<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

An Application of Low-Order Arma and Garch Models for Sea Level Fluctuations

Space Research Centre, Polish Academy of Sciences, Poland

Institute of Geography and Regional Development, University of Wrocław, Poland

Environmental Engineering and Land Surveying, University of Agriculture in Kraków, Poland

Artificial Satellites

{"article-title":"An Application of Low-Order Arma and Garch Models for Sea Level Fluctuations"}

The paper presents the analysis of geographically-dependent irregular sea level fluctuations, often referred to as residual terms around deterministic signals,...

An Application of Low-Order Arma and Garch Models for Sea Level Fluctuations

Published Online: Sep 16, 2010

Page range: 27 - 39

DOI: https://doi.org/10.2478/v10018-010-0003-x

Keywords
Sea level modelling, Tropical Instability Waves, TOPEX/Poseidon, Jason-1

This content is open access.

An Application of Low-Order Arma and Garch Models for Sea Level Fluctuations

Published Online: Sep 16, 2010

Page range: 27 - 39

DOI: https://doi.org/10.2478/v10018-010-0003-x

KeywordsSea level modelling, Tropical Instability Waves, TOPEX/Poseidon, Jason-1

This content is open access.

Keywords
Sea level modelling, Tropical Instability Waves, TOPEX/Poseidon, Jason-1