Simulating uncertainty in climate-pest models with fuzzy numbers.
Inputs in climate-pest models are commonly expressed as point estimates ('crisp' numbers), which implies perfect knowledge of the system in study. In reality, however, all model inputs harbor some level of uncertainty. This is particularly true for climate change impact assessments where the inputs (i.e., climate projections) are highly uncertain. In this study, uncertainties in climate projections were expressed as 'fuzzy' numbers; these are uncertain numbers for which one knows that there is a range of possible values and that some values are 'more possible' than others. A generic pest risk model incorporating the combined effects of temperature, soil moisture, and cold stress was implemented in a fuzzy spreadsheet environment and run with three climate scenarios: (1) present climate (control run); (2) crisp climate change; and (3) fuzzy climate change. Under the crisp climate change scenario, winter and summer temperatures and precipitation were altered using best estimates (averaged predictions from the 1995 assessment report of the Intergovernmental Panel on Climate Change [IPCC]). Under the fuzzy scenario, climate changes were expressed as triangular fuzzy numbers, utilizing the extremes (lowest and highest predictions from the IPCC report) in addition to the best estimates. Under each scenario, environmental favorability was calculated for six locations in two geographical regions (Central North America and Southern Europe) with two hypothetical pest species having temperate or mediterranean climate requirements. Simulations with the crisp climate change scenario suggested only minor changes in overall environmental favorability compared with the control run. When simulations were conducted with the fuzzy climate change scenario, however, important changes in environmental favorability emerged, particularly in Southern Europe. In that region, the possibility of considerably increased winter precipitation led to increased values of environmental favorability. However, the simulations also showed that this result harbored a very broad range of possible outcomes. The results support the notion that uncertainty in climate change projections must be reduced before reliable impact assessments can be achieved.