Horizontal surface heterogeneity and non-stationarity invalidate the assumptions inherent to Monin-Obukhov similarity theory (MOST). These impacts can be enhanced under stratified conditions prevalent in the nocturnal boundary layer (NBL). A critical shortcoming in equilibrium models, including MOST, modifications to MOST, or power-law formulations, is the assumption that advection is negligible in the momentum, thermal energy, and turbulence kinetic energy equations. When these models are applied instantaneously and locally, as in surface boundary conditions (SBCs) in large-eddy simulations (LES), their underlying assumptions are highly suspect. Yet, these models are routinely employed because of the lack of clear alternatives for atmospheric flows. In this study, the filtered versions of the momentum, thermal energy, and turbulence kinetic energy equations are examined using published direct numerical simulation data of stratified flows. Each term in these equations is evaluated as a function of filter scale, distance in the surface layer from the ground, and static stability for their contribution to the overall budget. Although vertical transport dominates as expected in the momentum budget, contributions from horizontal advection and pressure forces increase for smaller filter scales and with increasing static stability. Similar behavior is observed for the thermal and kinetic energy budgets. Analysis of these budgets suggests possible formulations for reduced-order models that weaken some assumptions used in commonly employed LES SBCs.