Numerical results show that the structure of the nocturnal valley boundary layer is substantially different for the draining and pooling configurations. The greater the pooling, the deeper and colder is the boundary layer. Down-valley winds are weaker in pooling and draining valleys than in equivalent valleys opening directly on a plain, because of the reduction of the along-valley pressure gradient due to the presence of the neighbouring valley.
Subsequently, we moved to the analysis of the thermodynamical processes controlling the evolution of the valley boundary layer. Following the idea of Schmidli and Rotunno (J. Atmos. Sci. 2010), the geometrical effects (expressed by the topographic amplification factor), can be separated from the processes controlling the valley heat budget (namely diabatic and transport processes), when examining the differential cooling between different along-valley sections. Quantities are averaged over the valley volume.
We firstly compared the heat budget of different cross-valley sections along the valley. Once the down-valley wind is fully developed, all the cases considered present a nearly-homogeneous cooling rate in the along-valley direction. The contribution of the diabatic processes to the valley heat budget, when appropriately weighted, hardly varies along the valley axis for both the pooling and draining cases. Conversely, the contribution of advection to the valley heat budget varies along the valley axis depending on the configuration: it decreases for a pooling configuration, and increases for a draining configuration. Hence, the temperature differences along the valley axis are controlled by the variations of the advection contribution along the valley axis, and modulated by the geometrical effects.
We then compared the heat budget of valley and plain sections. Pooling increases the temperature difference between the valley and the plain. For the moderate pooling case, the valley to plain temperature difference can be explained by the topographic amplification factor during the early night. That is because the greater the pooling, the weaker is the heat transfer between the valley and the plain. For moderate pooling, the larger heat input (i.e. warming) due to advection within the valley with respect to the plain, is comparable (in amplitude) to the heat loss (i.e. cooling) due to diabatic processes. The latter are larger in a valley with respect to a plain because of down-slope winds, that enhance the surface sensible heat fluxes on the slopes.
In the absence of significant dynamical processes, the valley to plain temperature differences can be possibly explained by the topographic amplification factor. Our results suggest that this condition can be reached in a relatively open valley by a balance between the extra' heat loss within the valley due to the surface sensible heat flux and the heat input due to advection; the along-valley constriction is key to reaching this balance.