Toward Generalizing the Impact of Surface Heating, Stratification, and Terrain Geometry on the Daytime Heat Export from an Idealized Valley

The convective export of heat from different types of idealized valleys for fair-weather daytime conditions is studied with the Weather Research and Forecasting (WRF) Model. The goal is to test the hypothesis that the total export of heat over the course of the day depends on a so-called breakup parameter B. The breakup parameter is the ratio between the energy required to neutralize the initially stably stratified valley atmosphere and the total energy provided by the surface sensible heat flux. To achieve this goal, simulations with different surface heating, initial stability, and terrain geometry are performed. The fraction of the sensible heat provided at the surface that is exported at crest height over the course of the day depends exponentially on B. The effects of variations of the valley width, crest height, forcing amplitude, and initial stratification on the total export of heat can be described by this function. The complete neutralization of the stratification in the valley is never reached if B exceeds a critical value of about 0.65 for an initially constant stratification. For a valley geometry with linear slopes and sharp crests, up to 60% of the provided heat is exported for the strongest forcing and the weakest stability (i.e., B ≈ 0.1), whereas less than 5% is exported for B > 0.65. The minimum heat export for larger B is higher for rounded crests (10%) and for a deep residual layer that extends to above crest height (17%).