Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction
The problem of forecasting the behavior of a complex dynamical system through analysis of observational timeseries data becomes difficult when the system expresses chaotic behavior and the measurements are sparse, in both space and/or time. Despite the fact that this situation is quite typical across many fields, including numerical weather prediction, the issue of whether the available observations are "sufficient" for generating successful forecasts is still not well understood. An analysis by Whartenby et al. (2013) found that in the context of the nonlinear shallow water equations on a β plane, standard nudging techniques require observing approximately 70 % of the full set of state variables. Here we examine the same system using a method introduced by Rey et al. (2014a), which generalizes standard nudging methods to utilize time delayed measurements. Here, we show that in certain circumstances, it provides a sizable reduction in the number of observations required to construct accurate estimates and highquality predictions. In particular, we find that this estimate of 70 % can be reduced to about 33 % using time delays, and even further if Lagrangian drifter locations are also used as measurements.
 Authors:

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 Univ. of California, San Diego, CA (United States). Dept. of Physics
 Univ. of California, San Diego, CA (United States). Dept. of Physics; Univ. of California, San Diego, CA (United States). Scripps Inst. of Oceanography, Marine Physical Lab.
 Publication Date:
 Grant/Contract Number:
 FG0297ER25308; PHY0961153
 Type:
 Accepted Manuscript
 Journal Name:
 Nonlinear Processes in Geophysics (Online)
 Additional Journal Information:
 Journal Name: Nonlinear Processes in Geophysics (Online); Journal Volume: 24; Journal Issue: 1; Journal ID: ISSN 16077946
 Publisher:
 European Geosciences Union  Copernicus
 Research Org:
 Krell Inst., Ames, IA (United States)
 Sponsoring Org:
 USDOE; National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 58 GEOSCIENCES
 OSTI Identifier:
 1366514
An, Zhe, Rey, Daniel, Ye, Jingxin, and Abarbanel, Henry D. I.. Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction. United States: N. p.,
Web. doi:10.5194/npg2492017.
An, Zhe, Rey, Daniel, Ye, Jingxin, & Abarbanel, Henry D. I.. Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction. United States. doi:10.5194/npg2492017.
An, Zhe, Rey, Daniel, Ye, Jingxin, and Abarbanel, Henry D. I.. 2017.
"Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction". United States.
doi:10.5194/npg2492017. https://www.osti.gov/servlets/purl/1366514.
@article{osti_1366514,
title = {Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction},
author = {An, Zhe and Rey, Daniel and Ye, Jingxin and Abarbanel, Henry D. I.},
abstractNote = {The problem of forecasting the behavior of a complex dynamical system through analysis of observational timeseries data becomes difficult when the system expresses chaotic behavior and the measurements are sparse, in both space and/or time. Despite the fact that this situation is quite typical across many fields, including numerical weather prediction, the issue of whether the available observations are "sufficient" for generating successful forecasts is still not well understood. An analysis by Whartenby et al. (2013) found that in the context of the nonlinear shallow water equations on a β plane, standard nudging techniques require observing approximately 70 % of the full set of state variables. Here we examine the same system using a method introduced by Rey et al. (2014a), which generalizes standard nudging methods to utilize time delayed measurements. Here, we show that in certain circumstances, it provides a sizable reduction in the number of observations required to construct accurate estimates and highquality predictions. In particular, we find that this estimate of 70 % can be reduced to about 33 % using time delays, and even further if Lagrangian drifter locations are also used as measurements.},
doi = {10.5194/npg2492017},
journal = {Nonlinear Processes in Geophysics (Online)},
number = 1,
volume = 24,
place = {United States},
year = {2017},
month = {1}
}