On the minimization of adjacency effects in SeaWiFS primary data products from coastal areas

Barbara Bulgarelli; Giuseppe Zibordi; Frédéric Mélin

doi:10.1364/OE.26.00A709

1. Introduction

Satellite remote sensing, which delivers a number of essential climate variables through the Global Climate Observing System [1], is a fundamental element for investigating climate and its changes [2]. A detailed identification of uncertainties affecting satellite data is thus a requirement in view of creating climate records [2].

The Ocean Color component of the Aerosol Robotic Network (AERONET-OC) of in situ autonomous radiometers [3] was specifically created to support the assessment of ocean color products through the provision of highly accurate, cross-site consistent, and globally distributed measurements, and it has been instrumental through the years to identify and quantify uncertainties affecting both data and retrieval algorithms [4,5].

AERONET-OC sites are all located in coastal regions. These areas are of utter environmental and economical importance, but definitely represent a challenging target for ocean color remote sensing. In fact, their bio-optical properties are turned into rather complex ones by the contemporary presence of non-covarying in-water optically significant components (i.e., pigments, colored dissolved organic matter and suspended sediments) and by potential perturbations from sea-bottom and nearby land. The difficulty to tackle such a complexity emphasizes the criticality of assessment exercises in these areas.

Recent evaluations of annual average biases from match-ups of SeaWiFS and in situ data at the Aqua Alta Oceanographic Tower (AAOT, 45.31N, 12.51E) AERONET-OC site for the period 2002-2010 [6] evidenced systematic underestimates of the normalized water-leaving radiance L_WN at 670 nm. For the same period, the analysis of intra-annual variation of biases showed that underestimates of L_WN at 670 nm are more pronounced in the July-October period, while L_WN is generally overestimated in winter, particularly at the blue and the red wavelengths [7].

Considering that the SeaWiFS Data Analysis System (SeaDAS) [8,9] utilized to process the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) images assumes an infinite water surface whereas the AAOT is located at 8 nautical miles from the coast, perturbations from the nearby land might still affect satellite data products. This kind of perturbations affecting the top-of-atmosphere (TOA) radiance and resulting from inhomogeneities in the surface reflectance are generally termed adjacency effects (AE) [10].

The hypothesis that average and intra-annual biases routinely observed at the AAOT might be partly induced by adjacency perturbations finds support in results from previous theoretical investigations indicating i) percent adjacency contributions to the radiometric signal in typical ocean color observations up to 2-3% in the NIR bands [11], ii) significant negative biases induced by AE on the water signal at blue and red wavelengths for correction schemes such as SeaDAS determining the atmospheric radiance from the NIR [12], and iii) remarkable seasonal variations of adjacency perturbations, displaying contributions significantly larger than the sensor radiometric sensitivity at the NIR wavelengths between March and October, and at the visible wavelengths between November and February [13]. These same theoretical analyses also suggest that the turbid water (TW) correction algorithm [14] implemented in SeaDAS might partially correct for AE by misinterpreting adjacency contributions in the NIR as water contributions [12].

The sensitivity of annual and intra-annual biases to the minimization of AE in the presence of TW perturbations is here further investigated utilizing a set of SeaWiFS images acquired at the AAOT in conjunction with in situ data. In specific, SeaDAS primary products (i.e., the aerosol optical thickness and, the remote sensing reflectance and its ratios) from sample original data and from data corrected at TOA for estimated adjacency contributions [11] are compared with reference in situ measurements, alternatively applying and excluding the TW correction algorithm.

Data and methods are presented in Section 2, while results are illustrated in Section 3 and discussed in Section 4. Conclusions are drawn in Section 5.

2. Data and methods

From a set of 492 SeaWiFS images acquired at the AAOT between 2002 and 2010, all suitable for match-up construction with in situ measurements, 82 images free from cloud contamination have been identified. This subset allows investigating sole AE induced by land, excluding cases of contamination by nearby clouds [15].

The following subsections briefly describe i) the processing applied to satellite data, ii) the methodology implemented for the theoretical estimate of the at-sensor adjacency contributions, iii) the match-up construction criteria, iv) the in situ measurements and v) the geophysical characteristics of the match-up data set.

2.1 Satellite data processing procedure

SeaWiFS Level-1 data (L1, i.e., TOA calibrated and geolocated) at 1.1 km spatial resolution, obtained from the Goddard Space Flight Center of the National Aeronautics and Space Administration (NASA-GSFC), have been processed to Level-2 (L2) with the SeaDAS version 7 (consistent with Reprocessing R2014).

Briefly, in SeaDAS the total radiance at the sensor L_tot for observations out of the region of sunglint contamination and in the absence of whitecaps is modeled as:

L_{t o t} = L_{R} + L_{A} + t L_{w},

where

L_{R}

and

L_{A}

represent the radiance due to scattering by gas molecules in the absence of aerosol and by aerosol in the presence of gas molecules, respectively, within an atmosphere bounded by a Fresnel water surface [16]; t is the diffuse atmospheric transmittance [17]; and

L_{w}

is the water-leaving radiance. While the Rayleigh radiance

L_{R}

is assumed exactly known, the aerosol radiance

L_{A}

at the visible wavelengths

λ_{V}

is determined using two NIR wavelengths

λ_{N}

(765 and 865 nm for SeaWiFS) at which L_w is assumed a priori known [16]. Specifically, in open oceanic waters

L_{w}

at

λ_{N}

is assumed to be negligible. In coastal waters a TW correction algorithm [14] is instead applied to iteratively estimate

L_{w}

in the NIR bands from retrieved values of the chlorophyll concentration Chl and of the spectral remote sensing reflectance

R_{r s}

. Precisely, the optical model implemented in the TW algorithm [14]:

i) assumes a spectral dependence for the backscattering coefficient $b_{b p}$ [m⁻¹] of the suspended particles given by: $b_{b p} (λ) = b_{b p} (670) \cdot {(\frac{670}{λ})}^{2.0 \cdot [1.0 - 1.2 \exp (- 0.9 \cdot R_{r s} (443) / R_{r s} (555))]}$
with λ in nm;
ii) determines the absorption coefficient of suspended particles and dissolved material $a_{p g}$ [m⁻¹] from the retrieved Chl [mg m⁻³] with: $a_{p g} (670) = e^{(l n (C h l) \cdot 0.9389 - 3.7589)};$
iii) and computes $R_{r s}$ [sr⁻¹] from: $R_{r s} (λ) = G (λ) \cdot \frac{b_{b} (λ)}{a (λ) + b_{b} (λ)},$

where a [m⁻¹] and

b_{b}

[m⁻¹] represent the total absorption and backscattering coefficients, respectively (which include the pure water contributions), and coefficients G are from [18].

As already anticipated, SeaDAS assumes an infinite water surface [16] and consequently neglects the presence of land in coastal waters. In fact, to account for AE, Eq. (1) should be more comprehensively written as:

L_{t o t} = L_{R} + L_{A} + t L_{w} + L_{a d j},

where the adjacency radiance

L_{a d j}

indicates the radiance difference at the sensor when accounting for or neglecting inhomogeneities in the surface reflectance, such as those due to land. As such,

L_{a d j}

can range from negative to positive values.

In order to investigate the sensitivity of satellite primary products to adjacency perturbations, and concurrently reveal possible mechanisms of compensation enacted by the TW correction algorithm, each sample image has been processed utilizing four different procedures P (Table 1).

Table 1. Procedures P utilized to correct SeaWiFS satellite data with the SeaDAS 7 processing scheme.

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Procedure P₀ ingests original L1 data and excludes the default TW correction algorithm [14]. This is equivalent to assume that $L_{w}$ at $λ_{N}$ and $L_{a d j}$ at any λ are all negligible. Procedure P_TW ingests original L1 data and implements the default TW correction algorithm (i.e., applies SeaDAS in standard mode). This implies to assume negligible $L_{a d j}$ at each λ, while estimating a non-null $L_{w}$ at $λ_{N}$ . Procedure P_AE ingests L1 data previously corrected for adjacency contributions through theoretically estimated adjacency correction factors $c_{A E}$ (see Section 2.2) and excludes the default TW correction algorithm. This corresponds to assuming a negligible water signal at $λ_{N}$ , while acknowledging non-null $L_{a d j}$ . Procedure P_AE+TW ingests L1 data previously corrected for estimated adjacency contributions, and implements the default TW correction algorithm, i.e., it assumes both non-null $L_{w} (λ_{N})$ and $L_{a d j} (λ)$ .

2.2 Theoretical quantification of AE

For each image i of the sample, adjacency correction factors have been computed as $c_{A E}^{i} = 1 - ξ_{L t o t}^{i}$ , where $ξ_{L t o t} = L_{a d j} / L_{t o t}$ and $L_{t o t} = L_{p a t h} + t L_{w} + L_{a d j}$ . The path radiance $L_{p a t h}$ accurately accounts for multiple scattering by aerosol and gas molecules within an atmosphere bounded by a water surface, and $L_{a d j}$ is modeled as (see Appendix A and [11]):

L_{a d j} = (\frac{ρ_{l}}{π} \cdot κ_{l} - R_{r s} \cdot κ_{w}) \cdot C^{ρ = 1} - W

In Eq. (6) the functions

C^{ρ = 1}

and W designate the cumulative radiance contribution at the sensor originating from the land assumed as an ideal Lambertian reflector [19] and as a Fresnel wind-roughened sea surface, respectively;

ρ_{l}

and

R_{r s}

represent the albedo of the land and the remote sensing reflectance (both assumed as homogeneous and isotropic); and parameters

κ_{l}

and

κ_{w}

are scaling factors to adjust the radiance reflected by an ideal Lambertian reflector to that reflected by an actual land surface and to that leaving the water volume, respectively (see Appendix A). This approach allows the decoupling of land and water optical properties from atmospheric scattering, while fully accounting for the sea surface roughness. It is noticed that the functions

C^{ρ = 1}

and W depend on the illumination and observation geometry, on the land/sea spatial extension, as well as on the atmospheric optical properties.

For the sake of a sensitivity analysis supporting the minimization of AE in satellite radiometric products, the values of functions S, $C^{ρ = 1}$ and W were obtained from pre-existing simulated data for representative and realistic observation conditions at the AAOT site [11]. In specific, values of S, $C^{ρ = 1}$ and W simulated for different illumination and atmospheric conditions were interpolated over the sensor viewing angle. For each image i, the values of $L_{a d j}$ were hence computed via Eq. (6) by ingesting the temporally closest climatological land albedo from a MODIS database of 16-day climatological land reflectances [20], and the reference in situ value of R_rs. A null water signal was assumed in the NIR acknowledging the negligible sensitivity of $L_{a d j}$ to non-null values of $L_{w} (λ_{N})$ [12]. It is here shortly mentioned that simulations of the functions $C^{ρ = 1}$ and W were performed with the Novel Adjacency Perturbation Simulator for Coastal Areas (NAUSICAA) full three-dimensional (3D) backward Monte Carlo (MC) code [11], accurately accounting for multiple scattering by aerosol and gas molecules within a stratified atmosphere bounded by a non-homogeneous reflecting surface with sea surface roughness modeled according to [21], and for the actual coastline. The finite element method (FEM) plane-parallel code [22,23] was instead applied to simulate atmospheric optical quantities such as S, t, $L_{p a t h}$ , $L_{R}$ and $L_{A}$ [see Eqs. (1), (5) and (6)].

It is remarked that the FEM numerical code has been extensively benchmarked with alternative popular radiative transfer codes [22,24–26], it has been already applied to perform radiative transfer simulations in realistic cases [25], and it is routinely used within the Modular Inversion and Processing System (MIP) [27–29]. The NAUSICAA MC code, whose precision is set to meet typical sensitivity of ocean color sensors [11], has been benchmarked with the FEM code [11], and with the approximate algorithm by Sei [11,30,31].

It is recognized that interpolated $ξ_{_{L t o t}}^{i}$ values represent a fair estimate, whose accuracy could be increased in view of an operational application by simulating functions $C^{ρ = 1}$ and W for the actual observation conditions in terms of aerosol content, land reflectance and illumination and observation geometries. It is further acknowledged that confidence on adjacency contributions at visible wavelengths and in winter is lower. In fact, the closeness between land and sea reflectances (see Table 4 of [11]) makes the adjacency radiance particularly sensitive to the anisotropy of the sea surface reflectance, and hence to the actual sun-sensor position with respect to land, and to actual wind speed and direction [11].

Spectral values of $ξ_{_{L t o t}}^{i}$ with uncertainties $δ_{ξ}^{i}$ computed by assuming uncorrelated contributions (see Section 5 of [11]) are separately presented in Fig. 1 for images acquired in summer (May-August), mid-seasons (March-April and September-October) and winter (November-February). The SeaWiFS spectral noise levels (NL), equal to the inverse of the signal-to-noise ratio (SNR) [32], are also indicated.

Fig. 1 Spectral values of $ξ_{_{L t o t}}^{i}$ for images acquired in November-February (N=12), in September-October and March-April (N=31), in May-August (N=39). Error bars identify uncertainties $δ_{ξ}^{i}$ . Red box bars indicate the SeaWiFS noise level NL.

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Notably, values of $ξ_{_{L t o t}}^{i}$ show a narrow spread towards the blue wavelengths. Conversely, they display a remarkable intra-annual variation in the NIR with values ranging from 0.2% to 5.1% at 865 nm in winter and summer, respectively. Adjacency contributions at $λ_{V}$ are all negative in November-February, while in the other periods of the year $ξ_{_{L t o t}}^{i}$ values may vary from positive to negative at the blue-green wavelengths, but they are always positive in the red. It is recalled that the seasonality of $ξ_{_{L t o t}}^{i}$ mainly depends on the combined effects of three key parameters: the albedo of land (vegetation is dormant in winter, while highly reflecting in summer), the albedo of sea (the water is relatively productive and laden with sediments in winter, while its albedo is minimum in summer), and the sun elevation [11,31].

Considering that adjacency contributions lower than or close to the sensor NL are regarded as not detectable, L1 data are corrected only for adjacency contributions exceeding NL by more than their expected uncertainty (i.e., only when $| ξ_{L t o t}^{i} | - N L > δ_{ξ}^{i}$ ). With reference to the SeaWiFS data applied in this study, corrections for AE are hence needed in ~20% of cases between 412 and 510 nm, ~78% of cases at 555 nm, ~50% of cases at 670 nm, and ~85% of cases at NIR wavelengths. Notably, the 15% of cases where AE at $λ_{N}$ are regarded as not detectable occur in winter.

2.3 Match-ups construction

For each of the SeaDAS procedures P illustrated in Section 2.1 (see Table 1), match-ups between satellite and in situ data have been constructed by using the 3x3-elements of image centered at the AAOT site for each L2 product. An established protocol [33] has been applied to exclude cases when default SeaDAS processing flags (predominantly detecting clouds or critical geometries) affect any of the 9 pixels, when the time difference between the satellite overpass and the field measurement exceeds 2-hours, and when there is evidence of spatial heterogeneity for remote sensing reflectance at 490 and 555 nm (i.e., when the coefficient of variation over the 9 elements of image exceeds 20%).

2.4 In situ measurements

In situ measurements of the aerosol optical thickness τ_a and of the remote sensing reflectance R_rs have been systematically performed at the AAOT since 2002 within the framework of AERONET-OC making use of autonomous above-water radiometer systems [34]. AERONET-OC L2 data applied in this study benefit of regular absolute calibration of the radiometers before and after any field deployment and additionally of a comprehensive quality assurance [34]. Corrections have been applied to match SeaWiFS center-wavelengths [35] and to minimize the effects of the anisotropic distribution of the in-water light field [18]. An estimate of overall uncertainties affecting AERONET-OC R_rs acquired at the AAOT indicates values of ~5% in the blue-green, and up to ~7% in the red [36,37]. The expected uncertainty on in situ measurements of τ_a is ~0.01-0.02 at all considered wavelengths [38].

2.5 Geophysical characteristics of the match-up data set

The geometric, atmospheric and water characteristics of satellite and in situ match-ups are summarized in Figs. 2 and 3. The parameters adopted for AE simulations at the site (see Section 2.2) are also displayed.

Fig. 2 Histograms of the geo-physical quantities characterizing the SeaWiFS images considered in this study (N=82). From upper left to lower right panel: sun zenith θ₀, sun azimuth ϕ₀, day of the year (Jday), sensor viewing angle θ_v, satellite azimuth angle ϕ_v, and Ångström exponent ν. The dashed lines indicate values applied for the MC simulations (see Section 2.2).

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Fig. 3 Spectral values of in situ τ_a (a) and $R_{r s}$ [sr¹] (b) contributing to match-ups for the periods May-August, September-October and March-April, and November-February. The dashed lines represent values of τ_a applied for the MC simulations (see Section 2.2). It is noted that while mid-season simulations were performed for a wide range of atmospheric conditions, summer and winter simulations were conducted for the sole average ones [11].

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Figure 3(a) indicates lower atmospheric turbidity in winter and higher in summer (consistent with the aerosol variability determined with automated measurements [39]). Figure 3(b) and Fig. 1 further illustrate that the water is highly reflecting in winter whereas land perturbations are the lowest. Conversely, water reflectance is relatively low in summer while land perturbations are the highest. The situation encountered in mid-seasons is in between the previous two extremes.

3. Results

Results from the analysis of satellite and in situ match-up values of τ_a and, $R_{r s}$ and its band ratios, are here illustrated for each SeaDAS procedure P listed in Table 1.

3.1 Statistical quantities applied for the analysis

The average of percentage differences ψ, the average of absolute percentage differences |ψ|, and the root mean square difference RMSD are used to present the comparison between primary products $ℜ$ (either τ_a, $R_{r s}$ or derived quantities) from satellite and in situ measurements. The quantity ψ indicates the bias between the compared quantities, while |ψ| (not to be mistaken with the absolute value of ψ) is an estimate for the dispersion.

For each image i, the values of ψ are computed as

ψ = \frac{1}{N} \sum_{i = 1}^{N} ψ_{i}

where N is the total number of match-ups included in the analysis, and ψ_i is defined as

ψ_{i} = 100 \frac{ℜ_{i}^{s} - ℜ_{i}^{R}}{ℜ_{i}^{R}} .

with

ℜ^{S}

indicating the quantity determined from satellite data and

ℜ^{R}

the in situ reference value.

The quantity |ψ_i| is used to compute the average absolute percentage difference |ψ| according to

| ψ | = \frac{1}{N} \sum_{i = 1}^{N} | ψ_{i} |

The root mean square difference RMSD is finally defined as:

R M S D = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {| ℜ_{i}^{s} - ℜ_{i}^{R} |}^{2}} .

3.2 τ_a and ν match-ups

Spectral values of ψ, |ψ| and RMSD for τ_a and for the Ångström exponent ν are summarized in Tables 2 and 3, respectively.

Table 2. Values of ψ and |ψ| (both in percent), and of RMSD (dimensionless), for τ_a determined at different center-wavelengths λ with the different procedures P. N=82.

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Table 3. Values of ψ and |ψ| (in percent) and of RMSD (dimensionless) for ν determined with the different procedures P. N=82.

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The values of |ψ| affecting τ_a (Table 2) are within those determined from the analysis of approximately 9000 match-ups of SeaWiFS derived and globally distributed AERONET values, which showed median absolute percent differences increasing from 17% at 443 nm to 23% in the NIR [40]. Further recalling that the uncertainty of AERONET τ_a measurements (here indicated as ϵ_τ) is ~0.01-0.02 [38], RMSD values at red and NIR center-wavelengths can be all regarded as not significant. At other center-wavelengths RMSDs exceed ϵ_τ, but this occurs regardless of the applied procedure, while RMSDs between τ_a from alternative procedures are always lower than 0.017 (i.e., in the order of ϵ_τ). Results therefore suggest that differences in satellite-derived τ_a from alternative procedures are below the uncertainties affecting both in situ and satellite data. Finally, the values of ψ in Table 3 suggest an improvement of ν when the TW correction is applied, although |ψ| does not show any sensitivity.

3.3 $R_{r s}$ match-ups

3.3.1 SeaDAS procedure without NIR correction

When assuming negligible NIR water-leaving radiance in the processing of SeaWiFS data (procedure P₀), average annual biases ψ are all negative with the largest values at the blue and red center-wavelengths, i.e., where the water signal is lower (see Fig. 4). At 670 nm, where the water signal is the lowest, misestimates are up to −43% and negative $R_{r s}$ occur in 9% of the cases. Overall, results suggest an overestimate of the aerosol radiance at the NIR wavelengths, commonly attributed to non-negligible values of the water signal in the NIR.

Fig. 4 Scatter plots of satellite (SAT) versus reference in situ (IN SITU) $R_{r s}$ values for procedure P₀.

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3.3.2 Standard SeaDAS procedure

By including the iterative estimate of TW contributions at NIR wavelengths in the processing of satellite data (i.e., by applying the standard SeaDAS procedure P_TW) ψ decreases to values lower than ± 5% between 412 and 555 nm, but it remains up to −31% at 670 nm (see Fig. 5), where the satellite-derived $R_{r s}$ is still negative in 10% of the cases. Notably, the values of ψ are in agreement with annual average biases determined from SeaWiFS and AERONET-OC match-ups at the AAOT for the period 2002-2010 [6].

Fig. 5 As in Fig. 4 but for procedure P_TW.

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3.3.3 Correcting for AE and TW contributions

When the standard SeaDAS scheme (i.e., including the TW algorithm) is applied to L1 SeaWiFS data previously corrected for AE (procedure P_AE+TW), the annual average bias drastically decreases to + 5% at 670 nm, but it appreciably increases at the blue center-wavelengths where it exceeds + 10% (Fig. 6). The dispersion of data does not significantly change with respect to procedure P_TW (Fig. 5), although RMSD slightly decreases in the red, and slightly increases in the blue. The observed increase of ψ in the blue might result from an underestimate of the atmospheric contribution induced by an overestimate of the global adjacency and water contributions at $λ_{N}$ (see Eq. (5), and/or by misestimates of $L_{a d j}$ at $λ_{V}$ where confidence on simulated results is lower (see Section 2.2). Notably, the number of cases characterized by negative satellite $R_{r s}$ drastically decreases, too.

Fig. 6 As in Fig. 4 but for procedure P_AE+TW.

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3.3.4 Correcting for the sole AE

If data are corrected for the sole AE, i.e., the TW algorithm is excluded (procedure P_AE), the annual relative biases are within ± 5% between 412 and 555 nm, and only up to −10% at 670 nm (Fig. 7). Remarkably, the number of cases presenting negative satellite $R_{r s}$ is still low.

Fig. 7 As in Fig. 4 but for procedure P_AE.

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It is noted that the RMSD values decrease less substantially by correcting for AE than for TW contributions. This finds explanation in observing that TW corrections, which are proportional to the water signal itself, are more important for cases characterized by higher values of $R_{r s}$ . Conversely, AE corrections, which are higher in summer when the water is scarcely productive, are more important for cases characterized by low $R_{r s}$ . Consequently, TW corrections introduce larger absolute variations in $R_{r s}$ (and hence in RMSD) than those introduced by AE corrections.

3.4 Band ratio match-ups

Results are additionally presented for remote sensing reflectance ratios $R_{r s} (λ) / R_{r s} (555)$ , which are commonly applied in bio-optical algorithms for the determination of chlorophyll concentration Chl (it is noted that $R_{r s} (555)$ is the least affected by the various retrieval procedures, as shown in Fig. 4 to 7). Average spectral values of RMSD, |ψ| and ψ are summarized in Table 4. As expected, band ratios for λ = 490 and 510 nm are not particularly sensitive to the alternative correction procedures, while ψ at the other center-wavelengths are consistent with values obtained for $R_{r s}$ alone.

Table 4. Values of ψ and |ψ| (in percent) and of RMSD for R_rs(λ)/R_rs(555) determined at different center-wavelengths λ with the different procedures P. N = 82 at all center-wavelengths except for λ = 510 where N = 47.

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4. Discussion

Acknowledging the seasonal dependence of both water reflectance [see Fig. 2(b)] and AE (see Fig. 1), as well as the intra-annual trend in biases for the whole set of SeaWiFS match-ups at the AAOT over the period 2002-2010 [6], results from Section 3.3 are analyzed at intra-annual level. Specifically, intra-annual values of ψ and RMSD for match-ups of $R_{r s}$ from the different correction procedures are summarized in Fig. 8.

Fig. 8 Upper and lower panels illustrate spectral values of average biases ψ (in percent) and of RMSD [sr⁻¹], respectively, between SeaWiFS and AERONET-OC $R_{r s}$ products for satellite images acquired in November-February (N = 12), in March-April and September-October (N = 31), and in May-August (N = 39). Empty stars refer to satellite data retrieved with procedure P₀, filled stars with procedure P_TW, empty circles with procedure P_AE, and gray circles with procedure P_{AE + TW} (see Table 1).

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It is noted that the seasonal trend of biases for the standard procedure P_TW shows a consistent underestimate of $R_{r s}$ at the red center-wavelength in summer (−62%), and a less important overestimate of $R_{r s}$ at blue center-wavelengths in winter ( + 10% and + 13% at 412 and 443 nm, respectively). This is in agreement with the trend observed for the complete set of SeaWiFS and in situ AERONET-OC match-ups at the AAOT site between 2002 and 2010 [6].

Biases of data acquired in summer, when the water reflectance is low [Fig. 2(b)] and AE are the highest (Fig. 1), do not show significant sensitivity to TW corrections. Indeed, values of ψ from the standard procedure P_TW are very similar to those from procedure P₀ (when the NIR correction is not applied), and both show large negative values at 670 nm and slightly negative values in the blue. This suggests an overestimate of the atmospheric contribution in the NIR, likely due to adjacency contributions interpreted as atmospheric ones. In support to this hypothesis, biases strongly decrease by correcting for AE, i.e., by implementing the procedures P_AE+TW and P_AE. Indeed, the large negative bias at 670 nm drastically decreases to −5% and −18%, respectively. As well, the RMSD at 670 nm decreases from 2.8⋅10⁻⁴ sr⁻¹ for the procedure P_TW, to 1.4⋅10⁻⁴ and 1.9⋅10⁻⁴ sr⁻¹ for the procedures P_AE+TW and P_AE, respectively. Nevertheless, while for the procedure P_AE the summer biases at the blue wavelengths remain within ± 6%, they exceed + 10% for the procedure P_AE+TW. The latter suggests a possible overestimate of the global AE and TW contributions at $λ_{N}$ for the procedure P_AE+TW, although misestimates of adjacency contributions at $λ_{V}$ might also occur.

Mid-season biases display their lowest values for the standard procedure P_TW. Considering that mid-season AE are considerably larger than the noise level NL at the NIR center-wavelengths (Fig. 1), this suggests that the standard SeaDAS procedure compensates adjacency perturbations by interpreting them as TW contributions. The overestimate of the water signal at the blue wavelengths for procedure P_AE+TW (i.e., + 9% and + 10% at 412 and 443 nm, respectively) again calls for an overestimate of the global AE and TW contributions at $λ_{N}$ .

In winter, when AE at $λ_{N}$ are generally negligible (see Fig. 1) and the water reflectance is the highest, biases from the procedures P_TW and P_AE both show an analogous overestimate of the water signal at the blue wavelengths (i.e., + 10% and + 13% at 412 and 443 nm, respectively). This again suggests an overestimate of TW contributions by the procedure P_TW, and an overestimate of the (negative) AE at $λ_{V}$ by the procedure P_AE. Noteworthy, the overestimate of the water signal at the blue center-wavelengths further increases when both corrections are applied (i.e., for procedure P_AE+TW with + 18% and + 19% at 412 and 443 nm, respectively).

To summarize, overall results suggest a significant bias reduction by correcting for AE (while acknowledging that possible misestimates of adjacency correction factors at $λ_{N}$ where confidence on simulations is lower, may affect the data), and likely a systematic overestimate of the TW contributions.

Underestimated (or neglected) AE and overestimated TW contributions can compensate each other in the standard SeaDAS procedure P_TW. This might occur when the first-iteration value of $b_{b p} (670)$ in Eq. (2) (and hence of $R_{r s}$ at 670 nm) is large enough and $L_{a d j} (λ_{N})$ is not too high, such as in mid-seasons. Moderate AE are then interpreted as TW contributions and so unintentionally corrected. Conversely, the compensation fails in summer when high NIR adjacency perturbations and low water reflectance simultaneously occur. In this case, uncompensated AE at NIR wavelengths lead to an overestimate of the atmospheric contribution with a consequent underestimate of $R_{r s}$ at $λ_{V}$ . This is particularly pronounced at 670 nm where $R_{r s}$ is very low. The compensation also fails in the absence of adjacency perturbations in the NIR (such as in winter or when SeaWiFS data are processed after correcting for AE as in the procedure P_AE+TW). TW contributions not compensated by AE lead to an underestimate of the atmospheric radiance and consequently to an overestimate of the water signal at $λ_{V}$ . This is more pronounced towards the blue where the atmospheric contribution is more relevant. Annual average biases illustrated in Section 3.3 for the procedure P_TW (see Fig. 5) appear hence to originate from a misinterpretation of NIR atmospheric contributions as TW ones in data acquired in winter, and from uncompensated adjacency effects in data acquired in summer.

Paradoxically, after correcting the original SeaWiFS data for AE, SeaDAS retrieves even higher water contributions in the NIR. Indeed, values of $R_{r s} (670)$ , which are largely underestimated by the standard SeaDAS procedure P_TW (see Fig. 5), significantly increase when correcting for AE (see Figs. 6 and 7). Larger retrieved values of $R_{r s} (670)$ correspond to larger initial values of $b_{b p} (670)$ in Eq. (2). Considering that the ratio $R_{r s} (443) / R_{r s} (555)$ defining the $b_{b p}$ spectral slope [see Eq. (2)] is instead not substantially affected by the alternative retrieval procedures (Table 3), the final effect is the determination of even higher values of $R_{r s} (λ_{N})$ . The annual average biases illustrated in Section 3.3 for the procedure P_AE+TW (see Fig. 6) thus appear to originate from a misinterpretation of NIR atmospheric contributions as TW ones.

The systematic overestimate of TW contributions is likely explained by the inability of the therein-adopted model [Eqs. (2)-(4)] to represent actual bio-optical conditions at the site. In fact, a worsening of the fitting capability of Eq. (2) for clearer waters has been reported [14]. Thus, considering that the AAOT exhibits only moderately turbid waters, the $b_{b p}$ spectral dependence at the site could be characterized by a steeper gradient from the red to the NIR than that actually determined with the TW scheme.

Evidence of overestimates of the water signal at $λ_{N}$ was already reported in Bulgarelli et al. (2017) [12] from the analysis of 162 SeaWiFS match-ups acquired in correspondence of the AAOT between 1997 and 2008, all indicating the presence of clear water. In that study, the empirical criterion $n L_{w} (670)<0 .1$ Wm⁻²μm⁻¹sr⁻¹ was used to indicate negligible values of the reference in situ water leaving radiance in the NIR. Satellite radiometric products derived from clear water observations should not be altered by TW corrections, and the NIR water signal determined by the satellite should be null. Nonetheless, the analysis indicated that in ~85% of the cases SeaDAS determined a non-null (overestimated) water signal at $λ_{N}$ . The same analysis conducted on the present SeaWiFS sample images indicates non-null (overestimated) water signals in about 90% of the clear water cases. The overestimate is particularly significant in mid-seasons.

It is here remarked that a direct comparison between water signal contributions at NIR center-wavelengths from satellite and in situ measurements is impracticable, being the in situ R_rs values available for the AAOT at 870 nm within the noise of measurements.

The hypothesis of compensations of AE (particularly in mid-seasons) as well as the overall need to correct for AE, are further supported by the comparison at the NIR center-wavelengths between water signal contributions $ς_{w}^{i} = t L_{w}^{i} / L_{t o t}^{i}$ (as estimated with the standard SeaDAS procedure) and adjacency contributions $ξ_{L t o t}^{i}$ (as theoretically estimated in Section 2.2). Results, summarized in Fig. 9, show that even assuming that $ς_{w}^{i}$ is accurately retrieved (yet likely overestimated), $ς_{w}^{i} < ξ_{L t o t}^{i}$ in 68% and 85% of the whole cases at 765 and 865 nm, respectively, and that such a percentage reaches 100% at 865 nm for images acquired in May-August.

Fig. 9 Scatter plot of $ξ_{L t o t}^{i}$ versus $ζ_{w}^{i}$ at 765 and 865 nm for the whole SeaWiFS data sample (N = 82). Filled circles represent data acquired in May-August, grey circles indicate data acquired in November-February, while empty circles represent data acquired in the remaining period of the year.

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A similar analysis performed on a larger sample of 1124 SeaWiFS images collected in correspondence of the AAOT between 1997 and 2008, all qualified for match-up construction with in situ data, predicts $ζ_{w}^{i} < {\bar{ξ}}_{L t o t}^{}$ in ~70% and ~85% of the cases at 765 and 865 nm, respectively (see Fig. 10), where ${\bar{ξ}}_{L t o t}^{}$ indicates the average adjacency contribution theoretically estimated at the AAOT for typical observation conditions [11]. The seasonal breakdown of data (see Fig. 11) evidences again that adjacency contributions are likely to outdo TW contributions for the vast majority of summer and mid-season cases, and for only few cases in winter.

Fig. 10 Frequency distribution of $ζ_{w}^{i}$ at 765 and 865 nm for a sample of 1124 SeaWiFS data acquired in correspondence of the AAOT between 1997 and 2008. Vertical full and dashed lines represent estimated average adjacency contribution $\bar{ξ}$ and standard deviation s, respectively [11].

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Fig. 11 Frequency distribution of $ζ_{w}^{i}$ at 865 nm nm for a sample of 1124 SeaWiFS images acquired in correspondence of the AAOT in different intra-annual periods between 1997 and 2008. Vertical full and dashed lines represent estimated average adjacency contribution $\bar{ξ}$ and standard deviation s, respectively [11].

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Results from these comparative analyses indicate that even assuming no overestimate of $L_{w} (λ_{N})$ , the latter would nonetheless be significantly lower than $L_{a d j} (λ_{N})$ in the large majority of cases between March and October. This surely calls for regarding adjacency perturbations at least as important as TW ones, while it further suggests that low biases in mid-season match-ups can only occur through compensation of adjacency perturbations.

5. Summary and conclusions

With the aid of a sample of 82 SeaWiFS match-ups from the AAOT site for the period 2002 and 2010 and in the absence of cloud contamination, the sensitivity of satellite primary products (i.e., the aerosol optical thickness τ_a, the remote sensing reflectance $R_{r s}$ and its band ratios) to AE and TW perturbations has been analyzed.

For each sample image, adjacency contributions at the sensor have been interpolated from accurate simulations performed for representative observation conditions at the AAOT site [11], while ingesting actual in situ remote sensing reflectance spectra and the closest climatological land albedos. Simulations were performed with the NAUSICAA 3D MC code, accounting for multiple scattering, sea surface roughness, off-nadir illuminations and observations, and the actual coastal profile. The FEM code was also utilized to compute the atmospheric radiometric contributions.

Results from the standard SeaDAS procedure show an average underestimate of summer $R_{r s}$ values at the red center-wavelengths and an average overestimate of winter $R_{r s}$ values at the blue center-wavelengths. These findings are in full agreement with intra-annual trends of biases observed for the whole set of match-ups between SeaWiFS and in situ data at the AAOT over the period 2002-2010 [6].

A significant bias reduction is obtained when correcting for AE the satellite data acquired from March to October, i.e., when AE significantly exceed the SeaWiFS radiometric sensitivity. Due to low sun elevation and dormant vegetation, AE do not generally affect observations at the site between November and February. Possible misestimates of AE at the visible wavelengths, where confidence on simulation results is lower, are also recalled.

The analysis further indicates systematic overestimates of the NIR water signal by the TW correction algorithm, likely due to the inability of the optical model therein implemented to reproduce actual bio-optical conditions at the AAOT: the spectral dependence of b_bp around the AAOT is probably characterized by a steeper decrease from the red to the NIR.

Within the standard SeaDAS procedure, underestimates of AE and overestimates of TW contributions appear to compensate each other when the difference between the two is not too high, i.e., in mid-seasons. The compensation fails in summer when NIR AE are the highest and the water reflectance is low, and also in winter when NIR AE are negligible and $R_{r s}$ is relatively high. In summer, uncompensated adjacency contributions are likely interpreted as atmospheric ones leading to an overestimate of the atmospheric radiance and thus to an underestimate of the water signal at $λ_{V}$ . This is particularly remarkable in the red where the water-leaving radiance is the lowest. In winter, overestimates of the TW contribution induce an underestimate of the atmospheric radiance with a consequent increase of the apparent water signal.

The need to regard AE at least as important as TW contributions is further supported by a comparative analysis indicating AE exceeding TW contributions at the NIR wavelengths in the vast majority of cases acquired between March and October, and thus additionally evidencing that low biases in mid-season match-ups can only occur through compensation of adjacency effects.

Overall, findings indicate that the intra-annual variation in biases observed in SeaWiFS primary products acquired at the AAOT between 2002 and 2010 [7] might originate from SeaDAS misinterpretation of NIR atmospheric contributions as TW ones in data acquired in winter, and from uncompensated AE in data acquired in summer.

Uncertainty reduction in SeaWiFS data thus requires the simultaneous accurate estimate of both AE and TW contributions, whereas the latter implies tailoring the optical model embedded in the TW correction algorithm to reproduce the actual bio-optical conditions of the observed waters.

The analysis of the seasonal impact of AE in satellite data at the AAOT performed for different ocean color sensors [13] suggests that results from the present exercise might be valid for MERIS and OLCI full resolution data, too. Data acquired by sensors with significantly larger radiometric sensitivity, such as MODIS-A low-resolution and MERIS and OLCI reduced-resolution, might instead be more consistently affected by AE at the visible wavelengths, especially in winter. This could lead to a lower compensation of AE by TW overestimates.

Present results are specifically valid for the considered region, regarded as representative of mid-latitude coastal areas covered by crop. Coastal lands covered by dry and green vegetation, snow, white sand and concrete lead to significantly higher AE at all wavelengths (only at the NIR wavelengths for green vegetation) [31]. It would thus be challenging to determine to what extent present findings are occurring elsewhere. Nonetheless, results surely warn that underestimates of land perturbations and potential overestimates of the NIR water signal (input to several bio-optical algorithms [41,42,43]) should be comprehensively addressed.

Appendix A

The adjacency radiance $L_{a d j}$ reaching a satellite sensor observing a target element located at (x₀,y₀) with observation direction Θ_v can be modeled as (see [11]):

L_{a d j} (x_{0}, y_{0}; Θ_{v}) = {[L_{l a n d} (x, y; Θ) - L_{w} (x, y; Θ) - L_{s s} (x, y; Θ)] \cdot M (x, y)} \otimes h (x, y; x_{0}, y_{0}; Θ, Θ_{v})

Where

L_{l a n d}

,

L_{w}

and

L_{s s}

are the upgoing two-dimensional radiance leaving the land, the water volume and the sea in (x,y) with direction Θ, respectively;

h (x, y; x_{0}, y_{0}; Θ, Θ_{v})

the atmospheric point-spread function; and

M (x, y)

the land-water matrix:

M (x, y) = {\begin{matrix} 1 f o r l a n d e l e m e n t s \\ 0 f o r w a t e r e l e m e n t s \end{matrix}

Under the assumption of isotropic and homogeneous reflectance of the land and water volume, the terms

L_{l a n d}

and

L_{w}

can be modeled as:

L_{l a n d} = \frac{ρ_{l}}{π} E_{d}^{ρ = ρ_{l}}

L_{w} = R_{r s} E_{d}^{ρ = ρ_{s e a}},

where

ρ_{l}

indicates the albedo of the land; R_rs the remote sensing reflectance;

ρ_{s e a}

the albedo of the sea (i.e., the spectral bi-hemispherical reflectance [19] of both water and sea surface) (pg. 193 of [44]); and

E_{d}^{ρ = ρ_{l}}

and

E_{d}^{ρ = ρ_{s e a}}

the total downward irradiance impinging on land and sea surface, respectively.

By introducing the functions

C^{ρ = 1} (x_{0}, y_{0}; Θ_{v}) = E_{d}^{ρ = 1} (x, y) / π \cdot M (x, y) \otimes h (x, y; x_{0}, y_{0}; Θ, Θ_{v})

and

W (x_{0}, y_{0}; Θ_{v}) = L_{s s} (x, y, Θ) \cdot M (x, y) \otimes h (x, y; x_{0}, y_{0}; Θ, Θ_{v})

representing the cumulative radiance contribution at the sensor from the land region assumed an ideal Lambertian surface [Eq. (A.5)] or as a wind-roughened Fresnel sea surface [Eq. (A.6)] respectively, Eq. (A.1) can be finally transformed in Eq. (6), with

κ_{l} = \frac{E_{d}^{ρ = ρ_{l}}}{E_{d}^{ρ = 1} / π}

and

κ_{w} = \frac{E_{d}^{ρ = ρ_{s e a}}}{E_{d}^{ρ = 1} / π} .

By further acknowledging that the total downward irradiance at the surface

E_{d}^{ρ}

can be computed from

E_{d}^{ρ = 0}

for a completely absorbing surface as

E_{d}^{ρ} = E_{d}^{ρ = 0} / (1 - ρ S)

, where S is the atmospheric spherical albedo of the bottom of the atmosphere and the term

(1 - ρ S)

accounts for multiple reflections at the surface, the parameters

κ_{l}

and

κ_{w}

simply become:

κ_{l} = \frac{π (1 - S)}{1 - ρ_{l} S}

κ_{w} = \frac{π (1 - S)}{1 - ρ_{s e a} S}

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On the minimization of adjacency effects in SeaWiFS primary data products from coastal areas

Abstract

1. Introduction

2. Data and methods

2.1 Satellite data processing procedure

2.2 Theoretical quantification of AE

2.3 Match-ups construction

2.4 In situ measurements

2.5 Geophysical characteristics of the match-up data set

3. Results

3.1 Statistical quantities applied for the analysis

3.2 τ_a and ν match-ups

3.3 $R_{r s}$ match-ups

3.3.1 SeaDAS procedure without NIR correction

3.3.2 Standard SeaDAS procedure

3.3.3 Correcting for AE and TW contributions

3.3.4 Correcting for the sole AE

3.4 Band ratio match-ups

4. Discussion

5. Summary and conclusions

Appendix A

References and links

Cited By

Figures (11)

Tables (4)

Equations (20)

Optics Express

λ		P₀	P_TW	P_{AE + TW}	P_AE
412	RMSD	0.037	0.037	0.042	0.038
	\|ψ\|	18	15	15	15
	ψ	11	2	−6	3
443	RMSD	0.034	0.034	0.040	0.035
	\|ψ\|	17	14	14	14
	ψ	9	1	−7	2
490	RMSD	0.031	0.031	0.034	0.031
	\|ψ\|	19	16	15	16
	ψ	11	3	−5	3
510	RMSD	0.030	0.030	0.034	0.031
	\|ψ\|	19	16	14	16
	ψ	11	3	−5	3
555	RMSD	0.026	0.026	0.028	0.026
	\|ψ\|	20	16	14	16
	ψ	12	3	−3	4
670	RMSD	0.020	0.020	0.021	0.020
	\|ψ\|	24	21	18	20
	ψ	15	10	2	7
865	RMSD	0.018	0.019	0.020	0.020
	\|ψ\|	23	24	24	22
	ψ	−3	−2	−8	−9

λ		P₀	P_TW	P_{AE + TW}	P_AE
412	RMSD	0.17	0.16	0.17	0.16
	\|ψ\|	16	15	16	15
	ψ	−7	1	10	2
443	RMSD	0.12	0.13	0.16	0.15
	\|ψ\|	10	11	14	12
	ψ	3	7	12	8
490	RMSD	0.09	0.09	0.10	0.09
	\|ψ\|	5	5	6	5
	ψ	0	1	3	2
510	RMSD	0.07	0.07	0.08	0.08
	\|ψ\|	5	5	6	6
	ψ	3	4	5	5
670	RMSD	0.07	0.06	0.03	0.03
	\|ψ\|	44	39	23	23
	ψ	−41	−32	2	−10

Abstract

1. Introduction

2. Data and methods

2.1 Satellite data processing procedure

2.2 Theoretical quantification of AE

2.3 Match-ups construction

2.4 In situ measurements

2.5 Geophysical characteristics of the match-up data set

3. Results

3.1 Statistical quantities applied for the analysis

3.2 τa and ν match-ups

3.3 Rrs match-ups

3.3.1 SeaDAS procedure without NIR correction

3.3.2 Standard SeaDAS procedure

3.3.3 Correcting for AE and TW contributions

3.3.4 Correcting for the sole AE

3.4 Band ratio match-ups

4. Discussion

5. Summary and conclusions

Appendix A

References and links

Cited By

Figures (11)

Tables (4)

Equations (20)

Optics Express

3.2 τ_a and ν match-ups

3.3 $R_{r s}$ match-ups