A Path Integral Method for Data Assimilation

We describe a path integral approach for data assimilation. It is based on the generalized hybrid Monte Carlo sampling scheme. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution, parameter estimation, and data/model initialization. This estimation method exploits gradient-following sampling and a nonlocal decorrelation strategy. The significant increase in computational efficiency comes with a cost: additional software –computation of the gradient –, and an increase in communication –a matrix-vector multiply –, when compared to basic Monte Carlo sampling. However, the increase in computational efficiency makes it a viable and practical method in a variety of moderately large estimation problems. The method is described and shown with examples to be capable of tracking the conditioned mean and uncertainty of a nonlinear process with non Gaussian statistics. The example chosen is an idealized flow/drifter problem which has been used as a testbed for assimilation strategies involving Lagrangian data. It is in this kind of context that the method may prove to be an invaluable assimilation tool in large scale oceanic studies.