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-<H2>DESCRIPTION</H2>
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+<h2>DESCRIPTION</h2>
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This program generates flowlines using a combined raster-vector
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approach (see <a href="http://skagit.meas.ncsu.edu/~helena/gmslab/papers/hmg.rev1.ps">Mitasova and
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-Hofierka 1993</A> and <a href="http://skagit.meas.ncsu.edu/~helena/gmslab/papers/ijgis.html">Mitasova et
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-al. 1995)</A>) from an input elevation raster map <I>elevin</I>
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+Hofierka 1993</a> and <a href="http://skagit.meas.ncsu.edu/~helena/gmslab/papers/ijgis.html">Mitasova et
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+al. 1995</a>) from an input elevation raster map <b>elevin</b>
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(integer or floating point), and optionally an input aspect raster map
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-<I>aspin</I> and/or an input barrier raster map <I>barin</I>. There are
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+<b>aspin</b> and/or an input barrier raster map <b>barin</b>. There are
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three possible output maps which can be produced in any combination
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-simultaneously: a vector map <I>flout</I> of flowlines, a raster map
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-<I>lgout</I> of flowpath lengths, and a raster map <I>dsout</I> of flowline
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+simultaneously: a vector map <b>flout</b> of flowlines, a raster map
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+<b>lgout</b> of flowpath lengths, and a raster map <b>dsout</b> of flowline
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densities (which are equal upslope contributed areas per unit width, when
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multiplied by resolution).
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+<p>
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+Aspect used for input must follow the same rules as aspect computed
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+in other GRASS programs (see <a href="v.surf.rst.html">v.surf.rst</a>
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+or <a href="r.slope.aspect.html">r.slope.aspect</a>).
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+<p>
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-<P>Aspect used for input must follow the same rules as aspect computed
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-in other GRASS programs (see <A HREF="v.surf.rst.html">v.surf.rst</A>
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-or <A HREF="r.slope.aspect.html">r.slope.aspect</A>).
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-
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-<P>Flowline output is given in a vector map <I>flout</I>, (flowlines generated
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+Flowline output is given in a vector map <b>flout</b>, (flowlines generated
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downhill). The line segments of flowline vectors have endpoints on edges
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of a grid formed by drawing imaginary lines through the centers of the
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cells in the elevation map. Flowlines are generated from each cell downhill
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-by default; they can be generated uphill using the flag <I>-u</I>. A flowline
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+by default; they can be generated uphill using the flag <b>-u</b>. A flowline
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stops if its next segment would reverse the direction of flow (from up
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to down or vice-versa), cross a barrier, or arrive at a cell with undefined
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-elevation or aspect. Another option, <I>skip</I>=val, indicates that only
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-the flowlines from every val-th cell are to be included in <I>flout</I>.
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-The default <I>skip</I> is max(1, <rows in elevin>/50, <cols in elevin>/50).
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-A high <I>skip</I> usually speeds up processing time and often improves
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-the readability of a visualization of <I>flout</I>.
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+elevation or aspect. Another option, <b>skip</b>=val, indicates that only
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+the flowlines from every val-th cell are to be included in <b>flout</b>.
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+The default <b>skip</b> is max(1, <rows in elevin>/50, <cols in elevin>/50).
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+A high <b>skip</b> usually speeds up processing time and often improves
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+the readability of a visualization of <b>flout</b>.
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+<p>
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-<P>Flowpath length output is given in a raster map <I>lgout</I>. The value
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+Flowpath length output is given in a raster map <b>lgout</b>. The value
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in each grid cell is the sum of the planar lengths of all segments of the
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-flowline generated from that cell. If the flag <I>-3</I> is given, elevation
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+flowline generated from that cell. If the flag <b>-3</b> is given, elevation
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is taken into account in calculating the length of each segment.
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-<P>Flowline density downhill or uphill output is given in a raster map
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-<I>dsout.</I> The value in each grid cell is the number of flowlines which
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+<p>Flowline density downhill or uphill output is given in a raster map
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+<b>dsout.</b> The value in each grid cell is the number of flowlines which
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pass through that grid cell, that means the number of flowlines from the
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entire map which have segment endpoints within that cell.
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-With the <em>-m</em> flag less memory is used as aspect at each cell is computed
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+With the <b>-m</b> flag less memory is used as aspect at each cell is computed
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on the fly. This option incurs a severe performance penalty. If this flag is given,
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the aspect input map (if any) will be ignored.
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<!-- doesn't exist
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-<P><B>-M</B> Use a fixed size memory and utilize page-swapping to handle
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+<p><b>-M</b> Use a fixed size memory and utilize page-swapping to handle
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large input files. This option incurs a severe performance penalty but
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is the only way to handle arbitrarily-large data files. If this flag is
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-given, the <B>-m</B> flag will be ignored.
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+given, the <b>-m</b> flag will be ignored.
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-->
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-The <em>barin</em> parameter is a raster map name with non-zero
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+The <b>barin</b> parameter is a raster map name with non-zero
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values representing barriers as input.
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-<H2>NOTES</H2>
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+<h2>NOTES</h2>
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For best results, use input elevation maps with high precision units (e.g.,
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centimeters) so that flowlines do not terminate prematurely in flat areas.
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To prevent the creation of tiny flowline segments with imperceivable changes
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@@ -67,7 +69,7 @@ and another segment of 1/2 degree different aspect is taken to be "very
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close" for that axis. Note that this distance (the so-called "quantization
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error") is about 1-2% of the resolution on maps with square cells.
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-<P>The values in length maps computed using the <B>-u</B> flag represent
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+<p>The values in length maps computed using the <b>-u</b> flag represent
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the distances from each cell to an upland flat or singular point. Such
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distances are useful in water erosion modeling for computation of the LS
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factor in the standard form of USLE. Uphill flowlines merge on ridge lines;
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@@ -75,7 +77,7 @@ by redirecting the order of the flowline points in the output vector map,
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dispersed waterflow can be simulated. The density map can be used for the
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extraction of ridge lines.
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-<P>Computing the flowlines downhill simulates the actual flow (also known
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+<p>Computing the flowlines downhill simulates the actual flow (also known
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as the raindrop method). These flowlines tend to merge in valleys; they
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can be used for localization of areas with waterflow accumulation and for
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the extraction of channels. The downslope flowline density multiplied by
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@@ -85,46 +87,44 @@ flux for the steady state conditions and can be used in the modeling of
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water erosion for the computation of the unit stream power based LS factor
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or sediment transport capacity.
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-<P>The program has been designed for modeling erosion on hillslopes and
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+<p>The program has been designed for modeling erosion on hillslopes and
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has rather strict conditions for ending flowlines. It is therefore not
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very suitable for the extraction of stream networks or delineation of watersheds
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unless a DEM without pits or flat areas is available
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(<a href=r.fill.dir.html>r.fill.dir</a> can be used to fill pits).
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-<P> To label the vector flowlines automatically, the user can use
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+<p> To label the vector flowlines automatically, the user can use
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<a href=v.category.html>v.category</a> (add categories).
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-<H2>Algorithm background</H2>
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+<h3>Algorithm background</h3>
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-<P>1. Construction of flow-lines (slope-lines): <em>r.flow</em> uses an original
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+<p>1. Construction of flow-lines (slope-lines): <em>r.flow</em> uses an original
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vector-grid algorithm which uses an infinite number of directions between
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0.0000... and 360.0000... and traces the flow as a line (vector) in the
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direction of gradient (rather than from cell to cell in one of the 8
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directions = D-infinity algorithm). They are traced in any direction using
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aspect (so there is no limitation to 8 directions here). The D8 algorithm
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produces zig-zag lines. The value in the outlet is very similar for both
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-r.flow and r.flowmd (GRASS 5 only) algorithms (because it is
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+<em>r.flow</em> and <em>r.flowmd</em> (GRASS 5 only) algorithms (because it is
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essentially the watershed area), however the spatial distribution of flow,
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especially on hillslopes is quite different. It is still a 1D flow routing
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so the dispersal flow is not accurately described, but still better than D8.
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-<P>2. Computation of contributing areas: <em>r.flow</em> uses a single flow
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+<p>2. Computation of contributing areas: <em>r.flow</em> uses a single flow
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algorithm, i.e. all flow is transported to a single cell downslope.
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-<H2>FURTHER NOTES</H2>
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-
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-<b>Differences between <em>r.flow</em> and <em>r.flowmd</em></b>
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+<h3><b>Differences between <em>r.flow</em> and <em>r.flowmd</em></b></h3>
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<p>
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<ol>
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<li> <em>r.flow</em> has an option to compute slope and aspect internally thus making
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-the program capable to process much larger data sets than r.flowmd. It has
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+the program capable to process much larger data sets than <em>r.flowmd</em>. It has
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also 2 additional options for handling of large data sets but it is not
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known that they work properly.
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<li> the programs handle the special cases when the flowline passes exactly
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(or very close) through the grid vertices differently.
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-<li> r.flowmd has the simplified multiple flow addition so the results are
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+<li> <em>r.flowmd</em> has the simplified multiple flow addition so the results are
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smoother.
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</ol>
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@@ -132,63 +132,62 @@ In conclusion, <em>r.flowmd</em> produces nicer results but is slower and it doe
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support as large data sets as <em>r.flow</em>.
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-<H2>DIAGNOSTICS</H2>
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+<h3>Diagnostics</h3>
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-<P>"ERROR: r.flow: " input " file's resolution differs from current" region
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+<p>"ERROR: r.flow: " input " file's resolution differs from current" region
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resolution
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-<P>The resolutions of all input files and the current region must match.
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+<p>The resolutions of all input files and the current region must match.
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-<P>"ERROR: r.flow: resolution too unbalanced (" val " x " val ")" The difference
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+<p>"ERROR: r.flow: resolution too unbalanced (" val " x " val ")" The difference
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in length between the two axes of a grid cell is so great that quantization
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error is larger than one of the dimensions. Resample the map and try again.
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+<h2>REFERENCES</h2>
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-<H2>SEE ALSO</H2>
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-
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-<A HREF="r.basins.fill.html">r.basins.fill</A>,
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-<A HREF="r.drain.html">r.drain</A>,
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-<A HREF="r.fill.dir.html">r.fill.dir</A>,
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-<A HREF="r.water.outlet.html">r.water.outlet</A>,
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-<A HREF="r.watershed.html">r.watershed</A>,
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-<A HREF="v.category.html">v.category</A>,
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-<A HREF="v.to.rast.html">v.to.rast</A>
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-
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-
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-<H2>AUTHORS</H2>
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-
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-<P><I>Original version of program:</I>
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-<BR>Maros Zlocha and Jaroslav Hofierka, Comenius University, Bratislava,
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-Slovakia,
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-
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-<P><I>The current version of the program (adapted for GRASS5.0)</I>:
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-<BR>Joshua Caplan, Mark Ruesink, Helena Mitasova, University of Illinois
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-at Urbana-Champaign with support from USA CERL.<br>
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-<a href=http://skagit.meas.ncsu.edu/~helena/gmslab/>GMSL/University of Illinois at
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-Urbana-Champaign</a>
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-
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-<H2>REFERENCES</H2>
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-
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-<P>Mitasova, H., L. Mitas, 1993, Interpolation by regularized spline with
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+<p>Mitasova, H., L. Mitas, 1993, Interpolation by regularized spline with
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tension : I. Theory and implementation. Mathematical Geology 25, p. 641-655.
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-(<a href=http://skagit.meas.ncsu.edu/~helena/gmslab/papers/lmg.rev1.ps>online</A>)
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+(<a href=http://skagit.meas.ncsu.edu/~helena/gmslab/papers/lmg.rev1.ps>online</a>)
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-<P>Mitasova and Hofierka 1993 : Interpolation by Regularized Spline with
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+<p>Mitasova and Hofierka 1993 : Interpolation by Regularized Spline with
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Tension: II. Application to Terrain Modeling and Surface Geometry Analysis.
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-Mathematical Geology 25(6), 657-669. (<a href=http://skagit.meas.ncsu.edu/~helena/gmslab/papers/hmg.rev1.ps>online</A>)
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+Mathematical Geology 25(6), 657-669. (<a href=http://skagit.meas.ncsu.edu/~helena/gmslab/papers/hmg.rev1.ps>online</a>)
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-<P>Mitasova, H., Mitas, L., Brown, W.M., Gerdes, D.P., Kosinovsky, I.,
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+<p>Mitasova, H., Mitas, L., Brown, W.M., Gerdes, D.P., Kosinovsky, I.,
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Baker, T., 1995: Modeling spatially and temporally distributed phenomena:
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New methods and tools for GRASS GIS. International Journal of Geographical
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Information Systems 9(4), 433-446.
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-<P>Mitasova, H., J. Hofierka, M. Zlocha, L.R. Iverson, 1996, Modeling
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+<p>Mitasova, H., J. Hofierka, M. Zlocha, L.R. Iverson, 1996, Modeling
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topographic potential for erosion and deposition using GIS. Int. Journal of
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Geographical Information Science, 10(5), 629-641. (reply to a comment to
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this paper appears in 1997 in Int. Journal of Geographical Information
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Science, Vol. 11, No. 6)
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-<P>Mitasova, H.(1993): Surfaces and modeling. Grassclippings (winter and
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+<p>Mitasova, H.(1993): Surfaces and modeling. Grassclippings (winter and
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spring) p.18-19.
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+<h2>SEE ALSO</h2>
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+
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+<a href="r.basins.fill.html">r.basins.fill</a>,
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+<a href="r.drain.html">r.drain</a>,
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+<a href="r.fill.dir.html">r.fill.dir</a>,
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+<a href="r.water.outlet.html">r.water.outlet</a>,
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+<a href="r.watershed.html">r.watershed</a>,
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+<a href="v.category.html">v.category</a>,
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+<a href="v.to.rast.html">v.to.rast</a>
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+
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+
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+<h2>AUTHORS</h2>
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+
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+<p><i>Original version of program:</i>
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+<br>Maros Zlocha and Jaroslav Hofierka, Comenius University, Bratislava,
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+Slovakia,
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+
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+<p><i>The current version of the program (adapted for GRASS5.0)</i>:
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+<br>Joshua Caplan, Mark Ruesink, Helena Mitasova, University of Illinois
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+at Urbana-Champaign with support from USA CERL.<br>
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+<a href=http://skagit.meas.ncsu.edu/~helena/gmslab/>GMSL/University of Illinois at
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+Urbana-Champaign</a>
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+
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<p><i>Last changed: $Date$</i>
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