Climate change is here, it’s real, and it won’t be easy for humans to deal with. But few things are all good or all bad, and so it may be for climate change, at least with respect to environmental science and management.

A vast literature has accumulated in the past two or three decades in geosciences, environmental sciences, and ecology acknowledging the pervasive—and to some extent irreducible—roles of uncertainty and contingency. This does not make prediction impossible or unfeasible, but does change the context of prediction. We are obliged to not only acknowledge uncertainty, but also to frame prediction in terms of ranges or envelopes of probabilities and possibilities rather than single predicted outcomes. Think of hurricane track forecasts, which acknowledge a range of possible pathways, and that the uncertainty increases into the future.

Forecast track for Hurricane Lili, September 30, 2002. The range of possible tracks and the increasing uncertainty over time are clear. Source: National Hurricane Center.

The foundation for time series analysis methods to detect chaos is the notion that phase spaces and dynamics of a nonlinear dynamical system (NDS) can be reconstructed from a single variable, based on Takens embedding theorem (Takens, 1981). Many years ago (Phillips, 1993) I showed that temporal-domain chaos in the presence of anything other than perfect spatial isotropy (and when does that ever happen in the real world?) leads to spatial-domain chaos. This implies an analogous principle in the spatial domain.

Assume an Earth surface system (ESS) characterized by n variables or components x_i, i = 1, 2, . . , n, which vary as functions of each other:

ESS = f(x₁, x_2, , , , x_n)

If spatial variation is directional along a gradient y (of e.g., elevation, moisture, insolation) then

dx_i/dy = f(x₁, x_2, , , , x_n)

dx₂/dy = f(x₁, x_2, , , , x_n)

.                 .                   .

Resistance of environmental systems is their capacity to withstand or absorb force or disturbance with minimal change. In many cases we can measure it based on, e.g., strength or absorptive capacity. Resilience is the ability of a system to recover after a disturbance or applied force to (or toward) its pre-disturbance condition—in many cases a function of dynamical stability. In my classes I illustrate the difference by comparing a steel bar and a rubber band. The steel bar has high resistance and low resilience—you have to apply a great deal of force to bend it, but once bent it stays bent. A rubber band has low resistance and high resilience—it is easily broken, but after any application of force short of the breaking point, it snaps back to its original state.