Early Warning Signals for Regime Transition in the Stable Boundary Layer: a Model Study

An idealized model for the nocturnal boundary layer is employed to study dynamics of the evening transition. The model consists of a horizontally homogeneous flow with a prescribed top velocity to mimic the wind speed around sunset. Although a fixed-wind-speed boundary may appear somewhat artificial, it is based on the observation that wind near the surface tends to weaken around sunset, while winds aloft accelerate. Consequently, an altitude exists, the so-called crossing point, where winds remain relatively constant for several hours. Furthermore, a fixed sensible heat flux is prescribed at the surface to mimic net radiative cooling. From earlier studies it is known that the nocturnal boundary layer manifests itself in one of two distinct regimes, depending on ambient synoptic conditions. Strong-wind or overcast conditions typically lead to weakly stable, turbulent nights, while clear-sky and weak-wind conditions, on the other hand, lead to very stable, weakly turbulent nights. Physically, this two-regime division may be understood as follows: for both neutral conditions (no gradients) and strongly stratified conditions (no mixing) the sensible heat flux becomes very small. As such, a maximum downward sensible heat flux must exist at intermediate stability. The magnitude of the maximum flux is strongly dependent on the wind speed. For low-heat capacity, insulated surfaces (e.g. fresh snow) the sensible heat flux acts as the main energy supply to the surface. In case of weak-wind and clear-sky conditions, the maximum heat flux (energy gain) may be significantly less than the net radiative cooling (energy loss). In such nights strong surface cooling may occur, leading to a strong inversion near the surface, which further inhibits the sensible heat flux. Understanding of the boundary layer behavior close to and beyond the critical point remains limited. At the same time, phenomena like ground frost or radiation fog are more likely to occur under such conditions. Previously, a similar idealized set-up (i.e. using a fixed wind speed at crossing level and a prescribed surface flux) was used to study the dynamical behavior near the transition between weakly stable and very stable boundary layers and to predict the transition point. The model used, however, relied on Monin-Obukhov (MO) similarity to describe turbulent transport. As first innovative aspect, we investigate a similar set-up, using direct numerical simulation. In contrast to MO-based models, this type of simulation does not rely on turbulent closure assumptions. By systematically increasing the surface cooling previous predictions are verified, but now independently of parameterizations for turbulence. Results show that turbulence intensity remains relatively unaffected by stability until close to the critical point. When the prescribed surface flux is increased beyond the critical point, turbulence intensity suddenly becomes very weak as the flow transitions to a very stable state. As second innovative aspect, specific changes in dynamical behavior of the turbulent flow in the weakly stable regime are investigated. These changes are closely related to the existence of a heat-flux maximum, as at the maximum itself, no change in stability could further increase the sensible heat flux. Based on MO similarity it is therefore hypothesized that the ratio between the change in sensible heat flux to the change in stability is an indicator for the distance to the critical point. Indeed, the results indicate that such changes signal the arrival of a regime-shift prior to the onset of the very stable state (see figure). Here, we show how these changes may be used to infer a quantitative estimate of the transition point. In addition, it is shown that the idealized, nocturnal boundary layer system, shares important similarities with generic non-linear dynamical systems that exhibit critical transitions. For such generic systems it is well known that the typical decay time of perturbations with respect to the equilibrium solution, tends to be larger in the vicinity of a regime shift. In the current system the typical time scale required to reach equilibrium is measured for different prescribed surface heat fluxes. It is shown that indeed the typical time scale for decay to equilibrium increases when the system is closer to the regime shift. ========================================================== Figure: Asterisks depict the ratio between change in sensible heat flux and change in stability as a function of the prescribed surface heat flux. Note that all units are dimensionless. Stability is measured by the time-averaged vertical temperature difference when the system is in steady state. Each asterisks depicts the steady state value of a single run. The thin grey line indicates a linear fit through the numerical results. By extrapolating the linear fit to the horizontal axis a closure-independent estimate for the transition point is obtained close to the observed transition point. ==========================================================