Spectral interdependence of remote-sensing reflectance and its implications on the design of ocean color satellite sensors Zhongping Lee,1,* Shaoling Shang,2 Chuanmin Hu,3 and Giuseppe Zibordi4 1

School for the Environment, University of Massachusetts Boston, Boston, Massachusetts 02125, USA 2

State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen 361005, China 3

College of Marine Science, University of South Florida, St. Petersburg, Florida 33701, USA

4

Institute for Environment and Sustainability, Joint Research Centre, 21027 Ispra (VA), Italy *Corresponding author: [email protected] Received 13 January 2014; revised 12 April 2014; accepted 14 April 2014; posted 22 April 2014 (Doc. ID 204584); published 19 May 2014

Using 901 remote-sensing reflectance spectra (Rrs λ; sr−1 , λ from 400 to 700 nm with a 5 nm resolution), we evaluated the correlations of Rrs λ between neighboring spectral bands in order to characterize (1) the spectral interdependence of Rrs λ at different bands and (2) to what extent hyperspectral Rrs λ can be reconstructed from multiband measurements. The 901 Rrs spectra were measured over a wide variety of aquatic environments in which water color varied from oceanic blue to coastal green or brown, with chlorophyll-a concentrations ranging from ∼0.02 to >100 mg m−3 , bottom depths from ∼1 m to >1000 m, and bottom substrates including sand, coral reef, and seagrass. The correlation coefficient of Rrs λ between neighboring bands at center wavelengths λk and λl , rΔλ λk ; λl , was evaluated systematically, with the spectral gap (Δλ  λl − λk ) changing between 5, 10, 15, 20, 25, and 30 nm, respectively. It was found that rΔλ decreased with increasing Δλ, but remained >0.97 for Δλ ≤ 20 nm for all spectral bands. Further, using 15 spectral bands between 400 and 710 nm, we reconstructed, via multivariant linear regression, hyperspectral Rrs λ (from 400 to 700 nm with a 5 nm resolution). The percentage difference between measured and reconstructed Rrs for each band in the 400–700 nm range was generally less than 1%, with a correlation coefficient close to 1.0. The mean absolute error between measured and reconstructed Rrs was about 0.00002 sr−1 for each band, which is significantly smaller than the Rrs uncertainties from all past and current ocean color satellite radiometric products. These results echo findings of earlier studies that Rrs measurements at ∼15 spectral bands in the visible domain can provide nearly identical spectral information as with hyperspectral (contiguous bands at 5 nm spectral resolution) measurements. Such results provide insights for data storage and handling of large volume hyperspectral data as well as for the design of future ocean color satellite sensors. © 2014 Optical Society of America OCIS codes: (120.0280) Remote sensing and sensors; (280.4788) Optical sensing and sensors; (280.4991) Passive remote sensing. http://dx.doi.org/10.1364/AO.53.003301

1. Introduction 1559-128X/14/153301-10$15.00/0 © 2014 Optical Society of America

It has long been concluded that the measurement of ocean (water) color with satellite sensors is an indispensable means to study the biology and 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS

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biogeochemistry of the global oceans as well as largesize inland lakes [1]. Indeed, it was not until the launch of the first satellite ocean color instrument, the Coastal Zone Color Scanner (CZCS), in 1978 that a global perspective of ocean biology was available for the first time [2]. The CZCS had four spectral bands in the visible (400–700 nm) domain; however, this was found inadequate for the separation of colored dissolved organic matter (CDOM or gelbstoff) from phytoplankton [3,4]. Subsequently, more bands in the visible domain were included in advanced ocean color sensors: six on the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS), eight on the Medium Resolution Imaging Spectrometer (MERIS), seven on the Moderate-Resolution Imaging Spectrometer (MODIS), and five on the newly launched Visible Infrared Imaging Radiometer Suite (VIIRS). On the other hand, airborne sensors such as the Airborne Visible-Infrared Imaging Spectrometer (AVIRIS) and the Portable Remote Imaging Spectrometer (PRISM), or experimental sensors such as the Hyperion and the Hyperspectral Imager for the Coastal Ocean (HICO) [5], have many more spectral bands in the visible. Further, for ocean color missions planned for the coming decades, such as the PreAerosol, Clouds, and ocean Ecosystem (PACE) [6] and the Geostationary Coastal and Air Pollution Events (GEO-CAPE) [7], there is a desire to take hyperspectral measurements. “Hyperspectral” is a generic term in the literature and is not uniformly defined, although it categorically represents measurements using a large number of spectral bands for a given spectral window. Here we set hyperspectral as contiguous bands with a 5 nm increment, along with a bandwidth of 1 nm for each band. Also, because most in situ measurements cover a spectral range of 400–800 nm and optically active constituents (OACs) generally contribute to color variations in the visible domain, we focus on the 400–700 nm range of such hyperspectral data. We then try to address the loss of spectral information for sensors that are likely not capable of obtaining hyperspectral measurements. About four decades ago, using 31 measurements of upwelling radiance (400–750 nm, 55 bands) over waters off the Oregon coast from a low-altitude airplane, Mueller [8] found that these radiance spectra could be well explained with four end-member spectra (or eigenvectors) through principal component analysis (PCA). Because these measurements include contributions from surface-reflected skylight, at least one of the four end members represents such skylight contributions. Thus, the results suggest that there are actually three end-member spectra to represent changes of spectral water-leaving radiance. Moore et al. [9] instead found that the ocean color of the global oceans might be better represented with eight end-member spectra. Sathyendranath et al. [10] found that reflectance spectrum of oceanic waters can be modeled with three independent variables, which is consistent with the findings of Mueller [8]. 3302

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Also through the use of PCA, Sathyendranath et al. [11] further found that for data measured over the New York Bight and for retrieving concentrations of chlorophyll-a and phycoerythrin, the retrievals were nearly the same if the spectral measurement (in a range of 413.5–762.3 nm) was dropped from 27 to 5 bands. When retrievals of bottom properties (depth and reflectance) of optically shallow waters were included, however, Lee and Carder [12] found that about 15 bands in the 400–800 nm domain were required. The increase of band number is to ensure the capture of the water-transparent window because this window differs between clear and turbid waters. Nevertheless, all these studies suggest that “optimized” or focused spectral bands can produce nearly identical results of aquatic environments to those from “hyperspectral” measurements, provided that the focus of remote sensing is the primary variables instead of subtle spectral features. Several limitations exist in the above studies, though. First, the dataset used in the studies is generally small, which thus may not be inclusive or representative for global ocean environments. Second, the studies are product driven, i.e., focused on several highly desired primary products such as the concentration of chlorophyll-a or total absorption coefficient or bottom depth. Thus the conclusions could be specific to those products and to the algorithms used to derive the products. Here, instead of focusing on the data product retrievals, we evaluate the spectral interdependence using a hyperspectral dataset as suggested in the IOCCG Report No. 1 [3] and practiced in other studies [13]. We realize that such an analysis is always data dependent, and in reality it is nearly impossible to obtain a spectral library that is representative of all water types. In this study, we assemble a dataset that is extremely inclusive, as it covers environments from blue oceanic waters to brown/green coastal waters with bottom depths ranging from ∼1 to >1000 m and substrates including sand, seagrass, and coral reef. After the analysis of spectral covariance, as in Wernand et al. [14], we further compare the hyperspectral measurements with those reconstructed from multiband data. The objective is to characterize the interdependence of the spectral information and to understand to what extent hyperspectral measurements could be reconstructed using measurements at a few “optimized” bands. Such knowledge will be important and useful for the design of future ocean color sensors as well as for the handling and processing of a large volume of hyperspectral data collected by an airborne or satellite sensor. 2. Data and Methods

Remote-sensing reflectance Rrs ; sr−1  is defined as the ratio of water-leaving radiance (Lw , W m−2 sr−1 ) to downwelling irradiance just above the surface (Ed 0; W m−2 ). Spectral Rrs λ is the critical input for the derivation of bio-optical properties of constituents in the upper water column that include

phytoplankton and CDOM as well as bottom properties of optically shallow waters through various algorithms [15,16]. For satellite ocean color remote sensing, both Lw and Ed 0 are derived from the satellite-measured signals through radiometric calibration and modeling of the atmospheric effects [17]. The Rrs spectra of this study were all measured in the field using the above-surface approach [18], with a data processing scheme described in the ocean optics protocol [18] and Lee et al. [19]. The instruments used for such measurements were hand-held spectroradiometers of either custom-made Spectrix [20], GER (Spectra Vista Corporation, Inc.), or RAMSES (TriOS GmbH). These instruments cover a spectral range of ∼400–850 nm (Spectrix), 350–1050 nm (GER), or 320–950 nm (TriOS), and provide a spectral resolution of ∼2–3 nm and half-value-bandwidth of ∼1–1.5 nm. The data were resampled to 5 nm spectral resolution and 1 nm bandwidth for easier data processing and handling. The visible spectral range of 400–700 nm was focused in this study because longer wavelengths contain no or limited information of the water-column OACs for most waters [3,15,16]. A total of 901 Rrs λ spectra were obtained from a wide range of environments (Fig. 1), which include blue oceanic waters in the Pacific Ocean, blue to green waters in the Gulf of Mexico, South China Sea, and northern Adriatic Sea, sediment-rich waters of the Mississippi River (United States) plume and

Changjiang River (China) plume, as well as optically shallow waters in the West Florida Shelf and around Key West (Florida). The range of chlorophyll concentrations ([Chl]) (measured fluorometrically) is ∼0.02 to >100 mg m−3 ; the range of suspended sediment matter is from sensor detection limit to >100 g m−3 ; the range of bottom depth is from ∼1 m to >1000 m with substrates of seagrass, sand, and coral reef. Figure 2(a) provides a small subset of the Rrs λ dataset as examples to highlight their variations in both magnitudes and spectral shapes, which are also illustrated in Fig. 2(b), where the coefficient of variation (ratio of standard deviation to the mean) at each band varied by 80% or more. Figure 2(b) also shows the mean Rrs λ spectrum of this dataset as a general measure of the Rrs λ library. To further highlight the diversity and variability of this Rrs dataset, Fig. 3 shows the distributions of Rrs at several bands and their ratios, where the range of Rrs 440 and Rrs 550 is 0.0001–0.017 sr−1 and 0.0001–0.035 sr−1 , respectively, with the Rrs 410∕Rrs 440 and Rrs 440∕ Rrs 550 ratios in a range of 0.2–1.4 and 0.1–7.8, respectively. These values indicate this Rrs dataset covers an extremely wide range of waters, and represents ∼99% of natural variability of aquatic environments. For this Rrs dataset, the Pearson correlation coefficient of Rrs between neighboring bands was calculated as

P P P N i Rirs λk Rirs λl  − Rirs λk  Rirs λl  i i rΔλ λk ; λl   r P 2r P 2 : P i P 2 2 i i i N Rrs λk  − N Rrs λl  − i Rrs λk  i Rrs λl  i

(1)

i

Fig. 1. Locations of data collection. Background of world map is from Paul’s House (http://paulsporterhouse.com/blank‑world‑map‑ printable‑pdf/blank‑world‑map‑printable‑pdf‑2). 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS

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Fig. 2. (a) Examples of measured Rrs λ. (b) Coefficient of variation (CV, dashed line) and average (solid line) of the Rrs λ dataset.

Here λk and λl represent the center wavelengths of neighboring spectral bands and λl  λk  Δλ, with λk starting at 400 nm. Rirs λk  is the ith Rrs at λk . N is the total number of measurements used in the regression analysis. Δλ is the spectral distance between λk and λl . Six Δλ were used in this study, which are 5, 10, 15, 20, 25, and 30 nm. For Δλ  5 nm, the first r5 is between 400 and 405 nm. Because rΔλ is influenced strongly by large Rrs values, five Rrs spectra (see Fig. 4) with extremely large Rrs values (>50 times of the mean Rrs values in the green wavelengths) were excluded in the above regression analysis. These five spectra were used to test the effectiveness of hyperspectral Rrs λ reconstruction, however.

3. Results and Discussion

Figure 5 presents the spectrum of rΔλ for the six Δλ, where a few general features emerge: 1) Rrs highly covaries between neighboring bands when Δλ is small (5–10 nm). 2) Except for wavelengths around 600 nm, r5 and r10 are >0.99. r20 is lower, but still >0.97. These results indicate that there is almost no information loss when Δλ is increased from 5 to 10 nm in the Rrs measurements, and the information loss is very limited when Δλ is increased to 20 nm. 3) The larger the Δλ, the lower the degree of spectral interdependence. If Δλ > 100 nm (e.g., between 440 and 550 nm), the correlation coefficient is 0.63

Fig. 3. Characteristics of the Rrs λ dataset. (a) Rrs 440 versus Rrs 550, with a correlation coefficient (CC) as 0.63. (b) Rrs 440∕Rrs 550 versus Rrs 410∕Rrs 440. (c) Frequency distribution of Rrs 550. (d) Frequency distribution of Rrs 670. 3304

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Fig. 4. Data with extremely high Rrs (shallow and bright sandy bottoms; solid black symbol with blue-dashed line) excluded in the spectral interdependence analysis. Also shown are the reconstructed hyperspectral data (open green symbol) using multispectral data. Solid red symbol, band locations used to reconstruct hyperspectral Rrs .

between Rrs 440 and Rrs 550, indicating that Rrs values at these two bands are quite independent [see Fig. 3(a)]. Note that for Case-1 waters [21], Rrs 440 and Rrs 550 highly covary. The strong interdependence of Rrs between neighboring bands with short spectral distance is consistent with previous studies [10]. Fundamentally, Rrs is a function of the absorption (a) and backscattering (bb ) coefficients through [22,23]

Rrs λ ∝

bb λ : aλ  bb λ

(2)

Here bb is a sum of the contributions from pure seawater (bbw ) and particulate matter (bbp ), while a is a sum of the contributions from pure water (aw ), detritus and gelbstoff (adg ), and phytoplankton pigments (aph ),

Fig. 5. Correlation coefficient (rΔλ λk ; λl ) of Rrs λ between neighboring bands for different spectral gaps, where the x axis represents λl . For instance, the first black point represents rΔλ λk ; λl  between Rrs 400 and Rrs 405 (λk  400 nm and λl  405 nm), the second black point represents rΔλ λk ; λl  between Rrs 405 and Rrs 410, the first pink point represents rΔλ λk ; λl  between Rrs 400 and Rrs 430, and the second pink point represents rΔλ λk ; λl  between Rrs 405 and Rrs 435.

bb λ  bbw λ  bbp λ;

(3)

aλ  aw λ  aph λ  adg λ:

(4)

The bbw spectrum is a constant for global seawaters. Although not a constant, the spectral variability of bbp is small [24,25]. Even for spectral bands affected strongly by phytoplankton absorption (i.e., around 440 and 670 nm), the spectral variation of bbp is broadband instead of narrow [24,26]. Indeed, because the spectral variability of bbp is small, the primary sources contributing to the spectral variability of Rrs come from the absorption components. Figure 6 shows typical spectral shapes of aph λ and adg λ, along with the spectral shapes and values of aw λ. The aw values are considered as global constants [27], although they vary slightly with temperature and salinity [28,29]. Because adg changes gradually and monotonically with wavelength [30,31] (i.e., a broadband effect), there will be no single, narrowband effect on the spectral Rrs if there are changes in gelbstoff or suspended detrital particles (including inorganic sediments and organic nonliving particles). The spectral shapes of aph λ are not narrow band either [32], so the effects of changes in pigment concentrations (chlorophyll-a or accessory pigments) on the spectral Rrs λ are also broadband. These facts form the basis for why the Rrs values highly covary between neighboring bands with narrow spectral distances. The same reasoning also applies to optically shallow waters where light reflected by the bottom contributes to Rrs , because the reflectance spectra of sand, coral reefs, and seagrass are all broadband [33]. Measurements with hyperspectral resolution thus generally provide redundant information instead of independent spectral signal. For wavelengths around 600 nm, rΔλ is always lower than that at other wavelengths. This is because aw quickly increases from ∼0.12 m−1 between 550 and 600 nm to ∼0.25 m−1 between 600 and 640 nm. This leads to a transparent window for wavelengths 600 nm may not, thus resulting in no or little correlation for Rrs between λ < 600 nm and λ > 600 nm. In addition to this effect, because of the higher aw λ > 600 nm values, small changes in aph and/or adg will not be captured by Rrs λ > 600 nm, thus resulting in reduced correlation for wavelengths around 600 nm. The same logic also applies to the spectral windows of ∼450 nm and ∼515 nm, where for clearer waters only Rrs in the shorter wavelengths may sense changes in phytoplankton and/or gelbstoff, resulting in lower rΔλ for λ around 450 and 515 nm. 4. Reconstruction of Hyperspectral R rs

Because Rrs highly covaries within narrow spectral windows, as demonstrated in Wernand et al. [14], it may be possible to reconstruct hyperspectral Rrs λ from multiband measurements. To evaluate the performance of such a reconstruction approach, Rrs at 15 bands between 400 and 710 nm were used to reconstruct hyperspectral Rrs λ between 400 and 700 nm through linear interpolation, Rrc rs λj  

15 X

K ij Rrs λi :

(5)

i1

Here the superscript “rc” represents reconstruction. In the equation, the 15 bands are 400, 425, 445, 460, 475, 495, 515, 545, 565, 580, 605, 640, 665, 685, and 710 nm (red symbols in Figs. 4 and 7), based on those proposed in Lee et al. [34], except that 615 nm is changed to 605 nm. While the resulting Rrc rs λj  is always hyperspectral, the performance of two types of Rrs λi  as inputs was evaluated: one with 1 nm band1−nm λi ) and the other with 10 nm bandwidth (Rrs λi ). This is because ocean color width (R10−nm rs satellite sensors (e.g., MODIS) are often designed to have a 10 nm bandwidth to ensure adequate

signal-to-noise ratio (SNR) [3,35]. As an approximation, R10−nm λi  was calculated from the hyperspecrs tral data by spectral binning. For instance, 1−nm 410 is the simple average of Rrs 405, R10−nm rs 1−nm 410, and R1−nm 415; R10−nm 415 is the simRrs rs rs 1−nm 1−nm ple average of Rrs 410, Rrs 415, and 1−nm Rrs 420; and so on. This scheme basically assumes that measurements of the three nearby 1 nm bands provide equivalent spectral information that would be measured by a 10 nm band. When R10−nm λi  is used as input, the shortest band bers comes 405 nm, a result of the three-band binning. K ij are linear scaling coefficients between Rrs λi  and Rrs λj , and they were derived by minimizing the difference between the measured hyperspectral Rrs (Rm rs λj ) and the reconstructed hyperspectral Rrs (Rrc rs λj ). These coefficients are slightly different 1−nm when using Rrs λi  and R10−nm λi  as the inputs of rs Eq. (5), and are provided as supplemental materials to Applied Optics or can be obtained from the authors. As an example, Fig. 7 shows a comparison be1−nm λi  as inputs) and the tween Rrc rs λj  (using Rrs measured Rrs λj  for four randomly selected stations of relatively clear waters Rrs 440∕Rrs 550 > 1.0, where the agreement is nearly perfect (i.e., they cannot be distinguished visually). For the five stations with extremely high Rrs values shown in Fig. 4, the reconstructed Rrc rs λj  also match the measured hyperspectral Rrs excellently. Note that the K ij values used in reconstructing the five Rrs spectra were derived without these spectra; thus the results actually represent an independent validation. Further, for each band, Fig. 8(a) shows the correlation coeffirc cient between Rm rs λj  and Rrs λj , with Fig. 8(b) showing the percentage difference (ratio of average of the absolute difference to the average of Rm rs λj  between rc Rm rs λj  and Rrs λj  calculated for this dataset. For every spectral band, the percentage difference is generally less than 1%, with a correlation coefficient close to 1.0. These results demonstrate that the reconstructed Rrs spectra, regardless of the bandwidth 1−nm λ  or R10−nm λ ), match the used in the inputs (Rrs rs i i measured Rrs spectra nearly exactly. More importantly, the differences are smaller than uncertainties in the field-measured Rrs [36,37], and much smaller than those from the satellite in situ comparisons [38]. To further highlight the agreement between measured and reconstructed hyperspectral Rrs λ, Fig. 9 shows the mean absolute error (MAE) between Rm rs and Rrc rs for each band, calculated as MAERrs λj  

Fig. 7. Examples to demonstrate the agreement between the measured (solid black symbol with blue-dashed line) and the reconstructed hyperspectral Rrs (open green symbol) using multispectral (1 nm bandwidth) data as inputs. Solid red symbol, band locations used to reconstruct hyperspectral Rrs . 3306

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1X m jRrs λj  − Rrc rs λj j: N i

(6)

The MAERrs λj  values are generally 0.0004 sr−1 . In this case, the MAERrs λj  is still much smaller than MODIS-Aqua Rrs uncertainties over the South Pacific, but 5%–10% of the stations with reconstructed Rrs having errors >0.0004 sr−1 in the visible domain. These results suggest that measurements with five bands may not be adequate

Fig. 10. (a) Same as Fig. 9, but Rrs λ at five bands (410, 495, 555, 620, and 670 nm) [14] with a 10 nm bandwidth was used to reconstruct hyperspectral Rrs λ. (b) Percent of stations with reconstructed Rrs having absolute errors >0.0004 sr−1 . For comparison, also shown in (b) is the reconstruction result with 15 bands (also with 10 nm bandwidth data as input). Clearly errors in the reconstructed hyperspectral Rrs λ are much smaller when Rrs λ at 15 bands were used as the inputs. 20 May 2014 / Vol. 53, No. 15 / APPLIED OPTICS

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Fig. 11. Spectral shapes in the visible range of major absorbing gases in the atmosphere.

for some aquatic environments to reconstruct hyperspectral Rrs λ with sufficient accuracy. The reconstructed Rrs data show slightly larger errors around 600 and 685 nm than in other wavelengths. This is due to the fact that (1) Rrs is not a linear function between spectral bands (also see discussions above), and (2) Rrs around 685 nm includes contributions from chlorophyll-a fluorescence [41,42]. The larger errors in these spectral windows could be easily reduced if a nonlinear interpolation method, such as using a Gaussian function for chlorophyll-a fluorescence [41], is used in the reconstruction scheme. 5. Implication to Ocean Color Satellite Sensors

Since the launch of the proof-of-concept CZCS ocean color instrument to observe the global oceans, there has long been a desire to have a satellite sensor with hyperspectral capabilities. Because the atmosphere contributes ∼80% or more of the total signal measured at the satellite altitude [17], a satellite sensor must have adequate SNR, in addition to robust calibration and processing algorithms, for the observation and derivation of water constituents [3,35]. SNR depends on many factors and can be generally expressed as SNR ∝ A × Δt × δλ:

(7)

Here A is the pixel size, Δt is the integration time, and δλ is the bandwidth for a specific band. For Sun-synchronize satellites, Δt is small. Then, to ensure high SNR, a sensor must have either large pixel size (A) (e.g., 1.1 km nominal spatial resolution for SeaWiFS and MODIS) or wide bandwidth (δλ) (e.g., 50–100 nm for Landsat). In general, δλ cannot be pushed too wide, for otherwise the sensor will lose its capability to detect the spectral features of desired targets [43]. On the other hand, δλ cannot be too narrow either (at least from the current technology), for otherwise either A or Δt will have to be increased in order to maintain adequate SNR. At present, the generally recommended δλ is 10 nm 3308

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for the observation of biogeochemical properties in the oceans [3]. For a sensor on a geostationary satellite, as the sensor can stare at the desired pixels, Δt can be longer than that of a Sun-synchronize satellite sensor [44,45], so that A can be smaller (e.g., 250 m × 250 m) while keeping δλ as 10 nm. However, in practice Δt cannot exceed a certain limit, for otherwise the satellite can only measure a small area instead of the full Earth disk. Separately, if δλ is kept at 10 nm, there will be strong overlapping between adjacent bands if it is sampled at every 5 nm, thus not producing independent spectral measurements at each band. Furthermore, because the water-leaving radiance has to pass through the entire atmosphere before being detected by a satellite sensor, it is critical to properly remove the effects due to gas absorption and scattering (i.e., atmospheric correction [17]). Figure 11 shows the spectral features associated with several major absorbing gases in the atmosphere, with data taken from the moderate resolution transmission model (MODTRAN). In the 400– 700 nm range, even if the absorption effects due to ozone (O3 ) could be adequately addressed as with the current ocean color data processing using near realtime O3 measurements, the absorption effects from water vapor (H2 O) and nitrogen (N2 ) do vary and are difficult to be corrected accurately [17,46,47]. Thus, it is better to avoid such spectral windows if concurrent and accurate measurements of H2 O and N2 are not available [3]. In view of the above, it appears easier to obtain reliable hyperspectral data that meet the requirements of SNR, the impact of gaseous absorption effects, and the storage and processing of a large volume of satellite data with a multiband senor. Separately, although all hyperspectral Rrs λ can be reproduced successfully from multiband measurements, as demonstrated above with a library of Rrs λ covering an extensive range of the natural aquatic environment, we do recognize that additional cases including floating vegetation, such as Trichodesmium, pelagic Sargassum spp., or the green macroalgae Ulva prolifera are not addressed in the study. However, these represent very special cases of algal blooms that can often be easily recognized by multiband measurements (e.g., Gower et al. [48] and Hu et al. [49,50]). 6. Conclusion

The analyses of an extensive hyperspectral Rrs λ dataset covering a wide range of aquatic environments further highlight that Rrs of the neighboring bands are highly correlated, and the correlation coefficients are greater than 0.99 for band gaps ≤10 nm. This is because the absorption and scattering effects of the OACs are all broadband, so that the changes of Rrs in one band are associated with the changes of Rrs in adjacent bands. It is also found that in situ hyperspectral Rrs λ data (400–700 nm with a 5 nm resolution) can be reconstructed nearly perfectly

(percentage difference < ∼ 1%) from predetermined 15-band Rrs measurements at 10 nm bandwidth. The errors in the reconstructed Rrs λ data are much smaller than uncertainties in the satellite-derived Rrs λ. Considering the difficulty to accurately remove gas absorption effects if a satellite sensor takes hyperspectral measurements, the effectiveness of the reconstruction suggests that it is practical to obtain hyperspectral Rrs λ data from multiband measurements that avoid the gas absorption bands. Even if a robust hyperspectral atmospheric correction at sensor level can be developed in the future, the superb reconstruction results also indicate an effective scheme to sample hyperspectral data to a few optimized bands for efficient data processing and storage for handling a large volume of satellite-based global hyperspectral measurements. We are grateful for the financial support from the University of Massachusetts (Boston) and the University of South Florida, the NASA Ocean Biology and Biogeochemistry and Water and Energy Cycle Programs (Lee, Hu), the JPSS VIIRS Ocean Color Cal/Val Project (Lee, Hu), and the National Natural Science Foundation of China (No. 40976068, Shang). We are in debt to many colleagues who helped in the collection and reduction of in situ remote-sensing reflectance data, in particular Gong Lin, Jushi Zhang, David English, Jennier Cannizzaro, Tom Peacock, Kendall Carder, Wesley Goode, Robert Arnone, Liping Li, and Xiaoquan Song. References 1. IOCCG, “Status and plans for satellite ocean-color missions: considerations for complementary missions,” in Reports of the International Ocean-Colour Coordinating Group, No. 2, J. A. Yoder, ed. (IOCCG, 1999). 2. H. R. Gordon, D. K. Clark, J. L. Mueller, and W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: comparisons with surface measurements,” Science 210, 63–66 (1980). 3. IOCCG, “Minimum requirements for an operational oceancolor sensor for the open ocean,” in Reports of the International Ocean-Color Coordinating Group, No. 1, A. Morel, ed. (IOCCG, 1998). 4. K. L. Carder, R. G. Steward, G. R. Harvey, and P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989). 5. R. L. Lucke, M. Corson, N. R. McGlothlin, S. D. Butcher, D. L. Wood, D. R. Korwan, R. R. Li, W. A. Snyder, C. O. Davis, and D. T. Chen, “The hyperspectral imager for the coastal ocean: instrument description and first images,” Appl. Opt. 50, 1501–1516 (2011). 6. NASA, “Responding to the challenge of climate and environmental change: NASA’s plan for a climate-centric architecture for Earth observations and applications from space” (2010). 7. J. Fishman, L. T. Iraci, and J. Al-Saadi, “The United States’ next generation of atmospheric composition and coastal ecosystem measurement: NASA’s Geostationary Coastal and Air Pollution Events (GEO-CAPE) mission,” Bull. Am. Meteorol. Soc. 93, 1547–1566 (2012). 8. J. L. Mueller, “Ocean color spectra measured off the Oregon coast: characteristic vectors,” Appl. Opt. 15, 394–402 (1976). 9. T. S. Moore, J. W. Campbell, and M. D. Dowell, “A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product,” Remote Sens. Environ. 113, 2424–2430 (2009).

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Spectral interdependence of remote-sensing reflectance and its implications on the design of ocean color satellite sensors.

Using 901 remote-sensing reflectance spectra (R(rs)(λ), sr⁻¹, λ from 400 to 700 nm with a 5 nm resolution), we evaluated the correlations of R(rs)(λ) ...
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