ALL MODELS ARE WRONG, OFTEN IN DIFFERENT WAYS: AN INTER-COMPARISON STUDY OF LANDSCAPE EVOLUTION MODELS

The stream power equation (SPE) is widely used in landscape evolution models (LEMs) to gain a better understanding of how landscapes respond to perturbations and how climate and tectonic signals can be deciphered in modern landscapes. Presumably different LEMs implementing the SPE produce the same solution when using the same parameter values and initial and boundary conditions. However, unlike other earth-science modeling communities (climate, geodynamics), geomorphologists have not carried out organized community-wide LEM intercomparisons to test this assumption. This begs the question: do all LEMs produce the same solution, when initialized and forced in the same way?

We explore this question using four different modeling libraries that each implement the SPE: CHILD, Landlab, Python FastScape, and TTLEM. LEMs built from these libraries solve the SPE using an explicit finite difference algorithm, the implicit FastScape solution, and the total variation diminishing finite volume method (TVD_FVM). In the history of LEMs, the FastScape and TVD_FVM are relatively new algorithms, but they are appealing in comparison with explicit finite difference methods for different reasons: the FastScape algorithm is unconditionally stable, allowing the use of long time steps without numerical instability; and TVD_FVM can more accurately preserve and propagate knickpoints.

We highlight differences in steady-state topography and transient landscape form produced using different LEMs. Steady state is reached following uniform rock uplift of initial topography. Transient landscape form results from an increase in rock uplift rate after steady state is reached. Within a single model, details of the final results, such as network organization, vary with the time step length (dt), even when the exact analytical solution is reached. Among the models, sensitivity to increasing dt varies. Some of the models become obviously unstable when long dt values are used, whereas other models are not obviously unstable, but the solution is wrong. In the transient experiments, long dt values produce incorrect solutions in all LEMs, but in some cases these incorrect solutions are more difficult to identify than classic sawtooth numerical instability. Importantly, many problems can be solved simply by using a stable time step.