Summary:

### Average Spread Area of a Fire

- Fire fighting capacity is influenced by socioeconomic conditions, affecting the average burned area of a fire.
- The average burned area of a fire without anthropogenic suppression is assumed to be elliptical in shape, calculated using the formula:
  - $a^* = \frac{\pi u_p^2 \tau^2}{4L_B} (1 + \frac{1}{H_B})^2 \times 10^{-6}$
  - Where $u_p$ is the fire spread rate, $\tau$ is the average fire duration, $L_B$ is the length-to-breadth ratio, and $H_B$ is the head-to-back ratio of the ellipse.
- The socioeconomic effect on fire spread area is represented by $F_{se}$, which is the product of the demographic effect ($F_d$) and the economic effect ($F_e$).
- The demographic and economic impact factors are parameterized differently for shrub/grass PFTs and tree PFTs outside tropical closed forests.
- These equations reflect that more developed and densely populated regions have higher fire fighting capabilities, leading to smaller average burned areas.