather forecasting problem, albeit at a significantly smaller scale, so it is quite reasonable that, at the end of the day, we arrived in this study at some hybrid of the leading two methods for large-scale data assimilation that are available today in the weather forecasting community.