Permafrost Modeling with Ku Model

1.5 hrs
Run online using:
  1. Jupyter
  2. Lab
     Jupyter logo.png

    Ethan Pierce at University of Colorado Boulder.

Ku output.png

The Kudryavtsev et al. (1974), or Ku model, presents an approximate solution of the Stefan problem. The model provides a steady-state solution under the assumption of sinusoidal air temperature forcing. It considers snow, vegetation, and soil layers as thermal damping to variation of air temperature. The layer of soil is considered to be a homogeneous column with different thermal properties in the frozen and thawed states. The main outputs are annual maximum frozen/thaw depth and mean annual temperature at the top of permafrost (or at the base of the active layer). It can be applied over a wide variety of climatic conditions.

The Ku model is part of the Permamodel Toolbox, see Overeem et al. 2018.

Classroom organization
In this lab, it includes two Jupyter Notebooks. In the first notebook, we will explore the Ku model to simulate the active layer thickness and soil temperature. In the second notebook, we will use the active layer depth results from Ku model to drive a depth-dependent hillslope diffusion model over the Eight Mile Lake study site. The second notebook gives one very simplistic example for how Ku can be used alongside landscape geomorphology models.

Learning objectives
  • Learn how to use "permamodel" Python module to run Ku model
  • Learn to load, rescale, and visualize DEM data in Python.
  • Learn how to use Ku model output and Landlab component to run depth-dependent diffusion model
Key concepts
  • What are important parameters for calculating active layer thickness

Lab notes

This lab can be run on the lab (for educators) and jupyter (for general use) instances of the OpenEarthscape JupyterHub: just click one of the links under the Run online using heading at the top of this page, then run the notebook in the "CSDMS" kernel.

If you don't already have a JupyterHub account, follow the instructions to sign up at If you're an educator, you can get JupyterHub accounts for students--please contact us through the CSDMS Help Desk:

  • Kudryavtsev, V.A. , L.S. Garagulya, K.A. Kondrat'yeva, and V.G. Melamed Fundamentals of Frost Forecasting in Geological Engineering Investigations Nauka, Moscow (1974), p. 431 (in Russian; English translation appears as U.S. Army Cold Regions Research and Engineering Laboratory Draft Translation 606)
  • Overeem, Irina, Jafarov, Elchin, Wang, Kang, Schaefer, Kevin, Stewart, Scott, Clow, Gary, Piper, Mark, and Elshorbany, Yasin, 2018: A Modeling Toolbox for Permafrost Landscapes. Eos, Transactions of the American Geophysical Union (Online).