Calibrating relative-humidity sensors

Relative humidity is the ratio of the actual water vapour pressure to the saturation vapour pressure at that temperature. The numerator is a property of the air; the denominator is a property of the thermometer reading. Saturation vapour pressure rises steeply with temperature — from 23.33 kPa at 20.0 °C to 24.07 kPa at 20.5 °C, a 3 % change for half a degree — so any temperature disagreement between the sensor and the reference turns straight into an RH disagreement, whatever the humidity generator is doing.

How much a half-degree costs

Hold the actual moisture content fixed and move only the sensor's temperature. The table below is that calculation run against the Magnus relation, for a sensor reading 0.5 °C warmer than the reference.

Two things follow. The error is proportional to the humidity, so a chamber qualified comfortably at 50 %rh can fail at 80 %rh for no reason other than thermal lag. And at 2.43 %rh, a half-degree at the high end is already larger than the 1–2 %rh calibration uncertainty a good laboratory would quote — which means the thermal condition, not the reference hygrometer, is setting the result.

Methods, in order of achievable uncertainty

• Humidity generator (two-pressure or two-temperature): the reference method, generating a known RH from first principles. Best uncertainty, highest cost.
• Comparison in a humidity chamber against a chilled-mirror hygrometer: the usual laboratory approach. Around 1–2 %rh at k = 2 with a good reference and proper stabilisation.
• Saturated salt solutions in a sealed jar (LiCl ≈ 11 %, MgCl₂ ≈ 33 %, NaCl ≈ 75 %, K₂SO₄ ≈ 97 %): cheap, portable, and strongly temperature-dependent — the quoted RH of each salt shifts with temperature, so the jar needs its own thermometer. Typically 2–3 %rh.
• One-point field check against a hand-held reference: a verification, not a calibration. Useful for catching gross failure, not for a certificate.

Stabilisation is the measurement

A capacitive RH sensor responds to humidity in seconds but to temperature in minutes, and the mass of its housing and cable slows it further. If you step the chamber and read at ten minutes, you are recording the sensor's thermal lag rather than its calibration error. Allow the whole assembly — sensor, sheath, cable gland — to come to equilibrium, and demonstrate that it has by showing a flat trace rather than by assuming a settling time.

Read down rather than up where you can. A capacitive sensor that has been held at 80 %rh carries hysteresis for some time afterwards; approaching each point from the same direction at least makes the effect consistent, and approaching from both quantifies it.

What goes on the certificate

• The RH value and its uncertainty at each point — and the temperature at which that point was realised.
• The direction of approach, if hysteresis was not separately evaluated.
• The stabilisation criterion actually used, not a nominal one.
• As-found and as-left values where an adjustment was made, so drift history survives the adjustment.

Capacitive sensors drift with contamination and exposure rather than with time on a shelf, so the interval should come from as-found history in the environment of use. A sensor in a clean laboratory and the same model in a warehouse loading bay do not deserve the same interval.