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Causality Relations Using Nonlinear Data Assimilation

Total Cost €


EC-Contrib. €






Project "CUNDA" data sheet

The following table provides information about the project.


Organization address
postcode: RG6 6AH

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country United Kingdom [UK]
 Project website
 Total cost 2˙597˙754 €
 EC max contribution 2˙597˙754 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-AdG
 Funding Scheme ERC-ADG
 Starting year 2016
 Duration (year-month-day) from 2016-09-01   to  2021-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE UNIVERSITY OF READING UK (READING) coordinator 2˙597˙754.00


 Project objective

A major problem in understanding complex nonlinear geophysical systems is to determine which processes drive which other processes, so what the causal relations are.

Several methods to infer nonlinear causal relations exist, but often lead to different answers, often perform hypothesis testing on causality, need long stationary time series, can be misleading if an unknown process drives the processes under study, or, if a numerical model is used, reflect model causality instead of real-world causality. Furthermore methods that use the governing evolution equations directly lead to intractable high-dimensional integrals.

In this proposal I will tackle these problems by firstly embedding causality into a Bayesian framework, moving from testing causality to estimating causality strength and its uncertainty in a systematic way. Knowledge from several causality methods can be combined, new knowledge can be brought in systematically, and time series can be short. Furthermore, new knowledge can be incorporated into the existing knowledge basis, and several methods can be combined in a consistent manner. Secondly, a new formulation to infer causal strength exploring evolution equations that avoids high-dimensional integrals will be explored. Thirdly, numerical models are combined with observations by exploring fully nonlinear data assimilation to study real-world causality.

I will test the new techniques on simple models and then apply them to a high-resolution model of the ocean area around South Africa where the Southern Ocean, the Indian Ocean, and the Atlantic Ocean meet. This area plays a crucial role in the global circulation of heat and salt by bringing warm and salty Indian Ocean water into the Atlantic in a highly turbulent manner. The techniques allow to infer what sets this interocean transport, the turbulent local dynamics or the global climate-related dynamics, crucial for understanding the functioning of the ocean in the climate system.


year authors and title journal last update
List of publications.
2018 Tijana Janjic, Roland Potthast, Peter Jan Van Leeuwen
published pages: 1189-1190, ISSN: 0035-9009, DOI: 10.1002/qj.3382
Quarterly Journal of the Royal Meteorological Society 144/713 2019-09-26
2018 Chris W. Hughes, Joanne Williams, Adam Blaker, Andrew Coward, Vladimir Stepanov
A window on the deep ocean: The special value of ocean bottom pressure for monitoring the large-scale, deep-ocean circulation
published pages: 19-46, ISSN: 0079-6611, DOI: 10.1016/j.pocean.2018.01.011
Progress in Oceanography 161 2019-07-03
2019 Flavia R. Pinheiro, Peter Jan van Leeuwen, Gernot Geppert
Efficient nonlinear data assimilation using synchronisation in a particle filter
published pages: , ISSN: 0035-9009, DOI: 10.1002/qj.3576
Quarterly Journal of the Royal Meteorological Society 2019-07-03
2019 V.N. Stepanov
The Impact of the Processes in the Southern Ocean on ENSO Development
published pages: , ISSN: 2328-5982, DOI:
Earth Sciences 2019-07-03
2019 M. Pulido and P.J. van Leeuwen
Sequential Monte Carlo with kernel embedded mappings: The mapping particle filter
published pages: , ISSN: 0021-9991, DOI:
Journal Of Computational Physics + OA Mirror 2019-07-03
2019 Peter Jan van Leeuwen, Hans R. Künsch, Lars Nerger, Roland Potthast, Sebastian Reich
Particle filters for high‐dimensional geoscience applications: A review
published pages: , ISSN: 0035-9009, DOI: 10.1002/qj.3551
Quarterly Journal of the Royal Meteorological Society 2019-09-04
2018 Javier Amezcua, Peter Jan van Leeuwen
Time‐correlated model error in the (ensemble) Kalman smoother
published pages: 2650-2665, ISSN: 0035-9009, DOI: 10.1002/qj.3378
Quarterly Journal of the Royal Meteorological Society 144/717 2019-04-18
2019 Jacob Skauvold, Jo Eidsvik, Peter Jan van Leeuwen, Javier Amezcua
A Revised Implicit Equal-Weights Particle Filter
published pages: , ISSN: 0035-9009, DOI: 10.1002/qj.3506
Quarterly Journal of the Royal Meteorological Society 2019-04-18
2018 Sanita Vetra-Carvalho, Peter Jan van Leeuwen, Lars Nerger, Alexander Barth, M. Umer Altaf, Pierre Brasseur, Paul Kirchgessner, Jean-Marie Beckers
State-of-the-art stochastic data assimilation methods for high-dimensional non-Gaussian problems
published pages: 1445364, ISSN: 1600-0870, DOI: 10.1080/16000870.2018.1445364
Tellus A: Dynamic Meteorology and Oceanography 70/1 2019-04-18
2018 Mengbin Zhu, Peter J. van Leeuwen, Weimin Zhang
Estimating model error covariances using particle filters
published pages: 1310-1320, ISSN: 0035-9009, DOI: 10.1002/qj.3132
Quarterly Journal of the Royal Meteorological Society 144/713 2019-04-18
2017 Michael Goodliff, Javier Amezcua, Peter Jan Van Leeuwen
A weak-constraint 4DEnsembleVar. Part II: experiments with larger models
published pages: 1271565, ISSN: 1600-0870, DOI: 10.1080/16000870.2016.1271565
Tellus A: Dynamic Meteorology and Oceanography 69/1 2019-04-18
2017 Javier Amezcua, Michael Goodliff, Peter Jan Van Leeuwen
A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments
published pages: 1271564, ISSN: 1600-0870, DOI: 10.1080/16000870.2016.1271564
Tellus A: Dynamic Meteorology and Oceanography 69/1 2019-04-18
2018 Flavia R. Pinheiro, Peter Jan van Leeuwen, Ulrich Parlitz
An ensemble framework for time delay synchronization
published pages: 305-316, ISSN: 0035-9009, DOI: 10.1002/qj.3204
Quarterly Journal of the Royal Meteorological Society 144/711 2019-04-18
2017 Matthew Lang, Philip Browne, Peter Jan van Leeuwen, Mathew Owens
Data Assimilation in the Solar Wind: Challenges and First Results
published pages: 1490-1510, ISSN: 1542-7390, DOI: 10.1002/2017SW001681
Space Weather 15/11 2019-04-18

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