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Permafrost Modeling - looking at future permafrost with climate models

1.5 hrs
Run online using:

This lab is part of the series Permafrost. Others in this series are:

    Irina Overeem at instaar.

Using the Frost number code and grids of climate model input data (CMIP5), allows you to map predictions of permafrost occurrence. This is lesson 4 in a mini-course on permafrost.

Classroom organization
This lab is the fourth in a series of introduction to permafrost process modeling, designed for inexperienced users. In this lesson, we explore the future of permafrost under a globally changing climate in the CSDMS Python Modeling Tool (Pymt). We implemented a basic configuration of the Air Frost Number (as formulated by Nelson and Outcalt in 1987). This series of labs is designed for inexperienced modelers to gain some experience with running a numerical model, changing model inputs, and analyzing model output. This fourth lab looks at permafrost occurrence trends over the 21st century for different regions in the Arctic

Basic theory on the Air Frost Number is presented in File:FrostNumberModel Lecture1.pptx.

This lab will likely take ~ 1,5 hours to complete in the classroom. Since this is the fourth lab in a mini-series, this estimated time assumes you are familiar with the Pymt and have now learned setting parameters, saving runs, downloading data and looking at output. If this is not the case, either start with Lab 1 in this series, or learn how to use Pymt ( The Pymt allows you to set up simulations and run notebooks.

We will use netcdf files for output, this is a standard output from all CSDMS models. If you have no experience with visualizing these files, Panoply software will be helpful ( Find instructions on how to use this software:

If you are a faculty at an academic institution, it is possible to work with us to get temporary teaching accounts. Work directly with us by emailing:

Download associated file: FrostNumberModel Lecture1.pptx
Basic theory on the Air Frost Number

Learning objectives
  • Use the Air Frost Number Model on Pan-Arctic maps
  • Use the output of global coupled atmosphere-ocean models (CMIP5) to drive a permafrost model
  • hands-on experience with visualizing NetCDF output with Panoply.
Key concepts
  • what is the primary control on the future occurrence of permafrost
  • how changes in global climate affect permafrost
  • learn about the permafrost-carbon feedback mechanism

Lab notes
Soil organic carbon.jpg
The total carbon storage is estimated to be 1035 +/- 150 Pg in the uppermost 3m of the permafrost zone, which means gross average carbon density is ~0.025 +/- 0.004 Pg per km3. If we are conservative, regions with Frost Number > 0.67, which we use here as a threshold for occurrence, declines about 6.68 million km2 by the end of the twenty-first century.
You can launch binder to directly run the Jupyter Notebook for this lab through a web browser.

>> Open a new browser window and open the Pymt read the docs page (

>> You will see that there are several example models.

>> Click on the 'Launch Binder' box and it will allow you to see this lab as a Jupyter Notebook.

>> You can execute the Jupyter notebook code cells using shift -enter.

In this lab we will select the Frost number GEO component as the driving model, we will combine it with temperature data from the CMIP5 climate simulations.

If you have done the previous labs, you now are familiar with the approach of the Air Frost number, it uses the mean annual air temperature of a location (MAAT), as well as the yearly temperature amplitude. In the Air Frost parametrization the mean monthly temperature of the warmest month and coldest month set that amplitude. In the model coupling here we have assumed the warmest month is July and the coldest month is January. The 'degree thawing days' are above 0 C, the 'degree freezing days' are below 0 C. To arrive at the cumulative freezing degree days and thawing degree days, the annual temperature curve is approximated by a cosine as defined by the warmest and coldest months, and one can integrate under the cosine curve (see also in Frost number presentation). The CMIP component is a 'data component' processed from the CRU-NCEP Climate Model Intercomparison Project - 5, also called CMIP 5. Data presented include the mean annual temperature for each gridcell, mean July temperature and mean January temperature over the period 1902 -2100. This dataset presents the mean of all the CMIP5 models, and the original atmosphere ocean models were run for the representative concentration pathway RCP 8.5. In RCP 8.5, greenhouse gas emissions continue to rise throughout the 21st century.

>> Link the Frost number GEO component with the CMIP component >> In the Frost number component parameters adapt the time to start in 1950, for 150 years. Set the model dimensions to xdim=40 and ydim=30. Make sure you request the frost-number-air output file.

>> Then open up the settings for the CMIP5 data component. Make sure you start reading the data from 1950 onwards. Make sure you match the xdim and ydim with the Frost number grid dimensions. In addition, you will need to specify what region in large PanArctic dataset you do want to read. The CMIP5 data are on a half-degree latitude-longitude grid, so it consist of 720 by 360 grid cells. The upper left corner of the grid is at the international date line. For Alaska, set the column offset as 26, and the row offset as 32. Of course, the climate models keep track of 100's of physical variables; for our simple approximation we only need temperature. So this data component is subsampled to only provide monthly air temperature to other components. In the component here, the data is masked to only comprise the present-day permafrost region. The rest of the grid has 'no data' values.

Download the zip file with your simulation output from the run status window. If you unzip the file you will find your output files, we will use the one called ''. You can open this file with Panoply and plot the steady Frost number over 150 years by clicking on the 'create plot' icon

What are typical mean annual temperatures over the North Slope of Alaska in the 1950's?

Do you see much change in the mean annual temperatures at the end of the 21st century?

What does the Frost Number map look like for 1955, and for 2095? What do these specific Frost numbers imply for the likelihood of permafrost occurrence?

We assume that the disappearance of permafrost (as predicted by the Frost number) indeed means all 3m of soil is thawed.

What would be a rough estimation of the amount of new carbon potentially exposed to the global atmosphere and carbon cycle?

How does that amount compare to the total amount of carbon in the atmosphere? (Hint, see Schuur et al., 2015).

Discuss the factors that would make this first-order estimation problematic?


These labs are developed with support from NSF Grant 1503559, ‘Towards a Tiered Permafrost Modeling Cyberinfrastructure’

  • Nelson, F.E., Outcalt, S.I., 1987. A computational method for prediction and prediction and regionalization of permafrost. Arct. Alp. Res. 19, 279–288.
  • Schuur, E. A. G. et al. 2015, Climate change and the permafrost carbon feedback, Nature, 520(7546), 171–179, doi:10.1038/nature14338.
  • Taylor, K. E., R. J. Stouffer, and G. A. Meehl. 2012, An overview of CMIP5 and the experiment design, Bull. Am. Meteorol. Soc., 93(4), 485–498, doi:10.1175/BAMS-D-11-00094.1.
  • Wei, Y., Liu, S., Huntzinger, D. N., Michalak, A. M., Viovy, N., Post, W. M., Schwalm, C. R., Schaefer, K., Jacobson, A. R., Lu, C., Tian, H., Ricciuto, D. M., Cook, R. B., Mao, J., Shi, X., 2014. The North American Carbon Program Multi-scale Synthesis and Terrestrial Model Intercomparison Project – Part 2: Environmental driver data. Geosci. Model Dev., 7, 2875–2893. 10.5194/gmd-7-2875-2014