[GRASS-SVN] r62164 - grass-addons/grass6/raster/r.landscape.evol
svn_grass at osgeo.org
svn_grass at osgeo.org
Thu Oct 2 14:55:46 PDT 2014
Author: isaacullah
Date: 2014-10-02 14:55:46 -0700 (Thu, 02 Oct 2014)
New Revision: 62164
Added:
grass-addons/grass6/raster/r.landscape.evol/r_landscape_evol_Flow_acc_vs_curvature.png
grass-addons/grass6/raster/r.landscape.evol/r_landscape_evol_Map1.png
grass-addons/grass6/raster/r.landscape.evol/r_landscape_evol_equation1.gif
grass-addons/grass6/raster/r.landscape.evol/r_landscape_evol_equation2.gif
grass-addons/grass6/raster/r.landscape.evol/r_landscape_evol_equation3.gif
grass-addons/grass6/raster/r.landscape.evol/r_landscape_evol_equation4.gif
grass-addons/grass6/raster/r.landscape.evol/r_landscape_evol_equation5.gif
grass-addons/grass6/raster/r.landscape.evol/r_landscape_evol_equation6.gif
Removed:
grass-addons/grass6/raster/r.landscape.evol/585d862d.gif
grass-addons/grass6/raster/r.landscape.evol/Flow_acc_vs_curvature.png
grass-addons/grass6/raster/r.landscape.evol/Map_showing_locations_for_the_different_surface_processes.png
grass-addons/grass6/raster/r.landscape.evol/de331ef.gif
grass-addons/grass6/raster/r.landscape.evol/m100fb7e.gif
grass-addons/grass6/raster/r.landscape.evol/m11de82c.gif
grass-addons/grass6/raster/r.landscape.evol/m2c6cce6a.gif
grass-addons/grass6/raster/r.landscape.evol/m2f9c13ec.gif
grass-addons/grass6/raster/r.landscape.evol/m8e0f3ca.gif
Modified:
grass-addons/grass6/raster/r.landscape.evol/description.html
Log:
Further changes to description.html, following advice from Markus. Removed more malformed code snippets and non-prefered syntax, changed image names to represent standard naming system, and made sure all special charcters were properly coded in html.
Deleted: grass-addons/grass6/raster/r.landscape.evol/585d862d.gif
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--- grass-addons/grass6/raster/r.landscape.evol/description.html 2014-10-02 21:06:47 UTC (rev 62163)
+++ grass-addons/grass6/raster/r.landscape.evol/description.html 2014-10-02 21:55:46 UTC (rev 62164)
@@ -17,53 +17,53 @@
flow, and vegetation cover. This map of net ED is then added to (for
deposition) or subtracted from (for erosion) the topography map of
the previous time step, to create a new topography map (i.e., as a
-DEM) after a cycle of landuse and landscape change.</p>
+DEM) after a cycle of landuse and landscape change.
<p><b>R</b>, <b>K</b>, and <b>C</b> are environmental factors in the
USPED equation that relate to the intensity of yearly rainfall, the
erodability of soil, and the degree to which vegetation cover
prevents erosion (See below for a detailed description of these
factors). These factors largely determine the amount of erosion or
deposition that occur on the hill-slopes. <b>cutoff1</b>, <b>cutoff2,
-</b><span style="font-weight: normal">and </span><b>cutoff3</b> are
+</b>and <b>cutoff3</b> are
values of flow accumulation (amount of upslope area in square meters)
that determine where surface processes change from soil-creep to
laminar overland flow (sheetwash), from laminar overland flow to
channelized overland flow (rills/gullies), and from channelized
overland flow to full stream flow respectively. <b>kappa</b> is the
rate of diffusion for soil-creep in meters per 1000 years. <b>sdensity</b>
-is the density of the soil in grams per cubic centimeters. <b>rain</b><span style="font-weight: normal">
+is the density of the soil in grams per cubic centimeters. <b>rain</b>
is the total annual precipitation measured in meters (or the average
-annual rainfall in meters per year). </span><b>raindays</b><span style="font-weight: normal">
+annual rainfall in meters per year). <b>raindays</b>
is the total number of days on which it rained in one year (or an
-average value of days per year). </span><b>infilt</b><span style="font-weight: normal">
+average value of days per year). <b>infilt</b>
is the proportion of rainfall that infiltrates into the soil and thus
-does not contribute to runoff (values are between 0 and 1). </span><b>Kt</b><span style="font-weight: normal">
+does not contribute to runoff (values are between 0 and 1). <b>Kt</b>
is the stream transport efficiency variable that describes the
-cohesivness of the stream channel beds (0.001 for normal
+cohesiveness of the stream channel beds (0.001 for normal
gravel/sandy/silt channel bed to 0.000001 for a bedrock channel bed).
-</span><b>loadexp</b><span style="font-weight: normal"> is the stream
+<b>loadexp</b> is the stream
transport type variable that determines the type of stream transport
modeled (1.5 for bedload transport, or 2.5 for suspended load
-transport). </span><b>alpha</b><span style="font-weight: normal"> is
+transport). <b>alpha</b> is
the critical slope threshold above which the model will simulate the
-cumulative effects of mass wasting (landsliding). These</span>
+cumulative effects of mass wasting (landsliding). These
measures all need to be determined empirically for a given landscape
under a given climatic condition, but the defaults are average values
for the Circum-Mediterranean Basin.
-</p>
+
<p>By default, <em>r.watershed</em> is used to calculate flow
-accumulation modeling using the MFD alglrithm included in GRASS 6.4
+accumulation modeling using the MFD algorithm included in GRASS 6.4
and higher. This can be made backwards compatible by checking the -f
-flag, which will use <i>r.terraflow </i><span style="font-style: normal">to
+flag, which will use <i>r.terraflow </i>to
compute a flow accumulation model using the SFD algorithm. This will,
however, produce much less accurate results, and users are therefore
-encouraged to used GRASS 6.4 or higher.</span></p>
+encouraged to used GRASS 6.4 or higher.
<p> The user may use the <b>statsout</b> option to define the name of
the file that contains the statistics of erosion, deposition, and
soil depths over all iterations. The default name is
<tt>"mapset"_"prefix"_lsevol_stats.txt</tt> (in
the users home directory).
-</p>
+
<h3>Calculating Erosion and Deposition</h3>
<p>Because physical laws that govern the flow of water across
landscapes and its ability to erode, entrain, transport, and deposit
@@ -91,7 +91,7 @@
larger streams and rivers. Therefore we use a different process
equation to model erosion and deposition in stream channels (see
below).
-</p>
+
<p>Net erosion and deposition rates on hillslopes are computed from
the change in sediment flow across cells of a DEM that have flow
accumulation values less than <b>cutoff3</b>. We approximate sediment
@@ -101,9 +101,9 @@
(R, MJ mm/ha h yr), soil erodability coefficient (K, Mg ha h/ha MJ
mm), and coefficient for the ability of vegetation to prevent erosion
(C, unitless) from RUSLE with with an estimate of topographically
-driven stream power as shown in equation (1)</p>
+driven stream power as shown in equation (1)
<center>
-<img src="m11de82c.gif"><br>
+<img src="r_landscape_evol_equation1.gif"><br>
</center>
<p>where <i>A</i> is the upslope contributing area (a measure of
water flowing through a cell) and <em>B</em> is the slope of the
@@ -113,7 +113,7 @@
The sediment flow rate is largely determined by the amount of water
flowing (contributing area), its velocity (a function of slope), the
erodability of the substrate (K factor), and the ability of the
-vegetation cover to prevent erosion (C factor).</p>
+vegetation cover to prevent erosion (C factor).
<p>Implementing the USPED algorithm in a GRASS script combines GIS
modules for calculating slope, aspect, and flow accumulation (the
amount of water that flows across each cell) using map algebra. Data
@@ -124,68 +124,69 @@
underlying bedrock topography map (a raster DEM) to limit the total
depth of unconsolidated sediment that can be eroded. Soil
erodability, vegetation cover, and rainfall are expressed as the
-K-factor <i>(K),</i> C-factor (<i>C</i><span style="font-style: normal">)</span>,
-and R-factor (<i>R</i>)<span style="font-style: normal"> components</span>
+K-factor <i>(K),</i> C-factor (<i>C</i>),
+and R-factor (<i>R</i>) components
of the RUSLE and have been calculated empirically for a variety of
setting (Boellstorff and Benito 2005; MartÃnez-Casasnovas, 2000;
Essa 2004; Hammad, et al. 2004; Renard, et al. 1997; Renard and
Freimund 1994).
-</p>
+
<p>For areas of the DEM that have flow accumulation values greater
-than <b>cutoff3 </b><span style="font-weight: normal">(ie. areas
+than <b>cutoff3 </b>(ie. areas
that are proper streams), we use a case of the transport limited
process law that is formulated for water flowing in stream channels
(Howard 1980; Tucker and Hancock 2010). This is done by first
-calculating the reach average shear stress (</span><FONT FACE="Times New Roman, serif"><span style="font-weight: normal">τ</span></FONT><span style="font-weight: normal">),
-here estimated for a cellular landscape simply as:</span>
+calculating the reach average shear stress (<FONT FACE="Times New Roman, serif">τ</FONT>),
+here estimated for a cellular landscape simply as:
<center>
-<p><img src="m2f9c13ec.gif">>br>
+<p><img src="r_landscape_evol_equation2.gif"><br>
</center>
-<p> <span style="font-weight: normal">Where: </span><i><span style="font-weight: normal">9806.65</span></i><span style="font-weight: normal">
-is a constant related to the gravitational acceleration of water, </span><i><span style="font-weight: normal">B</span></i><span style="font-weight: normal">
-is the slope of the cell in degrees, and </span><i><span style="font-weight: normal">D</span></i><span style="font-weight: normal">
-is the instantaneous depth of flowing water in the cell. </span><i><span style="font-weight: normal">D
-</span></i><span style="font-style: normal"><span style="font-weight: normal">is</span></span><span style="font-weight: normal">
+<p> Where: <i>9806.65</i>
+is a constant related to the gravitational acceleration of water, <i>B</i>
+is the slope of the cell in degrees, and <i>D</i>
+is the instantaneous depth of flowing water in the cell. <i>D
+</i>is
here assumed to be roughly equivalent to the depth of flow during the
-average minute of rainfall, calculated by:</span></p>
+average minute of rainfall, calculated by:
<center>
-<img src="m2c6cce6a.gif"><br>
+<img src="r_landscape_evol_equation3.gif"><br>
</center>
-<p><span style="font-weight: normal">Where: </span><i><span style="font-weight: normal">R</span></i><sub><i><span style="font-weight: normal">m</span></i></sub><span style="font-weight: normal">
-is the total annual precipitation in meters, </span><i><span style="font-weight: normal">i</span></i><span style="font-weight: normal">
-is the proportion of rainfall that infiltrates rather than </span><span style="font-weight: normal">runs
-off, </span><i><span style="font-weight: normal">A</span></i><span style="font-style: normal"><span style="font-weight: normal">
+<p>Where: <i>R</i><sub><i>m</i></sub>
+is the total annual precipitation in meters, <i>i</i>
+is the proportion of rainfall that infiltrates rather than runs
+off, <i>A</i>
is the uplsope accumulated area per unit contour width at the cell,
-</span></span><i><span style="font-weight: normal">R</span></i><sub><i><span style="font-weight: normal">d</span></i></sub><span style="font-style: normal"><span style="font-weight: normal">
+<i>R</i><sub><i>d</i></sub>
is the number of days on which it rained in a one year period, and
-</span></span><i><span style="font-weight: normal">1440</span></i><span style="font-style: normal"><span style="font-weight: normal">
-is a constant relating to the number of minutes in a day.</span></span></p>
-<p style="font-style: normal; font-weight: normal">Then the transport
-capacity is calculated by:</p>
-<p style="font-style: normal; font-weight: normal"><img src="m100fb7e.gif" name="Object4" align=absmiddle hspace=8 width=76 height=28></p>
-<p><span style="font-weight: normal">Where: </span><i><span style="font-weight: normal">K</span></i><sub><i><span style="font-weight: normal">t</span></i></sub><span style="font-style: normal"><span style="font-weight: normal">
+<i>1440</i>
+is a constant relating to the number of minutes in a day.
+<p>Then the transport capacity is calculated by:
+<center>
+<img src="r_landscape_evol_equation4.gif"><br>
+</center>
+<p>Where: <i>K</i><sub><i>t</i></sub>
is the transport efficiency factor related to the character of the
-stream bed (0.001 for normal sediment to 0.000001 for bedrock), and </span></span><i><span style="font-weight: normal">n</span></i><span style="font-style: normal"><span style="font-weight: normal">
+stream bed (0.001 for normal sediment to 0.000001 for bedrock), and <i>n</i>
is an empirically determined exponent related to the dominant type of
transport in the stream system (1.5 for bedload transport or 2.5
-suspended load transport).</span></span></p>
+suspended load transport).
<p>Net erosion and deposition rates are then computed across the
entire DEM as change in sediment flow in the x and y directions
-across a cell as follows”</p>
+across a cell as follows:
<center>
-<img src="m8e0f3ca.gif"><br>
+<img src="r_landscape_evol_equation5.gif"><br>
</center>
-<p><span style="font-weight: normal">where ED is net erosion or
-deposition rate for sediment and </span><em><FONT FACE="Times New Roman, serif"><span style="font-weight: normal">α</span></FONT></em><span style="font-weight: normal">
+<p>where ED is net erosion or
+deposition rate for sediment and <em><FONT FACE="Times New Roman, serif">α</FONT></em>
is the topographic aspect (i.e., direction of slope) for a cell.
Whether flowing water will erode or deposit sediment in a particular
-cell is determined by the </span><em><span style="font-style: normal"><U><span style="font-weight: normal">change</span></U></span></em><span style="font-weight: normal">
+cell is determined by the <em><U>change</U></em>
in sediment flow (transport capacity) from one cell to the next. If
the transport capacity increases (for example, due to an increase in
the steepness of the slope or amount of flowing water), more sediment
will be entrained and erosion will occur; if the transport capacity
decreases (for example, due to a decrease in slope or water flow)
-sediment will be deposited.</span></p>
+sediment will be deposited.
<p>The output of this GRASS implementation of these transport
equations must be modified in several ways in order to make it
appropriate for landscape evolution simulation. First, because of the
@@ -195,13 +196,13 @@
and creates oscillating "spikes" in positive and negative
flux values resulting in the calculation of alternating deep pits and
high mounds at sensitive areas on the landscape. To overcome this,
-<em>r.landscape.evol</em> uses a nieghborhood algorithm in <em>r.mapcalc</em>
+<em>r.landscape.evol</em> uses a neighborhood algorithm in <em>r.mapcalc</em>
to put the calculated value of <i>T</i> back into the cell that is
most uplsope from where it is originally calculated.
-</p>
+
<p>Additionally, control must be kept for the amount of erodible
sediment available to moved. <em>r.landscape.evol</em> explicitly
-tracks this by taking the difference between the input bedrcok
+tracks this by taking the difference between the input bedrock
elevation DEM, and the current surface topography DEM, and creating a
map of "soil" depth. This map tracks the amount of material
assumed to be available for entrainment and transport by surface
@@ -210,78 +211,80 @@
materials (ie. at bedrock outcrops). Where this condition occurs, <i>K</i>
or <i>K</i><sub><i>t </i></sub>is made to be very small, resulting in
only extremely small amounts of erosion.
-</p>
+
<p>Another major issue is that the total flux <i>T </i>is in units of
Tons/Ha, which means it must be converted in order to calculate the
change in elevation at each cell (<i>m</i><sub><i>vert</i></sub>).
This is done via a simple algorithm that uses the density of the soil
-and the cell resolution:</p>
+and the cell resolution:
<center>
-<img src="585d862d.gif"><br>
+<img src="r_landscape_evol_equation6.gif"><br>
</center>
<p>Where: <i>10000</i> is the number of meters per hectare, <i>Sd </i>is
the density of the soil, and <i>Res </i>is the cell resolution
(width). In order to convert the output back to Tons/Ha (standard
rate for USPED/RUSLE equations), you can multiply the <b>netchange</b>
-output map by "(10000 x resolution x soil density)" to
+output map by "(10000 x raster cell resolution x <b>sdensity</b>)" to
create a map of soil erosion/deposition rates across the landscape.
-</p>
+
<h3>Determining Cutoff Points</h3>
<p>
-To get started with r.landscape.evol, you need to determine the appropriate values for "cutoff1", "cutoff2", and "cutoff3", which are transition points between different types of erosive processes. These are in units of flow accumulation scaled to actual surface flow as determined in r.watershed from the values of rainfall and flow hindrance from vegetation. To do this, you should parameterize the module as best as possible, EXCEPT for the three "cutoffs". Then, run the module with the "-p" flag, which will make a random points vector file with the values of scaled flow accumulation (scaled to actual rainfall and vegetation), profile curvature, and tangential curvature in the associated table. Plotting the log of the scaled flow accumulation against each of these two curvatures will help you to determine reasonable values for the cutoffs, as each transition should show a unique relationship between curvature and flow accumulations. See the figures bel
ow for examples:
-</p>
+To get started with <em>r.landscape.evol</em>, you need to determine the appropriate values for <b>cutoff1</b>, <b>cutoff2</b>, and <b>cutoff3</b>, which are transition points between different types of erosive processes. These are in units of flow accumulation scaled to actual surface flow as determined in r.watershed from the values of rainfall and flow hindrance from vegetation. To do this, you should parameterize the module as best as possible, EXCEPT for the three "cutoffs". Then, run the module with the <b>-p</b> flag, which will make a random points vector file with the values of scaled flow accumulation (scaled to actual rainfall and vegetation), profile curvature, and tangential curvature in the associated table. Plotting the log of the scaled flow accumulation against each of these two curvatures will help you to determine reasonable values for the cutoffs, as each transition should show a unique relationship between curvature and flow accumulations. See
the figures below for examples:
+
<center>
-<img src="Flow_acc_vs_curvature.png" width="1000" height="500" alt="Log Scaled Flow Accumulation versus Topographic Curvatures"><br>
+<img src="r_landscape_evol_Flow_acc_vs_curvature.png" width="1000" height="500" alt="Log Scaled Flow Accumulation versus Topographic Curvatures"><br>
Log Scaled Flow Accumulation versus Topographic Curvatures.<br><br>
-<img src="Map_showing_locations_for_the_different_surface_processes.png" width="500" height="284" alt="Map showing the spatial patterns of the cutoffs determined from the previous figure"><br>
+<img src="r_landscape_evol_Map1.png" width="500" height="284" alt="Map showing the spatial patterns of the cutoffs determined from the previous figure"><br>
Map showing the spatial patterns of the cutoffs determined from the previous figure.<br><br>
</center>
-<p></p>
+<p>
<h3>Note About Climate Parameters</h3>
<p>
-r.landscape.evol accepts an external “climate file”, which should be a comma separated plain text file with four columns in the order of, "rain,R,storms,stormlength" (without headers). Each of these columns must exist, although there need not be values in every column (i.e., you can enter a single value for any of these parameters in the command line, and combine that with populated columns for the other values). Note that the climate file must have the same number of rows as there are iterations of the simulation (“years”).
-</p>
+r.landscape.evol accepts an external "climate file", which should be a comma separated plain text file with four columns in the order of, "<b>rain</b>,<b>R</b>,<b>storms</b>,<b>stormlength</b>" (without headers). Each of these columns must exist, although there need not be values in every column (i.e., you can enter a single value for any of these parameters in the command line, and combine that with populated columns for the other values). Note that the climate file must have the same number of rows as there are iterations of the simulation (<b>years</b>).
+
<h2>SEE ALSO</h2>
<ul>
- <li><p style="margin-bottom: 0in">The <a href="http://medland.asu.edu/">MEDLAND</a>
+ <li><p>The <a href="http://medland.asu.edu/">MEDLAND</a>
project at Arizona State University
- </p>
+
<li><p><a href="r.watershed.html">r.watershed</a>, <a href="r.terraflow.html">r.terraflow</a>,
<a href="r.mapcalc.html">r.mapcalc</a>
- </p>
+
+ <li><p>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.
+
+
</ul>
<h2>REFERENCES</h2>
<p>American Society of Agricultural Engineers 2003 Honoring the
Universal Soil Loss Equation: Historic Landmark Dedication Pamphlet.
Purdue University Department of Agricultural and Biological
Engineering.
-</p>
+
<p>Clevis, Q., G. E. Tucker, G. Lock, S. T. Lancaster, N. Gasparini,
A. Desitter and R. L. Bras 2006 Geoarchaeological simulation of
meandering river deposits and settlement distributions: A
three-dimensional approach. Geoarchaeology 21(8):843-874.
-</p>
+
<p>Degani, A., L. A. Lewis and B. B. Downing 1979 Interactive
Computer Simulation of the Spatial Process of Soil Erosion.
Professional Geographer 31(2):184-190.
-</p>
-<p style="margin-left: 0.5in; text-indent: -0.5in">Howard, A. D.
-1980. Thresholds in river regimes. <span style="font-style: normal">Thresholds
-in geomorphology</span>, 227–258.
-</p>
+
+<p>Howard, A. D. 1980. Thresholds in river regimes. Thresholds
+in geomorphology, 227-258.
+
<p>Mitas, L. and H. Mitasova 1998 Distributed soil erosion simulation
for effective erosion prevention. Water Resources Research
34(3):505-516.
-</p>
+
<p>Mitasova, H., J. Hofierka, M. Zlocha and L. R. Iverson 1996
Modelling topographic potential for erosion and deposition using GIS.
International Journal of Geographical Information Systems
10(5):629-641.
-</p>
+
<p>Mitasova, H. and L. Mitas 2001a Modeling Physical Systems. In
Geographic Information Systems and Environmental Modeling, edited by
B. O. Parks, M. Crane and K. C. Clarke, pp. 189-210. Prentice Hall,
@@ -289,7 +292,7 @@
management. In Landscape erosion and landscape evolution modeling,
edited by R. Harmon and W. Doe, pp. 321-347. Kluwer Academic/Plenum
Publishers, New York.
-</p>
+
<p>Mitasova, H., L. Mitas and W. M. Brown 2001 Multiscale simulation
of land use impact on soil erosion and deposition patterns. In
Sustaining the Global Farm. Selected Papers from the 10th
@@ -297,12 +300,12 @@
Purdue University, edited by D. E. Stott, R. H. Mohtar and G. C.
Steinhardt, pp. 1163-1169. USDA-ARS National Soil Erosion Research
Laboratory, Purdue.
-</p>
+
<p>Mitasova, H., L. Mitas, W. M. Brown and D. Johnston 1996
Multidimensional Soil Erosion/Deposition Modeling Part III: Process
based erosion simulation. Geographic Modeling and Systems Laboratory,
University of Illinois at Urban-Champaign.
-</p>
+
<p>Mitasova, H., C. Thaxton, J. Hofierka, R. McLaughlin, A. Moore and
M. L 2004 Path sampling method for modeling overland water flow,
sediment transport and short term terrain evolution in Open Source
@@ -310,50 +313,50 @@
Computational Methods in Water Resources (CMWR XV), edited by C. T.
Miller, M. W. Farthing, V. G. Gray and G. F. Pinder, pp. 1479-1490.
Elsevier, Chapel Hill, NC, USA.
-</p>
+
<p>Peeters, I., T. Rommens, G. Verstraeten, G. Govers, A. Van
Rompaey, J. Poesen and K. Van Oost 2006 Reconstructing ancient
topography through erosion modelling. Geomorphology 78(3-4):250-264.
-</p>
+
<p>Rawls, W. J. 1983 Estimating soil bulk denisty from particle size
analysis and organic matter content. Soil Science 135(2):123.
-</p>
+
<p>Renard, K. G., G. R. Foster, G. A. Weesies, D. K. McCool and D. C.
Yoder 1997 Predicting soil erosion by water: a guide to conservation
planning with the Revised Universal Soil Loss Equation (RUSLE). In
-Agriculture Handbook, pp. 1–251. vol. 703. US Department of
+Agriculture Handbook, pp. 1-51. vol. 703. US Department of
Agriculture, Washington, DC.
-</p>
+
<p>Renard, K. G. and J. R. Freimund 1994 Using monthly precipitation
data to estimate the R-factor in the revised USLE. Journal of
Hydrology 157(1-4):287-306.
-</p>
+
<p>Singh, R. and V. S. Phadke 2006 Assessing soil loss by water
erosion in Jamni River Basin, Bundelkhand region, India, adopting
universal soil loss equation using GIS. Current Science
90(10):1431-1435.
-</p>
+
<p>Tucker, G. E. and G. R Hancock 2010 Modelling landscape
-evolution. <span style="font-style: normal">Earth Surface Processes
-and Landforms</span> 35(1): 28–50.
-</p>
+evolution. Earth Surface Processes
+and Landforms 35(1): 28-50.
+
<p>Warren, S. D., H. Mitasova, M. G. Hohmann, S. Landsberger, F. Y.
Iskander, T. S. Ruzycki and G. M. Senseman 2005 Validation of a 3-D
enhancement of the Universal Soil Loss Equation for prediction of
soil erosion and sediment deposition. Catena 64:281-296.
-</p>
+
<p>Wischmeier, W. H. 1976 Use and Misuse of the Universal Soil Loss
Equation. Journal of Soil and Water Conservation 31:5-9.
-</p>
+
<p>Wischmeier, W. H., C. B. Johnson and B. V. Cross 1971 A Soil
Erodibility Nomograph for Farmland and Construction Sites. Journal of
Soil and Water Conservation 26:189-92.
-</p>
+
<p>Wischmeier, W. H. and D. D. Smith 1978 Predicting Rainfall-Erosion
Losses - A Guide to Conservation Planning. USDA Agriculture Handbook
282.
-</p>
+
<h2>AUTHORS</h2>
Isaac I. Ullah, C. Michael Barton, and Helena Mitasova
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