Understanding how flow_length accounts for slope

[AquaPore]

Dear Wflow modellers,

I am questioning how does flow_length depend on slope, as from my understanding flow_length should increase with increasing slope, which from my understanding does not seem to be the case in Wflow.

 flow_length[v] * surface_flow_width[v] = CellSize[v]

I understand that slope is incorporated in the parameter $\alpha$ of the Manning equation, and I am questionning if this is supposed to compensate for the slope in the flow_length?

With kindness,
Joseph A. P. Pollacco

[cookesan]

flow_length is the plan-view routing length through a grid cell, based on the local drain direction and the cell dimensions. So for D8-style routing it is effectively the horizontal cell length in the chosen direction, or the diagonal length for diagonal flow.

It is not stretched into a terrain-surface distance using the slope. In Wflow, slope enters the hydraulic/kinematic-wave calculations separately. The geometry side stays consistent with the cell area relationship, where effective overland width is derived from area divided by flow length.

So in practical terms: do not adjust flow_length to compensate for slope unless you intentionally want to change the model geometry. Use the slope parameter for the hydraulic gradient/topographic control part of the calculation.

[AquaPore]

Dear @cookesan,

I am ever so grateful for your time for clarifying the physical processes of Wflow model. I am aware of the $\alpha$ parameter of the surface flow routine:

$$\alpha =\left( \frac{n,,{P_w}^{{{3}\Bigg/{3}}}}{\sqrt{Slope}} \right) ^{\beta}$$

Based on your comprehensive reply I have 2 more questions:

Q1) Will you kindly let us know what you mean you intentionally want to change the model geometry , I guess that this would require rewriting the Wflow model by using for example Triangulated Irregular Network?

Q2) Let's imagine we have (a) gentle terrain and (b) a steep terrain, with the same land use. Would the manning parameter n of the steeper terrain need to be slightly higher compared to the n gentle sloping terrain to compensate for not correcting the extra distance the water would needs to travel?

With kindness,
Joseph A.P. Pollacco