# Calculation of river width in relation to contributing area

I'm looking for a mathematical method to estimate the river width based on the basic topographic information of the specific sections of stream under consideration.

Is there a formula to estimate the river width in a specific point based on the upstream contributing area (or any other relation with the geo-morphological characteristics of flow accumulation)? Could you please also refer to the corresponding literature?

Thank you

• What is the "basic topographic information of the specific sections of stream" that you have? Is it measured cross-sections of the river at various locations? Also which width of river are you after, the width at the water surface, or the average width, which takes in the submerged sides of the river? If you want the width at the water surface & you have measured cross sections you can simply take the width from the cross sections.
– Fred
Sep 28, 2020 at 21:55
• No @Fred, I was referring to all the information you get by processing a DEM (Flow direction, accumulation and so on). My domain is too big to directly measure the width water surface (which is fine for my purposes) on Google Earth. Sep 29, 2020 at 7:50

## 1 Answer

It's a function of flow volume rather than catchment area. The flow rate can be vary by an order of 10 to 100 for the same catchment area, https://www.google.com/search?q=average+river+width+based+on+flow+volume&tbm=isch There's so many variables like flow speed, inclination, bedrock type, flow rate.

This document includes the river width, it says there are too many variables.

https://www.nature.com/articles/s41598-019-44347-4

https://link.springer.com/article/10.1007/s11629-014-3265-0

here's a cool reference:

https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019GL082027

Did you know that a given type of rock gives mountains with all the same slope angles, i.e. there are mountains with ravines averaging 23 or 14 or 33 or 50% for the same mountain group, and screes inclines are rarely an irregular mix.

• Hi @aliential, thanks for you reply. I am aware of the relationship between flow (Q) and width (w) (w=aQ^b, being a and b empirically estimated constants) and the consequent relationships for the estimation of hydraulic geometry (as Q=wdv, width x depth x velocity), but unfortunately I cannot use the flow to calculate my (roughly) estimated width. Sep 29, 2020 at 8:38
• More promising looks the relation described in your last suggested article (de Moeres Frasson et al 2019): w= a x A^b, being a and b empirically estimated constants and A the catchment area. Unfortunately my domain is very broad, it spans different climate zones, and I'm afraid I wouldn't be able to estimate two a and b that could reasonably work throughout my river network. Sep 29, 2020 at 8:43
• @Nemesi you may not be able to do it using catchment, since catchment does not correlate well with the amount of water in the system, flow rate, or slope. sometimes the answer is that two things just are not related.
– John
Sep 29, 2020 at 20:20