Air Dispersion Screening: Method

Method, Equations and Sources

What the tool does

An air-permit application for a stack usually starts with a screening calculation: the highest ground-level concentration the source could cause under the worst weather, compared with an ambient air-quality standard. If the screening result is comfortably below the standard, no more modelling is normally asked for; if it is not, a refined model is run with real meteorology. This tool makes the screening estimate the way EPA's SCREEN3 program does for a single source in simple terrain: a steady-state Gaussian plume, Pasquill stability classes A to F, Briggs plume rise, and a search over every stability class and wind speed for the worst case. It reproduces SCREEN3's printed examples for a flare and a volume source to every digit (see the worked example). It is not SCREEN3 itself and it is not a regulatory model run: building downwash, complex terrain, fumigation and area sources, which SCREEN3 also covers, are left out and named in the results.

The plume equation

The 1-hour concentration at a receptor x downwind, y off the plume centreline and z_r above the ground is (ISC3 User's Guide Volume II, eq. 1-1)

C = Q V exp(−y² / (2 σ_y²)) / (2π u_s σ_y σ_z),

with Q the emission rate, u_s the wind speed at release height and σ_y, σ_z the lateral and vertical dispersion coefficients at x. With Q in g/s and the factor 10⁶ the result is in µg/m³. The vertical term V holds the Gaussian exp(−(z_r − H)² / (2 σ_z²)), its image in the ground exp(−(z_r + H)² / (2 σ_z²)) and, for the unstable and neutral classes, the images in the mixing lid at heights 2 i z_i ± H (i = 1, 2, …). When σ_z / z_i reaches 1.6 the plume is uniformly mixed below the lid and V = √(2π) σ_z / z_i. The stable classes E and F have no lid. H is the plume height: release height (after stack-tip downwash) plus the final plume rise, less the terrain height when simple elevated terrain is entered.

Dispersion coefficients

Rural: the Pasquill-Gifford curves in the equation form of the ISC3 guide. σ_y = 465.11628 x tan(θ) with θ = 0.017453293 (c − d ln x), x in km, and c, d by class (Table 1-1); σ_z = a x^b with a and b given by class and distance range (Table 1-2). Urban: the Briggs fits to the McElroy-Pooler data (Tables 1-3 and 1-4), for example σ_y = 0.16 x (1 + 0.0004 x)^−1/2 and σ_z = 0.14 x (1 + 0.0003 x)^−1/2 for class D with x in metres. σ_z is not allowed above 5,000 m. For class A the tool uses c = 24.1667 as the SCREEN3 program does; the ISC3 table prints 24.1670, a difference of two parts in a million in σ_y.

A buoyant plume spreads as it rises. Following Pasquill, the coefficients are enlarged by the buoyancy-induced term σ = Δh(x) / 3.5 added in quadrature, σ_y = (σ_y² + σ²)^1/2 and the same for σ_z, where Δh(x) is the transitional rise at the receptor distance (ISC3 Section 1.1.5.2).

Wind speed at release height

The screening wind speeds are 10 m values. The speed at release height is u_s = u_ref (h_s / z_ref)^p, never below 1 m/s, with the exponent p = 0.07, 0.07, 0.10, 0.15, 0.35, 0.55 for classes A to F in rural settings and 0.15, 0.15, 0.20, 0.25, 0.30, 0.30 in urban settings (ISC3 Section 1.1.3). For a release below 10 m the 10 m speed is used unchanged.

Plume rise (Briggs)

The buoyancy flux is F_b = g v_s d_s² (T_s − T_a) / (4 T_s) and the momentum flux F_m = v_s² d_s² T_a / (4 T_s) (ISC3 eqs. 1-8, 1-9). Whether buoyancy or momentum governs is decided by comparing T_s − T_a with a crossover temperature difference (eqs. 1-10, 1-11 and 1-18).

• Unstable and neutral, buoyant: Δh = 21.425 F_b^3/4 / u_s for F_b below 55 m⁴/s³, else 38.71 F_b^3/5 / u_s; final rise is reached at x_f = 49 F_b^5/8 or 119 F_b^2/5.
• Unstable and neutral, momentum: Δh = 3 d_s v_s / u_s.
• Stable, buoyant: Δh = 2.6 (F_b / (u_s s))^1/3 with the stability parameter s = g (∂θ/∂z) / T_a and ∂θ/∂z = 0.020 K/m for class E, 0.035 K/m for class F; x_f = 2.0715 u_s / √s. The program also applies the calm-wind limit 4 F_b^1/4 / s^3/8 when it is lower.
• Stable, momentum: Δh = 1.5 (F_m / (u_s √s))^1/3, not above the neutral momentum rise.
• Transitional rise before x_f: Δh(x) = 1.60 F_b^1/3 x^2/3 / u_s for buoyant plumes (eq. 1-22) and the jet relations of eqs. 1-23 and 1-25 for momentum plumes, never above the final rise.
• Stack-tip downwash: when v_s is less than 1.5 u_s the release height becomes h_s′ = h_s + 2 d_s (v_s / u_s − 1.5) (eq. 1-7).

Like SCREEN3, the tool places the plume at its final height at every distance when no building wake is involved, and uses the transitional rise only in the buoyancy-induced spread. Two details follow the SCREEN3 program where it differs from the printed ISC3 text: the stable crossover temperature difference is evaluated with the ambient temperature (the text of eq. 1-18 prints T_s), and g = 9.80616 m/s².

Worst-case meteorology and mixing height

Full meteorology examines the wind speeds 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 8, 10, 15 and 20 m/s at 10 m with the classes they can occur with: A up to 3 m/s, B up to 5, C up to 10, D up to 20, E up to 5 and F up to 4 m/s (SCREEN3 User's Guide, Table 2). The mechanical mixing height for the unstable and neutral classes is z_i = 320 u₁₀ (guide eq. 4), raised to H + 1 m when the plume would otherwise be above it, so that the plume is always kept below the lid, which is the conservative choice. Beyond 50 km speeds below 2 m/s are raised to 2 m/s. The maximum is found by scanning the envelope of all conditions between the entered distances and refining it to the nearest metre.

Flare and volume source

Flare (guide Sections 2.5 and 3.3): with H the total heat release in cal/s, 55 % is assumed radiated; the effective release height is the flare height plus 4.56×10⁻³ H^0.478 m (the flame is taken as tilted 45°), the gas is given an exit velocity of 20 m/s and a temperature of 1,273 K in air at 293 K, and the effective diameter 9.88×10⁻⁴ (0.45 H)^0.5 m then reproduces the guide's buoyancy flux F_b = 1.66×10⁻⁵ H (its eq. 6). The tool takes the heat release in watts and converts with 4.1868 J/cal.

Volume source (guide Section 2.7): no plume rise; the initial dimensions σ_y0 and σ_z0 are honoured by adding virtual distances x_y and x_z, found by inverting the coefficient formulas, to the receptor distance. Receptors closer than 2.15 σ_y0 are inside the source and get no value. The guide's rules for the initial dimensions: side length divided by 4.3 for σ_y0; vertical dimension divided by 2.15 for a surface-based source, building height divided by 2.15 for a source on or next to a building, and vertical dimension divided by 4.3 for an elevated source.

Longer averaging times

EPA's screening procedures (EPA-454/R-92-019, Section 4.2, Step 5) estimate the maximum for longer averaging times by multiplying the 1-hour maximum by 0.9 (± 0.1) for 3 hours, 0.7 (± 0.2) for 8 hours, 0.4 (± 0.2) for 24 hours and 0.08 (± 0.02) for the annual average. The values in parentheses are the limits within which the factor may be changed for a particular source with the agreement of the reviewing agency (toward the high side for low releases and downwash or terrain problems). The tool applies the general-case factor, lets it be edited and warns when it is outside the limits.

ppm and the standard

For a gas, ppm by volume = C [µg/m³] × V_m / (1,000 M), with M the molecular weight in g/mol and V_m = R T / P = 24.465 L/mol at the reference conditions of 40 CFR 50.3 (25 °C, 760 mm Hg). The preset standards are the levels of 40 CFR Part 50 as in force on 1 October 2025: sulfur dioxide 75 ppb (1 hour) and 0.5 ppm (3 hours, secondary), nitrogen dioxide 100 ppb (1 hour) and 53 ppb (annual), carbon monoxide 35 ppm (1 hour) and 9 ppm (8 hours), PM10 150 µg/m³ (24 hours), PM2.5 35 µg/m³ (24 hours) and 9.0 µg/m³ (annual). They are cited values in editable fields: check the current rule, the form of the standard and any state or local limit. Because the concentration is proportional to the emission rate, the tool also reports the emission rate at which the screening total, with the entered background, would just equal the standard.

Limits

• Building downwash is not modelled. EPA's rule of thumb (screening procedures eq. 4.11) is that a stack at least h_b + 1.5 L_b tall, with h_b the height of a building within five times L_b and L_b the lesser of its height and projected width, is unlikely to be affected; a shorter stack needs the downwash and cavity calculations of SCREEN3 or a refined model.
• Simple terrain only: receptors at or below the release height. The terrain height entered lowers the plume height for every receptor.
• No inversion break-up or shoreline fumigation, no area sources, no deposition or settling, no chemistry.
• One source at a time; add the background and other nearby sources before a comparison.
• The current preferred screening model under 40 CFR 51 Appendix W is AERSCREEN, the screening version of AERMOD (Section 4.2.1.1 of the Guideline), which also handles building downwash and complex terrain. Ask the reviewing agency which screening method it expects before relying on a SCREEN3-type estimate.

Checks

The library reproduces every printed line of the flare example (pages 29 to 31) and the volume-source example (page 40) of the SCREEN3 User's Guide, and the buoyancy and momentum fluxes of its point-source example (page 22); an independent numpy and scipy implementation written from the ISC3 text agrees on twenty random stacks; the crosswind-integrated mass flux equals the emission rate.