Effects of boundary-layer stability on urban heat island-induced circulation

Summary The effects of atmospheric boundary-layer stability on urban heat island-induced circulation are numerically and theoretically investigated using a nonlinear numerical model (ARPS) and a two-layer linear analytical model. Numerical model simulations show that as the boundary layer becomes less stable, a downwind updraft cell induced by the urban heat island strengthens. It is also shown that as the boundary layer becomes less stable, both the height of the maximum updraft velocity and the vertical extent of the downwind updraft cell increase. Hence, in the daytime with a nearly neutral or less stable boundary layer the urban heat island-induced circulation can become strong, even though the urban heat island is weak. It is suggested that these findings can be a mechanism for urban-induced thunderstorms observed in the late afternoon or evening with a nearly neutral or less stable boundary layer. The boundary-layer stability affects the spatial distribution of scalar concentration through its influencing urban heat island-induced circulation. Analytical results from a two-layer model with different boundary-layer stabilities in the lower and upper layers are in general qualitatively consistent with the numerical simulation results, although the low-level maximum vertical velocity does not change monotonically with lower-layer stability.     

在细网格模式中引入总体边界层参数化方案的数值试验

本文把MM4模式中的总体边界层参数化方案引入到十一层细同治原始方程数值模式中去，用它与仅考虑简单边界层国擦的细网格模式对一典型江淮气旋天气过程分别作了24小时对比模拟试验；初步试验结果表明：边界层总体参数化方案的引入是可行的，对模式的预报效果在某些方面有显著改进．     

Large-Eddy Simulation of the Stable Atmospheric Boundary Layer using Dynamic Models with Different Averaging Schemes

Large-eddy simulation (LES) of a stable atmospheric boundary layer is performed using recently developed dynamic subgrid-scale (SGS) models. These models not only calculate the Smagorinsky coefficient and SGS Prandtl number dynamically based on the smallest resolved motions in the flow, they also allow for scale dependence of those coefficients. This dynamic calculation requires statistical averaging for numerical stability. Here, we evaluate three commonly used averaging schemes in stable atmospheric boundary-layer simulations: averaging over horizontal planes, over adjacent grid points, and following fluid particle trajectories. Particular attention is focused on assessing the effect of the different averaging methods on resolved flow statistics and SGS model coefficients. Our results indicate that averaging schemes that allow the coefficients to fluctuate locally give results that are in better agreement with boundary-layer similarity theory and previous LES studies. Even among models that are local, the averaging method is found to affect model coefficient probability density function distributions and turbulent spectra of the resolved velocity and temperature fields. Overall, averaging along fluid pathlines is found to produce the best combination of self consistent model coefficients, first- and second-order flow statistics and insensitivity to grid resolution.     

Nocturnal boundary-layer height: Observations by acoustic sounders and predictions in terms of surface-layer parameters

Acoustic sounder measurements of the stable boundary-layer height taken during the EPRI Plume Model Validation and Development Project experiment are examined. Comparison of simultaneous measurements by two sodars located 15 km apart shows good agreement. Several widely used diagnostic formulas for estimation of the boundary-layer height, based on wind speed and surface-layer parameters, such as friction velocity and Monin-Obukhov length, are tested against the sodar data. Of these, best performance is found using a simple linear relationship with friction velocity or, alternatively, wind speed at 10 m height. No evidence is found to support the more often used Zilitinkevich (1972) formula. Tests using selected data from the Cabauw site in the Netherlands confirm the results found on the basis of EPRI data.     

Estimation of Surface-Layer Scaling Parameters in the Unstable Boundary Layer: Implications for Orographic Flow Speed-Up

A method is proposed for estimating the surface-layer depth \((z_s)\) and the friction velocity \((u_*)\) as a function of stability (here quantified by the Obukhov length, L) over the complete range of unstable flow regimes. This method extends that developed previously for stable conditions by Argaín et al. (Boundary-Layer Meteorol 130:15–28, 2009), but uses a qualitatively different approach. The method is specifically used to calculate the fractional speed-up \((\varDelta S)\) in flow over a ridge, although it is suitable for more general boundary-layer applications. The behaviour of \(z_s \left( L\right) \) and \(u_*\left( L\right) \) as a function of L is indirectly assessed via calculation of \(\varDelta S\left( L\right) \) using the linear model of Hunt et al. (Q J R Meteorol Soc 29:16–26, 1988) and its comparison with the field measurements reported in Coppin et al. (Boundary-Layer Meteorol 69:173–199, 1994) and with numerical simulations carried out using a non-linear numerical model, FLEX. The behaviour of \(\varDelta S\) estimated from the linear model is clearly improved when \(u_*\) is calculated using the method proposed here, confirming the importance of accounting for the dependences of \(z_s\left( L \right) \) and \(u_*\left( L \right) \) on L to better represent processes in the unstable boundary layer.     

Determination of boundary-layer parameters using a vertical gill anemometer

The paper presents a simple method to compute the stability parameter Z/L and boundary-layer parameters such as friction velocity U ^* and surface heat flux Q ₀ on an operational basis. The method is based on the autocorrelation function of the vertical velocity which is relatively insensitive to averaging times except for very large lag times. Eddy correlation techniques on the other hand are very sensitive to averaging times.     

A model for the height of the internal boundary layer over an area with an irregular coastline

A model for the time and space variation of the internal boundary-layer height over a land area with an irregular coastline is presented. It is based on the analytical model of the boundary-layer height proposed by Gryning and Batchvarova (1990) and Batchvarova and Gryning (1991), The model accounts for the temperature jump and the mean vertical air motion at the top of the internal boundary-layer. Four cases from experiments in Nanticoke and Vancouver are used for model validation. The agreement between the calculated and measured internal boundary layer height at the observational sites is fairly good. The input information for the model consist of wind speed and direction, friction velocity and kinematic heat flux in time and space for the area, and the potential temperature gradient and the mean vertical air motion above the internal boundary layer. For the experiments used in the validation the effect of subsidence is relatively important in the afternoon under low wind speed high pressure conditions, lowering the height of the internal boundary layer by up to 10%, and it is negligible in the morning hours. The effect of the mixing height over the sea is found to be negligible.     

A Method for Increasing the Turbulent Kinetic Energy in the Mellor–Yamada–Janjić Boundary-Layer Parametrization

A method for enhancing the calculation of turbulent kinetic energy in the Mellor–Yamada–Janjić planetary boundary-layer parametrization in the Weather Research and Forecasting numerical model is presented. This requires some unconventional selections for the closure constants and an additional stability dependent surface length scale. Single column model and three-dimensional model simulations are presented showing a similar performance with the existing boundary-layer parametrization, but with a more realistic magnitude of turbulence intensity closer to the surface with respect to observations. The intended application is an enhanced calculation of turbulence intensity for the purposes of a more accurate wind-energy forecast.     

Direct Numerical Simulation of Stable Channel Flow at Large Stability

We consider a model for the stable atmospheric boundary at large stability, i.e. near the limit where turbulence is no longer able to survive. The model is a plane horizontally homogeneous channel flow, which is driven by a constant pressure gradient and which has a no-slip wall at the bottom and a free-slip wall at the top. At the lower wall a constant negative temperature flux is imposed. First, we consider a direct numerical simulation of the same channel flow. The simulation is computed with the neutral channel flow as initial condition and computed as a function of time for various values of the stability parameter h/L, where h is the channel height and L is related to the Obukhov length. We find that a turbulent solution is only possible for h/L < 1.25 and for larger values turbulence decays. Next, we consider a theoretical model for this channel flow based on a simple gradient transfer closure. The resulting equations allow an exact solution for the case of a stationary flow. The velocity profile for this solution is almost linear as a function of height in most of the channel. In the limit of infinite Reynolds number, the temperature profile has a logarithmic singularity at the upper wall of the channel. For the cases where a turbulent flow is maintained in the numerical simulation, we find that the velocity and temperature profiles are in good agreement with the results of the theoretical model when the effects of the surface layer on the exchange coefficients are taken into account. Frans Nieuwstadt, a recently retired member of the BLM Editorial Board and a well-known member of the boundary-layer/turbulence community, died unexpectedly on 18 May 2005. An obituary will appear in a later issue of BLM.     

IMPACT OF SEA SPRAY ON TROPICAL CYCLONE STRUCTURE AND INTENSITY CHANGE

In this paper,the effects of sea spray on tropical cyclone(TC)structure and intensity variation are evaluated through numerical simulations using an advanced sea-spray parameterization from the National Oceanic and Atmospheric Administration/Earth System Research Laboratory(NOAA/ESRL),which is incorporated in the idealized Advanced Research version of the Weather Research and Forecast (WRF-ARW)model.The effect of sea spray on TC boundary-layer structure is also analyzed.The results show that there is a significant increase in TC intensity when its boundary-layer wind includes the radial and tangential winds,their structure change,and the total surface wind speed change.Diagnosis of the vorticity budget shows that an increase of convergence in TC boundary layer enhances TC vorticity due to the dynamic effect of sea spay.The main kinematic effect of the friction velocity reduction by sea spray produces an increment of large-scale convergence in the TC boundary layer,while the radial and tangential winds significantly increase with an increment of the horizontal gradient maximum of the radial wind, resulting in a final increase in the simulated TC intensity.The surface enthalpy flux enlarges TC intensity and reduces storm structure change to some degree,which results in a secondary thermodynamic impact on TC intensification.Implications of the new interpretation of sea-spray effects on TC intensification are also discussed.     

Large-Eddy Simulation of Thermally Stratified Atmospheric Boundary-Layer Flow Using a Minimum Dissipation Model

A generalized form of a recently developed minimum dissipation model for subfilter turbulent fluxes is proposed and implemented in the simulation of thermally stratified atmospheric boundary-layer flows. Compared with the original model, the generalized model includes the contribution of buoyant forces, in addition to shear, to the production or suppression of turbulence, with a number of desirable practical and theoretical properties. Specifically, the model has a low computational complexity, appropriately switches off in laminar and transitional flows, does not require any ad hoc shear and stability corrections, and is consistent with theoretical subfilter turbulent fluxes. The simulation results show remarkable agreement with well-established empirical correlations, theoretical predictions, and field observations in the atmosphere. In addition, the results show very little sensitivity to the grid resolution, demonstrating the robustness of the model in the simulation of the atmospheric boundary layer, even with relatively coarse resolutions.     

An interpolation method of randomly distributed atmospheric data in the height-time domain

A numerical method for objective interpolation of boundary-layer data in the height-time domain is presented. The method is based on a diffusive transport hypothesis and allows for the determination of the optimal ratio between the height and time scales to be used for non-dimensionalising the independent variables z and t. This ratio, with dimensions of a velocity, may be related to the vertical transfer properties of the atmosphere. A few cases during springtime with different stability conditions are discussed, showing that this ratio varies by at least one order of magnitude between day and night.     

The Effect of Surface Heating on Hill-Induced Flow Separation

A series of two-dimensional mixing length model simulations of boundary-layer flow over idealised ridges of varying steepness are conducted to investigate the effect of surface heating on flow separation. The relatively simple numerical approach used permits characterisation of the influence of heating for a variety of initial conditions and parameter values. For steep terrain, increased surface heating is shown to enhance the strength and extent of hill-induced separation. For more moderate terrain, a critical heating strength is required for a given hill width and background flow speed before separation is initiated. Sensitivity tests show the results to be insensitive to model parameters or the choice of mixing length. The results are accounted for using a scaling analysis in terms of a non-dimensional stability parameter.     

On the solution of the stationary,baroclinic Ekman-layer equations with a finite boundary-layer height

The stationary, Ekman-layer equations have been solved in closed form for two expressions of the eddy viscosity as a function of height, z: v _τ=cu*z(1?z/h)and v _τ=cu*z(1?z/h) ², where u* is the friction velocity, h the boundary-layer height and c a constant. The main difference between both solutions is that the quadratic K-profile leads to a velocity discontinuity at the top of the boundary layer, while the solution for the cubic profile approaches the geostrophic wind at z=h smoothly. We discuss the characteristics of the solutions in terms of a dimensionless parameter C=fh/cu*, where f is the Coriolis parameter. The dependence on C can be interpreted in terms of a varying boundary-layer height or in terms of stability. The results for C ~ 1 are related to a neutral boundary layer. They agree well with results of a second-order model. The limit C → 0 is investigated in detail. We find that the stress profile becomes linear. The velocity profile shows different characteristics depending on whether we consider a shallow or a very unstable boundary layer. The results agree with observations. Finally we consider the influence of baroclinicity on the wind and stress profiles.     

A moving grid finite-element model of the bulk properties of the atmospheric boundary layer

A moving-grid finite-element model has been developed to model numerically the vertically integrated properties of the atmospheric boundary layer (ABL) in one dimension. The model equations for mean wind velocity and potential temperature are combined with a surface energy budget and predictive equations for boundary-layer height to simulate both stable and unstable ABLs. The nodal position defining the top of the boundary layer is one of the model unknowns and is determined by boundary-layer dynamics. The finite-element method, being an integral method, has advantages of accurate representation of both bulk values and their vertical derivatives, the latter being essential properties of the nocturnal boundary layer. Compared with observations and results of other models, the present model predicts bulk properties very well while retaining a simple and economical form.Journal Paper No. J-12996 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa, Project No. 2779.     

Velocity and Temperature Dissimilarity in the Surface Layer Uncovered by the Telegraph Approximation

We consider the Janjic (NCEP Office Note 437:61, 2001) boundary-layer model, which is one of the most widely used in numerical weather prediction models. This boundary-layer model is based on a number of length scales that are, in turn, obtained from a master length multiplied by constants. We analyze the simulation results obtained using different sets of constants with respect to measurements using sonic anemometers, and interpret these results in terms of the turbulence processes in the atmosphere and of the role played by the different length scales. The simulations are run on a virtual machine on the Chameleon cloud for low-wind-speed, unstable, and stable conditions.

     

鄱阳湖地区零平面位移及动力粗糙度的计算

利用2013年7月1日至2014年6月30日鄱阳湖东岸70 m铁塔涡动相关观测资料,应用Martano方法和TVM（Temperature Variance Method）方法分别计算了该地地表零平面位移d和粗糙度z₀,通过代回Monin-Obukhov相似性理论的风廓线关系计算摩擦速度,以验证与实测摩擦速度的一致性。速度和温度标准差的归一化拟合线分别与Panosky等和Tillman给出的曲线趋势一致,表明该站观测数据总体满足近地层相似性。Martano方法计算结果随季节变化较大,春夏季的粗糙度是秋冬季的6.3倍;陆面方向零平面位移和粗糙度分别为来自湖面的2倍和10倍;Martano方法比TVM方法对季节和方向的敏感性更强。Martano方法计算得到零平面位移和粗糙度对摩擦速度造成了约9.9%的高估;而TVM方法对摩擦速度造成了约32.8%的高估;Martano方法计算的摩擦速度和观测值的一致性更好。     

A bulk model of the well-mixed boundary layer

A bulk boundary-layer model is developed to predict surface fluxes and conditions in the well-mixed layer between the surface and the lower troposphere. The model includes the effects of all the dominant processes, including advection, in a dry boundary layer. The numerical model is compared with theoretical predictions for the growth of an internal boundary layer, and it is used to simulate the generation of a sea breeze by the diurnal cycle of radiative heating.     

A simple and efficient procedure for the numerical simulation of wind fields in complex terrain

In spite of recent progress in the prognostic numerical simulation of the atmospheric boundary layer, the explicit simulation of turbulent flows in actual complex terrain is generally still very complicated and time consuming for many environmental applications. In an attempt to develop simpler and more efficient application oriented techniques, although less refined, we propose a multi-step procedure for simulating wind fields. Once obtained the necessary meteorological input, the mass-consistent modelling technique is used to perform high-resolution mean wind flow simulations taking into account recent developments in the atmospheric boundary-layer theory. Besides, a procedure based on a generalisation of the local logarithmic law-of-the-wall over complex terrain is used to estimate the effective parameters characterising the simulated wind profiles. Turbulence intensities and spectral properties are then calculated through the estimated effective parameters, in particular through the effective friction velocity parameter. Finally, time series of the instantaneous velocity field are simulated by the Monte Carlo technique. Two applications of the proposed approach are discussed briefly: the first one is related to a coastal area in southern Italy (the Messina Straits), where the construction of the world’s longest central span bridge is being planned; the second one corresponds to the flow in a mountainous area in northern Italy (the Albenga Airport).