The Influence of Thermally-Induced Mesoscale Circulations on Turbulence Statistics Over an Idealized Urban Area Under a Zero Background Wind

The influence of mesoscale circulations induced by urban-rural differential surface sensible heat flux and roughness on convective boundary-layer (CBL) flow statistics over an isolated urban area has been examined using large-eddy simulation (LES). Results are analyzed when the circulations influence the entire urban area under a zero background wind. For comparison, the CBL flow over an infinite urban area with identical urban surface characteristics under the same background meteorological conditions is generated as a control case (without circulations). The turbulent flow over the isolated urban area exhibits a mix of streaky structure and cellular pattern, while the cellular pattern dominates in the control case. The mixed-layer height varies significantly over the isolated urban area, and can be lower near the edge of the urban area than over the rural area. The vertical profiles of turbulence statistics over the isolated urban area vary horizontally and are dramatically different from the control case. The turbulent kinetic energy (TKE) sources include wind shear, convergence, and buoyancy productions, compared to only buoyancy production in the control case. The normalized vertical velocity variance is reduced compared to the control case except in the central urban area where it is little affected. The low-level flow convergence is mainly responsible for the enhanced horizontal velocity variance in the central urban area, while wind shear is responsible for the additional local maximum of the horizontal velocity variance near the middle of the CBL outside the central area. Parameterizations in the prognostic equation for TKE used in mesoscale models are evaluated against the LES results over the isolated urban area. We also discuss conditions under which the urban-induced circulations occur and when they may affect the entire urban area. Given that urban-induced circulations can influence the entire urban area within hours for an urban area of a realistic size, it is inappropriate to directly apply empirical relations of turbulence statistics derived under horizontally-homogenous flow conditions to an urban area.     

Heterogeneity-Induced Heat-Flux Patterns in the Convective Boundary Layer: Can they be Detected from Observations and is There a Blending Height?—A Large-Eddy Simulation Study for the LITFASS-2003 Experiment

An understanding of how the convective boundary layer (CBL) is mixed under heterogeneous surface forcing is crucial for the interpretation of area-averaged turbulence measurements. To determine the height and degree to which a complex heterogeneous surface affects the CBL, large-eddy simulations (LES) for two days of the LITFASS-2003 experiment representing two different wind regimes were undertaken. Spatially-lagged correlation analysis revealed the turbulent heat fluxes to be dependent on the prescribed surface flux pattern throughout the entire CBL including the entrainment layer. These findings prompted the question of whether signals induced by surface heterogeneity can be measured by airborne systems. To examine this question, an ensemble of virtual flights was conducted using LES, according to Helipod flight measurements made during LITFASS-2003. The resulting ensemble-averaged heat fluxes indicated a clear dependence on the underlying surface up to the top of the CBL. However, a large scatter between the flux measurements in different ensemble runs was observed, which was the result of insufficient sampling of the largest turbulent eddies. The random and systematic errors based on the integral length scale did not indicate such a large scatter. For the given flight leg lengths, at least 10–15 statistically independent flight measurements were necessary to give a significant estimate of heterogeneity-induced signals in the CBL. The need for ensemble averaging suggests that the observed blending of heterogeneity-induced signals in the CBL can be partly attributed to insufficient averaging.     

Laboratory and Numerical Studies of the Convective Boundary Layer Capped by a Strong Inversion

The convective boundary layer (CBL) with a wide range of stability is simulated experimentally using a thermally stratified wind tunnel, and numerically by direct numerical simulation (DNS). The turbulence structures and flow characteristics of various CBL flows, capped by a strong temperature inversion and affected by surface shear, are investigated. The various vertical profiles of turbulence statistics similar to those from the observed CBL in the field are successfully simulated in both the wind-tunnel experiment and in DNS. The comparison of the wind-tunnel data and DNS results with those of atmospheric observations and water-tank studies shows the crucial dependence of the turbulence statistics in the upper part of the layer on the strength of the inversion layer, as well as the modification of the CBL turbulence regime by the surface shear.     

Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation

A Lagrangian stochastic (LS) model, which is embedded into a parallelised large-eddy simulation (LES) model, is used for dispersion and footprint evaluations. For the first time an online coupling between LES and LS models is applied. The new model reproduces concentration patterns, which were obtained in prior studies, provided that subgrid-scale turbulence is included in the LS model. Comparisons with prior studies show that the model evaluates footprints successfully. Streamwise dispersion leads to footprint maxima that are situated less far upstream than previously reported. Negative flux footprints are detected in the convective boundary layer (CBL). The wide range of applicability of the model is shown by applying it under neutral and stable stratification. It is pointed out that the turning of the wind direction with height leads to a considerable dependency of source areas on height. First results of an application to a heterogeneously heated CBL are presented, which emphasize that footprints are severely affected by the inhomogeneity.     

Parameterization of Sheared Convective Entrainment in the First-Order Jump Model: Evaluation Through Large-Eddy Simulation

In this note, two different approaches are used to estimate the entrainment-flux to surface-flux ratio for a sheared convective boundary layer (CBL); both are derived under the framework of the first-order jump model (FOM). That suggested by Sun and Wang (SW approach) has the advantage that there is no empirical constant included, though the dynamics are described in an implicit manner. The second, which was proposed by Kim et al. and Pino et al. (KP approach), explicitly characterizes the dynamics of the sheared entrainment, but uncertainties are induced through the empirical constants. Their performances in parameterizing the CBL growth rate are compared and discussed, and a new value of the parameter A ₃ in the KP approach is suggested. Large-eddy simulation (LES) data are employed to test both approaches: simulations are conducted for the CBL growing under varying conditions of surface roughness, free-atmospheric stratification, and wind shear, and data used when the turbulence is in steady state. The predicted entrainment rates in each case are tested against the LES data. The results show that the SW approach describes the evolution of the sheared CBL quite well, and the KP approach also reproduces the growth of the CBL reasonably, so long as the value of A ₃ is modified to 0.6.     

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.     

A Variable Mesh Spacing for Large-Eddy Simulation Models in the Convective Boundary Layer

A variable vertical mesh spacing for large-eddy simulation (LES) models in a convective boundary layer (CBL) is proposed. The argument is based on the fact that in the vertical direction the turbulence near the surface in a CBL is inhomogeneous and therefore the subfilter-scale effects depend on the relative location between the spectral peak of the vertical velocity and the filter cut-off wavelength. From the physical point of view, this lack of homogeneity makes the vertical mesh spacing the principal length scale and, as a consequence, the LES filter cut-off wavenumber is expressed in terms of this characteristic length scale. Assuming that the inertial subrange initial frequency is equal to the LES filter cut-off frequency and employing fitting expressions that describe the observed convective turbulent energy one-dimensional spectra, it is feasible to derive a relation to calculate the variable vertical mesh spacing. The incorporation of this variable vertical grid within a LES model shows that both the mean quantities (and their gradients) and the turbulent statistics quantities are well described near to the ground level, where the LES predictions are known to be a challenging task.     

A note on the top-down and bottom-up gradient functions over a forested site

The dimensionless bottom-up and top-down gradient functions in the convective boundary layer (CBL) are evaluated utilizing long-term well-calibrated carbon dioxide mixing ratio and flux measurements from multiple levels of a 447-m tall tower over a forested area in northern Wisconsin, USA. The estimated bottom-up and top-down functions are qualitatively consistent with those from large-eddy simulation (LES) results and theoretical expectations. Newly fitted gradient functions are proposed based on observations for this forested site. The integrated bottom-up function over the lowest 4% of the CBL depth estimated from the tower data is about five times larger than that from LES results for a ‘with-canopy’ case, and is smaller than that from LES results for a ‘no-canopy’ case by a factor of 0.7. We discuss the uncertainty in the evaluated gradient functions due to stability, wind direction, and uncertainty in the entrainment flux and show that while all of these have a significant impact on the gradient functions, none can explain the differences between the modelled and observed functions. The effects of canopy features and atmospheric stability may need to be considered in the gradient function relations.     

Entrainment Processes in the Convective Boundary Layer with Varying Wind Shear

Large-eddy simulations (LES) are performed to investigate the entrainment andthe structure of the inversion layer of the convective boundary layer (CBL) withvarying wind shears. Three CBLs are generated with the constant surface kinematicheat flux of 0.05 K m s^-1 and varying geostrophic wind speeds from 5 to 15m s^-1. Heat flux profiles show that the maximum entrainment heat flux as afraction of the surface heat flux increases from 0.13 to 0.30 in magnitude withincreasing wind shear. The thickness of the entrainment layer, relative to the depthof the well-mixed layer, increases substantially from 0.36 to 0.73 with increasingwind shear. The identification of vortices and extensive flow visualizations nearthe entrainment layer show that concentrated vortices perpendicular to the meanboundary-layer wind direction are identified in the capping inversion layer for thecase of strong wind shear. These vortices are found to develop along the mean winddirections over strong updrafts, which are generated by convective rolls and to appearas large-scale wavy motions similar to billows generated by the Kelvin–Helmholtzinstability. Quadrant analysis of the heat flux shows that in the case of strong windshear, large fluctuations of temperature and vertical velocity generated by largeamplitude wavy motions result in greater heat flux at each quadrant than that inthe weak wind shear case.     

Perturbations to the Spatial and Temporal Characteristics of the Diurnally-Varying Atmospheric Boundary Layer Due to an Extensive Wind Farm

The effect of extensive terrestrial wind farms on the spatio-temporal structure of the diurnally-evolving atmospheric boundary layer is explored. High-resolution large-eddy simulations of a realistic diurnal cycle with an embedded wind farm are performed. Simulations are forced by a constant geostrophic velocity with time-varying surface boundary conditions derived from a selected period of the CASES-99 field campaign. Through analysis of the bulk statistics of the flow as a function of height and time, it is shown that extensive wind farms shift the inertial oscillations and the associated nocturnal low-level jet vertically upwards by approximately 200 m; cause a three times stronger stratification between the surface and the rotor-disk region, and as a consequence, delay the formation and growth of the convective boundary layer (CBL) by approximately 2 h. These perturbations are shown to have a direct impact on the potential power output of an extensive wind farm with the displacement of the low-level jet causing lower power output during the night as compared to the day. The low-power regime at night is shown to persist for almost 2 h beyond the morning transition due to the reduced growth of the CBL. It is shown that the wind farm induces a deeper entrainment region with greater entrainment fluxes. Finally, it is found that the diurnally-averaged effective roughness length for wind farms is much lower than the reference value computed theoretically for neutral conditions.     

对流边界层大涡模式的改进及对夹卷速度的研究

对已建的对流边界层(CBL)大涡模式进行了改进，将次网格闭合方案改为次网格能量闭合，并考虑了水汽的源汇项和水汽相变潜热的作用。通过对均匀下垫面上由热扰动发展的对流边界层的模拟及与实验结果的比较表明，模式较好地模拟了对流边界层的主要物理结构，较好地反映了各物理量之间的对应关系。本文在一定的对流理查森数(Ri*)范围内给出了一些算例，对无量纲夹卷速度(We/W*)进行了研究。结果表明，无量纲夹卷速度随地表热通量(Qs)的增大而增大，随对流边界层上部温度递减率（γ)的增大而减小。当9.06≤Ri*≤45.29时，无量纲夹卷速度We/W*可以拟合成A(Ri*)-1的形式，其中A=0.226。并且与我们的对流槽实验结果，Sullivan等人的大涡模拟结果以及Deardorff等人的对流槽实验结果作了比较，四者吻合较好。     

风切变对边界层对流影响的大涡模拟研究

利用"西北干旱区陆-气相互作用野外观测实验"加密观测期间在敦煌站的观测资料以及大涡模式,模拟了对流边界层的发展,以及示踪物从混合层向残留层传输的时空变化。模拟的对流边界层的结构及演变特征与实测结果基本一致。进一步通过有风切变和无风切变的敏感性数值试验,研究了风切变对垂直速度、位温和示踪物浓度的水平分布以及示踪物传输高度的影响。研究结果表明,在有风切变的试验中(甚至风切变仅存在于近地层中),对流边界层的增长加强,而且示踪物被传输的高度也较高。与浮力驱动的对流边界层相比,由浮力和风切变共同驱动的边界层中上升气流较弱而下沉气流较强,但前者的上升气流与下沉气流的分布在垂直方向上更为倾斜。由于夹卷作用的增强,浮力和风切变共同驱动的对流边界层较浮力驱动的对流边界层暖。在夹卷层,浮力和风切变共同驱动的边界层对流的上升气流和下沉气流都比浮力驱动的边界层对流中的强,而且垂直速度的概率密度函数分布也较对称,其位温和示踪物浓度的概率密度函数分布也比浮力驱动的边界层中的平直。对湍流动能收支的分析也表明风切变对湍流动能有重要影响,尤其对夹卷层中的湍流动能切变产生项影响较大。示踪物浓度的概率密度函数垂直分布显示,浮力驱动的边界层中示踪物浓度随高度变化较小,而浮力和风切变共同驱动的边界层中示踪物浓度随高度递减,但是示踪物传输的高度比较高。     

Parameterization of sheared entrainment in a well-developed CBL. Part I: Evaluation of the scheme through large-eddy simulations

The entrainment flux ratio A _e and the inversion layer (IL) thickness are two key parameters in a mixed layer model. A _e is defined as the ratio of the entrainment heat flux at the mixed layer top to the surface heat flux. The IL is the layer between the mixed layer and the free atmosphere. In this study, a parameterization of A _e is derived from the TKE budget in the firstorder model for a well-developed CBL under the condition of linearly sheared geostrophic velocity with a zero value at the surface. It is also appropriate for a CBL under the condition of geostrophic velocity remaining constant with height. LESs are conducted under the above two conditions to determine the coefficients in the parameterization scheme. Results suggest that about 43% of the shear-produced TKE in the IL is available for entrainment, while the shear-produced TKE in the mixed layer and surface layer have little effect on entrainment. Based on this scheme, a new scale of convective turbulence velocity is proposed and applied to parameterize the IL thickness. The LES outputs for the CBLs under the condition of linearly sheared geostrophic velocity with a non-zero surface value are used to verify the performance of the parameterization scheme. It is found that the parameterized A _e and IL thickness agree well with the LES outputs.     

On the Nature of the Transition Between Roll and Cellular Organization in the Convective Boundary Layer

Both observational and numerical studies of the convective boundary layer (CBL) have demonstrated that when surface heat fluxes are small and mean wind shear is strong, convective updrafts tend to organize into horizontal rolls aligned within 10–20\(^\circ \) of the geostrophic wind direction. However, under large surface heat fluxes and weak to negligible shear, convection tends to organize into open cells, similar to turbulent Rayleigh-Bénard convection. Using a suite of 14 large-eddy simulations (LES) spanning a range of \(-z_i/L\) between zero (neutral) and 1041 (highly convective), where \(z_i\) is the CBL depth and L is the Obukhov length, the transition between roll- and cellular-type convection is investigated systematically for the first time using LES. Mean vertical profiles including velocity variances and turbulent transport efficiencies, as well the “roll factor,” which characterizes the rotational symmetry of the vertical velocity field, indicate the transition occurs gradually over a range of \(-z_i/L\); however, the most significant changes in vertical profiles and CBL organization occur from near-neutral conditions up to about \(-z_i/L \approx \) 15–20. Turbulent transport efficiencies and quadrant analysis are used to characterize the turbulent transport of momentum and heat with increasing \(-z_i/L\). It is found that turbulence transports heat efficiently from weakly to highly convective conditions; however, turbulent momentum transport becomes increasingly inefficient as \(-z_i/L\) increases.     

On the Effect of Surface Heat-Flux Heterogeneities on the Mixed-Layer-Top Entrainment

We used a set of large-eddy simulations to investigate the effect of one-dimensional stripe-like surface heat-flux heterogeneities on mixed-layer top entrainment. The profiles of sensible heat flux and the temporal evolution of the boundary-layer depth revealed decreased entrainment for small heat-flux amplitudes and increased entrainment for large heat-flux amplitudes, compared to the homogeneously-heated mixed layer. For large heat-flux amplitudes the largest entrainment was observed for patch sizes in the order of the boundary-layer depth, while for significantly smaller or larger patch sizes entrainment was similar as in the homogeneous case. In order to understand the underlying physics of this impact, a new approach was developed to infer local information on entrainment by means of the local flux divergence. We found an entrainment maximum over the centre of the stronger heated surface patch, where thermal energy is accumulated by the secondary circulation (SC) that was induced by the surface heterogeneity. Furthermore, we observed an entrainment maximum over the less heated patch as well, which we suppose is to be linked to the SC-induced horizontal flow convergence at the top of the convective boundary layer (CBL). For small heat-flux amplitudes a counteracting effect dominates that decreases entrainment, which we suppose is the horizontal advection of cold air in the lower, and warm air in the upper, CBL by the SC, stabilizing the CBL and thus weakening thermal convection. Moreover, we found that a mean wind can reduce the heterogeneity-induced impact on entrainment. If the flow is aligned perpendicular to the border between the differentially-heated patches, the SC and thus its impact on entrainment vanishes due to increased horizontal mixing, even for moderate wind speeds. However, if the flow is directed parallel to the border between the differentially-heated patches, the SC and thus its impact on entrainment persists.     

Development of a Single-Column Model in RegCM4 and Its Preliminary Application for Evaluating PBL Schemes in Simulating the Dry Convection Boundary Layer

A single-column model (SCM) is developed in the regional climate model RegCM4. The evolution of a dry convection boundary layer (DCBL) is used to evaluate this SCM. Moreover, four planetary boundary layer (PBL) schemes, namely the Holtslag-Boville scheme (HB), Yonsei University scheme (YSU), and two University of Washington schemes (UW01, Grenier-Bretherton-McCaa scheme and UW09, Bretherton-Park scheme), are compared by using the SCM approach. A large-eddy simulation (LES) of the DCBL is performed as a benchmark to examine how well a PBL parameterization scheme reproduces the LES results, and several diagnostic outputs are compared to evaluate the schemes. The results show that the SCM is proper constructed. In general, with the DCBL case, the YSU scheme performs best for reproducing the LES results, which include well-mixed features and vertical sensible heat fluxes; the simulated wind speed, turbulent kinetic energy, entrainment flux, and height of the entrainment zone are all underestimated in the UW09; the UW01 has all those biases of the UW09 but larger, and the simulated potential temperature is not well mixed; the HB is the least skillful scheme, by which the PBL height, entrainment flux, height of the entrainment zone, and the vertical gradients within the mixed layer are all overestimated, and a inversion layer near the top of the surface layer is wrongly simulated.Although more cases and further testing are required, these simulations show encouraging results towards the use of this SCM framework for evaluating the simulated physical processes by the RegCM4.     

Large-Eddy Simulations of Surface Heterogeneity Effects on the Convective Boundary Layer During the LITFASS-2003 Experiment

We investigate the impact of observed surface heterogeneities during the LITFASS-2003 experiment on the convective boundary layer (CBL). Large-eddy simulations (LES), driven by observed near-surface sensible and latent heat fluxes, were performed for the diurnal cycle and compare well with observations. As in former studies of idealized one- and two-dimensional heterogeneities, secondary circulations developed that are superimposed on the turbulent field and that partly take over the vertical transport of heat and moisture. The secondary circulation patterns vary between local and roll-like structures, depending on the background wind conditions. For higher background wind speeds, the flow feels an effective surface heat-flux pattern that derives from the original pattern by streamwise averaging. This effective pattern generates a roll-like secondary circulation with roll axes along the mean boundary-layer wind direction. Mainly the upstream surface conditions control the secondary circulation pattern, where the fetch increases with increasing background wind speed. Unlike the entrainment flux that appears to be slightly decreased compared to the homogeneously-heated CBL, the vertical flux of sensible heat appears not to be modified in the mixed layer, while the vertical flux of latent heat shows different responses to secondary circulations. The study illustrates that sufficient time averaging and ensemble averaging is required to separate the heterogeneity-induced signals from the raw LES turbulence data. This might be an important reason why experiments over heterogeneous terrain in the past did not give any clear evidence of heterogeneity-induced effects.     

边界层对流对示踪物抬升和传输影响的大涡模拟研究

利用"西北干旱区陆气相互作用野外观测实验"加密观测期间敦煌站的实测资料以及大涡模式, 通过一系列改变地表热通量和风切变的敏感性数值试验, 分析了地表热通量和风切变对边界层对流的强度、形式, 以及对对流边界层结构和发展的影响。模拟结果显示风切变一定, 增大地表热通量时, 由于近地层湍流运动增强, 向上输送的热量也较多, 使对流边界层变暖增厚, 而且边界层对流的强度明显增强, 对流泡发展的高度也较高。当地表热通量一定, 增大风切变时, 由于风切变使夹卷作用增强, 将逆温层中的暖空气向下卷入混合层中, 使对流边界层增暖增厚, 但是对流泡容易破碎, 对流的强度也较弱。另外通过在模式近地层释放绝对浓度为100的被动示踪物方法, 用最小二乘法定量地分析了地表热通量和风切变分别与示踪物抬升效率和传输高度的关系。分析结果表明, 风切变小于10.5×10-3 s-1时, 增大地表热通量加强了上层动量的下传, 使示踪物的抬升效率也线性增大;地表热通量小于462.5 W m-2时, 增大风切变减弱了边界层对流的强度, 从而使示踪物的抬升效率减弱。当风切变一定时, 示踪物的平均传输高度随地表热通量增加而增大, 而地表热通量一定, 只有风切变大于临界值时, 示踪物平均传输高度才随风切变的增加而增大, 而临界风速的大小由地表热通量决定。     

Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-Eddy Simulations. Part II: Forced Convection

Forced convection in a quasi-steady atmospheric boundary layer is investigated based on a large-eddy simulation (LES) model. The performed simulations show that in the upper portion of the mixed layer the dimensionless (in terms of mixed layer scales) vertical gradients of temperature, humidity, and wind velocity depend on the dimensionless height z/z _i and the Reech number Rn. The peak values of variances and covariances at the top of the mixed layer, scaled in terms of the interfacial scales, are functions of the interfacial Richardson number Ri. As a result expressions for the entrainment rates, in the case when the interfacial layer has a finite depth, and a condition for the presence of moistening or drying regimes in the mixed layer, are derived. Profiles of dimensionless scalar moments in the mixed layer are proposed to be expressed in terms of two empirical similarity functions F _m and F _i , dependent on dimensionless height z/z _i , and the interfacial Richardson number Ri. The obtained similarity expressions adequately approximate the LES profiles of scalar statistics, and properly represent the impact of stability, shear, and entrainment. They are also consistent with the parameterization proposed for free convection in the first part of this paper.     

日间对流边界层中的非局地动量混合

日间对流边界层最显著的结构特征是在热力作用下所形成的组织化对流。与小尺度湍涡不同的是，组织化对流具有边界层尺度的垂直相干性，可实现垂直贯穿边界层的非局地物质和能量传输。本文针对对流边界层中的动量混合，探究组织化对流对动量输送的贡献。以高精度大涡模拟数据为研究资料，通过傅里叶变换、本征正交分解和经验模态分解3种滤波方法，分离组织化对流和背景湍涡，计算与两者相关的非局地和局地动量通量，发现与组织化对流相关的非局地动量通量是总通量的重要组成部分，并主导混合层中的垂直动量输送。而后，基于协谱和相位谱分析，探究组织化对流的空间结构对动量传输的影响，发现在热力主导的不稳定环境中，单体型环流结构对动量的传输效率较低。而在风切较强的近中性环境中，滚涡型组织化结构可使垂直和水平流向扰动速度的相位差减小，从而提升动量传输效率。研究结果表明，边界层方案需要包含非局地动量通量项，其参数化应考虑整体稳定度对传输效率的影响。