an improved method of absolute calibration to satellite altimeter: a case study in the yellow sea,...

An improved method of absolute calibration to satellite altimeter: A case study in the Yellow Sea, ChinaLIU Yalong1,2,3, TANG Junwu1,2*, ZHU Jianhua2, LIN Mingsen3, ZHAI Wanlin2, CHEN Chuntao2

1 Ocean University of China, Qingdao 266100, China2 National Ocean Technological Center, State Oceanic Administration, Tianjin 300112, China3 National Satellite Ocean Application Service, State Oceanic Administration, Beijing 100081, China

Received 16 April 2013; accepted 8 October 2013

©The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2014

AbstractAn improved absolute calibration technology based on indirect measurements was developed through two probative experiments, the performance of which was evaluated by applying the approach to in situ sea sur-face height (SSH) at the Tianheng Island (tidal gauge) and the satellite nadir (GPS buoy). Using Geoid/MSS (mean sea surface) data, which accounted for a constant offset between nadir and onshore tidal gauge water levels, and TMD (tidal model driver), which canceled out the time-varying offsets, nadir SSH (sea surface height) could be indirectly acquired at an onshore tidal gauge instead of from direct offshore observation. The approach extrapolated the onshore SSH out to the offshore nadir with an accuracy of (1.88±0.20) cm and a standard deviation of 3.3 cm, which suggested that the approach presented was feasible in absolute altimeter calibration/validation (Cal/Val), and the approach enormously facilitated the obtaining SSH from the offshore nadir.Key words: radar altimeter, absolute calibration, Yellow Sea

Citation: Liu Yalong, Tang Junwu, Zhu Jianhua, Lin Mingsen, Zhai Wanlin, Chen Chuntao. 2014. An improved method of absolute calibration to satellite altimeter: A case study in the Yellow Sea, China. Acta Oceanologica Sinica, 33(5): 103–112, doi: 10.1007/s13131-014-0476-8

1 IntroductionGlobal Changes, especially destructive climate and disas-

trous environmental events that have arisen in recent years, have increasingly attracted people’s attention. As a sensitive indicator of changes in the climate and environment, sea level variability plays a crucial role in the global change study (Ablain et al., 2009; Beckley et al., 2010; Lubin and Massom, 2005), and reflects the global change quantitatively in a relatively short timescale (Cazenave and Nerem, 2004; Griffies and Bryan, 1997; Nerem et al., 1999). Consequently, the evolution of climate and environment (e.g., global circulation, meso-scale eddies, El Niño and La Niña phenomen) can be monitored through sea level observation (Bonnefond et al., 2003b; Traon and Dibarbo-ure, 2004). Space-Borne radar altimeters, compared with tidal gauges and GPS buoys, have obtained sea surface height (SSH) globally and continuously for decades, and have become a criti-cal approach to the global change study by acquiring a sea level anomaly (SLA) (Bonnefond et al., 2010; Cazenave and Nerem, 2004; Watson, 2005).

It is true that altimeters not only provide a new perspective that had not happened before in oceanography, but also fa-cilitate geophysics and geodesy researches (Deng et al., 2001; Evensen and Van Leeuwen, 1994; Skagseth et al., 2004; Strub and James, 2000). Space-borne altimetry is qualified as a standard tool for oceanography (Chelton et al., 2001). Nevertheless, the accuracy of altimetry restricts its application: for instance, geo-tropic current studies require centimeter-level precision, and annual sea level variability needs 2 mm or better (Bonnefond

et al., 2003b; Chelton et al., 2001; Cheng et al., 2010; Evans et al., 2005). Long-term sea level change observations, however, necessitate the high consistency of multi-altimeters (Ablain et al., 2010; Beckley et al., 2010).

Calibration for altimeters, is one of the most critical issues, which promotes quality, enhances accuracy, and extends the applications of altimetry data (Beckley et al., 2010; Bonnefond et al., 2003b; Haines et al., 2010; Nerem et al., 2010). There has been a variety of Cal/Val activities conducted to qualify the geo-physical data record (GDR) data. The T/P (Topex/Poseidon) al-timeter was calibrated by Christensen et al. (1994), Haines et al. (2003), and Ménard et al. (1994) at harvest and Lampedusa cali-bration sites, respectively. With regard to Jason-1 and Jason-2 al-timeters, calibration activities were conducted at the Harvest oil platform (Haines et al., 2010; Haines et al., 2003), the Bass Strait (Watson et al., 2003; Watson et al., 2011; Watson et al., 2004; Wat-son, 2005), and Corsica (Bonnefond et al., 2010; Bonnefond et al., 2003a; Bonnefond et al., 2003b; Bonnefond et al., 2011). The calibration activities mentioned above were achieved by elabo-rate technology at the dedicated calibration sites. Although it is vital and necessary to calibrate altimeters at dedicated sites, problems remain as described below. It is expensive to construct a dedicated calibration site for altimetry, along with taking a long time to select a site. Furthermore, the geographically cor-related errors derived from orbit accuracy cannot be accounted for at a few sites (Jayles et al., 2010; Labroue et al., 2004; Watson, 2005). Bonnefond et al. (2010) suggested that both dedicated sites and tidal gauges should collaborate to characterize the er-

Acta Oceanol. Sin., 2014, Vol. 33, No. 5, P. 103–112

DOI: 10.1007/s13131-014-0476-8

http://www.hyxb.org.cn

E-mail: [email protected]

Foundation item: The Marine Public Welfare Projects of China under contract No. 201105032; the National High-Tech Project of China under con-tract No. 2008AA09A403.*Corresponding author, E-mail: [email protected]

LIU Yalong et al. Acta Oceanol. Sin., 2014, Vol. 33, No. 5, P. 103–112104

rors/bias in an absolute sense. More importance should be attached to calibrating altim-

etry data by tidal gauges due to the number of available, widely distributed tidal gauges and convenient maintenance to devic-es compared with GPS buoys (Bonnefond et al., 2010). In ad-dition, they provide continuous measurements for long-term Cal/Val, which the direct GPS buoy solution cannot. However, agreement between tidal gauges and GPS buoys is the key to Cal/Val activities. Continued efforts have been made in improv-ing precision. For example, Christensen et al.(1994) used GPS-based estimates to assess the Harvest tidal gauge system with a uncertainty of 1.5 cm, while Watson (2005) reported a subcen-timeter level.

There are challenges when calibrating altimeters using tidal gauges including extrapolating water level from the tidal benchmark to the nadir, and the knowledge of geoid undulation (White et al., 1994). In this study, a solution with tidal gauge, GPS buoy, well-developed tidal model data, and 1'×1' Geoid/MSS data was presented to calibrate not only for China HY-2 in a truly absolute sense, but also for Jason-2 and subsequent al-timetry missions (e.g., Saral 2013, Sentinel-3 2014, Jason-3 2014, Jason-CS 2017, SWOT 2020).

2 Site configuration and calibration methodology

2.1 Test field and instrumentsTwo probative experiments were conducted by the NOTC

(National Ocean Technological Center) to verify the feasibil-ity of extrapolation of the tidal level from the tidal benchmark out to the nadir of the altimeter. There were path-breaking ex-periments nationally aimed for the altimetry calibration. One was designed to demonstrate the consistency between a GPS buoy and tidal gauge at the same place on 18 October 2012, and another was intended to connect the water level measured by the gauge and GPS buoy at two sites with a distance of approxi-mately 15 km, from 24 October 2012 to 20 November 2012.

In the first experiment, the in situ water levels jointly mea-sured by the tidal gauge and the GPS buoy at Shazikou lasting for approximately 5 h were used to ensure the homogeneity be-tween the time series (Fig. 1). The Valeport 740 automatic tidal

gauge, with a nominal accuracy of ±0.1% in full scale and a reso-lution of 1 mm, was deployed at the test field along the bank (Fig. 1a). A buoy with a TOPCON NET-G3A GPS receiver (preci-sion: 5 mm+0.5×10−6 m) equipped inside was deployed near the bank (Fig. 1b). Water levels were observed by tidal gauge and GPS buoy simultaneously. The location where the GPS buoy was deployed was approximately 100 m away from the gauge. Within this distance, the water levels difference caused by ei-ther Geoid/MSS or tide was negligible.

The second experiment was implemented at Tianheng Is-land where the tidal gauge was installed; the GPS buoy was placed 15 km away from the tidal gauge (Fig. 1). The second observation was designed to resolve the issue of extrapolating water levels from the tidal gauge out to the nadir. The distance between the tidal gauge and GPS buoy was considered to mini-mize the baseline length for GPS buoy processing and maximize the distance from nadir to land (to circumvent the contamina-tion from land) (Watson, 2005). In addition, two reference sta-tions were built on the bank for GPS data processing, and the data from the reference stations and GPS buoy were processed by a number of routines in the GPS analysis suite “GAMIT”.

2.2 MethodIn this study, a solution, which transfers water levels from

the tidal gauge to the comparison point (nadir), was presented based on Geoid/MSS undulation data and tidal model harmon-ic data. The technique-derived water levels (by extrapolation at the nadir) were regarded as indirect measurements (Bonnefond et al., 2011). Examples include National Centre for Space Stud-ies (CNES) calibration activities (Bonnefond et al., 2003a), the United Kingdom project (Dong et al., 2002; Woodworth et al., 2004), and the GAVDOS calibration project (Erricos and Stelios, 2004). Bonnefond et al., (2011) and Watson (2005) pointed out that this indirect method provided continuous estimates of wa-ter levels at the nadir beyond the intensive calibration phase. While the tidal differences between the two sites, for which the water levels observed at the tidal gauge can be transferred to the nadir, were predicted by standard tidal prediction procedures (Watson et al., 2004; Watson, 2005).

Differences between tidal gauge measurements and GPS

nadir

Shazikou

Tianheng Island

121°10′ E121°00′120°50′120°40′120°30'E

36°3

0'N

36°20′N

36°10′

36°N

Qingdao

Huanghai Sea

China

“HY-2” Pass-147“H

Y-2”

Pas

s-52

a

b

c

15 km

Fig.1. Test locations and field instruments.

LIU Yalong et al. Acta Oceanol. Sin., 2014, Vol. 33, No. 5, P. 103–112 105

buoy observations consisted of the discrepancy between the tidal level and Geoid/MSS undulation at two separate sites (about 15 km away). Therefore, water levels at the nadir can be expressed as:

na ga= +H H H , (1)

where Hga is the water level measured at the tidal gauge, and H is the difference between two sites, which includes the Geoid/MSS undulation and tidal level:

Geoid/MSS ti= + .H H H (2)

Then, inserting Eq. (2) into Eq. (1), Hna can be rewritten as:

na ga Geoid/MSS ti= + + .H H H H (3)

Meanwhile, the Hna can also be acquired by the GPS buoy as:

na GPS= .H H (4)

The aim of this study was to obtain Hna through Hg, HGeoid/MSS and Hti. Compared with HGPS, the error, consequently, was de-termined by

er ga Geoid/MSS ti GPS= + + .H H H H H (5)

With reference to HGeoid/MSS, the 1'×1' global Geoid/MSS data were used by means of interpolation (Pavlis et al., 2008), and the tidal difference, Hti, was calculated based on (1/30)º × (1/30)º tidal model data, which can be expressed as:

ti ti ti= L1, L2,H H T H T . (6)

L1 and L2 denote different locations; T is time; and Hti is the tidal level predicted by a set of procedures:

ti 0, = cos +j Lj j Ljj

H L T f H T V u K , (7)

where HLj is the amplitude of tidal constituents at the tidal gauge and nadir in this study, and j indicates different tidal con-stituents (e.g., M2, S2, K1, O1); KLj is the lag phase of tidal constit-uents; f is the nodal correction factor for the constituents; V0+u represents the initial phase of tidal constituents with reference to Greenwich; and j is the frequency of tidal constituents.

Then Hti is calculated through a standard harmonic tidal analysis procedure, the OTIS (Oregon State University tidal in-version software) (http://www.coas.oregonstate.edu/research/po/research/tide/index.html) (Egbert et al., 1994; Egbert and Erofeeva, 2002). The solution consists of regional and global

tidal constituents with different spatial resolutions, which have assimilated various altimetry data (Topex/Poseidon, Topex Tan-dem, ERS, and GFO) and in situ data (e.g., tidal gauges, ship-borne ADCP).

3 DataThe data used in this study consisted of two categories, in-

cluding field observation data (from the tidal gauge and GPS buoy) and model data (geoid, MSS and Tidal model data). In the first verification experiment (Shazikou, Fig. 1), the GPS buoy was tethered approximately 100 m from the tidal gauge, and the bias derived from this distance is detailed in Section 4.

In the second tidal level difference extrapolation experiment (Tianheng Island and nadir; Fig. 1), field data were intended to derive the SSH differences between the two sites, whereas the model data were aimed to offset the differences.

With regard to the model data, two reference ellipsoids were utilized, comprising the WGS84 ellipsoid and Topex/Poseidon ellipsoid (Table 1). All model data referred to the WGS84 ellip-soid with the exception of the DTU MSS model data, which re-lated to the Topex/Poseidon ellipsoid.

3.1 In situ dataTwo groups of data were obtained from each experiment,

consisting of water levels independently measured by a tidal gauge and GPS buoy, respectively. The tidal gauge typically measured water level at 1min interval, while the kinematic GPS was processed at 1 Hz with short baseline distance. GAMIT soft-ware was used for the GPS data processing. Limitations of the GPS water level were depended on the location, surrounding environment, and number of satellites (less than the minimum of five prevented reliable and robust solution) (Watson, 2005).

Both high-rate GPS data and low-rate tidal gauge data (logged every 1 min, with each value an average of 60, 1-second samples) required filtering to eliminate waves, swell effects, and noise (Bonnefond et al., 2003a; Ménard et al., 1994). Meanwhile, all data were transformed to universal time.

Due to the sampling frequency discrepancy between the ki-nematic GPS and tidal gauge, the gauge data were resampled identically with GPS 1 Hz data by an ordinary interpolation.

3.2 Model dataWater levels observed at Tianheng Island and the nadir, were

intended to calculate differences between the levels. Neverthe-less, the model data were used to account for the differences. The Geoid/MSS model data were used to compensate for the constant difference. The disagreement between geoid and MSS is that the latter takes into account the mean dynamic topogra-phy (MDT):

mss Ge MDT= +H H H , (8)

where Hmss is the mean sea surface height, HGe indicates geoid

Table 1. The parameters of two relevant ellipsoids

Ellipsoid Equatorial Radius (a)/m Polar radius (b)/m Reciprocal Flattening (1/f) Eccentricity(e)

T/P 6 378 136.3 6 356 751.600 563 298.257 0.081 819 221 456

WGS84 6 378 137.0 6 356 752.314 245 298.257 223 56 0.081 819 190 843


undulation, and HMDT means mean dynamic topography. MSS and geoid data were used to analyze the influence of MDT.

Ideally, MSS and geoid data should cancel out the constant difference. Nevertheless, the tidal model data aimed to explain the remainders, Hti.

3.2.1 Geoid dataThe geoid undulation values referring to WGS 84 were cal-

culated from the EGM2008 official earth gravitational model, which was released by the US National Geospatial-Intelligence Agency (NGA) EGM Development Team (NGA, 2008). This grav-itational model is complete to a spherical harmonic with degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159 (Pavlis et al., 2008). At present, the NGA provides two grids of precomputed geoid undulations: one at 1 min × 1 min resolution and another at 2.5 min × 2.5 min resolution. The former are used to determine the difference in levels in this study.

The widely used EGM 2008 geoid undulation, according to Pavlis et al. (2008), compared within dependent data, intro-duced a RMSE of 5.2 cm and a slope of 0.3 seconds, while the previous version, EGM96 had a RMSE of 20.0 cm. The differ-ence between EGM96 and EGM2008 was large in the Yellow Sea, especially at the second experiment site. It was approximately 7 m for EGM2008, but more than 8 m for EGM96 (Fig. 2). Al-though both are used worldwide as geoid models, the EGM2008 exceeded EGM96 in precision and resolution.

3.2.2 MSS dataMSS model data, derived from The Danish Technical Uni-

versity’s DTU10 MSS, were developed through the averaging of satellite altimetry (Andersen, 2010), and improved based on the DNSC08MSS global mean sea surface (Andersen and Knudsen, 2008). Compared with its previous version, DNSC08MSS, this MSS data extended altimetry data from 12 a (1993–2004) to 17 a (1993–2009). In addition, the altimetry data (with which the MSS was derived) were refined in orbit, wet troposphere, ocean tide, and sea state bias (Andersen, 2010).

The difference between MSS data and EGM2008 was the mean dynamic topography according to Eq. (8), which gave rise to tens of centimeters difference as a result (left panel of Fig. 3). The right panel of Fig. 3 presents the MSS distribution similar to the geoid undulation (Fig. 2)

3.2.3 Tidal model dataIn order to extrapolate the water levels from the tidal gauge

to the nadir GPS buoy, the geoid and MSS data were expected to account for a constant difference, whereas the tidal model data were used to account for the time-varying periodic difference,

Hti (Eq. (6)).The TMD (tidal model driver) is the current version of a

global model of ocean tides, which best fits, in a least-squares sense, the Laplace tidal equations and along-track averaged data from TOPEX/Poseidon and Jason (on TOPEX/POSEIDON tracks since 2002) obtained with Oregon State University Tidal

nadir

Shazikou

Tianheng Island

a

4.74 – 5.965.96 – 7.157.15 – 8.288.28 – 9.41>9.41

EGM

2008

/m

nadir

Shazikou

Tianheng Island

b

Diff

eren

ce/m

< −1.14

> −0.41

−1.14 – −0.96−0.96 – −0.78−0.78 – −0.61−0.61 – −0.41

3.4 – 4.74

Fig.2. Geoid undulation of EGM2008 (a) and difference between EGM2008 and EGM96 geoids (b).

nadir

Shazikou

Tianheng Island

a<0.530.53 – 0.560.56 – 0.590.59 – 0.620.62 – 0.660.66 – 0.700.70 – 0.74>0.74

MD

T/m

nadir

Shazikou

Tianheng Island

b<5.225.22 – 6.356.35 – 7.427.42 – 8.468.46 – 9.59>9.60

MSS

/s

Fig.3. Time-averaged mean dynamic topography and mean sea surface with reference to ellipsoid (T/P).


Inversion Software (OTIS). The methods used to compute the model are described in detail by Egbert et al. (1994) and further by Egbert and Erofeeva (2002).

The model provided in the China’s sea as complex ampli-tudes comprised eight major harmonic constituents (M2, S2, N2, K2, K1, O1, P1, Q1), on a 901 × 1 201, (1/30)° resolution grid (for versions 6.* and later), which has been improved continuously. The latest version of each model is of better quality compared with the earlier versions since: (1) it assimilates a longer satellite time series; (2) more data sites are included in assimilation; and (3) bathymetry has improved from version to version. Accord-ing to VOLKOV/OCE/ORST (http://volkov.oce.orst.edu/tides/global.html), 55 coastal tidal gauges and six “true shallow” tidal gauges were used to validate (but not assimilate) the model.

Tidal levels in the study region could then be predicted based on the TMD model mentioned above, which were referenced to the mean sea level. In order to avoid introducing unnecessary errors in datum transformation, it was preferable to calculate tidal difference between two sites instead of acquiring absolute tidal levels at each site.

4 ResultsThe determination of absolute bias of altimeters requires

accurate in situ SSH (nadir). As described above, a long-term and continuous observation of water levels far away from the continent (to avoid waveform contamination from the land) poses a challenge to the GPS buoys, which require calm weath-er condition and sea state, and guarding. Extrapolating the SSH from the onshore tidal gauge out to the offshore nadir provides a feasible solution. However, this solution entails high precision from both measurements. In order to verify the feasibility and accuracy of the solution, the differences (SSH difference, here-inafter referred to as Hss,d) between the two instruments (same instruments for both field experiments) should be estimated at the same site (for consistency) and then at different sites (for extrapolation):

ss,d ss,gb ss,tg= .H H H (9)

First, the Hss,d between the two measurements at Shazikou

(Fig. 1; 36º5 48.48 N, 120º32 1.32 E) were analyzed to check the agreement of SSH derived from different instruments at the same site. Second, the offsets from Geoid/MSS and time-vary-ing tidal difference were calculated to cancel out Hss,d at the two sites (Fig. 2; approximately 15 km apart) and to demonstrate the accuracy of the extrapolation.

In short, the objective of the first field experiment was to ascertain whether the observations from the two instruments were identical. Based on the first experiment, the second one demonstrated agreement of SSH observation from two the in-struments with a relatively large distance.

During the second field experiment, there was one point available from the “Jason-2” observation, however, the absolute bias of “Jason-2” could not be determined statistically due to the small sample size.

4.1 In situ SSH mutual verification between gauge and buoy As the SSH was measured by two instruments, the agree-

ment between the two observations needed to be ascertained. Although the first experiment at Shazikou lasted approximately 5 hours, 154 min was taken to acquire concurrent SSH (Fig. 4). The 1 Hz raw SSHs measured by the GPS buoy were smoothed to filter out surface waves, swell, and high-frequency noise. The lag length of 3 min was adopted in smoothing (Fig. 4a, green line), which was longer than waves and swell periods, but was also short enough to avoid over-smoothing (a change in the tendency of raw data).

For SSH, the two ways agreed well one another except ap-proximately 11 min of data since 15:50 that showed a relatively large difference, corresponding to degraded GPS satellite cover-age. Figure 4a presents the SSH from the two instruments, and Fig. 4b is the Hss,d time series in which the green lines denote the mean value and dash lines denote the 95% confidence interval of Hss,d. The gray patches from Figs 4a and b are SSH with a large discrepancy. The degraded Hss,d showed a mean value of 4.72 cm, in light of the short distance between the gauge and buoy (approximately 100 m), however, a difference this large was un-acceptable. After the degraded data were removed, the Hss,d pre-sented a mean value of 1.07 cm and standard deviation of 1.19 cm, which was comparable with the result from Watson (2005).

14:24 14:52 15:21 15:50 16:19 16:48

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Time

SSH

diff

eren

ce/m

b

Hss, g−Hss, b

mean value95% confidence interval

14:24 14:52 15:21 15:50 16:19 16:485. 0

5. 5

6. 0

6. 5

7. 0

7. 5

8. 0

Time

SSH

/m

a

GPS buoy: 1 Hz raw SSHtidal gauge: 1 min averaged SSHGPS buoy: filtered SSH

Fig.4. SSH from tidal gauge and buoy (a) and Hss,d (b).


Table 2. Statistics of SSH difference (m) between gauge and

buoy

Statistics Dataset1) Dataset2) Dataset3)

Mean −0.010 7 0.047 2 −0.006 5

Std 0.011 9 0.013 4 0.019 1

Upper bound 0.014 3 0.081 1 0.050 8

Lower bound −0.034 2 0.026 5 −0.033 8

Notes: 1) SSH difference without the area covered by the gray patch (Fig. 4); 2) gray patch covered data; 3) entire difference data.

4.2 Extrapolation of water level from bank to nadirThere were many factors contributing to the Hss,d that de-

rived from onshore SSH minus offshore (nadir) SSH, but two were dominant in determine the difference: Geoid/MSS differ-ence (constant) and tidal offsets (time-varying). The Hss,d was then canceled out by the two factors based on geoid undula-tion/MSS data and TMD data, respectively.

GPS buoy 1 Hz raw SSH from the synchronization experi-ment (Tianheng Island and nadir), was smoothed based on ro-bust local regression using weighted linear least squares and a second degree polynomial model (Cohen, 1999) to average out surface waves, swell, and random noise with a length of 3 min.

Nevertheless, it was not necessary to apply smooth technology to the tidal gauge 1-min SSH due to the fact that the SSH records were averaged values from the integrated water level at 1-min intervals.

All data sets (in situ and model data) referred to the WGS84 ellipsoid, except MSS data that referred to the Topex/Poseidon ellipsoid (Table 1). The impact from datum transfer was also analyzed later.

4.2.1 Difference accounted for by constant offsetGeoid undulation or MSS data were not equivalent between

Tianheng Island (tidal gauge) and the nadir (GPS buoy), which gave rise to differences of SSH (Fig. 2): geoid undulation did not take mean MDT (dynamic topography) into account, and MSS data included both geoid undulation and MDT. The influence of MDT in extrapolating water level out to the offshore site could be evaluated by comparing the difference between the two model data with constant offset.

The mean SSH difference was regarded as a constant offset, which was not equivalent in the whole Hss,d time series, and presented a larger difference between peak and trough than in other positions (Fig. 5). The mean Hss,d had a mean value of 0.425 2 m, which was theoretically supposed to be aligned to zero (Fig. 6).

09:36 12:00 14:24 16:48 19:12 21:36

0

5

0

5

0

5

0

5

Time

7.

7.

8.

8.

9.

9.

10.

10.

SSH

/m

GPS buoy: 1 Hz raw SSHGPS buoy: filtered SSHtidal gauge: 1 min averaged SSH

Fig.5. SSH observed by the GPS buoy and tidal gauge.

09:36 12:00 14:24 16:48 19:12 21:36−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Time

SSH

diff

eren

ce/m

0.425 2 m

0.018 8 m

0.090 2 m

Hss, b−Hss, gHss, b−Hss, g+ΔHgHss, b−Hss, g+ΔHm

Fig.6. SSH difference and geoid/MSS offsets.


The mean SSHDiff (mean difference between Hs,b and Hss,g) was 42.52 cm (Fig. 6). After shifting a mean value of 33.5 cm (the difference of the geoid between the Tianheng Island and the nadir; green dashed line in Fig. 6), there was still 9.02 cm to be canceled out, resulting in 21.21% a relative deviation. Regard-ing MSS data, after compensating for the mean value of 44.4 cm (difference of MSS between the two sites), there was an overes-timate of 1.88 cm (red dashed line in Fig. 6), reaching a relative deviation of 4.42%. Compared with the geoid model, the MSS offset was more effective, and the MSS had higher performance due to consideration of the MDT.

4.2.2 Difference accounted for by periodic time-varying offsetsAfter removing the constant offset, the remaining time series

fluctuated with time, which were determined by tides (Figs 7 and 8). Namely, the differences between tides at the two sites led to time varying offsets (Fig. 7, green patch). The major tidal con-stituents, which were used to estimate the tidal level as well as time-varying Hss,d, could be extracted by applying the standard harmonic tidal analysis to the water level data, provided that there were long-term observed water level time series available.

However, with tens of hours' time series length, the eight major tidal constituents could not be identified. Therefore, the TMD solution was preferable to solve the periodic offsets (Eqs (6) and (7)). The eight major tidal constituents were extracted from the TMD data to calculate tidal offsets (Table 3). Compared with the onshore tidal level, the nadir tidal level presented an ap-proximate 2° phase lag in the M2 dominant constituents, which showed an amplitude of 0.069 6 m (Table 3). Except for M2, S2 and N2 constituents, the remaining constituents had a subtle influence at the two sites, since the amplitudes of constituents were at the millimeter level or smaller.

Based on the eight major tidal constituents (amplitude and phase lag), Hss,d could be offset by predicting water levels using the TMD solution (Fig. 8). Afterwards, the differences between SSHDiff and the predicted tidal differences could be determined, shown as the blue line in Fig. 8. Note that before the differences were obtained, the mean Hss,d should be aligned, to 0 which the predicted water levels were referred.

The results suggested that the predicted data agreed with Hss,d except local parts (Fig. 8). The predicted data fits well the shape feature of fluctuating Hss,d time series, as expected. The

09:36 12:00 14:24 16:48 19:12 21:36

7.0

7.5

8.0

8.5

9.0

9.5

10.0

Time

SSH

/m

time−varying differencestidal gauge: plus canstant offset (0.425 2 m)GPS buoy: filtered SSHtidal gauge: 1 min averaged SSH

Fig.7. Theoretical time varying differences.

09:36 12:00 14:24 16:48 19:12 21:36

−0.15

−0.10

−0.05

0

0.05

0.10

0.15

Time

Hss,d predicted tidal level residual

Hss

,d/m

Fig.8. Hss,d and predicted tidal level.

Table 3. Major tidal amplitude and phase lag of Hss,d (Hgps−Hg)

Constituent M2 S2 N2 K2 K1 O1 P1 Q1

Amplitude/m −0.069 6 −0.021 8 −0.012 1 −0.004 8 −0.005 9 −0.002 7 −0.001 1 −0.000 3

Phase lag/(º) −1.889 9 −2.496 9 −1.866 1 −2.476 4 −0.014 7 −0.710 5 −0.930 9 −0.709 7


residual revealed normally distributed shape indicating that there was no higher order nonlinear behavior in Hss,d (Watson, 2005) (Fig. 9). Meanwhile, the residual had a standard deviation of 3.33 cm, while the Hss,d and the predicted water levels pres-ent standard deviations of 9.74 and 8.33 cm, respectively, dem-onstrating that the TMD solution provided accurate offsets to explain the time-varying Hss,d.

−0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.100

500

1 000

1 500

Residual/m

Freq

uenc

y

σ =3.33 cm

Fig.9. Histogram of residual and normal distribution probability density function.

5 DiscussionAccording to the results, the SSH at the tidal gauge could

be extrapolated out to the nadir by taking the constant and time-dependent differences into account. However, other fac-tors were omitted, for instance, tidal model impact (TMD solu-tion), currents, wind setup, atmospheric pressure, and ellipsoid transformation (Crétaux et al., 2011; Watson, 2005). Concerning tides, errors rose from imperfect representation by the model of real ocean tides, due to inadequate knowledge of bathymetry, inaccurate lateral boundary, and imprecise parameterizations (e.g. bed friction). The bathymetry especially played an impor-tant role in tidal propagation (Benveniste and Vignudelli, 2009; Lyard et al., 2006). For example, the M4 constituent influenced by shallow water (Andersen, 2011), reached a significant am-

plitude (Rosmorduc et al., 2011). The research concluded that this constituent had a significant amplitude about 5 to 10 cm in some parts of the Atlantic Ocean, but a noise level in the deep ocean (Lyard et al., 2006). In this study, the tidal difference was calculated without including any long periods of tidal and the shallow-water constituents, which may have led to a millime-ter-level or larger error (although the short distance between the two sites, the M4 constituent, for example, was sensitive to the shallow water).

The currents also affected the Hss,d. Watson (2005) suggested that the speed of along-shore currents, is typically less than 10 cm/s, inducing an approximate maximum difference of 6.5 mm with an offshore distance of 15 km (Fig. 10a; h is current-induced bias, f is the Coriolis parameter, u is current speed, g is gravity acceleration, and y is offshore distance). Concerning the ellipsoid conversion, the transformation between WGS84 and T/P resulted bias is less than the millimeter-level due to the subtle difference between latitudes of the two sites (Figs 1 and 10b). Meteorological factors (wind setup and atmospheric pressure), had a negligible impact to Hss,d due to the close geo-graphic location (Crétaux et al., 2011).

The extrap.olated SSH at the nadir was acquired by add-ing constant and time-dependent offsets (hereinafter referred to as Hss,re). The ordinary least square regression analysis was applied to Hss,b and Hss,re, which showed scale parameter, a , of 0.995 9±0.000 3 and intercept parameter, b, of (3.4±0.26) cm (Fig. 11). The coefficient a appeared significantly close to one (the theoretical slope of regression), while the intercept seemed relatively large, most likely caused by incompletely filtered noise. Moreover, the incompletely filtered noise induced a ragged feature in either the filtered GPS buoy data or tidal gauge data (Fig. 12), which theoretically vary smoothly. According to the constant and time-varying offsets, the tidal gauge SSH was extrapolated out to the nadir with a remaining offset of 1.88 cm and standard deviation of 3.3 cm. It can be concluded that the accuracy of this extrapolation was (1.88±0.20) cm (0.20 cm de-notes the standard error related to sample number 831/3). Fig-ure12 shows that the extrapolated the SSH (yellow line) dove-tailed with Hss,b, which suggested that the extrapolation method detailed in this study is feasible in acquiring the nadir SSH.

6 ConclusionsThe absolute in situ calibration and validation (Cal/Val)

0 5 10 15 20

a b

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

∆h=−∆yfu/g

∆h/c

m

Speed /cm∙s−1

80°S 60°S 40°S 20°S 0° 20°N 40°N 60°N 80°N

6.36

6.37

Earth

Rad

ius/

106 m

WGS84T/PWGS84−T/P

0.700

0.705

0.710

0.715

Diff

eren

ce/m

Fig.10. Influence from currents and ellipsoid transformation.


were the vital components of the altimeter measurement sys-tem, and it was imperative to have the altimeter calibration at the centimeter level or better for operational application. This study demonstrated that the SSH extrapolation from the onshore tidal gauge out to the offshore site performed well by taking into the MSS model (DTU10 MSS) and the tidal model (TMD) data. It also suggested that MSS data, which included the MDT impact, were more reasonable in accounting for con-stant offset than the purely geoid model. The periodic time-varying offsets were canceled out using the TMD model data with a standard deviation of 3.3 cm (from 9.74 cm).

Based on the methodology detailed above, the tidal gauge observed SSH was employed to extend the cycle-by-cycle comparison with altimeters with an accuracy of 1.88±0.20 cm, which enormously facilitated the altimeter Cal/Val activities and provided a feasible way to calibrate/validate altimeters. The result presented in this study was compared with similar works published in the world (Bonnefond et al., 2011; Gwenaële et al., 2004; Ménard et al., 2003), and sufficed as the in situ altimeter Cal/Val.

In order to better sustain the operational and stable Cal/Val of altimeters in the future, the accuracy could be improved by means of the following ways. First, the shape of the GPS buoy should be reconstructed to decrease the impacts of waves, swell

effects and noise. Second, long-term concurrent time series (water levels from both the tidal gauge and GPS buoy) should be observed to preclude necessity of determination of the marine geoid and to simplify the solution involving just the geometrical framework. Third, filtering algorithms entail more focus. In ad-dition, contributions including wind setup, along/cross shore currents, loading tides, solid tides, and other factors should be taken into account.

AcknowledgementsThe authors would like to thank all colleagues from the Re-

mote Sensing Group the National Ocean Technological Center, the State Oceanic Administrator, for their hard work in the two experiments and proposals in data processing.

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7.0

7.5

8.0

8.5

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