Underwater light field and remote sensing signals are mainly determined by inherent optical properties (IOPs), which are affected by the different physicochemical properties of water constituents (Jerlov, 1976; Morel and Ahn, 1990; Morel and Bricaud, 1991; Morel et al., 2006; Wozniak et al., 1991, 1995; Semovski, 1999). Studies of lake ecosystems and successful application of remote sensing to retrieve the concentrations of water constituents requires accurate determination of the relationships between IOPs and water constituents. Therefore, studies of the bio-optical properties of inland lake water are keys to understanding the influence of water constituents on the underwater optical field and stability of the bio-optical algorithm of lake water (Dickey et al., 1993; Bricaud et al., 2002). Many studies on bio-optical properties have been carried out, and indicated that the temporal and spatial variations of bio-optical models are significant (Gordon and Morel, 1983; Loisel and Morel, 1998; Gould et al., 1999; Morel and Maritorena, 2001; Morel and Belanger, 2006; Morel and Claustre, 2007; Morel, 2009). This is due to many factors. For instance, the refractive index and particle size influence the scattering and backscattering coefficients (Sun et al., 2009; Huang et al., 2012), and the package effect influences the phytoplankton absorption coefficients (Le et al., 2009). The relationship between IOPs and the water constituent concentration can be considered in terms of the relationship between chlorophyll-a concentration (CChl–a) and phytoplankton absorption (or backscattering coefficient). This is because of its role in ocean-color and of primary production estimation (Smith et al., 1984, 1996; Platt, 1986; Platt and Sathyendranath, 1988; Platt et al., 1990, 1991; Siegel et al., 2001).
However, resuspended sediments induced by waves and underset significantly modify the underwater light field and the principal optically-active constituents in inland shallow lakes. Minerals become the main optically-active constituents when sediments are resuspended. IOPs are fundamental parameters of water optical properties. Indeed, not only do they respond to physicochemical properties of the water constituents, but they also directly determine the underwater light field and remote sensing reflectance. Thus, more attention should be paid to the bio-optical relationships between IOPs and minerals in highly turbid inland water, where minerals are the main optically-active constituents. This is particularly true for shallow eutrophic lakes in monsoon areas, such as Taihu lake (Qin et al., 2004).
In the current study, the bio-optical relationships between IOPs (i.e. absorption, scattering, backscattering, and attenuation) and chlorophyll-a concentrations (Cchl–a) are reexamined. The concentration of inorganic suspended matter (ISM) is taken into account as an optically-active component more important than chlorophyll-a (chl-a) in Taihu lake. The bio-optical property of Taihu lake is discussed by touching upon the relationships between its IOPs, diffuse attenuation coefficients, and ISM.
The purpose of this study is: i) to establish the bio-optical relationships between IOPs and ISM; and ii) to determine the photosynthetically active radiation (PAR) capacity of ISM and OSM in a high dynamic ratio [(square root of area)/depth] inland shallow lake. The bio-optical relationships between IOPs and ISM could be used to quantify the influence of water constituents changed by hydrodynamics on the underwater light field and on the remote sensing signals of lake water. Furthermore, they could also be used to predict the optical properties and underwater light field via water constituents concentration, irrespective of measurement type (in situ or simulated by hydrodynamic model).
Study area and sample collection
Taihu lake is a typical inland shallow eutrophic lake. It is located in the East Asia Monsoon Area (EAMA), precisely in the Yangtze river delta. The inhabitants of the surrounding cities of WuXi, SuZhou, and HuZhou regularly drink its water. The mean depth of Taihu lake is 1.9 m and the area is 2338 km2 (Qin et al., 2004). The dynamic ratio [(square root of area)/depth] can reach 25.4. Thus, sediment in Taihu lake is extremely easy to resuspend, as demonstrated in the study by Bachmann et al. (2000).
Water sample collection and optical measurements were carried out in Taihu lake during five cruises in August 2006 (15 points in Meiliang Bay, no backscattering and scattering data), November 2006 (69 points in the whole Taihu lake), March 2007 (15 points in Meiliang Bay), November 2007 and November 2008 (69 points in the whole Taihu lake for both months) (Fig. 1).
Water constituents sample analysis
Water samples (placed inside 6-litre polyethylene bottles) were collected from all stations just below the surface (20 cm). Total suspended matter (TSM) was obtained by measuring the difference in weight of pre-combusted (450°C for 4 h) and dried (105°C for 4 h) 0.7-µm Whatman GF/F glass fibre filters before and after filtration of whole-water field samples. The filters were re-combusted at 450°C for 4 h to remove the weight of organic suspended matter (OSM), and weighed again to obtain ISM (Pegau et al., 2003). On the other hand, OSM was obtained by subtracting ISM from TSM. Samples of chl-a were filtered on Whatman GF/C filters. Chl-a was extracted with ethanol (90%) at 80°C and analysed spectrophotometrically at 750 and 665 nm, with correction for phaeopigments (Chen et al., 2006). Detailed information on water samples is provided in Tab. 1.
Optical property measurements in situ
Inherent optical property measurements
The spectral absorption a(λ) and beam attenuation c(λ) coefficients of the particles were measured 20 cm below the water surface using an AC-S profiler (WET Labs Inc., Philomath, OR, USA). The instrument provided an 85-wavelength output over approximately 400-760 nm.
The AC-S profiler was calibrated with pure water and air to ensure that its performance was within factory specifications (±0.005 m–1). The change in absorption due to temperature and salinity was corrected according to Sullivan et al. (2006):
amts(λ) is the corrected absorption;
am(λ) is the measured raw data;
ψt and ψs are the corrected parameters for temperature and salinity;
t and S are temperature and salinity measured in situ;
tr and Sr indicate the reference temperature and salinity.
The influence of salinity was ignored because Taihu lake is a fresh water lake.
The absorption was corrected for scattering errors according to Zaneveld et al. (1994):
ap + g(λ) is the absorption coefficient of dissolved matter;
at(λ) is the total absorption coefficient;
aw(λ) is the absorption coefficient of pure water;
amts(λref)is the corrected absorption at reference wavelength (λref =715 nm).
The scattering coefficient of coloured dissolved organic matter (CDOM) was ignored during the calculation of scattering coefficient of particle [bp (λ)]. The term bp(λ) could be calculated by following this formula (Moore et al., 2004):
cp + g(λ) is the attenuation and absorption coefficients of the particulate;
ap + g(λ) is the attenuation and absorption coefficients of the dissolved matter.
The backscattering coefficient of particle bbp(λ) was measured 20 cm below the water surface using a BB9 profiler (WET Labs Inc., Philomath, OR, USA). The BB9 profiler measures scattering at a single angle in a backward direction (117°) at nine wavelengths (412, 440, 488, 510, 532, 595, 660, 676, and 715 nm).
For the population of photons scattered within the remote sample in front of the sensor, there is attenuation along the path from the light source through the sample volume to the detector. This result, however, underestimates the true volume scattering in the hydrosol. Consequently, a weighted function was used to calibrate this attenuation effect.
β(117°, λ)* is the raw total volume scattering coefficient;
Scale Factor(λ) is the calibrated scale factor;
Output(λ) is the measured signal output of the scattering metre;
Dark Counts(λ) is the signal obtained by covering the detector with black tape and submersing the sensor in water; Both Scale Factor(λ) and Dark Counts(λ) were provided in the scattering metre calibration sheet for different wavelengths by WET Labs.
After the scaling factor was calibrated, only the absorption of the incident beam required correction. The calculated raw total volume scattering coefficient [β(117°, λ)*] at a given value of absorption coefficient was corrected to zero absorption:
β(117°, λ) is the corrected total volume scattering coefficient (in m–1sr–1);
a(λ) is the corresponding total absorption coefficient that can be obtained using an AC-S profiler.
The particulate volume scattering coefficient [βp(117°, λ)] was obtained by subtracting the volume scattering coefficient of pure water from β(117°, λ) (Morel, 1974), and bbp(λ) was calculated using equation (6) with an uncertainty of 4% (Boss et al., 2001):
Xp is a parameter determined from measurements of the volume scattering coefficient with a high angular resolution in various types of water (Boss et al., 2001).
Downward irradiance measurements
The spectra of downward irradiance [Ed(λ)] were measured at discrete depths (20, 40, 60, 80, 100, and 120 cm) with RAMSES-ACC-VIS (Trios, Rastede, Germany). The output wavelength range of this instrument covered 320-950 nm, with a channel width of approximately 3.3 nm. The detection accuracy was better than 6% (depending on the spectral range). The downward irradiance obtained at different depths z [Ed(z,λ)], was corrected for the slight shift in incoming solar radiation (monitored on the deck) during the experiment. All optical measurements in the current study were performed under sunny and steady conditions. The influence of ship shadow was avoided by using a long crane operated from the stern and oriented in the direction of the sun. The surface wave influence was offset using the method provided by Zaneveld et al. (2001).
Ed(z,λ) spectra, corresponding to the same incident radiation at the same sites, were used to calculate the diffuse attenuation coefficient of the downward irradiance Kd(λ) (Smith and Baker, 1981; Darecki and Stramski, 2004):
z and zr are depth and reference depth z;
l is one (number);
ln is Napierian Logarithm operation
Ed(z, λ) is the downward irradiance at depth z;
Ed(zr, λ) is the downward irradiance at the reference depth zr;
Kdw(λ) is the diffuse attenuation coefficient of pure water;
Kdbio(λ) is the diffuse attenuation coefficient except the pure water at wavelength λ.
Kdw(λ) can be expressed as[aw(λ)+bbw(λ)]/(0.017/0.0194), where aw(λ)and bbw(λ) are absorption and backscattering coefficients of pure water, respectively. The sum of aw(480) and bbw(480) was 0.017 (Pope and Fry, 1997), and Kdw(480) was 0.0194, as estimated by Baker and Smith (1982). After the diffuse attenuation coefficient for pure water [Kdw(λ)] was subtracted from Kd, the Kdbio was obtained.
Absorption measurements in laboratory
Total particulate absorption measurements
The quantitative filter technique (QFT) method (Yentsch, 1962; Mitchell and Kiefer, 1988; Mitchell, 1990) was used to quantify the total particle absorption [ap(λ)]. Water samples (100-200 mL) were filtered through a 47-mm diameter Whatman fiberglass GF/F filter under a low vacuum pressure. If too thick, the water samples were first diluted to ensure that the measured optical density of particulate matter was less than 0.4. Absorption spectra were recorded every 1 nm from 350 to 800 nm using a Shimadzu UV-2550PC UV-Vis spectrophotometer (Shimadzu Corporation, Kyoto, Japan). The optical density of the sample filters (ODf) at 750 nm was adjusted to zero. Subsequently, the path length amplification factor (β), which was the increased path-length of light due to multi-scattering in the filter, had to be corrected (Mitchell and Keifer, 1984; Hoepffner and Sathyendranath, 1992, 1993; Cleveland and Weidemann, 1993; Arbones et al., 1996). The corrected optical density (ODs) of the sample filters was calculated as follows:
A and B are empirical coefficients. In the current study, they were set to 0.378 and 0.532 according to Zhang (2009). The absorption coefficients of particle ap(λ) were calculated according to Cleveland and Weidemann (1993):
2.303 is the factor used to convert the base 10 to a natural logarithm;
ODs(λ) is the corrected optical density at wavelength (λ);
S is the filter clearance area;
V is the filtered volume;
R is semidiameter of fiberglass GF/F filter.
Non-pigment particulate absorption measurements
Pigment in the water samples was removed using 0.1% sodium hypochlorite (NaClO) (Mueller, 2003). The absorption peak of chl-a at 675 nm was examined to determine whether the pigment had been removed completely. If an absorption peak existed at this wavelength, some pigment remained in the water. This process was repeated until the peak value disappeared. Then, the absorption spectra of the bleached water samples were measured again to obtain the absorption coefficient of non-pigment particles aNAP(λ) by using the same method used for total particulate absorption.
Pigment particulate absorption measurements
The absorption coefficient of pigment aph(λ) was obtained by subtracting the absorption coefficient of non-pigment particles aNAP(λ) from the absorption coefficient of particle ap(λ):
Colored dissolved organic matter absorption measurements
Water samples were collected in 2 L acid-cleaned plastic bottles and held in an icebox while they were in the field. Water samples were first filtered through a 47 mm diameter Whatman fiberglass GF/F filter with 0.70 µm pores, and then refiltered through a 25 mm diameter Millipore filter (Millipore Corporation, Billerica, MA, USA) with 0.22 µm pores. The absorption spectra of the filtered water were measured between 240 and 800 nm at 1 nm intervals using a Shimadzu UV-2550PC Uv-Vis spectrophotometer (Shimadzu Corporation, Kyoto, Japan) with a 1×4 cm quartz cuvette, where Milli-Q water (Millipore Corporation, Billerica, MA, USA) was used as the reference. The absorption coefficient of CDOM was obtained using the following equation (Bricaud et al., 1981):
aCDOM(λ´) is the uncorrected CDOM absorption coefficient at wavelength λ;
2.303 is the factor used to convert the base 10 to a natural logarithm;
D(λ) is the optical density at wavelength λ
r is the cuvette light path length in metre.
The absorption coefficient was corrected by backscattering small particles and colloids that had passed through the filters using the following equation (Bricaud et al., 1981; Green and Blough, 1994; Keith et al., 2002):
aCDOM(λ) is the corrected absorption coefficient at a given wavelength (λ);
aCDOM(λ´) is the uncorrected CDOM absorption coefficient at wavelength λ;
aCDOM(750´) is the uncorrected absorption coefficient at 750 nm.
Results and Analysis
Spatial and temporal variation of water inherent optical properties
Significant spatial and temporal variations of optical properties were found in Taihu lake. The range of the IOPs and the parameters associated with them for each water constituent are listed in Tab. 2. On the whole, the data range of IOPs and the parameters is very wide and the difference among time series is very big. The scattering coefficient related to the concentration of TSM in November 2007 and 2008 is much bigger than that recorded in November 2006 and March 2007. The backscattering coefficient in March 2007 was grouped in a value area bigger than other time series data. This is because the percentage of ISM is much higher, although in March 2007 TSM is not much bigger than in other time series data. The backscattering ratio [B(λ)=bb(λ)/b(λ)] can be used as an indicator of the ratio between ISM and OSM (Jerlov, 1976; Aas, 1981; Twardowski et al., 2001). A high backscattering ratio corresponds with a high percentage of ISM (i.e. high concentration of ISM), and B should linearly correlate with ISM/OSM. However, the multi-scattering effect restrains the covariation of B and ISM in high ISM concentrations. Consequently, a significant logarithmic relationship between B and ISM/OSM was found in this study, except for the data obtained in November 2006 (November 2008: R2=0.6216, P<0.001; November 2007: R2=0.5084, P<0.001; March 2007: R2=0.4398, P<0.005; November 2006: R2=0.1354, P<0.1).
The variations of scattering and attenuation coefficients were given not only by the values, but also by the spectral shape [IOPs decrease with wavelength by power law exponent, namely, IOP(λ)=IOP(λ0)(λ / λ0)SIOP]. The wavelength dependence of the scattering and attenuation coefficients is significant. The particle size distribution of the water constituents can be traced by the spectral shape of the attenuation coefficients (Sc)(Boss and Pegau, 2001). Small-sized particles lead to high Sc. The largest value of Scwas found in March 2007, followed by November 2008, and November 2006. The Scin November 2007 was similar to that in November 2006. The spectral shape of the scattering coefficient (Sb)in the current study was beyond the range of those inprevious studies. Sb in Taihu lake was steeper than -0.6 (Morel et al., 2006) and -0.48 (Snyder et al., 2008), but much smoother than -0.93 (Bernard et al., 2001). Small Sb indicates high absorption of CDOM and non-pigments at short wavelengths (this is the primary influencing factor), and relatively high scattering at long wavelengths (such as that in November 2006). The absorption values of CDOM and non-pigments in March 2007, November 2007, and November 2008 were smaller than that in November 2006. On the contrary, Sb values in March 2007, November 2007, and November 2008 were steeper than that in November 2006. The spectral shape of the backscattering coefficient (Sbb) in Taihu lake was much steeper than the values of -1.15 (Song and Tang, 2006) and -0.94±0.21 (Snyder et al., 2008) found in ocean water because of the high backscattering property of small particles at short wavelengths. Tab. 2 shows the range of Sc, Sb, and Sbb at each time series.
Relationship between inherent optical properties and chlorophyll-a concentration
Fig. 2 provides the attenuation coefficients at 440 nm [c(440 nm)], the absorption coefficients at 677 nm [aTotal(677 nm)], and the scattering [b(532 nm)] and backscattering coefficients at 532 nm [bb(532 nm)] of particles (pure water absorption and scattering coefficients were subtracted) (N=222) in comparison with the concentration of chl-a. A poor relationship between IOPs and chl-a was found (Fig. 2A-D), indicating that chl-a may not be the main optically-active constituent in Taihu lake. Moreover, the high absorption of non-pigments at short wavelengths caused the correlation between c(440 nm) and chl-a to become significantly low.
Carder et al. (1991) suggested that the chl-a dependence of the aphcould differ between regions and times. In the current study, the relationship between aph (675 nm) and chl-a was compared before and after the package effect was corrected. The package effect is defined as the ratio of aph* (the specific absorption coefficient of pigmented cells) to asol* (the specific absorption coefficient of the same cellular matter ideally dispersed into the solution). This dimensionless factor [defined as Qa’] was theoretically formulated by Morel and Bricaud (1981) and Bricaud and colleagues (1990, 1995, 1998):
p′(λ) is a process variable, no specify physical significance.
ρ′(λ) is process variable, no specify physical significance.
a*sol(λ) is the intracellular chlorophyll-specific absorption coefficient;
CIis the intracellular chl-a concentration;
d is the phytoplankton cell diameter.
The a*sol(λ) coefficient of chl-a was 0.0201 at 675 nm, as given in Bidigare et al. (1990). Qa’(λ) was calculated by following the method of Le et al. (2009). Fig. 3 presents aph(λ) in comparison with chl-a before and after the package effect was corrected. The package effect caused by high Cchl-a destroys the correlation between the pigment absorption coefficient at 675 nm [aph(675 nm)] and Cchl-a (Fig. 3A,B, and B’). The coefficient determined between aph (675 nm) and Cchl-a after the package effect correction was significantly improved. The package effect is a primary influencing factor for the bio-optical model between aph (675 nm) and chl-a in Taihu lake.
Relationship between inherent optical properties and inorganic suspended matter
The correlations between IOPs and ISM were examined as well. Fig. 4 A-D provides the attenuation coefficient at 532 nm [c(532 nm)], the absorption coefficient at 440 nm [aTotal(440 nm)], the scattering coefficient at 532 nm [b(532 nm)], and the backscattering coefficient at 532 nm [bb(532 nm)] of particles in comparison with ISM. Specific symbols were used to discriminate between the datasets of the four time series. Fig. 4 indicates that ISM is the main optically-active constituent in Taihu lake. The resuspended sediment dramatically increases the ratio of ISM to TSM. The highest percentage of ISM to TSM can reach up to 95%, and the mean percentage of ISM can reach up to 65.21%. ISM is the main contributor to the scattering and backscattering coefficients (Stramski et al., 2004; Snyder et al., 2008). Thus, the main optical property in Taihu lake is scattering. A single scattering ratio [b(λ)/c(λ)] can reach up to 0.93 (mean value of all sample sites and wavelengths) (Fig. 4E, F).
Tab. 3 provides the relationships of the attenuation and scattering coefficients at 532 nm with ISM and the relationships of absorption at 440 nm with ISM. The c(532 nm) (R2=0.80, P<0.0001, n=213), b(532 nm) (R2=0.82, P<0.0001, n=213), and bb(532 nm) (R2=0.57, P<0.0001, n=213) significantly increase with ISM. The aTotal(440 nm) (R2=0.61, P<0.001, n=213) also increases with it. Fig. 4B presents the scattering plot of aTotal(440 nm) with ISM. The correlations between c(532 nm), b(532 nm), and ISM are stronger than that between aTotal(440 nm) and ISM. This is because water constituents in inland water are independent of one another, and the absorption peak for chlorophyll may be found at 440 nm. However, as a result of the temporal variations of the IOPs, the parameters and the correlation coefficients (R2) determined in each relationship between IOPs and ISM are significantly different (Tab. 3). In each function, the parameters, i.e. the slope, intercept, and R2 of the function for c(532 nm), aTotal(440 nm), b(532 nm), and bb(532 nm) with ISM at each time series, were compared with one another. The variation coefficient (VC) of the slope, intercept, and R2 in each relationship was as follows:
c(532 nm) with ISM:VC of slope=0.14;
VC of intercept=0.12; VC of R2=0.10);
b(532 nm) with ISM: VC of slope=0.2;
VC of intercept=0.12; VC of R2=0.11);
aTotal(440 nm) with ISM: VC of slope=0.53;
VC of intercept=0.49; VC of R2=0.23.
As it is manifest, VCs for c(532 nm) and b (532 nm) with ISM were much smaller than that for a Total (440 nm) with ISM. This implies that the temporal variations of the c(532 nm) and b(532 nm) influencing factors are smaller than the aTotal(440 nm) influencing factors. Therefore, the functions for c(532 nm) and b(532 nm) with ISM are more valid compared to aTotal(440 nm) with ISM. The backscattering coefficient was highly determined by ISM for its high refractive index. Thus, owing to the different physicochemical properties of water constituents at each time series, the variation coefficients of slope, intercept, and R2 for bb(532 nm) with ISM are 0.20, 0.38, and 0.02, respectively. The R2 of each function for bb(532 nm) with ISM at different time series is very high (2006-11:0.80; 2007-3: 0.84; 2007-11: 0.82; 2008-11: 0.85). In contrast, the R2 of function for bb(532 nm) (0.5723) with ISM for all the sampling points is very small. This indicates that the relationship between bb(532 nm) and ISM is valid at each time series, while it is not valid for all the sampling points. Consequently, different functions should be used to describe the relationship between bb(532 nm) and ISM.
The variation of diffuse attenuation coefficient of particles with chlorophyll-a concentration and organic suspended matter
The apparent optical property (AOP) (diffuse attenuation coefficient of particle, Kdbio) was expressed by the main optical active constituent in Case 1 water (refferred to as phytoplankton dominant clear water) to study the bio-optical properties of oceanic waters (Gordon, 1987; Morel and Maritorena, 2001; Morel et al. 2007). Although various parameterisations of Kdbio have been proposed in previous studies, all its functions were parameterised by Cchl–a. Being Taihu lake a typical inland shallow lake, the composition of its water constituents is significantly affected by terrigenous and resuspended sediment. Thus, in the study, the traditional main optically-active constituent (Cchl–a) was replaced by ISM in order to extend the previous idea that Kdbio can be expressed by the main optically-active component to Taihu lake and to confirm the main optically-active constituent. The relationships between Kdbio(675 nm) and Cchl–a (Fig. 5A) and the relationship between Kdbio(440 nm) and OSM were detected (Fig. 5B). The poor relationship of Kdbio(440 nm) and Kdbio (675 nm) with Cchl–a and OSM was also explored. Total OSM significantly correlates with Cchl–a (P<0.0001, R2=0.88, including the point in the ellipse; P<0.005, R2=0.63, excluding the point in the ellipse) (Fig. 5C). Thus, phytoplankton debris is the primary component of OSM but is not the primary contributor to Kdbio. This is similar to results in previous studies on Taihu lake (Zhang et al., 2004a, 2004b).
The diffuse attenuation coefficient of particle variation with inorganic and total suspended matter
ISM is the primary component of TSM (mean percentage of ISM for all sample points is 65%, SD=0.19) (Fig. 6C). This is mainly caused by the resuspended sediments. Consequently, ISM is taken into account as an important optically-active component to describe the bio-optical properties in Taihu lake. The relationship between Kdbio and ISM and TSM was determined (Fig. 6 A,B) and out of it some remarkable linear functions were found:
0.094 can be treated as the specific diffuse attenuation coefficient of ISM at 532 nm;
1.51 could be the contribution of OSM and CDOM at 532 nm to the Kdbio;
RMSE is the Root Mean Square Error.
0.062 can be treated as the specific diffuse attenuation coefficient of TSM at 532 nm;
1.38 could be the contribution of CDOM at 532 nm to the Kdbio;
RMSE is the Root Mean Square Error.
The regressive result between Kdbio and TSM is not as good as that between Kdbio and ISM. This is because OSM hinders the stability of the regressive function for Kdbio and TSM (the departure from linearity between Kdbio and TSM is expressed by a large percentage of OSM; sample points are in the ellipse in Fig. 6B). The linear parameters in equation (15) are very close to the laboratory experiment results in the study by Zhang et al. (2004b).
Separate regression analyses of inorganic and organic suspended matter for Kdbio at wavelength λ
According to its linear additive rule, Kdbio(λ) can be expressed as:
K*dISM(λ) is the specific diffuse attenuation coefficient of inorganic particles;
CISM is the concentration of ISM;
K*dOSM(λ) is the specific diffuse attenuation coefficient of organic particles;
COSM is the concentration of OSM.
Equation (17) can be used to derive the average specific diffuse attenuation coefficient of organic and inorganic particles in Taihu lake. First, the Kdbio(λ) values at each wavelength are divided by COSM (or CISM). Second, a linear regression (R2≥0.60, P<0.005) between Kdbio(λ)/COSM [or Kdbio(λ)/CISM] and CISM/COSM (or COSM/CISM) for each dataset is used to obtain the slope of line, [i.e., K*dISM(λ) and K*dOSM(λ)] (Fig. 7). The spectral property of K*dOSM(λ) at approximately 675 nm indicates the chl-a absorption peak. Furthermore, the value of K*dOSM(λ) is much larger than the specific diffuse attenuation coefficient of chl-a [K*dchl–a(λ)] in previous studies (Smith and Baker, 1978; Morel, 1988; Mitchell and Holm–Hansen, 1991; Stambler et al., 1997; Figueroa, 2002). The spectral property of K*dISM(λ) in the 420-750 nm range is smooth and similar to the scattering and absorption spectral properties of ISM. The K*dISM(λ) at 532 nm is 0.0898, i.e. it is approximately close to the slope of the linear function between Kdbio and ISM – 0.0942 – retrievable in equation 15. The coefficient for K*dISM determined in the 350-450 nm range is much lower. ISM has a low contribution to short wavelengths during absorption. Hence, the coefficient for K*dOSM determined over the whole wavelength range is very high. This is because the OSM absorption coefficient is very large at short wavelengths, and CDOM significantly correlates with OSM (R2=0.51, P<0.005).
In conclusion, as an important optically-active constituent, ISM highly correlates with IOPs and significantly determines the underwater light field (Kdbio) in Taihu lake. On the basis of the present data, the following conclusions can be drawn. First, the active optical factor in Case 1 water (chl-a) is replaced by ISM in the Taihu lake water and in it IOPs are more sensitive to ISM. Second, the IOPs significantly correlate with ISM, and the equation parameters of the present data do not differ significantly from each other at different cruises, particularly for the function of c(532 nm) and b(532 nm) with ISM. Thus, the parameters in the models are valid. Third, the diffuse attenuation coefficient is significantly affected by ISM and linearly correlates with it. The specific diffuse attenuation coefficients of organic and inorganic particles are different, especially in the wavelength range of 350-450 nm. K*dOSM(λ), which includes the chl-a absorption property at 675 nm, is larger than K*dISM(λ). Hence, the attenuation ability of OSM is stronger than that of ISM.