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: [email protected]
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