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Semi-analytical prediction of Secchi depth transparency in Lake Kasumigaura using MERIS data

  • Takehiko Fukushima
  • Bunkei Matsushita
  • Wei Yang
  • Lalu Muhamad Jaelani
Research paper


To investigate the long-term trend of light conditions in Lake Kasumigaura (a shallow eutrophic lake with high turbidity) in Japan, 215 images of MERIS data from the period 2003–2012 were processed at four stations using a semi-analytical algorithm to retrieve their inherent optical properties after atmospheric correction. Previously obtained Secchi depths (SDs) were somewhat underestimated by the proposed algorithms, and the ratio of the predicted SD to the measured SD changed with the ratio of tripton to chlorophyll a. A submodel was then built describing the ratio of scattering to backscattering based on the ratio of tripton to chlorophyll a (a trend supported by a number of previous reports) and applied to the prediction of SD in this lake. The model showed a gradually increasing trend at all stations in the predicted SD over the period, which was validated by the observations. The relationship between the measured and predicted SDs within a 2-day period was scattered, but showed a positive correlation at a significant level. In addition, this proposed method with the submodel describing the ratio of scattering to backscattering was applied to in situ reflectance spectra, and a correlation at a significant level was confirmed between the measured and predicted SDs.


Secchi depth Lake Kasumigaura Semi-analytical prediction of IOPs MERIS Scattering/backscattering 


Assessing the transparency of water bodies is one of the key issues in environmental monitoring and management, because it can affect both ecosystems and water amenities. The Secchi depth (SD) is an optical measure of water transparency assessed with the naked eye. It is determined by all optically active substances in the water; i.e., phytoplankton (represented by chlorophyll a), tripton (non-planktonic suspended solids), colored dissolved organic matter (CDOM), and pure water (Mancino et al. 2009). Although the SD measurement is easy, the frequent collection of these data for high numbers or large water bodies is costly and challenging for monitoring agencies (Nelson et al. 2003). Remote sensing using satellite images offers several advantages, including spatially and temporally extensive coverage and the possibility of measuring many water bodies simultaneously (Koponen et al. 2002). Therefore, combining remote sensing techniques and precise knowledge of water optics might be an efficient method of monitoring water transparency.

Many research groups have investigated the relationship between in situ measurements of SD and the spectral response of satellite sensors such as Landsat, MODIS (MODerate resolution Imaging Spectroradiometer on NASA’s Terra/Aqua), SeaWiFS (Sea-viewing-Wide-Field-of-view Sensor on the GeoEye’s OrbView-2 satellite), and MERIS [Medium Resolution Imaging Spectrometer on the European Space Agency’s (ESA) Envisat], as mentioned in Fukushima et al. (2016). However, most of these studies focused on empirical approaches, and thus the final applications tended to be time- and site-specific. Thus, an algorithm developed for a particular set of conditions cannot be applied to a water region/period with different conditions.

At the same time, significant efforts have been made to predict SD using quasi-analytical algorithms. For example, Chen et al. (2007) estimated the SD in Tampa Bay, Florida, by processing SeaWiFS satellite imagery with a two-step process: first, they estimated the diffuse attenuation coefficient at 490 nm [Kd (490)] using a semi-analytical approach; then, they assessed the SD using the empirical relationship with Kd (490) to obtain an excellent estimate of in situ SD values. Doron et al. (2007) proposed a semi-analytical algorithm that can predict the absorption coefficient at 490 nm [a (490)] and the backscattering coefficient at 490 nm [bb (490)]. They then obtained the relationship between (Kd (490) + c (490)) and (Kd (ν) + c (ν)), where c is the attenuation coefficient, and ν indicates the average over-photic range (400–750 nm; Doron et al. 2007), and they successfully applied these algorithms to MERIS, MODIS and SeaWiFS data in oceans (Doron et al. 2011).

For lakes with a wide range of turbidity conditions, Fukushima et al. (2016) used the maximum chlorophyll index (MCI) in semi-analytical retrieval procedure of inherent optical properties (IOPs) in clear (MCI < MCIthreshold; MCIthreshold = 0.0001 or 0.0016) or turbid waters (MCI ≥ MCIthreshold), and applied the chosen procedure to the targeted lake. SD values were then predicted based on the transmittance theory (Tyler 1968; Preisendorfer 1986), which integrated (Kd (λ) + c (λ)) over the photic range with the weights of both the photopic response of the human eye and the downwelling irradiance at the water surface. Further, the coupling constant was determined using the data from Davies-Colley (1988). Fairly good agreement was obtained between the predicted and observed SD values, but two problems remained in our previous study (Fukushima et al. 2016). The first problem was that only in situ-measured remote-sensing reflectance was used for our previous analysis, indicating the need for further testing of our previous method using space-borne data. The second problem was the underestimation of the SD prediction that was generally observed using the previous method in Lake Kasumigaura.

In the present study, we first modified the SD prediction algorithm (Fukushima et al. 2016) applicable to MERIS data and checked the performance using in situ-measured remote sensing reflectance. Then, the changes in SD in Lake Kasumigaura were predicted using the MERIS data from 2003 to 2012, processed by a newly developed atmospheric correction method (Jaelani et al. 2015) and compared with the observed values. Finally, we examined a modification of the SD prediction algorithm and compared it to other semi-analytical SD prediction schemes to enhance the accuracy of SD prediction. Because the SD changes observed in this lake for the targeted period were around 50 cm, as shown below, the SD prediction accuracy should be less than this value.

Data and methods

Study site

Lake Kasumigaura is the second largest lake in Japan, with a surface area of 171 km2 (Fig. 1). This lake is characterized by high turbidity, as shown below, and eutrophic conditions (total phosphorus: 0.101 mg l−1; total nitrogen: 0.99 mg l−1 during 2000–2011 at St. 9) due to its shallowness (mean depth of 4.0 m; maximum depth of 7.3 m) and the intensive human activities in the watershed (Fukushima and Arai 2015). Compared with the period before 2000, an increase in suspended solids (a significant increase from 13.8 mg l−1 during 1990–1999 to 16.9 mg l−1 during 2000–2011 at St. 9) and a decrease in chlorophyll a (a significant decrease from 71.7 µg l−1 during 1990–1999 to 53.2 µg l−1 during 2000–2011 at St. 9) were observed, suggesting a higher percentage of inorganic matter in water (Fukushima et al. 2005; Terrel et al. 2012; Fukushima and Arai 2015). This increase in suspended solids in the lake water accompanied by the increase in total silicon was likely attributable to sediment resuspension (Seki et al. 2006; Arai et al. 2012). At almost the same time, a shift of dominant phytoplankton species from cyanobacteria to diatoms was reported, probably resulting from the increase in total silicon (Arai and Fukushima 2014). However, one report indicated a tendency toward a decreasing tripton concentration (subtracted particulate organic matter from suspended solids) after 2007 (Nakamura and Aizaki 2016). In particular, a substantial increase of SD after 2010 (to be shown below) was observed, and this increase corresponded to a remarkable decrease in suspended solids (e.g., 16.3, 17.7, 13.0 and 12.3 mg l−1 in 2008, 2009, 2010 and 2011, respectively). In this manner, large and rapid changes in turbidity and in the composition of particulate matter are common in Lake Kasumigaura.
Fig. 1

Lake Kasumigaura and NIES water-quality monitoring stations

In addition, Lake Kasumigaura is so shallow that vertical stratification is easily destroyed by moderately strong winds (Muraoka and Fukushima 1986). Ishikawa et al. (1989) also reported that diurnal stratification resulted in a weak thermocline with a temperature difference of about 1 °C in summer, but this thermocline did not exist for more than a few days. Thus, we assumed that the characteristics of particle- and dissolved-matter-related optical properties do not change vertically.

Data and atmospheric correction

In-situ-measured remote sensing reflectance data were obtained at 10 lakes in Japan including Lake Kasumigaura, from 2009 to 2014 using a FieldSpec Hand Held spectroradiometer (Analytical Spectral Devices, Boulder, CO, USA) in the range of 325–1075 nm at 1-nm intervals. Details of the surveys were provided in Fukushima et al. (2016). We used only the data for Lake Kasumigaura (SD, chlorophyll a, suspended solids, etc.). SDs were measured using a white circular panel (0.3 m diameter) for all water regions. Reflection and SD measurements were performed from 9:30 to 16:00 h local time. In addition, we used the SD data from four stations (Fig. 1), which have been monitored monthly from 1976 to the present by the National Institute for Environmental Studies (NIES) (2016). SD measurements were performed using the same method [see NIES (2016)] by different observers between 10:00 and 15:00 h local time.

Full-resolution MERIS data (300 m) were obtained from EOLi (ESA’s Link to Earth Observation), the ESA’s client for the Earth Observation Catalogue and Ordering Services (2014). A total of 492 images were taken of all or part of Lake Kasumigaura during the period 2003–2012, and 215 images were used for the subsequent analysis, after cloud-covered images were excluded. The images were photographed between 9:30 and 10:30 h local time. The averaged value of a 3 × 3 pixel window (900 m × 900 m) was used to compare the estimated SD with the corresponding in situ measured SD. The use of the 3 × 3 pixel window rather than a single pixel can reduce the potential error in the geometric correction and in the dynamics of water bodies, as well as the potential error in spatial variability (Han and Jordan 2005). Therefore, NASA provides a protocol for a validation procedure (Bailey and Werdell 2006). In addition, Lake Kasumigaura is very turbid, as explained above, and thus is considered as optically deep. Therefore, it is not necessary to consider bottom contamination in this lake. There is a potential for land contamination, however, as pixels close to the lake shore are possibly affected by land. Since the stations chosen in this study were at least 1 km away from the nearest shores (i.e., using the pixels only located in water region), this influence was not considered.

The new standard Gordon and Wang algorithm with an interactive process and a bio-optical model (N-GWI) (Jaelani et al. 2015) was used for atmospheric correction. This algorithm was developed for application to MERIS data involving very turbid inland waters, such as Lake Kasumigaura, by modifying the GWI (Gordon and Wang 1994). The usefulness of the N-GWI has been confirmed in Lake Kasumigsura (Jaelani et al. 2015).

Semi-analytical SD prediction algorithm

This algorithm is composed of two stages (Fukushima et al. 2016). The first stage is the process for retrieving the IOPs based on the reflectance spectrum as follows.

Step 1: Judgment using MCI for selection between clear and turbid water regions.

Step 2: Estimation of the absorption coefficient (a) and backscattering coefficient of particulate matter (bbp) using QAA_v5 (Lee et al. 2009) in clear waters or QAA_turbid (Yang et al. 2013) in turbid waters. In the analysis of MERIS data obtained in Lake Kasumigaura, we compared QAA_turbid (as a standard) and QAA_v5, although large portions of the cases suggested the use of QAA_turbid (e.g., 87% for MCI ≥ 0.0001, 66% for MCI ≥ 0.0016 at St. 9). Underestimation of QAA_v5 was reported in Fukushima et al. (2016).

Step 3: Calculation of the beam attenuation coefficient (c) and diffuse attenuation coefficient (Kd). The value of c is the sum of a and b. The scattering coefficient (b) is calculated using the following equation:
$$ b = b_{\text{p}} + b_{\text{w}} = b_{\text{bp}} \times {\text{coef}}_{\text{bp}} + b_{\text{bw}} \times {\text{coef}}_{\text{w}} , $$
where bp is scattering by particle, bw is scattering by pure water, bbp is backscattering by particle, and bbw is backscattering by pure water (Morel 1974). As the first approximation, coefbp (the ratio of bp to bbp) was set to 55.6 based on the results of studies such as Mobley et al. (1993), and coefw (the ratio of bw to bbw) was set to 2 due to isotropic scattering. A modification of coefbp was attempted as explained below. The estimation of Kd was accomplished using both the relationship given by Kirk (1984) using b and the one given by Lee et al. (2005) using bb. The solar zenith angle used in the above models was calculated based on the sampling date, time, latitude, and longitude. In the case of satellite image analysis, SD prediction was done for the time when the image was taken.
The second stage is estimating SDs from IOPs (Fukushima et al. 2016) as follows:
$$ {\text{SD}} = \frac{\varGamma }{{\mathop \int \nolimits_{\lambda 1}^{\lambda 2} {\text{Eye}} \left( \lambda \right) \cdot {\text{Isurface}}(\lambda )[c(\lambda ) + {K}{\text{d}}(\lambda )]{\text{d}}\lambda \text{ / }\mathop \int \nolimits_{\lambda 1}^{\lambda 2} {\text{Eye}} \left( \lambda \right) \cdot {\text{Isurface}}(\lambda ){\text{d}}\lambda }}, $$
where c and \( K{\text{d}} \)d are the depth-averaged beam (from the water surface to the SD) and diffuse attenuation coefficients, respectively. When these coefficients do not vary vertically, they are expressed simply as c and Kd, respectively. Hereafter, we assume their vertical constancy. Eye (λ) and Isurface (λ) are the photopic response of the human eye and the downwelling irradiance at the water surface, respectively, and they are a function of the wavelength (λ). The denominator of Eq. (2) indicates the sum of c and Kd weighted toward the wavelength dependency of the photic response and the downwelling irradiance over the range of visible wavelengths from λ1 to λ2 (Preisendorfer 1986). The photopic function has a maximum of around 550 nm and is near zero at the two ends λ1 and λ2 (Takami 2011). In this study, λ1 and λ2 were set at 400 nm and 750 nm, respectively. We used the smoothed “global tilt” (Reference Solar Spectral Irradiance—ASTM G-173) as the downwelling irradiance at the water surface. The photopic function and the downwelling irradiance are shown in Supplementary Fig. 1.
In Eq. (2), Γ is a coupling constant that depends on variations in ambient conditions during measurements (Preisendorfer 1986). Equation (3) was deduced from the regression analysis between SD and (c + Kd) using the data from Davies-Colley (1988) (eight lakes with an SD range of 0.42–7.7 m). Davies-Colley considered this tendency to result from a change in the angle subtended by the target disc at the eye with SD.
$$ \varGamma = 8.12 \times \left( {\mathop \int \limits_{\lambda 1}^{\lambda 2} {\text{Eye}} \left( \lambda \right) \cdot {\text{Isurface}}(\lambda )[c(\lambda ) + K{\text{d}}(\lambda )]{\text{d}}\lambda \text{ / }\mathop \int \limits_{\lambda 1}^{\lambda 2} {\text{Eye}} \left( \lambda \right) \cdot {\text{Isurface}}(\lambda ){\text{d}}\lambda } \right)^{0.1076}$$

Correspondence to MERIS data

In order to compare the SDs predicted from 1-nm interval data and MERIS data, in situ remote sensing reflectance spectra were transformed to MERIS band-based spectra using Response function original 1. While MERIS has 15 bands, we used only the information from the first 10 bands (Band 1–10) to calculate the integral over the visible range as expressed in Eq. (2). The weight values on the respective bands used to calculate the integral were determined using the reflectance spectra observed in Lake Kasumigaura. In the QAA_turbid, the reflectance value at 780 nm corresponding to Band 12 is needed to calculate the parameter expressing the spectral slope (Y). However, since we used the SeaWiFS Data Analysis System (SeaDAS, for processing MERIS data, only 10 bands (Bands 1–10) remained after atmospheric correction was carried out. To prepare for cases without the Band-12 information, the equations for estimating the value of Y were investigated for reflectance at 440, 560, 681, 709 and 750 nm using the synthetic dataset extracted from IOCCG (2006). The following three equations were compared with the original equation (Yang et al. 2013):
$$ Y_{1} = - 0.2605 x^{2} + 1.2725 x + 0.8695, \quad x = \log \frac{\mu (440)}{\mu (560)} $$
$$ Y_{2} = 22.751 x^{2} - 5.116 x - 2.3773,\quad x = \log \frac{\mu (709)}{\mu (750)} $$
$$ Y_{3} = 168313 x^{6} - 117931 x^{5} + 31160x^{4} - 3834.9x^{3} + 238.03x^{2} - 6.308x - 0.0557, \quad x = \log \frac{\mu (681)}{\mu (709)}, $$
where μ(λ) is equal to bb(λ)/(a(λ) + bb(λ)), which is calculated with above-surface or subsurface remote-sensing reflectance. However, the values of x for Y2 and Y3 calculated for Lake Kasumigaura were rather different from those obtained by the calibrated dataset (IOCCG 2006), indicating an inappropriate application of regression Eqs. (5) and (6); thus, we did not use these equations, but we show them for further consideration in other water regions.
A standard case was set as QAA_turbid with Eqs. (1), (2), (3), and (4). Modified cases were expressed with the modified component(s) as shown later in Table 1.
Table 1

Comparison of predicted Secchi depths (SDs) using different components for in situ measured reflectance spectra (n = 33)


Case 1 (standard)

Case 2

Case 3

Case 4

Case 5

Case 6 (proposed)

Case 7

Case 8

Measured SD

Prediction algorithm

QAA turbid

QAA turbid

QAA turbid

QAA turbid

QAA turbid

QAA turbid

QAA clear No. 1

QAA clear No. 2


(Y estimation model)

750 vs 780 ratio

440 vs 560 ratio

750 vs 780 ratio

750 vs 780 ratio

440 vs 560 ratio

440 vs 560 ratio


Wavelength used for SD

Visible range

Visible range

490 nm

Visible range

Visible range

Visible range

Visible range

Visible range


Kd estimation










Reflectance spectra

1 nm

1 nm

1 nm

1 nm

MERIS band

MERIS band

1 nm

1 nm


b:bb model






New submodel




Average (m)










Standard deviation (m)










r with measured SD










r with case 1 (standard)










r correlation coefficient, * p < 0.05, ** p < 0.01

[Prediction algorithm] QAA turbid: SD prediction in turbid waters (Fukushima et al. 2016), QAA clear no. 1: in clear waters (Fukushima et al. 2016), QAA clear no. 2: Doron et al. (2011)

[Y estimation model] 750 vs 780: using Yang et al. (2013), 440 vs 560: Eq. (4) in the text

[Wavelength used] visible range: Fukushima et al. (2016), 490 nm: Doron et al. (2007)

[Kd estimation] b: Kirk (1984), bb: Lee et al. (2005)

[Reflectance spectra] 1 nm: in situ measurement using spectrophotometer, MERIS band: calculating using MERIS response function original 1

[b:bb model] constant: 55.6 for coefbp in Eq. (1), new submodel: Eq. (11)

Estimation of chlorophyll a and tripton concentrations

The semi-analytical model-optimizing and look-up-table (SAMO-LUT) (Yang et al. 2011) was used to retrieve the concentrations of chlorophyll a and tripton. This method was based on three previous semi-analytical models that estimated chlorophyll a, tripton and CDOM. Look-up tables and an iterative searching strategy were used to obtain the most appropriate parameters in the models. The accuracy of the MERIS-derived chlorophyll a concentration has been evaluated in our previous work by comparing it to the measured chlorophyll a concentrations obtained from the Lake Kasumigaura database (Matsushita et al. 2015). The results showed acceptable accuracy for all test sites (i.e., Sts. 3, 7, 9, and 12) with relative error in the range of 24–34%. In addition, the MERIS-derived chlorophyll a concentrations also showed similar seasonal and yearly variations with the measured chlorophyll a concentrations (correlation coefficient: r between 0.59 and 0.78, n = 63–68, p < 0.001). For the MERIS-derived tripton concentration, the estimation accuracy was only evaluated using the data collected from two field campaigns in Lake Kasumigaura (February 18, 2006 and August 7, 2008) due to the lack of measured tripton data in the Lake Kasumigaura database (with a normalized root mean square error of 23.2%, Yang et al. 2011).

Comparison with previously proposed methods

Doron et al. (2007) proposed the relationship between (Kd (490) + c (490)) and (Kd (ν) + c (ν)), in which c is the attenuation coefficient, and ν indicates the average over the photic range as shown below. Using this relationship, integration over the visible range as expressed by Eq. (2) is unnecessary.
$$ {K\text{d}}\left( \nu \right) + c\left( \nu \right) = 0.0989x^{2} + 0.8879x - 0.0467, \quad x = {K\text{d}} \left( {490} \right) + c(490) $$

Another semi-analytical algorithm proposed for MERIS and SeaWiFS sensors (Doron et al. 2011) was also compared in the estimation process of a (490) and bb (490) using two wavelengths at 490 and 560 nm instead of the original one using two wavelengths at 490 and 709 nm (Doron et al. 2007).

Evaluation of predicted SDs using MERIS images

We compared the predicted SDs with the measured SDs at the four stations in Lake Kasumigaura (Fig. 1; station numbers based on NIES). Bailey and Werdell (2006) recommended a time difference between the satellite data and in situ measurements of less than 3 h when the two were compared. However, to increase the available matchups, we relaxed this condition and assumed that water quality does not vary much within 2 days (e.g., only 8 matchups for 0-day difference). Therefore, the condition of a time difference of less than 3 days (i.e., 0, 1 or 2-day difference) was used for further analysis. Their agreement between the sets of SDs was analyzed by considering the wind speed at the time when the MERIS image was taken, as well as characteristics of particulate matter in lake waters. The mean wind speed at Tsuchiura (AMeDAS) (2016) and the ratio of tripton to chlorophyll a, respectively, also estimated by MERIS images, were used for these analyses.

Comparison of SD prediction components using in situ remote-sensing reflectance spectra

A variety of SD prediction components — e.g., the SD prediction algorithm (turbid or clear waters), Y estimation model [original or Eq. (4)], wavelength used for SD prediction (visible range or 490 nm), Kd estimation model (b or bb), reflectance spectra resolution (1-nm resolution or MERIS bands), and the b:bb model [Eqs. (1) or (11) explained below]—were compared with each other and with the measured SD values based on in situ measured-reflectance spectra (n = 33). The methods (cases 1–8) are compared in Table 1. Cases 2–5 were compared with case 1 as a standard in order to evaluate the influence of each component related to the Y estimation model, the wavelength used for SD prediction, the Kd estimation model, and the reflectance spectra resolution, respectively. Case 6 was a variant of case 5 with regard to the b vs bb submodel, as shown below. Cases 7 and 8 were SD prediction models for clear water proposed by Fukushima et al. (2016) and Doron et al. (2011), respectively. We also compared other cases, e.g., two or three components arranged conjointly.

Accuracy assessment

We used the root-mean-square error (RMSE), the mean normalized bias (MNB), and the normalized root-mean-square error (NRMS) to assess the model performance, defined as:
$$ {\text{RMSE}} = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{N} \left( {X_{\text{pred,i}} - X_{\text{meas,i}} } \right)^{2} }}{N}} $$
$$ {\text{MNB}} (\% ) = \bar{\varepsilon } = \frac{{\mathop \sum \nolimits_{i = 1}^{N} \varepsilon_{i} }}{N} $$
$$ {\text{NRMS}} (\% ) = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{N} \left( {\varepsilon_{i} - \bar{\varepsilon }} \right)^{2} }}{N}} , $$
where Xpred,i and Xmeas,i are the predicted and measured values, respectively. N is the number of measurements and \( \varepsilon_{i} (\% ) = 100 \cdot \frac{{(X_{\text{pred,i}} - X_{\text{meas,i}} )}}{{X_{\text{meas,i}} }} \) is the percent difference between the predicted and measured values. The RMSE values depend on the range of SD; in contrast, MNB and NRMS are independent of this range.


Comparison of SD prediction components using in situ remote-sensing reflectance spectra

The algorithm for clear waters (cases 7 and 8) gave significantly higher SD values that were only weakly correlated (r = 0.161 for case 7 and r = 0.415* for case 8; no asterisk: p ≥ 0.05, *: p < 0.05) with the measured ones (Table 1). In contrast, the SD values predicted using the algorithm for turbid waters (cases 1–6) were underestimated, but were well correlated with the measured ones, similarly to Fukushima et al. (2016). Differences in the Y estimation model (case 1 vs case 2), the wavelength used for calculation (case 1 vs case 3), the Kd estimation model (case 1 vs case 4), and the reflectance spectra resolution (case 2 vs case 5) had negligible effects on the predicted SD values, and the cases with two or three components arranged showed results quite similar to case 1 (data not shown). Thus, the following analyses using MERIS images were conducted using Y estimation with Eq. (4), the whole visible range, Kd estimation by scattering coefficient (b), and the MERIS bands (corresponding to case 5, and subsequently to case 6).

SD prediction using MERIS data

Underestimated SD values were obtained using MERIS data (Fig. 2 for St. 9). Similar tendencies were also observed at Sts. 3, 7 and 12 (results not shown). The underestimation for MERIS images was the same as that for in situ data, indicating problem(s) in the SD prediction model.
Fig. 2

Temporal changes in measured and predicted SDs at the center of Lake Kasumigaura (St. 9). The prediction was obtained using QAA_turbid with Eqs. (1), (2), (3) and (4) (standard case: fixed coefbp)

In order to clarify the reason(s) for the underestimation, we compared the influence of wind speed, season, and the characteristics of particulate matter on the prediction results. We considered wind speed because whitecaps might affect reflectance spectra (no whitecap detection algorithm was applied in our prediction system) and/or wave movement might disturb the SD measurement. Seasonal difference was investigated because the conditions of lake water stratification might affect SD values. In addition, the characteristics of particulate matter might have influenced the scattering of particles through a change in coefbp [Eq. (1)]. Figure 3 suggests that the last influence was dominant in determining the ratio of predicted to measured SD. The values of the average (±standard deviation) of RSD (=predicted SD/measured SD) were 0.57 (±0.27) for < 3 m s−1 and 0.69 (±0.15) for ≥ 3 m s−1 (insignificant difference p > 0.05; insignificant differences also were found for the threshold wind speed: 2 and 4 m s−1, respectively). In addition, the sampling seasons did not correspond to significant differences in the values of RSD (figure not shown; 0.60 ± 0.22 from July to September and 0.67 ± 0.30 from January to March, p > 0.05). On the other hand, RSD = 0.82 (±0.20) for tripton/chlorophyll a < 350 and RSD = 0.45 (±0.18) for tripton/chlorophyll a ≥ 350 (significant difference p < 0.01). These results indicate the possibility that the dominance of non-phytoplanktonic particles causes an underestimation of SD.
Fig. 3

Correlation between measured and predicted SDs within a 2-day difference (standard method: see text). Color classification by the ratio of tripton to chlorophyll a

Submodel for the relationship between bp and bbp

The abovementioned result suggested the need for a new submodel for the relationship between bp and bbp. We applied 15 different values (60, 55.6, 52.5, 50, 47.5, 45, 42.5, 40, 35, 30, 25, 20, 15, 10, and 5; 55.6 was the previous standard) to coefbp to find the value of the coefficient that produced the best agreement between the measured and predicted SD. The thus-determined coefbp was considered to be the actual ratio of b to bb. We then investigated the relationship between the value of the coefbp that gave the best agreement and the ratio of chlorophyll a to tripton as estimated from the satellite image (Fig. 4). The value of coefbp increases with the chlorophyll a to tripton ratio, indicating that the backscattering proportion of the total scattering increased with the tripton percentage in particulate matter. The logistic model between them was found to be as follows:
$$ \frac{{b_{\text{p}} }}{{b_{\text{bp}} }} = {\text{coef}}_{\text{bp}} = 53.78 - \frac{36.72}{{1 + \left( {\frac{r}{3.85}} \right)^{1.73} }}, $$
where r is the ratio of chlorophyll a to tripton multiplied by 1000. We used not the ratio of tripton to chlorophyll a but that of chlorophyll a to tripton because a type of logistic model with an upper limit corresponding to phytoplankton was expected. We referred to the method using Eq. (11) instead of the constant coefbp in Eq. (1) as the modified method. A linear model was also applied, but gave a worse regression coefficient.
Fig. 4

Relationship between the chlorophyll a/tripton ratio and bp/bbp values that produce the best agreement of predicted SD to observed SD

Predicted SD time series

Predicted SD changes were compared with the measured changes at the four stations (Fig. 5). The proposed model using Eq. (11) (case 6 in Table 1) was used for the prediction. At all stations, there were gradual increasing trends in the predicted SD, which were validated by the observed trends. The relationship between the measured and predicted SDs within a 2-day period between them (Fig. 6) was rather scattered, but showed a significant positive correlation (r = 0.234, p < 0.01, RMSE = 0.21 m, MNB = 7.2%, NRMS = 39.5%). The values of RSD for these data were 1.03 ± 0.33 (n = 35) at St. 3, 1.21 ± 0.48 (n = 35) at St. 7, 0.99 ± 0.35 (n = 33) at St. 9 and 1.04 ± 0.38 (n = 31) at St. 12, respectively. Slightly overestimated SD values were obtained at St. 7. In addition, this proposed method except for the Y estimation was applied to in situ reflectance spectra with a 1-nm resolution, and a good correlation with a slope close to unity was confirmed (Fig. 7; r = 0.529, p < 0.01, RMSE = 0.17 m, MNB = −2.7%, NRMS = 27.5%). These spectra had no influence from the atmosphere and had a higher spectrometric resolution compared with MERIS images.
Fig. 5

Temporal changes in measured and predicted SDs. The proposed model with Eq. (11) (case 6 in Table 1) was used for prediction. a St. 3, b St. 7, c St. 9, d St. 12

Fig. 6

Correlation between measured and predicted SDs using MERIS images at four stations in Lake Kasumigaura. The method is the same as in case 6 in Table 1

Fig. 7

Correlation between observed SD and predicted SD using in situ measured-reflectance spectra (1-nm resolution). The method is the same as in case 6 in Table 1 except the Y estimation using the ratio of the reflectance at 750 nm to the reflectance at 780 nm


Evaluation of our proposed model

Semi-analytical algorithms for retrieving IOPs in clear waters, i.e., QAA_v5 clear No. 1 and No. 2, gave SD values that were considerably higher than the observed ones. This result indicates that semi-analytical algorithms for clear waters are not applicable to turbid waters, although they give an excellent estimation of SD in clear waters (Fukushima et al. 2016; Doron et al. 2011). QAA_v5 uses reflectance information at shorter wavelengths of around 490–560 nm as the reference, while QAA_turbid uses longer wavelengths of around 750 nm. This means that QAA_v5 is not able to accurately predict the values of the absorption and scattering coefficients at longer wavelengths in turbid waters, and then gives overestimated SD values.

In contrast, the use of Eq. (7) for integrating the visible wavelength gave results similar to those from the integration using Eq. (2), even in turbid waters, when we used the semi-analytical algorithm for IOPs in turbid waters. Doron et al. (2007) proposed Eq. (7) using in situ COASTIOOC data covering a wide range of Kd (490) + c(490) from 0.1 to 30 m−1, probably resulting in its good performance for Lake Kasumigaura. The selection of Kd corresponded to negligible differences in SD prediction, probably because the estimation equations for Kd were obtained by numerical simulations for wide ranges of Kd values. With regards to the Y estimation model, we hope to perform a future estimation using the reflectance at 750 and 780 nm after a new method of atmospheric correction at 780 nm is developed.

Although our proposed model (case 6 in Table 1) solved the underestimation problem in the previous model (corresponding to cases 1 to 5), the SD values predicted by it were not in fairly good agreement with the measured ones, particularly for MERIS images (Fig. 6). These discrepancies may have been partly due to the time differences between the in situ measurements and satellite images. There were at most 2% differences among the obtained SD values when we predicted SD by changing the sampling times of the image from 9:30 to 15:00 h local time corresponding to the SD measurement. Further, the variability of the observed SD values was usually observed due to differences in observer eyesight and/or observation experience (Fukushima et al. 2016). Therefore, it might be more important that our proposed model was able to describe the long-term change in SD accompanied by the change in particulate matter content.

The predicted SD values for MERIS images were overestimated at St. 7 (Fig. 5b; RSD: 1.21), while fairly good agreement between them was obtained at other stations. A slight overestimation (less than 2%) of the predicted SD was expected because the SD measurement at this station was generally done from 14:00 to 15:00 h local time while the image was taken from 9:30 to 10:30 h local time. In addition, this station was the most turbid station in this study (averaged measured SD: 0.56 m at St. 3, 0.51 m at St. 7, 0.68 m at St. 9 and 0.63 m at St. 12), probably due to its close proximity to a large influent river (the River Sakura) and/or to gravel digging activity. The difference in tripton characteristics may affect Eq. (11), but a further study is needed to solve this problem.

bp:bbp ratio (coefbp)

Twardowski et al. (2001) reported an increase in the dimensionless backscattering ratio at 532 nm from 0.004 to 0.02 (bbp/bp; i.e., the reciprocal of coefbp) with depth in the Gulf of California and considered that the proportion of inorganic tripton (biogenetic and/or nonbiogenetic minerals) in the particulate matter raised the ratio (lowered the coefbp). They indicated that the change in the backscattering ratio was due to the change in the bulk particulate refractive index np from 1.04 to 1.05 in phytoplankton to 1.14–1.18 in inorganic matter. Loisel et al. (2007) reported low bbp/bp values (i.e., high coefbp) for a particle population made up of low refractive material such as phytoplankton, whereas high bbp/bp values were generally observed in the presence of a relatively high concentration of inorganic particles (this ratio at 650 nm ranged from 0.003 to 0.05) in the eastern English Channel and southern North Sea. Bowers et al. (2014) also reported that the backscattering ratio (bbp/bp; i.e., the reciprocal of coefbp) increased with the ratio of minerals to total suspended solids in the Irish Sea, Celtic Sea and English Channel and proposed a model describing this relationship. Using a global data set, Whitmire et al. (2007) indicated that the bbp/bp values at several wavelengths decreased with the chlorophyll a concentration.

In inland waters, characteristics similar to seawater have been shown. Shi et al. (2014) found that the value of the mass-specific scattering coefficient at 532 nm for inorganic suspended materials (0.71 m2 g−1) was approximately 1.6 times greater than that for organic suspended materials (0.45 m2 g−1). Thus, these results support the tendency of Eq. (11) theoretically.

Nakamura and Aizaki (2016) estimated the concentrations of tripton and particulate organic materials using the concentrations of particulate organic nitrogen and suspended solids, and showed that the tripton concentration decreased while particulate organic materials increased from 2004 to 2010. Our analysis period corresponds to this transition timing; therefore, the submodel related to bbp/bp should be involved. When the characteristics of particulate materials change substantially, it is necessary to understand and model the relevant material constituents to perform long-term monitoring of lake light conditions. Because the materials in the respective lakes differ, the submodel should be arranged based on site-specific characteristics.

Applicability of our SD prediction system

Our proposed SD prediction model (case 6 in Table 1) is composed of atmospheric correction, estimation of IOPs, prediction of tripton and chlorophyll a concentrations, and the SD prediction model. All of these activities should be applicable to turbid waters and can be obtained solely from satellite data. Methods for estimating the diffuse attenuation coefficient and euphotic zone depth, which are also important parameters describing lake light environments, are available for turbid waters (Yang et al. 2014, 2015).

The proposed method was only applied to MERIS data in this study. Its applicability to other ocean color sensors such as MODIS, SeaWiFS, and VIIRS should be tested in a future study to increase the frequency of estimated SD values. The applicability to other turbid water regions should be tried because the light characteristics of those regions may differ significantly. It is likely that the optical properties of inorganic particles and/or dissolved organic substances could affect the light regimes. Thus, the submodel relating to bbp/bp and/or the estimation model of chlorophyll a and tripton concentrations should be arranged corresponding to the light regimes. The indices expressing the characteristics, e.g., Kd × SD (Koenings and Edmundson 1991) may be useful for evaluating the applicability of the submodel, but a deliberate examination of plenty of data is needed.


The long-term trends of SD in a turbid lake were successfully predicted based on satellite images. A semi-analytical algorithm for retrieving IOPs in turbid waters and a submodel describing the relationship between bp and bbp were necessary to obtain reasonable SD values and their trend. Further studies on the light characteristics of particulate materials and their modeling are necessary to achieve accurate SD estimation in a wide variety of turbid water regions.



This research was supported in part by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sport, Science and Technology (MEXT), Japan (Nos. 23404015 and 26281039), the Global Environment Research Fund (S9-4) of the Ministry of Environment, Japan, and the River Fund (27-1271-001) in charge of The River Foundation, Japan. Monitoring data on SD were provided by the National Institute for Environmental Studies (NIES). We express our appreciation to 2 anonymous reviewers for constructive criticisms on earlier versions of the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10201_2017_521_MOESM1_ESM.pdf (11 kb)
Supplementary material 1 (PDF 11 kb)


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Copyright information

© The Japanese Society of Limnology 2017

Authors and Affiliations

  • Takehiko Fukushima
    • 1
  • Bunkei Matsushita
    • 1
  • Wei Yang
    • 2
  • Lalu Muhamad Jaelani
    • 3
  1. 1.Graduate School of Life and Environmental StudiesUniversity of TsukubaTsukubaJapan
  2. 2.Center for Environmental Remote SensingChiba UniversityChibaJapan
  3. 3.Department of Geomatics EngineeringInstitut Technologi Sepuluh NopemberSurabayaIndonesia

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