**-m**- -m Apply smoothing (useful to mitigate possible unstable conditions in streams)
**-p**- -p Run a sampling procedure to generate a vector points map with scaled flow accumulation values suitable for determining transport equation thresholds. Overrides all other output.
**-k**- -k Keep ALL temporary maps (overides flags -drst). This will make A LOT of maps!
**-d**- -d Don't output yearly soil depth maps
**-r**- -r Don't output yearly maps of the erosion/deposition rates ("ED_rate" map, in vertical meters)
**-s**- -s Keep all slope maps
**-t**- -t Keep yearly maps of the Transport Capacity at each cell ("Qs" maps)
**-e**- -e Keep yearly maps of the Excess Transport Capacity (divergence) at each cell ("DeltaQs" maps)
**--overwrite**- Allow output files to overwrite existing files
**--help**- Print usage summary
**--verbose**- Verbose module output
**--quiet**- Quiet module output
**--ui**- Force launching GUI dialog

**elev**=*name***[required]**- Input elevation map (DEM of surface)
**initbdrk**=*name***[required]**- Bedrock elevations map (DEM of bedrock)
- Default:
**prefx**=*basename***[required]**- Name for output basename raster map(s)
- Default:
*levol_* **outdem**=*basename***[required]**- Name stem for output elevation map(s) (preceded by prefix and followed by numerical suffix if more than one iteration)
- Default:
*elevation* **outsoil**=*basename***[required]**- Name stem for the output soil depth map(s) (preceded by prefix and followed by numerical suffix if more than one iteration)
- Default:
*soildepth* **number**=*integer***[required]**- Number of iterations (cycles) to run
- Default:
*1* **k**=*name*- Soil erodability index (K factor) map or constant (values <= 0.09 [t.ha.h /ha.MJ.mm])
- Default:
*0.05* **c**=*name*- Landcover index (C factor) map or constant (values <=1.0 [unitless])
- Default:
*0.005* **p**=*name*- Landuse practices factor (P factor) map or constant (values <=1.0 [unitless])
- Default:
*1.0* **sdensity**=*name*- Soil density map or constant for conversion from mass to volume (values typically >=1000 [kg/m3])
- Default:
*1218.4* **transp_eq**=*string*- The sediment transport equation to use (USPED: Tc=R*K*C*P*A^m*B^n, Stream power: Tc=Kt*gw*1/N*h^m*B^n, or Shear stress: Tc=Kt*tau^m ).
- Options:
*StreamPower, ShearStress, USPED* - Default:
*StreamPower* **exp_m**=*string*- Exponent m relates to the influence of upslope area (and thus flow depth, discharge) on transport capacity. Values generally thought to scale inversely with increasing depth of flow between the two cutoff thresholds specified: "thresh1,m1,thresh2,m2"
- Default:
*10,2,100,1* **exp_n**=*string*- Exponent n relates to the influence of local topographic slope on transport capacity. Default values set to scale inversely with increasing local slope between the two slope cutoff thresholds specified: "thresh1,n1,thresh2,n2"
- Default:
*10,2,45,0.5* **r**=*name***[required]**- Rainfall (R factor) map or constant (Employed only in the USPED equation) (values typically between 500 and 10000 [MJ.mm/ha.h.yr])
- Default:
*720* **rain**=*name***[required]**- Precip total for the average erosion-causing storm map (Employed in stream power and shear stress equations) (values typically >=30.0 [mm])
- Default:
*30* **storms**=*name***[required]**- Number of erosion-causing storms per year map or constant (Employed in stream power and shear stress equations) (values >=0 [integer])
- Default:
*2* **stormlength**=*name***[required]**- Average length of the storm map or constant (Employed in stream power and shear stress equations) (values >=0.0 [h])
- Default:
*24.0* **stormi**=*name***[required]**- Proportion of the length of the storm where the storm is at peak intensity map or constant (Employed in stream power and shear stress equations) (values typically ~0.05 [unitless proportion])
- Default:
*0.05* **climfile**=*string*- Path to climate file of comma separated values of "rain,R,storms,stormlength,stormi", with a new line for each year of the simulation. This option will override values or maps entered above.
**manningn**=*name*- Map or constant of the value of Manning's "N" value for channelized flow. (Employed in stream power and shear stress equations) (0.03 = clean/straight stream channel, 0.035 = major river, 0.04 = sluggish stream with pools, 0.06 = very clogged streams [unitless])
- Default:
*0.03* **flowcontrib**=*name*- Map or constant indicating how much each cell contributes to downstream flow (this typically relates to vegetation or conservation practices). If no map or value entered, routine will assume 100% downstream contribution (values between 0 and 100 [unitless percentage])
- Default:
*100* **convergence**=*integer*- Value for the flow convergence variable in r.watershed. Small values make water spread out, high values make it converge in narrower channels.
- Options:
*1, 2, 3, 4, 5, 6, 7, 8, 9, 10* - Default:
*5* **statsout**=*name*- Name for the statsout text file (optional, if none provided, a default name will be used)

- DESCRIPTION
- NOTES
- Transport capacity equations.
- Scalar m and n exponents to simulate changing process across landscapes.
- Scaling other input values.
- Creating a hydrologically-appropriate base DEM.
- Estimating soil depth.
- Climate data file.
- Rainfall excess and flow accumulation.
- Temporal Interval
- Approximation of depth of flow for Stream Power and Shear Stress equations.
- Conversion of output of divergence to calculated erosion and deposition in vertical meters of elevation change.
- Computing elevation changes from one year to next.

- KNOWN ISSUES
- SEE ALSO
- REFERENCES
- AUTHORS

*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.

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).

```
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.

```
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.

```
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.

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.

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

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.

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.

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**.

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.

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.

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.

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.

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).

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.

The MEDLAND project at Arizona State University

r.watershed, r.terraflow, r.mapcalc

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

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

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