Burn it all down

The occurrence rate of forest fires that burn $\SI{100}{\kilo\meter\squared}$ is $\num{0.5}$ which means that they happen once every 2 years.

If the slope analysis shows that $\beta = 1.2,$ then the frequency of forest fires of size $\SI{10000}{\kilo\meter\squared}$ would scale according to $\begin{aligned} p(\SI{10000}{\kilo\meter\squared}) &= p\left(\SI{100}{\kilo\meter\squared}\right) \times \left(\frac{\SI{100}{\kilo\meter\squared}}{\SI{10000}{\kilo\meter\squared}}\right)^{1.2} \\ &= p\left(\SI{100}{\kilo\meter\squared}\right) \times \frac{1}{100^{1.2}} \\ &\approx p\left(\SI{100}{\kilo\meter\squared}\right)\times\frac{1}{250} \end{aligned}$ so that $p\left(\SI{10000}{\kilo\meter\squared}\right)\approx p\left(\SI{100}{\kilo\meter\squared}\right)/250$ or roughly $\SI{0.002}{occurrences\ per\ year},$ or once every 500 years.