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  • Nicolis, G. and C. Nicolis 2012. Foundations of Complex Systems : nonlinear dynamics, statistical physics, information and prediction, World Scientific. Second edition.

Edited volume

  • Vannitsem S., D. Wilks, J. Messner (Eds): Statistical Postprocessing of Ensemble Forecasts, Elsevier, The Netherlands, 347 pp, 2018 (ISBN: 978-0-12-812372-0)  

International Journals with peer-review

Manuscripts under review

  •  Roulin, E. and Vannitsem, S.: Post-processing of seasonal predictions – Case studies using the EUROSIP hindcast data base, Nonlin. Processes Geophys. Discuss.,, in review, 2019.
  • Stéphane Vannitsem, John Bjørnar Bremnes, Jonathan Demaeyer, Gavin R. Evans, Jonathan Flowerdew, Stephan Hemri, Sebastian Lerch, Nigel Roberts, Susanne Theis, Aitor Atencia, Zied Ben Bouallègue, Jonas Bhend, Markus Dabernig, Lesley De Cruz, Leila Hieta, Olivier Mestre, Lionel Moret, Iris Odak Plenković, Maurice Schmeits, Maxime Taillardat, Joris Van den Bergh, Bert Van Schaeybroeck, Kirien Whan, Jussi Ylhaisi, Statistical Postprocessing for Weather Forecasts -- Review, Challenges and Avenues in a Big Data World, submitted to BAMS, 2020.


  • Christian L.E. Franzke Susana Barbosa Richard Blender Hege‐Beate Fredriksen Thomas Laepple Fabrice Lambert Tine Nilsen Kristoffer Rypdal Martin Rypdal Manuel G. Scotto Stéphane Vannitsem Nicholas W. Watkins Lichao Yang Naiming Yuan, The structure of climate variability across scales, Reviews of Geophysics, in press, March 2020
  • Demaeyer, J. and Vannitsem, S.: Correcting for model changes in statistical postprocessing – an approach based on response theory, Nonlin. Processes Geophys., 27, 307–327,, 2020.
  • Tao, L., Duan, W. & Vannitsem, S. Improving forecasts of El Niño diversity: a nonlinear forcing singular vector approach. Clim Dyn (2020).
  •  Tondeur, M., A. Carrassi, S. Vannitsem & M. Bocquet, On temporal scale separation in coupled data assimilation with the ensemble Kalman Filter, in press, J. Stat. Phys., 2020.
  • Van Ginderachter, M., Degrauwe, D., Vannitsem, S., and Termonia, P.: Simulating model uncertainty of subgrid-scale processes by sampling model errors at convective scales, Nonlin. Processes Geophys., 27, 187–207,, 2020.
  •  Vannitsem, S., Duan, W. On the use of near-neutral Backward Lyapunov Vectors to get reliable ensemble forecasts in coupled ocean–atmosphere systems. Clim Dyn (2020).


  • Faranda D., G. Messori and S. Vannitsem, Attractor dimension of time-averaged climate observables: insights from a low-order ocean-atmosphere model, Tellus A, 71, 1-11, 2019. link
  • Vannitsem, S., R. Sole-Pomies and L. De Cruz, Routes to long-term atmospheric predictability in reduced-order coupled ocean-atmosphere systems -- Impact of the ocean boundary conditions, Quart. J. Royal Met. Soc., 145, 2791-2805, 2019. link, arxiv
  • Vannitsem, S., Q. Dalaiden & H. Goosse, Testing for dynamical dependence - Application to the surface mass balance over Antarctica. Accepted in Geophys. Res. Lett., 2009. link


  • De Cruz, L., S. Schubert, J. Demaeyer, V. Lucarini, and S. Vannitsem, Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models,  Nonlinear Processes in Geophysics, 25, 387-412, 2018. pdf
  • Demaeyer J. and S. Vannitsem, Stochastic parameterization of subgrid-scale processes: A review of recent physically-based approaches, in “Advances in Nonlinear Geosciences”, Ed. A.A. Tsonis, ISBN: 978-3-319-58894-0, Springer, 55-85, 2018.
  • Demaeyer J. and S. Vannitsem, A comparison of stochastic parameterizations in the framework of a coupled ocean-atmosphere model, Nonlinear Processes in Geophysics, 25, 605-631, 2018. pdf
  • Nicolis, C., Nonlinear dynamical approach to atmospheric predictability, in “Advances in Nonlinear Geosciences”, Ed. A.A. Tsonis, ISBN: 978-3-319-58894-0, Springer, 393-425, 2018
  • Nicolis, C., Climatic responses to systematic time variations of parameters: a dynamical approach, Nonlin. Processes Geophys., 25, 649-658,, 2018
  • Termonia, Piet, Bert Van Schaeybroeck, Lesley De Cruz, Rozemien De Troch, Steven Caluwaerts, Olivier Giot, Rafiq Hamdi, Stéphane Vannitsem, Patrick Willems, Hossein Tabari, Els Van Uytven, Parisa Hosseinzadehtalaei, Nicole Van Lipzig, Hendrik Wouters, Sam Vanden Broucke, Jean-Pascal van Ypersele, Philippe Marbaix, Cecille Villanueva-Birriel, Xavier Fettweis, Carolyn Wyard, Chloé Scholzen, Sébastien Doutreloup, Koen De Ridder, Anne Gobin, Dirk Lauwaet, Trissevgeni Stavrakou, Maite Bauwens, Jean-François Müller, Patrick Luyten, Stéphanie Ponsar, Dries Van den Eynde, Eric Pottiaux, The initiative as a foundation for climate services in Belgium, in press in Climate Services, 11, 49-61, 2018. 
  • Van Schaeybroeck B. and S. Vannitsem, , Applications of Postprocessing for long range forecasts, Chapter 10 in Statistical postprocessing of ensemble forecasts, eds. S. Vannitsem, D. Wilks, J. Messner, p. 267-290, 2018.
  • Vannitsem, S., Que nous apprennent les modèles météorologiques et climatiques simplifiés sur la prévisibilité à long terme de l’atmosphère? La Météorologie, 102, 22-30, 2018.
  • Vannitsem S. and P. Ekelmans, Causal dependences between the coupled ocean-atmosphere dynamics over the Tropical Pacific, the North Pacific and the North Atlantic, Earth System Dynamics. 9, 1063-1083, 2018. pdf
  • Wilks, D. and S. Vannitsem, Uncertainty forecasts from deterministic dynamics, Chapter 1 in Statistical postprocessing of ensemble forecasts, eds. S. Vannitsem, D. Wilks, J. Messner, p. 1-13, 2018.


  •  Demaeyer J. and S. Vannitsem, Stochastic parameterization of subgrid-scale processes in coupled ocean-atmosphere systems: Benefits and limitations of response theory, Quart. J. Royal Met. Soc., 143, 881-896, 2017.
  •  C. Nicolis and G. Nicolis 2017. Stochastic resonance across bifurcation cascades. Phys. Rev. E 95, 032219
  •  C. Nicolis and G. Nicolis 2017. Coupling-enhanced stochastic resonance. Phys. Rev. E 96, 042214
  • Pelosi, A., H. Medina, J. Van den Bergh, S. Vannitsem, G. Battista Chirico, Adaptive Kalman filtering for post-processing ensemble numerical weather predictions, Monthly Weather Review, 145, 4837-4854, 2017.
  • Vannitsem S. and M. Ghil, Evidence of coupling in the Ocean-Atmosphere dynamics over the North Atlantic, Geophys. Res. Lett., 44, 2016-2026, 2017. LinkSpotlight EOS
  • Vannitsem S. Predictability of large-scale atmospheric motions: Lyapunov exponents and error dynamics, Chaos 27, 032101, 2017, link, Arxiv pdf.


  • Carrassi A. and S. Vannitsem, Deterministic treatment of model error in geophysical data assimilation, Springer-Indam volume "Mathematical Paradigms of Climate Science, F. Ancona et al (Eds), Vol 15, 175--213, 2016.
  • De Cruz, L., J. Demaeyer, and S. Vannitsem, A Modular Arbitrary Order Ocean-Atmosphere Model: MAOOAM v1.0, Geoscientific Model Development, 9, 2793-2808, 2016.pdf
  • C. Nicolis, Error dynamics in extended-range forecasts, Q. J. R. Meteorol. Soc. 142, 1222-1231 (2016).
  • C. Nicolis and G. Nicolis, Dynamical systems approach to extreme events, in “Extreme events: observations, modeling, and economics”, M. Chavez, M. Ghil and J. Urrutia-Fucugauchi Editors, AGU Monograph Series vol. 214 , 23-34 (2016).
  • G. Nicolis and C. Nicolis, Detailed balance, nonequilibrium states and dissipation in symbolic sequences, Phys. Rev. E93, 052134 (2016).
  • G. Nicolis and C. Nicolis, Stochastic resonance, self-organization and information dynamics in multistable systems, Entropy 18, 172 (2016).  
  • Van Schaeybroeck B. and S. Vannitsem, A probabilistic approach to forecast the skill with ensemble spread, Mon. Wea. Rev., 144, 451-468, 2016.
  • Van Schaeybroeck B. and S. Vannitsem, Assessement of calibration assumptions under strong climate changes, Geophys. Res. Lett., 43, 1314-1322, 2016.
  • Vannitsem, S. and V. Lucarini, Statistical and dynamical properties of covariant Lyapunov vectors in a coupled ocean-atmosphere model - Multiscale effects, geometric degeneracy and error dynamics, J. Phys. A, 49, 224001, 2016.


  •  Barth A., M Canter, B. Van Schaeybroeck, S. Vannitsem, F. Massonnet, V. Zunz, P. Mathiot; A. Alvera-Azcaratea, J.-M. Beckers, Assimilation of sea surface temperature, sea ice concentration and sea ice drift in a model of the Southern Ocean, Ocean Modelling, 93, 22-39, 2015.
  •  Nicolis C. and G. Nicolis, The Fluctuation-Dissipation Theorem Revisited: Beyond the Gaussian Approximation, J. Atmos. Sci. 72, 2642-2656 (2015).
  • Nicolis C. and G. Nicolis, Extreme events and dynamical complexity, Chaos, Solitons and Fractals, 74, 46-54 (2015).
  • Nicolis C. 2015. Stochastic resonance and information processing, in Chaos, Information Processing and Paradoxical games, World Scientific, Singapore.
  • Nicolis C. and G. Nicolis 2015. Dynamical systems approach to extreme events, in Extreme events: Observations, Modeling and Economics, M. Chavez, M. Ghil and J. Urrutia-Fucugauchi Eds, AGU, in press.
  • Roulin E. and S. Vannitsem. ‘Post-processing of medium-range probabilistic hydrological forecasting: Impact of the presence of forcing, initial condition and model errors’ , Hydrol. Process. 29, 1434–1449, 2015.
  • Vannitsem, S., J. Demaeyer, L. De Cruz, M Ghil: Low-frequency variability and heat transport in a low-order nonlinear coupled ocean-atmosphere model. Physica D, 309, 71-85, 2015.
  • Vannitsem, S., The role of the ocean mixed layer on the development of the North Atlantic Oscillation: A dynamical system’s perspective, Geophys. Res. Lett., 42, doi:10.1002/2015GL065974, 2015.



  •  Nicolis C. and G. Nicolis, Dynamical responses to time-dependent control parameters in the presence of noise: A normal form approach, Phys. Rev. E89, 022903 (2014)
  • Nicolis G. and C. Nicolis 2014. Thermodynamic approach to chemical networks, Adv. Chem. Phys. 157, 85-94.
  • Provata A., C. Nicolis and G. Nicolis 2014. DNA viewed as an out-of equilibrium structure, Phys. Rev. E89, 052105.
  • Provata, A., C. Nicolis and G. Nicolis 2014. Complexity measures for the evolutionary categorization of organisms, Computational Biology and Chemistry, 53, 5-14.
  • Vannitsem, S., Stochastic modelling and predictability : Analysis of a low-order coupled ocean-atmosphere model. Phil Trans Roy Soc, A372, 20130282, 2014. abstract
  • Vannitsem S. and L. De Cruz, A 24-variable low-order coupled ocean-atmosphere model: OA-QG-WS v2. Geoscientific Model Development, 7, 649-662, 2014.pdf
  •  Vannitsem S., Dynamics and predictability of a low-order wind-driven ocean – atmosphere coupled model. Climate Dynamics, 42, 1981-1998, 2014.




  • Nicolis G. and C. Nicolis 2013. Toward a complex systems approach to information, in Without Bounds: a Scientific Canvas of Nonlinearity and Complex Dynamics, R. Rubio et al. Edts, Springer, Berlin. 
  • Van Schaeybroeck B. and S. Vannitsem. Reliable probabilities through statistical post-processing of ensemble forecasts. Proceedings of the European Conference on Complex Systems 2012, T Gilbert, M. Kirkilionis, G. Nicolis (eds.), Springer proceedings on complexity, XVI, p. 347-352, 2013.


  • Carrassi, A., R. Hamdi, P. Termonia and S. Vannitsem, Short time augmented extended Kalman filter for soil analysis, Atmospheric Science Letter, doi: 10.1002/asl.394
  •  Nicolis, C., Stochastic resonance in multistable systems: The role of dimensionality, Phys. Rev. E 86, 011133, 2012.
  • Nicolis C. and G. Nicolis 2012. Extreme events in multivariate deterministic systems, Phys. Rev. E85, 056217. 
  • Nicolis G. and C. Nicolis 2012. Kinetics and thermodynamics of fluctuation-induced transitions in multistable systems, Adv. Chem. Phys. 151, 1-23.
  • Nicolis, G., J.J. Kozak and C. Nicolis 2012. Modelling early stages of sequential versus hierarchical self-assembly in supramolecular architectures, Molecular Phys. 110, 395-402.  
  • Roulin E and S. Vannitsem. Post-processing of ensemble precipitation predictions with extended logistic regressions based on hindcasts. Mon. Wea. Rev., 140, 874-888, 2012.


  • Carrassi A and S Vannitsem, Treatment of the error due to unresolved scales in sequential data-assimilation. International Journal of Bifurcation and Chaos, 21, 3619-3626, 2011.
  • Carrassi A and S. Vannitsem. State and parameter estimation with extended Kalman Filter. An alternative formulation of the model error dynamics. Q. J. Royal Met. Soc., 137, 435-451, 2011.
  • Ghil, M., P. Yiou, S. Hallegate, B.D. Malamud, P. Naveau, A. Soloviev, P. Friederichs, V. Keilis-Borok, D. Kondrashov, V. Kossobokov, O. Mestre, C. Nicolis, H.W. Rust, P. Shebalin, M. Vrac, A. Witt, I. Zaliapin 2011. Extreme events: dynamics, statistics and Prediction, Nonlin. Processes Geophys. 18, 295-350, doi:10.5194/npg-18-296-2011. 
  • Nicolis G. and S. Vannitsem. Foreword of the Special Issue ‘The complexity paradigm : Understanding the dynamics of weather and Climate’. International Journal of Bifurcation and Chaos, 21, 3387-3388, 2011.
  • Van Schaeybroeck B and S. Vannitsem, Post-processing through linear regression. Nonlinear Processes in Geophysics, 18, 147-160, 2011.
  • Vannitsem S., Bias correction and post-processing under climate change, Nonlinear Processes in Geophysics, 18, 911-924, 2011.
  • Vannitsem S. and R Hagedorn, Ensemble forecast post-processing over Belgium : Comparison of deterministic-like and ensemble regression methods. Meteorol. Appl., 18, 94-104, 2011.


  • Carrassi A and S. Vannitsem, Model error and variational data assimilation. A deterministic formulation. Mon. Wea. Rev., 138, 3369-3386, 2010.
  • Nicolis C., 2010. Stochastic resonance in multistable systems: the role of intermediate states, Phys. Rev. E82, 011139.
  • Nicolis C., and G. Nicolis 2010. Stability, complexity and the maximum dissipation conjecture, Q.J.R.Meteorol. Soc., 136, 1161-1169.
  • Van de Vyver H., and C. Nicolis 2010. Probabilistic properties of ranges of sums in dynamical systems, Phys. Rev. E82, 031107.    


  • Carrassi A., S. Vannitsem, D. Zupanski and M. Zupanski, 2009, The maximum likelihood ensemble filter performances in chaotic systems. Tellus A, 61, 587-600, 2009.
  • Nicolis C., and G. Nicolis 2009. The butterfly effect, Scholarpedia 4(5), 1720.
  • Nicolis C., and S.C. Nicolis 2009. Propagation of extremes in space, Phys. Rev. E80, 026201.
  • Nicolis G., and C. Nicolis 2009. Foundations of complex systems, European Review, 17, 237-248.
  • Nicolis C. and G. Nicolis 2009. Memory effects in recurrent and extreme events, Phys. Rev. E80, 061119.   
  • Nicolis, C., R. Perdigao and S. Vannitsem, Dynamics of prediction errors under the combined effect of initial condition and model errors. J. Atmos. Sci., 66, 766-778, 2009.
  • Vannitsem, S., A unified Linear Model Output Statistics scheme for both deterministic and ensemble forecasts. Quart. J. Roy. Met. Soc., 135, 1801-1815, 2009.


  • Carrassi, A., M. Ghil, A. Trevisan and F. Uboldi, 2008: Data assimilation as a nonlinear dynamical sysem problem: Stability and convergence of the prediction-assimilation system.
    Chaos, 18, 023112.
  • Carrassi, A., A. Trevisan, L. Descamps, O. Talagrand and F. Uboldi, 2008: Controlling instabilities along a 3DVar analysis cycle by assimilating in the unstable subspace: a comparison with the EnKF. Nonlinear Processes in Geophysics, 15, 503-521.
  • Carrassi, A., S. Vannitsem and C. Nicolis, 2008: Model error and sequential data assimilation: A deterministic formulation. Quart. J. Royal Meteorol. Soc., 134, 1297-1313.
  • Nicolis, G., V. Balakrishnan and C. Nicolis, 2008: Probabilistic aspects of extreme events generated by periodic and quasi-periodic deterministic dynamics. Stochastics and Dynamics, 8, 115-125.
  • Nicolis, C. and G. Nicolis, 2008: Irreversible thermodynamics of multi-step transitions. Phys. Rev. E, 77, 051101.
  • Vannitsem, S., 2008: Dynamical properties of MOS forecasts. Analysis of the ECMWF operational forecasting system. Wea. Forecasting, 23, 1034-1043.
  • Vannitsem S. et C. Nicolis, 2008: Dynamical properties of Model Output Statistics forecasts. Mon. Wea. Rev., 136, 405-419.


  • Kozak, J., C. Nicolis and G. Nicolis 2007. Modeling the early stages of self-assembly in nanophase materials, J. Chem. Phys., 126, 154701(8).
  • Nicolis, C. 2007. Dynamics of model error : the role of the boundary conditions, J. Atmos. Sci., 64, 204-215.
  • Nicolis, C. and G. Nicolis, 2007. Dynamics of switching in nonlinear kinetics, J. Phys.:Condens. Matter 19, 065131(13).
  • Nicolis C. and G. Nicolis 2007: Stochastic resonance, Scholarpedia,, p. 26389. 
  • Nicolis, C. and S. C. Nicolis 2007. Return time statistics of extreme events in deterministic dynamical systems, Europhys. Lett, 80, 40003-1-6. 
  • Nicolis G. and C. Nicolis 2007: Complex systems, Scholarpedia,, p. 25053. 
  • Vannitsem, S. 2007. Statistical properties of the temperature maxima in an intermediate order Quasi-Geostrophic model, Tellus, 59, 80-95.
  • Vannitsem S. et P. Naveau, 2007: Spatial dependences among precipitation maxima over Belgium. Nonlin. Proc. Geophys., 14, 621-630.


  • Nicolis, C., V. Balakrishnan and G. Nicolis 2006. Extreme events in deterministic dynamical systems, Phys. Rev. Lett. 97, 210602(4).
  • Vannitsem, S. 2006. The role of scales in the dynamics of parameterization uncertainties, J. Atmos. Sci, 63, 1659-1671


  • Nicolis, G. and C. Nicolis, 2005. Kinetics of phase transitions in the presence of an intermediate state : a generic model, Physica A, 351, 22-29.
  • Nicolis, C. 2005. Can error source terms in forecasting models be represented as Gaussian Morkov noises? Q. J. R. Meteorol. Soc., 131, 2151-2170. 
  • Nicolis, G. A. Garcia Cantu and C. Nicolis 2005. Dynamical aspects of interaction networks, Bifurcation and Chaos, 15, 3467-3480.
  • Nicolis, C. and G. Nicolis 2005. Stochastic resonance in the presence of slowly varying control parameters, New J. Phys, 7, 1-14.
  • Roulin, E. and S. Vannitsem 2005. Skill of medium range hydrological ensemble prediction, J. Hydromet., 6, 729-744.
  • Vannitsem, S. and F. Chomé, 2005. One-way nested regional climate simulations and domain size. J. Clim., 18, 229-233.


  • Nicolis, G., V. Basios and C. Nicolis, C. 2004. Pattern formation and fluctuation-induced transitions in protein crystallization, J. Chem. Phys., 120, 7708-7719.
  • Nicolis, C. 2004. Dynamics of model error : the role of unresolved scales revisited, J. Atmos. Sci., 61, 1740-1753.
  • Nicolis, C. and G. Nicolis 2004. Noisy limit point bifurcation with a slowly increasing parameter, Europhys. Lett., 66, 185-191.

National journals or proceedings with peer review


  • A. Carrassi and S. Vannitsem. Accounting for model error in data assimilation Workshop “Mathematical and Algorithmic Aspects of Atmosphere-Ocean Data Assimilation”, DOI: 10.4171/OWR/2012/58, Mathematisches Forschungsinstitut Oberwolfach, 21-22, 2012. pdf
  • B Van Schaeybroeck and S. Vannitsem. Toward post-processing of ensemble forecasts based on hindcasts. Publications scientifiques et techniques, N° 61, IRM, 2012. pdf

Other proceedings of interest

Seleshi, Y., Demaree, G., & Vannitsem, S. (1992, July). Statistical analysis of long-term monthly and annual Ethiopian precipitation series and their relationship with ENSO events. In Proc. International Workshop on Climate Variabilities (pp. 80-92).pdf


Special issues

Z. Toth, O. Talagrand, and S. Vannitsem (Eds.), Quantifying predictability. Nonlinear Processes in Geophysics, Special issue, 2005,link

2. Z. Toth, O. Talagrand, S. Vannitsem and G. Balint (Eds.), Predictability in Earth Sciences. Nonlinear Processes in Geophysics, Special issue, 2008,link

3. G. Nicolis et S. Vannitsem (Eds). ‘The complexity paradigm : Understanding the dynamics of weather and Climate’. International Journal of Bifurcation and Chaos, Special Issue, 21, issue 12,