Incipient channelization in mountainous landscapes is often associated with the presence of first-order valleys at a regular wavelength under diverse hydroclimatic forcings. Here we provide a formal linear stability analysis of a landscape evolution model in detachment-limited erosion conditions to quantify the impact of the erosion law on the regular valley formation. The linear stability analysis is conducted for the unchannelized hillslope solutions along a long mountain ridge, where the perturbed equations constitute a third-order differential eigenvalue problem. The solutions to the posed eigenvalue problem are obtained by a spectral Galerkin technique with numerical quadrature. Results reveal the dependence of the erosion threshold and the emergent ridge/valley wavelength on the exponents in the power-law scaling coupling fluvial erosion with specific drainage area (m) and local slope (n). As the exponent m increases for a fixed n, the emergent valley spacing expands and the erosion limit for the first channel instability declines. Conversely, the erosion threshold for the first channelization rises with an increase in n at a particular value of m. We also show that predictions of the stability analysis conform with numerical simulations for different degrees of nonlinearity in the erosion mechanism and agree well with topographic data of a natural landscape.

In this comment, we clarify that the specific contributing area is defined in the limit of an infinitesimal contour length. We also confirm that not all solutions obtained from the minimalist landscape evolution model of Bonetti et al. (2020) are rescaled copies of each other because of the crucial role of the boundary conditions. We use dimensional analysis and numerical simulations for a case where only one horizontal length scale enters the physical law to establish this point.