Quantifying pollutant release and atmospheric transport from wildfires
2026-02-27
In the summer of 2023, wildfire smoke from Quebec and Ontario turned the skies over New York City orange. PM2.5 concentrations reached 11 times the WHO daily guideline, schools cancelled outdoor activities, and the United States issued its worst-ever air quality alerts across the Northeast. The smoke had travelled more than 1,500 km from fires consuming millions of hectares of boreal forest. The public health impact — measured in respiratory hospital admissions, reduced visibility, and premature deaths — rivalled the fires’ direct destruction of property. And it was predictable: atmospheric transport models had been forecasting the smoke plume’s trajectory for days before it arrived.
Wildfire smoke is a complex mixture of gases and particles produced by incomplete combustion of organic material. The quantities emitted depend on what is burning (fuel type and loading), how efficiently it is burning (flaming versus smouldering), and how much area has burned. Each fuel type has characteristic emission factors — grams of PM2.5, carbon monoxide, or volatile organic compounds per kilogram of fuel consumed — derived from laboratory burns and field measurements. Once released, the smoke plume rises due to thermal buoyancy (Briggs plume rise equations), is advected by the mean wind, and disperses by turbulent mixing. The Gaussian plume model — the workhorse of atmospheric dispersion for point and area sources — predicts concentrations downwind as a function of emission rate, wind speed, atmospheric stability, and distance. This model derives the emission accounting, implements plume rise, and calculates ground-level concentrations from wildfire smoke using the Gaussian framework.
What is the air quality impact 50 km downwind from this wildfire?
Fire emissions:
Pollutants released during combustion.
Major species: - CO₂ (carbon dioxide): ~1650 g/kg fuel - CO (carbon monoxide): ~60-100 g/kg - PM₂.₅ (fine particles): ~10-20 g/kg - NOₓ (nitrogen oxides): ~1-3 g/kg - VOCs (volatile organics): ~10-30 g/kg - CH₄ (methane): ~5-10 g/kg
Health impacts:
PM₂.₅ primary concern: - Respiratory issues - Cardiovascular stress - Premature mortality
Air quality standards:
EPA: 35 μg/m³ (24-hour PM₂.₅)
Wildfire smoke: 100-500 μg/m³ common, >1000 μg/m³ near fires
Applications: - Air quality forecasting - Evacuation decisions - Health advisories - Climate forcing calculations - Carbon accounting
Mass of pollutant per mass of fuel:
EF_i = \frac{m_i}{m_{\text{fuel}}}
Where: - EF_i = emission factor for species i (g/kg) - m_i = mass of species emitted - m_{\text{fuel}} = dry fuel consumed
Total emissions:
E_i = A \times B \times C \times EF_i
Where: - A = area burned (ha) - B = fuel loading (kg/ha) - C = combustion completeness (fraction, 0-1)
Modified combustion efficiency (MCE):
MCE = \frac{\Delta CO_2}{\Delta CO_2 + \Delta CO}
Flaming: MCE > 0.95 (high efficiency, less PM)
Smoldering: MCE < 0.85 (low efficiency, more PM, CO)
PM₂.₅ increases as MCE decreases:
EF_{PM_{2.5}} = a - b \times MCE
Typical: a = 60, b = 50 → flaming = 12.5 g/kg, smoldering = 17.5 g/kg
Buoyancy-driven ascent:
Hot emissions rise above fire.
Final plume height:
H = H_s + \frac{1.6 F^{1/3}}{U s^{1/3}}
Where: - H = plume top height (m) - H_s = stack (fire) height (m) - F = buoyancy flux (m⁴/s³) - U = wind speed (m/s) - s = stability parameter
Buoyancy flux:
F = g \frac{Q_H}{c_p T_a \rho_a}
Where: - g = 9.81 m/s² - Q_H = sensible heat flux (W) - c_p = 1005 J/kg/K - T_a = ambient temperature (K) - \rho_a = air density (kg/m³)
Typical wildfire:
Q_H = 10^8 W → plume rise 1000-3000 m
Concentration downwind:
C(x,y,z) = \frac{Q}{2\pi U \sigma_y \sigma_z} \exp\left(-\frac{y^2}{2\sigma_y^2}\right) \left[\exp\left(-\frac{(z-H)^2}{2\sigma_z^2}\right) + \exp\left(-\frac{(z+H)^2}{2\sigma_z^2}\right)\right]
Where: - C = concentration (μg/m³) - Q = emission rate (μg/s) - U = wind speed (m/s) - \sigma_y, \sigma_z = dispersion parameters (m) - H = effective release height (m) - Second exponential = ground reflection
Dispersion parameters:
Power-law with distance:
\sigma_y = a x^b \sigma_z = c x^d
Constants depend on atmospheric stability class.
Ground-level concentration (z=0):
C(x,y,0) = \frac{Q}{\pi U \sigma_y \sigma_z} \exp\left(-\frac{y^2}{2\sigma_y^2}\right) \exp\left(-\frac{H^2}{2\sigma_z^2}\right)
Fuel consumption:
FC = A \times FL \times CC
Where: - FC = fuel consumed (kg) - A = burned area (m²) - FL = fuel loading (kg/m²) - CC = combustion completeness
Species emission:
E_i = FC \times EF_i \times 10^{-6} (tonnes)
Example:
Area = 1000 ha = 10⁷ m²
Fuel loading = 1.5 kg/m² (forest)
CC = 0.9
EF_{PM_{2.5}} = 15 g/kg
FC = 10^7 \times 1.5 \times 0.9 = 1.35 \times 10^7 \text{ kg}
E_{PM_{2.5}} = 1.35 \times 10^7 \times 15 \times 10^{-6} = 202.5 \text{ tonnes}
Over 200 tonnes of PM₂.₅!
Temporal distribution:
Fire burns over time T (hours/days).
Emission rate:
Q(t) = \frac{E_i}{T} \times f(t)
Where f(t) = temporal distribution (peak during active burning).
Simplified: Assume constant during active burning period.
Q = \frac{E_i}{T \times 3600} (g/s)
Pasquill-Gifford classes:
A: Extremely unstable (strong solar heating, light winds)
B: Moderately unstable
C: Slightly unstable
D: Neutral
E: Slightly stable
F: Moderately stable (clear night, light winds)
Affects dispersion:
Unstable (A-C): Rapid vertical mixing, lower ground concentrations
Stable (E-F): Limited mixing, concentrated plume
Wildfire context:
Heat from fire creates instability → often class C-D even at night.
Problem: Calculate PM₂.₅ emissions and downwind concentration.
Fire characteristics: - Burned area: 500 ha - Fuel type: Conifer forest - Fuel loading: 2.0 kg/m² - Combustion completeness: 85% - Burn duration: 8 hours
Meteorology: - Wind speed: 5 m/s - Stability: Class C (slightly unstable) - Plume height: 800 m
Location of interest: - Downwind distance: 20 km - Lateral offset: 2 km
Calculate total PM₂.₅ and ground-level concentration.
Step 1: Fuel consumed
A = 500 \times 10^4 = 5 \times 10^6 \text{ m}^2
FC = 5 \times 10^6 \times 2.0 \times 0.85 = 8.5 \times 10^6 \text{ kg}
Step 2: PM₂.₅ emission
EF_{PM_{2.5}} = 15 g/kg (typical conifer)
E_{PM_{2.5}} = 8.5 \times 10^6 \times 15 = 1.275 \times 10^8 \text{ g} = 127.5 \text{ tonnes}
Step 3: Emission rate
Q = \frac{1.275 \times 10^8}{8 \times 3600} = \frac{1.275 \times 10^8}{28800} = 4427 \text{ g/s}
Step 4: Dispersion parameters (Class C, x=20 km)
From standard tables:
\sigma_y = 0.20 \times 20000^{0.894} = 0.20 \times 8913 = 1783 \text{ m}
\sigma_z = 0.14 \times 20000^{0.885} = 0.14 \times 8318 = 1164 \text{ m}
Step 5: Concentration at (x=20 km, y=2 km, z=0)
C = \frac{4427}{\pi \times 5 \times 1783 \times 1164} \exp\left(-\frac{2000^2}{2 \times 1783^2}\right) \exp\left(-\frac{800^2}{2 \times 1164^2}\right)
= \frac{4427}{32.5 \times 10^6} \times \exp(-0.63) \times \exp(-0.24)
= 1.36 \times 10^{-4} \times 0.533 \times 0.787
= 5.7 \times 10^{-5} \text{ g/m}^3 = 57 \text{ μg/m}^3
Step 6: Interpret
57 μg/m³ exceeds EPA standard (35 μg/m³)
Health advisory warranted at this location.
Directly downwind (y=0): Concentration would be ~107 μg/m³ (worse)
Below is an interactive smoke dispersion simulator.
<label>
Burned area (ha):
<input type="range" id="burned-area" min="100" max="5000" step="100" value="1000">
<span id="area-val">1000</span>
</label>
<label>
Wind speed (m/s):
<input type="range" id="wind" min="2" max="15" step="1" value="5">
<span id="wind-val">5</span>
</label>
<label>
Plume height (m):
<input type="range" id="plume-height" min="200" max="2000" step="100" value="800">
<span id="height-val">800</span>
</label>
<label>
Stability class:
<select id="stability">
<option value="A">A (Very unstable)</option>
<option value="B">B (Unstable)</option>
<option value="C" selected>C (Slightly unstable)</option>
<option value="D">D (Neutral)</option>
<option value="E">E (Slightly stable)</option>
</select>
</label>
<div class="smoke-info">
<p><strong>Total PM₂.₅:</strong> <span id="total-pm">--</span> tonnes</p>
<p><strong>Max concentration:</strong> <span id="max-conc">--</span> μg/m³</p>
<p><strong>Distance to standard:</strong> <span id="dist-standard">--</span> km</p>
</div><canvas id="smoke-canvas" width="700" height="400" style="border: 1px solid #ddd;"></canvas>Observations: - Concentration decreases with distance as plume disperses - Higher plume rise reduces ground-level concentrations - Unstable atmosphere promotes mixing (lower peak concentrations) - EPA standard often exceeded 10-30 km downwind - Larger fires produce proportionally more emissions - Wind speed dilutes concentrations but transports farther
Key insights: - Smoke impacts extend far beyond fire perimeter - Atmospheric stability critically affects dispersion - PM₂.₅ health risks significant at large distances - Multiple factors determine air quality impacts
PM₂.₅ exposure effects:
Short-term (hours-days): - Respiratory irritation - Asthma attacks - Reduced lung function
Long-term (weeks-months): - Cardiovascular events - Premature mortality - Chronic conditions
Vulnerable populations: - Children - Elderly - Respiratory disease - Cardiovascular disease
2020 California fires:
Estimated 1200-3000 premature deaths from smoke exposure.
Economic impact: $10-80 billion (health costs).
BlueSky framework:
Operational use:
NOAA Smoke Forecasting System (daily products).
Applications: - Public health advisories - School closures - Outdoor event cancellations - Hospital preparedness
CO₂ emissions:
E_{CO_2} = FC \times 1650 \text{ g/kg}
Example: 10 million hectares burned globally (annual average)
Fuel loading ~1.5 kg/m², CC = 0.9:
FC = 10^{10} \times 1.5 \times 0.9 = 1.35 \times 10^{10} \text{ kg}
E_{CO_2} = 1.35 \times 10^{10} \times 1650 \times 10^{-12} = 22.3 \text{ Gt CO}_2
~5% of global fossil fuel emissions!
Plume rise depends on fire intensity, atmospheric stability.
Under-prediction:
Plume rises higher than modelled → lower ground concentrations (false alarm).
Over-prediction:
Plume doesn’t rise → higher ground concentrations (missed hazard).
Example - 2003 Canberra:
Pyrocumulonimbus (fire-generated thunderstorm) injected smoke to 15 km (vs predicted 3 km).
Solution: Real-time satellite observations (GOES, MODIS).
Gaussian model assumes flat terrain, uniform meteorology.
Mountains: - Channeled flows (valleys) - Slope winds - Thermal circulations
Result: Smoke pooling in valleys, unpredicted transport.
Solution: CALPUFF (puff model) or WRF-Chem (3D meteorology + chemistry).
Simple models: Transport PM₂.₅ as inert tracer.
Reality:
Photochemical aging: - VOCs + NOₓ → ozone, secondary PM - PM₂.₅ mass increases downwind - Composition changes
Solution: Chemical transport models (CMAQ, WRF-Chem).
Model predicts fire contribution only.
Total exposure:
PM_{total} = PM_{background} + PM_{fire}
Urban areas:
PM_{background} = 10-20 μg/m³ (normal)
Fire adds 30 μg/m³ → total = 40-50 μg/m³
Exceeds standard even though fire alone wouldn’t.
Bottom-up (models):
Fire area × fuel × EF (this model’s approach).
Top-down (satellites):
Directly observe emissions from space.
Fire radiative power (FRP):
Thermal emission from fire (MW).
FRP to emissions:
E_i = FRP \times CE_i
Where CE_i = conversion efficiency (g/MJ).
Advantages: - Near real-time - No fuel data needed - Global coverage
Sensors: - MODIS: 1 km, 4× daily - VIIRS: 375 m, 2× daily - GOES: 2 km, 5-15 min
Example - GFAS (Global Fire Assimilation System):
Copernicus service, daily global fire emissions.
f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)
Where: - \mu = mean - \sigma = standard deviation
Properties: - Symmetric around \mu - Total area = 1 (probability distribution) - 68% within ±σ, 95% within ±2σ
f(x,y) = \frac{1}{2\pi\sigma_x\sigma_y} \exp\left(-\frac{x^2}{2\sigma_x^2} - \frac{y^2}{2\sigma_y^2}\right)
Dispersion plume:
Concentration follows Gaussian in crosswind (y) and vertical (z).
Peak concentration: On centerline (y=0, z=H).