A data-driven kernel method assimilation technique for geophysical modelling

Abstract

Incorporating the quantity and variety of observations in atmospheric and oceanographic assimilation and prediction models has become an increasingly complex task. Data assimilation allows for uneven spatial and temporal data distribution and redundancy to be addressed so that the models can ingest massive data sets. Traditional data assimilation methods introduce Kalman filters and variational approaches. This study introduces a family of algorithms, motivated by advances in machine learning. These algorithms provide an alternative approach to incorporating new observations into the analysis forecast cycle. The application of kernel methods to processing the states of a quasi-geostrophic numerical model is intended to demonstrate the feasibility of the method as a proof-of-concept. The speed, efficiency, accuracy and scalability in recovering unperturbed state trajectories establishes the viability of machine learning for data assimilation.

Keywords:

• machine learning
• geophysical modelling
• data-driven model
• data assimilation

AMS Subject Classification:

• 68T
• 82C

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The Chebyshev nodes on the interval are defined by , for all . Interpolation polynomials built upon those nodes are minimizing Runge's phenomenon.

2. Sources are available at http://www.seas.harvard.edu/climate/eli/Downloads/QG200205011455.tar.gz.

Additional information

Funding

The authors acknowledge the following grants: NSF AGS0831359 and NA17RJ1227 for providing financial support for this work. The opinions expressed herein are those of the authors and not necessarily those of the NSF. Theodore Trafalis was supported by RSF grant 14-41-00039 and he conducted research at National Research University Higher School of Economics.