GEOSC 340 Spring 2015
DiBiase
Lab 2: Cinder cone evolution
Objectives
In this lab, you will use ArcGIS to analyze the morphology of some cinder cones in the San Francisco
Volcanic Field just north of Flagstaff, Arizona (Fig. 1). You will then compare your results to predictions
from a simple numerical model of hillslope “diffusion”.
R. DiBiase
Figure 1. SP Crater, San Francisco Volcanic Field, Arizona
Background
Cinder cones are ideal landforms for testing models of hillslope evolution because 1) Their initial
geometry is well-constrained, and 2) Cinder Cones can be dated using a variety of techniques. Often
times, only a few individual flows within a cinder cone field will be radiometrically dated due to the
effort and expense limitations. Establishing a chronology for an entire cinder cone field relies on
morphometric analysis, and helps us learn about the timing and nature of volcanism and assess potential
volcanic hazards.
2.0 File geodatabase and supplied datasets
You have been supplied with the File Geodatabase “lab_02_data.gdb”, which contains the raster
“sfvf_dem”, a digital elevation model of the San Francisco Volcanic Field in northern Arizona.
Remember to navigate to the Geodatabase “lab_02_data.gdb”, right click, and select Make
Default Geodatabase. Now load the raster “sfvf_dem” into your map, and save your map to a
new .mxd file.
2.1 Projecting raster data
More often than not, datasets you acquire will need to be projected into a coordinate system that
has x-y units of meters, rather than elliptical coordinates of latitude and longitude. You have been
given a digital elevation model (DEM) of a portion of the San Francisco Volcanic Field, just
north of Flagstaff, Arizona. This data was downloaded from the USGS National Map website,
and needs to be projected into a Cartesian coordinate system before we can do any calculations.
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To do this, go to ArcToolbox, and navigate to \\Data Management Tools\Projections and
Transformations\Raster\Project Raster. This will bring up a window with lots of important
parameters to adjust (Fig. 2).
Figure 2. Project Raster dialog. Make sure to select CUBIC resampling technique!
For the Output Raster Dataset, navigate to the geodatabase folder “lab_02.gdb”, and name it
something like “sfvf10_dem”, as this will be a 10 m resolution DEM. For the Output
Coordinate System, navigate to \\Projected Coordinate Systems\UTM\NAD 83\NAD 1983
UTM Zone 12N. This is the local UTM grid for Arizona. Next, and this is CRITICAL, change
the Resampling Technique to “CUBIC”. If you leave it as is, your output DEM will have
annoying artifacts after the transformation. Finally, let’s round the output cell size to 10.0 for both
X and Y, and click OK.
Now, to clean things up, we need to remove the original, unprojected raster “sfvf_dem” and
change the coordinate system for the Data Frame. Double click on Layers in the Table of
Contents window, and navigate to the Coordinate System tab (Fig. 3).
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GEOSC 340 Spring 2015
DiBiase
Figure 3. Data Frame Properties dialog showing selection of Coordinate System.
Here, you can either navigate through the menu system, or simply scroll down to the “Layers”
folder, which will show you the current projections in use. Make sure to choose
“NAD_1983_UTM_Zone_12N” and click “OK”. The map should now look a little stretched in
the active window, as we are now viewing the projected image.
2.2 Making a “slopeshade” map.
Follow the directions from last week to generate both a hillshade and a slope map of the layer
“sfvf10_dem”. Remember to save these to your geodatabase and use the nomenclature
“sfvf10_hillshade” and “sfvf10_slope” to help keep things organized.
Last week, we saw how a hillshade map can aid in “popping” out the topography with a simulated
illumination. Because you must choose a direction from which to illuminate, the hillshade map
will always have a directional bias to which features are accentuated. To help overcome this bias,
we can use the slope map to provide a more unbiased view of the topography.
First, let’s change the symbology of the slope map such that it is a linear “min-max” stretch with
black corresponding to high slopes and white to low slopes (Fig.4).
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GEOSC 340 Spring 2015
DiBiase
Figure 4. Layer properties dialog showing symbology for slopeshade map.
I set the cutoff values to 0 and 50 degrees, but you can adjust these to your liking. Next, let’s set
the transparency to 30%, and overlay the slope on the hillshade. Again, you can adjust the
transparency to your liking. The resulting map is called a “slopeshade” map, because the steep
areas are shaded. Notice the similarities and differences to the hillshade. As before, you can
always color code the elevation on top if you like – if I do this, I usually set the elevation
transparency to 70% to really accentuate the relief.
2.3 Adding x-y data
For this lab, we are going to be comparing the morphology of cinder cones to their independently
determined ages. To see which cinder cones have been dated, we need to add the excel table
“cinder_cone_locations.xlsx” to our map. First, open it up in excel and take a quick peek at the
information. The “Easting” and “Northing” columns contain the X-Y data needed to plot the
locations on our map.
Go to File/Add Data/Add XY Data… to open the Add XY Data dialog box. Click the folder,
and navigate to the file “cinder_cone_locaions.xlsx”. Select “sheet 1” and click Add. Now, make
sure the columns for X Field and Y Field correspond to “Easting” and “Northing” respectively,
set the coordinate system to NAD_1983_UTM_Zone_12N, and click OK (Fig. 5).
There is now a layer called “Sheet1$Events” loaded in the map. To save this data as a point
feature class, we need to right click on it and select Data\Export Data (Fig. 6). Change the file
type to “File and Personal Geodatabase feature classes”, and give it a name like
“cinder_cone_locations”. Once it is added to the map, you can remove the “Sheet1$Events” layer.
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GEOSC 340 Spring 2015
DiBiase
Figure 5. Add XY Data dialog
Figure 6. Export data dialog.
2.4 Extracting profiles of cinder cones
Much of the lab this week will involve analyzing topographic profiles extracted across cinder
cones of various ages. Take some time to explore the map, take some profiles, and observe the
variations in morphology. If you need a reminder on how to extract profiles, there are detailed
instructions in Lab 1.
Because many of the cones have been modified either during eruption or afterwards, it is best to
take profiles starting from the center and radiating out, focusing on the most pristine sector of the
cone (Fig 7).
Figure 7. Radial cross section of cinder cone showing planar side slope in red, and transition to depositional
apron at yellow dot. The total relief is 160 m. The height of the debris apron is ~40 m.
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GEOSC 340 Spring 2015
DiBiase
We can see that in general the crater rims are convex up, the side slopes are planar, and the toe
slopes are concave up. If you look at the youngest cinder cones you can get a sense for what they
look like when they first erupt.
If you look at the cinder cones in Google Earth (see .kmz file in lab folder), or add the Imagery
basemap to ArcMap, you can get a sense of how the shape and surface expression of these cinder
cones changes over time. Note the presence or lack of vegetation, accumulation of windblown
dust, and presence of small rill networks (fine-scale runoff features).
For your assignment, you will make analyze radial cross sections of the 5 dated cinder cones. In
order to annotate the cross sections, it will be easiest to load them into Layout View. First, label
each cross section with the cinder cone name, and perhaps the direction that the profile radiates
away from the center of the crater (i.e., N, NE, SSW…). Make sure the axes are labeled, and
stretch them so they are all at roughly the same scale and vertical exaggeration – I will show you
how to do this in lab. When you like how they look, right click each profile, select Copy as
Graphic, and paste into Layout View, where you can arrange them on the same page as your
overview map (you may need to resize them again to get the scales right).
Now, in layout view, annotate your cross sections using the Drawing Toolbar to add lines where
the slopes are planar, and a dot that indicates the transition from the original cinder cone to the
concave-up debris apron (see Fig. 7). Also annotate the age and total relief of each cinder cone
and the mean slope of the planar segment of the hillslope in degrees. Remember, the slope angle
= tan-1(Δy/Δx) in degrees. It may be also be useful to make a legend for any annotations on your
cross section (note that you will need to make this legend from scratch using drawing elements).
2.5 Plotting up morphology-age relationships
Now that we have made some measurements, let’s see how our observations compare to a simple
numerical model for cinder cone evolution. First, create a new Microsoft Excel workbook, and
make a table containing the following data columns for each of the 5 dated cinder cones:
Name; Age (ka); Mid-slope angle (degrees); Total relief (m); Height of apron (m); Hilltop curvature
The name and age for each cinder cone is given in the excel spreadsheet
“cinder_cone_locations.xlsx” and the point feature class on your map. The mid-slope angle, total
relief, and apron height are all what you measured for each cross section as described above. For
hilltop curvature, just give me a qualitative assessment of how sharp or broad the crater rim is
(i.e., very sharp, somewhat rounded, subdued).
Next, create 2 scatter plots; one of Mid-slope angle on the y-axis vs. Age on the x-axis, and one
of Total Relief on the y-axis vs. Age on the x-axis. Plot the data as points, and we will add on
curves that show predictions from a simple diffusion model.
2.6 Diffusion modeling of cinder cone evolution
Included in your lab folder is an excel spreadsheet called “cinder_cone_diffusion_model.xlsx”.
This is a simple 1-dimensional numerical model that simulates hillslope processes acting to
transport the unconsolidated cinders and scoria that make up the landform. Because this model
uses a transport law where hillslope sediment flux is linearly proportional to slope, it is often
referred to as a “diffusion” model, and the solutions are identical to problems relating to heat flow
and chemical dispersion, among others.
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GEOSC 340 Spring 2015
DiBiase
There are three spreadsheets – one that forms the interface for us to enter parameters and see
results plotted, and two that contain the numerical “guts” of the model as a large matrix of
operations. If you are interested in the numerical methods, this is a “forward time, central space”
finite difference model of the diffusion equation.
For this lab, the only parameter you will be changing is the age of the cone (highlighted in
yellow). There are two solutions shown as radial cross sections: one for a cone with an initial
height of 300 m (Fig. 8), and one that is the same shape, but 150 m high (Fig. 9). The black lines
show the initial condition, and the red and blue lines show the final profiles.
Figure 8. Model output for t = 70 ka, initial cone height of 300 m, and diffusivity of 0.02 m2/yr.
Figure 9. Model output for t = 70 ka, initial cone height of 150 m, and diffusivity of 0.02 m2/yr. Note the axes!
Change the age of the cone and observe how the morphology changes as a function of both time
and the initial size of the cone (remember, cinder cones are not all the same size when erupted!).
Also shown are the mid-slope angle and the total relief for the final (colored) profiles. Now,
systematically vary the age of the cone from 0-1000 ka (in increments of 100 ka), and record the
mid slope angle and total relief for both the tall and short cone in the spreadsheet that contains
your cinder cone morphology data. Add these to the appropriate plots as lines to see how they
compare to what you measured from the DEM.
Finally, once your data table and plots are finished, you can simply copy and paste them as
objects into the layout view of ArcMap. You should have plenty of room to arrange your map,
cross sections, table, and plots if you are careful, but if you need to, you can change the page size
in File\Page and Print Setup.
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GEOSC 340 Spring 2015
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Lab 2 deliverables, due Friday January 30 before lecture (40 pts total)
Please submit as single PDF file to the Lab 2 drop box on Angel
Map, cross sections, plots, and data table should all fit on one page
(5 pts) One overview slopeshade map, including appropriate legend, scale bar, and north arrow
• Slopeshade should be white-black, and may be overlain on hillshade.
• Be sure to indicates the units of slope on your legend!
• There is no need to include topography, but if you would like to, you may overlay a nonobstructive contour map on the slopeshade.
(10 pts) Five annotated topographic cross sections of the dated cinder cones
• All cross sections must contain cinder cone name, age, and axes labels. You may either indicate
the radial direction of the cross section, or show the cross section location on the map.
• All cross sections must be at the same horizontal and vertical scale, and include 1) a colored line
object indicating the extent of the planar midslope, and 2) a colored point object indicating the
top of the debris apron (see Fig. 7).
(5 pts) A table summarizing your measurements of cinder cone morphology
• Make sure to include the Name, Age, mid-slope angle (in degrees), total relief (see Fig. 7), height
of apron (Fig.7), and a qualitative measure of hilltop curvature for each of the five cinder cones.
• Remember, the slope angle = tan-1(Δy/Δx) in degrees – it shouldn’t be too tough to measure Δy
and Δx off your cross sections, and you can convert to degrees either in Excel or by googling
“atan(M) in degrees” where M = Δy/Δx.
(5 pts) Two plots comparing cinder cone morphology to model predictions
• One plot of Mid-slope angle vs Age, with the dated cinder cones as points and the 2 model
predictions as lines. Make sure to label your axes and include an appropriate legend.
• One plot of Total Relief vs. Age, with the dated cinder cones as points and the 2 model
predictions as lines. Make sure to label your axes and include an appropriate legend.
(15 pts) A written report no more than 2 pages long, which should include the following
• A brief introduction (no more than 1 paragraph)
• A description of the morphology visual appearance of cinder cones of different ages. (~1-2
paragraphs focused on observations and measurements)
• A discussion comparing how well the diffusion model describes the evolution of cinder cone
morphology – where does it work well? Where does it do poorly? Which is a better indicator of
cinder cone age, slope or total relief? Are there other metrics you might use to describe the
changing morphology? (~2 paragraphs focused on interpretation)
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