# The definition(s) of humidity

Reference Equations: The calculation of humidity in one set of units from measurements made in a different set of humidity units or under different conditions is common practice.

For example, from measurements of relative humidity and temperature, the dew-point temperature or the mixing ratio are frequently calculated. These (and virtually all) humidity calculations require evaluation of humidity reference equations − the saturation vapour pressure equation which relates the saturation vapour pressure to the saturation temperature, and the enhancement factor equation, which accounts for the interaction between water molecules and those in the dry gas. The reference equations ensure that the result of a humidity calculation can be linked to the SI (the International System of units) and thus it is essential that they are well defined and correctly used.

As part of a general study of the propagation of uncertainty for humidity calculations we have shown how the uncertainty associated with the reference equations can be propagated and have presented complete sets of sensitivity coefficients for a variety of humidity calculations associated with humidity generation and measurement. Our work on the propagation of uncertainty for humidity calculations highlights

- the need to distinguish the uncertainty deriving from a reference equation from that propagating through it from another source;
- the need to account for correlations between two evaluations of the reference equations and hence,
- the need for reference functions to be published with sufficient information for their autocorrelation functions to be calculated.

In comparing two-pressure (2−P) and single-pressure (1−P) humidity generation, for example, the transition from a 2−P regime (where reference function uncertainty is an issue) to a 1−P regime (where reference function uncertainty can be ignored) is ill-defined. In the latter regime, it is clear that reference function errors cancel. Consequently, as the 2−P approaches the 1−P regime, we expect that errors will increasingly cancel but without more information than is usually given, we cannot tell by how much.

We have shown that the uncertainty associated with the reference function may be captured in the parameter covariance, from which the autocorrelation function is generated. Work is continuing to determine whether existing reference functions can be reinterpreted in this way.

**Definition of relative humidity:** Impedance-based relative humidity sensors, which are responsible for a high proportion of humidity measurement world-wide, are increasingly being used in conditions where traditional and standard definitions of relative humidity are not valid. The standard definition holds that the relative humidity of a gas at temperature t and pressure P is the ratio of the actual vapour pressure to the same vapour pressure the gas would exert if saturated at the same pressure and temperature. However this definition breaks down when the theoretical vapour pressure is greater than the actual pressure, i.e. when saturation cannot be achieved under these conditions. Without a valid definition, manufacturers and users resort to a variety of looser definitions which, though locally useful, have serious implications for calibration and traceability and for the ability of the measurement to be used to calculate other humidity quantities. Having identified the definition of “saturation” as the source of the problem, we investigated the various ways saturation could be achieved and championed a simple and useful definition of relative humidity which extends the traditional definition to cover the whole range.

### More information

For further information on the humidity definitions, contact Jeremy Lovell-Smith

### Key publications

Lovell-Smith, J.W. “Propagation of uncertainty in humidity measurement”. *Proceedings of TEMPMEKO 2001, 8th International Symposium on Temperature and Thermal Measurements in Industry and Science*, Berlin, 911-916, 2001.

Lovell-Smith, J.W. “On Correlation in the water vapour pressure formulations” *Metrologia* **43** 556–60, 2006.

Lovell-Smith, J.W. and Pearson H. “On the concept of relative humidity” *Metrologia* **43** 129–134, 2006.