Probability and Statistics

Environmental phenomena, and the methods by which these phenomena are measured, are characterized by variability and uncertainty. In developing environmental models, several sources of variability and uncertainty appear routinely and complicate both predictions and the decisions on which they are based:Variability of physical properties in space and/or time. Section 1.1 introduced the concept of an inhomogeneous field. In such fields, the field quantity varies across the space at some point in time. These same fields may evolve in time, and so there is variation in the field quantity for a particular point in space at different times. A full description of the environmental field requires characterizing this spatial inhomogeneity and temporal evolution.Variability of physical properties across a population. Two individuals exposed to the same state of the environment may have different states of health. This might, for example, be because of intersubject variability in breathing rates, body mass, etc. A full description of the risk from an environmental field requires characterization of this variation between individuals.Random sampling by a measurement method. Measurement methods provide completely reliably measures of field quantities only when performed over a very long period of time with a large number of samples. In practice, a finite, manageable, sample size must be taken. This leads to variation in measurements of a field quantity, even at a single point in space. This variation is not a property of the field itself (that component of variation is accounted for by the first bullet above), but rather of the measurement system.