Machine and Deep Learning Regression of Chlorophyll-a Concentrations in Lakes Using PRISMA Satellite Hyperspectral Imagery
"> Figure 1
<p>Summary of available data (pixels with information of Chl-a maps and PRISMA acquisitions) within the study’s AOI. In the reference map is highlighted the approximate location of the AOI within Europe (red dot).</p> "> Figure 2
<p>Schematic of pre-processing operations on the input data.</p> "> Figure 3
<p>Schematic of the anomalous pixels removal procedure.</p> "> Figure 4
<p>QQ-plot of training and test sets. Blue dots represent quantiles of pixel values distribution from reference Chl-a maps in the training set (X-axis) and test set (Y-axis).</p> "> Figure 5
<p>Predictions and reference Chl-a map and their absolute difference (Abs. difference) computed from Experiment SVR-4 applied to each of the acquisitions in the test set.</p> "> Figure 6
<p>Distribution of the errors of Experiment SVR-4 applied to each of the acquisitions in the test set.</p> "> Figure 7
<p>Schematic of the inference procedures on 30 m spatial resolution output.</p> "> Figure 8
<p>Predictions and reference Chl-a map and their absolute difference (Abs. difference) computed from Experiment RF-12 trained and evaluated at 30-m spatial resolution data and applied to each of the acquisitions in the test set.</p> "> Figure 9
<p>Distribution of the errors of Experiment RF-12 trained and evaluated at 30-m spatial resolution data and applied to each of the acquisitions in the test set.</p> ">
Abstract
:1. Introduction
2. Data and Methods
2.1. Data Procurement and Preprocessing
2.2. Training and Test Datasets Preparation
2.3. PRISMA Images Normalization and Dimensionality Reduction
2.4. Machine and Deep Learning Regression Models for Chl-a Concentration
- Normalization approach: A set of experiments was conducted to determine the best normalization approach among the ones discussed in Section 2.3.
- Spectral dimensionality reduction: An experiment was conducted to investigate whether the PCA technique contributes or not to the model performances.
- Tests on best input spatial resolution: First, all experiments used 300 m spatial resolution inputs and then, considering the best experiment for each model typology, it was repeated using inputs at 30 m resolution to determine which of the two approaches performed better. This approach was followed because, despite the different spatial resolution, the data derives from the same original distribution, ensuring that the model selection step remains unaffected.
Parameter | Description |
---|---|
Number of estimators | It is the number of decision trees built. Higher values are expected to improve performance while increasing computational time. |
Minimum number of samples per leaf | It sets the minimum samples required for a leaf node, reducing over-fitting with higher values. |
Maximum depth of each decision tree | It controls model complexity; large values can lead to over-fitting. |
Parameter | Description |
---|---|
Gamma | Kernel coefficient for the RBF. It governs the shape of the decision boundary. A high value leads to an extended or complex decision boundary, which, if not carefully controlled, may result in over-fitting. |
C | It influences the width of the margin and the tolerance for misclassified data points. It is a regularization hyperparameter which enables to balance between training and testing errors. |
Parameter | Description |
---|---|
Number of layers | The number of LSTM or GRU cells stacked on top of each other. |
Dropout in the recurrent neural network cells | Effective regularization method that contrast over-fitting by randomly deactivating a portion of neurons [61]. When dealing with recurrent neurons, dropout is specifically applied to the connections between consecutive recurrent hidden cells. |
Dropout in the fully connected layer | Proportion of dropout applied to the fully connected layers’ outputs. |
Directionality | Both unidirectional and bidirectional networks were investigated. The difference is that bidirectional networks calculate the hidden state at each time step using information from both past and future inputs, whereas unidirectional networks utilize only past inputs in their calculations. |
Hidden size | The number of features in the hidden state. |
3. Results and Discussion
3.1. RF Regressor
3.2. SVR
3.3. LSTM Network
3.4. GRU Network
3.5. Summary of Best Models and Inference on 30 m
4. Conclusions and Outlook
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
AHSI | Advanced Hyperspectral Imager |
ANN | Artificial Neural Networks |
AOI | Area of Interest |
ASI | Italian Space Agency |
Chl-a | Chlorophyll-a |
CNN | Convolutional Neural Network |
DESIS | German Aerospace Center Earth Sensing Imaging Spectrometer |
DN | Digital Number |
EeTeS | EnMAP end-to-end Simulator Software |
EnMAP | Environmental Mapping and Analysis Program |
ESA | European Space Agency |
FCN | Fully-connected Network |
GRU | Gated Recurrent Unit |
HICO | Hyperspectral Imager for the Coastal Ocean |
LSTM | Long-short Term Memory |
MAE | Mean Absolute Error |
MARS | Multivariate Adaptive Regression Spline |
MDN | Mixture Density Network |
NASA | National Aeronautics and Space Administration |
OLCI | Ocean and Land Colour Instrument |
PCA | Principal Component Analysis |
PCs | Principal Components |
PLS | Partial Least Squares |
PRISMA | PRecursore IperSpettrale della Missione Applicativa |
QQ-plot | Quantile-Quantile plot |
RBF | Radial Basis Function |
RF | Random Forest |
RMSE | Root Mean Square Error |
RNN | Recurrent Neural Network |
SIMILE | Informative System for the Integrated Monitoring of Insubric Lakes and their Ecosystems |
SSI | Spectral Sampling Interval |
SVM | Support Vector Machines |
SVR | Support Vector Regressor |
SWIR | Short-Wave Infrared |
TSM | Total Suspended Matter |
US | United States |
VNIR | Visible and Near-infrared |
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ID Acquisition | PRISMA Acquisition Date | Lake Como | Lake Maggiore | Lake Lugano | Reference Chl-a Map Date |
---|---|---|---|---|---|
1 | 24 April 2020 | YES | NO | YES | 23 April 2020 |
2 | 24 April 2020 | YES | NO | NO | 23 April 2020 |
4 | 25 April 2020 | NO | YES | NO | 23 April 2020 |
6 | 3 July 2020 | NO | YES | NO | 5 July 2020 |
10 | 9 July 2021 | YES | NO | YES | 9 July 2021 |
13 | 31 August 2021 | YES | NO | NO | 31 August 2021 |
17 | 16 October 2021 | NO | YES | NO | 16 October 2021 |
18 | 22 October 2021 | YES | NO | NO | 22 October 2021 |
19 | 22 October 2021 | YES | NO | YES | 22 October 2021 |
21 | 26 November 2021 | NO | NO | YES | 24 November 2021 |
23 | 9 February 2022 | NO | YES | NO | 9 February 2022 |
24 | 27 March 2022 | YES | NO | NO | 25 March 2022 |
Exp. ID | Exp. Setting | Res [m] | PCA | Norm. | Data Augm. | N Trees | Min. Leaf | Max. Depth | MAE [µg/L] | RMSE [µg/L] |
---|---|---|---|---|---|---|---|---|---|---|
RF-1 | Norm. | 300 | No | Minmax | No | 1000 | 3 | 10 | 0.931 | 1.112 |
RF-2 | Norm. | 300 | No | Std. | No | 1000 | 3 | 10 | 0.931 | 1.112 |
RF-3 | Norm. | 300 | No | Reflect. | No | 1000 | 3 | 10 | 0.931 | 1.112 |
RF-4 | Spec. red. | 300 | 30 PCs | Std. | No | 1000 | 3 | 10 | 1.020 | 1.245 |
RF-5 | Data augm. | 300 | No | Std. | Yes | 1000 | 3 | 10 | 1.106 | 1.296 |
RF-6 | Model hyperp. | 300 | No | Std. | No | 1000 | 3 | 5 | 1.032 | 1.192 |
RF-7 | Model hyperp. | 300 | No | Std. | No | 1000 | 3 | 20 | 0.930 | 1.113 |
RF-8 | Model hyperp. | 300 | No | Std. | No | 100 | 3 | 20 | 0.947 | 1.128 |
RF-9 | Model hyperp. | 300 | No | Std. | No | 10,000 | 3 | 20 | 0.924 | 1.107 |
RF-10 | Model hyperp. | 300 | No | Std. | No | 10,000 | 2 | 20 | 0.915 | 1.099 |
RF-11 | Model hyperp. | 300 | No | Std. | No | 10,000 | 10 | 20 | 0.934 | 1.114 |
RF-12 | Spatial res. | 30 | No | Std. | No | 1000 | 2 | 20 | 0.986 | 1.181 |
Exp. ID | Exp. Setting | Res [m] | PCA | Norm. | Data Augm. | Gamma | C | MAE [µg/L] | RMSE [µg/L] |
---|---|---|---|---|---|---|---|---|---|
SVR-1 | Norm. | 300 | No | Minmax | No | 0.001 | 15 | 1.285 | 1.431 |
SVR-2 | Norm. | 300 | No | Std. | No | 0.001 | 15 | 0.699 | 0.898 |
SVR-3 | Norm. | 300 | No | Reflect. | No | 0.001 | 15 | 1.253 | 1.394 |
SVR-4 | Spec. red. | 300 | 30 PCs | Std. | No | 0.001 | 15 | 0.687 | 0.895 |
SVR-5 | Data augm. | 300 | 30 PCs | Std. | Yes | 0.001 | 15 | 0.909 | 1.126 |
SVR-6 | Model hyperp. | 300 | 30 PCs | Std. | No | 0.0001 | 15 | 0.752 | 0.993 |
SVR-7 | Model hyperp. | 300 | 30 PCs | Std. | No | 0.01 | 15 | 0.956 | 1.152 |
SVR-8 | Model hyperp. | 300 | 30 PCs | Std. | No | 0.001 | 1.5 | 0.756 | 0.955 |
SVR-9 | Model hyperp. | 300 | 30 PCs | Std. | No | 0.001 | 150 | 1.106 | 1.307 |
SVR-10 | Spatial res. | 30 | 30 PCs | Std. | No | 0.001 | 15 | 1.260 | 1.555 |
Exp. ID | Exp. Setting | Res [m] | PCA | Norm. | Hidden Size | N Layers | Drop. RNN | Drop. FCN | Bidir. | MAE [µg/L] | RMSE [µg/L] |
---|---|---|---|---|---|---|---|---|---|---|---|
LSTM-1 | Norm. | 300 | No | Minmax | 10 | 2 | 0.6 | 0.4 | No | 1.443 | 1.584 |
LSTM-2 | Norm. | 300 | No | Std. | 10 | 2 | 0.6 | 0.4 | No | 1.303 | 1.431 |
LSTM-3 | Norm. | 300 | No | Reflect. | 10 | 2 | 0.6 | 0.4 | No | 1.897 | 2.012 |
LSTM-4 | Spec. red. | 300 | 30 PCs | Std. | 10 | 2 | 0.6 | 0.4 | No | 1.298 | 1.428 |
LSTM-5 | Model hyperp. | 300 | 30 PCs | Std. | 5 | 2 | 0.6 | 0.4 | No | 1.386 | 1.522 |
LSTM-6 | Model hyperp. | 300 | 30 PCs | Std. | 15 | 2 | 0.6 | 0.4 | No | 1.323 | 1.452 |
LSTM-7 | Model hyperp. | 300 | 30 PCs | Std. | 10 | 4 | 0.6 | 0.4 | No | 1.494 | 1.635 |
LSTM-8 | Model hyperp. | 300 | 30 PCs | Std. | 10 | 1 | 0.6 | 0.4 | No | 1.334 | 1.490 |
LSTM-9 | Model hyperp. | 300 | 30 PCs | Std. | 10 | 2 | 0.2 | 0.4 | No | 1.342 | 1.475 |
LSTM-10 | Model hyperp. | 300 | 30 PCs | Std. | 10 | 2 | 0.8 | 0.4 | No | 1.278 | 1.407 |
LSTM-11 | Model hyperp. | 300 | 30 PCs | Std. | 10 | 2 | 0.8 | 0.6 | No | 1.366 | 1.498 |
LSTM-12 | Model hyperp. | 300 | 30 PCs | Std. | 10 | 2 | 0.8 | 0.2 | No | 1.305 | 1.434 |
LSTM-13 | Dir. flow | 300 | 30 PCs | Std. | 10 | 2 | 0.8 | 0.4 | Yes | 1.211 | 1.345 |
LSTM-14 | Spatial res. | 30 | 30 PCs | Std. | 10 | 2 | 0.8 | 0.4 | Yes | 1.278 | 1.455 |
Exp. ID | Exp. Setting | Res [m] | PCA | Norm. | Hidden Size | N Layers | Drop. RNN | Drop. FCN | Bidir. | MAE [µg/L] | RMSE [µg/L] |
---|---|---|---|---|---|---|---|---|---|---|---|
GRU-1 | Norm. | 300 | No | Minmax | 10 | 2 | 0.6 | 0.4 | No | 1.367 | 1.499 |
GRU-2 | Norm. | 300 | No | Std. | 10 | 2 | 0.6 | 0.4 | No | 1.287 | 1.416 |
GRU-3 | Norm. | 300 | No | Reflect. | 10 | 2 | 0.6 | 0.4 | No | 1.559 | 1.698 |
GRU-4 | Spec. red. | 300 | 30 PCs | Std. | 10 | 2 | 0.6 | 0.4 | No | 1.305 | 1.433 |
GRU-5 | Model hyperp. | 300 | No | Std. | 5 | 2 | 0.6 | 0.4 | No | 1.435 | 1.575 |
GRU-6 | Model hyperp. | 300 | No | Std. | 20 | 2 | 0.6 | 0.4 | No | 1.235 | 1.366 |
GRU-7 | Model hyperp. | 300 | No | Std. | 40 | 2 | 0.6 | 0.4 | No | 1.221 | 1.352 |
GRU-8 | Model hyperp. | 300 | No | Std. | 60 | 2 | 0.6 | 0.4 | No | 1.186 | 1.321 |
GRU-9 | Model hyperp. | 300 | No | Std. | 100 | 2 | 0.6 | 0.4 | No | 1.271 | 1.408 |
GRU-10 | Model hyperp. | 300 | No | Std. | 60 | 1 | 0.6 | 0.4 | No | 1.236 | 1.373 |
GRU-11 | Model hyperp. | 300 | No | Std. | 60 | 10 | 0.6 | 0.4 | No | 1.231 | 1.362 |
GRU-12 | Model hyperp. | 300 | No | Std. | 60 | 2 | 0.2 | 0.4 | No | 1.272 | 1.419 |
GRU-13 | Model hyperp. | 300 | No | Std. | 60 | 2 | 0.8 | 0.4 | No | 1.194 | 1.340 |
GRU-14 | Model hyperp. | 300 | No | Std. | 60 | 2 | 0.6 | 0.2 | No | 1.202 | 1.355 |
GRU-15 | Model hyperp. | 300 | No | Std. | 60 | 2 | 0.6 | 0.8 | No | 1.260 | 1.399 |
GRU-16 | Dir. flow | 300 | No | Std. | 60 | 2 | 0.6 | 0.4 | Yes | 1.213 | 1.363 |
GRU-17 | Spatial res. | 30 | No | Std. | 60 | 2 | 0.6 | 0.4 | No | 1.203 | 1.382 |
Exp. ID | Model | MAE Overall | RMSE Overall | MAE-4 | RMSE-4 | MAE-23 | RMSE-23 | MAE-24 | RMSE-24 |
---|---|---|---|---|---|---|---|---|---|
SVR-4 | SVR | 0.687 | 0.895 | 0.544 | 0.688 | 0.712 | 0.961 | 0.806 | 1.036 |
RF-10 | RF | 0.915 | 1.099 | 0.464 | 0.622 | 0.903 | 1.106 | 1.378 | 1.570 |
GRU-8 | GRU | 1.186 | 1.321 | 0.929 | 0.997 | 1.262 | 1.420 | 1.365 | 1.544 |
LSTM-13 | LSTM | 1.211 | 1.345 | 0.992 | 1.053 | 1.288 | 1.442 | 1.355 | 1.538 |
Exp. ID | Model | Train. Res. [m] | Eval. Res. [m] | MAE Overall | RMSE Overall | MAE-4 | RMSE-4 | MAE-23 | RMSE-23 | MAE-24 | RMSE-24 |
---|---|---|---|---|---|---|---|---|---|---|---|
RF-10 | RF | 300 | 30 | 1.076 | 1.241 | 0.988 | 1.071 | 0.836 | 1.068 | 1.405 | 1.585 |
RF-12 | RF | 30 | 30 | 0.986 | 1.181 | 0.815 | 0.921 | 0.707 | 0.987 | 1.435 | 1.635 |
SVR-4 | SVR | 300 | 30 | 1.107 | 1.266 | 1.578 | 1.620 | 0.778 | 1.017 | 0.964 | 1.161 |
SVR-10 | SVR | 30 | 30 | 1.260 | 1.555 | 1.052 | 1.571 | 1.043 | 1.235 | 1.686 | 1.859 |
LSTM-13 | LSTM | 300 | 30 | 1.234 | 1.369 | 0.826 | 0.905 | 1.413 | 1.556 | 1.462 | 1.648 |
LSTM-14 | LSTM | 30 | 30 | 1.278 | 1.455 | 1.004 | 1.112 | 1.004 | 1.214 | 1.826 | 2.039 |
GRU-8 | GRU | 300 | 30 | 1.248 | 1.393 | 0.643 | 0.746 | 1.294 | 1.448 | 1.808 | 1.986 |
GRU-17 | GRU | 30 | 30 | 1.203 | 1.382 | 0.598 | 0.727 | 1.518 | 1.732 | 1.493 | 1.686 |
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Amieva, J.F.; Oxoli, D.; Brovelli, M.A. Machine and Deep Learning Regression of Chlorophyll-a Concentrations in Lakes Using PRISMA Satellite Hyperspectral Imagery. Remote Sens. 2023, 15, 5385. https://doi.org/10.3390/rs15225385
Amieva JF, Oxoli D, Brovelli MA. Machine and Deep Learning Regression of Chlorophyll-a Concentrations in Lakes Using PRISMA Satellite Hyperspectral Imagery. Remote Sensing. 2023; 15(22):5385. https://doi.org/10.3390/rs15225385
Chicago/Turabian StyleAmieva, Juan Francisco, Daniele Oxoli, and Maria Antonia Brovelli. 2023. "Machine and Deep Learning Regression of Chlorophyll-a Concentrations in Lakes Using PRISMA Satellite Hyperspectral Imagery" Remote Sensing 15, no. 22: 5385. https://doi.org/10.3390/rs15225385