Local similarity in the stable boundary layer and mixing-length approaches: consistency of concepts

In stably stratified flows vertical movement of eddies is limited by the fact that kinetic energy is converted into potential energy, leading to a buoyancy displacement scale z B . Our new mixing-length concept for turbulent transport in the stable boundary layer follows a rigid-wall analogy, in the sense that we assume that the buoyancy length scale is similar to neutral length scaling. This implies that the buoyancy length scale is: ¿ B = ¿ B z B , with ¿ B ¿ ¿, the von Karman constant. With this concept it is shown that the physical relevance of the local scaling parameter z/¿ naturally appears, and that the ¿ coefficient of the log-linear similarity functions is equal to c/¿ 2, where c is a constant close to unity. The predicted value ¿ ¿ 1/¿ 2 = 6.25 lies within the range found in observational studies. Finally, it is shown that the traditionally used inverse linear interpolation between the mixing length in the neutral and buoyancy limits is inconsistent with the classical log-linear stability functions. As an alternative, a log-linear consistent interpolation method is proposed

Exploring the possible role of small scale terrain drag on stable boundary layers over land

This paper addresses the possible role of unresolved terrain drag, relative to the turbulent drag on the development of the stable atmospheric boundary layer over land. Adding a first-order estimate for terrain drag to the turbulent drag appears to provide drag that is similar to the enhanced turbulent drag obtained with the so-called long-tail mixing functions. These functions are currently used in many operational models for weather and climate, although they lack a clear physical basis. Consequently, a simple and practical quasi-empirical parameterization of terrain drag divergence for use in large-scale models is proposed and is tested in a column mode. As an outcome, the cross-isobaric mass flow (a measure for cyclone filling) with the new scheme, using realistic turbulent drag, appears to be equal to what is found with the unphysical long-tail scheme. At the same time, the new scheme produces a much more realistic less-deep boundary layer than is obtained by using the long-tail mixing function

Dynamic root growth in response to depth-varying soil moisture availability:a rhizobox study

Plant roots are highly adaptable, but their adaptability is not included in crop and land surface models. They rely on a simplified representation of root growth, which is independent of soil moisture availability. Data of subsurface processes and interactions, needed for model setup and validation, are scarce. Here we investigated soil-moisture-driven root growth. To this end, we installed subsurface drip lines and small soil moisture sensors (0.2 L measurement volume) inside rhizoboxes (length × width × height of 45 × 7.5 × 45 cm). The development of the vertical soil moisture and root growth profiles is tracked with a high spatial and temporal resolution. The results confirm that root growth is predominantly driven by vertical soil moisture distribution, while influencing soil moisture at the same time. Besides support for the functional relationship between the soil moisture and the root density growth rate, the experiments also suggest that the extension of the maximum rooting depth will stop if the soil moisture at the root tip drops below a threshold value. We show that even a parsimonious one-dimensional water balance model, driven by the water input flux (irrigation), can be convincingly improved by implementing root growth driven by soil moisture availability

Why does fog deepen?: An analytical perspective

The overall depth of a fog layer is one of the important factors in determining the hazard that a fog event presents. With discrete observations and often coarse numerical grids, however, fog depth cannot always be accurately determined. To address this, we derive a simple analytical relation that describes the change in depth of a fog interface with time, which depends on the tendencies and vertical gradients of moisture. We also present a lengthscale estimate for the maximum depth over which mixing can occur in order for the fog layer to be sustained, assuming a uniform mixing of the vertical profiles of temperature and moisture. Even over several hours, and when coarse observational resolution is used, the analytical description is shown to accurately diagnose the depth of a fog layer when compared against observational data and the results of large-eddy simulations. Such an analytical description not only enables the estimation of sub-grid or inter-observation fog depth, but also provides a simple framework for interpreting the evolution of a fog layer in time.</p

Modelling the Arctic Stable boundary layer and its coupling to the surface

The impact of coupling the atmosphere to the surface energy balance is examined for the stable boundary layer, as an extension of the first GABLS (GEWEX Atmospheric Boundary-Layer Study) one-dimensional model intercomparison. This coupling is of major importance for the stable boundary-layer structure and its development because coupling enables a realistic physical description of the interdependence of the surface temperature and the surface sensible heat flux. In the present case, the incorporation of a surface energy budget results in stronger cooling (surface decoupling), and a more stable and less deep boundary layer. The proper representation of this is a problematic feature in large-scale numerical weather prediction and climate models. To account for the upward heat flux from the ice surface beneath, we solve the diffusion equation for heat in the underlying ice as a first alternative. In that case, we find a clear impact of the vertical resolution in the underlying ice on boundary-layer development: coarse vertical resolution in the ice results in stronger surface cooling than for fine resolution. Therefore, because of this impact on stable boundary-layer development, the discretization in the underlying medium needs special attention in numerical modelling studies of the nighttime boundary layer. As a second alternative, a bulk conductance layer with stagnant air near the surface is added. The stable boundary-layer development appears to depend heavily on the bulk conductance of the stagnant air layer. This result re-emphasizes the fact that the interaction with the surface needs special attention in stable boundary-layer studies. Furthermore, we perform sensitivity studies to atmospheric resolution, the length-scale formulation and the impact of radiation divergence on stable boundary-layer structure for weak windy condition