Erosion and deposition patterns for steep hillslope application

[Nate Abramson]

Hi Tom, 

I am hoping to get your input on some issues I’m having with my application of CAESAR-Lisflood to a steep reclaimed mine tailings embankment (slopes ~ 0.25 -0.4 m/m). The goal is to use CAESAR to model event-based rill erosion for short-duration high-intensity rainfall events where we have repeat topographic surveys and high-resolution rainfall data for each event. We are modeling two specific events (with peak 5-minute rainfall intensities of about 130 and 250 mm/hr) and total storm duration of about 1 hour. Overall, I have been able to get good model results which generally match the spatial distribution of observed rill erosion across the embankment for the two events. The issue I am running into is that erosion and deposition are alternating along the hillslope profile where a rill dumps out sediment intermittently and then picks back up again. This results in a somewhat unrealistic pattern of erosion and deposition where instead of depositing most of the sediment at the bottom of the hillslope there are discontinuous rills along the steep hillslope profile.

See example CL output of a change map attached (Pictures 1 and 2) for a section of the embankment with flow direction from bottom of image towards the top of image (erosion in blue and deposition in red). I’m curious if this might be related to model instability or some parameters choices in attached xml file. I am using a 1m resolution LiDAR derived DEM (2400 x 400m some of which has been masked out as no data) and 5-minute rainfall gage data using multiple gages across the DEM. Attached is the xml file. Please let me know if you have any suggestions or see any red flags as far as model parameters go that might help to improve this issue. Happy to provide more info if needed. 

One other note is that I have modified the removal of vegetation within the erode() routine so that when tau >vegTauCrit the vegetation is completely removed as this is what we observe at our study site. However, I get similar results and erosion patterns with the distributed version using the grass now function at beginning of run so don’t believe the issue I am having is related to the modification below. 

// veg components

                            // here to erode the veg layer..

                            if (veg[x, y, 1] > 0 && tau > vegTauCrit)

                            {

                                // now to remove from veg layer..

                               // veg[x, y, 1] -= mult_factor * time_factor * Math.Pow(tau - vegTauCrit, 0.5) * 0.00001;

                                veg[x, y, 1] = 0;

                            }

Look forward to any input. 

Thanks, 

Nate

[tom.co...@gmail.com]

Hi Nate – is flow from bottom to top on those images? If so it looks like the material is being dumped out as splays next to the channels rather than at the bottom as you expected..? That sound about right?

 

Eyeballing your config file, Mannings is at 0.5 – which seems really high.. 0.05 is better? (eg https://www.fsl.orst.edu/geowater/FX3/help/8_Hydraulic_Reference/Mannings_n_Tables.htm )

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[Nate Abramson]

Hi Tom, 

Thanks for the reply. Yes the flow direction is from bottom of image towards top of image and I would agree with your summary that material is being dumped out periodically on the hillslope rather than carried down to the bottom of the slope. Also attached are a few screenshots of the water depth during a run showing some discontinuity and diagonal intermittent flow patterns. Curious if you have seen this and if it might be causing some of these issues?

Due to the steepness of the hillslopes and only slightly convergent topography in places (mostly planar design) the overland flows are very shallow. Manning's n was chosen from the literature (Hydraulics of overland flow on hillslopes - Emmett 1970) but that being said we have not measured this in the field so I will see if 0.05 removes this issue.

Thanks, 

Nate 

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[Tom Coulthard]

Hi Nate - I’ll look more later but in case you’re still working - try lowering the min depth for erosion to 0.001? It may be that ‘threshold’ is too high at 0.01 on these sterp slopes. 

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From: caesar-...@googlegroups.com <caesar-...@googlegroups.com> on behalf of Nate Abramson <abrams...@gmail.com>
Sent: Monday, August 7, 2023 5:59:23 PM
To: caesar-...@googlegroups.com <caesar-...@googlegroups.com>
Subject: Re: Erosion and deposition patterns for steep hillslope application

 

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[Nate Abramson]

Hi Tom, 

Thanks for your input. Regarding the threshold for erosion, I have this at 0.01 and find the results quite sensitive to this parameter since as you suggest it may be close to the water depths on steep slopes (this is still using manning's n = 0.5). Reducing the threshold for erosion to 0.001 or even 0.005 m leads to an overprediction of erosion but does not eliminate the intermittent rilling. For the two events I am trying to model this threshold value of 0.01 seems like the best fit as there is slight underprediction of erosion with the lower intensity event and overprediction of erosion with the larger intensity event. 

I have also tried reducing manning's n to 0.05 as you suggested. The main noticeable change I see is that the shear stress drops by almost an order of magnitude and no rill erosion is predicted where tau>100 pa, which is what I have my vegetation shear strength set to at the beginning of the run. This is true for both events with peak rainfall intensities of 130 and 250 mm/hr. Not sure if this has to do with the formulation of shear stress including manning's n? For example using n = 0.05, a water depth of 0.085 m and velocity of 0.99 m/s gives shear stress ~ 55 pa, where when using n = 0.5, a water depth of 0.03 m and velocity of 0.14 m/s gives shear stress of ~150 pa. I'm sure this is really a non-issue when modeling fluvial erosion in channels but not sure how to best proceed with the hillslope application. If you have a set of parameters that has been successfully used in a steep hillslope application with a high resolution DEM I'd be interested in comparing with what I have to see if there are any major differences. Like I said in the first post, the model is working well in that it is generally predicting the correct locations of erosion for both events, I was just hoping to find a fix to the intermittent rill erosion. 

Thanks, 

Nate

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[tom.co...@gmail.com]

Hi Nate,

Ok – here’s my thinking on this.

It looks like you’re getting erosion and deposition that suddenly switches off and on as you move downslope. Which is resulting in the ‘splays’ then incision, then splays then incision. So taking that at stage further something in the model is switching on and off – and I think this may be the erosion, where the hard thresholds are the water depth erosion threshold.. On a steep slope – the velocity of a 1cm deep flow is likely enough to move fine grained material without a problem, and when that drops below 1cm it suddenly stops… I think this may also explain the diagonal artefacts you talked about earlier in the water depth pics – its likely this may be the switching on and off… On a 10m grid cell, a 0.01m depth threshold is likely fine, but on a 1m or smaller it can make a big difference. The work we carried out on 0.2m resolution plot simulations for Australian mines, needed to have really low min depth in order to make any sensible hydraulic connections across the DEM – BUT these were pretty low gradient situations – especially compared to yours.

 

A couple of other hopefully helpful comments – Shear stress is not calculated by a depth slope product in the model (which I think you are doing in your message below? Sorry if not) – it’s a product of vel^2 and a drag coefficient (ci)

 

                            double ci = gravity * (temp_mannings * temp_mannings) * Math.Pow(water_depth[x, y], -0.33);

                            //tauvel = 1000 * ci * vel * vel;

                            if (slopetot > 0) slopetot = 0;

                            //tauvel = 1000 * ci * vel * vel * (1 + (1 * (slopetot)));

                            tau = 1000 * ci * vel * vel * (1 + (1 * (slopetot / vel)));

 

(the slopetot/vel thing is to reduce tau when there are negative bed slopes) – this will have a big effect on your depth/slope tau calcs – as reducing n will lower flow depths – but increase the velocity..

 

Its also worth bearing in mind that – unfortunately – things based around mannings and mannings roughness probably start to break down on steep slopes (above 0.1) so we’re at the limits of how the model should be operating – and as you are doing calibrating to get the right results with a wide range of parameters is probably the way forward.

 

Not sure all of this helps – sorry! But hopefully the explanations help….

Tom

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[Nate Abramson]

Hi Tom, 

Thank you for the explanations, they do help and it makes sense that the depth threshold close to water depths may likely be causing the switching on and off.  This provides me with a path forward so appreciate your input. I will continue to work on it and will write back if I'm able to find a good solution to the switching of erosion and deposition.

Regarding my comment on the shear stress and manning's n, the numbers I was referring to were using the formulation in the code in your last response. My point was that I saw a large reduction in shear stress across the DEM (likely from drag term ci) when changing manning's n from 0.5 to 0.05, where reducing manning's n leads to much lower shear stress even where water depth and velocity increase (table below for example - these were just two random points I picked out during each run so not necessarily the same location or timing). I recognize that this is likely not an issue in the normal range of manning's n and applications with the model, however it seemed to make a large difference in my runs. Good to know that manning's n may break down at higher slopes and I realize that this model was not built for steep hillslope applications so will keep that in mind as I apply it in somewhat extreme applications. 

Tau (Pa)	Ci	vel (m/s)	manning's n	water depth (m)
54	0.06	0.99	0.05	0.085
153	7.8	0.14	0.5	0.030

Thanks, 

Nate

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[Tom Coulthard]

Yes the Ci will behave quite differently with very shallow flows. I think I’ve tried it in the past with a forced minimum or constant… maybe worth trying that? 

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From: caesar-...@googlegroups.com <caesar-...@googlegroups.com> on behalf of Nate Abramson <abrams...@gmail.com>

Sent: Thursday, August 10, 2023 5:19:49 PM

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[Nate Abramson]

Thanks, good idea. I will give it a shot. 

Nate

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