Mathematical foundations of hybrid data assimilation from a synchronization perspective

Penny, Stephen G.

doi:10.1063/1.5001819

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Mathematical foundations of hybrid data assimilation from a synchronization perspective

2017
By Penny, Stephen G.
Source: Chaos 27, 126801

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Journal Title:

Chaos: An Interdisciplinary Journal of Nonlinear Science
Personal Author:

Penny, Stephen G.
Corporate Authors:

United States. National Oceanic and Atmospheric Administration. Office of Oceanic and Atmospheric Research ; Modeling, Analysis, Predictions, and Projections Program (U.S.) ; United States. National Weather Service. ; National Centers for Environmental Prediction (U.S.)

United States. National Oceanic and Atmospheric Administration. Office of Oceanic and Atmospheric Research ; Modeling, Analysis, Predictions, and Projections Program (U.S.) ; United States. National Weather Service. ; National Centers for Environmental Prediction (U.S.) Less -
NOAA Program & Office:

OAR (Oceanic and Atmospheric Research) ; CPO (Climate Program Office) ; NWS (National Weather Service) ; NCEP (National Centers for Environmental Prediction)

OAR (Oceanic and Atmospheric Research) ; CPO (Climate Program Office) ; NWS (National Weather Service) ; NCEP (National Centers for Environmental Prediction) Less -
Description:

The state-of-the-art data assimilation methods used today in operational weather prediction centers around the world can be classified as generalized one-way coupled impulsive synchronization. This classification permits the investigation of hybrid data assimilation methods, which combine dynamic error estimates of the system state with long time-averaged (climatological) error estimates, from a synchronization perspective. Illustrative results show how dynamically informed formulations of the coupling matrix (via an Ensemble Kalman Filter, EnKF) can lead to synchronization when observing networks are sparse and how hybrid methods can lead to synchronization when those dynamic formulations are inadequate (due to small ensemble sizes). A large-scale application with a global ocean general circulation model is also presented. Results indicate that the hybrid methods also have useful applications in generalized synchronization, in particular, for correcting systematic model errors.

Data assimilation is a mathematical discipline that arose out of the development of numerical weather prediction (NWP), which required initialization of numerical models based on a set of relatively sparse observations. In recent years, popular solution approaches for this state estimation problem have evolved into two main categories: variational methods and ensemble-based Kalman filters. As each approach has its own unique benefits, researchers began creating hybrid combinations of these methods to take advantage of the strengths of both. We describe how data assimilation can be interpreted as a type of synchronization problem in which a modeled system is driven by observations of a natural system and extend this formalism to include the aforementioned hybrid data assimilation techniques.
Content Notes:

The author would like to acknowledge support from the National Oceanic and Atmospheric Administration (NOAA) Next Generation Global Prediction System (NGGPS) Research to Operations (R2O) Program (NA15NWS4680016), and the NOAA Climate Program Office (CPO) and Modeling, Analysis, Predictions, and Projections (MAPP) Program (NA16OAR4310140).
Keywords:

[+]

Atmospheric Science Electromagnetic Compatibility Information Visualization Kalman Filtering Lyapunov Exponents Models Numerical Methods Ocean Circulation Oceanography Variational Methods Covariance And Correlation Data Visualization
Source:

Chaos 27, 126801
DOI:

https://doi.org/10.1063/1.5001819
ISSN:

1054-1500
Format:

PDF
Publisher:

AIP Publishing
Pubmed ID:

29289051
Document Type:

Journal Article
Funding:

Grant no. NA16OAR4310140 ; Grant no. NA15NWS4680016

Grant no. NA16OAR4310140 ; Grant no. NA15NWS4680016 Less -
Rights Information:

Other
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Submitted
Main Document Checksum:

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urn:sha256:1301969fb569e55776fce5a598300ce09d88f2c65861400b49e456e9e44e1444
Download URL:

https://repository.library.noaa.gov/view/noaa/28438/noaa_28438_DS1.pdf
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Mathematical foundations of hybrid data assimilation from a synchronization perspective

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