ISCST3 Tech Guide

Gaussian Plume Air Dispersion Model

5. Symbols

Symbol Definition
A Linear decay term for vertical dispersion in Schulman-Scire downwash (dimensionless)
Ae Effective area for open pit emissions (dimensionless)
D Exponential decay term for Gaussian plume equation (dimensionless)
DB Brownian diffusivity (cm/s)
Dr Relative pit depth (dimensionless)
de Effective pit depth (m)
dp Particle diameter for particulate emissions (µm)
ds Stack inside diameter (m)
Fb Buoyancy flux parameter (m4/s3)
Fd Dry deposition flux (g/m2)
Fm Momentum flux parameter (m4/s2)
FQ Plume depletion factor for dry deposition (dimensionless)
FT Terrain adjustment factor (dimensionless)
Fw Wet deposition flux (g/m2)
f Frequency of occurrence of a wind speed and stability category combination (dimensionless)
g Acceleration due to gravity (9.80616 m/s2)
hb Building height (m)
he Plume (or effective stack) height (m)
hs Physical stack height (m)
hter Height of terrain above stack base (m)
hs´ Release height modified for stack-tip downwash (m)
hw Crosswind projected width of building adjacent to a stack (m)
>k von Karman constant (= 0.4)
L Monin-Obukhov length (m)
Ly Initial plume length for Schulman-Scire downwash sources with enhanced lateral plume spread (m)
Lb Lesser of the building height and crosswind projected building width (m)
Alongwind length of open pit source (m)
P(x,y) Profile adjustment factor (dimensionless)
p Wind speed power law profile exponent (dimensionless)
QA Area Source pollutant emission rate (g/s)
Qe Effective emission rate for effective area source for an open pit source (g/s)
Qi Adjusted emission rate for particle size category for open pit emissions (g/s)
Qs Pollutant emission rate (g/s)
Q Total amount of pollutant emitted during time period (g)
R Precipitation rate (mm/hr)
Ro Initial plume radius for Schulman-Scire downwash sources (m)
R(z,zd) Atmospheric resistance to vertical transport (s/cm)
r Radial distance range in a polar receptor network (m)
ra Atmospheric resistance (s/cm)
rd Deposition layer resistance (s/cm)
s Stability parameter = FUNC {g {{ theta}/ z } over {T_a}}
S Smoothing term for smoothing across adjacent sectors in the Long Term model (dimensionless)
SCF Splip correction factor (dimensionless)
Sc Schmidt number = FUNC { upsilon /D_B } (dimensionless)
St Stokes number = FUNC { (v_g/g)```(u_*^2/upsilon) } (dimensionless)
Ta Ambient temperature (K)
Ts Stack gas exit temperature (K)
uref Wind speed measured at reference anemometer height (m/s)
us Wind speed adjusted to release height (m/s)
u* Surface friction velocity (m/s)
V Vertical term of the Gaussian plume equation (dimensionless)
Vd Vertical term with dry deposition of the Gaussian plume equation (dimensionless)
vd Particle deposition velocity (cm/s)
vg Gravitational settling velocity for particles (cm/s)
vs Stack gas exit velocity (m/s)
X X-coordinate in a Cartesian grid receptor network (m)
xo Length of side of square area source (m)
Y Y-coordinate in a Cartesian grid receptor network (m)
Direction in a polar receptor network (degrees)
x Downwind distance from source to receptor (m)
xy Lateral virtual point source distance (m)
xz Vertical virtual point source distance (m)
xf Downwind distance to final plume rise (m)
x* Downwind distance at which turbulence dominates entrainment (m)
y Crosswind distance from source to receptor (m)
z Receptor/terrain height above mean sea level (m)
zd Dry deposition reference height (m)
zr Receptor height above ground level (i.e. flagpole) (m)
zref Reference height for wind speed power law (m)
zs Stack base elevation above mean sea level (m)
zi Mixing height (m)
zo Surface roughness height (m)
Entrainment coefficient used in buoyant rise for Schulman-Scire downwash sources = 0.6
Jet entrainment coefficient used in gradual momentum plume rise calculations FUNC {~=~{1 over 3} + {{u_s} over {v_s}}}
Plume rise (m)
Potential temperature gradient with height (K/m)
Escape fraction of particle size category for open pit emissions (dimensionless)
Precipitation scavenging ratio (s-1)
Precipitation rate coefficient (s-mm/hr)-1
pi = 3.14159
Decay coefficient = 0.693/T1/2 (s-1)
Stability adjustment factor (dimensionless)
Fraction of mass in a particular settling velocity category for particulates (dimensionless)
Particle density (g/cm3)
Density of air (g/cm3)
Horizontal (lateral) dispersion parameter (m)
Initial horizontal dispersion parameter for virtual point source (m)
Effective lateral dispersion parameter including effects of buoyancy-induced dispersion (m)
Vertical dispersion parameter (m)
Initial vertical dispersion parameter for virtual point source (m)
Effective vertical dispersion parameter including effects of buoyancy-induced dispersion (m)
Viscosity of air 0.15 cm2/s
Absolute viscosity of air 1.81 x 10-4 g/cm/s
Concentration (µg/m3)
Concentration with dry deposition effects)