# Model help:Erode-D8-Global

## Erode-D8-Global

Erode is a Fluvial Landscape Evolution Model

## Model Introduction

Erode-D8-Global is a raster, D8-based fluvial landscape evolution model (LEM). The original version was written in 2004 in IDL (Interactive Data Language). In support of an NSF-funded CMG grant, it has been converted from IDL to Python using I2PY 2.0, then refactored to have an IRF interface and wrapped as a CSDMS/CCA component. The current version makes use of the Numerical Python package to achieve performance similar to the IDL version. Results can now be saved as "grid stacks", or a sequence of spatial grids indexed by time, in netCDF format and then viewed with VisIt and other visualization packages. It is possible to save elevations (z), slopes (S), upstream areas (A), discharges (Q) and sediment discharges (Qs) as grid stacks.

Erode uses another component called D8-Global that is currently visible in the palette but which does not need to be coupled to ErodeGlobal within the CMT. The D8-Global component can perform many other tasks related to working with D8 flow grids, including their extraction from a DEM and the creation of contributing area grids, etc.

As a raster-based, CSDMS/CCA compliant component with an IRF interface, it can easily be linked to other raster models such as a distributed hydrologic model.

There is another, experimental implementation of the Erode model called Erode-D8-Local, also visible in the palette, that uses an algorithm based on local vs. global timesteps. It will have its own help page soon.

## Model parameters

Parameter Description Unit
component status component status enabled/Disabled
Input directory -
Output directory -
Site prefix prefix for the study site -
Case prefix prefix for a given scenario -
Number of steps number of time step -
Grid nx number of columns in DEM -
Grid ny number of rows in DEM -
Grid cell dx grid cell xsize m
Grid cell dy grid cell ysize m
Parameter Description Unit
CFL factor prefactor for CFL stability condition -
Area exponent area exponent -
Slope exponent -
Erodibility -
Q-A exponent -
Mean rainrate geomorphically effective rainrate m/yr
Mean uplift rate mm/yr
Base lowering rate base-level lowering rate mm/yr
BC method boundary-condition method (Bottom/Right/Four-sides) -
Fill pits toggle option to fill pits in each DEM -
Parameter Description Unit
make z0 method method to make initial DEM (Flat/Plane/Corner_Plane/Read_file) -
z0 plane dz/dx dz/dx for make_z0_method = PLANE m/m
z0 plane dz/dy dz/dy for make_z0_method = PLANE m/m
z0 filename filename for make_z0_method = READ_FILE -
Noise method (Midpoints, Gaussian, O_Noise) -
Random seed random number seed (long int) -
Parameter Description Unit
Save grid dt time interval between saved grids years
Save z grids toggle option to save computed z grids (Yes/No) m / m
Save z grids file filename for z grid stack -
Save S grids toggle option to save computed S grids (Yes/No) -
Save S grids file filename for S grid stack -
Save A grids toggle option to save computed A grids (Yes/No) -
Save A grids file filename for A grid stack -
Save Q grids toggle option to save computed Q grids (Yes/No) -
Save Q grids file filename for Q grid stack -
Parameter Description Unit
Save time series dt time interval between time series values years
Save z time series toggle option to save computed z time series (Yes/No) -
Save z pixels file filename for time series of z -
Save S time series toggle option to save computed S time series (Yes/No) -
Save S pixels file filename for time series of S -
Save A time series toggle option to save computed A time series (Yes/No) -
Save A pixels file filename for time series of A -
Save Q time series toggle option to save computed Q time series (Yes/No) -
Save Q pixels file filename for time series of Q -
Save Qs time series toggle option to save computed Qs time series (Yes/No) -
Save Qs pixels file filename for time series of Qs -

## Uses ports

• Meteorology (shown, but not used yet)
• Uplift (shown, but not used yet)

## Provides ports

• LEM (Landscape Evolution Model)

## Main equations

• Change in elevation at a grid cell in one timestep (m)
 $\displaystyle{ \Delta z = [ U + \left ( -Q_{out} + \Sigma Q_{in} \right ) / \left ( \Delta x \Delta y \right ) ] \cdot \Delta t }$ (1)
• Water discharge
 $\displaystyle{ Q = R \cdot A^p }$ (2)
 $\displaystyle{ Q_{s} = K \cdot Q^m \cdot S^n }$ (3)

## Notes

All variables and their units can be seen by expanding the Nomenclature section above.

Equation (1) above is just conservation of mass for sediment, often referred to as Exner's equation. It states that the change in elevation at any grid cell is determined by the net amount of sediment that flows into and out of the grid cell. If more flows in than out, then (Δ z > 0) and sediment is deposited. Otherwise, (Δ z < 0) and erosion occurs in that cell. Transport rates for water, Q, and sediment, Qs, are parameterized with grids of slope, S, and upstream contributing area, A. (See equations (2) and (3).) Values of the exponents m and n are both typically between 1 and 2. If the uplift rate, U, is greater than 0, then it is as if additional sediment is being deposited in a grid cell at that rate. The typical grid cell dimensions are 10 to 500 meters and typical simulated times are 1000 to 100,000 years. Longitudinal profiles (elevations along streamlines) tend to be concave down for some time as drainage networks are formed and then eventually become concave up.

Erode provides several different ways to create an initial elevation grid at the start of a simulation, including flat or tilted planes, with or without added noise. The currently available methods are called: FLAT, PLANE, CORNER_PLANE and READ_FILE. Methods for adding noise to the initial surface include: GAUSSIAN (uncorrelated normal random variables), MIDPOINTS (create a fractal surface using midpoint replacement algorithm) and NO_NOISE. A scale factor can be applied to the noise and the seed for the random number generator can be specified (for reproducibility of model runs). Depressions are filled in the initial elevation grid prior to the simulation and can optionally be filled at each timestep. By default, however, Erode allows depressions to be filled naturally by sediment deposition so that the landscape evolves to a depressionless or "hydrologically sound" state.

Base-level lowering can be specified to occur on all four sides (FOUR_SIDES), on the bottom side (BOTTOM) or the right side (RIGHT). In the latter two cases, "side boundaries" are periodic. Elevation values for grid cells that lie within the set of "base-level grid cells" (e.g. those on an edge) are changed by this rate.

In the GUI dialog, basic model parameters are organized under the "Input Parameters" tab, initial surface parameters are under the "Z0 Method" tab and output options are under the "Output" tab.

Coming soon!

• Coming soon!