| 22 Jul 2026
Coupled hydrology, weathering geochemistry and surface-process evolution in a parallel global landscape evolution model
Abstract. goSPL (Global Scalable Paleo Landscape Evolution) is an open-source, parallel, finite-volume landscape evolution model designed to simulate the co-evolution of topography, drainage and sedimentary basins from catchment to planetary scale over geological time. Here, I present the new capabilities which extend the model from a fluvial–hillslope–marine sediment-routing engine into a coupled surface-process, near-surface-hydrology and weathering-geochemistry framework. The principal additions are (i) an implicit Dupuit–Boussinesq water table and a generic capillary-fringe duricrust that armours erodibility (forming either in situ or, with a groundwater-discharge gate, by lateral accumulation confined to valley discharge zones) and is archived in the stratigraphic record; (ii) a mass-conservative solute geochemistry module in which one or more lumped weathering tracers are dissolved, transported along the groundwater flux, precipitated as crust and routed down the river network to the ocean, with per-species typing, source provenance, spatially variable (lithology-controlled) weatherability and optional in-transit and marine coupling; (iii) a soil/regolith model; (iv) a mesh-native orographic-rain solver; (v) a diagnostic glacial-erosion model; and (vi) a parallel finite-volume flexural isostasy solver for planar meshes. All components are opt-in and are formulated as implicit or steady solves on a distributed PETSc DMPlex mesh, with solver choices (Krylov method, preconditioner, iteration scheme) driven by the conditioning of each operator. I describe the governing equations and the numerical and design choices behind each component, the YAML-based experiment configuration, the analytical-benchmark and regression test suite, and strong-scaling measurements on global production meshes of up to 23.7 million nodes. Finally I summarise the online documentation, the conda/PyPI/Docker distributions, the application interface and post-processing tools, and a suite of fifteen generic examples spanning regional and global scales. goSPL is distributed under the GNU GPL v3 licence.
This paper describes the quite comprehensive landscape evolution model goSPL. Similar to the older model eSCAPE by the same first author, the community somehow knows that it is powerful, but my impression is that it still does not receive the attention it deserves. Having a model description paper on goSPL (in a addition to the 2019 model description paper of eSCAPE) would probably help to make the model more popular. So I would definitely recommend publication as a model description paper after some (moderate) revisions.
On the other hand, I find the recent paper less clear than the older paper about eSCAPE. Overall, understanding the concept requires much knowledge about numerics. The model goSPL is, of course, much more comprehensive than eSCAPE. So it is clear that the author cannot go as deep into the individual model components as in the previous paper. Nevertheless, I feel that reducing the level a bit might help to make goSPL more popular.
While it is not clear whether it is really possible to make the paper more accessible at reasonable length, I would suggest to address the following points in a revised version. Some of these points contradict a bit to my own experience with landscape evolution modeling, which makes me curious about the author's opinion. Sorry for referring mainly to my own work here.
Title: As far as I remember, name and version of the model should be included in the title.
Line 104: The occurrence of the local precipitation rate in Eq. 2 is not very intuitive to me, given that Q is (time-averaged) discharge.
Line 110: Just for completeness, the oldest reference to the implicit O(n) scheme made popular by Braun & Willett (2013) is either (Hergarten, 2001, doi 10.1103/PhysRevLett.86.2689, but a bit short to see that it is the same) or Hergarten (2002, doi 10.1007/978-3-662-04390-5, very detailed, but only in a book).
Line 120: I think that some properties occurring in Eq. 3 are not explained.
Sect. 3.5: To my experience, diffusion suffers from strong scaling problems if fluvial erosion and diffusion are applied simultaneously (e.g., described in the already cited paper of Hergarten & Pietrek 2023 and in several papers cited therein). In my opinion, this is a fundamental problem of combining rivers as linear elements with two-dimensional hillslopes. How are diffusion and fluvial erosion coupled in goSPL? What happens to the sediment brought into the rivers?
Line 171: This form of the equation would not be correct for spatially variable D.
Line 174: Perhaps mention the full version for q_h (with the denominator) and not only the truncated series.
Line 176: Perhaps a few more words about the treatment of the nonlinear diffusivity.
Lines 221-223: To my experience, Eulerian treatment of horizontal movement causes severe problems (Hergarten & Fraters, 2026, doi 10.5194/egusphere-2026-2060) in the form that rivers do not follow the movement perpendicular to their flow direction? Was this explicitly tested? It would be interesting to see whether the scheme used here overcomes this problem.
Lines 223-224: I did not find information about the end-of-interval semi-Lagrangian interpolation in the cited reference.
Line 228: I think that D should be somewhere between the nabla-operators in Eq. 4 instead of in front of nabla^4 if it is spatially variable. Some readers might also worry about using the same symbol D as for the diffusivity.
Line 258: Is z_bed = eta?
Line 272: Why does block-Jacobi/ILU yield a physically unreasonable behavior here?
Lines 276-297: The description of the duricrust formation is a bit difficult to follow.
Sect 5.1: Some information about the geometry of the benchmark scenarios would be helpful.
Line 431: Perhaps clear for those who are familiar with stream power erosion, but the notation is not fully consistent with the previous notation and not all properties are explained.
Figure 2(c): I am a bit confused about the quite strong deviation in the celerity of knickpoint migration. Of course, taking the full Voronoi cell overestimates the discharge. But how is the discharge computed in the analytical solution?
Line 509: Given that K is the same property as before, why is it nondimensional?
Line 525: The data given here refer to peak elevation, while Fig. 5 refers to mean elevation.
Figure 5: Why were the simulations stopped at t = 100 kyr? Will they come closer to each other over longer time intervals?
Line 565: Given that kappa_h is the diffusivity, the value for land looks quite high to me. As far as I remember, other studies typically use something like 0.01 m^2 yr^-1.
Lines 566-567: Eq. 4 is not written directly in terms of the parameters defined here (although the relations are clear for those who are really familiar with the topic).
Line 697: For me, the wording "targets a narrower niche" makes goSPL smaller than it is. My impression is that coupling of mantle dynamics and atmospheric processes with landscape evolution is becoming a "hot topic".
General: Some of the inline equations are a bit too long and should be replaced by displayed and numbered equations. Also, y and yr should be used consistently.
In sum, this manuscript provides an overwhelming amount of information. It is impressing to see which level the model has reached in the meantime. In turn, the amount of information can also be seen as a weakness. To be honest, the writing even seems to be a bit rushed to me. In this sense, a bit less material in combination with a more thorough check for details and consistency might make the paper more accessible to a wider readership.
Anyway, there is nothing that cannot be fixed by a moderate revision and nothing that questions my initial statement that a model description paper helps to make goSPL more popular in the community.
Best regards,
Stefan Hergarten