# Description

The Duff moisture code ($$DMC$$\)) is one of the three fuel moisture code components of the Canadian forest fire weather index ($$FWI$$) system. The $$DMC$$ represents the moisture content of loosely compacted, decomposing organic matter weighing about 5 kg/m2 when dry. It assesses fuel consumption in moderate duff layers and medium-size woody material at mid-afternoon. It requires temperature, relative air humidity, precipitation (at noon), and current month (in order to take daylength into account) as input data (Van Wagner 1987).

As the two other fuel moisture codes of the $$FWI$$ (cf. $$FFMC$$ and $$DC$$), the $$DMC$$ comprises two phases: one for wetting by rain and one for drying.

# Formula

The $$DMC$$ is calculated as follows (Van Wagner and Pickett 1985):

The previous day's $$DMC$$ becomes $$DMC_{t-1}$$

In case of rain (i.e. if $$P>1.5$$), the following procedure for wetting phases has to be chosen:

Effective rainfall $$P_e$$ [mm] is first calculated:

$P_e=0.92\cdot P-1.27, \mbox{ for P}>1.5$

Second, the duff moisture content from previous day $$M_{t-1}$$ is calculated:

$M_{t-1}=20+e^{5.6348-\frac{DMC_{t-1}}{43.43}}$

Third, the slope variable in $$DMC$$ rain effect $$b$$ is calculated:

${b}= \begin{cases} \dfrac{100}{0.5+0.3\cdot DMC_{t-1}}, & \mbox{for }DMC_{t-1}\leqslant{33} \\ & \\ 14-1.3\cdot\ln (DMC_{t-1}), & \mbox{for }33 < DMC_{t-1}\leqslant{65} \\ & \\ 6.2\cdot\ln (DMC_{t-1})-17.2, & \mbox{for }DMC_{t-1}>65 \end{cases}$

Fourth, the duff moisture content after rain $$M_{r_t}$$ is calulated:

$M_{r_t}=M_{t-1}+\dfrac{1000\cdot P_e}{48.77+b\cdot{P_e}}$

Finally, $$M_{r_t}$$ is converted to the $$DMC$$ after rain $$DMC_{r_t}$$, which becomes the new $$DMC_{t-1}$$:

$DMC_{r_t}=244.72-43.43\cdot\ln (M_{r_t}-20), \mbox{ if }DMC_{r_t}<0\mbox{, then } DMC_{r_t}=0$

NB: if $$P\leqslant{1.5}$$, the above rainfall routine must be omitted.

Then, the log drying rate in $$DMC$$ $$K$$ has to be calculated:

$K=1.894\cdot(T_{12}+1.1)\cdot(100-H_{12})\cdot{L_e}\cdot{10^{-6}}, \mbox{ if }T_{12}<{-1.1}\mbox{, then } T_{12}={-1.1}$

where the effective day-length $$L_e$$ for each month is given in the following table.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
$$L_f$$ 6.5 7.5 9.0 12.8 13.9 13.9 12.4 10.9 9.4 8.0 7.0 6.0

Finally, the $$DMC$$ can be calculated as follows:

$DMC_t= \begin{cases} DMC_{t-1}+100\cdot K, & \mbox{for }P\leqslant{1.5} \\ & \\ DMC_{r_t}+100\cdot K, & \mbox{for }P>{1.5} \end{cases}$

The $$DMC$$ is supposed to be calculated on a daily basis. The meteorological data used for its calculation have to be recorded at noon (for fire danger prediction at about 4 pm).

The $$DMC$$ calculation starts, in regions normally covered by snow in winter, on the third day after snow has essentially left the area. In regions where snow cover is not a significant feature, the calculation starts on the third successive day with noon temperature greater than 12 °C (Lawson and Armitage 2008). The starting value of the index has to be set to 6.

# References

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

Other publication:
Lawson and Armitage (2008)