Heat transport through short and closed vegetation such as grass is modelled by a simple diffusion process. The grass is treated as a homogeneous ‘sponge layer’ with uniform thermal diffusivity and conductivity, placed on top of the soil. The temperature and heat-flux dynamics in both vegetation and soil are described using harmonic analysis. All thermal properties have been determined by optimization against observations from the Haarweg climatological station in The Netherlands. Our results indicate that both phase and amplitude of soil temperatures can be accurately reproduced from the vegetation surface temperature. The diffusion approach requires no specific tuning to, for example, the daily cycle, but instead responds to all frequencies present in the input data, including quick changes in cloud cover and day– night transitions. The newly determined heat flux at the atmosphere–vegetation interface is compared with the other components of the surface energy balance at this interface. The budget is well-closed, particularly in the most challenging cases with varying cloud cover and during transition periods. We conclude that the diffusion approach (either implemented analytically or numerically) is a physically consistent alternative to more ad hoc methods, like ‘skin resistance’ approaches for vegetation and bulk correction methods for upper soil heat storage. However, more work is needed to evaluate parameter variability and robustness under different climatological conditions. From a numerical perspective, the present representation of vegetation allows for both slow and rapid feedbacks between the atmosphere and the surface. As such, it would be interesting to couple the present surface parametrization to turbulence-resolving models, such as large-eddy simulations.@en

In polar regions, where the boundary layer is often stably stratified, atmospheric models produce large biases depending on the boundary-layer parametrizations and the parametrization of the exchange of energy at the surface. This model intercomparison focuses on the very stable stratification encountered over the Antarctic Plateau in 2009. Here, we analyze results from 10 large-eddy-simulation (LES) codes for different spatial resolutions over 24 consecutive hours, and compare them with observations acquired at the Concordia Research Station during summer. This is a challenging exercise for such simulations since they need to reproduce both the 300-m-deep convective boundary layer and the very thin stable boundary layer characterized by a strong vertical temperature gradient (10 K difference over the lowest 20 m) when the sun is low over the horizon. A large variability in surface fluxes among the different models is highlighted. The LES models correctly reproduce the convective boundary layer in terms of mean profiles and turbulent characteristics but display more spread during stable conditions, which is largely reduced by increasing the horizontal and vertical resolutions in additional simulations focusing only on the stable period. This highlights the fact that very fine resolution is needed to represent such conditions. Complementary sensitivity studies are conducted regarding the roughness length, the subgrid-scale turbulence closure as well as the resolution and domain size. While we find little dependence on the surface-flux parametrization, the results indicate a pronounced sensitivity to both the roughness length and the turbulence closure.@en

We perform direct numerical simulation of the Couette flow as a model for the stable boundary layer. The flow evolution is investigated for combinations of the (bulk) Reynolds number and the imposed surface buoyancy flux. First, we establish what the similarities and differences are between applying a fixed buoyancy difference (Dirichlet) and a fixed buoyancy flux (Neumann) as boundary conditions. Moreover, two distinct parameters were recently proposed for the turbulent-to-laminar transition: the Reynolds number based on the Obukhov length and the "shear capacity," a velocity-scale ratio based on the buoyancy flux maximum. We study how these parameters relate to each other and to the atmospheric boundary layer. The results show that in a weakly stratified equilibrium state, the flow statistics are virtually the same between the different types of boundary conditions. However, at stronger stratification and, more generally, in nonequilibrium conditions, the flow statistics do depend on the type of boundary condition imposed. In the case of Neumann boundary conditions, a clear sensitivity to the initial stratification strength is observed because of the existence of multiple equilibriums, while for Dirichlet boundary conditions, only one statistically steady turbulent equilibrium exists for a particular set of boundary conditions. As in previous studies, we find that when the imposed surface flux is larger than the maximum buoyancy flux, no turbulent steady state occurs. Analytical investigation and simulation data indicate that this maximum buoyancy flux converges for increasing Reynolds numbers, which suggests a possible extrapolation to the atmospheric case.@en

A conceptual model is used in combination with observational analysis to understand regime transitions of near-surface temperature inversions at night as well as in Arctic conditions. The model combines a surface energy budget with a bulk parameterization for turbulent heat transport. Energy fluxes or feedbacks due to soil and radiative heat transfer are accounted for by a "lumped parameter closure," which represents the "coupling strength" of the system. Observations from Cabauw, Netherlands, and Dome C, Antarctica, are analyzed. As expected, inversions are weak for strong winds, whereas large inversions are found under weak-wind conditions. However, a sharp transition is found between those regimes, as it occurs within a narrow wind range. This results in a typical S-shaped dependency. The conceptual model explains why this characteristic must be a robust feature. Differences between the Cabauw and Dome C cases are explained from differences in coupling strength (being weaker in the Antarctic). For comparison, a realistic column model is run. As findings are similar to the simple model and the observational analysis, it suggests generality of the results. Theoretical analysis reveals that, in the transition zone near the critical wind speed, the response time of the system to perturbations becomes large. As resilience to perturbations becomes weaker, it may explain why, within this wind regime, an increase of scatter is found. Finally, the so-called heat flux duality paradox is analyzed. It is explained why numerical simulations with prescribed surface fluxes show a dynamical response different from more realistic surface-coupled systems.

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The evening transition is investigated in an idealized model for the nocturnal boundary layer. From earlier studies it is known that the nocturnal boundary layer may manifest itself in two distinct regimes, depending on the ambient synoptic conditions: strong-wind or overcast conditions typically lead to weakly stable, turbulent nights; clear-sky and weak-wind conditions, on the other hand, lead to very stable, weakly turbulent conditions. Previously, the dynamical behaviour near the transition between these regimes was investigated in an idealized setting, relying on Monin–Obukhov (MO) similarity to describe turbulent transport. Here, we investigate a similar set-up, using direct numerical simulation; in contrast to MO-based models, this type of simulation does not need to rely on turbulence closure assumptions. We show that previous predictions are verified, but now independent of turbulence parametrizations. Also, it appears that a regime shift to the very stable state is signaled in advance by specific changes in the dynamics of the turbulent boundary layer. Here, we show how these changes may be used to infer a quantitative estimate of the transition point from the weakly stable boundary layer to the very stable boundary layer. 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. Therefore, the presence of other, generic early warning signals is tested as well. Indeed, indications are found that such signals are present in stably stratified turbulent flows.

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This study aims to find the typical growth rate of the temperature inversion during the onset of the stable boundary layer around sunset.The sunset transition is a very challenging period for numerical weather prediction, since neither accepted theories for the convective boundary layer nor those for the stable boundary layer appear to be applicable. To gainmore insight in this period, a systematic investigation of the temperature inversion growth rate is conducted. A statistical procedure is used to analyze almost 16 years of observations from the Cabauw observational tower, supported by observations from two additional sites (DomeCandKarlsruhe). The results show that, on average, the growth rate of the temperature inversion (normalized by the maximum inversion during the night) weakly declines with increasing wind speed. The observed growth rate is quantitatively consistent among the sites, and it appears insensitive to various other parameters. The results were also insensitive to the afternoon decay rate of the net radiation except when this decay rate was very weak. These observations are compared to numerical solutions of three models with increasing complexity: a bulk model, an idealized single-column model (SCM), and an operational-level SCM. It appears only the latter could reproduce qualitative features of the observations using a first-order closure. Moreover, replacing this closure with a prognostic TKE scheme substantially improved the quantitative performance. This suggests that idealized models assuming instantaneous equilibrium flux-profile relations may not aid in understanding this period, since history effects may qualitatively affect the dynamics.

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