Ib Troen

Surface-layer flow in complex terrain: Comparison of models and full-scale observations

Four models of surface boundary-layer flow in complex terrain are compared with observations made at Blashaval Hill, North Uist, Scotland. The field experiment is described by Mason and King (1985). Three of the models are derived from the two-dimensional theory of Jackson and Hunt (1975) and are described in Mason and King (1985), Walmsley et al. (1986) and Troen and Petersen (1989). The fourth is a mass-consistent code based on Traci et al. (1979). The model results are in good agreement with each other and are generally within the observed range of variation ( ~ ± 16%) in normalized wind speed. For most wind direcions (7 of 11), model results of normalized wind speed at the summit were within 7% of the observed mean values. For some wind directions, calculations using the “Guidelines” of Walmsley et al. (1989) suggested that variations in surface roughness were important. This led us to apply one of our models incorporating nonuniform surface roughness. The lack of significant improvement for cases when water lay upstream of Blashaval Hill is attributed to compensating changes at summit and reference sites and to very local effects on the wind data. Sensitivity to topography lying to the west and northwest of Blashaval was also investigated. Results suggested an influence from those distant topographic features for some wind directions. When those features were incorporated, maximum errors in normalized wind speed at the summit were reduced from 18 to 13%.

Response of neutral boundary layers to changes of roughness

When air blows across a change in surface roughness, an internal boundary layer (IBL) develops within which the wind adapts to the new surface. This process is well described for short fetches, > 1 km. However, few data exist for large fetches on how the IBL grows to become a new equilibrium boundary layer where again the drag laws can be used to estimate the surface wind.To study this problem, data have been sampled for two years from four 30-m meteorological masts placed from 0 to 30 km inland from the North Sea coast of Jutland in Denmark. The present analysis is limited to neutral stratification, and the surface roughness is the main parameter. The analysis of wind data and two simple models, a surface layer and a planetary boundary layer (PBL) model, are described.Results from both models are discussed and compared with data analysis. Model parameters have been evaluated and the model sensitivity to those parameters has been investigated. Using the model parameters, a large-scale roughness length has been estimated.

A stochastic equation for dispersion in inhomogeneous conditions

The Langevin equation is used to describe dispersion of pollutants in the atmosphere. It is shown that the Langevin equation can describe dispersion in complex circumstances. In particular, the equation is applied to dispersion in a convective boundary layer where it reproduced the measurements accurately. Two forms of the Langevin equation, which have both been used in practical applications, are compared and it is concluded that in terms of their theoretical properties they are not very different in spite of important differences in practical application.

Turbulence and diffusion over inhomogeneous terrain

This paper provides an overview of some aspects of atmospheric boundary-layer dispersion processes over homogeneous and complex terrain. Special emphasis is placed on a discussion of the boundarylayer scaling regimes over homogeneous terrain and the characteristics of the dispersion processes associated with each of these regimes. The paper points out that vertical concentration profiles usually deviate substantially from a Gaussian distribution. The mean flow and turbulence over a low hill is dealt with, and in the inner layer the turbulence levels are increased due to the mean flow speed-up. In the outer layer the turbulence is modified by the rapid distortion effect. In a middle layer the turbulence is reduced due to the effect of a hill-induced streamline curvature. The paper concludes that the flow perturbations introduced by large-scale hills and valleys invalidate the use of simple approximations for describing atmospheric dispersion processes, and that it is necessary to utilize the full set of equations of motion.

PPI-Theory for Particle Dispersion

For many problems with turbulent dispersion the Lagrangian approach as introduced by Taylor (1921) is the most appropriate. Extension of this theory to atmospheric dispersion problems is, however, complicated by the inhomogeneity and instationarity of atmospheric turbulence. Here we first describe a method based on the Preferred Path Integration (PPI) theory relating the probability distribution of particle displacement to the probability for a particle to move along the most probable or preferred path. The theory is based on the assumption that the particle velocity fluctuations are governed by a first order autoregressive process equivalent to the Langevin model of dispersion (Lin and Ried (1962), Novikov (1963), Smith (1968), Hanna (1978) and Gifford (1982)). The PPI-model yields conditional probability distributions in the case of stationary conditions. The Langevin model has been proposed also for instationary conditions in Monte-Carlo simulations of particle dispersion (Durbin (1980), Wilson et al. (1981)), and here are presented some analytical results based on this type of model for the case of dispersion in decaying turbulence.