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Abstract
High-precision radiometric calibration (RC) coefficients are required to retrieve reliable water quality parameter products in turbid inland/coastal waters. However, unreliable RC coefficients when satellite sensors lack accurate and in-time RC may lead to pronounced uncertainties in the products through error propagation. To address this issue, a novel approach for estimating water quality parameters, taking suspended particulate matter (SPM) as a case, was proposed by coupling the procedures of RC and SPM model development. The coupled models were established using digital numbers (DNs) from target sensors and “in-situ” SPM measurements from concurrent well-calibrated reference sensors, with the RC coefficients introduced as unknown model parameters. The approach was tested and validated in varied Chinese inland/coastal regions, including the Hongze lake (HL), Taihu lake (TL), and Hangzhou bay (HB). The results show: (1) the DN-based SPM models can achieve a degree of accuracy comparable to reflectance-based SPM models with determination coefficients (R2) of 0.94, 0.92, and 0.72, and root-mean-square errors (RMSE) of 7.02 mg/L, 15.73 mg/L, and 619.2 mg/L for the HL, TL, and HB, respectively, and the biases less than 3% between the derived and official gain RC coefficients; (2) the uncertainty of SPM products increases exponentially as the RC uncertainty increases for exponential reflectance-based SPM models; (3) the DN-based SPM models are less sensitive to the uncertainties of atmospheric correction and RC coefficients, while the reflectance-based models suffer deeply. This study provides encouraging results to the improvement of SPM retrieval using the DN-based models by coupling RC and SPM retrieving processes, especially for sensors without precise RC coefficients.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Inland/coastal water quality plays an important role in environmental ecosystems and human society [1]. Suspended particulate matter (SPM), an important indicator of water quality, should be accurately and reliably acquired so that we can better understand the bio-geomorphic dynamics of inland/coastal water ecosystems and develop effective water management and protection techniques [2]. SPM plays an important role in the ecological function of water ecosystems and the biogeochemical cycles [3], and affects phytoplankton productivity [4], nutrient dynamics [5], and transport of micropollutants [6]. Traditional field sampling methods, limited by spatial and temporal coverage, are often insufficient to develop robust models and to obtain statistically meaningful results [7]. Remote sensing techniques are widely used to obtain spatiotemporal information of SPM concentrations (${\textrm{C}_{SPM}}$) because they can monitor the water ecosystems at a large scale and a high frequency [8].
The radiometric calibration (RC) of satellite sensors is crucial to sensors’ ability to retrieve bio-geophysical parameters accurately. RC uncertainty should be lower than 5%, and RC stability should be better than 0.5% over a decade [9]. The uncertainty requirement is essential to derive remote sensing products, and the stability requirement is crucial to determine long-term trends. Radiometric degradation of satellite sensors will greatly affect the accuracy of satellite-derived products. Specifically, a 0.3% radiometric change can result in a 5% bias approximately in the ocean color satellite products of water-leaving radiance (${L_w}$) and chlorophyll-a (Chl-a) concentration [10].
To avoid inconsistencies in satellite-derived products obtained by multiple satellite images and algorithms, RC corrects for the sensor sensitivity and reduces the inaccuracy of algorithms that are used to derive water quality parameters [11]. Satellite observations and products are sensitive to RC uncertainties due to sensor degradation, and vicarious calibration (VC) efforts are made to ensure the RC accuracy of satellite sensors. VC determines vicarious adjustment gain-factors for absolute RC coefficients [12] through simulation of top-of-atmosphere (TOA) radiance (${\textrm{L}_{TOA}}$) using highly accurate in-situ measurements [10,13]. The gain-factors can be used to update the RC coefficients, account for characterization errors, and interpret ocean color data physically to achieve the desired accuracy on the satellite-derived products [13,14]. VC is a key procedure to maintain the radiometric accuracy of ocean color sensors [10,14]. However, VC efforts are often limited because of labor intensity and high cost, and cross-calibration which can radiometrically calibrate a sensor easily is used when VC efforts are not available or conducted long before [15]. In traditional retrievals of ${\textrm{C}_{SPM}}$, the satellite sensors are well-calibrated either by onboard VC or by cross-calibration.
Mainstream ocean color sensors, such as the MODerate-resolution Imaging Spectroradiometer (MODIS), the Visible Infrared Imaging Radiometer Suite (VIIRS), and the Geostationary Ocean Color Imager (GOCI), are well-calibrated for water targets [16]. For terrestrially-oriented satellite sensors, such as the Operational Land Imager (OLI) onboard the Landsat-8 and the Wide-Field-of-View (WFV) onboard the Chinese Gaofen-1, however, sets of RC coefficients are needed to improve the accuracy of SPM products [17]. Highly accurate RC coefficients are only achievable at extremely stable sites with advanced approaches [10]. Thus, reducing the impacts of RC coefficients is vital to the accuracy of the satellite-derived SPM products.
Many SPM algorithms that require accurate RC coefficients are widely used, including semi-analytical models [2,18], empirical and semi-empirical models [19]. In these algorithms, atmospheric correction (AC) is also crucial to retrieve ${\textrm{C}_{SPM}}$ accurately, however, the standard AC based on near-infrared (NIR) bands (NIR-AC) for turbid inland/coastal waters is often difficult [20–22] because of (1) invalid “black water” assumption at NIR bands, (2) incorrect cloud and land mask, and (3) land adjacency effects. To avoid the problems of NIR-AC, short-wave infrared (SWIR) bands were introduced to conduct AC (SWIR-AC) over turbid inland/coastal waters [23], because the “black water” assumption is still valid. However, due to the longer extrapolation distance from the SWIR to visible bands, the SWIR-AC is more sensitive to the aerosol models [24]. The performance of SWIR-AC is also influenced by the signal-to-noise (SNR) ratio of SWIR bands [25]. In addition, some sensors (e.g. WFV) lack SWIR bands, and some water reflections are still strong in the SWIR bands (e.g. 1609 nm of OLI) [20]. These SPM models are wildly applied for SPM estimations with some alternative AC approaches, such as only correcting Rayleigh scattering (RC-AC) [8], using ultraviolet wavelength as reference to conduct AC (UV-AC) [26], and using Second Simulation of the Satellite Signal in the Solar Spectrum code (6S-AC) [27].
To avoid the dependence of accurate RC coefficients in the conventional ocean color modeling process, this study aims to develop a coupled approach for RC and parameter retrieval to improve SPM estimations over turbid inland/coastal waters. The main idea is to employ digital numbers (DNs) directly, rather than remote sensing reflectance (${R_{rs}}$) which requires accurate RC coefficients, to retrieve ${\textrm{C}_{SPM}}$ with the RC coefficients introduced as model parameters. AC approaches including RC-AC, UV-AC, and 6S-AC are analyzed to select a suitable AC algorithm for the DN-based SPM models over inland/coastal waters. To determine the validity of the proposed models, we test our approach at three typical inland/coastal waters in China: Hongze lake (HL), Taihu lake (TL), and Hangzhou bay (HB). The approach is then implemented to the Chinese Gaofen-1 WFV (designed for land applications) to evaluate its potential in providing SPM products for inland/coastal waters.
2. Regions and materials
2.1 Study regions
Hongze Lake (HL, 33°06′–33°40′N, 118°10′–118°52′E, Fig. 1(a)), is a typical inland lake with complex optical properties located in southeastern China. HL is a dynamic shallow lake with an average water depth of 1.9 m and a surface area of 1597 km2 [28]. Algal blooms may occur during the summer and autumn. Thus, SPM at HL varies greatly in both space and time [29].
Fig. 1. Location of study regions: (a) Hongze Lake (HL), (b) Taihu Lake (TL), and (c) Hangzhou Bay (HB).
Taihu Lake (TL, 30°56′–31°34′N, 119°54′–120°36′E, Fig. 1(b)), the third-largest freshwater lake in China, is located in the well-developed region in eastern China. TL is also a typical shallow turbid water with a 1.9 m average water depth and a 2338 km2 water surface. SPM varies spatially and temporally at TL because of terrestrial factors and sediment resuspension [30].
Hangzhou Bay (HB, 30°00′–39°50′N, 120°27′–121°55′E, Fig. 1(c)), located at the mouth of the Yangtze River, has a surface area of 8500 km2 and an average depth of 8 to 10 m during low tides. HB is a wide and shallow estuary receiving sediment from the Yangtze and Qiantang rivers whose hydrodynamics and sedimentation are profoundly influenced [26].
The satellite-derived SPM products are up to 150 mg/L, 300 mg/L, and 5,000 mg/L for HL, TH, and HB, respectively (Table 1). In HL, SPM and Chl-a have a strong influence on the total absorption coefficients [29]. SPM at TH shows clear seasonal variability due to the seasonal changes of wind speed [30]. Because HB is an extremely turbid coastal water body that is much more turbid than the typical inland waters like HL and TL, SPM at HB are greatly influenced by the variations of tidal phases, tidal magnitudes, and strong wind events [26].
Table 1. SPM models for the study regions.
2.2 Pseudo-field SPM measurements
While in-situ SPM measurements are preferred to establish SPM models, however, it is difficult to obtain sufficient concurrent in-situ measurements for different water bodies and at various image acquisition times. Thus, SPM retrieved by previous studies are used as “in-situ” SPM measurements, a technique that has proven to be successful in the past [31]. The SPM data were gathered at HL using VIIRS [29], at TL using MODIS [30], and at HB using GOCI [32]. The SPM algorithms employed to retrieve “in-situ” SPM measurements are listed in Table 1.
While “in-situ” SPM measurements from prior studies may induce additional uncertainties to the DN-based SPM models, these products can be used due to the following reasons: (1) the errors of SPM products are estimated in those studies (2) when accessing the performance of SPM models, the uncertainties of the SPM products can be considered, and (3) most importantly, the uncertainties of SPM products are included in the uncertainties of DN-based SPM models.
2.3 Satellite images
The OLI can provide satellite observations of inland/coastal waters with a relatively high spatial resolution (30 m), which is particularly helpful in the monitoring of inland/coastal environmental problems [33,34]. The WFV is a sensor with a higher spatial resolution (16 m), providing great potential to monitor inland/coastal waters on both small and large scales. Because both sensors are terrestrially-oriented with a high spatial resolution, it is of great interest to assess their ability to determine ${\textrm{C}_{SPM}}$ [35].
The OLI data were downloaded from the United States Geological Survey (USGS, https://earthexplorer.usgs.gov/), the WFV data were acquired from the China Centre for Resources Satellite Data and Application (CCRSDA, http://www.cresda.com/CN/), the MODIS and VIIRS data were obtained from the Level-1 and Atmosphere Archive & Distribution System Distributed Active Archive Center (LAADS DAAC, https://ladsweb.modaps.eosdis.nasa.gov/search/), and the GOCI data were acquired from the Korea Ocean Satellite Center (KOSC, http://kosc.kiost.ac.kr/eng/p10/kosc_p11.html). The cloud-free image-pairs and datasets for modeling and validation are listed in Table 2, which were visually examined to avoid thick aerosol and cloud, and their complex interactions [36].
Table 2. The acquisition time of the image-pairs (Greenwich Mean Time) as well as modeling and validation strategies used in this study.
To match the satellite images with the pseudo-field SPM measurements, the difference between the spatial resolution of satellite data (OLI or WFV) and “in-situ” observations (VIIRS, MODIS, and GOCI) should be addressed. In this paper, the satellite images and the “in-situ” SPM observations were first projected to geographic coordinates, and then geometrically registered with error controlled to within one pixel. Finally, the satellite images were resampled to the spatial resolution of the “in-situ” observations using mean filtering.
Generally, an N*N window (e.g. 3*3) is needed to obtain the matching pairs between satellite images and in situ measurements [8]. However, in this study, the pseudo-field measurements (MODIS, VIIRS, and GOCI) were coarser than the satellite images (OLI and WFV), and no N*N window was applied at the “in-situ” measurements because (1) the pseudo-field SPM measurements matched the mean values of satellite images, indicating that a window was implicitly applied at the satellite images and (2) there were two more parameters (gain and offset coefficients) to be determined for the DN-based SPM models which involved a larger number of matching pairs to ensure the model’s performance.
3. Methods
3.1 Theoretical background
For turbid inland/coastal waters, SPM, an optical property, is closely related to ${R_{rs}}(\lambda )$ at the NIR bands:
The optical properties of SPM are approximately proportional to ${C_{SPM}}$, and the NIR signal is important and effective to retrieve ${C_{SPM}}$ in turbid waters [32]. The ${C_{SPM}}$ can be estimated through empirical or semi-empirical SPM models, which are written as:According to Eqs. (3) and (4), ${R_{rs}}$ can then be written as:
For simplicity, the wavelength dependence of these variables has been suppressed. Because sensors respond linearly to the incoming signal, the ${L_{TOA}}$ can be calculated from the quantized standard DNs using the RC coefficients [40] according to ${L_{TOA}} = A\cdot DN + B$, where A is the gain coefficient, and $B$ is the offset coefficient. Finally, the ${R_{rs}}$ is rewritten as: where $\textrm{k} = {F_0}\textrm{cos}{\theta _0}{t_v}{t_s}$.In the applications for SPM retrieval over turbid inland/coastal waters, ${L_{path}}$ may be calculated using different methods such as RC-AC [8], UV-AC [26], and 6S-AC [27]. After ${L_{path}}$ is determined, the ${R_{rs}}$ becomes a function of DN and RC coefficients. The A and B are unreliable in some cases such as the sensors are newly launched lacking of accurate RC, the sensors are degraded without in-time RC, and inconsistent RC coefficients are obtained through various approaches. Since the incoming signal responds linearly to DN, the A and B can be considered as model parameters which make the RC coefficients more suitable for SPM models and AC algorithms. Finally, SPM can be retrieved using DN directly, with RC coefficients determined in model development and path scattering calculated by AC algorithms as following:
3.2 Development of DN-based SPM models
In general, simple and easy to be implemented empirical models for SPM retrieval are established by quantifying the relationship between water’s optical properties and its constituents [38]. For inland/coastal waters, semi-empirical exponential models of the red and/or NIR bands are widely used to calculate stable and acceptable ${\textrm{C}_{SPM}}$ [8,42]. Based on the exponential model of a single red or NIR band, the DN-based SPM model is as followings:
where ${p_1}$, ${p_2}$, A, and B are fitting parameters, and ${L_{Path}}$ is calculated by the 6S code. Unlike traditional SPM models, the DN-based SPM model designates the RC coefficients as unknown parameters. With enough “in-situ” SPM measurements, the model accuracy is unaffected because there are only two more parameters. In the development of empirical DN-based SPM algorithms, the model coefficients as well as RC coefficients that provide the best fit between the “in-situ” SPM data and retrieved ${R_{rs}}$ are obtained.3.3 Model accuracy assessment
To evaluate the performance of the algorithm, the determination coefficient (${R^2}$), the average absolute percentage difference (APD, in percentage), the root-mean-square error (RMSE), and the unbiased RMSE (URMSE, in percentage), are used to assess the model performance. These parameters are expressed as follows:
4. Results
4.1 Selection of AC schemes
AC is a crucial procedure to retrieve SPM accurately for turbid inland/coastal waters, however, there is no standard AC approach. Several AC schemes are commonly used, including UV-AC, RC-AC, RC-AC (1240) (a modified version RC-AC that removes the Rayleigh-corrected reflectance at 1240 nm band [8]), and 6S-AC. Thus, it is essentially necessary to determine a suitable AC scheme for retrieving SPM products. The relationships between ${R_{rs}}$ at red band of MODIS derived by the four AC algorithms are displayed in Fig. 2.
Fig. 2. The relationships between ${R_{rs}}\; ({645} )$ derived from the four AC schemes including UV-AC (first column), RC-AC (1240) (second column), RC-AC (third column) and 6S-AC (fourth column) at HL (first and second rows), TL (third and fourth rows), and HB (fifth and sixth rows).
Overall, the derived ${R_{rs}}\; ({645} )$ values using the four approaches exhibit strong correlations with each other (${R^2}$>0.80; p < 0.001). However, the gains of the regression lines are not close to 1.000, indicating a linear difference between the four methods. Specifically, ${R_{rs}}\; ({645} )$ values derived by RC-AC and 6S-AC are larger than those calculated using UV-AC and RC-AC (1240). In addition, the ${R_{rs}}\; ({645} )$ values derived from RC-AC are more consistent with those calculated with 6S-AC (${R^2}$>0.90; p < 0.001), while the ${R_{rs}}\; ({645} )$ values from UV-AC are better correlated with those calculated by RC-AC (1240), which may be due to the fact that RC-AC and 6S-AC only involve a single band, whereas UV-AC and RC-AC (1240) require more bands.
In the development of empirical SPM models, concurrent datasets consisting of ${R_{rs}}$ estimated from satellite images and “in situ” SPM data are established within a ± 3 h time window [8]. The RC-AC method was selected for the developments of our SPM models for several reasons:(1) RC-AC is simple and can be calculated exactly [43]; (2) RC-AC has been already successfully used to establish SPM models [16]; (3) visual examinations were conducted to avoid thick aerosols and aerosol contribution is small in the TOA signal; (4) there is just a linear difference between derived ${R_{rs}}$ values using different AC schemes which only results in different model parameters; (5) the WFV bands are too limited to perform NIR-AC, SWIR-AC, and UV-AC; and (6) it is difficult to remove the atmospheric influence using the 6S-AC, without simultaneously retrieved or observed aerosol information [44].
4.2 Model development and validation
Based on exponential models of a single band, a more sensitive band will result in better SPM values. To determine the best band for SPM retrieval for the three water bodies, the band of the SPM models was shifted from OLI band 1 to band 9. The R2 and RMSE of the SPM models are shown in Fig. 3. Clearly, band 4 (655 nm) of OLI at HL and TL (Figs. 3(a) and 3(b)), and band 5 (865 nm) of OLI at HB (Fig. 3(c)) are the wavelengths most sensitive to ${C_{SPM}}$.
Fig. 3. Sensitive bands for SPM retrieval at (a) HL, (b) TL, and (c) HB based on exponential models.
The exponential models of red and/or NIR bands have been proven useful in determining SPM for turbid inland/coastal waters [45]. However, HB is an extremely turbid water body with ${C_{SPM}}$ up to 5,000 mg/L [26], which is much higher than those of HL (<100 mg/L) [29] and TL (<300 mg/L) [30]. In the extremely turbid water of HB, longer bands are needed to retrieve SPM because the bands at shorter wavelengths may saturate [46]. However, for wavelengths larger than 1300 nm (band 8 and band 9 of OLI), the pure water absorption is too large and no leaving-water signal can be received even for the most turbid waters, thus, shorter SWIR (950–1150 nm) bands are important to derive SPM in extremely turbid waters [47]. The band 8 and band 9 of OLI are 1609 and 2201 nm, respectively. Thus, the band 865 nm is possibly the most suitable band of OLI to retrieve SPM at HB.
Correlation analysis indicated that there was a significant correlation between the OLI-derived SPM and the “in-situ” SPM measurements at HL and TL (${R^2}$>0.90; p < 0.001, Figs. 3(a) and 3(b)). The robust correlation between ${R_{rs}}({red} )$ and the “in-situ” SPM measurements was similar to the findings of numerous previous studies [28,29,41]. However, for the extremely turbid HB, band 865 nm had the best performance among the OLI bands (${R^2}$>0.70; p < 0.001, Fig. 3(c)) which was suggested by previous studies [26]. The development and validation results of the SPM models are shown in Fig. 4. The developed SPM models based on the OLI derived ${R_{rs}}$ data are written as:
Fig. 4. Calibration of ${R_{rs}}$-based SPM models (a, d, g) and DN-based SPM models (b, e, h), and validation (c, f, i) for estimating SPM in turbid HL, TL, and HB. ${R_{rs}}$ was derived from the OLI data using RC-AC.
Consistency was also found in the spatial distributions between “in-situ” SPM measurements and SPM estimations from the OLI using DN-based SPM models (Fig. 5), except for the SPM in the red frame (Fig. 5(j)). SPM in the central-eastern part of HL and the southern part of TL are higher, and both lakes have a high dynamic SPM range (0–100 mg/L for HL and 0–300 mg/L for TL). However, in the red frame of Fig. 5(j), the SPM retrieval and UV-AC failed. One of the basic assumptions of UV-AC is that the ${L_w}$ at UV wavelengths is neglected compared to that at longer wavelengths. In turbid waters, the ${L_w}$ at the UV bands may be much less than that at the NIR bands, however, it can still not be neglected in some cases.
Fig. 5. Maps of “in-situ” SPM values (b, f, j) and estimated SPM values from DN-based SPM models using OLI (d, h, l) at HL, TL, and HB. The first bands of the selected satellite images are displayed in panels a, c, e, g, i, and k. Unusual SPM retrievals are shown in the red frame.
4.3 Validation and application for Gaofen-1/WFV
The Gaofen-1 satellites include four high-resolution (16 m) WFV cameras. Images from these cameras can be used for many purposes, from evidence in criminal cases to real-time monitoring of natural disasters [48]. Imagery from these high-resolution sensors is of great interest to the monitoring of inland/coastal water bodies [35]. Due to the lack of onboard calibrators on the Gaofen-1 satellites, it is naturally valuable to implement the DN-based SPM models to WFV images, because those models don’t require highly accurate RC coefficients.
The DN-based SPM models were only applied to the WFV images for HL and TL because WFV only has blue (450–520 nm), green (520–590 nm), red (630–690 nm) and NIR (770–890 nm) bands, which makes the model unsuitable for images of the extremely turbid HB water body (Fig. 4(i)). WFV1 and VIIRS images were downloaded on 2015/12/07 for model development at HL, and WFV2 and MODIS data were required on 2013/12/12 to establish the DN-based SPM model using WFV. RC-AC was performed on these images. The models and their statistical parameters are summarized in Table 3. Overall, the models were reasonable with the R2 larger than 0.60 and the RMSE/Range less than 12%.
Table 3. DN-based SPM models for WFV images at HL and TL. Note ${{\boldsymbol \rho }_{\boldsymbol r}}$ represents the Rayleigh scattering reflectance.
The WFV SPM models were then validated with SPM derived from OLI. Figure 6 shows the comparison of WFV1 and OLI SPM maps at HL, and WFV2 and OLI SPM maps at TL. Clearly, the retrieved SPM maps of WFV agreed well with OLI-derived SPM maps. Generally, the relative biases between the WFV and OLI SPM products are less than 20% in the center of the lakes (Figs. 6(c) and 6(g)), while larger biases occur in the near land pixels which might be caused by the adjacent effects [49].
Fig. 6. The SPM maps of OLI (a, e) and WFV (b, f), the biases (c, g) and statistical results (d, h) between them at HL and TL, respectively.
Statistical analysis performed between retrieved SPM from WFV and OLI yielded R2 values of 0.98 and 0.80, and RMSE values of 13.14 mg/L and 17.46 mg/L at HL and TL, respectively. Because the two-day time difference between the WFV and OLI SPM products may introduce more potential uncertainties, the WFV and OLI SPM retrievals are more consistent at HL. However, the WFV1-derived SPM map is relatively higher than that derived by the OLI at east-central HL. The slope of the regression analysis (Fig. 6(d)) is 0.99, while the offset is 14.49 which means the WFV1-derived SPM data are about 14 mg/L higher than the OLI-derived SPM data. This might be caused by the differences in the SPM model. The SPM at east-central HL ranged from approximately 80 mg/L to 100 mg/L, indicating that the offset only results in <20% biases (Fig. 6(c)). Overall, the performance of WFV is comparable to that of OLI, and with a higher spatial resolution (16 m), WFV has the potential to perform better in SPM retrievals, such as resolving the fine structures of SPM in the inland/coastal regions and monitoring the SPM distribution in small lakes and rivers.
To further validate the coupled approach, SPM derived from WFV using DN-based SPM models and traditional reflectance-based SPM models were compared. Figure 7 shows the statistical comparisons of SPM at HL and TL, as well as the bias histograms. The RMSE and APD of DN-based models are similar to those of reflectance-based models (Figs. 7(a) and 7(c)). A larger number of pixels of SPM from DN-based models are within small biases when compared with OLI SPM data (the red area in Figs. 7(b) and 7(d)). Overall, the performance of the DN-based SPM model is comparable to that of the reflectance-based SPM model.
Fig. 7. Statistical results between OLI and WFV SPMs derived from the reflectance-based and DN-based model (a, c), and the biases between them (b, d) at HL and TL, respectively.
5. Discussion
In this section, the impacts of RC, AC, and imaging geometry on the SPM models are analyzed, and the potential for near-real-time RC and SPM retrieval based on the DN-based models is also discussed.
The reflectance-based and DN-based SPM model using band single exponential model and RC-AC can be written as:
Based on the Eq. (15), some analysis was conducted: (1) in the analysis of impacts of RC coefficients, Gaussian-distributed random noises are added to ${L_{TOA}}$ which means ${L_{TOA}}$ is replaced with ${L_{TOA}} + {\delta _{TOA}}\ast {L_{TOA}}$. ${\delta _{TOA}}$ was set from 0% to 100% with an interval of 1% to represent the uncertainties of RC coefficients; (2) in the analysis of impacts of AC uncertainties, Gaussian-distributed random noises are added to ${L_{RC}}$ which means ${L_{RC}}$ is replaced with ${L_{RC}} + {\delta _{RC}}\ast {L_{RC}}$. ${\delta _{RC}}$ was set from 0% to 200% with an interval of 1% to represent the uncertainties of AC; (3) in the analysis of impacts of imaging geometry, SZA-VZA-SAA-VAA at each pixel instead of at the central pixel was used; (4) ${p_3}$ and ${p_4}$ corresponding to different uncertainties were analyzed to explore the potential for near-real-time RC and SPM retrieval.
5.1 Impacts of unreliable RC coefficients on reflectance-based SPM models
Reflectance-based SPM models require highly accurate RC coefficients. To better understand the impacts that RC coefficients have on the performance of the SPM models, the Gaussian-distributed random noises, from 0% to 100% with an interval of 1%, were added to OLI RC coefficients. Figure 8 shows the R2, APD and URMSE variations of the reflectance-based SPM models at HL, TL, and HB. Because the SPM models are exponential, R2 decreases exponentially as the noises of RC coefficients increases. Thus, for exponent SPM models, the accuracy might be greatly affected by the precision of the RC coefficients. Additionally, a coefficient noise of only 10% results in a nearly two-fold increase in APD. However, the URMSE increases at a much slower rate because the noises on RC coefficients are Gaussian-distributed. RC coefficients are crucial to reflectance-based SPM models, and ideally, they should be as accurate as possible to minimize SPM uncertainties. In this respect, there is a distinct advantage to use DN-based SPM models because they consider RC coefficients as model parameters that have been embedded in the SPM models.
5.2 Impacts of AC on reflectance- and DN-based SPM models
While only reflectance-based SPM models are sensitive to the RC coefficients, both DN-based and reflectance-based SPM models are affected by the AC accuracy. To determine the influence of AC on SPM models, Gaussian-distributed random noises, from 0% to 200% with an interval of 1%, were added to the path signal contribution to the TOA signal calculated by the Acolite system. The variations of R2 and RMSE for the DN-based and reflectance-based models are plotted in Fig. 9. Both the R2 and RMSE values of DN-based SPM models are stable relative to the added AC noise, indicating that the DN-based SPM models are more robust.
Fig. 9. The influence of AC uncertainty on the DN-based and reflectance-based SPM models for (a) HL, (b) TL, and (c) HB.
However, the reflectance-based SPM models are influenced by the AC. Compared to the influence of RC coefficients, the impact of AC noises is much slighter. The R2 decreases by less than 6% with the noise of 100% added to the AC. This effect may be a consequence of the fact that we used visual examinations to ensure that aerosol concentrations in the images were low and that only the Rayleigh scattering signal would need to be removed.
Overall, the performance of DN-based SPM models is more stable than that of reflectance-based SPM models because the DN-based models treat the RC coefficients as unknown items. Conversely, with two more parameters to be determined, DN-based SPM models are a little more difficult to develop. However, with enough matched points (Table 3), the accuracy of the calculation to four parameters is nearly the same as that of the calculation for two parameters. Thus, DN-based SPM models are better than reflectance-based models in terms of robustness.
5.3 Impacts of single image angle pair on SPM models
The metadata of both OLI and WFV images only contain a single SZA-VZA-SAA-VAA for the whole image; however, ocean color sensors such as MODIS, VIIRS, and GOCI provide each pixel with an SZA-VZA-SAA-VAA. Thus, it is necessary to analyze the influence of single SZA-VZA-SAA-VAA for a whole image when OLI or WFV is used for ocean color applications such as retrieving SPM [25].
To provide additional information about the scene geometry for some applications, USGS/NASA hosts Landsat Angles Creation Tools in a LINUX environment, that can generate angles for each pixel of each band in OLI images (https://landsat.usgs.gov/sites/default/files/documents/L8_ANGLES_2_7_0.tgz). Thus, the difference between using single SZA-VZA-SAA-VAA for a whole image and using different SZA-VZA-SAA-VAAs for varied pixels are analyzed by comparisons of derived surface reflectance using the 6S model. According to 6S model manuals (http://6s.ltdri.org/pages/manual.html), the TOA radiance can be converted to atmospherically-corrected surface reflectance (acr) by:
The imaging angles of OLI pixels over HL, TL, and HB are listed in Table 4, including the maximum, minimum, mean, and STD of SZA-VZA-SAA-VAA angles. The input ${L_{TOA}}$ and output of 6S model for HL, TL and HB are summarized in Table 5.
Table 4. Statistics of the imaging geometries of pixels for the OLI images at HL, TL, and HB.
Table 5. Input ${{\boldsymbol L}_{{\boldsymbol TOA}}}$ and output of 6S model with angles for each pixel.
Clearly, the SZA and SAA over a small region like HL, TL, and HB change little, and the STDs are smaller than 0.5%, indicating the position of the sun is stable during the imaging period. However, the VZA and VAA vary a lot, particularly the VAA, which is influenced by the imaging method. More details on solar illumination and sensor viewing angle for OLI can be found on the Landsat website (https://www.usgs.gov/land-resources/nli/landsat/solar-illumination-and-sensor-viewing-angle-coefficient-files).
The coefficients of variations (CVs) of $xa$, $xb$, and $xc$ at the three water bodies are less than 0.3%, which result in surface reflectance uncertainties of 0.10%, 0.09%, and 0.08% and biases of 1.6%, 1.3%, and 2.8% in SPM products for HL, TL, and HB, respectively. The uncertainties induced by the single image angles are negligible compared to the uncertainties of RC and AC [51]. Thus, for sensors with a small coverage, like OLI and WFV, the SZA-VZA-SAA-VAA at the center pixel can be used for the whole image.
5.4 Potential for near-real-time RC and SPM retrieval
The DN-based SPM models consider RC coefficients as unknown parameters; thus, it is possible to derive the RC coefficients in the process of developing SPM models. The official and derived RC coefficients of OLI are listed in Table 6. The biases between the official and derived gain coefficients are less than 3%, while the biases of the offset coefficients are about 10%. Overall, the derived RC coefficients are quite closed to the official RC coefficients, indicating that DN-based SPM models have the potential to calibrate satellite sensors and retrieve SPM in real-time.
Table 6. The official RC coefficients of OLI and the estimated RC coefficients in the DN-based SPM models.
If the AC is accurate and the OLI is well-calibrated, biases of RC coefficients are mainly caused by errors in the “in-situ” SPM measurements. Those biases can be considered as the “inherent” uncertainty of the DN-based SPM model. If assuming the “in-situ” SPM measurements are error-free, the AC is the only source of uncertainty. The influence of uncertainty of AC on the model-derived RC coefficients at HL, TL, and HB is plotted in Fig. 10. Obviously, the bias of the RC coefficient increases as the AC uncertainty increases. An AC uncertainty of 100% induces gain RC coefficient variations of 2%, 5% and 0.4% for HL, TL, and HB, respectively. The variations caused by AC uncertainty is greater at HL and TL, potentially because the atmospheric contribution to the TOA signal is smaller at the two lakes than it is for HB. The ${L_w}$ at more turbid waters in HB is stronger, and the atmospheric contribution to the TOA signal at HB is less significant.
Fig. 10. The influence of the AC uncertainty on model-derived RC coefficients at (a) HL, (b) TL, and (c) HB.
Biases introduced by the SPM models are comparable to that induced by a 100% AC error, thus, in-situ SPM measurements used to develop SPM models should be heavily scrutinized for accuracy and robustness. AC also plays a significant role in the SPM models and should be calculated as accurately as possible. Fortunately, these uncertainties are reflected in the biases of the RC coefficients, which means that smaller biases of derived RC coefficients indicate that both in-situ SPM measurements and AC are more accurate. The derived RC coefficients can then be used as a benchmark to evaluate the accuracy of all the procedures needed to develop an SPM model.
6. Conclusions
A novel method for retrieving SPM has been proposed in this study to reduce the dependence on the RC coefficients, and to improve the robustness of the SPM retrievals. The method is different from the prior reflectance-based approaches, which require accurate RC coefficients. By coupling the processes of retrieving SPM and RC, the uncertainties of the SPM models are reduced. There are several findings from the developments of the DN-based SPM models for turbid and extremely turbid inland/coastal waters, which have significant implications for SPM retrievals.
Firstly, as ${\textrm{C}_{SPM}}$ increases, the band most sensitive to SPM shifts to longer wavelengths, which makes shorter SWIR bands important for retrieving SPM in extremely turbid waters. Secondly, the DN-based SPM models can fold the AC uncertainties into the uncertainties of derived RC coefficients, which is rarely probed in previous studies. Thirdly, the performance of exponential SPM models decreases exponentially as the uncertainty of RC coefficients increases, indicating that SPM models should be selected carefully. Furthermore, the biases between the derived RC coefficients and the actual RC coefficients can be considered as a set of benchmarks that can determine whether the SPM model is good. In addition, for high-resolution land sensors with limited scene coverage, it is reasonable to use a single angle pair for the whole image.
However, the spatial resolution issue should be addressed between the “in-situ” measurements and satellite images, because the pseudo-field SPM data from MODIS, VIIRS, or GOCI are coarser than the satellite data from OLI of WFV. Whether the established SPM models with a low spatial resolution can be directly applied to satellite images with a high spatial resolution needs more investigations.
Overall, the current study demonstrates the great potential of the Chinese Gaofen series sensors in ocean color remote sensing applications, and DN-based SPM models in maintaining accurate and consistent SPM products for various sensors. The concept of coupling the RC and retrieval processes can be adopted as a regular strategy to obtain water quality parameters from DN values directly.
Funding
National Key Research and Development Program of China (2018YFB0504900, 2018YFB0504904); National Natural Science Foundation of China (41571344, 41701379).
Acknowledgments
The authors would like to thank the USGS for providing the Landsat-8 OLI data and Landsat Angles Creation Tools, the NASA for providing the MODIS and VIIRS data, the KOSC for providing the GOCI data, the CCRSDA for providing Gaofen-1/WFV data, and the RBINS for providing the ACOLITE software. We also thank the anonymous reviewers for their valuable comments on this work.
Disclosures
The authors declare no conflicts of interest.
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