This study focuses on dynamics and optically complex waters in the Belgian coastal zone (BCZ). The BCZ is a relatively shallow (< 50 m) well-mixed shelf sea connected to the North Sea in the north and the English Channel in the west . It is characterized by a relatively high suspended sediment concentration, with a gradient from several hundreds of grams per cubic metre near the shore to < 1 g m⁻³ in the offshore waters, which is inversely related to the bathymetry . Strong tidal currents and the tidal resuspension of sediments are the main causes of the high turbidity in the nearshore area . Annually recurring phytoplankton blooms are observed in spring and summer. These blooms are generally composed of diatoms and Phaeocystis globose . In recent years, blooms have been occurring earlier, likely in response to sea surface temperature increases and changes in nutrient outputs . The water type is turbid coastal to turbid coastal with a high organic content. The water at Research Tower 1 (RT1) near Oostende (51.24643° N, 2.91933° E), used in the validation of the various datasets in this work, is turbid with tidal variability and with an occasional outflow from the port of Oostende (Belgium) reaching the site.

The ocean colour satellite products used in this study are generated following the methodology applied in the high-resolution Copernicus Marine Service using a multi-algorithm approach which aims to combine the best-suited algorithms for different water types. The year 2020 was chosen for the test period, as this year has the largest unbroken time series of independent in situ data at the Oostende RT1 station used to validate the super-resolution DINEOF product and its potential to capture the coastal turbidity dynamics. To facilitate Sentinel-2 and Sentinel-3 product generation, the processor is fully automated and set up in the DIAS cloud environment CREODIAS (https://creodias.eu/, last access: 30 March 2025). This processor starts from L1C and L1 data for Sentinel-2/MSI and Sentinel-3/OLCI respectively and combines atmospheric correction processing (C2RCC + ACOLITE dark-spectrum fitting), IDEPIX pixel classification, ocean colour algorithm application, and product quality control (e.g. glint flagging or bottom reflection flagging) to provide analysis-ready data layers (ARDLs), i.e. chlorophyll (CHL), turbidity (TUR), and suspended particulate matter (SPM). A schematic overview of the different processing steps taken is provided in Fig. .

The RRS products were validated using the Pan-and-Tilt Hyperspectral Radiometer system (PANTHYR, ) for the period 2019–2022. An autonomous PANTHYR system was deployed at RT1 near Oostende (51.24643° N, 2.91933° E). The PANTHYR system has two TriOS RAMSES radiometers mounted on a pan-and-tilt head, one for upwelling and downwelling spectral radiances and one with a cosine collector to measure spectral irradiance, enabling us to determine the RRS signal. The PANTHYR system measures autonomously every 20 min at programmed relative azimuth angles to the Sun. In the present study, measurements were made at a 270° azimuth angle. Because of the hyperspectral measurements, one significant advantage of the PANTHYR datasets when compared to AERONET-OC and typically used to validate ocean colour satellites is that the hyperspectral instrument permits the validation of all MSI and OLCI VNIR bands within the 400–900 nm range, including several near-infrared bands not available with the AERONET-OC instrument. RRS data were finally convolved to the relative spectral response functions of the MSI and OLCI instruments on Sentinel-3 A and B and Sentinel-2 A and B.

Match-ups for the PANTHYR stations were extracted from locations slightly to the east (RT1_shifted; 51.24643° N, 2.9206°0 E) of the deployment tower to avoid platform effects such as direct pixel contamination and shadows as well as in-water wakes. For the match-up extraction, a maximum time difference of 2 h between in situ observation and satellite overpass was allowed. However, the high-frequency measurement protocol from the in situ measurement stations resulted in shorter time differences between in situ and satellite observations. The match-up validation protocol described by was applied to remove erroneous match-ups from the analysis. Macro-pixels of 15 × 15 60 m pixels for Sentinel-2/MSI and 3 × 3 300 m pixels for Sentinel-3/OLCI were extracted from the L2 products. This box allows for the evaluation of spatial stability, or homogeneity, at the validation point. For the satellite data it was required that at least 60 % of the pixels in the defined box be valid (i.e. unflagged) to ensure statistical confidence in the mean values retrieved. The arithmetic mean and standard deviation of the non-masked pixels were determined, enabling the computation of the coefficient of variation (standard deviation divided by the filtered mean). Satellite retrievals with extreme variation between pixels in the defined box (coefficient of variation > 0.15) were excluded from the match-up analysis.

DINEOF is used to calculate the reconstruction of the data and to enhance the resolution of the combined Sentinel-2 and Sentinel-3 dataset. It computes the missing data from a three-dimensional dataset by calculating a truncated empirical orthogonal function (EOF) basis. These EOFs are calculated increasingly (starting from one until the optimal number of EOFs is found) and iteratively until a convergence is reached, and at each iteration the estimate of the missing data is updated using the latest EOF modes. About 3 % of valid data (in the form of clouds, following ) are masked at the beginning of the procedure, and these data are used to determine the number of EOFs that minimize the reconstruction error (in terms of its root mean square error or RMSE). When three consecutive EOFs provide an increasingly higher RMSE, the procedure is stopped and the final reconstruction is performed with the optimal number of EOFs determined by this cross-validation.

In addition to the reconstruction of missing data in several variables (e.g. sea surface temperature, ; chlorophyll, ; turbidity, ; salinity, ; and multi-variate reconstructions, ), DINEOF has been used to detect outliers in satellite data and shadows in high-spatial-resolution satellite data . DINEOF has therefore shown that it can perform a wide range of analyses of satellite data with the aim of improving their quality and completeness.

In order to obtain a super-resolution reconstruction from the combination of Sentinel-3/OLCI and Sentinel-2/MSI data mentioned in Sect. , the initial gappy matrix is prepared as follows: Sentinel-2 data are used preferentially and, on days with no Sentinel-2 coverage, Sentinel-3 data, interpolated at the Sentinel-2 spatial resolution of 60 m, are used. The matrix therefore consists of a mixture of Sentinel-2 and Sentinel-3 data. The interpolation of Sentinel-3 data onto the Sentinel-2 grid using the nearest-neighbour method is done to preserve the size of the matrix, which has to be constant in order to be used in DINEOF and to determine the spatial resolution of the final dataset, but no gain in resolution is made at this step.

On days when Sentinel-2 and Sentinel-3 data are available, only Sentinel-2 data are used. We could slightly increase the spatial coverage on these days by combining both data streams, but we found the increase to be very small, since cloud distribution does not change substantially between the Sentinel-3 and Sentinel-2 passes. In addition, depending on the tidal currents, the difference in turbidity between the two satellite passes can be quite high, and this can lead to discontinuities between both estimates, which in turn can be retained in the final dataset. We have therefore decided to avoid this problem by using a unique data source on a given day.

The initial dataset with the combined Sentinel-2 and Sentinel-3 data has 210 time steps, of which 63 % are Sentinel-3 data and 37 % are Sentinel-2 data. Days with overly high cloud coverage (more than 98 % missing data over the study region) are not used, which brings the final size to 163 d, distributed from 18 January to 17 December 2020.

The combined dataset is fed into DINEOF as a unique matrix. As DINEOF does not re-grid the data, it is important that the initial data are already gridded to the final grid that we want to obtain (i.e. the high-spatial-resolution grid). Through the EOF basis calculation, the high spatial information of Sentinel-2 is extracted by the EOFs, and this information is then projected into the final dataset by the EOF basis, effectively increasing the spatial resolution of the initial dataset.

Super-resolution DINEOF (Sect. ) has been applied to the turbidity data in the Oostende region described in Sect. . The initial matrix has 45 % of missing data. DINEOF was applied to the combined Sentinel-2 and Sentinel-3 data for 2020, and 23 EOFs were retained as optimal for the reconstruction, with a cross-validation error of 1.4 FNU. The size of the matrix was 946 × 789 × 210 (longitude, latitude, and time), and the DINEOF run took 8 h to complete (on an Intel Core i9-10900X CPU at 3.70 GHz). The only two optional parameters to set in DINEOF are related to the filtering of the temporal covariance matrix and were fixed to α=0.01 (the amplitude of the filter) and n=3 (the number of iterations of the filter). These result in a filter of about 1.1 d. As shown in , the use of this filter can result in more EOFs being retained as optimal, which in turn results in a higher variability in the final results. Several tests were performed for values α=0.01 to α=0.1 and n=1 to n=10, and the combination that maximized the number of EOFs was retained. The first three EOFs explain 59.04 %, 25.73 %, and 3.74 % of the total variability of the dataset, and the 23 EOFs retained explain the total of 97.9 % of the variability. When analysing the spatial and temporal structures of these EOFs, we can observe the influence of small-scale variability contained in them. The first EOF mode (Fig. ) displays an inshore–offshore gradient on which more turbid waters are found in the nearshore region. An increasing turbidity along the coast is found towards the region of the Scheldt estuary. The factors responsible for the higher turbidity in this region have been attributed to tides and meteorological conditions and show peaks in January, April, June, and September–October 2020. This mode shows large-scale processes, and there is no apparent small-scale variability present in the first spatial EOF.

The second EOF mode (not shown) already displays small-scale spatial variability. We show here the third EOF mode (Fig. ), which shows a NE–SW gradient with high variability in the temporal mode. In the detailed panel shown in the figure we can also appreciate a thin region along the coast with behaviour opposite to the more offshore waters. Thanks to its high spatial resolution, it has been shown (https://www.esa.int/Applications/Observing_the_Earth/Copernicus/Sentinel-2/Near-shore_phytoplankton_bloom_captured_from_space, last access: 30 March 2025) that Sentinel-2 is able to capture small-scale variability that was previously unknown, i.e. a variability that has been captured by the EOF basis to produce the final, super-resolution datasets that will be shown in this section. The validation of the initial data and the super-resolution reconstruction will be presented in Sect. .

Figure  shows the initial turbidity data on 9 May 2020, a day with, initially, Sentinel-3 data (i.e. low-resolution data). A day with low cloud coverage was chosen in order to show the ability of DINEOF to enhance the spatial resolution. The initial data (Fig. a) show a series of high- and low-turbidity regions, a pattern that is due to the presence of sandbanks close to the Belgian coast. The changes in depth in this region induce large differences in turbidity from day to day. High-turbidity values in the east of the figure are due to the Scheldt–Rhine plume, which is located to the east of the domain. The reconstructed image (Fig. b) reproduces all of these features, as also seen in the contours added to this figure. A north–south transect is also included in the figure to show the small-scale variability that has been included in the reconstruction. The initial data (in blue in Fig. c) do not contain this small-scale variability and instead present a step-like nature due to the low spatial resolution of the initial dataset. This step-like variability is absent from the final, super-resolution data, which instead show smaller-scale variability. A percentage change map is also included, showing differences between the initial and final products over the whole domain, with a dominance of along-shore structures following the sandbanks present in the region that cause changes in turbidity. Most of the changes between the initial and final products therefore affect the structures of these sandbanks and other high-turbidity features offshore. The difference in resolution between the initial and final products is also responsible for the changes observed in this figure. Sentinel-2 data have a 60 m resolution, Sentinel-3 data have a 300 m resolution, and the DINEOF reconstruction should be between these two. The sandbanks have different TUR intensities in all the products, and since they present sharp gradients this will be felt in the percentage change map.

Figure  shows a similar reconstruction to Fig.  but this time for a date on which Sentinel-2 data are available (i.e. high-spatial-resolution data). This example shows that the variability of the super-resolution DINEOF reconstruction is similar to that of the initial dataset, and there is only a limited amount of variability lost with the analysis, mostly in regions with low-turbidity values (Fig. c). The presence of high-turbidity regions caused by the presence of sandbanks is also visible in this image, and a sharp inshore–offshore turbidity gradient can be seen that is retained well by the reconstruction. The contours in both images show the small-scale variability retained in the reconstruction. Turbid waters in the easternmost part of the domain, close to the Scheldt estuary and the shallowest region of the domain, can also be seen. The percentage change map in this figure shows smaller-scale features, i.e. long and thin structures in an along-shore direction, showing that the turbidity around the sandbanks and in offshore high-turbidity features is being modified between the initial and final datasets. Again, the difference in resolution between the different initial products is reflected in the representation of sharp turbidity gradients in the final product.

The results shown so far are from images that have good data coverage, but DINEOF also provides super-resolution data on days with high cloud coverage. Two examples in the Supplement show the reconstruction on a day with almost no initial data (Fig. S1) and a day with a high amount of noise in the initial data (Fig. S2). On days with almost no data (Fig. S1 on 12 April 2020), DINEOF is still able to provide a reconstruction with good spatial variability. Reconstruction of the turbidity's spatial distribution on days with high amounts of missing data is possible because of the three-dimensional nature of DINEOF, which exploits the spatio-temporal coherence of the data and enhances temporal correlations . The accuracy of the reconstruction can however be affected when persistent clouds obscure a specific region for several days e.g.. The method proposed by would allow us to obtain a pixel-by-pixel estimation of the reconstruction error variance and can be used to assess the influence of persistent cloud cover on the final result.

At some moments, there can be outliers or noise in the initial dataset despite the strong quality controls applied to the data, as in Fig. S2. The fact that DINEOF uses a truncated EOF basis to compute the missing data results in a partial loss of variability. However, this truncated EOF basis guarantees that the presence of outliers will not influence the overall quality of the reconstruction. As an example, in Fig. S2 we can see the turbidity on 28 May 2020, with a region in the northern part affected by the presence of noisy data. These are probably due to undetected thin clouds. The north–south transect shows that the variability of these data far exceeds the normal variability expected for the region. The DINEOF super-resolution results provide a reduced amount of noise and an improved quality of the final product while still providing an accurate depiction of small-scale variability.

Using the in situ data described in Sect. , a quality assessment of the initial data and the DINEOF results has been realized. Figure  shows the RRS match-ups between Sentinel-2/MSI and the PANTHYR in situ instrument installed on RT1. The metrics used are described in the Appendix. In the considered deployment period between 11 December 2019 and 1 August 2023, 528 MSI L1C images were available for processing with 53 match-ups with the PANTHYR instrument, which passed the quality flagging of the individual atmospheric corrections (i.e. ACOLITE/DSF and C2RCC), IDEPIX quality flagging, and match-up quality flagging. When using the merged approach for atmospheric correction, the best-performing bands are 490, 560, 665, and 704 nm, which are typically used for retrieval of turbidity and turbid-water chlorophyll a. For these bands the median absolute percentage error (MAPE) ranges between 9.88 % and 17.20 %.

Figure  shows the RRS match-ups between the Sentinel-3/OLCI and PANTHYR instruments installed on RT1. In the deployment period between 11 December 2019 and 1 August 2023, 2334 OLCI L1FR images were available for processing with 168 common match-ups with the PANTHYR instrument, which passed the quality flagging of the individual atmospheric corrections (i.e. ACOLITE/DSF and C2RCC), the IDEPIX quality flagging, and the match-up quality flagging. For the merged approach of atmospheric correction, the best-performing bands are 443, 490, 560, 665, and 709 nm, which are typically used for retrieval of turbidity and turbid-water chlorophyll a. For these bands the MAPE ranges between 10.74 % and 19.00 %.

The accuracy of the DINEOF super-resolution products was validated for the Belgian coastal zone region by using the hyperspectral in situ dataset from the autonomous PANTHYR system deployed at RT1 near Oostende to generate an in situ turbidity product which was directly compared with the satellite-derived turbidity products. This resulted in a turbidity time series with a temporal resolution of 20 min when daylight was available. The in situ turbidity product was generated with the same algorithm as used for the satellite products. Figure  shows the turbidity time series for 2020 overlaying the in situ data, the Sentinel-2 and Sentinel-3 turbidity products, and the final super-resolution DINEOF gap-filled product showing that the DINEOF product is able to capture the in situ turbidity signal between March and September. In January and February the DINEOF product shows slightly lower values, which can be caused by the fact that in those months the availability of cloud-free satellite products from Sentinel-2 and Sentinel-3 is very low. In situ observations for the period September–December were unavailable as the PANTHYR system was taken down for maintenance.

An objective intercomparison was achieved through a match-up analysis. The match-up validation protocol described by was applied to remove erroneous match-ups from the analysis based on macro-pixels of 3 × 3 pixels from the satellite turbidity products. Figure  shows the results of the match-up analysis for Sentinel-2, Sentinel-3, and the gap-filled DINEOF super-resolution products. These graphs show that the Sentinel-2 and Sentinel-3 products are in good agreement with the in situ observations, with mean average percentage differences of around 6 %. The temporal frequency of Sentinel-3 overpasses over the region of interest results in more than 3 times more match-ups. Considering the DINEOF super-resolution match-ups, this number of match-ups is increased by another 34 %, with very similar statistics compared to the Sentinel-3 match-ups, thus showing DINEOF's ability to retain the turbidity information provided by the source products. We do see a slight underestimation of the turbidity values by both satellites, especially for higher values (turbidity > 50 FNU). Further inspection indicates that this underestimation mostly happens in the winter months (January–February), probably due to the high cloud cover (data not shown).

In order to determine which scales are reconstructed in the super-resolution DINEOF approach, a test using the multi-sensor satellite chlorophyll data at 1 km spatial resolution described in Sect.  was performed. These data are downscaled to 5 km using a nearest-neighbour interpolation (to avoid smoothing the data). Following the same procedure as with the combined Sentinel-2 and Sentinel-3 turbidity dataset, we intercalate the 1 km data and the 5 km data. The ratio of this mixed dataset is one high-resolution image (at 1 km) to every three low-resolution images (at 5 km) in order to mimic the ratio of the Sentinel-2 and Sentinel-3 combination used in the previous section. This allows us to compare the scales reconstructed on this dataset with the initial 1 km data on days when 1 km data and 5 km data were used. In addition, we have made a reference reconstruction of the original, 1 km data so that we can assess how a full high-spatial-resolution reconstruction compares with the mixed-dataset reconstruction.

The DINEOF reconstruction of the mixed dataset used 22 EOFs, and an example of the reconstruction is shown in Fig. . On this date, 1 June 2022, the initial dataset has a spatial resolution of 5 km. A north–south transect shows that the reconstruction (in blue) is able to increase the variability of the 5 km data to mimic the variability of the reference dataset, which only uses 1 km resolution data (in green). This effectively increases the spatial resolution of the results with respect to the downgraded dataset (in black), which shows a step-like structure. A percentage difference map is also included, which in addition to showing the regions with higher or lower values in the reconstruction (positive or negative percentage values respectively) shows a square pattern that comes from the partial removal of the low-resolution information.

In order to investigate this pattern further, Fig.  shows a detail of the reconstruction on 1 June 2022, in which 5 km data are initially present. The super-resolution DINEOF reconstruction (in Fig. c) is shown to provide higher spatial resolution than the initial data, similar to what is obtained with the reference reconstruction at 1 km (shown in Fig. b), despite the coarse resolution of the initial field. There are some remaining edge effects showing the initial 5 km grid at the super-resolution, but this comes from the choice of nearest-neighbour interpolation. A linear interpolation would avoid such a pattern in the final results, although this would need to be tested.

On a day with 1 km data initially (Fig. , 9 July 2022), we can see that the variabilities observed in the north–south transect for the reference run and the super-resolution reconstruction are very similar, showing the ability of the super-resolution approach to retain small-scale variability.