In a nutshell: stable equilibrium states of systems can change drastically with small changes in parameters. That there is a clean a very useful theory was clear to people like Victor Arnol'd, Rene Thom, and Floris Takens, famous mathematicians in their day.  They are the silent leadership in this organization and are rubbing their hands upon reading the latest UN climate report. 

We are happy to explain their teaching and incorporate uncertainty quantification as we understand that too.

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Rather than saying that an event is possible, it is often much more useful to determine the probability (or likelihood) of the event.  It is not often the case that such a probability can be determined by pure thought. A more typical case is through Monte Carlo numerical simulation and particle filtering. In this case one:

•  Uses one or more computer models, 

• Varies the initial conditions over a prior distribution of initial conditions. This captures  uncertainty of the actual weather state including the movements of butterflies on other continents,

•  Assesses the distribution of outcomes of each. 

So for example, given the current state (and uncertainty in the current state) of the weather now, and the threatening weather patterns near the Sahara, one can rigorously determine the probability that Alabama is outside the cone of uncertainty of the oncoming hurricane.   

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According to https://en.wikipedia.org/wiki/Risk#Descriptions_of_risk

" In simple terms, risk is the possibility of something bad happening.[1] Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environment), often focusing on negative, undesirable consequences.[2] Many different definitions have been proposed. The international standard definition of risk for common understanding in different applications is “effect of uncertainty on objectives. [3]

The understanding of risk, the methods of assessment and management, the descriptions of risk and even the definitions of risk differ in different practice areas (business, economics, environment, finance, information technology, health, insurance, safety, security etc). This article provides links to more detailed articles on these areas. The international standard for risk management, ISO 31000, provides principles and generic guidelines on managing risks faced by organizations.[4] 

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