Can we define "drainage density" for a soil column (point-scale)?

Question

From what I read all over the web and articles, drainage density is a parameter that is defined for a catchment.

I want to use a hydrological model to simulate the percolation from the bottom of a soil column, therefore my spatial scale is point-scale.

This model both works in point-scale mode and distributed mode. In the point-scale, I still need to choose a value for the drainage density (DD).

As described in this paper :

$$ DD = \dfrac{1}{2 HL} ,$$

where $HL$ is the length of hillslope.

Any idea how to calculate $HL$ for a soil column?

Can I say $HL$ is equal to the depth of the soil column (surface to the seepage face)?

Or it doesn't make sense to define DD in the point-scale?

In this model, DD affects the ratio of $\dfrac{lateral flow}{percolation}$. As for the lateral flow in the soil column, beside the topographical slope and soil textures, is there any other parameters that is important to consider?

Please let me know if I did not explain my question clearly.

Answer 1

Fundamentally it doesn't make sense to describe the point scale model with hillslope length and drainage density. If you are looking to model a soil column, you could use Darcy's law or Richard's equation. If you are looking to model the catchment, the point scale is not appropriate, although you could always incorporate those point-scale appropriate equations into a more complete hydrologic model if you wish (something like HydroGeoSphere does), but that is still a catchment scale model.

In either case, this comes back to 1) what is the purpose of your modelling exercise, and 2) making sure that your choice of model is appropriate for that purpose. A hydrologic model that uses hillslope length for a point scale is not an appropriate choice for what (I think) you are trying to do.