the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 12 Feb 2025
The discontinuous Galerkin coastal and estuarine modelling system (DGCEMS v1.0.0): a three-dimensional, mode-nonsplit, implicit-explicit Runge–Kutta hydrostatic model
Abstract. Numerical method of discontinuous Galerkin (DG) discretization for coastal ocean modelling have advanced significantly, but there are still challenges in accurately simulating phenomena such as wetting and drying process and baroclinic flows in coastal and estuarine regions. This study develops a novel 3D coastal and estuarine modelling system, DGCEMS, using a quadrature-free nodal DG method. The model adopts σ-coordinates, employs a non-split mode framework, and integrates a semi-implicit Runge–Kutta scheme with second-order accuracy in both space and time. A series of numerical experiments demonstrate the model’s second-order convergence, low spurious mixing, and capability to simulate salt-freshwater interactions in the presence of wetting and drying boundaries.
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RC1: 'Comment on gmd-2024-240', Anonymous Referee #1, 28 Feb 2025
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In this paper, the authors describe their development of a novel 3D coastal and estuarine modelling system called DGCEMS based on the nodal discontinuous Galerkin method. Through some tests, it has been demonstrated that the model has second-order convergence, low spurious mixing, and capability to simulate salt-freshwater interactions in the presence of wetting and drying boundaries. The subject of the paper is well presented, and definitely of interest to the modeling community. I’d recommend the paper for publication, after addressing the following comments.
1.In the governing equations, no specific vertical stratification was given, but Figure 1 shows 2 layers, while 10(Line 230) and 20 layers(Line 254) were used in Section 3.1 and 3.2, respectively. How is vertical stratification determined?
2.When presenting the model algorithm, it is necessary to highlight the innovative points of the solution, which can help readers better understand.
3.In model validation, the sources of analytical and experimental solutions should be provided first. In other words, from cases in Section 3.1 to 3.4, which ones are referenced from others and which ones are used for the first time, there should be more specific explanations.
Citation: https://doi.org/10.5194/gmd-2024-240-RC1 -
AC1: 'Reply on RC1', Qinghe Zhang, 28 Feb 2025
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Thank you for the suggestions and evaluation.
Answer1: The vertical layering of the model can theoretically be arbitrary. The more layers there are, the higher the accuracy of vertical flow velocity will be, but it will not increase the convergence order of the solution and will also increase the calculation time of the model. The two layers shown in Figure 1 are intended to clearly express the spatial distribution of interpolation nodes in the vertical direction. We will add necessary explanations in the revised version.
Answer2: Thank you. We will emphasize the significance of using the wet dry treatment and limiters in the mode nonsplit model algorithm. The 3D limiters are always applied after achieving the physical field to prevent pathological solutions, and then we can obtain the vertically averaged physical field. The WD treatment is carried out after obtaining the vertically averaged physical field to ensure the conservation of water elevation and depth-average momentum.
Answer3: Thanks for the suggestion. The artificial analytical solution in Section 3.1 is a re-derivation of the analytical expression in the sigma coordinate system based on Kärnä et al. (2018). The case in Section 3.4 is inspired by the examples used in Chen et al. (2022) and conducted research using our own designed grid.
Citation: https://doi.org/10.5194/gmd-2024-240-AC1
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AC1: 'Reply on RC1', Qinghe Zhang, 28 Feb 2025
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