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Use of boundary-layer meteorological parameters in the Gaussian model ‘STACKS’

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Abstract

The advanced Gaussian model STACKS includes improved descriptions of some boundarylayer meteorological parameters to calculate atmospheric dispersion from stacks. Instead of describing the influence of meteorology by making use of stability classes, the dispersion parameters σ y and σ x , with profiles and the height of the boundary layer are given as continuous functions of boundary-layer parameters. σ y and σ z are direct functions of turbulence parameters. Two ways to obtain the essential meteorological parameters (turbulence, vertical profiles and mixing height) are given: (i) use of an extended data set with detailed hourly measurements and (ii) application of boundary-layer relations based on the scaling concepts and using a synoptic data set.

Frequency distributions of stability classes as well asz i-values are investigated from the extended data set. Using our method of stability determination, much lower frequencies of the neutral class D are found compared to the traditional PGT (Pasquill-Gifford-Turner) stability classification scheme: instead of 70% neutral according to PGT, about 30% neutral (20% unstable and 50% stable) is estimated with our method for Dutch circumstances. This is also found when Golders' (1972) method is applied (with Obukhov length scale L). Also, in comparingz i-values independently derived from the extended data set (using an analysis of 3 years of balloon soundings), a shift is found toward smaller values compared to those found by recently reported advanced models (OML, HPDM, UKADM). Theoretical formulations for σ v , σ w andT j are evaluated with the extended data set resulting in correlation coefficients of about 0.8.

The effect of two basic parameters (turbulence andz i-values) on the long-term-averaged concentration pattern is shown and compared with the results of three other models: the OML and OPS models (representatives of other advanced models) and the Dutch National Model (DNM), representative of traditional models. For tall stacks, the concentration pattern calculated by the advanced models strongly differs from the one of DNM, which is typical for all comparisons between traditional and advanced models. Hence, it is recommended that one considers not only performance characteristics such as mean bias and standard error, but also the long-term-averaged concentration patterns.

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Abbreviations

B, C :

Constants for computingz i

D :

Wind direction (deg)

f :

Coriolis parameter (s−1)

F b :

Buoyancy flux from the stack (m4/s3)

F r :

Residual buoyancy during plume rise (m4/s3)

g :

Acceleration due to gravity (m/s2)

H * :

Stability parameter (m2/s3)

h 3 :

Effective stack height (m)

L :

Obukhov length scale (m)

M :

Month in the year (1–12)

p :

Plume inversion-penetration fraction

R :

Correlation coefficient

R r :

Dimensionless ratio in (8)

t :

Travel time (s)

T a :

Ambient temperature (K)

ΔT :

Temperature jump at inversion heght (K)

T e :

Eulerian timescale of turbulent fluctuations (s)

T l :

Lagragian timescale of turbulent fluctuations (s)

T ly :

Lagrangian timescale of lateral turbulent fluctuations (s)

T lz :

Lagrangian timescale of vertical turbulent fluctuations (s)

u(z) :

Wind speed at heightz (m/s)

u h :

Wind speed at stack height (m/s)

u * :

Friction velocity (m/s)

w * :

Convective velocity scale (m/s)

x :

Distance from the stack (m)

z :

Height (m)

z b :

Bottom of atmospheric layer (m)

z T :

Top of atmospheric layer (m)

z i :

Inversion height; mixing height (m)

z 0 :

Surface roughness length (m)

Δh :

Plume rise (m)

θ:

Potential temperature (K)

θ v :

Virtual potential temperature (K)

κ:

Von Kárman constant

σ v :

Standard deviation of cross-wind speed fluctuations (m/s)

σ v f :

Same; for the turbulent fluctuations (m/s)

σ v s :

Same; for the slow fluctuations (m/s)

σ w :

Standard deviation of vertical wind speed fluctuations (m/s)

σ y :

Horizontal dispersion parameter (m)

σ y f :

Horizontal dispersion parameter — turbulent component (m)

σ y s :

Horizontal dispersion parameter — non-turbulent component (m)

σ z :

Vertical dispersion parameter (m)

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    J. J. Erbrink

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Erbrink, J.J. Use of boundary-layer meteorological parameters in the Gaussian model ‘STACKS’. Boundary-Layer Meteorol 74, 211–235 (1995). https://doi.org/10.1007/BF00712119

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