Measurements and Parametrizations of the Atmospheric Boundary-Layer Height at Dome C,Antarctica

An experimental campaign, Study of the Atmospheric Boundary Layer Environmental at Dome C, was held during 2005 at the French-Italian station of Concordia at Dome C. Ground-based remote sensors, as well as in situ instrumentation, were used during the experimental campaign. The measurements allowed the direct estimation of the polar atmospheric boundary-layer height and the test of several parametrizations for the unstable and stable boundary layers. During the months of January and February, weak convection was observed while, during the polar night, a long-lived stable boundary layer occurred continuously. Under unstable stratification the mixing-layer height was determined using the sodar backscattered echoes and potential temperature profiles. The two estimations are highly correlated, with the mixing height ranging between 30 and 350 m. A simple prognostic one-dimensional model was used to estimate the convective mixing-layer height, with the correlation coefficient between observations and model results being 0.66. The boundary-layer height under stable conditions was estimated from radiosounding profiles as the height where the critical Richardson number is reached; values between 10 and 150 m were found. A visual inspection of potential temperature profiles was also used as further confirmation of the experimental height; the results of the two methods are in good agreement. Six parametrizations from the literature for the stable boundary-layer height were tested. Only the parametrization that considers the long-lived stable boundary layer and takes into account the interaction of the stable layer with the free atmosphere is in agreement with the observations.     

Stratified Atmospheric Boundary Layers

Various features of different stability regimes of the stable boundary layer are discussed. Traditional layering is examined in terms of the roughness sublayer, surface layer, local similarity, z-less stratification and the region near the boundary-layer top. In the very stable case, the strongest turbulence may be detached from the surface and generated by shear associated with a low level jet, gravity waves or meandering motions. In this case, similarity theory and the traditional concept of a boundary-layer break down. The elevated turbulence may intermittently recouple to the surface. Inability to adequately measure turbulent fluxes in very stable conditions limits our knowledge of this regime.     

An Auxiliary Tool to Determine the Height of the Boundary Layer

Results from radiosoundings, performed both over land and over sea, show that the ascent rate of a radiosounding balloon, the vertical velocity of the balloon, can be used to determine the height of the boundary layer. In many cases the balloon has a higher ascent rate in the boundary layer and a lower, less variable, ascent rate above. The decrease in ascending velocity appears as a jump at the top of the boundary layer. Two examples of potential temperature profiles for unstable stratification and one profile for stable conditions are shown with the corresponding ascent rates. A comparison between the boundary-layer height determined from potential temperature profiles and from ascent rates is presented for a larger dataset. The different ascent rates of the balloon in the boundary layer and above can be explained by a decrease in drag on the balloon in combination with a lowering of the critical Reynolds number in the boundary layer caused by turbulence. Hence, by simply logging the time from release of a radiosonde, it is possible to obtain additional information that can be used to estimate the height of both the unstable and stable boundary layers.     

Role of land-surface temperature feedback on model performance for the stable boundary layer

At present a variety of boundary-layer schemes is in use in numerical models and often a large variation of model results is found. This is clear from model intercomparisons, such as organized within the GEWEX Atmospheric Boundary Layer Study (GABLS). In this paper we analyze how the specification of the land-surface temperature affects the results of a boundary-layer scheme, in particular for stable conditions. As such we use a well established column model of the boundary layer and we vary relevant parameters in the turbulence scheme for stable conditions. By doing so, we can reproduce the outcome for a variety of boundary-layer models. This is illustrated with the original set-up of the second GABLS intercomparison study using prescribed geostrophic winds and land-surface temperatures as inspired by (but not identical to) observations of CASES-99 for a period of more than two diurnal cycles. The model runs are repeated using a surface temperature that is calculated with a simple land-surface scheme. In the latter case, it is found that the range of model results in stable conditions is reduced for the sensible heat fluxes, and the profiles of potential temperature and wind speed. However, in the latter case the modelled surface temperatures are rather different than with the original set-up, which also impacts on near-surface air temperature and wind speed. As such it appears that the model results in stable conditions are strongly influenced by non-linear feedbacks in which the magnitude of the geostrophic wind speed and the related land-surface temperature play an important role.     

A simple model of the atmospheric boundary layer; sensitivity to surface evaporation

A simple formulation of the boundary layer is developed for use in large-scale models and other situations where simplicity is required. The formulation is suited for use in models where some resolution is possible within the boundary layer, but where the resolution is insufficient for resolving the detailed boundary-layer structure and overlying capping inversion. Surface fluxes are represented in terms of similarity theory while turbulent diffusivities above the surface layer are formulated in terms of bulk similarity considerations and matching conditions at the top of the surface layer. The boundary-layer depth is expressed in terms of a bulk Richardson number which is modified to include the influence of thermals. Attention is devoted to the interrelationship between predicted boundary-layer growth, the turbulent diffusivity profile, countergradient heat flux and truncation errors.The model predicts growth of the convectively mixed layer reasonably well and is well-behaved in cases of weak surface heat flux and transitions between stable and unstable cases. The evolution of the modelled boundary layer is studied for different ratios of surface evaporation to potential evaporation. Typical variations of surface evaporation result in a much greater variation in boundary-layer depth than that caused by the choice of the boundary-layer depth formulation.     

Surface Heterogeneity Effects on Regional-Scale Fluxes in the Stable Boundary Layer: Aerodynamic Roughness Length Transitions

The effects of abrupt streamwise transitions of the aerodynamic roughness length ( $z_\mathrm{o}$ z o ) on the stable atmospheric boundary layer are evaluated using a series of large-eddy simulations based on the first Global Energy and Water Cycle Experiment Atmospheric Boundary Layer intercomparison study (GABLS1). Four $z_\mathrm{o}$ z o values spanning three orders of magnitude are used to create all possible binary distributions with each arranged into patches of characteristic length scales equal to roughly one-half, one, and two times the equivalent homogeneous boundary-layer height. The impact of the heterogeneity on mean profiles of wind speed and temperature, on surface fluxes of heat and momentum, and on internal boundary-layer dynamics are considered. It is found that $z_\mathrm{o}$ z o transitions do not significantly alter the functional relationship between the average surface fluxes and the mean profiles of wind speed and potential temperature. Although this suggests that bulk similarity theory is applicable for modelling the stable boundary layer over $z_\mathrm{o}$ z o heterogeneity, effective surface parameters must still be specified. Existing models that solve for effective roughness lengths of momentum and heat are evaluated and compared to values derived from the simulation data. The existing models are unable to accurately reproduce both the values of the effective aerodynamic roughness lengths and their trends as functions of patch length scale and stability. A new model for the effective aerodynamic roughness length is developed to exploit the benefits of the other models tested. It accurately accounts for the effects of the heterogeneity and stratification on the blending height and effective aerodynamic roughness length. The new model provides improved average surface fluxes when used with bulk similarity.     

On the Temperature and Humidity Dissimilarity in the Marine Surface Layer

The dissimilarity of temperature and humidity transfer in the marine surface layer (MSL) is investigated through the relative transport efficiency and correlation coefficient of these two scalars. We examine their variability and relationship with mean values, as well as spectral characteristics. It is shown that the dissimilarity between these two scalars in the MSL is a function of stability, the boundary-layer depth, and flow steadiness. In general the temperature and humidity are less correlated in shallow marine boundary layers compared to deep marine boundary layers, due to the stronger impact of the boundary-layer scale in breaking the “same source, same sink” assumption for scalar similarity. This is supported by the combination of our spectral analysis of scalar fluxes and corresponding measured and modelled boundary-layer depth. This assumption is also broken in near-neutral conditions, when there is an efficient latent heat transfer but negligible sensible heat transfer. Our data suggest that parametrization of humidity fluxes via similarity theory could still be reliable when the correlation coefficient $>$ 0.5, and in near-neutral conditions the humidity flux can be estimated without use of the sensible heat flux.     

PARAMETERISING SUB-GRID SCALE VERTICAL TRANSPORT IN ATMOSPHERIC MODELS UNDER STATICALLY STABLE CONDITIONS

Five different formulations of the stability functions used forvertical turbulent transfer in atmospheric models are compared in a 1-Dmodel of the nocturnal boundary layer. One of them has a critical valueof the Richardson number around 0.2 and leads to the traditional log-linear profile, while other more empirical formulations maintain sometransfer at values of Ri around 1.0. Although no new observationalevidence is presented, it is suggested that the latter formulations aremore appropriate for use in atmospheric models because the unresolvedvariability inside a model grid box induces some turbulent transfer evenat super-critical values of the mean Ri. The study shows that themagnitude of the stability functions is principally important in theeffective range of Ri values found in the stable boundary layer and thattheir slopes near the origin are less important. This permits the use inatmospheric models of a simple explicit function of Ri containing asingle parameter, with results similar to those obtained with earlier morecomplex formulations. The results of the simulation with the 1-D model are used toexamine the errors introduced by the relatively thick surface layers of most atmospheric models, in which, for the stable case, the traditionalassumption of constancy of the fluxes with height is often clearlyviolated. When a height variation of the fluxes is introduced in surface-layer formulations, the error in the magnitude of the surface fluxes isdecreased with some of the formulations but not all of them. This lackof sensitivity is explained by a compensation mechanism in which theassumed decrease of the fluxes with height implies a correspondingdecrease of the Obukhov length which acts in the oppositedirection, reducing, and sometimes eliminating, the adverse effect of theunrealistic specification of the fluxes. It may be argued that thiscompensation mechanism also explains the wide range of validity of theMoini-Obukhov similarity theory.     

Boundary-Layer Similarity Under an Axisymmetric,Gradient Wind Vortex

We present similarity solutions for the mean boundary-layer profiles under an axisymmetric vortex that is in gradient wind balance; the similarity model includes the nonlinear momentum advection and curvature terms. These solutions are a generalization of the Ekman layer mean flow, which is the canonical boundary-layer basic state under a uniform, geostrophically-balanced flow. Near-surface properties such as inflow angle, surface wind factor, diffusive transport of kinetic energy into the surface layer and dissipational heating are calculated and shown to be sensitive to the choice of turbulence parameterization.     

Surface energy balance,parameterizations of boundary-layer heights and the application of resistance laws near an Antarctic Ice Shelf front

A study of the surface energy balance with turbulent fluxes obtained by the Monin-Obukhov similarity theory and a comparison with results for resistance laws are presented for the strong baroclinic conditions in the vicinity of the Filchner/Ronne Ice Shelf front. The data are taken from a field experiment in the Antarctic summer season 1983/84. For the first time in the coastal Antarctic region, this data set comprises synchronous energy balance measurements over the polynya and the ice shelf together with soundings of the boundary layer, yielding vertical profiles of the wind velocity and temperature over the ice shelf, at the ice shelf front and over the polynya.Over the ice shelf, the radiation balance is the largest component of the energy fluxes and is mainly compensated by the subsurface energy flux and the turbulent heat flux in the daily mean. Over the polynya, turbulent fluxes of sensible and latent heat lead to large energy losses of the water surface in the night-time and in situations of very low air temperatures.Different parameterizations for boundary-layer height are compared using tethered sonde and energy balance measurements. With the height of the inversion base over the polynya and the height of the critical bulk Richardson number over the ice shelf, external parameters for the application of resistance laws were determined. The comparison of turbulent surface fluxes obtained by the energy balance measurements and by the resistance laws shows good agreement for the convective conditions over the polynya. For the stably stratified boundary layer over the ice shelf with small amounts of the turbulent heat flux, the deviation is large for the case of a cold air outflow with a superposed inertial oscillation.     

Intercomparison of Planetary Boundary-Layer Parametrizations in the WRF Model for a Single Day from CASES-99

This study compares five planetary boundary-layer (PBL) parametrizations in the Weather Research and Forecasting (WRF) numerical model for a single day from the Cooperative Atmosphere-Surface Exchange Study (CASES-99) field program. The five schemes include two first-order closure schemes—the Yonsei University (YSU) PBL and Asymmetric Convective Model version 2 (ACM2), and three turbulent kinetic energy (TKE) closure schemes—the Mellor–Yamada–Janjić (MYJ), quasi-normal scale elimination (QNSE), and Bougeault–Lacarrére (BouLac) PBL. The comparison results reveal that discrepancies among thermodynamic surface variables from different schemes are large at daytime, while the variables converge at nighttime with large deviations from those observed. On the other hand, wind components are more divergent at nighttime with significant biases. Regarding PBL structures, a non-local scheme with the entrainment flux proportional to the surface flux is favourable in unstable conditions. In stable conditions, the local TKE closure schemes show better performance. The sensitivity of simulated variables to surface-layer parametrizations is also investigated to assess relative contributions of the surface-layer parametrizations to typical features of each PBL scheme. In the surface layer, temperature and moisture are more strongly influenced by surface-layer formulations than by PBL mixing algorithms in both convective and stable regimes, while wind speed depends on vertical diffusion formulations in the convective regime. Regarding PBL structures, surface-layer formulations only contribute to near-surface variability and then PBL mean properties, whereas shapes of the profiles are determined by PBL mixing algorithms.     

Mean Profiles of Moisture Fluxes in Snow-Filled Boundary Layers

Profiles of moisture fluxes have been examined for convective boundary layers containing clouds and snow, using data derived from aircraft measurements taken on four dates during the 1983/1984 University of Chicago lake-effect snow project. Flux profiles were derived from vertical stacks of aircraft cross-wind flight legs taken at various heights over Lake Michigan near the downwind shore. It was found that, if ice processes are taken into account, profiles of potential temperature and water content were very similar to those presented in past studies of convective boundary layers strongly heated from below. Profiles of total water content and equivalent potential temperature adjusted for ice were nearly invariant with height, except very near the top of the boundary layer, suggesting that internal boundary-layer mixing processes were rapid relative to the rates at which heat and vapour were transported into the boundary layer through entrainment and surface fluxes. Ice was found to play a significant, measurable role in boundary-layer moisture fluxes. It was estimated that 40 to 57% of the upward vapour flux was returned to the surface in the form of snow, converting about 45 to 64% of the surface latent heat flux into sensible heat in the snow-producing process. Assuming advective fluxes are relatively small (thought to be appropriate after the first few tens of km over the lake as suggested by past studies), the boundary layer was found to warm at a rate faster than could be explained by surface heat fluxes and latent heat releases alone, the remainder of the heating presumably coming from radiational processes and entrainment. Discussions of moisture phase change processes throughout the boundary layer and estimates of errors of these flux measurements are presented.     

Theoretical studies of the parameterization of the non-neutral surface boundary layer

The parameterization of the non-neutral atmospheric surface layer has been reexamined using the basic principles of small-scale energetics and thermodynamics. On the basis of this more complete treatment, theK-parameterization has been reformulated. It is found that the linear regression laws between fluxes and driving gradient forces of the turbulent heat and humidity exchanges in the surface layer can be derived in a much more comprehensive manner than by using the commonly used K-theory. With respect to stationary conditions and in the context of similarity concepts, a system of algebraic equations has been formulated which provides reasonable estimates of the distributions of the dimension less rates of viscous energy dissipation as well as turbulent kinetic and thermal-diffusive energy transport as functions of the variablez/L. Quantitative calculations have been performed using the scaling height formulations of Takeuchi and Yokoyama, Prandtl, and von Karman as closure conditions of the equations.     

Measurements and Modelling of the Wind Speed Profile in the Marine Atmospheric Boundary Layer

We present measurements from 2006 of the marine wind speed profile at a site located 18 km from the west coast of Denmark in the North Sea. Measurements from mast-mounted cup anemometers up to a height of 45 m are extended to 161 m using LiDAR observations. Atmospheric turbulent flux measurements performed in 2004 with a sonic anemometer are compared to a bulk Richardson number formulation of the atmospheric stability. This is used to classify the LiDAR/cup wind speed profiles into atmospheric stability classes. The observations are compared to a simplified model for the wind speed profile that accounts for the effect of the boundary-layer height. For unstable and neutral atmospheric conditions the boundary-layer height could be neglected, whereas for stable conditions it is comparable to the measuring heights and therefore essential to include. It is interesting to note that, although it is derived from a different physical approach, the simplified wind speed profile conforms to the traditional expressions of the surface layer when the effect of the boundary-layer height is neglected.     

Regional surface fluxes from satellite-derived surface temperatures (AVHRR) and radiosonde profiles

Radiometric surface temperatures, derived from measurements by the AVHRR instrument aboard the NOAA-9 and the NOAA-11 polar orbiting satellites, were used in combination with wind velocity and temperature profiles measured by radiosondes, to calculate surface fluxes of sensible heat. The measurements were made during FIFE, the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment, in a hilly tall grass prairie area of northeastern Kansas. The method of calculation was based on turbulent similarity formulations for the atmospheric boundary layer. Good agreement (r = 0.7) was obtained with reference values of sensible heat flux, taken as arithmetic means of measurements with the Bowen ratio method at six ground stations. The values of evaporation (latent heat fluxes), derived from these sensible heat fluxes by means of the energy budget, were also in good agreement (r = 0.94) with the corresponding reference values from the ground stations.     

Estimating heat fluxes by merging profile formulae and the energy budget with a variational technique

A variational technique (VT) is applied to estimate surface sensible and latent heat fluxes based on observations of air temperature, wind speed, and humidity, respectively, at three heights (1 m, 4 m, and 10 m), and the surface energy and radiation budgets by the surface energy and radiation system (SERBS). The method fully uses all information provided by the measurements of air temperature, wind, and humidity profiles, the surface energy budget, and the similarity profile formulae as well. Data collected at Feixi experiment station installed by the China Heavy Rain Experiment and Study (HeRES) Program are used to test the method. Results show that the proposed technique can overcome the well-known unstablility problem that occurs when the Bowen method becomes singular; in comparison with the profile method, it reduces both the sensitivities of latent heat fluxes to observational errors in humidity and those of sensible heat fluxes to observational errors in temperature, while the estimated heat fluxes approximately satisfy the surface energy budget. Therefore, the variational technique is more reliable and stable than the two conventional methods in estimating surface sensible and latent heat fluxes.     

Evaluation and model impacts of alternative boundary-layer height formulations

We study bulk formulations for the boundary-layer height which are currently in use for atmospheric modelling. The formulations are based on various forms of the Richardson number, and these are evaluated with Cabauw field data in stable conditions. Results for both a large-eddy simulation model and anE-ε turbulence closure model for neutral boundary layers are also utilised. An updated formulation is introduced, which combines the effects of shear in the outer region of the boundary layer with surface friction. The updated formulation has a better performance for neutral boundary layers with upper level stratification. The findings are illustrated with a single-column model for a case with relatively high winds over the tropical ocean including shallow cumulus convection, and for a case with fair weather over land. We also show that for stable conditions, the updated formulation performs better than estimates on the basis of surface friction alone.     

Theoretical Studies of the Parameterization of the Non-Neutral Surface Boundary Layer

The parameterization of the non-neutral atmospheric surface layer has been reexamined using the basic principles of small-scale energetics and thermodynamics. On the basis of this more complete treatment, the K- parameterization has been reformulated. It is found that the linear regression laws between fluxes and driving gradient forces of the turbulent heat and humidity exchanges in the surface layer can be derived in a much more comprehensive manner than by using the commonly used K-theory. With respect to stationary conditions and in the context of similarity concepts, a system of algebraic equations has been formulated which provides reasonable estimates of the distributions of the dimension-less rates of viscous energy dissipation as well as turbulent kinetic and thermal-diffusive energy transport as functions of the variable z/L. Quantitative calculations have been performed using the scaling height formulations of Takeuchi and Yokoyama, Prandtl, and von Kármán as closure conditions of the equations.     

地表热力非均匀性对近地层相似理论适用性影响的大涡模拟

利用非均匀地表加热的大涡模拟试验,研究了不稳定条件下地表热力非均匀性对近地层相似理论适用性的影响。结果发现,边界层的平均廓线基本不受地表热力非均匀性的影响。进一步分析发现,较大尺度的地表非均匀加热可以激发出有组织的大尺度次级环流,冷暖斑块的通量直到边界层上部才混合均匀;而当地表非均匀尺度较小时,次级环流难以形成有组织的结构,冷暖斑块的通量很快就可以混合均匀。然而,不管是哪种尺度的非均匀地表,非均匀斑块间的平流都对各斑块近地层结构产生重要影响,进而斑块近地层通量—梯度关系与相似理论产生偏差,其中风速梯度关系的偏差更为明显。最后,对目前大气模式中常用的基于相似理论的次网格非均匀地表通量参数化方法——Mosaic方法提出了改进思路。