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Abstract
The equivalence of two radiometric methods relying on a single nadir-view optical sensor to determine the water-leaving radiance LW, namely the Single Depth Approach (SDA) and the Sky-Blocked Approach (SBA), was investigated applying identical hyperspectral radiometers operated on the same deployment platform. Values of LW from SDA and SBA measurements performed in the Black Sea across a variety of waters during ideal illumination conditions and with low-to-slight sea state, exhibited mean absolute differences within 0.5% in the blue-green spectral region and 2% in the red. This result, benefitting of a comprehensive parameterization of optical processes in combination with the characterization of sensors non-linearity, in-water response and reproducibility of absolute radiometric calibrations, indicated ample equivalence of the two near-surface methods in terms of performance and data reduction needs.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In situ reference measurements are essential to support ocean color applications such as bio-optical modelling, validation of satellite data products and system vicarious calibration. These applications call for increasing accuracy requirements putting constrains on measurement conditions and methods [1]. Best practice, therefore, suggests the collection of in situ reference measurements through consolidated protocols satisfying application requirements. However, measurement methods evolve with science and technology. This implies a thorough and continuous assessment of the evolving methods in view of evaluating their performance, and to ultimately allow for a comprehensive quantification of uncertainties affecting measurements.
Within such a broad context, this work aims at comparing two radiometric methods based on near-surface measurements for the determination of the water-leaving radiance ${L_W}$ relevant for the validation of satellite data products. The first method, hereafter called Single-Depth Approach (SDA), has been extensively applied in validation activities [2,3] and relies on near-surface in-water nadir-view measurements performed at a single fixed depth. The other method, called Skylight-Blocked Approach (SBA), was early applied by Y. H. Ahn [4] and relies on near-surface above-water nadir-view measurements performed shielding the sky- and sun-glint contributions. This method has been comprehensively documented over time [5–7] and applied in various investigations [8–10].
The final objective of this work is to compare the two methods by exploiting contemporaneous measurements performed with equivalent radiometers operated on the same deployment platform during ideal illumination and low-to-slight sea state conditions.
2. Methods
The SDA method illustrated in Fig. 1(a) relies on a near-surface in-water nadir-view radiance sensor operated at a nominal depth below the sea surface. This measurement method is generally implemented through a floating platform (e.g., a buoy) hosting the radiometer [11,12]. The implementation of the method implies the capability to account for the attenuation of the water layer between radiometer optical window and surface, the water-air radiance transmission coefficient, and additionally the shading perturbations by radiometer and floating platform [13–15].
Fig. 1. Schematics of (a) the Single-Depth Approach (SDA) and of (b) the Skylight-Blocked Approach (SBA). The self-shaded volumes refer to the idealized self-shading solely due to the direct sun light interacting with the bottom components of the two optical systems (i.e., they neglect any 3-D shading contribution from radiometers and shield). The shield-shaded volume refers to the shading by the immersed portion of the shield. The symbol z0 indicates the depth of the optical window of the SDA sensor and of the bottom of the SBA shield. The symbol τs indicates the distance between the optical window for SDA or the bottom of the shield for SBA, and the ideal point at which the field-of-view leaves the self-shaded volume.
The SBA method illustrated in Fig. 1(b) relies on a near-surface above-water nadir-view radiance sensor operated at some height from the surface with a shield preventing glint perturbations into the sensor field-of-view [5,7]. Current implementation of the method consists of a floating buoy hosting the radiometer, implicitly assuming that the shield ideally touches the surface and the optical window of the sensor fore optics is dry. This implementation only requires the basic capability to account for the shading perturbations of any component of the system [16]. However, when the shield is partially immersed and the optical window is wet due to waves action, the method should also account for: i. perturbations by the shield-shaded water volume between the depth of the shield bottom and surface; and ii. perturbing effects due to the presence of water on the optical window. These latter two elements were not considered (or at least not declared) in former works presenting or applying SBA.
3. Field measurements
Field measurements were performed in the Western Black Sea during May 2019 (see Fig. 2) across a variety of water types representing intermediate Jerlov’s coastal waters [17]. Specifically, measurements were collected with an Optical Floating System (OFS) equipped with two TriOS (Rastaede, Germany) RAMSES-ARC hyperspectral radiance sensors (i.e., one supporting SDA and the other SBA measurements) operated on 20 cm long arms symmetrically arranged with respect to the main axis of the system (see Fig. 3). Additionally, a Satlantic (Halifax, Canada) Tilt Heading Sensor (THS) operated on OFS at some distance from the radiometers, allowed for the collection of data to flag SDA and SBA measurements affected by excessive tilt.
RAMSES sensors exhibit a nominal spectral range of 320-950 nm, with spectral sampling and resolution of 3.3 nm and 10 nm, respectively. The integration time, autonomously determined as a function of the intensity of the measured signal, varies between 4 and 8192 ms. RAMSES-ARC sensors have an in-air full-angle field-of-view of 7° that reduces to approximately 5° in the water. Relevant is the low sensitivity to polarization of RAMSES-ARC sensors, typically within 0.5% in the blue-green spectral region and slightly exceeding 1% in the red [18].
The THS acquisition rate was set to 10 Hz. This ensured oversampling of tilt data during SDA and SBA radiometric measurements generally performed with integration times of 64 - 512 ms. It is emphasized that to minimize the impact of uncertainties affecting the comparison of the two methods, measurements benefitted of the use of identical RAMSES-ARC sensors i. radiometrically calibrated applying the same method and laboratory standards, and ii. characterized for non-linearity and in-water response (this latter characterization, leading to the determination of the immersion factor, only applies to the SDA in-water sensor). Additionally, the self-shading perturbations were ideally forced to equally affect both SDA and SBA data. In fact, aside deploying the SDA sensor at the same depth of the bottom of the SBA shield (6 cm, on average), the size of the front plate of the SDA sensor was artificially increased through the application of a 4 cm radius flange equivalent to the radius of the SBA shield (see Fig. 1). This solution makes identical the distance τs between the optical window for SDA or the bottom of the shield for SBA, and the ideal point at which the field-of-view leaves the shadow. Still, it is recognized that the actual 3D geometry of radiometers and SBA shield, affects the adjacent radiance field and has a secondary unaccounted contribution to self-shading effects. Finally, by recalling the very low sensitivity to polarization of RAMSES-ARC sensors, it is underlined that the nadir-view characterizing both SDA and SBA measurements excludes any appreciable polarization effect by the water-air interface and consequently any related impact on comparison results.
OFS was deployed from the stern of the ship while this latter was slowly moving in the direction defined by the sun azimuth. This solution allowed for the collection of data with both SDA and SBA radiometers symmetrically deployed with respect to the sun, thus ensuring minimization of the shading effects by the buoys of the floating system.
Measurements were only performed with sky and sea state conditions most favorable for the validation of satellite ocean color data. This implied i. clear sky conditions (sun not covered by clouds and cloudiness lower than 3 oktas), and ii. low-to-slight sea state (always lower than 4 of the Douglas scale) with wave height generally not exceeding 1 meter.
Data were collected during sequences lasting 3 minutes with radiance measurements performed at 5 second intervals, which led to the collection of 36 pairs of SDA and SBA radiance samples per sequence. It is mentioned that hyperspectral measurements of the downward irradiance ${E_s}(\lambda )$ were also collected with a TriOS RAMSES-ACC sensor operated on a 6 m mast onboard the research vessel at the same time of the SDA and SBA sensors. These irradiance data, however, were not applied in the following analysis except for documenting the water remote-sensing reflectance spectra, Rrs(λ), relevant to the study.
In view of supporting an accurate determination of the water-leaving radiance ${L_W}(\lambda )$ from both near-surface methods fully accounting for the involved attenuation and shading processes, a number of optical quantities were experimentally determined during the execution of the SDA and SBA radiometric measurements. These are the near-surface diffuse attenuation coefficient of the upwelling radiance ${K_L}(\lambda )$, the diffuse-to-direct in-air downward irradiance ratio ${I_r}(\lambda )$ and finally the seawater absorption and backscattering coefficients $a(\lambda )$ and ${b_b}(\lambda )$, respectively. ${K_L}(\lambda )$ was determined from the linear regression as a function of depth z of the log-transformed upwelling multispectral radiance ${L_u}(z,{\lambda _i})$ measured at the center-wavelengths ${\lambda _i}$ with a Satlantic µPRO free-fall profiler equipped with OCR-507 sensors. ${I_r}(\lambda )$ was determined with the aid of a shadow-band operated in conjunction with the RAMSES–ACC sensor allowing to measure the total and the diffuse (when shading the sun to the sensor) downward irradiances. The coefficient $a(\lambda )$ was computed adding the absorption coefficient of pure seawater for the spectral intervals below [19] and above [20] 550 nm, to the absorption coefficients of colored dissolved organic matter and of pigmented and non-pigmented particles quantified through laboratory spectrophotometric analysis of field samples [21,22]. Finally, ${b_b}(\lambda )$ was determined from the exponential fit of ${b_b}({\lambda _j})$ multispectral values measured with a HOBI Labs (Philomath, Oregon) Hydroscat-6 backscattering meter at the center-wavelengths ${\lambda _j}$.
Hyperspectral ${K_L}(\lambda )$ have been determined by multiplying the interpolated (extrapolated) multispectral ratio ${K_L}({\lambda _i})/[{a({\lambda_i}) + {b_b}({\lambda_i})} ]$ by the hyperspectral values of $[{a(\lambda ) + {b_b}(\lambda )} ]$ according to:
It is anticipated that the in-water free-fall profiles performed with the µPRO system just before OFS deployments to determine ${K_L}({\lambda _i})$, were also applied to compute multispectral water-leaving radiances $L_W^{\mu P}({\lambda _i})$ relevant for a fully independent assessment of the SDA and SBA data products. These $L_W^{\mu P}({\lambda _i})$ have been determined applying the multi-cast approach [23] and benefit of a radiometric calibration of the OCR-507 radiance sensor performed concurrently with those of the SDA and SBA sensors by applying the same methodology and laboratory standards.
Summary values of various quantities characterizing the radiometric measurements exploited in this study, are provided in Table 1.
Table 1. Minimum, maximum and mean values of quantities characterizing the field radiometric measurements applied in this study. The symbol ${\theta _0}$ indicates the sun zenith angle, ${K_L}(490)$ the diffuse attenuation coefficient of upwelling radiance at 490 nm, $a(490)$ the seawater absorption coefficient, ${b_b}(490)$ the seawater back-scattering coefficient, ${I_r}(490)$ the diffuse-to-irradiance ratio, $S$ the salinity and $T$ the water temperature.
4. Data processing
The RAMSES raw data were converted to physical quantities by applying corrections for the dark signal and non-linear response [24] and using the relevant calibration coefficients [25]. The SDA radiances were additionally corrected for the in-water change in response by applying the experimental immersion factors ${I_f}(\lambda )$ determined for RAMSES-ARC sensors [26], adjusted to account for the local values of water temperature and salinity [27].
Data from each measurement sequence were retained for successive analysis when i. performed with tilts lower than 3 degrees (i.e., approximately 85% of the data); ii. the heading of the floating frame was within approximately ± 20 degrees from the ideal direction determined by the sun azimuth, and iii. SDA and SBA spectral radiance values in the 400 − 700 nm range were within two standard deviations (2σ) from the mean of the measurement sequence. This last exclusion criterion was mostly applied to remove any data affected by large measurement perturbations such as wave focusing-defocusing, bubbles, and significant changes in the average water depth of the SDA radiance sensor or of the immersed portion of the SBA shield. Its application flagged approximately 10% and 12% of the SDA and SBA data, respectively. Overall, the 2σ criterion led to the removal of 15% of the collected data because of the wide correspondence of SDA and SBA flagged cases.
Practical aspects of the SBA applied in study are i. the use of a shield immersed by a few centimeters (i.e., 6 cm on average) and not ideally touching the sea surface, and ii. the assumption of a wet optical window resulting from the high probability of immersing the sensor during OFS deployments and the successive action of waves occasionally wetting the window (the actual condition of wet optical window was verified at the end of each deployment). Both aspects have significant impact and, if ignored, may lead to appreciable errors (biases) in the comparison of the two methods.
With reference to the schematic in Fig. 1(a), by defining ${L_u}({z_0},\lambda )$ the spectral upwelling radiance measured by the SDA sensor at depth ${z_0}$, the water-leaving radiance $L_W^{SDA}(\lambda )$ is determined by:
The correction ${C_{{K_L}}}(\lambda ,{K_L},{z_0}) = {e^{{K_L}(\lambda ) \cdot {z_0}}}$, in the ideal absence of the instrument, propagates the radiance ${L_u}({z_0},\lambda )$ from z0 to the ideal depth ${0^ - }$ accounting for ${K_L}(\lambda )$ in the subsurface layer.
Finally, the water-air radiance transmission coefficient ${t_{wa}}(\lambda )/n_w^2(\lambda )$ is computed with the assumption of a small field-of-view, with ${t_{wa}}(\lambda )$ the transmittance of the water-air interface and ${n_w}(\lambda )$ the spectral refractive index of water largely depending on salinity and temperature.
With reference to the schematic in Fig. 1(b), by defining ${L_W}({z_0},\lambda )$ the spectral radiance measured by the SBA sensor with the lower side of the shield at depth z0, the SBA water-leaving radiance $L_W^{SBA}(\lambda )$ is determined by:
The correction ${C_{{K_L}}}(\lambda ,{K_L},{z_0})$, in the ideal absence of the screen, propagates the upwelling radiance at depth ${z_0}$ to the depth ${0^ - }$. The additional term ${C_{is}}(\lambda ,a,{b_b},{z_0}) = {e^{[{a(\lambda ) + {b_b}(\lambda )} ]\cdot {z_0}}}$ attempts a first-order correction for the attenuation of the upwelling radiance in the shield-shaded water volume. It is emphasized the equivalence of the combined ${C_{{K_L}}}(\lambda ,{K_L},{z_0}) \cdot {C_{is}}(\lambda ,a,{b_b},{z_0})$ correction implemented for shield-shading, with the self-shading correction detailed in Gordon and Ding [28]. In fact, both correction schemes imply the determination of i. the radiance transmitted along the shadowed optical paths (i.e., the self-shaded or the shield-shaded ones) in the absence of the shading obstacle (i.e., the sensor or the shield) and ii. the radiance attenuation in the related shadowed water volumes.
Finally, ${C_{ww}}(\lambda ) = {t_{wa}}(\lambda ) \cdot {t_{wg}}(\lambda )/{t_{ag}}(\lambda )$ accounts for the wet optical window (idealized as a homogenous water film on the optical window) determined by the ratio of the combined transmittances of air-water and water-window interfaces ${t_{wa}}(\lambda ) \cdot {t_{wg}}(\lambda )$ to that of an air-window interface ${t_{ag}}(\lambda )$, all computed applying the small angle approximation.
5. Results
Figure 4 shows the $R_{rs}^{SBA}(\lambda )$ spectra (i.e., $R_{rs}^{SBA}(\lambda ) = L_W^{SBA}(\lambda )/{E_s}(\lambda )$) determined with the SBA data applying the corrections, calibrations, quality checks and processing detailed in the previous section. The spectra, only displayed in the 400 − 700 nm interval away from both the low sensitivity of RAMSES sensors in the ultraviolet and the negligible water-leaving radiance signal in the near-infrared, exhibit a large variability likely resulting from different concentrations of suspended and dissolved matter, as well as phytoplankton pigments.
Fig. 4. $R_{rs}^{SBA}(\lambda )$ spectra from the 472 SBA quality checked data collected in the Western Black Sea during 25 independent measurement sequences.
Results from the study are presented and discussed through the analysis of the $L_W^{SDA}(\lambda )$ and $L_W^{SBA}(\lambda )$ data products. It is noted that this choice does not imply any loss of information, in fact, the alternative analysis of $R_{rs}^{SDA}(\lambda )$ and $R_{rs}^{SBA}(\lambda )$ would lead to identical conclusions due to the application of the same values of ${E_s}(\lambda )$ while computing the remote sensing reflectance for the two measurement methods.
The comparison between SDA and SBA radiometric data products, omitting the index identifying the individual measurements, is presented through the unbiased percent differences $\varepsilon (\lambda )$ between $L_W^{SBA}(\lambda )$ and $L_W^{SDA}(\lambda )$ pairs:
Fig. 5. (a) Percent differences $\varepsilon (\lambda )$ between the 472 pairs of $L_W^{SBA}(\lambda )$ and $L_W^{SDA}(\lambda )$ spectra qualified for the comparison (the grey lines indicate individual spectra, the red dashed line indicates null differences, the blue dashed line indicates the mean values of $\varepsilon (\lambda )$ and finally the error bars indicate ± 1 σ). (b) Percent differences $\varepsilon (\lambda )$ between the 472 pairs of $L_W^{SBA}(\lambda )$ and $L_W^{SDA}(\lambda )$ samples at selected spectral bands (the colored bars present the distribution of differences while the error bars indicate ± 1 σ).
In view of supporting the comparison of results from this study with those from alternative investigations focused on the equivalence of a variety of radiometric methods, Fig. 6 displays the scatter plots of $L_W^{SBA}(\lambda )$ versus $L_W^{SDA}(\lambda )$ at the 412, 489, 555 and 665 nm center-wavelengths. Graphs are complemented by the mean of signed and unsigned differences, i.e., $\bar{\Psi } = 1/N \cdot \sum {\varepsilon (\lambda )} $ and $|{\bar{\Psi }} |= 1/N \cdot \sum {|{\varepsilon (\lambda )} |} $, provided as indices for bias and dispersion, respectively. The values of these statistical indices are comparable to those from the best comparison results published for above- and in-water methods [31] or, of different in-water methods [32] and SBA assessments [5,7].
Fig. 6. Scatter plots of $L_W^{SBA}({\lambda _i})$ versus $L_W^{SDA}({\lambda _i})$ at a few bands identified by their center-wavelengths (i.e., 412, 489, 555 and 665 nm) across the visible spectral region. The regression values are represented by the dashed lines. $\bar{\Psi }$ indicates the mean of the $\varepsilon (\lambda )$ values, while $|\bar{\Psi }|$ is the mean of the absolute values of $\varepsilon (\lambda )$.
6. Discussion
6.1 Impact of corrections
The corrections applied for SDA and SBA data processing are summarized in Fig. 7. These include: i. the corrections for sensors non-linearity ${C_{nl}}$ applied before the absolute radiometric calibration and leading to a net mean impact up to + 0.5% on $\varepsilon (\lambda )$ in the red, as determined by the difference between the corrections applied to the SDA and SBA radiometers; ii. the self-shading corrections $C_{ss}^{SDA}$ and $C_{ss}^{SBA}$ with mean values varying in the range of approximately 2-5% in the blue-green spectral region and approaching 10% in the red, and exhibiting slightly different values for SDA and SBA as a result of differences in ${f^{SDA}}$ and ${f^{SBA}}$; iii. the corrections for the water attenuation ${C_{{K_L}}}$ with mean values varying in the range of 1-1.5% in the blue spectral region, and reaching 4% in the red; and finally the corrections ${C_{is}}$ for radiance attenuation in the shield-shaded water volume exhibiting mean values in the range of 1-2% in the blue-green and approaching 4% in the red spectral region.
Fig. 7. Correction factors: ${C_{nl}}(\lambda )$ applied for sensor non-linearity; $C_{ss}^{SDA}(\lambda )$ and $C_{ss}^{SBA}(\lambda )$ applied for self-shading and computed accounting for the ${f^{SDA}} \simeq 0.1$ and ${f^{SBA}} \simeq 0.2$ ratios; ${C_{{K_L}}}(\lambda )$ applied for radiance propagation from the depth ${z_0}$ to ${0^ - }$; and finally ${C_{is}}(\lambda )$ applied for radiance attenuation in the shield-shaded water volume. The error bars indicate ± 1 σ with respect to the mean values represented by the continuous thick lines.
For completeness, it is mentioned that the corrections for the wet optical window ${C_{ww}}$ exhibit values of approximately 1.3% slightly varying with λ in the 400-700 nm spectral interval. Laboratory verifications of such a correction showed values varying from a fraction of a percent to several percent depending on the size and spatial distribution of water drops on the optical window. Because of this, ${C_{ww}}$ must be considered an idealized correction, still representative of the impact of water on the optical window of the SBA sensor.
It is additionally reported that the application of the experimental factors ${I_f}(\lambda )$ to SDA measurements performed with a RAMSES-ARC, leads to a radiance increase of ∼1% with respect to the application of the theoretical immersion factors.
To conclude, it is worthwhile recalling that the uncertainties affecting the determination of ${C_{{K_L}}}$, ${C_{is}}$, $C_{ss}^{SBA}$ and $C_{ss}^{SDA}$, which are more pronounced in the red, may largely impact the accuracy of both $L_W^{SDA}(\lambda )$ and $L_W^{SBA}(\lambda )$. Because of this, with specific reference to the self-shading corrections, it is once more stressed the importance of using small size radiometers in combination with deployment platforms and measurement strategies minimizing shading perturbations.
6.2 Impact of data averaging
In the previous section the comparison results have been presented applying pairs of individual quality checked measurements. A reduction of the random uncertainties affecting these individual measurements is then expected by the averaging of the quality checked data from each measurement sequence. This lessening of uncertainties has relevance for applications such as the validation of satellite data that require the minimization of random perturbations affecting data collected in a relatively short period at a specific location.
The impact of averaging of data from measurement sequences is illustrated in Fig. 8 through the unbiased percent differences $\bar{\varepsilon }(\lambda )$ determined from the mean $\bar{L}_W^{SBA}(\lambda )$ and $\bar{L}_W^{SDA}(\lambda )$ of the averaged $L_W^{SBA}(\lambda )$ and $L_W^{SDA}(\lambda )$ from each sequence. As expected, while the mean of the $\bar{\varepsilon }(\lambda )$ values in Fig. 8 do not show any difference with respect to the corresponding mean of the $\varepsilon (\lambda )$ values presented in Fig. 5(a), the related standard deviations are appreciably lower. Specifically, they exhibit values varying from approximately 2% in the blue-green to 3% in the red, while for the individual measurements they are 4% in the blue-green and 8% in the red. For completeness, Fig. 9 illustrates the variation coefficients CV for the $\bar{L}_W^{SBA}(\lambda )$ and $\bar{L}_W^{SDA}(\lambda )$ values from the various (i.e., 25) measurement sequences. These results indicate very close variability for both $L_W^{SDA}(\lambda )$ and $L_W^{SBA}(\lambda )$, and consequently for the related ${L_u}({z_0},\lambda )$ and ${L_w}({z_0},\lambda )$ measurements.
Fig. 8. Percent differences $\bar{\varepsilon }(\lambda )$ between the $\bar{L}_W^{SBA}(\lambda )$ and $\bar{L}_W^{SDA}(\lambda )$ spectra determined from the averaging of measurements from each individual sequence (the grey lines indicate mean spectra determined from the various measurement sequences, the red dashed line indicates null differences, the blue dashed line indicates the mean of the $\bar{\varepsilon }(\lambda )$ values and finally the error bars indicate ± 1 σ).
Fig. 9. Coefficients of variation CV determined for the individual values of $\bar{L}_W^{SBA}(\lambda )$ and $\bar{L}_W^{SDA}(\lambda )$ pairs from each measurement sequence. The blue dashed lines indicate the mean values.
6.3 Independent assessment of SDA and SBA retrieved ${L_W}(\lambda )$
The mean values of $\varepsilon (\lambda )$ (or of the equivalent $\bar{\varepsilon }(\lambda )$) indicate a bias between SDA and SBA water-leaving radiance retrievals of approximately -0.5% in the blue-green and -2% in the red. These biases, at least in the blue-green spectral region, could be explained by the repeatability of absolute radiometric calibrations (both SDA and SBA radiometers were calibrated at the same time in the same facility). An analysis of the absolute calibration repeatability of RAMSES radiometers achievable at the Marine Optical Laboratory of the Joint Research Centre where the SDA and SBA sensors were both calibrated, shows values varying from approximately 0.7% in the blue to 0.6% in the red (close to the mean of $\varepsilon (\lambda )$ and $\bar{\varepsilon }(\lambda )$ in the blue-green spectral regions). Still, differences in self-shading perturbations due to the SDA and SBA system components (i.e., radiometers, supports, flange, shield) and also the uncertainty in the determination of the combined correction ${C_{{K_L}}} \cdot {C_{is}}$ due to the immersed portion of the SBA shield, could also explain the systematic differences between methods more pronounced in the red part of the spectrum.
An independent assessment of the accuracy of the retrieved $\bar{L}_W^{SDA}(\lambda )$ and $\bar{L}_W^{SBA}(\lambda )$ is supported by their agreement with the water-leaving radiance $L_W^{\mu P}({\lambda _i})$ determined from in-water radiometric profiles performed with a µPRO multispectral free-fall system, and corrected for self-shading effects applying the same approach used for SDA and SBA data. Results from this comparison are shown in Fig. 10 at the center-wavelengths λi of the µPRO OCR-507 radiance sensor (i.e., 412, 443, 489, 510, 555 and 665 nm). The spectrally averaged values of the mean of the unbiased percent differences determined with $\bar{L}_W^{SDA}({\lambda _i})$ and $L_W^{\mu P}({\lambda _i})$ or, alternatively with $\bar{L}_W^{SBA}({\lambda _i})$ and $L_W^{\mu P}({\lambda _i})$, exhibit values of -1.6% for the first and of -1.1% for the second. The corresponding spectrally averaged values of the absolute differences exhibit values of 7.6% in both cases. These values are slightly higher than those spectrally presented in Fig. 6 for $L_W^{SBA}(\lambda )$ versus $L_W^{SDA}(\lambda )$. Nevertheless, the differences are fully justified by the independence of in-water profiling and near-surface measurements, and additionally by the use of radiometers based on different technologies (i.e., hyperspectral with varying integration time versus multispectral with fixed acquisition rate), both differently affecting the accuracy of data products.
Fig. 10. Scatter plot of $\bar{L}_W^{SDA}({\lambda _i})$ versus $L_W^{\mu P}({\lambda _i})$ and of $\bar{L}_W^{SBA}({\lambda _i})$ versus $L_W^{\mu P}({\lambda _i})$, at the µPRO center-wavelengths (i.e., 412, 443, 489, 510, 555 and 665 nm) across the visible spectral region. $\bar{\Psi }^{\prime}$ and $\bar{\Psi }^{\prime\prime}$ indicate the spectrally averaged values of the mean of the unbiased percent differences determined with $\bar{L}_W^{SDA}$ and $L_W^{\mu P}$ or, alternatively with $\bar{L}_W^{SBA}$ and $L_W^{\mu P}$, respectively. $|\bar{\Psi }^{\prime}|$ and $|\bar{\Psi }^{\prime\prime}|$ indicate the corresponding spectrally averaged values of the mean of the absolute unbiased percent differences.
Fig. 11. Spectral ratio $L_W^{SBA}(\lambda )/L_u^{SDA}({0^ - },\lambda )$ from the individual measurements qualified for the comparison. The red line indicates the theoretical value of ${t_{wa}}(\lambda )/n_w^2(\lambda )$ while the dashed blue line indicates the mean of the $L_W^{SBA}(\lambda )/L_u^{SDA}({0^ - },\lambda )$ spectral values. The error bars indicate ± 1 σ.
6.4 Water-air radiance transmission coefficient
The SDA and SBA comparison is complemented with the experimental analysis of the ratios of $L_W^{SBA}(\lambda )$ to $L_u^{SDA}({0^ - },\lambda )$ (i.e., the subsurface radiance from SDA), theoretically expressed by the radiance transmission coefficient ${t_{wa}}(\lambda )/n_w^2(\lambda )$ [33,34] commonly applied to convert subsurface ${L_u}({0^ - },\lambda )$ to above-water ${L_W}(\lambda )$ radiances.
The mean values of $L_W^{SBA}(\lambda )/L_u^{SDA}({0^ - },\lambda )$ presented in Fig. 11 as a function of wavelength exhibit an excellent agreement with the theoretical values of ${t_{wa}}(\lambda )/n_w^2(\lambda )$, with mean differences equivalent to those determined for the SDA and SBA water-leaving radiance comparison (i.e., $\varepsilon (\lambda )$). These results show a much higher agreement between theoretical values and mean of experimental data, than those presented in a former investigation [9]. Recognizing that the current study is restricted to a fewer water types and to data only collected during ideal illumination conditions and low-to-slight sea states, it is stressed that these results ultimately benefit from a comprehensive parameterization of the optical processes, the characterization of optical sensors, and additionally, of a deployment platform and measurement methods enforcing equivalence of the self-shading perturbations affecting SDA and SBA data.
6.5 Equivalence of SDA and SBA methods
The overall former results indicate equivalence of the implemented methods. In fact, both require information on the water optical properties (e.g., $a(\lambda )$, ${K_L}(\lambda )$) to estimate shading perturbations and to quantify the attenuation effects by the water layer between the sensor optical window and sea surface for SDA, or between the depth of the immersed portion of the shield and sea surface for SBA. Definitively, in both cases the impact of water attenuation can be minimized by reducing the depth of the SDA sensor and of the immersed portion of the shield for SBA. However, the effects of sea state would likely affect this ideal condition and imply the application of filtering techniques challenged by the very small percent differences characterizing measurements performed with immersed and non-immersed optical windows (the first condition affecting SBA and the second SDA). Specifically, by considering the absolute radiometric calibration factors ${C_f}(\lambda )$, the equation providing ${L_W}(\lambda )$ from raw data $D{N_{i - w}}(\lambda )$ of in-water nadir-view radiance measurements is:
When evaluating individual drawbacks of the two near-surface methods as implemented in this study, SDA undergoes uncertainties affecting i. the accurate determination of the immersion factor ${I_f}(\lambda )$ and ii. the spectral determination of the water-air radiance transmission coefficient that varies with the water refractive index primarily function of salinity and temperature, when excluding extremely high concentrations of suspended particles. On the contrary, SBA may exhibit i. larger dependence on uncertainties affecting self-shading corrections with respect to SDA (i.e., considering identical radiometers, SBA is more impacted by self-shading due to the application of the shield increasing the perturbed water volume) and additionally ii. uncertainties resulting from the occasional or systematic impact of water on the optical window. Once more, current implementations of both methods require the capability to account for the water attenuation because of the non-null depth of the SDA sensor and of the immersed portion of the SBA shield.
7. Summary and conclusions
This work investigated the equivalence of two methods relying on the application of a single near-surface nadir-view radiometer for the determination of the water-leaving radiance: namely the Single-Depth Approach (SDA) and the Sky-Blocked Approach (SBA).
SDA relies on a radiance sensor measuring the water-leaving radiance at a fixed depth below the water surface. This method requires the accurate determination of the immersion factor, of corrections for shading effects by the sensor and deployment structure, of the attenuation by the water layer between the optical window of the sensor and sea surface, and finally, of the water-air radiance transmission coefficient.
SBA relies on a radiance sensor measuring the water-leaving radiance from above the sea surface with the application of a shield screening any potential glint contribution into the sensor field-of-view. Ideally, this method only requires corrections for the shading effects by any component of the system. Still, practical implementations of the method allowing to operate in a variety of sea states, implies i. to have a portion of the shield immersed to maximize the possibility of collecting data not affected by glint, and also ii. to assume the optical window is likely wet. These operational conditions require further corrections to account for the impact of the water volume shaded by the immersed portion of the shield, and, for changes in response by the wet optical window.
Measurements performed in the Black Sea during ideal illumination conditions, with sea state not exceeding 4 (Douglas scale) and diverse marine bio-optical conditions, exhibit mean absolute differences within 0.5% in the blue-green and 2% in the red, between SBA and SDA pairs of water-leaving radiance ${L_W}(\lambda )$. These differences, supported by the application of an accurate parameterization of optical processes in combination with the characterization of sensors non-linearity, immersion factors and reproducibility of absolute radiometric calibrations, demonstrate ample equivalence of the two near-surface methods implemented in this study, without any major advantage of one with respect to the other in terms of performance and data reduction needs.
Funding
Joint Research Centre.
Acknowledgments
The authors would like thank Violeta Slabakova and Yavor Vekov from IO-BAS for the support provided during field operations onboard the R/V Akademik in the Black Sea. Pietro Sciuto and Lukasz Jankowski are acknowledged for their contribution to realize and test the OFS system. Zhongping Lee and two anonymous reviewers are also duly acknowledged for their constructive comments to the manuscript.
Disclosures
The authors declare no conflicts of interest.
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