1. Introduction

2. Materials and Methods

2.6. ML Model Selection

A pipeline (Figure 10) was established to predict the SSC velocities. The initial phase involved selecting appropriate models, with LSTM and GRU architectures identified as the optimal choices. This decision was informed by their demonstrated effectiveness in processing time-series data, rendering them particularly suitable for this task, as shown in studies by A. M. Ali et al. [30] and I. I. Zulfa et al. [31]. By utilising these models, we can accurately predict the dispersion of marine debris around Malta’s coastal waters, addressing both the temporal dynamics and spatial complexities inherent in SSC movements.

2.6.1. Data Preprocessing and Geospatial Filtering

While the initial plan was to train a model on a year’s worth of data to forecast SSC for the next month, the complexity and four-dimensional nature of the data led to sub-optimal predictions. Consequently, the strategy was revised to extend the dataset used for training, which spanned from February 25^th 2020 to August 1^st 2023. Given the substantial volume of data points and the need for geospatial filtering, a decision was made to concentrate on a smaller area of interest along the northern coast of Malta, as illustrated in Figure 5. The method involved predicting the u and v components individually for each longitude and latitude pair within the defined area. These individual predictions were subsequently merged into a single file and finally inputted into the Lagrangian simulation.

The dataset was geospatially filtered to only include data points within the designated area of interest, as shown in Figure 6. This filtering resulted in a focused dataset consisting of 37 data points. The data did not require any normalisation as it had already been scaled between -1 and 1 during the data collection phase. Each coordinate pair was then processed into individual comma-separated-values (CSV) files. These files were systematically named and organised according to the corresponding latitude and longitude coordinate points. These CSV files served as the basis for training the AI models for every individual data point location.

Areas closer to the coast had fewer data points (more NaNs), as illustrated in the heat map in Figure 7. This lack of data near coastal regions is likely attributed to several factors. These include radar interference from nearby land or structures, obstruction of radar beams by coastal terrain or buildings, and refraction of radar waves at the coast, all contributing to distorted data collection. Efforts to solve this issue included experiments with data interpolation and filling missing values with the mean. However, these methods yielded worse results compared to those obtained by eliminating the NaN values. Due to this, the most effective strategy proved to be the removal of NaN values, a decision informed by testing and alignment with the methodologies applied for the Lagrangian model, as discussed in Section 2.5.

Prior to creating the pipeline, preliminary testing was conducted on a single model to determine the most effective features and targets. Experimentation involved the integration of both u and v as features, revealing marginally improved outcomes compared to using each as a single feature, prompting a focus on using both features for the predictions. Notably, the model yielded good results when predicting a single target, but the accuracy of predictions noticeably diminished upon testing the model to predict both u and v as targets. This observation led to the decision to develop separate models for each target variable to maximise the accuracy of the results. Therefore, we implemented a series of 37 models to predict the u component and repeated this process for the v component, ensuring precise and reliable predictions.

2.6.2. The Main Loop

Inspired by the approach of H.-M. Choi et al. [32], who developed a model for every individual coordinate pair, we established a pipeline that iterates through each pair of coordinates in the dataset (total of 37) and trains a dedicated model for each individual pair. This approach made possible the predictions across the entire area of interest, which are later utilised for the Lagrangian simulations. The u and v columns in the data files prepared earlier are extracted as input features. The dataset is then divided into training, validation, and testing sets in a 70-15-15 split respectively, a common split for ensuring a balance between adequate model training and thorough evaluation. Given the time series nature of the data, it was necessary to sequence the data appropriately; this was achieved using the TimeseriesGenerator library3. Iterative testing of different parameter combinations revealed that a window size of 72 hours, a batch size of 64, and a sampling rate of 1 unit yielded the best overall results. This means that the data is sequenced into continuous blocks of 72 hours of data as input and paired with the value immediately following these 72 hours as the target output. This step allows the model to predict the next hour based on the preceding 72 hours of data.

TensorFlow4 was used to implement the models. Various architectures and hyperparameters were tested to determine which ones yielded the best results, including a partial grid search for hyperparameter tuning. To ensure a fair comparison, we applied identical hyperparameters and layer configurations across both the LSTM and GRU architectures. The most effective architecture involved ten hidden layers, composed of four LSTM/GRU layers, three dropout layers, and two dense layers activated by ReLU, followed by an additional dropout layer after each dense layer. The models were set up with a learning rate of 0.001, ADAM optimiser, and the MSE loss function. Importantly, the model was reinitialised in each iteration of the loop, ensuring that each dataset was trained on a fresh instance without any residual weights from previous iterations. This approach is crucial when dealing with multiple datasets to avoid any data leakage or influence from previously trained models (clean slate training). It also helps maintain the integrity of the learning process for each distinct dataset. Early stopping with a patience of 8 epochs was implemented to halt training and prevent overfitting. Model checkpoints were utilised to save the best-performing epoch automatically. After each training epoch, plots comparing training versus validation loss were generated to monitor the performance of each model. To ensure that each model was trained adequately, predictions were made on the test set and subsequently visualised by comparing actual versus predicted values, as illustrated in Figure 8. Finally, adopting a similar evaluation approach to Adhikari et al. [20], MAE, MSE and RMSE error metrics were computed and displayed to evaluate the model’s performance on the test set.

2.6.3. Making Real-World Predictions

In the final phase of the AI model pipeline, we undertook a simulation mirroring a real-world scenario by feeding historical data spanning 72 hours to predict the subsequent 24 hours. This 24-hour prediction window is chosen as it provides a balance between short-term accuracy and computational feasibility, which is typically used for time series forecasting in dynamic environments like SSC. The dates of 4^th August and 4^th November 2023 were selected to assess the model’s performance under different seasonal conditions, from here on referred to as Test 1 and Test 2 respectively. Specifically, data from 1^st to 3^rd August 2023 were used as input to predict conditions for Test 1, data from 1^st to 3^rd November were used for Test 2. This setup allowed us to compare the predictions with actual historical data from our dataset. The process began with a loop to systematically extract SSC data across 72 hours for all 37 individual coordinate pairs. Subsequently, actual observed data for the following 24-hour period on 4^th August (Test 1) was extracted for comparative purposes, and both sets were saved as CSV files. Given the requirement for 72 consecutive hours of data to be able to make predictions and 24 hours for comparison, spline interpolation 5 was utilised to address any present NaN values, ensuring the dataset’s completeness. Using the rolling forecasting method shown in Figure 9, predictions were generated for the subsequent 24-hour period for the individual targets u and v. We note that predictions based on interpolated data serve as inputs for subsequent forecasts, potentially diminishing their precision. This effect is particularly noticeable in longer-term predictions, where accuracy tends to decrease as the forecast horizon extends, expectedly showing a decline in prediction accuracy the further the prediction extends into the future.

This process was repeated for all 37 data points and the predictions are converted into NetCDF format to be subsequently used in the Lagrangian model. Finally, the same error metrics were calculated to be used later for evaluation. This pipeline is repeated four times, encompassing two LSTM models and two GRU models, one for each of the u and v components respectively. The architecture of the AI models pipeline is illustrated in Figure 10 below:

Figure 10. Overview of the entire pipeline.

Figure 10. Overview of the entire pipeline.

2.7. Integrating the ML Models with the Lagrangian Model

The final stage of the pipeline involves integrating the AI models’ predictions with the physics-based Lagrangian model to produce a 24-hour forecast simulation of sea surface debris dispersion.

This process was conducted separately for both the LSTM and GRU model predictions. The initial and most critical step involves the preprocessing and merging of the predicted u and v values as NetCDF data. Following this, the procedures outlined in Section 2.5 were implemented once again to set up the Lagrangian simulation framework. This involved the configuration of the land-sea mask, FieldSet, number of particles, kernels, and timestep. The only difference lies in the particle initialisation phase. Given that the AI model predictions were specific to the area of interest (as depicted in Figure 6), we decided to set the centroid of the polygon as the starting position. More specifically, the coordinates are at a latitude of 35.9895° and a longitude of 14.4944°. This approach is advantageous as it allows for an unbiased observation of dispersion patterns. The reason being, that since the centroid is equidistant from all edges of the polygon, it provides a neutral starting point that does not inherently favour any flow direction. In terms of the offset of the initial particles, the same random seed was used for both LSTM and GRU simulations. This ensures a fair comparison as the initial locations of the particles are identical for both models.

Finally, the Lagrangian simulations for both the LSTM and GRU models were executed and stored. The resulting particle movements and dispersion patterns were visualised. These visualisations (Figure 11 and Figure 19) allowed us to observe the surface debris movement predictions and facilitate the evaluation of the results produced by the LSTM and GRU models.

Figure 11. LSTM and GRU initial vs final debris movement for Test 1 (4^th August).

Figure 11. LSTM and GRU initial vs final debris movement for Test 1 (4^th August).

3. Results

3.2. Geospatial Analysis

Another test focused on determining whether an increased volume of data correlates with enhanced predictive accuracy, whether data points closer to the coast, typically characterised by less data, yield poorer performance, and whether the time of year and seasonality of the data impact the results. The primary goal was to assess whether the geographical location of data points influences the accuracy of the predictive models. Additionally, we sought to compare the final Lagrangian simulations generated by both the LSTM and GRU models to evaluate their similarities in modelling sea surface debris.

3.2.1. A Hypothesis

As highlighted in Section 2.6.1 and Section 2.8, the dataset contains considerable missing data, with data points closer to the coast having more NaNs present, as evidenced in Figure 7. This is corroborated by Figure 12, which illustrates how some data points have significantly less data available. Figure 7 is instrumental in demonstrating the correlation between model performance and geographic location, thereby paving the way for a focused analysis on the impact of data availability at specific locations. Based on these observations, we formulated a hypothesis:

Hypothesis–Data points near the coast exhibit reduced data availability due to environmental and technical challenges that interfere with radar performance. This scarcity of data consequently impairs the accuracy of predictive models for SSC velocities near the coast. Specifically, it suggests that models predicting SSC at coastal locations perform less effectively compared to those further offshore, where radar data tends to be more complete.

We investigated the hypothesis by conducting a comparative analysis with the heat map in Figure 7. This analysis helped us validate or refute our assumption regarding the influence of geographical location on model accuracy.

3.2.2. Heat Maps Results and Analysis

As discussed in Section 2.8, heat maps were utilised to geospatially analyse the performance of the models, focusing on the MAE across all 37 models. These visualisations were crucial for testing the validity of our hypothesis regarding the impact of data availability on predictive accuracy near coastal areas. Heat maps for the MAE error metrics were produced for both the u and v components of both LSTM and GRU models, covering both the predictions made in Test 1 and Test 2. To enhance the clarity of these visualisations and minimise the influence of outliers, we applied a clipping method at the 95^th percentile of the data. This method effectively limited the range of data considered for colour scaling in the heat maps, allowing for more nuanced visual comparisons between most data points by excluding extreme outliers. The resultant heat maps for Test 1 are displayed in Figure 13 and Figure 14 below.

The heat maps for Test 2 are are displayed in Figure 15 and Figure 16 below.

These visualisations clarify that while models near the coast generally perform worse, presumably due to less data being available, there are notable exceptions where coastal predictions maintained good accuracy. This observation challenges the assumption that greater data volume directly correlates with higher predictive accuracy. Instead, it suggests that the models’ capabilities to handle noise and extract meaningful patterns from sparse data can significantly impact their effectiveness. Furthermore, the differential accuracy between the u and v components highlights the complexity of environmental factors and model sensitivities, which contribute to a diverse spectrum of outcomes that are not solely determined by the amount of data available.

Comparing the results obtained by the two tests reveals a stark contrast; predictions for August are markedly more accurate, underscoring the potential impact of seasonal variations. The outliers observed in Test 1 are inconsistent with those of Test 2, highlighting the temporal variability of missing data and its non-uniform impact across different points and times. It becomes evident that no consistent pattern exists, thus challenging any definitive conclusions. While certain models excel in predicting the u component, their performance diminishes when applied to the v component. These observations attest to the intricate dynamics at play in predictive modelling, where factors like the models’ ability to manage noise and the inherent directional properties of data lead to outcomes where less data does not always result in less accuracy. Therefore, these findings not only challenge but effectively refute the hypothesis.

3.2.3. Comparison of Lagrangian Simulations

In the final component of the evaluation framework, the performance similarities between the LSTM and GRU models was assesed by analysing centroids, spreads, and skewness within the respective Lagrangian simulation outputs. The findings for Test 1 are shown in Figure 17.

In this case, the average centroid distances for the LSTM and GRU models were around 2 km, suggesting both models achieved markedly different geographical accuracy. The standard deviation of these distances was 1.54 km, indicating a moderate spread around the centroids. However, the GRU model demonstrated a more compact spread of 0.54 km compared to the LSTM’s 1.81 km, suggesting GRU’s predictions were more tightly grouped. The skewness metrics showed a mild eastward and southward bias in the LSTM predictions, whereas the GRU exhibited a stronger westward bias and a slight northward tendency, highlighting directional tendencies in their prediction patterns. Next, the results for Test 2 are shown in Figure 18.

The results from the second test showed improvements in clustering, with mean and median centroid distances reduced to approximately 1.63 km and 1.91 km, respectively. This reduction, coupled with a decreased standard deviation of 0.70 km, suggests enhanced prediction accuracy and consistency for this period. Interestingly, LSTM showed a more consistent spread of 1.60 km, whereas GRU’s predictions were more dispersed, with a spread of 2.58 km. Skewness values also shifted, indicating changes in predictive behaviour that might be influenced by different environmental conditions or model sensitivities to the input data at that time.

Overall, the analyses highlight that the LSTMs generally offer more consistent and reliable performance, marked by less variability in spread and skewness compared to GRUs. While GRUs seemed to adjust its performance based on different conditions, suggesting a possible sensitivity to seasonal or environmental changes, the LSTMs maintained steadiness across the evaluated metrics. This consistent performance makes LSTMs the more suitable model for this application.

3.2.4. Comparison of Final Lagrangian Visualisations

The visual comparisons between Figure 11 and Figure 19 indicate notable differences in the outcomes of the LSTM and GRU simulations. Specifically, the August simulations (Figure 11) reveal distinct disparities in the final particle locations between the LSTM and GRU models. Conversely, the November simulations (Figure 19) display a high degree of similarity. This observation lends support to findings from our previous observations in Section 3.2.3, where the November results demonstrated greater alignment between the models when compared to August. Such disparities point out the variable nature of these predictions and highlight the complex interplay of various factors that significantly impact the accuracy and consistency of the final outcomes. This variability is illustrative of the inherent challenges in modelling time series data, where slight variations in input or parameters can lead to markedly different predictions.

Figure 19. LSTM and LSTM initial vs final debris movement for Test 2 (4^th November).

Figure 19. LSTM and LSTM initial vs final debris movement for Test 2 (4^th November).

4. Discussion and Conclusions

Abbreviations

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