On the detectability of adjacency effects in ocean color remote sensing of mid-latitude coastal environments by SeaWiFS, MODIS-A, MERIS, OLCI, OLI and MSI

2.1. Simulation procedure

The methodology described in Bulgarelli et al. (2014) has been adopted to estimate percent adjacency contributions at the sensor level ξ_Ltot = L_adj/L_tot · 100, where L_tot is the TOA signal, and the adjacency radiance L_adj is modeled as:

with L_l^TOA representing the land contribution (i.e., the radiance at the sensor originating from the area covered by land), and ${\tilde{L}}_w^{\mathit{TOA}}$ and ${\tilde{L}}_{\mathit{ss}}^{\mathit{TOA}}$ indicating the masked water and the masked sea surface contributions, respectively (i.e., the water-leaving radiance and the sea surface radiance that would reach the sensor from the same area if still covered by the sea). It is mentioned that the term ${\tilde{L}}_{\mathit{ss}}^{\mathit{TOA}}$ is sometimes called the Fresnel mask (Santer and Schmechtig, 2000). Eq. (1) can be further parameterized as (see Bulgarelli et al., 2014 for details):

where ρ_l represents the albedo of the land assumed isotropic and spatially homogeneous; S is the atmospheric spherical albedo of the bottom of the atmosphere; ρ_sea is the albedo of the sea (Mobley, 1994); and the expressions for functions C and W are given in Bulgarelli et al. (2014). The functions C and W depend on the illumination and observation geometry, on the land/sea spatial extension, as well as on the atmospheric optical properties. The described approach allows decoupling the land and water optical properties from atmospheric scattering, yet fully accounting for sea surface roughness. It is pointed out that the term 1/(1 − ρ_seaS) in Eq. (2) is exclusively used in the determination of ${\tilde{L}}_w^{\mathit{TOA}}$ to account for multiple reflections by the sea surface of atmospherically scattered light, whereas the bi-directional reflectance properties of a wind-roughed sea surface are accurately accounted for in the computation of ${\tilde{L}}_{\mathit{ss}}^{\mathit{TOA}}$. While the simulation of C and W requires a full 3D description of the propagating system, the simulation of S can be performed with a plane-parallel radiative transfer code, while the input parameters ρ_l and R_rs can be extrapolated from satellite-derived or in situ data. Therefore, once functions C and W are computed for a given geometric and atmospheric case, the proposed modeling allows a straightforward evaluation of AE for a wide variety of land and water spectral signatures.

The 3D Novel Adjacency Perturbation Simulator for Coastal Areas (NAUSICAA) MC code (Bulgarelli et al., 2014), whose accuracy was set to meet average SeaWiFS, MODIS and MERIS radiometric sensitivities, has been utilized to perform the simulations of functions C and W. The FEM plane-parallel numerical code (Bulgarelli et al., 1999), already extensively benchmarked with other popular radiative transfer codes (Bulgarelli et al., 1999, Bulgarelli and Doyle, 2004, Bulgarelli et al., 2003) and additionally used to perform radiative transfer simulations in realistic cases (Bulgarelli et al., 2003, Bulgarelli and Mélin, 2003, Bulgarelli and Zibordi, 2003, Zibordi and Bulgarelli, 2007), has also been utilized to simulate the atmospheric radiance and its components. Simulations have been carried out at the SeaWiFS-equivalent center-wavelengths i.e., for λ = 412, 443, 490, 510, 555, 670, 765 and 865 nm.

2.2. Selected test cases

Simulations have been performed for typical mid-latitude observation conditions (identified by a sun zenith angle θ₀ = 45°, Ångström coefficient α = 0.05, Ångström exponent ν = 1.7, aerosol scale height H_a = 1.2 km) assuming a stratified atmosphere resolving the vertical distribution of gas molecules and aerosol (Bulgarelli et al., 2014). Simulated values are provided from 1 to 36 km off the coast (at 2 km increments) along a study transect extending perpendicularly to a half-plane of uniform and isotropic land albedo, and whose coastline is oriented in the South-North direction (Fig. 1). Both cases of a land located in the western and eastern half-planes have been considered. It is noted that a previous analysis evidenced the feasibility to neglect the actual coastal morphology without any loss in accuracy, apart for enclosed basins (Bulgarelli et al., 2014).

The same set of parameters utilized to describe solar and sensor geometries for SeaWiFS, MODIS-T, MODIS-A and MERIS observations in the northern Adriatic Sea (Bulgarelli et al., 2014) has been considered suitable to describe observation conditions for OLCI, OLI and MSI (Table 1 and Fig. 1). Indeed, the equatorial crossing time (ECT) of OLCI and OLI is the same as MERIS (10:00 Mean Local Solar (MLS) time in descending node), while the ECT of MSI (10:30 MLS time in descending node) coincides with that of MODIS-T. As such, the same illumination geometry applies. For OLCI, all viewing angles θ_v = 5°, 20° and 50° are suitable. Conversely, for MSI (whose field-of-view (FOV) is 20.6°) only θ_v = 5° and 20° apply, while for OLI (whose FOV is 15°) θ_v = 5° is the sole appropriate.

A large set of optical properties for the two half-planes covered by uniform land and water, have been selected. Adjacency contributions have been quantified for a total of 12 × 6 land-water cases (see 2.2.1, 2.2.2). For each test case, all suitable observation geometries (Table 1 and Fig. 1) for both sea/land configurations and all reference wavelengths have been considered.

2.3. Sensors radiometric sensitivity

Higher radiometric sensitivity allows resolving smaller changes of the target signal, but it also implies higher sensitivity to spurious perturbations such as those generated by nearby land. A critical parameter describing the radiometric resolution of a sensor is the signal-to-noise ratio, SNR. The comparison of AE among different sensors requires the SNR to be defined and computed in a harmonized way, i.e., for the same input signal. Nonetheless the radiometric sensitivity of each sensor is unfortunately specified for different radiance values. To overcome this, Hu et al. (2012) carried out a re-quantification of the SNR of SeaWiFS, MODIS-A, and MERIS under uniform conditions. A typical at-sensor spectral radiance L_typ was determined from MODIS-A cloud-free ocean scenes and the SNR of SeaWiFS, MODIS-A and MERIS was directly estimated from data characterized by TOA radiances close to L_typ. For comparison, pre-launch SNRs of SeaWiFS and MODIS-A from sensors specifications were also adjusted to the same input radiance L_typ assuming proportionality between the SNR and the square root of the input signal. It is indeed recalled that in modern radiometers, detector and readout noise are dominated by the shot (or photon) noise that describes the variation in the number of photons N_p detected by the sensor per unit time. Since the latter follows a Poisson distribution, whose standard deviation is the square root of N_p, the overall noise can be assumed proportional to the square root of the input radiance (Moses et al., 2012). This scheme has been here utilized to scale the latest on-orbit performance SNR of OLCI, OLI and MSI (specified at different reference input radiances L_ref) to the same input radiance L_typ (see SNR@L_typ values listed in Table 2, Table 3, Table 4, respectively). Results from Hu et al. (2012) suggest that until the input reference radiance is within ± 50% of L_typ, uncertainties on SNR@L_typ are generally lower than 10%. For the aim of the present study it should hence be considered that uncertainties on SNR@L_typ might exceed 10% at all bands for the MSI sensor and at the red and infrared bands for OLI. Furthermore, considering that at these bands L_ref is larger than L_typ, the computed SNR@L_typ are likely to underestimate the actual values (Hu et al., 2012).

Remarkably, sample cloud-free SeaWiFS images acquired at the AAOT between 2002 and 2008 and suitable for match-ups with in situ data show TOA radiances in optimal agreement with L_typ provided by Hu et al. (2012) (see values displayed in Fig. 4). This confirms the suitability of the recomputed SNRs for satellite observations of mid-latitude coastal waters.

The harmonized SNR values for the considered sensors are spectrally represented in Fig. 5 at the SeaWiFS-equivalent center-wavelengths. Selected center-wavelengths for OLCI, OLI and MSI are highlighted in Table 2, Table 3, Table 4. MODIS-A selected center-wavelengths are those of the ocean color bands at 1 km spatial resolution. MERIS selected center-wavelengths coincide to those chosen for OLCI. It is remarked that the OLCI and MERIS band at 778 nm has been chosen among the other bands close to 765 nm because it is utilized to perform the atmospheric corrections (Antoine and Morel, 1999). Notably, OLCI and MERIS acquire data in full (0.3 km, FR) and reduced (1.2 km, RR) spatial resolution with a significantly different SNR. The highest radiometric sensitivity characterizes MODIS-A, MERIS-RR and OLCI-RR. In specific, MERIS-RR is the most sensitive sensor at blue-green wavelengths, MODIS-A around 555 nm, OLCI-RR at longer wavelengths. The radiometric sensitivity of MERIS-FR is slightly larger than that of SeaWiFS, while the radiometric performance of OLCI-FR (equal to ¼ of that of OLCI-RR) is slightly lower. As expected, the lowest SNR values are found for the MSI and OLI sensors that were developed for land applications. Indeed, land observations require a high spatial resolution to capture the large spatial variability of land optical properties and a high radiometric range to accommodate signals from bright targets. Conversely, they do not need the high radiometric resolution required by ocean color sensors to discriminate small variations of the water signal. Notably, the SNR of the MSI band at 443 nm (characterized by the coarsest spatial resolution) is significantly high, and close to that of MERIS-FR. At other center-wavelengths the SNR of MSI becomes instead the lowest. It is mentioned that MODIS-A land bands (with 250–500 m spatial resolution), also used for ocean color applications, are characterized by SNR values laying in between those of OLI and MSI.

In the following of the paper the percent noise level (NL) values (i.e., NL = 1/SNR·100) displayed in Fig. 6 are utilized for comparison with ξ_Ltot. Any adjacency radiance contribution lower than NL is regarded as not discriminable from noise, i.e., not detectable.

3.1. Adjacency contributions at the sensor

The absolute value of mean adjacency contributions ${\overline{\xi }}_{L_{\mathit{tot}}}$ (for 24 observation geometries obtained by combining parameters detailed in Table 1) is summarized in Fig. 7 together with sensors NL. Results are presented at sample wavelengths for NADR waters and representative land covers. Data for fine and coarse snow are neither presented nor discussed being equivalent to those of medium grain snow. Data for conifers and grass, brown sand, and pale brown loam have been omitted being similar to those of deciduous trees and brown loam, respectively.

As expected, values of $\left|{\overline{\xi }}_{L_{\mathit{tot}}}\right|$ monotonically decrease with the distance from the coast and their magnitude increases with the spectral albedo of the land cover. For all sensors, mean adjacency contributions in the presence of snow, white sand, concrete and dry vegetation, are above the spectral NL values throughout the study-transect and at all wavelengths. Conversely, in the presence of bare soil and green vegetation, adjacency contributions might become lower than NL within the transect at a distance that increases with the radiometric sensitivity of the sensor. As an example, average perturbations for brown loam at 443 nm become lower than NL at ~ 9 km offshore for OLI, ~ 19 km for OLCI-FR, ~ 25 km for SeaWiFS, ~ 33 km for MERIS-FR, while they are above the noise level throughout the whole 20 km-transect for MSI and at 36 km offshore for MODIS-A, OLCI-RR and MERIS-RR. It is remarked that mean adjacency contributions drop below the noise level at distance from the coast shorter than 36 km (20 for MSI): i) at the sole red center-wavelengths with green vegetation for the highly sensitive MODIS-A, MERIS-RR and OLCI-RR; ii) at all visible center-wavelengths for SeaWiFS, OLCI-FR and MERIS-FR, OLI and MSI; iii) at additional NIR center-wavelengths for MSI and OLI measurements in the presence of bare soil. It is mentioned that adjacency contributions at the blue wavelengths for green vegetation and bare soil are negative.

Different observation geometries, as well as the mutual location of sun, sensor and land, influence the actual adjacency contributions. In particular, results confirm a general increase of AE with the viewing angle (see Fig. 8 for green grass and snow at 443 and 865 nm). Adjacency perturbations also show a dependence on the position of the sun with respect to the land (see Fig. 9). Indeed, due to the anisotropy of the sea surface, the value of term W (the Fresnel mask) in Eq. (2) increases with the portion of land laying in the solar half-plane. This dependence is clearly more significant when land and sea albedos are closer (as for green vegetation and bare soil at blue wavelengths), because the contribution of W to L_adj is more important. Under these same conditions, results are expected to be more sensitive to actual roughness of the sea surface. Conversely, when the land reflectance is consistently larger than the sea one (i.e., throughout the spectrum for snow, dry vegetation, white sand and concrete, or at the sole NIR wavelengths for green vegetation and bare soil), AE become sensitive to the position of the sensor with respect to the land (see Fig. 9). This is mainly relevant for slanted observations, for which AE appear consistently larger when the sensor is observing the sea from over the land.

Results from Fig. 8, Fig. 9, Fig. 10 allow concluding that actual adjacency contributions are expected to be below the average values illustrated in Fig. 7 for quasi-nadir observations and when the sensor is located over the sea. Conversely, they likely are above the average values for slanted observations and when the sensor is located over the land.

It is further remarked that adjacency perturbations are expected to become much more dependent on the sun-sensor position for a coast oriented in the East-West direction.

Adjacency perturbations show a slight sensitivity to the water type at the sole blue wavelengths. Specifically, when varying the water type the largest relative changes in the adjacency contributions occur in the presence of poorly reflecting land covers, such as green vegetation or bare soil. In this case, AE decrease with the water optical complexity and are the largest for oligotrophic EMED waters (see the left panel of Fig. 11 for green grass). Conversely, the largest absolute changes occur in the presence of highly reflecting land covers, such as snow, dry vegetation, concrete and white sand. In these cases AE increase with water absorption and are the largest for the BLTS waters (see the right panel of Fig. 11 for dry grass).

Simulations have been performed assuming a constant remote sensing reflectance along the transect. In agreement with results presented and discussed above, ξ_Ltot is expected to be sensitive to spatial variations of the water optical complexity at sole blue wavelengths. Results from Fig. 11 suggest that an increase of R_rs towards the coast would lead to a slight increase of adjacency contributions (as compared to Fig. 7) in the presence of green vegetation and bare soil. A slight decrease of adjacency contributions would instead be expected in the presence of more reflecting land covers.

Average adjacency contributions quantified for selected land covers and water types are also summarized in Table 5, Table 6, Table 7 at several distances from the coast and for selected center-wavelengths.

3.2. Benchmark with data from literature

Simulated data have been benchmarked with results obtained with the approximate algorithm by Sei (2007) that provides an analytical estimate of L_adj at nadir for two Lambertian half-spaces. For all considered combinations of land and water types, the comparison has been performed for nadir values of L_adj/L_path, where the path radiance L_path, computed with the FEM numerical code (Bulgarelli et al., 1999), describes the radiance due to both atmospheric scattering along the optical path and to specular reflection by the sea surface of the atmospherically scattered light. Results at 865 nm are given in Fig. 12 for a) brown loam, b) deciduous trees, and c) white sand. Values of L_adj from the application of the algorithm by Sei (2007) have been computed by implementing the environment weighting function defined by Reinersman and Carder (1995), but analogous values have been produced when adopting the approximations by Vermote et al. (1997) and by Tanré et al. (1981). Values of L_adj from the application of the NAUSICAA code have been obtained by both assuming a Lambertian sea (in agreement with the assumption adopted in the approximate algorithm by Sei (2007)) and fully accounting for the sea surface anisotropy.

Results show extremely good agreement, particularly in the proximity of the coast where discrepancies between NAUSICAA simulations (fully accounting for the sea surface roughness) and data simulated with the approximate algorithm by Sei (2007) are clearly due to the assumption of an isotropic sea surface in the latter algorithm. The faster convergence with distance from the coast of values simulated with the algorithm by Sei (2007) is the likely consequence of the exponential decay of the environment weighting function. A slower convergence of MC simulations with respect to their exponential approximation was also reported by Reinersman and Carder (1995) (see their Fig. 27).

Analytical results from the algorithm by Sei (2007), extending till the coastal edge, allow evidencing a very steep increase of AE in the first few hundred meters close to the coast where L_adj might reach or even exceed L_path in the presence of a bright land (such as vegetation and white sand, as illustrated in Fig. 12b and c). For the poorly reflecting brown loam, L_adj always remains lower than L_path (Fig. 12a). These results, indicating L_adj exceeding L_path at the coastal edge only, find confirmation in simulations by Santer and Schmechtig (2000). In specific, their additional reflectance Δρ^∗ (owing to AE) for nadir observations over two Lambertian half-planes of albedo ρ_l = 0.3 and ρ_sea = 0 (see their Table 3) exceed corresponding values of the atmospheric reflectance ρ_atm (see their Table 1) only at zero distance from the coast line, while at 1 km off the coast it is already Δρ^∗ < ρ_atm (corresponding to L_adj < L_path). Values of Δρ^∗ exceeding ρ_atm at some distance from the coast are predicted by the same authors only for slanted observations from over the land (see their Fig. 18) and for a dark water disk surrounded by homogenous and infinite land (see their Fig. 2 and Table 2).

Recent empirical estimates of AE determined from MODIS-A NIR data covering clear coastal waters off the Madagascar Island evidenced instead contributions exceeding L_path up to ~ 1.5 km from the coast (Feng and Hu, 2017). The authors of this work noted the difference with AE simulated in the northern Adriatic Sea by Bulgarelli et al. (2014), albeit represented by different statistical indices. Indeed, while both studies assume negligible R_rs at NIR wavelengths (i.e., L_tot = L_path + L_adj), the parameter Ratio by Feng and Hu (2017) indicates the ratio between the at-sensor radiance from adjacency contaminated and adjacency-free offshore pixels (i.e., Ratio = L_tot/L_path), whereas the parameter ξ_Ltot by Bulgarelli et al. (2014) describes the contribution of adjacency radiance at the sensor (i.e., ξ_Ltot = L_adj/L_tot). By accounting for the diversity in the indices adopted in the two approaches, a fully quantitative comparison of AE in the proximity of the coast (~ 1 km) leads to ξ_Ltot > 50% in Feng and Hu (2017) and to ξ_Ltot ~ 11% in Bulgarelli et al. (2014).

A thorough explanation of these differences would require accounting for the combined effects of averaging over space, uncertainties in the geolocation of satellite data, SNR in the NIR bands, eventual residual NIR contributions from bottom resuspension, anisotropic reflectance of the land surface that may influence AE in the NIR (Bulgarelli et al., 2014), and finally the different observation conditions (i.e., land albedo, atmospheric structure and composition, illumination geometry, and coastal morphology).

It is indeed remarked that the eastern coast of Madagascar Island is characterized by a broad leaf non-deciduous forest (IGBP, 2000) and white sand beaches, whose albedos are significantly larger than that of the land facing the northern Adriatic Sea. Further, sun elevation is higher in the tropics than at mid-latitudes, and simulations with the algorithm by Sei (2007) easily show that L_adj/L_path tends to decrease with increasing SZA (see Fig. 13a for results at 865 nm in the presence of a white sand land cover) as a consequence of the simultaneous increase of L_path and decrease of L_adj (as evidenced in Bulgarelli et al., 2014). Finally, it is recalled that the horizontal scale of AE (i.e., the distance at which L_adj decreases by a factor e) reflects the scale height of the atmosphere (Tanré et al., 1981, Santer and Schmechtig, 2000, Sei, 2007, Reinersman and Carder, 1995), which in turn depends on the load and scale height of the aerosol. Simulations of L_adj/L_path at 865 nm, performed with the algorithm by Sei (2007) for H_a = 1.2 km and for varying aerosol optical thicknesses τ_a(865), evidence how an increase of aerosol content leads to AE characterized by higher values at the coast and a faster decrease with distance (see Fig. 13b).

It is finally mentioned that the hypothesis by Feng and Hu (2017) that the differences between the two independent quantifications of AE in the NIR at the coastal edge might arise from the assumption of a high sea surface albedo (i.e., 0.04) in the simulations by Bulgarelli et al. (2014) can be definitely excluded. In fact, the methodology applied by Bulgarelli et al. (2014) computes the Fresnel mask (i.e., the term ${\tilde{L}}_{\mathit{ss}}^{\mathit{TOA}}$ in Eq. (1)) fully accounting for the bi-directional reflectance of a wind roughed sea surface, while parameter ρ_sea (approximated as ~ 0.04 + πR_rs in Bulgarelli et al., 2014) is exclusively used in the determination of the masked water-leaving radiance contribution ${\tilde{L}}_w^{\mathit{TOA}}$ to account for multiple reflections at the sea surface (see Eq. (2)). Notably, when the remote sensing reflectance is negligible (as it is assumed in the NIR), the term ${\tilde{L}}_w^{\mathit{TOA}}$ is null and consequently the parameter ρ_sea does not contribute to any simulated quantity in the NIR.

3.3. Biases induced by AE on satellite radiometric products

Adjacency perturbations in satellite radiometric products strictly depend on the AC procedure applied. Estimates of biases induced by AE on the water-leaving radiance derived from satellite data are here presented making reference to the algorithm proposed by Gordon and Wang (1994) and implemented in SeaDAS (Ahmad et al., 2010, Franz et al., 2007), for which the radiance L_tot reaching a space sensor looking at a water element out of the region of sunglint and in the absence of whitecaps is modeled as:

where t is the diffuse atmospheric transmittance (Yang and Gordon, 1997), L_w is the water-leaving radiance, L_R is the radiance resulting from multiple scattering by air molecules in the absence of aerosol, and L_A is the radiance resulting from multiple scattering by aerosol in the presence of air molecules. The latter two terms are intended for an atmosphere bounded by a Fresnel reflecting surface. While the term L_R is assumed exactly known, the aerosol radiance L_A at the visible wavelengths λ_V is derived from the NIR wavelengths λ_N (e.g., 765 and 865 nm, or equivalent), where L_w is assumed a priori known.

Eq. (3) is strictly valid for open-ocean observations, where it is feasible to assume a homogenous underlying water surface. In the vicinity of the coast, Eq. (3) more correctly becomes

As detailed in Bulgarelli et al. (2017), the bias induced by AE on the derived water-leaving radiance at TOA, tL_w, can be expressed as:

where ψ_LA represents the bias induced by AE on L_A modeled as:

with f representing the function used to infer the aerosol properties from the NIR wavelengths.

Taking this into account, Eq. (5) can be written as:

to indicate the presence of two sources of land perturbations at each wavelength: one induced by AE at the visible wavelength itself, L_adj(λ_V)/tL_w(λ_V), and one induced by AE at NIR wavelengths, $-{\psi }_{L_A}·\frac{L_A\left({\lambda }_V\right)}{t{L}_w\left({\lambda }_V\right)}$ (Bulgarelli et al., 2017).

It is evident from Eq. (7) that when ξ_Ltot(λ_V) < NL, the overall bias equals the sole ψ_tLw[L_adj(λ_N)] term. This might for example happen for OLCI-FR radiometric products at 443 nm from ~ 8 km to ~ 10 km offshore in the presence of green vegetation and bare soil, respectively.

In this study, biases are quantified computing ψ_LA in single scattering approximation (see Bulgarelli et al., 2017). It is reminded that this approximation is considered appropriate for an aerosol optical thickness at 865 nm, τ_a(865), up to 0.2 (Gordon and Wang, 1994), and it is consequently applicable for the value of 0.06 considered in this study. It is moreover noticed that the single scattering approximation is only applied for the evaluation of ψ_LA, while all other terms (L_A included) are computed carefully accounting for multiple scattering.

Mean biases ${\overline{\psi }}_{t{L}_w}$ are illustrated in Fig. 14 for the same set of cases selected in Fig. 7. Results indicate that for any given wavelength the largest values of ${\overline{\psi }}_{t{L}_w}$ do not necessarily correspond to the largest spectral land albedo. For example, biases for green vegetation are the largest throughout the spectrum, although its albedo at visible wavelengths is the lowest (see Fig. 2). Additionally, although the albedo for dry vegetation is much larger than that of brown loam at all wavelengths, the corresponding values of ${\overline{\psi }}_{t{L}_w}$ are very similar. Furthermore, regardless of the largest spectral albedo of snow (Fig. 2), values of ${\overline{\psi }}_{t{L}_w}$ at 555 and 670 nm for a land covered by snow are comparable to those occurring in the presence of dry vegetation, concrete and brown loam. Notably, the lack of correlation between ${\overline{\psi }}_{t{L}_w}$ and the spectral strength of the land albedo, as well as the non-monotonic spatial trend of ${\overline{\psi }}_{t{L}_w}$ in the proximity of highly reflecting land covers (e.g., snow), show similarities with statistically determined AE in satellite-derived R_rs in the presence of clouds (Feng and Hu, 2016).

Results illustrated in Fig. 14 are explained by recalling that the two components ${\overline{\psi }}_{t{L}_w}\left[L_{\mathit{adj}}\left({\lambda }_V\right)\right]$ and ${\overline{\psi }}_{t{L}_w}\left[L_{\mathit{adj}}\left({\lambda }_N\right)\right]$ of Eq. (7) may compensate each other, as illustrated in Fig. 15, Fig. 16, Fig. 17 for NADR waters and deciduous trees, white sand and snow, respectively. For deciduous trees, both components are negative and sum each other leading to values of ${\overline{\psi }}_{t{L}_w}$ up to − 200% at 443 nm at the coast (Fig. 15). For white sand, the positive values of ${\overline{\psi }}_{t{L}_w}\left[L_{\mathit{adj}}\left({\lambda }_V\right)\right]$ compensate the negative values of ${\overline{\psi }}_{t{L}_w}\left[L_{\mathit{adj}}\left({\lambda }_N\right)\right]$, hence ${\overline{\psi }}_{t{L}_w}$ becomes almost negligible besides in the right proximity of the coast (see Fig. 16). In the presence of snow (see Fig. 17), AE at blue wavelengths are so high that ${\overline{\psi }}_{t{L}_w}\left[L_{\mathit{adj}}\left({\lambda }_N\right)\right]$ cannot counterweight ${\overline{\psi }}_{t{L}_w}\left[L_{\mathit{adj}}\left({\lambda }_V\right)\right]$ at 443 nm, but compensations still occur at 555 and 670 nm.

Biases are chiefly sensitive to the seawater type at blue wavelengths where differences in the water-leaving radiance from different marine regions are the largest (see Fig. 3). Fig. 18 shows biases for CDOM-dominated BLTS waters, whose reflectance at blue wavelengths is very low. In comparison to results in Fig. 14 (for NADR oligotrophic waters), biases at 443 and 490 nm are largely increased (about 4 and 3 times larger, respectively) while they remain almost unchanged at 670 nm.

It is recalled that findings presented so far assume a constant L_w along the whole transect. Following results from Fig. 14, Fig. 18, a decrease of the water signal towards the coast would increase absolute biases. The opposite would occur for increasing L_w. Where the land albedo is consistently larger than the sea albedo, the adjacency radiance is not expected to be sensitive to L_w. Hence the decrease of biases towards the coast for increasing water turbidity is expected to be proportional to the increase of L_w (Bulgarelli et al., 2017).

Overall results confirm that for an atmospheric correction scheme inferring the aerosol properties from the NIR wavelengths, biases are not directly correlated to the strength of the land spectral albedo. Consequently, the water-leaving radiance determined from satellite data in coastal areas might exhibit larger misestimates for a low reflecting land than for a highly reflecting one.

Finally, Fig. 19 illustrates spectral values of ${\overline{\psi }}_{L_A}$ at 9 km from the coast for representative land covers. In agreement with considerations from Bulgarelli et al. (2017), results show that while ${\overline{\psi }}_{L_A}\left(865\right)$ is proportional to ρ_l(865), larger values of the land albedo in the NIR do not necessarily correspond to larger values of ${\overline{\psi }}_{L_A}$ at blue wavelengths. For example, the albedo of concrete in the NIR is about 50% smaller than the albedo of dry vegetation and very close to that of bare soil, nonetheless, ${\overline{\psi }}_{L_A}\left(412\right)$ for concrete is very close to that for dry vegetation, while it is significantly larger than that for bare soil. White sand and snow albedos are quite similar in the NIR, nevertheless white sand leads to values of ${\overline{\psi }}_{L_A}\left(412\right)$ significantly lower than those occurring for snow. These results find their explanation on ψ_LA that does not only depend on the magnitude of the land albedo at NIR wavelengths, but on its spectral dependence too (Bulgarelli et al., 2017).

It is mentioned that the atmospheric contribution in OLI and MSI data is generally quantified utilizing one or two SWIR bands (Vanhellemont and Ruddick, 2015). As well, SWIR bands can be alternatively used to derive the aerosol optical properties from MODIS data (Wang and Shi, 2007). The analysis of adjacency effects in the SWIR (where the land albedo might consistently differ from values in the NIR) is out of the scope of the present work. Nonetheless, the occurrence of analogous mechanisms of propagation of adjacency perturbations from SWIR to visible, as well as of potential compensations between adjacency perturbations at SWIR and visible wavelengths are expected. A decrease of the impact AE from NIR to SWIR is further envisaged as a consequence of a decrease of atmospheric scattering, sensors SNR (see Table 7 of Hu et al. (2012) for MODIS-A, and Table 2 for OLCI, OLI and MSI), and land albedo (with the exception of bare soil).