A shared property of all models is the looseness of the approximations on which they rely (e.g., linear theory with turbulent viscosity parametrisation, or purely phenomenological arguments on the nature of dynamical interactions between granules and their potential large-scale instabilities). Completely distinct theoretical arguments can easily be tuned to produce results that are all broadly consistent with observations. This degeneracy makes it impossible to discriminate between various scenarios and to come up with a proper theoretical explanation for the origin of supergranulation that could be unambiguously validated by observations.
Finally, it is possible but certainly not obvious that supergranulation can be explained quantitatively by a simple mathematical theoretical model. In any case, one of the most urgent tasks to overcome some of the previously mentioned shortcomings is to figure out if the basic assumptions and arguments on which current theoretical models rely (linear theory, effective boundary conditions, convection in uniform magnetic fields, etc.) are justified, and to test them quantitatively with the help of large-scale numerical simulations.
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