1. Introduction
The atmospheric boundary layer (ABL) is the layer of the troposphere that is directly influenced by Earth’s surface. The depth of this layer varies in time, ranging in depth from tens of meters to kilometers. In clear-sky conditions the sun warms Earth’s surface during the day and generates an unstable surface layer. The resulting convective boundary layer is relatively deep and actively turbulent. Around sunset, when the surface shortwave flux approaches zero, Earth’s radiative energy budget changes sign. The resulting cooling gives rise to a near-surface temperature gradient that marks the onset of the stable boundary layer (van Hooijdonk et al. 2017). Conditions of static stability frequently occur in the Arctic especially during the polar night, and can also occur when warm air is advected over a cold surface.
The stable boundary layer has been classified into different regimes based on the interplay between the temperature gradient and the turbulent transports (Mahrt 2014). The weakly stable boundary layer (wSBL) generally occurs under cloudy skies or in the presence of moderate to strong horizontal pressure gradients and is characterized by the presence of continuous turbulent mixing. In contrast, the very stable boundary layer (vSBL) typically occurs under clear skies and in the presence of weak horizontal pressure gradients. Under these circumstances turbulence can weaken to the point of cessation. The lower and upper parts of the near-surface flow can largely decouple as strong atmospheric stability inhibits vertical turbulent transport (Derbyshire 1999; Banta et al. 2007; Williams et al. 2013; Mahrt 2011). This phenomenon, referred to as the collapse of turbulence, is a traditional characterization of the transition from the wSBL to the vSBL.
There are many feedbacks that complicate the dynamics of regime transitions in the stable boundary layer (SBL). For sufficiently strong temperature gradients turbulent transports of heat from above are weak. Surface cooling further weakens turbulent transports and enhances the inversion. Lower near-surface atmospheric temperatures are associated with a weakening of the downwelling longwave radiation which cools the surface further. These positive feedbacks are counteracted by negative feedbacks such as the fact that decreased surface temperatures result in a lower emission of blackbody radiation which leads to less cooling. Furthermore, cooling of the surface increases the subsurface temperature gradient which can lead to warming of the surface as the heat flux to the subsurface increases.
Understanding and predicting the structure of the SBL is important to society (Steeneveld 2014). Human health hazards arise in stable atmospheric conditions when pollutants become trapped near the ground and affect air quality (Nappo 1991; Arya 1999; Salmond and McKendry 2005). Fog and frost formation (Holtslag et al. 2013) has significant consequences for agriculture as well as for ground transportation and aviation. Predictions of the near-surface wind speed are also needed for wind power assessments (Petersen et al. 1998). Any forecast of the future state of the atmospheric boundary layer necessitates the use of models.
Developing an accurate representation of the SBL in weather and climate models is particularly challenging for several reasons. Turbulence occurs on small spatial scales and these subgrid-scale effects must be parameterized. In addition, turbulence can be weak or intermittent and boundary layer depths are so shallow that they are not well resolved. Numerical models on scales from the mesoscale to larger-scale models used for numerical weather prediction (NWP) and climate modeling have particular difficulty representing the dynamics of the very stable boundary layer (Holtslag et al. 2013; Derbyshire 1999; Viterbo et al. 1999). Many atmospheric models use classic Monin–Obukhov similarity theory (MOST) to model the surface layer (Mahrt 1998; Pahlow et al. 2001; Mahrt 2014). This theory assumes that turbulent fluxes scale with their distance from the surface. However, under very stable conditions the scale of turbulent eddies is determined by the stratification independent of the distance from the surface. Therefore, MOST generally holds well in the wSBL, but not in the surface layer of the vSBL (Mahrt 1998; Pahlow et al. 2001).
Under conditions of very strong static stability turbulent transports are weak, which limits the downward sensible heat flux, leading to even colder temperatures at the surface and a further increase of stability. When this positive feedback occurs in models it can lead to runaway cooling giving rise to a cold bias in near-surface temperatures especially during the winter and in polar regions (Derbyshire 1999; Viterbo et al. 1999). To improve the overall model performance, the parameterizations of turbulence used in NWP and climate models are often tuned by altering some of the turbulent process parameters away from observationally based values. One way of tuning the model to avoid conditions of extreme stability is by increasing the magnitude of the turbulent diffusivities (Sandu et al. 2013; Walters et al. 2014). A common justification of these enhanced mixing schemes is the argument that they represent localized mixing events that are not explicitly accounted for due to submesoscale motions such as density-driven currents, solitary waves, and internal gravity waves (Sandu et al. 2013). However, artificially enhanced diffusion can lead to a warm bias near the surface in cold conditions and cloud dissipation (Tjernström et al. 2005; Sandu et al. 2013; Holtslag et al. 2013). The improvement of parameterizations that account for physical processes such as gravity waves, flow over topography, and other mesoscale motions requires improved understanding of the physical mechanisms governing turbulent transitions.
As the wSBL–vSBL transition is primarily radiatively driven (over land), idealized models of this process have not needed to account for Coriolis effects or mechanical driving by the large-scale pressure gradient force (ReVelle 1993; Van de Wiel et al. 2007; Acevedo et al. 2012; Van de Wiel et al. 2012a,b; Holdsworth et al. 2016). Van de Wiel et al. (2007) showed that a simple Couette flow model with fixed surface sensible heat flux was able to qualitatively represent transitions from the wSBL to the vSBL. The transition was explained by appealing to the idea of a maximum sustainable heat flux (MSHF) (Van de Wiel et al. 2012b): the sensible heat flux is limited to a maximum under the influence of strong temperature gradients because turbulent transports are suppressed by the stratification, and in near-neutral conditions by the weak temperature gradient. The maximum heat flux occurs under conditions of intermediate stability. If the surface radiative energy flux exceeds this maximum, the downward transport of energy cannot meet this demand and rapid surface cooling occurs. Holdsworth et al. (2016) showed that the transition behavior of Couette flow described by the MSHF framework is qualitatively insensitive to the parameterization of turbulence, and that when the flow is dynamically unstable only one unstable mode exists. They confirmed the conjecture that for this system weakly stable and very stable regimes corresponded to the dynamically stable and dynamically unstable branches, respectively (Taylor 1971; Van de Wiel et al. 2007, 2012a; Holdsworth et al. 2016). Monahan et al. (2015) classified the observations from the Cabauw Experimental Site for Atmospheric Research (CESAR) in the Netherlands (51.971°N, 4.927°E) (Van Ulden and Wieringa 1996) into two distinct regimes using hidden Markov model analysis, which corresponded well to the unstable and stable branches. However, these Couette flow models assume that the heat flux at the surface is fixed, while in the atmosphere the heat flux varies as a function of the surface energy budget.
Van de Wiel et al. (2017) used a conceptual model that combined the effects of soil heat transport and radiative budget together and considered the “coupling strength” between the surface and the lower atmosphere. They compared this model to observations from Cabauw and Dome C in Antarctica and showed that the differences between these cases can be interpreted in terms of changes in the coupling strength. Many models of the SBL have assumed a prescribed surface sensible heat flux (Gohari and Sarkar 2017) and a relatively shallow fixed height for the boundary layer (Van de Wiel et al. 2007, 2012a; Acevedo et al. 2012; McNider et al. 1995). Since the heat flux varies depending on the properties of the underlying surface, coupling the simulated atmosphere with the surface energy budget allows for an interdependence between the surface temperature and the surface sensible heat flux (Steeneveld et al. 2006).
The idea that there exists a critical wind speed that marks the transition between the wSBL and the vSBL can be traced at least as far back at Nieuwstadt (1984), who restricted his analysis of the SBL to wind speeds above 5 m s−1 to ensure continuous turbulence. Transition wind speeds from 3 to 7 m s−1 have been reported (Van de Wiel et al. 2012a; Acevedo et al. 2012; Van de Wiel et al. 2012b). Denoting the transition wind speed by Umin, Van Hooijdonk et al. (2015) defined the shear capacity as the dimensionless ratio U/Umin so that the wSBL is separated from the vSBL at U/Umin = 1. While this parameter provides a useful heuristic, the estimated value of Umin is empirically based using clear-sky data at Cabauw and may not be generalizable. Similarly, Sun et al. (2012) found that for a given height the relationship between turbulence intensity and mean wind speed changes for a critical (transition) value of the wind speed. This criterion is referred to as the hockey-stick transition (HOST) since the relationship resembles a hockey stick where the elbow of the stick marks the transition wind speed (Sun et al. 2015, 2016). Still, the connection between the coupling strength of the surface and this transition wind speed is not well understood.
In this study we develop an idealized single-column model to examine the collapse and recovery of turbulence in the SBL under the influence of a large-scale pressure gradient force, the effect of rotation, and an explicit model of the surface that separates the factors controlling the coupling strength. The model is described in section 2. In section 3a the sensitivity of the model to different parameterizations of turbulence is explored. Section 3b examines the role of rotation in the development and evolution of the SBL as a function of the pressure gradient force (geostrophic wind). In section 3c we explore the role of different variables influencing the surface energy budget such as the cloud cover, surface type, and the subsurface temperature on regime transitions. Discussion of the results is presented in section 4 and the conclusions appear in section 5.
2. Numerical model





Schematic diagram for the SCM of pressure-driven flow in the SBL including a force-restore surface radiative budget. Here
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
List of model parameters (independent variables).
The geostrophic wind components are defined by
After 3 h, (a) the wind speed at 40 m on the primary axis with the horizontal pressure gradient
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1

















The upper boundary of the model, at which we impose the boundary condition that the flow is geostrophic, is fixed at h = 5000 m. This domain is large enough for the height of the SBL to evolve freely for the geostrophic wind speeds used in this study (varying between 2 and 30 m s−1). At the upper boundary a no-flux condition is implemented so that the sensible heat flux
The model implements the surface energy scheme of Blackadar (1976), known as the force-restore method, defined by Eq. (4) and illustrated in Fig. 1. The surface, represented as an infinitesimally thin layer with temperature








The equations are integrated in time using a fourth-order Runge–Kutta method. The spatial discretization is obtained using finite differences on a logarithmic grid. This grid has 100 vertical levels with a much finer resolution in the boundary layer than aloft and is determined by






3. Results
The HOST criterion was first applied to the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) (Sun et al. 2012) and has been applied in several subsequent studies (i.e., Mahrt et al. 2015; Russell et al. 2016; Maroneze et al. 2019). The criterion relates the mean horizontal wind speed to the turbulent intensity at a given height. These quantities were averaged in time to capture fluctuations. To apply the HOST criterion to our model results, we use the time-averaged horizontal wind speed
The relationship between the mean horizontal wind speed
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
Temperature profiles for different (top to bottom) stability functions and (left to right) geostrophic wind speeds at the times indicated by the legend at the bottom. The height is nondimensionalized by the height of the boundary layer. The inset plots show the evolution of the surface temperature.
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
Figure 3a demonstrates that when turbulence is said to collapse there is still some turbulent activity. The collapse of turbulence is the transition from the wSBL to the vSBL and the recovery is the transition from the vSBL to the wSBL.
a. Choice of parameterization
The stability functions used to parameterize the turbulent diffusivities were largely formulated using empirical fits to atmospheric data. These functions are subject to large uncertainty and problems with sampling (Nieuwstadt 1984; Mahrt 1985) especially in the very stable regime (Clarke 1970; Webb 1970; Businger et al. 1971; Hicks 1976; Holtslag and De Bruin 1988; Chenge and Brutsaert 2005; Brown et al. 2008). This fact has been used to justify the modifications of these functions to improve model performance (Sandu et al. 2013). A commonly used expression for the similarity functions is
The surface parameters for the control simulation correspond to dry sand (Table 2) with
The evolution of the temperature profile normalized by the time-evolving height of the boundary layer for the different stability functions is shown in Fig. 4. Each column represents a different geostrophic wind speed (as indicated at the top). These speeds were selected to be representative of speeds in the vSBL, near the transition wind speed, and in the wSBL, respectively. Inset plots of surface temperature show that, consistent with the air temperature profiles, cooling near the surface is generally smaller for larger
Figure 2b shows the inversion strength as a function of the geostrophic wind at t = 3 h. The strength of the simulated inversion is calculated as the temperature difference between 40 m and the lowest model level. All of the formulations exhibit similar dependence of inversion strength on
In Fig. 2b the solid diamond markers indicate cases of turbulent collapse, crosses indicate cases with turbulent collapse and recovery, and the open circles indicate a persistent wSBL. For the BD function with
Several previous studies have related the temperature inversion to the geostrophic winds (van der Linden et al. 2017; Baas et al. 2018) or to the speed at a fixed height above the surface
Figure 5 shows the wind speed and temperature profiles at t = 6 h for all of the stability functions with
Vertical profiles of (left) wind speed and (right) temperature for the different stability functions are shown at t = 6 h. Two different wind speed classes are shown representing (a),(b) the vSBL with
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
Figure 5 shows that BH, HD, and LD result in temperature profiles that are more similar near the top of the profile to observations from Cabauw than the BD functions (cf. Fig. 5 of van der Linden et al. 2017). While the wind speed profiles and height of the boundary layer are very similar for BH, LD, and HD functions, Fig. 4 (first column) and Fig. 5b show that, although all three of these functions exhibit a negative curvature near the surface in the vSBL, the curvature of the HD temperature profile is more pronounced. Negative curvature is observed to be associated with near-surface clear-air radiative cooling in the vSBL (André and Mahrt 1982) and is evident in composite profiles from Cabauw for weak winds in Fig. 3 of Baas et al. (2018). This curvature is consistent with the model results of Edwards (2009a,b) who used a force-restore method with high spatial and high spectral resolution. The HD function is recommended by Andreas (2002) who argued for the existence of a critical Richardson number and turbulent Prandtl number of order one. Based on the strong negative curvature of the temperature profile in the vSBL and similar morphology to the Cabauw profiles, we will use the HD function for the remainder of our analysis.
Figure 6 shows the evolution of various stable boundary layer variables for the control simulation, for a range of different geostrophic wind speeds. The similarity of the modeled friction velocities and surface heat fluxes with observations from Cabauw is remarkable given the simplicity of our model and the biases in the boundary layer structure for weak winds [cf. Fig. 2 of Baas et al. (2018) and Fig. 3 of van der Linden et al. (2017)]. The evolution of
The evolution of surface characteristics for the control simulations with geostrophic wind speeds in the legend at the bottom: (a) bulk Richardson number, (b) inversion strength at z = 40 m, (c) square of the friction velocity, and (d) turbulent heat flux. The HD stability function is used.
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
b. The role of the Coriolis effect
The idealized model presented here builds on studies of regime shifts in the SBL that have neglected the Coriolis effect in the momentum equation (Van de Wiel et al. 2002a,b, 2007; Holdsworth et al. 2016). The justification for this simplifying assumption is that the time scale of turbulent collapse is much smaller than the time scale of geostrophic adjustment. The validity of this assumption is investigated here by fixing
Van de Wiel et al. (2012a) defines the pseudo–steady state (PSS) as the short period of time after the nocturnal transition when the wind and temperature gradients near the surface are relatively stationary, and the time scale of the PSS
(left) The evolution of the wind speed profile in the PSS is shown for
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
Some model studies implement a constant speed condition at the upper boundary located at a relatively low altitude within or just above the SBL (McNider et al. 1995; Van de Wiel et al. 2007, 2012b; Acevedo et al. 2012). This boundary condition is justified by appealing to the idea that there exists a crossing point at which the initial wind speed profile (t = 0) intersects the profile at
Figures 7c and 7f show the strength of the temperature inversion 1 h after sunset, calculated at different fixed heights, as a function of
To explore the effect of changing the value of the Coriolis parameter
(a),(d) Profiles of the wind speed and (b),(e) temperature as well as (c),(f) the evolution of the normalized wind speed are shown after 6 h for (a)–(c) very stable and (d)–(f) transition wind speeds. (g)–(i) Relationship between (g) surface stress, (h) maximum heat flux, and (f) inversion strength and the geostrophic wind. The units of the Coriolis parameter f0 in the legend are 10−4 s−1.
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
The bottom row in Fig. 8 illustrates how the value of
Gohari and Sarkar (2017) found that turbulent collapse and recovery is influenced by inertial oscillations in their direct numerical simulations. However, it is difficult to directly assess the role of rotation from our analysis because changing
We find that neglecting rotation is a reasonable assumption when studying the collapse of turbulence for very weak pressure gradients. However it must be noted that there are noticeable effects of Coriolis in the wind and temperature profiles immediately after sunset. In the pseudo–steady state the dependence of inversion strength on the pressure gradient is similar, qualitatively, for both simulations. Over longer time scales, there are more pronounced differences as Coriolis effects reduce local shear affecting both the timing of collapse and the regime occupation.
c. The role of the surface energy budget
We now investigate how cloud cover, surface type, and subsurface temperature affect the evolution of the SBL for different geostrophic wind speeds. Figure 9 shows the relative contribution of each of the terms in the energy budget [Eq. (4)] for three values of
The evolution of surface energy budget [Eq. (4)] for the control simulation (dry sand) with (a) weak
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
Using the Regional Atmospheric Climate Model (RACMO) single-column model to simulate the SBL at Cabauw, Baas et al. (2018) suggested that such differences in the relative importance of sensible heat flux and subsurface heat flux are characteristic features of the vSBL and wSBL. Figure 10 (top row) shows
(left to right) Selected surface types. (a)–(c) Evolution of the bulk Richardson number is shown for different
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
The corresponding surface energy budgets for Sg = 8 m s−1 are shown with solid lines in Figs. 10d–f. The total surface cooling is relatively large for new snow, weaker for old snow, and weaker still for ice. Sensible heat fluxes dominate subsurface heat fluxes in the vSBL new snow simulation (Fig. 10d), while the opposite is true in the wSBL ice simulation (Fig. 10f). This result indicates that the relationship between sensible and subsurface heat fluxes suggested by Baas et al. (2018) is not a generic feature of the distinction between the two SBL regimes. That study concluded that in the vSBL the sensible heat flux constitutes only a small fraction of the surface energy budget. While this is true for our control simulations shown in Fig. 9 (dry sand), the surface budgets shown in Fig. 10 demonstrate that this conclusion is not generalizable. The relative contribution of each term in the surface energy budget is dependent on the properties of the underlying surface.
To further study the role of the subsurface heat flux in the surface energy budget a series of simulations were performed with
Figure 11a shows the strength of the temperature inversion as a function of
The strength of the temperature inversion at 3 h between z = 40 m and the surface for (a) surface types and (b) cloudiness. In (a) the size of the marker is determined by the thermal conductivities found in Table 2.
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
To examine the influence of clouds on static stability, the inversion strength in a series of simulations with different values of cloud cover
For different amounts of cloud cover Figs. 12a–c show the variation in
The evolution of (a)–(c) the bulk Richardson number and (d)–(f) surface cooling budget [Eq. (4)] for the control simulation under varying amounts of cloud cover.
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
Finally, to explore the influence of the subsurface temperature a series of simulations are shown for different values of
For different subsurface temperatures, (a) the temperature inversion is shown as a function of the geostrophic wind. When
Citation: Journal of the Atmospheric Sciences 76, 5; 10.1175/JAS-D-18-0312.1
4. Discussion
Our idealized model demonstrates that the most commonly used parameterizations of turbulence are able to simulate both the collapse and recovery of turbulence in the vSBL in the presence of a large-scale horizontal pressure gradient, Coriolis effects, and a surface energy budget. Because of the simplicity of the model and the neglect of processes such as intermittent turbulence in the vSBL, the timing and magnitudes of changes across transitions may not be accurately represented. While in this study we often compare our results to observations at Cabauw, we do not attempt to replicate observations at any particular site exactly. Closer matches between the model and any specific set of observations could use site-specific initial conditions and surface characteristics or a more sophisticated model of the surface energy budget. Furthermore, more complicated parameterizations of turbulence could be considered including for example more detailed treatments of the mixing length or adding a turbulent Prandtl number (He et al. 2019). We do find that the representation of the vSBL in our model for very weak geostrophic winds exhibits boundary layers which are too shallow. The representation of the stable boundary layer under very stable conditions remains a challenge to NWP and climate models.
Our results have illustrated how enhanced mixing from the buildup of shear and subsurface heat flux feedbacks can drive the recovery of turbulence. Further study is needed to understand the role that other neglected processes such as density-driven currents, solitary waves, and internal gravity waves (Sun et al. 2002, 2004) play in regime transitions and to represent them in NWP and climate models. A good starting point for such a study would be to represent these processes in idealized models like the one presented here.
Related idealized model studies with much coarser vertical resolution reported abrupt shifts between regimes (limit cycle behavior) (Van de Wiel et al. 2002b; ReVelle 1993; McNider et al. 1995) not found in this much higher-resolution model. In fact, the near-surface resolution we consider is much finer than is used by operational models. For wind speeds that are characteristic of the very stable regime the height of the boundary layer is on the order of a few tens of meters (Fig. 6b) which is too shallow to be resolved by standard NWP and climate models. Changes to the vertical resolution in such models is a significant undertaking because many of the model parameterizations are tuned to the existing resolution. Nevertheless, studies show that poor vertical resolution in the SBL can lead to large errors in the radiative flux (Räisänen 1996) and may be essential to preventing the surface warm bias (McNider et al. 2012). More work is needed to determine if an increase in model resolution is necessary to capture the effects of these near-surface dynamics.
The above analysis considered the influence of the geostrophic winds, cloud cover, thermal conductivity, and the subsurface temperature on regime transitions in the SBL. These quantities were held constant over the duration of the night in our simulations. In the real atmosphere, these forcings all evolve in time, adding another layer of complexity to the dynamics. Moreover, the representation of clouds in our model is rather simplistic and it would be interesting to see how the type of clouds or their location in the atmosphere might affect SBL dynamics.
Our simulations are restricted to a particular set of initial conditions. Preliminary investigations of the onset of the SBL indicate that the system may be sensitive to the atmospheric conditions around sunset (van Hooijdonk et al. 2017). More research is needed to explore the influence of realistic initial conditions on this complex dynamical system.
5. Conclusions
This study examined the influence of the large-scale horizontal pressure gradient on conditions of stratification in the SBL using an idealized single-column model with parameterized turbulence and a force-restore surface radiative scheme. A range of stability functions were considered, all of which were capable of qualitatively representing the vertical wind and temperature profiles from the Cabauw tower (van der Linden et al. 2017; Baas et al. 2018; Van de Wiel et al. 2017; Vignon et al. 2017), but there were some quantitative differences. We found that the Holtslag and De Bruin (1988) stability function resulted in shapes of profiles that matched most closely with the observations.
The idealized SCM model showed that the parameterizations of turbulence used in operational models are capable of representing the collapse and recovery of turbulence when coupled with a surface energy budget. This result does not of course indicate that the simulation of either collapse or recovery is quantitatively accurate. For very weak winds the model exhibits relatively shallow boundary layers compared with the observations.
Simulations were performed with and without rotation for a fixed pressure gradient force. Although differences in the wind speed and temperature were apparent between the rotating and nonrotating cases at the start of the simulation, the two simulations exhibited similar trends in atmospheric stability. Simulations with f = 0 exhibit more rapid turbulent collapse and deeper boundary layers. Simulations performed with variable f0 and fixed Sg indicate that when the inertial period is short compared to the length of the night, inertial oscillations are associated with a vSBL–wSBL transition. Further study is needed to determine whether inertial oscillations are actually the cause of this transition.
In agreement with observations (Monahan et al. 2015; van der Linden et al. 2017; Baas et al. 2018), we found that the strength of the large-scale pressure gradient strongly influences regime occupation in the SBL because the it controls the amount of turbulent mixing near the surface. The regime occupied by the SBL for a given geostrophic wind speed depends on the ambient cloud cover, the thermal conductivity of the surface, and the temperature of the subsurface through their influence on the surface energy budget (as in Van de Wiel et al. 2017). Cloud cover affects the amount of downwelling longwave radiation making wSBLs more likely for increasing cloud cover. Surfaces with larger thermal conductivities transfer heat more efficiently from the subsurface to the surface and relatively warm subsurface temperatures increase the subsurface gradient.
Occupation of either the weakly stable or very stable regimes is not simply a tug of war between the surface radiative cooling and the downward transport of turbulence controlled by the geostrophic winds. Rather it is the combined effect of the rate of heat transport from the subsurface together with the turbulent transport of heat from above that counters the radiative cooling of the surface (although, in contrast with the findings of previous studies, the occupied regime is not simply determined by the relative magnitude of the sensible and subsurface heat fluxes). Moreover, the relative importance of these terms is found to depend strongly on the thermal conductivity of the surface and the ambient cloud cover and weakly on the temperature of the subsurface. The idealized SCM shows that the subsurface can play an important role in the vSBL–wSBL transition depending on the thermal conductivity. The influence of cloud cover is more pronounced affecting both the collapse and recovery of turbulence.
Acknowledgments
The authors sincerely thank Otávio Acevedo and two anonymous reviewers whose suggestions have improved the quality of the manuscript. Thanks to Carsten Abraham, Ivo van Hooijdonk, and Bas van de Wiel for useful discussions about our work. We acknowledge support by the Natural Sciences and Engineering Research Council of Canada (NSERC).
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