Globally validated non-unique inversion framework to estimate optically active water quality indicators using in situ and space-borne hyperspectral data sets
. Department of Civil Engineering, Indian Institute of Technology (BHU), Varanasi 221005, India . Space Application Centre, ISRO, Ahmedabad 380015, India . Institute of Environment and Sustainable Development, Banaras Hindu University (BHU), Varanasi 221005, India
As water quality is a combination of multiple optically active parameters, there is a growing interest in probabilistic models to predict water quality. This study aims to add to the water quality prediction studies by introducing ensemble learning with deep learning-based mixture density networks with multiple probabilistic Gaussian distributions. We named the approach as Ensembled Gaussian Mixture Density Network (GMDN). Many existing water quality algorithms rely on localized data sets, which limits their applicability. This research addresses this by developing and evaluating the proposed model using the global in situ water quality data set GLORIA (Global Reflectance community data set for Imaging and optical sensing of Aquatic environments). We focused on estimating two key biogeochemical components (BPs): Total Suspended Solids (TSS) and Chlorophyll-a(Chla), along with one inherent optical property (IoP), the absorption coefficient of colored dissolved organic matter (αCDOM). The proposed approach performs quite reliably when evaluated on the data samples of individual countries. The GMDN algorithm has been fine-tuned on the satellite-matchup for the river Ganga near Varanasi city. The fine-tuning was implemented using the remote sensing reflectance (Rrs) of the spaceborne hyperspectral data set PRISMA (PRecursore IperSpettrale della Missione Applicativa). The contribution of the riverbed floor to the Rrs of PRISMA has been computed using physics-based simulations in the Water Color Simulator (WASI). Overall, the simultaneous use of multiple probabilistic distributions and ensembled architectures improves the predictive accuracy of WQ parameters compared to the existing operational algorithms.
Prashant K. Srivastava,Anurag Ohri,Shard Chander, et al. Globally validated non-unique inversion framework to estimate optically active water quality indicators using in situ and space-borne hyperspectral data sets[J]. Front. Environ. Sci. Eng.,
2025, 19(1): 10.
Fig.1 Global distribution of in situ measured remote sensing reflectance (Rrs) and associated water quality (WQ) parameters within the GLORIA benchmark data set.
Fig.2 Logarithmic scale distribution of the WQ components frequency curve: TSS, Chla, and αCDOM. The distribution illustrates the sample count across WQ parameters, with statistical parameters such as mean, median, and standard deviation in the individual plots.
Fig.3 Spectral smoothening of the atmospherically corrected reflectance curve with Savitzky Golay Filter (SGF).
Fig.4 Schematic illustration of the proposed Ensembled Gaussian Mixture Density Network (GMDN) architecture. PI refers to the parameter initialisation.
Hyperparameters
Best values
Original model
Fine-tuned model
Hidden Neurons
2223
361
Hidden Layers
9
4
Iterations
677
119
Learning rate
0.001
0.04
Dropout rate (in every hidden layer)
0.29
0.29
Epsilon
0.001
0.062
Optimiser
Adam
Adam
Tab.1 Optimal values of Hyperparameters during the training process of the GMDN on the GLORIA data set and during the fine-tuning of the pre-trained model on the PRISMA data set
Tab.2 Input Rrs corresponding to the individual wavelengths of the GLORIA data set correspond to the central wavelengths of the PRISMA data cube
Parameters
Model1
Model2
TSS
TSS1 (Novoa et al., 2017)
TSS2 (Balasubramanian et al., 2020)
Chla
Chla1 (Gurlin et al., 2011)
Chla2 (Smith et al., 2018)
αCDOM
CDOM1 (Ficek et al., 2011)
CDOM2 (Zhu and Yu, 2012)
Tab.3 Existing operational models implemented in this research for the purpose of accuracy assessment with respect to the GMDN architecture
Fig.5 In situ and estimated TSS of the test subset of the 50–50 data split using (a) GMDN and existing operational models, (b) TSS1, and (c) TSS2. Uncertainty (ε), bias (µ), Slope (S) and R2 have also been mentioned in individual plots.
Fig.6 In situ and estimated Chla of the test subset of the 50–50 data split using (a) GMDN and existing operational models, (b) Chla1, and (c) Chla2. Uncertainty (ε), bias (µ), Slope (S) and R2 have also been mentioned in individual plots.
Fig.7 In situ and estimated αCDOM of the test subset of the 50–50 data split using (a) GMDN and existing operational models, (b) CDOM1, and (c) CDOM2. Uncertainty (ε), bias (µ), Slope (S) and R2 have also been mentioned in individual plots.
Fig.8 Cross-validation results of the GMDN architecture and operational algorithms for (a) TSS, (b) Chla, and (c) αCDOM. Here, samples from each nation have been considered a single source. The dashed lines represent the median value of the MAPE. Here, KR stands for Republic of Korea.
Parameters
Unit
Range
Mean
TSS
g/m3
37.51–256.47
97.3
Chla
mg/m3
7.93–37.29
16.6
αCDOM
m−1
0.92–3.24
1.4
Tab.4 Range and mean values of in situ samples in Varanasi
WQ parameters
Algorithms
ε
µ
MAPE
TSS
GMDN
5.85
−1.37
4.65
TSS1
23.22
−15.55
19.63
TSS2
19.55
−9.22
16.29
Chla
GMDN
4.11
−1.81
3.45
Chla1
19.68
10.91
17.37
Chla2
16.61
6.36
15.22
αCDOM
GMDN
7.59
−1.98
6.92
CDOM1
27.97
11.91
18.76
CDOM2
33.21
17.23
21.24
Tab.5 Tabulated illustration of the performance metrics to evaluate the fine-tuned GMDN model and the alternative operational algorithms with respect to the in situ samples of river Ganga
Fig.9 Visual product maps derived for TSS with the atmospherically corrected PRISMA for river Ganga in the vicinity of Varanasi city using (a) GMDN and existing operational models (b) TSS1 (c) TSS2.
Fig.10 Visual product maps derived for Chla with the atmospherically corrected PRISMA for river Ganga in the vicinity of Varanasi city using (a) GMDN and existing operational models (b) Chla1 (c) Chla2.
Fig.11 Visual product maps derived for αCDOM with the atmospherically corrected PRISMA for river Ganga in the vicinity of Varanasi city using (a) GMDN and existing operational models (b) CDOM1 (c) CDOM2.
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