Chapter 11
WHAT IS DATA ASSIMILATION REALLY
SOLVING, AND HOW IS THE CALCULATION
ACTUALLY DONE?
Ichiro Fukumori
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USA
Abstract: Data assimilation is reviewed in the context of an inverse problem. The
mathematical nature of the problem is examined and some of its common
solutions are described, clarifying some of the implicit assumptions that underlie
both problem and solution. For instance, Kalman filtering and Rauch-TungStriebel smoothing can be identified as recursive least-squares inversions of the
assimilation problem but of different parts of the problem. The temporal
evolution of a filtered solution is not physically consistent, but that of a smoothed
solution is. Understanding these characteristics is essential in effectively
assimilating observations as well as in utilizing and further improving the
assimilated solution. Practical steps in implementing a filtering and smoothing
algorithm are illustrated by examples from the Consortium for “Estimating the
Circulation and Climate of the Ocean” (ECCO).
Keywords: Data assimilation, Kalman filter, smoother, consistency, ECCO.
1. Introduction
Data assimilation is a procedure in which observations are combined
with models. The observations correct model errors on the one hand, and
the models extrapolate the data information in space, time, and among
different properties on the other. The result of assimilation is generally a
more complete and more accurate description of the state of the modeled
system than those obtained by either observations or model simulations
alone. However, data assimilation is not a panacea for correcting every
model error or for compensating all deficiencies of observations.
Because ocean models have finite degrees of freedom, model estimates
are inherently different from observations regardless of errors in
317
E. P. Chassignet and J. Verron (eds.), Ocean Weather Forecasting, 317-342.
© 2006 Springer. Printed in the Netherlands.
WHAT IS DATA ASSIMILATION REALLY
SOLVING, AND HOW IS THE CALCULATION
ACTUALLY DONE?
Ichiro Fukumori
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USA
Abstract: Data assimilation is reviewed in the context of an inverse problem. The
mathematical nature of the problem is examined and some of its common
solutions are described, clarifying some of the implicit assumptions that underlie
both problem and solution. For instance, Kalman filtering and Rauch-TungStriebel smoothing can be identified as recursive least-squares inversions of the
assimilation problem but of different parts of the problem. The temporal
evolution of a filtered solution is not physically consistent, but that of a smoothed
solution is. Understanding these characteristics is essential in effectively
assimilating observations as well as in utilizing and further improving the
assimilated solution. Practical steps in implementing a filtering and smoothing
algorithm are illustrated by examples from the Consortium for “Estimating the
Circulation and Climate of the Ocean” (ECCO).
Keywords: Data assimilation, Kalman filter, smoother, consistency, ECCO.
1. Introduction
Data assimilation is a procedure in which observations are combined
with models. The observations correct model errors on the one hand, and
the models extrapolate the data information in space, time, and among
different properties on the other. The result of assimilation is generally a
more complete and more accurate description of the state of the modeled
system than those obtained by either observations or model simulations
alone. However, data assimilation is not a panacea for correcting every
model error or for compensating all deficiencies of observations.
Because ocean models have finite degrees of freedom, model estimates
are inherently different from observations regardless of errors in
317
E. P. Chassignet and J. Verron (eds.), Ocean Weather Forecasting, 317-342.
© 2006 Springer. Printed in the Netherlands.