# Deep Learning Approaches for Numerical Modeling and Historical Reconstruction of Water Quality Parameters in Lower Seine

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Study Area and Data Acquisition

#### 2.2. Data Analysis

#### 2.3. Nomenclature and Abbreviation

#### 2.4. Model Description

#### 2.4.1. Models’ Architecture

#### Long Short-Term Memory (LSTM)

#### Bidirectional Long Short-Term Memory (BiLSTM)

#### Gated Recurrent Unit (GRU)

#### Convolution Neural Network (CNN)-Based Bi-Directional Long Short-Term Memory (BiLSTM) with Attention Mechanism

#### Attention Mechanism

#### 2.4.2. Model Evaluation Metrics

#### 2.4.3. Model Hyperparameters Tuning

#### 2.5. Modelling and Historical Reconstruction Approaches

## 3. Results and Discussion

#### 3.1. Modelling Task

#### 3.1.1. Simulating Water Quality Parameters Using Only Water Level Data

#### 3.1.2. Simulating Water Quality Parameters in Many Scenarios

#### 3.2. Historical Reconstruction

^{2}= 0.813 in the case of Rouen and R

^{2}= 0.814 in the case of Tancarville. The mean monthly values are close to the reference at the beginning and end of the year. However, some low robustness appeared in simulating the end of the summer season, especially in the case of Rouen.

## 4. Conclusions and Future Works

- ✓
- The classical correlation analysis used to decrypt the relationships of interdependence between the parameters involved in this study does not allow us to identify clear relationships due to the strong nonlinearity that links them.
- ✓
- Training DL networks to reconstruct variations in water quality parameters based on water level has been shown to be effective, particularly in predicting electrical conductivity at stations located near the sea. This is because of the strong correlation between water level and increasing or decreasing seawater intrusion during tide oscillations. However, at predominantly fluvial stations, the water level data are not sufficient to simulate the electrical conductivity.
- ✓
- Reconstructing a water quality parameter for a given station using a network trained with the same parameter but collected at other stations proves to be an effective solution, especially when the data from the stations used are subject to the same environmental influences.
- ✓
- Deep learning tools are also powerful in identifying temporal interdependencies of each parameter to accurately predict missing data using available historical data. While our initial results using a small modelling data period are promising, it is important to consider that this approach may require longer records and additional parameters, including meteorological data, TSS, TDD, Chloride, etc., to achieve even greater accuracy and more reliable reconstructed data. Therefore, future studies should explore the potential benefits of using larger datasets.
- ✓
- The DL tools were able to extract the hidden correlations that exist between the different quality data recorded at the bottom and at the surface at each station. It was also found that the surface station data are more contaminated by noise and can be recovered with the DL tools using the bottom data as input.
- ✓
- Prediction of electrical conductivity data was more accurate than prediction of dissolved oxygen, which in turn was more accurate than prediction of turbidity. Therefore, the electrical conductivity data were reconstructed prior to the dissolved oxygen and turbidity data. This provided an important database for the final reconstruction of turbidity, which is the most complex parameter in this reconstruction.
- ✓
- The accuracy of the reconstructions depends on the type of network and the amount and nature of input data used. In this respect, the CNN-BiLSTM attention model outperformed the other networks in complex reconstructions, especially when the input data are varied. Meanwhile, the GRU model showed particularly strong performance when the input and target features had similar trends.
- ✓
- The historical reconstruction in high frequency was validated by some measurements in low frequency, with which we highlighted that the physico-chemical conditions of the studied area before 2000, which are different from those of the recent period over which the training data are acquired, make the reconstruction before this period inaccurate and valid for the period between 2000 and 2015. This highlights the strong dependence of ML tools on the nature of the features of the training data.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A2.**Basic additional statistical information for the available electrical conductivity input parameters.

**Figure A3.**Basic additional statistical information for the available dissolved oxygen input parameters.

**Figure A5.**Model architectures: (

**a**) LSTM cell diagram, (

**b**) GRU cell diagram, (

**c**) CNN-BiLSTM-Attention model structure, and (

**d**) Attention mechanism process.

**Figure A6.**GRU model performance in simple monitoring tasks across multiple targets. Results of training, validation and test are displayed with the corresponding evaluation metrics (RMSE, rRMSE and ${R}^{2}$). The GRU network simulates the water parameters with high accuracy.

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**Figure 1.**Study area and monitoring stations in the Seine River. The orange and blue dots are dedicated to water level and quality data sampling sites respectively.

**Figure 2.**The measurement time windows for the available data cover 30 years, from 1990 to 2022. In this database, water levels are archived since 1990, but quality parameters are measured only since the last decade. The goal of this work is to reconstruct historical quality data to complete this database.

**Figure 3.**Long-term (seasonal) and short-term (daily) dynamic trends in water quality indicators (water level, conductivity, dissolved oxygen and turbidity) at Tancarville. Long-term seasonal trends are difficult to identify because the interdependencies between variables are masked by daily fluctuations. However, correlation trends are recognizable at the tidal scale.

**Figure 4.**Long-term (seasonal) and short-term (daily) dynamic trends of water quality indicators (water level, conductivity, dissolved oxygen) in Rouen. Despite the fact that this station is located far from the sea, the influence of the tidal cycle is clearly noticeable, especially in the variations of the water level, but its influence on the variability of the physico-chemical parameters remains rather limited compared to the downstream stations. Consequently, the quality parameters at this station are largely dependent on the water cycle, as shown by the seasonal variations in electrical conductivity and dissolved oxygen, which evolve in a correlated but opposite manner.

**Figure 5.**Input parameters correlation matrix, using the Pearson correlation coefficient R, supported by a Dendrogram diagram.

**Figure 6.**Flowchart of the historical reconstruction methodology for water quality parameters. This diagram illustrates the flow mechanism for a specific historical reconstruction step, including the process of dividing parameters into available and remaining categories and generating all possible input combinations. The diagram highlights an automatic search process that selects the best target parameter, the optimal neural network model, and suitable input combinations based on the maximum ${R}^{2}$ value from a database of modeling results. The selected target parameter is then filled and added to the available parameters for the subsequent reconstruction steps.

**Figure 7.**The results of evaluating the four proposed models for predicting water quality data with different input selections, including only water level data. For each model the ${R}^{2}$ on the overall test dataset are presented. The combination of the water level WLCa_WLDu_WLRo emerges as the best input combination, in most of the cases. Simulating the electrical conductivity in stations near to the sea (Tancarville & Fatouville) showed to be more accurate than the other parameters and location.

**Figure 8.**The results of evaluating the four proposed models for predicting water quality data with different input selections, including only water level data. For each model the rRMSE on the overall test dataset are presented. The combination of the water level WLCa_WLDu_WLRo emerges as the best input combination, in most of the cases.

**Figure 9.**Comparative performance analysis for the four proposed models in predicting water quality data (conductivity and dissolved oxygen) at the bottom layer of three stations (Fatouville, Tancarville and Rouen) using different input selections.

**Figure 10.**Comparative performance analysis for the four proposed models in predicting water quality data (conductivity and dissolved oxygen) at the surface layer of two stations near to the sea (Fatouville, Tancarville) using different input selections.

**Figure 11.**Comparative performance analysis for the four proposed models in predicting water turbidity at Fatouville using different input selections.

**Figure 12.**Comparison results of the observed and predicted water quality data for some steps in the historical reconstruction. The results on training, validation and test are displayed with the corresponding evaluation meterics (RMSE, rRMSE and ${R}^{2}$). Each subfigure corresponds to a specific historical reconstruction step. The model used in each step, in addition to the input selection and the filled target are mentioned at the top of each subfigure. An additional data correction results are displayed in the step 8.

**Figure 13.**Historical Reconstruction of several water quality data in many stations over the last 25 years.

**Figure 14.**Example of reconstructed water quality data (electrical conductivity and dissolved oxygen) at Rouen between 1993 and 1997: the reconstructed data indicates that increasing conductivity is associated with a decrease in dissolved oxygen, in accordance with the expected physical relationship between these two water quality parameters. This finding further validates the accuracy of the historical reconstruction process in capturing such relationships.

**Figure 15.**An example of reconstructed water quality data for conductivity, dissolved oxygen, and turbidity at Tancarville in 1991–2004. The reconstructed data confirms the expected physical relationship between the water quality parameters: an increase in water conductivity is associated with a decrease in dissolved oxygen, with recognizable correlation trends even at the tidal scale. The study also observes the expected lag between the parameters, further validating the accuracy of the historical reconstruction process in capturing these relationships at different stations.

**Figure 16.**Comparison of the original, and historical reconstructed dissolved oxygen data with the historical random reference samples data provided by NAIADES-Eau-France for two stations: (

**a**) Rouen and (

**b**) Tancarville. The figure includes hourly reconstructed data to illustrate the range variability in the reconstructed data, for better visualizing/evaluating the placement of the historical samples among the reconstructed one as the measured time and error are unknown.

**Figure 17.**Comparison of mean monthly reconstructed dissolved oxygen data in 2010 with monthly reference data from the work of Le Pichon et al. [34] for two stations: (

**a**) Rouen and (

**b**) Tancarville. Hourly reconstructed data is included also to illustrate high-frequency variability in the reconstructed data not captured by the monthly reference data. Error confidence intervals are added to the mean monthly data to account for added uncertainty resulting from high-frequency variability in hourly data and potential errors in extracting the reference monthly data, which were digitalized from a figure.

Feature Name | Abbreviation |
---|---|

Water_Level_Honfleur (m) Water_Level_Tancarville (m) Water_Level_Caudebec (m) Water_Level_Duclair (m) Water_Level_Rouen (m) | WLHo WLTa WLCa WLDu WLRo |

Electrical Conductivity_Tancarville_Surface (μS·cm^{−1})Electrical Conductivity_Tancarville_Bottom (μS·cm ^{−1})Electrical Conductivity_Fatouville_Surface (μS·cm ^{−1})Electrical Conductivity_Fatouville_Bottom (μS·cm ^{−1})Electrical Conductivity_Rouen_Surface (μS·cm ^{−1})Electrical Conductivity_Valdesleux_Surface (μS·cm ^{−1}) | CTaS CTaB CFaS CFaB CRoS CVaS |

Turbidity_Tancarville_Bottom (NTU) Turbidity_Fatouville_Bottom (NTU) | TTaB TFaB |

Dissolved_Oxygen_Tancarville_Surface (mg·L^{−1})Dissolved_Oxygen_Tancarville_Bottom (mg·L ^{−1})Dissolved_Oxygen_Fatouville_Surface (mg·L ^{−1})Dissolved_Oxygen_Fatouville_Bottom (mg·L ^{−1})Dissolved_Oxygen_Rouen_Surface (mg·L ^{−1})Dissolved_Oxygen_Valdesleux_Surface (mg·L ^{−1}) | DTaS DTaB DFaS DFaB DRoS DVaS |

Hyper-Parameters | Range |
---|---|

BiLSTM/GRU Number of layers | From 1 to 4 |

BiLSTM/GRU Number of Unit | From 10 to 500 |

Batch-size | {32, 64, 128, 256} |

Learning rate | From 0.001 to 0.1 |

Drop-out | {0.1, 0.2, 0.3} |

CNN Filter size | {4, 9, 16, 25, 36, 49, 64, 81} |

CNN Activation Function | ‘Sigmoid’, ‘Relu’ |

Look-Back (Input Sequence size) | From 1 day to 12 months |

**Table 3.**Historical reconstruction steps with the appropriate input and model selection for each step.

Steps | Target to Be Filled at the Specific Step | Selected Input | Selected Model |
---|---|---|---|

1 | CTaB | WLCa_WLDu_WLRo | Bi_LSTM |

2 | CFaB | WLCa_WLDu_WLRo | CNN_Bi_LSTM_Attention |

3 | CFaS | CFaB | CNN_Bi_LSTM_Attention |

4 | CRoS | WLHo_WLTa_WLCa_CFaB | CNN_Bi_LSTM_Attention |

5 | DRoS | CRoS | Bi_LSTM |

6 | DTaS | WLCa_WLDu_WLRo_CRoS_DRoS | Bi_LSTM |

7 | CVaS | WLCa_WLDu_WLRo_CRoS_DRoS | Bi_LSTM_Attention |

8 | DVaS | DRoS | GRU |

9 | CTaS | WLHo_WLTa_WLCa_CTaB | GRU |

10 | DFaB | WLCa_WLDu_WLRo_DTaS | GRU |

11 | DFaS | WLHo_WLTa_WLCa_CFaB_DFaB | Bi_LSTM_Attention |

12 | DTaB | WLHo_WLTa_WLCa_CFaB_DFaB | CNN_Bi_LSTM_Attention |

13 | TFaB | WLHo_WLTa_WLCa_CFaB_DFaB_CTaB_DTaB | CNN_Bi_LSTM_Attention |

14 | TTaB | WLHo_WLTa_WLCa_TFaB | CNN_Bi_LSTM_Attention |

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**MDPI and ACS Style**

Janbain, I.; Jardani, A.; Deloffre, J.; Massei, N.
Deep Learning Approaches for Numerical Modeling and Historical Reconstruction of Water Quality Parameters in Lower Seine. *Water* **2023**, *15*, 1773.
https://doi.org/10.3390/w15091773

**AMA Style**

Janbain I, Jardani A, Deloffre J, Massei N.
Deep Learning Approaches for Numerical Modeling and Historical Reconstruction of Water Quality Parameters in Lower Seine. *Water*. 2023; 15(9):1773.
https://doi.org/10.3390/w15091773

**Chicago/Turabian Style**

Janbain, Imad, Abderrahim Jardani, Julien Deloffre, and Nicolas Massei.
2023. "Deep Learning Approaches for Numerical Modeling and Historical Reconstruction of Water Quality Parameters in Lower Seine" *Water* 15, no. 9: 1773.
https://doi.org/10.3390/w15091773