Physical modelling of flow and dispersion over complex terrain

Atmospheric motion and dispersion over topography characterized by irregular (or regular) hill-valley or mountain-valley distributions are strongly dependent upon three general sets of variables. These are variables that describe topographic geometry, synoptic-scale winds and surface-air temperature distributions. In addition, pollutant concentration distributions also depend upon location and physical characteristics of the pollutant source. Overall fluid-flow complexity and variability from site to site have stimulated the development and use of physical modelling for determination of flow and dispersion in many wind-engineering applications. Models with length scales as small as 1:12,000 have been placed in boundary-layer wind tunnels to study flows in which forced convection by synoptic winds is of primary significance. Flows driven primarily by forces arising from temperature differences (gravitational or free convection) have been investigated by small-scale physical models placed in an isolated space (gravitational convection chamber). Similarity criteria and facilities for both forced and gravitational-convection flow studies are discussed. Forced-convection modelling is illustrated by application to dispersion of air pollutants by unstable flow near a paper mill in the state of Maryland and by stable flow over Point Arguello, California. Gravitational-convection modelling is demonstrated by a study of drainage flow and pollutant transport from a proposed mining operation in the Rocky Mountains of Colorado. Other studies in which field data are available for comparison with model data are reviewed.     

A wind tunnel boundary-layer simulation of wind flow over complex terrain: Effect of terrain and model construction

The report presents the results of a wind-tunnel study of the flow of the natural wind over complex terrain. A 1:4000 undistorted scale model of Gebbies Pass in the South Island of New Zealand was prepared and tested in the boundary-layer wind tunnel in the Department of Mechanical Engineering at the University of Canterbury.Three forms of construction, viz., terraced, contoured and roughness-added, were compared. Velocity and turbulence profiles, Reynolds stresses and spectra were measured, and correlation of results between different types of construction was calculated. The terraced form was much simpler to construct but was found to be unsatisfactory. The correlation between the contoured and roughness-added models was as high as 0.94, although the roughness-added model made a significant difference to the results in the lower 20%; of the boundary layer. The results of these tests will be compared with results from the field in a future report.     

Observations of complex terrain flows using acoustic sounders: Drainage flow structure and evolution

This paper presents an analysis of nocturnal drainage flows in a mountainous coastal environment where the elevation of the terrain is comparable with the elevation of the marine temperature inversion. The analysis traces the initiation, evolution, and breakup of the drainage flow using acoustic sounder facsimile data and tethered sonde measurements of wind and temperature. Conditions addressed include (1) opposing seabreeze flow ranging from 2 to 8m s^-1, (2) aiding flow, and (3) large-scale and drainage-induced subsidence. The effect of deep marine temperature inversions pervades the observations, as seen in deeper, more stratified echo layers, weaker drainage, and delayed destruction of the inversion in the morning.     

Simulation of three-dimensional wind flow over complex terrain in the atmospheric boundary layer

A three-dimensional model for wind prediction over rough terrain has been developed for practical use. It is a compromise between hydrodynamic and objective wind models. The proposed model includes: (1) a statistical model to predict the wind velocity and potential temperature at anemometer height at observing stations, (2) the drainage wind model expressed by Prandtl's analytic solution for the slope wind, (3) the Businger-Dyer surface-layer formulation which considers the surface energy budget and (4) the model for three-dimensional boundary-layer solutions to the stationary flow. In this model, mass consistency is guaranteed by using flow fields that satisfy the continuity equation. Model predictions show good agreement with the observations.     

The use of mesoscale numerical models to assess wind distribution and boundary-layer structure in complex terrain

Mesoscale models which can be used to assess wind and turbulent structure in complex terrain are overviewed. The different types of models — diagnostic and prognostic are discussed and the significant physical processes which each can handle realistically are reviewed. Examples of specific applications of these models are presented.     

Mesoscale flow over complex terrain — A field study in the Lake Kinneret area

A two week observation program was carried out in the summer of 1981 in the Lake Kinneret (Northern Israel) area. The main purpose was to study the mesoscale flow patterns in and around the lake valley and compare them with the results of mesoscale model simulations in the same area. The main effort of the program was directed to the determination of three dimensional trajectories from various points around the valley. For that purpose a new method for the deployment of relatively long term no-lift balloons was used. In addition, surface observations as well as upper air wind observations using pibals were taken at four fixed locations along a straight line across the lake valley. Based on previous studies using surface observations and model results it appeared that the flow regime was determined by the combination of three main mechanisms: the Mediterranean sea breeze, the lake breeze and the mountain-valley wind. This combination results in a daily cycle divided into three distinct flow regimes. The results of the present experiment confirm this basic classification as well as the general structure of the flow for each of the three regimes. The experiment also confirmed the assumption that the large scale synoptic flow has only a minor influence in the valley, and contributes only to the general direction of the winds. In spite of the overall agreement several deficiencies of the model simulations came to light as a result of the experiment. These have to do with the horizontal and vertical resolutions employed in the models, with the fact that all of them were two dimensional (even though several of the models are capable of three dimensional simulations), and with the fact that most of them use the hydrostatic approximation. Due to the lack of appropriate equipment no vertical soundings were performed in order to determine the thermal and humidity stratification. These will have to be completed in subsequent experiments in order to provide the missing data.     

Modeling heavy precipitation in complex terrain

Summary A numerical prediction model is described which uses the full set of prognostic equations on a domain roughly the size of the United States with a 96 km horizontal grid resolution and six sigma-coordinate levels. Within this grid resides a nested domain of approximately 1000×1000 km with 24 km horizontal resolution. In this nested grid only modifications to the wind field by the better resolved terrain are considered on the lowest two sigma levels. The terrain effects necessitate adjustments in the location of these two sigma levels. Adjusted wind fields cause modifications in the mass and moisture divergence fields, hence in precipitation. These modifications are averaged into the appropriate meteorological fields on the larger grid.The algorithms used by our model allow continuous interaction between both grids with high computational efficiency.The relative importance of synoptic forcing and terrain is demonstrated for the cases of the Big Thompson, Colorado, flood of 1976 and the Cheyenne, Wyoming, flood of 1985.With 15 Figures     

An assessment of mixing-length closure schemes for models of turbulent boundary layers over complex terrain

The effectiveness of closure assumptions implemented in turbulent boundary-layer models is rather uncertain over complex terrain. Different closure schemes for Reynolds shear stress based on the mixing-length concept are compared with data from wind tunnel experiments over complex terrain and the results are analysed on the basis of second-order moment equations. A good estimation of the vertical momentum flux velocity scale turns out to be given by the standard deviation of the vertical velocity while the turbulent kinetic energy scaling gives less satisfactory results in regions where turbulence anisotropy is large. Fairly good results are given by closure models implementing a shear-limited mixing-length already proposed for non-logarithmic wind profiles, while large errors characterize traditional mixing-length formulations.     

Mass consistent models for wind distribution in complex terrain — Fast algorithms for three dimensional problems

Mass consistent models for wind distribution in complex terrain are extremely useful and readily applied to many practical situations, such as the siting of wind turbines, or as input in the estimation of diffusion and transport of pollutants in complex terrain. These models are based on the numerical solution of the steady state three dimensional continuity equation for the mean wind components. The momentum and energy equations are not solved explicitly, but considered indirectly using parametric relations and wind data. In practical applications the equations must be solved numerous times (e.g. for each time interval). Standard techniques for numerical solution of three dimensional problems are frequently very expensive and thus not suitable for practical needs. In the present work, great emphasis is given to the development of fast algorithms, and techniques based on the multigrid approach are shown. Two mass consistent programs are described, the first based on the parametric representation of one of the wind components, and the second based on a few wind measurements and a variational principle. To verify the reliability of the variational approach, a measurement program related to a project of wind energy, is being performed at Har-Ahim, a site located in the Galilee.     

Transport and diffusion in complex terrain (review)

This paper reviews activities over the past nine years involving the evaluation, verification and development of atmospheric transport and diffusion models applied to air pollution assessments in complex/ mountainous terrain settings. Results from experiments performed at different complex terrain settings under stably stratified flow conditions have been emphasized. Comparisons of model predictions to observations are made. Physical modeling laboratory tests simulating flow conditions for full-scale experiments complement the data bases and provide information on systematic variations of modeling parameters and input conditions for mathematical model development purposes. Principal findings from these and other experiments on specific technical issues are summarized.     

Turbulent dispersion of pollutant over complex terrain

A two-dimensional turbulent diffusion equation is derived in a streamline coordinate system, defined for rotational flow over complex terrain and limited aloft by an elevated, impenetrable inversion. In the first instance, the steady-state equation is solved for an inner region of the boundary layer, in which the effect of curvature is negligible and, for simplicity, it is assumed that vorticity has a power-law dependence upon stream function. A variational method of solution is also discussed, in which vorticity may have a more general representation. A numerical calculation is performed for a special case of symmetrical flow over an isolated hill. The dependence of pollutant concentration upon the flow field, downwind distance and source is examined and the effect of wind acceleration in the neighbourhood of the top of the hill is discussed. It is pointed out that the diffusion model can be applied to any realistic flow field, provided that the streamlines are specified.     

Vertical distributions of sulfur species simulated by large scale atmospheric models in COSAM: Comparison with observations

A comparison of large‐scale models simulating atmospheric sulfate aerosols (COSAM) was conducted to increase our understanding of global distributions of sulfate aerosols and precursors. Earlier model comparisons focused on wet deposition measurements and sulfate aerosol concentrations in source regions at the surface. They found that different models simulated the observed sulfate surface concentrations mostly within a factor of two, but that the simulated column burdens and vertical profiles were very different amongst different models. In the COSAM exercise, one aspect is the comparison of sulfate aerosol and precursor gases above the surface. Vertical profiles of SO₂, SO²⁻₄, oxidants and cloud properties were measured by aircraft during the North Atlantic Regional Experiment (NARE) experiment in August/September 1993 off the coast of Nova Scotia and during the Second Eulerian Model Evaluation Field Study (EMEFSII), in central Ontario in March/April 1990. While no single model stands out as being best or worst, the general tendency is that those models simulating the full oxidant chemistry tend to agree best with observations although differences in transport and treatment of clouds are important as well.     

Observations of complex terrain flows using acoustic sounders: Echo interpretation

We examine methods for the interpretation of sodar facsimile records obtained in the study of complex terrain flows. Acoustic scattering theory is presented first and then interpreted using a simpolified second-order turbulence closure scheme. The use of this theory suggests the strong sensitivity of acoustic scatter to changes in the wind shear. With this introduction, detailed sodar facsimile records, temperature and wind profiles, and model calculations follow. Characteristic scattering patterns are described for simple drainage jets, complex basin flows, convection with a capping inversion, stratus, and dynamical instabilities. Examples are also shown of bistatic facsimile records detailing the strong temporal and spatial variability in small-scale turbulence.     

A comparison between two stochastic diffusion models in a complex three-dimensional flow

A Random Displacement Model (RDM) and a Langevin Equation Model (LEM) are used to simulate point releases in a complex flow around a building. The flow field is generated by a three-dimensional finite element model that uses the standardk- model to parameterize the turbulence. The RDM- and LEM-calculated concentration fields are compared, with particular emphasis on the structure in regions with high turbulence and/or recirculation. RDM and LEM results are similar qualitatively, but RDM tends to predict lower concentration levels. In part this is due to the higher early-time diffusion. However, the expected convergence at later times is prevented by the interaction of the diffusion with the strongly inhomogeneous mean flow.Notation a _i coefficient in the Langevin equation - b _ij coefficient in the Langevin equation - C ₀ the universal constant associated with the Lagrangian structure function - H building height (22.5 m) - K eddy viscosity - K _k eddy viscosity used in the definition of the off-diagonal Reynolds stresses - k turbulent kinetic energy - LEM Langevin Equation Model - p ₁ local unit vector in thexy-plane, orthogonal tos - p ₂ local unit vector, orthogonal to boths andp ₁ - RDM Random Displacement Model - s local unit vector in the streamline direction - T local decorrelation time (Lagrangian time scale) - U magnitude of the local Eulerian mean wind velocity - u _s total velocity in the streamline direction - u ₁ velocity component in thexy-plane, orthogonal to the streamline direction - u ₂ velocity component orthogonal to bothu _s andu ₁ - _i mean Eulerian wind velocity - W _i stochastic vector-valued Wiener process - x unit vector inx-direction - y unit vector iny-direction - z unit vector inz-direction - angle between thexy-plane and the mean wind streamline - angle between the projection in thexy-plane of the streamline and thex-axis - _ij the Kronecker delta function - rate of turbulence dissipation - _i/g_a the part ofa _i that contains mean wind and turbulence gradients - _ij inverse of a Reynolds stress tensor component - _ij shorthand for a quantity that defines a part of _i/g_a - _i shorthand for a quantity that defines a part of _i/g_a - _ij Reynolds stress tensor component     

Atmospheric properties of ENSO: models versus observations

Two important atmospheric features affecting El Niño-Southern Oscillation (ENSO) are atmospheric noise and a nonlinear atmospheric response to SST. In this article, we investigate the roles of these atmospheric features in ENSO in observations and coupled Global Climate Models (GCMs). We first quantify the most important linear couplings between the ocean and atmosphere. We then characterize atmospheric noise by its patterns of standard deviation and skewness and by spatial and temporal correlations. GCMs tend to simulate lower noise amplitudes than observations. Additionally, we investigate the strength of a nonlinear response of wind stress to SST. Some GCMs are able to simulate a nonlinear response of wind stress to SST, although weaker than in observations. These models simulate the most realistic SST skewness. The influence of the couplings and noise terms on ENSO are studied with an Intermediate Climate Model (ICM). With couplings and noise terms fitted to either observations or GCM output, the simulated climates of the ICM versions show differences in ENSO characteristics similar to differences in ENSO characteristics in the original data. In these model versions the skewness of noise is of minor influence on ENSO than the standard deviation of noise. Both the nonlinear response of wind stress to SST anomalies and the relation of noise to the background SST contribute to SST skewness. The ICM is not yet fully evolved, the results rather show that this is a promising route. Overall, atmospheric noise with realistic standard deviation pattern and spatial correlations seems to be important for simulating an irregular ENSO. Both a nonlinear atmospheric response to SST and the dependence of noise on the background SST influence the El Niño/La Niña asymmetry.