365 Days of Climate Awareness 75 - Uncertainty

Error and uncertainty are intimately related, but not the same. It's easy, but not correct, to use the two interchangeably in conversation. Error is the difference between a measurement and the true value, and is generally impossible to know. Uncertainty is an estimate of error—that is, the accuracy and precision of a measurement. Scientifically we estimate uncertainties because true error cannot be measured.

It's a sad fact of life in science and in general that we cannot produce absolute measurements. We can have highly accurate standards—the international standard kilogram is kept in Paris, the meter is defined via wavelengths of red light, and the second is defined by the oscillations of a cesium atom--but we can never measure something with perfect accuracy.

The measurement tool itself has only limited resolution (however fine, such as 0.002 deg C for a CTD used in ocean profiling). Small variations in the environment, such as changes in sound speed through the water column when using sonar, small changes in the electrical current within the instrument--many tiny factors, and sometimes large ones, combine to corrupt the accuracy of every measurement.

Error has two components: systemic and random. Systemic error, also known as bias, is due to a constant factor in the system or environment which has a consistent effect on measurements. Once discovered, the cause--such as an interfering sound source in subsea sonar work--might be removed, or the effect removed in processing (such as the changing draft of a boat). Systemic error can be discovered.

Random error, however, is due to rapid, tiny variations in the environment and instruments themselves (such as changes temperature in the environment and in the instrument, or tiny variations in internal voltage). These minute random errors are too small and quick to be measured. We reduce the error by averaging a number of measurements, and with the concept of uncertainty. Uncertainty is the concept whereby we attempt to estimate the errors inherent in a measurement, so as to generate an estimate of confidence in it.

Precision versus accuracy.

Precision and accuracy of a system are two related terms which are also, wrongly, used interchangeably. The accuracy of a system refers to how close it comes to the true value. This cannot be measured absolutely but an instrument can be calibrated against another and adjusted to improve its performance. Comparing instruments' measurements against a known standard is a typical way of proving their fitness for use. Precision, on the other hand, refers to how consistent, or repeatable, an instrument's measurements are. The illustration shows the four possibilities: accurate and precise (the goal); accurate but not precise; not accurate, but still precise; neither accurate nor precise.

Tomorrow: NASA and climate science.

Be well!