| 28 Jan 2026
A novel ALE scheme with the internal boundary for coupling tectonic and surface processes in geodynamic models
Abstract. Recent advancements in modelling the deformation of the Earth's crust and upper mantle, coupled with surface processes, have significantly deepened our understanding of how the Earth responds to integrated tectonic and erosional forces, which are intricately linked to climate dynamics. This study presents a novel coupling framework within the Arbitrary Lagrangian-Eulerian with Internal Boundary (ALE-IB) scheme, which integrates the geodynamic codes Underworld 2 with the surface process code Badlands. Our innovative approach addresses the limitations of previous Eulerian-based coupling frameworks by maintaining the integrity of internal interfaces and providing precise surface tracking. This ensures accurate representation of material boundaries and enhances the fidelity of simulations involving complex geological processes. We detail the principles underlying the coupling of surface processes with tectonic deformation, leveraging the strengths of the ALE-IB scheme to model free surfaces and moving boundaries effectively. By comparing our model's performance with an Eulerian-based approach, we highlight key differences in structural and dynamic behaviour under varying surface process intensities. This comparison offers valuable insights into the intricate interactions between surface and deep Earth processes. Our findings contribute to a more comprehensive understanding of geomorphological and tectonic evolution, providing a robust framework for future research in geodynamic and climate-related geological studies.
Lu et al. present a novel coupling framework within ALE-IB scheme, which couples the thermo-mechanical code Underworld 2 with the landscape evolution code Badlands. They suggest that this module could give an accurate material boundary and prevent numerical artifacts. The topic is timely and relevant to the geodynamic modeling community. I suggest publication after addressing the following comments.
Main concerns:
1) This new coupling module is based on the previous UWGeodynamics module, which is also coupled to the geodynamic code Underworld 2 with surface process codes such as Badlands. What are the detailed differences between your coupling module and the UWGeodynamics module? I speculate that you added the IB scheme, but the description in Section 2.2.2 is not clear about how it is implemented. Some details about this IB scheme need to be added. How exactly is the velocity evaluated on the S-surface and transferred to Badlands? What interpolation methods are used? The particle adjustment process based on surface changes (distinguishing sediment from air) requires more detail.
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2) The benchmark results in Fig. 4 are not very clear to me (see details below).
3) The sediment distribution differences between schemes (Figure 10a,b) are subtle, yet the tectonic deformation is more different at the collision front (Fig. 10c,d). Why?
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Minor:
38, typo: FasScape -> FastScape
Eqs 4-5, the C and phi are messed up. It’s better to define the starting cohesion (C_0) and friction angle (phi_0).
131, do you have a criterion for choosing the subtimesteps dt_sp?
138-139, Is the grid used in Badlands the triangular grid as shown in Figure 1? Although the ALE-IB scheme avoids interpolation from particles to grid nodes at the surface in Underworld 2, how is the processing carried out in the process of converting from surface rectangular grids in Underworld 2 to more refined rectangular grids and further triangular grids in Badlands? If interpolation is still used, what impact will it have on the result?
140-144, As mentioned above, a more detailed ALE-IB implementation scheme needs to be described.
167, the air density is set to be 0 kg/m3. Do you solve the energy equation, and does it have problems?
208, add units for Kd & Kf
Fig. 4, SP should add the abbr. for SP-surface process in the figure caption.
Fig. 4, why isn’t the deposition/sedimentation at the trough? Did the two models use the same random noise? Does the change of random noise have a significant impact? Besides, a figure of the differences in topography and erosion/deposition between these two schemes can better show the distinctions between the two schemes.
Fig. 5, drainage colorbar adds unit
Table 2, your rheological model has no pressure dependence, activation volume is not used, but you show it here. So, do you use the activation volume in your viscosity?
Fig. 12 is not used in the main text; you may want to refer to it at line 248 (Fig. 12e, not 11e?)
Table 2 defines the model names for two groups of experiments: Ex.1 vs. Ex. 2. It’s very confusing when referring to e.g., CM1 from Ex.1 or Ex.2. Please use a better approach for clarity.