Remote Sensing of Chlorophyll-a in Clear vs. Turbid Waters in Lakes

Abstract

Chlorophyll-a (Chl-a), a proxy for phytoplankton biomass, is one of the few biological water quality indices detectable using satellite observations. However, models for estimating Chl-a from satellite signals are currently unavailable for many lakes. The application of Chl-a prediction algorithms may be affected by the variance in optical complexity within lakes. Using Lake Winnipeg in Canada as a case study, we demonstrated that separating models by the lake’s basins [north basin (NB) and south basin (SB)] can improve Chl-a predictions. By calibrating more than 40 commonly used Chl-a estimation models using Landsat data for Lake Winnipeg, we achieved higher correlations between in situ and predicted Chl-a when building models with separate Landsat-to-in situ matchups from NB and SB (R² = 0.85 and 0.76, respectively; p < 0.05), compared to using matchups from the entire lake (R² = 0.38, p < 0.05). In the deeper, more transparent waters of the NB, a green-to-blue band ratio provided better Chl-a predictions, while in the shallower, highly turbid SB, a red-to-green band ratio was more effective. Our approach can be used for rapid Chl-a modeling in large lakes using cloud-based platforms like Google Earth Engine with any available satellite or time series length.

1. Introduction

Recent increases in the frequency, prevalence, and intensity of harmful phytoplankton blooms in lakes worldwide have raised significant environmental concerns [1,2,3]. These blooms contribute to toxin production, water odor, taste degradation, and esthetic decline [4,5]. They also reduce biodiversity through habitat degradation and alter energy and nutrient fluxes within food webs [5,6,7]. Addressing these challenges requires a thorough understanding of past, current, and potential future occurrences of phytoplankton blooms, necessitating regular, lake-wide monitoring of phytoplankton biomass [8]. However, traditional in situ monitoring methods are costly, time-consuming, and limited in spatial and temporal coverage [9].

Satellite sensors offer a cost-effective solution for monitoring chlorophyll-a (Chl-a), a proxy for phytoplankton biomass, across lakes by mapping its concentration [10]. Estimating Chl-a from satellite spectral data relies on the absorption and scattering of light by phytoplankton at specific wavelengths [11]. In waters with straightforward optical properties, phytoplankton and related substances predominantly determine the color of the water and thus the signals received by satellite sensors [12]. However, in optically complex waters like many inland and coastal areas, non-phytoplankton optically active constituents (OACs) such as detritus and colored dissolved organic matter (CDOM) also influence the color of water, complicating Chl-a estimation from satellite data [12]. These OACs vary widely in type, quantity, and light absorption and scattering behavior across different water bodies [13], posing challenges for developing universal Chl-a prediction models [14,15].

Successful Chl-a estimation from satellite data requires the development of region-specific models, known as regional models, which account for the optical characteristics of the target water body [11,16,17]. Efforts to create such models often rely on lake-wide approaches that overlook within-basin variations in water optical properties [18]. On the other hand, some approaches classify lake pixels into optical water types (OWTs) before model prediction, with unique Chl-a models developed for each OWT [19,20,21]. Chl-a models using the OWT approach require in situ Chl-a training data for each of the OWTs [20] that are not available for many lakes. The Chl-a products of the European Space Agency (ESA)’s Lakes-Climate Change Initiative (Lakes-CCI) developed using the OWT approach are still unavailable for many lakes. Additionally, these Chl-a products are often too coarse for studying the spatial variability of Chl-a (e.g., 300 m spatial resolution in the best case compared to Landsat with 30 m spatial resolution). Further, because Lakes-CCI products began in 1992, they do not offer the longest possible time series for studying the temporal variability of Chl-a (e.g., compared to Landsat starting in 1984).

This study provides a simple and intuitive method for creating accurate models to predict Chl-a that addresses the optical heterogeneity and variability in lakes without requiring a comparatively large in situ training dataset. Using Lake Winnipeg (LW), Canada, as a case study, we hypothesize that improving Chl-a predictions can be achieved by separating the lake into its optically distinct basins. We evaluate their efficacy by comparing “basin-specific” models against conventional “lake-wide” models. Enhanced Chl-a predictions using basin-specific models could facilitate Chl-a modeling on platforms like Google Earth Engine (GEE), which is crucial for processing and analyzing long-term satellite data at broad spatial scales using medium- to high-resolution imagery, often computationally intensive outside cloud-based environments.

2. Materials and Methods

2.1. Case Study Area

LW, with a surface area of 23,750 km², is recognized as the world’s 10th largest, North America’s 7th largest, and Canada’s 3rd largest freshwater lake [22,23]. It is a shallow, wind-mixed, polymictic lake, which is divided into two physically and biogeochemically distinct basins: the north basin (NB) and the south basin (SB) (Figure 1) [22]. Compared to the SB, the NB is larger, encompassing 74% of the total lake area, and deeper, with an average depth of 13.3 m and a maximum depth of 18.0 m. The water in the NB is relatively transparent. In contrast, the SB encompasses 11% of the total lake area and is shallower, with an average depth of 9.0 m and a maximum depth of 12.0 m. The Red River transports a large amount of sediments to the SB, combined with sediment resuspension, making the SB highly turbid. A deep, narrow channel, known as the Narrows, separates the NB and SB. The Narrows is characterized by its relatively rapid water flow, with a maximum depth of approximately 60.0 m and a width of around 2.6 km [22].

2.2. LW Turbidity

To distinguish the basins based on their turbidity, we used in situ turbidity data (Nephelometric Turbidity Units; NTU) measured throughout LW, provided by Manitoba Agriculture and Resource Development during the peak phytoplankton biomass season (July to October) from 2002 to 2018 (Figure 1). A non-parametric, one-way analysis of variance by ranks (Kruskal–Wallis H test) was employed to determine whether turbidity differed between the two basins (NB and SB) and the Narrows [24]. A non-parametric test was chosen based on the non-normal distribution of the data (Shapiro–Wilcoxon test; p > 0.05). A significant result from the Kruskal–Wallis test (p < 0.05) indicated that at least one basin differed from the others. We then applied a multi-step a posteriori pairwise testing procedure based on studentized range statistics (non-parametric multiple comparison Dunn’s procedure) to identify which basins were significantly different from each other [25].

2.3. Modeling Chl-a

A flowchart (Figure 2) summarizes the sequence of methods described in this study, including (a) acquiring in situ Chl-a data, (b) pre-processing satellite data, (c) developing Chl-a prediction models, and (d) applying models to a time series of satellite data. A description of each step is discussed below.

2.3.1. In Situ Data Acquisition

In situ Chl-a measurements (μg L⁻¹) were provided by Manitoba Sustainable Development, Water Quality Management Section 2019. Chl-a data were collected from 32 stations distributed throughout the lake (13 stations in the NB, 15 in the SB, and 3 in the Narrows; Figure 1) during the peak phytoplankton biomass season (July to October) between 2002 and 2018 at depths ranging from 0 to 17.79 m [22]. All Chl-a data were measured using spectrophotometric methods (American Public Health Association (APHA) 10200H [26]). Because satellite-derived Chl-a information is limited to the uppermost water layer, we only used samples taken from the surface of the lake (≤0.1 m depth); these samples were taken in 2010 and 2011. Although using Chl-a samples from deeper layers (≤0.5 m depth) increased the number of matchups between in situ samples and satellite image acquisitions from 53 to 143, the performance of the Best-Performing Models (BPMs) as measured by the coefficient of determination (R²) decreased from 0.85 to 0.16 in the NB and from 0.76 to 0.12 in the SB (see Figure S1). Our criteria for in situ Chl-a sample selection resulted in no samples from the Narrows, as all samples there were from deeper than 0.1 m. Due to the log-normal distribution of Chl-a in nature [27], all Chl-a data were logarithmically transformed (using natural log) before analysis.

2.3.2. Landsat Data

Landsat 4–5 Level 1 Collection 2 Thematic Mapper (TM) and Landsat 7 Enhanced Thematic Mapper Plus (ETM+) images covering the entirety of LW were used in this study (https://www.usgs.gov/landsat-missions/landsat-collection-2, accessed on 21 January 2024). Both sensors (TM and ETM+) have a spatial resolution of 30 m. We used four visible bands: blue (B, 450–520 nm), green (G, 520–600 nm), red (R, 630–690 nm), and near-infrared (NIR, 770–900 nm). Matchups between Chl-a sample times and Landsat image acquisition times were extracted from 9 TM and 20 ETM+ images (6 TM and 6 ETM+ path/rows). Images with more than 90% cloud or cloud shadow cover were excluded.

2.3.3. Pre-Processing Landsat Level 1 Data

Partial atmospheric correction was applied to Landsat Level 1 data (Figure 2) because Level 2 products may introduce higher uncertainty in aerosol calculations over inland waters, leading to erroneous results [28,29]. All pre-processing steps for transforming Landsat data to partially corrected satellite top-of-atmosphere (TOA) reflectance were performed in GEE (see Supplementary Materials for the code). The individual pixels were then pre-processed in four steps.

• Step 1. Cloud mask

Land pixels and those covered by cloud or cloud shadow during satellite image acquisition were masked using a standard LW boundary shapefile and Pixel Quality Assessment bands provided with Landsat Level 2 products.

• Step 2. Radiometric correction

Landsat Level 1 data are stored as digital numbers (DNs). During the radiometric correction, we recalibrated the DNs to the satellite TOA radiance (L_λ) using the standard equation [30] (1):

$${\mathrm{L}}_{\mathsf{\lambda }}=\left({\mathrm{D}\mathrm{N}}_{\mathsf{\lambda }}\times {\mathrm{G}}_{\mathsf{\lambda }}\right)+{\mathrm{B}}_{\mathsf{\lambda }}$$

(1)

where

• L_λ is the TOA radiance for band λ;
• DN_λ is the DN for band λ;
• G_λ is the multiplicative rescaling factor for band λ;
• B_λ is the additive rescaling factor for band λ.

• Step 3. Partial atmospheric correction

L_λ values were corrected for Rayleigh scattering using a partial atmospheric correction algorithm [31]. We used an inverse algorithm based on a simplified radiative transfer model to calculate the Rayleigh scattering radiance (or Rayleigh path radiance) for each band (L_r(λ)) [31] (2):

$${\mathrm{L}}_{\mathrm{r}\left(\mathsf{\lambda }\right)}=\left({\displaystyle \frac{{\mathrm{E}\mathrm{S}\mathrm{U}\mathrm{N}}_{\mathsf{\lambda }}\times \mathrm{c}\mathrm{o}\mathrm{s}{\mathsf{\theta }}_{\mathrm{s}}\times {\mathrm{P}}_{\mathrm{r}}}{4\mathsf{\pi }\times \left(\mathrm{c}\mathrm{o}\mathrm{s}{\mathsf{\theta }}_{\mathrm{s}}+\cos \mathsf{\theta }\right)}}\right)\times \left(1-\exp \left({-\mathsf{\tau }}_{\mathrm{r}}\left(\mathsf{\lambda }\right)\times \left(\left({\displaystyle \frac{1}{\mathrm{c}\mathrm{o}\mathrm{s}{\mathsf{\theta }}_{\mathrm{s}}}}\right)+\left({\displaystyle \frac{1}{\cos \mathsf{\theta }}}\right)\right)\right)\right)\times {\mathrm{t}}_{\mathrm{o}\mathrm{z}}\uparrow \left(\mathsf{\lambda }\right)\times {\mathrm{t}}_{\mathrm{o}\mathrm{z}}\downarrow \left(\mathsf{\lambda }\right)$$

(2)

where

• ESUN is the mean solar exo-atmospheric irradiance;
• P_r is the Rayleigh scattering phase function;
• θ_s is the solar zenith angle (degrees);
• θ is the satellite viewing angle (degrees) (set to 0°);
• τ_r is the Rayleigh optical thickness;
• t_oz↑ and t_oz↓ are upward and downward ozone transmittance, respectively.

The phase function P_r was calculated using (3):

$${\mathrm{P}}_{\mathrm{r}}={\displaystyle \frac{3}{4}}\times {\displaystyle \frac{1-\mathsf{\gamma }}{1+2\mathsf{\gamma }}}\times \left(1+{\mathrm{c}\mathrm{o}\mathrm{s}}^2\mathsf{\Theta }\right)+{\displaystyle \frac{3\mathsf{\gamma }}{1+2\mathsf{\gamma }}}$$

(3)

where

• Θ (the view zenith angle) is the scattering angle (180° − θ_s);
• γ = δ/(2 − δ) [32];
• δ is the depolarization factor [33], which denotes the polarization of anisotropic particles at right angles and is dependent on the wavelength, atmospheric pressure, and air mass (with the last two variables being constant values) [34].

The Rayleigh optical thickness, τ_r, was calculated using [35,36] (4):

$${\mathsf{\tau }}_{\mathrm{r}}=0.008569{\mathsf{\lambda }}^{-4}\times \left(1+0.0113{\mathsf{\lambda }}^{-2}+0.00013{\mathsf{\lambda }}^{-4}\right)$$

(4)

where

• λ is the band-specific mid-wavelength value (nm).

t_oz↑ and t_oz↓ were calculated using [37] ((5) and (6)):

$${\mathrm{t}}_{\mathrm{o}\mathrm{z}}\uparrow =\exp \left(-{\mathsf{\tau }}_{\mathrm{o}\mathrm{z}}\right)$$

(5)

$${\mathrm{t}}_{\mathrm{o}\mathrm{z}}\downarrow =\exp \left({\displaystyle \frac{{-\mathsf{\tau }}_{\mathrm{o}\mathrm{z}}}{\mathrm{c}\mathrm{o}\mathrm{s}{\mathsf{\theta }}_{\mathrm{s}}}}\right)$$

(6)

where

• t_oz is the constant ozone optical thickness [38].

Finally, the Rayleigh-corrected radiance, ${\widehat{\mathrm{L}}}_{\mathsf{\lambda }}$, was obtained by subtracting the Rayleigh scattering radiance (L_r) from the TOA radiance (L_λ) (7):

$${\widehat{\mathrm{L}}}_{\mathsf{\lambda }}{=\mathrm{L}}_{\mathsf{\lambda }}-{\mathrm{L}}_{\mathrm{r}}$$

(7)

• Step 4. Converting radiance to reflectance

The TOA reflectance for each band ($\mathsf{\rho }\mathsf{\lambda }$), was calculated using (8):

$${\mathrm{R}}_{\mathrm{r}\mathrm{s}}\mathsf{\lambda }={\displaystyle \frac{\mathsf{\pi }\times {\widehat{\mathrm{L}}}_{\mathsf{\lambda }}\times {\mathrm{d}}^2}{{\mathrm{E}\mathrm{S}\mathrm{U}\mathrm{N}}_{\mathsf{\lambda }}\times {\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\theta }}_{\mathrm{s}}}}$$

(8)

where

• R_rsλ is TOA reflectance for wavelength range or band λ;
• d is the Earth-to-sun distance in astronomical units [30].

2.3.4. Extracting Matchups

We extracted remote sensing reflectance (R_rs) for each band (B, G, R, and NIR; Section 2.3.3) and paired it with the corresponding sampling points (Section 2.3.1) in GEE (See Supplementary Materials for the code). To increase the chance of matching satellite observations with sampled Chl-a, we considered Landsat images within ±3 days of the sampling dates. Larger temporal windows were not used due to the highly dynamic nature of blooms in LW [39]. Satellite data were extracted from corresponding pixels to sampling point locations (single pixels; spatial windows of 1 × 1 pixels). To mitigate potential errors in digitization [40], we also extracted R_rs using the median of pixels corresponding to sampling locations and their 8 (spatial window of 3 × 3 pixels) and 24 neighboring pixels (spatial window of 5 × 5 pixels). Based on these criteria, a total of 42 samples (18 in the NB and 24 in the SB) from 28 stations (13 in the NB and 15 in the SB) were identified (Figure 1,

Table 1. Matchups for NB, SB, and LW using different temporal windows (0 to ±3 days). The values were the same for different spatial windows (1 × 1, 3 × 3, and 5 × 5 pixels).

Basin	Temporal Window (Days)	In Situ Chl-a (µg L−1)	# of Samples	# of Stations	# of Images	# of Matchups	Landsat Sensors	Landsat Scenes (Path/Row)	Year	Month
NB	0	10.1–147	2	2	1	2	5	3322	2011	9
	±1	1.91–147	8	6	6	10	5, 7	3223, 3322/23	2010, 2011	7, 8, 9, 10
	±2	1.91–147	13	11	8	17	5, 7	3223, 3322/23	2010, 2011	7, 8, 9, 10
	±3	1.91–147	18	13	9	23	5, 7	3223, 3322/23	2010, 2011	7, 8, 9, 10
SB	0	3.05–4.01	2	2	2	3	5, 7	3124/25	2010	7, 8
	±1	3.05–6.68	5	5	5	7	5, 7	3025, 3124/25	2010, 2011	7, 8
	±2	2.67–9.55	15	12	8	20	5, 7	3025, 3124/25	2010, 2011	7, 8, 10
	±3	2.67–147	24	15	11	30	5, 7	3025, 3124/25	2010, 2011	7, 8, 9, 10
LW	0	3.05–147	4	4	3	5	5, 7	3322, 3124/25	2010, 2011	7, 8, 9
	±1	1.91–147	13	11	11	17	5, 7	3223, 3025, 3124/25, 3322/23	2010, 2011	7, 8, 9, 10
	±2	1.91–147	28	23	16	37	5, 7	3223, 3025, 3124/25, 3322/23	2010, 2011	7, 8, 9, 10
	±3	1.91–147	42	28	20	53	5, 7	3223, 3025, 3124/25, 3322/23	2010, 2011	7, 8, 9, 10

). We found 9 Landsat images for the NB, 11 for the SB, and 20 for the entire LW matching the time and location of the sampling points, providing 23 matchup points in the NB, 30 in the SB, and 53 for the entire LW (Table 1). We created 36 sets of matchups with different temporal windows (0 to ±3 days), different spatial windows (1 × 1, 3 × 3, and 5 × 5 pixels), and different basins of the lake [NB or SB, each with significantly different turbidity levels, determined through in situ turbidity measurements (p < 0.05)], as well as the entire lake (LW).

2.3.5. Model Calibration

For each set of matchups (Section 2.3.4), we tested the performance of 45 models, including all possible bands and band ratios and various commonly used multiband combinations (Supplementary Materials, Table S1) to predict Chl-a in the NB, SB, and LW using regression analyses. Each model was fitted using the matchup natural log-transformed in situ Chl-a values against the partially corrected R_rs using simple linear regression equations (Table S1). We then identified the BPM for each set of matchups as the model that exhibited the highest R² and was statistically significant (p < 0.05). Model calibration on the BPMs was performed using 5-fold cross-validation, chosen to balance bias and variance given the number of matchups available [41,42]. During model calibration, for each fold of the 5-fold cross-validation, the models were fitted to the training dataset (natural log-transformed in situ Chl-a values against partially corrected R_rs) using simple linear regression equations. We then estimated the average predictive performance of each model during the calibration stage using the average R² of the five cross-validation folds.

2.3.6. Model Validation

To assess the predictive capacity of the BPMs identified during the initial calibration phase for each set of matchups (Section 2.3.5), we validated each model by applying the slope and intercept from each calibration to its associated test matchup set in the cross-validation fold (k = 5). The predictive performance of the BPMs was measured using Root Mean Square Error (RMSE; µg L⁻¹) for each cross-validation fold as follows (9):

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\displaystyle \frac{\left({\left({\mathrm{y}}_{\mathrm{o}}-{\mathrm{y}}_{\mathrm{p}}\right)}^2\right)}{\mathrm{n}}}\right)}$$

(9)

where

• ${\mathrm{y}}_{\mathrm{o}}$ represents the observed Chl-a values, and
• ${\mathrm{y}}_{\mathrm{p}}$ represents the predicted Chl-a values.

We normalized the RMSE (NRMSE) for each cross-validation fold as follows (10):

$$\mathrm{N}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}={\displaystyle \frac{\sqrt{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left(\frac{\left({\left({\mathrm{y}}_{\mathrm{o}}-{\mathrm{y}}_{\mathrm{p}}\right)}^2\right)}{\mathrm{n}}\right)}}{\overline{\mathrm{y}\mathrm{o}}}}$$

(10)

where

• $\overline{\mathrm{y}\mathrm{o}}$ is average observed Chl-a.

We calculated the Root Mean Squared Logarithmic Error (RMSLE; µg L⁻¹) as follows (11):

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{L}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left(\log \left[{1+\mathrm{y}}_{\mathrm{o}}\right]-\mathrm{l}\mathrm{o}\mathrm{g}{[1+\mathrm{y}}_{\mathrm{p}}\right]{)}^2}$$

(11)

We also calculated the Mean Absolute Error (MAE; µg L⁻¹) and Mean Absolute Percentage Error (MAPE; %) for the five cross-validation folds to measure the predictive performance of the models as follows ((12) and (13)):

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{y}}_{\mathrm{o}}-{\mathrm{y}}_{\mathrm{p}}\right|}{\mathrm{n}}}$$

(12)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=100\times \mathrm{m}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n} \mathrm{o}\mathrm{f}\left[{\displaystyle \frac{\left|{\mathrm{y}}_{\mathrm{o}}-{\mathrm{y}}_{\mathrm{p}}\right|}{{\mathrm{y}}_{\mathrm{p}}}}\right]\mathrm{f}\mathrm{o}\mathrm{r} 1=1,\dots ,\mathrm{n}.$$

(13)

Bias was measured as follows (14):

$$\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}={\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{y}}_{\mathrm{o}}-{\mathrm{y}}_{\mathrm{p}}\right)}{\mathrm{n}}}$$

(14)

Finally, we compared the performances of the models based on the average errors for all the cross-validation folds [19].

2.4. Application of the BPMs to Landsat OLI

Landsat TM and ETM+ sensors were launched in 1984 and 1999 (respectively), and the Landsat Operational Land Imager (OLI) was launched in 2013. In our study, all matchups since 2013 were discarded because the in situ Chl-a data in those years were taken from depths below 0.1 m, which did not meet our matchup selection criteria (Section 2.3.1). To test the applicability of our BPMs for predicting Chl-a using OLI, we applied the models to concurrent OLI and ETM+ data (with ± 1 day difference between the two sensors’ overpass times from 16 stations distributed throughout LW between 2013 and 2017) (Figure 1).

For each OLI matchup, Level 1 Collection 2 OLI data (https://www.usgs.gov/landsat-missions/landsat-collection-2, accessed on 21 January 2024) for the bands used in the BPMs (i.e., B, G, and R) were pre-processed in GEE using the same approach as for Landsat TM and ETM+ (Section 2.3.3). After applying the BPMs to ETM+ and concurrent OLI data, we compared the modeled Chl-a derived from each sensor (a total of 26 matching points) using a simple linear regression model.

2.5. Comparing Chl-a Predictions Using Basin-Specific vs. Lake-Specific BPMs

To compare Chl-a predictions using basin-specific versus lake-specific BPMs, we applied the BPMs from each approach to all Landsat images during the peak Chl-a period (July to October) from 1984 to 2023 in GEE. We then compared the ability of the predictions from the two approaches to capture spatial and temporal changes in peak Chl-a in LW. All Landsat images were pre-processed to partially corrected R_rs in GEE (Section 2.3.3) prior to model application.

To study spatial changes in peak Chl-a in LW, we calculated the median of peak Chl-a for each pixel within each basin for all years from 1984 to 2023. To study temporal changes in peak Chl-a in LW, we calculated the median peak Chl-a for all pixels within each basin for each year from 1984 to 2023.

3. Results

3.1. Spatial Heterogeneity in LW Turbidity

Our results revealed statistically significant (p < 0.05) differences in turbidity levels in the different basins during the peak phytoplankton biomass season (July to October). Specifically, turbidity in the NB was consistently lower than in the SB and the Narrows (p < 0.05), whereas no significant difference was observed between the SB and the Narrows (p ≥ 0.05;

Table 2. Comparison of turbidity (Nephelometric Turbidity Units; NTU) in the NB and SB and the Narrows (median values) during the peak phytoplankton biomass season (July to October). The number of sample data points is added in the parenthesis next to the median values. Different letters indicate statistically significant (p < 0.05) differences between basins.

	July	August	September	October	All Months
NB	5.53 a (176)	3.81 a (95)	5.55 a (207)	9.44 a (41)	5.50 a (723)
SB	19.00 b (58)	14.90 b (73)	19.75 b (58)	20.50 b (80)	15.00 b (396)
Narrows	21.80 b (62)	17.45 b (70)	17.90 b (23)	14.70 a,b (8)	16.10 b (243)

Source: raw in situ data from Manitoba Agriculture and Resource Development. Kruskal–Wallis and Dunn’s test (p < 0.05). Data were not normally distributed (Shapiro–Wilcoxon test; p > 0.05).

).

3.2. Best Performng Models

The performance of basin-specific models in predicting Chl-a was superior to that of lake-specific models (Figure 3 and Table S1). The NB-specific and SB-specific BPMs achieved R² values of 0.85 (10 matchups) and 0.76 (7 matchups), respectively (p < 0.05; Figure 3 and Tables S2 and S3). In contrast, the lake-specific BPM showed a lower R² of 0.38 (17 matchups; p < 0.05; Figure 3 and Table S4).

The NB-specific BPM (R² = 0.85) used matchups from ±1 day with a 1 × 1 pixel spatial window (Figure 3 and Table S2). Increasing the spatial window to 3 × 3 and 5 × 5 pixels decreased the R² to 0.70 and 0.60, respectively, while increasing the temporal window to ±2 and ±3 days decreased the R² to 0.75 and 0.57, respectively. Despite these changes, increasing the temporal window to ±2 days still provided a high R² of 0.75 with reduced errors (NRMSE decreased from 1.98 to 0.73; bias reduced from 9.39 to 2.04).

The SB-specific BPM (R² = 0.76) used matchups from ±1 day with a 1 × 1 pixel spatial window (Figure 3 and Table S3). Increasing the spatial window to 3 × 3 and 5 × 5 pixels decreased the R² to 0.74 and 0.63, respectively, while increasing the temporal window to ±2 and ±3 days decreased the R² to 0.61 and 0.32, respectively. The temporal window of ±2 days provided 17 matchups with an R² of 0.61 and reduced bias (bias decreased from 0.25 to 0.23).

Like the basin-specific models, the LW-specific model (R² = 0.38, based on matchups from ± 1 day with a 1 × 1 pixel spatial window) exhibited decreasing R² values with larger spatial and temporal windows (Figure 3 and Table S4).

3.3. Best Chl-a Prediction Models

From the BPMs in Section 3.2, the basin-specific models (NB and SB) using a 1 × 1 pixel spatial window and a temporal window of ±2 days were selected for their balanced performance (high R² and low errors) and increased confidence due to the larger number of matchups used.

In the NB, a two-band model based on the R_rs of the band ratio of G to B showed the highest performance (R² = 0.74) (

Table 3. Calibration and validation results for the NB- and SB-specific BPMs (spatial window of 1 × 1 pixels and temporal window of ±2 days) and the LW-specific BPM (spatial window of 1 × 1 pixels and temporal window of ±1 day). All the calibration R² were significant at p < 0.05.

Basin	Model	Calibration R2	RMSE (µg L−1)	RMSLE (µg L−1)	NRMSE	MAE (µg L−1)	MAPE (%)
NB	G/B	0.74	20.53	0.65	0.88	14.51	55.43
SB	R/G	0.62	1.14	0.20	0.24	1.00	22.81
LW	G/B	0.38	21.57	0.87	1.29	13.57	64.27

and Figure 4a) (15):

$$\ln (\mathrm{C}\mathrm{h}\mathrm{l}-a)=8.153\times \left[\mathrm{G}/\mathrm{B}\right]-5.622$$

(15)

In the SB, a two-band model based on the R_rs of the band ratio of R to G performed best (R² = 0.62) (Table 3 and Figure 4b) (16):

$$\ln (\mathrm{C}\mathrm{h}\mathrm{l}-a)=4.313\times \left[\mathrm{R}/\mathrm{G}\right]-2.603$$

(16)

In the entire LW, a two-band model based on the R_rs of the band ratio of G to B achieved the highest performance (R² = 0.38) (Table 3 and Figure 4c) (17):

$$\ln (\mathrm{C}\mathrm{h}\mathrm{l}-a)=5.836\times \left[\mathrm{G}/\mathrm{B}\right]-4.005$$

(17)

Validation tests using five-fold cross-validation further supported the superiority of basin-specific models over the LW-specific model (Table 3).

3.4. Application of the Models to Landsat OLI

Cross-comparison between ETM+ and OLI sensors indicated a robust linear relationship between Chl-a predictions using OLI (dependent variable) and those using ETM+ (independent variable) (R² = 0.87, p < 0.05) (Figure 5). Notably, the correlation was stronger in the NB (R² = 0.89, p < 0.05) than in the SB (R² = 0.68, p < 0.05) (Figure 5).

3.5. Comparing Chl-a Predictions Using the Basin-Specific vs. Lake-Scpecific BPMs

Figure 6 illustrates the median of natural log-transformed peak Chl-a (µg L⁻¹) in the NB and SB during peak phytoplankton biomass (July to October) from 1984 to 2023 using basin-specific (Figure 6a) and lake-specific (Figure 6b) BPMs. Basin-specific models predicted higher Chl-a concentrations in the NB compared to the SB (Figure 6a), while lake-specific model showed the opposite pattern (Figure 6b).

Figure 7 illustrates the annual time series of peak Chl-a in the NB and SB during peak phytoplankton biomass (July to October) using basin-specific and lake-specific BPMs. In the NB, lake-specific model consistently predicted lower Chl-a concentrations than basin-specific model (Figure 7). Conversely, in the SB, lake-specific model predicted higher Chl-a concentrations than basin-specific model (Figure 7). Temporal variations in peak Chl-a in the SB from 1984 to 2023 also exhibited distinct patterns between basin-specific and lake-specific models, reflecting different spatial dynamics within LW (Figure 7).

4. Discussion

Remote sensing is a crucial tool for the rapid and consistent monitoring of spatial and temporal changes in surface water Chl-a. Limnologists often use satellite-derived Chl-a products developed using global models designed for optically complex waters [39,43,44] without considering variations in water optical properties among lakes [19]. Chl-a prediction using remote sensing reflectance can be improved by developing models that account for potential within-lake variance in optical properties. Such models can be delineated based on optical properties or, as in our study, by morphometric characteristics that distinguish lake basins with unique optical properties. Our study demonstrates that by considering within-basin differences in optical properties and dividing the lake into optically distinct parts, the Chl-a prediction can be improved.

4.1. Basin-Specific Chl-a Prediction Models

The physical and biogeochemical differences between the NB and SB [22,39] create different optical properties, favoring basin-specific models over lake-specific models in both basins. BPMs in both basins used band ratios. Compared to single bands, band ratios enhance Chl-a estimations by reducing the atmospheric, irradiance, and air–water surface effects on reflectance [45]. Band ratios also minimize the impact of non-phytoplankton OACs found in inland waters, which can alter the spectral profile observed by the sensor [46,47]. This is significant because the varying concentrations of these constituents can explain the lack of correlation between observed Chl-a and single bands in lakes [45], as observed in our study (Table S1).

Many models based on band ratios have been proposed for estimating Chl-a in inland, coastal, and open ocean waters [11,48]. These models leverage the scattering and absorption patterns of sunlight by Chl-a. With increasing Chl-a, the relative energy between 520 and 600 nm (Landsat G band) increases, while the energy between 450 and 520 nm (Landsat B band) decreases [49]. In our study, while BPMs in both the NB and SB included the G band, this band was the dividend of the ratio in the NB and the denominator in the SB, and the other part of the ratio was the B band in the NB and the R band in the SB.

In the NB, where the water is deeper and clearer [22] and Chl-a reaches higher concentrations during bloom events [22,38], the G-to-B band ratio provided the highest correlation with observed Chl-a (R² > 0.80). The B-to-G band ratio is widely used in estimating Chl-a in lakes with low concentrations of inorganic suspended matter or in eutrophic and hypertrophic waters where phytoplankton are the predominant constituents and non-phytoplankton constituents have a minor effect on reflectance [50,51,52].

In the SB, where the water is shallow, well mixed, and highly turbid [22,39], the R-to-G band ratio provided the highest correlation with observed Chl-a (R² > 0.70). The SB creates optically complex water conditions, where non-phytoplankton OACs create turbid conditions that interfere with spectral bands—particularly the B band [53]. This interference complicates Chl-a estimation in turbid waters using the B band [46,54,55], and therefore the R-to-G band ratio is commonly used for estimating Chl-a in highly turbid waters [45,56,57,58]. Many Chl-a prediction models developed for turbid, optically complex waters are also based on the red and near-infrared regions of the electromagnetic spectrum [45,59]. Like the red region, the near-infrared region (near 700 nm wavelength) shows less sensitivity to non-phytoplankton particles’ interference than the blue region [60]. However, near-infrared-based models are successful, with satellites having a band centered at the red- near-infrared edge, like MERIS [60,61]. Multispectral sensors like Landsat have broad NIR bands (770–900 nm in TM and ETM+ and 845–885 nm in OLI), which are unsuitable for estimating Chl-a [45]. Our study could not improve the relationship between observed and modeled Chl-a using NIR in either the basin-specific or lake-specific models.

4.2. Comparing Chl-a Predictions Using the Basin-Specific vs. Lake-Specific BPMs

The differences between predictions using basin-specific and lake-specific models were striking for both basins. We have higher Chl-a predictions in the SB using the lake-specific model than using the SB-specific model and, conversely, lower Chl-a predictions in the NB using the lake-specific model than using the NB-specific model. This is primarily due to the optical differences of the two basins and the choice of band ratio algorithm (G-to-B band ratio).

The SB is turbid with non-phytoplankton OACs (e.g., CDOM and sediments) that influence the reflectance of the B and G bands and, therefore, introduce errors in the G-to-B band ratio [46,62]. Conversely, the NB is less turbid than the SB. The inclusion of the SB data in the same model as the NB lowered the regression slope due to the error introduced because of non-phytoplankton OACs. The lake-specific model predicts lower Chl-a concentrations in the NB compared to the NB-specific model, and higher Chl-a concentrations in the SB compared to the SB-specific model.

4.3. Application of the Models to Landsat OLI

Our in situ data (2010 and 2011) coincided with operations of Landsat TM and ETM+ sensors but were before the period of Landsat OLI operation (2013 to present). OLI is different from TM and ETM+ in terms of image quality and the number and width of spectral bands. Despite these differences, the similar spatial and spectral resolutions allowed intercalibration between these sensors [63]. Our cross-comparison analysis showed that the TM and ETM+ Chl-a models developed in this study complemented OLI (Figure 5). Similarly, other studies successfully applied models developed based on TM or ETM+ to OLI images or vice versa, e.g., [3,64].

4.4. Future Applications

Overall, the high correlations between modeled and observed Chl-a obtained using the basin-specific models suggests these models can reliably capture relative changes in Chl-a in LW. Therefore, the models can be used to predict Chl-a in LW with Landsat data to study spatial and temporal variabilities of Chl-a [64,65]. However, due to our matchup selection criteria, the lack of in situ Chl-a data with concentrations above 10 µg L⁻¹ in the SB may affect the accuracy of absolute Chl-a predictions in this basin [64]. Moreover, separating a lake into visually distinctive basins is conceptually simple and intuitive. Our matchup selection criteria also excluded all samples from the Narrows. Like the SB, the Narrows is optically complex, where non-phytoplankton particles are primary determinants of water transparency [22]. However, applying the SB-specific model to the Narrows requires in situ Chl-a data to validate these models’ performance in this part of the lake.

Applying models to Landsat imagery (available since 1984) in GEE (see Supplementary Materials for the code) can provide the longest available Chl-a time series for most water bodies. The length of this time series (40 years) allows for the study of long-term climate trends or oscillations' impacts on changes in Chl-a. At least 30-40 years of continuous and consistent data on water temperature (a critical indicator of climate change) and Chl-a is required to separate climate change signals from natural variability [21,66,67,68,69]. This information will also provide ecosystem managers and scientists with a better understanding of the sensitivity of different regions of their study area to environmental perturbations. This can lead to more accurate predictions of future lake ecosystem responses to increasing anthropogenic pressures in the face of a changing climate. Ecosystem managers can use this knowledge to design contextual and more efficient management strategies towards eutrophication and phytoplankton blooms in lakes.

5. Conclusions

In this study, we predicted concentrations of Chl-a in a large lake using simple empirical equations applied to Landsat data. Our results highlight the importance of considering optical differences within lakes when developing Chl-a prediction models. Separating a lake into basins with distinct water optical properties, we significantly improved the relationships between in situ and modeled Chl-a. These models can be easily applied in cloud-based platforms like Google Earth Engine (GEE) for computationally intensive modeling of Chl-a on broad spatial and temporal scales. The user-friendly GEE code requiring minimal adjustments of the times and locations of in situ Chl-a samples developed for this study is freely available, facilitating the development of models for optically distinct lakes worldwide.