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Precipitation duration

Fire » Generic composite input variables » Precipitation duration

Definition

Precipitation duration in hours is used by 100-hr and 1000-hr fuel moisture indices of the NDRFS.
When absent it can be estimated usinga a formula proposed by Bradshaw et al. (1983).

Formula

Bradshaw et al. (1983) proposed to replace the \(P_{Dur}\) as follows:

\[ P_{Dur}= min( 8, \dfrac{P + 0.02)}{p_r}) \]

with the precipitation rate \(p_r\) [inch/h] defined as

\[ p_r = \begin{cases} 0.25, & \mbox{for } Climate {\ 1\ or\ 2} \\ &\\ 0.05, & \mbox{for } Climate {\ 3\ or\ 4} \\ \end{cases} \]

where \(P\) is the 24-hours precipitation in inches and \(Climate \) is the climate class according to Deeming (1977).

References

Literature:
Bradshaw et al. (1983)
Deeming (1977)

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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