Quality assessment of the mapping of satellite ocean altimeter data

Based on the orbital data of the Jason3 satellite, the absolute dynamic topography (ADT) of 1/8°×1/8° and 1/4°×1/4° products distributed by AVISO (hereinafter referred to as AVISO1/8° and AVISO1/4°) was interpolated into the Jason3 orbit, and the effective resolution and merged product error of the two products were evaluated with the Northwest Pacific Ocean as the target area. In addition, combined with independent SST data and drifting buoy data, the ground conversion field in the merged data was tested, and the results showed that although the spatial resolution of AVISO1/8° was doubled compared with AVISO1/4°, its effect was not significantly improved, and the error in some areas was even slightly greater than that of AVISO1/4°. Finally, these two merged datasets were used to identify mesoscale vortices. AVISO1/8° have higher precision and make identifying vortex structures easier. The two products are consistent in identifying vortices with relatively large radius, while there are differences in identifying vortices with relatively small radius.


Introduction
The 21st century is an important period in ocean science and exploration, with coastal nations placing higher demands on marine rights and development [1].Satellite remote sensing of oceans, with its advantages of large coverage, near-real-time, and continuous observations, has been the main technological means for significant progress in marine science since the late 20th century [2].Satellite altimetry plays a crucial role in observing global oceans and is important for geodesy, physical oceanography, and global climate change research [3].Recognizing the importance of satellite altimetry technology, countries worldwide have launched and implemented next-generation scientific satellite programs to continuously innovate and advance technological developments for enhancing marine scientific research capabilities [4].
ADT is one of the most important indicators of climate change, as it reflects the response of the climate system to human forcing and natural variability.High-precision satellite altimeters for sea surface height (SSH) measurements provide all-weather high-resolution observations of SSH fields, which are essential for ocean analysis and forecasting.Compared with along-track data from satellite altimeters, merged products with temporal and spatial continuity can intuitively reflect oceanic geostrophic currents and dynamic processes, thus possessing high practical value [5].

Along-track data from satellite altimeters
Currently, the most widely used satellite altimeter data come from the Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO) organization of the French Space Agency.Among the products released by AVISO, there are two global gridded sea-level height products: sea level anomaly (SLA) and absolute dynamic topography (ADT).The SLA represents the sea-level height anomaly by subtracting the Mean Sea Surface Height (MSSH), which is typically based on a 20-year (1993-2012) average sea level height.ADT was obtained by adding SLA to the Mean Dynamic Topography (MDT), which was calculated using 4.5 years of gravity recovery and climate experiment (GRACE) data, along with 15 years of altimeter data and in situ measurements.The working principles of satellite altimeters and the relationships between various relevant physical quantities are illustrated in Figure 1.

Sea surface temperature data from NOAA satellites
The National Oceanic and Atmospheric Administration (NOAA) satellites are third-generation operational meteorological observation satellites in the United States [8].They are used for daily weather observations and typically operated in pairs.As each satellite can observe the same area at least twice a day, the use of two satellites allows for more than four observations per day.The orbital heights of these satellites were 870 km and 833 km, with orbital inclinations of 98.9° and 98.7°, respectively, and period of 101.4 minutes.The orbit is nearly perfectly circular and subsynchronous.NOAA satellites are primarily equipped with two types of sensors: the Advanced Very High-Resolution Radiometer (AVHRR/2) and TIROS Operational Vertical Sounder (TOVS).AVHRR/2 is a remote sensing instrument used to observe cloud and temperature distributions over the Earth's surface, primarily in marine areas.In this study, sea surface temperature data observed by the AVHRR sensor were utilized, with a spatial resolution of 1/4° × 1/4° and a temporal resolution of 1 d.

NOAA drifter buoy data
The drifter buoy data were obtained from the NOAA.It comprises a collection of surface buoys tracked using GPS.The data had a temporal resolution of 1 h and included variables such as the latitude, longitude, buoy ID, buoy status, time, and current velocity.

Error analysis and comparison of the two merged data
The Northwestern Pacific region (0-50°N, 100-150°E) was chosen as the study area.AVISO1/8° and 1/4° were interpolated onto the along-track orbit of Jason3, and a comparison and error analysis of the results were conducted.
To illustrate the performance of the ADT interpolation from the two merged datasets onto the Jason3 orbit, the mean ADT for the entire year of 2020 was calculated and displayed for both AVISO1/8° and AVISO1/4°.The results are shown in Figure 2.  2 shows that the ADT distributions for AVISO1/8° and AVISO1/4° were essentially the same.Subsequently, the ADT of AVISO1/8° was subtracted from that of AVISO1/4° to obtain the distribution of the difference between the two.Figure 2c shows that in the target area, the difference between the ADT values of AVISO1/8° and AVISO1/4° is positive and approximately 0.005m, indicating that the values of AVISO1/8° are slightly larger than those of AVISO1/4°.In the southwestern part of the region, the difference is mainly negative and close to zero, indicating that the ADT of AVISO1/8° is smaller than those of AVISO1/4° (approximately 0.01m).In the southern part of Japan, there are small areas with positive differences, around 0.03m, indicating that the ADT of AVISO1/8° is larger in this region.
Next, the-root-mean-square error (RMSE) was calculated for the interpolation of the two products onto the Jason3 orbit, and the resulting distribution is shown in Figure 3.The two plots in Figure 3 show that the distributions of the RMSE for AVISO1/8° and AVISO1/4° products were generally similar, with AVISO1/8° exhibiting a slightly higher RMSE in certain localized regions.In some specific areas, such as the southeastern part of the Philippines and the southern part of Japan, both products have larger RMSE values, reaching around 0.1m.However, in the other regions, the RMSE values were relatively small and did not exceeding 0.05m.
To provide a more intuitive representation of the difference in the RMSE between the two merged datasets, a skill score index is defined as follows: Where, MSE(AVISO1/4°) and MSE(AVISO1/8°) represent the mean square errors of AVISO1/4° and AVISO1/8°, respectively.A skill score greater than zero indicated that the RMSE of AVISO1/4° was smaller than that of AVISO1/8°.Figure 4 shows that in the southwestern region of Japan, the overall skill score was greater than zero, indicating that the RMSE of AVISO1/4° was smaller than that of AVISO1/8°.In northeastern Japan, the overall skill score was < 0, indicating that the RMSE of AVISO1/4° was larger than that of AVISO1/8°.

Evaluation of interpolation along the Jason3 orbit for the two merged data
Evaluation of AVISO1/8° and AVISO1/4° merged data involved interpolating them onto the Jason3 orbit and assessing their performance.
Effective resolution is an important indicator of the merged data quality, representing the minimum scale at which oceanic eddies can be resolved.From a spectral analysis perspective, it is defined as the smallest spatial scale where the ratio of the energy spectral density between the fusion data and the true signal exceeds 0.5.First, the energy spectral density was calculated using Jason3 along-track data.Simultaneously, AVISO1/8° and AVISO1/4° were interpolated to the along-track data points, and the same spectral analysis was performed.This allowed us to determine the scale at which the energy spectral density ratio between the two merged datasets and the along-track data reached 1/2.This scale represents the effective resolution of the merged data.
The ratio of energy spectral density is depicted in Figure 5. Figure 5 shows that the effective resolution for both AVISO1/8° and AVISO1/4° is approximately 190 km, with the former having a slightly higher effective resolution than the latter when compared with the Jason3 along-track data.
To clearly assess the fit between the merged data and Jason3 along-track data, further analysis of the merged data errors was conducted.A comparative distribution map of AVISO1/8° and AVISO1/4° merged data with the Jason3 along-track ADT data for the entire year of 2020 was created.The fitting maps of the two products are shown in Fig. 6. indicates the correlation of the linear regression coefficients, and RMSD represents the RMSE (unit: meters) (similarly for other statistics).Comparing the two plots in figure, it can be observed that both products exhibit some deviations from the SSH observed by along-track satellite measurements [9].However, AVISO1/4° had a slightly smaller RMSD than AVISO1/8°.Additionally, AVISO1/4° showed a slightly higher correlation and a larger correlation coefficient with the assumed true values from the along-track satellite data than AVISO1/8°.
Based on the above conclusions, the ADT obtained from AVISO1/8° is comparable to that obtained from AVISO1/4°.Next, we compared the fittings of the two products.Because AVISO1/8° has a higher resolution than AVISO1/4°, we extracted the ADT from AVISO1/8° at the same latitude and longitude as AVISO1/4° for comparison.This is illustrated in Fig. 7.As shown in Figure 7, the fitting coefficient (C) between the two products reached 0.9928, with a correlation (R) of 0.9856 and RMSD of 0.027m.This indicated that the difference between the two products was minimal.When the ADT is approximately less than 0.5m, the fitting curve was above the black dashed line, suggesting that AVISO1/8° had slightly higher ADT values than AVISO1/4°.Conversely, when the ADT is approximately greater than 0.5m, the fitting curve is below the black dashed line, indicating that AVISO1/8° has slightly lower ADT values compared to AVISO1/4°.

Independent data comparison
Satellite SST data provides complete two-dimensional images.Although there is no direct correspondence between SST and ADT, the spatial structure of SST often reveals the spatial positions and structures of mesoscale eddies and other mesoscale circulations during ADT.Herein, we present the distribution of geostrophic currents obtained from the merged products and the SST distribution obtained from the AVHRR sensor on the NOAA satellite on July 1, 2020.[10] on July 1st, 2020.Figure 8 shows that in the southeastern Yellow Sea and southeastern Japan, the SST displays multiple ocean frontal zones and local warm and cold core structures.Because of the difference in spatial resolution between the two merged products, AVISO1/8° exhibited higher precision in depicting geostrophic currents, making it easier to identify vortex structures.However, the overall distribution of the geostrophic currents obtained from the merged products was essentially the same.
In summary, the geostrophic currents reflected by the AVISO-merged products were generally consistent.In comparison, AVISO1/8° had a higher spatial resolution, resulting in denser and more easily recognizable geostrophic flow vectors and vortex structures.However, in some areas, AVISO1/4° accurately identified mesoscale eddies.
Ocean geostrophic currents were calculated based on the buoy positions and other auxiliary data.Because the stabilizers of the drifting buoys were located at a depth of 15m, the geostrophic flow at 15m depth was computed using these independent data.Although there may be some deviations, this method remains effective in the absence of reliable independent data.with buoy geostrophic flow velocities (GDP) (unit: m/s) [11].Figure 9 presents a scatter plot distribution of the geostrophic flow velocities from both merged products compared to the buoy geostrophic flow velocities.The geostrophic flow velocities from both AVISO products were relatively weaker than the buoy velocities, whereas AVISO1/8° exhibited stronger geostrophic flow velocities in the range of 0.1-0.5 m/s compared to AVISO1/4°.Additionally, the fitting coefficients and correlations between the two merged products were consistent.However, the RMSE between the geostrophic flow velocities from AVISO1/8° and buoy geostrophic flow velocities was 0.2064 m/s, whereas that for AVISO1/4° was 0.2111 m/s.This indicates that AVISO1/8° has a smaller RMSE between the geostrophic flow velocities and the buoy geostrophic flow velocities than AVISO1/4°.products.The results consistently indicate that the ADT from AVISO1/4° aligned more closely with the buoy trajectory direction than that from AVISO1/8°.

Application of mesoscale vortices in the northwest Pacific Ocean
Based on AVISO1/4° and AVISO1/8° merged data, the daily mesoscale vorticity in the Northwest Pacific Ocean in 2020 was identified using the vortex detection and tracking method, and its distribution characteristics and intensity changes were analysed.First, the top five vortices were selected according to the vortex radius from largest to smallest, and the vortex-related parameters of AVISO1/4° and AVISO1/8° were obtained.Owing to space constraints, only the vortices identified on January 1, 2020, are shown in Tables 1 and 2.
Table 1 1 and 2, from, the radii of the vortices identified by AVISO1/8° were generally larger than those of AVISO1/4°, and the corresponding centre positions and amplitudes were also different.Among the five vortices, more cold vortices and fewer warm vortices were identified.In particular, for AVISO1/4°, four fifths of the vortices are cold vortices.
The next step is to show the scroll identification map.Owing to space limitations, only the scroll identification map for July 1, 2020, is presented here.As can be seen from Figure 11, the vorticity in the Northwest Pacific Ocean on July 1 was mainly concentrated in the eastern part of the East China Sea, the eastern part of the South China Sea, and the southeastern part of Japan, with the majority of anti-gas vorticity.There are three strong air vortices in the eastern and northeastern Ryukyu Islands.In comparison, the two products are consistent in recognizing strong vortices, but there are some deviations in recognizing the scope of the vortices, mainly because the scope of the anti-gas vortices recognized by AVISO1/8° is smaller than that of AVISO1/4°.There were also some differences in the recognition of relatively weak vortices.For example, near (119°E and 22°N), AVISO1/4° recognized multiple mesoscale vortices within a small range, whereas AVISO1/8° did not.Vortices identified in AVISO1/8° were not identified in AVISO1/4°.

Conclusion
The main conclusions of this study can be summarized as follows: (1) Comparison between AVISO merged data and Jason3 along-track data: The RMSE for AVISO1/8° was 0.0334m, with a correlation coefficient of 0.9811.AVISO1/4° had an RMSE of 0.0328m, and a correlation coefficient of 0.9817.The fitting curve also indicates a slightly better performance for AVISO1/4°.The average values of the two merged datasets were calculated for the entire year, and the RMSE was calculated accordingly.The results indicate that the distributions of the RMSE for AVISO1/8° and AVISO1/4° were similar, with a slightly larger RMSE in certain areas for AVISO1/8°.In some local areas, such as southeastern Philippines and southern Japan, the RMSE reached approximately 0.1m, while in other areas, the RMSE was small, not exceeding 0.05m.The evaluation score based on the RMSE showed that in the southwest Japan, the overall Skill Score was greater than zero, indicating that the RMSE of AVISO1/4° was smaller than that of AVISO1/8°.In northeastern Japan, the overall Skill Score was less than 0, indicating that the RMSE of AVISO1/4° was greater than that of AVISO1/8°.
(2) Effective resolution of the merged data: The effective resolution of the two merged datasets was evaluated and compared with the Jason3 along-track data.The results showed that both AVISO1/8° and AVISO1/4° had an effective resolution of approximately 190 km, with a slightly higher resolution for the former than for the latter.
(3) Comparison with independent data: The results revealed that the geostrophic currents of both AVISO products were relatively weaker than the buoy velocities, whereas AVISO1/8° showed a relatively stronger geostrophic current in the 0.1-0.5 m/s range.Simultaneously, the RMSE between the geostrophic currents of AVISO1/8° and buoy velocities was smaller than that of AVISO1/4°.The ADT of AVISO1/4° showed better agreement with the buoy trajectory directions than AVISO1/8°.
(4) Identification of mesoscale vortices: Owing to the different spatial resolutions of the two merged datasets, AVISO1/8° has higher precision and makes it easier to identify the vortex structure.The two products were consistent in recognizing vortices with relatively large intensities, whereas there were differences in the recognition of vortices with relatively small intensities.

Figure 2 .
Figure 2. Distribution of average ADT interpolation for AVISO1/8° (a) and AVISO1/4° (b) for the full year of 2020.The difference obtained by interpolating the two AVISO products into the Jason3 track(c).A comparison of the first two plots in Figure2shows that the ADT distributions for AVISO1/8° and AVISO1/4° were essentially the same.Subsequently, the ADT of AVISO1/8° was subtracted from that of AVISO1/4° to obtain the distribution of the difference between the two.Figure2cshows that in the target area, the difference between the ADT values of AVISO1/8° and AVISO1/4° is positive and approximately 0.005m, indicating that the values of AVISO1/8° are slightly larger than those of AVISO1/4°.In the southwestern part of the region, the difference is mainly negative and close to zero, indicating that the ADT of AVISO1/8° is smaller than those of AVISO1/4° (approximately 0.01m).In the southern part of Japan, there are small areas with positive differences, around 0.03m, indicating that the ADT of AVISO1/8° is larger in this region.Next, the-root-mean-square error (RMSE) was calculated for the interpolation of the two products onto the Jason3 orbit, and the resulting distribution is shown in Figure3.

Figure 5 .
Figure 5. Ratio of energy spectral density.

Figure 6 .
Figure 6.Scatterplot and linear regression curves of AVISO1/8° and AVISO1/4° products with Jason3 along-track data.The black dots represent the scatter of merged data with satellite data.The black dashed line represents a ratio of 1, indicating perfect agreement between the two.The correlation coefficient (C) between the merged data and satellite data is shown in the top left corner.The red solid line represents the fitted line of the scatterplot, with the equation (y) displayed in the top left corner.The coefficient of determination (R)indicates the correlation of the linear regression coefficients, and RMSD represents the RMSE (unit: meters) (similarly for other statistics).Comparing the two plots in figure, it can be observed that both products exhibit some deviations from the SSH observed by along-track satellite measurements[9].However, AVISO1/4° had a slightly smaller RMSD than AVISO1/8°.Additionally, AVISO1/4° showed a slightly higher correlation and a larger correlation coefficient with the assumed true values from the along-track satellite data than AVISO1/8°.Based on the above conclusions, the ADT obtained from AVISO1/8° is comparable to that obtained from AVISO1/4°.Next, we compared the fittings of the two products.Because AVISO1/8° has a higher resolution than AVISO1/4°, we extracted the ADT from AVISO1/8° at the same latitude and longitude as AVISO1/4° for comparison.This is illustrated in Fig.7.

Figure 8 .
Figure 8.Comparison of geostrophic currents (vector arrows) from AVISO1/4°(a) and AVISO1/8°(b) merged products and SST (filled colors) from AVHRR sensor on NOAA satellite[10] on July 1st, 2020.Figure8shows that in the southeastern Yellow Sea and southeastern Japan, the SST displays multiple ocean frontal zones and local warm and cold core structures.Because of the difference in spatial resolution between the two merged products, AVISO1/8° exhibited higher precision in depicting geostrophic currents, making it easier to identify vortex structures.However, the overall distribution of the geostrophic currents obtained from the merged products was essentially the same.In summary, the geostrophic currents reflected by the AVISO-merged products were generally consistent.In comparison, AVISO1/8° had a higher spatial resolution, resulting in denser and more easily recognizable geostrophic flow vectors and vortex structures.However, in some areas, AVISO1/4° accurately identified mesoscale eddies.Ocean geostrophic currents were calculated based on the buoy positions and other auxiliary data.Because the stabilizers of the drifting buoys were located at a depth of 15m, the geostrophic flow at 15m depth was computed using these independent data.Although there may be some deviations, this method remains effective in the absence of reliable independent data.

Figure 9 .
Figure 9. Scatter plot distribution, fitting curve, correlation coefficient, correlation, and RMSE of geostrophic flow velocities (GDP) from AVISO1/8° and AVISO1/4° comparedwith buoy geostrophic flow velocities (GDP) (unit: m/s)[11].Figure9presents a scatter plot distribution of the geostrophic flow velocities from both merged products compared to the buoy geostrophic flow velocities.The geostrophic flow velocities from both AVISO products were relatively weaker than the buoy velocities, whereas AVISO1/8° exhibited stronger geostrophic flow velocities in the range of 0.1-0.5 m/s compared to AVISO1/4°.Additionally, the fitting coefficients and correlations between the two merged products were consistent.However, the RMSE between the geostrophic flow velocities from AVISO1/8° and buoy geostrophic flow velocities was 0.2064 m/s, whereas that for AVISO1/4° was 0.2111 m/s.This indicates that AVISO1/8° has a smaller RMSE between the geostrophic flow velocities and the buoy geostrophic flow velocities than AVISO1/4°.

Figure 10 .
Figure 10.Comparison of ADT fields from AVISO1/4° (left) and AVISO1/8° (right) products with buoy trajectories (blue for current day, red for previous and following days' trajectories, arrow indicates buoy movement direction, buoy ID: 63123200) on February 14th, 2020(a) [10].And the other buoy ID is 63344700 on February 16th, 2020(b).Affected by the geostrophic flow, the buoy trajectories moved along the contour lines of the ADT field.Figures 10 presents comparisons between the three different buoy trajectories and the fused ADT

Figure 11 .
Figure 11.Mesoscale vortices identified by AVISO1/4° (a) and AVISO1/8° (b) merged data on July 1, 2020.The depth of colour in the figure represents the SLA (cm); the negative area, also known as the dashed line area, represents the gas vortex, generally known as the cold vortex; the positive area, also known as the solid line area, represents the anti-gas vortex, generally known as the warm vortex; the