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) |
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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) |
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Entrainment coefficient used in buoyant rise for Schulman-Scire downwash sources = 0.6 |
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Jet entrainment coefficient used in gradual momentum plume rise calculations FUNC {~=~{1 over 3} + {{u_s} over {v_s}}} |
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Plume rise (m) |
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Potential temperature gradient with height (K/m) |
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Escape fraction of particle size category for open pit emissions (dimensionless) |
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Precipitation scavenging ratio (s-1) |
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Precipitation rate coefficient (s-mm/hr)-1 |
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pi = 3.14159 |
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Decay coefficient = 0.693/T1/2 (s-1) |
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Stability adjustment factor (dimensionless) |
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Fraction of mass in a particular settling velocity category for particulates (dimensionless) |
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Particle density (g/cm3) |
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Density of air (g/cm3) |
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Horizontal (lateral) dispersion parameter (m) |
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Initial horizontal dispersion parameter for virtual point source (m) |
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Effective lateral dispersion parameter including effects of buoyancy-induced dispersion (m) |
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Vertical dispersion parameter (m) |
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Initial vertical dispersion parameter for virtual point source (m) |
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Effective vertical dispersion parameter including effects of buoyancy-induced dispersion (m) |
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Viscosity of air 0.15 cm2/s |
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Absolute viscosity of air 1.81 x 10-4 g/cm/s |
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Concentration (µg/m3) |
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Concentration with dry deposition effects) |