Sea-breeze scaling from numerical model simulations,part II: Interaction between the sea breeze and slope flows

Numerical model simulations of sea-breeze circulations in the presence of idealized topography are subjected to dimensional analysis in order to capture the dynamics of the sea-breeze circulation combined with an upslope-flow circulation. A secondary objective is to reconcile previous results based on observations. The analysis is based on a scaling analysis of sea-breeze speed, depth and volume flux. This study is motivated by the fact that the literature of sea breezes interacting with upslope flows is generally qualitative. Results show clear scaling regimes and strong interaction between the two thermally driven circulations. We distinguish three regimes, depending on slope length, slope angle, stability and surface heat flux. The first and third regimes obey the scaling laws of pure sea-breeze scaling. The second regime shows a significant decrease in the scaled volume flux relative to pure sea-breeze scaling. Dynamical relations in the second regime show a strong influence on the circulation of upslope stable air advection.     

Stable Boundary-Layer Scaling Regimes: The Sheba Data

Turbulent and mean meteorological data collected at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are analyzed to examine different regimes of the stable boundary layer (SBL). Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification. Scaling arguments and our analysis show that the SBL can be classified into four major regimes: (i) surface-layer scaling regime (weakly stable case), (ii) transition regime, (iii) turbulent Ekman layer, and (iv) intermittently turbulent Ekman layer (supercritical stable regime). These four regimes may be considered as the basic states of the traditional SBL. Sometimes these regimes, especially the last two, can be markedly perturbed by gravity waves, detached elevated turbulence (‘upside down SBL’), and inertial oscillations. Traditional Monin–Obukhov similarity theory works well in the weakly stable regime. In the transition regime, Businger–Dyer formulations work if scaling variables are re-defined in terms of local fluxes, although stability function estimates expressed in these terms include more scatter compared to the surface-layer scaling. As stability increases, the near-surface turbulence is affected by the turning effects of the Coriolis force (the turbulent Ekman layer). In this regime, the surface layer, where the turbulence is continuous, may be very shallow (< 5 m). Turbulent transfer near the critical Richardson number is characterized by small but still significant heat flux and negligible stress. The supercritical stable regime, where the Richardson number exceeds a critical value, is associated with collapsed turbulence and the strong influence of the earth’s rotation even near the surface. In the limit of very strong stability, the stress is no longer a primary scaling parameter.     

Nocturnal Boundary-Layer Regimes

This study analyzes turbulence data collected over a grassland site in the nocturnal boundary layer. Examination of the dependence of the nocturnal boundary layer on stability suggests three regimes: a) the weakly stable case, b) a transition stability regime where many of the variables change rapidly with increasing stability and c) the very stable case. The value of z/L where the downward heat flux is a maximum defines the stability boundary between the weakly stable and transition regimes, where L is the Obukhov length. In the present analysis, the downward heat flux reaches a maximum at z/L approximately equal to 0.05 for 10 m, although comparison with other data indicates that this is not a universal value. For weaker stability, the heat flux decreases with decreasing z/L due to weaker temperature fluctuations. In the transition stability regime, the heat flux decreases rapidly with increasing stability due to restriction of vertical velocity fluctuations by the increasing stratification.For weakly stable conditions, the variances scale according to Monin-Obukhov similarity theory. For very stable conditions, the variances are contaminated by non-turbulent horizontal motions and do not follow the scaling laws. An alternative length scale based on variances is developed which explains more of the variance of the transfer coefficients compared to the Obukhov length.     

A Note on Wave-Turbulence Interaction and the Possibility of Scaling the Very Stable Boundary Layer

Success in scaling the very stable boundary layer has been mixed. One possible reason for this is that wave-turbulence interaction can result in significant energy coupling between turbulence within the planetary boundary layer and the mean flow outside the PBL. Three regimes are described where wave-turbulence interaction forms a significant part of the dynamics. In the first, energy and momentum flows are confined within the PBL and do not preclude local scaling. In the other two, which involve topographically forced waves and propagating waves respectively, energy/momentum transfers across the PBL make success in local scaling unlikely.     

Some aspects of the turbulent stable boundary layer

We consider the structure of the stable boundary layer using the concept of local scaling. In this scaling approach turbulence variables, non-dimensionalized with measurements taken at the same height, can be expressed as a function of a single parameter z/, where z is the height and a local Obukhov length. One of the consequences is that locally scaled variables become constant above the surface layer. This behavior is illustrated with observations of the Richardson number. With local scaling as a closure hypothesis we then formulate a model of the stable boundary layer. Its solution for steady-state conditions is given. One result we obtain is the well-known Zilitinkevich equation for the boundary-layer height. A comparison of this equation with observations results in a reasonable agreement. Also we discuss some alternative expressions for the stable boundary-layer height and compare them with observations. Another result of our model is an explicit profile for the K-coefficient as a quadratic function of height. We discuss the consequences of this expression for the dispersion of a point source emission. We find that the time scale of diffusion in this case is about 5 hours.     

Variability Of The Stable And Unstable Atmospheric Boundary-Layer Height And Its Scales Over A Boreal Forest

Radiosondes releases during the NOPEX-WINTEX experiment carried out in late winter in Northern Finland were analysed for the determination of the height h of the atmospheric boundary layer. We investigate various possible scaling approaches, based on length scales using micrometeorological turbulence surface measurements and the background atmospheric stratification above h. Under stable conditions, the three previously observed turbulence regimes delineated by values of z/L (L is the Obukhov length) appears as a blueprint for understanding the departures found for the suitability of the Ekman scaling based on L_E = u_/f (u is the friction velocity and f the Coriolis parameter). The length scale L_N = u_/N (where N is the Brunt–Väisälä frequency) appears to be a useful scale under most stable conditions, especially in association with L. Under unstable conditions, shear production of turbulence is still significant, so that the three scales L, L_N and L_E are again relevant and the dimensionless ratios _N = L_N/L and L_N/L_E = N/f describe well the WINTEX data. Furthermore, in the classical scaling framework, the unstable domain may also be divided into three regimes as reflected by the dependence ofu_/f on instability (z/L).     

The Scaling Behaviour of a Turbulent Kinetic Energy Closure Model for Stably Stratified Conditions

We investigate the scaling behaviour of a turbulent kinetic energy (TKE) closure model for stably stratified conditions. The mixing length scale for stable stratification is proportional to the ratio of the square root of the TKE and the local Brunt–Väisälä frequency, which is a commonly applied formulation. We analyze the scaling behaviour of our model in terms of traditional Monin–Obukov Similarity Theory and local scaling. From the model equations, we derive expressions for the stable limit behaviour of the flux–gradient relations and other scaling quantities. It turns out that the scaling behaviour depends on only a few model parameters and that the results obey local scaling theory. The analytical findings are illustrated with model simulations for the second GABLS intercomparison study. We also investigate solutions for the case in which an empirical correction function is used to express the eddy diffusivity for momentum as a function of the Richardson number (i.e. an increasing turbulent Prandtl number with stability). In this case, it seems that for certain parameter combinations the model cannot generate a steady-state solution. At the same time, its scaling behaviour becomes unrealistic. This shows that the inclusion of empirical correction functions may have large and undesired consequences for the model behaviour.     

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

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.     

The Effects of Thermal Stratification on Clustering Properties of Canopy Turbulence

The intermittent structure of turbulence within the canopy sublayer (CSL) is sensitive to the presence of foliage and to the atmospheric stability regime. How much of this intermittency originates from amplitude variability or clustering properties remains a vexing research problem for CSL flows. Using a five-level set of measurements collected within a dense hardwood canopy, the clustering properties of CSL turbulence and their dependence on atmospheric stability are explored using the telegraphic approximation (TA). The binary structure of the TA removes any amplitude variability from turbulent excursions but retains their zero-crossing behaviour, and thereby isolating the role of clustering in intermittency. A relationship between the spectral exponents of the actual and the TA series is derived across a wide range of atmospheric stability regimes and for several flow variables. This relationship is shown to be consistent with a relationship derived for long-memory and monofractal processes such as fractional Brownian motion (fBm). Moreover, it is demonstrated that for the longitudinal and vertical velocity components, the vegetation does not appreciably alter fine-scale clustering but atmospheric stability does. Stable atmospheric stability conditions is characterized by more fine scale clustering when compared to other atmospheric stability regimes. For scalars, fine-scale clustering above the canopy is similar to its velocity counterpart but is significantly increased inside the canopy, especially under stable stratification. Using simplified scaling analysis, it is demonstrated that clustering is much more connected to space than to time within the CSL. When comparing intermittency for flow variables and their TA series, it is shown that for velocity, amplitude variations modulate intermittency for all stability regimes. However, amplitude variations play only a minor role in scalar intermittency. Within the crown region of the canopy, a ‘double regime’ emerges in the inter-pulse duration probability distributions not observed in classical turbulence studies away from boundaries. The double regime is characterized by a power-law distribution for shorter inter-pulse periods and a log-normal distribution for large inter-pulse periods. The co-existence of these two regimes is shown to be consistent with near-field/far-field scaling arguments. In the near-field, short inter-pulse periods are controlled by the source strength, while in the far-field long inter-pulse periods are less affected by the precise source strength details and more affected by the transport properties of the background turbulence.     

The Turbulence Structure of the Stable Atmospheric Boundary Layer Around a Coastal Headland: Aircraft Observations and Modelling Results

The turbulence structure of a stable marine atmospheric boundary layer in the vicinity of a coastal headland is examined using aircraft observations and numerical simulations. Measurements are drawn from a flight by the NCAR C-130 around Cape Mendocino on the coast of northern California on June 7 1996 during the Coastal Waves 96 field program. Local similarity scaling of the velocity variances is found to apply successfully within the continuously turbulent layer; the empirical scaling function is similar to that found by several previous studies. Excellent agreement is found between the modelled and observed scaling results. No significant change in scaling behaviour is observed for the region within the expansion fan that forms downstream of the Cape, suggesting that the scaling can be applied to horizontally heterogeneous conditions; however, the precise form of the function relating scaled velocities and stability is observed to change close to the surface. This result, differences between the scaling functions found here and in other studies, and the departure of these functions from the constant value predicted by the original theory, leads us to question the nature of the similarity functions observed. We hypothesize that the form of the functions is controlled by non-local contributions to the velocity variance budgets, and that differences in the non-local terms between studies explain the differences in the observed scaling functions.     

Characterisation of the Nocturnal Boundary Layer at a Site in Northern Spain

The availability of well-calibrated meteorological data for a 10-month period on a 100-m tower has allowed a statistical study to be carried out of many boundary-layer variables. The analyses are restricted to nighttime conditions with stable stratification most of the time, allowing the checking of a number of similarity proposals and the quantifying of the frequency of the different nighttime regimes. We study in detail two typical nights at the site: one weakly stable and one with very strong stratification, highlighting the different aspects between the nights.     

Sea-breeze scaling from numerical model simulations,Part I: Pure sea breezes

Numerical model simulations of sea-breeze circulations under idealized conditions are subjected to dimensional analyses in order to resolve sea-breeze dynamical relations and unify previous results based on observations. The analysis is motivated by the fact that sea-breeze depth scaling and volume flux scaling are only partially understood. The analysis is based on nonlinear numerical modelling simulations in combination with recent observational scaling analyses. The analysis confirms scaling laws for sea-breeze strength dependence on governing variables and shows how the sea-breeze speed scale is controlled by surface heat flux. It also shows that the sea-breeze depth scale is controlled by stability. By combining sea-breeze speed and depth scales, the sea-breeze volume flux scale is determined by an equilibrium between the accumulated convergence of heat over land since sunrise and stable air advection from the sea surface.     

Impact of the Diurnal Cycle of the Atmospheric Boundary Layer on Wind-Turbine Wakes: A Numerical Modelling Study

The wake characteristics of a wind turbine for different regimes occurring throughout the diurnal cycle are investigated systematically by means of large-eddy simulation. Idealized diurnal cycle simulations of the atmospheric boundary layer are performed with the geophysical flow solver EULAG over both homogeneous and heterogeneous terrain. Under homogeneous conditions, the diurnal cycle significantly affects the low-level wind shear and atmospheric turbulence. A strong vertical wind shear and veering with height occur in the nocturnal stable boundary layer and in the morning boundary layer, whereas atmospheric turbulence is much larger in the convective boundary layer and in the evening boundary layer. The increased shear under heterogeneous conditions changes these wind characteristics, counteracting the formation of the night-time Ekman spiral. The convective, stable, evening, and morning regimes of the atmospheric boundary layer over a homogeneous surface as well as the convective and stable regimes over a heterogeneous surface are used to study the flow in a wind-turbine wake. Synchronized turbulent inflow data from the idealized atmospheric boundary-layer simulations with periodic horizontal boundary conditions are applied to the wind-turbine simulations with open streamwise boundary conditions. The resulting wake is strongly influenced by the stability of the atmosphere. In both cases, the flow in the wake recovers more rapidly under convective conditions during the day than under stable conditions at night. The simulated wakes produced for the night-time situation completely differ between heterogeneous and homogeneous surface conditions. The wake characteristics of the transitional periods are influenced by the flow regime prior to the transition. Furthermore, there are different wake deflections over the height of the rotor, which reflect the incoming wind direction.     

Concentration Fluctuations in Smoke Plumes Released Near the Ground

Near-ground artificial cloud releases in the turbulent atmospheric boundary layer were investigated experimentally by Lidar measurement techniques. Simple scaling relations between the average concentration and the lowest order moments are suggested by simple analytical models, and the experimental results are tested against these hypotheses. We find strong evidence for a simple scaling of the standard deviation, skewness and kurtosis with the average concentrations at the downwind distances observed in our experiments. Near-ground concentration fluctuations in fixed as well as moving frames of references are investigated. The scaling is supported by data from several experimental sites and different atmospheric stability conditions. One conclusion of the study is that relatively accurate estimates for the standard deviation, skewness and kurtosis can be obtained for the concentration fluctuations, given a reliable estimate of the space-time varying average concentration field.     

The influence of atmospheric stratification on the growth of water waves

The atmospheric surface layer over sea has a density stratification which varies with moisture content and air/sea temperature difference. This influences the growth of water waves. To study the effect quantitatively, the Reynolds equations are solved numerically. For given wind speed and surface roughness, wave growth is found to be more rapid in unstably stratified conditions than in stable conditions. This is due to an increase in turbulence, primarily caused by an increase of mixing length.Under the assumption of a Charnock relation between surface roughness and friction velocity, it is found that for large inverse wave age (u _*/c>0.07), the effect of stratification on wave growth is weell described by Monin-Obukhov scaling of the friction velocity. For smaller values ofu _*/c, Monin-Obukhov scaling overpredicts.The effect on duration-limited wave growth is studied with the third-generation WAM surface wave model driven by 10 m winds. Effects of stratification on the significant wave height are found to be of the order of 10%. The results are comparable to those of a recent reanalysis of field measurements, although the measured stratification effect is somewhat stronger. Implementation of a stratification-dependent growth in wave models is recommended, as it can lead to small but significant improvements in wave forecasts when accurate air and sea temperatures are available.     

Multifractal analysis of 1-min summer rainfall time series from a monsoonal watershed in eastern China

Multifractal analysis can provide parameters associated with different scales of rainfall, which may be useful for setting up parsimonious downscaling models of rainfall, or for revealing climate-specific properties. Time series of rain rate with 1-min resolution collected from ten stations over a monsoon watershed in eastern China were used to study the multifractal properties. The power spectra estimated by fast Fourier transform (FFT) and discrete Haar wavelet transform (DWT) showed three scaling regimes: the sub-hourly scaling regime with β?≈?1.2, the scaling regime from 1 h to 1 day with β close to 0.6, and the low-frequency spectra plateau with β?≈?0.1. From the hyperbolic tails of exceeding probability distributions, the estimated values of parameter q _c are in 2–2.5, which were consistent with the critical order of K(q) curves. The statistical moments display two main scaling regimes: the high-frequency regime from 3 min to 5 days and the scaling regime beyond 5 days. The scales of 5–10 days seem a transitional regime. The reason that the regimes, revealed by the power spectra, disagree with the statistical moments may be that both FFT and DWT power spectra have limited abilities of analyzing low-frequency scaling but are sensitive to the properties in high-frequency scales. The H values estimated for the regime of sub-hourly scales are larger than 0.4, and the values for the regime 1 h–1 day are close to 0.1. For the low-frequency scales beyond 1 day, negative H is obtained by DWT power spectra. The parameters of universal multifractal models were also estimated. The values of α for the scaling range of 1 min–5 days are 0.486?±?0.047, and for the low-frequency scaling range, its values are 0.808?±?0.323. For the high- and low-frequency scaling ranges, the values of C ₁ are 0.5 and 0.169, respectively, which is different from the values for daily rainfall series collected at the same rain gages.     

A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer

Currently no expression for the equilibrium depth of the turbulent stably-stratified boundary layer is available that accounts for the combined effects of rotation, surface buoyancy flux and static stability in the free flow. Various expressions proposed to date are reviewed in the light of what is meant by the stable boundary layer. Two major definitions are thoroughly discussed. The first emphasises turbulence and specifies the boundary layer as a continuously and vigorously turbulent layer adjacent to the surface. The second specifies the boundary layer in terms of the mean velocity profile, e.g. by the proximity of the actual velocity to the geostrophic velocity. It is shown that the expressions based on the second definition are relevant to the Ekman layer and portray the depth of the turbulence in the intermediate regimes, when the effects of static stability and rotation essentially interfere. Limiting asymptotic regimes dominated by either stratification or rotation are examined using the energy considerations. As a result, a simple equation for the depth of the equilibrium stable boundary layer is developed. It is valid throughout the range of stability conditions and remains in force in the limits of a perfectly neutral layer subjected to rotation and a rotation-free boundary layer dominated by surface buoyancy flux or stable density stratification at its outer edge. Dimensionless coefficients are estimated using data from observations and large-eddy simulations. Well-known and widely used formulae proposed earlier by Zilitinkevich and by Pollard, Rhines and Thompson are shown to be characteristic of the above interference regimes, when the effects of rotation and static stability (due to either surface buoyancy flux, or stratification at the outer edge of the boundary layer) are roughly equally important.     

Methodology for bulk approximation of the wind profile power-law exponent under stable stratification

The variation of the wind profile power-law exponent (p) with respect to changes in atmospheric stability is depicted using the formulation of Ku et al. (1987) for specifying the Monin-Obukhov scaling length (L) under stable atmospheric conditions. The theoretical estimates for the bulk approximation of p as a function of L under stable conditions compare well with power-law exponent data from various sources and the theoretical analysis from Irwin (1979).     

Gradient-Based Turbulence Estimates from Multicopter Profiles in the Arctic Stable Boundary Layer

Boundary-Layer Meteorology - We explore the potential of a new method for the estimation of profiles of turbulence statistics in the stable boundary layer (SBL). By applying gradient-based scaling...     

A Simple Parameterisation for Flux Footprint Predictions

Flux footprint functions estimate the location and relative importance of passive scalar sources influencing flux measurements at a given receptor height. These footprint estimates strongly vary in size, depending on receptor height, atmospheric stability, and surface roughness. Reliable footprint calculations from, e.g., Lagrangian stochastic models or large-eddy simulations are computationally expensive and cannot readily be computed for long-term observational programs. To facilitate more accessible footprint estimates, a scaling procedure is introduced for flux footprint functions over a range of stratifications from convective to stable, and receptor heights ranging from near the surface to the middle of the boundary layer. It is shown that, when applying this scaling procedure, footprint estimates collapse to an ensemble of similar curves. A simple parameterisation for the scaled footprint estimates is presented. This parameterisation accounts for the influence of the roughness length on the footprint and allows for a quick but precise algebraic footprint estimation.