Computation of the erosion rate

[cyrilgarneau@gmail.com]

Dear mohiders,

I'm reviewing the erosion model described in "An advanced modelling tool for simulating complex river systems" from Trancoso et al. 2009 and I have a question about the erosion equation of the Drainage Network module (subroutine ComputeErosionFluxes):

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                            !kg m-2 s-1 = kg m-2 s-1 * m2
                            ErosionRate = Property%ErosionCoefficient                       &
                                        * Property%BottomConc (NodeID)                      &
                                        / SedimentConc (NodeID)                             &
                                        * aux


As far as I understand the code, the erosion rate is normalized by the ratio of the bottom concentration of the property divided by the "sediment concentration". My first question is: Why do we normalize since we already inputed an erosion coefficient? In my case, I want to erode particulate metals to which I give a Bottom Concentration many orders of magnitude lower than the "sediment concentration" and I know its erosion rate.

My second question: Isn't it dangerous to normalize all erosion rates by the TSS or Cohesive Sediment property? I mean that these two properties are independent and are not, for example, the sum of all particulate properties (or at least, I hope so!). This means that if, for example again, my cohesive sediment's bottom concentration is null (or very low) in a reach, the erosion rate will raise to unrealistic levels. Once again, in my case, I need at least two fractions of TSS (fine and coarse). If I define the Cohesive Sediment as the fine fraction, then I risk a division by zero in my model.

In my opinion, this normalization is tricky and might lead to misinterpretations. But before modifying my code, I would like your opinion.

Thank you,

Cyril

[davidbrito]

Hello Cyril,

1. There is no option that you have a division by zero since before that evaluation this if is tested ( SedimentConc (NodeID) > AllmostZero)

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if3:                    if (Me%ShearStress (ReachID) > Property%ErosionCriticalShear .and.  &
                            CurrNode%VolumeNew > AllmostZero .and.                          &
                            SedimentConc (NodeID) > AllmostZero) then


2. Normalization
This division of property by sediment (property enrichment of the sediment) was added because particulate properties that we use are linked to cohesive sediment or total suspended sediment. When you erode sediment than a proportion of property material attached goes with it. And it is assumed that the proportion that is eroded is the proportion of the material existing in the bed.

Advantages
Without this ratio (property enrichment of the sediment) it would erode the same amount of sediment and the same amount of other particulated properties even that, for instance, in the bottom exists double of the property matter adsorbed to one unit of fine sediment.

Disavantages
It assumes homogenization and does not distinguish material that deposited in different instants and can have different property enrichments. This disavantage comes form the fact that we do not account for layers, what exists in one cell is homogenized in the bottom.

The erosion coefficient is the sediment "erodibility" and so effectively I do not change it from property to property.
So for your case you say that you adapt property erosion coefficient that is the similar you are trying to say that less metals exist per unit of sediment so you reduce the erosion coefficient.
With the ratio used, the amount of metals per sediment may change with time and with space depending on the deposition rates and discharges for instance and the amount eroded is proportional to the ratio existing in the bottom at any given cell and given time.

If it was not clear please say and I will try again.

If you think that this procedure is not correct please show us and we will be glad to improve the model.
This can be and optional component for instance.

Best regards,
David