IAP-25-081

Coastal Hydrodynamic Water Quality Modelling using Machine Learning Techniques

Designated bathing waters in England are monitored under the Bathing Water Directive, with the Environment Agency using Pollution Risk Forecasts (PRFs) to warn of poor water quality. However, PRFs rely on statistical models that overlook combined sewer overflows, leading to frequent inaccuracies and limited predictive capability. Incorporating real time telemetry from water companies could improve forecasting, however, current systems still lack validation and the capability to predict the evolution of the pollution. Developing an advanced hydrodynamic water quality model would enable accurate prediction of pollution transport, targeted sampling and effective mitigation. This would offer a more reliable, science based approach to coastal water quality management.

Coastal hydrodynamics and pollutant transport involve complex physical and biochemical processes. Accurate modelling requires capturing phenomena such as vorticity, tidal and wind driven currents, turbulent mixing as well as biochemical reactions affecting pollutant behaviour. Assuming advection dominated transport processes, pollutant movement is governed by advection–diffusion–reaction equations of parabolic type [1], making precise representation of flow dynamics essential. Therefore, developing a reliable hydrodynamic model is critical for accurately simulating transport and dispersion in coastal environments. However, such models are typically computationally expensive and not well suited for near real-time simulations, which are essential for applications such as monitoring and sampling pollution plumes, as well as issuing safety warnings. Machine learning techniques offer a promising solution to this limitation by enabling real time, reliable simulations of water quality in coastal areas.

Developing a computationally efficient hydrodynamic model for coastal regions is a key challenge. Common approaches are based on the non-linear Shallow Water, Boussinesq and Serre–Green–Naghdi equations. The non-linear Shallow Water Equations are first-order and hyperbolic, effectively capturing surf-zone wave dynamics and energy dissipation due to wave breaking, while neglecting dispersive effects [2]. The Boussinesq equations, with weak non-linearity, include dispersive effects for small-amplitude waves but require additional mechanisms to model wave breaking [3]. The Serre–Green–Naghdi equations extend applicability by removing the weak non-linearity assumption but are computationally demanding due to the need to solve elliptic problems [4]. Multi-layer formulations of these equations improve representation of vertical velocity variation and non-linear dispersive properties while maintaining computational efficiency, offering advantages for coupled transport modelling [5-7].

The proposed approach adopts the multi-layer non-hydrostatic formulation of Antuono et al. [8-9], modified to remove the assumption of irrotational flow. This method offers a unified framework for coastal modelling by intrinsically representing wave breaking through the gradual reduction of dispersive terms, eliminating the need for ad-hoc breaking mechanisms. The multi-layer structure provides a computationally efficient means of approximating three-dimensional flow and transport dynamics, combining depth-averaged Boussinesq-type equations for horizontal motion with a Poisson equation for vertical dynamics. Further improvements are anticipated through the application of advanced high-order numerical solvers and the inclusion of turbulence and vorticity effects. Additionally, the advection–diffusion–reaction equations will be fully coupled with the hydrodynamic equations.

To complement the high-fidelity numerical model and mitigate its computational cost, a surrogate modelling framework will be developed. The new multi-layer hydrodynamic water quality solver will generate a dataset of wave–structure interaction scenarios, from which a machine learning surrogate will be trained to reproduce key hydrodynamic responses such as free-surface elevation, near-field velocities and run-up. The surrogate model will be constructed using regression surfaces interpolated by Gaussian processes, providing smooth and uncertainty-aware approximations of model behaviour. Evolutionary algorithms will then be applied to efficiently explore the surrogate model across a broad parameter space, enabling systematic sensitivity and scenario analyses while remaining consistent with the underlying physics.

Research objectives:
This PhD research focuses on developing a computationally efficient coastal hydrodynamic and water quality modelling framework that accurately simulates wave dynamics, transport and dispersion processes while enabling real time prediction through surrogate modelling. The research is structured around the following objectives and corresponding tasks:

• Development of the hydrodynamic model. Tasks: (1) Develop a multi-layer hydrodynamic model based on the approach of Antuono et al. [Ref], modified to remove the assumption of irrotational flow; (2) Incorporate turbulence and vorticity terms to enhance the accuracy of the model; (3) Validate the model against benchmark cases and experimental data for surf-zone and nearshore wave dynamics.
• Coupling with transport and reaction processes. Tasks: (1) Integrate the advection–diffusion–reaction equations with the hydrodynamic solver to simulate pollutant transport; (2) Ensure the coupled framework captures mixing and biochemical processes governing contaminant evolution; (3) Evaluate model accuracy in representing transport and dispersion under varying conditions.

• Development of a surrogate modelling framework. Tasks: (1) Generate a high-fidelity dataset from the multi-layer hydrodynamic and water quality solver for a range of wave–structure interaction scenarios; (2) Train a machine learning surrogate using Gaussian process regression to emulate key hydrodynamic and transport responses, including free-surface elevation and near-field velocities. (3) Incorporate uncertainty quantification within the surrogate model to ensure reliability and interpretability of predictions.

• Model optimisation and application. Tasks: (1) Employ evolutionary algorithms to explore the surrogate model efficiently across a broad parameter space; (2) Conduct sensitivity analyses and scenario evaluations to identify key physical drivers influencing hydrodynamic and transport behaviour. (3) Demonstrate the framework’s potential for real-time water quality forecasting and decision support in coastal management applications.

Year 1

a. Literature review and problem definition. Establish a comprehensive understanding of coastal hydrodynamic and water quality equations, as well as machine learning applications in hydrodynamics.
b. Development and validation of a Coastal Hydrodynamic Model.

Year 2

a. Development and validation of a pollutant transport model
b. Development of a surrogate modelling framework
c. Preliminary results and preparation of the first journal article

Year 3

a. Performance evaluation and optimisation of the surrogate machine learning model
b. Publication of journal articles and participation in international conferences
c. Preparation of the initial chapters of the thesis

Year 3.5

a) Thesis write up

– Advanced programming
– Hydrodynamic and water quality model implementation
– Application of machine learning techniques