403where MaxFire = 1547 hectares and is 10 % of the area sum of all shrubland–wood-
land ecological systems. Equation 13.6 combines two Gompertz functions to
accommodate negative and positive values of PDSI. The first part of Eq. (13.6) after
MaxFire, representing fine fuels production, is a classic Gompertz function where a
weighted sum is applied to soil moisture during 2 previous years (70 % of PDSI in
year t−1 and 30 % of PDSI in year t−2). Wetter years (PDSI > 0) increase the value
of this function (fine fuels accumulation) to a maximum of one. The first part is
multiplied by the second function representing the current year, which is one minus
another Gompertz function bound between zero and one. Increasingly drier soil
moisture (PDSI < 0) causes the second part of Eq. (13.6) to increase to a maximum
of one (maximum ignition probability). The PDSI values from the scenarios without
and with climate change were used to calculate future area burned. Equation 13.6 is
not the final temporal multiplier, however, because it is not divided by its average.
In the absence of climate change effects, yearly values of Eq. (13.6) were divided by
their temporal average over 75 years, whereas each yearly value of Eq. (13.6) with
climate change was divided by the no-climate change average to reflect the hypoth-
esis of altered levels.
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13 State-and-Transition Models: Conceptual Versus Simulation Perspectives...