SECTION I

THE ultimate objective of the application of MODIS (Moderate-Resolution Imaging Spectroradiometer) imagery over the ocean is to study the primary production, as well as its spatial and temporal variation, of the oceans on a global scale, in order to better understand the ocean's role in the global carbon cycle [1]. A required component in the estimation of primary productivity is the concentration of chlorophyll a. Estimation of the concentration of chlorophyll a from MODIS imagery requires water-leaving reflectance. Due to the relationships which connect bio-optical parameters to water-leaving reflectance, the water-leaving reflectance plays a central role in the application of ocean color imagery to the oceans, and atmospheric correction becomes a critical factor in determining the fidelity with which bio-optical parameters may be retrieved [2].

The NASA standard ocean color products have been routinely derived using the two MODIS near-infrared (NIR) bands (748 and 869 nm) for atmospheric correction [3], [4], with assumption of a black ocean in the NIR for the open ocean and modifications to account for NIR ocean contributions for productive near-shore or coastal waters [1]. For turbid waters in coastal and inland regions, however, the “clear water” assumption and its modifications are often invalid [5], [6], leading to large errors in the MODIS-derived ocean color products [7]. The “clear water” method and its modified methods fail in turbid waters due to the fact that water-leaving reflectance at NIR is not negligible, and is not only related to phytoplankton abundance, but also to suspended sediment concentration [8], [9]. This limitation is a disadvantage to MODIS measuring water-leaving reflectance over the turbid waters and curtails applications in coastal and inland areas, such as monitoring sediment transport and observing phytoplankton abundance where the two occur together.

To solve this problem, several atmospheric correction models have been developed to process satellite data when water-leaving reflectance is non-negligible at near-infrared wavelengths [5], [8], [9], [10], [11], [12]. An iterative method was also developed to correct for non-negligible water reflectance in the NIR arising from moderate to high phytoplankton abundances [5]. However, the modified “clear water” method fails in the presence of even modest quantities of suspended particle matter because NIR water-leaving reflectance is not negligible, and is not related to phytoplankton abundance [13]. Hu *et al.* [14] suggested that the aerosol type observed over adjacent (less turbid waters to the turbid water pixels) may be applied to the relevant study regions. The studies carried out by Hu *et al.* [14] revealed that the aerosol type dose not vary much over relatively small spatial scales ($\sim$50–100 km). Consequently, the adjacent method may be violated in inland lakes, because it cannot always find the suitable “clear water” for this method within the range of $<50\sim 100\ {\rm km}$. Recently, an atmospheric correction algorithm using the shortwave infrared bands (SWIR algorithm) has been demonstrated to improve ocean color products in turbid coastal waters measured by the MODIS [6], [15]. With the in situ measurements from the China east coastal region, Wang and Shi [15] demonstrated that using shortwave infrared algorithm the MODIS ocean color products may be improved in the extremely turbid waters. Unfortunately, there are some noise errors in the short-infrared-derived data mainly due to the considerably lower sensor signal-noise ratio (SNR) values for the MODIS short infrared bands, which would influence the accuracy and stability in water-leaving reflectance estimation [6], [16]. Thus, an accurate atmospheric correction algorithm for turbid waters is still under development.

In this study, a simple atmospheric correction algorithm based on a “known” empirical spectral relationship at four bands of MODIS sensor has been developed as a modification to the current MODIS atmospheric correction to estimate water-leaving reflectance from MODIS top-of-atmosphere radiometric measurements. The simple atmospheric correction algorithm (SACA) would discard the bands selected method of the “clear water” atmospheric correction algorithm. The spectral bands which have a strong empirical spectral relationship with each other would be potential selected bands for the SACA algorithm. However, the SACA algorithm would still use the aerosol and Rayleigh scattering look-up table method of the “clear water” method to extrapolate the aerosol and Rayleigh scattering from the “known” wavelength to the “unknown” wavelength.

SECTION II

China's Taihu Lake, which is located between longitudes $119^{\circ}54^{\prime}{\rm E}$ and $120^{\circ}36^{\prime}{\rm E}$, and latitudes $30^{\circ}56^{\prime}{\rm N}$ and $31^{\circ}33^{\prime}{\rm N}$, provides normal water usage for several million residents in the nearby city of Wuxi [17]. The water quality of inland freshwater lakes such as Taihu Lake is vital to local human activities and needs, and plays a critical role in the regional ecosystem, which may also impact climate changes. Taihu Lake is the third-largest inland freshwater lake in China, with an average water depth of $\sim$2 m [18]. Taihu Lake's waters are consistently highly turbid, with the exceptions of East Taihu Bay and some of the East Lake regions, where waters are often clear [19]. In addition, Taihu Lake undergoes frequent algae blooms in the spring-summer, polluting the lake water. The spring 2007 blue-green algae (Microcystis) bloom event which occurred in Taihu Lake caught the worlds' attention. Algae-polluted waters in the lake have adversely affected the lives of the several million local residents. Thus, there is an urgent need to effectively monitor and manage the water quality in Taihu Lake, and to better understand the optical, biological and ecological processes and phenomena which occur there [19].

Recent advances in optical sensor technology have provided new opportunities to study biogeochemical processes in aquatic environments at spatial and temporal scales which were not previously possible [20]. These advances allowed scientists to utilize satellite images to synoptically investigate large-scale surface features in Taihu Lake [21]. However, the water-leaving reflectance detected by satellite sensor is fairly weak. For example, the component of the measured reflectance, backscattering out of the water and transmitting to the top of the atmosphere is less than 10% in the blue band, and typically much smaller in the green and near-infrared bands [22], [23]. In order to obtain useful water-leaving information from Taihu Lake, one must remove the atmospheric absorption and scattering effects. Thus, it is necessary to perform research on atmospheric correction in this area to effectively monitor and manage water color in Taihu Lake.

In this study, the Root-Mean-Square (RMS) of the ratio of modeled-to-measured values will be used to assess the accuracy of atmospheric correction. This statistic will be referred to as RMS and is described by the following equation: TeX Source $$RMS=\sqrt{\sum\limits_{i=1}^{n}\left({x_{{\rm mod},i}-x_{obs,i}\over x_{obs,i}}\right)^{2}\over n}\times 100\%\eqno{\hbox{(1)}}$$ where, $x_{{\rm mod},i}$ is the modeled value of the $i^{\rm th}$ element, $x_{{\rm obs},i}$ is the observed value of the $i^{\rm th}$ element, and $n$ is the number of elements.

The field measurements (Fig. 1(a)) carried out from September 1 to 9, 2009 in the Yellow River Estuary, from October 14 to 15, 2010 in the Changjiang River Estuary, and from March 21 to 23 in Jiaozhou Bay, respectively, were used to construct the optimal empirical spectral relationship for the SACA algorithm. The MODIS/TERRA data on October 27, 2003 in Taihu Lake (containing 2187 pixel at 748 nm) and the MODIS/Aqua data on October 28, 2003 in Taihu Lake (containing 2228 pixel at 748 nm), respectively, were used to illuminate the work frames of the SACA algorithm. In order to evaluate the performance of the SACA model in predicting water-leaving reflectance from turbid waters, the almost simultaneously in situ measurements (Fig. 1(b)) were recorded in Taihu Lake from October 27–28, 2003.

The field measurements of the three datasets were performed from 10:00 to 14:00 local time. Taken from aboard a boat, the reflectance was measured with a spectroradiometer with 25° fiber-optic, covering the spectral range of 350 nm–2500 nm (Spectral Devices, Boulder, CO, ASD). Although data were collected in the range of 350–2500 nm, with a spectral resolution of 3 nm (full-width-at-half-maximum, FWHM) and a 1.4 nm sampling interval for the 350 nm–1050 nm spectral range [24], the data in the range of 400–900 nm, which is the wavelength generally used for water color remote sensing [25], [26], [27], were mainly used for this study. Following the ocean optics protocols for satellite ocean color sensor validation [28], various measurements (three repeated measurements in a short time) were repeated at each station in order to estimate the uncertainty (RMS values of three repeated measurements) associated with each measurement, and the average measurements (mean values of three repeated measurements) with <5% RMS at each station would be selected for model calibration and validation.

During the measurements, the tip of the optical fiber was kept directly on the water surface by means of a 3 m long, hand-held black pole. In order to effectively avoid the interference of the direct solar radiation, the optical fiber was positioned at an angle of 90–135° with the plane of the incident radiation facing away from the sun [28]. The view of the water surface was controlled between 30–45° with the aplomb direction to avoid the ship's shadow. Immediately after measuring the water radiance, the spectroradiometer was rotated upwards by 90–120° to measure skylight. The view zenith angle in this measurement was kept the same as that in measuring water radiance [29].

Water-leaving remote sensing reflectance, $R_{\rm rs}(\lambda)$ was calculated as follows: TeX Source $$\eqalignno{R_{\rm rs}(\lambda)=&\,{L_{w}(\lambda)\over E_{d}^{0+}(\lambda)}&\hbox{(2a)}\cr\rho_{\rm w}(\lambda)=&\,\pi R_{\rm rs}(\lambda)&\hbox{(2b)}}$$ where $\rho_{\rm w}(\lambda)$ is the water-leaving reflectance; $R_{\rm rs}(\lambda)$ is the water-leaving remote sensing reflectance; $L_{\rm w}(\lambda)$ is the water-leaving radiance; and $E_{d}^{0+}(\lambda)$ is the total incident irradiance of the water surface. $L_{\rm w}(\lambda)$ and $E_{d}^{0+}(\lambda)$ in (2) are further calculated as follows: TeX Source $$\eqalignno{L_{w}(\lambda)=&\,L_{sw}(\lambda)-rL_{sky}(\lambda)&\hbox{(3)}\cr E_{d}^{0+}(\lambda)=&\,{\pi L_{p}(\lambda)\over\rho_{p}(\lambda)}&\hbox{(4)}}$$ where $L_{\rm sw}(\lambda)$ denotes the total radiance received from the water surface; $L_{\rm sky}(\lambda)$ represents the diffused radiation of the sky, which contains no information of water properties and hence must be eliminated; $r$ refers to the reflectance of the skylight at the air-water interface, the value of which depends upon the solar azimuth, measurement geometry, wind speed, and surface roughness; $L_{\rm p}(\lambda)$ is the radiance of the gray plate; and $\rho_{\rm p}(\lambda)$ is the reflectance of the gray plate. In this study, $r$ is calculated with assumption of the black water body at wavelengths ranging from 1000 to 1020 nm [30] and wavelength-independent [31]. The water-leaving remote sensing reflectance calculated by (2) is shown in Fig. 1.

In order to accurately remove the influence of Rayleigh scattering and aerosol multi-scattering, the look-up table of Rayleigh and aerosol, which is included in the SeaDAS software package, and atmospheric parameters including total ozone, zonal winds speeds at 10 m above the water surface and the atmospheric pressure at mean sea level on October 27 and 28, 2003, on Taihu Lake, were collected from the official NASA website (ftp://oceans.gsfc.nasa.gov).

The total signal received by a satellite sensor at the top-of-atmosphere in a spectral band centered at a wavelength, $\lambda$, $\rho_{\rm t}(\lambda)$, is composed of several parts [1], expressed as: TeX Source $$\displaylines{\rho_{\rm t}(\!\lambda,\theta_{s},\varphi_{s},\theta_{v},\varphi_{v}\!)\!=\!\rho_{\rm r}(\!\lambda,\theta_{s},\varphi_{s},\theta_{v},\varphi_{v}\!)+\rho_{\rm a}(\!\lambda,\theta_{s},\varphi_{s},\theta_{v},\varphi_{v}\!)\hfill\cr\hfill+\rho_{\rm ra}(\lambda,\theta_{s},\varphi_{s},\theta_{v},\varphi_{v})\!+\!t(\theta_{s},\lambda)\rho_{\rm w}(\lambda)\quad\hbox{(5a)}}$$

For briefly, solar zenith and azimuth angles and satellite zenith and azimuth angles in (5a) are usually omitted in most currently literatures [1], [15], [16], [19], [32], and the (5a) can be rewritten as: TeX Source $$\rho_{\rm t}(\lambda)=\rho_{\rm r}(\lambda)+\rho_{\rm a}(\lambda)+\rho_{\rm ra}(\lambda)+t(\theta_{s},\lambda)\rho_{\rm w}(\lambda)\eqno{\hbox{(5b)}}$$ where $\rho_{\rm r}(\lambda)$ is the contribution from Raleigh scattering, $\rho_{\rm a}(\lambda)$ is the contribution from aerosol scattering, $\rho_{\rm ra}(\lambda)$ represents the contribution from the interaction of Rayleigh and aerosol scattering, $t$ is the diffuse transmittance, and $\theta_{\rm s}$ and $\varphi_{\rm s}$ are solar zenith and azimuth angles, respectively, $\theta_{\rm s}$ and $\varphi_{\rm s}$ refer to satellite zenith and azimuth angles. Due to the fact that the water-leaving reflectance is nearly diffused, it is regarded as the diffused transmittance. It may be computed approximately (yet accurately enough for the purposes of this study) by completely ignoring the aerosol, as follows [1], [33]: TeX Source $$t(\lambda)=t(\theta_{s},\lambda)=\exp\left[-{0.5\tau_{\rm r}(\lambda)+\tau_{\rm oz}(\lambda)\over\cos\theta_{s}}\right]\eqno{\hbox{(6a)}}$$ where $\tau_{\rm oz}(\lambda)$ is the ozone optical depth. In this study, at any surface pressure $P$, the Rayleigh optical depth, $\tau_{\rm r}(\lambda)$, may be determined as follows [34]: TeX Source $$\tau_{\rm r}(\lambda)={P_{0}\over P}\tau_{{\rm r},0}(\lambda)\eqno{\hbox{(6b)}}$$ where $\tau_{{\rm r},0}(\lambda)$ represents the Rayleigh optical depth at the standard atmospheric pressure $P_{0}$ of 1013.25 mb, and the ozone optical depth is determined as follows: TeX Source $$\tau_{\rm oz}(\lambda)=\tau_{{\rm oz},0}(\lambda){DU\over 1000}\eqno{\hbox{(6c)}}$$ where $\tau_{{\rm oz},0}(\lambda)$ is the specific ozone optical depth and $DU$ is the total ozone concentration (265 and 262 DU, respectively, on October 27 and 28, 2003, in Taihu Lake). The $\rho_{\rm r}(\lambda)$ at all visible and NIR wavelengths depends on the atmospheric molecular composition of the atmosphere, the sun and viewing geometry [22], [32], and to a lesser extent, on water-surface roughness [1]. Therefore, the $\rho_{\rm r}(\lambda)$ may be computed quite accurately without the use of the remotely sensed data, owing to the stability distribution of the atmospheric components associated with Rayleigh scattering [13]. According to the study results carried out by Gordon and Franz [32] and Hu and Carder [33], the $\rho_{\rm r}(\lambda)$ may be calculated by the lookup table method as long as the atmospheric pressure is known. As long as $\rho_{\rm r}(\lambda)$ and $\tau_{\rm r}(\lambda)$ are known, we concentrate on determining the aerosol, which is the key parameter to using the two-channel method to extrapolate the aerosol optical depth from the “known” wavelength to the “unknown” wavelength. Hence, the single scattering approximation of the path reflectance at $\lambda$ is given by the following equation: TeX Source $$\eqalignno{\!\!\!\!\!\!\rho_{\rm at}(\lambda)\!=\!&\,\rho_{\rm t}(\lambda)\!-\!\rho_{\rm r}(\lambda)\!=\!\varepsilon(\lambda,\lambda_{1})\rho_{\rm as}(\lambda_{1})\!+\!t(\lambda)\rho_{\rm w}(\lambda)&\hbox{(7a)}\cr\!\!\!\!\!\!\varepsilon(\lambda,\lambda_{1})\!\approx\!&\,{\rho_{\rm as}(\lambda)\over\rho_{\rm as}(\lambda_{1})}\approx Exp\left[\eta(\lambda_{1}\!-\!\lambda)\right]&\hbox{(7b)}}$$

Where, $\eta$ is Angstrom exponent, $\varepsilon$ is the two-channel model, $\rho_{\rm as}(\lambda)$ is aerosol single scattering contribution, and $\lambda_{1}$ is the reference band. The water-leaving reflectance at a given spectral band central of wavelength $\lambda_{\rm i}$ may be denoted as follows: TeX Source $$\rho_{\rm w}(\lambda_{i})={\rho_{\rm at}(\lambda_{i})-\rho_{\rm as}(\lambda_{i})\over t(\lambda_{i})}\eqno{\hbox{(8)}}$$ where $i$ refers to 1, 2, 3, and 4. Assume that the $\rho_{\rm w}(\lambda_{1})$ vs. $\rho_{\rm w}(\lambda_{2})$ and $\rho_{\rm w}(\lambda_{3})$ vs. $\rho_{\rm w}(\lambda_{4})$ meet a “known” empirical linear relationship, as follows: TeX Source $$\eqalignno{\rho_{\rm w}(\lambda_{2})\approx&\,a_{1}\rho_{\rm w}(\lambda_{1})+b_{1}&\hbox{(9a)}\cr\rho_{\rm w}(\lambda_{4})\approx&\,a_{2}\rho_{\rm w}(\lambda_{3})+b_{2}&\hbox{(9b)}}$$ where $a_{1}$, $a_{2}$, $b_{1}$, and $b_{2}$ are empirical constant coefficients. The underlying assumption of (9) must meet the following conditions: (1) the reflectance at $\lambda_{\rm i}$ should be “spectrally flat” enough in order to minimize the influence of different spectral response function (SRF); and (2) $\lambda_{2}$ or $\lambda_{4}$ should be quite close to $\lambda_{1}$ or $\lambda_{3}$ in order to minimize the impact of difference in spectral shape aerosol contribution and water-leaving contribution. Substituting (8) into (9), yields the following: TeX Source $$\eqalignno{\rho_{\rm at}(\lambda_{2})=&\,a_{1}{t(\lambda_{2})\over t(\lambda_{1})}\rho_{\rm at}(\lambda_{1})+b_{1}t(\lambda_{2})+\rho_{\rm as}(\lambda_{2})\cr&-a_{1}{t(\lambda_{2})\over t(\lambda_{1})}\rho_{\rm as}(\lambda_{1})&\hbox{(10a)}\cr\rho_{\rm at}(\lambda_{4})=&\,a_{2}{t(\lambda_{4})\over t(\lambda_{3})}\rho_{\rm at}(\lambda_{3})+b_{2}t(\lambda_{4})+\rho_{\rm as}(\lambda_{4})\cr&-a_{2}{t(\lambda_{4})\over t(\lambda_{3})}\rho_{\rm as}(\lambda_{3})&\hbox{(10b)}}$$

Substituting (7) into (10) yields the following: TeX Source $$\eqalignno{{\hskip-30pt}\rho_{\rm at}(\lambda_{2})=&\,{a_{1}t(\lambda_{2})\over t(\lambda_{1})}\rho_{\rm at}(\lambda_{1})+b_{1}t(\lambda_{2})\cr&+\left[\varepsilon(\lambda_{2},\lambda_{4})-{a_{1}t(\lambda_{2})\over t(\lambda_{1})}\varepsilon(\lambda_{1},\lambda_{4})\right]\rho_{\rm as}(\lambda_{4})&\hbox{(11a)}\cr{\hskip-30pt}\rho_{\rm at}(\lambda_{4})=&\,{a_{2}t(\lambda_{4})\over t(\lambda_{3})}\rho_{\rm at}(\lambda_{3})+b_{2}t(\lambda_{4})\cr&+\left[\varepsilon(\lambda_{4},\lambda_{4})-{a_{2}t(\lambda_{4})\over t(\lambda_{3})}\varepsilon(\lambda_{3},\lambda_{4})\right]\rho_{\rm as}(\lambda_{4})&\hbox{(11b)}}$$

The parameters of $a_{1}$, $a_{2}$, $b_{1}$, and $b_{2}$ can be computed from field measurements using robust regression method, and the $\rho_{\rm at}(\lambda_{1})$, $\rho_{\rm at}(\lambda_{2})$, $\rho_{\rm at}(\lambda_{3})$, $\rho_{\rm at}(\lambda_{4})$, $t(\lambda_{1})$, $t(\lambda_{2})$, $t(\lambda_{3})$, and $t(\lambda_{4})$ can be estimated from MODIS images using (6) and (7) as long as known the parameters of total ozone and the atmospheric pressure at mean sea level. Hence, the (11) only contains two unknowns, namely, $\rho_{\rm as}(\lambda_{4})$ and $\eta$. The studies carried out by Hu *et al.* [14] revealed that the aerosol type dose not change in a small spatial extent (50 $\sim$ 100 km). The underlying assumption of “clear water” method indicates that the aerosol optical depth result in insignificant or only slight changes over small spatial scales [13], [15], [16], [20]. In regions with the range of 50 $\sim$ 100 km, the $\theta_{\rm s}$ may be approximated as constants. If one accepts these assumptions, then, for a small study region such as Taihu Lake, the slopes and biases in (11) could be approximately equal to a “constant” which is unchanged with the pixel. Since Taihu Lake is an eutrophic shallow lake [35], the signal received by sensors may be polluted by water bottom reflectance in some regions, such as southeast Taihu Lake, in addition to the adjacency effect (scattering of light from highly reflecting pixels in the atmosphere into the reflectance signal from low reflectance pixels) is very high at visible wavelengths due to the high reflectance of vegetation in the surrounding area of the lake [36]. This makes it very difficult to accurately estimate the aerosol type and aerosol scattering contribution from (11) on a point-by-point basis. Instead, the analysis approach made use of image statistics based on large area common in the band's pairs are suggested for aerosol scattering reflectance estimation, i.e. the regions with low $\rho_{\rm at}(667)$ values were selected to compute the aerosol type and aerosol scattering contribution for (11) by the robust regression method, but areas surrounding the lake were excluded.

As long as the aerosol type and aerosol single-scattering contribution are known from (11) (only one value of aerosol type and aerosol single-scattering concentration for one MODIS image in Taihu Lake), aerosol multi-scattering contribution may be estimated by the look-up table method as follows: TeX Source $$\rho_{\rm ms}(\lambda)=\gamma_{1}(\lambda)+\gamma_{2}(\lambda)\rho_{\rm as}(\lambda)+\gamma_{3}(\lambda)\left[\rho_{\rm as}(\lambda)\right]^{2}\eqno{\hbox{(12)}}$$ where $\rho_{\rm ms}(\lambda)$ refers to the aerosol multi-scattering contribution, whose value is equal to $\rho_{\rm a}(\lambda)+\rho_{\rm ra}(\lambda)$, and $\gamma_{1}(\lambda)$, $\gamma_{2}(\lambda)$, and $\gamma_{3}(\lambda)$ are empirical coefficients, which may be interpolated from the aerosol look-up table by the given viewing

geometric conditions. Then, the water-leaving reflectance at $\lambda$ may be computed by the following equation: TeX Source $$\rho_{\rm w}(\lambda)={\rho_{\rm at}(\lambda)-\rho_{\rm ms}(\lambda)\over t(\lambda)}\eqno{\hbox{(13)}}$$

SECTION III

The spectral characteristics in the three datasets, shown in Fig. 1, are quite similar to typical reflectance spectral collected in turbid waters [37], [38]. The water-leaving reflectance in the blue range (400–500 nm) is very low. The $\rho_{\rm w}(\lambda)$ in this spectral region do not have any remarkable features. A reflectance trough near 440 nm, corresponding to the chlorophyll-a absorption peak, is not distinct. $\rho_{\rm w}(\lambda)$ in the green range (500–600 nm) is much higher than in the blue range. Many factors contribute to the water-leaving reflectance features in the blue and green ranges; these ranges mainly contain absorption by dissolved organic matter and suspended sediment as well as backscattering by suspended particles. In the red range (600–700 nm), the reflectance is highly variable.

The MODIS is a scanning radiometer which has six bands at 443, 531, 552, 667, 678, and 748 nm with a bandwidth of 10 nm, and three bands at 412, 488, and 869 nm with a bandwidth of 15 nm, and is designed for ocean color application. According to the SRF of the MODIS sensor, as shown in Fig. 2, it is found that SRFs of two pairs of bands overlap each other. These bands are 531, 551, 667, and 678 nm, respectively. By comparison, the overlapped portion between 667 and 678 nm is larger than that between 531 and 551 nm. Additionally, the wavelength spacing between 667 and 678 nm is 10 nm smaller than it is between 531 and 552 nm. It is widely known that the water-leaving reflectance would be strongly related with the neighboring wavelengths [39], [40]. To summarize the above arguments, there may be a strong correlation between these pairs of bands, and the correlation between 667 and 678 nm is higher than between 531 and 552 nm.

Fig. 3 shows the spectral characteristics in spectral bands centered at 531, 551, 667, and 678 nm. It is found that the water-leaving reflectance is very “spectrally flat” at these wavelengths, which is useful for constructing the stability and accuracy empirical spectral.

A algorithm. In order to illuminate the strongly correlation between these bands as previously analyzed, the average measurements at each station in Fig. 1(a) is used to construct the linear relationship of $\rho_{\rm w}(531)$ vs. $\rho_{\rm w}(551)$ and $\rho_{\rm w}(667)$ vs. $\rho_{\rm w}(678)$. Fig. 4(a) shows that the water-leaving reflectance at 531 and 667 nm is very linearly fit for it at 551 and 678 nm, respectively, and the corresponding $R^{2}$ are 0.9964 and 0.9970 $(n=74)$, respectively. It is noted that the high correlation coefficient of $\rho_{\rm w}(531)$ vs. $\rho_{\rm w}(551)$ and $\rho_{\rm w}(667)$ vs. $\rho_{\rm w}(678)$, indicating that the band positions at 531, 551, 667, and 678 nm are the acceptable bands meeting the underlying assumption of (9).

To illuminate effects of uncertainty (<5%) associated with each measurement on regression results of $\rho_{\rm w}(531)$ vs. $\rho_{\rm w}(551)$ and $\rho_{\rm w}(667)$ vs. $\rho_{\rm w}(678)$, all repeated various measurements at each station are used to regress the these linear relationships, as shown in Fig. 4(b). Compared to regression results as shown in Fig. 4(a), the items of $[a_{1}t(551)/t(531)\rho_{\rm w}(531)+b_{1}t(551)]$ and $[a_{1}t(678)/t(667)\rho_{\rm w}(667)+b_{1}t(678)]$ are insensitive to the uncertainty of measurements, which is $<0.0001\ {\rm sr}^{-1}$. It seems that each repeated measurement is systematically affected by measuring uncertainty. Compared to “noise equivalent reflectance” ($\sim$0.0001) calculating by Gordon and Voss [1], the regression uncertainty associated with measurements is negligible.

Given the surface atmospheric pressure (to determine the value of $\tau_{\rm r}(\lambda)$), viewing and solar geometric conditions, and the surface wind speed (to define the roughness of the water surface), reflectance contributed by Rayleigh scattering may be computed accurately, even accounting for polarization effects [3], [32]. In this study, the reflectance associated with

Rayleigh scattering is removed by the look-up table method advised by Gordon and Voss [1] and Gordon and Wang [3]. The region of interest is masked by checking the reflectance at top-of-atmosphere at 667 nm after Rayleigh scattering correction, namely, the regions with $\rho_{\rm at}(667)<0.07\ {\rm sr}^{-1}$ expected for areas surrounding the lake. The $\rho_{\rm as}(678)$ and $\eta$ are estimated from (11) using the robust regression method $(n>1124,R^{2}>0.993)$. Once the $\rho_{\rm as}(678)$ and $\eta$ are known, the aerosol multi-scattering contribution at a given wavelength can also be known by the look-up table method suggested by Gordon and Voss [1], given the solar and viewing geometric conditions, as shown in Fig. 5.

To compare SACA-based $\rho_{\rm ms}(\lambda)$ with other methods, the results of the SWIR algorithm are also provided here. Due to the fact that four of the MODIS/Aqua detectors at the wavelength 1640 nm are dysfunctional [16], the SWIR band set of 1240 and

2130 nm are used for MODIS data processing. In order to minimize the bottom reflecting interfering and adjacency effects in the optically shallow Taihu Lake, a “clear water” pixel is selected from among the pixels with values not within the bottom 1% of the histogram at 2130 nm for computing the aerosol scattering contribution using the SWIR algorithm, because the pixels belonging to the bottom 1% were considered to be error values [41]. Providing an overall SACA algorithm performance evaluation in a reference to the SWIR method, Fig. 5 shows comparisons of the MODIS-derived $\rho_{\rm ms}(\lambda)$ using the SACA and SWIR methods. The overall $\rho_{\rm ms}(\lambda)$ comparisons indicate that SWIR-derived $\rho_{\rm ms}(\lambda)$ is averaged 0.0057 and 0.0108 ${\rm sr}^{-1}$ larger than SACA-derived $\rho_{\rm ms}(\lambda)$ on October 27 and 28, 2003, respectively. Therefore, in general the MODIS $\rho_{\rm w}(\lambda)$ values derived using SACA method are slightly larger than those derived using the SWIR method.

The accuracy of the atmospheric correction algorithms was evaluated through comparison of the retrieved and observed water-leaving reflectance. The observation stations within a ±3 hour time window of satellite overpass and measurement were selected. The atmospheric conditions are reasonably stable within the ±3 hour period [6], [42], [43]. For the data match-up analysis, the procedure of Bailey and Werdell [42] was used to produce the satellite data for comparison with in situ measurements. Briefly, for a given MODIS-derived water-leaving reflectance, pixels with a 3 × 3 box centered at the location of the in situ measurement were extracted, and the retrievals of 3 × 3 pixels were averaged for the validation. To evaluate the accuracy of SACA and SWIR algorithms in water-leaving reflectance prediction, 16 field independent measurements were collected from Taihu Lake within a ±3 hour time window of satellite overpass on October 27 and 28, 2003.

Fig. 6 provides comparisons of MODIS-derived water-leaving reflectance in (13) plotting against field measurements in (2b), demonstrating that the SACA algorithm produces a superior performance at seven visible bands, but provides a poor result at two NIR bands to SWIR algorithm in predicting water-leaving reflectance. Fig. 7 shows the RMS of SACA and SWIR algorithms, in predicting MODIS-derived water-leaving reflectance. Correlation coefficients of SACA model-derived $\rho_{\rm w}(\lambda)$ vs. field measured $\rho_{\rm w}(\lambda)$ and SWIR model-derived

$\rho_{\rm w}(\lambda)$ vs. field measured $\rho_{\rm w}(\lambda)$ are 0.8398 and 0.6384, respectively. By comparison, use of the SACA algorithm in retrieving water-leaving reflectance in Taihu Lake decreases the uncertainty of estimation by >10% at visible bands but increases >10% RMS at NIR bands from the SWIR algorithm. Thus, using the SACA algorithm the MODIS ocean color products may be improved in the turbid waters, with the exception of NIR bands. Fortunately, this situation may be alleviated by using a combined method, i.e. for visible bands the SACA algorithm is executed, while for NIR bands the SWIR algorithm is used. Results indicate that the suggested combined method is capable of successfully producing <20% RMS in estimating water-leaving reflectance from MODIS data.

The SACA model was initialized using data recorded over coastal waters in the Changjiang River Estuary, Yellow River Estuary, and Jiaozhou Bay, and the specific form of this model as expressed in Fig. 4 was applied for predicting water-leaving reflectance in the optically shallow Taihu Lake. It was found that this algorithm does not require further optimization of site-specific parameterization to accurately estimate $\rho_{\rm w}(\lambda)$ in water bodies with widely varying bio-optical characteristics.

Findings in this paper are in accord with the results of match-up analyses of the SACA and SWIR algorithms. It was found that using the SACA algorithm for ocean color data processing has reduced the bias errors in $\rho_{\rm w}(\lambda)$. In comparison with the results from the official NASA algorithm reported by researchers such as Gordon and Voss [1], Hu *et al.* [14], Lavender *et al.* [13], etc., the SACA algorithm improves the MODIS-derived $\rho_{\rm w}(\lambda)$ products in optically shallow turbid inland waters, e.g. the negative $\rho_{\rm w}(\lambda)$ are reduced significantly (Fig. 8). Therefore, in the optically shallow turbid inland waters, the SACA algorithm is usually superior to the NIR method.

During the past several years, the SWIR algorithm has been successfully used for water-leaving reflectance in turbid waters of the U.S. east coast, the U.S. west coast, Adriatic Sea, Brazilian east coast, China east coast, and China Taihu Lake [6], [16]. In this study, while comparing the performance of the SACA algorithm with the optimal results of the SWIR algorithm in these regions, it was found that the RMS of water-leaving prediction was comparable: <14% RMS in the SACA algorithm

vs. >20% RMS in the SWIR algorithm at 412 through 488 nm [6], [16]. At 531 through 869 nm, the water-leaving reflectance retrieved by the SACA algorithm was the same as the SWIR algorithm. Thus, the SACA algorithm, especially the combined SACA algorithm, is an acceptable atmospheric correction algorithm for deriving the water-leaving reflectance from MODIS data in shallow turbid waters.

An empirical model (Fig. 4) was used by the SACA model to estimate $\rho_{\rm w}(\lambda)$ from the MODIS data. This type of model is quite easy to implement, however it lacks physical foundation, and the relationships are more geographically specific and cannot be applied other areas [9], [44]. Thus, the SACA model is still a site-specific model to some extent. In some complicated bio-optical waters which are different from aquatic environment conditions for model developments used in this study, local information may still require reinitialization of the statistical parameters of the empirical model shown in (9). The researchers also suggest calibration and validation of the algorithms based on more in situ measurements of waters with different optical properties.

Another limitation of this study is that the SACA model assumes that the aerosol type and aerosol optical depth dose insignificant or only slight change over small spatial scales, which is also the underlying assumption of “clear water” method developed by Gordon and Wang [3]. Similarly to “clear water” method, the SACA model may violate in some region, where the aerosol type or aerosol optical depth are spatially dramatically changes, even though the case study in Taihu Lake, China, indicates that SACA model is an acceptable atmospheric correction algorithm for turbid waters of Taihu Lake. The researchers also suggest calibration and validation of SACA model in more other regions, and discussion on impacts of spatial changes of aerosol type and aerosol optical depth on water-leaving reflectance retrieval accuracy in future.

SECTION IV

For optically shallow turbid inland lakes, a simple SACA algorithm is developed to remove the atmospheric influences from MODIS imageries. The algorithm is based on the spectral relationships of $\rho_{\rm w}(531)$ vs. $\rho_{\rm w}(551)$ and $\rho_{\rm w}(667)$ vs. $\rho_{\rm w}(678)$. Due to the high adjacency effects and water bottom reflectance in this shallow inland lake, the image statistics method would operate more reasonably than the point-by-point method while computing aerosol contribution using (11). Evaluated using an independently collected dataset collected in Taihu Lake, China, on October 27 and 28, 2003, the SACA algorithm is found to have an acceptable performance in removing atmospheric influences from the MODIS data. To compare the SACA-based $\rho_{\rm w}(\lambda)$ with other methods, the results of the SWIR algorithm are also presented in this paper. By comparison, use of the SACA algorithm in retrieving water-leaving reflectance in Taihu Lake decreases the uncertainty of estimation by >10% at 412 through 678 nm, but increase >10% RMS at 748 and 869 nm from the SWIR algorithm. However, the poor performance of the SACA algorithm at NIR bands may be improved by a combined method: the SACA algorithm is operated at the visible band, while the SWIR algorithm is executed at the NIR bands. Due to the fact that an empirical model was adopted by the SACA model, the SACA model may be a site-specific model. Thus, some local information may be still require improvement of the site-specific statistical parameters of the SACA model, while the bio-optical properties of water bodies are different from the aquatic environment conditions for model developments. It is concluded that the SACA algorithm should be used for deriving water-leaving reflectance from MODIS data in shallow turbid waters, although it may be essential to reinitialize the statistical parameters of “known” spectral relationship models.

The authors would like to express their gratitude to the three anonymous reviewers for their useful comments and suggestions.

This work was supported by the Science Foundation for 100 Excellent Youth Geological Scholars of China Geological Survey (GZH201200036), the open fund of the Key Laboratory of Marine Hydrocarbon Resources and Environmental Geology (MRE201109), the High-tech Research and Development Program of China (2007AA092102), and Dragon 3 Project (10470). (Corresponding author: J. Chen.)

J. Chen is with the School of Ocean Sciences, China University of Geosciences (Beijing), Beijing. He is also with the Key Laboratory of Marine Hydrocarbon Resources and Environmental Geology, Qingdao, China, Qingdao Institute of Marine Geology, Qingdao, Shandong, China (e-mail: cjun@cgs.cn).

W. T. Quan is now with the Shanxi Remote Sensing Information Center Agriculture, China (e-mail: cloudy1112@gmail.com).

M. W. Zhang is now with the Center for Earth Observation and Digital Earth, Chinese Academy of Sciences, Beijing, China (e-mail: mwzhang@ceode.ac.cn).

T. W. Cui is now with the First Institute of Oceanography, State Oceanic Administration, Qingdao, China (e-mail: cuitingwei@fio.org.cn).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

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