A new large-eddy simulation model for simulating air flow and warm clouds above highly complex terrain. Part I: The dry model

This paper presents the dry version of a new large-eddy simulation (LES) model, which is designed to simulate air flow and clouds above highly complex terrain. The model is three-dimensional and nonhydrostatic, and the governing equations are sound filtered by use of the anelastic approximation. A fractional step method is applied to solve the equations on a staggered Cartesian grid. Arbitrarily steep and complex orography can be accounted for through the method of viscous topography. The dynamical model core is validated by comparing the results for a spreading density current against a benchmark solution. The model accuracy is further assessed through the simulation of turbulent flow across a quasi two-dimensional ridge. The results are compared with wind-tunnel data. The method of viscous topography is not restricted to moderately sloped terrain. Compared to models using curvilinear grids, it allows this model to be applied to a much wider range of flows. This is illustrated through the simulation of an atmospheric boundary-layer flow over a surface mounted cube. The results show that the dry model version is able to accurately represent the complex flow in the vicinity of three-dimensional obstacles. It is concluded that the method of viscous topography was successfully implemented into a micrometeorological LES model. As will be shown in Part II, this allows the detailed study of clouds in highly complex terrain.     

On the parameterization of drag over small-scale topography in neutrally-stratified boundary-layer flow

Predictions of the surface drag in turbulent boundary-layer flow over two-dimensional sinusoidal topography from various numerical models are compared. For simple 2D terrain, the model results show that the drag increases associated with topography are essentially proportional to (slope)² up to the steepness at which the flow separates. For the purposes of boundary-layer parameterisation within larger-scale models, we propose a representation of the effects of simple 2D topography via an effective roughness length, z ₀ ^eff. The form of the varation of z ₀ ^eff with terrain slope and topographic wavelength is established for small slopes from the model results and a semi-empirical formula is proposed.     

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.     

Parameterization of the thermal impacts of sub-grid orography on numerical modeling of the surface energy budget over East Asia

Summary A parameterization scheme for the thermal effects of subgrid scale orography is incorporated into a regional climate model (developed at Nanjing University) and its impact on modeling of the surface energy budget over East Asia is evaluated. This scheme includes the effect of terrain slope and orientation on the computation of solar and infrared radiation fluxes at the surface, as well as the surface sensible and latent heat fluxes. Calculations show that subgrid terrain parameters alter the diurnal cycle and horizontal distributions of surface energy budget components. This effect becomes more significant with increased terrain slope, especially in winter. Due to the inclusion of the subgrid topography, the surface area of a model grid box changes over complex terrain areas. Numerical experiments, with and without the subgrid scale topography scheme, show that the parameterization scheme of subgrid scale topography modifies the distribution of the surface energy budget and surface temperature around the Tibetan Plateau. Comparisons with observations indicate that the subgrid topography scheme, implemented in the climate model, reproduces the observed detailed spatial temperature structures at the eastern edge of the Tibetan Plateau and reduces the tendency to overestimate precipitation along the southern coastal areas of China in summer.     

贵州高原起伏地形下日照时间的时空分布

由于坡度、坡向和地形之间相互遮蔽等局地地形因子的影响, 实际起伏地形下的日照时间与水平面上的日照时间有一定差异。该文建立了一种基于数字高程模型 (DEM) 的起伏地形下日照时间的模拟方法, 计算了起伏地形下贵州高原100 m×100 m分辨率日照时间的时空分布。结果表明:坡度、坡向、地形遮蔽对日照时间的影响较大, 实际起伏地形下日照时间的空间分布具有明显地域特征。1月太阳高度角较低, 坡度、坡向的作用非常明显, 地形遮蔽面积较大, 日照时间的空间差异较多, 日照时间为16~142 h, 最大值约为最小值9倍; 7月太阳高度角较高, 地形遮蔽面积相对较小, 日照时间的空间差异相对较少, 日照时间为133~210 h, 最大值为最小值1.6倍, 但由于7月日照时间相对较多, 局地地形对日照时间影响仍明显。4月、10月日照时间及其变化幅度介于1月和7月之间。     

Nocturnal drainage flow on simple slopes

Observations of nocturnal slope flow have been made at two sites with quite different topography and vegetation. In both cases, continuous measurements of wind and temperature profiles were made from towers that extended through the depth of the katabatic flow. At the simpler site, which approximates a tilted plane, three towers were located at different distances down the slope to measure the development of slope flow with downslope distance.Slope flow depth, downslope wind speed, and temperature deficit are found to change with downslope distance at rates that are consistent with the predictions of Manins and Sawford's (1979) layer-averaged model of slope flow, while measured entrainment rates are found to be comparable to those predicted by Ellison and Turner's (1959) laboratory experiments. The depth of slope flow is found to be roughly 0.05 times the vertical drop from the top of the slope, a relationship that also follows from combining Manins and Sawford's model and Ellison and Turner's laboratory data. Analysis of the wind spectra and a simple numerical model suggest that the turbulent kinetic energy profiles in slope flow are dependent on the speed and direction of the ambient wind and can differ substantially from those found over flat terrain. At the more complex of the two measurement sites, the occurrence of slope flow was found to correlate well with a dimensionless number 5 that is a function of the ridge-top wind speed and of the strength and depth of the inversion and that is an estimate of the ratio of the buoyancy deficit to the external horizontal pressure gradient.Prepared for the U.S. Department of Energy under Contract DE-AC06-76RLO 1830     

Spectral Maxima In A Perturbed Stable Boundary Layer

Wind velocity data have been collected on Nansen Ice Sheet, Antarctica, close to the base of a steeply sloping glacier along which frequently flow katabatic winds. The aim of this study is to investigate how turbulent energy and momentum flux are perturbed by the flow interaction with topography and by the strong mechanical mixing produced by downslope flows. Spectral and cospectral analyses, performed on the wind velocity components, provide evidence that such a perturbation, at any stability, is restricted to frequencies lower than the inertial subrange. Longitudinal spectra display an energy increment, due to turbulence generated by topography and by mechanical forcing related to the katabatic wind structure. The energy, supplied by the topographic forcing, displaces the turbulent energy maximum toward lower frequencies. In near-neutral stratification the spectral maximum occurs at a reduced frequency, which seems to be consistent with the height of the steepest part of the slope, and seems to shift toward higher frequencies as a linear ,function of the local stability parameter,L_l. The parameterisation of the orographic perturbation by means of a similarity relationship allows us to scale u spectra in the same way as over uniform terrain. The scaled, perturbed spectra collapse onto a unique curve in the mid-frequency as well in the inertial subrange, while maxima are grouped in a cluster. Lateral and vertical velocity spectra exhibit shapes independent of stability, suggesting a topographic perturbation that is predominantly over stability effects.     

The influence of topography on the cloud-to-ground lightning density in South Brazil

A comparative analysis between cloud-to-ground (CG) lightning density and terrain parameters (altitude and terrain slope) in South Brazil is presented. This region is characterized by a contrasting topography, where a mountain chain separates lower (depression) and higher (plateau) landscapes. The altitude and terrain slope data were obtained from the Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM). Two years of CG lightning data (from June 2005 to May 2007) obtained by the Brazilian Lightning Detection Network (BrasilDAT) were used in the study. To avoid intracloud contamination, positive CG flashes with peak currents less than 20 kA were removed from the data set. A relative detection efficiency model was used to correct the lightning data. The results indicate that, for localized areas (following the mountain shape) within this region of Brazil, the CG lightning density is correlated with the terrain slope and not the altitude. This suggests that terrain slope has more influence than altitude on the thunderstorm occurrence and lightning activity. In addition, a temporal analysis shows that over high altitude regions the diurnal variation (amplitude) of lightning activity is stronger and the peak occurs 1 h earlier than over low altitude regions.     

Influence of Topography and Large-scale Forcing on the Occurrence of Katabatic Flow Jumps in Antarctica： Idealized Simulations

The Regional Atmospheric Modeling System （RAMS）, which is a non-hydrostatic numerical model, has been used to investigate the impact of terrain shape and large-scale forcing on the Antarctic surface-wind regime, focusing on their roles in establishing favorable flow conditions for the formation of katabatic flow jumps. A series of quasi-2D numerical simulations were conducted over idealized slopes representing the slopes of Antarctica during austral winter conditions. Results indicate that the steepness and variations of the underlying slope play a role in the evolution of near-surface flows and thus the formation of katabatic flow jumps. However, large-scale forcing has a more noticeable effect on the occurrence of this small-scale phenomenon by establishing essential upstream and downstream flow conditions, including the upstream supercritical flow, the less stably stratified or unstable layer above the cold katabatic layer, as well as the cold-air pool located near the foot of the slope through an interaction with the underlying topography. Thus, the areas with steep and abrupt change in slopes, e.g. near the coastal areas of the eastern Antarctic, are preferred locations for the occurrence of katabatic flow jumps, especially under supporting synoptic conditions.     

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.     

山地上冰雹云的数值试验研究

建立了一个适用于复杂地形的冰雹云模式。模式是二维、弹性、非静力、采用地形跟随价值、包含双变参数冰相微物理过程参数化。使用实测的初值条件和环境场进行试验。对理论对称型山地的不同初始位温扰动作模拟。结果表明,当初始位温扰动在迎风坡和山顶时冰雹云发展较弱,而当初始位温扰动在背风坡和平原时冰雹云发展较强。当初始位温扰动在背风坡时冰雹云的降雹量约为当初始位温扰动在迎风坡时冰雹云降雹量的６倍。山地上冰雹云的发     

Large-Eddy Simulation of Katabatic Flows

A large-eddy simulation model with rotated coordinates and an open boundary is used to simulate the characteristics of katabatic flows over simple terrain. Experiments examine the effects of cross winds on the development of the slope-flow boundary layer for a steep (20°) slope and the role of drainage winds in preventing turbulence collapse on a gentle slope (1°). For the steep flow cases, comparisons between model average boundary-layer velocity, temperature deficit, and turbulence kinetic energy budget terms and tower observations show reasonable agreement. Results for different cross slope winds show that as the cross slope winds increase, the slope flow deepens faster and behaves more like a weakly stratified, sheared boundary layer. Analysis of the momentum budget shows that near the surface the flow is maintained by a balance between downslope buoyancy forcing and vertical turbulence flux from surface drag. Above the downslope jet, the turbulence vertical momentum flux reverses sign and acceleration of the flow by buoyancy is controlled by horizontal advection of slower moving ambient air. The turbulence budget is dominated by a balance between shear production and eddy dissipation, however, buoyancy and pressure transport both are significant in reducing the strength of turbulence above the jet. Results from the gentle slope case show that even a slight terrain variation can lead to significant drainage winds. Comparison of the gentle slope case with a flat terrain simulation indicates that drainage winds can effectively prevent the formation of very stable boundary layers, at least near the top of sloping terrain.     

Evaluation of an alternative method for numerically modeling nonhydrostatic flows over irregular terrain

Modeling nonhydrostatic atmospheric flow requires the solution of the vertical equation of motion and a prognostic or diagnostic equation for pressure. If the nonhydrostatic components of the flow are relatively small, they can be approximated and incorporated into a purely hydrostatic model, which usually is conceptually simpler and computationally more efficient. A method to do this for a linear model of local thermally-induced circulations is further developed and adapted to a non-linear numerical model of the neutral atmospheric boundary layer. A hydrostatic model and the quasi-nonhydrostatic version were used to simulate neutral flow over simple terrain features. One set of observations taken over a simple change in roughness and another set taken over a change in both roughness and terrain were simulated by both models to assess the capabilities of the quasi-nonhydrostatic technique.It is found that (as expected) the pressure deviation from the hydrostatic state is negligible for the roughness change, but it is an important aspect of neutral flow over terrain. Thus, for flow encountering a simple roughness change, the hydrostatic approximation is good, even for small horizontal scales. However, the quasi-nonhydrostatic model qualitatively produces the features in the observations for flow over a terrain change that the hydrostatic model cannot produce.Journal Paper No. J-12737 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2779.     

PRELIMINARY NUMERICAL STUDY OF TOPOGRAPHIC EFFECTS OF THE TIBETAN PLATEAU ON SURFACE DIRECT RADIATION*

To improve the simulating ability of a model,this paper presents a scheme of calculating direct radiation at land surface with topography in the model.A numerical study is conducted for the topographic effects of the Tibetan Plateau on the direct radiation using NCEP terrain data.Results show that,after taking account into the topographic radiation effect,the regional average of the radiation over the Plateau obviously increases in the local early morning and late afternoon,but changes less around noon.The effect is stronger in winter than that in summer.And heterogeneous topography has also affected the distribution of the radiation in this area.A simple numerical experiment shows that considering the effect will lead ground temperature to increase on the slope having more sunshine,and vice versa.     

PRELIMINARY NUMERICAL STUDY OF TOPOGRAPHIC EFFECTS OF THE TIBETAN PLATEAU ON SURFACE DIRECT RADIATION

To improve the simulating ability of a model,this paper presents a scheme of calculatingdirect radiation at land surface with topography in the model.A numerical study is conducted forthe topographic effects of the Tibetan Plateau on the direct radiation using NCEP terrain data.Results show that,after taking account into the topographic radiation effect,the regional averageof the radiation over the Plateau obviously increases in the local early morning and late afternoon,but changes less around noon.The effect is stronger in winter than that in summer.Andheterogeneous topography has also affected the distribution of the radiation in this area.A simplenumerical experiment shows that considering the effect will lead ground temperature to increase onthe slope having more sunshine,and vice versa.     

Weakly nonlinear oscillatory flow over an isolated seamount

Abstract

Numerical models can show large errors in the modelling of flow around tall topography. We present a weakly nonlinear analytical solution of barotropic oscillatory flow over a tall axisymmetric seamount and compare the results to a numerical tidal model. The comparison is formulated for a flat topped seamount with parabolic sides and for a standing wave boundary condition in order to make the problem analytically tractable and to reduce it to a series of ordinary differential equations. The comparison shows reasonable agreement within the confines of the analytical formulation confirming that the numerical model can exploit tall topography. Comparisons to a Gaussian seamount and Kelvin wave forcing illustrate the generality of the results.

The analytical formulation produces an equation relating relative errors in the comparison to discontinuities in topographical slope; the numerical model should have smaller errors over smoother topography. Residual velocities are found to be proportional to the aspect ratio of the topography.     

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