ESCI 4701/8701: Geomorphology
Lab Exercise
A. Wickert, Fall 2020; modified Fall 2022 and (slightly) Fall 2023

Hillslope Geomorphology and QGIS (95 points total)

This lab is in two parts. You may do these in a group with others, though you must each turn in your own assignment.

Your hand-in will be a single PDF document. There are many tools that you may use to stich PDFs together (web searches are your friend).

[Learning] Goals

• Become familiar with QGIS, a free and open source GIS
  • Install a QGIS plug-in to incorporate commercially-available (but viewable for free) imagery in a geospatial framework
  • Import a *.bil – an old but common binary data format for a geospatially-registered raster data file – into QGIS
  • Create and edit a GeoPackage layer
• Identify hillslope and fluvial geomorphic process domains based on topography
• Think through where you may find different soils
• Present your arguments and reasoning in writing
  • Well-reasoned arguments lead to a good grade, even if you are wrong!
  • Grammar, spelling, punctuation, and style may all be graded. Professional writing skills are essential and must be practiced. (Fancy is not necessary, but correct is.)
• Analyze a small region of southeastern Minnesota using 1-meter LiDAR topography to understand and apply hillslope processes.
• Use slope to identify zones of landsliding vs. hillslope creep.
• Work to understand landslide susceptibility as a function of slope, pore-fluid pressure, and cohesion.
• Use hilltop curvature to estimate the overall landscape erosion rate and project it into the future.

Part 1: Introduction to QGIS (+ thoughts on soils)

Deliverables: 20 points total

1. (5 points) An exported map showing a DEM imported into QGIS, set up with a semi-transparent elevation color ramp over a shaded-relief map. Include a scale. Use the Print Layout tool to produce this. (See Step 7.)
2. (3 points) This same map, but with overhead imagery (using HCMGIS) replacing the colored elevation data set.
3. (7 points) This same map once more, but this time with the semi-transparent colored DEM replaced by semi-transparent GIS vector layers delineating hillslope vs. channel process domains in a subset of this landscape. Additionally, include an explanation of how you chose different process domains, as described in Step 11, below.
4. (5 points) Identify graphically and in words the locations on the landscape in which you expect to find the shallowest and deepest soils, as well as the youngest and oldest soils. Here, it is your reasoning that counts! Think back to soil-production functions and think about what factors may cause hillslope material to erode quickly or to stay in place for a long time. See Step 12 for more information on this.

Steps

1. Download QGIS

Mac, Windows: https://qgis.org/en/site/forusers/download.html

Ubuntu Linux:

sudo apt install qgis qgis-dev

2. Download and unzip the DEM

DEM ZIP

Note that this ZIP archive has many files in it! Each contains some data or metatadata, such as binary values that combine to give topographic information or geospatial referencing information.

If you like: check out http://arcgis.dnr.state.mn.us/maps/mntopo/ to see where it came from. MnTopo is a great portal for high-resolution topography from across the state of Minnesota.

3. Open QGIS and set the projection

• Start QGIS.
• Start a new project.
• Click on "Project → Properties" to set the Coordinate Reference System (AKA map projection AKA CRS) for the project. For this lab, we will use UTM Zone 15N, as it encompasses this region of southwestern Minnesota.

4. Import the DEM

• Click on “Open Data Source Manager”

• Select “Raster”, and for the source, navigate to the *.bil file that you just extracted. Click “Add”.

• You should now have a grayscale map on your screen that looks like this:

5. Add a little color to the DEM

Double-click on “dem_3m_m” in the “Layers” panel.

The window that appears has all of the layer information. It will default to “information”. This gives the size of the raster layer, its projection information, and so forth. If you are interested, take a look at the map projection.

Click symbology → singleband pseudocolor

Set the color ramp. the following instructions are just a suggestion – you may use whatever you like!

• Under “color ramp”, click “create new color ramp”
• From the next dialog, select “Catalog: cpt-city”
• Select “Topography”
• Choose one that you like. I use “Wiki Schwarzwald” in these notes.
• Click “OK” (maybe twice)

Note: if you are really into the cognitive science behind color maps, as well as colorblind-friendliness, you should take a look at Scientific Colour Maps.

6. Create a hilshade map.

• Right-click on the DEM in the Layers palette, and click “Duplicate Layer”
• Rename the copied layer to “Hillshade” via the right-click menu.
• While you’re at it, rename the original DEM to “DEM”
• Double-click on the hillshade map, and choose its render type as “hillshade” in the “Symbology” of the Layer Properties dialog. Keep the defaults and click “OK”.

Note: this method of generating a hillshade "on the fly" may make it look blocky when zooming in. Raster → Analysis → Hillshade will give you a way to create a brand-new file for the hillshade that sidesteps these issues.

7. Overlay a semi-transparent colored DEM atop the hillshade

With the new “Hillshade” map below the “DEM” in the layers palette (so it disappears beneath it), double-click on the DEM. Using the “transparency” tab, set a transparency that lets you see some detail of the hillshade alongside the transparent DEM.

8. If you have not done so yet, save your project.

For real! Save it!

9. Build a presentable map

Click Project → New Print Layout. Using the “Add a new map to the layout” button, , create a map canvas area. Play around with the tools to position your map on the page as you like.

Then, add a scale bar using the proper tool.

Finally, export a PDF.

10. Overlay aerial imagery and other products

In addition to the mat that you’re making, Google and others have good mapping resources – including imagery. This can be useful when mapping as well.

It is possible to view these in QGIS at the same time as your own maps and data files!

Click Plugins → Manage and Install Plugins Type “HCM” in the search bar. Install HCMGIS

Next, click HCMGIS → BaseMap → Google Satellite to create a satellite-map layer atop yours.

To see how the satellite photo intersects your topography, try the following:

• Uncheck “DEM” to hide it
• Double-click on the Google Maps layer and change its opacity (“Transparency” tab) to a moderately low value, maybe 30–50%. This will show you how the lakes, forests, and farms intersect the hills and low points of the topography.
• With this overlay on, you can click on and off of the “DEM” layer to see how this intersects the lakes, etc. It will not be a pretty picture – color mish-mash instead! But it will be informative to toggle between the two and look at what you notice.

Using the print layout, create a figure containing this semi-transparent imagery overaying the shaded-relief basemap, along with a scale bar.

11. Process Domains

Now that you have had a chance to explore some different ways of using QGIS to visualize data and create maps, it's time to think about geomorphology.

• Zoom into a small area of the map, which encompasses both hillslope and channels. An example of a representative area with some varied terrain for you to think about lies below; note that I created a true shaded-relief map using the "raster" menu in order to build this map.
  
• Create a new GeoPackage (gpkg) layer following the example below; note the field called "domain". This is a vector layer, made up of edges and vertices. Specifically, it is a polygon layer, which means that it encompasses an area. The other maps, on the other hand, are raster data sets.
  
• Classify the land surface into regions that you think may be dominated my channel (also called fluvial) or hillslope processes. Use your text-label field to indicate which one is which. To perform your classification, it may be helpful to build other maps, such as those showing slope or flow accumulation. Feel free to play around with QGIS and its features! The main idea here though is that you have a first idea of what these different zones are.
  • It might not be quite so easy to separate channel from hillslope! That's okay. Aim to produce good -- not perfect -- polygons, and to learn about the processes shaping the landscape.
  • There is a reason that finding a perfect cutoff is not easy: there is a region between the obvious channel adn the obvious hillslope in which you may see evidence of both channel and hillslope processes occuring. This is typical of many geomorphic process domains: there are "simple" zones within one domain, and more complex zones that combine aspects of multiple process domains. Seeing this is good experience.
• Next, prepare a map of your polygons as a semi-transparent layer over the hillshade. You will want to use the "categorized" option under "symbology" to make them show up as distinct colors. You may add additional maps to your report as well if you think that they are supportive of your work.
• Finally, write a justification for how you chose your different process domains. Describe the criteria and data that you used and how you addressed ambiguities. Because of the methods used, this may well be qualitative, and that is okay. Quantification in geomorphology comes after building a basic intuition for the landscape. There is no set number of words or paragraphs, but it must be necessary to present and defend your choices, and link them to the features that you are observing in the landscape.

12. Soils

Geomorphology encompasses the relationship between erosion (or deposition) and soil production. Pick three points in the subset of the map where you analyzed process domains, and describe whether you think the soils will be thick or thin, and how that relates to the processes occurring (and their rates). As this is an exploratory assignment, your answers need not be right to be graded highly, but if they are wrong without an explanation, your grade will be poor! Make sure to provide reasoning behind all of your point placements.

Be sure to submit a copy of your map with labeled points in your write-up. You learned how to create GeoPackages above, and this could be a great way to work with this as well. In Layer Properties, QGIS allows you to set labels on your points, which could also be helpful.

Part 2: Hillslope Processes

1. Distribution of slope in a landscape governed by fluvial and hillslope processes (10 points)

(a) 5 points: Produce a slope histogram for a portion of this southeastern Minnesota landscape

First, be sure that your project coordinate system is in UTM 15N with the NAD 83 datum. The EPSG code of the projection is 26915.

Then, look to the "processing toolbox" to the right. If you cannot see it, go to view → panels → processing toolbox.

You'll want to become acquainted with this -- it holds many useful tools for computing and comparing geographic and geomorphic features. This toolbox gives access to many built-in features wihtin QGIS, as well as powerful functions from GDAL (https://gdal.org/), which underlies all modern GIS software, and from the feature-rich open-source GRASS GIS (https://grass.osgeo.org/).

In the search bar, type "clip", and select GDAL's "clip raster by extent".

Then, using this tool, follow the coordinate set that I have used here:

Bounding box: 558200,560400,4918200,4920200

Choose to save your output to a reasonable place on your computer (not to a temporary file unless you feel like losing your work) and hit "Run".

After this, use the built-in QGIS tool to compute the slope angle (in degrees):

Once you have completed this, use the "histogram tool" (also accessed via the processing toolbox) to compute a histogram and save it to an HTML file somewhere. (I'm not sure why QGIS saves this as a HTML, but it's good enough for what we need it to do: visualize some data.) The x axis is the slope angle, and the y axis is the number of cells that fall within that angle.

• Use 100 bins
• y axis: n cells
• x axis: bin (i.e., slope angle)

Computing the histogram might take some time, and it will get stuck on 99%. Don't worry! Maybe do before making a snack / using the bathroom. Going on a jog works too, but it's more a few minutes than a few tens, at least on my old-ish computer.

(b): 5 points: Why does this histogram look the way it does?

Why does the distribution of slopes on the DEM look the way it does? Think about different processes that could be intfluencing the topography. (Note: significant erosion has occurred in this region since the Mississippi River incised between ~2.5 and 0.8 million years ago: Over this time, the landscape has eroded on average.)

Take a screenshot of the histogram and annotate it, and write a paragraph supporting your conjectures. For example: Is the histogram continuous or not, and why? How does the set of slopes compare wtih the angle of repose, and is this as expected or is it surprising? Do you think that the slope map is more representative of channels or hillslopes? Can you see zones where gradual creep vs. sudden mass-wasting processes may be dominant? Support your ideas based on what we have learned about the mechanics of these landscapes.

2. Obtaining erosion rate and extent from hillslope diffusion and hilltop curvature (40 points)

In the geosciences, we often obtain rates from sets of dates -- typically, radiometric dates. However, the topography also tells a story, and by interpreting it, you can also start to infer how quickly geological processes operate -- and project into the future.

We're going to start with the hillslope-diffusion equation in one dimension:

$$\frac{\partial z}{\partial t} = k_h \frac{\partial^2 z}{\partial x^2}$$

(a) 5 points: Dimensional analysis of hillslope diffusivity

$k_h$ is the hillslope-diffusion coefficient, or "hillslope diffusivity". Its numerical value is often around 0.05 for poorly-consolidated materials (e.g., glacial till, soils fine-grained sedimentary or metasedimentary rock). What are its SI units? Demonstrate this using dimensional analysis of the differential equation terms to the left and right of the "equals" sign.

Hint: the terms in the differential equation are really just giving you differences over an infinitesimally small distance. Remember that these have units! It might be helpful for your thinking to change the $\partial$s to $\Delta$s, or to entirely remove the derivative symbols (and to replace the letters with units).

(b) 15 points: Diffusion length

i: 5 points

Showing your work, use a similar approach to the dimensional analysis to show how you could intuit a how the characteristic horizontal $(x)$ length scale of hillslope diffusion relates to the a time scale, $t$. You can think of this length scale as the distance away from the channel that the hillslope has responded to river incision (or, if you prefer to personify a landscape, the distance over which the hills can "feel" the effects of the river). The time scale is the time since some sudden event, such as a rapid pulse of river incision. In the upper Mississippi valley, this pulse occurred sometime between 0.8 and 2.5 million years ago.

ii: 5 points

After writing this scaling argument, sketch half of a valley cross section, from the center line of the channel (your lowest point) and going perpndicularly out of the valley and towards the hills. Do so for three time steps, $t_0$, $t_1$, and $t_2$. Hint: at your first time step, $t_0$, you can draw the landscape as a sideways "L", with a river that has cut a vertical slot canyon and the hill still being just a cliff. There is no need to have real values on the axes; the point is that you can intuit how hillslopes might respond to a sudden river incision over time.

iii: 5 points

The actual solution for this scaling (part i) is:

$$L = 2 \sqrt{k_m t},$$

where $L$ is a characteristic length scale. Yes, I just gave you (sort of) the answer to this first part! And so this is why you have to show your work: I need to know that you know how you get to this length-scale--time-scale proportionality. (n.b. I write "proportionality" here because you would need to actually solve the PDE to obtain the coefficient of 2. The dimensional analysis approach that I ask you to apply above should give you the proper functional relationship between the variables but without information on coefficients. Still, it is nice to see that you can take apart an equation quickly and gain information on how its solutions might scale.)

Considering that the bluffs of the upper Mississippi valley are made of dolostone, which is considerably less erodible than glacial till (though it can weather), I assume that:

$$k_m = 0.01$$.

This value may be a bit high, but it sure makes the math easier!

The question for you: If it has been 2 million years since the Mississippi first incised, setting off hillslope diffusion, then how far from a channel might hillslope diffusion have reached in this time? How does this compare to the distances in the DEM subset that you used for Question 2? Based on this, would you expect that most regions between these valleys might be experiencing hillslope diffusion everywhere, or do you think that there could be some high plateaus that have not yet "felt" the river incision?

(c) 20 points: Solving for mean landscape erosion rate using hilltop curvature.

Let's return to the hillslope diffusion equation:

$$\frac{\partial z}{\partial t} = k_h \frac{\partial^2 z}{\partial x^2}$$

We'll make the simplifying assumption that the entire landscape -- at least within the valleys and hills close to the Mississippi -- is eroding at the same rate. Let's call this rate $\dot{\varepsilon}$, with $\varepsilon$ standing for "erosion" and the dot indicating that it is a rate. Because this is steady in time and uniform in space, it is a constant.

$$\dot{\varepsilon} = k_h \frac{\mathrm{d}^2 z}{\mathrm{d} x^2}$$

By using this and analyzing the topography, you will be able to estimate the whole-landscape erosion rate.

i: 5 points

Mapping hilltop curvature

First, install the Profile Tool plugin from via the drop-down menu: Plugins → Manage and Install Plugins...:

Next, use the layer manager to import the line that I drew crossing a hillslope between two incising valleys.

Select this single line in the "layers" panel and open the Profiler Tool. Choose "selected layer" in the profiler tool for the source of the line, and add your DEM as the source for the elevation data.

Take a screenshot of your computer at this stage to demonstrate that you have successfully extracted your own data. This will be the basis for the 5 points -- basically, I want to give you some credit for griding through the mechanics of QGIS.

Then, go to the "Table" tab and copy the data table to the clipboard. This will contain $x$ (distance along the profile) and $z$ (elevation) data.

Paste this data set in your desired spreadsheet program. You are ready to begin the next step.

ii: 10 points

Solve for erosion rate

• First, create a plot of your data as a set of x,z points (or as a continuous line: your choice).
• Second, create a curve fit to this as a second-order polynomial.
• Third, note that the parabolic fit, strictly speaking, is only valid near the top of the hill. Consider trimming some of the river valleys and surrounding regions. I expect you to obtain a good fit regardless, and for the result to be relatively insensitive to this.

Your mission now Once you have this fit, use it with the above ordinary differential equation to find the average erosion rate. For this, assume (as before), that $k_m = 0.01$ in units of meters and years. When considering the sign of your solution, recall that erosion is defined such that down is positive. (Right? Becuase otherwise it wouldn't be... eroding.)

Also: Project how much additional erosion (distance) might occur in the next 1 million years if the overall shape of the hillslopes remains similar.

Turn in:

• An image of your spreadsheet-generated plot with data, curve fit, and the curve-fit parameters (coefficients and goodness of fit)
• Your computed average erosion rate, including your math/work to get there
• The estimated additional erosion after 1 million years of further hillslope evolution

iii: 5 points

You have solved for a natural backgorund erosion rate. Stan Trimble, geomorphologist from UCLA, studied erosion following Euro-American settlement in Coon Creek, a river basin on the Wisconsin side of the Mississippi valley. From his paper (linked here for those with UMN libraries access), he estimates an average depth of erosion of 13.2 cm over the course of time from 1853 to 1975, which encompasses the major phase of Euro-American settlement, land clearing, and unsustainable plowing practices.

Compare the natural erosion rate to the 19th--20th century rate, and (in a few sentences) and describe why you expect this discrepancy exists. Dave Montgomery's Nobel Conference lecture at Gustavus may provide some inspiration towards your reasoning.

4. Identifying zones of likely mass-wasting processes in the landscape (25 points)

(a) 5 points: Comparing slopes to the angle of repose

Using the slope map that you built in Question 2, compute a binary raster based on slopes that are above the angle of repose (computed in Step 1). According to Byerlee's Law, most geological materials have frictional properties that are similar to sand $(\mu = 0.6)$. The best way to do this is by using the "Raster Calculator", built in to QGIS. Produce a map with a descriptive legend as your output. Brownie points (but no real points) if you decide to create a nice-looking map with overlays or do something creative with the QGIS map composer.

(b) 5 points: Topographic observations

What do you notice that is different between the sections of the landscape that are above vs. below the anlge of repose? Describe this in ~2 sentences.

(c) 10 points: Cohesion

Regions of the landscape whose slopes are near or above the angle of repose can fail suddenly. Consider a 45-degree hillslope. What is the minimum cohesion $(\sigma_c)$ that would be required to maintain this slope as barely stable (i.e., at incipient failure)?

Recall the general equation for slope stability (see the hillslopes notes for more complete descriptions):

$\tau = \mu \sigma_\mathrm{eff} \cos \theta + \sigma_c$

along with the supporting equations for shear stress $(\tau)$, which is the same as the driving stress $(\sigma_d$, the stress pushing the system towards failure):

$$\sigma_d \equiv \tau = \left((1 - \lambda_p) \rho_r + \lambda_p f_w \rho_w\right) g h \sin \theta$$

and the effective normal stress, $\sigma_\mathrm{eff}$, which is part of the resisting stress term:

$$\sigma_\mathrm{eff} = \sigma - P_f = (1 - \lambda_p) \rho_r g h$$

Use the following parameters

• Slope angle $\theta$ = 45 degrees
• Rock density $\rho_r$ = 2840 kg/m³ (dolomite)
• Water density $\rho_w$ = 1000 kg/m³
• Porosity $\lambda_p$ = 0.2
• Fractional pore content $f_w$ = 0
• The coefficient of internal friction $\mu$ = 0.6
• The thickness of the landslide block, $h$ = 1 meter (roughly known due to the joint spacing in the bedrock)

Don't forget to include units! For a better learning experience (but no extra credit), think about how much equivalent thickness of weight of water this cohesion represents, and think about that weight pushing in a way that holds the hillslope together.

(d) 5 points: Impact of rainfall on landslide hazard

What would happen to your perfectly balanced hillslope from part (c) if the water content in the rock, $f_w$, increased? Show your work about which direction it would tip the stress balance. Would it make the hillslope more or less stable?

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