Uncertainty

Uncertainty simply means lack of knowledge. There are four types of uncertainty that are important to water resources.

1. Engineering Uncertainty

Engineering uncertainty is "exact value" uncertainty. In engineering, the basis of design is the pre-determined target. Because the target is known, the main concerns are accuracy and precision.

Accuracy: how close an attemp is to the center of the target.

Bias: the expected error, or the distance from the average attempt location to the center of the target.

Precision: the spread across all attempts, or how close the attempts are grouped together. The inverse of precision is variability.

Variance: the expected, or average, distance for all attempts from the average attempt location.

2. Scientific Uncertainty

Scientific uncertainty is why hypothesis testing is the core of the scientific method. In this case, the “target” is unknown, but is hypothesized, and we are not able to directly communicate with The Architect. To address this type of uncertainty, we seek to add extra variability to indirect measurements and predictions to explicitly constrain or describe the actual amount of knowledge. The result is a range of values, and likelihoods (or probabilities) are used to describe certainty and uncertainty. The location of the “Truth” population is unknown and extra variability acts to increase the diameter of the “Extra Variability” circle which means that some “good” attempts may actually be worse than some of the “bad” attempts.

Truth: the unknown center of the bullseye. It is unknown because it is not directly observed, but estimated using indirect information.

Biased Truth Estimate: indirect estimate of unknown truth made using calculations based off of other observed quantities.

Extra Variability: required because "truth" is unknown. The goal for extra variability is to make the target area large enough to include feasible values given uncertainty, but not so large that all attempts are "good" attempts.

3. Planning Uncertainty including 4. Future Uncertainty

Planning uncertainty includes scientific uncertainty and future uncertainty. Future conditions are unknown. The farther into the future, the greater the uncertainty. The result is a “cone” of uncertainty for future conditions with the cone spreading, and uncertainty increasing, as progress into the future. To robustly plan, present-day scientific uncertainty must be compounded with inherent “future uncertainty”.

The cone of uncertainty, shown in the associated figure, is the Annual Mean Temperature cone of uncertainty from CMIP5 RCP4.5 and RCP8.5 scenarios. Note that the cone is depicted with probabilities and increases in width moving into the future. The increase in cone width corresponds to increased uncertainty, which is addressed by increasing the variability of projected values.

Scientific uncertainty is shown for approximately present day. Note that there is the same amount of scientific uncertainty in the distant future, i.e., 2095. Future uncertainty is expected to be larger in the distant future, and planning uncertainty is the sum of future uncertainty and scientific uncertainty.