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Abstract
Several atmospheric correction algorithms for turbid waters have been developed based on an assumption of zero reflection in short–wave infrared (SWIR) bands. However, for the Landsat8–Operational Land Imager (OLI), some water reflections are so strong in the 1609 nm band that they cannot be ignored. In this study, we developed a novel atmospheric correction algorithm based on a zero assumption for the short–wave infrared band (ACZI). The ACZI algorithm uses the black pixel index (BPI) and the floating algae index (FAI) to distinguish black pixels, which are used to estimate the aerosol scattering of non–black pixels based on the assumption of spatial homogeneity of aerosol types. In Lake Taihu, compared with the SeaDAS (SeaWiFS Data Analysis System) –SWIR algorithm, the ACZI algorithm achieved better precision for visible bands MAPE (the mean absolute percentage error), < 30%, RMSE (the root mean square error) < 0.0117 sr–1) and provided more available water pixels. The accuracy of ACZI was close to that of the DSF (dark spectrum fitting) algorithm and was better than that of the EXP (exponential extrapolation) algorithm and L8SR (Landsat 8 OLI Surface Reflectance) product. The ACZI algorithm showed good applicability in turbid waters.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The OLI (Operational Land Imager) (Table 1) on Landsat–8 was launched on February 11, 2013, and has a ground track repeat cycle of 16 days with an equatorial crossing time [1]. Compared with medium– and low–resolution satellite sensors (e.g., MODIS, Moderate Resolution Imaging Spectroradiometer), the OLI has better spatial information with a spatial resolution of 30 m [2]. In addition, the OLI has two short–wave infrared (SWIR) bands (1609 and 2201 nm) for atmospheric correction. Although Landsat satellites are mainly used for land monitoring, studies using the OLI data of Landsat–8 for water–related research have shown success in coastal [3,4] and inland waters [4–6].
Table 1. Bands of the OLI on Landsat–8, with band range, band center, ground sampling distance (GSD), and signal–to–noise ratio (SNR) at the reference radiance [1].
Atmospheric correction (AC) is the key to remote sensing of water color. Wang and Gordon (1994) developed a mature and effective atmospheric correction algorithm [7], GW94. GW94 is based on the black pixel assumption for NIR (near infrared) bands, i.e. the TOA (top of atmosphere) radiance in NIR bands is dominated by atmospheric radiance from Rayleigh and aerosol scattering. Therefore, the water–leaving radiance (Lw), or water–leaving reflectance (ρw), in visible bands can be derived by removing the Rayleigh and aerosol scattering through extrapolation from the NIR ranges, and has been determined in clear water or open ocean.
However, the “black pixel” assumption is often invalid for turbid coastal and inland waters [8]. Overestimation of the aerosol contribution in the NIR bands and the overcorrection of atmospheric effects results in very low and even negative values at shorter wavelengths in the visible region [9]. Therefore, some AC algorithms often use the clean water to correct the non–clean water based on the assumption of spatial homogeneity of aerosol types [9,10]. As turbid waters still have very strong absorption capacity in the SWIR bands, the black pixel assumption is generally valid for SWIR bands, even for extremely turbid waters [11–13]. These SWIR–based AC algorithms have achieved good results in coastal and turbid inland waters [11,14,15]. However, the water–leaving reflectance of algae waters in SWIR bands was strong and no longer met the “black pixel” assumption when blooms occurred [16]. The reflectance contribution in 1609 nm band of Landsat 8–OLI was not only from the atmosphere, but also from waters with high content of algae particles. Therefore, the AC algorithms based on the black pixel assumption failed in algal bloom waters. Although some AC algorithms identified clean water as black pixel, there is usually no clean water to offer black pixels in some inland waters. Overall, it is essential to develop a more suitable and accurate atmospheric correction algorithm that relies on non–clean water to provide black pixels.
In this study, the “black pixel” in turbid waters for the Landsat 8–OLI data is first defined; second, the black pixels are identified using the black pixel index (BPI) (details of the BPI index are shown in section 3.2) and the floating algae index (FAI), then the black pixels are used to estimate the aerosol scattering of non–black pixels. Third, the improved AC algorithm for turbid waters is developed based on the identified black pixels. Finally, the improved AC algorithm is compared with the SeaDAS (SeaWiFS Data Analysis System)–SWIR, ACOLITE (atmospheric correction for OLI lite) and Landsat 8 surface reflectance (L8SR) products.
2. Study area and data
2.1. Study area
Lake Taihu (30°56′–31°34′N, 119°54′–120°36′E, Fig. 1) is the third–largest freshwater lake in China, with a surface area of 2338 km2 and mean depth of 1.9 m. Lake Taihu is a very important drinking source in the Yangtze Delta [17,18], but Lake Taihu has suffered from frequent algal blooms since the 1990s, which severely impacts the normal life of several million nearby residents [19]. Lake Taihu represents typical case II waters with complex optical properties and high spatial variability [20–22], and it is an ideal area to test the performance of atmospheric correction for turbid inland water remote sensing.
Fig. 1 Study lake and in situ sampling points in Lake Taihu. Triangles and crosses represent the in situ sampling locations on May 27, 2017 and December 21, 2017, respectively.
2.2. Field measurements
Field data were obtained to assess the AC algorithms in two surveys on May 27, 2017 and December 21, 2017 in Lake Taihu, and algal blooms occurred in these two days.
Remote sensing reflectance (Rrs) were measured by a spectrometer (ASD FieldSpec 4, which was sold by LICA United Technology Limited company) following NASA Ocean optics protocols [23]. The total water–leaving radiance (Lt) range from 350 to 2500 nm, radiance of reference panel (Lp), and sky radiance (Lsky) were measured via this instrument at 90° azimuth with respect to the sun and with a nadir viewing angle of 45° at each station. ρp is the reflectance of reference panel. The water surface reflectance factor σ was assumed to be 0.028 [24] considering the wind speed (< 5 m/s) and sky conditions (under clear sky or low cloud) of the field measurements. For each site, the measurements were conducted 15 times to obtain the Rrs [25], from the ratio of water–leaving radiance (Lw) to incident downwelling plane irradiance (Ed):
The water samples were collected near the water surface (< 0.3 m), and were stored in the dark at 4 °C before laboratory analysis. According to NASA protocols, the concentration of chlorophyll–a (Chla) was measured spectrophotometrically using a Shimadzu UV–2600 spectrophotometer [26,27]. The concentrations of suspended particulate matter (SPM) was determined gravimetrically in laboratory by burning organic matter from the filters [21,28]. The spectral absorption coefficients of particulate involved phytoplankton (aph(λ)), and non–algal particulates (ad(λ)) were determined using the quantitative filter technique [29]. The spectral absorption coefficients of colored dissolved organic matter (ag(λ)) were determined using a Shimadzu UV–2600 spectrophotometer with Milli–Q water as the reference. The absorption coefficients of pure water (aw(λ)) was obtained from Pope and Fry [30]. Further details of the field measurements of bio–optical parameters, and processing methods can be found in previous studies [31,32].
2.3. Satellite data and data matching
The Level–1 OLI images were acquired from the USGS (United State Geological Survey) (http://earthexplorer.usgs.gov/). The cloud free OLI images were processed to the Rrs products via the atmospheric correction described in Section 3, and compared with in situ Rrs data. To minimize the effects of temporal and spatial mismatches between the satellite and in situ data, the time window was narrowed to ~ ± 3h of the Landsat–8 overpass. To ensure spatial data consistency, model–measured Rrs spectral data were derived by averaging a 3 × 3 pixel area surrounding the in situ data location. 60 sampling points were matched, 22 points of which were from May 27 and 38 points of which were from December 21, 2017 (Fig. 1).
3. Method
The processing procedure of the ACZI algorithm is divided into three main steps (Fig. 2): First, the Rayleigh correction reflectance data are produced by 6SV (the vector version of Second Simulation of the Satellite Signal in the Solar Spectrum)–LUT (look–up table) for OLI; second, the aerosol scattering ratio is calculated based on black pixels identified by BPI (the black pixel index) and FAI (the floating algae index) [19,33]; third, the aerosol scattering ratio of black pixels is used to estimate aerosol scattering of non–black pixels. Finally, the Rrs data of OLI image is obtained.
3.1 The basic theory of the improved AC algorithm
The digital number data (DN) from Level 1 OLI images were converted to radiance of top–of–atmosphere (TOA):
where Lt is the radiance of TOA, ML is the multiplicative factor (gain), and AL is the additive factor (offset).ρt is reflectance of TOA, d is the sun–earth distance in Astronomical Units, θ0 is the sun zenith angle, and F0 is the band averaged extraterrestrial [10].The ρt is assumed to be the sum of the Rayleigh reflectance (ρr), aerosol reflectance (ρa) and the water–leaving reflectance (ρw) with transmittance (t).
According to sun and sensor geometry, the Rayleigh reflectance and transmittance are obtained from a LUT generated for all OLI bands using 6SV [34]. The Rayleigh corrected reflectance (ρrc) can be derived as: ε is the aerosol scatting ratio:ρa(λi) and ρa(λj) are the aerosol reflectance at short wavelengths (λi, NIR bands) and long wavelengths (λj, SWIR bands), respectively. C is easily calculated using NIR or SWIR bands that satisfy the “black pixel” assumption. Here, the aerosol model is assumed to be relatively stable at the small scale [9,10], and C is a fixed value for one OLI image. The water–leaving reflectance in the SWIR band is almost zero due to the strong absorption of water in the SWIR band [11,12], so Eq. (7) can be converted to: where, the superscript b represents black pixels. The C can be calculated by ρrc(SWIR).For most waters except for floating algae, 2201 nm still has very strong absorption, and the ρw(SWIR2) is considered to be zero [16,35], therefore the ρw(λ) can be derived from ρrc(λ):
This atmospheric correction algorithm based on a zero reflectance in short–wave infrared band is abbreviated as ACZI in this study. The key step in the new atmospheric correction algorithm is to define and collect black pixels.3.2 Black pixels
3.2.1 What kind of water pixel is black pixel?
Figure 3 shows the distribution of ρrc(SWIR) and its ratio from OLI images of four water regions in eastern China: Xin’ anjiang Reservoir (Figs. 3(a)–3(e)) is a typical clean water [36,37], the Yangtze River estuary (Figs. 3(f)–3(j)) and Lake Hongze (Figs. 3(k)–3(o)) are (extremely) turbid water regions [32,38], and Lake Taihu (Figs. 3(p)–3(t)) is eutrophic waters [20,39]. In Xin’anjiang Reservoir (Fig. 3(e)), the Yangtze River estuary (Fig. 3(j)), and Lake Hongze (Fig. 3(o)), the frequencies of ρrc(1609)/ρrc(2201) had only one peak, and its average and SD (standard deviation) values were 1.63 ± 0.14, 1.55 ± 0.16 and 1.58 ± 0.12, respectively. Figure 3(p) showed the algal bloom (red circle) in Lake Taihu, the high value distribution in Figs. 3(p)–3(s) was consistent with the water bloom distribution in Fig. 3(p). The histogram in Fig. 3(t) covered a range from 1 to 2.5 with a secondary peak around 1.7, and its average and SD value were 1.46 ± 0.24. The water area in Fig. 3(f) (~23084 km2) was larger than Lake Taihu (~2338 km2), and the spatial variation of ρrc(1609)/ρrc(2201) was small (Figs. 3(i) and 3(j)). This means that the spatial distribution of the aerosol type can be considered homogeneous, and thus if the waters in SWIR bands are black, the spatial distribution of ρrc(1609)/ρrc(2201) will be uniform. Noted that the ρrc(1609)/ρrc(2201) in the small water that distributed around Lake Taihu in Fig. 3(s) unfold a blue color similar to that of some parts of Lake Taihu, which proved that the assumption of spatial homogeneity of aerosol types is true in Lake Taihu. However, the high value in Figs. 3(q)–3(s) was prominent and consistent with the algal bloom distribution, indicating that some of the waters do not conform to the “black pixel” assumption, i.e., the signal from the water body was still present in the SWIR bands and cannot be ignored [16].
Fig. 3 OLI–RGB images, ρrc(SWIR) images and frequency of ρrc(1609)/ρrc(2201) in the Xin’ anjiang Reservoir (a–e), Yangtze River estuary (f–j), Lake Hongze (k–o) and Lake Taihu (p–t).
Based on prior knowledge and previous studies [16,39,40], the waters were divided into five types: floating bloom, submerged macrophytes, extremely turbid water, turbid water and clean water, where turbid water was considered a water type that meets the “black pixel” hypothesis [12]. The average ρrc from 1000 pixels was extracted from typical water regions in which the five water types were located (Fig. 3). There were significant differences in the ρrc spectra of the five water types (Fig. 4), for instance, the peak of the turbid water was at the 561 nm band (ρrc(561)), and the ρrc(655) was close to ρrc(561), but ρrc(865) was obvious low (Fig. 4(d)). These features can be used to build the BPI index for distinguishing the turbid water type from other water types.
Fig. 4 Average ρrc spectra of five water types: (a) floating bloom, (b) submerged macrophytes, (c) extremely turbid water, (d) turbid water, and (e) clean water. The average ρrc of each water type was extracted from 1000 pixels of images in Fig. 3.
3.2.2 Identification of black pixel
In this study, the basic processes for identification of dark pixels and determination of the aerosol type epsilon are as follows:
First, the BPI for identifying black pixel for turbid water was developed based on the spectral characteristics of the five water types in Fig. 4:
As shown in Fig. 4, compared to the submerged macrophytes, extremely turbid water and clean water, the ρrc(561) and ρrc(655) of the floating bloom and turbid water were very close, so the difference between ρrc(655) and ρrc(561) can be used to distinguish the floating bloom and turbid water from other three water types. On the other side, the ρrc(865) of the turbid water was much smaller than the ρrc(655), while the ρrc(865) of the floating bloom was larger than the ρrc(655), therefore the (ρrc(655) – ρrc(865)) of the turbid water will be a positive number, and the (ρrc(655) – ρrc(865)) of the floating bloom will be a negative number. Thus the ratio between the absolute value of (ρrc(655) – ρrc(561)) and (ρrc(655) – ρrc(865)) will have positive small BPI in the turbid water, while the floating bloom waters will have the negative BPI values.
Second, the FAI is often used to identify algal blooms [19,33], and it can be used to mask the floating algae pixels whose signals are not negligible in the SWIR bands. Therefore, to reduce misclassification of the BPI threshold, the FAI was used to remove the non–black pixels.
Finally, after screening of the BPI and FAI, the lowest 1% of the remaining water pixels were selected, and their average value was used as the εd(λ).
3.2.3 Threshold of the BPI and FAI
To determine the BPI threshold for water classification, statistical analysis of the histograms was performed by visually interpreting pixels of five water types (Fig. 4). It was reasonable to set 0–0.1 as the threshold of the BPI to efficiently distinguish turbid water in this study (Fig. 5), and histogram statistics of the water pixels of the five water types also have a clear distinction at 0–0.1. Only pixels from turbid waters were in the range of BPI varying from 0 to 0.1, and there were no pixels from other water types. Thus, 0–0.1 was defined as the BPI threshold for turbid waters, which is considered as a black pixel in this study; otherwise, it is a non–black pixel. When the BPI was greater than 1, the clean water seems to be distinguishable from other water types. However, the original in situ data for Fig. 5 were checked, and it was found that the BPI of more than 15 pixels from submerged macrophytes were greater than 1, hence it has to be strictly verified using the BPI to distinguish clean waters. In addition, it was difficult to search for clean water in some inland waters such as Lake Taihu, the in situ data from inland waters with clean water was lacked to evaluate the atmospheric correction algorithm based on clean water. The BPI was not used to distinguish clean waters in this study. The FAI thresholds of 73 cloud–free OLI images were calculated by visual image interpretation and the FAI threshold was set as −0.03, which can ensure exclusion of the water pixels without floating algae or algal bloom. In addition, there are valid pixels that can be used to identify black pixels (when the FAI is less than −0.05, it is difficult to obtain valid water pixels).
Fig. 5 Histogram of the BPI index of water pixels. The colors indicate different water types: dark is floating bloom, yellow is turbid water, pink is extremely turbid water, green is submerged macrophyte, and blue is clean water.
3.3 Algorithm accuracy analysis
To evaluate the performance of the algorithm, the root mean square error (RMSE), mean absolute percentage error (MAPE) and bias were used to determine the differences between the measured data and the modelled data. The parameters are defined as follows:
where Rirs is the in situ data, Rmrs is the OLI data after atmospheric correction, and n is the number of match–up pairs.4. Results and discussion
4.1 Bio–optical properties of Lake Taihu
The measured Rrs within 400–900 nm associated with the 60 sites from Lake Taihu (Fig. 1) are shown in Fig. 6. It indicated that the spectral characteristic of Lake Taihu are optically complex. In Lake Taihu, the spectral characteristics of Rrs of turbid waters were observed, and other spectra showed distinct increased Rrs within the NIR region, i.e., 700 to 900 nm. In the sampling spectrum on May 27, 2017, five sampling points show spectral characteristics of algal bloom with high Rrs in NIR ranges.
Fig. 6 Measured remote sensing reflectance (Rrs) of Lake Taihu onMay 27 and December 21 2017. The red lines represent data on May 27, 2017, and the black lines represent data on December 21, 2017.
The sampling results for the two dates showed similar bio–optical properties (Table 2): Chla showed high variability from 22.39 to 382.03 μg/L and 9.7 to 318.64 μg/L on May 27 (n = 18) and December 21 (n = 22), 2017, respectively, with a SD greater than 76 μg/L. Similarly, the ag(440), ad(440) and aph(665) of Lake Taihu covered wide ranges. These parameters indicate that Taihu is a highly eutrophic lake with complex optical properties. In addition, the mean values of bio–optical properties showed that content of phytoplankton and CDOM of May 27, 2017 was higher than that of December 21, 2017.
Table 2. Variations in the bio–optical properties of Lake Taihu. SD is the standard deviation. Note that not all the sample sites had bio–optical parameters in the two cruises.
4.2 Black pixel mask
Taking the OLI images of Lake Taihu on May 27 and December 21, 2017 as examples, in contrast to the RGB image, the floating algae and its surrounding water pixels were masked, as shown in Fig. 7. The spatial distribution of ρrc(1609)/ρrc(2201) is shown in blue (Figs. 7(c) and 7(g)) and the average and SD values of the ρrc(1609)/ρrc(2201) were 1.48 ± 0.15 (May 27, 2017) and 1.37 ± 0.07 (December 21, 2017) with range from 1.2 to 1.5 (Figs. 7(d) and 7(h)), which meet the requirements of the black pixel distribution hypothesis that was described in section 3.2.1. This means that the pixels identified by the BPI and FAI are in accordance with the characteristics of dark pixels, which could be clearly distinguished from non–black pixels using the BPI and FAI. It indicates that the BPI and FAI thresholds are reasonable. Notably, not all the black pixels should be identified in the ACZI algorithm, as the identified black pixels are just used to calculate the aerosol scattering ratio.
Fig. 7 Two examples of the identification of black pixels in OLI images of Lake Taihu on May 27 and December 21, 2017. The dark areas are masked pixels, and red indicates identified black pixels (b and f). The spatial distribution (c and g) and frequency histograms (d and h) of ρrc(1609)/ρrc(2201) are also illustrated.
4.3 Assessment of ACZI algorithm
To evaluate the performance of the ACZI algorithm, the 60 match–up sample points of in situ Rrs data and OLI derived Rrs were used. In addition, the standard atmospheric correction method from SeaDAS (this algorithm was referred to as SeaDAS–SWIR) [12] was also evaluated for comparison. Due to stronger water absorption in SWIR (short–wave infrared) bands than that in NIR bands, the SeaDAS–SWIR algorithm replaces NIR bands with SWIR bands [12]. Here, we used SeaDAS 7.4 [41] to process the satellite data via the SeaDAS–SWIR algorithm. As more water pixels were masked in the SeaDAS–SWIR algorithm, only 54 match–up sample points of in situ data were remained to evaluate the SeaDAS–SWIR algorithm.
As demonstrated in Fig. 8 and Table 3, the Rrs derived from ACZI were underestimated in the visible bands (the bias was negative), while the results of SeaDAS–SWIR were overestimated; and the two AC algorithms overestimated the Rrs in the 865 nm band (bias > 84.84%). For the SeaDAS–SWIR algorithm, the smallest MAPE was from the 561 nm band (MAPE ~19.46%) and the second smallest was from the 655 nm band (MAPE ~27.23%). For the ACZI algorithm, the 655 nm band provided the minimum MAPE (MAPE ~19.00%), followed by the 561 nm band (MAPE ~19.64%). Compared with the SeaDAS–SWIR algorithm, the ACZI algorithm achieved better accuracy for the bands at 443, 482, 655, and 865 nm. The performance of SeaDAS–SWIR was better than that of ACZI at 561 nm (Table 3). The two AC algorithms failed at the 865 nm band (RMSE > 0.0105 sr−1; MAPE > 91.08%). Notably, when the in situ Rrs was less than 0.01 sr–1, the ACZI–Rrs scatters were close to the 1:1 line whereas the results derived from ACZI were dispersed when the in situ Rrs was greater than 0.01 sr–1. The high values in the 865 nm band were caused by algal bloom, thus it can be inferred that the ACZI and SeaDAS–SWIR algorithms failed for the algal bloom water. The validation results indicate that the ACZI algorithm generally has better performance than the SeaDAS–SWIR algorithm.
Fig. 8 Comparison of the in situ data and atmospheric correction algorithm–driven Rrs in 443, 482, 561, 655, 865 nm.
Table 3. Band errors between the in situ Rrs and OLI Rrs obtained with SeaDAS–SWIR and ACZI atmospheric correction algorithm. The minimal statistical value is shown in bold.
There were some discrete points in Fig. 8, especially in 865 nm. These discrete points in Fig. 8 did reduce the statistical accuracy of the algorithm. It may be due to the low precision of the algorithm at the corresponding points. Another possible reason is the time window difference although the time window was strictly set to ± 3h, and AC– driven Rrs data were derived by averaging a 3 × 3 pixels area surrounding the in situ data location to ensure spatial data consistency. Noted that the Rrs(865) of these discrete points were large (> 0.01 sr–1), indicating that the chlorophyll–a content of these points were high. These discrete points may come from the floating algae waters. The mobility of floating algae is high, which bring challenge to the matching of in situ data and satellite data. It is difficult to define whether the discrete point is due to algorithm accuracy or time window, or both.
Two examples for Lake Taihu are shown in Fig. 9 to illustrate the Rrs at different bands derived from the two atmospheric correction approaches. Although the “proc_ocean” option of SeaDAS was set to “2–force all pixels to be processed as ocean”, the water pixels of floating algae were masked by SeaDAS–SWIR in all bands. Taking the Rrs(443) of Lake Taihu on May 27, 2017 as an example, the SeaDAS–SWIR–derived Rrs(443) data produced a total of 1737655 available water pixels (approximately 1563 km2), while ACZI–driven Rrs(443) data had a total of 2595556 water pixels (approximately 2336 km2). The ACZI algorithm could detect more effective water pixels, but it overcorrected some pixels of floating algae at the 443 nm band. Overall, the ACZI algorithm performed better and could obtain more available pixels than the SeaDAS–SWIR algorithm.
Fig. 9 Comparison of SeaDAS–SWIR and ACZI for OLI Rrs retrievals over Lake Taihu on May 27 and December 21, 2017. The “proc_ocean” option of SeaDAS was set to “2–force all pixels to be processed as ocean”.
4.4 Comparison with ACOLITE and OLI reflectance products
ACOLITE is a popular software for OLI imagery that integrates two AC algorithms: EXP (exponential extrapolation) and DSF (dark spectrum fitting).
The EXP algorithm is based on exponential extrapolations of the ratio of multiple scattered SWIR aerosol reflectance. The LUTs (lookup tables) of aerosol models are not used in the EXP. The EXP reduces the noise from SWIR bands through spatial smoothing [10]. Two SWIR bands (1609 nm and 2201 nm) of OLI were used for aerosol determination in ACOLITE (acolite_py_win_20180925.0).
The DSF algorithm was developed by Vanhellemont et al. (2018) [34] and integrated into a Python version of ACOLITE (version: acolite_py_win_20180925.0). The ‘black pixels’ for atmospheric correction in DSF are more flexible than those in EXP and SWIR. In GW94, SWIR or EXP, the dark target pixels in NIR or SWIR are fixed during the dynamic band selection of ‘dark targets’ in the DSF algorithm. The darkest pixels in DSF are searched from all the image pixels. The aerosol optical thickness (AOD) is derived from the darkest pixels using a LUT, and used in the AC process.
Landsat 8 OLI Surface Reflectance (L8SR) is generated using the Landsat Surface Reflectance Code (LaSRC), which makes use of the coastal aerosol band to perform aerosol inversion tests using auxiliary climate data from MODIS, and based on Second Simulation of the Satellite Signal in the Solar Spectrum Vectorial (6SV) model [42].
As shown in Fig. 10 and Table 4, compared with the EXP, DSF and L8SR, ACZI provided the smallest MAPE and bias at 443 nm (MAPE ~28.70%, bias ~-3.95%), 482 nm (MAPE ~23.12%, bias~-4.58%) and 655 nm (MAPE ~19.00%, bias ~-9.62%); the DSF derived the smallest RMSE (< 0.0077 sr–1) in the visible bands, and the ACZI–derived RMSE were similar to the DSF– derived RMSE at the 443 nm, 482 nm and 655 nm bands. The EXP and ACZI algorithms underestimated the water–leaving reflectance in the visible bands, while the DSF and L8SR overestimated them, all four AC algorithms failed at the 865 nm band (RMSE > 0.0103 sr–1; MAPE > 73.60%; bias > 62.86%). Generally, the performance of ACZI was comparable to that of DSF and was better than that of EXP and L8SR.
Fig. 10 Comparison of the in situ data and atmospheric correction algorithm–driven Rrs in 443, 482, 561, 655, 865 nm.
Table 4. Band errors between the in situ Rrs and OLI Rrs obtained with four atmospheric correction algorithms (EXP, DSF, L8SR, and ACZI). The minimal statistical value is shown in bold.
4.5 Performances of ACZI and DSF in SPM estimation
Four AC algorithms (ACZI, SeaDAS–SWIR, EXP, DSF) and L8SR products were evaluated in Section 4.3 and 4.4, which showed that ACZI and DSF were the optimal algorithms. In order to understand the performance of ACZI and DSF in remote sensing retrieval of water color, a retrieval model for SPM in Lake Taihu was developed using in situ data. The SPM data of Lake Taihu were collected from four field cruises (December 06, 2016, March 08, 2017, March 14, 2017, and April 30, 2017) with 72 samples, of which 37 samples were used to develop the SPM model and the remaining 35 samples were used to validate the SPM model. The Rrs used to develop SPM model was from in situ measurements, not from AC–derived Rrs. It may make the measured and estimated SPM match well using Rrs derived by AC algorithms, however, in the process of developing the SPM model (using band ratio driven by AC algorithm), it indicated that the uncertainties and errors of AC algorithms would affect the SPM models. That is to say, the SPM models derived by different AC algorithms may be different. The purpose of this section was to compare the performance of ACZI and DSF in remote sensing retrieval of SPM. Therefore, the measured Rrs were used to develop and validate the SPM model.
The in situ data of algal blooms were eliminated in this section because the reflective signals of the water column were weak or even absent in algal bloom waters (the floating algae on water surface will block light into the water column). Based on the measured Rrs and SPM, the empirical algorithm with the highest coefficient of determination was obtained through regression analyses among different band combinations that estimate SPM, as follows:
The coefficient of determination, R2, for the best regression relationship of the logarithmic function between the simulated measured Rrs(865) and in situ SPM data was 0.68 (P < 0.005) (Fig. 11(a)). The proposed model performed well for the validation data set (Fig. 11(b)). The R2 and RMSE of the SPM model for the in situ data set were 0.81, 19.61 mg/L, respectively. It indicated that the proposed model could be used to estimate SPM with satisfactory performance in these inland waters.Fig. 11 (a) Calibration: relationship between in situ Rrs and measured SPM. (b) Scatter plots of validation data using measured SPM and estimated SPM.
The spatial distributions of the ACZI–derived and the DSF–derived SPM were consistent (Figs. 12(b) and 12(c)). As shown in Fig. 12(e), the frequency peak derived from ACZI was around 100 mg/L, while the frequency peak derived from DSF was around 180 mg/L. The SPM values derived by DSF was higher than that derived by ACZI algorithm. The R2 of the regression relationship between the simulated in situ– measured SPM and OLI–estimated SPM derived by ACZI and DSF were 0.75 and 0.56, respectively (Fig. 12(d)). Based on the statistical indices, the estimation accuracy of the ACZI–driven SPM was higher than that of the DSF–driven SPM.
Fig. 12 OLI true color image (a), and distribution of estimated SPM patterns in Lake Taihu on May 27, 2017: ACZI (b) and DSF (c). Comparison of measured SPM and OLI–estimated SPM derived by ACZI and DSF algorithms (d). The frequency of OLI–estimated SPM on May 27, 2017 (e).
4.6 Limitations of ACZI in application
There is not enough clean water to offer black pixels in some coastal and inland waters, therefore the ACZI algorithm focuses on atmospheric correction using turbid water pixels that conform to the “black pixel” assumption. The ACZI algorithm uses the BPI to identify the black pixels in turbid waters, which have a zero water–leaving reflectance in the SWIR bands. The model structure of the BPI causes the water pixels acquired by the BPI to be turbid waters, rather than the clean water pixels sought by other AC algorithms such as that used by Hu et. al (2000). In this case, due to the limitations of the BPI index, the ACZI algorithm is not suitable for the areas that only have clean waters because clean water cannot offer the black pixels determined by the BPI. Figure 13 showed an example that the water pixels of Xin'anjiang Reservoir (representative of a clean water region) are almost masked by the BPI and FAI indexes. For clean waters, the GW94 or other AC method based on NIR bands can also obtain accurate results. For areas where it is difficult to obtain enough clean waters, ACZI can be an alternative atmospheric correction algorithm. In future research, we will add an index to identify clean water pixels to expand the applicable area of the ACZI algorithm. In addition, the black pixels defined by the ACZI algorithm can be used in other studies that need black pixels, such as the inversion of AOD.
Fig. 13 An example of the identification of black pixels in an OLI image of Xin’ anjiang Reservoir (March 11, 2018).
5. Conclusions
There is usually no clean water to offer black pixels in some inland waters, such as Lake Taihu. It is essential to develop a more suitable and accurate atmospheric correction algorithm that relies on non–clean water to provide black pixels. However, not all waters meet the assumption of “zero reflectance in SWIR bands” due to waters with algal blooms have strong water reflection in the 1609 nm band that cannot be ignored. Therefore, the BPI and the FAI index were constructed to distinguish turbid waters as the black pixels in this study, and the black pixels were used to estimate the aerosol scattering of non–black pixels based on the assumption of spatial homogeneity of aerosol types. The ACZI was developed for inland waters, and the assessment results showed that the accuracy of the ACZI algorithm is as good as or better than that of the SeaDAS–SWIR, EXP, DSF, and L8SR algorithms. The ACZI is suitable for waters lacking clean water pixels such as Lake Taihu.
Funding
State Key Program of National Natural Science of China (41431176); National Natural Science Foundation of China (41771366, 41471287 & 41701416), the key project of Nanjing Institute of Geography and Limnology (NIGLAS2017GH03) and the China Postdoctoral Science Foundation (BX20190155).
Acknowledgments
The authors would like to thank the USGS for providing the Landsat–8 OLI data; NASA for providing the SeaDAS; the Remote Sensing and Ecosystem Modelling (REMSEM) team for providing the ACOLITE software; Zhigang Cao, Ming Shen, Junfeng Xiong, Tianci Qi, and Xu Fang for their hard work. We also thank for the data support from “Lake–Watershed Science Data Center, National Earth System Science Data Sharing Infrastructure, National Science & Technology Infrastructure of China (http://lake.geodata.cn) and the ESA/MOST Dragon 4 program for facilitating this collaboration.
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