CHAPTER 3 GLOBAL MODELS OF MEAN SEA SURFACE AND GRAVITY
3.5 Computation and Analysis of Global Gravity Anomaly Model
To evaluate the accuracy of the NCTU01 gravity grid, we made comparison between the predicted and shipborne gravity anomalies in 12 areas in the world oceans (see Table 3.1 for the boundaries). These shipborne gravity data are from the National Geophysical Data Center. The corresponding ship tracks are shown in Figure 3.4. The 12 areas are so selected that deep and shallow waters, and low and high latitudes are covered in the comparison. The comparing procedure and the adjustment of shipborne gravity data were detailed in Hwang et al. (1998). Briefly, long wavelength biases in the shipborne gravity anomalies were first adjusted using altimetry-derived gravity anomalies. A pointwise comparison was then made for the adjusted shipborne gravity anomalies. Table 3.4 shows the result of the comparison.
In Table 3.4, the gravity grid from Hwang et al. (1998) is also compared. It has been shown that the gravity grid of Hwang et al. (1998) has a better accuracy than that of Sandwell and Smith’s (1997). As shown in Table 3.4, the accuracy of the current gravity grid has indeed improved over the gravity grid of Hwang et al. (1998). The improvement is most dramatic in the deep oceans such as the East Pacific Rise. In the Caribbean Sea, the improvement is also significant. Other areas with significant improvements are the Ross Sea and Kerguelen Plateau, which are situated in the Antarctica. In general, large difference between predicted and shipborne gravity anomalies may be due to either or both of the following reasons: (1) bad altimeter data quality, including data scarcity, and (2) large gravity signatures, for example, in areas with trenches and seamounts. The largest difference in the Fiji Plateau and then the Mediterranean Sea should be attributed to the first reason. Due to possibly bad
tide correction and contamination of altimeter waveforms by land mass and reefs, the predicted gravity anomalies in the Fiji Plateau are not expected to be in good quality.
A recent detailed analysis of errors in altimeter-derived gravity anomalies is given by Trimmer et al. (2001). To have a dramatic improvement of gravity accuracy in such an area, a better tide model and improved determination of SSH by retracking altimeter waveforms will be needed. Improved SSHs by wave retracking have been reported in, e.g., Anzenhofer and Shum (2001), Deng et al. (2001), and Fairhead and Green (2001).
Figure 3.4: Distributions of shipborne gravity anomalies in the 12 areas where the NCTU01 gravity anomaly grid is evaluated.
Table 3.4: RMS differences (in mgal) between predicted and shipborne gravity anomalies in 12 areas
Comparison area This work Hwang et al. (1998) Improvement
(1) Alaska Abyssal 4.887 5.168 0.281
(2) East Pacific Rise 3.057 6.786 3.729
(3) Caribbean Sea 9.840 11.399 1.559
(4) Reykjanes Ridge 5.122 5.202 0.080 (5) Sierra Leone Basin 3.678 3.688 0.010 (6) Mediterranean Sea 13.026 13.480 0.454 (7) Carlsberg Ridge 7.347 7.397 0.023 (8) Kerguelen Plateau 6.017 6.931 0.914 (9) South China Sea 8.004 8.229 0.225 (10) Mariana Trench 11.561 11.814 0.253 (11) Fiji Plateau 13.365 14.148 0.783
(12) Ross Sea 7.634 8.477 0.843
CHAPTER 4
SHALLOW-WATER ALTIMETRY GRAVITY RECOVERY: DATA PROCESSING AND
COMPARISON OF METHODS
4.1 Introduction
Satellite altimetry can be useful in coastal area, such as coastal geoid modeling and offshore geophysical explorations, see, e.g., Hwang (1997), Andersen and Knudsen (2000). Recent global altimeter-derived gravity anomaly grids by, e.g., Sandwell and Smith (1997), Andersen et al. (2001), and Hwang et al. (2002), confirm that the accuracies of estimated gravity anomalies range from 3 to 14 mgals, depending on gravity roughness, data quality and areas of comparison. These papers made their comparisons with shipborne gravity anomalies mostly in the open oceans.
Research has shown that over shallow waters, altimeter data are prone to measurement errors and errors in geophysical corrections. For example, Deng et al.
(2002) shows that within about 10 km to the coastlines, altimeter waveforms are not what the onboard tracker has expected and use of ocean mode product altimetry leads to error in range measurement. The footprint of a radiometer is also large enough to make the water vapor contents measurement near shores highly inaccurate, yielding bad wet tropospheric corrections. Large tide model errors and large wave heights, among others, add to the problem of poor quality in altimeter data over shallow waters. Worst still, there is no data on land for near-shore gravity computation and this
(for example, transforming gravity anomaly to geoid requires global integration).
Thus, gravity anomaly prediction over shallow waters has been a challenging task, due mainly to problems with both data and theory. In view of these problems, this chapter compares two methods of gravity computation from altimetry discussed in (2.3.1) and (2.3.2), and a method of removing outliers in altimeter data based on a nonlinear filter is also discussed. The test area is over shallow waters in Taiwan Strait and East China sea. Figure 4.1 shows the bathymetry based on the ETOPO5 depth grid. The water west of Taiwan is a part of the east Asia continental shelf with depths less than 200 meters, while the waters east of Taiwan is deep due to the subducting Philippine Sea Plate.
4.2 Data Processing：Outlier Detection and Filtering
Outliers which are anomalous measurements in data will create a damaging result. There are methods abundant in literature for removing outliers in one-dimensional time series, see, e.g., Kaiser (1999), Gomez et al. (1999) and Pearson (2002). In this chapter we use an iterative method to remove outliers in along-track altimeter data. Consider the measured height or the differenced height as a time series with along-track distance as the independent variable. First, a filtered time series is obtained by convolving the original time series with the Gaussian function
2
where σ is the 1/6 of the given window size of convolution. The definition of Gaussian function is the same as that used in GMT (Wessel and Smith, 1995). For all data points the differences between the raw and filtered values are computed, and the
Figure 4.1: Contours of slected depths around Taiwan, unit is meter
standard deviation of the differences is found. The largest difference that also exceeds three times of the standard deviation is considered an outlier and the corresponding data value is removed from the time series. The cleaned time series is filtered again and the new differences are examined against the new standard deviation to remove a possible outlier. This process stops when no outlier is found.
We choose pass d64 of Geosat/ERM, which travels across Taiwan, to be used for the test of outliers detection. Figure 4.2 shows the ground track of pass d64 and Figure 4.3 shows the result of outlier removing. In Figure 4.3, we clearly see that erroneous differenced heights are successfully removed (discrete points) after outlier
ERS-1/gm and Geosat/gm, we do outlier detection as well as filtering for the differenced heights with a 14-km wavelength in order to reduce the data noise. There is no need of filtering for the differenced heights from the repeat missions because their data noises will be reduced due to time averaging. As an example, we choose pass a27 of Geosat/GM for testing outlier removal and filtering. Figure 4.4 shows the ground pass a27 and Figure 4.5 shows the result. Again, our algorithm removes outliers and filter the data successfully.
Furthermore, Figure 4.6 and 4.7 show the result of outlier detection along Tracks d0222 and a3083 of Geosat/GM. Both tracks pass through Peng-Hu Island in the Taiwan Strait, where most of the outliers occur and the differenced heights contain large variation. These examples from the Geosat altimeter show that differenced height is very sensitive to sudden change of height, and is particularly useful for outlier detection in the above iterative method.
We also tested this outlier detection method using altimeter data from the repeat and non-repeat missions in the East China Sea area. The altimeter data type used is also differenced height. It turns out outliers in differenced heights are very sensitive to this method, especially when along-track SSHs experience an abrupt change. A spike of SSH will translate into two large height differences. As an example, Figure 4.9 shows the result of outlier detection along two tracks of Geosat/ERM. In this case, the outliers are removed using a 28-km window size to generate the filtered time series.
Another test was carried out using data from a non-repeat mission--Geosat/GM.
Figure 4.11 shows the result of the test along two tracks of Geosat/GM. In this case, we used an 18-km window size. According to our experiments, different window sizes
for outlier detection should be used for altimeter data from different missions. Based on numerous tests, in this chapter we adopt 28 km as the optimal window sizes for the repeat missions, and 18km and 14km for non-repeat missions, respectively, over the ECS and the TS.
Figure 4.2: The ground track of pass d64 of Geosat/ERM
Figure 4.3: Raw data points (red) and outliers (blue) detected with a 28-km window for pass d64 of Geosat/ERM.
Figure 4.4: The ground track of pass a27 of Geosat/GM
Figure 4.5: Raw data points (blue) and filtered and outlier-free points (red) using a 14-km window for pass a27 of Geosat/gm.
Figure 4.6: The ground tracks of Geosat/GM d0222 and a3083
Figure 4.7: Differenced heights for passes a3083 and d0222 of Geosat/gm, crosses represent outliers.
Figure 4.8: Ascending and descending passes of Geosat/ERM for outlier detection.
Figure 4.9: Results with a 28-km window size. Outliers are not connected by the lines.
Figure 4.10: Ascending and descending passes of Geosat/GM for outlier detection.
Figure 4.11: Results with a 18-km window size. Outliers are not connected by the lines.
4.3 Results of Tests
We use multi-satellite altimeter data mentioned in chapter 2 for testing two methods (by using three kinds of altimeter data types). These data have different noise levels, which work as weights in LSC computations. In all computations, the standard remove-restore procedure is employed. In this procedure, the long wavelength part of altimeter-derived data (differenced height, height slope or DOV) implied by the EMG96 geopotential model (Lemoine et al. 1998) to degree 360 is removed. With the residual data, the residual gravity anomaly is computed and finally the gravity anomaly implied by the EMG96 model is restored. The needed isotropic covariance functions are computed using the error covariance of EGM96 and the Tscherning/Rapp Model 4 signal covariance (Tscherning and Rapp, 1974). All needed covariance functions are tabulated at an interval at of 0.01°. The local covariance values in a prediction window are scaled by the ratio between the data variance and the global variance.
For the gravity grids from methods 1 and 2, a further filtering be 2 2-D median filter improved the result. Table 4.1 and 4.2 shows the results of such filtering. Based on the testing result for method 2 in Table 4.1 and for method 1 in Table 4.2, we decide to use 16 km as the filter parameters in Taiwan Strait and to use 20 km as the filter parameters in East China Sea.
To evaluate the accuracy of the gravity anomalies derived from three different methods mentioned, we made comparisons between the predicted and shipborne anomalies in the Taiwan Strait and the East China Sea area. The shipborne gravity anomaly data in Taiwan are from Hsu et al. (1998) and that in the East China Sea are
Table 4.1: RMS differences (in mgals) between predicted and shipborne gravity anomalies using different filter parameters over the Taiwan Strait.
Filter parameter RMS
No filter 11.2687
Filter wavelength = 8 km 10.8739 Filter wavelength = 16 km 10.4353 Filter wavelength = 24 km 10.5682
Table 4.2: RMS differences (in mgals) between predicted and shipborne gravity anomalies using different filter parameters over the East China Sea.
Filter parameter RMS
No filter 10.80
Filter wavelength = 10 km 10.01 Filter wavelength = 16 km 9.82 Filter wavelength = 18 km 9.76 Filter wavelength = 20 km 9.59 Filter wavelength = 22 km 9.61 Filter wavelength = 24 km 9.64
comparison was made for both of them. The ship tracks are shown in Figure 4.12 and Figure 4.13. Table 4.3 and Table 4.4 show the result of the comparisons in TS and in ECS. The conclusions we get from the two tables are similar and the only difference is that the inverse Vening Meinesz method with DOV produces the worst result in Table 4.3 The gravity grid from method 1 has a better accuracy than those from the other two methods in the two area. The least square collocation with slope height gives results which are very close to but a little bit worse than use of differenced height as data type in method 1. By using of least square collocation with differenced height, the RMS differences between the predicted and shipborne gravity anomalies lower 1.67 mgal and 2.27 mgal comparing to method 3 (Hwang et al., 2002) in TS and ECS respectively.
Figure 4.12: Distribution of shipborne gravity data in Taiwan Strait area.
Figure 4.13: Distribution of shipborne gravity data in the East China Sea.
Table 4.3: Statistics of differences (in mgals) between altimeter-derived and shipborne gravity anomalies
Method (data type) RMS (1) LSC (differenced height) 9.06 (1) LSC (height slope) 10.26
(1) LSC (DOV) 10.44
(2) inverse Vening Meinesz (DOV) 10.73
Table 4.4: Statistics of differences (in mgals) between altimeter-derived and shipborne gravity anomalies in the East China Sea.
Method (data type) RMS
(1) LSC (differenced height) 9.59
(1) LSC (height slope) 9.77
(1) LSC (DOV) 13.10
(2) inverse Vening Meinesz (DOV) 11.86
CHAPTER 5
GRAVITY ANOMALY OVER EAST CHINA SEA AND TAIWAN STRAIT: CASE STUDY AND
ANALYSIS
5.1 Introduction
Over shallow waters Satellite altimetry has been very useful in earth sciences, see, e.g., Fu and Cazenave (2001) and Hwang et al. (2004a). One example of geodetic application is coastal gravity field modeling: both coastal altimetry data and terrestrial gravity anomalies were got together to determine gravity field model that are far better than the existing models that only used terrestrial gravity data (Li and Sideris, 1997; Andersen and Knudsen, 2000). Furthermore, the potential of satellite altimetry to help to learn about sea surface topography have been tested in Hipkin (2000). Sea surfacetopography is the essential parameter for a world vertical datum (Rapp and Balasubramania, 1992). For oceanographic applications, shallow-water altimetry has been used to derive M-2 internal tides (Niwa and Hibiya, 2004) and variations of surface circulations (Yanagi et al., 1997). There are other examples of geophysical applications of altimetry in the literature; we refer to Cazenave and Royer (2001) for a review.
Altimeter-gravity conversion is one of the most important parts in the geodetic and geophysical applications of satellite altimetry. Currently, the achieved accuracies of altimeter-derived gravity anomalies vary from one oceanic region to another,
depending on gravity roughness, altimeter data quality and density (Sandwell and Smith, 1997; Hwang et al., 2002; and Andersen et al., 2005). Accuracy analyses associated with global gravity anomaly grids were mostly made over the open oceans.
However, altimeter data quality over shallow waters can be seriously degraded because of (1) bad tidal correction, (2) bad wet tropospheric correction because of corruption in radiometer measurements, (3) large sea surface variability and (4) contaminated altimeter waveforms (Deng et al., 2003). Inferior or erroneous altimeter data will lead to gravity anomalies containing artifacts and in turn false interpretations of the underlying geophysical phenomena.
The East China Sea and the Taiwan Strait are two typical shallow-water areas which are defined as waters with a depth less than 500 meters. In these areas the gravity fields are relatively smooth, but large gravity variations occur over regions with thick sediments, structural highs and at the margin of the continental shelf.
Figure 5.1 shows the bathymetry in the ECS and the TS.
Over the ECS, one publicly accessible database of shipborne gravity data can be found at the National Geophysical Data Center (NGDC) (http://www.ngdc.noaa.gov), and the data are sparsely distributed. In the TS, the shipborne gravity data were mostly collected by research ships studying marine geophysics around Taiwan.
Global altimeter-derived gravity anomaly grids have been important sources of gravity anomalies in these areas.
The purposes of this chapter is to (1) compare global gravity models and tide models over ECS and TS to analyze the errors in altimeter-gravity conversion over shallow waters, and to detect outliers. (2) perform case studies and analysis using shipborne gravity data over the ECS and the TS. (3) to demonstrate how we can
improve the accuracy of altimeter-derived gravity anomaly by using land data.
Figure 5.1: Bathymetry (dashed lines) in the East China Sea and Taiwan Strait. Lines represent shipborne gravity data for comparison with altimeter-derived gravity anomalies.
5.2 Comparison of Two Global Gravity Anomaly Grids over ECS and TS
To show the problems of the altimeter-gravity conversion over shallow waters, we compare two global, altimeter-derived gravity anomaly grids over the ECS and the TS. The two grids were computed by Sandwell and Smith (1997), Andersen et al.
(2005), which are designated as SS02 and KMS02, respectively. The differences over areas of various depths are summarized in Table 5.1. Table 5.1 shows no clear correlation between depth and gravity anomaly difference at depths less than 500 meters, but in general the differences at depths greater than 500 meters are smaller than other areas. Since some of the systematic errors may be eliminated when differencing any two grids, the true errors in the gravity anomaly grids may be actually larger than what have been shown in Table 5.1. Figure 5.2 shows the distribution of the differences. As expected, large differences occur over the waters off the coasts of China, Japan, Korea, and the Ryukyu Island Arc. Note that large differences exist over almost the entire TS. Furthermore, the areas distant from the coasts also contain large differences, e.g., a spot off the east coast of China centering at about latitude= 28°N and longitude = 124°E.
Table 5.1: Statistics of the differences between the SS02 and KMS02 global gravity anomaly grids over the area 118°−130°E ,22°−35°N
Depth (m) 0-100 100-200 200-500 > 500
Mean (mgal) 0.27 0.05 0.56 0.12
RMS (mgal) 4.96 4.06 5.65 4.21
No. of points 50491 14964 7426 39450
Figure 5.2: Differences between the SS02 and KMS02 global gravity anomaly grids.
In order to see the possible causes of the differences, we investigate the qualities of SSHs and two selected tide models here. Figure 5.3 shows the standard deviations of mean SSHs from the Geosat/ERM, ERS-1/35day and ERS-2/35day repeat missions.
Here a standard deviation of SSH is the result of SSH measurement error and SSH variability. The standard deviations of Geosat/ERM SSHs are relatively small because
used in averaging ERS-1 and ERS-2 repeat SSHs. The pattern of ERS-1 standard deviations resembles that of ERS-2 standard deviations. In general, standard deviation of SSH increases with decreasing depth. As seen in Figures 5.2 and 5.3, gravity anomaly difference is highly correlated with standard deviation of SSH. In general, gravity anomaly difference (absolute value) increases with standard deviation of SSH.
Figure 5.3: Standard deviations of sea surface heights from the Geosat/ERM, ERS-1/35 day and ERS-2/35 day repeat missions.
Figure 5.4 shows the tidal height differences at a selected epoch from the NAO tide model (Mastsumoto et al., 2000) and the CSR4.0 tide model (Eanes, 1999). Again, large tidal height differences occur in the same places where large standard deviations of SSHs (Figure 5.3) and large gravity anomaly differences (Figure 5.2) occur, showing these three quantities are geographically correlated. Figure 5.5 shows the normalized values of depths, standard deviations of ERS-1 SSHs, tidal height differences (CSR4.0 vs. NAO 99) along Tracks 1 and 2 (Figure 5.1). A normalized value, y, is obtained by
x
x y x
σ
= − (5.1)
where x is the raw value, x is the mean value, σxis the standard deviation of the time series. As seen in Figure 5.5, the standard deviation of ERS-1 SSH and the tidal height difference along Tracks 1 and 2 have a correlation coefficient of 0.9, and both increase with decreasing depth. The NAO and CSR4.0 tide models are derived from the TOPEX/Poseidon (T/P) altimeter data. Over areas with bad T/P SSHs, mostly caused by bad range measurements and bad geophysical corrections, both of these tide models will produce inaccurate tidal heights. Also, by neglecting shallow-water tidal areas in the tide models creates additional errors. Those areas with large differences in Figure 5.4 are just where NAO and CSR4.0 produce inaccurate tidal heights. By using of these inaccurate tidal heights to correct for the tidal effects in altimeter data will inevitably lead to have poorer quality of SSHs, and creates large standard deviations seen in Figure 5.3.
Figure 5.4: Differences between the NAO and CSR4.0 tidal heights at a selected epoch.
Figure 5.5a: Time series of normalized standard deviation of ERS-1 SSH, tide height difference and depth, along Track 1.
Figure 5.5b: Time series of normalized standard deviation of ERS-1 SSH, tide height difference and depth, along Track 2.
According to Jan et al. (2004) and Lefevre et al. (2000), ocean tides over ECS and TS are complex with high-frequency spatial variations in tidal amplitude and
According to Jan et al. (2004) and Lefevre et al. (2000), ocean tides over ECS and TS are complex with high-frequency spatial variations in tidal amplitude and