---

NAME

r.landscape.evol - Simulates the cumulative effect of erosion and deposition on a landscape over time.

KEYWORDS

raster, hydrology, erosion modeling, landscape evolution

SYNOPSIS

r.landscape.evol --help

DESCRIPTION

r.landscape.evol takes as input a raster digital elevation model (DEM) of surface topography and an input raster DEM of bedrock elevations, as well as several environmental variables, and computes the net change in elevation due to erosion and deposition Stream Power equation, the Shear Stress equation, or the USPED equation.

NOTES

Transport capacity equations.

Users may select to use the Stream Power equation, the Shear Stress equation, or the USPED equations with variable transp_eq. All three equations estimate transport capacity as [kg/m.s], and thus eventually erosion/deposition rate as [kg/m2.s], which is transformed to [vertical meters/cell] using the variable sdensity (see below for details of these conversions).

It is important to note that in this new version of r.landscape.evol, only one transport equation will be used to model sediment flux across the entire landscape. Chane in process will be simulated through scalar m and n exponents (see below for details).

1) Stream power equation:

Tc=Kt*gw*1/N*h^m*B^n

  where: h = depth of flow = (i*A)/(0.595*t) and: B = slope (rise over run)

a) GIS Implementation:

Tc=K*C*P*gw*(1/N)*((i*A)/(0.595*t))^m*(tan(S)^n) 

b) Variables:

• Tc = Transport Capacity [kg/meters.second]
• K*C*P ~ Kt = mitigating effects of soil type, vegetation cover, and land-use practices. [unitless]
• gw = Hydrostatic pressure of water 9810 [kg/m2.second]
• N = Manning's coefficient (0.3-0.6 for different types of stream channels) [unitless]
• i = rainfall intensity [m/rainfall event]
• A = upslope accumulated area per contour (cell) width [m2/m] = [m]
• 0.595 = constant for time-lagged peak flow (assumes symmetrical unit-hydrograph)
• t = length of rainfall event [seconds]
• S = topographic slope [degrees]
• m = transport coefficient for upslope area [unitless]
• n = transport coefficient for slope [unitless]

c) Converted to Map Algebra:

    ${K}*${C}*${P} * exp(${manningn}, -1) * 9810. *
exp((((${rain}/1000.)*\
    ${flowacc})/(0.595*${stormtimet})), graph(${flowacc}, ${exp_m1a},\
    ${exp_m1b}, ${exp_m2a},${exp_m2b}) ) * exp(tan(${slope}), graph(${slope},\
    ${exp_n1a},${exp_n1b}, ${exp_n2a},${exp_n2b}))

d) NOTES:

• This is likely the best of the three equations for simulating erosion at the scale of small watersheds, including overland flow on hillslopes and channelized flow in gullies and streams.
• It is likely not appropriate for simulating erosion and deposition processes in larger rivers, especially meandering flood plains.
• K*C*P should equal an appropriate value of Kt: 0.001 for a soft substrate, 0.0001 for a normal substrate, 0.00001 for a hard substrate, 0.000001 for a very hard substrate. See note below about methods for scaling these values.
• N should likely scale with channel vegetation so that 0.03 = clean/straight stream channel, 0.035 = major free-flowing river, 0.04 = sluggish stream with pools, 0.06 = very clogged streams. See below for methods to scale these values.

2) Shear stress equation:

Tc=Kt*tau^m

  where: tau = shear stress = gw*h*B and: B = slope (rise over run) and:
  h = depth of flow = (i*A)/(0.595*t)

a) GIS Implmentation:

Tc=K*C*P*(gw*((i*A)/(0.595*t)*(tan(S))))^n 

b) Variables:

• Tc = Transport Capacity [kg/meters.second]
• K*C*P ~ Kt = mitigating effects of soil type, vegetation cover, and land-use practices. [unitless]
• gw = Hydrostatic pressure of water 9810 [kg/m2.second]
• N = Manning's coefficient ~0.3-0.6 for different types of stream channels [unitless]
• i = rainfall intensity [m/rainfall event]
• A = upslope accumulated area per contour (cell) width [m2/m] = [m]
• 0.595 = constant for time-lagged peak flow (assumes symmetrical unit-hydrograph)
• t = length of rainfall event [seconds]
• B = topographic slope [degrees]
• n = transport coefficient (here assumed to be scaled to slope) [unitless]

c) Converted to Map Algebra:

     ${K}*${C}*${P} *
exp(9810.*(((${rain}/1000)*${flowacc})/(0.595*\
     ${stormtimet}))*tan(${slope}), graph(${flowacc}, ${exp_n1a},${exp_n1b},\
      ${exp_n2a},${exp_n2b}))

d) NOTES:

• This implementation of the Shear Stress equation assumes the critical shear stress is 0.
• This means the equation is likely to over predict erosion in situations where shear stress is less than the actual critical shear stress, such as on vegetated hillslopes.
• K*C*P should equal an appropriate value of Kt: 0.001 for a soft substrate, 0.0001 for a normal substrate, 0.00001 for a hard substrate, 0.000001 for a very hard substrate. See note below about methods for scaling these values.
• N should likely scale with channel vegetation so that 0.03 = clean/straight stream channel, 0.035 = major free-flowing river, 0.04 = sluggish stream with pools, 0.06 = very clogged streams. See below for methods to scale these values.

3) USPED equation:

Tc=R*K*C*P*A^m*B^n`

  where: B = slope (rise over run)

a) GIS Implementation:

Tc=R*K*C*P*A^m*tan(S)^n 

b) Variables:

• Tc = Transport Capacity [kg/meters.second]
• R = Rainfall intensity factor [MJ.mm/ha.h.yr]
• K*C*P ~ Kt = mitigating effects of soil type, vegetation cover, and land-use practices. [unitless]
• A = upslope accumulated area per contour (cell) width [m2/m] = [m]
• S = topographic slope [degrees]
• m = transport coefficient for upslope area [unitless]
• n = transport coefficient for slope [unitless]

c) Converted to Map Algebra:

    (${R}*${K}*${C}*${P}*exp((${flowacc}*${res}),graph(${flowacc},
${exp_m1a},\
    ${exp_m1b}, ${exp_m2a},${exp_m2b}))*exp(sin(${slope}), graph(${slope},
    \ ${exp_n1a},${exp_n1b}, ${exp_n2a},${exp_n2b})))

d) NOTES:

• The USPED equation is best suited for modeling erosion and deposition on hillslopes and small gullies.
• It will vastly over predict erosion/deposition in channels and streams.

Scalar m and n exponents to simulate changing process across landscapes.

Exponents m and n are used to influence the behavior of the transport equations by differentially weighting the influence of upslope accumulated area (and thus depth of flow) (m) or the influence of local slope (n). Depending on how these are each weighted, transport estimates can be made for overland flow processes, rilling and gullying, or channelized flow (see references below, but in particular Peckham 2003, Mathier et al 1989, and Kwang and Parker 2017). Following a suggestion in Peckham 2003, this new version of r.landscape.evol simulates change in process across the landscape by scaling m and n to changes in topography and flow accumulation. As this is largely an experimental process, the specifics of this scaling are exposed to the user via the m and n variables. The user can define the scalar relationship of m to surface flow accumulation, and n to local slope. Sensible default values are included to help the user know where to start.

Exponent m relates to the influence of upslope area (and thus flow depth, discharge) on transport capacity in the Stream Power and USPED, but is not used in the Shear Stress equation. Values of m are generally thought to be between 2 and 1, and experimentation suggests that they should scale inversely with increasing depth of flow. Exponent m will scale linearly with the value of flow accumulation between the two cutoff thresholds specified: "thresh1,m1,thresh2,m2". So, for example, if you would like the value of exponent m to scale from 1.2 to 1 between a flow accumulation value of 5 and 50, enter the following into the variable m: "5,1.2,50,1". The exponent m will remain 1.2 for all cells where flow accumulation is below 5, and will remain 1 for all cells with flow accumulation above 50. It will scale linearly between 1.2 and 1 for all cells with values of flow accumulation between 5 and 50.

A literature search indicates that maximum values of m should be less than or equal to 2, and that scaling between 1.2 and 1 is probably a good range to start with.

Exponent n relates to the influence of local topographic slope on transport capacity, and is used in the Stream Power, Shear Stress, and USPED equations. Values of n are generally thought to be between 2 and 1, and experimentation suggests that they should scale inversely with increasing local slope. Exponent n will scale linearly with slope between the two slope cutoff thresholds specified: "thresh1,n1,thresh2,n2". So, for example, if you would like the value of exponent n to scale from 1.3 to 1 between a slope value of 10 and 30, enter the following into the variable n: "10,1.3,30,1". The exponent n will remain 1.3 for all cells where slope is below 5, and will remain 1 for all cells with slope above 30. It will scale linearly between 1.3 and 1 for all cells with values of slope between 5 and 30.

A literature search indicates that maximum values values of n should be less than or equal to 2, and that scaling between 1.3 and 1 is probably a good range to start with.

Scaling other input values.

To ensure proper behavior for landscape evolution simulation over long periods, it is important that most of the important variables be allowed to vary spatially as they would on a real landscape. The three most important sets of variables are a) Soil, vegetation cover, and land use factors k, c, p, which together approximate erodibility factor Kt, b) Manning's N manningn which is used to estimate stream power/shear stress of flowing water in different types of channels and surface conditions, and c) flowcontrib, the rainfall excess rate (percentage of direct precipitation that will flow off of a cell), which is used to estimate the flow depth (see below).

Because upslope accumulated area A is a major influencing factor in each of the three equations, transport capacity (and thus erosion/deposition rate) will be inordinately governed by A as values of flow accumulation approach very large numbers (e.g., >> 10,000). This will be partially mitigated with scalar m and n (see above), but will need additional dampening by scaling Kt, N, and rainfall excess.

Kt is composed of the K, C, and P factors. If empirical patterns of K, C, and P are known (e.g., digitized or classified from remotely senses data products), these should be entered as maps in input variables k, c, and p.

If empirically determined maps of these variables are not available, it is possible to use constants in their place, but it will be much better to create maps using some theoretical concepts. The simplest way is to scale C to a wetness index using the principle that the more water accumulation, the denser the vegetation. From a DEM, it is possible to calculate the TCI topographic wetness index using r.watershed with output parameter tci. Here is an example set of r.recode rules to create a C map from TCI to enter in input variable c:

0:3:0.1:0.01 3:7:0.01:0.005 7:10:0.005:0.004 10:*:0.004

Here, low values of TCI will be coded as shrubs or open woodlands. Moderate values of TCI will become wooded, and high values of TCI will coded as dense riparian vegetation. It's important to note that this should be done with a TCI map created with r.watershed on the same DEM that will be used as the initial DEM for the simulation.

From here, it is possible to map rainfall excess to values of C. The following recode rules will achieve a reasonable mapping:

0.1:0.05:85:80 0.05:0.01:80:60 0.01:0.005:60:45 0.005:0.001:45:35

Here, as vegetation becomes more protective of detachment, it is also scaled to become more conducive to water infiltration, and thus more prohibitive to excess water escaping from the cell. The resulting map should be entered into input variable flowcontrib.

Finally, Manning's N can be scaled to flow accumulation (i.e., computed with r.watershed) using the following recode rules to create an input map for variable manningn:

0:10:0.03:0.04 10:100:0.04:0.05 100:10000:0.05:0.06 10000:*:0.06

Here, the assumption is that as flow accumulation increases, the channel will become more complex. These particular rules assume that the scale of analysis is at the level of small watershed feeding into a small trunk stream, not a large free-flowing river. If some empirical data about channel conditions are known, then the values used in the recode statement should be adjusted to reflect this. Again, it's important to note that this should be done with a flow accumulation map created with r.watershed on the same DEM that will be used as the initial DEM for the simulation. Further, the -a flag in r.watershed should be checked so that the output flow accumulation will contain only positive numbers

Creating a hydrologically-appropriate base DEM.

It is vitally important the the input starting DEM be hydrologically valid and at an appropriate raster resolution. Resolution should be scaled to the size of the region being modeled, with the caveat that the assumptions of the way the transport equations are implemented will start to break down at larger cell resolutions. As a general rule of thumb, cell resolution should be <= 10m. This can be achieved through resampling/interpolation from coarser data sets (e.g., a 30m SRTM DEM). If interpolation is used, it is best to use an interpolation procedure that will result in relatively smooth interpolated DEM with minimal depressions. Generally, v.surf.bspline achieves good results when the spline step is double to triple the cell resolution of the coarser input map, and the smoothing parameter is set to provide some additional smoothing (e.g., ~0.1). This results in an interpolated DEM with a smooth surface and minimal localized depressions caused by over-fitting to localized surface trends. Although v.surf.rst can also be used, it often produces rectilinear artifacts from it's segmentation procedure that can adversely affect simulation of water flow on the interpolated DEM.

The DEM should be clipped to a contiguous watershed boundary (e.g., extracted with r.watershed or r.water.outlet). Rectilinear input maps will produce erroneous results outside of internally contiguous watersheds leading to faulty statistics, so it is more useful to clip to the watershed of interest (e.g., using r.mapcalc).

Finally, in order to assure that water will flow naturally across the DEM, it is important to ensure that the DEM is depressionless. This could be achieved with r.fill.dir to fill any interior basins to an elevation level with their spill point, but doing so creates many flat areas where otherwise channelized flow will diverge (and thus deposit). This can be partially addressed by adjusting convergence to a low value, which forces the flow accumulation routine in r.watershed to send a higher proportion of the flow to the most downstream cell.

However, a much better, if more complicated approach is to create a depressionless DEM by carving the main streams through any blockages. The module r.carve can do this relatively simply, but you are only able to use a uniform stream width and depth. Ideally, the width and depth of the carved channels should decrease in width and depth from the basin outlet to the stream sources. To do this requires several steps. First extract an appropriately-scaled stream network using r.watershed and/or r.stream.extract and an appropriate interior basin threshold parameter to isolate main trunk streams with some smaller tributary branches. Use this output raster streams map as the input to the addon module r.stream.order with the output option for the Shreve stream order. This will create a raster streams map where trunk streams are coded with a large number, and tributaries with smaller numbers. Use r.univar to determine the maximum Shreve value, and then use r.mapcalc to standardize the values between 0 and 1 by dividing the Shreve-scaled streams map by the maximum Shreve order value (ensure that you use a decimal point behind the maximum value number so that a floating point map will be made). The standardized Shreve order streams raster map is then converted to a line vector map with r.to.vect with option column set in order to write the scaled Shreve order into the table. This vector map is then input into v.buffer with option column set to the column where the scaled Shreve order values were saved and flag t is selected so that the attribute table will transfer to the new file. Also set option scale to the maximum channel width (in meters) of the largest trunk stream in the streams map, which will create a vector areas map with streams scaled to the appropriate widths. This vector areas map should then be converted back to a raster map with v.to.rast, making sure that the option use is set to “attr” and the option attribute_column is set so that the scaled Shreve order values will be saved as the raster values. Finally, use r.mapcalc to scale the Sherve order values into the depth of the carved streams by multiplying the converted buffer raster map by the maximum desired depth of the largest trunk stream. This final output raster map will now be scaled to both width and depth throughout the stream network. Use r.mapcalc to “carve” into the DEM by subtracting this scaled width/depth map from the DEM. As a final measure to ensure that there is no stream blockage, you can use the module *r.carve with the streams vector map and the “precarved” DEM, which will ensure that no high areas exist in the channel bottoms. Finally, you may wish to re-interpolate the carved DEM so that harsh angles on the edges of the carved banks are removed. Using a bicubic interpolation in v.surf.bspline with relatively long spline step and high smoothing should accomplish this.

Estimating soil depth.

Soil depth is important in the routine, as it provides a depth-based limitation on the amount of erosion that can occur at any particular cell (see below). The depth of soil available to erode is the difference between the current surface elevations (DEM) and the bedrock elevation map initbdrk. The simplest way to estimate the bedrock elevation map is to subtract a constant from the starting DEM map used for elev using r.mapcalc. A more complex bedrock topography can be estimated using the addon module r.soildepth. In either case, it is important to use the same DEM to derive the bedrock elevations as you will use for the initial starting topography in the simulation.

Climate data file.

Users can use constants for climate data, or can use an input climate file with columns of comma separated values arranged in order of: "R,rain,storms,stormlength,stormsi" A new line should be used for each year of the simulation. The file can have a one-line header or no header. Do not included a column containing dates, but ensure that the number of rows matches the value you input for number.

Note that only the USPED equation needs a value for R factor, and USPED does not need the remaining climate variables. In the case of using USPED, only the first column needs to contain data (for R factor), but you still need to include all columns (the remaining columns can be with zeros or NaN's).

In the case of using the Stream Power or Shear Stress equations, you still must create a CSV file with 5 columns, but the first column (for R Factor) can be filled with zeros or NaN's.

When using a climate file, you enter the path to the text file as variable climfile. This will override values or maps entered into variables r, rain, storms, stormlength, or stormsi. A fatal error message will be raised if the number of rows in the input climate file does not match the value entered for the variable number.

Rainfall excess and flow accumulation.

This module will take rainfall totals into account when calculating the value of flow accumulation. It does so using r.watershed and the value of flowcontrib to calculate flow accumulation scaled by the percentage of rain that will flow off the cell (i.e., rainfall - infiltration). See above for a method to scale flowcontrib to C factor.

Temporal Interval

The USPED equation relies on the value of R from the RUSLE equation to define the temporal interval for landscape evolution. Typically, R is estimated at a yearly temporal interval, so it is important to understand the time step of your R input data before simulation with the USPED equation.

The Stream Power and Shear Stress equations, on the other hand, accept storm-level data. This can be aggregated at any time step (per-storm, daily, weekly, monthly, yearly, decadal, etc.). The time step does not need to be an even interval; this means you can model on a per-storm basis where the interval between storms is not the same. To do so, you would use the option to enter a climate file where each line would detail the timing and intensity of each storm. You would then run the simulation with variable number equal to the total number of storms in your study interval.

Approximation of depth of flow for Stream Power and Shear Stress equations.

Flow depth is an important component for estimating stream power or shear stress. Here, it is estimated using upslope accumulated area (as modified by rainfall excess), rain fall in a typical erosion causing event (e.g., greater than ~30mm), and the length of the typical erosion causing event. Depth at peak flow is then estimated by assuming a symmetrical unit-hydrograph where total flow is the area below the hydrograph curve, and the total length equal to duration of the storm. The constant 0.595 is used to estimate the depth at peak flow under a symmetrical hydrograph where the area under the graph equals A (upslope accumulated area), and the horizontal width of the base of the hydrograph is equal to the length of the storm in seconds (stormlength).

One of the benefits of this approach is that it is not tied to any specific time scale; any amount of time equal to or greater than 1 second can be modeled. For example, hourly rainfall totals can be entered as rain in sequence, with stormtime set to 3600 seconds, storms set to 1, and stormi set to 1. Hourly data could be aggregated to the level of the individual storm with the total for each storm entered as rain, stormtime equal to the total number of seconds each storm lasted, storms set to 1, and stormi set to some proportion of the storm where flow was at or near peak depths (e.g. 0.05). Daily rainfall totals can be entered as rain in sequence, with stormtime set to 84600 seconds, storms set to 1, and stormi set to some proportion where flow is at peak (e.g., 0.05). Monthly totals can be broken up into proportions per rain day, entered as rain with stormtime set to 84600 seconds, storms set to the number of storms that occurred that month, and stormi set to some proportion where flow is at or near peak depth (e.g., 0.05). Weekly, yearly, decadal, etc., totals can be entered in the same manner.

This approach is more flexible than using R factor to encapsulate rainfall intensivity, as with USPED, as often R factor can only be estimated from rainfall totals at the timescale of the year or decade.

Conversion of output of divergence to calculated erosion and deposition in vertical meters of elevation change.

In order to convert the changes in transport capacity into the amount of elevation gained or lost by deposition or erosion, first the divergence in transport capacity is calculated in the EW and NS directions. These are then added back together to calculate the divergence in transport capacity (flux) in the direction of flow across the cell. Once this is done, the units are in kg/m2.s of sediment gained or lost. This is converted to meters of elevation gained or lostby dividing by soil density [kg/m3]. For USPED, which is tied to the temporal interval of R factor, this typically provides [m/year] as the output units. For the shear stress and stream power equations, however, this first comes out in units of [m/s]. It is then necessary to multiply by the number of seconds at peak flow depth (stormi * stormtime) and then by the number of erosive storms (storms) per year to get [m/year] elevation change.

Computing elevation changes from one year to next.

To compute the new surface elevation after erosion and deposition have occurred, it is necessary to add this year's ED map to last year's DEM, checking first if the amount of erodible soil in a given cell is less than the amount of erosion calculated. The cell will be prevented from eroding past this amount. If there is some soil depth remaining in the cell, then if the amount of erosion is more than the amount of soil, the routine will remove all the remaining soil and stop. Otherwise it will remove the amount of calculated erosion. If there is deposition, then it will be added on top of current depth of sediment (even if no sediment is currently in the cell).

Finally, this routine is sensitive to edge effects carried forward from calculation of slope or other neighborhood routines used earlier in the module. To prevent null cells at the edges of maps, (the edge cells have no upstream cell, so get turned null), the initial DEM is patched underneath. Thus, the perimeter cells will never change in elevation throughout the simulation. Users are therefore strongly suggested to use a watershed boundary for their input maps (e.g., extracted from r.watershed, and then clipped with the map calculator), as cells at the watershed boundary should not change in elevation much in real world scenarios over the time spans of landscape evolution intended to be modeled with this module (100's to 1000's of years).

KNOWN ISSUES

This module is sensitive to the geometry of the input DEM. False flat areas and very steep slope transitions that are in the path of the flowlines will result in erroneous values, and perhaps even lead to instability in the landscape evolution algorithms that will exhibit as large “spikes” and “pits” in the output DEM's after several iterations, and may lead to numerical instability and NULL values in the various output maps. Preconditioning the input DEM to reduce these issues, which can be introduced during initial interpolation, or by the process of filling basins with r.fill.basins or carving streams with r.carve.

The module is also sensitive to input climate parameters and the exponents of flow and how they are scaled. It is important to test these out extensively before use.

At this time, this module should be considered to be at a robust alpha stage. It appears stable enough, but needs to be tested more extensively before it can be considered stable and ready for production use.

SEE ALSO

The MEDLAND project at Arizona State University

r.watershed, r.terraflow, r.mapcalc

Mitasova, H., C. M. Barton, I. I. Ullah, J. Hofierka, and R. S. Harmon 2013 GIS-based soil erosion modeling. In Remote Sensing and GIScience in Geomorphology, edited by J. Shroder and M. P. Bishop. 3:228-258. San Diego: Academic Press.

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AUTHORS

Isaac I. Ullah, C. Michael Barton, and Helena Mitasova

SOURCE CODE

Available at: r.landscape.evol source code (history)

Latest change: Thu Feb 3 09:32:35 2022 in commit: f17c792f5de56c64ecfbe63ec315307872cf9d5c

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