.. _manning:
==========================
Manning friction term
==========================
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:
:math:`(hu)_t + \cdots = -\gamma (hu),`
:math:`(hv)_t + \cdots = -\gamma (hv),`
The form built into GeoClaw is the Manning formulation, in which
:math:`\gamma` is a function of the depth and momentum:
:math:`\gamma = \frac{gn^2\sqrt{(hu)^2 + (hv)^2}}{h^{7/3}}.`
with :math:`g` the gravitational constant and :math:`n` the "Manning
coefficient". This is an empirical formula and the proper value of
:math:`n` to use depends on the roughness of the terrain or seabed, as shown
for example in
`this table `_.
Often for generic tsunami modeling, the constant value :math:`n=0.025` is used.
An enhancement of GeoClaw planned for the future is to allow
spatially-varying Manning coefficient.
The friction term is only applied in regions where the depth is below a
threshold specified by *friction_depth* (see :ref:`setrun_geoclaw`).
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 :ref:`setrun_geo`.
.. warning:: 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 :math:`n` (less friction) will generally
lead to greater inundation.
.. warning:: 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 :math:`n` 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.