Inherent Optical Properties in Lake Taihu Derived from VIIRS Satellite Observations

Abstract

Using in situ remote sensing reflectance and inherent optical property (IOP) measurements, a near-infrared (NIR)-based IOP algorithm is developed and tuned for Lake Taihu, in order to derive the particle backscattering coefficient b_bp(λ), total absorption coefficient a_t(λ), dissolved and detrital absorption coefficient a_dg(λ), and phytoplankton absorption coefficient a_ph(λ), with satellite observations from the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (SNPP). The IOP algorithm for Lake Taihu has a reasonably good accuracy. In fact, the determination coefficients between the retrieved and in situ IOPs are 0.772, 0.638, and 0.487 for a_t(λ), a_dg(λ), and a_ph(λ), respectively. The IOP products in Lake Taihu that have been derived from VIIRS-SNPP observations show significant spatial and temporal variations. Southern Lake Taihu features enhanced b_bp(λ) and a_dg(λ), while northern Lake Taihu shows higher a_ph(λ). The seasonal and interannual variability of a_dg(λ) and b_bp(λ) in Lake Taihu is quantified and characterized with the highest b_bp(λ) and a_dg(λ) in the winter, and the lowest in the summer. In the winter, b_bp(443) and a_dg(443) can reach over ~1.5 and ~5.0 m⁻¹, respectively, while they are ~0.5–1.0 and ~2.0 m⁻¹ in the summer. This study shows that in Lake Taihu a_dg(λ) is the most significant IOP, while a_ph(λ) is the least in terms of the IOP values and contributions to remote sensing reflectance. The highest b_bp(λ) and a_dg(λ) occurred in the winter between 2017–2018, and the lowest b_bp(λ) and a_dg(λ) occurred in the summer of 2014. In comparison, the seasonal and interannual variability of mean a_ph(λ) for Lake Taihu is less significant, even though enhanced seasonal and interannual variability can be found in some parts of Lake Taihu, such as in the northern Lake Taihu region.

1. Introduction

Lake Taihu is China’s third largest fresh water lake, and it is located in the Yangtze River Delta (Figure 1). It covers an area of ~2300 km² with an average water depth of ~2 m. Lake Taihu features constantly turbid waters and frequent breakouts of algal blooms in the spring-summer. For example, a massive blue-green algae bloom broke out in the spring of 2007 and became an environmental crisis, which polluted the water supply for nearby urbanized and heavily populated regions [1,2,3].

Numerous studies have been conducted with both in situ measurements and satellite ocean color observations in order to develop satellite algorithms for geophysical and biological parameter retrievals, study the environmental changes, and to characterize and quantify the physical, biological, and biogeochemical dynamics, such as water quality, phytoplankton algal blooms, lake eutrophication, chlorophyll-a (Chl-a) concentration, water diffuse attenuation coefficient at the wavelength of 490 nm K_d(490) [4] or at the domain of photosynthetically available radiation (PAR) K_d(PAR) [5], primary production and color dissolved organic matters (CDOM), etc. Using the Moderate Resolution Imaging Spectroradiometer (MODIS) observations, Wang et al. [2] analyzed the massive blue-green algae bloom event during the spring of 2007, and derived the water properties for water quality monitoring, assessments, and management in Lake Taihu [2]. The intense blooms of cyanobacteria (primarily Microcystis aeruginosa) in Lake Taihu were also characterized with MODIS observations [6]. The annual frequency of significant blooms was found to increase from the time period of 2000–2004 to 2006–2008 [6]. The total suspended matter (TSM) concentration can also be retrieved and evaluated in Lake Taihu with satellite observations [7,8]. The long-term variability of the TSM concentration in Lake Taihu was characterized and quantified [7].

In recent years, the environment in Lake Taihu has been deteriorating significantly [9]. The water quality in northern Lake Taihu is getting worse due to urban pollutant discharge. The eutrophication in eastern Lake Taihu is caused by intensive aquaculture [9]. Climate variability and poor lake management are attributed to the crisis of the blue-green algal bloom in 2007. Similar to the lakes in the middle and low reaches of the Yangtze River, Lake Taihu also experienced eutrophication and the corresponding ecosystem responses, including the extinction of underwater plants and frequent cyanobacterial blooms [10]. The annual average total nitrogen concentration in Lake Taihu is ~2–3 mg L⁻¹, and the phosphorus concentration is ~0.2 mg L⁻¹, with significant spatial and temporal variations. The phytoplankton growth in Lake Taihu is controlled by nitrogen and phosphorus inputs, as well as by climatic factors [6,11].

In Lake Taihu, Chl-a concentration typically peaks in the summer and reaches its minimum in the winter. The maximum primary production usually occurs in the spring and summer seasons [12]. The CDOM shows the spatial and seasonal dynamics in Lake Taihu [13]. CDOM absorption is significantly higher in the winter than in the summer [14]. This is caused by the degradation and release of fixed carbon in the phytoplankton and the underwater vegetation [15]. The spectral slope for the exponential decrease of the CDOM absorption a_g(λ) is ~0.015 nm⁻¹ [16] with seasonal variations. The backscattering spectra from the blue to near-infrared (NIR) wavelengths in Lake Taihu are flat [17]. In fact, they are highly related to the TSM concentrations [7,17,18]. Shi et al. [7] show that TSM concentrations in Lake Taihu have significant spatial and temporal variability. Seasonal changes in the TSM concentration for all parts of Lake Taihu are in the range of 25–80 mg L⁻¹. The TSM in southern Lake Taihu can reach over ~100 mg L⁻¹ in the wintertime, while low TSM concentrations of ~20–30 mg L⁻¹ are located in the northern parts of Lake Taihu, such as Meiliang Bay and Gonghu Bay [7].

The lake water inherent optical properties (IOPs) include the absorption and scattering of the pure water, color dissolved and detrital organic matter, and particles in the water column. These are the intrinsic optical properties, which determine the normalized water-leaving radiance spectra nL_w(λ), that can be measured or retrieved from the in situ or satellite radiometry sensors [19,20,21,22]. In comparison to these nL_w(λ) spectra, retrievals of biological and biogeochemical parameters such as Chl-a, TSM, K_d(490) and IOPs can provide comprehensive information about the constituents in the water column, and interaction between different constituents in order for researchers to better understand the ecosystem dynamics in both regional and global ocean waters [23,24].

For the global ocean, several algorithms were developed in order to retrieve IOPs, i.e., the particle backscattering coefficient b_bp(λ), the absorption coefficient of the phytoplankton a_ph(λ), etc. In the Garver-Siegel-Maritorena (GSM) IOP algorithm [19,25], a nonlinear least-square scheme is used in order to best fit the modeled remote sensing reflectance R_rs(λ) with R_rs(λ) spectra from the satellite or in situ measurements. This IOP algorithm uses a fixed b_bp(λ) power law slope η, and a constant exponential degradation slope S for the dissolved and detrital matters (a_dg(λ)). In the Quasi-Analytical Algorithm (QAA) [21], a couple of empirical formulae are used first to compute backscattering coefficients at a reference wavelength b_bp(λ₀) and the b_bp(λ) power law slope η. Then total absorption a_t(λ) is further decomposed into a_ph(λ) and a_dg(λ) using the empirical formulae with a_t(410), a_t(443), as well as remote sensing reflectance beneath the surface r_rs(λ) at the blue and green bands. On the other hand, the generalized IOP (GIOP) algorithm is a generic IOP algorithm, which allows the researcher to specify the modeling assumption for the IOP parameters, construct and develop new semi-analytical IOP algorithms, and tune into regional IOP algorithms [22].

These three IOP retrieval algorithms generally work well in the open ocean and less-turbid coastal and inland waters. However, significant errors with these three IOP algorithms can occur in turbid coastal and inland waters, such as Lake Taihu. Specifically, for the QAA algorithm, r_rs(λ) in the blue and green bands are the major inputs to estimate the b_bp(λ₀) and b_bp(λ) power law slope η. The saturation of the r_rs(λ) in the visible bands over highly turbid waters shows that r_rs(λ) loses its sensitivity to the change of b_bp(λ) [26,27,28], thereby resulting in significant errors in coastal and inland turbid waters, such as those in Lake Taihu.

Satellite-measured nL_w(λ) spectra at the red and NIR wavelengths are rarely used in the open ocean, since their values are close to 0. However, over turbid coastal and inland waters, nL_w(λ) spectra feature enhanced nL_w(λ) at the red and NIR wavelengths [2,28,29,30]. This spectral feature of the coastal and inland waters is caused by the strong water absorption at the red and NIR wavelengths [31,32], as well as a significant decrease of absorptions by CDOM at the red and NIR wavelengths and the near zero absorption of the phytoplankton at the NIR wavelengths [21,33]. Thus, nL_w(λ) spectra at the red and NIR wavelengths can provide unique information to address the complexity of turbid coastal and inland waters, while the spectral features at the traditional blue and green wavelengths often fail. Over coastal and inland water regions, Chl-a [34], K_d(490) [4,35], TSM [7,36,37], the floating algae index [38] and normalized difference algae index [39], can all be produced using the optical measurements at the red and NIR wavelengths from the in situ and satellite observations. These products from the ocean color observations can be used to study the long-term environmental variability, characterize and quantify the coastal and lake ecosystems, evaluate the dynamics of the coastal environment, and monitor the natural hazards and environmental events.

In Lake Taihu, several studies were conducted in order to develop an improved algorithm to accurately retrieve the IOPs. By shifting the wavelength reference for b_bp(λ₀) from 551 nm or 640 nm to 701 nm in the QAA algorithm, the IOP retrievals in Lake Taihu are improved [40]. Another study shows an improved QAA algorithm with double-reference bands, and divides the entire Lake Taihu into two types of waters using the spectral slopes of remote sensing reflectance between 677 and 701 nm [41].

Even though these two algorithms showed some improvements in comparison with the QAA retrievals, they are in situ focused, and are not designed to be applied to the satellite observations in Lake Taihu.

Recent studies [42,43,44] show that the semi-analytical radiance model [20] can be simplified for the nL_w(λ) at the NIR wavelengths because the sea water absorption a_w(λ) is normally ~1–2 orders higher than the other IOP components at the NIR wavelengths. Consequently, the b_bp(λ) spectra for all wavelengths between the short blue and NIR can be computed analytically from b_bp(λ) values at the two NIR bands (745 and 862 nm) in coastal and inland turbid waters [42]. In comparison, the b_bp(λ) spectra derived from other IOP algorithms, e.g., QAA [21], significantly underestimate the true b_bp(λ) values. Shi and Wang [42] suggest that the NIR-based b_bp(λ) retrievals in turbid coastal and inland waters can be extended to the second step of the QAA IOP algorithm to further derive other IOP components, i.e., decompose the total absorption a_t(λ) into phytoplankton absorption a_ph(λ) and absorption coefficient a_dg(λ) for the dissolved and detrital matters in the water column.

In this study, in situ IOP measurements in Lake Taihu are used to tune the NIR-based IOP algorithm for satellite ocean color observations from the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (SNPP). The performance of the IOP algorithm is evaluated and analyzed. This IOP algorithm is then applied to VIIRS observations between 2012 and 2018 to derive IOP b_bp(λ), a_ph(λ), and a_dg(λ) products in Lake Taihu. Climatology, seasonal variability of b_bp(λ), a_ph(λ), and a_dg(λ) are computed, characterized, and quantified. Time series of b_bp(λ), a_ph(λ), and a_dg(λ) in Lake Taihu between 2012 and 2018 are also evaluated.

2. In Situ Data and VIIRS-SNPP Data

2.1. In Situ Measurements of R_rs(λ), a_ph(λ), and a_dg(λ)

During the period between 2006 and 2007, extensive in situ measurement campaigns were conducted by the Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences. Five cruises were carried out in 7–9 January 2006, 29 July–1 August 2006, 12–15 October 2006, 7–9 January 2007, and 25–27 April 2007. In each cruise, 50 stations covering the entire Lake Taihu (Figure 1) were set up. The measurements included hyperspectral remote sensing reflectance for wavelengths between 350 and 1050 nm, K_d(PAR), TSM concentration, Chl-a, detrital particle absorption coefficient a_d(λ), CDOM absorption coefficient a_g(λ), and phytoplankton absorption coefficient a_ph(λ) between 300 and 750 nm. The absorption coefficient of dissolved and detrital matter a_dg(λ) is the sum of a_d(λ) and a_g(λ). It is noted that no b_bp(λ) was measured in these experiments due to technical difficulties in measuring the backscattering coefficient in the turbid shallow waters.

The optical measurements and the water samples were taken at depths of 50 cm below the water surface. In situ remote sensing reflectance and PAR at each station were measured under low wind conditions between local time 8:30–16:30. At each station, an ASD field spectrometer (Analytical Devices, Inc., Boulder, CO, USA) was used to measure the downwelling irradiance and upwelling radiance. To reduce the radiance measurement error and increase the signal-to-noise ratio (SNR), the radiance was measured 10 times at each station. The downwelling irradiance and upwelling radiances are used to compute the remote sensing reflectance R_rs(λ). The protocols and the procedures to measure and compute the reflectance, PAR, K_d(PAR), and IOP properties are detailed in [35,45]. Note that nL_w(λ) spectra and remote sensing reflectance just below the surface r_rs(λ) can be directly converted from the remote sensing reflectance R_rs(λ) as shown in Appendix A.

The quantitative filter technique (QFT) was used to determine the detrital absorption coefficient a_d(λ) and phytoplankton absorption coefficient a_ph(λ). Methanol was used to partition the absorption of detritus and phytoplankton. Water samples were first filtered through a 47-mm-diameter Whatman 0.70 μm GF/F filter, and then re-filtered through a 25-mm-diameter 0.22 μm Millipore filter to measure CDOM absorption a_g(λ). The absorption coefficients of a_d(λ) and a_ph(λ) were measured with a Shimadzu UV-2401PC UV-Vis spectrophotometer. Details of the measurement process were described by Zhang et al. [14].

In this study, these in situ measurements are used to tune and validate the NIR-based IOP algorithm for the VIIRS-SNPP observations, in order to develop a satellite-based IOP algorithm to retrieve the IOP properties from the VIIRS-derived nL_w(λ) spectra for Lake Taihu. Assuming that the biogeochemical parameters that determine the spectra of IOPs, such as the particle size distribution, composition, texture, and refractive index, do not change with time, the in situ tuned IOP algorithm for the VIIRS-SNPP is still valid, even though these in situ measurements were taken prior to the SNPP launch in late 2011.

2.2. VIIRS-SNPP Satellite Observations

Launched on 28 October 2011, VIIRS-SNPP provides continuous observations of Earth’s atmosphere, land and ocean [46], similar to the data derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) onboard the Aqua and Terra satellites [47]. The reflective solar bands in VIIRS for ocean color observations are similar to MODIS, in order to produce continued and consistent global ocean color products. Specifically, the nominal central wavelengths of the visible bands (M1–M5) for the VIIRS ocean color observations are 410, 443, 486, 551, and 671 nm, with a bandwidth of 20 nm and a spatial resolution of 750 m. The nominal central wavelengths for the two NIR bands (M6 and M7) are 745 and 862 nm, and the wavelengths for the three shortwave infrared (SWIR) bands (M8, M10, and M11) are 1238, 1601, and 2257 nm. The measurements at the NIR and SWIR bands are used to carry out an atmospheric correction in the satellite ocean color data processing [48,49,50].

As a key product suite derived from VIIRS, ocean color Environmental Data Records (EDR) are derived using the Multi-Sensor Level-1 to Level-2 (MSL12) ocean color data processing software package from Sensor Data Records (SDR) (or Level-1B) [51]. In particular, the SWIR-based and NIR-SWIR combined atmospheric correction algorithms are used in turbid coastal and inland waters in order to derive accurate nL_w(λ) spectra from the short blue to the NIR wavelengths. A couple of studies have already shown that good quality nL_w(λ) spectra can be achieved for both the open ocean and coastal regions from MODIS-Aqua, VIIRS-SNPP, etc. [2,49,52,53]. Previous studies have also shown that the SWIR-based atmospheric correction with MODIS can be used to drive nL_w(λ) spectra with good accuracy in Lake Taihu [2,54]. Specifically, the mean ratios and standard deviations of nL_w(λ) between the satellite retrievals and the in situ measurements are 1.074 ± 0.206 and 0.950 ± 0.153 at the wavelengths of 443 and 555 nm, respectively [2]. In this study, a total of 3813 VIIRS-SNPP granules over Lake Taihu between 2012 and 2018 are used to derive nL_w(λ) spectra with the NIR-SWIR atmospheric correction in MSL12. These nL_w(λ) spectra are further used to derive the IOPs using the NIR-based IOP algorithm.

3. The NIR-Based IOP Algorithm in Lake Taihu and Its Performance

3.1. The NIR-Based IOP Algorithm

To compute the IOPs using the nL_w(λ) spectra from the VIIRS observations, it is critical to accurately estimate b_bp(λ) in the first step. In QAA, the total absorption coefficients a_t(λ) at the reference green/red wavelengths are empirically estimated. The reference a_t(λ₀) is then applied to the water-leaving reflectance model to calculate b_bp(λ₀) at the green/red wavelengths. Following the b_bp(λ₀) and the empirical power law slope η of b_bp(λ) calculated from R_rs(λ) in the visible bands, b_bp(λ) spectra are consequently estimated. The a_t(λ) spectra are then further derived from the surface remote-sensing reflectance model with the known b_bp(λ).

Following the retrievals of the b_bp(λ) and a_t(λ) spectra, these a_t(λ) spectra are further decomposed into the dissolved and detrital absorption coefficient a_dg(λ) and the phytoplankton absorption coefficient a_ph(λ) in the second step. Further details of the decomposition procedure are shown in Appendix A.

The a_w(λ) spectrum shows a_w(λ) is significantly enhanced at the NIR wavelengths [31]. Thus, a_w(λ) is one to two orders higher than the absorption coefficients of the other constituents at the NIR wavelengths in turbid coastal and inland waters, i.e., a_w(λ) >> a_ph(λ), a_g(λ), and a_d(λ). Thus, b_b(λ)/[a(λ)+b_b(λ)] can be approximated as

$$\left(\frac{b_b(\lambda )}{a(\lambda )+b_b(\lambda )}\right)\approx \left(\frac{b_b(\lambda )}{a_w(\lambda )+b_b(\lambda )}\right)$$

(1)

Figure 2a shows the in situ measurements of these a_ph(λ), a_d(λ), and a_g(λ) spectra in comparison with a_w(λ) at [31.387°N, 120.267°E] measured on 7 January 2007, in Lake Taihu. The remote sensing reflectance R_rs(λ) spectrum (Figure 1b) peaks at the red wavelength, and the R_rs(λ) values are ~0.015 sr−¹ and ~0.010 sr−¹ at 745 and 862 nm, respectively. This suggests that Lake Taihu is a typical turbid inland lake. The a_ph(λ), a_d(λ), and a_g(λ) spectra at this station indeed show that a_w(λ) at the NIR wavelengths is significantly higher than the other three IOP components, even though a_ph(λ), a_d(λ), and a_g(λ) are the dominant IOPs in the visible bands. Results in Figure 2a demonstrate that Equation 1 is a valid assumption for turbid coastal and inland waters. Thus, it can be used to derive the IOPs for coastal and inland waters.

In a recent study, Shi and Wang [42] demonstrated that the NIR-based b_bp(λ) algorithm can be safely used for highly turbid waters with nL_w(745) and nL_w(862) < ~6 and 4 mW cm⁻² μm⁻¹ sr⁻¹, respectively. In Lake Taihu, the MODIS and VIIRS observations show that nL_w(859) or nL_w(862) < ~2 mW cm⁻² μm⁻¹ sr⁻¹ for all seasons [2,7]. This further shows that Equation 1 is valid for all seasons in Lake Taihu. Thus, this IOP algorithm can be applied to all VIIRS-SNPP observations between 2012 and 2018, in order to characterize and quantify the spatial and temporal IOP variations over Lake Taihu.

With this assumption, b_bp(λ) at the two NIR bands can be analytically estimated, and the b_bp(λ) power law slope η and b_bp(λ) in the visible bands can be consequently calculated. In a recent study, Shi and Wang [42] demonstrated that b_bp(λ) can be derived with good accuracy using the NIR-based backscattering algorithm and b_bp(λ) data for global turbid coastal waters can be produced [42].

Following b_bp(λ) retrievals in turbid coastal and inland waters like Lake Taihu, derived b_bp(λ) data can be further extended to calculate a_t(λ) spectra with the remote-sensing reflectance model [20]. The other IOPs such as a_ph(λ) and a_dg(λ) are then further derived following a similar approach to step 2 of the QAA algorithm, i.e., to decompose a_t(λ) into a_ph(λ) and a_dg(λ). Note that the coefficients and formulae to decompose a_t(λ) into a_ph(λ) and a_dg(λ) in QAA are empirical, and default coefficients are tuned with in situ data for the global applications. IOP parameters such as the exponential decay slope S for a_dg(λ) can vary significantly from one region to another due to the difference of the particle size distribution, texture and composition, and particle refractive index [42]. As an example, the exponential decay slope S for a_dg(λ) can range from 0.008 to 0.018 [22]. Thus, it is necessary to re-tune it for Lake Taihu with the in situ IOP and nL_w(λ) measurements, in order to optimize the coefficients and formulae in the second step in order to decompose a_t(λ) further into a_ph(λ) and a_dg(λ).

3.2. Performance of the NIR-Based IOP Algorithm in Lake Taihu

The default values in the quadratic equation for the remote sensing reflectance model in Gordon et al. [20] are 0.0949 for g₁ and 0.0794 for g₂ (see Appendix A). In this study, we optimize the retrievals of IOPs from the remote sensing reflectance in Lake Taihu by tuning g₁ and g₂ in order to obtain the best matches between retrieved a_t(λ) and the in situ a_t(λ) for VIIRS-SNPP application. We also use the in situ IOP and nL_w(λ) measurements to recalculate the exponential decay slope S for a_dg(λ) as a function of nL_w(410) and nL_w(443) in Lake Taihu to further decompose a_t(λ) into a_ph(λ) and a_dg(λ) from VIIR-SNPP observations.

Following the procedure as described in Appendix A, we used the in situ measurements of a_dg(λ) and a_ph(λ) to tune the coefficients g₁ and g₂ of the quadratic formula in Gordon et al. (1988), so as to optimize the retrievals of a_t(λ) from the remote sensing reflectance in Lake Taihu. In this study, the values for the tuned g₁ and g₂ are 0.0626 and 0.0289, respectively.

We also tune the coefficients and formulae to decompose the a_t(λ) into a_ph(λ) and a_dg(λ) using the in situ IOP and nL_w(λ) data in Lake Taihu. It is found that the exponential slope S₀ in Equation (A12) of Appendix A is set to 0.01056 in order to produce the best matches between the derived a_ph(λ) and a_dg(λ) using the in situ R_rs(λ) spectra and in situ a_ph(λ) and a_dg(λ) measurements. Details of the IOP algorithm for VIIRS-SNPP are described in Appendix A. Figure 3 shows the scatter plots of the derived IOP data versus the in situ IOP measurements for IOP parameters of a_t(λ) (Figure 3a), a_ph(λ) (Figure 3b), and a_dg(λ) (Figure 3c). In general, the in situ a_t(λ) measurements in Lake Taihu match well with a_t(λ) retrievals using the in situ R_rs(λ) spectra. The coefficient of determination R² for these two a_t(λ) is 0.772 (

Table 1. Coefficients of determination R² between the derived- and in-situ-IOPs in Lake Taihu.

IOP	Coefficient of Determination R2
	All Bands	410 nm	443 nm	486 nm	551 nm	671 nm
at(λ)	0.772	$0.761$	0.760	0.810	0.784	0.745
adg(λ)	$0.638$	$0.672$	0.681	0.656	0.662	0.523
aph(λ)	0.487	0.398	0.594	0.474	0.439	0.537

). Table 1 also shows that these a_t(λ) retrievals have good performances for all the VIIRS bands with the best R² of 0.810 for a_t(486).

The mean ratio of a_t(λ) between retrievals and the in situ a_t(λ) data is 0.970 ± 0.233 (

Table 2. Statistics of the ratios with standard deviation (STD) values between the derived- and in-situ-IOPs in Lake Taihu.

IOP.	IOP Ratio of Derived/In Situ (Mean ± STD).
	All Bands	410 nm	443 nm	486 nm	551 nm	671 nm
at(λ)	0.970 ± 0.233	0.975 ± 0.265	0.953 ± 0.238	0.905 ± 0.202	0.897 ± 0.186	1.118 + 0.276
adg(λ)	$0$.948 ± 0.298	$0.928$ ± 0.273	1.001 ± 0.296	0.956 ± 0.297	0.943 ± 0.292	0.910 ± 0.331
aph(λ)	1.196 ± 0.728	1.272 ± 0.718	0.932 ± 0.641	0.967 ± 0.753	1.126 ± 0.891	1.683 ± 0.640

). The ratios of a_t(λ) are also generally good at most of the VIIRS bands. The ratio of a_t(671) is 1.118 ± 0.276. The relatively high a_t(671) ratio and standard deviation (STD) can be attributed to the significantly small a_t(671) values in Lake Taihu. It is noted that there are no results for b_bp(λ), because there are no in situ b_bp(λ) data, due to the difficulty of the b_bp(λ) measurement in turbid waters like Lake Taihu. Since the radiance model shows that b_bp(λ) can be determined from a_t(λ) and R_rs(λ), the good match between retrievals and the in situ a_t(λ) data suggests that b_bp(λ) retrievals from the IOP algorithm are expected to match the true b_bp(λ) values.

Figure 3b shows the matchup (scatter plot) results for the IOP parameter a_dg(λ). The coefficient of determination for the match between the derived and in situ-measured a_ag(λ) data is 0.638 (Table 1). The mean a_dg(λ)/a_dgi(λ) for all the VIIRS bands are 0.948 ± 0.298. Table 1 and Table 2 also show that a_dg(λ) retrievals from the remote sensing reflectance have good accuracies for all of the VIIRS bands.

Lower accuracies and higher uncertainties can be found for a_ph(λ) retrievals even though fair comparison results are shown in the a_ph(λ) scatter plot between derived and in situ-measured a_ph(λ) data (Figure 3c). The coefficient of determination R² for these two a_ph(λ) is 0.487 (Table 1), and the mean ratio of the derived/in situ in a_ph (λ) for all VIIRS bands is 1.196 ± 0.728 (Table 2). In comparison to the matchup plot of a_dg(λ) in Figure 3b, a large uncertainty can be found for a_ph(λ) retrievals, especially when a_ph(λ) is lower than ~1 m⁻¹.

It is noted that the IOP retrievals show significant improvements in comparison to the un-tuned original IOP algorithm. The R² values for the un-tuned IOP algorithm are 0.578, 0.302, and 0.251, while the IOP ratios are 1.02 ± 0.285, 0.56 ± 0.243, and 2.24 ± 1.19 for a_t(λ), a_dg(λ), and a_ph(λ), respectively. The IOP algorithm from Lee et al. [21] has a performance similar to the un-tuned original IOP algorithm. This suggests that it is necessary to tune the IOP algorithm in Lake Taihu in order to produce accurate IOP products for characterizing and quantifying the IOP dynamics in Lake Taihu, and the tuned IOP algorithm with g₁ and g₂ of 0.0626 and 0.0289, respectively, is optimal for Lake Taihu.

Even though there are no in situ measurements of b_bp(λ) due to the technical difficulties, a conversion was also conducted to use the in situ R_rs(λ) spectra and a_t(λ) to further compute the corresponding b_bp(λ) at the VIIRS bands using the tuned quadratic Equation (A3). As expected, the derived “in situ b_bp(λ)” match well with the b_bp(λ) retrievals at the corresponding VIIRS bands from the IOP algorithm. The coefficient of determination R² for these two b_bp(λ) is 0.779, and the IOP ratio of derived/in situ b_bp(λ) is 1.010 ± 0.216.

The IOP in situ measurements for tuning the IOP algorithms were collected across Lake Taihu, and covered all four seasons. Thus, all variations of the parameters are related to the IOPs, such as particle size distribution, particle type, shapes, refractive index, a*_ph(λ) spectral shapes, a*_dg(λ) spectral shapes, etc., have already been included in this in situ dataset. Correspondingly, the IOP algorithm tuned with the in situ dataset should be insensitive to the changes of these IOP parameters. Consequently, the tuned IOP algorithm can be applied to the entire Lake Taihu and for all seasons to derive the IOP properties, in order to study the IOP spatial variability and temporal dynamics from the satellite observations. The IOP retrieval accuracy should be comparable to the IOP accuracy as described in Table 1 and Table 2.

Retrievals of a_t(λ), a_dg(λ), and a_ph(λ) at the VIIRS bands are also compared with the corresponding in situ data at different stations. Figure 4 provides the examples of these comparisons at various measurement stations. At station #06 [31.504°N, 120.179°E] on 7 January 2007, retrieved a_t(λ) generally match the in situ a_t(λ) spectrum in the blue and green bands (Figure 4a). The curvature of the derived a_dg(λ) spectrum matches well with the in situ data (Figure 4b). Similarly, a_ph(λ) retrievals also show a good match with the in situ a_ph(λ) (Figure 4c).

Figure 4. shows a_t(λ), a_dg(λ), and a_ph(λ) retrievals in comparison with the corresponding in situ measurements at station #09 [31.506°N, 120.146°E] on 29 July 2006. The a_t(λ) retrievals generally match well with in situ a_t(λ), except that a notable underestimation in the derived a_t(λ) at the 410 nm band is observed (Figure 4d). Similarly, a_dg(λ) retrievals also show a good match with the in situ measurements (Figure 4e). The derived a_ph(λ) data are consistent with the a_ph(λ) measurements (Figure 4f). At station #39 on 30 July 2006, a_t(λ), a_dg(λ), and a_ph(λ) retrievals also show good matches with those from the in situ measurements (Figure 4g–i).

4. IOPs from VIIRS-SNPP Observations between 2012–2018

4.1. Climatology IOPs between 2012 and 2018

Figure 5 shows the VIIRS-SNPP-derived climatology b_bp(λ) (Figure 5a–c), a_dg(λ) (Figure 5d–f), and a_ph(λ) (Figure 5g–i) at the bands 443, 551, and 671 nm from observations between 2012 and 2018. For each pixel, the climatology value is calculated as the median value of all the valid IOPs for this pixel from the VIIRS observations between 2012 and 2018. Of the three IOPs, a_ph(λ) is the lowest one in comparison with the corresponding b_bp(λ) and a_dg(λ). In general, b_bp(λ), a_dg(λ), and a_ph(λ) are not in phase with each other in terms of the spatial distributions and the spectral variations. At the bands 443 and 551 nm, a_dg(443) and a_dg(551) are the dominant IOPs in the three IOPs for most of Lake Taihu. At the VIIRS red band 671 nm, b_bp(671) for Lake Taihu is generally larger than a_dg(671) and a_ph(671), except for northern Lake Taihu.

For b_bp(λ), enhanced b_bp(λ) can be found in southern and southwestern Lake Taihu, while relatively low b_bp(λ) is found in the northern part of Lake Taihu. The spatial distribution of b_bp(λ) is consistent with the TSM in Lake Taihu [7]. It is also noted that b_bp(λ) slowly decreases spectrally from b_bp(443) to b_bp(671). In fact, this also suggests that the b_bp(λ) spectral power law slope η is slightly positive and close to 0 [7].

The IOP parameter a_dg(λ) data are composed of a_d(λ) from the non-algae detrital particles and a_g(λ) from the dissolved matters. Lake Taihu is featured with enhanced a_dg(443), having values over ~4 m⁻¹ in the eastern and southern regions of the lake. The a_dg(λ) decreases exponentially from a_dg(443) to a_dg(671). The spatial pattern of a_dg(λ) is not the same as the spatial pattern of b_bp(λ) in Lake Taihu, even though both a_d(λ) and b_bp(λ) are proportional to the TSM concentration, i.e., TSM × specific a_d*(λ) or b_bp*(λ). Specifically, in Gonghu Bay, a_dg(λ) is significantly pronounced, while b_bp(λ) in these regions are relatively low in comparison to those in southern Lake Taihu. This further implies that the a_g(λ) in Meiliang Bay and Zhushan Bay are higher than those in the other parts of Lake Taihu.

In comparison to a_dg(λ) and b_bp(λ), a_ph(λ) is usually low for most regions of Lake Taihu. However, pronounced a_ph(λ) can indeed be observed with a_ph(443) over ~1 m⁻¹ in northern Lake Taihu, such as Meiliang Bay and Zhushan Bay, while no enhanced a_dg(443) is observed. The enhanced a_ph(443) is consistent with reports of algal blooms in those regions [55].

4.2. Seasonal Variability of IOPs in Lake Taihu

In Lake Taihu, seasonal variations of IOPs are significant. Figure 6 shows the b_bp(λ), a_dg(λ), and a_ph(λ) in the spring season. Spatial distributions in b_bp(λ) in the spring (Figure 6a–c) are similar to those of the climatology b_bp(λ) with highs in southern Lake Taihu and lows in northern Lake Taihu. Enhanced a_dg(λ) (Figure 6d–f) can be found for the entire lake with a_dg(443) larger than ~4 m⁻¹. In the near-shore region of Lake Taihu, Zhushan Bay, and Meiliang Bay, a_ph(443) can reach over ~1 m⁻¹, while it is ~0.5 m⁻¹ for most of Lake Taihu.

The summer season is the least turbid season in Lake Taihu, with the lowest b_bp(λ) (Figure 7a–c). In the summer, a_dg(λ) also shows a significant drop in comparison with a_dg(λ) in the other seasons (Figure 7d–f). In fact, a_dg(443) in Lake Taihu is ~2–3 m⁻¹, which is less than half of the a_dg(443) in the spring season. The values of a_ph(λ) in the summer are generally larger than those in the spring. Enhanced a_ph(λ) can also be found in the western coastal region and northern region of Lake Taihu.

It is noted that a large portion of the data noise in a_ph(λ) from a single observation can be filtered out when tens of a_ph(λ) observations are used to produce the seasonal IOPs. The previous study [12] also shows that a peak Chl-a occurs in the summer season. The in situ data from 2006–2007 in the lake show that the average a_ph(443) in the spring, summer, autumn, and winter were 1.22, 1.45, 0.95, and 0.34 m⁻¹, respectively, while the corresponding VIIRS values from 2012–2018 are 0.65, 0.76, 0.59, and 0.46 m⁻¹, respectively. The in situ mean a_dg(443) for the spring, summer, autumn, and winter were 3.12, 2.50, 2.77, and 6.92 m⁻¹, respectively, compared with the corresponding VIIRS-derived mean a_dg(443) from 2012–2018 for these four seasons of 4.51, 2.14, 3.94, and 5.72 m⁻¹. Thus, the seasonal variations in IOPs from the in situ data in Lake Taihu qualitatively agree with the IOP retrievals from VIIRS-SNPP measurements, and further demonstrate that a_ph(λ) and a_dg(λ) products from these VIIRS observations are reliable, and can be used to study the spatial and temporal dynamics of phytoplankton in Lake Taihu.

Figure 8 shows the IOP spatial distributions in the autumn season. A broad increase of b_bp(λ) can be found in the autumn in comparison to the summer season (Figure 8a–c). Similarly, a_dg(λ) also shows significant increase in the summer (Figure 8d–f) with enhanced a_dg(λ) in the western coastal region and northern Lake Taihu. Also, it is noted that the spatial patterns of a_dg(λ) are not exactly the same as those of b_bp(λ) in this and other seasons. This can be attributed to the contribution of a_g(λ) in this season. In comparison to the changes of b_bp(λ) and a_dg(λ) from the summer to autumn, the change of a_ph(λ) from the summer to autumn is less significant for most of Lake Taihu. In Zhushan Bay and Meiliang Bay, a_ph(λ) decreases from the summer to autumn.

The highest b_bp(λ) and a_dg(λ) can be found in the winter season (Figure 9a–f). In southern Lake Taihu, b_bp(443) and a_dg(443) reach over ~1.5 m⁻¹ and above 4–5 m⁻¹, respectively. On the other hand, b_bp(λ) is ~1 m⁻¹, and a_dg(λ) is significantly smaller than the corresponding b_bp(λ) in northern Lake Taihu. Furthermore, a_ph(λ) is flat for the entire Lake Taihu, and no enhanced a_ph(λ) can be found in northern Lake Taihu.

4.3. Time Series of IOPs in Lake Taihu between 2012 and 2018

Figure 10 shows the IOP variations in Lake Taihu between 2012 and 2018. Of IOPs b_bp(λ), a_dg(λ), and a_ph(λ), a_dg(λ) is the most prominent one. This is also evident in Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9. Specifically, a_dg(443) is significantly larger than the corresponding b_bp(443) and a_ph(443). In the seven-year period, b_bp(λ) changed between ~0.3 and 2 m⁻¹ with the notable seasonal variability. As shown in Figure 6, Figure 7, Figure 8 and Figure 9, the highest b_bp(λ) occurred in the winter season and the lowest b_bp(λ) in the summer season. Interannual variability was also significant in these seven years. In the summers of 2014 and 2015, the b_bp(λ) was only ~0.3–0.4 m⁻¹. The highest b_bp(λ) occurred in the winter between 2017 and 2018 with b_bp(443) over ~2 m⁻¹ in Lake Taihu. Note that there is also an increasing trend for b_bp(443) in the period of 2016–2018.

Overall, b_bp(λ) and a_dg(λ) show similar seasonal and interannual trends in Lake Taihu (Figure 10b). In comparison to b_bp(λ), a_dg(λ) shows more seasonal and interannual variabilities between 2012 and 2018. In the winter season, a_dg(443) reached over ~4 m⁻¹, with the maximum a_dg(443) over ~6.0 m⁻¹ in the winter between 2017 and 2018. The low a_dg(443) occurred in the summer season with a_dg(443) ~2.0 m⁻¹ for most summers between 2012 and 2018. However, in the summer of 2014, a_dg(443) was only ~0.5 m⁻¹.

In comparison to b_bp(λ) and a_dg(λ), the phytoplankton absorption coefficient a_ph(λ) is the least significant IOP in terms of the magnitude and its contribution to the reflectance in the IOP model (Figure 10c). Seasonal and interannual variabilities in a_ph(λ) are not as significant as b_bp(λ) and a_dg(λ), e.g., a_ph(443) ranging between 0.5 and 1.0 m⁻¹. In the summer of 2013 and the spring-summer of 2016, a_ph(443) reached ~1.0 m⁻¹. This suggests that the phytoplankton blooms in the summer of 2013 and the spring-summer of 2016 were more significant than in the other years.

5. Discussion

The nL_w(λ) spectra in this study are derived using the SWIR-based atmospheric correction algorithm from the VIIRS observations. This is similar to the SWIR-based atmospheric correction algorithm for the MODIS observations [2]. In fact, the same MSL12 ocean color data processing system has been used in both studies. We examined the nL_w(λ) climatology derived from VIIRS observations [7] and MODIS observations in Lake Taihu [2,28], and concluded that the climatology nL_w(λ) spectra from these two studies are very close/similar in terms of both the magnitudes and the spatial patterns. This shows that VIIRS-derived nL_w(λ) spectra are reliable, and can be used to produce the IOP products in Lake Taihu.

On the other hand, nL_w(λ) bias in highly turbid waters may indeed occur in the blue band. It can reach up to ~0.5 mW cm⁻² μm⁻¹ sr⁻¹ at the blue band for extremely turbid waters like Hangzhou Bay [27], and much less at the other bands. The water reflectance spectra in Lake Taihu [7,28] suggest that the winter is the only season when the low biased nL_w(443) can occur. VIIRS-derived nL_w(443) may be biased low ~ < 0.2 mW cm⁻² μm⁻¹ sr⁻¹ with the SWIR-based atmosphere correction algorithm. The assessment of the nL_w(λ) in Lake Taihu implies that there should be little bias for b_bp(λ), a_t(λ), a_dg(λ), and a_ph(λ) in the spring, summer, and autumn seasons.

In the winter season, however, no or insignificant bias is expected for the b_bp(λ) product since b_bp(λ) is derived directly from nL_w(λ) at the NIR wavelengths. However, VIIRS-derived a_t(443), a_dg(443), and a_ph(443) may be biased high, within ~10%.

It has long been a challenge to derive the IOP products from satellite ocean color observations in turbid coastal and inland waters. This challenge comes from two issues, i.e., an atmospheric correction for deriving accurate nL_w(λ) spectra, and a valid IOP algorithm to retrieve IOPs in turbid coastal and inland waters. In the studies by Wang et al. [2,54], it has been shown that the SWIR-based atmospheric correction algorithm can be used to derive good quality nL_w(λ) spectra from satellite observations. On the other hand, an NIR-based algorithm was proposed, developed, validated, and demonstrated to derive the backscattering coefficient b_bp(λ) in turbid coastal and inland waters [42]. Based on the retrievals of b_bp(λ) with the NIR-based algorithm, this study shows that the other IOPs such as a_dg(λ) and a_ph(λ) can also be subsequently retrieved after tuning and optimizing the coefficients in the procedure to decompose a_t(λ) into a_dg(λ) and a_ph(λ) with the in situ measurements. With the in situ IOP data, we developed the IOP algorithm in Lake Taihu from the VIIRS-SNPP observations. The comparison between IOP data derived from the NIR-based IOP algorithm and the in situ measurements shows that a_t(λ), a_dg(λ), and a_ph(λ) can be calculated with reasonable accuracy in Lake Taihu. A high determination coefficient between the derived a_t(λ) and in situ-measured a_t(λ) also suggests that b_bp(λ) retrievals from the NIR-based IOP algorithm should also be reasonably accurate.

In this NIR-based IOP algorithm, the b_bp(λ) spectral slope η is computed from b_bp(745) and b_bp(862), as shown in Equation A8 in Appendix A. Even though it is not an input/output parameter, η is critical in defining the spectral shapes of the IOPs and in determining the accuracy of the IOP retrievals. In Lake Taihu, the η calculated from the in situ R_rs(λ) range between −0.2 and 2.5 with the mean η of 1.13. Seasonal change of η is significant. Low η ~ 0 normally occurs in the winter season with enhanced R_rs(λ), while η is generally high in the summer and autumn seasons with low R_rs(λ). Examination of the VIIRS-SNPP observations also shows the similar seasonal variability in Lake Taihu.

The spatial patterns and temporal variations of the IOPs in Lake Taihu are driven by the physical and biogeochemical dynamics in Lake Taihu. In northern Lake Taihu, the enhanced a_ph(λ) in the summer and autumn seasons can be attributed to the frequent occurrence of the cyanobacterial blooms in that region [10]. In the spring and winter seasons, the enhanced b_bp(λ) in southern and western Lake Taihu is consistent with the enhanced TSM concentrations caused by the sediment resuspensions due to high winds in these two seasons [7]. The spatial and temporal variations of a_dg(λ) in Lake Taihu are also driven by the physical and biogeochemical changes. The enhanced a_dg(λ) in the spring and winter seasons can be attributed to the high TSM in the water column [7] and degradation and release of fixed carbon in the phytoplankton and the underwater vegetation [15].

Both a_d(λ) and b_bp(λ) are proportional to the TSM concentration. Figure 5, Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10 show that the changes of a_dg(λ) and b_bp(λ) are different from each other. The main reason for the difference of the changes in a_dg(λ) and b_bp(λ) is the role of a_g(λ). In a turbid region like southern Lake Taihu, the a_d(λ), which is proportional to the TSM concentration just like b_bp(λ), is dominant in the a_dg(λ). However, in the less turbid waters of northern Lake Taihu, e.g., Meiliang Bay, a_g(λ) is significantly enhanced due to a high CDOM centration from the phytoplankton decay. Thus, a_g(λ) can be larger than a_d(λ) in this region. This leads to the different changes in a_dg(λ) and b_bp(λ).

It is also noted that no obvious seasonality of mean a_ph(λ) in the entire Lake Taihu shown in Figure 10c does not necessarily represent the regional a_ph(λ) seasonality in Lake Taihu. Figure 6, Figure 7, Figure 8 and Figure 9 clearly show that the northern and northwestern Lake Taihu regions experience notable seasonal variations of a_ph(λ). Enhanced a_ph(λ) can be observed in the summer-autumn seasons, while low a_ph(λ) occurs in the winter season. In the summer, a_ph(443) reaches over ~1.5 m⁻¹, while a_ph(443) is generally below ~0.5 m⁻¹ in the winter season.

Even though one of the purposes in this study is to develop the IOP algorithm for satellite observations in Lake Taihu, the approach for the regional NIR-based IOP algorithm can be further expanded to develop similar regional IOP algorithms for other coastal and inland water regions from a broad global perspective. On the other hand, the particles in Lake Taihu, the Yangtze River Estuary, and the Hangzhou Bay are all from the Yangtze River [56]. Thus, the nL_w(λ) spectral shapes for these waters are similar [28]. Since the coefficients, such as the exponential decay coefficient S, are determined by the mineral type, composition, texture, particle refractive index, etc., this further implies that the particle type and composition for these waters are similar. Thus, the IOP algorithm for Lake Taihu in this study can be correspondingly applied to the other similar waters, such as the Yangtze River Estuary and Hangzhou Bay, in order to decompose a_t(λ) into a_dg(λ) and a_ph(λ) in those regions.

6. Conclusions

In this study, we applied the NIR-based IOP algorithm to VIIRS-SNPP observations to characterize and quantify the dynamics of the b_bp(λ), a_dg(λ), and a_ph(λ) in Lake Taihu. In Lake Taihu, b_bp(λ), a_dg(λ), and a_ph(λ) show significant spatial variability in the period between 2012 and 2018. The southern Lake Taihu region features enhanced b_bp(λ) and a_dg(λ), while a_ph(λ) in northern Lake Taihu is significantly higher than those in the other regions. Of the three IOPs b_bp(λ), a_dg(λ), and a_ph(λ), a_dg(λ) is the most significant IOP, while a_ph(λ) is the least one in terms of the IOP magnitude. Enhanced a_dg(λ) in northern Lake Taihu also implies that the CDOM absorption coefficient a_g(λ) plays an important role.

This study also shows the significant temporal variability of b_bp(λ) and a_dg(λ) in Lake Taihu in the period between 2012 and 2018. The highest b_bp(λ) and a_dg(λ) occurred in the winter and the lowest b_bp(λ) and a_dg(λ) occurred in the summer. In the winter, b_bp(443) and a_dg(443) could reach over 1.5 and 5.0 m⁻¹, respectively, while they are ~0.5–1.0 and ~2.0 m⁻¹ in the summer. The highest b_bp(λ) and a_dg(λ) occurred in the winter between 2017–2018, and the lowest b_bp(λ) and a_dg(λ) occurred in the summer of 2014. In comparison to b_bp(λ) and a_dg(λ), both the seasonal and interannual variations of a_ph(λ) are small.