Multilevel Regression Modeling of Nonlinear Processes: Derivation and Applications to Climatic Variability

By Sergey Kravtsov, D. Kondrashov, Michael Ghil. 2005

154 citations recorded by the source corpus.

Subfields: Applied Mathematics, Artificial Intelligence, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/567ce8a96ad04a18159abded6a6af44d9386f2cf

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Citations in the corpus

FUNDAMENTAL LIMITATIONS OF AD HOC LINEAR AND QUADRATIC MULTI-LEVEL REGRESSION MODELS FOR PHYSICAL SYSTEMS (2012, unknown): “One disadvantage of the approach is that a huge number of non-unique coefficients need to be measured by the least squares procedure, of order 10(3) for fifteen variables with three levels [15].”
A mathematical theory of climate sensitivity or, How to deal with both anthropogenic forcing and natural variability? (2015, methodology): “EMR models based on this approach have proven to be particularly skillful at capturing and simulating the power spectrum of higher-order models, as well as their PDF in the phase space of the leading empirical orthogonal functions (Kravtsov et al., 2005).”
Data-driven non-Markovian closure models (2014, methodology): “Nevertheless, the considerations in this subsection demonstrate the intuitive relevance of the multilevel structure inherent in the EMR methodology — albeit initially designed from a different perspective [18, 26] — for the derivation of closure models from a multivariate time series of partial obse”
Reconciling Non-Gaussian Climate Statistics with Linear Dynamics (2009, background): “Some role for deterministic nonlinear dynamics has also been argued, for instance, in tropical SST variability (e.g., Penland and Sardeshmukh 1995; Monahan and Dai 2004; An and Jin 2004), extratropical atmospheric circulation variability (e.g., Kravtsov et al. 2005; Kondrashov et al. 2006; Newman ”
Physics constrained nonlinear regression models for time series (2012, methodology): “On the other hand, the ad hoc quadratic regression models proposed in [11] can satisfy linear stability at the origin and still exhibit pathological finite-time blow up of statistical solutions since condition (B) above is not satisfied with general nonlinear quadratic terms (that is, B(x, x) that d”
The physics of climate variability and climate change (2019, methodology): “-called intermediate-range memory. This way relies on a methodology that was developed at rst quite independently of the MZ formalism, namely empirical model reduction (EMR: Kondrashov et al., 2005b; Kravtsov et al., 2005, 2009). b. Empirical model reduction (EMR) methodology. The purpose of EMR dev”