An application of low-order ARMA and GARCH models for sea level fluctuations

• Autorzy: Niedzielski T. , Kosek W.

Identyfikatory

DOI

10.2478/v10018-010-0003-x

• Języki publikacji: EN

Abstrakty

EN

The paper presents the analysis of geographically-dependent irregular sea level fluctuations, often referred to as residual terms around deterministic signals, carried out by means of stochastic low-order autoregressive moving average (ARMA) and generalised autoregressive conditional heteroscedastic (GARCH) models. The gridded sea level anomaly (SLA) time series from TOPEX/Poseidon (T/P) and Jason-1 (J-1) satellite altimetry, commencing on 10th January 1993 and finishing on 14th July 2003, has been examined. The aforementioned models, limited to low-orders being combinations of 0,1 and 2, have been fitted to the SLA data. The root mean square and the Shapiro-Wilk test for the normal distribution have been used to calculate statistics of the residuals from these models. It has been found that autoregressive (AR) models as well as ARMA ones serve well the purpose of adequate modelling irregular sea level fluctuations, with a successful fit in some patchy bits of the equatorial Pacific. In contrast, GARCH models have been shown to be rather inaccurate, specifically in the vicinity of the tropical Pacific, in the North Pacific and in the equatorial Indian Ocean. The pattern of the Tropical Instability Waves (TIWs) has been noticed in the statistics of AR and ARMA model residuals indicating that the dynamics of these waves cannot be captured by the aforementioned linear stochastic processes.

Słowa kluczowe

EN

sea level modelling; Tropical Instability Waves; TOPEX; Poseidon; Jason-1

• Wydawca: Centrum Badań Kosmicznych PAN ; De Gruyter
• Czasopismo: Artificial Satellites : Journal of Planetary Geodesy
• Rocznik: 2010
• Tom: Vol. 45, No. 1
• Strony: 27--39
• Opis fizyczny: Bibliogr. 25 poz., rys., tab.

Twórcy

autor

Niedzielski T.

• Space Research Centre, Polish Academy of Sciences, Poland
• Institute of Geography and Regional Development, University of Wrocław, Poland

autor

Kosek W.

• Space Research Centre, Polish Academy of Sciences, Poland
• Environmental Engineering and Land Surveying, University of Agriculture in Kraków, Poland

Bibliografia

• Ablain M., Cazenave A., Valladeau G., Guinehut S. (2009) A new assessment of the error budget of global mean sea level rate estimated by satellite altimetry over 1993-2008, Ocean Science, Vol. 5, 193-201.
• Barbosa S.M., Silva M.E., Fernandes M.J. (2006) Multivariate autoregressive modelling of sea level time series from TOPEX/Poseidon satellite altimetry, Nonlinear Processes in Geophysics, Vol. 13, 177-184.
• Barbosa S.M., Silva M.E., Fernandes M.J. (2008) Time Series Analysis of Sea-Level Records: Characterising Long-Term Variability, Nonlinear Time Series Analysis in the Geosciences, Lecture Notes in Earth Sciences, Vol. 112, 153-173.
• Beckley B.D., Lemoine F.G., Luthcke S.B., Ray R.D., Zelensky N.P. (2007) A reassessment of global rise and regional mean sea level trends from TOPEX/Poseidon and Jason-1 altimetry based on revised reference frame orbits, Geophysical Research Letters, Vol. 34, L14608, doi:10.1029/2007GL030002.
• Cazenave A., Lombard A., Llovel W. (2008) Present-day sea level rise: A synthesis, Comptes Rendus Geoscience, Vol. 340, 761-770.
• Douglas B.C. (1991) Global sea level rise, Journal of Geophysical Research, Vol. 96, No. C4, 6981-6992.
• Iz H.B. (2006) How do unmodeled systematic mean sea level variations affect long-term sea level trend estimates from tide gauge data? Journal of Geodesy, Vol. 80, 40-46.
• Jevrejeva S., Grinsted A., Moore J.C., Holgate S. (2006) Nonlinear trends and multiyear cycles in sea level records, Journal of Geophysical Research, Vol. 111, C09012, doi:10.1029/2005JC003229.
• Katz E.J., Busalacchi A., Buschnell M., Gonzales F., Gourdeau L., McPhaden M., Picaut J. (1995) A comparison of coincidental time scales of the ocean surface height by satellite altimeter, mooring and inverted echo sounder, Journal of Geophysical Research, Vol. 100, No. C12, 25101-25108.
• Kosek W. (2001) Long-term and short period global sea level changes from TOPEX/Poseidon altimetry, Artificial Satellites, Vol. 36, 71-84.
• Lawrence S.P., Angell J.P. (2000) Evidence for Rossby Wave Control of Tropical Instability Waves in the Pacific Ocean, Geophysical Research Letters, Vol. 27, No. 15, 2257-2260.
• Legeckis R. (1977) Long waves in the eastern equatorial Pacific; A view from a geostationary satellite, Science, Vol. 197, 1177-1181.
• Leuliette E.W., Nerem R.S., Mitchum G.T. (2004) Calibration of TOPEX/Poseidon and Jason altimeter data to construct a continuous record of mean sea level change, Marine Geodesy, Vol. 27, 79-94.
• Liu W.T., Xie X., Polito P.S. Xie S.-P., Hashizume H. (2000) Atmospheric Manifestation of Tropical Instability Wave Observed by QuikSCAT and Tropical Rain Measuring Mission, Geophysical Research Letters, Vol. 27, No. 16, 2545-2548.
• Miller L., Douglas B.C. (2004) Mass and volume contributions to twentieth-century global sea level rise, Nature, Vol. 428, 406-409.
• Niedzielski T., Kosek W. (2005) Multivariate stochastic prediction of the global mean sea level anomalies based on TOPEX/Poseidon satellite altimetry, Artificial Satellites, Vol. 40, 185-198.
• Niedzielski T., Kosek W. (2009) Forecasting sea level anomalies from TOPEX/Poseidon and Jason-1 satellite altimetry, Journal of Geodesy, Vol. 83, 469-476.
• Niedzielski T. (2010) Non-linear sea level variations in the eastern tropical Pacific, Arti- ficial Satellites, Vol. 45, 1-10.
• Niedzielski T., Kosek W. (2010) El Niño’s impact on the probability distribution of sea level anomaly fields, Polish Journal of Environmental Studies, Vol. 19, No. 3, 611-620.
• Pezzi L., Caltabiano A., Challenor P. (2006) Satellite observations of the Pacific tropical instability wave characteristics and their interannual variability, International Journal of Remote Sensing, Vol. 27, No. 8, 1581-1599.
• Philander S.G.H, Hurlin W.J., Pacanowski R.C. (1986) Properties of Long Equatorial Waves in Models of the Seasonal Cycle in the Tropical Atlantic and Pacific Oceans, Journal of Geophysical Research, Vol. 91, No. C12, 14207-14211.
• Raudsepp U., Toompuu A., Kõuts T. (1999) A stochastic model for the sea level in the Estonian coastal area, Journal of Marine Systems, Vol. 22, 69-87.
• Royston P. (1995) A Remark on Algorithm AS 181: The W Test for Normality, Applied Statistics, Vol. 44, 547-551.
• Shapiro S.S., Wilk M.B. (1965) An analysis of variance test for normality (complete samples), Biometrika, Vol. 52, 591-611.
• Wagner C.A., Tai C.K., Kuhn J.M. (1994) Improved ocean tide from TOPEX/POSEIDON and Geosat Altimetry, Journal of Geophysical Research, Vol. 99, No C12, 24853-24865.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).