pyTopoComplexity

pytopocomplexity is an open-source Python package designed to measure the topographic complexity (i.e., surface roughness) of land surfaces using digital elevation model (DEM) data. This package includes modules for three methods commonly used in the fields of geomorphology and oceanography for measuring topographic complexity, which are not fully available in Geographic Information System (GIS) software like QGIS.

In this repository, each module has a corresponding example Jupyter Notebook file that includes detailed instructions on module usage and brief explanations of the applied theories with cited references. Example raster file data are included in the ~/example/ folder.

There is also an additional Jupyter Notebook, nonlineardiff_landlab.ipynb, which leverages the power of landlab to perform forward simulation of landscape smoothing through non-linear hillslope diffusion process.

**[!CAUTION] This package is under developement and has not officially released. Use it with caution.**

Installation

pip install pytopocomplexity

Citation

The current version is still a pre-release. If you use the current version of pytopocomplexity and associated Jupyter Notebooks (including nonlinear diffusion simulation) in your work, please cite the Zenodo DOI:

• Lai, L. S.-H. (2024). pyTopoComplexity. Zenodo. https://doi.org/10.5281/zenodo.11239338

Modules for Surface Complexity Measurement

1. pycwtmexhat: 2D Continuous Wavelet Transform Method

from pytopocomplexity import pycwtmexhat

The module pycwtmexhat uses two-dimensional continuous wavelet transform (2D-CWT) with a Mexican Hat wevalet to measure the topographic complexity (i.e., surface roughness) of a land surface from a Digital Elevation Model (DEM). Such method quanitfy the wavelet-based curvature of the surface, which has been proposed to be a effective geomorphic metric for identifying and estimating the ages of historical deep-seated landslide deposits.

The method and early version of the code was developed by Dr. Adam M. Booth (Portland State Univeristy) in 2009, written in MATLAB (Source code available from Booth's personal website). This MATLAB code was later revised and adapted by Dr. Sean R. LaHusen (Univeristy of Washington) and Dr. Erich N. Herzig (Univeristy of Washington) in their research (LaHusen et al., 2020; Herzig et al. (2023)). Dr. Larry Syu-Heng Lai (Univeristy of Washington), under the supervision of Dr. Alison R. Duvall (Univeristy of Washington), translated the code into this optimized open-source Python version in 2024.

See pycwtmexhat_example.ipynb for detailed explanations and usage instructions.

2. pyfracd: Fractal Dimentsion Analysis

from pytopocomplexity import pyfracd

The pyfracd module calculates local fractal dimensions to assess topographic complexity. It also computes reliability parameters such as the standard error and the coefficient of determination (R²). The development of pyfracd is made possible through the gratitude of Dr. Eulogio Pardo-Iguzquiza, who kindly shared his Fortran code used in his recent publication Pardo-Igúzquiza and Dowd (2022).

The local fractal dimension is determined by intersecting the surface within a moving window with four vertical planes in principal geographical directions, simplifying the problem to one-dimensional topographic profiles. The fractal dimension of these profiles is estimated using the variogram method, which models the relationship between dissimilarity and distance using a power-law function. While the fractal dimension value does not directly scale with the degree of surface roughness, smoother or more regular surfaces generally have lower fractal dimension values (closer to 2), whereas surfaces with higher fractal dimension values tend to be more complex or irregular. This method has been applied in terrain analysis for understanding spatial variability in surface roughness, classifying geomorphologic features, uncovering hidden spatial structures, and supporting geomorphological and geological mapping on Earth and other planetary bodies.

See pyfracd_example.ipynb for detailed explanations and usage instructions.

3. pyrugosity: Rugosity Index

from pytopocomplexity import pyrugosity

The module pyrugosity measure rugosity index of the land surface, which is widely used to assess landscape structural complexity. The development of this module is influenced by another open-source tool Rugosity_Calculator created by drk944.

The rugosity index is determined as the ratio of the real surface area to the geometric surface area, highlighting smaller-scale variations in surface height. This module adapt triangulated irregular networks method (Jenness, 2004032[0829:CLSAFD]2.0.CO;2)), which approximate the surface area of with within each 9 cell as the sum of 8 truncated-triangle area connecting each cell centerpoint with the centerpoints of the 8 surrounding cells. The geometric surface area is assumed to be the planimetric area of the center cell. By definition, the rugosity index is as a minimum value of one (completely flate surface). Typical valuesrange from one to three although larger values are possible in very steep terrains. Such method has been applied in classifying seafloor types by marine geologists and geomorphologist, small-scale hydrodynamics by oceanographers, and studying available habitats in the landscape by ecologists and coral biologists.

See pyrugosity_example.ipynb for detailed explanations and usage instructions.

Forward Simulation of Landscape Smoothing by Nonlinear Hillslope Diffusion Process

In the ~/example/ folder, the Jupyter Notebook file nonlineardiff_landlab.ipynb demonstrates the use of landlab, an open-source Python framework for simulating landscape evolution, to model topographic smoothing driven by near-surface soil disturbance and downslope soil creep processes. Specifically, this notebook employs the TaylorNonLinearDiffuser component from LandLab, described as one element in the terrainBento package (developed by Barnhart et al. (2019), to simulate topographic smoothing over time through non-linear hillslope diffusion processes (Roering et al., 1999).

Users need to define the diffusion coefficient (K) for the simulation. The code will automatically detect the units of the XYZ directions (must be in feet or meters) of the input DEM raster file and convert the unit for K accordingly.

[!WARNING] There is a known/unresolved stability issue when running TaylorNonLinearDiffuser component with a DEM with reprojected coordinate reference system (CRS) through GIS softwares. When using the example DEM, users may only use the pre-reprojected DEM with CRS: NAD83/Washington South (ftUS) (EPSG: 2286) and Z unit in US survey feet (e.g., the DEM files named with "_f_3ftgrid" or "_f_6ftgrid").

Example DEM Raster Files

Along with he example Jupyter Notebook files, this repository include example LiDAR DEM files under ~/example/ExampleDEM/ that cover the area and nearby region of a deep-seated landslide occurred in 2014 at Oso area of the North Fork Stillaguamish River (NFSR) valley, Washington State, USA. The souce LiDAR DEM files were compiled from 'Stillaguamish 2014' and 'Snohoco Hazel 2006' projects that was originally contracted by Washington State Department of Transportation (WSDOT), downloaded from the Washington Lidar Portal on April 4, 2024.

A goal of this work allow users to reproduce the research by Booth et al. (2017) and permit comparison of topographic complexity metrics derived from other regions using pytopocomplexity package and the nonlineardiff_landlab.ipynb simulation tools presented in this repository.

The example DEM raster files have various grid size, coordinate reference system (CRS), and unit of grid value (elevation, Z).

[!NOTE] When testing the code with the example DEM files, users should place the entire ~/ExampleDEM/ subfolder in the same directory as the Jupyter Notebook files. Both the pytopocomplexity package and the nonlineardiff_landlab.ipynb land-smoothing modeling tool have the capability to automatically detect the grid spacing and the units of the XYZ directions (must be in feet or meters) of the input DEM raster and compute the results in SI units.

License

pyTopoComplexity is licensed under the Apache License 2.0.