Set Eta Init – spatially varying initial surface elevation

Prior to Version 5.7.0, GeoClaw had a single scalar parameter sea_level and the water surface is initialized to this value in every cell where the GeoClaw cell-averaged topography value B is smaller, i.e., the water depth in each cell is initialized to:

h[i,j] = max(0, sea_level - B[i,j]).

In some cases it is desirable to initialize the depth so that the surface is spatially varying.

Starting in v5.7.0, the library routine $CLAW/geoclaw/src/2d/shallow/set_eta_init.f90 can be used to set the desired initial water surface eta = B + h in a spacially varying manner. In order to invoke this routine, in you should set:

rundata.qinit_data.variable_eta_init = True

Default behavior, adjusting sea level by seismic deformation

The default library routine $CLAW/geoclaw/src/2d/shallow/set_eta_init.f90 is set up for the use case in which a region subsides or is uplifted by a local earthquake. In tsunami modeling of a nearfield event, the seafloor deformation due to the earthquake often extends onto shore in the region being modeled. If the coastal region subsides, for example, then the land drops near the shore and the water adjacent drops as well. If a grid patch was initialized before the deformation specified in the dtopo file by the formula above, then the depth h[i,j] does not decrease during the subsidence, which is the correct behavior.

However, in some cases the tsunami does not arrive at the shore quickly and so it is desirable to use coarser grids in early stages of the computation, introducing highly refined grids only after some specified time. When new levels of refinement are first introduced into a simulation then the formula given above is used to initialize cells near the coast. But if the coast subsided (or is uplifted), the the formula above should be replaced by:

h[i,j] = max(0, sea_level + dz[i,j] - B[i,j])

where dz[i,j] is obtained by interpolating the co-seismic deformation specified in the dtopo file to the cell center. Failure to do this can sometimes result in large areas being flooded by the initialization that should not be flooded by the tsunami.

The default version of $CLAW/geoclaw/src/2d/shallow/set_eta_init.f90 loops over all (possibly time-dependent) dtopo files and interpolates from these files to the points on the grid patch, at the specified time, to adjust the initial constant sea_level value at each point on the patch.

Note that this set_eta_init function is only called when a grid cell is first initialized at a given AMR level. It is called from qinit.f90 to initialize any patches that exist at the initial time (which may be before the earthquake starts, in which case no adjustment to sea_level would be made).

It is also called if a region is refined to a higher level than previously, but the resulting value is used only in cells where the the water surface level h+B cannot be interpolated from coarser levels, due to the fact that one or more neighboring cells was dry (in which case h+B=B may be huge if the land rises steeply, and using this value in an interpolation of the sea surface would lead to artificially high surface elevation, and hence incorrect depth h when this is computed as eta - B. So such cells near the coast must be filled with water up to the value specified by set_eta_init. In previous versions they were always filled to the level specified by sea_level, but this was incorrect in regions where the water level subsided (or was uplifted) along with the land.

As noted above, this is particularly important in coastal regions where there is seismic deformation but it takes some time for the tsunami to arrive and so the fine grids needed to resolve the region are not introduced until some time after the seismic deformation.

Other use cases

For other uses one can copy the library routine $CLAW/geoclaw/src/2d/shallow/set_eta_init.f90 to the application directory and modify it as desired (and change the Makefile to point to the modified version).

For example, there may be onshore lakes whose initial surface elevation should be different than sea_level. This could be added to the existing routine, so that siesmic displacement of both the offshore water and onshore lakes is also handled, or the dtopo adjustments can be removed if not needed.

When modeling dam break problems, there may one or more lakes of interest at different initial elevations. As an example, to develop a custom routine in the case where a lake behind a dam is desired to be set to one elevation while everywhere else there should be no water, this routine could check the (x,y) location of each cell and set eta_init either to the lake elevation, if in a specified region, or to a very negative value lower than any topography (to force h = 0), when outside the region covered by the lake.