Evaluating the Potential of Sea Surface Height Observations and Depth Datum Calculation Using GNSS/IMU Buoys

Abstract

This study evaluates the potential of GNSS/IMU buoys for sea surface height observations and depth datum verification. GNSS/IMU buoys were deployed alongside 34 tide gauges around Taiwan for synchronous sea surface height measurements. The collected GNSS data were processed through relative positioning and loosely coupled GNSS/IMU integration methods. Analysis revealed that the average of the means of the differences was −2.5 cm across all stations, indicating that most tide gauge datums agreed well with the GNSS/IMU buoy measurements. Significant discrepancies were observed at only a few stations, likely due to local subsidence. Notably, the Shuitou station showed a mean difference of 63.4 cm, resulting from its remarkable deviation from tidal zero since 2019, suggesting a potential datum issue. The mean of the standard deviation (STD) of the differences across the stations was 3.8 cm, with the highest STD observed at the Shuitou station (9.4 cm). These findings demonstrate that GNSS/IMU buoys can effectively complement tide gauge measurements for observing sea surface heights and defining the depth datum, particularly in areas where local vertical land movements affect tide gauge data accuracy.

1. Introduction

With global climate change, accurately monitoring sea level variations has become a critical research focus in oceanography and geophysics. Sea level changes not only reflect global climate trends but also directly affect coastal infrastructure, human livelihoods, and ecosystems [1]. Currently, the main methods for monitoring sea level variations include tide gauges and satellite altimetry. While tide gauges provide stable long-term data, they only represent relative sea levels and are affected by vertical land movements [2], limiting their precision in measuring absolute sea level changes. Additionally, due to high installation costs and strict environmental requirements, tide gauges are mainly deployed in coastal areas, limiting their coverage of remote or offshore regions [3]. Satellite altimetry offers significant advantages in measuring global sea surface heights with wide coverage. However, in coastal areas, the complex topographic environment, which distorts the reflected waveforms at the sea surface and limits the accuracy of geophysical correction models, reduces the overall precision of satellite altimeter measurements [4,5].

To overcome the limitations of traditional techniques, Global Navigation Satellite System (GNSS) buoys have been introduced into marine surveying to provide absolute sea surface measurements. Since the 2000s, GNSS buoy technology has gained growing attention and has proven effective in collecting high-frequency sea surface variation data [6,7]. For example, GNSS buoys can be used to calibrate satellite altimetry observations [8,9], monitor high-frequency ocean signals such as tsunamis [10], and support accurate definitions of coastal depth datums [11,12]. Additionally, GNSS buoys provide accurate measurements of water surface heights in estuaries, coastal regions [13], and offshore wind farm areas [14], and they can be used to determine wave parameters [15].

However, during observations, GNSS buoys themselves can be affected by factors such as wind, waves, and currents, leading to tilting or swaying, affecting their accuracy [16]. To address this issue, previous studies have introduced the Inertial Measurement Unit (IMU) to compensate for errors caused by buoy attitude changes [17]. The IMU records the buoy’s three-axis accelerations and attitude angles, and when integrated with GNSS signals, it significantly enhances positioning accuracy in dynamic environments. The application of the GNSS/IMU integrated system has been validated in multiple studies, demonstrating superior accuracy, particularly in monitoring high-frequency sea surface variations [17,18].

The accuracy of GNSS single-point positioning is typically limited to meter-level precision. However, centimeter-level positional accuracy is essential for studying oceanographic phenomena such as tides and waves. Consequently, numerous studies have been dedicated to enhancing the positioning capabilities of GNSS buoys. Early research indicated that relative positioning could achieve centimeter-level accuracy over short distances. Kato et al. [19] proposed long-term offshore monitoring using GNSS buoys with real-time kinematic (RTK) positioning technology, but the relative positioning accuracy decreases over longer baselines due to error accumulation [20]. Precise Point Positioning (PPP) technology has addressed this issue, allowing buoy positioning with centimeter-level accuracy without requiring a reference station [15,20,21]. Kuo et al. [20] utilized PPP for sea level monitoring, achieving a root mean square error (RMSE) of less than 10 cm in the vertical direction. The significant wave height (SWH) values computed with PPP by [15] also showed good consistency with those from dedicated wave buoys, with a correlation coefficient of 0.935 and a difference of 0.82 cm ± 4.63 cm.

Traditionally, the mean sea surface for coastal depth datums relies on long-term stable tide gauge records, while satellite altimetry data are used for open ocean areas [22]. However, as mentioned, limitations in tide gauges and satellite altimetry observation data result in lower accuracy and inconsistency for the mean sea surface within 10 km of the coast [5,23]. Additionally, the high construction and maintenance costs of tide gauges restrict their use in some areas [3]. GNSS/IMU buoys offer a flexible and cost-effective alternative by providing high-frequency, absolute sea surface height measurements across various locations, effectively filling gaps left by tide gauge and altimetry observations in computing the mean sea surface for depth datums [24].

This study aims to evaluate the potential of GNSS/IMU buoys in analyzing the sea surface height and mean sea surface for depth datums by comparing their observations with tide gauge records of 34 stations in Taiwan. Tide gauges are traditionally recognized as reliable instruments for measuring sea level height and defining depth datums. Unlike previous studies that relied on the relative datum of orthometric height, this research employs the absolute datum of ellipsoidal height, showcasing the buoys’ ability to verify and correct tide gauge datums, particularly in areas affected by vertical land motion. In addition, this study employs a loosely coupled GNSS/IMU integration method, combining centimeter-level GNSS positioning with 20 Hz high-frequency IMU data to enhance the accuracy of positioning and altitudes in dynamic marine environments. A key innovation is the large-scale deployment of 34 GNSS/IMU buoys near tide gauge stations across diverse coastal environments in Taiwan. This not only provides robust validation of tide gauge data but also highlights the potential of GNSS/IMU buoys to complement traditional systems, surpassing earlier studies that focused on only one or a few locations. The findings of this study provide new technical support for marine surveying and are expected to enhance the reliability and accuracy of sea surface observations in coastal zones.

2. Data and Methodology

2.1. Tide Gauge

This study used data from 34 tide gauge stations in Taiwan, with their locations shown in Figure 1. The tide gauges are primarily distributed along the coast of Taiwan’s main island, with more distant stations located in Kinmen, Shuitou, and Mazu, covering diverse environmental conditions. Relevant information about the gauges is presented in

Table 1. Information on 34 tide gauge (TG) stations used in the study and their corresponding benchmarks and elevations.

TG ID	Name	Lat (°)	Lon (°)	Benchmark ID	TWD97[2010] (m) *	TWVD2001 (m) **
112	Hsinchu	24°50′55″ N	120°55′14″ E	82043	22.399	3.451
113	Waipu	24°39′05″ N	120°46′17″ E	TG06A	23.199	4.199
1102	Tamsui	25°10′33″ N	121°25′29″ E	TG31	23.068	3.448
1116	Jhuwei	25°07′05″ N	121°14′36″ E	TG04	21.535	2.300
1156	Boziliao	23°37′07″ N	120°08′15″ E	TG08	20.492	0.969
1166	Dongshi	23°27′00″ N	120°8′22″ E	TG10X	22.612	2.904
1176	Jiangjun	23°12′45″ N	120°04′59″ E	TG32	22.040	2.400
1186	Donggang	22°27′54″ N	120°26′18″ E	TG33	23.235	2.480
1196	Houbihu	21°56′45″ N	120°44′43″ E	TG34	23.882	1.905
1206	Linshanbi	25°17′02″ N	121°30′37″ E	TG02	22.408	2.686
1226	Longdong	25°05′51″ N	121°55′05″ E	TG21	23.528	2.785
1236	Wushi	24°52′02″ N	121°50′15″ E	TG35A	22.505	1.989
1246	Su-ao	24°35′33″ N	121°52′01″ E	TG20A	22.194	2.183
1256	Hualien	23°58′50″ N	121°37′25″ E	TG19	23.307	2.458
1276	Chenggong	23°05′50″ N	121°22′49″ E	TG17-1	28.023	2.664
1356	Penghu	23°33′37″ N	119°34′37″ E	TG73	20.718	2.247
1366	Wengang	23°28′00″ N	120°07′21″ E	TG09	25.410	5.682
1386	Liuchiu	22°21′12″ N	120°23′00″ E	TG74	24.276	3.430
1396	Lanyu	22°03′29″ N	121°30′25″ E	TG75-1	27.922	2.807
1436	Taichung Port	24°17′16″ N	120°31′59″ E	TG07	22.215	3.504
1456	Mailiau	23°47′10″ N	120°09′37″ E	ML01	23.882	4.676
1486	Kaohsiung	22°36′52″ N	120°17′18″ E	TG12	21.775	1.535
1496	Syunguangzui	21°59′08″ N	120°42′43″ E	TG14X	23.802	1.921
1516	Keelung	25°09′18″ N	121°45′08″ E	TG01	21.990	1.554
1552	Heping Port	24°18′11″ N	121°45′22″ E	HP02	29.621	9.921
1566	Shihti	23°29′41″ N	121°30′22″ E	TG18	27.539	4.213
1586	Fugang	22°47′27″ N	121°11′35″ E	TG16-1	27.055	2.319
1596	Dawu	22°20′15″ N	120°53′50″ E	TG15	26.390	3.011
1676	Lyudao	22°39′44″ N	121°27′53″ E	TG76	27.444	2.654
1786	Yongan	22°49′08″ N	120°11′51″ E	TG11X	24.203	4.146
1926	Mazu	26°09′42″ N	119°56′34″ E	TG71-1	17.375	3.327
1956	Kinmen	24°24′31″ N	118°25′48″ E	TG72XB	15.298	3.447
1966	Shuitou	24°25′16″ N	118°17′21″ E	KM28	15.331	4.143
11781	Sicao	23°01′25″ N	120°06′43″ E	CC01	22.482	2.815

* Ellipsoidal height (Geodetic Reference System 1980). ** The orthometric height systems for Taiwan’s main island (TWVD2001) and its offshore islands are different.

. The tide gauge stations are established and maintained by various organizations, including the Ministry of the Interior, the Central Weather Administration of the Ministry of Transportation and Communications, the Transportation Technology Research Center, and the Water Resources Agency of the Ministry of Economic Affairs, among others. Data management is centralized under the Central Weather Administration, which provides data at a sampling interval of 6 min.

The reference datum for the tide gauge stations is based on benchmark elevations, Taiwan Vertical Datum 2001 (TWVD2001) for stations on Taiwan’s main island, and the offshore mean sea level for offshore islands. In addition to orthometric heights provided by the tide gauge benchmarks, the National Land Surveying and Mapping Center has also used continuous GNSS observations to determine the ellipsoidal heights of the Taiwan Datum 1997 (TWD97[2010]), which spatially covers the main island and offshore islands of Taiwan. Therefore, the tide gauge records can be converted to ellipsoidal heights. The definitions of ellipsoidal height and orthometric height, as well as their relationship, can be found in [25]. The orthometric and ellipsoidal heights of the 34 tide gauge benchmarks are given in Table 1. All tide gauge observations underwent a complete quality control procedure.

As the observation periods of 34 GNSS/IMU buoys cover only a few hours, the quality controls of the tide gauge data primarily focused on assessing data completeness and detecting datum shifts at the corresponding time points [26]. No datum shift issues were found in any of the tide gauge data.

2.2. GNSS/IMU Buoy

Most commercially available high-precision GNSS positioning equipment is designed for terrestrial surveying applications. However, prolonged use in harsh marine environments often leads to equipment and antenna degradation, eventually resulting in malfunction. To address this issue, Taiwan’s first buoy was designed and developed specifically for GNSS and IMU data collection and wireless transmission in marine environments. This GNSS/IMU buoy employs a Trimble OEM GNSS core module and Mouser ADIS series chip IMU and integrates proprietary control, recording, and wireless transmission circuitry from SkyBees Technology Co., Ltd. in Taipei, Taiwan, as shown in Figure 2. The GNSS/IMU buoy has the following features:

(1)

It is a fully enclosed IP68 waterproof device, resistant to seawater corrosion, and suitable for repeated deployments.

(2)

It is equipped with a high-capacity rechargeable battery and an inductive charging system, and it operates for over 10 h on a full charge.

(3)

The Trimble OEM module supports multi-frequency, multi-constellation signals, including GPS L1/L2/L5, GLONASS L1/L2, BeiDou B1/B2, Galileo E1/E5, and QZSS L1/L2/L5. Additionally, it integrates a low-cost IMU.

(4)

The IMU used is a Mouser ADIS series chip, which includes sensors such as a gyroscope, accelerometer, magnetometer, barometer, and thermometer, with sampling rates of 20 Hz.

(5)

Data are first stored on an SD card with a capacity of up to 256 GB. An internal wireless transmission module, coupled with a custom-developed mobile app, enables control over data recording functions, GNSS data collection, and uploading to a backend server. The app can also query the buoy’s current GNSS positioning and GNSS/IMU status (as shown in Figure 3).

(6)

The buoy is designed as a single unit with a diameter of approximately 50 cm, a height of 35 cm, and a weight of around 12 kg, ensuring portability and ease of deployment.

Furthermore, to ensure high-quality data collection, four checklists were developed to cover pre-deployment preparations, setup procedures, station retrieval, and nighttime operation readiness, thus ensuring accurate field operations.

2.3. Methodology

In this study, GNSS/IMU buoys were deployed near 34 tide gauges (Figure 1), with the deployment locations chosen to avoid signal obstruction from the coast. Simultaneously, an onshore GNSS receiver at the tide gauge benchmark was set up as a GNSS reference station to conduct synchronous observations, with observation durations ranging from 6 to 8 h. Due to obstructions affecting observations at both the buoy and reference station, PPP was not used, as it requires 20–30 min for a stable solution after cycle slips. Instead, the relative positioning method was employed with the following procedure. First, virtual observation data (RINEX files) from a Virtual Reference Station (VRS) near the reference station was obtained from the National Land Surveying and Mapping Center and used for relative positioning computations to determine the reference station’s coordinates. Afterward, the calculated coordinates were compared with the ellipsoidal height provided by the National Land Surveying and Mapping Center to evaluate accuracy. The onshore GNSS reference station and VRS were then selected as reference stations to perform multi-baseline kinematic solutions of the GNSS/IMU buoy, jointly resolving the sea surface heights relative to the reference stations. Due to varying environmental conditions around each tide gauge and differing buoy observation situations, it was necessary to evaluate the plausibility of the calculated buoy sea surface height variations (including tidal fluctuations). If the GNSS solutions did not show ocean tidal variations, the sky visibility at the onshore reference station was re-assessed, and the VRS was adjusted as the primary reference station and the onshore observation station as an auxiliary station before recalculating. Finally, the calculated results were then converted to the TWD97[2010] coordinate system.

In this study, relative positioning solutions were processed using the GrafNav software version 8.70 developed by Novatel in Canada, which employs a dynamic carrier-phase Kalman filter for fast and stable processing. Both static and kinematic solutions were obtained using ARTK (Advanced RTK) to resolve integer ambiguities in the carrier-phase measurements. ARTK is an on-the-fly (OTF) algorithm that addresses cycle slips in differential solutions, significantly improving dynamic positioning accuracy to the centimeter level. As the goal of this study is to achieve continuous kinematic positioning, the data were processed in both the forward (from earlier to later records) and reverse (from later to earlier records) directions. The combined forward–reverse solutions further enhanced the accuracy [27].

IMU errors can accumulate rapidly over prolonged navigation periods, but high-precision GNSS measurements can update and correct IMU navigation results. Additionally, during GNSS signal disruptions or obstructions, which cause signal interruptions or cycle slips, and buoy tilts, IMU measurements provide corrective navigation information, aid the GNSS receiver in reacquiring signals, and supply precise orientation. The loosely coupled architecture treats the IMU and GNSS as two independent systems, where the IMU uses the navigation equations, and GNSS uses an independent Kalman filter for solutions. Finally, an extended Kalman filter [28,29] and the Rauch–Tung–Striebel (RTS) smoother [30] are used to obtain optimal integrated solutions. This study integrated the GNSS positioning results with the IMU data in a loosely coupled solution, outputting three-dimensional positions, velocities, attitudes, and precision indicators [31].

The outputted three-axis attitude angles (roll, pitch, and heading) provide information for correcting tilt errors in the GNSS/IMU buoy, thereby compensating for the height reduction caused by the buoy’s tilt under wind and waves. Figure 4 illustrates the correction of the buoy tilt angle. The equation for the buoy tilt angle (γ) is as follows [32]:

$$\gamma ={\cos }^{-1}[\cos (\alpha )\ast \cos (\beta )]$$

(1)

where α is the roll angle and β is the pitch angle. Since the distance from the buoy’s equator to the sea surface, denoted as H2, is very small, it is assumed to be zero. The distance from the Antenna Reference Point (ARP) to the buoy’s equator (H1) is known (left panel of Figure 4). When the buoy tilts (right panel of Figure 4), the distance from the ARP to the sea surface (H3) can be calculated using the trigonometric relationship between H1 and the tilt angle γ. The height correction (HC) due to buoy’s tilt is obtained as the difference between H3 and H1, as shown in the following equation [32].

The distance from the ARP to the sea surface (H3) is given as follows:

$$H3=(H1+H2)\times \cos (\gamma )$$

(2)

The height correction (HC) is given as follows:

HC = H1 − H3

(3)

3. Results

The study describes an experiment where GNSS/IMU buoys were utilized simultaneously nearby 34 tide gauges, and satellite signals were unobstructed as much as possible. The observation dates for the buoys are listed in

Table 2. Mean and STD of sea surface height differences from tide gauges and GNSS/IMU buoys.

TG ID	Name	Observation Epoch	Mean of Differences (m)	STD of Differences (cm)
112	Hsinchu	31.07.2019	0.055	8.8
113	Waipu	01.08.2019	0.021	8.8
1102	Tamsui	02.08.2019	−0.019	6.5
1116	Jhuwei	30.07.2019	−0.043	6.1
1156	Boziliao	16.08.2019	−0.213	3.2
1166	Dongshi	03.12.2019	−0.214	1.1
1176	Jiangjun	19.08.2019	−0.033	4.1
1186	Donggang	05.12.2019	−0.023	3.3
1196	Houbihu	06.12.2019	−0.124	2.7
1206	Linshanbi	28.07.2019	−0.040	1.7
1226	Longdong	10.08.2019	−0.033	2.9
1236	Wushi	10.08.2019	−0.049	2.1
1246	Su−ao	12.08.2019	−0.032	1.8
1256	Hualien	14.08.2019	0.056	3.7
1276	Chenggong	22.08.2019	0.001	3.8
1356	Penghu	25.12.2019	−0.031	1.4
1366	Wengang	18.08.2019	−0.175	2.4
1386	Liuchiu	08.10.2019	0.018	1.8
1396	Lanyu	25.09.2019	0.053	3.1
1436	Taichung Port	15.08.2019	−0.068	5.2
1456	Mailiau	07.10.2019	−0.223	3.1
1486	Kaohsiung	20.08.2019	0.014	2.5
1496	Syunguangzui	28.09.2019	−0.159	2.3
1516	Keelung	19.09.2019	−0.022	2.7
1552	Heping Port	13.08.2019	−0.110	3.2
1566	Shihti	21.08.2019	−0.152	4.4
1586	Fugang	24.09.2019	−0.035	2.6
1596	Dawu	23.09.2019	−0.026	3.6
1676	Lyudao	26.09.2019	−0.056	3.9
1786	Yongan	18.10.2019	0.019	2.6
1926	Mazu	04.09.2019	0.014	6.0
1956	Kinmen	12.10.2019	0.108	4.3
1966	Shuitou	13.10.2019	0.634	9.4
11781	Sicao	27.08.2019	0.027	3.6
Mean			−0.025	3.8

. Figure 5 and Figure 6 show field photos from the Linshanbi and Su-ao stations, illustrating the GNSS/IMU buoy in operation, GNSS measurements at the tide gauge benchmarks, and observation sites in the harbors (indicated by red circles).

After processing the GNSS observational data by relative positioning, GNSS/IMU integration was performed using a loosely coupled solution. The GNSS/IMU integrated solution was recorded at a frequency of 1 Hz, while the tide gauge data were recorded with sampling intervals of 6 min (1/360 Hz). For comparison, the GNSS/IMU data were averaged to one data point every 6 min, excluding data points with less than 70% of observations. The tide gauge and GNSS/IMU data were then compared after both were converted to the TWD97[2010] ellipsoid heights. The STD of the differences between the tide gauge and GNSS/IMU data was calculated, and the GNSS/IMU integrated solution (one data point every 6 min) was considered an outlier if the difference was larger than 3 STD. Finally, the mean and STD of the differences between the two datasets were calculated.

Using the Linshanbi and Su-ao tide gauges as examples, Figure 7 and Figure 8 illustrate the comparison between the GNSS/IMU buoy and tide gauge data for these two stations. The mean values of the differences were −4.0 cm and −3.2 cm, respectively, and may be primarily have been caused by crustal movement and incomplete datum alignment at the tide gauges. The STDs of the differences were 1.7 cm and 1.8 cm, respectively, primarily reflecting the observation accuracy of the GNSS/IMU buoys and tide gauges. This study completed datum analyses for all 34 tide gauges, and Table 2 summarizes the comparison of the GNSS/IMU buoy results with the tide gauge records. The averages of the mean and STD of the differences across all stations were −2.5 cm and 3.8 cm, respectively, with the largest STD of 9.4 cm observed at the Shuitou tide gauge. The comparisons indicate that most tide gauge datums were reliable, with only a few stations showing mean differences greater than 10 cm, including the Boziliao, Dongshi, Houbihu, Wengang, Mailiau, Heping Port, Shihti, Kinmen, and Shuitou tide gauge stations.

The Shuitou station showed a mean of the differences of 63.4 cm and an STD of the differences of 9.4 cm, suggesting a questionable datum at this station. For future applications, the Shuitou tide gauge datum should be adjusted to align with the buoy. As an offshore island tide gauge, the Shuitou datum is based on the long-term mean sea level at the tide gauge, meaning the sea level variations should oscillate around the zero value when the tide gauge records are relative to TWVD2001 (orthometric height). However, since 2019, the Shuitou tide gauge records have been noticeably below the tide gauge zero (Figure 8), resulting in a significant discrepancy between the Shuitou tide gauge data and GNSS/IMU buoy observations. The Boziliao, Dongshi, Wengang, and Mailiau tide gauges are located in southwestern Taiwan, while Heping Port and Shihti are in Hualien County, where significant subsidence has been observed, particularly in the southwest, which exhibits the highest subsidence rates [33,34]. This has caused tide gauge data in these areas to be greater than the GNSS/IMU buoy measurements.

4. Discussion and Conclusions

In this study, GNSS/IMU buoys were deployed near 34 tide gauges around Taiwan to synchronously monitor sea surface height variations and assess the accuracy of tide gauge datums. The analysis revealed that the STD of the differences across all stations was 3.8 cm, with the highest STD of 9.4 cm observed at the Shuitou tide gauge, indicating the potential of GNSS/IMU buoys for sea surface height observation. Additionally, the average of the mean of the differences was −2.5 cm across all stations. Among the 34 tide gauges, the datums were reliable at most stations, with only a few stations showing a mean of the differences between the buoy and tide gauge greater than 10 cm, including Boziliao, Dongshi, Houbihu, Wengang, Mailiau, Heping Port, Shihti, Kinmen, and Shuitou stations. Notably, the Shuitou station data showed a significantly larger mean of the differences compared to the STD, with a sea level value significantly below the tidal zero since 2019, suggesting a questionable datum at this station. Other stations are located in subsidence areas, resulting in tide gauge data appearing higher than the GNSS/IMU buoy measurements. Therefore, in order to use tide gauge data for sea level changes or depth datum calculations, it is essential to thoroughly verify ground displacement. Co-located GNSS and tide gauges provide the optimal solution for this purpose.

This study demonstrates that the GNSS/IMU buoys achieved high accuracy in the sea surface height measurements, with a mean difference of −2.5 cm and a STD of 3.8 cm. These differences are minimal compared to the total signal amplitude, such as tidal and wave variations, ranging from tens of centimeters to several meters. Additionally, the GNSS/IMU buoys provide a cost-effective and flexible alternative to traditional tide gauges, particularly in regions requiring rapid deployment or affected by vertical land motion.

This study thus highlights the importance of GNSS/IMU buoy systems as a complement to traditional tide gauges, particularly in areas where land movements affect the accuracy of tide gauge data. GNSS provides 1 Hz centimeter-level positioning, while IMU delivers 20 Hz attitude and acceleration data, enabling precise measurement of both low-frequency tidal variations and high-frequency ocean surface waves [18]. These results are comparable to those reported in [35]. GNSS/IMU buoys can provide critical support for marine surveying and coastal management under changing climatic and geophysical conditions.