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The interannual variation of tropical Pacific sea surface temperature
(SST) is an important factor in the variability of the global climate
system. The dominant feature of this field is the episodic warming and
cooling of ocean waters with periods of approximately 3-5 years,
namely, the El Nino Southern Oscillation (ENSO) phenomenon. In recent
years, long-lead predictions of tropical Pacific SSTs have improved
greatly in light of better observational networks, analysis schemes,
and understanding of the processes that govern the interaction of the
atmosphere and ocean. Although statistical methods for SST prediction
have performed as well or better than deterministic, physically derived
dynamical methods (Barnston et al., 1999), there is often a perception
in the climate community that much of the potential of statistical
models has been exhausted. Of course, such suggestions refer to a
collection of particular forms of statistical models; our approach is
based on an alternative, Bayesian statistical formulation and prediction
procedure that expresses a variety of qualitative notions and
principles present in the literature regarding SSTs and their
evolution. The Bayesian approach also allows for the quantification of
uncertainty related to our physical understanding and its stochastic
representation. That is, we build a Bayesian Hierarchical Dynamic Spatial Model to
forecast SSTs in the Tropical Pacific Ocean. In all subsequent
discussion, we refer to these models as HiDyn Models.
Our model is "statistical" in that, although it is guided by a
qualitative expression of the physics, no formal physical model is
included. This is not a limitation of the Bayesian approach. See
Royle et al. (1998) and Wikle et al. (2001) for examples of Bayesian
analyses relying on physical models. Indeed, the Bayesian statistical
view does not recognize a strict dichotomy between statistical and
deterministic approaches.
It offers opportunities to incorporate deterministic
models into statistical long-lead SST forecasting, in a fashion that
accounts for a variety of uncertainties. Furthermore, Bayesian
predictions and associated uncertainties are efficient inputs to
decision-making and forecasting the impacts of SST behavior. (See Berger,
1985, and Bernardo and Smith, 1994, for a general discussion of Bayesian
statistics.)
Many of the long-lead statistical prediction schemes for SSTs that
have been used to date have focused on relatively simple linear models
(Barnston et al., 1999). The statistical sciences have undergone a
dramatic change in recent years as computationally based nonlinear
methodologies have been developed and applied in complex settings. In
particular, the hierarchical Bayesian statistical paradigm has
benefited from this revolution. The tropical-Pacific-SST-forecasting
problem provides an exceptional context in which to demonstrate the
long-lead predictive power of, and associated quantification of
uncertainties possible with, a statistical approach based on HiDyn Models.
The HiDyn Model that we have developed forecasts a spatial field of
monthly tropical Pacific SST anomalies at a seven-month lead
time. This lead time was chosen
to demonstrate how the
methodology could be applied to produce operational forecasts at least
six months in advance, with the consideration that time is required to
acquire new data for the new forecast. The methodology can be readily
adapted to different lead times. The mathematical details can be found
in Berliner,
Wikle, and Cressie (2000); key to
the HiDyn Model is incorporation of the following technical features:
- For each time (month) we consider a spectral model for the data,
focusing on a reduced empirical orthogonal function (EOF) basis set.
- We assume that the spectral
coefficients of the model are stochastic and time-varying. That is, they
are assumed to follow a multivariate time-series model.
- The parameters of that time-series model are themselves
time-varying, yielding a methodology that is inherently nonlinear.
Models reflecting warm, normal, and cool regimes are
considered.
- Prognostic variables that indicate possible future transitions
among regimes are modeled as random with probabilities that depend
upon the behavior of surface-wind anomalies in the western Pacific,
which is a qualitative expression of physical processes associated
with tropical Pacific SSTs.
Variabilities inherent in the various processes are included in the HiDyn Model,
and the SST-anomaly forecasts are obtained with these variabilities properly
accounted for. Furthermore, we note that since the HiDyn Model is a desktop
workstation model, achieving even comparable results to deterministic models run
on supercomputers represents a significant advance relative to
computational effort.
As a disclaimer, this HiDyn Model may not give dramatically
superior forecasts to existing ones, but it is the first to
quantify properly the variability in the forecasts. There is much more
that could be done to the present HiDyn Model to improve it, as is noted
throughout the exposition of Berliner, Wikle, and Cressie (2000).
(Based on material presented in Berliner,
Wikle, and Cressie, 2000.)
References:
Barnston, A.G., Glantz, M.H., and He, Y. (1999). Predictive skill of
statistical and dynamical climate models of SST forecasts during the
1997-98 El Nino episode and the 1998 La Nina onset. Bulletin of the
American Meteorological Society, 80, 217-243.
Berger, J.O. (1985). Statistical Decision Theory and Bayesian
Analysis. Springer-Verlag: New York, 617 pp.
Berliner, L.M., Wikle, C.K., and Cressie, N. (2000). Long-Lead Prediction of Pacific SSTs
via Bayesian Dynamic Modeling. Journal of Climate, 13, 3953-3968.
Bernardo, J.M., and Smith, A.F.M. (1994). Bayesian Theory. Wiley:
New York, 586 pp.
Royle, J.A., Berliner, L.M., Wikle, C.K., and Milliff, R. (1998). A
hierarchical spatial model for constructing wind fields from
scatterometer data in the Labrador Sea. Case Studies in Bayesian
Statistics, C. Gatsonis et al. (eds.). Springer-Verlag:
New York, 367-382.
Wikle, C.K., Milliff, R.F., Nychka, D., and Berliner, L.M. (2001).
Spatial-temporal hierarchical Bayesian modeling: Tropical ocean
surface winds. Journal of the American Statistical Association,
96, 382-397.
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