GeoClaw topo_type == 3 is essentially the same as the ESRI ASCII Raster format but it is important to note which grid registration is used. (topo_type == 2 uses the same header conventions, so this discussion also applies to these files.)
The third and fourth lines of the header file contain labels that tell whether the registration is llcorner (lower left corner) or llcenter (lower left center). GeoClaw also recognizes lower, which is currently handled in a way equivalent to llcenter. This is also the assumed default registration if the string is not one of these recognized values.
According to the documentation linked above for ESRI raster format, the topography data given in the file should be viewed as cell averages of the topography over DEM cells of dimension dx by dy where in this format dx = dy and is given by the cellsize parameter. (We use DEM cell to denote the cell in the Digital Elevation Model provided in the topofile, not be be confused with the computational grid cells used by the finite volume method.)
The registration indicates whether the (x,y) (longitude, latitude) value given in the header corresponds to the location of the lower left corner of the SW-most DEM cell, or to the center of this cell. Using the example from Topography data, a file containing:
2 mx 2 my 0. xllcenter 20. yllcenter 10. cellsize -9999 nodatavalue -1000. -2000. -3000. -4000.
would specify DEM cells with centers at (0,30), (10,30), (0,20), (10,20), which are the same points specified in the topo_type == 1 example on Topography data.
By contrast, the file:
2 mx 2 my 0. xllcorner 20. yllcorner 10. cellsize -9999 nodatavalue -1000. -2000. -3000. -4000.
would specify DEM cells with lower left corners at the 4 points listed above, and hence cell centers at (5,35), (15,35), (5,25), (15,25).
In the GeoClaw Fortran code, we assume the DEM values are actually pointwise values and these are used to construct a piecewise bilinear function interpolating these values. This function is then integrated over the computational grid cells in order to get the cell-averaged topography values that are stored in aux(1,:,:) and used in the finite volume method. The computational cells over which this function is integrated can vary as adaptive refinement is performed.
If the topography is smoothly varying, then the cell average over a DEM cell agrees with the pointwise value at the cell center, so for our purpose it is best to view the DEM values as being located at cell centers. Hence if llcorner registration is specified, the lower left corner (and all other (x,y) points spaced according to cellsize) should all be shifted by cellsize/2 in both x and y before being used.
Starting with Version 5.5.0, this is done in the Fortran code when the DEM topofile is read in. It is also done in the Python topotools module at the time of reading the file, so the internal representation has Topography.x and Topography.y corresponding to the cell centers or points where the data should be interpreted in a pointwise view. This is also best when producing contour plots, for example. When writing a topography file using Topography.write(), a new optional argument grid_registration has been added. The (x,y) values in the header will be printed properly based on the registration chosen.
Note that if you use Topography.crop() with a coarsen parameter in order to generate a coarser version of the DEM, this simply subsamples the topography. This followed by Topography.write() should print out the proper llcorner or llcenter value for the coarsened topography based on the location of the subsamples, but crop() does not currently average topography over large cells as the ESRI standard suggests should be done. In the future a coarsen_method parameter might be added to crop() to allow this.
Earlier versions of GeoClaw always viewed the (x,y) value in the header as the location of the SW-most data point, i.e., always assumed llcenter == lower registration. So if you rerun a previous example that had a topofile specifying llcorner in the header, the results may change since the DEM data will now be (more properly) viewed as specified at slightly different points. If you need to try to reproduce your earlier results, you could change llcorner to lower in the header lines, for example.
For GeoClaw topo_type=1, each row contains x, y, z data for a single point and we interpret z as the pointwise data at the specified x, y.
For netCDF files the data points are generally interpreted as pointwise values at the points specified in the lat and lon arrays included in the file (or as cell-averaged values with these points as the cell centers).