Minimum Eroded Volume

Consider a bowl. Its volume can be found by delineating two things: a plane across its rim and its curved inner surface. Finding the volume of a watershed is much the same. A capping surface can be constructed by connecting a set of points located along the divide, while the inner surface is the modern topography represented by the DEM. The volume is simply the difference between the cap elevation and topography. “Minimum Eroded Volume” is called “Minimum Bulk Erosion (Ebulk)” by Bellin et al. (2014), but its hopeless getting through to the Belgians (#Piorot). Continue reading

Terrain Roughness – 13 Ways

Topographic roughness (ruggedness) is defined differently depending on the calculation used. Topographic roughness may be based on standard deviation of slope, standard deviation of elevation, slope convexity, variability of plan convexity (contour curvature), or some other measure of topographic texture. Scale is important in any roughness analysis – both that of the DEM and that of the landscape features you intend to characterize. In many cases, starting with a smoothed DEM produces a more interpretable roughness raster (see Relative Topographic Position). Here are several ways to calculate topographic roughness. Continue reading

ArcGIS to Illustrator

There are good reasons for completing maps in Adobe Illustrator (Ai). Illustrator is intuitive and layer-based. Compared to the clunky Layout workspace in ArcGIS, Ilustrator’s Artboards are great for editing, proofing, and printing. ArcGIS exports directly to the Ai native format, though there are few caveats (text and transparency handling).

See the documents below for help on bringing in vector and raster files from ArcGIS 10.2 into Adobe Illustrator CC. Continue reading

Stream Power Notes

Stream power is the rate the energy of flowing water is expended on the bed and banks of a channel. Said another way, it is the potential for flowing water to perform geomorphic work. Stream power can be calculated on the cheap from DEM data because of the area-discharge relationship, but recognize that the DEM doesn’t provide everything you need. Continue reading

Sampling Grid & Map Ref Grid

Two kinds of grids are described here. A “survey sampling grid”, created with the Fishnet tool, is a shapefile with vector properties. Sampling grids are useful in survey planning. A “map reference grid” is a pre-formatted border that is inserted into a Layout much like a Neatline, but with more flair. Both are customizable. Continue reading

Terrace Extraction I

Terraces are distinctive landforms composed of two morphologic elements: the sloping riser and the relatively flat tread (Leopold et al., 1964). They preserve a history of past fluvial and/or glacial outwash activity. Terrace flats are rarely steeper than ~13% slope. The treads are bounded by the riser on the downhill side (a slope breakline). On the uphill side, the flats often transition to an alluvial fan, the toeslope of another riser, or bedrock outcrops.

This lesson needs to be cleaned up. Continue reading

Least Cost Path (Carnivores)

** Currently under construction **

Least-Cost Path Model for Grizzly & Wolverine in North-central Washington State
Grizzly Team: Tate Mason, Temsha Huttanus, Shane Skaar, Tempe Regan, Michelle Jeffries
Wolverine Team: Allie Anderson, Shawn Smith, Heidi Ware, Bryce Robinson

Methods described here were modified from Singleton et al. (2002), “Landscape permeability for large carnivores in Washington: A geographic information system weighted-distance and least-cost corridor assignment”, U.S. Forest Service Research Paper PNW-RP-549 PDF.

The work here involves three parts, a.) the acquisition and preparation of 5 input rasters, b.) creation of the “travel cost” raster, and c.) calculation of a specific least cost “travel path” from Point A to Point B, as determined by the user. Each of the 5 input rasters are classified and each class assigned a weighting factor (a coefficient between 0.0 and 1.0). The analysis is performed using 90m pixels, so all 5 input rasters must be standardized to this cell size prior to calculation. The travel cost equation is:

Elevation x
Slope x Population Density x Road Density x Habitat Type

1.) Set up ArcMap:
– Open new, blank .mxd document.
– Set Data Frame Coordinate System to a projected system (Ex: UTM_NAD83_Zone11).
– Set Data Frame Display Units appropriately (Ex: Meters).
– Turn on Spatial Analyst extension.
– Turn off Background Processing (Geoprocessing menu > Geoprocessing Options).
– Set working folder or set Environments for Workspace and Scratch Space.
– Determine your study area boundary. Create a polygon shapefile of the study area.

2.) Acquire 30m ASTER DEM from EarthExplorer. Data arrives in GCS_WGS84. Unzip files. Load DEM(s) into ArcMap.

3.) Optional: Mosaic DEMs (Data Management > Raster > Raster Dataset > Mosaic to New Raster tool). See additional info HERE.

4.) Fill sinks and holes in DEM (Spatial Analyst > Hydrology > Fill).

5.) Resample DEM to 90m pixels (Raster > Raster Processing > Resample tool). Singleton et al. (2002) used 90m pixel in their analysis.

6.) Convert DEM to integer format (Spatial Analyst > Math > Trigonometric > Int tool).

7.) Reclassify elevation (meters) using 4 classes and the following value ranges, Break Values, and new values:

0-1000 –> 1
1000-1500 –> 2
1500-2000 –> 3
2000-max –> 4

8.) Create slope raster in percent rise from 30m DEM – the filled, projected one NOT the one resampled to 90m (Spatial Analyst > Surface > Slope).

9.) Reclassify Slope raster based on criteria provided in Singleton et al. (2002)…….

10.) For this project, we’ll used Landfire data ( Download

11.) Group Landfire habitat/vegetation classes (field name?) to reasonably match categories shown in Singleton et al. (2002)…….Do this in Excel…

12.) Find/Replace PERM values with those from Singleton et al. (2002)…

13.) Join Excel table to Landfire raster…

14.) Acquire human population data (census blocks) from Look for the latest TIGER/Line Shapefiles. Download “Block” data for the entire state, then clip to study area boundary (Geoprocessing > Clip tool).

15.) Clip census data to study area boundary (Geoprocessing menu > Clip tool).

16.) Calculate population density by census block polygon:

– Open Attribute table
– Add new field, AREA_KM2, Float format
– Calculate geometry (km2) for the field
– Add another new field, POPDENSE, Float format- Use Field Calculator to divide POP10/AREA_KM2 to get density in persons per km2

17.) Convert population density shapefile to a raster:

– Input = clipped population density shapefile
– Field = POPDENSE
– Output = blk10pop
– Output cell size = 30

18.) Focal Statistics tool to determine population in 0.9 km2 radius neighborhood. The output will contain a value representing the number of people within 900m of each pixel.

– Input = blk10pop
– Output = blk10pop_fs
– Neighborhood = Circle
– Radius = 900
– Units = Map (make sure Display Units are Meters)
– Statistics Type = SUM

19.) Reclassify population layer using 5 classes, Break Values of 10, 25, 50, 100, 10000, and New Values of 1,2,3,4,5 respectively. So the value ranges for the five classes are assigned new values 1 through 5:

0-10 –> 1
10-25 –> 2
25-50 –> 3
50-100 –> 4
100-10000 –> 5

– Input = blk10pop_fs
– Field = VALUE
– Output = blk10reclass

20.) Edit table for blk10reclass. Open attribute table and add a new field named GRIZZ_WT, Float format.

21.) Open Editor toolbar, start editing blk10reclass. Replace values of 1,2,3,4,5 with the weighting values provided in Singleton et al. (2002)…..When done, stop editing and save edits.

22.) Resample population raster to 90m pixels (Raster > Raster Processing > Resample tool).

23.) Road density data is available from…

.) The travel cost raster equation is shown below. Make sure all input rasters are 90m pixels and in Float format. Double check your syntax in raster calculator.

Travel Cost (Permeability) Equation:
Slope x Elevation x Road Density x Population Density x Habitat Type

Syntax in Raster Calculator:

.) Create start and destination points or polygons. Use either existing files or create new ones with Draw tools and Convert Graphics to Features….

.) Cost Distance tool…

.) Cost Backlink tool…

.) Cost Path tool…

.) Convert path to polyline (Conversion tools > Raster to Polyline tool)…


Topographic Wetness Index (TWI)

The Topographic Wetness Index (TWI), also called Compound Topographic Index (CTI), is a steady-state wetness index. In some areas, TWI has been shown in some study areas to predict solum depth (i.e., Gessler et al., 1995). It involves the upslope contributing area (a), a slope raster, and a couple of geometric functions. The value of a for each cell in the output raster (the CTI raster) is the value in a flow accumulation raster for the corresponding DEM. Higher CTI values represent drainage depressions, lower values represent crests and ridges. Continue reading

Channel & Hillslope Relief

Channels incision determines the “local base level” and the nature of valley hillslopes. Local base can also describe the surface created by connecting channel long profiles. Here, we’ll just describe two metrics for a single basin and its corresponding channel and ridgeline long profiles: Continue reading

Channel Sinuosity

For single-thread stream channels, the sinuosity index is calculated for each reach using its two endpoints (Upstream point A, Downstream point B). The ratio of the sinuous length tho the straight-line distance is Channel Sinuosity value for the reach. The sinuous length is measured down the centerline of the channel. Divide the sinuous length by the straight-line distance between the same two points. Continue reading

Landforms I: Hammond

Hammond-type macro landform mapping is accomplished using a DEM and the Spatial Analyst extension. Hammond’s method was created for region-scale landform delineation. The steps below were reworked from Morgan et al. (2005). You should have this paper handy. I have retained Morgan’s workflow, but modified the size and shape of their focal statistics neighborhood operator (changed from a 20×20 pixel radius to a 50×50 pixel rectangle), clarified reclassification routines, and updated language to match that used by ArcGIS Desktop. Input and output filenames are in quotes. We’ll do the Hammond/Dikau landform model here. Look for the MORAP landform model in its own lesson. Instructions revised May 2016. Continue reading

Viewshed from a Tower

A viewshed is the portion of a landscape visible from a particular vantage point. That point may be on the ground or, like this example, above ground level in a tower. Viewsheds are commonly used in environmental planning (scenic views/historic vista preservation), communications tower site prospecting, and wildlife radio collar telemetry. Continue reading

Channel Concavity

Channel concavity (θ) is the longitudinal change in the slope of a reach. Most channel profiles are concave due to detachment-limited erosion of bedrock in headwater areas and the usual downstream relationships: increase in discharge, decrease in bed grainsize, and increase in channel width. Continue reading

LS Factor & RUSLE Equation

Instruction document by my former Boise State University students Jim Pelton, Eli Frazier, Erin Pikcilingis:
LS Factor in RUSLE with ArcGIS 10.docx

Instructions and worked example by my former Boise State University students Richard Martinez & Keisha Tomaszewski:
RUSLE Soil Loss Project_Martinez and Tomaszewski.pptx

“There are still a lot of concepts and assumptions embedded in erosion estimation models that need to be verified” – C. Wu, 2000

The Revised Universal Soil Loss Equation can be used to estimate soil loss from agricultural fields and certain rangeland areas. RUSLE has limited application in steep, complex mountainous terrain. RUSLE generates the value A, the average loss in tons over a “field slope”, a concept somewhat at odds with distributive nature of DEMs. DEM data was not used during development of the model, rather DEM data was substituted in later.

The RUSLE equation accounts for:
– Rainfall
– Soil Erodibility
– Slope Length
– Slope Steepness
– Cover Management Type
– Conservation Practice

The RUSLE equation is:

A = R x K x L x S x C x P


Of all the inputs, the LS factor is perhaps the most confusing.

(Area/22.1)^m * (sin(t)/0.09)^n * (m+1)

Constants “m” and “n” have been empirically derived by others. There is a range for each. The idea is that you select values that best suit your particular landscape you are working (climate, soils, etc.). See instruction doc by Pelton et al. and references therein.

L = (λ / 22.13)m

22.13 meters = 72.6 feet
λ = length of slope in the field (or data layer)

Values for L
0.2 on uniform, < 1% slopes
0.3 for 1-3% slopes
0.4 for 3.5-4.5% slopes
0.5 for >5% slopes

The m Exponent
m = exponent representing the Rill-to-Interrill Ratio

m = β / (1+β)
m = (sinθ / 0.896) / (3(sinθ)0.8 + 0.56)
m = (Gr/Gi) / (1 + Gr/Gi) = Gr/(Gr + Gi)
m = Gr/G

G = Gr + Gi
Gr = sediment load contributed from Rill erosion
Gi = sediment load contributed from Interrill erosion

Values for Exponent m
0.02 – 0.05 for low β slopes
0.04 – 0.71 for moderate β slopes
0.07 – 0.83 for high β slopes


ResearchGate forum conversation LINK
Renard et al. (1997) USDA-ARS Agricultural Handbook 703 PDF
Foster et al. (1977) Transactions of the Amer. Society of Agricultural Engineers, v. 20
Foster (1994) Journal of Soil and Water Conservation v.49
McCool et al. (1989) Transactions of the Amer. Society of Agricultural Engineers, v. 32
McCool (1994) Journal of Soil and Water Conservation v.49
Moore and Wilson (1992) Journal of Soil and Water Conservation v.47
Moore and Wilson (1994) Journal of Soil and Water Conservation v.49
Wischmeier and Smith (1978) USDA-ARS Agricultural Handbook 537
Wu, C-C., 2000, L Factor for short, steep slopes, in Laflen, J.M et al. (editors), Soil Erosion and Dryland Farming, CRC Press, p. 591-600


Additional Notes:
Length of Overland Flow can be calculated in several ways, including the list below.

A. Field measurements.
B. Regional estimation method (Troeh et al. 1991).
C. Unit stream power method (Mitasova 1993, Mitasova et al. 1996, Moore and Wilson, 1992, Moore and Burch 1986).
D. Upslope contributing area proxy method (Desmet and Govers 1995, 1996).
E. Slope length from high points (ridges/peaks) and the flow direction raster (Hickey 2000).
F. Cell-by-cell Non-cumulative Slope Length (NCSL) method: FlowAcc * SR, where FlowAcc = Flow accumulation raster (orientation of maximum downhill slope), SR = Cell size of raster (i.e., 30 x 30m).
G. TIN analysis (Cowen 1993).
H. Average length of overland flow by the equation:

Average Length of Overland Flow = 1 / (2Dd √1 – (Sc / Sg)2 or 1 / 2Dd



RUSLE Equation Notes:
The LS factor in the Revised Universal Soil Loss Equation is:
(Area/22.1)^m * (sin(t)/0.09)^n * (m+1)


m+1 is the mysterious 1.4, where m=0.4. Careful though, m=0.4 isn’t always appropriate.


Additional Online Resources:
Jeffrey Evans, ESRI Forum:
The original USLE assumed little slope curvature and no deposition. To account for flow convergence in complex terrain, modifications were made to the LS factor with an equation that incorporates flow accumulation. Because they are now used interchangeably, when you see reference to slope-length most likely it is in reference to the LS factor, as calculated below.

To calculate the LS factor for the RUSLE equation, first calculate flow accumulation (flowacc) and slope in degrees (slope). Then a bit of map algebra in the raster calculator yields LS.

Power(flowacc * cell resolution / 22.1, 0.4) * Power(Sin(slope * 0.01745) / 0.09, 1.4) * 1.4

Van Remortel et al. articles on SL in GIS:
PDF Computers & Geosciences
PDF ResearchGate/Geography v30
Robert Hickey article (2000):
Camposano thesis (2004):
Thread related to Camposano thesis:
How to Lesson from CSU:
Wiki: USLE:

From Da Ouyang and Jon Bartholic:

A detailed description of these factors is available from the web site. Among these factors, terrain factor – “L” is most difficult to compute. Fortunately, the soil loss equation is much less sensitive to L factor than another terrain factor – S factor which can easily be computed from the digital elevation model (DEM).

L factor and S factor are usually considered together to combine the effect of slope and slope-length, which basically reflects the terrain on a given site. For this project, an approach developed by Moore and Burch (1985) is used to compute LS factor. They developed an equation to compute length-slope factor:

LS = (As / 22.13) ^m * (sin β / 0.0896) ^n (2)

m = 0.4 – 0.6 and n = 1.2 – 1.3.
LS = computed LS factor.
As = specific catchment area, i.e. the upslope contributing area per unit width of contour (or rill), in m‘ / m. It is calculated in Are/Info using the function called “flow accumulation” multiply by the squared cell size and divided by the cell size.
As = calculated flow accumulation * 30 * 30 / 30 (for cell size = 30 m).
β = slope angle in degrees. It is calculated in Arc/Info using the function called “slope” with option “percent rise” which is 100 times Tan β. Then β is calculated using “Atan” function in Arc/Info.
Tan β = slope (in percent rise) / 100
β = Atan (Tan β)
RUSLE 1.06 Tutorial LINK
Ouyang & Bartholic, LINK
Kim & Julien, PDF
NRCS RUSLE for Western States (press release) LINK
Renard et al. (1997) Predicting Soil Erosion by Water, USDA Agricultural Handbook, #703
Cowen (1993) Proceedings 13th ESRI User Conference
Desmet and Govers (1995) Catena 25
Desmet and Govers (1996) Journal of Soil and Water Conservation 51
Hickey, R. (2000) Cartography 29
Mitasova (1993) GRASSclippings 7
Mitasova et al. (1996) International Journal of GIS 10
Moore and Burch (1986) Soil Science Society of America Journal 50
Moore and Wilson (1992) Journal of Soil and Water Conservation 47
Renard et al. (1997) USDA Agricultural Handbook #703
Troeh et al. (1991) Soil and Water Conservation (2nd edition), Chapter 6
Wischmeier and Smith (1978) Predicting rainfall erosion losses-A guide to conservation planning: Agricultural Handbook #537

Long Profiles (partial)

Stream channels typically display a concave profile (upward concave) over their length. Channels tend to develop and maintain this quasi-equilibrium shape over time due to several contributing factors, including subsidence of the adjacent basin, sea level rise, progradation of the delta, downstream fining of transported and stored sediment, abrasion (fining with distance downstream), and tributary effects on sediment concentration with distance downstream (Paola et al., 1992; Sinha & Parker, 1996). Convexities in the profile commonly occur where a channel crosses a fault, resistant band of rock, a collection of in-stream boulders, a paleosurface, or an precipitation boundary. Continue reading

Low Order Stream Gradients

Low-order catchments comprise a large proportion of a mountain watershed. Low order streams in many ranges are shaped by and preserve evidence of recent tectonic, depositional, and climatic perturbations. In some mountains, the low order streams feel the effects of the perturbation sooner than downstream reaches. High elevation watersheds (non-glaciated) tend to be steep, wet, cold, rocky (thinner soils, more impervious), and have flashy flood profiles. Where the low-order portion of a stream network is oriented across a fold or the axis of active uplift, some tributaries may be flowing in the direction of tilt and others against it. In this case, gradients may be compared to tease out tectonic effects (Merritts & Hesterberg, 1994). Continue reading