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Abstract
For coastal waters, the radiation signals received by the sensor are affected by the high reflectance of the coastal land, inducing reduced image contrast and significant adjacency effect. Eliminate the atmospheric attenuation and adjacency effect, and obtain the accurate remote sensing reflectance above water surface is an important prerequisite for the quantitative water color remote sensing. Based on the in situ spectral data of the coastal Hangzhou Bay, China on July 23, 2017 and the Taihu Lake, China on April 29, 2016, as well as the synchronous Gaofen-1 wide field-of-view camera (GF-1/ WFV) images, the 6S model was used to eliminate the atmospheric attenuation, and a point spread kernel function was used to correct the adjacency effect. The experimental results show that the images after adjacency effect correction are clearer, with increased image contrast and more abundant information of the water body. Compared to the atmospheric correction results only after the 6S model, the average relative errors of three in situ synchronous samples in Hangzhou Bay after adjacency effect correction are reduced by 8.39%, 10.81% and 7.29%, and that in Taihu Lake after adjacency effect correction are reduced by 10.8%, 5.24% and 0.39%, respectively. The adjacency effect correction improves the radiation detection accuracy of the remote sensing reflectance above water surface and can be a reference for quantitative water color remote sensing in coastal waters.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
For the quantitative inversion of water color parameters using remote sensing images, the radiation signals received by the sensor include atmospheric path radiation, water-leaving reflectance, and cross radiation of surrounding background pixels, that is, adjacency effect [1]. The adjacency effect will blur the edges of features in remote sensing images and reduce the image contrast. The effective water-leaving radiation signal received by the sensor only accounts for about 10% of the total radiance at the top of the atmosphere [2]. Therefore, eliminating the atmosphere interference and adjacency effects effectively is very important to the quantitative inversion of water color parameters by remote sensing [3].
In recent decades, a lot of researches have focused on the adjacency effect in satellite observation of land information, resulting in many atmospheric correction models that consider the influence of adjacent pixels [4–6]. However, most of these studies focus on terrestrial areas, and few have specifically addressed the adjacency effect of coastal waters [7–8]. For coastal waters, in addition to the radiation attenuation caused by atmospheric absorption and scattering, the adjacent land, especially the high reflectance of urban surface, has a significant impact on the coastal water pixels with low reflectance (adjacency effect) [9]. Santer [7] used 5S code to simulate a circular dark target (lake water, the reflectance is 0) with a radius of 20 km surrounded by reflecting surface with 30% reflectance, and found that the reflectance deviation of the center position was about 0.15%, and the deviation increased to 2.31% at the edge. If the radius of the circular lake is 5 km, the adjacency effect of the background reflection on the central pixel of the circular lake is about 50%. Odermatt [10] believed that the adjacency effect led to a significant increase in the aerosol optical depth of coastal water pixels at 550 nm, which in turn affected the inversion effect of water quality in Constance rivers based on MERIS data. The simulation results of Bulgarelli [8] show that the radiation of water pixels detected by the ocean color sensors in the range of several kilometers from the shore is affected by a very significant adjacency effect in both the visible and near-infrared bands. The influencing factors were analyzed and results found that when the difference between the reflectance of the target and the reflectance of adjacent pixels is large, that is, the aerosol optical thickness is large, the symmetry of the scattering phase function is strong, and the apparent reflectance of the satellite sensor is more sensitive to the reflectance of adjacent pixels, the adjacency effect is more obvious and the range of the effect will expand to tens of kilometers [1].
Besides, different from the open ocean, the coastal waters have small spatial scales and obvious spatial differences in water quality, and therefore the remote sensing images of medium and high-resolution are required in water color remote sensing [11]. With the popularization of the application of high-resolution remote sensing images in water color remote sensing, a large number of atmospheric correction algorithms have been proposed for water color remote sensing with high-resolution images [12–15], but these algorithms seldom consider the influence of adjacency effect. With the increasing resolution of the remote sensing images, the problem of mixed pixel within one pixel has been gradually transformed into the problem of adjacency effect between pixels. Compared to the remote sensing images with medium or low spatial resolution, the atmospheric correction of high-resolution images is more likely to be affected by the adjacency effect [16]. Kaufman [5] shows that the influence of adjacency effect is inseparable from the sensor resolution, when the spatial resolution of the sensor is smaller than the scale height of atmospheric molecules and aerosols, the influence of adjacency effect cannot be ignored and it is an important factor that needs to be considered for accurate quantitative remote sensing. Lyapustin [17] points out that the influence of adjacency effect should be fully considered when performing atmospheric correction on remote sensing images with sub-satellite point resolution higher than 1 km, and the adjacency effect is becoming more and more prominent with the increasing resolution of the sub-satellite point. Previous research also shows that the smaller the pixel scale is, the more significant the adjacency effect is [18], so the adjacency effect in addition to the atmospheric correction of high-resolution images should be especially considered [4,17].
Therefore, the problem of adjacency effect should be especially considered when the high-resolution images are used for the remote sensing inversion of water quality parameters in coastal waters. Based on the Gaofen-1 wide field-of-view camera (GF-1/WFV) images and the synchronously measured in situ spectra on July 23, 2017, in Hangzhou Bay and April 29, 2016, in Taihu Lake, the atmospheric attenuation was firstly removed by the 6S model [19], and the adjacency effect was then corrected by using the kernel function as the atmospheric point spread function. Finally, the results after adjacency effect correction were compared with the remote sensing reflectance of the in situ spectra of measured samples, in order to analyze the effect of the adjacency effect correction on the radiation detection accuracy of the high-resolution images in coastal waters.
2. Research area and data
Hangzhou Bay is located in the northeast of Zhejiang Province and the south of Shanghai, with the East China Sea in the east and the Qiantang River in the west. Hangzhou Bay is 90 km long from east to west, 100 km wide at the bay mouth, and about 21 km wide at the top of the bay. It is a trumpet-shaped estuary that runs from east to west (Fig. 1), with an average water depth of about 10 m and a total water area of about 5,000 km2. Under the combined influence of the southward flow of the Yangtze Estuary, the runoff of the Qiantang River, and the tidal waves of the East China Sea, Hangzhou Bay is characterized by strong tidal currents and high suspended sediment content [20,21]. In this paper, the Ganpu section of Hangzhou Bay is taken as the research area. Field experiment was carried out in Hangzhou Bay on July 23, 2017. There are 3 sample points that are quasi-synchronous with the transit of GF1/WFV. The scope of the study area and the distribution of 3 sample points are shown in Fig. 1.
Fig. 1. In situ synchronous samples and GF-1/WFV image (with RGB composite of 4,3,2) of the Hangzhou Bay
Taihu Lake is located in the south of the Yangtze River Delta, which is the third largest freshwater lake in China (Fig. 2). The cities along the Taihu Lake are densely populated, and the long-term high-intensity development has led to the deterioration of the ecological environment in this area. In the highly developed northwest Taihu Lake area with plain river network, the industrial pollution and water environment problem is increasingly serious [22]. The northwest of Taihu Lake was taken as the research area. Field experiment was carried out in Taihu Lake on April 29, 2016, and the 3 sampling points quasi-synchronous with the transit of GF1/WFV image are shown in Fig. 2.
Fig. 2. In situ synchronous samples and GF-1/WFV image (with RGB composite of 4,3,2) of the Taihu Lake
The hyperspectral reflectance above the water surface was measured by the ASD Field Spectroradiometer (Analytical Spectral Devices Inc., Boulder, CO, USA) with 512 bands from 350 nm to 1050 nm and increments of 1.5 nm. During the spectral measurement, this instrument was positioned at 0.5 m to 1 m high above the water surface, in a specific viewing geometry to avoid the effects of direct solar radiation and prevent the ship from interfering with the water surface [23]. The water and sky were repeatedly measured ten times, and the median value of which was selected to calculate the remote sensing reflectance. The spectra with wavelengths shorter than 400 nm or longer than 900 nm were discarded owing to the spectral noise [24]. Using the spectral response function of GF-1/WFV (from the website of China Resources Satellite Application Center), the equivalent remote sensing reflectance of each band of WFV was simulated and calculated using the in situ spectral reflectance.
The WFV imaging system onboard the Chinese GF-1 optical satellite with technical specifications shown in Table 1 was used in this study. The GF-1/WFV images of the Hangzhou Bay on July 23, 2017 and Taihu Lake on April 29, 2016 synchronous with the field experiment were obtained, and the transit time of the satellites were at 11:04 and 11:26 Beijing time, respectively. The images are of good quality, and they were geometrically corrected with precision within 1 pixel based on the topographic maps of the study areas. The corrected images were clipped to cover the measured sample points (Fig. 1 and Fig. 2).
Table 1. Technical specifications of GF-1/ WFV image
3. Algorithm theory
3.1 Calculation of TOA
The GF-1/WFV image was firstly calibrated according to the radiation calibration Formula 1, where L(λ) is the converted radiance, Gain is the band gain, digital number value (DN) is the satellite load observation value, and Offset is the offset. The gain and bias parameters of the WFV camera can be obtained from the website of China Resources Satellite Application Center.
The apparent reflectance (atmospheric top reflectance) ${\rho _{TOA}}$ was calculated based on the calibrated radiance according to the Formula 2, in which L is the radiance, d is the relative distance between the sun and the earth, θs is the solar zenith angle and Eλ is the band average solar radiation value. The d value varies slightly with the date and was set to 1 in this study. The Eλ can be calculated based on the spectral response function of the WFV sensor and the solar spectral function of the corresponding spectral interval.
3.2 Removal of the atmospheric attenuation
Assuming an ideal ground-atmosphere radiative transfer case, that is, the land surface is homogeneous and Lambertian, the temperature and composition of the atmosphere are horizontally uniform with only vertically changes, ignoring adjacency effects and multiple ground-air bounces, the apparent reflectance of the top of the atmosphere received by the satellite sensor can be expressed as Formula 3.
In Formula 3, ${\rho _{TOA}}$ is the reflectance at the top of the atmosphere, S is the downward hemispherical albedo of the atmosphere, Lp is the atmospheric path radiation, $T({\theta _s})$ and $T({\theta _v})$ are the atmospheric transmittance in the sun incidence direction and the observation direction, and ${\rho}^{\ast}$ is the surface reflectance.
The radiance reaching the ground target is reflected by the surface and then attenuated by the atmosphere before entering the sensor. Therefore, the difference between the reflectance at the top of the atmosphere ${\rho _{TOA}}$ and the surface reflectance ${\rho}^{\ast}$ can be regarded as the effect of atmospheric attenuation.
The 6S model (Second Simulation of the Satellite Signal in the Solar Spectrum) is an improved version developed by Vermote et al. [19]. on the basis of the 5S model, which is a highly developed and commonly used atmospheric correction model. When entering some satellite and atmospheric parameters, it can simulate the atmospheric radiative transfer process. In formula 3, the parameters related to the atmosphere such as S, Lp, $T({\theta _s})$ and $T({\theta _v})$ can be calculated after solving the 6S radiative transfer equation, and then the surface reflectance ${\rho}^{\ast}$ was calculated using MATLAB.
The input parameters of the 6S model are shown in Table 2. It is proved that all the input parameters except for aerosol models have little effect to the atmospheric correction results [25], therefore some uniform parameters were set for both images. The observation geometry comes from the satellite’s own parameters. The Midlatitude Summer (MLS) atmospheric model was used for Hangzhou Bay image according to the image date and latitude. The customized atmospheric model with experience value of H2O-vapor and O3 content was used for the Taihu Lake image [25]. Using the altitude and spectral condition settings of the GF-1/WFV sensor, it is assumed that the ground surface is Lambertian uniform surface and the ground feature type is lake water.
Table 2. The input parameters for 6S model
The aerosol models including the aerosol types and concentrations have big effect to the atmospheric correction results [26]. There are seven default aerosol types in 6S model, and the continental aerosol model were used for both images. As to the aerosol concentration, the visibility of 40 km was used for the Hangzhou Bay image and the aerosol optical depth (AOD) at 550 nm was used for the Taihu Lake. Since the AOD at 550 nm cannot be directly obtained from AERONET, the AOD values at 440 nm, 500 nm, 675 nm, and 870 nm provided by AERONET were used to perform binomial fitting, and the AOD at 550 nm was obtained by interpolation [25].
3.3 Adjacency effect correction
Considering the interference of the adjacency effect of the background pixels, the surface reflectance ${\rho}^{\ast}$ calculated above is the combined radiation of the target pixel and the background pixel. The contribution of background pixels can be calculated from the convolution of the reflectance of background pixels and the atmospheric point spread function. At present, the commonly used methods for calculating the atmospheric point spread functions include Monte Carlo simulation [27], analytical equation approximation [28,29], artificial neural network simulation [30] and etc. The Monte Carlo simulation is much more complicated, because it is based on a large number of statistical results and the accuracy is related to the number of calculations [31]. A simple kernel function in Formula 4 was directly used in this study to express the atmospheric point spread function [6].
In Formula 4, the $\xi$ and $\eta$ are the point positions, $H(\xi ,\eta )$ is the point spread kernel function, and $\int\limits_{ - \infty }^{ + \infty } {\int\limits_{ - \infty }^{ + \infty } {H(\xi ,\eta )} } {d_\xi }{d_\eta } = 1$; R represents the distance from the background pixel to the target pixel, and $R = \sqrt {{\xi ^2} + {\eta ^2}}$. If the discrete form of the pixels is considered, the relationship between ${\rho}^{\ast}$ and the true surface reflectance ρ can be expressed as Formula 5 [6].
In Formula 5, ${t_d}({\theta _v})$ is the atmospheric diffuse transmittance function in the viewing direction, which can be calculated from $T({\theta _v})$, with $T({\theta _v}) = {t_d}({\theta _v}) + {e^{ - \tau ({\theta _v})/\cos ({\theta _v})}}$ and $\tau ({\theta _v})$ is the atmospheric optical depth corresponding to the vertical direction. $r = a \cdot \sqrt {{i^2} + {j^2}}$, and a is the pixel size, with the unit of km. x and y are the pixel coordinates. N is the window radius indicating the influence range of the adjacency effect, and it was set to 20 pixels in this study.
4. Results and discussion
4.1 Image changes before and after correction
Comparing the false color images (with RGB composite of 4,3,2) before and after the adjacency effect correction (Fig. 3(a) and (e) for Hangzhou Bay and Fig. 3(c) and (g) for Taihu Lake), it can be seen that the remote sensing images after the adjacency effect correction are clearer, the boundary of the coastal water body is clear, and the images can reflect more surface features. The grayscale images at the near-infrared band (B4) before and after the adjacency effect correction was also compared (Fig. 3(b) and (f) for Hangzhou Bay and Fig. 3(d) and (h) for Taihu Lake), the water surface texture in the image after the adjacency effect correction is more abundant, the contrast of the coastal water and land is improved, and the information amount of water body is more abundant.
The information entropy (entropy) was used to test the image contrast before and after adjacency effect correction [32]. The entropy is a concept used in information theory to measure the amount of information in a system. It is the sum of the probability of information occurrence and expressed in Formula 6.
In Formula 6, H is the entropy, ${P_i}$ represents the occurrence probability of pixels with DN of i, and $\max$ is the maximum DN value when it was used to calculate the entropy of an image. The more gray values of the image, the more uniform the distribution, the larger the H value, and vice versa.
The information entropy results of images before and after correction are shown in Table 3. It can be seen that the calculated entropy values of all bands are larger in images after correction, implying that the images after adjacency effect correction have bigger amount of information, the image textures are more abundant, and more ground feature information can be identified.
Table 3. Information entropy values of images before and after adjacency effect correction
4.2 Spectral changes before and after correction
Draw the spectral profiles of several points along the coast of Hangzhou Bay (shown by the red line in Fig. 3(a)) and Taihu Lake (shown by the green line in Fig.3(c)), and compare the changes in pixel spectral reflectance before and after adjacency effect correction in the blue band (B1) and near-infrared band (B4) (Fig. 4). It can be seen that after the correction of the adjacency effect, the reflectance of the pixels with high reflectance is increased, while the reflectance of the pixels with low reflectance is reduced. The spectral contrast is enhanced and the expressed detail information of image features is more abundant.
Fig. 4. Spatial profiles of reflectance for band B1 and B4 before and after adjacency effect correction (a) and (b) is for Hangzhou Bay, and (c) and (d) is for Taihu Lake
Using the sample points in the Hangzhou Bay and Taihu Lake synchronously measured during the WFV image transit time, the in situ remote sensing reflectance, the reflectance after correction by the 6S model, and the reflectance after correction by the adjacency effect were compared, with results shown in Fig. 5 and Fig. 6. Overall, the remote sensing reflectance after the adjacency effect correction was more closer to the in situ spectra compared to the results only after 6S model.
Fig. 5. Spectral reflectance before and after adjacency effect correction of in situ synchronous samples in Hangzhou Bay
Fig. 6. Spectral reflectance before and after adjacency effect correction of in situ synchronous samples in Taihu Lake
As to Hangzhou Bay, it can be seen that after the adjacency effect correction, the spectra of all four bands of sample A are decreased, which are closer to the measured spectra. There is little difference in the spectral reflectance in the blue and green bands before and after the adjacency effect correction of sample B and C, but the spectral reflectance after the adjacency effect correction in the red and near-infrared bands are much closer to the measured spectra. The relative errors after 6S correction of sample A, B, C are 22.54%, 41.05%, 35.46%, and that after adjacency effect correction is 14.16%, 30.24%, 28.16%, respectively. Compared with the 6S correction results, the average relative errors of the three samples were reduced by 8.39%, 10.81% and 7.29% respectively after the adjacency effect correction.
As to Taihu Lake, the spectra of all four bands at the sample point A after the adjacency effect correction are closer to the measured spectra compared to that by 6S. The spectra are nearly the same by both two correction methods at sample B and C, but the spectra in R and NIR bands are decreased after the adjacency effect correction, which are closer to the measured spectra. The average relative errors of the three samples were also reduced by 10.8%, 5.24% and 10.39%, respectively after the adjacency effect correction compared with the 6S correction results.
4.3 Adjacency effect correction
The adjacency effect correction significantly improved the image contrast compared with the 6S atmospheric correction results (Fig. 3, Fig. 4). When retrieving the radiation signals of coastal water bodies by sensors, the combined effect of water vapor, molecules, and aerosols in the atmosphere reduces atmospheric transparency, and the high background reflectance of coastal land interferes with water body radiation signals. The distribution range of the remote sensing reflectance above water surface retrieved by satellite is narrower than that of the actual reflectance, and the image contrast is also decreased. In the images after adjacency effect correction, the real reflectance of the features is restored, the brightness and clarity of the image are increased, the image textures are more abundant, and more water body information can be identified.
Besides, the obtained remote sensing reflectance after adjacency effect correction is more accurate in coastal waters compared with the 6S atmospheric correction results (Fig. 5, Fig. 6). The adjacency effect problem is solved using surface environmental factors in the 6S radiative transfer model, but the diffuse reflection effect on the horizontally non-uniform surface needs to be known in actual calculation and it is generally unknown [28]. The subsequent adjacency effect correction in this study significantly improves the accuracy of the remote sensing reflectance in coastal waters, reducing the deviation between the inverted pixel reflectance and the in situ spectra, which can be applied in the remote sensing inversion of water quality parameters in coastal waters.
Our results also show that the adjacency effect correction has greater improvement of the detection accuracy of remote sensing reflectance on the water body pixels closer to the shore. As to Hangzhou Bay, the distances from the three sample points to the shore are 12 km, 8.7 km, and 11.8 km, respectively. Among them, the sample point B is nearest from the shore, and its accuracy improvement by adjacency effect correction is greater than the other two samples. As to Taihu Lake, the distances from the three samples A, B, C to the shore are 3.5 km, 4.5 km, and 0.5 km, respectively, and point B is the farthest from the shore. The accuracy improvements of the adjacency effect correction at points A and C are more obvious. However, although point C is the closest to the shore, its accuracy improvement (with the average relative errors of 58.54% and 48.15% before and after adjacency effect correction) was still slightly lower than that of point A (with errors of 29.55% and 18.76%) due to the algae in water during sampling. Our results illustrate that the adjacency effect may not be neglected for the coastal pixels, even for pixels at distance larger than 10 km from the shore. Previous simulation results also show that the influence of the adjacency effect of coastal land on water pixels can generally reach several kilometers [8].
From the adjacency effect correction results in Fig. 5 and Fig. 6, we can see that there is a significant accuracy improvement of the remote sensing reflectance in NIR band compared to other bands. But the correction performance after both the 6S and adjacency effect correction in the blue band (see Fig. 5(a b c)) and green band (see Fig. 6(b) and (c)) are poor. The contrast between land and water is weak and the water pixels are more easily contaminated by the adjacency effect in this wavelength area [33]. Santer [34] also found that the applied adjacency correction strongly decreases the water-leaving reflectance values in the NIR and only a slight decrease can be observed for the visible bands.
There are many researches about the PSF in the adjacency effect correction in coastal waters with medium or high-resolution images, such as the SIMEC model [33,35], the Monte Carlo simulated PSF [8–37], the simulated PSF by single scattering approximate solution [7,38]. However, these studies mainly focus on theoretical simulations and experimental tests [39–41], and few of them can be actually applied to specific satellite images [28,33]. The adjacency effect correction method based on the kernel PSF proposed in this study is simple, and performs good on the GF1/WFV image. The more application of this method on satellite images and its influence on the remote sensing inversion of water color parameters in coastal waters will be discussed in the future.
5. Conclusion
The 6S radiative transfer model was used to remove atmospheric attenuation, the kernel function was used to express the atmospheric point spread function, and the adjacency effect correction was performed on the GF-1/WFV images covering the coastal waters of Hangzhou Bay and Taihu Lake. The results show that after the correction of the adjacency effect, the high-resolution image has an enhanced image contrast and can reflect more abundant feature information. Compared with the atmospheric correction results only using 6S model, the remote sensing reflectance after the adjacency effect correction is closer to the in situ spectral reflectance of the synchronously sampled points, with average relative errors reduced by 8.39%, 10.81% and 7.29% for three samples in Hangzhou Bay and by 8.39%, 10.81% and 7.29% for three samples in Taihu Lake. The adjacency effect correction must be considered in the atmospheric correction of high-resolution images, and the removal of adjacency effect is of great significance for the radiation detection and the remote sensing inversion of water quality parameters of high-resolution images in coastal waters.
The key to the correction of the adjacency effect of high-resolution images is the determination of the atmospheric point spread function. Accurately expressing the atmospheric point spread function suitable for the high-resolution image and comparing the results with the results based on Monte Carlo simulation is the key issue of promoting the adjacency effect correction accuracy. Future research will further analyze and determine the atmospheric point spread function for high-resolution images facing coastal waters, quantitatively evaluate the influence of adjacency effect in water color remote sensing and build a high-precision adjacency effect correction model.
Funding
Natural Science Foundation of Zhejiang Province of China (LQ21D010001).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data is available upon reasonable request to the first author.
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