# Uncertainty Analysis

## UNCERTAINTY ANALYSIS

For any variable or quantity that requires a measurement, short of a "perfect" measurement (which does not exist), the true value cannot be obtained from any known detector or analysis. For example, the measurement of an environmental pollutant will be subject to errors in instrument design, sampling rate, and analytical methods. These errors will lead to measured concentrations that may approach a true value, but will not be 100 percent accurate due to random or systematic processes during detection. Variables or quantities that are subject to uncertainty include: (1) empirical metrics (e.g., concentrations); (2) constants (e.g., diffusion coefficients); (3) decision variables (e.g., acceptable/unacceptable limits); and (4) modeling domains or boundaries (e.g., grid size). Of these variables, the empirical metrics are usually the most uncertain, since each may have many independent variables that can individually or synergistically control the total uncertainty attached to a measurement.

There are different sources of uncertainty for a variable, including:

1. Random error, which is derived from weaknesses or imperfections in measurement techniques or independent interferences.
2. Systematic error, which is due to biases in the measurement, analytical technique, or models; these can be associated with calibration, detector malfunctions, or assumptions about processes that affect variables.
3. Unpredictability, which is due to the inability to control the stability of a system or process, such as the partitioning of a semivolatile compound between the vapor and particle phase in the atmosphere.

Other sources of less importance include the lack of an empirical basis for individual values (theoretical predictions) and dependence/correlation of variables (interdependence of controlling variables in a system). Some uncertainties in variables or systems can be reduced, either by improving the methods of measurement and analysis or by improving the formulation of a model. Some nonreducible uncertainty, however, is inherent within the physical, chemical, or biological system that is being studied and can only be quantified by statistical analyses of data collected from the system.

A number of methods are used to quantify the uncertainty of a system. Analytical uncertainty analysis involves a description of the output or response variable that is a function of the uncertainty of each input variables (independent) that affects the response variable. This technique is only useful for simple systems, however; more complex systems require sophisticated techniques to determine uncertainty and its propagation within a system, such as Monte Carlo distributional methods, Latin hypercube sampling, and the stochastic response surface method.

At times uncertainty is mistaken for variability. Variability consists of the range of values that truly can be ascribed to a variable within a system. In principle, variability is based upon the differences in a variable frequently found within a system (e.g., a population distribution or concentration pattern). It is based on the number and frequency of observations of one or more variables in the system, or on the probability of the occurrence of a specific value (e.g., concentration) in the system under consideration. In this case, the uncertainty would be the quantitative error around the measurement of a single value or all values frequently observed in the system.

PAUL J. LIOY