fastscapelib.DiffusionADIEroder#

class fastscapelib.DiffusionADIEroder#

Hillslope erosion using linear diffusion.

It numerically solves the diffusion equation using an Alternating Direction Implicit (ADI) scheme.

The equation is given by:

\[\frac{\partial h}{\partial t} = K \nabla^2 h\]

where \(K\) is an erosion coefficient (diffusivity) and \(\nabla^2 h\) is the local curvature of the topographic surface.

This equation implies that the amount of sediment eroded is linearly proportional to the local gradient of the topographic surface.

Notes: only raster grids are supported. This eroder assumes Dirichlet boundary conditions at the border nodes of the raster grid.

__init__(self, grid: RasterGrid, k_coef: float | numpy.ndarray) → None#

DiffusionADIEroder initializer.

Parameters:

  • grid (RasterGrid) – A raster grid instance.

  • k_coef (float or numpy.ndarray) – Spatially uniform or variable erosion coefficient (diffusivity) value. For the spatially variable case, the shape of the array must match the shape of the raster grid.

Methods

__init__(self, grid, k_coef)

DiffusionADIEroder initializer.

erode(elevation, dt)

Slove diffusion for one time step.

Attributes

k_coef

Erosion coefficient (spatially variable or uniform).
erode(elevation: numpy.ndarray, dt: float) → numpy.ndarray#

Slove diffusion for one time step.

Parameters:

  • elevation (numpy.ndarray) – Surface topography elevation at each grid node (shape must match the shape of the raster grid).

  • dt (float) – Duration of the time step.

Returns:

erosion (numpy.ndarray) – Diffusion vertical erosion (> 0) or accumulation (< 0) computed for the time step. Same shape than the input elevation array.

property k_coef#

Erosion coefficient (spatially variable or uniform).