3D lithological structure in a steady state model drives ...

3D lithological structure in a steady

state model drives divide migration

E. Graf1, S. Mudd1, F. Kober2, A. Landgraf2, A. Ludwig2

1 School of Geosciences, University of Edinburgh, UK2 National Cooperative for the Disposal of Radioactive Waste (Nagra), Switzerland

vEGU2021 – April 2021

In order to confidently model scenarios of future

topography, we want to account for variations in

lithology as well as potential changes in drainage

patterns (e.g. through river capture).

We present a model capable of incorporating 3D

geological data and adapting to alternative

drainage axes.

We demonstrate the model using a site in the

Swiss Jura Mountains. Values of erodibility K are

calibrated for different lithological units, and the

model is then run for selected incision and

alternative drainage scenarios.

Motivation

Right: Location of the study area in northern Switzerland (figure modified from Yanites et al., 2017). Black rectangle delineates the extent of the

study area according to the maps on subsequent slides.

The MuddPILE (Parsimonious Integrated Landscape Evolution)

Model (Mudd, 2017):

• calculates local relief using steady state solutions of the

stream power incision model (where gradient is related to

drainage area via a concavity index and a steepness index)

• quantifies hillslope relief using a very simple critical slope

gradient where hillslope angles are set to a critical value on

pixels that have a small drainage area

• allows drainage divides to migrate to minimize sharp breaks

in relief across them

For the 3D lithological structure, we use a 3D geological model

of the study area by Gmünder et al. (2013). See litho-

stratigraphic scheme at end of display.

Model overview

Right: model domain, draining into the fixed Rhine-Aare channel (blue).

Digital terrain model: DHM25 © Swisstopo.

We calibrate the values of erodibility, K, for each lithological unit by:

1) Extracting ranges of apparent K from the present-day

landscape based on drainage area and gradient along the

drainage network

2) Using a Monte Carlo approach to create combinations of K

values based on these ranges

3) Picking the best fit combination of K values by minimising

differences between the real and model landscape.

Calibrating values of K

Right: Geological map of the study area, following Isler et al. (1984). See end

of display for full legend. Digital terrain model: DHM25 © Swisstopo.

To extract K from the present-day landscape, we first calculate the

normalised channel steepness ksn for each node in the channel

network, as the gradient in χ–elevation space (following Mudd et al.

(2014).

Then we calculate erodibility K according to:

𝐾 =𝐸

𝑘𝑠𝑛𝑛

where E is erosion rate, and n is slope exponent in stream power law.

The calculations are performed on a 25 m digital terrain model (©

Swisstopo). The erosion rate was set to 0.0001 m/y, roughly based

on assumptions from an earlier modelling study in the area (Yanites

et al. 2017).

K extraction from topography

Right: channel network coloured by K. Note that the main Rhine/Aare channel is excluded

from the calculations since we do not have the full drainage area within the model extent.

E = 0.0001 m/yr, m = 0.45 and n = 1.

We group the lithological units, based on the geological map of

northern Switzerland 1:100,000 (Isler et al. 1984), as follows:

1) All bedrock units considered separately.

2) Quaternary units aggregated into Rhine Aare Domain

and Local Topography Domain (see right-hand side

map). This aims at separating the effects of the

predominantly flat, alluvial morphology along the Rhine

and Aare main valley bottoms.

3) Higher elevated parts of the Folded Jura excluded from

the K extraction (grey area in southwestern part of the

map, reflecting a different uplift history).

K extraction – grouping scheme

See end of display for full legend.

Digital terrain model: DHM25 © Swisstopo.

K ranges

Quat.

Distribution of K values within each lithological unit. Each “violin” shows an estimate of the underlying distribution of K values for the

corresponding lithological unit, such that the range of the violins extends past the extreme data points. The lower and upper dotted lines in

each violin indicate the 25th and 75th percentile, respectively, and the dashed lines indicate the median. The number of channel nodes in each

lithological unit, N, is given above the corresponding violin. The colour of each violin and unit IDs correspond to the legend at the end of the

display, with units appearing in the same order as in the legend.

• For the given assumptions, median K values for bedrock units are in the order of 10-06.

• We cannot easily distinguish between bedrock units based on K range

• The scatter within individual units can have various causes, such as:

• Transient stages in parts of the landscape

• Lithologic variability within individual units

• Partial deviations from the assumption of spatially uniform uplift / incision rates

• K is uncertain for some units due to a small number of data points.

• The Rhine-Aare and local topography Quaternary domains show a clear difference in

median K and K range

Insights from extracting apparent K

Monte Carlo grouping scheme

For the Monte Carlo simulation, we further

aggregate the bedrock units into five erodibility

groups (in addition to the two Quaternary groups)

based on lithologic considerations, thus also

increasing the sample sizes.

For each erodibility group, we randomly sample

values of K between the 25th and 75th percentile of

the corresponding K range extracted from channel

steepness.

Digital terrain model: DHM25 © Swisstopo.

To test the fit of each combination of K values, we run the model to

steady state and then compare the real and model landscape by

1) Extracting source points (see figure)

2) Plotting the distribution of source point elevations

3) Assessing the goodness of fit between distributions of real and

model landscape source point elevations using a two-sample

Kolmogorov-Smirnov test.

We run 5,000 combinations.

Monte Carlo simulations

Right: Source points (black) in the real landscape, with source points within the Rhine-

Aare domain and the folded Jura removed.

E = 0.0001 m/yr, m = 0.45 and n = 1 for Monte Carlo simulations.

Digital terrain model: DHM25 © Swisstopo.

Monte Carlo simulations

Distribution of source point elevation in the real and model

landscape for the best fit K combination. Each “violin”

shows an estimate of the underlying distribution of elevation

values for the corresponding landscape, such that the range

of the violins extends past the extreme data points.

The lower and upper dotted lines in each violin indicate the

25th and 75th percentile, respectively, and the dashed lines

indicate the median.

Monte Carlo simulations

We additionally explore the distribution of

goodness of fit across the landscape by

grouping source points according to the

erodibility group they are located in.

Note that the source point elevation is

cumulative, being the result of the entire

river profile, and therefore the distributions

aren't exclusively a product of a given

erodibility group.

Note: Rhine-Aare domain (Group 0) excluded from

calculations

Distribution of source point elevation by erodibility group in the real and model landscape for the best fit K combination. Each “violin” shows an

estimate of the underlying distribution of elevation values for the corresponding landscape, such that the range of the violins extends past the

extreme data points. The lower and upper horizontal dotted lines in each violin indicate the 25th and 75th percentile, respectively. The horizontal

dashed lines indicate the median.

Monte Carlo simulations

Using this best fit K combination, the real and model landscape are very similar in terms of source point elevation

distribution (see above), whereas they partly differ in terms of local relief and location of drainage divides.

REAL (*) MODEL

(*) Digital terrain model: DHM25 © Swisstopo.

Monte Carlo simulations

A given combination of K values that achieves good fit is not necessarily the “correct” combination,

since multiple combinations can produce similar results in terms of goodness of fit (equifinality).

We pick the K combination resulting in the highest p-value and assign these values to the

corresponding erodibility classes in the 3D geological model (see end of display for detailed scheme,

including assignment of hillslope gradients).

Table: K combinations resulting in the 5 highest p-values. Shaded in red is the best-fit combination, which is used in the subsequent simulations

with 3D lithology.

Applications: Incision scenarios

3D UNIFORM

Final model topography using 3D lithology and uniform lithology, respectively, with 350 m main channel incision in both cases. White boxes indicate

characteristic areas of divide migration. Left: 3D lithology using the best-fit combination of K values from the Monte Carlo simulations. Right: Uniform

lithology, using K = 3.5E-06 and Sc = 0.21, which corresponds to Group 2 (Tertiary Sediments) in the best-fit combination. E = 0.0001 (implying

duration of incision = 3.5 My); m = 0.45; n = 1. Note that the uplift component is just indirectly simulated via the cumulative main channel incision,

partly resulting in hypothetical model elevations near or even below sea level.

Applications: Incision scenarios

3D UNIFORM

Lithologies exposed in the final model landscape using 3D lithology and uniform lithology, respectively, with 350 m main channel incision in

both cases. Left: 3D lithology using the best-fit combination of K values from the Monte Carlo simulations. Right: Uniform lithology, using K =

3.5E-06 and Sc = 0.21, which corresponds to Group 2 (Tertiary Sediments) in the best-fit combination. E = 0.0001 (implying duration of

incision = 3.5 My); m = 0.45; n = 1. See end of display for full legend of the 3D geological model..

Applications: Alternative drainage

We next simulate the incision scenario in

combination with the reactivation of a paleo-

channel, thus assessing the effect of lateral

changes of the main channel axis on local relief

and drainage divide migration.

Left: Base level channel for the alternative drainage scenario (blue).

The original course of the Aare is plotted in red. Digital terrain model:

DHM25 © Swisstopo.

Applications: Alternative drainage

Final model topography (left) and lithologies exposed in the final model landscape (right) with 350 main channel incision

using the alternative drainage pathway and 3D lithology. White box is added for comparison with slide 15. K values used are

the best-fit combination from the Monte Carlo simulations. E = 0.0001 (implying duration of incision = 3.5 My); m = 0.45; n =

1. Note that the uplift component is just indirectly simulated via the cumulative main channel incision, partly resulting in

hypothetical model elevations near or even below sea level. See end of display for full legend of the 3D geological model.

• We approximated reasonable values of erodibility K from modern landscapes using normalised

channel steepness and geological maps.

• Calibration of K values might be further refined by using additional approaches to assess

goodness of fit.

• We simulated 350 m of main channel incision over 3.5 My and demonstrate that drainage

divides are affected by explicitly accounting for 3D lithology, as opposed to uniform lithology.

• This further indicates the need to include 3D geological models when modelling future

topography.

• Additionally, alternative drainage pathways can be relevant to predictions of future topography.

Discussion points/Conclusions

Gmünder, C., Jordan, P., and J. K. Becker (2013). Documentation of the Nagra regional 3D Geological Model 2012. Nagra Arbeitsber. NAB

13–28

Isler, A., Pasquier, F., and Huber, M. (1984). Geologische Karte der zentralen Nordschweiz 1:100’000 - mit angrenzenden Gebieten von

Baden-Württemberg. Geologische Spezialkarte Nr. 121.

Ludwig, A. (2018). Local topography and hillslope processes in the Jura Ost siting region (and surrounding area). Nagra Arbeitsber. NAB 17–

42.

Mudd, S. M., Attal, M., Milodowski, D., Grieve, S. W. D., and Valters, D. A. (2014). A statistical framework to quantify spatial variation in

channel gradients using the integral method of channel profile analysis. Journal of Geophysical Research: Earth Surface, 119(2):138–152. doi:

10.1002/2013JF002981.

Mudd, S. M (2017) Detection of transience in eroding landscapes. Earth Surface Processes and Landforms, 42(1):24-41.

doi:10.1002/esp.3923.

Yanites, B. J., Becker, J. K., Madritsch, H., Schnellmann, M., and Ehlers, T.A. (2017). Lithologic effects on landscape response to base level

changes: A modeling study in the context of the Eastern Jura Mountains, Switzerland. Journal of Geophysical Research: Earth Surface,

122(11):2196–2222. doi: 10.1002/2016JF004101.

Model documentation and code

Documentation: https://lsdtopotools.github.io/LSDTT_documentation/LSDTT_MuddPILE.html

Code: https://github.com/LSDtopotools/MuddPILE

References

Map legend, modified after Isler et al. (1984) – all units

Unit ID corresponds to violin plot (for bedrock units). Q = Quaternary unit; B = bedrock unit.

Map legend, mod. after Isler et al. (1984) – Quat. separation

Unit ID corresponds to violin plot. QD = Quaternary domain; B = bedrock unit; EC = erodibility class, corresponding to grouping of units for the Monte Carlo simulations. See map on slide 6 for spatial separation of QD1 and QD2.

Legend 3D Geol. Model (mod. from Gmünder et al. 2013)

Assignment of K and hillslope gradients Sc to the

lithologic units of the 3D Geological Model

Erodibility classes (EC) were

assigned based on lithologic

considerations, using K values

according to the best fit Monte

Carlo simulation (see above).

Sc values were derived from

Ludwig (2018), corresponding to

characteristic hillslope gradients of

the present-day landscape.