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Spatial-Temporal Parametric Model with Covariance Structure based on Multiple Satellite Altimetry for Predicting and Interpolating Sea Surface Heights in the South China Sea Background The measurement and prediction of the amplitude and phase of ocean tides have been important for commerce and science for thousands of years. In addition to the obvious need to understand the tides for ocean commerce and mitigate their effects on coastal communities, tides also have strong influence on modeling of coastal or continental shelf circulations. Accurate prediction of ocean tides is critical in many contemporary research and applications of interdisciplinary nature, including the study of ocean circulation using radar altimeter measurements, tidal mixing and dissipation associated with ocean heat transport, interpretation of mechanism of Earths wobble and variable rotation, refining the knowledge of tidal perturbation on near-Earth satellites for precision orbit determination, understanding the mechanism of tidal friction and its quantification, study of the dispersive property of the solid Earth and rheology, and study of climate-sensitive signals occurring near known tidal frequencies. Background The measurement and prediction of the amplitude and phase of ocean tides have been important for commerce and science for thousands of years. In addition to the obvious need to understand the tides for ocean commerce and mitigate their effects on coastal communities, tides also have strong influence on modeling of coastal or continental shelf circulations. Accurate prediction of ocean tides is critical in many contemporary research and applications of interdisciplinary nature, including the study of ocean circulation using radar altimeter measurements, tidal mixing and dissipation associated with ocean heat transport, interpretation of mechanism of Earths wobble and variable rotation, refining the knowledge of tidal perturbation on near-Earth satellites for precision orbit determination, understanding the mechanism of tidal friction and its quantification, study of the dispersive property of the solid Earth and rheology, and study of climate-sensitive signals occurring near known tidal frequencies. Aims and Objectives The purpose of this ongoing study is to develop parametric models for the SSH with a covariance structure in order o predict and interpolate the sea surface height anomalies, SSHA, in the South China Sea. Toward this end, the project objectives are: 1.To investigate the statistical properties of the various satellite altimetry data. 2.To construct appropriate spatial and temporal stochastic models for the SSHA 3.To validate the performance of new stochastic models together with the fixed effect models for predicting and interpolating SSH variations in the South China Sea. This poster presents our preliminary findings regarding the first objective. Satellite Altimetry Data The study region (see fig on the right) as been sampled over time by ENVISAT, ERS-1, ERS-2 (red tracks), GFO (green tracks), JASON-1, TOPEX, TOPEX-TTM, (blue tracks). Approximately 5,000,000 measurements were processed. See below the raw JASON SSH measurements. Satellite Altimetry Data The study region (see fig on the right) as been sampled over time by ENVISAT, ERS-1, ERS-2 (red tracks), GFO (green tracks), JASON-1, TOPEX, TOPEX-TTM, (blue tracks). Approximately 5,000,000 measurements were processed. See below the raw JASON SSH measurements. H. Bki Iz Dept. of Land Surveying and Geo-Informatics The Hong Kong Polytechnic Univ., Hong Kong, China. C. K. Shum, H. S. Fok, Y. Yi School of Earth Sciences, The Ohio State University Columbus, Ohio 43210-1308, U.S.A. Regional Properties of SSHA Standard deviations (table below) indicate varying quality of satellite data All SSHA anomalies show the presence of satellite biases as indicated by deviations from zero. SSHA data are significantly left skewed (marked in red on the table) for all satellites, which may be caused by autoregressive heteroscadasticity in the data due to the unmodeled effects. Between Satellite Variations: Two Way ANOVA Even after removing relative satellite biases from the SSHA time series via averaging for each satellite, we still find that the differences in the mean SSHA among different satellites are significant at 5 % significance level over the same grids using two way ANOVA. Given the homogeneity of the SSHA among grids for each satellite, this result indicate that the differences are as a result of satellite specific biases which are not removed by simple averaging over their time series. Between Satellite Variations: Two Way ANOVA Even after removing relative satellite biases from the SSHA time series via averaging for each satellite, we still find that the differences in the mean SSHA among different satellites are significant at 5 % significance level over the same grids using two way ANOVA. Given the homogeneity of the SSHA among grids for each satellite, this result indicate that the differences are as a result of satellite specific biases which are not removed by simple averaging over their time series. Within Grid and Among Grid Variations: One Way ANOVA Satellites generates 3 -7 data points within a quarter degree grid during a pass over the region (left figure below). Hence, 3 7 time series are generated for each grid by a satellite. One way ANOVA results show that the replicated SSHA series within a quarter degree grids are in agreement at 5 % significance level. Similarly, the null-hypothesis: SSHA time series within larger grids are in agreement is also accepted at 5 % significance level (variations in the mean values of the SSHA calculated from ENVISAT measurements are displayed in the figure below). Theses results shows that the SSHA in the South China Sea region is spatially homogeneous. Within Grid and Among Grid Variations: One Way ANOVA Satellites generates 3 -7 data points within a quarter degree grid during a pass over the region (left figure below). Hence, 3 7 time series are generated for each grid by a satellite. One way ANOVA results show that the replicated SSHA series within a quarter degree grids are in agreement at 5 % significance level. Similarly, the null-hypothesis: SSHA time series within larger grids are in agreement is also accepted at 5 % significance level (variations in the mean values of the SSHA calculated from ENVISAT measurements are displayed in the figure below). Theses results shows that the SSHA in the South China Sea region is spatially homogeneous. Conclusions and Upcoming Work SSHA descriptive statistics and ANOVA results demonstrated the presence of non stationary random effect structures in the mean and variance for all the satellite data. Hence, new parametric models are needed for the South China Sea SSH variations with the following three error components with covariance structures: 1.Grid to grid random variations at a given epoch 2.Time dependent autoregressive stochastic effects within a given grid time series. 3.Measurement errors with stochastic properties that vary from satellite-to-satellite. Conclusions and Upcoming Work SSHA descriptive statistics and ANOVA results demonstrated the presence of non stationary random effect structures in the mean and variance for all the satellite data. Hence, new parametric models are needed for the South China Sea SSH variations with the following three error components with covariance structures: 1.Grid to grid random variations at a given epoch 2.Time dependent autoregressive stochastic effects within a given grid time series. 3.Measurement errors with stochastic properties that vary from satellite-to-satellite. Acknowledgement The authors acknowledge the RGC grant B-Q02D by the University Grant Council of Hong Kong, for funding this research. Acknowledgement The authors acknowledge the RGC grant B-Q02D by the University Grant Council of Hong Kong, for funding this research. Sea Surface Height Anomalies The SSHA, SSHA were calculated by removing; variations due to the ocean tides as predicted by NAO99.b model, solid earth tide corrections, atmospheric effects (ionospheric, wet and dry tropospheric corrections), electromagnetic biases, inverted barometer effects, and altimeter-specific corrections. See below for a display of SSHA calculated from JASON data. Email: lshbiz@polyu.edu.hk Autocorrelation Sample variograms, such as left figure, show that SSHA are correlated for all satellite data irrespective of their time separation, which may be induced by unmodeled mean sea level changes. Autocorrelation Sample variograms, such as left figure, show that SSHA are correlated for all satellite data irrespective of their time separation, which may be induced by unmodeled mean sea level changes. H.S. Fok 1, H. Baki Iz 2, C.K. Shum 1, Yuchan Yi 1, Ole Andersen 3, Alexander Braun 4, Yi Chao 5, Guoqi Han 6, C.Y. Kuo 7, Koji Matsumoto 8, Y. Tony Song 5