3d lithological structure in a steady state model drives
TRANSCRIPT
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.