Singular Spectrum Analysis

The analysis of observed -- or numerically generated -- time series is often a prerequisite for progress in modeling and forecasting the physical system of interest. Two complementary approaches attempt to detect regularities in climate time series, via multiple weather regimes or climatic states, on the one hand, and via harmonic or relaxation oscillations, on the other. Multiple planetary flow regimes have been classified via cluster analysis or estimation of the system dynamics' probability density function (pdf) and its maxima. Markov chains between such preferred states and and statistical learning method called random forests have been used for long-range forecasting (LRF) of the atmosphere's LFV.

A team consisting of TCD members and collaborators has developed a technique called Singular-Spectrum Analysis (SSA) which extracts as much reliable information as possible from short, noisy time series without prior knowledge of the dynamics underlying the series. SSA is a form of principal-component analysis applied to lag-correlation structures of uni- and multivariate time series. SSA decomposes a time series by data-adaptive filters into oscillatory, trending, and noise components; generates statistical significance information on these components; and provides reconstructed components. It has been applied to a wide range of data types -- from geophysical to financial -- for a variety of purposes, including forecast of Niño-3 sea surface temperature anomalies that exhibit both regular and irregular behavior.

The SSA-MTM Toolkit is now available for use on computers with X-Windows capabilities.

Emprical Model Reduction (EMR)

Modern climate dynamics uses a two-fisted approach in attacking and solving the
problems of atmospheric and oceanic flows. The two fists are: (i) observational analyses;
and (ii) simulations of the geofluids, including the coupled atmosphere–ocean system, using
a hierarchy of dynamical models. These models represent interactions between many of
processes that act on a broad range of spatial and time scales, from a few kilometers to tens
of thousands, and from diurnal to multi-decadal, respectively. The evolution of virtual
climates simulated by the most detailed and realistic models in the hierarchy is typically as
difficult to interpret as that of the actual climate system, based on the available
observations thereof. Highly simplified models of weather and climate, though, help gain a
deeper understanding of a few isolated processes, as well as clues on how the interaction
between these processes and the rest of the climate system may participate in shaping
climate variability. Finally, models of intermediate complexity, which resolve well a subset
of the climate system and parameterize the remainder of the processes or scales of motion,
serve as a conduit between the models at the two ends of the hierarchy.


We developed a methodology for constructing intermediate models based almost
entirely on the observed evolution of selected climate fields, without reference to dynamical
equations that may govern this evolution; these models parameterize unresolved processes
as multivariate stochastic forcing. This methodology may be applied with equal success to
actual observational data sets, as well as to data sets resulting from a high-end model
simulation. This methodology has benn successfully applied to: (i) observed and
simulated low-frequency variability of atmospheric flows in the Northern Hemisphere; (ii)
observed evolution of tropical sea-surface temperatures; and (iii) observed air–sea
interaction in the Southern Ocean. In each case, the reduced stochastic model represents surprisingly well a
variety of linear and nonlinear statistical properties of the resolved fields. Our
methodology thus provides efficient means of constructing reduced, numerically
inexpensive climate models. These models can be thought of as stochastic–dynamic
prototypes of more complex deterministic models, as in examples (i), but work just
as well in the situation when the actual governing equations are poorly known, as in (ii) and
(iii). These models can serve as competitive prediction tools, as in (ii), or be included as
stochastic parameterizations of certain processes within more complex climate models, as in (iii).

Invited and Contributed Talks

EMR model of ENSO and forecast

Ocean–Atmosphere Interaction over the Southern Ocean:
Satellite Data and Stochastic Models.

TCD Members:
P. Billant, M. Dettinger, M. Ghil, K. Ide, A.W. Robertson,
Y. Tian, D. Kondrashov, P. Yiou, S. Kravtsov.
References:
Allen, M. R., and A. W. Robertson, 1996: Distinguishing modulated oscillations from colored noise in multivariate datasets. Climate Dyn., 12, 775-784.
Dettinger, M. D., M. Ghil, C. M. Strong, W. Weibel and P. Yiou, 1995: Software expedites singular-spectrum analysis of noisy time series, Eos, Trans. AGU, 76, pp. 12, 14, 21.
Dettinger, M. D., M. Ghil and C. L. Keppenne, 1995: Interannual and interdecadal variability in United States surface-air temperatures, 1910-87, Climatic Change, 31, 35-66.
Ghil, M., and R. Vautard, 1991: Interdecadal oscillations and the warming trend in global temperature time series, Nature, 350, 324-327.
Ghil, M., and P. Yiou, 1996: Spectral Methods: What they can and cannot do for climatic time series, Decadal Climate Variability: Dynamics and Predictability, D. Anderson and J. Willebrand (Eds.), Elsevier, pp. 446-482.
Jiang, N., M. Ghil and D. Neelin, 1996: Forecasts of Niño 3 SST anomalies and SOI based on singular spectrum analysis combined with the maximum entropy method. Experimental Long-Lead Forecast Bulletin, Vol. 5, Nos. 2-4. National Meteorological Center, NOAA, U.S. Department of Commerce.
Keppenne, C. L., and M. Ghil, 1992: Adaptive filtering and prediction of the Southern Oscillation index, J. Geophys. Res., 97, 20449-20454.
Keppenne, C. L., and M. Ghil, 1993: Adaptive filtering and prediction of noisy multivariate signals: An application to subannual variability in atmospheric angular momentum, Intl. J. Bifurcation & Chaos, 3, 625-634.
Kravtsov S, Kondrashov D, Ghil M, 2005: 
Multilevel regression modeling of nonlinear processes: Derivation and applications to climatic variability. 
J. Climate, 18 (21): 4404-4424. 
Kondrashov D, Kravtsov S, Robertson AW and Ghil M., 2005: 
A hierarchy of data-based ENSO models .
J. Climate, 18 (21): 4425-4444. 
Penland, C., and M. Ghil, 1993: Forecasting Northern Hemisphere 700-mb geopotential height anomalies using empirical normal modes, Mon. Wea. Rev., 121, 2355-2372.
Penland, C., M. Ghil, and K. M. Weickmann, 1991: Adaptive filtering and maximum entropy spectra, with application to changes in atmospheric angular momentum, J. Geophys. Res., 96, 22659-22671.
Plaut, G., M. Ghil and R. Vautard, 1995: Interannual and interdecadal variability in 335 years of Central England temperatures, Science, 268, 710-713.
Vautard, R., and M. Ghil, 1989: Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series, Physica D, 35, 395-424.
Vautard, R., K. C. Mo, and M. Ghil, 1990: Statistical significance test for transition matrices of atmospheric Markov chains, J. Atmos. Sci., 47, 1926-1931.
Vautard, R., P. Yiou, and M. Ghil, 1992: Singular-spectrum analysis: A toolkit for short, noisy chaotic signals, Physica D, 58, 95-126.