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A new scheme has been proposed by Lee et al. (2014) to reconstruct hyperspectral (400 - 700 nm, 5 nm resolution) remote sensing reflectance (Rrs(λ), sr−1) of representative global waters using measurements at 15 spectral bands. This study tested its applicability to optically complex turbid inland waters in China, where Rrs(λ) are typically much higher than those used in Lee et al. (2014). Strong interdependence of Rrs(λ) between neighboring bands (≤ 10 nm interval) was confirmed, with Pearson correlation coefficient (PCC) mostly above 0.98. The scheme of Lee et al. (2014) for Rrs(λ) re-construction with its original global parameterization worked well with this data set, while new parameterization showed improvement in reducing uncertainties in the reconstructed Rrs(λ). Mean absolute error (MAERrs(λi)) in the reconstructed Rrs(λ) was mostly < 0.0002 sr−1 between 400 and 700nm, and mean relative error (MRERrs(λi)) was < 1% when the comparison was made between reconstructed and measured Rrs(λ) spectra. When Rrs(λ) at the MODIS bands were used to reconstruct the hyperspectral Rrs(λ), MAERrs(λi) was < 0.001 sr−1 and MRERrs(λi) was < 3%. When Rrs(λ) at the MERIS bands were used, MAERrs(λi) in the reconstructed hyperspectral Rrs(λ) was < 0.0004 sr−1 and MRERrs(λi) was < 1%. These results have significant implications for inversion algorithms to retrieve concentrations of phytoplankton pigments (e.g., chlorophyll-a or Chla, and phycocyanin or PC) and total suspended materials (TSM) as well as absorption coefficient of colored dissolved organic matter (CDOM), as some of the algorithms were developed from in situ Rrs(λ) data using spectral bands that may not exist on satellite sensors.
© 2015 Optical Society of America
1. Introduction
Spectral remote sensing reflectance (Rrs(λ), sr−1) above the water surface provides quantitative information on optically significant constituents (OSCs) present in natural aquatic environments [1–7]. Due to large ranges of the OSCs, Rrs(λ) spectra show large variability in both magnitude and spectral shape [8–12]. The goal of ocean color remote sensing is to provide synoptic observation of aquatic systems routinely, while the goal of bio-optical inversion is to derive geophysical properties (e.g., OSCs) from these observations (e.g., Rrs(λ)).
Although hyperspectral Rrs(λ) (in this context, continuous spectral coverage in the visible and near-infrared domain, mainly 400-700nm with 5-nm increments) provides complete spectral information, due to technical limitations only multi-band measurements have been the primary source from satellite sensors such as the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Medium Resolution Imaging Spectrometer (MERIS). On the other hand, not all spectral bands from the hyperspectral data are independent. Lubac and Loisel (2007) showed that three modes of the empirical orthogonal function (EOF) could explain most (93%) of the total variance of Rrs(λ) data collected from the eastern English Channel and southern North Sea [13]. Craig et al. (2012) demonstrated that the first two EOF modes could account for 97.5 of the total variance of hyperspectral Rrs(λ), observed at the Compass Buoy station during the period of Feb. 2009-Mar. 2010 [14]. Similar findings were also reported by Flink et al. (2001) [15] and Toole and Siegel (2001) [16].
For the same reason of spectral inter-dependence, Dekker et al. (1992) suggested that 9 bands should be needed to capture the spectral curvatures in the 500-800 nm range for the Loosdrecht lakes [17]. Sathyendranath et al. (1994) demonstrated that the wavelengths used in pigment retrieval algorithms could be reduced from 32 to 6 without much information loss for the New York Bight [18]. Wernand et al. (1997) reported that the full reflectance spectrum (20 nm increments between 400 and 720 nm) could be regenerated from five key bands (412, 492, 556, 620, and 672 nm) for the Dutch and Belgian coastal waters as well as the Dover Strait [19]. More recently, Lee et al. (2014, hereafter referred to as the “Lee_2014 scheme”) compiled a library of Rrs(λ) collected from both open-ocean and coastal waters, and showed that the use of 15 spectral bands could successfully reconstruct hyperspectral Rrs(λ) data with uncertainties lower than those induced by the sensor noise and atmospheric correction artifacts [20]. The selection of the 15 bands followed the earlier works by Lee and Carder (2002) [21] and Lee et al. (2007) [22], where 15 bands were found to be sufficient in retrieving inherent optical properties (IOPs) of the OSCs as well as the benthic properties of shallow waters.
The Lee_2014 study used a total of 901 Rrs(λ) spectra from a wide variety of aquatic environments covering blue open ocean waters, blue to green gulf waters, sediment-rich river plumes, and optically shallow coastal waters, representing a variability of ~99% of the global water bodies [20]. However, as noted in Lee et al. (2014) [20], highly turbid inland lakes, where the Rrs(λ) spectra may be highly variable in both magnitudes and spectral shapes, were not included in the study. Indeed, most of the inland water Rrs(λ) spectra showed significant difference from those used in Lee et al. (2014) [20] (Fig. 1).
Fig. 1 (A) Rrs(λ) spectra used to develop the spectra reconstruction method in Lee et al. (2014) [20]. (B-E) Rrs(λ) spectra collected from several inland water bodies (Lake Taihu, Lake Chaohu, Three Gorges reservoir, and Lake Dianchi, respectively) in China, used in this study to test the Lee_2014 scheme and to determine the parameterization. Note the dramatic difference between Rrs(λ) in (A) and (B-E).
Furthermore, while the Lee_2014 scheme showed excellent accuracy in the reconstructed Rrs(λ), some of the required bands are not available on several popular ocean color sensors such as MODIS and MERIS. How these existing bands can be used to reconstruct Rrs(λ) remains to be studied.
Thus, the goal of this study is three folds: 1) to evaluate the performance of the Lee_2014 scheme with its original parameterization (15 bands) for data collected from several turbid inland lakes of China (Fig. 1(B-E)); 2) to fine tune the parameterization for the Lee_2014 scheme (15 bands) on reconstructing hyperspectral Rrs(λ) in Fig. 1(B-E); 3) to test the performance of the scheme on MODIS and MERIS bands. The final parameterization and its implications on inversion algorithm development are also discussed.
2. Data and methods
2.1 Data collection areas
Rrs(λ) data were collected from four inland water bodies of China, including Lake Taihu, Lake Chaohu, Three Gorges reservoir, and Lake Dianchi (Fig. 2). Lake Taihu has a surface area of 2338 km2 and a mean depth of ~1.9 m [23]. Lake Chaohu has an area of 820 km2 and a mean depth of ~4.5 m [24]. They are both located in the downstream of the Yangtze River. Three Gorges reservoir is an artificial lake created by the Three Gorges Project. The reservoir is approximately 600 km long and 1.1 km wide. Lake Dianchi is located in Yunnan Province on a plateau at an altitude of 1886.5 m. It has an area of ~298 km2 and a mean depth of 5.5m. These water bodies have been adversely affected by pollutants released from nearby industries, agricultural fields, and household wastewater [23–25], resulting in water quality degradation and recurrent algal blooms in recent years [11].
Fig. 2 Data collection locations in four turbid waters of China. Four cruise surveys were conducted in Lake Taihu, two cruise surveys were conducted in Lake Dianchi, and some stations were sampled repeatedly from different cruises. One cruise survey was carried out in Lake Chaohu and Three Gorges Reservoir, respectively.
2.2 Field measurements
Eight field investigations were carried out to collect Rrs(λ) data and water samples from the 4 inland lakes between April 2009 and May 2011 (Table 1). In total, 232 stations were surveyed. At each sampling station, Rrs(λ) data were collected between 10:00 and 14:00 h local time using a 512-channel ASD FieldSpec spectroradiometer (350 – 1050 nm, 1.5 nm increments).
Table 1. Field measurement locations, dates, and number of stations.
The radiance spectra of the reference panel, water, and sky were collected according to the above-water measurement method [26]. To effectively avoid the interference of the ship with the water surface and the influence of direct solar radiation, the instrument was positioned at an angle of φv ~135° relative to the sun and a zenith angle of θv ~40° for collecting the water radiance. Immediately after measuring the water radiance, the spectroradiometer was rotated upwards to measure the skylight radiance at an angle mirroring the water measurement. Ten spectra were acquired for each target, and then averaged after eliminating abnormal spectra.
The Rrs(λ) data was acquired also following the Ocean Optical Protocols [26]:
where Lt is the radiance from water, Lsky is the sky radiance, Lp is the radiance measured from a gray reference panel with a diffuse reflectance of ρp = (30% with minimal spectral dependence), and r is the surface reflectance of the water depending on the wind speed (2.2% for calm weather, 2.5% for <5 m s−1 wind, 2.6-2.8% for 10 m s−1 wind) [27, 28].The water samples were collected near the surface, and used to analyze the concentrations of OSCs in the lab, including Chla and TSM. Chla concentration was determined spectrophotometrically using the method of Lorenzen (1967) [29] and Chen et al. (2006) [30]. TSM concentration was gravimetrically determined via a series of processes, including filtration, stoving, and weighing [31].
2.3 Rrs(λ) correlation and reconstruction
The reconstruction scheme has been detailed in Lee et al. (2014) [20]. For completeness of this manuscript it is briefly introduced here.
First, Rrs(λ) data were binned to 1-, 5-, and 10-nm bandwidths, resulting in Rrs1nm(λ), Rrs5nm(λ), and Rrs10nm(λ), respectively. Then, the Pearson Correlation Coefficient (PCC) between any two wavelengths in the 400-750 nm range was calculated to form a 2-D correlation matrix for each bandwidth selection.
To reconstruct the hyperspectral Rrs(λ) using multi-bands, the following relationship was used:
where Rrsrc(λj) denotes the reconstructed Rrs(λ) for the j-th band, Rrs(λi) denotes the input Rrs(λ) for the i-th band for spectrum reconstruction, Kij and K0j are coefficients determined from multi-variant regression. The 15 bands used to reconstruct the Rrs(λ) for each of the 3 bandwidths are listed in Table 2. The selection of these bands followed the recommendations of Lee et al. (2007, 2014) [20, 22].Table 2. Spectral bands used to reconstruct hyperspectral Rrs(λ) data.
To evaluate the effectiveness of the Rrs(λ) reconstruction approach, an independent data set collected from Lake Taihu during October 2010 was used. This data covered 31 stations in the lake. The mean absolute error (MAERrs(λi)) and mean relative error (MRERrs(λi)) between the measured Rrs(λ) and reconstructed Rrsrc(λ) for all bands were calculated as below:
3. Results
3.1 Variation of in situ Rrs(λ)
Figure 1(B-E) shows the in situ Rrs(λ) collected from the 4 lakes, which exhibited large variability in both magnitudes and spectral shapes. The Rrs(λ) spectra showed typical characteristics of turbid inland waters, for instance the reflectance trough near 675 nm due to Chla absorption, low reflectance at <450 nm attributed to absorption by CDOM and phytoplankton, and two reflectance peaks near 570 nm and 700 nm due to combined effects and absorption and backscattering of OSCs and water molecules. These characteristics are similar to those reported for other turbid waters [8, 32, 33]. Figure 3 shows a summary of Fig. 1(B), where the mean and standard deviation spectra as well as the coefficient of variation (CV) are plotted against wavelength. CV varied from 20% to 50%, with two local minima around 550 nm and 700 nm. For three representative wavelengths in the blue, green, and red, Table 3 lists the statistics of their Rrs(λ) together with Chla and TSM. Overall they all showed large dynamic range with significant variability.
Fig. 3 Mean and standard deviation (SD) spectra of Rrs(λ) from in situ measurements (Fig. 1(B)). The coefficient of variation (CV) is derived as SD over the mean.
Table 3. Statistical description of Rrs(λ) and water quality parameters.
3.2 Spectral interdependence of Rrs(λ)
The spectral distributions of the PCC between different bands for Rrs1nm(λ), Rrs5nm(λ), and Rrs10nm(λ), respectively (note that the superscript represents the bandwidth), are shown in Fig. 4. The 2-D spectral distributions in the left column show the PCC between a single band and all other bands, while the 1-D distributions in the right column show the PCC between neighboring bands. There are three wide spectral regions with high PCC values: 400-530 nm, 580-690 nm, and 710-750 nm. In general, PCC slightly decreased with increasing band widths from Rrs1nm(λ), Rrs5nm(λ), to Rrs10nm(λ). For the 1-nm bandwidth, PCC between neighboring bands with different spectral intervals (<30 nm) was all significant (>0.90, p<0.0001) except near 700 nm (Fig. 4(B)). When the spectral intervals were below 10 nm, PCC was all above 0.97 (p<0.0001) except near 700 nm. For the 5-nm and 10-nm bandwidths, similar correlations were found among neighboring bands with slightly lower PCC values. Overall, the correlation analysis showed that except for the wavelengths around 700 nm, all neighboring spectral bands are highly correlated regardless of the bandwidths. This provides the basis for reconstructing hyperspectral Rrs(λ) using only several bands.
Fig. 4 Spectral distribution of Pearson correlation coefficient (PCC). A and B: 1nm bandwidth; C and D: 5nm bandwidth; E and F: 10nm bandwidth. The left column shows the 2-D spectral distribution of PCC, while the right column shows the PCC between neighboring bands with different spectral intervals.
3.3 Hyperspectral Rrs(λ) reconstruction using 15 bands
Using 15 spectral bands with bandwidths from 1 to 10 nm (Table 2), the multi-variant regression coefficients between any single wavelength and those 15 bands were determined using Eq. (2). Figure 5 shows the regression coefficients and their corresponding R2 values. Each number in Fig. 5(A-C) represents the regression coefficient between the input (x-axis) and output (y-axis) bands. The coefficients for the same input and output wavelengths (their band numbers are different) are all equal to 1.0. Although R2 decreased with increasing bandwidth (Fig. 5(D)), for λ < 720 nm they were all > 0.998 with a significance level of p<0.0001, and for λ < 700 nm they were close to 1.0 (>0.9995). Even for the near-IR bands between 720 and 750 nm, the R2 values were still > 0.960 (p<0.0001).
Fig. 5 Two-dimensional distribution of the model coefficients in constructing Rrs in any spectral band (y-axis) using the 15 bands (x-axis) for (A) 1-nm, (B) 5-nm, and (C) 10-nm bandwidths. These coefficients were determined using in situ Rrs(λ) data and a multi-variant regression in Eq. (1). The coefficients of determination (R2) are presented in (D). The three x-axis of (A)-(C) denote the coefficients of K0j, K1j, K2j, ……, K15j in Eq. (1), but marked here as 1, 2, 3, ……,16 owing to limited space.
An independent in situ Rrs(λ) data set (N = 31) collected from Lake Taihu in October 2010 was used to evaluate the above reconstruction approach with the newly establish parameterization. Four stations with significant spectral differences were selected as examples from the data set to show the agreement between the measured and reconstructed Rrs(λ) in Fig. 6. Even with a 10-nm bandwidth, the reconstructed Rrs(λ) showed excellent agreement with the measured Rrs(λ). One can barely distinguish the two spectra visually, especially for wavelengths < 700 nm. For all 31 Rrs(λ) spectra, Fig. 7 shows the MAERrs(λi) and MRERrs(λi) in the reconstructed Rrs(λ) with different bandwidths. The MAERrs(λi) was <0.0002 sr−1 for λ< 680 nm, and it reached about 0.0006 sr−1 near 700 nm. The corresponding MRERrs(λi) was < 1% for λ< 680 nm, and it approached ~2% at 700 nm. These results suggest that the hyperspectral Rrs(λ) can be reconstructed accurately for most visible wavelengths using 15 carefully selected bands.
Fig. 6 Reconstructed and measured Rrs(λ) for four selected stations. These data were not used in the model development. Blue solid lines represent the measured Rrs(λ), while the red symbols represent the reconstructed Rrs(λ) using 15 bands with 10nm bandwidth.
3.4 Hyperspectral Rrs(λ) reconstruction using MODIS and MERIS bands
The above process was repeated with the in situ Rrs(λ) data (N = 232), but using MODIS (7 bands) and MERIS (9 bands) instead of the 15 bands for the Rrs(λ) reconstruction. Rrs(λ) data corresponding to MODIS and MERIS bands (Table 4) were first calculated using the relative spectral response functions, and then used through the multi-variant regression model to reconstruct the hyperspectral Rrs(λ) with different bandwidths (1 nm, 5 nm, and 10 nm) (Fig. 8). For MODIS, R2 was > 0.96 (p<0.0001) for λ < 700nm, that it approached 1.0 for λ < 550 nm. There is no noticeable difference in the reconstruction accuracy for different bandwidths. For MERIS, R2 was mostly > 0.998 (p<0.0001) for λ<700 nm, and it showed slightly lower R2 values near 540 nm and 580 nm than in other wavelengths. The reconstruction accuracy was further evaluated using the independent in situ data set (N = 31), where the 4 examples are shown in Fig. 9 and error statistics in Fig. 10. MAERrs(λi) for MODIS bands reconstructed data was < 0.001 sr−1 for λ <700 nm, and was much lower for λ between 400 and 550 nm (<0.0002 sr−1). MRERrs(λi) was < 3% for λ between 400 and 700 nm, and <0.7% for λ < 550 nm (Fig. 10). For MERIS, MAERrs(λi) was < 0.0004 sr−1, while MRERrs(λi) was mostly <1% for λ between 400 and 700 nm. These results suggest that while the use of fewer than 15 bands would degrade the Rrs(λ) reconstruction accuracy, for most spectral bands in the visible the use of MODIS and MERIS spectral bands to reconstruct hyperspectral Rrs(λ) could result in satisfactory results with acceptable errors.
Table 4. MODIS and MERIS bands used to reconstruct hyperspectral Rrs(λ).
Fig. 8 Similar to Figs. 5(B, D), but MODIS and MERIS bands instead of the 15 bands were used to reconstruct the hyperspectral Rrs(λ). The left-column panels show the two-dimensional distribution of the model coefficients in constructing Rrs in any spectral band (y-axis) for 5-nm bandwidth using the MODIS (A) and MERIS (C) bands (x-axis). The corresponding coefficients of determination (R2) are presented in (B) and (D) for MODIS and MERIS, respectively.
Fig. 9 Similar to Fig. 6, but hyperspectral Rrs(λ) was reconstructed using MODIS (left) and MERIS (right) bands instead of the 15 bands. Blue solid lines represent the measured Rrs(λ), while the red symbols represent the reconstructed Rrs(λ) with 10nm bandwidth.
Fig. 10 Similar to Fig. 7, but MODIS and MERIS bands were used to reconstruct the hyperspectral Rrs(λ) (N = 31) with three bandwidths.
4. Discussion
4.1 Interpretation of Rrs(λ) interdependence
The strong interdependence of Rrs(λ) between neighboring bands has been shown previously by Sathyendranath et al. (1989) [34], Wernand et al. (1997) [19], and Lee et al. (2014) [20]. The present study echoes these previous findings with data collected from highly turbid lakes in China. Such interdependence can be attributed to the fact that the water’s IOPs change gradually with wavelength (the broadband effect), as demonstrated and argued in Lee et al. (2014) [20]. The Rrs(λ) values thus co-vary highly between neighboring bands. For wavelengths around 700 nm, PCC values are always lower than at other wavelengths (Fig. 4(B, D, & F)). This is because that aph (phytoplankton pigment absorption) rapidly decreases near 700 nm [35–40] and aw (pure water absorption) quickly increases near 700 nm [41]. In addition to these fast changing IOPs, chlorophyll a fluorescence and the so-called “red edge” effect also affects Rrs(λ) around 700 nm [42–44]. Consequently, relatively high variations (i.e., the narrowband effect) from aph, aw, and chlorophyll fluorescence contributed to the relatively lower spectral interdependence near 700 nm than at other visible wavelengths. This also suggests that for sensor design, more spectral bands are required around 700 nm than in other visible wavelengths.
4.2 Comparison with Lee_2014 scheme
Based on a global data set, Lee et al. (2014) developed a Rrs(λ) reconstruction scheme with a global parameterization (the Lee_2014 scheme) [20]. Can it be applied directly to the data set used in this study, which were collected from highly turbid lakes in China? Figure 11 shows reconstructed Rrs(λ) for the four sample Rrs(λ) using the 15 spectral bands with the Lee_2014 global parameterization. Overall, the reconstructed Rrs(λ) showed excellent agreement with the measured Rrs(λ) except at several wavelengths for Station 2 (~550 nm, 610-630 nm, ~700 nm). This is possibly due to lack of such a spectral shape in the original global data set used in Lee et al. (2014) [20]. In contrast, when such a spectral shape was included in the model development, the new parameterization of this study yielded improved reconstruction performance (Fig. 11). Such an improvement is also reflected in the statistical measures as shown in Fig. 12. In summary, the improvement for wavelengths < 510 was minimal (1% for λ < 430 nm and 0.5% for 430 – 510 nm), but increased for longer wavelengths (λ between 510 and 700 nm). The parameterization for hyperspectral Rrs(λ) reconstruction in the present study works well for the highly turbid waters from the four lakes, yet its performance still needs to be evaluated for other optically complex waters. Even without local parameterization, the Lee_2014 scheme with its global parameterization could yield MRERrs(λ) <2% for most visible wavelengths, indicating the robustness of this general approach in reconstructing hyperspectral Rrs(λ).
Fig. 11 Comparison between measured and reconstructed Rrs(λ) for four selected stations with distinctive spectral shapes and magnitudes. Rrs(λ) was reconstructed using 15 spectral bands and the Lee_2014 scheme with its global parameterization, and using the same 15 spectral bands with new parameterization obtained from this study using Rrs(λ) collected from highly turbid lakes.
Fig. 12 Spectral distribution of mean errors in the reconstructed Rrs(λ) (N = 31, 5nm bandwidth). Rrs(λ) was reconstructed using 15 bands and the Lee_2014 scheme with its global parameterization as well as the parameterization determined from this study.
4.3 Credibility of the reconstructed Rrs(λ)
The reconstructed Rrs(λ) is certainly not error free. However, given the fact that the satellite-derived Rrs(λ) also contains errors, the reconstructed Rrs(λ) may be used as surrogates in the absence of satellite-based hyperspectral measurements. For clear waters, Hu et al. (2013) showed that both MODIS- and SeaWiFS-derived Rrs(λ) contained uncertainties of ~0.0006 sr−1, ~0.0003 sr−1, and ~0.0001 sr−1 in the blue, green, and red wavelengths (red curves in Fig. 13(A), also see Table 3 of Hu et al. (2013) [45]). These Rrs(λ) uncertainties were used as reference to evaluate the credibility of the reconstructed Rrs(λ) using 15 bands (5-nm bandwidth), 7 MODIS bands, and 9 MERIS bands. Figure 13(A) shows that for λ < 550 nm, all reconstructed Rrs(λ) showed lower uncertainties than those in the satellite-derived Rrs(λ). Most of the reconstructed Rrs(λ) showed uncertainties < 0.00005 sr−1, approaching the noise level of MODIS [46]. For λ > 550 nm, uncertainties in the reconstructed Rrs(λ) are comparable to those from the satellite observation except for the Rrs(λ) data reconstructed using the 7 MODIS bands.
Fig. 13 (A) Rrs uncertainties (MAE, sr−1) in the reconstructed data. The input Rrs data to the reconstruction scheme were assumed error free, but the data were binned to 15 bands, 7 MODIS bands, and 9 MERIS bands, respectively. B: Same as in A, but Rrs uncertainties from MODIS retrievals of turbid waters (Moore et al., 2015 [47], symbols) were added to the input Rrs, which were then used in the Rrs reconstruction.
However, the reconstructed Rrs(λ) in Fig. 13(A) assumed error-free Rrs(λ) input. In practice, when satellite-derived Rrs(λ) data are used as the reconstruction input, the input already contains some degrees of uncertainties. Such uncertainties vary from clear waters [45] to turbid coastal waters [47]. Moore et al. (2015) classified their global data set into seven optical water types (OWT), where OWT 5, 6, and 7 were used to represent optically complex waters [47]. Because the focus of this study is on turbid coastal waters and inland waters, the uncertainty estimates from MODIS measurements for OWT 5 – 7 of Moore et al. (2015) [47] (green symbols in Fig. 13(B)) were added to the input Rrs(λ) in the reconstruction scheme. Figure 13(B) shows that when the input Rrs(λ) contained realistic uncertainties for turbid waters, the uncertainties in the reconstructed Rrs(λ) are about 0.0010-0.0015 sr−1 for λ <550 nm, comparable to the uncertainties in the input Rrs(λ). These results suggest that the additional uncertainties resulted from the reconstruction are much smaller than those in the input Rrs(λ). Thus, in the absence of hyperspectral satellite measurements, hyperspectral Rrs(λ) data for 400-700 nm may be reconstructed using MERIS and MODIS measurements in turbid optically complex waters, regardless of the intrinsic satellite-derived uncertainties.
4.4 Benefits to inversion algorithms
Inversion algorithms developed from in situ Rrs(λ) sometimes rely on spectral bands that do not exist on satellite sensors. For instance, Gower (1980) proposed a fluorescence line height (FLH) approach to estimated Chla concentrations by using three wavelengths at 650, 685, and 730 nm [48]. Some Chla algorithms utilized 675 nm and 700 nm [43, 49]. Gons et al. (1999) used 672 nm and 704 nm to estimate Chla concentrations [50]. Dall’Olmo et al. (2003) applied a three-band model to use 670, 710, and 740 nm to estimate Chla [51]. Gitelson et al. (2007) optimized the two-band and the three-band models by using in situ reflectance data from Chesapeake Bay, resulting in R(720)/R(670) and [R−1(675)-R−1(695)]*R(730) as thee algorithm inputs [8]. Le et al. (2009) used a four-band model (662, 693, 705, and 740 nm) to estimate Chla for highly turbid lakes [52]. Most of these wavelengths used for the Chla retrievals are not available from satellite sensors.
Similar cases were also found for inversion algorithms for TSM, CDOM, and phycocyanin (PC) concentrations. For TSM retrievals, the following wavelengths were used: 490, 550, 555, 665, 670, and 720-740nm [53–58]. For CDOM retrievals, the following wavelengths were used: 412, 443, 490, 510, 551, 555, 590, and 670nm [59–66]. For PC retrievals, the following wavelengths were used: 510, 556, 600, 615, 620, 624, 625, 648, 650, 665, 709, 710, and 725nm [67–75]. Similar to the Chla retrieval algorithms, most of these wavelengths are not available on current satellite sensors. It is thus desirable to reconstruct Rrs at these wavelengths using existing MODIS and MERIS bands in order to utilize the in situ Rrs-based inversion algorithms.
Figure 14 shows the reconstruction accuracy for the above frequently-used algorithm bands. For Chla algorithms, the reconstructed Rrs using either 15 bands or MERIS bands showed MRE < 2% for all frequently-used bands except those between 710 and 740 nm. When MODIS data were used, the reconstructed Rrs showed MRE <2% for λ ≤685 nm. For TSM algorithms, reconstructed Rrs using either 15 bands, MODIS bands, or MERIS bands all showed MRE < 0.5% for all but the NIR bands. This is because that the input bands used for the reconstruction are all close to the TSM algorithm bands. For the same reason, the reconstructed Rrs for the CDOM algorithm bands showed MRE <1% except for the reconstructed data at 590 nm using MODIS bands. For PC algorithms, the reconstructed Rrs using either 15 bands or MERIS bands showed MRE <1% for all but the 725-nm band. The reconstructed Rrs using MODIS bands showed higher MRE values but they were still <4% for the visible bands below 700 nm.
Fig. 14 Rrs reconstruction accuracy (MRE, %) for the frequently used bands for inversion algorithms. Rrs for those bands was reconstructed using 15 bands, MERIS bands, and MODIS bands from in situ Rrs data. (A) For Chla algorithms, the bands are: 650, 662, 670, 672, 675, 685, 693, 695, 700, 704, 705, and 710-740nm; (B) For TSM algorithms, the bands are: 490, 550, 555, 665, 670, and 720-740nm; (C) For CDOM algorithms, the bands are: 412, 443, 490, 510, 551, 555, 590, and 670nm; (D) For PC algorithms, the bands are: 510, 556, 600, 615, 620, 624, 625, 648, 650, 665, 709, 710, and 725nm.
The results shown in Fig. 14 suggest that when the algorithm bands, optimized from in situ Rrs data, are not available, MODIS and especially MERIS bands could be used to reconstruct those algorithm bands with sufficient accuracy for most (primarily the visible) wavelengths. This is particularly important before a sensor with hyperspectral or 15-band capacity is put in orbit.
Note that the inversion algorithms that can benefit from the Rrs reconstruction are those that use wavebands unavailable on current sensors. These algorithms were developed using wavebands to optimize retrievals of water constituents in optically complex waters, regardless of whether these optimal wavebands exist on current sensors. For the same reason, algorithms that are optimized to use existing wavebands of current sensors, such as the GSM algorithm [76, 77], would not benefit from the Rrs reconstruction. However, the reconstructed hyperspectral data is expected to play a significant role in applying existing algorithms and in developing new algorithms as the availability of virtually all wavelengths can help develop new applications. Indeed, this type of waveband reconstruction has received considerable attention by the community since the 1990s [13, 16–19, 22], and a recent progress by Lee et al. (2014) [20] reinforced its feasibility. As highly turbid inland lakes may have Rrs(λ) spectra highly variable in both magnitudes and spectral shapes that are not represented in the global data set in the Lee et al. (2014) [20] study, the current study complements the results of Lee et al. (2014) [20] through inclusion of more data from several inland turbid lakes of China, thus making the Rrs-construction more robust.
5. Conclusion
Through the use of a large Rrs data set collected from several highly turbid lakes in China, this study confirms the findings of Lee et al. (2014) [20] that most of the hyperspectral Rrs data can be reconstructed from the carefully selected 15 spectral bands. Local parameterization can also improve the reconstruction accuracy. The study also shows that hyperspectral Rrs data or Rrs data at spectral bands commonly used for inversion algorithms can be reconstructed using MERIS or MODIS bands with sufficient accuracy for most of the bands. This is particularly important because current satellite sensors are not equipped with all the 15 spectral bands. Specifically, MERIS bands can be used to reconstruct the bands below 700 nm for algorithms to retrieve Chla, TSM, CDOM, and PC. We expect to apply this approach to improve algorithm performance using MERIS or MODIS data in the near future.
Appendix
The multivariate coefficients of this study, used for reconstructing hyperspectral reflectance, have been provided as an appended document of this publication.
Acknowledgments
This research was supported by the National Natural Science Foundation of China (No. 41101340, 41276186, 41201332), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and a Case Study of Pearl River Science and Technology Star of Guangzhou (No. 2013J2200073). We gratefully acknowledge the important contribution of Zhongping Lee (University of Massachusetts at Boston) who provided the Lee_2014 scheme and numerous suggestions for this manuscript. We also thank the three anonymous reviewers for their valuable comments.
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