A Simple Boundary Condition for Model Studies of the Diurnal Cycle and Surface Heterogeneity

For idealized model studies, the prescription of the heat flux or the temperature is a popular method to specify the boundary condition associated with the thermodynamic variable. A disadvantage of such an approach is that the evolution of the heat flux and temperature at the surface are integrally part of the atmospheric dynamics itself. Therefore, these type of ‘enforced’ conditions have a limited use when studying the dynamical evolution of atmospheric flows. Alternatively, more realistic set-ups employ a model for the surface energy budget (SEB), allowing for a dynamical interaction between the evolution of the state of atmosphere and the processes that impact the heat release to the atmosphere at the surface. This work presents a simple boundary condition based on a combination of a prescribed heat flux and a dynamical negative feedback. Using both a single-column model and turbulence resolving methods, we show that the present formulation is able to represent some of the most important system-dynamical aspects of the SEB approach. Furthermore, due to its simplicity, the new boundary condition can readily be implemented in virtually all existing model codes. The present work reports on the application of the present boundary condition to two scenarios. First, the diurnal cycle and second, heterogeneous surfaces. We conclude that the present approach can form an interesting alternative to existing surface-parameterizations for model studies where there is a trade-off between model-system complexity and physical realism.