Buildup index

Description

The Buildup index (\(BUI\)) is one of the two intermediate indices required for calculating the Canadian fire weather index (\(FWI\)\)). The \(BUI\) represents the total amount of fuel available to the spreading fire. It is a combination of the \(DMC\) and the \(DC\) (Van Wagner 1987).

The \(BUI\) is affected mainly by the \(DMC\). The \(DC\) only has a limited and variable weight in the equation (Van Wagner 1987).

Formula

For \(DMC\leqslant{0.4\cdot DC}\) the \(BUI\) is calculated as follows (Van Wagner and Pickett 1985):

\[BUI=0.8\cdot\dfrac{DMC\cdot{DC}}{DMC+0.4\cdot DC}, \mbox{ for DMC}\leqslant{0.4\cdot DC}\]

and for \(DMC>{0.4 \cdot DC}\) as follows:

\[BUI=DMC-\bigg(1-\dfrac{0.8\cdot DC}{DMC+0.4\cdot DC}\bigg)\cdot\big[0.92+(0.0114\cdot DMC)^{1.7}\big], \mbox{ for DMC}>{0.4\cdot DC}\]

where \(DMC\) is the Duff moisture code and \(DC\) the Drought code.

References

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

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Symbols

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)	d
\(rr\)	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