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This webpage was designed by Noel Cressie with the assistance of Mark
Irwin. It presents research that began with a project between Cressie
and Christopher Wikle while Wikle was a postdoctoral researcher in
the Geophysical Statistics Project at the National Center for
Atmospheric Research (NCAR). Subsequently, Cressie and Wikle were
joined by Mark Berliner, and the research was funded by the
U.S. EPA - Science to Achieve Results (STAR) Program Grant # R827257-01-0. (Disclaimer: Although
the research described on this webpage has been funded in part
by the U.S. Environmental Protection Agency's STAR program, it
has not been subjected to any EPA review and therefore does not
necessarily reflect the views of the Agency, and no official
endorsement should be inferred.)
Berliner, Wikle, and Cressie (2000) presented a Bayesian dynamic
forecasting model for prediction, with seven-month leads, of the
tropical Pacific (29°S-29°N latitude and 124°E-70°W
longitude) SST monthly anomalies. The model focuses on a statistical
description of the temporal evolution of SST fields, though the
Bayesian hierarchical dynamical approach taken is different from more classical
statistical models of SSTs. Roughly speaking, one regresses future
SST anomaly fields on past ones, as represented via empirical
orthogonal functions. The regression coefficients are modeled as
time-varying and follow a dynamic stochastic model. The Bayesian
approach used seeks to (1) incorporate qualitative understanding of
potential influences on SST evolution; (2) predict the regime status
and regime shifts commonly associated with warmer-than-normal (i.e., "El
Nino"-like), normal, and cooler-than-normal (i.e., "La Nina"-like)
anomalies; and (3) provide both forecast information and quantification
of uncertainty in the forecasts. We refer to the model as a Hierarchical
Dynamic (HiDyn) Model. The authors would like to acknowledge the help
of NCAR scientists (particularly Ralph Milliff and Dennis Shea) as the
HiDyn Model was being developed.
The HiDyn Model uses current values of SST anomalies, the Southern Oscillation
Index (SOI), and a summary of westerly surface-wind bursts as
predictor variables. Rather than viewing the prediction as restricted
to a single model, several statistical prediction models are developed.
These models condition on the current regime state (Warm, Normal, or
Cool), classified according to the current value of SOI, and then
provide probabilistic forecasts of the future regime state (Warm,
Normal, or Cool) seven months
later. The probabilities of the future states are estimated based on
the current SOI and the wind-burst statistic. The HiDyn Model yields
predictive distributions that were computed by using a Markov Chain
Monte Carlo (MCMC) program written by Christopher Wikle. The model was
trained on monthly data beginning in 1970.
The HiDyn-Model output is the predictive distribution for SSTs in the Tropical
Pacific Region, with a seven-month lead. Key summaries of this distribution
include (i) probabilities of each of the three temperature regimes;
(ii) SST mean-field estimates for each temperature regime; (iii) a combined
mean-field estimate (the probability weighted average of the three
fields in (ii)), and (iv) prediction intervals. One of the advantages
of the HiDyn Model is that it allows us to focus easily on selected features of
SSTs. Specifically, forecasts of the Nino 3.4 Region (see map below) can be
easily obtained. In addition to "point forecasts" (e.g., means or
medians) of Nino 3.4 (the average of SST anomalies over all pixels in the Nino 3.4 Region), the predictive distribution can be obtained and
summarized. All these summaries are available on this webpage.
Reference:
L.M. Berliner, C.K. Wikle, and N. Cressie, 2000. Long-Lead Prediction
of Pacific SSTs via Bayesian Dynamic Modeling. Journal of
Climate, 13, 3953-3968.
Tropical Pacific Region of Interest with Nino 3.4 Region Outlined
SST Anomalies:
SST anomalies are defined with respect to a base anomaly period. In
our case, this period was January 1971 through December 2000. For each
pixel, all January months, then all February months, etc are averaged
during this base period, to obtain a set of 12 monthly climatology
estimates for each month of the year. Then
an SST anomaly for March 1999, say, is obtained for each pixel by
subtracting the March climatology estimate from the March-1999 SST
value. All results on this web site are shown in terms of SST
anomalies.
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