A New Large-Eddy Simulation Model for Simulating Air Flow and Warm Clouds Above Highly Complex Terrain. Part II: The Moist Model and its Application to Banner Clouds

In Part I the dry version of a new large-eddy simulation (LES) model was presented that is specifically designed to simulate air flow and clouds above highly complex terrain. Here the implemented moisture physics are described and a new method for the generation of turbulent inflow conditions for meteorological LES is proposed. As a typical area of application the new model is applied to simulate banner clouds developing downwind of pyramidal mountain peaks. Banner clouds are shown to be primarily a dynamical phenomenon, and form in the lee of steep mountain peaks as a result of dynamically forced lee upslope flow. Due to the highly asymmetric flow field induced by the extreme orography, banner clouds can form even under horizontally homogeneous initial conditions regarding both moisture and temperature. Thus, additional leeward moisture sources, distinct air masses on both windward and leeward sides, or radiation effects are no prerequisite for banner-cloud formation. The probability of banner-cloud formation increases with increasing obstacle height and steepness and is, to a first approximation, independent of the pyramid’s orientation. Simulations with and without moisture physics reveal that, for the set-up chosen, moisture is of only secondary importance for banner-cloud dynamics. The reinforcement of lee upslope flow and corresponding cloud formation due to latent heat release turns out to be almost negligible. Nevertheless moisture physics are shown to induce a dipole-like structure in the vertical profile of the Brunt-Väisälä frequency, which in turn leads to a moderate increase in leeward turbulence.     

Flow over Hills: A Large-Eddy Simulation of the Bolund Case

Simulation of local atmospheric flows around complex topography is important for several applications in wind energy (short-term wind forecasting and turbine siting and control), local weather prediction in mountainous regions and avalanche risk assessment. However, atmospheric simulation around steep mountain topography remains challenging, and a number of different approaches are used to represent such topography in numerical models. The immersed boundary method (IBM) is particularly well-suited for efficient and numerically stable simulation of flow around steep terrain. It uses a homogenous grid and permits a fast meshing of the topography. Here, we use the IBM in conjunction with a large-eddy simulation (LES) and test it against two unique datasets. In the first comparison, the LES is used to reproduce experimental results from a wind-tunnel study of a smooth three-dimensional hill. In the second comparison, we simulate the wind field around the Bolund Hill, Denmark, and make direct comparisons with field measurements. Both cases show good agreement between the simulation results and the experimental data, with the largest disagreement observed near the surface. The source of error is investigated by performing additional simulations with a variety of spatial resolutions and surface roughness properties.     

Comparison of Measured and Numerically Simulated Turbulence Statistics in a Convective Boundary Layer Over Complex Terrain

The Weather Research and Forecasting (WRF) model can be used to simulate atmospheric processes ranging from quasi-global to tens of m in scale. Here we employ large-eddy simulation (LES) using the WRF model, with the LES-domain nested within a mesoscale WRF model domain with grid spacing decreasing from 12.15 km (mesoscale) to 0.03 km (LES). We simulate real-world conditions in the convective planetary boundary layer over an area of complex terrain. The WRF-LES model results are evaluated against observations collected during the US Department of Energy-supported Columbia Basin Wind Energy Study. Comparison of the first- and second-order moments, turbulence spectrum, and probability density function of wind speed shows good agreement between the simulations and observations. One key result is to demonstrate that a systematic methodology needs to be applied to select the grid spacing and refinement ratio used between domains, to avoid having a grid resolution that falls in the grey zone and to minimize artefacts in the WRF-LES model solutions. Furthermore, the WRF-LES model variables show large variability in space and time caused by the complex topography in the LES domain. Analyses of WRF-LES model results show that the flow structures, such as roll vortices and convective cells, vary depending on both the location and time of day as well as the distance from the inflow boundaries.     

Large-Eddy Simulations of Atmospheric Flows Over Complex Terrain Using the Immersed-Boundary Method in the Weather Research and Forecasting Model

Atmospheric flow over complex terrain, particularly recirculation flows, greatly influences wind-turbine siting, forest-fire behaviour, and trace-gas and pollutant dispersion. However, there is a large uncertainty in the simulation of flow over complex topography, which is attributable to the type of turbulence model, the subgrid-scale (SGS) turbulence parametrization, terrain-following coordinates, and numerical errors in finite-difference methods. Here, we upgrade the large-eddy simulation module within the Weather Research and Forecasting model by incorporating the immersed-boundary method into the module to improve simulations of the flow and recirculation over complex terrain. Simulations over the Bolund Hill indicate improved mean absolute speed-up errors with respect to previous studies, as well an improved simulation of the recirculation zone behind the escarpment of the hill. With regard to the SGS parametrization, the Lagrangian-averaged scale-dependent Smagorinsky model performs better than the classic Smagorinsky model in reproducing both velocity and turbulent kinetic energy. A finer grid resolution also improves the strength of the recirculation in flow simulations, with a higher horizontal grid resolution improving simulations just behind the escarpment, and a higher vertical grid resolution improving results on the lee side of the hill. Our modelling approach has broad applications for the simulation of atmospheric flows over complex topography.     

A Large-Eddy Simulation Study of Turbulent Flow Over Multiscale Topography

Most natural landscapes are characterized by multiscale (often multifractal) topography with well-known scale-invariance properties. For example, the spectral density of landscape elevation fields is often found to have a power-law scaling behaviour (with a −2 slope on a log–log scale) over a wide span of spatial scales, typically ranging from tens of kilometres down to a few metres. Even though the effect of topography on the atmospheric boundary layer (ABL) has been the subject of numerous studies, few have focussed on multiscale topography. In this study, large-eddy simulation (LES) is used to investigate boundary-layer flow over multiscale topography, and guide the development of parametrizations needed to represent the effects of subgrid-scale (SGS) topography in numerical models of ABL flow. Particular emphasis is placed on the formulation of an effective roughness used to account for the increased aerodynamic roughness associated with SGS topography. The LES code uses the scale-dependent Lagrangian dynamic SGS model for the turbulent stresses and a terrain-following coordinate transformation to explicitly resolve the effects of the topography at scales larger than the LES resolution. The terrain used in the simulations is generated using a restricted solid-on-solid landscape evolution model, and it is characterized by a −2 slope of the elevation power spectrum. Results from simulations performed using elevation fields band-pass filtered at different spatial resolutions indicate a clear linear relation between the square of the effective roughness and the variance of elevation.     

Impacts of topography and land degradation on the sea breeze over eastern Spain

Summary A three-dimensional non-hydrostatic atmospheric model RAMS, version3b, is used to examine the impact of complex topography on the sea breeze under heterogeneous and degradation land use characteristics. In the study, it is shown that topography plays an important role in the sea-breeze circulation by aligning the sea breeze front to the coastline and locating the convergence zones close to the mountain range. When the sea breeze is coupled with the upslope wind, the sea-breeze circulation is strengthened by the topography.Sensitivity analyses are carried out to determine the influence of vegetation and soil moisture, i.e., land surface modifications, to this thermally driven flow. Land degradation results in an enhanced sea-breeze circulation which is characterized by a stronger onshore flow, a stronger return current, a larger updraft velocity associated with the sea-breeze front and further inland penetration. Other important features are a deeper sea-breeze depth, a larger downdraft velocity behind the sea-breeze front, and a longer offshore extent. The results also show how land changes modify the sea breeze temporal evolution resulting in an earlier onset and later end. The study stresses the convenience of using three-dimensional models with detailed land surface information to model the sea breeze in complex terrain where land use is rapidly modified.Received February 25, 2002; accepted October 7, 2002 Published online April 10, 2003     

Heavy rainfall in complex terrian: insights from a numerical model

Summary A numerical model is employed to study heavy rainfall events in complex terrain. The model uses a limited-fine-mesh grid and a nested grid, but does not utilize the same set of equations on both grids. Two similar, heavy rainfall cases are contrasted with each other and with a moderate precipitation case. Sensitivity experiments illustrate the effects of topography, synoptic forcing and diabatic heating on these episodes. Model results indicate that heavy rainfall in complex terrain requires a suitable superposition of mass, momentum and moisture fields in relation to the topography. It is the mass and momentum fields, however, which primarily control the location of heaviest precipitation. Synoptically similar events may be different in their underlying causes. The diabatic heating distribution may in some cases be essential to creating such episodes heavy rain.With 22 Figures     

Analyses of variance and flux budgets in cumulus-topped boundary layers

A large-eddy simulation (LES) of a cumulus-topped boundary layer (CTBL) has been made, based on observations gathered on 10 September 1974 during the GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment (GATE). On this day there were light winds, making buoyancy production the only important mechanism for generating turbulent kinetic energy. Cumulus clouds with a depth of a few hundred meters covered about 10% of the sky. A comparison between LES results and observed variances and fluxes will be made.In order to understand the dynamics of the cumulus, we will investigate the physical mechanisms by which variances and fluxes are produced in CTBL's. This will be done by analyzing the budget equations which describe the time evolution of the variances and fluxes. The production, transport and destruction terms, that appear in these equations, will be calculated explicitly with the LES model.Budgets are calculated from the GATE simulation and two slightly modified GATE simulations, in which only the initial water vapor specific humidity is increased. As a result in these two modified GATE simulations the vertical extent of the clouds and the cloud cover is larger. In this way, the influence of the cumulus clouds on the budgets can be investigated more thoroughly. Finally, the budgets are compared with the results obtained from an earlier simulation based on the Puerto Rico Field Experiment and other results found in the literature.     

A simple model of neutrally stratified boundary-layer flow over complex terrain with surface roughness modulations (MS3DJH/3R)

The MS3DJH series of simple models of flow over low hills and other terrain features described in earlier papers (see Taylor et al., 1983) required that the terrain was of uniform surface roughness. In the present paper, we describe an approximate theory of flow above variations in surface roughness using a similar structure to that established by Jackson and Hunt (1975) for flow over hills. This then allows us to include the calculation of flow perturbations due to roughness variations within a modified version of our model which we designate as MS3DJH/3R. Comparisons are made with alternative calculations for simple two-dimensional flows; and sample three-dimensional calculations are presented. The model retains its essential features of high spatial resolution and low computing cost.Summer student, 1981     

An improved method for integrating the Mixed Spectral Finite Difference (MSFD) model equations

In their Mixed Spectral Finite Difference (MSFD) model for flow over complex terrain, Beljaars et al. (1987) solve a set of coupled, second-order ordinary differential equations (ODEs) for the first-order perturbations to the logarithmic velocity profile caused by nonuniform surface roughness and topography. To solve this set of ODEs, they employ a Forward Euler Shooting Method. It is demonstrated here that the shooting method is computationally unstable for this problem. An absolutely stable finite-difference method based on a block tridiagonal LU factorization of the finite-difference matrix is presented. The advantages of the present algorithm over the method used by Beljaars et al. are demonstrated both by theoretical argument and numerical experiment.     

The Numerical Simulation on Atmospheric Transport and Dispersion of the Spray Atomized from Flood Discharging by Hydropower Station over Complex Terrain

Summary  A three-dimensional, nonhydrostatic numerical model with high spatial resolution, in which a simple energy closure scheme is employed, has been developed to simulate the spray dispersion over complex terrain. The evaporation, condensation, and dispersion of the spray and moisture are taken into account in model equations. The term of latent heat due to phase transformation is considered in detail to account for its effects on the temperature field and airflow. As an application of the model, the spray concentration and air relative humidity are calculated under neutral condition. The results indicate that under the neutral condition, the spray is transported to about 0.6 km downwind from the source, and its effects on the air humidity reach a further distance of 0.9 km downwind from the source. Attention is given to the dependence of the results upon the various factors influencing the simulation, such as the intensity of the source, the atmospheric stratification, and the dynamic factor of the terrain. Some numerical tests were carried out to provide extra insight to the effects of these factors. It has been demonstrated that the simulation results such as relative humidity and temperature are sensitive to these factors, especially to the thermal stratification. Under unstable conditions, the effects of the spray source increase significantly, and the variation extent of the temperature, relative humidity and flow field is larger than that under neutral condition. The effects of dynamic and thermal factors on the air flow field are discussed through the comparison of the modeling results over complex terrain and flat terrain. Received June 8, 1998 Revised April 17, 1999     

Simulation of orographically generated waves in a nonhydrostatic model of an adiabatic atmosphere

Results of numerical experiments on the simulation of a flow moving around an isolated mountain are presented. The influence of the sizes of a barrier and of the flow velocity on characteristics of wave oscillations is discussed. All calculations are carried out with the authors’ two-dimensional (in the vertical plane) version of a nonhydrostatic dynamic scheme, in which equations of the dry quasi-incompressible atmosphere are solved with a semi-implicit semi-Lagrangian method. This method uses large time steps as compared to explicit-implicit Eurlerian methods. The results of calculations agree with results obtained by other authors, which gives hope for finding physically correct solutions in the simulation of nonhydrostatic processes in the atmosphere.     

Relaxation Factor Effects in the Non-Linear Mixed Spectral Finite Difference Model of Flow Over Topographic Features

The nonlinear version of the mixed spectral finite difference model of atmospheric boundary-layer flow over topography is reviewed. The relations between the stability of the iteration scheme and its relaxation parameter are discussed. Suitable choice of the relaxation factor improves the computational stability on terrain with maximum slope up to 0.5 or 0.6 in certain circumstances. Examples of relatively high slope terrain are used to test the stability. A two-dimensional version of the model is considered. More detailed simulations are studied and analyzed for a comparison with wind-tunnel flow over periodic sinusoidal surfaces. An application on real topography is given for Bolund hill in Roskilde, Denmark.     

The influence of a water surface on mesoscale dynamics as a function of atmospheric stability

Several numerical experiments have been undertaken with a three-dimensional mesoscale model in order to determine to what extent a water surface such as a lake can influence mesoscale flow patterns.It is shown that the influence of the lake is important when cumulus clouds are present. These clouds, generated by evaporation from the water surface are small but induce significant secondary circulations which disrupt the flow field on the mesoscale.Artificial suppression of cloud activity results in a situation where the lake exerts little influence on the atmospheric environment in comparison to the control experiment where the body of water is absent. Atmospheric stability controls the intensity of perturbations to the mean flow when clouds are present.The study is of interest when modeling a number of complex phenomena simultaneously; the results shown here indicate that under certain stability conditions, a small lake can be ignored as to its dynamic and thermodynamic influence on atmospheric processes, thus leading to a neglect of a number of equations taking into account moisture terms explicitly.     

A non-linear extension of the mixed spectral finite difference model for neutrally stratified turbulent flow over topography

A non-linear extension of the mixed spectral finite difference model for neutrally stratified surface-layer flow over complex terrain is developed. The non-linear terms are treated as additional source terms in the present model. The solution is calculated iteratively in spectral space, while the source terms are evaluated in physical space (at each iteration step) with the help of a Fast Fourier Transform algorithm.Results for simple 2D sinusoidal topography are shown to compare well with full non-linear finite difference results. The method, compared to conventional finite difference methods, has the advantage of rapid convergence and substantial savings in computer time.     

一次山地积云并合扩展层化过程的数值模拟

因复杂地形下热力和动力抬升对近地面空气的扰动作用,贵州地区容易形成内部嵌有许多小对流单体的积层混合云.选取2005年5月29日发生在贵州省的一次积层混合云降水个例进行分析,并利用WRF模式模拟该云系的生成、发展过程.结果表明:积层混合云由积云并合扩展层化形成,其发展过程经历三个典型的并合阶段.云系的降水特点是降水范围很大,分布不均匀,雨区中存在多个强降水中心,降水量累计最大值可达60 mm,且强降水中心与云中小对流单体的位置对应;积层混合云形成过程中,地面产生强降水的最终原因是,云并合过程中释放的不稳定能量改变了云中的气流场和含水量场.     

Local advection of momentum,heat, and moisture in micrometeorology

The local advection of momentum, heat and moisture in micrometeorology due to a horizontal inhomogeneity in surface conditions is numerically investigated by a higher-order turbulence closure model which includes equations for the mean quantities, turbulent fluxes, and the viscous dissipation rate. The application of the two-dimensional model in this paper deals with the simulation of the flow from an extensive smooth dry area to a grassy wet terrain. The mean wind speed, temperature, and humidity distributions in the resulting internal boundary layer downstream of the surface discontinuity are determined such that the energy and moisture balances at the Earth's surface are satisfied.Numerical calculations of the mean temperature and humidity profiles are compared with available observed ones. The results include the advective effects on turbulent flux distributions, surface energy balance, evaporation rate, and Bowen ratio. The sensitivity of the predicted mean profiles and turbulent flux distributions to the surface relative humidity, thermal stratification, and the roughness change is discussed.NRC-NAS Resident Research Associate at AFCRL.     

A mixed spectral finite-difference model for pollutant concentrations over a hill

Given incident logarithmic profiles of wind and pollutant concentration above a rough, absorbing surface, the three-dimensional distribution of pollutant concentration over a hill of gentle slope is determined from a linearized model. The model is applied in neutrally stratified flow, without chemistry, and is integrated using spectral methods in the horizontal and a finite-difference scheme in the vertical. This approach allows for flexibility in choosing a closure scheme and a variety of surface boundary conditions. This was not possible in the analytic approach of Padro (1987) who added pollutant concentration and flux to the MS3DJH/1 model of Walmsley et al. (1980). The present model requires as input the turbulent kinetic energy, E, dissipation, , and the perturbation vertical velocity, w, from the three-dimensional boundary-layer flow model of Beljaars et al. (1987), hereinafter referred to as MSFD, The latter model also supplies wind velocity perturbations at the upper boundary, as input to upper boundary conditions on the pollutant flux perturbations.The present study describes applications of the model to idealized terrain features: isolated two- and three-dimensional hills and ridges and an infinite series of ridges. (Application to real terrain, however, presents no difficulties.) Comparisons were made with different (though uniform) surface roughnesses. Tests were performed to examine the effect of upstream terrain features in the periodic domain and to illustrate the importance of the vertical resolution of the output for interpreting results from the sinusoidal terrain case.