1000-hour timelag dead fuel moisture model


The 1000-hour timelag fuel moisture \(MC_{1000}\)is the moisture content of the 1000-hour timelag fuels, which consist of dead roundwood 3 to 8 inches in diameter and/or the forest floor more than 4 inches below the surface (Deeming et al. 1977).

The calculation of the 1000-hour timelag fuel moisture model requires latitude (in degrees or radians, cf. below), maximum and minimum daily air temperature [°F] and relative humidity [%] at early to midafternoon time, as well as precipitation duration during the previous 24 hours [hr] as input variables (Bradshaw et al. 1983).

NB: the calculation of the 1000-hour timelag fuel moisture model requires precipitation duration (in hours) as input variable, which is not a standard meteorological variable.


Similarly to the 100-hour fuel class, the 1000-hour fuel class responds very slowly to changes in environmental conditions. Therefore, an equilibrium moisture content (\(EMC\)) representing the average drying-wetting potential of the atmosphere for the preceding 24 hours is used for its calculation (Cohen & Deeming 1985).

The 1000-hour dead fuel moisture model is calculated as follows (Cohen & Deeming 1985):

First, the weighted 24-hour average EMC is calculated (similar to that of the 100-hr timelag moisture model):


where \(N_{nfdrs}\) is the daylight hours (cf. NFDRS formulation), \(EMC_{max}\) the 24-hr maximum \(EMC\), and \(EMC_{min}\) the 24-hr minimum \(EMC\). The 24-hour average \(EMC_{max}\) is obtained by substituting \(T\) [°F] and \(H\) [%] by \(T_{max}\) and \(H_{min}\) in the standard \(EMC\) equation (cf. Equilibrium moisture content), and the 24-hour average \(EMC_{min}\) is obtained by substituting \(T\) [°F] and \(H\) [%] by \(T_{min}\) and \(H_{max}\) in the standard \(EMC\) equation.

Then, the weighted 24-hour average moisture condition \(D\) [%], which is different from that for the 100-hour timelag moisture model, is calculated as follows (Cohen & Deeming 1985):


where \(P_{dur}\) is the 24-hours precipitation duration (in hours).

Based on \(D\), the seven day running average moisture condition \(\bar{D}\) on day i has to be calculated:


Finally, the 1000-hour timelag fuel moisture model \(MC_{1000}\) [%] on day i is calculated as follows (Cohen & Deeming 1985):

\[MC_{1000_t}=MC_{1000_{t-1}}+(\bar{D_t}-MC_{1000_{t-1}})\cdot(1-0.82\cdot e^{-0.168})\]

where \(MC_{1000_{t-1}}\) is the \(MC_{1000}\) value from the previous day.

The 1000-hour timelag fuel moisture model is aimed 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).

NB1: The model used in the 1978 NFDRS version (cf. Burgan et al. 1977 and Deeming et al. 1977) to calculate the 1000-hour timelag fuel moisture differs from the model presented here (cf. Cohen & Deeming 1985): in the 1978 version, daylength was not considered, and the 24-hour average \(EMC\) was a function of the simple averages of the 24-hour temperature and relative humidity extremes.

NB2: In order to stabilize the prediction of the 1000-hour timelag fuel moisture, the calculation of the model should be started at least four weeks before the beginning of the fire season. Usally, the starting value of the 1000-hour timelag fuel moisture is set to 30 [%], but if the four-week rule is adhered to, accurate starting values are not needed (Deeming et al. 1977).


Burgan et al. (1977)
Deeming et al. (1977)
Bradshaw et al. (1983)
Cohen & Deeming (1985)


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