22/11/2005t. niedzielski & w. kosek; coastal governance, planning, design and gi, 21st - 26th...
TRANSCRIPT
FORECASTI NG THE GLOBAL SEA LEVEL VARI ATIONS FROM TOPEX/ POSEIDON SATELLI TE ALTI METRY BY
THE MULTIVARIATE AUTOREGRESSIVE MODELS
Tomasz Niedzielski , Wiesław Kosek a,b a
a
b
Space Research Centre, Polish Academy of Sciences, Bartycka 18A, 00-716 Warsaw, Poland
Department of Geomorphology, I nstitute of Geography and Regional Development, University of Wrocław,
pl. Uniwersytecki 1, 50-137 Wrocław, Poland
22/11/2005 T. NIEDZIELSKI & W. KOSEK; Coastal Governance, Planning, Design and GI, 21st - 26th November 2005, Nice, France
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STRUCTURE OF THE PRESENTATI ON
P O L I S H A C A D E M Y
O F S C I E N C E S
S P A C ER E S E A R C H
C E N T R E
DONE
Niedzielski T., Kosek W., 2005. Multivariate stochastic prediction of the global mean sea level anomalies based on TOPEX/ Poseidon satellite altimetry. Artificial Satellites - J ournal of Planetary Geodesy 40, 185-198.
TO BE DONE
22/11/2005 T. NIEDZIELSKI & W. KOSEK; Coastal Governance, Planning, Design and GI, 21st - 26th November 2005, Nice, France
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• Forecasting sea level anomalies (SLA)» Differences between the best
estimate of the see surface height and the mean sea surface
• Application of the sea surface temperature (SST) as an explanatory variable for SLA predictions
• DataA. SLA – TOPEX/Poseidon satellite altimetry,
monthly (gridded)B. SST – NOAA OI.v2 SST monthly
fields (gridded)
OBJECTIVES, RATI ONALE AND DATA
P O L I S H A C A D E M Y
O F S C I E N C E S
S P A C ER E S E A R C H
C E N T R E
0.40.0
0.4
0.8
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Period (years)
Coh
ere
nce
SLA & SST
Aver
aged
22/11/2005 T. NIEDZIELSKI & W. KOSEK; Coastal Governance, Planning, Design and GI, 21st - 26th November 2005, Nice, France
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METHODS
P O L I S H A C A D E M Y
O F S C I E N C E S
S P A C ER E S E A R C H
C E N T R E
• Multivariate time series techniques– The multivariate time series corresponds to the multivariate stochastic
process
– Transformation of the data to obtain residuals– Modelling residuals using multivariate autoregressive models (MAR)
– Forecasting a MAR process– Forecasting the „real” data
Tkttt XXX )()1( ,...,
EYAYAY ptptt ...11
22/11/2005 T. NIEDZIELSKI & W. KOSEK; Coastal Governance, Planning, Design and GI, 21st - 26th November 2005, Nice, France
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RESULTS AND CONCLUSI ONS
P O L I S H A C A D E M Y
O F S C I E N C E S
S P A C ER E S E A R C H
C E N T R E
• MAR(2) is fitted to the residuals by the Bayes-Schwartz Criterion (SBC)
• MAR(11) is fitted to the residuals by Akaike Information Criterion (AIC)
• The forecasts based upon MAR(11) are more accurate than the predictions based on MAR(2)
• The precision of the bivariate (SLA&SST) MAR-based forecast is better than for the forecast based on univariate autoregressive models of the same order
MARMAR(2) MAR(11)
22/11/2005 T. NIEDZIELSKI & W. KOSEK; Coastal Governance, Planning, Design and GI, 21st - 26th November 2005, Nice, France
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PROJ ECT - AN APPROACH
P O L I S H A C A D E M Y
O F S C I E N C E S
S P A C ER E S E A R C H
C E N T R E
• To perform the similar procedure for each of the available grids
• 10-variate time series
• As a result we yield a set of maps (forecasts) (1-month, 2-month,…)
• Problems:A. Automatic selection of an order of a
MAR process at each locationB. Can we extrapolate the global results
and utilize AIC
SLA( , )SST( , )
i ji j
SLA( +1, )i j
SLA( +1, +1)i j
SLA( +1, 1)i j-
SLA( -1, +1)i j
SLA( -1, 1)i j-
SLA( -1, )i j
SLA( , +1)i j
SLA( , 1)i j-
Source: http://www.cbk.waw.pl/~kosek
22/11/2005 T. NIEDZIELSKI & W. KOSEK; Coastal Governance, Planning, Design and GI, 21st - 26th November 2005, Nice, France
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WHAT MAY WE GAIN?
P O L I S H A C A D E M Y
O F S C I E N C E S
S P A C ER E S E A R C H
C E N T R E
• The project will lead to the answers to the following questions:
– How does the SST influence the SLA forecasts at the dissimilar locations?
– What is the difference between the accuracies of predictions at the dissimilar location?
– How does the vicinity of the land influence the precision of forecasts?– Is it possible to forecast El Nino extreme events?
• The possible outputs for users
– An automatic computer algorithm which generates and updates the SLA forecast for dissimilar locations in the World
– Queries seeking locations at which the SLA predictions fulfill the previously assumed conditions
THANK YOU FOR YOUR ATTENTION
Cross your fingers, please!