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10-hour timelag dead fuel moisture model


The 10-hour timelag fuel moisture \(MC_{10}\) is the moisture content of the 10-hour timelag fuels, which consist of dead roundwood 0.25 to 1 inch in diameter and the layer of litter extending from just below the surface to 0.75 inch below the surface (Deeming et al. 1977).

The calculation of the 10-hour timelag fuel moisture model requires the use of fuel sticks. However, an estimation of the 10-hour fuel moisture at midafternoon without the use of fuel sticks is possible according to the formula described here (Bradshaw et al. 1983).

As for the calculation of the 1-hour timelag fuel moisture model, the calculation of the 1-hour timelag fuel moisture model requires daily temperature [°F], relative humidity [%] and fraction of sky cover at early to midafternoon time (Bradshaw et al. 1983).


When fuel sticks are not used, the 10-hour fuel moisture \(MC_{10}\) [%] for midafternoon observation time is estimated in a manner similar to that for the 1-hour fuel moisture model (Cohen & Deeming 1985):


where \(EMC_{f/a}\) is the same \(EMC\) used to calculate the 1-hour timelag dead fuel moisture model.

NB: According to Bradshaw et al. (1983), this model works well for early afternoons in strong continental areas at the approximate latitude of Nebraska (~41°N) in the late summer, but tends to underpredict fuel stick moisture under other conditions.

The 10-hour timelag fuel moisture model is supposed to be calculated on a daily basis. The meteorological data used for its calculation have to be recorded at early to mid-afternoon time (1 to 3 pm).


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


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