4.1. Linear Mixed Effect Model Results
Our study agrees with previous studies to the effect that Lake Erie is to be considered as a Case II water. O’Donnell et al.
(2010) employed modern instrumentation to measure IOPs and AOPs in the western basin of Lake Erie. The study also concluded that the characterization of IOPs and AOPs supports the fact that the western basin of Lake Erie is an optically complex Case II system. Therefore, in such case, red and NIR band ratios are the most reliable predictors in regression algorithms to estimate chl-a concentration in Lake Erie. Results from the LME models calibration show that the band ratio of B07:665 nm to B09:708.75 nm is highly negatively correlated with the variations of chl-a concentration in Lake Erie. Gitelson et al.
(2007) applied a two-band model, as the special case of a conceptual three-band model [39
], to the turbid (Case II) waters of Chesapeake Bay to estimate chl-a concentration [40
]. The tuning process found the ratio of 720 nm to 670 nm as the optimal spectral band ratio, with the maximal R2
of 0.79 in a positive correlation. Water samples collected from Chesapeake Bay contained widely variable chl-a concentrations (9 to 77.4 mg·m−3
), when SDD ranged from 0.28 to 1.5 m. Duan et al.
(2010) also found the band ratio of 710/670 nm to be positively correlated with chl-a concentration in eutrophic Lake Chagan with R2
= 0.70. Chl-a concentration in this lake was between 6.40 and 58.21 mg·m−3
and SDD rarely exceeded 0.50 m [11
]. Simis et al.
(2005, 2007) correlated the absorption of chl-a to MERIS band ratio of 708.75 to 665 nm for turbid, cyanobacteria-dominated lakes in the Netherlands and Spain. Hicks et al.
(2013) reported that the logarithmic scale of SDD measurements and logarithmic scale of Landsat 7 ETM+ band ratio of B01(0.450–0.515 nm)/B03(0.630–0.690 nm) were positively correlated with a high correlation (R = 0.82). This study was conducted for shallow lakes (ranging from 1.8 to 8.7 m depth) in the Waikato region in New Zealand, with SDD in situ
observations varying between 0.005 and 3.78 m [41
]. In our study, the highest correlation between MERIS band ratios and SDD variations in Lake Erie was estimated for the band ratio of B06:620 nm to B04:510 nm.
The selected band ratios were used to develop two separate LME models to estimate chl-a concentration and SDD in Lake Erie. The models were evaluated using the testing data in a cross validation approach. Results showed that LME model was in a high agreement with the chl-a in situ
observations with RMSE and MBE values of 0.31, and 0.018, respectively, in a logarithmic scale. The overestimation of chl-a concentration derived from the LME model can be attributed to the contribution of TSM in the red/NIR region of the spectrum that is not necessarily correlated with chl-a concentration. In turbid waters such as Lake Erie, the signals measured in the red and NIR regions can no longer be attributed to the chl-a concentration absorption and fluorescence and water alone, while TSM can also confound the signal [1
]. Although, formation of blooms in a thick surface layer can dominate the reflectance and eliminate much of the contribution of TSM to reflectance [42
]. The LME model is particularly overestimating while not showing sensitivity to chl-a values lower than 0.1 in logarithmic scale (see Figure 6
a). Binding et al.
(2013) assessed the sensitivity of maximum chlorophyll index (MCI; measures a peak in red/NIR region near 708 nm relative to a baseline which is drawn between two suitable wavelengths) to mineral sediments. The modeling results in this study suggested that the sensitivity of MCI to mineral turbidity particularly increases at low chlorophyll concentrations when mineral sediments can contribute to reflectance and lead to substantial increase in the resulted MCI [42
]. This study derived a strong linear relationship between in situ
MCI and chl-a concentration in Lake Erie with R2
value of 0.70, suggesting a minimal contamination of the MCI signal from sediments under intense surface algal blooms [42
]. A blue/green band ratio algorithm was tested for western basin Lake Erie in Ali et al.
(2014) and resulted in R2
value of 0.46. For chl-a concentrations below 6 mg·m−3
, a closer 1:1 relationship with the in situ
measurements was derived [43
]. However, Witter et al.
(2009) found systematic overestimation of low chl-a concentration in the western basin of Lake Erie applying regionally calibrated quadratic algorithms (employing blue/green bands as the predictor) on SeaWiFS imagery. Therefore, the difficulties associated with estimation of chl-a using blue/green band ratio algorithms in turbid, optically complex waters is demonstrated. In this region of spectrum, CDOM confounds the signals as well as TSM and chl-a concentrations [44
Moore et al.
(2014) applied a blending approach, to manage the selection between two band ratio algorithms in the blue/green and red/NIR regions, based on the optical water type classification of Lake Erie. RMSE and MBE values were 0.32, and 0.023 in logarithmic chl-a units [18
]. Sá et al.
(2015) evaluated CC chl-a products including: OC4, NN, and merged products, for the Western Iberian coast. The uncertainty estimation analysis was presented on the logarithmic scale of chl-a (0.249 < RMSE < 0.278, 0.139 < MBE < 0.200; for 3-hour time intervals) [45
]. The derived LME model for SDD estimation resulted in RMSE and MBE values of 0.19, and 0.006, in logarithmic units. Wu et al.
(2008) estimated SDD in Poyang Lake in China from two multiple regression models. The models were developed using spectral bands of Landsat TM and MODIS, separately. In both models the blue and red bands were used in the regression. The logarithmic scale of SDD was predicted with RMSE values of 0.20 and 0.37 for the models, respectively [14
]. Results from our study indicate that the LME models can be used to derive the bio-optical quantities; the models provide accuracies comparable to that of other studies. A good agreement between the selected band ratios (B07/B09 for chl-a and B06/B04 for SDD) of atmospherically corrected CC L2R MERIS data and in situ
measurements of chl-a and SDD in logarithmic scale were derived for Lake Erie for the 2004–2012 study period.
4.2. Interpretation of Spatial and Temporal Variations in Chl-a and SDD
Monthly maps of chl-a concentration and SDD for Lake Erie (Figure 7
and Figure 8
) show that Maumee Bay, Sandusky Bay, Rondeau Bay and Long Point Bay have persistent intense algal blooms. These specific areas are known to experience cyanobacteria blooms due to constant nutrient enrichment [1
]. Maumee River drains a large watershed which is dominated by agricultural fields, and also is a tributary of the largest storm runoff within the Lake Erie basin [46
]. There was also a north-south gradient in western basin for chl-a concentration and SDD estimations. This gradient can be explained by inflows from the Detroit River. The Detroit River is a major source of flows from the upper Great Lakes into Lake Erie, which carries contaminated sediments and nutrients from a highly urbanized and industrialized watershed into western Lake Erie [1
]. However, the comparatively clearer water that is carried through this river from the upper Great Lakes can create the north-south gradient in Lake Erie [1
]. Also, Dolan (1993) reported that municipal phosphorus loads from US sources have a higher magnitude compared to the Canadian ones during the period 1986–1990 [49
]. Therefore, if the same trend of phosphorus loads in those years occurs during the time period of this study, the observed differences between north and south near-shore algal productivity can be enlightened [1
Re-suspension, shoreline erosion and loading from different sources such as rivers are among the most important factors influencing SDD estimates. Wind, as the primary source of kinetic energy, affects the sediment redistribution in the water column in Lake Erie [50
]. The high-energy and short-lived winter storms are a characteristic of Lake Erie wave climate that interrupts a long period of relative calm weather [47
]. These strong storms usually occur before the lake freezes (in October, November, and December) and also in spring after ice break-up (March and April) [1
]. However, it should be noted that the depth of the lake directly affects the amount of kinetic energy generated by wind. In other words, the re-suspension of sediment loads generated by wind in the shallower areas can be more pronounced than in the deeper areas of Erie. Comparing SDD estimates (Figure 8
) with lake depths in Figure 9
, it can clearly be seen that the deeper areas are relatively clearer, while the shallow areas are more turbid. The maximum depth of the western basin is only 11 m [51
]. Hence, being the shallowest area, the western basin is the most vulnerable to physical processes such as re-suspension. Therefore, re-suspension of TSM can result in a prolonged constant turbidity in West Erie basin. Rivers and streams can supply suspended matters to the lake; and result in SDD reduction. The Detroit River (1.6 million tons/year) and the Maumee River (1.2–1.3 tons/year) have the major role in loading fine-grained sediments into Lake Erie [52
]. Rainstorms can even strengthen the contribution of river discharges to load sediments in the lakes [53
The largest variations in chl-a concentration (Figure 7
) and SDD (Figure 8
) occur in the western basin in March. This area of the lake is the estuary of the Detroit River and close to Maumee Bay and Sandusky Bay. Precipitation and runoff during this time of year, after the ice break-up period on the lake, cause more variations in nutrient availability and water column re-suspension effect on algal biomass and lake turbidity. The offshore areas and eastern basin have the least variations in chl-a concentration and SDD patterns. These lake sections appear to experience low fluctuations in the availability of required resources for algal bloom such as nutrients. Also, eastern basin of Lake Erie is the deepest with an average depth of 24 m (max depth = 64 m). Physical processes such as re-suspension have the least effect on the turbidity and its variations in the deep parts of the lake, as opposed to the shallow western basin.
Meteorological forcings can also have an impact on the magnitude and timing of blooms. In general, a temperature increase leads to higher rates of photosynthesis and therefore to a greater phytoplankton growth rate under adequate resource supplies such as nutrients and light. Light-limited photosynthesis rate is insensitive to temperature, whereas a light-saturated one increases with temperature [54
]. The resource availability of light and nutrients can be accompanied by vertical mixing. Therefore, the seasonal cycles of stratification and wind-induced vertical mixing are the key variables that condition the growth rate of phytoplankton in the water column [54
]. Stratification results in a nutrient-depleted condition at the water surface, when the upward flux of nutrients from the deep water layers is suppressed. Also, the overall impact of windiness decreases light availability in the lower depth due to re-suspension of sediments [54
]. As a result, the balance found between meteorological forcings, which sometimes can have opposite effects, is one of the driving factors determining the bloom condition. Phytoplankton production is a complex function and can be controlled by resources dynamics, species composition, and predator–prey interactions in the ecosystem [54
4.3. Limitations and Uncertainties of the Applied Linear Mixed Effect Model on MERIS
The influence of other existing particulates in a Case II water, such as CDOM and TSM, will be significantly decreased employing the chosen wavelengths to develop the chl-a LME model, as opposed to empirical blue-to-green band ratio algorithms. The absorption of CDOM is greatest in the blue region and certainly decreases exponentially with increasing wavelength, being near negligible in the NIR for the majority of the Great Lakes waters [1
]. The wavelengths (665 and 708.75 nm) have a minimal sensitivity to other CPAs, but the absorption and scattering of suspended matters can still interfere within the chl-a algorithm selected wavebands. Increasing sediment loads result in the reflectance peak to move from blue to green to red in turbid waters [55
]. Therefore, the semi-empirical models need to be tuned for each water body of interest characterized by different optical properties, in order to obtain the optimized wavelengths that can discriminate algal from suspended matters, and result in improved retrieval accuracy. Binding et al.
(2012) presented a method to discriminate algal from particulate matters. The method simultaneously extract algal and suspended matters for Lake Erie from red and NIR bands of MODIS-Aqua sensor. The study resulted in estimated concentrations in close agreement with in situ
observations with RMSE and R2
values of 2.21 mg·m−3
and 0.95 for chl-a and 1.04 g·m−3
and 0.91 for TSM, respectively [1
In addition, one has to consider that there is a relatively higher level of errors in computing remote sensing reflectance at longer wavelengths. Water absorption in red-NIR is strong and produces less remote sensing reflectance and, accordingly, a lower signal-to-noise ratio. This error is even higher in the case of clear waters where there is a low concentration of CDOM and TSM to produce remote sensing reflectance [1
]. In Lake Erie, however, the contribution of suspended and dissolved matters in remote sensing reflectance is high enough to allow the use of the proposed wavelengths from this study and produce a strong agreement between the modeled and observed values.
Atmospheric corrections are a critical step over water bodies, since the radiance signal emerging from the water column is much less than that of land. Atmospheric corrections become even more challenging in highly turbid inland and coastal waters where the ‘black pixel’ assumption of negligible water-leaving radiance in the near-infrared (NIR) is no longer valid due to scattering from suspended matters [50
]. Thus, typical atmospheric corrections fail and other schemes based on radiative transfer models or other approaches are required [13
]. The accuracy of atmospheric correction algorithms used in different models is very important to evaluate the satellite-derived water quality products. However, in a band ratio algorithm with bands near each other, atmospheric effects are normalized [13
In the northern part of the western basin of Lake Erie, benthic algae can be seen at the surface when the water is clear enough. Consequently, in some remote sensing methods, benthic algae can contribute to the remote sensing reflectance [1
]. In the present study, however, there is no need to distinguish benthic algae from surface algae. The rapid in-water attenuation of the wavelengths selected in this study for chl-a model means that the remote sensing reflectance in these wavelengths originates mostly from the upper 30 cm of water column in the lake (depends on the diffuse attenuation coefficient) [50
]. Therefore, there is no contribution of reflectance from algae at the bottom of the lake or subsurface. The estimated chl-a concentration is attributed to the surface or near surface algae even in the shallow areas or sections of the lake with clear water. The in situ
samples to measure chl-a concentration in Lake Erie were collected from the surface mixed layer. There is a constant relationship between chl-a concentration at the surface and the one averaged over the mixed layer, as Lake Erie is shallow and exposed to strong wind-driven mixing to create a mainly mixed water column condition [50
data are required for algorithm evaluation purposes and also for parameterizing the LME models. The water quality parameters measured in the field can change at a scale smaller than that of the satellite image pixel resolution (300 m for MERIS), especially in Lake Erie due to different river inputs and wind effect. Thus, multiple measurements around stations are necessary to consider spatial heterogeneity. Also, the time lapse between satellite overpasses and in situ
data collection may characterize a large change in the water quality parameter magnitude. The extent of these variations depends on the particular condition in the water body and defines the time window to be considered between satellite and in situ
measurements. A time window of 3 h between satellite overpass and in situ
data collection is recommended for open ocean waters [56
]. However 2-day time window was selected for inland waters of Lake Erie to increase the number of matchups for validation and training purposes. There are also some uncertainties associated with in situ
data collections. Over- or underestimation of chl-a concentration measurements in the field is inevitable when the collected samples contain all of the pigments, due to spectral absorption overlaps [57
]. SDD measurements are subjective and may vary depending on the operator’s ability. In shallow water bodies, disk contrast disappears at a shorter depth due to bottom reflections. Also, the disk can reach the bottom of the shallow parts of the lake without disappearing [28
], which is not the case in Lake Erie as the depth measured in the survey was always larger than SDD [1
Although MERIS is no longer active, the upcoming Sentinel-3a and b satellite missions of ESA, which will each carry the OLCI (Ocean and Land Colour Instrument) sensor (heritage of MERIS), will mark a new era in the measurement of lake water quality parameters from space. OLCI has an optimized design to minimize sun-glint and will provide 21 spectral bands compared to the 15 bands available from MERIS. Therefore the band ratio selection is between a larger numbers of bands that are improved with regards to radiometric correction.