A Modelling Study of Flux Imbalance and the Influence of Entrainment in the Convective Boundary Layer

It is frequently observed in field experiments that the eddy covariance heat fluxes are systematically underestimated as compared to the available energy. The flux imbalance problem is investigated using the NCAR’s large-eddy simulation (LES) model imbedded with an online scheme to calculate Reynolds-averaged fluxes. A top–down and a bottom–up tracer are implemented into the LES model to quantify the influence of entrainment and bottom–up diffusion processes on flux imbalance. The results show that the flux imbalance follows a set of universal functions that capture the exponential decreasing dependence on u _*/w _*, where u _* and w _* are friction velocity and the convective velocity scale, respectively, and an elliptic relationship to z/z _i , where z _i is the mixing-layer height. The source location in the boundary layer is an important factor controlling the imbalance magnitude and its horizontal and vertical distributions. The flux imbalance of heat and the bottom–up tracer is tightly related to turbulent coherent structures, whereas for the top–down diffusion, such relations are weak to nonexistent. Our results are broadly consistent with previous studies on the flux imbalance problem, suggesting that the published results are robust and are not artefacts of numerical schemes.     

Resolved Versus Parametrized Boundary-Layer Plumes. Part III: Derivation of a Statistical Scheme for Cumulus Clouds

We present a statistical cloud scheme based on the subgrid-scale distribution of the saturation deficit. When analyzed in large-eddy simulations (LES) of a typical cloudy convective boundary layer, this distribution is shown to be bimodal and reasonably well-fitted by a bi-Gaussian distribution. Thanks to a tracer-based conditional sampling of coherent structures of the convective boundary layer in LES, we demonstrate that one mode corresponds to plumes of buoyant air arising from the surface, and the second to their environment, both within the cloud and sub-cloud layers. According to this analysis, we propose a cloud scheme based on a bi-Gaussian distribution of the saturation deficit, which can be easily coupled with any mass-flux scheme that discriminates buoyant plumes from their environment. For that, the standard deviations of the two Gaussian modes are parametrized starting from the top-hat distribution of the subgrid-scale thermodynamic variables given by the mass-flux scheme. Single-column model simulations of continental and maritime case studies show that this approach allows us to capture the vertical and temporal variations of the cloud cover and liquid water.     

Length Scales of Scalar Diffusion in the Convective Boundary Layer: Laboratory Observations

A laboratory study of scalar diffusion in the convective boundary layer has found results that are consistent with a 1999 large-eddy simulation (LES) study by Jonker, Duynkerke and Cuijpers. For bottom-up and top-down scalars (introduced as ‘infinite’ area sources of passive tracer at the surface and inversion, respectively) the dominant length scale was found to be much larger than the length scale for density fluctuations, the latter being equal to the boundary-layer depth h. The variance of the normalized passive scalar grew continuously with time and its magnitude was about 3–5 times larger for the top-down case than for the bottom-up case. The vertical profiles of the normalized passive scalar variance were found to be approximately constant through the convective boundary layer (CBL) with a value of about 3–8c_*² for bottom-up and 10–50c_*² for top-down diffusion. Finally, there was some evidence of a minimum in the variance and dominant length scale for scalar flux ratios (top-down to bottom-up flux) close to −0.5. All these convection tank results confirm the LES results and support the hypothesis that there is a distinct difference in behaviour between the dynamic and passive variables in the CBL.     

Measurements Of Thermal Updraft Intensity Over Complex Terrain Using American White Pelicans And A Simple Boundary-Layer Forecast Model

An examination of boundary-layer meteorological and avian aerodynamic theories suggests that soaring birds can be used to measure the magnitude of vertical air motions within the boundary layer. These theories are applied to obtain mixed-layer normalized thermal updraft intensity over both flat and complex terrain from the climb rates of soaring American white pelicans and from diagnostic boundary-layer model-produced estimates of the boundary-layer depth z_i and the convective velocity scale w_*. Comparison of the flatland data with the profiles of normalized updraft velocity obtained from previous studies reveals that the pelican-derived measurements of thermal updraft intensity are in close agreement with those obtained using traditional research aircraft and large eddy simulation (LES) in the height range of 0.2 to 0.8 z_i. Given the success of this method, the profiles of thermal vertical velocity over the flatland and the nearby mountains are compared. This comparison shows that these profiles are statistically indistinguishable over this height range, indicating that the profile for thermal updraft intensity varies little over this sample of complex terrain. These observations support the findings of a recent LES study that explored the turbulent structure of the boundary layer using a range of terrain specifications. For terrain similar in scale to that encountered in this study, results of the LES suggest that the terrain caused less than an 11% variation in the standard deviation of vertical velocity.     

The Role of Shear in the Morning Transition Boundary Layer

We use large-eddy simulation (LES) to better define the early stages of the morning transition boundary layer. Previous LES studies relating to the morning transition boundary layer focus on the role of the entraining convective boundary layer (CBL). By using a combination of different domain sizes and grid lengths, the full evolution from the stable boundary layer (SBL) to the CBL is modelled here. In the early stages of the morning transition the boundary layer is shown to be a combination of a shallow mixed layer capped by a significant shear driven stable boundary layer (the so-called mixed CBL–SBL state). The mixed CBL–SBL state is the key to understanding the sensitivity to shear. Turbulent kinetic energy budgets also indicate that it is shear driven. The negative flux from the mixed CBL–SBL state extends much further above the minimum than is typically found for the CBL later in the day, and the depth of penetration scales as w _m /N _i , where w _m is the combined friction and convective velocity scale and N _i the static stability at the inversion top.     

Airborne measurements of turbulent trace gas fluxes and analysis of eddy structure in the convective boundary layer over complex terrain

Using the new high-frequency measurement equipment of the research aircraft DO 128, which is described in detail, turbulent vertical fluxes of ozone and nitric oxide have been calculated from data sampled during the ESCOMPTE program in the south of France. Based on airborne turbulence measurements, radiosonde data and surface energy balance measurements, the convective boundary layer (CBL) is examined under two different aspects. The analysis covers boundary-layer convection with respect to (i) the control of CBL depth by surface heating and synoptic scale influences, and (ii) the structure of convective plumes and their vertical transport of ozone and nitric oxides. The orographic structure of the terrain causes significant differences between planetary boundary layer (PBL) heights, which are found to exceed those of terrain height variations on average. A comparison of boundary-layer flux profiles as well as mean quantities over flat and complex terrain and also under different pollution situations and weather conditions shows relationships between vertical gradients and corresponding turbulent fluxes. Generally, NO_x transports are directed upward independent of the terrain, since primary emission sources are located near the ground. For ozone, negative fluxes are common in the lower CBL in accordance with the deposition of O₃ at the surface.The detailed structure of thermals, which largely carry out vertical transports in the boundary layer, are examined with a conditional sampling technique. Updrafts mostly contain warm, moist and NO_x loaded air, while the ozone transport by thermals alternates with the background ozone gradient. Evidence for handover processes of trace gases to the free atmosphere can be found in the case of existing gradients across the boundary-layer top. An analysis of the size of eddies suggests the possibility of some influence of the heterogeneous terrain in mountainous area on the length scales of eddies.     

Subfilter-Scale Modelling Using Transport Equations: Large-Eddy Simulation of the Moderately Convective Atmospheric Boundary Layer

We perform large-eddy simulation (LES) of a moderately convective atmospheric boundary layer (ABL) using a prognostic subfilter-scale (SFS) model obtained by truncating the full conservation equations for the SFS stresses and fluxes. The truncated conservation equations contain production mechanisms that are absent in eddy-diffusivity closures and, thus, have the potential to better parametrize the SFS stresses and fluxes. To study the performance of the conservation-equation-based SFS closure, we compare LES results from the surface layer with observations from the Horizontal Array Turbulence Study (HATS) experiment. For comparison, we also show LES results obtained using an eddy-diffusivity closure. Following past studies, we plot various statistics versus the non-dimensional parameter, Λ _w /Δ, where Λ _w is the wavelength corresponding to the peak in the vertical velocity spectrum and Δ is the filter width. The LES runs are designed using different domain sizes, filter widths and surface fluxes, in order to replicate partly the conditions in the HATS experiment. Our results show that statistics from the different LES runs collapse reasonably and exhibit clear trends when plotted against Λ _w /Δ. The trends exhibited by the production terms in the modelled SFS conservation equations are qualitatively similar to those seen in the HATS data with the exception of SFS buoyant production, which is underpredicted. The dominant production terms in the modelled SFS stress and flux budgets obtained from LES are found to approach asymptotically constant values at low Λ _w /Δ. For the SFS stress budgets, we show that several of these asymptotes are in good agreement with their corresponding theoretical values in the limit Λ _w /Δ → 0. The modelled SFS conservation equations yield trends in the mean values and fluctuations of the SFS stresses and fluxes that agree better with the HATS data than do those obtained using an eddy-diffusivity closure. They, however, underpredict considerably the level of SFS anisotropy near the wall when compared to observations, which could be a consequence of the shortcomings in the model used for the pressure destruction terms. Finally, we address the computational cost incurred due to the use of additional prognostic equations.     

Observations of planview flux patterns within convective structures of the marine atmospheric surface layer

Air/sea flux variability on horizontal scales from 50 m to several km results, in part, from the presence of coherent convective structures within the atmospheric boundary layer. The horizontal distribution of fluxes within these convective updrafts and downdrafts is, therefore, central to studies of air/sea interaction and remote sensing of sea surface wind and wave fields. This study derives these flux patterns from observations of the Marine Atmospheric Surface Layer (MASL).Research aircraft flights through the MASL provide an optimal means for sampling large numbers of the above-mentioned coherent structures. The NCAR Electra flew numerous legs through the MASL at a height of 50 m during the 1987 stratocumulus phase of Project FIRE (First ISSCP (International Satellite Cloud Climatology Program) Regional Experiment).In situ measurements from these legs serve as the dataset for this paper. The data are processed in such a way as to retain only the turbulence fluctuations. Conditional sampling, based on the vertical velocity field, results in the isolation of convective updrafts and downdrafts. Compositing of the data for these two classes of convective drafts results in horizontal planviews of the vertical fluxes of buoyancy, absolute humidity, along-meanwind component of momentum, and vertical velocity. To ensure dynamical similarity, these horizontal planviews are oriented in a coordinate system aligned with the mean wind.     

Vertical velocity field in the convective boundary layer as observed with an acoustic Doppler sodar

The morning development of the daytime convective boundary layer (CBL) during fine weather has been observed with an acoustic Doppler sodar of the C.R.P.E. In particular, the vertical profile of the vertical velocity third-order statistic W* ³ has been obtained. This quantity is a maximum near 0.3z _I where z _I, is the height of the CBL. The histogram of vertical velocity in the CBL shows a relationship between W ³ and the convective velocity W _* and is useful for convective plume determination.     

Resolved Versus Parametrized Boundary-Layer Plumes. Part I: A Parametrization-Oriented Conditional Sampling in Large-Eddy Simulations

A conditional sampling based on the combination of a passive tracer emitted at the surface and thermodynamic variables is proposed to characterise organized structures in large-eddy simulations of cloud-free and cloudy boundary layers. The sampling is evaluated against more traditional sampling of dry thermals or clouds. It enables the characterization of convective updrafts from the surface to the top of the boundary layer (or the top of cumulus clouds), describing in particular the transition from the sub-cloud to the cloud layer, and retrieves plume characteristics, entrainment and detrainment rates, variances and fluxes. This sampling is used to analyze the contribution of boundary-layer thermals to vertical fluxes and variances.     

Resolved Versus Parametrized Boundary-Layer Plumes. Part II: Continuous Formulations of Mixing Rates for Mass-Flux Schemes

The conditional sampling of coherent structures in large-eddy simulations of the convective boundary layer (Couvreux et al. Boundary-layer Meteorol 134:441–458, 2010) is used to propose and evaluate formulations of fractional entrainment and detrainment rates for mass-flux schemes. The proposed formulations are physically-based and continuous from the surface to the top of clouds. Entrainment is related to the updraft vertical velocity divergence, while detrainment depends on the thermal vertical velocity, on buoyancy and on the moisture contrast between the mean plume and its environment. The proposed formulations are first directly evaluated in simulations of shallow clouds. They are then tested in single-column simulations with the thermal plume model, a mass-flux representation of boundary-layer thermals.     

The impact of soil moisture on dispersion-related characteristics

This study investigates the impact of soil moisture availability on dispersion-related characteristics: surface fric-tion velocity (u*), characteristic scales of temperature and humidity (T* and q*), the planetary boundary layer height (h) and atmospheric stability classified by Monin-Obukhov length (L), Kazanski-Monin parameter (μ) and convective velocity scale (w*) during daytime convective condition using a one-dimensional primitive equation with a refined soil model.     

Numerical simulation of turbulent convective flow over wavy terrain

By means of a large-eddy simulation, the convective boundary layer is investigated for flows over wavy terrain. The lower surface varies sinusoidally in the downstream direction while remaining constant in the other. Several cases are considered with amplitude up to 0.15H and wavelength ofH to 8H, whereH is the mean fluid-layer height. At the lower surface, the vertical heat flux is prescribed to be constant and the momentum flux is determined locally from the Monin-Obukhov relationship with a roughness lengthz _o=10^–4 H. The mean wind is varied between zero and 5w _*, wherew _* is the convective velocity scale. After rather long times, the flow structure shows horizontal scales up to 4H, with a pattern similar to that over flat surfaces at corresponding shear friction. Weak mean wind destroys regular spatial structures induced by the surface undulation at zero mean wind. The surface heating suppresses mean-flow recirculation-regions even for steep surface waves. Short surface waves cause strong drag due to hydrostatic and dynamic pressure forces in addition to frictional drag. The pressure drag increases slowly with the mean velocity, and strongly with /H. The turbulence variances increase mainly in the lower half of the mixed layer forU/w _*>2.     

Simulating Dispersion in the Evening-Transition Boundary Layer

We investigate dispersion in the evening-transition boundary layer using large-eddy simulation (LES). In the LES, a particle model traces pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent subgrid-scale motions. The LES is forced with both a sudden switch-off of the surface heat flux and also a more gradual observed evolution. The LES shows ‘lofting’ of plumes from near-surface releases in the pre-transition convective boundary layer; it also shows the subsequent ‘trapping’ of releases in the post-transition near-surface stable boundary layer and residual layer above. Given the paucity of observations for pollution dispersion in evening transitions, the LES proves a useful reference. We then use the LES to test and improve a one-dimensional Lagrangian Stochastic Model (LSM) such as is often used in practical dispersion studies. The LSM used here includes both time-varying and skewed turbulence statistics. It is forced with the vertical velocity variance, skewness and dissipation from the LES for particle releases at various heights and times in the evening transition. The LSM plume spreads are significantly larger than those from the LES in the post-transition stable boundary-layer trapping regime. The forcing from the LES was thus insufficient to constrain the plume evolution, and inclusion of the significant stratification effects was required. In the so-called modified LSM, a correction to the vertical velocity variance was included to represent the effect of stable stratification and the consequent presence of wave-like motions. The modified LSM shows improved trapping of particles in the post-transition stable boundary layer.     

Comparison of Kansas Data with High-resolution Large-eddy Simulation Fields

The surface layer of an atmospheric boundary layer (ABL) is most accessible to field measurements and hence its ensemble-mean structure has been well established. The Kansas field measurements were the first detailed study of this layer, providing numerous benchmark statistical profiles for a wide range of stability states. Large-eddy simulation (LES), in contrast, is most suitable for studying the mixed layer of the ABL where the energy-containing range of the vertical velocity field is well resolved. In the surface layer, typical large-eddy simulations barely resolve the energy-containing vertical-velocity fields and hence do not provide sufficient data for a detailed analysis.We carried out a nested-mesh simulation of a moderately convective ABL (-z_i/L = 8) in which the lower 6% of the boundary layer had an effective grid resolution of 512³. We analyze the LES fields above the 6th vertical grid level (z = 23 m) where the vertical velocity field has a well formed inertial subrange, for a detailed comparison with the Kansas results. Various terms in the budgets of turbulent kinetic energy, temperature variance, Reynolds stress, temperature flux, and some higher order moments are compared. The agreement is generally quite good; however, we do observe certain discrepancies, particularly in the terms involving pressure fluctuations.     

A Comparison of Higher-Order Vertical Velocity Moments in the Convective Boundary Layer from Lidar with In Situ Measurements and Large-Eddy Simulation

We have analyzed measurements of vertical velocity w statistics with the NOAA high resolution Doppler lidar (HRDL) from about 390 m above the surface to the top of the convective boundary layer (CBL) over a relatively flat and uniform agricultural surface during the Lidars-in-Flat-Terrain (LIFT) experiment in 1996. The temporal resolution of the zenith-pointing lidar was about 1 s, and the range-gate resolution about 30 m. Vertical cross-sections of w were used to calculate second- to fourth-moment statistics of w as a function of height throughout most of the CBL. We compare the results with large-eddy simulations (LES) of the CBL and with in situ aircraft measurements. A major cause of the observed case-to-case variability in the vertical profiles of the higher moments is differences in stability. For example, for the most convective cases, the skewness from both LES and observations changes more with height than for cases with more shear, with the observations changing more with stability than the LES. We also found a decrease in skewness, particularly in the upper part of the CBL, with an increase in LES grid resolution.     

Coherent Structures near the Surface in a Strongly Sheared Convective Boundary Layer Generated by Large-Eddy Simulation

Well-developed low speed and high temperature streaks in association with the alignment of convection cells are observed in a large-eddy-simulation (LES) generated strongly sheared convective boundary-layer flow, which is driven by a geostrophic wind speed of 15 m s^-1 and a surface kinematic heat flux of 0.05 K m s^-1. Vortices that drive streaky structures are identified through an eigenvalue method (lambda;₂method) near the surface. These vortices are highly elongated along the quasi-streamwise direction alternating sign of the x-component of vorticity (_x). By conditional sampling of fully developed vortices, a statistically significant coherent structure is educed. The educed vortex is elongated to the streamwise direction with the elevation angle of about 17° above the horizontal surface. However, the horizontal tilting is not clearly demonstrated in the present simulation. Fluctuation fields in the domain of the educed vortex show the existence of a low speed and high temperature streak as a direct consequence of momentum and heat transport by vortical motions. The strong ejection(upward transport of low momentum or high temperature)occurring at the higher level than that of the strong sweep (downward transport of high momentum and low temperature) can be explained from the spatial distribution of the fluctuationfields of velocity and temperature. The contribution of ejection to the Reynolds stress at z/h₁ = 0.18 is about 75%, which is slightly greater than that (70% at z/h₁ = 0.173) for the neutrally stratified atmospheric boundary layer. Ejection is also found to be dominant for the turbulent heat flux.     

The limitations on stress parameterization imposed by intermittency in turbulent flow

The indirect dissipation technique is used to estimate 1-min averages of friction velocity u _*in the surface layer over the tropical ocean. These estimates are compared to estimates of u _*obtained using a drag coefficient and the relative difference between the two is examined in relation to stability and averaging time. Plumes and downdrafts are found to be responsible for an anomalous behavior of the drag coefficient estimates. Certain factors relating to plume properties, derived using conditional sampling as described in Khalsa (1980), are shown to be related to the variance between the two estimates of friction velocity. An investigation into the effects of increasing the averaging time reveals that plume spacing, which is dependent on stability, and the mean wind speed determine the minimum time for smoothing the influence of plumes and downdrafts.Department of Atmospheric Sciences contribution number 513.     

Large-eddy simulations of thermally forced circulations in the convective boundary layer. Part I: A small-scale circulation with zero wind

We have conducted large-eddy simulations (LES) of the atmospheric boundary layer with surface heat flux variations on a spatial scale comparable to the boundary layer depth.We first ran a simulation with a horizontally homogeneous heat flux. In general the results are similar to those of previous large-eddy simulations. The model simulates a field of convective eddies having approximately the correct velocity and spatial scales, and with the crucial property that kinetic energy is transported vigorously upwards through the middle levels. However, the resolved temperature variance is only about half what is observed in the laboratory or the atmosphere. This deficiency — which is shared by many other large-eddy simulations — has dynamic implications, particularly in the pressure/temperature interaction terms of the heat flux budget. Recent simulations by other workers at much higher resolution than ours appear to be more realistic in this respect.The surface heat flux perturbations were one-dimensional and sinusoidal with a wavelength equal to 1.3 times the boundary-layer depth. The mean wind was zero. Results were averaged over several simulations and over time. There is a mean circulation, with ascent over the heat flux maxima (vertical velocity ~0.1w _*) and descent over the heat flux minima. Turbulence is consistently stronger over the heat flux maxima. The horizontal velocity variance components (calculated with respect to the horizontal average) become unequal, implying that convective eddies are elongated parallel to the surface heat flux perturbations.A consideration of the budgets for temperature and velocity suggests several simplifying concepts.The research reported in this paper was conducted while the first author was on study leave at Colorado State University.     

论边界层中的大气扩散PDF模式

基于大气扩散Ｋ理论，用作为风速脉动均方差和拉氏时间尺度函数的湍流交换系数，得到了直接利用风速脉动几率密度而不用扩散参数的大气扩散ＰＤＦ模式。分别研究了对流边界层上升气流区与下降区垂直速度的统计特征，求得双正态ＰＤＦ模式。在给定ＣＢＬ自身参数如对流特征速度ｗ＊，顶高ｈｉ和源高度上的平均风速时，该模式计算出的无量纲浓度分布与室内外测试结果一致。