Comparative analysis of significant wave height between a new Southern Ocean buoy and satellite altimeter

Jinjun Kng , Runyu Mo Yiting Chng Hongli Fu

a National Ocean Technology Center, Tianjin, China

b National Marine Data and Information Service, Tianjin, China

Keywords:Mooring buoy Southern ocean Satellite altimeter Significant wave height

A B S T R A C T In-situ observation is restricted by the strong wind and waves in the Southern Ocean. A Westerlies Environmental Monitoring Buoy (WEMB) was firstly deployed in the Southern Ocean during China’s 35th Antarctic Expedition,facilitating further understanding of the oceanic environmental characteristics of this region. With the development of technology and the improvement of data processing methods, the accuracy of satellite altimeter products is constantly improved, thus making it possible to inspect and evaluate the in-situ observation data. Based on the L3 products of multiple satellite altimeters, this paper analyzes and corrects the significant wave height (SWH)data of WEMB by means of data matching, error statistics, and linear least-squares fitting. Through this study,the authors obtained the following results. The effect of gravitational acceleration changes with latitude on SWH accuracy is fairly small. Due to the low response of WEMB to high-frequency waves, there is a systematic deviation. A feasible correction method is therefore proposed to improve the SWH accuracy of WEMB. The temporal variation of the corrected SWH is highly consistent with that of the 10 m wind during the observation period,and its average value reaches 3.8 m.

1.Introduction

Ocean waves have become an increasing concern worldwide due to their great significance to marine engineering, marine resources development, navigation and transportation, fishing, and aquaculture. To date, a variety of ocean wave observation technologies have been developed, such as buoys, satellite altimeters, shipborne wave radars, and image wave measurements. The moored accelerometer buoy seems to be one of the most popular choices as it measures the actual surface movement and is not impacted by any theoretical approximations and the water vapor in the air ( Niclasen and Simonsen, 2007 ). At the same time, the satellite altimeter can provide long-term observational time series covering the globe, which has become an indispensable tool for wave observation in the past few decades. Recently, much research on the inspection and correction of satellite data products has been conducted based on buoy observations ( Dobson et al., 1987 ; Ray and Beckley, 2003 ; Caires and Sterl, 2003 ; Queffeulou, 2005 ; Durrant et al., 2009 ;Zieger et al., 2009 ; Zhao et al., 2012 ; Passos et al., 2013 ; Sepulveda et al.,2015 ; Jayaram et al., 2016 ; Peng and Lin, 2016 ). With the development of technology, the accuracy of satellite altimeter products is constantly improved, and has reached a level comparable to the accuracy of buoy measurements ( Queffeulou, 2005 ), making it possible to inspect and evaluate the

in-situ

observation data. Challenor and Cotton(2003) compared the significant wave height (SWH) of different buoy networks with that of the altimeter data corrected by National Data Buoy Center (NDBC) buoy data and gave the difference between them.Durrant et al. (2009) also analyzed the difference in SWH between NDBC and Canadian buoy network data when they compared to the corrected altimeter data.

Mooring buoy stations have a very limited distribution in high latitudes, especially in the Southern Ocean, where strong winds and storms are perennial. In 2010, Australia set up the first air—sea flux mooring buoy station at (47°S, 142°E) ( Schulz et al., 2012 ). The Woods Hole Oceanographic Institution deployed a set of buoys at (55°S, 90°W) with a lifespan covering 2017—18, where wave data are not available (from the NDBC website). On 8 February 2017, with the assistance of the New Zealand Defense Force, a mooring wave buoy was deployed near Campbell Island in the south of New Zealand (52°45.71 ′ S, 169°02.54 ′ E). After 170 days, the buoy was drifting eastwards ( Barbariol et al., 2019 ).During China’s 35th Antarctic Expedition, the Westerlies Environmental Monitoring Buoy (WEMB) was deployed in the Southern Ocean, providing many variables such as wind, sea surface temperature and salinity,and especially ocean waves, which is extremely valuable for the study of the Southern Ocean.

This paper focuses on analyzing the difference between WEMB and the L3 satellite altimeter products derived from the Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO). The possible reasons for the differences are discussed. Furthermore, an SWH correction method for WEMB is suggested in order to modify the systematic errors.

2. Data and methods

2.1. Data

2.1.1.

Buoy

data

On 1 January 2019, WEMB ( Fig. 1 ), developed by the National Marine Technology Center (NOTC) of China for the severe sea conditions in the westerlies, was deployed in the Southern Ocean (52.6122°S,175.3819°E) during China’s 35th Antarctic Expedition. It can provide hourly real-time observation data. The data were disrupted in April 2020 due to a power system breakdown. The sensors aboard WEMB were NOTC “SBS2—1 ″ equipped with a vertical accelerometer,a two-dimensional horizontal accelerometer, and a solid-state threeaxis magnetometer-based compass. For further details of WEMB, see Feng et al. (2019) . The SWH accuracy is ± (0.1 m + 5%

H

), where

H

is the measurement value. The accuracy of wave measurement is to a great extent affected by the following-wave performance. Steel et al. (1985) indicated that the NDBC 10-m buoy underestimated the SWH of highfrequency waves (0.3 Hz) by 26.4% owing to the influence of followingwave characteristics. In this study, the original data from 1 January 2019 to 10 March 2020, without deviation correction, are used, in which the data loss is serious from 26 June to 24 September 2019.

Fig. 1. Location of WEMB buoy and satellite passes around the buoy.

In addition, to verify the rationality of the data processing method and some conclusions, the dataset from 1 January 2019 to 10 March 2020 of NDBC buoy 46035 in high latitudes was selected and compared to altimeter data. The averaged SWH of NDBC 46035 is 3.06 m, which is slightly less than that of WEMB (3.8 m). The daily 10-m wind data are from the National Centers for Environmental Prediction (NCEP) datasets( Kalnay et al., 1996 ) and interpolated to the same resolution as the observation station data in order to analyze the causes of ocean waves.

2.1.2.

Satellite

altimeter

data

The wave datasets were retrieved from multiple satellites (Jason-3,Saral, Cryosat-2, Sentinel-3a, and Sentinel-3b). We extracted the data from January 2019 to March 2020 to correct the buoy data in the westerlies. The Jason-3 mission took over from and continued with the missions of TOPEX/Poseidon, Jason-1, and OSTM/Jason-2. The Jason-3 mission was conducted under a cooperation among the French Space Agency (Centre National d’Etudes Spatiale (CNES)), NASA, EUMETSAT(the European organisation for the Exploitation of Meteorological Satellites), and NOAA (the National Oceanic and Atmospheric Administration). It was launched on 17 January 2016, with a repetition period of 9.9 days ( Picot et al., 2018 ) (see Fig. 1 (a)). SARAL (Satellite with ARgos and ALtiKa) was launched on 25 February 2013. The SARAL mission is a joint collaboration between the Indian Space Research Organization and CNES, with a repetition period of 30 days ( Sepulveda et al., 2015 ;Jayaram et al., 2016 ) (see Fig. 1 (e)). Cryosat-2 is the first ice measurement satellite in Europe. It was launched on 8 April 2010, with a repetition period of 369 days. The Sentinels represent an important part of the European Union’s Copernicus environmental monitoring network.Sentinel-3a was launched on 16 February 2016, and Sentinel-3b on 25 April 2018 ( Yang et al., 2019 ), with a repetition period of 27 days. Here,the L3 SWH products are used, which have been corrected by buoy data( Taburet and Husson, 2017 ).

2.2. Methods

The buoy—satellite data matching method and evaluation metrics used to compare the buoy observations with the satellite altimeter data are described in the following sections.

2.2.1.

Matching

method

The data from buoys and satellite altimeters cannot be completely consistent, both from a temporal and spatial perspective. As such, a set of reasonable matching criteria needs to be established. Firstly, two parameters need to be determined: the temporal window and spatial window.Monaldo (1988) proposed 50 km and 30 min as the spatial and temporal windows for data matching, which have been widely adopted in subsequent research to become the standard for such work ( Zieger et al.,2009 ).

The buoy is usually used as the center, selecting all altimeter data within the given temporal window and radius range. So, a buoy observation value corresponds to a certain amount of altimeter observation values. Some researchers have averaged all satellite data and matched their mean with the buoy data ( Jayaram et al., 2016 ; Feng et al., 2019 ).Others eliminated values greater than ± 2 standard deviations of the altimeter itself, and interpolated buoy observations before and after satellite observation into the satellite observation time ( Durrant et al., 2009 ;Zieger et al., 2009 ; Sepulveda et al., 2015 ). The former method is usually applied to the comparison of multiple buoys with one satellite. This study has only one set of buoy data with a period of more than one year,but there are multiple sets of satellite altimeter data. In order to increase the sample size from the limited amount of buoy data, the latter method was adopted for buoy—satellite matching.

In this study, a 30 min temporal window was selected and the spatial window varied from a 50 km radius to a 200 km radius with a 10 km separation. The statistical results for different spatial windows were analyzed in order to select the best one. It was found that the sample size increases significantly as the window radius increases. It is over 5000 with the 200 km-radius spatial window. According to the assumption that higher consistency between buoy and altimeter data should have a smaller root-mean-square error (RMSE), the spatial window was selected where the deviations of the RMSE among different altimeter were minimal (see Section 3.3 for details). The calculation methods for the RMSE and standard deviation are given in the next section.

2.2.2.

Evaluation

metrics

Due to its lower accuracy in the past, the satellite altimeter product was corrected by the ordinary least squares method based on

insitu

buoys. The accuracy of the satellite altimeter gradually improved with the advancement of technology and has now reached a comparable level to that of buoys ( Caires and Sterl, 2003 ). Since then, the total least squares (TLS) has been adopted in order to correct and evaluate altimeter products ( Durrant et al., 2009 ; Passos et al., 2013 ). In this study, the bias, RMSE, correlation coefficient (

R

), scattering index (SI),and standard deviation (

σ

) are used to evaluate the rationality and accuracy of the data. These parameters are calculated as follows:

3. Results

3.1. Gravitational acceleration correction

An accelerometer is a sensor to measure the acceleration of a carrier. It records the voltage change of the sensitive element caused by the gravitational change induced by the inertial force of the carrier. The sensor uses the parameter of gravitational acceleration

g

. Studies indicate that gravitational acceleration

g

changes along with latitude at the sea surface, as shown in Eq. (6) (1985 International Gravity Formula). The WEMB is located at 52.6122°S, corresponding to

g

= 9.8338. However,it is taken as a constant (

g

= 9.8) in the SBS2—1 without the change with latitude. So, the acceleration correction is to multiply a conversion coefficient

κ

(

φ

) based on the original acceleration

a

(

t

) , as shown in Eq. (7) :

3.2. Spatial window selection

As described in Section 2.2.1 , the spatial window was increased from 50 km to 200 km in 10 km steps, forming 15 sample groups. The statistical results for different spatial windows were compared to select the best spatial window. Fig. 2 shows good consistency between the buoy and altimeter data. Whereas, the result of NDBC 46035 is better than that of WEMB. The spatial window is taken as 80 km (70 km), where the minimum deviation of WEMB (NDBC 46035) occurs. Therefore, subsequently, the time window was set to 30 min and the spatial window to 80 km for WEMB, and 70 km for NDBC 46035. The total amount of data pairs was 4766 for WEMB and 5108 for NDBC46035.

Fig. 2. (a) RMSEs between the L3 product of AVISO and the WEMB buoy data. (b) RMSEs between the L3 product of AVISO and the NDBC 46,035 buoy. (c) As in(a) except for the standard deviation of RMSEs. (d) As in (b) except for the standard deviation of RMSEs.

Under the given temporal and spatial windows, the amount of data pairs for different satellites depends on the satellite’s characteristic parameters, such as the distance between the selected satellite track and the buoy, the amount of the selected satellite orbit, the standard deviations of satellites, and so on. Table 1 indicates the amount of data pairs for different satellites; that is, the size of samples used for statistical analysis.

Table 1 Comparisons between the original buoy data and L3 altimeter data.

Table 2 Comparison between the modified buoy data and L3 altimeter data.

3.3. Error statistics

Table 1 compares the SWH between the original buoy and altimeter L3 data according to the evaluation metrics. It is shown that the WEMB SWH is obviously lower than that of the altimeter L3 product by about 54.30—59.77 cm. Furthermore, the RMSE is large (59.38—68.58 cm). The bias between NDBC 46035 and the altimeter is about 2.95—10.25 cm,and the RMSE is about 25.47—30.16 cm.

Based on the total the amount of data pairs, the formula of the linear relation between the WEMB and altimeter SWH (between NDBC 46035 and altimeter SWH) can be obtained by the TLS method ( Fig. 3 ). Here,for each buoy observation value, the average value of the satellite observation within the specified temporal and spatial window around it is shown by the circles in Fig. 3 . These circles are located near the fitted line. So, the fitted line can to a certain extent represent the relationship between buoy and satellite observations. The fitted line between WEMB and the altimeter moves upward relative to the diagonal line as a whole,while it cannot be seen for the fitted line between NDBC 46035 and the altimeter. This further confirms the existence of systematic deviation of WEMB.

Fig. 3. Linear relation (black solid line) of SWH between buoys and AVISO L3: (a) WEMB against AVISO L3 SWH; (b) NDBC against AVSIO L3 SWH. Circles represent the average value of satellite observations within the specified temporal and spatial window around each buoy observation. The dotted line is the diagonal line.

Fig. 4. Time series of SWH from the original (green) and modified (blue) WEMB, along with the AVISO L3 (red asterisks) data, during the observation period.

Many studies have suggested that there is a systematic discrepancy in the wave data for different buoy networks. Challenor and Cotton (2003) found that there were discrepancies of 6%, 4%,and ? 5% between NDBC and three other buoy networks, operated by the Canadian Marine Environmental Data Service (MEDS), the UK Met-Office, and the Japan Meteorological Agency, respectively.Durrant et al. (2009) pointed that there is a 28 cm difference between MEDS and NDBC.

3.4. Error analysis

The WEMB buoy is a special buoy designed for severe sea conditions in the westerlies. Therefore, considerable attention has been paid to the system reliability. For the sake of improving the structural integrity and mooring reliability, the weight and anchor tension of the buoy were increased, which possibly influences the following-wave performance of the buoy. The WEMB SWH was not calibrated before deployment because it is very difficult to test the following-wave characteristics in the real ocean.

Referring to Steele et al. (1985) ’s theory on wave error correction of buoys, the factors affecting the wave power spectrum include correction factors caused by digital filtering (

R

), correction factors caused by analog filtering (

R

), correction factors caused by sensors and quadratic integration (

R

), and correction factors caused by the hull and mooring system (

R

), as shown in Eq. (11) :

R

,

R

, and

R

can be obtained from laboratory tests. The SBS2—1 wave sensor has been verified by laboratory static tests at the National Center of Ocean Standard Metrology. The measurement accuracy is greater than 5%, and

R

,

R

, and

R

can be approximately 1. It implies that

R

is the main factor affecting the accuracy of buoy measurements. According to the relationship between

R

and frequency given by Steele et al. (1985) , the hull and mooring system mainly affects the measurement at high frequency. In other words, WEMB’s systematic deviation may be related to the low response of the buoy to high frequency.

According to the results of Sepulveda et al. (2015) , the RMSE of the buoy and altimeter is 0.2 m when the SWH is less than 3 m, and increases obviously when the SWH is greater than 3 m. When the SWH reaches 5 m, the RMSE of SARAL and Jason-2 relative to buoy observations is close to or greater than 0.4 m. As shown in Fig. 3 , the RMSE tends to increase along with the wave height.

3.5. Error correction

With the development of technology, altimeter products now have the same accuracy as buoys, which provides a simple and effective method for buoy evaluation and deviation correction. The AVISO L3 product has been calibrated, filtered and corrected by many buoy observations, which has high accuracy and reliability. Therefore, this study uses AVISO L3 as a standard dataset to correct the SWH measured by WEMB:

Table 3 Occurrence days (frequency) for difference ocean wave ranks (ratio of days occurred to total days observed) and the corresponding averaged SWH and wind speed. Averaged SWH and wind speed during the whole observation period are 3.8 m and 9.5 m s ? 1 .

Fig. 5. (a) Time series of the daily corrected SWH from the WEMB buoy (red; units: m) and 10-m wind speed from NCEP datasets (blue; units: m s ? 1 ) at the observation station. (b) As in (a) except for the five-day running average.

3.6. Analysis of SWH characteristics

The time series of the daily corrected SWH during the observation was compared to that of the 10-m wind speed, as shown in Fig. 5 (a).The peaks and valleys of the two time series are in good agreement. After applying a five-day running average to these time series, the degree of coincidence between them becomes better ( Fig. 5 (b)). Therefore, the ocean waves in the observed sea area are mainly driven by winds. The effective observation covers 372 days. During this period, the averaged SWH is 3.8 m, and the averaged 10-m wind speed is 9.5 m s. According to the daily observed SWH, the waves during the observation period were classified, and the occurrence days (frequency) for each classification counted (ratio of the days occurred to total days observed), and the corresponding averaged SWH and wind speed were also calculated( Table 3 ). The results indicate that ocean waves in the Southern Ocean are concentrated in four levels: moderate sea; rough sea; very rough sea;high sea. The occurrence frequency of rough sea is the highest, reaching 0.57, with an average SWH of 3.25 m.

4. Conclusions

During China’s 35th Antarctic Expedition, a marine environment monitoring buoy was deployed in the Southern Ocean for the first time.It can observe a range of variables at the air—sea interface in real time,providing valuable data for further understanding the environmental characteristics of strong winds, big waves, and strong currents. Through comparison with the L3 altimeter data provided by AVISO, the error of SWH measured by WEMB was analyzed, leading to the proposal of a correction method. Based on the corrected SWH data, the characteristics of ocean waves in the westerly zone were analyzed. The main conclusions are as follows:

(1) Based on the consistency among different L3 altimeter products, a selection principle for the spatial window for use in the matching between buoy and altimeter data is proposed.

(2) Although the change in gravitational acceleration with latitude can lead to errors in wave measurement, the error is small and can be ignored.

(3) A systematic deviation was found in the SWH measured by WEMB,which is mainly due to the low response of the buoy to highfrequency waves.

(4) A correction method is proposed by using the TLS method.The corrected SWHs are much closer to those of the AVISO L3 product.

(5) The variation of the corrected SWH is highly consistent with that of the 10-m wind speed, with an averaged SWH of 3.8 m, and the ocean waves reach the “rough sea ”level in most of the time.

Funding

This study was supported by the National Key R&D Program of China[grant number 2017YFC1403300 and 2016YFC1401701].

Acknowledgments

We would like to extend our gratitude to China’s 35th Antarctic Expedition team for its efforts in the deployment. Our thanks also go to AVISO for providing the altimetry data and NDBC for providing the buoy data.