Interaction Between Waves and Turbulence Within the Nocturnal Boundary Layer

The presence of waves is proven to be ubiquitous within nocturnal stable boundary layers over complex terrain, where turbulence is in a continuous, although weak, state of activity. The typical approach based on Reynolds decomposition is unable to disaggregate waves from turbulence contributions, thus hiding any information about the production/destruction of turbulence energy injected/subtracted by the wave motion. We adopt a triple-decomposition approach to disaggregate the mean, wave, and turbulence contributions within near-surface boundary-layer flows, with the aim of unveiling the role of wave motion as a source and/or sink of turbulence kinetic and potential energies in the respective explicit budgets. By exploring the balance between buoyancy (driving waves) and shear (driving turbulence), a simple interpretation paradigm is introduced to distinguish two layers, namely the near-ground and far-ground sublayer, estimating where the turbulence kinetic energy can significantly feed or be fed by the wave. To prove this paradigm, a nocturnal valley flow is used as a case study to detail the role of wave motions on the kinetic and potential energy budgets within the two sublayers. From this dataset, the explicit kinetic and potential energy budgets are calculated, relying on a variance–covariance analysis to further comprehend the balance of energy production/destruction in each sublayer. With this investigation, we propose a simple interpretation scheme to capture and interpret the extent of the complex interaction between waves and turbulence in nocturnal stable boundary layers.

Diurnal evolution of negative atmospheric ions above the boreal forest: From ground level to the free troposphere

At SMEAR II research station in Hyytiälä, located in the Finnish boreal forest, the process of new particle formation and the role of ions has been investigated for almost 20 years near the ground and at canopy level. However, above SMEAR II, the vertical distribution and diurnal variation of these different atmospheric ions are poorly characterized. In this study, we assess the atmospheric ion composition in the stable boundary layer, residual layer, mixing layer and free troposphere, and the 5 evolution of these atmospheric ions due to photochemistry and turbulent mixing through the day. To measure the vertical profile of atmospheric ions, we developed a tailored setup for online mass spectrometric measurements, capable of being deployed in a Cessna 172 with minimal modifications. Simultaneously, instruments dedicated to aerosol properties measured in a second Cessna. We conducted a total of 16 measurement flights in May 2017, during the spring, which is the most active new particle formation season. A flight day typically consisted of three distinct flights through the day (dawn, morning and afternoon) to 10 observe the diurnal variation and at different altitudes (from 100 m to 3200 m above ground), and to capture the boundary layer development from stable boundary layer, residual layer to mixing layer, and the free troposphere. Our observations showed that the ion composition is distinctly different in each layer and depends on the air mass origin and time of the day. Before sunrise, the layers are separated from each other and have their own ion chemistry. We observed that the ions present within the stable layer are of the same composition as the ions measured at the canopy level. During daytime when the mixing layer evolved and the compounds are vertically mixed, we observed that highly oxidised organic molecules are distributed to the top of the boundary layer. The ion composition in the residual layer varies with each day, showing similarities with either the stable boundary layer or the free troposphere. Finally, within the free troposphere, we detected a variety of carboxylic acids and ions that are likely containing halogens, originating from the Arctic Sea.

Flux–Profile Relationships in the Stable Boundary Layer—A Critical Discussion

Flux–profile relationships are crucial for parametrizing surface fluxes of momentum and heat, that are of central relevance for applications such as climate modelling and weather forecast. Nevertheless, their functional forms are still under discussion, and a generally accepted formulation does not exist yet. We reviewed the four main formulations proposed in the literature so far and assessed how they affect the theoretical behaviour of the kinematic heat flux (H0) and the temperature scale (T*) in the stable boundary layer, as well as their consequences on the existence of critical values for both the gradient and the flux Richardson numbers. None of them turned out to be fully consistent with the literature published so far, with two of them leading to very unreliable expressions for both H0 and T*. All considered, a convincing description of flux–profile relationships still needs to be found and seems to represents a considerable challenge.

Evaluation of a Method for Calculating the Height of the Stable Boundary Layer based on Wind Profile Lidar and Turbulent Fluxes

The height of the stable boundary layer (SBL), known as the nocturnal boundary layer height, is controlled by numerous factors of different natures. The SBL height defines the state of atmospheric turbulence and describes the diffusion capacity of the atmosphere. Therefore, it is unsurprising that many alternative (sometimes contradictory) formulations for the SBL height have been proposed to date, and no consensus has been achieved. In our study, we propose an iterative algorithm to determine the SBL height h based on the flux–profile relationship using wind profiles and turbulent fluxes. This iterative algorithm can obtain temporally continuous, accurate estimates of h and is widely applicable. The predicted h presents relatively good agreement with four observation-derived SBL heights, hJ, h1, hi, and hθ (hJ: maximum wind speed height, h1: zero wind shear height, hi: temperature inversion height, and hθ: height at which 0.8 times the inversion strength appears for the first time), especially with hθ, which shows the best fit. In addition, h exhibits a low absolute difference and relative difference with hJ, which presents the second-best result. The agreement with hi and h1 may be satisfactory, but small differences are observed, and the one standard deviation of the mean relative difference is large. In addition, the predicted h is compared with other SBL height estimation methods, including diagnostic, λ1, λ2 and λ3 (three typical dimensional scale height parameters) and prognostic equation-based methods, λ(h) (an equation for the growth of h developed). The diagnostic formulas are found to be appropriate, especially under extremely stable conditions. Additionally, the equation of λ3 presents the best result of all the dimensional scale height parameters. However, the prognostic equation λ(h) in our study is very unsatisfactory.

An Investigation of the Grid Sensitivity in Large-Eddy Simulations of the Stable Boundary Layer

We revisit the longstanding problem of grid sensitivity, i.e., the lack of grid convergence in large-eddy simulations (LES) of the stable boundary layer. We use a comprehensive set of LES of the well-known Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study 1 (GABLS1) case with varying grid spacings between 12.5 m and 1 m to investigate several physical processes and numerical features that are possible causes of grid sensitivity. Our results demonstrate that there are two resolution regimes in which grid sensitivity manifests differently. We find that changing the numerical advection schemes and the subgrid-scale models alters the simulation results, but the options tested do not fully address the grid-sensitivity issue. Moreover, sensitivity runs suggest that the surface boundary condition and the interaction of the surface with the near-surface flow, as well as the mixing with the free atmosphere, are unlikely to be the causes of the observed grid sensitivity. One interesting finding is that the grid sensitivity in the fine grid-spacing regime (grid spacings $$\le 2\,\mathrm{m}$$ ≤ 2 m ) is closely related to the reduction in the energy content of large-scale turbulence, leading to less turbulence kinetic energy and hence lower boundary-layer heights. The present work demonstrates that there is still an urgent need to address this grid-sensitivity issue in order to perform reliable LES of the stable boundary layer.

Intuitionism and the Sorites Paradox

This chapter revisits and further develops all the principle themes and concepts of the preceding chapters. Epistemicism about vagueness postulates a realm of distinctions drawn by basic vague concepts that transcend our capacity to know them. Its treatment of their subject matter is thus broadly comparable to the Platonist philosophy of mathematics. An intuitionist philosophy of vagueness, as do many philosophies of the semantics and metaphysics of vague expressions, finds this idea merely superstitious and rejects it. The vagueness-intuitionist, however, credits the epistemicist with a crucial insight: that vagueness is indeed a cognitive, rather than a semantic, phenomenon—something that is not a consequence of some kind of indeterminacy, or open-endedness in the semantics of vague expressions but rather resides in our brute inability to bring, for example, yellow and orange right up against one another, so to speak, so as to mark a sharp and stable boundary. A solution to the Sorites paradox is developed that is consonant with this basic idea but, by motivating a background logic that observes (broadly) intuitionistic restrictions on the proof theory for negation, allows us to treat the paradoxical reasoning as a simple reductio of its major premise, without the unwelcome implication, sustained by classical logic, of sharp cut-offs.

A Calculation Method of Power System Static Stability Margin

This paper establishes a hybrid power network equation with node voltage and branch current as state variables. The characteristic equation representing the stable boundary of the system is derived. Then the boundary conditions of static stability of the power system on the critical circle of voltage static stability are formed. Find the closest distance equation between the load point and the corresponding stable boundary through geometric analysis. The introduction of the distance equation avoids artificially setting the direction of load growth. The distance equation and boundary characteristic equation are added to the hybrid power network equations as additional equations for analyzing the minimum load boundary. The equations are solved by Newton's iterative algorithm. In order to avoid the Jacobian matrix singularity near the load boundary, the algorithm adopts the method of replacing the critical point in the Jacobian matrix to calculate. The simulation results show that the method is correct and effective.

Quantifying wind plant blockage under stable atmospheric conditions

Wind plant blockage reduces the wind velocity upstream undermining turbine performance for the first row of the plant. We assess how atmospheric stability modifies the induction zone of a wind plant in flat terrain. We also explore different approaches to quantifying the magnitude and extent of the induction zone from field-like observations. To investigate the influence from atmospheric stability, we compare simulations of two stable boundary layers using the Weather Research and Forecasting model in large-eddy simulation mode, representing wind turbines using the generalized actuator disk approach. We find a faster cooling rate at the surface, which produces a stronger stably stratified boundary layer, amplifies the induction zone of both an isolated turbine and of a large wind plant. A statistical analysis on the hub-height wind speed field shows wind slowdowns only extend far upstream (up to 15D) of a wind plant in strong stable boundary layers. To evaluate different ways of measuring wind plant blockage from field-like observations, we consider various ways of estimating the freestream velocity upstream of the plant. Sampling a large area upstream is the most accurate approach to estimating the freestream conditions, and thus of measuring the blockage effect. Also, the choice of sampling method may induce errors of the same order as the velocity deficit in the induction zone.