# 100-hour timelag dead fuel moisture model

# Description

The 100-hour timelag fuel moisture \(MC_{100}\) is the moisture content of the 100-hour timelag fuels, which consist of dead roundwood in the size range of 1 to 3 inches in diameter and the forest floor from 0.75 inch to 4 inches below the surface (Deeming et al. 1977).

The calculation of the 100-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 100-hour timelag fuel moisture model requires precipitation duration (in hours) as input variable, which is not a standard meteorological variable.

# Formula

The 100-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 100-hour dead fuel moisture model is calculated as follows (Cohen & Deeming 1985):

First, the weighted 24-hour average \(EMC\) is calculated:

\[EMC_{24}=\dfrac{N_{nfdrs}\cdot{EMC_{min}}+(24-N_{nfdrs})\cdot{EMC_{max}}}{24}\]

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 \(D\) [%] is calculated as follows (Cohen & Deeming 1985):

\[D=\dfrac{(24-P_{dur})\cdot{EMC_{24}}+P_{dur}\cdot(0.5\cdot{P_{dur}}+41)}{24}\]

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

Finally, the 100-hour timelag fuel moisture model \(MC_{100}\) [%] on day i is calculated as follows (Cohen & Deeming 1985):

\[MC_{100_{t}}=MC_{100_{t-1}}+(D_t - MC_{100_{t-1}})\cdot(1-0.87e^{-0.24})\]

where \( MC_{100_{t-1}}\) is the \(MC_{100}\) value from the previous day.

The 100-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 100-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: If the starting value is not known or accurate, usally a starting value of 30 [%] is set. This usually allows consistent results after a four-weeks calculation period (Deeming et al. 1977).

# References

Burgan et al. (1977)

Deeming et al. (1977)

Bradshaw et al. (1983)

Cohen & Deeming (1985)