[GRASS-SVN] r59445 - grass-addons/grass7/raster/r.stream.order

[svn_grass at osgeo.org]

Author: martinl
Date: 2014-03-27 09:54:50 -0700 (Thu, 27 Mar 2014)
New Revision: 59445

Modified:
   grass-addons/grass7/raster/r.stream.order/r.stream.order.html
Log:
r.stream.order: manual syntax clean up


Modified: grass-addons/grass7/raster/r.stream.order/r.stream.order.html
===================================================================
--- grass-addons/grass7/raster/r.stream.order/r.stream.order.html	2014-03-27 16:48:35 UTC (rev 59444)
+++ grass-addons/grass7/raster/r.stream.order/r.stream.order.html	2014-03-27 16:54:50 UTC (rev 59445)
@@ -1,216 +1,282 @@
 <h2>DESCRIPTION</h2>
 
+The <em>r.stream.order</em> calculates Strahler's and more streams
+hierarchy. It's a basic module for topological analysis of drainage
+network.
+
 <h2>OPTIONS</h2>
 <dl>
 <dt><b>-z</b></dt>
-<dd>Creates zero-value background instead of NULL. For some reason (like map
-algebra calculation) zero-valued background may be required. This flag produces
-zero-filled background instead of null (default).</dd>
+<dd>Creates zero-value background instead of NULL. For some reason
+(like map algebra calculation) zero-valued background may be
+required. This flag produces zero-filled background instead of null
+(default).</dd>
 <dt><b>-a</b></dt>
-<dd>Uses accumulation map instead of cumulated stream length to determine main
-branch at bifurcation. Works well only with SFD networks</dd>
+<dd>Uses accumulation map instead of cumulated stream length to
+determine main branch at bifurcation. Works well only with SFD
+networks</dd>
 <dt><b>-m</b></dt>
-<dd>Only for very large data sets. Use segment library to optimise memory
-consumption during analysis</dd>
+<dd>Only for very large data sets. Use segment library to optimise
+memory consumption during analysis</dd>
 <dt><b>stream_rast</b></dt>
-<dd>Name of input stream map on which ordering will be performed produced by
-r.watershed or r.stream.extract. Because streams network produced by r.watershed
-and r.stream.extract may slightly differ in detail it is required to 
-use both stream and direction map produced by the same module. Stream background
-shall have NULL value or zero value. 
-Background values of NULL are by default produced by r.watershed and
-r.stream.extract. If not 0 or NULL use <a href="r.mapcalc.html">r.mapcalc</a> to
-set background values to null.  
+<dd>Name of input stream map on which ordering will be performed
+produced by <em><a href="r.watershed.html">r.watershed</a></em> or
+<em><a href="r.stream.extract.html">r.stream.extract</a></em>. Because
+streams network produced
+by <em><a href="r.watershed.html">r.watershed</a></em> and
+<em><a href="r.stream.extract.html">r.stream.extract</a></em> may
+slightly differ in detail it is required to use both stream and
+direction map produced by the same module. Stream background shall
+have NULL value or zero value. Background values of NULL are by
+default produced by <em><a href="r.watershed.html">r.watershed</a></em> or
+<em><a href="r.stream.extract.html">r.stream.extract</a></em>. If not
+0 or NULL use <em><a href="r.mapcalc.html">r.mapcalc</a></em> to set background
+values to null.
 </dd>
 <dt><b>direction</b></dt>
-<dd>Name of input direction map produced by r.watershed or r.stream.extract. If
-r.stream.extract output map is used, it only has non-NULL values in places where
-streams occur. NULL (nodata) cells are ignored, zero and negative values are
-valid direction data if they vary from -8 to 8 (CCW from East in steps of 45
-degrees). Direction map shall be of type CELL values. Region resolution and map
-resolution must be the same. 
-Also <em>stream</em> network and <em>direction</em> maps must have the same
-resolution. It is checked by default. If resolutions differ the module informs
-about it and stops. Region boundary
-and maps boundary may be differ but it may lead to unexpected results.</dd>
+<dd>Name of input direction map produced by <em><a href="r.watershed.html">r.watershed</a></em> or
+<em><a href="r.stream.extract.html">r.stream.extract</a></em>. If
+<em><a href="r.stream.extract.html">r.stream.extract</a></em> output
+map is used, it only has non-NULL values in places where streams
+occur. NULL (nodata) cells are ignored, zero and negative values are
+valid direction data if they vary from -8 to 8 (CCW from East in steps
+of 45 degrees). Direction map shall be of type CELL values. Region
+resolution and map resolution must be the same.
+Also <b>stream_rast</b> network and <b>direction</b> maps must have
+the same resolution. It is checked by default. If resolutions differ
+the module informs about it and stops. Region boundary and maps
+boundary may be differ but it may lead to unexpected results.</dd>
 <dt><b>accumulation</b></dt>
-<dd>Flow accumulation (optional, not recommended): name of flow accumulation
-file produced by r.watershed or used in r.stream.extract. This map is an option
-only if Horton's or Hack's ordering is performed. Normally both Horton and Hack
-ordering is calculated on cumulative stream length which is calculated
-internally. Flow accumulation can be used if user want to calculate main stream
-as most accumulated stream. Flow accumulation map shall be of DCELL type, as is
-by default produced by r.watershed or converted do DCELL with r.mapcalc.</dd>
+<dd>Flow accumulation (optional, not recommended): name of flow
+accumulation file produced by <em><a href="r.watershed.html">r.watershed</a></em> or
+<em><a href="r.stream.extract.html">r.stream.extract</a></em>. This
+map is an option only if Horton's or Hack's ordering is
+performed. Normally both Horton and Hack ordering is calculated on
+cumulative stream length which is calculated internally. Flow
+accumulation can be used if user want to calculate main stream as most
+accumulated stream. Flow accumulation map shall be of DCELL type, as
+is by default produced by r.watershed or converted do DCELL with
+<em><a href="r.mapcalc.html">r.mapcalc</a></em>.</dd>
 <dt><b>elevation</b></dt>
 <dd>Used to calculate geometrical properties of the network stored in the
 table.</dd>
 </dl>
-<h2>OUTPUTS</h2>
 
-<p>At least one output map is required: </p>
+<h3>OUTPUTS</h3>
+
+<p>At least one output map is required:
+
 <dl>
 <dt><b>stream_vect</b></dt>
-<dd>Vector network with table where stream network topology can be stored.
-Because r.stream.order is prepared to work both with r.watershed and
-r.stream.extract, it may be used to create correct vector from r.watershed
-results.<dd>
+<dd>Vector network with table where stream network topology can be
+stored. Because <em><a href="r.stream.order.html">r.stream.order</a></em>
+is prepared to work both with <em><a href="r.watershed.html">r.watershed</a></em> or
+<em><a href="r.stream.extract.html">r.stream.extract</a></em>, it may
+be used to create correct vector
+from <em><a href="r.watershed.html">r.watershed</a></em> results.<dd>
 
 <dt><b>strahler</b></dt>
-<dd>Name of Strahler's stream order output map: see notes for detail. </dd>
+<dd>Name of Strahler's stream order output map: see notes for
+detail. </dd>
 
 <dt><b>shreve</b></dt>
 <dd>Name of Shreve's stream magnitude output map: see notes for detail.</dd>
 
 <dt><b>horton</b></dt>
-<dd>Name of Horton's stream order output map (require accum file): see notes for
-detail.</dd>
+<dd>Name of Horton's stream order output map (require accum file): see
+notes for detail.</dd>
 
 <dt><b>hack</b></dt>
-<dd>Name of Hack's main streams output map : see notes for detail.</dd>
+<dd>Name of Hack's main streams output map : see notes for
+detail.</dd>
 
 <dt><b>topo</b></dt>
 <dd>Name of topological dimensions streams output map: see notes for
 detail.</dd>
 </dl>
 
-<h3>Stream ordering example:</h3>
+<h2>NOTES</h2>
+
+Module can work only if direction map, stream map and region map has
+same settings. It is also required that stream map and direction map
+come from the same source. For lots of reason this limitation probably
+cannot be omitted. This means if stream map comes from
+<em><a href="r.stream.extract.html">r.stream.extract</a></em> also
+direction map
+from <em><a href="r.stream.extract.html">r.stream.extract</a></em>
+must be used. If stream network was generated with MFD method also MFD
+direction map must be used. Nowadays f direction map comes from
+<em><a href="r.stream.extract.html">r.stream.extract</a></em> must be
+patched by direction map
+from <em><a href="r.watershed.html">r.watershed</a></em>. (with <em><a href="r.patch.html">r.patch</a></em>).
+
+<h3>Stream ordering example</h3>
 <center>
 <img src="orders.png" border="1"><br>
 </center>
 
-<p>
 <h4>Strahler's stream order</h4>
-Strahler's stream order is a modification of Horton's streams order which fixes
-the ambiguity of Horton's ordering. 
-In Strahler's ordering the main channel is not determined; instead the ordering
-is based on the hierarchy of tributaries. The 	
-ordering follows these rules:
+
+Strahler's stream order is a modification of Horton's streams order
+which fixes the ambiguity of Horton's ordering. In Strahler's
+ordering the main channel is not determined; instead the ordering is
+based on the hierarchy of tributaries. The ordering follows these
+rules:
+
 <ol>
 <li>if the node has no children, its Strahler order is 1.
-<li>if the node has one and only one tributary with Strahler greatest order i,
-and all other tributaries have order less than i, then the order remains i.
-<li>if the node has two or more tributaries with greatest order i, then the
-Strahler order of the node is i + 1.
+<li>if the node has one and only one tributary with Strahler greatest
+order i, and all other tributaries have order less than i, then the
+order remains i.
+<li>if the node has two or more tributaries with greatest order i,
+then the Strahler order of the node is i + 1.
 </ol>
-Strahler's stream ordering starts in initial links which assigns order one. It
-proceeds downstream. At every node it verifies that there are at least 2 equal
-tributaries with maximum order. If not it continues with highest order, if yes
-it increases the node's order by 1 and continues downstream with new order. 
-<br>
-<b>Advantages and disadvantages of Strahler's ordering: </b>
- Strahler's stream order has a good mathematical background. All catchments with
-streams in this context are directed graphs, oriented from the root towards the
-leaves. Equivalent definition of the Strahler number of a tree is that it is the
-height of the largest complete binary tree that can be homeomorphically embedded
-into the given tree; the Strahler number of a node in a tree is equivalent to
-the height of the largest complete binary tree that can be embedded below that
-node. The disadvantage of that methods is the lack of distinguishing a main
-channel which may interfere with the analytical process in highly elongated
-catchments
+Strahler's stream ordering starts in initial links which assigns order
+one. It proceeds downstream. At every node it verifies that there are
+at least 2 equal tributaries with maximum order. If not it continues
+with highest order, if yes it increases the node's order by 1 and
+continues downstream with new order.
 
+<h4>Advantages and disadvantages of Strahler's ordering</h4>
+
+Strahler's stream order has a good mathematical background. All
+catchments with streams in this context are directed graphs, oriented
+from the root towards the leaves. Equivalent definition of the
+Strahler number of a tree is that it is the height of the largest
+complete binary tree that can be homeomorphically embedded into the
+given tree; the Strahler number of a node in a tree is equivalent to
+the height of the largest complete binary tree that can be embedded
+below that node. The disadvantage of that methods is the lack of
+distinguishing a main channel which may interfere with the analytical
+process in highly elongated catchments
+
 <h4>Horton's stream ordering</h4>
-Horton's stream order applies to the stream as a whole but not to segments or
-links since the order on any channel remains unchanged from source till it
-"dies" in the higher order stream or in the outlet of the catchment. The main
-segment of the catchment gets the order of the whole catchment, while its
-tributaries get the order of their own subcatchments. The main difficulties of
-the Horton's order are criteria to be considered to distinguish between "true"
-first order segments and extension of higher order segments. That is the reason
-why Horton's ordering has rather historical sense and is substituted by the more
-unequivocal Strahler's ordering system. There are no natural algorithms to order
-stream network according to Horton' paradigm. The algorithm used in
-r.stream.order requires to first calculate Strahler's stream order (downstream)
-and next recalculate to Horton ordering (upstream). To make a decision about
-proper ordering it uses first Strahler ordering, and next, if both branches have
-the same orders it uses flow accumulation to choose the actual link. The
-algorithm starts with the outlet, where the outlet link is assigned the
-corresponding Strahler order. Next it goes upstream and determines links
-according to Strahler ordering. If the orders of tributaries differ, the
-algorithm proceeds with the channel of highest order, if all orders are the
-same, it chooses that one with higher flow length rate or higher catchment area
-if accumulation is used. When it reaches the initial channel it goes back to the
-last undetermined branch, assign its Strahler order as Horton order and goes
-upstream to the next initial links. In that way stream orders remain unchanged
-from the point where Horton's order have been determined to the source. 
+
+Horton's stream order applies to the stream as a whole but not to
+segments or links since the order on any channel remains unchanged
+from source till it "dies" in the higher order stream or in the outlet
+of the catchment. The main segment of the catchment gets the order of
+the whole catchment, while its tributaries get the order of their own
+subcatchments. The main difficulties of the Horton's order are
+criteria to be considered to distinguish between "true" first order
+segments and extension of higher order segments. That is the reason
+why Horton's ordering has rather historical sense and is substituted
+by the more unequivocal Strahler's ordering system. There are no
+natural algorithms to order stream network according to Horton'
+paradigm. The algorithm used in r.stream.order requires to first
+calculate Strahler's stream order (downstream) and next recalculate to
+Horton ordering (upstream). To make a decision about proper ordering
+it uses first Strahler ordering, and next, if both branches have the
+same orders it uses flow accumulation to choose the actual link. The
+algorithm starts with the outlet, where the outlet link is assigned
+the corresponding Strahler order. Next it goes upstream and determines
+links according to Strahler ordering. If the orders of tributaries
+differ, the algorithm proceeds with the channel of highest order, if
+all orders are the same, it chooses that one with higher flow length
+rate or higher catchment area if accumulation is used. When it reaches
+the initial channel it goes back to the last undetermined branch,
+assign its Strahler order as Horton order and goes upstream to the
+next initial links. In that way stream orders remain unchanged from
+the point where Horton's order have been determined to the source.
   
-<br>
-<b>Advantages and disadvantages of Horton's ordering:</b> 
-The main advantages of Horton's ordering is that it produces natural stream
-ordering with main streams and its tributaries. The main disadvantage is that it
-requires prior Strahler's ordering. In some cases this may result in unnatural
-ordering, where the highest order will be ascribed not to the channel with
-higher accumulation but to the channel which leads to the most branched parts of
-the catchment. 
-<p>
+<h4>Advantages and disadvantages of Horton's ordering</h4> 
+
+The main advantages of Horton's ordering is that it produces natural
+stream ordering with main streams and its tributaries. The main
+disadvantage is that it requires prior Strahler's ordering. In some
+cases this may result in unnatural ordering, where the highest order
+will be ascribed not to the channel with higher accumulation but to
+the channel which leads to the most branched parts of the catchment.
+
 <h4>Shreve's stream magnitude</h4>
-That ordering method is similar to Consisted Associated Integers proposed by
-Scheidegger. It assigns magnitude of 1 for every initial channel. The magnitude
-of the following channel is the sum of magnitudes of its tributaries. The number
-of a particular link is the number of initials which contribute to it. 
 
+That ordering method is similar to Consisted Associated Integers
+proposed by Scheidegger. It assigns magnitude of 1 for every initial
+channel. The magnitude of the following channel is the sum of
+magnitudes of its tributaries. The number of a particular link is the
+number of initials which contribute to it.
+
 <h4>Scheidegger's stream magnitude</h4>
-That ordering method is similar to Shreve's stream magnitude. It assigns
-magnitude of 2 for every initial channel. The magnitude of the following channel
-is the sum of magnitudes of its tributaries. The number of a particular link is
-the number of streams -1 contributing to it. Consisted Associated Integers
-(Scheidegger) is available only in attribute table. To achieve Consisted
-Associated Integers (Scheidegger) raster the result of Shreve's magnitude is to
-be multiplied by 2: 
-<p>
-<code>r.mapcalc scheidegger=shreve*2</code>
-<p>
+
+That ordering method is similar to Shreve's stream magnitude. It
+assigns magnitude of 2 for every initial channel. The magnitude of the
+following channel is the sum of magnitudes of its tributaries. The
+number of a particular link is the number of streams -1 contributing
+to it. Consisted Associated Integers (Scheidegger) is available only
+in attribute table. To achieve Consisted Associated Integers
+(Scheidegger) raster the result of Shreve's magnitude is to be
+multiplied by 2:
+
+<div class="code"><pre>
+r.mapcalc scheidegger=shreve*2
+</pre></div>
+
 <h4>Drwal's stream hierarchy (old style)</h4>
-That ordering method is a compromise between Strahler ordering and Shreve
-magnitude. It assigns order of 1 for every initial channel. The order of the
-following channel is calculated according Strahler formula, except, that
-streams which do not increase order of next channel are not lost. To increase
-next channel to the higher order R+1 are require two channels of order R, or
-one R and two R-1 or one R, and four R-2 or one R, one R-1 and two R-2 etc. The
-order of particular link show the possible value of Strahler'order if the
-network was close to idealised binary tree. Drwal's order is aviallable only in
-attribute table.To achieve Drwal's raster the result of Shreve's magnitude is
-to be recalculated according formula: <b>floor(log(shreve,2))+1</b>
-<p>
-<code>r.mapcalc drwal=int(log(shreve,2))+1</code>
-<p>
-<b>Advantages and disadvantages of Drwal's hierarhy:</b> 
-The main advantages of Drwal's hierarchy is that it produces natural stream
-ordering with which takes into advantage both ordering and magnitude. It shows
-the real impact of particular links of the network run-off. The main
-disadvantage is that it minimise bifuraction ratio of the network.
 
-<p>
+That ordering method is a compromise between Strahler ordering and
+Shreve magnitude. It assigns order of 1 for every initial channel. The
+order of the following channel is calculated according Strahler
+formula, except, that streams which do not increase order of next
+channel are not lost. To increase next channel to the higher order R+1
+are require two channels of order R, or one R and two R-1 or one R,
+and four R-2 or one R, one R-1 and two R-2 etc. The order of
+particular link show the possible value of Strahler'order if the
+network was close to idealised binary tree. Drwal's order is
+aviallable only in attribute table.To achieve Drwal's raster the
+result of Shreve's magnitude is to be recalculated according
+formula: <tt>floor(log(shreve,2))+1</tt>
+
+<div class="code"><pre>
+r.mapcalc drwal=int(log(shreve,2))+1
+</pre></div>
+
+<h4>Advantages and disadvantages of Drwal's hierarhy</h4> 
+
+The main advantages of Drwal's hierarchy is that it produces natural
+stream ordering with which takes into advantage both ordering and
+magnitude. It shows the real impact of particular links of the network
+run-off. The main disadvantage is that it minimise bifuraction ratio
+of the network.
+
 <h4>Hack's main streams or Gravelius order</h4>
-This method of ordering calculates main streams of main catchment and every
-subcatchments. Main stream of every catchment is set to 1, and consequently all
-its tributaries receive order 2. Their tributaries receive order 3 etc. The
-order of every stream remains constant up to its initial link. The route of
-every main stream is determined according to the maximum flow length value of
-particular streams. So the main stream of every subcatchment is the longest
-stream or stream with highest accumulation rate if accumulation map is used. In
-most cases the main stream is the longest watercourse of the catchment, but in
-some cases, when a catchment consists of both rounded and elongated
-subcatchments these rules may not be maintained. The algorithm assigns 1 to
-every outlets stream and goes upstream according to maximum flow accumulation of
-every branch. When it reaches an initial stream it step back to the first
-unassigned confluence. It assigns order 2 to unordered tributaries and again
-goes upstream to the next initial stream. The process runs until all branches of
-all outlets are ordered. 
-<br>
-<b>Advantages and disadvantages of main stream ordering:</b>
-The biggest advantage of that method is the possibility to compare and analyze
-topology upstream, according to main streams. Because all tributaries of main
-channel have order of 2, streams can be quickly and easily filtered and its
-proprieties and relation to main stream determined. The main disadvantage of
-that method is the problem with the comparison of subcatchment topology of the
-same order. Subcatchments of the same order may be both highly branched and
-widespread in the catchment area and a small subcatchment with only one stream. 
+
+This method of ordering calculates main streams of main catchment and
+every subcatchments. Main stream of every catchment is set to 1, and
+consequently all its tributaries receive order 2. Their tributaries
+receive order 3 etc. The order of every stream remains constant up to
+its initial link. The route of every main stream is determined
+according to the maximum flow length value of particular streams. So
+the main stream of every subcatchment is the longest stream or stream
+with highest accumulation rate if accumulation map is used. In most
+cases the main stream is the longest watercourse of the catchment, but
+in some cases, when a catchment consists of both rounded and elongated
+subcatchments these rules may not be maintained. The algorithm assigns
+1 to every outlets stream and goes upstream according to maximum flow
+accumulation of every branch. When it reaches an initial stream it
+step back to the first unassigned confluence. It assigns order 2 to
+unordered tributaries and again goes upstream to the next initial
+stream. The process runs until all branches of all outlets are
+ordered.
+
+<h4>Advantages and disadvantages of main stream ordering</h4>
+
+The biggest advantage of that method is the possibility to compare and
+analyze topology upstream, according to main streams. Because all
+tributaries of main channel have order of 2, streams can be quickly
+and easily filtered and its proprieties and relation to main stream
+determined. The main disadvantage of that method is the problem with
+the comparison of subcatchment topology of the same
+order. Subcatchments of the same order may be both highly branched and
+widespread in the catchment area and a small subcatchment with only
+one stream.
+
 <h4>Topological dimension streams order</h4>
-This method of ordering calculates topological distance of every stream from
-catchment outlet.
-<br>
 
+This method of ordering calculates topological distance of every
+stream from catchment outlet.
+
 <h4>Stream network topology table description connected with vector file</h4>
+
 <ul>
 	<li><b>cat</b> integer: category;
 	<li><b>stream</b>integer: stream number, usually equal to cat;
@@ -239,16 +305,6 @@
 	<li><b>out_drop</b> double precision: drop at the outlet of the stream;
 	<li><b>gradient</b> double precision: drop/length;
 </ul>
-<h2>NOTES</h2>
-<p>
-Module can work only if direction map, stream map and region map has same
-settings. It is also required that stream map and direction map come from the
-same source. For lots of reason this limitation probably cannot be omitted. This
-means if stream map comes from r.stream.extract also direction map from
-r.stream.extract must be used. If stream network was generated with MFD method
-also MFD direction map must be used. Nowadays f direction map comes from
-r.stream.extract  must be patched by direction map from r.watershed. (with
-r.patch). 
 
 <h2>EXAMPLE</h2>
 
@@ -262,6 +318,30 @@
 r.stream.order stream_rast=streams direction=direction elevation=elevation accumulation=accum stream_vect=river_vector
 </pre></div>
 
+<h2>REFERENCES</h2>
+<ul>
+<li>Drwal, J., (1982), <i>Wyksztalecenie i organizacja sieci hydrograficznej jako
+podstawa oceny struktury odplywu na terenach m;odoglacjalnych</i>, <b>Rozprawy i
+monografie</b>, Gdansk 1982, 130 pp (in Polish)
+<li>Hack, J., (1957), <i>Studies of longitudinal stream profiles in Virginia and
+Maryland</i>, 
+<b>U.S. Geological Survey Professional Paper</b>, 294-B
+<li>Horton, R. E. (1945), <i>Erosional development of streams and their drainage
+basins: hydro-physical approach to quantitative morphology</i>,<b>Geological
+Society of America Bulletin</b> 56 (3): 275-370<br>
+Scheidegger A. E., (1966), <i>Statistical Description of River Networks</i>.
+<b>Water Resour. Res.</b>, 2(4): 785-790
+<li>Shreve, R.,  (1966),<i>Statistical Law of Stream Numbers</i>, <b>J. Geol.</b>,
+74, 17-37.
+<li>Strahler, A. N. (1952), <i>Hypsometric (area-altitude) analysis of erosional
+topology</i>,<b>Geological Society of America Bulletin</b> 63 (11): 1117-1142
+<li>Strahler, A. N. (1957), <i>Quantitative analysis of watershed
+geomorphology</i>,<b>Transactions of the American Geophysical Union</b> 8 (6):
+913-920.
+<li>Woldenberg, M. J., (1967), <i>Geography and properties of surfaces,</i>
+<b>Harvard Papers in Theoretical Geography</b>, 1: 95-189.
+</ul>
+
 <h2>SEE ALSO</h2>
 
 <em>
@@ -269,33 +349,12 @@
 <a href="r.stream.extract.html">r.stream.extract</a>,
 <a href="r.stream.basins.html">r.stream.basins</a>,
 <a href="r.stream.stats.html">r.stream.stats</a>,
-<a href="r.mapcalc.html">r.mapcalc</a>,
+<a href="r.mapcalc.html">r.mapcalc</a>
 </em>
 
-<h2>REFERENCES</h2>
-Drwal, J., (1982), <i>Wykształecenie i organizacja sieci hydrograficznej jako
-podstawa oceny struktury odpływu na terenach młodoglacjalnych</i>, <b>Rozprawy i
-monografie</b>, Gdańsk 1982, 130 pp (in Polish)<p>
-Hack, J., (1957), <i>Studies of longitudinal stream profiles in Virginia and
-Maryland</i>, 
-<b>U.S. Geological Survey Professional Paper</b>, 294-B<p>
-Horton, R. E. (1945), <i>Erosional development of streams and their drainage
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-
 <h2>AUTHOR</h2>
-Jarek  Jasiewicz
+Jarek Jasiewicz
 
-<p><i>Last changed: $Date$</i>
+<p>
+<i>Last changed: $Date$</i>