# The Long-Term Consequences of Forest Fires on the Carbon Fluxes of a Tropical Forest in Africa
## 2 Materials and Methods
### The New Fire Model ForFire  
For the simulation of fire events with the individual-based forest model FORMIND, a separate fire model ForFire (Forest Fire model) was developed (Figure 5), which combines the advantages of the abovementioned fire models. The detailed dynamics of the fire spread are not relevant for this study, as the time step of the forest model is one year. For the fire model ForFire, it is important that the appearance of forest fires, the total spread of the fire area, and the generation of heterogeneous landscapes can be represented. First, a stochastic process is introduced that counts the number of fires in a year (F in yr\({}^{-1}\)). This number of annual forest fires is assumed to be Poisson distributed:  
\[F(t)\sim Poisson\left(\frac{1}{\lambda}\right) \tag{1}\]  
where \(\lambda\) (yr) is the mean time interval between two fire events. If a fire breaks out in one year, the fire center is randomly determined on the entire simulated forest area. The size of the fire area (S in % of total forest area) is realized via an exponential distribution:  
\[S(t)\sim Exponential\left(\frac{1}{\beta}\right) \tag{2}\]  
where \(\beta\) (%) is the relative size of the mean fire area with respect to the total simulated forest area. The area of the forest fire is chosen in such a way that, from a randomly chosen fire  
Figure 5: Schematic representation of the fire model ForFire. This fire model was integrated in the forest model FORMIND. In each time step (here: 1 year) the random number of fires in this time step is determined. Then, an exponential distribution is used to specify the size of the forest fire. To ensure that the fire can break out, each sub-area (20 m plot) of the total simulation area is checked for whether there is enough biomass and for whether the top layer of soil is not too wet. After that, the type of fire is determined randomly, either a strong crown fire or a lighter ground fire. However, not all trees in the fire area burn and die. The probability of a tree dying from fire depends on the strength of the fire, the size of the tree, and the fire tolerance depending on the species. center, fire breaks out on randomly neighboring areas. This creates an irregular contiguous area around the fire center. However, fire can only break out on a forest plot if there is enough flammable material. If there is less than 200 g/m2 of biomass in the area, the possibility for a fire to spread is almost non-existent [45]. In addition, the possibility of a fire breaking out is also dependent on climatic conditions, such as soil moisture, cf. SPITFIRE in LPJ [46]. This is integrated in the fire model ForFire by only starting a fire with a certain probability B on a plot within the fire area, depending on the soil water content (\(\theta\) in Vol%) in the toposoil layer. For this purpose, the relative water saturation m (%) is calculated, which indicates how water-saturated the toposoil layer is [21]:  
\[m(\theta)=\theta-MSW/_{\text{P}or-MSW} \tag{3}\]  
where \(MSW\) and Por are parameters of the soil [47]. For the ignition probability \(B\) (Figure 6) we get:  
\[B(m)=e^{-\pi\ (m/n_{e})}+0.2 \tag{4}\]  
where \(m_{e}\) (%) is the saturation of the upper soil layer with water, above which it is very unlikely that a fire will start [21]. After determining the forest area in which the fire occurs, the next step considers all individual trees in the fire area. Every tree in the fire area is potentially at risk of burning and dying. The probability that a tree will burn depends on its species-specific fire tolerance and its trunk diameter [43]. Fire tolerance can be divided into four groups: Species with fire tolerance group 1 burn in any fire, whereas fire tolerance group 4 is very resistant to fire.