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# Modelling of Heat Transfer

The modelling of heat transfer in the soil is done by the heat transfer equation, which is solved by an implicit finite difference scheme.

The hydrologically particularly important freezing of soil water and the thawing of frozen soils is modelled in detail by accounting for the change in energy (supply or abstraction) that is needed to obtain a certain temperature change. This energy is a function of several parameters, including the soils grain size distribution is - especially withing the temperature range of phase change. In very fine porous soils liquid water exists even below -10°C, in other soils already barely below about -1 to -2°C. Between 0°C and -10°C (this are the limits for WaSiM), the relative ratio of liquid water and ice is changing continuously. There is no fixed temperature at which water suddenly turns into or vice versa. These complex relationships are modeled in detail in the model, thus allowing a detailed process analysis.

The soil is subdivided into the same layers as they are used in the modelling of water flows in the Richard model (actually, the modelling of heat transfer is done in the soil model)

The solution of the heat transport equation can be done either for diffusion only, or for diffusion and advection (program parameters in the control file). If advection is taken into account, the thermal energy of rainfall and melting water infiltrating into the ground is also considered.

Since the implicit solution scheme has been implemented, the module is relatively insensitive to long-time sub steps - there will be no oscillations in most cases - yet the automatically defined internal time step should not be limited to a too large minimum time step. Otherwise the model results would become more and more inaccurate.

Details on the modeling of heat transfer, also the complete set of equations, can be found in the WaSiM model documentation.