Construction of embedding for empirical prognostic models of climate

Abstract:

Empirical approach to modeling and forecasting complex dynamical systems becomes more and more popular in climate science because of two reasons: (i) not confidence reproducing and forecasting some of key climate modes by existing global climate models, and (ii) increasing number and duration of climatic time series which can be considered as a source of information about dynamical laws underlying observational variability. Such an approach is aimed to construction of prognostic models by way of direct analysis of data without involving any detailed physical equations. We developed a method for empirical modeling basing on reconstruction of prognostic evolution operator in a form of random dynamical system [1] – stochastic mapping the current state of the system to the next one. The most crucial point in application of the method to the analysis of real climatic data is the construction of proper embedding: the optimal set of variables – “principal modes” – determining the phase space the model works in. This task is non-trivial due to huge dimension of time series of typical space-distributed climatic fields. We outline two main features these modes should have to capture the main dynamical properties of the system: (i) capturing teleconnections in the atmosphere-ocean system by taking into account time-lagged couplings in data and (ii) reflecting the nonlinear interactions between the time series at different grid points. In this report we present the methodology of empirical forecasting which includes the construction of an embedding on the basis of the above principals: multichannel singular spectrum analysis (MSSA) together with nonlinear principal component analysis (NPCA) are used for phase space construction from data. The proposed methodology is applied to the analysis of sea surface temperature and atmospheric pressure fields. Capabilities to predict various indices of climate (such as SOI, PDO, NAO, NTA, etc.) is demonstrated.

This research was supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with Institute of Applied Physics RAS)

1. Molkov, Y. I., Loskutov, E. M., Mukhin, D. N. & Feigin, A. M. Random dynamical models from time series. Phys. Rev. E 85, 036216 (2012)