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Initial spread index


The Initial spread index (\(ISI\)) is one of the two intermediate indices required for calculating the Canadian fire weather index (\(FWI\)). The \(ISI\) represents the rate of fire spread without the influence of variable quantities of fuel. It is a combination of the effects of wind speed and fine fuel moisture content on fire spread, and thus requires wind speed and the \(FFMC\) as input variables (Van Wagner 1987).

The name of this index refers to the basic rate at which a fire would spread when the fine fuel is dry but drying in depth not advanced (Van Wagner 1987).

As the \(ISI\) combines the influences of wind and fine fuel moisture, it is well appropriated for predicting burnt area (Van Wagner 1987).


The \(ISI\) is the product of a wind and a fine fuel moisture functions.

The wind function is obtained as follows (Van Wagner and Pickett 1985):

\[f(U)=e^{0.05039\cdot U_{12}}\]

where \(U_{12}\) is wind speed [km/h] at noon.

And the fine fuel moisture function as follows (Van Wagner 1985):

\[f(F)=(91.9\cdot {e^{-01386\cdot{m}}})\cdot{\bigg(1+\dfrac{m^{5.31}}{4.93\cdot{10^7}}\bigg)}\]

where \(m\) is the fuel moisture content [%] and dermined as follows (Van Wagner 1985):


where \(FFMC\) is the Fine fuel moisture code.

The \(ISI\) is finally obtained with the following equation (Van Wagner 1985):



Original publications:
Van Wagner and Pickett (1985)
Van Wagner (1987)


Variable Description Unit
\(T\) air temperature °C
\(T_{dew}\) dew point temperature °C
\(H\) air humidity %
\(P\) rainfall mm
\(U\) windspeed m/s
\(w\) days since last rain
(or rain above threshold)
\(rr\) days with consecutive rain d
\(\Delta t\) time increment d
\(\Delta{e}\) vapor pressure deficit kPa
\(e_s\) saturation vapor pressure kPa
\(e_a\) actual vapor pressure kPa
\(p_{atm}\) atmospheric pressure kPa
\( PET\) potential evapotranspiration mm/d
\(r\) soil water reserve mm
\(r_s\) surface water reserve mm
\(EMC\) equilibrium moisture content %
\(DF\) drought factor -
\(N\) daylight hours hr
\(D\) weighted 24-hr average moisture condition hr
\(\omega\) sunset hour angle rad
\(\delta\) solar declination rad
\(\varphi\) latitude rad
\(Cc\) cloud cover Okta
\(J\) day of the year (1..365/366) -
\(I\) heat index -
\(R_n\) net radiation MJ⋅m-2⋅d-1
\(R_a\) daily extraterrestrial radiation MJ⋅m-2⋅d-1
\(R_s\) solar radiation MJ⋅m-2⋅d-1
\(R_{so}\) clear-sky solar radiation MJ⋅m-2⋅d-1
\(R_{ns}\) net shortwave radiation MJ⋅m-2⋅d-1
\(R_{nl}\) net longwave radiation MJ⋅m-2⋅d-1
\(\lambda\) latent heat of vaporization MJ/kg
\(z\) elevation m a.s.l.
\(d_r\) inverse relative distance Earth-Sun -
\(\alpha\) albedo or canopy reflection coefficient -
\(\Delta\) slope of the saturation vapor pressure curve kPa/°C
\(Cc\) cloud cover eights
\(ROS\) rate of spread m/h
\(RSF\) rate of spread factor -
\(WF\) wind factor -
\(WRF\) water reserve factor -
\(FH\) false relative humidity -
\(FAF\) fuel availability factor -
\(PC\) phenological coefficient -

Suffix Description
\(-\) mean / daily value
\(_{max}\) maximum value
\(_{min}\) minimum value
\(_{12}\) value at 12:00
\(_{13}\) value at 13:00
\(_{15}\) value at 15:00
\(_{m}\) montly value
\(_{y}\) yearly value
\(_{f/a}\) value at fuel-atmosphere interface
\(_{dur}\) duration
\(_{soil}\) value at soil level

Constant Description
\(e\) Euler's number
\(\gamma\)psychrometric constant
\(G_{SC}\)solar constant
\(\sigma\)Stefan-Bolzmann constant