This manuscript considers analytical solutions based on some of the rheological models widely used for modeling rapid mass movements. As far as I can see, there is nothing fundamentally wrong in the manuscript. On the other and, however, I am left with the feeling that I did not learn much.

The presented analytical solution refers to an infinite sheet of constant thickness on a planar slope. It is basically the same as that presented by Pudasaini and Krautblatter (2022), but extended by a linear term in velocity, which makes it additionally applicable to the rheology proposed by O'Brien and Julien (1988).

However, the analytical solutions are not used extensively in the rest of the manuscript. Practically, only the asymptotic velocity, which is approached on a long slope, is used. It is, however, already stated in the manuscript that this asymptotic velocity is obtained easily without solving a differential equation, just by balancing friction with driving force. The only property used beyond the asymptotic velocity is the time constant that describes how fast the asymptotic velocity is approached. This time constant is, however, only used for finding out that the asymptotic velocity is typically approached quickly. This results was also already described more or less in detail in previous studies, which are already cited (e.g., Pudasaini and Krautblatter 2022, Hergarten and Robl 2015).

The biggest part of the manuscript is devoted to writing the asymptotic velocity and the time constant for different rheologies. The comparison is, however, somewhat superficial. The considered (assumed to be typical) parameter combinations yield different asymptotic velocities and time constants and the meaning of the time constant is different for different rheologies. Analyzing which of the parameters have the biggest effect on the asymptotic velocity is a good idea in principle, but the results obtained from Sobol's sensitivity analysis do not tell much. As an example, it is clear for Voellmy's rheology that the parameter mu has a big effect if the slope is only a bit steeper than mu, but otherwise the effect of the other parameter, xi, becomes dominant. Since Sobol's analysis considers the entire "realistic" parameter range, it just predicts similar effects of both parameters (Table 3).

Section 4 comes back to the model calibration announced in the title of the paper. However, it is only showing that the asymptotic velocity can be helpful for calibration if the velocity and the flow thickness were measured at a suitable location. This is true, but not very surprising.

This section also comes back to a point raised earlier in the context of the O'Brien and Julien (1988) rheology. It is stated in Sect. 3 that the viscosity only occurs in combination with a nondimensional parameter, which tells that both cannot be obtained independently from experiments. This is described as an interesting observation, but such concepts are not unusual. The idea behind such concept is separating well-defined physical parameters from more empirical factors in the model equations. In general, it could be useful if fluids with different viscosities were considered. As an example from hydrogeology, Darcy's law involves the ratio of permeability and viscosity, with the permeability being a property of the porous medium and the viscosity a property of the fluid. So having such a product of properties in a model is not unusual, and checking numerically that the results really depend only on the product of the parameters is unnecessary.

My overall impression is that this manuscript misses several chances to bring new and important scientific results. How do the considered rheologies differ when calibrated to the same asymptotic velocity at the same slope? Is the time scale of adjustment then inherently linked to the asymptotic velocity? Is the adjustment always fast or does it rely on specific parameter combinations? And finally, could measuring the velocity at a suitable point and the shape of the deposits help to find out which rheology is finally the best (single-phase) rheology for debris flows? There is definitely some potential, and I would encourage the authors to go ahead. At the moment, however, I feel that the results are still not sufficient for a full research paper.