1. 1. Kondrashov, D., M. D. Chekroun, X. Yuan, and M. Ghil, 2018:

Data-adaptive Harmonic Decomposition and Stochastic Modeling of Arctic Sea Ice,

In: Tsonis A. (eds) Advances in Nonlinear Geosciences. Springer, doi:10.1007/978-3-319-58895-7_10.

  1. 2.Ghil, M., A. Groth, D. Kondrashov, and A.W. Robertson, 2018:

Extratropical sub-seasonal–to–seasonal oscillations and multiple regimes: The dynamical systems view.,

In The Gap between Weather and Climate Forecasting: Sub-Seasonal to Seasonal Prediction.

A.W . Robertson and F. Vitart (eds), Elsevier.

  1. 3.Chekroun, M. D., and D. Kondrashov, 2017:

Data-adaptive harmonic spectra and multilayer Stuart-Landau models,

Chaos, 27, 093110: doi:10.1063/1.4989400, HAL preprint.

  1. 4.Kondrashov, D., M.D. Chekroun, and M. Ghil, 2015:
    Data-driven non-Markovian closure models,

Physica D, 297, 33-55, doi:10.1016/j.physd.2014.12.005.

  1. 5.Chekroun, M. D., D. Kondrashov and M. Ghil, 2011:

Predicting stochastic systems by noise sampling,
and application to the El Niño-Southern Oscillation

Proc. Nat. Acad. Sciences, 108 (29), 11766–11771, doi: 10.1073/pnas.1015753108.

  1. 6. S. Kravtsov, D. Kondrashov and M. Ghil, 2009:

Empirical Model Reduction and the Modeling Hierarchy in Climate Dynamics,

invited chapter in Stochastic Physics and Climate Modeling,

(T. Palmer and P. Williams, Eds.) Cambridge Univ. Press, pp. 35–72.


  1. Matlab packages:

  2. Multilayer Stochastic Modeling (MSM)

  3. Past-Noise Forecasting (PNF)

  4. Data-adaptive Harmonic Decomposition (DAHD)


Supported by grants ONR-MURI N00014-16-1-2073, NSF OCE-1243175 and OCE-1658357


These tools demonstrate recently developed data-driven nonlinear stochastic-dynamic methods for analysis, modeling and prediction of data from partially-observed systems.  

  1. 1.Several examples of Empirical Model Reduction [Kondrashov et al, 2005, Kravtsov et al. 2009] within a general class of nonlinear Multilayer Stochastic Models (MSM) with memory effects and complex noise structure

   [Kondrashov et al. 2015, Ghil et al. 2018].

2. “Past-noise forecasting” example [Chekroun et al. 2011].

3. Data-adaptive Harmonic Decomposition [Chekroun and Kondrashov, 2017; Kondrashov et al. 2018] example to  identify coherent spatio-temporal modes in a shorty and noisy dataset.