modelling Level 3

Fire Weather and Ignition Potential

What weather conditions create extreme wildfire risk? Fire weather combines temperature, humidity, wind, and fuel conditions to determine ignition potential and fire behavior. This model derives fuel moisture equations, implements vapor pressure deficit calculations, demonstrates fire weather indices, and maps ignition probability across landscapes.

Prerequisites: fuel moisture, vapor pressure deficit, fire weather indices, ignition probability

27 Feb 2026 Updated 12 Mar 2026 13 min read

1. The Question

Will today’s weather conditions trigger catastrophic wildfires?

Fire weather:

Meteorological conditions controlling fire ignition and spread.

Critical factors:

Temperature: Higher → drier fuels, more volatilization
Humidity: Lower → drier fuels, faster spread
Wind: Stronger → rapid spread, spot fires
Precipitation: Recent rain → wet fuels, low risk

Fire triangle:

Fuel (vegetation)
Oxygen (atmosphere)
Heat (ignition source)

Weather affects all three:

Fuel moisture content
Wind supplies oxygen
Temperature affects ignition threshold

Applications:

Fire danger rating systems
Red flag warnings
Prescribed burn planning
Firefighting resource allocation
Evacuation decisions

Indices:

Fire Weather Index (FWI, Canada)
Keetch-Byram Drought Index (KBDI, USA)
Haines Index (atmospheric instability)
Hot-Dry-Windy Index (HDW)

2. The Conceptual Model

Fuel Moisture Content

Definition:

\[MC = \frac{m_{\text{water}}}{m_{\text{dry}}} \times 100\%\]

Where:

$MC$ = moisture content (%)
$m_{\text{water}}$ = mass of water
$m_{\text{dry}}$ = dry fuel mass

Categories:

Fine fuels (1-hour): Grasses, needles, <6mm diameter
Medium fuels (10-hour): Twigs, 6-25mm
Heavy fuels (100-hour): Branches, 25-75mm
Large fuels (1000-hour): Logs, >75mm

Equilibrium moisture content (EMC):

\[EMC = 0.03 + 0.2626 \times RH^{0.935} - 0.00104 \times T\]

Where:

$RH$ = relative humidity (%)
$T$ = temperature (°C)

Ignition thresholds:

Dead fuels: MC < 15% (flammable)
Dead fuels: MC < 8% (extreme fire danger)
Live fuels: MC < 80% (drought-stressed, flammable)

Vapor Pressure Deficit

Atmospheric drying power:

\[VPD = e_s - e_a\]

Where:

$e_s$ = saturation vapor pressure (kPa)
$e_a$ = actual vapor pressure (kPa)

Saturation vapor pressure (Tetens equation):

\[e_s = 0.611 \exp\left(\frac{17.27 T}{T + 237.3}\right)\]

Actual vapor pressure:

\[e_a = \frac{RH}{100} \times e_s\]

High VPD (>3 kPa): Rapid fuel drying, plant stress

Low VPD (<1 kPa): Slow drying, less fire danger

Wind Effects

Rate of spread:

\[ROS = ROS_0 (1 + C \times U^B)\]

Where:

$ROS$ = rate of spread (m/min)
$ROS_0$ = no-wind spread rate
$U$ = wind speed (km/h)
$C, B$ = empirical constants (fuel-dependent)

Typical: Wind doubles spread rate every 10 km/h increase

Critical wind speeds:

25 km/h: Moderate spread
40 km/h: Fast spread, difficulty controlling
60+ km/h: Extreme spread, spotting, ember storms

Gustiness: Variable winds → unpredictable fire behavior

3. Building the Mathematical Model

Time-Lag Fuel Moisture

Exponential approach to equilibrium:

\[MC(t) = EMC + (MC_0 - EMC) e^{-t/\tau}\]

Where:

$MC(t)$ = moisture at time $t$
$MC_0$ = initial moisture
$EMC$ = equilibrium moisture content
$\tau$ = time lag (hours)

Time lags:

1-hour: $\tau = 1$ h (fine fuels)
10-hour: $\tau = 10$ h
100-hour: $\tau = 100$ h
1000-hour: $\tau = 1000$ h

Example:

Initial MC = 20%, EMC = 8%, after 3 hours (1-hour fuel):

\[MC(3) = 8 + (20 - 8) e^{-3/1} = 8 + 12 \times 0.050 = 8.6\%\]

Rapid drying in 3 hours!

Fire Weather Index (FWI)

Canadian FWI System:

Fine Fuel Moisture Code (FFMC):

Moisture in litter/fine fuels (0-101 scale).

\[FFMC_{\text{new}} = 59.5 \times \frac{250 - MC}{147.2 + MC}\]

High FFMC (>90): Very dry, high ignition potential

Duff Moisture Code (DMC):

Moderate duff/humus moisture.

Drought Code (DC):

Deep organic layer moisture (cumulative dryness).

Initial Spread Index (ISI):

\[ISI = 0.208 \times FFMC \times \left(1 + \frac{U}{10}\right)\]

Combines fuel moisture and wind.

Fire Weather Index:

\[FWI = 0.05 \times ISI \times \sqrt{BUI}\]

Where $BUI$ = buildup index (from DMC, DC).

Interpretation:

FWI < 5: Low danger
FWI 5-10: Moderate
FWI 10-20: High
FWI 20-30: Very high
FWI > 30: Extreme

Keetch-Byram Drought Index

Cumulative moisture deficit:

\[KBDI_{\text{new}} = KBDI_{\text{old}} + \Delta KBDI - P_{\text{eff}}\]

Drought factor:

\[\Delta KBDI = \frac{(800 - KBDI) \times (0.968 \times e^{0.0486T} - 8.3)}{1 + 10.88 e^{-0.001736 \times MAP}}\]

Where:

$T$ = temperature (°C)
$MAP$ = mean annual precipitation (mm)
$P_{\text{eff}}$ = effective precipitation (mm)

Scale: 0-800

0-200: Soil/fuel moisture adequate
200-400: Soil moisture declining
400-600: Drought affecting fire potential
600-800: Severe drought, extreme fire danger

4. Worked Example by Hand

Problem: Calculate fire danger indices for given weather.

Weather conditions:

Temperature: 35°C
Relative humidity: 20%
Wind speed: 30 km/h
No precipitation last 7 days

Fuel state:

Initial 1-hour fuel MC: 18%
Initial FFMC: 85

Calculate EMC, VPD, updated FFMC, ISI, and fire danger level.

Solution

Step 1: Equilibrium Moisture Content

\[EMC = 0.03 + 0.2626 \times 20^{0.935} - 0.00104 \times 35\] \[= 0.03 + 0.2626 \times 15.2 - 0.036\] \[= 0.03 + 3.99 - 0.036 = 3.98\%\]

Very dry equilibrium!

Step 2: Vapor Pressure Deficit

\[e_s = 0.611 \exp\left(\frac{17.27 \times 35}{35 + 237.3}\right)\] \[= 0.611 \exp\left(\frac{604.45}{272.3}\right) = 0.611 \times e^{2.22} = 0.611 \times 9.21 = 5.63 \text{ kPa}\] \[e_a = \frac{20}{100} \times 5.63 = 1.13 \text{ kPa}\] \[VPD = 5.63 - 1.13 = 4.50 \text{ kPa}\]

Very high VPD (extreme drying)

Step 3: 1-hour fuel moisture after 3 hours

\[MC(3) = 3.98 + (18 - 3.98) e^{-3/1}\] \[= 3.98 + 14.02 \times 0.050 = 3.98 + 0.70 = 4.68\%\]

Approaching equilibrium, very dry

Step 4: Updated FFMC

\[FFMC = 59.5 \times \frac{250 - 4.68}{147.2 + 4.68}\] \[= 59.5 \times \frac{245.32}{151.88} = 59.5 \times 1.615 = 96.1\]

Very high FFMC (>90 = extreme)

Step 5: Initial Spread Index

\[ISI = 0.208 \times 96.1 \times \left(1 + \frac{30}{10}\right)\] \[= 19.99 \times 4 = 80.0\]

Extremely high ISI

Step 6: Fire danger assessment

FFMC = 96.1: Extreme
VPD = 4.5 kPa: Extreme drying
Wind = 30 km/h: Moderate-high
ISI = 80: Extreme

Overall: EXTREME FIRE DANGER

Red flag warning criteria met. Any ignition likely to become rapidly spreading, uncontrollable fire.

5. Computational Implementation

Below is an interactive fire weather simulator.

Temperature (°C): 30 Relative Humidity (%): 30 Wind Speed (km/h): 20 Days since rain: 7

VPD: -- kPa

1-hr fuel MC: --%

FFMC: --

Fire danger: --

Observations:

VPD peaks in afternoon when temperature highest and humidity lowest
Fuel moisture content reaches minimum in afternoon
Fire danger typically greatest 2-4 PM
Extended dry periods drive fuel moisture to dangerous levels
Red line (VPD): Atmospheric drying power
Blue line (Fuel MC): Equilibrium moisture content
Green dashed: Peak danger period

Key insights:

Hot, dry, windy conditions create extreme fire danger
Diurnal cycle important for fire behavior prediction
Multi-day drying cumulative effect critical
Combined indices provide comprehensive fire danger assessment

6. Interpretation

Red Flag Warnings

National Weather Service criteria (USA):

Combination of:

RH ≤ 15%
Wind ≥ 25 mph (40 km/h)
Unstable atmosphere (Haines Index)

During red flag:

No outdoor burning
Heightened firefighting readiness
Public awareness campaigns
Prescribed burns cancelled

Example - California 2020:

Labor Day heat wave:

T = 45°C, RH = 8%, winds 50 km/h
Multiple megafires ignited
4+ million acres burned (record)

Prescribed Burn Windows

Safe conditions required:

Fuel MC: 10-18% (will burn but controllable)
Wind: 8-25 km/h (enough spread, not too fast)
RH: 30-60% (moderate)
Atmospheric stability (smoke dispersal)

Narrow windows:

Spring/fall often best (temperature moderate, some moisture).

Example - Florida:

Winter burns common (cooler, higher humidity baseline).

Seasonal Fire Danger

Mediterranean climate (California):

Peak danger: Late summer-fall (hot, dry, Santa Ana winds)

Monsoonal (Southwest USA):

Peak: May-June (pre-monsoon drought)
Relief: July-September (monsoon rains)

Temperate forest (PNW):

Peak: July-August (summer drought)
Low: October-May (wet season)

7. What Could Go Wrong?

Haines Index Ignored

Atmospheric instability amplifies fire behavior.

Haines Index:

Combines:

Stability (temperature lapse rate)
Moisture (dew point depression aloft)

High Haines (5-6):

Extreme fire behavior potential:

Plume-driven spread
Erratic winds
Rapid fire growth

2003 Canberra fires:

Moderate FFMC but high Haines → catastrophic fire behavior.

Lesson: Surface indices insufficient alone.

Fuel Load Not Considered

FFMC measures moisture, not quantity.

Heavy fuel load:

Years of accumulation (fire suppression) → more available energy.

Light fuel load:

Recent fire or minimal vegetation → less fire spread even if dry.

Solution: Integrate fuel maps (biomass, fuel type).

Topography Effects

Slope increases spread:

\[ROS_{\text{slope}} = ROS_{\text{flat}} \times e^{k \times \text{slope}}\]

Where $k \approx 0.05-0.1$ (per degree slope).

Chimneys/canyons:

Funneled winds, preheating → extreme spread.

Aspect:

South-facing slopes (northern hemisphere): Hotter, drier → more flammable.

Solution: Incorporate terrain into fire danger mapping.

Spotting Not Predicted

Ember transport downwind.

Distance: 0.5-5 km typical, up to 30 km in extreme conditions.

Creates new fires ahead of main front.

Example - 2009 Black Saturday (Australia):

Spotting from eucalyptus bark ignited fires 20+ km ahead.

Unpredictable with standard fire weather indices.

8. Extension: Lightning Fire Prediction

Dry lightning:

Thunderstorms with minimal rain → fire ignition.

Prediction:

Lifted Index (LI):

\[LI = T_{500} - T_{\text{parcel,500}}\]

Where $T_{500}$ = environment temperature at 500 mb.

Negative LI: Unstable, thunderstorms likely

Precipitation efficiency:

Low = dry lightning.

Combined model:

\[P_{\text{ignition}} = P_{\text{lightning}} \times (1 - P_{\text{rain}}) \times f(MC)\]

Where:

$P_{\text{lightning}}$ from convective indices
$P_{\text{rain}}$ from precipitation forecast
$f(MC)$ = fuel moisture ignitability

9. Math Refresher: Exponential Decay

General Form

\[y(t) = y_{\infty} + (y_0 - y_{\infty}) e^{-t/\tau}\]

Where:

$y(t)$ = value at time $t$
$y_0$ = initial value
$y_{\infty}$ = equilibrium value
$\tau$ = time constant

Half-life:

\[t_{1/2} = \tau \ln 2 \approx 0.693 \tau\]

Time to 90% equilibrium:

\[t_{90\%} = \tau \ln 10 \approx 2.3 \tau\]

Application to Fuel Moisture

Fuel approaches EMC exponentially.

Time lag = $\tau$

1-hour fuel: 63% to EMC in 1 hour, 90% in 2.3 hours.

100-hour fuel: Takes 230 hours (9.6 days) to reach 90% of EMC.

Summary

Fire weather combines temperature, humidity, wind, and precipitation to determine fire danger
Fuel moisture content critical threshold below 15% for ignition, below 8% for extreme danger
Vapor pressure deficit quantifies atmospheric drying power affecting fuel and vegetation
Fire Weather Index integrates fuel moisture, wind, and cumulative dryness into single metric
Equilibrium moisture content derived from temperature and relative humidity relationships
Time-lag fuels respond at different rates from hours to weeks
Red flag warnings issued when RH ≤15%, wind ≥40 km/h, and unstable atmosphere
Applications span prescribed burn planning, firefighting readiness, public warnings
Challenges include atmospheric instability effects, topographic modifications, spotting
Critical tool for wildfire risk assessment and fire management operations