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Using hyperspectral measurements made in the field, we show that the effective sea-surface reflectance ρ (defined as the ratio of the surface-reflected radiance at the specular direction corresponding to the downwelling sky radiance from one direction) varies not only for different measurement scans, but also can differ by a factor of 8 between 400 nm and 800 nm for the same scan. This means that the derived water-leaving radiance (or remote-sensing reflectance) can be highly inaccurate if a spectrally constant ρ value is applied (although errors can be reduced by carefully filtering measured raw data). To remove surface-reflected light in field measurements of remote sensing reflectance, a spectral optimization approach was applied, with results compared with those from remote-sensing models and from direct measurements. The agreement from different determinations suggests that reasonable results for remote sensing reflectance of clear blue water to turbid brown water are obtainable from above-surface measurements, even under conditions of high waves.
©2010 Optical Society of America
1. Introduction
The remote-sensing reflectance of water (Rrs, sr−1) is defined as the ratio of the water-leaving spectral radiance (LW, W m−2 nm−1 sr−1) to downwelling spectral irradiance just above the surface (Ed(0+), W m−2 nm−1). Rrs (or LW) is the basis for development of remote-sensing algorithms as well as for satellite sensor vicarious calibration [1–3]. Because of various technique limitations and the random motion of the water surface, accurate determination of Rrs remains a challenge [2–5]. The measurement of Rrs in marine environments usually involves one of these approaches: 1) measure the vertical distributions of upwelling radiance (Lu(z)) and downwelling irradiance (Ed(z)) within the water, and then propagate these measurements upward across the sea surface to calculate Rrs [6]; 2) use one sensor to measure Lu a few centimeters below the surface and use another sensor to measure Ed(0+) above the surface, and then propagate Lu across the surface to calculate Rrs [7]; 3) measure all relevant quantities from an above-surface platform [1–5,8–12], and then calculate LW (or Rrs) by removing surface-reflected light (LSR). This third approach is widely used in the field and for continuous measurements [3,4,11,12], although each approach has its own advantages and disadvantages [2,10].
When measurements are made from above the sea surface [see Fig. 1(a) ], the measured signal is the total upwelling radiance (LT), which is the sum of the water-leaving radiance (LW) and the surface-reflected radiance (LSR). It is necessary to avoid viewing surface foam, the shadow of the platform structure, and obvious solar glint spots. Some surface-reflected light (mostly from downwelling sky radiance, but possibly including some sun glint) is inevitable, however. A correction is therefore required to remove the surface-reflected light from LT in order to compute LW and Rrs [2,4,8]. One approach to the removal of surface-reflected radiance was proposed by Mobley [13] (a similar description can be found in Morel [1]). In this technique, all LSR is expressed as the product of ρ – an effective surface reflectance – and sky radiance (LSky) measured for an angle reciprocal to the measurement of LT (see Fig. 1 in Ref. [13]). The value of ρ depends on sea state, sky conditions, and viewing geometry [13,14]. Two approaches have then been proposed for the determination of ρ: One is to derive the value of ρ from measured LT and LSky by assuming LW approaches 0 at near-infrared wavelengths (e.g. at 780 nm) [1]; the other is to use a table of ρ values derived from numerical simulations with various wind speeds and viewing geometries [13]. Both approaches [1,13], however, assume that the ρ value is spectrally constant. To minimize the impact of sun glint on the derivation of LW (or Rrs), Hooker et al. [2] and Zibordi et al. [4] suggested filtering out the higher measured total radiance (LT) values, and reasonably good results were achieved for LW in the 412–555 nm range (larger uncertainties were found at 670 nm [4]). Here, after describing the general dependence of ρ, we show with hyperspectral measurements that ρ in general varies with wavelength, and that the spectral variation can be significant. We further compare two physical-mathematical approaches and a direct measurement scheme for the removal of LSR in deriving Rrs.
Fig. 1 (a) Schematic illustration of above-surface measurement of LT. (b) Example of roughened sea surface when looking down from an above-surface platform. The different shades of blue result from light reflected from different parts of the sky.
2. Theoretical background
When a radiance instrument takes measurements of spectral upwelling radiance (LT(λ)) from an above-surface platform, it collects not only the radiance emerging from below the water surface (the so-called water leaving radiance, LW(λ)), but also surface-reflected light (LSR(λ)). If the measurement angle is θ from nadir and φ (azimuth) from the solar plane [see Fig. 1(a)], then for a level sea surface, LSR(λ) comes from the zenith angle θ’ = θ and the same azimuthal angle (φ). For the more common situation of a constantly moving, roughened, surface (see Fig. 1(b) for an example), and for typical instrument integration times of order of one second or longer (integration time is much shorter for multiband sensors [3]), LSR(λ) actually comes from a large portion of the sky (see Fig. 1 and Fig. 2 of Mobley [13]) and may include solar radiance (sun glint). So, in general, the spectral upwelling radiance measured from an angular geometry (θ,φ) is
Here subscript “i” represents the i th small wave facet viewed by the sensor; wi is the relative weighting of solid angle of the i th facet to the sensor’s field-of-view solid angle; F is the Fresnel reflectance of the i th facet; and LSky is the downwelling radiance incident onto the i th facet, which is reflected into senor’s viewing angle.Because LSR(λ) is assembled in an unknown manner according to Eq. (1), removal of LSR(λ) becomes a challenge in the field when measurements are taken from above the sea surface (or sea-surface remote sensing in analogy to satellite remote sensing). For this removal, to a first order approximation, Eq. (1) is simplified as [1,13]
Here LSky(θ’,φ) is the sky radiance in the same plane as that of LT, but with θ’ the reciprocal (specular) angle of θ [2,4,8,9]. ρ(θ,φ) is the effective surface reflectance that accounts for reflected sky light from all directions for the given sensor direction, and is assumed to be independent of wavelength. ρ(θ,φ) equals the Fresnel reflectance of the sea surface only if the surface is flat (without waves). Values of ρ(θ,φ) for various viewing directions, sun zenith angles, and wind speeds were evaluated with numerical simulations in [13]. Based on these simulations, it was suggested to use θ = 40° from the nadir and φ = 135° from the sun to minimize LSR when measuring Rrs in the field.Comparing Eqs. (1) and (2) gives
or,Because LSky in general has different spectral shapes for different directions [1] (e.g., for a clear sky at noon, LSky from the horizon appears whiter than that from the zenith), ρ in Eq. (2) or Eq. (3a) will in general be spectrally dependent, especially when solar light is inevitably reflected into sensor’s viewing angle by roughened surface, unless the sky is completely overcast.3. Data and methods
To demonstrate the spectral variation of ρ, hyperspectral measurements over clear oceanic waters were utilized, where the contribution of water to LT is negligible in the longer wavelengths. The measurements were made on Feb. 23, 1997 around 12:50 pm (local time), for waters near Hawaii at 21.33 N, 158.16 W. The sky was clear with no clouds, the water appeared blue, the wind speed was around 8 m s−1, and the surface wave amplitude was ~2 to 3 feet (~1 m).
Upwelling total radiance (LT, 9 scans), downwelling sky radiance (LSky, 5 scans), and “gray-card” radiance (LG, 3 scans) reflected from a standard diffuse reflector (Spectralon®) were measured with a handheld spectroradiometer (SPECTRIX [15]), which covers a spectral range ~360 – 900 nm with a spectral resolution ~2 nm and has an integration time about 1.5 seconds for the collection of LT. The orientation to measure LT was 30° from nadir and 90° from the solar plane. LSky was measured in the same plane as LT, but at an angle 30° from zenith. Downwelling irradiance was determined by assuming that the Spectralon is a lambertian reflector, so that Ed = πLG/RG, with LG the average of the three scans and RG the reflectance of the diffuse reflector (~10%). The measurement was taken at the bow of a large ship with a sensor to water-surface distance about 5 meters. The SPECTRIX has a 10° field of view, which then observed a surface area of ~1 m2 for this setup.
To evaluate the value and variations of the effective surface reflectance (ρ), Eq. (2) is converted to reflectances, where the total remote-sensing reflectance (Trs, ratio of LT to Ed) and sky remote-sensing reflectance (Srs, ratio of LSky to Ed) were calculated for each LT and LSky scan, respectively. From Eq. (2), these Trs, Rrs, and Srs are related as
orFurther, ρ is calculated asFor the calculation of ρ, Rrs(λ,30°,90°) (assumed equal to Rrs(λ,0°,0°), and for λ in a range of 400 – 800 nm) was estimated with the bio-optical model of Morel and Maritorena [16] and using a chlorophyll-a concentration of Chl = 0.05 mg m−3, which is an estimate based on observations of MODIS for these waters in February. The model coefficients of Morel and Maritorena [16] cover wavelengths up to 700 nm. For the study here, the model coefficients of wavelengths greater than 700 nm are considered the same as that at 700 nm, except for the attenuation coefficient of pure water, which was replaced with the absorption coefficient of clear natural water [17].4. Results
4.1 Variation of ρ
For this station, Trs and Srs are presented in Figs. 2(a) and 2(b), respectively. Because the sea surface is roughened by waves, as commonly encountered in the field, we did not get identical Trs for the 9 independent measurements of LT. This is because each LT measurement observed a different sea surface, hence a different sky coverage, and thus a different LSR. Nor did we get identical measurements of the 5 Srs because the boat was also constantly moving, and thus the sensor could not maintain the exactly same angular geometry for the different sky-viewing measurements.
For illustration purposes, Fig. 3 shows values of ρ calculated for the 9 Trs scans and with Srs from the first measurement used as the denominator in Eq. (5). It is seen, not surprisingly, that the ρ values differ among the different LT measurements. More importantly, the ρ values differ spectrally, and this difference can be as high as a factor of eight between 400 nm and 800 nm (a factor of five between 400 nm and 700 nm). The increase of ρ with wavelength occurs mainly because (1) Trs collects LSR from all directions, including the sun and near-horizon directions [recall the whitish patches in Fig. 1(b)]. Compared to sky light from zenith, radiances from these directions are richer in the longer wavelengths. (2) Srs is measured from one fixed angular geometry, and this Srs is usually blue rich (dominated by contributions from Rayleigh scattering).
Fig. 3 ρ values calculated from measured Trs and Srs. Rrs was modeled with Chl = 0.05 mg m−3 based on the bio-optical model of Morel and Maritorena [16].
To evaluate the impacts of incorrect Rrs, which were estimated from a spectral model with roughly estimated chlorophyll concentration, on the calculated ρ values, Fig. 4 compares the ρ values calculated from the 9 Trs measurements and the first Srs, but with Chl = 0.05 and 0.1 mg m−3, respectively. For wavelengths in the range of ~400 – 500 nm, because Rrs makes strong contributions to Trs, wide variations of ρ values were found, which highlights the limitation of calculating the effective ρ from field measurements when the water contribution is high. For wavelengths longer than ~550 nm, however, it is found that the impact of different Chl values (then different Rrs) on ρ is nearly negligible. This is because for such clear waters phytoplankton contribution to Rrs is nearly negligible at the longer wavelengths. This is further illustrated in Fig. 5 via scatter plots between ρ(Chl = 0.05) and ρ(Chl = 0.025), and between ρ(Chl = 0.05) and ρ(Chl = 0.1). This figure shows that Chl has very little impact on ρ values of ρ > 0.07 (corresponding to ~550 nm for the measurements in this study). The same results were found when the first Srs was replaced by any of the other measurements of LSky (results not shown here).
Fig. 4 Similar as Fig. 3, but with two different Chl values. Green: Chl = 0.05 mg m−3; blue, Chl = 0.1 mg m−3.
Fig. 5 Scatter plot between ρ(Chl = 0.05) and ρ(Chl = 0.025), blue symbol; and between ρ(Chl = 0.05) and ρ(Chl = 0.1), green symbol.
If there are clouds in the sky (assuming the sun itself is not blocked by clouds), this ρ value could vary widely with wavelength, because Srs could be measured from a small portion of the clear sky (very blue) or aimed at a cloud, while LSR will include radiance from clouds (nearly white) and the background blue sky. These results indicate that applying a ρ value calculated in the near infrared (e.g. 780 nm) to the shorter wavelengths will cause large uncertainties in Rrs in the blue bands [2], unless the measurements are made under nearly ideal conditions (no clouds, low wind, no foam on surface, and very short integration time).
4.2 Removal of LSR
The above analysis indicates that when the sea surface is not flat, 1) ρ is not a constant among measurement scans; and 2) ρ values change with wavelength, at least for the longer wavelengths (> ~550 nm) in this study. With such an observation, even if wind speed and angular geometry are all known exactly (note that the effective ρ also depends on the orientation of waves), it will still be a daunting challenge to accurately remove LSR via Eq. (2) or Eq. (4). Earlier, Hooker et al. [2] and Zibordi et al. [4] proposed to filter out the higher LT measurements before applying Eq. (4b) for the removal of LSR. This technique is generally supported by the results shown in Fig. 3, where higher spectral contrast of ρ is found for the high ρ(800) value (high LT). However, because it can never be known exactly which LSky is reflected into the view of an LT measurement, it is unclear how to select a proper ρ value that is relevant for the smaller LT measurements, as using the smallest LT to derive LW via Eq. (4b) may result in underestimation of LW [18].
For this station, the wind speed was about 8 m s−1, so a ρ value of 0.05 was assumed for the angular geometry (based on Fig. 8 in Mobley [13]) and applied for the calculation of Rrs via Eq. (4). Since there were 9 measurements of Trs and 5 measurements of Srs, 45 Rrs were derived. Figure 6 shows the average Rrs with ± 1 standard deviation as computed from the 45 spectra. As a qualitative check, the modeled Rrs for Chl = 0.05 mg m−3 is also included in Fig. 6. It is found that the average Rrs from measurements match modeled Rrs reasonably well for the ~400-550 nm range, but there are significant differences for the longer wavelengths. Since there are large uncertainties in the modeled Rrs (resulted from, likely, both inaccurate Chl value and imprecise Rrs model), we are not expecting the two Rrs matching each other exactly. However, because the water-leaving radiance (or Rrs) of such waters is nearly negligible at longer wavelengths, it can be safely argued that the Rrs derived from Eq. (4) is overestimated for those wavelengths. This observation is consistent with Fig. 13 (left) of Mobley [13].
Fig. 8 Color photos of the river water (a) and sky (b) measured on September 13, 2010, ~11 am local time.
Fig. 6 Average Rrs (solid blue) and the one standard deviation (dotted lines), calculated using Eq. (4b). Green line is modeled Rrs with Chl = 0.05 mg m−3 using the Morel-Maritorena bio-optical model [16].
The commonly measured properties (except grey card) are LT at angle (θ,φ) and LSky at (θ’,φ). Also, because the actual total LSR is not measured directly, we re-write Eq. (1) as
Here w 0 represents the weighting of sky light coming from the specular direction (θ’,φ), and the sum now includes sky light from all other directions. Further, since sky light from the specular direction (θ’,φ) dominates LSR from the field-of-view centered at (θ,φ) [13], Eq. (6) is approximated (by setting w0 = 1) as,or, in terms of reflectance,Now in Eq. (8) both Trs and Srs for the specular direction are directly determined from measurements. F(θ,φ) is the Fresnel reflectance of water surface for (θ,φ), which is known for a given angular geometry. For the calculation of Rrs from Eq. (8) for any measurement of LT and LSky, it is thus necessary to determine the last term on the right-hand side of Eq. (8). Because it is not known yet how this last term varies spectrally, this term is assumed for expediency to be spectrally independent [9]. Thus Eq. (8) becomesor [9],Thus, for each set of spectral Trs and Srs, there is a spectrally constant value (Δ, a bias) that must be determined before Rrs can be derived. For oceanic waters where Rrs is negligible in the red and near infrared, Δ can be estimated by assuming Rrs near 750 nm is 0 [19]. For coastal turbid waters, however, this assumption is no longer valid. For such environments, one approach [19,20] is to model the spectral Rrs as a function of spectral inherent optical properties (IOPs), and then solve for Δ by comparing modeled spectral Rrs with spectral Rrs derived from Eq. (9b) using all measured spectral information (so-called spectral optimization) [21–24].Basically, for optically deep waters, the spectral Rrs can be conceptually summarized as
where a(λ) is the absorption coefficient, and bb(λ) is the backscattering coefficient. The inherent optical properties a(λ) and bb(λ) can be modeled with bio-optical models of optically active components [22,24,25], so that Eq. (10) becomes explicit functions asHere λ1 to λn are the sensor’s wavelengths, aw and bbw are the known absorption and backscattering coefficients of pure seawater, and P, G, and X represent the magnitude of the absorption coefficient of phytoplankton, gelbstoff, and the backscattering coefficient of particles, respectively. To derive the value of Δ in Eq. (9b), an objective function is defined aswith from Eq. (11) while Rrs from Eq. (9b). represents the average of an array between 400 nm and 675 nm. The upper bound of wavelength (800 nm) can be extended to a longer wavelength for turbid lake or river waters when sensor has measurements in those wavelength ranges. Err is then a function of 4 variables (P, G, X, and Δ) for optically deep waters, and they are derived numerically when Err reaches a minimum – spectral optimization [22,26]. Rrs is therefore computed by applying this numerically derived Δ to Eq. (9b). Note that in the correction of LSR the focus is the estimation of Δ, although values of P, G, and X are also determined.For the measurements at this station, again, 45 spectral Rrs were determined with this spectral optimization method, and their average and standard deviation are presented in Fig. 7 . The overestimations of Rrs in the longer wavelengths (> ~550 nm) are generally removed, as compared to Fig. 6. At the same time, the average Rrs matches the modeled Rrs (with Chl = 0.05 mg m−3) very well in the ~400-550 nm range, although it is not our intension (the measured and Chl-modeled Rrs do not necessarily represent the same water environments).
Fig. 7 Similar as Fig. 6, but Rrs was calculated based on Eq. (9) and with a spectral optimization scheme. Green line is modeled Rrs with Chl = 0.05 mg m−3 using the Morel-Maritorena [16] bio-optical model.
To further test the above evaluation and the optimization approach of removing LSR, new measurements (September 13, 2010; ~11 am local time) were carried out (with SPECTRIX) over turbid river water (Pearl River, Mississippi, USA. Figure 8 shows color photos of the water and sky when measurements were taken). This shallow (~0.5 m) and very turbid water makes it nearly impossible to obtain Rrs from measurements of vertical profiles of Lu and Ed [6]. During the experiment, the surface was calm [see Fig. 8(a)] and the sky was blue [Fig. 8(b)] with some thin cirrus clouds. Two different measurement schemes were carried out. One followed the traditional scheme [10] that measures LG, LT and LSky (see Section 3), with θ = 30° from nadir and φ = 90° from the solar plane, and the sensor to water-surface distance was ~1 meter (the sensor then covered a surface area ~0.05 m2). Rrs were derived, separately, from these measurements following the simple approach [Eq. (4b), ρ = 0.022 is used for calm surface. Rrs-simp in the following] and following the optimization approach (Rrs-opt in the following) mentioned above.
Another measurement followed a novel scheme proposed by Ahn et al [27], where a small black tube (~4 cm in diameter) was placed in front of the sensor to block LSR (see Fig. 9 for a schematic illustration). When LT was measured the tube was dipped just below the sea surface (~5 cm) while the sensor itself was kept above the surface. Therefore there will be no LSR into the sensor in this setup and the instrument records a direct measurement of LW. Rrs (Rrs-direct in the following) was then derived as the ratio of measured LW to Ed (from measurement of LG).
Fig. 9 Scheme to measure LW directly (re-drawn from Ahn et al [27]). The open box is a black tube to block surface reflected light, which is inserted just below (~5 cm) the surface when measuring LW.
Figure 10 shows the derived Rrs from the three measurement-determination schemes; blue is Rrs-direct, green is Rrs-opt, and cyan is Rrs-simp. The three Rrs curves show similar spectral shapes, which are typical of turbid, high-CDOM river waters (note the yellow-brown color in Fig. 8). Rrs-simp is considerably higher than both Rrs-direct and Rrs-opt, suggesting incomplete removal of LSR even for this quite calm situation (it may be that some sun glitter could not be completely avoided for the (30°,90°) viewing geometry and integration times of ~1-2 seconds). On the other hand, Rrs-direct and Rrs-opt are very consistent across the ~400-850 nm range, with a coefficient of variation about ~11% (which is about 46% between Rrs-simp and Rrs-direct). The slight negative Rrs (both Rrs-direct and Rrs-opt) for wavelengths shorter than 400 nm may result from a combination of 1) SPECTRIX has lower signal-to-noise ratio for wavelengths shorter than ~400 nm [15], and 2) the extremely low upwelling signal in the blue-to-UV wavelengths of this CDOM-rich water. Nevertheless, the deduced Rrs of this turbid water (along with the result of blue oceanic waters) strongly indicates that Eq. (9b) with an optimization scheme to determine the value of Δ is adequate in obtaining Rrs in the field when measurements are made above the sea surface under un-ideal conditions and that LSR is not blocked during measurements. However, neither Rrs-direct nor Rrs-opt are error free, because Rrs-direct encounters some self-shading and/or contributions from reflectance inside the tube, while Rrs-opt suffers from the approximation from Eq. (6) to Eqs. (7) and (9a).
Fig. 10 Comparison between directly measured Rrs (blue line) of water showing in Fig. 8(a) and Rrs obtained after correcting surface-reflected light.
5. Conclusions
Using measurements from a clear-water station, we demonstrated that the effective surface reflectance (ρ) varies not only with each measurement scan but also with wavelength. Consequently, application of a spectrally constant ρ value for the removal of LSR from above-surface measurements is a crude approximation, especially if the sea surface is significantly roughened by waves and the sensor has a long integration time (as do most high-spectral resolution sensors). Earlier studies [2,4,18] have shown that it is wise to filter out the higher LT measurements before the derivation of LW when the simple formula [e.g., Eq. (4b)] is used for the derivation. Here we show that for clear to turbid waters, a spectral optimization scheme [28] is also adequate to remove LSR in LT measurements and derive reasonable Rrs. Further, the scheme to block LSR by equipping a black tube in front of the sensor and dipping it just below the surface shows promise to obtain reliable measurement of LW without the difficult post-processing. Further effort is required by the remote-sensing community to evaluate these approaches for a wide range of environments and measurement conditions (e.g. Hooker et al. [2] and Toole et al [7]) and then to establish a consensus for the optimum way to determine Rrs in the field when measurements are made from an above-surface platform, especially for situations such as turbid waters and partly cloudy skies.
Acknowledgements
We are grateful for the financial support provided by the Naval Research Laboratory (Z.-P. Lee and R. Arnone), the Northern Gulf Institute (Z.-P. Lee), the Water Cycle and Energy and Ocean Biology and Biogeochemistry Programs of NASA (Z.-P. Lee), and the Environmental Optics Program of the U. S. Office of Naval Research (C. D. Mobley). The comments and suggestions from the two anonymous reviewers are greatly appreciated.
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28. A Microsoft Excel template of this processing scheme is available for interested practitioners.
