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The PERMAFROST model simulates the flow and storage of heat, and the thermodynamics (ice, brine, and methane hydrate) of a sediment or soil column.

The temperature at the top surface is assumed to be set by the climate; its value is imposed as the top boundary condition to the model. The other is the conductive heat flow from below (geothermal heat).

If the temperature drops below the freezing temperature of ice of hydrate, these phases may form. When they do, the salt remains in the fluid phase (brine). Freezing stops when the brine is salty enough to depress the freezing temperature of the solid phase (ice of hydrate) so that it matches the local temperature. The saltiness of the water determines the thermodynamic activity of water; when it's very cold, the brine will be very salty and the activity of water will be low.

If the temperature is potentially low enough to form both phases (hydrate and ice), the brine salinity will decide which phase to form. In the permafrost zone, ice can tolerate a higher salinity than methane hydrate can (upper region in the plot on the right), so hydrate is salted out and doesn't form.

For calculating the abundance of methane hydrate, the model assumes unlimited availability of methane, and so it is calculating the highest possible amount of methane hydrate in the system. Usually, in the real world, the methane hydrate inventory will be much lower than this.

Left Temperature as a function of depth below the sediment or soil surface. The dashed lines show the freezing temperatures for ice and methane hydrate, at the salinity in the brine. The actual temperature (solid line) follows the ice equilibrium in the permafrost zone, and hydrate equilibrium in the hydrate stability zone.

Middle The fraction of the pore volume that is taken up by ice and by methane hydrate as a function of depth below the surface. The methane hydrate inventory is calculated assuming unlimited methane availability, so hydrate forms until it is limited by water.

Right Salinity is the controlling variable determining ice vs. methane hydrate stability. The line colors and types are the same as in the temperature plot. In the permafrost zone, ice can tolerate higher salinity than methane hydrate can, so you only find ice.

There are two stages to the model behavior: an initial steady state calculation, which you can tweak by changing the parameters in the Model Setup box, and a subsequent time-dependent model evolution, which is triggered if you change a parameter in the Run box.

When the model has only run a steady state calculation, a table will appear in the lower right giving the inventories of ice and methane hydrate (in meters, as if you separated out all the ice and measured the height of it in a pure column).

When a time-depentend Run is triggered, the box changes to time-dependent plots of temperature at the top and bottom of the model domain (top), and the time-evolving inventories of ice and hydrate, in the same units as in the box.

Make a plot of the ice and methane hydrate inventories as a function of the Initial Surface Temperature, using the steady state model results.
How does the Unfrozen Salinity affect the amount of ice you get and the potential for forming methane hydrate?
Contrast the melting response time of permafrost, between a place close to the edge of the permafrost zone (say, an Initial Surface Temperature of -2 degrees C) versus someplace much colder (say, -10 degrees C). Do a transient run by setting a New Surface Temperature, say, 4 degrees warmer, and see how long it takes for the ice to reach a new steady state.
How does the Unfrozen Salinity affect the time scale for melting ice and hydrate?
How does the Geothermal Temperature Gradient affect the ice and hydrate inventories?
Under what conditions can you achieve the fastest meltdown of methane hydrate? What time scale is this?
The model is formulated on a one-dimension verticl grid. The grid cells store temperatures, inventories of the phases of ice, methane hydrate, pore fluid, and soil matrix. The temperatures of the phases are assumed equal in a depth-box.

The model tracks the diffusion of heat by conduction using a time-implicit method, solving simultaneously for the temperatures and resulting heat fluxes at the end of each time step using Newton's methane and a tridiagonal matrix solver.

Also, each time step, alternating with the diffusion of heat, the composition and heat partitioning of each grid cell are calculated according to the equilibrium condition. For example, if both ice and fluid are present, the salinity of the fluid phase must produce a freezing-point depression to match the temperature of the box. The equilibrium temperature for the ice phase then matches the local temperature, at that salinity.

The model is based on a components of a more complex model called SpongeBOB, described in its treatment of permafrost and methane hydrate here.