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:
(hu)t+⋯=−γ(hu),
(hv)t+⋯=−γ(hv),
The form built into GeoClaw is the Manning formulation, in which γ is a function of the depth and momentum:
γ=gn2√(hu)2+(hv)2h7/3.
with g the gravitational constant and n the “Manning coefficient”. This is an empirical formula and the proper value of 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 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 Specifying GeoClaw parameters in setrun.py).
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 General geo parameters.
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 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 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.