Experimental analysis of the measurement precision of spectral water-leaving radiance in different water types: comment

Giuseppe Zibordi

doi:10.1364/OE.421786

1. Introduction

The compelling need to ensure the highest accuracy to satellite ocean color data products for environmental and climate applications, is driving advances in in situ measurement technology, methods and quality assurance schemes. These advances, resulting from a major community effort, aim at minimizing uncertainties in in situ reference measurements of spectral water-leaving radiance L_w(λ) and remote sensing reflectance R_RS(λ), applied for the indirect calibration of the space sensor (so called system vicarious calibration) and the validation of the related satellite-derived radiometric products. These efforts may naturally reflect different views, still they need to adhere to best practice and metrology.

This work provides comments on a recent paper that erroneously addressed uncertainty requirements for system vicarious calibration of ocean color sensors and incorrectly applied radiometry principles for the quantitation of differences between radiances collected by nadir-view optical sensors operated below and above the water surface.

2. Uncertainty requirements

Uncertainty requirements for in situ reference measurements supporting satellite ocean color missions are matter of continuous discussion and investigation. Uncertainties of quantities such as L_w(λ) definitively need to satisfy requirements that may vary for different applications (e.g., system vicarious calibration and validation) across bio-optical regions. The most demanding requirements are certainly those associated with system vicarious calibration devoted to support climate studies. With this respect, a community work [1] indicated target uncertainties for in situ reference measurements of L_w(λ) of 3-4% in the blue-green spectral regions and of 5% in the red in oligotrophic-mesotrophic regions (still difficult to achieve with current measurement methodologies and technology).

The 1-2% uncertainty requirement mentioned in Wei et al. [2] is not supported by any investigation. It simply results from the incorrect interpretation of the ideal concept of 1% radiometry introduced by McClain et al. [3] and further elucidated in successive publications [4]. The 1% radiometry concept indicates the need to keep below 1-2% each uncertainty source contributing to the uncertainty budget of radiometric quantities relevant for ocean color applications, and definitively not the need to keep below 1-2% the overall uncertainty budget. The appreciation of such a point is fundamental in view of avoiding the spread of currently unsupported and unfeasible uncertainty requirements.

3. Near-surface measurements

Near-surface measurements include the Sky-Blocked Approach (SBA) that relies on an above-water nadir-view radiance sensor operated at a nominal height from the surface with a shield screening skylight and consequently preventing glint perturbations in the sensor field-of-view (see Fig. 1). The method, whose concept appears in an early report [5], was extensively investigated in fully independent studies [e.g., 6–8]. The generic implementation of the method comprises a floating system hosting the nadir-view sensor whose shield is assumed to ideally touch the sea surface or more realistically having its lower side immersed in the water by a few centimeters.

Fig. 1. Schematics of the Skylight-Blocked Approach (SBA). The self-shaded volume refers to the idealized self-shading solely due to the direct sun light interacting with the bottom component of the optical system (i.e., it neglects any shading contribution from sensor and shield not affecting the radiance measured). The shield-shaded volume refers to the shading by the immersed portion of the shield.

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Waves may challenge this measurement concept: in fact, as a result of wave motion, the shield may emerge from the water, which leads to glint perturbations in the field-of-view of the sensor; similarly the instrument and consequently its optical window may be submerged by water, which affects the basic assumption of in-air measurements at the basis of SBA.

Discussing the impact of wave perturbations on SBA measurements, Wei et al. [2] conclude that the radiance collected by the sensor in water (i.e., with the optical window of the sensor immersed) is smaller than the radiance collected in air (i.e., with the optical window out of the water and the shield well positioned with respect to the surface). This quantification of radiance differences is definitively wrong: it results from an incorrect analysis of the processes characterizing radiance measurements. This is demonstrated by the following scrutiny relying on the basic equations for SBA measurements performed with the sensor in air and alternatively in water.

The measurement equations are proposed assuming that:

a. The SBA radiance in-air measurements ${L_{a - w}}(\lambda )$ referring to the optical window in air with the shield correctly positioned, or alternatively the SBA in-water measurements ${L_{i - w}}(\lambda )$ referring to the optical window immersed, are performed with identical observation conditions, determined applying the same calibration coefficients derived for in-air measurements and not applying the immersion factor I_f (λ) accounting for the responsivity change of the sensor when operated in water with respect to in air [9].
b. The small-angle approximation applies to quantify the Fresnel transmittance and the change in the field-of-view for the radiance crossing media with different refractive indices.
c. Shading perturbations are only due to self-shading [10], which would ideally equally affect the in-air and in-water SBA radiance measurements (i.e., any potential perturbation by the shield-shaded water volume [8] illustrated in Fig. 1, is neglected).
d. For the exclusive benefit of simplification, perturbations by water on the optical window are negligible when the instrument is operated in air. These perturbations, created by wave motion, may result from the formation of water films or even water drops on the optical window of the sensor.
e. Finally, multiple reflections in the optical window as well as polarization sensitivity of the sensor, have negligible impact.

In agreement with the previous assumptions:

(1)$${L_{a - w}}(\lambda ) = {L_u}({0^ - },\lambda ) \cdot \frac{{{t_{aw}}(\lambda )}}{{n_w^2(\lambda )}} \cdot {C_{ss}}(\lambda ),$$

where ${L_u}({0^ - },\lambda )$ is the nadir spectral upwelling radiance just below the water surface, ${t_{aw}}(\lambda )/n_w^2(\lambda )$ is the water-air radiance transmission coefficient [11,12] with ${t_{aw}}(\lambda )$ Fresnel transmittance of the air-water interface, $n_w^{}(\lambda )$ refractive index of the water and ${C_{ss}}(\lambda )$ the correction term for self-shading perturbations.

Consistently:

(2)$${L_{i - w}}(\lambda ) = {L_u}({0^ - },\lambda ) \cdot \frac{{{t_{wg}}(\lambda )}}{{{t_{ag}}(\lambda ) \cdot n_w^2(\lambda )}} \cdot {C_{ss}}(\lambda ) \cdot {e^{\mathop {-K}\nolimits_L (\lambda ) \cdot z}},$$

where ${t_{wg}}(\lambda )/[{t_{ag}}(\lambda ) \cdot n_w^2(\lambda )]$ expresses the change in responsivity of the sensor as a result of the optical window immersed in the water [9], and ${e^{\mathop {-K}\nolimits_L (\lambda ) \cdot z}}$ quantifies the attenuation by the water layer between sea surface and depth z of the optical window as a function of the diffuse attenuation coefficient of the upwelling radiance ${K_L}(\lambda )$. The terms ${t_{wg}}(\lambda )$ and ${t_{ag}}(\lambda )$ indicate the Fresnel transmittance of the water-window and of the air-window interfaces, respectively, both determined assuming the optical window has refractive index $n_g^{}(\lambda )$.

It is mentioned that the term $1/{n_w}{(\lambda )^2}$ quantifies the unavoidable change characterizing the field-of-view of the sensor when operated in water with respect to in air [9]. It is also recalled that for any in-water measurement method, the impact of ${t_{wg}}(\lambda )/[{t_{ag}}(\lambda ) \cdot n_w^2(\lambda )]$ is corrected through the application of I_f (λ) in the calibration process, but not accounted for in the calibration of SBA data.

By combing (1) and (2):

(3)$$\frac{{{L_{i - w}}(\lambda )}}{{{L_{a - w}}(\lambda )}} = \frac{1}{{{t_{aw}}(\lambda )}} \cdot \frac{{{t_{wg}}(\lambda )}}{{{t_{ag}}(\lambda )}} \cdot {e^{\mathop {-K}\nolimits_L (\lambda ) \cdot z}}.$$

With z = 0 and, mean spectral values $n_w^{}$ = 1.34 and $n_g^{}$ = 1.46 (typical of fused silica commonly used to manufacture optical windows [13]), the ratio ${L_{i - w}}(\lambda )/{L_{a - w}}(\lambda )$ gives 1.057, which shows that ${L_{i - w}}(\lambda )$ is ∼6% higher than ${L_{a - w}}(\lambda )$ (away from being lower as stated in Wei et al. [2], or even much lower). When assuming z = 0.05 m, the ratio ${L_{i - w}}(\lambda )/{L_{a - w}}(\lambda )$ would be 1.051 with K_L= 0.1 and 1.005 with K_L = 1.0.

The above ratios, which indicate values of ${L_{i - w}}(\lambda )$ slightly higher than ${L_{a - w}}(\lambda )$ when z → 0, are explained by the water-air radiance transmission coefficient exhibiting values close to the responsivity change of the sensor operated in water (a key element likely overlooked in Wei et al. [2]).

As already anticipated by Zibordi and Talone [8], contrary to what stated by Wei et al. [2], the closeness of SBA ${L_{i - w}}(\lambda )$ and ${L_{a - w}}(\lambda )$ values supported by (3) with the underlined assumptions, makes difficult flagging those measurements performed with the optical window immersed. This difficulty is expected to increase with sea state that rises the variability of z, and also to vary with wavelength and water type as a result of the spectral dependence of K_L(λ).

4. Concluding remarks

The comments to the work of Wei et al. [2] aim at taking the attention of the ocean color community on:

i. the actual significance of the ideal concept of 1% radiometry expressing the need to keep each uncertainty contribution to the uncertainty budget of relevant in situ radiometric quantities (i.e., L_w(λ) and R_RS(λ)) below 1-2%, and not targeting an unsupported and unfeasible 1-2% uncertainty budget;
ii. the radiometric processes governing SBA measurements affected by waves, which challenge the capability of discerning data collected with the optical window in air or in water and add complexity to the accurate determination of measurement uncertainties.

Disclosures

The author declares no conflicts of interest.

References

1. G. Zibordi, F. Mélin, K. J. Voss, B. C. Johnson, B. A. Franz, E. Kwiatkowska, J. P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: Requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015). [CrossRef]

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5. Y.-H. Ahn. “Development of red-tide and water turbidity algorithms using ocean color satellite,” Korea Ocean Research & Development Institute (KORDI), BSPE 98721-00-1224-01, (in Korean) (1999).

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8. G. Zibordi and M. Talone, “On the equivalence of near-surface methods to determine the water-leaving radiance,” Opt. Express 28(3), 3200–3214 (2020). [CrossRef]

9. G. Zibordi, “Immersion factor of in-water radiance sensors: assessment for a class of radiometers,” J. Atmos. Ocean. Tech. 23(2), 302–313 (2006). [CrossRef]

10. H. R. Gordon and K. Ding, “Self shading of in-water optical instruments,” Limnol. Oceanogr. 37(3), 491–500 (1992). [CrossRef]

11. R. W. Austin, “The remote sensing of spectral radiance from below the ocean surface,” in Optical Aspects of Oceanography, (Academic, 1974).

12. K. J. Voss and S. Flora, “Spectral Dependence of the Seawater–Air Radiance Transmission Coefficient,” J. Atmos. Ocean. Tech. 34(6), 1203–1205 (2017). [CrossRef]

13. W. L. Wolfe, “Optical materials,” in The Infrared Handbook, 4^th printing (Infrared Information Analysis Center, 1993).

Experimental analysis of the measurement precision of spectral water-leaving radiance in different water types: comment

Abstract

1. Introduction

2. Uncertainty requirements

3. Near-surface measurements

4. Concluding remarks

Disclosures

References

Cited By

Figures (1)

Equations (3)

Optics Express