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<section id="manning-friction-term">
<span id="manning"></span><h1>Manning friction term<a class="headerlink" href="#manning-friction-term" title="Permalink to this heading">¶</a></h1>
<p>When using GeoClaw to model inundation, it is important to include an
appropriate bottom friction term in the equations. This takes the form of a
source term added to the right hand side of
the momentum equations:</p>
<blockquote>
<div><p><span class="math notranslate nohighlight">\((hu)_t + \cdots = -\gamma (hu),\)</span></p>
<p><span class="math notranslate nohighlight">\((hv)_t + \cdots = -\gamma (hv),\)</span></p>
</div></blockquote>
<p>The form built into GeoClaw is the Manning formulation, in which
<span class="math notranslate nohighlight">\(\gamma\)</span> is a function of the depth and momentum:</p>
<blockquote>
<div><p><span class="math notranslate nohighlight">\(\gamma = \frac{gn^2\sqrt{(hu)^2 + (hv)^2}}{h^{7/3}}.\)</span></p>
</div></blockquote>
<p>with <span class="math notranslate nohighlight">\(g\)</span> the gravitational constant and <span class="math notranslate nohighlight">\(n\)</span> the “Manning
coefficient”. This is an empirical formula and the proper value of
<span class="math notranslate nohighlight">\(n\)</span> to use depends on the roughness of the terrain or seabed, as shown
for example in
<a class="reference external" href="http://www.engineeringtoolbox.com/mannings-roughness-d_799.html">this table</a>.
Often for generic tsunami modeling, the constant value <span class="math notranslate nohighlight">\(n=0.025\)</span> is used.
An enhancement of GeoClaw planned for the future is to allow
spatially-varying Manning coefficient.</p>
<p>The friction term is only applied in regions where the depth is below a
threshold specified by <em>friction_depth</em> (see <a class="reference internal" href="setrun_geoclaw.html#setrun-geoclaw"><span class="std std-ref">Specifying GeoClaw parameters in setrun.py</span></a>).</p>
<p>New in 5.0: A list of Manning coefficients can be specifed to be used in
different regions based on the topography B, e.g. one value offshore and a
different value onshore. See <a class="reference internal" href="setrun_geoclaw.html#setrun-geo"><span class="std std-ref">General geo parameters</span></a>.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>Changing the Manning coefficient can have a significant effect
on the extent of inundation and runup. If GeoClaw (or any other code) is
used for estimating real-world hazards, users should think carefully
about chosing an appropriate value, and may want to run sensitivity
studies. A smaller value of <span class="math notranslate nohighlight">\(n\)</span> (less friction) will generally
lead to greater inundation.</p>
</div>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>A bug was recently discovered in GeoClaw that was corrected
in Version 4.6.3: The exponent (7/3) was used in the Fortran code, which
evaluates as 2 in integer arithmetic rather than 2.3333. This has now
been corrected by writing it as (7.d0/3.d0). This can make a difference in
the extent of inundation and runup. Given the uncertainty in the proper
value of <span class="math notranslate nohighlight">\(n\)</span> to use and the inadequacy of using the same value
everywhere, the effect of this bug on the resulting accuracy was probably
small, but users may want to test this.</p>
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