Model:1D Particle-Based Hillslope Evolution Model

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1D Particle-Based Hillslope Evolution Model


Also known as
Model type Single
Model part of larger framework
Note on status model
Date note status model
Incorporated models or components:
Spatial dimensions 1D
Spatial extent Landscape-Scale, Watershed-Scale, Reach-Scale
Model domain Terrestrial, Coastal, Geodynamic
One-line model description 1D probabilistic, particle-based model of hillslope evolution for studying hillslope equilibration and response to perturbations.
Extended model description This module implements a particle-based model of hillslope evolution, which has an associated continuum description (introduced here: The model takes as input a few simple parameters which determine the equilibrium hillslope shape and dynamics, and can be used to produce equilibrium profiles and study the response of the hillslope to perturbations. The model benefits from straightforward implementation, as well as the flexibility to incorporate sophisticated perturbations and to be accessorized by local or nonlocal fluxes.

Hillslope Model, Particle-based, Landscape Evolution,

Name Jacob Calvert
Type of contact Model developer
Institute / Organization University of California, Berkeley
Postal address 1 Department of Statistics
Postal address 2 451 Evans Hall
Town / City Berkeley
Postal code 94709
State California
Country United States
Email address

Supported platforms
Unix, Linux, Mac OS, Windows
Other platform
Programming language


Other program language
Code optimized
Multiple processors implemented
Nr of distributed processors
Nr of shared processors
Start year development 2016
Does model development still take place? Yes
If above answer is no, provide end year model development
Code development status
When did you indicate the 'code development status'?
Model availability As code
Source code availability
(Or provide future intension)
Through CSDMS repository
Source web address
Source csdms web address
Program license type GPL v2
Program license type other
Memory requirements
Typical run time

Describe input parameters The model takes as input (i) p, dynamics asymmetry parameter; (ii) L, the hillslope length; (iii) H, the hillslope height; (iv) N, the number of steps of the simulation; and (v) a choice of initial hillslope profile.
Input format
Other input format
Describe output parameters The model can be customized to produce many different kinds of output but, typically, the output consists of (i) h, a final hillslope profile; (ii) h_diffs, a vector which summarizes how the profile changed over the duration of the simulation; and (iii) a vector expressing the fluxes of particles through a site along the hillslope.

However, the same code can be used to produce a video of the hillslope evolution, a vector containing the absolute difference between the hillslope profile and a reference profile, and many other observables of interest.

Output format
Other output format
Pre-processing software needed? No
Describe pre-processing software
Post-processing software needed? No
Describe post-processing software
Visualization software needed? No
If above answer is yes
Other visualization software

Describe processes represented by the model Overall, the module simulates a particle-based model of hillslope evolution in 1D.

The module contains several scripts and functions, the most important of which are the following. (1) zrp.m is the script wherein the parameters are set and from which the following functions are called. (2) init_x.m is the function which generates an initial profile for the hillslope. (3) make_moves.m is the function which samples the probabilistic dynamics. (4) calc_rates.m is the function which determines the rates at which the particles are moving.

In addition to these, there are the following. (5) perturb.m is the function which implements the hillslope perturbation and is called by the main script. (6) calc_flux.m and calc_fluxes.m are the functions which infer fluxes along the hillslope.

Describe key physical parameters and equations The key physical parameters are the hillslope length and height, as well as a parameter which specifies the underlying asymmetry in the particle dynamics. The process of determining these parameters is described in the simulation section of a corresponding paper (which can be accessed here:
Describe length scale and resolution constraints Although the hillslope length and height are specified, these are dimensionless numbers from the perspective of the module. Accordingly, the resolutions supported by the module are primarily constrained by the language in which it is implemented. However, the process of "dimensionalizing" the module's outputs may place practical constraints on resolution. The associated paper discusses this issue.
Describe time scale and resolution constraints The time scale over which the simulation occurs is specified in zrp.m as an input parameter. Since the module is computationally lightweight, millions of time steps can be simulated quickly.

Translating between discrete steps of the particle model and continuous, real-world time may be inferred during the dimensionalization process.

Describe any numerical limitations and issues

Describe available calibration data sets
Upload calibration data sets if available:
Describe available test data sets
Upload test data sets if available:
Describe ideal data for testing

Do you have current or future plans for collaborating with other researchers?
Is there a manual available? No
Upload manual if available:
Model website if any
Model forum / discussion board
Comments Questions which arise about the module, the model it implements, and the associated theory, may be addressed by the preprint available at

This part will be filled out by CSDMS staff

OpenMI compliant No but possible
BMI compliant No but possible
WMT component No but possible
PyMT component
Is this a data component
DOI model 10.5281/zenodo.1436771
For model version v1.0
Year version submitted 2018
Link to file
Can be coupled with:
Model info
Jacob Calvert

  • Download 1D Particle-Based Hillslope Evolution Model version: v1.0
    Doi: 10.5281/zenodo.1436771
Nr. of publications: 1
Total citations: 1
h-index: 1
m-quotient: 0.17
Qrcode 1D Particle-Based Hillslope Evolution Model.png
Link to this page




Nr. of publications: 1
Total citations: 1
h-index: 1
m-quotient: 0.17

Featured publication(s)YearModel describedType of ReferenceCitations
Calvert, J.; Balázs, M.; Michaelides, K.; 2018. Unifying Particle-Based and Continuum Models of Hillslope Evolution With a Probabilistic Scaling Technique. Journal of Geophysical Research: Earth Surface, 123, 3124–3146. 10.1029/2018JF004612
(View/edit entry)
2018 1D Particle-Based Hillslope Evolution Model
Model overview 1
See more publications of 1D Particle-Based Hillslope Evolution Model



Input Files

Output Files