**-l**- Allows running in lat/lon: dx is f(lat) at grid N-S midpoint
**--overwrite**- Allow output files to overwrite existing files
**--help**- Print usage summary
**--verbose**- Verbose module output
**--quiet**- Quiet module output
**--ui**- Force launching GUI dialog

**method**=*string***[required]**- Solution method: Finite Diff. or Superpos. of analytical sol'ns
- Options:
*FD, SAS* **input**=*name***[required]**- Raster map of loads (thickness * density * g) [Pa]
**te**=*name***[required]**- Elastic thickness: scalar or raster; unis chosen in "te_units"
**te_units**=*string***[required]**- Units for elastic thickness
- Options:
*m, km* **output**=*name***[required]**- Output raster map of vertical deflections [m]
**solver**=*string*- Solver type
- Options:
*direct, iterative* - Default:
*direct* **tolerance**=*float*- Convergence tolerance (between iterations) for iterative solver
- Default:
*1E-3* **northbc**=*string*- Northern boundary condition
- Options:
*0Displacement0Slope, 0Moment0Shear, 0Slope0Shear, Mirror, Periodic, NoOutsideLoads* - Default:
*NoOutsideLoads* **southbc**=*string*- Southern boundary condition
- Options:
*0Displacement0Slope, 0Moment0Shear, 0Slope0Shear, Mirror, Periodic, NoOutsideLoads* - Default:
*NoOutsideLoads* **westbc**=*string*- Western boundary condition
- Options:
*0Displacement0Slope, 0Moment0Shear, 0Slope0Shear, Mirror, Periodic, NoOutsideLoads* - Default:
*NoOutsideLoads* **eastbc**=*string*- Eastern boundary condition
- Options:
*0Displacement0Slope, 0Moment0Shear, 0Slope0Shear, Mirror, Periodic, NoOutsideLoads* - Default:
*NoOutsideLoads* **g**=*float*- gravitational acceleration at surface [m/s^2]
- Default:
*9.8* **ym**=*float*- Young's Modulus [Pa]
- Default:
*65E9* **nu**=*float*- Poisson's ratio
- Default:
*0.25* **rho_fill**=*float*- Density of material that fills flexural depressions [kg/m^3]
- Default:
*0* **rho_m**=*float*- Mantle density [kg/m^3]
- Default:
*3300*

The flexural solution is generated for the current computational region, so be sure to check *g.region* before running the model!

**input** is a 2-D array of loads in a GRASS raster. These are in units of stress, and equal the density of the material times the acceleration due to gravity times the thickness of the column. This is not affected by what you choose for **g**, later: it is pre-calculated by the user.

**te**, written in standard text as T_{e}, is the lithospheric elastic thickness.

Several boundary conditions are available, and these depend on if the solution method is finite difference (FD) or superposition of analytical solutions (SAS). In the latter, it is assumed that there are no loads outside of those that are explicitly listed, so the boundary conditions are "NoOutsideLoads". As this is the implicit case, the boundary conditions all default to this.

The finite difference boundary conditions are a bit more complicated, but are largely self-explanatory:

**0Displacement0Slope**- 0-displacement-0-slope boundary condition
**0Moment0Shear**- "Broken plate" boundary condition: second and third derivatives of vertical displacement are 0. This is like the end of a diving board.
**0Slope0Shear**- First and third derivatives of vertical displacement are zero. While this does not lend itself so easily to physical meaning, it is helpful to aid in efforts to make boundary condition effects disappear (i.e. to emulate the NoOutsideLoads cases)
**Mirror**- Load and elastic thickness structures reflected at boundary.
**Periodic**- "Wrap-around" boundary condition: must be applied to both North and South and/or both East and West. This causes, for example, the edge of the eastern and western limits of the domain to act like they are next to each other in an infinite loop.

All of these boundary conditions may be combined in any way, with the exception of the note for periodic boundary conditions. If one does not want the boundary conditions to affect the solutions, it is recommended that one places the boundaries at least one flexural wavelength away from the load.

*r.flexure* may be run in latitude/longitude coordinates (with the "**-l**" flag), but its grid constraint is that it can have only one *dx* and one *dy* for the entire domain. Thus, it chooses the average *dx* at the midpoint between the northernmost and southernmost latitudes for which the calculations are made. This assumption can break down at the poles, where the East–West dimension rapidly diminishes.

The Community Surface Dynamics Modeling System, into which **gFlex** is integrated, is a community-driven effort to build an open-source modeling infrastructure for Earth-surface processes.

Wickert, A. D., G. E. Tucker, E. W. H. Hutton, B. Yan, and S. D. Peckham (2011), Feedbacks between surface processes and flexural isostasy: a motivation for coupling models, in *CSDMS 2011 Meeting: Impact of time and process scales*, Student Keynote, Boulder, CO.

van Wees, J. D., and S. Cloetingh (1994), A Finite-Difference Technique to Incorporate Spatial Variations In Rigidity and Planar Faults Into 3-D Models For Lithospheric Flexure, *Geophysical Journal International*, *117*(1), 179–195, doi:10.1111/j.1365-246X.1994.tb03311.x.

Available at: r.flexure source code (history)

Latest change: Thu Feb 3 09:32:35 2022 in commit: f17c792f5de56c64ecfbe63ec315307872cf9d5c

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