The manuscript describes a modeling approach of the flow in unsaturated sand in order to explain so-called Bauters’ paradox. A semi-continuum model approach is presented that can imitate the finger flow phenomena with the oversaturation in the tip and the whole transition towards a diffusion-type infiltration plume as function of the initial soil moisture condition. The model was successfully tested by description of the Bauters’ experiment.

General Comments

The manuscript tackles an important problem that is in the focus of the journal. Methods and results are novel and can much contribute to progress in describing unsaturated flow phenomena. My main critical comment is that for in-depth understanding the physical basis of the modeling approach and finally also of the results, a better explanation of the semi-continuum’s model concept would help.

In addition, I found the introduction is much too far reaching, of course, everything is somehow connected. The review on global water cycle, the flow phenomena, sample volume dependency, REV concepts and Richards’ equations, and other aspects, all does not help much to better understand the problem, and are not discussed later any more.

What I did not understand was the semi-continuum model concept, especially what is different from a numerical discretization of a continuum model? Perhaps you did it already in other papers. It seems relatively simple and more empirical because of the block size selection and the scaling relations. Maybe it helps to include an illustration? The idea of scaling the retention function with block size is also unclear to me. I did not read the cited references, but the present paper seems to apply the previously developed model concept to describe the specific experiment, yes? It is suggested in the manuscript that the initial water saturation is the variable controlling the finger formation. What about the wettability (i.e., surface tension), which is of course connected with water saturation but can change with time?

Overall, this valuable contribution could become even better if more focussed and with more specific explanations on the physical basis of the approaches.

The paper analyses the process of infiltration of a liquid into an unsaturated porous medium, which is characterized by different regimes depending on the level of saturation. The liquid is assumed to be wettable with respect to the homogeneous medium. Then, the authors introduce a semi-continuum model that lends itself well to the interpretation of the infiltration regime.

The topic is of interest and deals with a process that even in extremely simple situations reveals a degree of complexity.

However, I see the major limitation in the absence of experimental validation: the numerical scheme, although of interest, appears limited in its interpretation of physical reality. Moreover, and this is a second major issue, there is a lack of sensitivity analysis, since the only estimator comes from repeating the numerical tests by changing only the intrinsic permeability distribution. In this sense, it is necessary for the authors to thoroughly analyse the uncertainty of the parameters (viscosity, degree of saturation, etc.) and analyse the variability of the governed quantities.

There is one point of particular interest: if Bauter's paradox occurs even when intrinsic permeability is homogeneous, how does the proposed model behave in this situation?

Last, the authors tell us about the behavior of their model, but the interpretation of why appears to be missing.

Minor comments

Figure 3: specify units for the colorbar

Figures 5-6: add the frame to panel b diagram

Please see the pdf.

As there are several points unclear to me, I wanted to skip ticking the points 1), 2) and 3) above. This did not work out, so I just ticked "Good" everywhere. This is just to proceed.