I am attempting to create a very simple hydraulic erosion simulation against a heightmap.

I am using Manning's equation to calculate velocity and discharge. I have taken samples of Hjulstrom's diagram to represent critical limits for eroding or depositing material from the stream bed--for now assuming a uniform particle size, but I plan to add 4 different sizes later. I am using information from various sources to select a relative best fit for Manning's Roughness Coefficient in different situations.

What I have not been able to find are formulas for the following:

  1. Stream capacity for a particle size
  2. Rate or quantity to erode for a particle size
  3. Rate or quantity to deposit for a particle size

Plenty of material has alluded to increases in velocity or discharge effectively squaring or cubing an output, for example, but I have not seen anything like a formula except to find the critical limits themselves.

Can anyone either provide some basic formulas for the above, or point me to some material that can help me estimate? Perfect accuracy is not required, so even a very rough approximation would do.

  • $\begingroup$ Deposit a layer of "Colored" sand like novelty toys and chart progress it takes to erode various layers. $\endgroup$
    – LazyReader
    Commented Sep 26, 2021 at 8:43
  • $\begingroup$ @LazyReader Thank you for the advice, but I do not think that would help me. I need to be able to estimate these values for arbitrary particle sizes, velocities, etc. So given certain values for velocity, discharge, hydraulic radius, particle diameter, etc, what is the stream capacity, rate or quantity eroded, and/or rate or quantity deposited? $\endgroup$
    – Daniel
    Commented Sep 28, 2021 at 1:38


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