Thursday, August 13, 2015

Domain Options: Terrain Following vs. Orthogonal Grids

by Lindsay Bearup
Keywords: Terrain Following Grid, Solid Files, Domain Geometry

Manual Location
Defining the Problem – Chapter 3.1
TFG example (Little Washita) – Chapter 3.6.2
TFG formulation – Chapter 5.3
ParFlow Solid Files (.pfsol) – Chapter 6.5

Two primary methods are available for defining the gridded domain of a watershed in ParFlow: orthogonal methods (implemented using solid files) and the terrain following method (TFG). The strengths and limitations of each approach are discussed below.

Depiction of orthogonal (upper) and the terrain following (lower) grid formulations for a topographic land-surface and (left) schematics of the associated finite difference stencils. Note in this figure that ij, and k are the xy, and z cell indices, respectively, and that the limits of the domain would be at i = nxj = ny and k = nz. Note also that nz is different (greater) in the orthogonal formulations (upper) than in the terrain formulation (lower) due to the difference in inactive cells between formulations. Figure from: Maxwell 2013 AWR.

Terrain Following Grid (TFG)
The terrain following grid formulation transforms the ParFlow grid to conform to topography. This formulation can be very useful for coupled surface-subsurface flow problems where groundwater flow follows the topography. This method also requires fewer inputs because it uses the provided surface slope files to determine the geometry. The following key is used to run with TFG and can only be used with Solver Richards (currently not available with Solver Impes): 

pfset Solver.TerrainFollowingGrid           True

TFG is typically applied using a "Box" input type to define the discretization. See the Little Washita example in Chapter 3.6.2 of the ParFlow Manual and the LW_var_dz.tcl script in the ParFlow test directory for an example of the TFG formulation applied to a watershed with a variable vertical discretization. 

pfset GeomInput.domaininput.GeomName  domain
pfset GeomInput.domaininput.InputType  Box 

Solid Files
Solid files rely on traditional orthogonal formulations of the geometry and discretization of the model domain. This approach provides more freedom to define irregular geologic layers and nonuniform watershed depths but requires the user to generate a pfsol file to define active/inactive cells. A solid file is a triangulated information network (TIN) file that defines the domain using a system of points, triangles, and patches. Patches are critical for applying boundary conditions to the domain and are listed in a specific order. For more information regarding solid files and patches, check out the blog entry on patch order here.  A fortran file named pf_solid_file_create.f90 is shipped with ParFlow (v.693 at the time of writing) and is located at $PARFLOW_DIR/pftools/prepostproc. This script can be modified to generate a solid file from a DEM. As written, this script assumes that the rest of the domain is rectangularly shaped and is the same size as the extents of the DEM. The keys required to use a solid file are:
pfset GeomInput.solidinput.InputType  SolidFile
pfset GeomInput.solidinput.GeomNames  domain
pfset GeomInput.solidinput.FileName   name.pfsol

Maxwell, Reed M. A terrain-following grid transform and preconditioned for parallel, large-scale, integrated hydrologic modeling. Advances in Water Resources 53, doi:10.1016/j.advwatres.2012.10.001, 2013.

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