CHAPTER 4 DATA PROCESSING AND METHODS OF GRAVITY
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 phase. The strong, fast-changing tidal currents over TS also increase the roughness of the sea surface and in turn increase the noise level of altimeter ranging (Sandwell and Smith, 2001). This explains why the tide model error over TS is large throughout the entire area (Figure 5.4). In addition, the monsoonal winds in winter and summer
induce large waves over ECS and TS (Jacobs et al., 2000; Wang, 2004), resulting in a large sea surface variability lasting more than half of a year. Therefore, one would expect that the noise level of altimeter measurements in these two areas is higher than that over a calm sea. In conclusion, inferior altimeter range measurements and inferior geophysical corrections combine to produce inferior SSHs, which in turn result in degraded gravity anomalies. More discussions on the limitations of gravity recovery from altimetry can be found in Sandwell and Smith (2001).
5.3 Coastal Land and Sea Data for Accuracy Enhancement
Altimeter-gravity conversion at the land-sea boundary is an extrapolation process since land altimeter data cannot be used for gravity derivation. At the immediate waters off the coast, there could be no reliable altimeter data due to waveform contamination (Deng et al., 2003). Also, because of depth limitation a large research ship cannot approach closely the coasts, so there are always void zones of shipborne gravity. This deficiency can be improved by using data near the coasts, including gravity anomalies from relative and airborne gravity surveys (Torge, 1989), DOVs from astro-geodetic surveys and geoidal heights from Global Positioning System (GPS) and leveling surveys (Wolf and Ghilani, 2002). A GPS-leveling-derived geoidal height is defined as
H h
N = − (5.2)
where N, h and H are geoidal height, ellipsoidal height and orthometric height, respectively. Due to the need in engineering and mapping applications, geoidal
heights from GPS and leveling in coastal areas could be abundant. In the case of combining altimeter and other data for gravity derivation, it would be difficult to use a FFT-based method even if it is possible (e.g., the input-output system method (Li and Sideris, 1997)). The LSC method outlined in chapter 2 is an efficient method for data combination, only requiring related models of covariance functions. A good weighting scheme for different types of data is essential for obtaining a good result. The usefulness of land gravity data in enhancing the accuracy of altimeter-derived gravity anomaly will be demonstrated in Section 5.5.2.
5.4 Outlier Distribution
The altimeter data we used are from the non-repeat missions ERS-1/GM and Geosat/GM, and the repeat missions Geosat/ERM, ERS-1/35-day, ERS-2/35-day and TOPEX/Poseidon 10-day repeats. Since no reliable estimate of SST is available here, it was set to zero. Neglecting SST here will introduce error at sub-mgal level (Hwang, 1997). For LSC computations, standard errors of the altimeter data are needed. For repeat missions, the standard errors of the altimeter data are derived from repeat observations, while for non-repeat missions, the standard errors are based on empirical values (Hwang et al., 2002). All altimeter data were screened against outliers using differenced heights. Figure 5.6 and 5.7 show the distribution of outliers over ECS and TS all altimeter missions. Outliers can occur anywhere in the oceans.
Table 5.2 and Table 5.3 show the summary of outlier rejection over ECS and TS respectively. The outliers in the open oceans come largely from the non-repeat missions (Geosat/GM and ERS-1/GM). Due to data editing in extracting SSHs from the geophysical data records (GDRs), most of the bad altimeter data in the immediate
vicinity of coasts have already been removed before outlier detection. In general, there is a higher concentration of outliers near the coasts and islands than other areas.
In particular, clusters of outliers were found at the southern Korean coast, the estuary of the Yangtze River and Peng-Hu Island over TS.
Figure 5.6: Distribution of altimeter data outliers in the East China Sea.
Figure 5.7: Distribution of altimeter data outliers in Taiwan Strait.
Table 5.2: Summary of outliers rejection in the East China Sea (119/131/25/35) data No. of passes No. of differenced ssh outliers Reject%
Geosat/gm 615 96392 873 0.9
Geosat/erm 37 15797 452 2.8
ERS2/35d 39 3509 80 2.2
ERS1/35d 37 3528 75 2.1
ERS1/gm 368 37173 334 0.9
Seasat 50 5631 67 1.2
T/P 12 1236 52 4.0
Table 5.3: Summary of outliers rejection around Taiwan (117/125/20/28)
data No. of passes No. of differenced ssh to be used outliers reject%
Geosat/gm 406 55579 555 1.0
5.5.1 The East China Sea
The first case study to assess the accuracies of gravity anomaly from the three altimeter-derived observations (mentioned in section 2.3 and 4.3) was carried out over ECS. We experimented with four cases of altimeter-gravity conversion. In these four cases, we used two methods of conversion: LSC and the inverse Vening Meinesz method (Hwang, 1998), and three altimeter-derived observations: DOV, differenced height and height slope. To identify the best case, we compared the altimeter-derived gravity anomalies with shipborne gravity anomalies. Figure5.1 shows the tracks of two selected ship cruises in the ECS (Tracks dmm07 and c1217) and two cruises in the TS (Tracks 1 and 2). The shipborne gravity data over ECS are from NGDC.
Before comparison, for each track we removed a bias and a trend in the shipborne gravity relative to the altimeter-derived gravity anomalies (Hwang and Parsons, 1995).
Table 5.4 shows the statistics of the differences between the altimeter-derived and shipborne gravity anomalies. The best result is from the case of using LSC with
differenced height, followed by the case of using LSC with height slope. The case of using LSC with DOV yields the least accurate gravity anomalies. Figure 5.8 shows the shipborne and altimeter-derived gravity anomalies along c1217 and dmm07. In general, the altimeter-derived gravity anomalies are smoother than the shipborne gravity anomalies. This is due to the filtering of the altimeter observations before the gravity derivations. At large spatial scales, the shipborne and altimeter-derived gravity anomalies agree very well, but at small spatial scales the differences become random and are not correlated with standard deviation of SSH, tidal difference or depth.
To see the possible sources causing the differences between altimeter-derived and shipborne gravity anomalies, we computed the normalized values of gravity anomaly differences (Case 1 gravity anomaly vs. shipborne gravity anomaly), depths, standard errors of ERS-1 SSH, tidal height differences (CSR4.0 vs. NAO 99) along Cruises c1217 and dmm07. As seen in Figure 5.9 and 5.10, the gravity anomaly differences fluctuate rapidly and do not possess a particular pattern with respect to the other three quantities. Over the shallow waters (depth less than 100 meters) of the ECS, both gravity anomaly differences and tidal height differences are relatively large.
In general, the standard error of ERS-1 SSH increases with decreasing depth.
Furthermore, the tidal height difference is larger over shallow waters than over the deep waters, and this agrees with the conclusion drawn in Section 5.2.
Table 5.4: Statistics of differences (in mgals) between altimeter-derived and shipborne gravity anomalies in East China Sea.
Case Mean RMS Min Max
LSC with differenced height -5.33 13.02 -49.24 43.96 LSC with height slope -5.45 13.19 -50.77 44.38
LSC with DOV -4.61 16.99 -85.59 74.65
Inverse Vening Meinesz with DOV -4.11 15.53 -52.23 80.53
Table 5.5: Statistics of differences (in mgals) between altimeter-derived gravity and two tracks of shipborne gravity anomalies in Taiwan Strait
Case Mean RMS Minimum Maximum
LSC with differenced height 7.91 9.82 -7.68 23.58
LSC with height slope 7.65 10.30 -9.13 28.30
LSC with DOV 9.39 12.16 -9.14 28.87
Inverse Vening Meinesz with DOV 9.14 11.61 -14.88 27.79
Table 5.6: Statistics of difference (in mgals) between altimeter-derived and shipborne gravity anomalies in the Taiwan Strait
Method and data for gravity derivation Mean RMS Min Max LSC with differenced heights only 8.01 9.06 -12.21 24.84
LSC with differenced heights and land gravity anomalies
6.22 8.22 -11.85 22.73
Figure 5.8: Gravity anomalies along Cruises c1217 and dmm07 in the East China Sea
Figure 5.9: Time series of normalized difference of gravity anomaly, standard error of ERS-1 SSH, tide model difference and depth, along Cruise dmm07.
Figure 5.10: Time series of normalized difference of gravity anomaly, standard error of ERS-1 SSH, tide model difference and depth, along Cruise c1217.
5.5.2 The Taiwan Strait
Next we carried out experiments over TS using the same four cases as in the ECS. We used shipborne gravity data along Tracks 1 and 2 (Figure 5.1) to evaluate the altimeter-derived gravity anomalies. These shipborne gravity data were compiled
by Hsu et al. (1998), who has crossover adjusted the shipborne gravity data and removed bad values. Table 5.5 shows the results of the comparisons between altimeter-derived and shipborne gravity anomalies in the four cases. The conclusion from Table 5.5 is similar to what has been drawn from Table 5.4, that is, the least square collocation method with DOV produces the worst result. Again, use of differenced heights produces the best results provided that the same altimeter-gravity conversion method is used.
Since land gravity data are available along the coast of TS, we also assessed the impact of land gravity data on the accuracy of altimeter-derived gravity anomaly.
Figure 5.11 shows the distribution of land gravity and altimeter data around Taiwan.
Note that there is no altimeter at the immediate coastal waters off the west coast of Taiwan. We experimented with the method of LSC using differenced heights, and with and without land gravity data (two cases). Table 5.6 shows the statistics of the differences between shipborne and altimeter-derived gravity anomalies. Figure 5.12 shows the shipborne and altimeter-derived gravity anomalies along Tracks 1 and 2.
Note that there is no altimeter at the immediate coastal waters off the west coast of Taiwan. We experimented with the method of LSC using differenced heights, and with and without land gravity data (two cases). Table 5.6 shows the statistics of the differences between shipborne and altimeter-derived gravity anomalies. Figure 5.12 shows the shipborne and altimeter-derived gravity anomalies along Tracks 1 and 2.