Correct Rothermel ROS model for SPITFIRE

[XiulinGao]

Task description

As already pointed out by Oberhagemann et al. 2025 that the implementation of Rothermel ROS model in SPITFIRE is wrong due to:

1. the weighthing factor for calculating average fuel load, SA:V, and bulk density is based on fuel load contribution by each fuel size class (namely, the fractional fuel load); however, Rothermel model uses the fractional total surface area contributed by fuel classes. The difference between fuel-load vs fuel SA:V weighted fuel characteristics is that: the former will aways be weighted toward large/heavy fuel size (e.g. basically all woody fuels) and the latter will always be weighted toward finer fuels with large SA:V (e.g., leaf litter, live grass and maybe also 1h fuel). This creates a huge difference between the averaged SA:V of a heterogenous fuel bed, especially when the fuel bed has considerable amount of woody fuels. See figures below for the comparison.

Note: fuel model 161 and 149 have woody fuels with 161 having a much higher fractional fuel load in 1h-100h fuel class.
Fig1. Average SA:V calculated using Rothermel model

Fig2. Average SA:V calculated using SPITFIRE model

2. Rothermel model treats live and deal fuel as distinct fuel category by calculating reaction intensity, mean fuel moisture content, fuel moisture of extinction separately for live vs dead fuels. To calculate ROS, reaction intensity of dead and live fuels are summed later on. However, SPITFIRE calculate ROS by ignoring the difference between dead and live fuels and mix the two into one average fuel using the fuel load weighting factor, and from there evrything is calculated based on this average fuel trait (e.g., averaged fuel moisture, averaged fuel moisture of extinction, and reaction intensity based on the averaged FMC and MEF).

We originally thought that this might not be a big problem we have to fix now (e.g., overestimated or underestimated ROS under certain wind speed according to Oberhagemann et al. 2025). But during the process of validating crown fire model, I noticed that calculated crowning index using EQ. 20 in Scott and Reinhard 2001 is always smaller than the actual crowning index (wind speed at which an active crown fire will happen). This is due to the wrong calculation of average fuel bed SA:V in SPITFIRE model while EQ. 20 is based on the correct Rothermel model. This mismatch create a weird pattern where we see that a passive crown fire can occur after wind speed passes the torching index, however, we did not see a gradual transition to active crown fire, rather a transition from passive crown fire to surface fire and then to active crown fire. This is largely due to the fact that when wind speed in in-between the calculated, false crowning index and the true crowning index, neither the passive crown nor the active crown fire condition is met, thus the model determines there is no crown fire and switches back to surface fire.

Fig. 3: crown fraction burned by crown fire. 0<CFB<1 indicates a passive crown fire; CFB=1 indicates a active crown fire; 0 means surface fire.

I'm currently working on a branch that try to correct Rothermel model in FATES-SPITFIRE. There is another issue I have discovered: all existing fuel models define surface fuel bed as anything, live or dead, inbetween the ground surface and ~6ft above the ground, so tree saplings are also considered surface fuels. But FATES only consider live grasses as live fuels, so in tree-dominant systems we have ZERO live fuels. This can create a problem for some of the Rothermel model calculations when live fuel acts as the denominator in the equation. While it's not hard to redefine our surface fuel category, I also realized that we always need to calculte fuel fraction burnt in order to determine fire intensity, which is then used to determine fire impacts (e.g crown fraction burnt) for calculating post-fire cohort mortality. For cohorts that also act as surface fuels this becomes circular.....

Any comments are welcomed. And I will submit a PR later for fixing the Rothermel model

[rosiealice]

Thanks for finding this @XiulinGao . I remember stumbling across this weighting towards the am large fuel classes a while ago, but I hadn't realised that the correct approach was to weight by surface area. That makes a lot more sense. So you know how much of an increase ROS occurs as a result (approx)?