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  • 1
    Electronic Resource
    Electronic Resource
    Tidal flow forecasting using reduced rank square root filters (1997)
    Springer
    Stochastic environmental research and risk assessment 11 (1997), S. 349-368 
    Details
    ISSN: 1436-3259
    Keywords: Data assimilation ; Kalman filter ; Square root filter
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The Kalman filter algorithm can be used for many data assimilation problems. For large systems, that arise from discretizing partial differential equations, the standard algorithm has huge computational and storage requirements. This makes direct use infeasible for many applications. In addition numerical difficulties may arise if due to finite precision computations or approximations of the error covariance the requirement that the error covariance should be positive semi-definite is violated. In this paper an approximation to the Kalman filter algorithm is suggested that solves these problems for many applications. The algorithm is based on a reduced rank approximation of the error covariance using a square root factorization. The use of the factorization ensures that the error covariance matrix remains positive semi-definite at all times, while the smaller rank reduces the number of computations and storage requirements. The number of computations and storage required depend on the problem at hand, but will typically be orders of magnitude smaller than for the full Kalman filter without significant loss of accuracy. The algorithm is applied to a model based on a linearized version of the two-dimensional shallow water equations for the prediction of tides and storm surges. For non-linear models the reduced rank square root algorithm can be extended in a similar way as the extended Kalman filter approach. Moreover, by introducing a finite difference approximation to the Reduced Rank Square Root algorithm it is possible to prevent the use of a tangent linear model for the propagation of the error covariance, which poses a large implementational effort in case an extended kalman filter is used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02427924
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    Paper (German National Licenses)
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  • 2
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    Lagrangian ocean analysis : fundamentals and practices (2018)
    Elsevier
    Details
    Publication Date: 2022-05-26
    Description: © The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Ocean Modelling 121 (2018): 49-75, doi:10.1016/j.ocemod.2017.11.008.
    Description: Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.
    Description: EvS has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 715386). This research for PJW was supported as part of the Energy Exascale Earth System Model (E3SM) project, funded by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research. Funding for HFD was provided by Grant No. DE-SC0012457 from the US Department of Energy. PB acknowledges support for this work from NERC grant NE/R011567/1. SFG is supported by NERC National Capability funding through the Extended Ellett Line Programme.
    Keywords: Ocean circulation ; Lagrangian analysis ; Connectivity ; Particle tracking ; Future modelling
    Repository Name: Woods Hole Open Access Server
    Type: Article
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    PAPER (OA)
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