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A Comprehensive Review of Phase-Averaged and Phase-Resolving Wave Models for Coastal Modeling Applications

Md Meftahul Ferdaus, Nathan Alton Cooper, Austin B. Schmidt, Pujan Pokhrel, Elias Ioup, Mahdi Abdelguerfi, Julian Simeonov

TL;DR

<3-5 sentence high-level summary> Numerical wave modelling for coastal and oceanographic applications is reviewed, contrasting phase-averaged spectral models with phase-resolving approaches. The paper surveys fundamental theory, mathematical formulations, and numerical methods (including DIA/ST6, Boussinesq/non-hydrostatic, unstructured grids, and GPU acceleration), and assesses major models (SWAN, WW3, WAM, MIKE 21 SW, TOMAWAC, FUNWAVE-TVD, SWASH, BOSZ) through validation and intercomparison. It discusses computational challenges, high-performance computing, and hybrid coupled frameworks, offering practical guidance for model selection across scales, from global forecasts to detailed nearshore simulations. The review also identifies gaps in physics parameterizations, data assimilation, and uncertainty quantification, and highlights future directions in multi-physics coupling and AI-assisted approaches for coastal resilience and climate adaptation.

Abstract

Predicting ocean wave behavior is challenging due to the difficulty in choosing suitable numerical models among many with varying capabilities. This review examines the development and performance of numerical wave models in coastal engineering and oceanography, focusing on the difference between phase-averaged spectral models and phase-resolving models. We evaluate the formulation, governing equations, and methods of widely used third-generation phase-averaged spectral models (SWAN, WAVEWATCH III, MIKE 21 SW, TOMAWAC, and WAM) alongside advanced phase-resolving models (FUNWAVE, SWASH, COULWAVE, and NHWAVE) that employ Boussinesq-type equations and non-hydrostatic formulations. The review begins with early parameterized models and progresses to contemporary third-generation models, which solve the wave action conservation equation with few spectral constraints. A comparison of the models' efficiency, accuracy in nearshore conditions, ability to resolve nonlinear wave-wave interaction, simulate wave breaking, diffraction, and wave-current interactions is provided. Applications in operational forecasting, extreme event simulation, coastal structure design, and assessing climate change impacts are discussed. The validation of these models and the statistical metrics and intercomparison studies used are addressed. A discussion of the limitations in computational scalability, physics parameterization, and model coupling is provided, along with emerging trends in high-resolution modeling and hybrid models. This review guides researchers in evaluating which models to use in coastal and oceanographic research.

A Comprehensive Review of Phase-Averaged and Phase-Resolving Wave Models for Coastal Modeling Applications

TL;DR

<3-5 sentence high-level summary> Numerical wave modelling for coastal and oceanographic applications is reviewed, contrasting phase-averaged spectral models with phase-resolving approaches. The paper surveys fundamental theory, mathematical formulations, and numerical methods (including DIA/ST6, Boussinesq/non-hydrostatic, unstructured grids, and GPU acceleration), and assesses major models (SWAN, WW3, WAM, MIKE 21 SW, TOMAWAC, FUNWAVE-TVD, SWASH, BOSZ) through validation and intercomparison. It discusses computational challenges, high-performance computing, and hybrid coupled frameworks, offering practical guidance for model selection across scales, from global forecasts to detailed nearshore simulations. The review also identifies gaps in physics parameterizations, data assimilation, and uncertainty quantification, and highlights future directions in multi-physics coupling and AI-assisted approaches for coastal resilience and climate adaptation.

Abstract

Predicting ocean wave behavior is challenging due to the difficulty in choosing suitable numerical models among many with varying capabilities. This review examines the development and performance of numerical wave models in coastal engineering and oceanography, focusing on the difference between phase-averaged spectral models and phase-resolving models. We evaluate the formulation, governing equations, and methods of widely used third-generation phase-averaged spectral models (SWAN, WAVEWATCH III, MIKE 21 SW, TOMAWAC, and WAM) alongside advanced phase-resolving models (FUNWAVE, SWASH, COULWAVE, and NHWAVE) that employ Boussinesq-type equations and non-hydrostatic formulations. The review begins with early parameterized models and progresses to contemporary third-generation models, which solve the wave action conservation equation with few spectral constraints. A comparison of the models' efficiency, accuracy in nearshore conditions, ability to resolve nonlinear wave-wave interaction, simulate wave breaking, diffraction, and wave-current interactions is provided. Applications in operational forecasting, extreme event simulation, coastal structure design, and assessing climate change impacts are discussed. The validation of these models and the statistical metrics and intercomparison studies used are addressed. A discussion of the limitations in computational scalability, physics parameterization, and model coupling is provided, along with emerging trends in high-resolution modeling and hybrid models. This review guides researchers in evaluating which models to use in coastal and oceanographic research.

Paper Structure

This paper contains 96 sections, 28 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Review Methodology
  3. Literature Search Strategy
  4. Inclusion and Exclusion Criteria
  5. Gaps in Existing Review Literature
  6. Motivation and Objectives
  7. Organization of the Review
  8. Wave Theory, Model Classification, Selection, and Validation
  9. Fundamental Wave Theory
  10. Classification of Numerical Wave Models
  11. Phase-Averaged vs. Phase-Resolving Models
  12. Generations of Wave Models
  13. Phase-Resolving Model Development
  14. Spectral Representation
  15. Hybrid and Coupled Approaches
  16. ...and 81 more sections

Figures (3)

  • Figure 1: Evolution of numerical wave models from 1960 to 2025, showing parallel development of phase-averaged spectral models (top track) and phase-resolving models (bottom track)
  • Figure 6: Phase-resolving models (left) compute deterministic wave elevation for local domains ($10^{-2}$ to $10^{2}$ km$^2$) from non-hydrostatic 3D to simplified formulations; phase-averaged models (right) solve wave action balance for statistical spectra over large domains ($10^{2}$ to $10^{8}$ km$^2$) with 10--200$\times$ lower computational cost. Comparative table quantifies key differences in resolution, duration, and applications.
  • Figure 7: Examples of different grid types used in numerical wave models: (a) regular structured grid with uniform spacing, (b) curvilinear grid conforming to coastline geometry, (c) unstructured triangular grid with local refinement in coastal regions, and (d) nested grid approach with fine-resolution domain embedded in coarse-resolution domain. Each grid type offers distinct advantages for specific applications and computational requirements.