Modelling Ground Temperatures for the Climate Model LPJmL4
by Julia Niebsch
Climate models are used to make predictions about the future development of the climate. These models use a variety of factors like aerial CO2 levels, sea temperatures and forestation to determine possible outcomes of the ongoing climate crisis. These physical and chemical processes can be described through mathematical models.
One aspect that plays an important part in climate models is the temperature of the ground. Depending on the temperature of the ground, different species of plants can grow on the soil, so a change in temperature can drastically change the vegetation of a region. But the truly catastrophic effect that a rise in ground temperatures has on the climate reveals itself in permafrost regions. Permafrost is frozen soil that remains frozen for a long period of time – though there is no real consensus on what constitutes a long period of time. When ground temperatures rise the frozen soil slowly begins to thaw. Most permafrost regions came into existence tens of thousands of years ago and in the formation process deceased animals and other organic matter got locked up in the ice. This makes permafrost soil a massive storage of methane and carbon dioxide. Once the permafrost is melted, bacteria will begin to decompose the organic matter, releasing all the stored carbon dioxide and methane into the atmosphere. The released gases then contribute to the greenhouse effect, causing temperatures to rise further.
The effect that the melting of permafrost has on the climate makes it necessary to properly model the temperature of the ground. For the past couple of months, I have been working on optimizing the modelling of ground temperatures for the climate model LPJmL4. The main idea is to solve the linear 1-dimensional heat equation numerically through a finite-element method. The 3-dimensional heat equation would paint a more accurate picture, but only modelling the temperature for the depth of the soil simplifies the calculations and describes the process well enough. To make the model more accurate, I had to consider several factors. Initially I assumed that the boundary condition at the surface of the soil to be a Dirichlet boundary condition. But if we have an air temperature of 10°C, using a Dirichlet condition would be equivalent to holding a 10°C heat source directly to the surface of the ground. The heat exchange between air and soil is slower than that, and using a Robin boundary condition describes this heat exchange more accurately. Another crucial physical property to consider is latent heat. As I already mentioned, the modelling of the temperature is especially interesting in permafrost regions where ice thaws and freezes again. During the process of thawing, the temperature of the ice does not change as all the energy is used for thawing. This idea can be implemented into the model by using an enthalpy method. This means that instead of modelling the temperature of the soil, I model the enthalpy which already includes the effects of thawing. However, for the enthalpy method the differential equation is no longer linear. This makes the process of finding the numerical solution slightly more involved. While doing all of these model adjustments, it is important to remember that the calculation process cannot take too long. Running an entire climate model often requires thousands of calculations and if the calculations of the individual programmes are not quick enough, the model might take an eternity to finally tell us that – despite what some politicians might say – the climate does indeed change for the worse.