workshop rh hygrometer fernicola

EUROMET Workshop on Uncertainty in Humidity Measurements1

Istituto di Metrologia "G. Colonnetti"Vito C. Fernicola

AN INTRODUCTION TO UNCERTAINTY IN RELATIVE HUMIDITY

HYGROMETERS

Vito FernicolaIMGC-CNR

Cavtat, Dubrovnik, 21st June 2004



Synopsis

�RH measurement methods

�RH hygrometers calibration approach

�Sources of uncertainty in RH:

�Relative humidity generator

�Relative humidity sensor

�Influence quantities

�Uncertainty estimate



RH measurement methods

Dew point temperature& gas temperature

Impedance-based sensor(capacitance, etc.)

Wet-bulb psychrometers

s

c

cscc

ssssPP

tePtftePtf

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)(),()(),(

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Direct output in RH unit

)()()(

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RH hygrometers calibration approach

DIRECT: in a test chamberconnected to a DP generator

BY COMPARISON in a climaticchamber:

� using a dew point hygrometeras a reference

� using a psychrometer as areference (e.g., WMO)

Other methods (e.g., saturated saltsolutions, etc.)

Dew pointhygrometer

Impedancesensor

Psychrometer



Sources of uncertainty in RH calibration

Standards

Method

Ambient conditions

Hygrometer undercalibration (HUC)

Dew point generator, dew-pointhygrometer, PRT’s

Calibration approachmeasuring equipment (bridge, DMM)aux. apparatus (scanner, bath)calibration cycle (e.g. hysteresis)

Environment influence on standardsand HUC

Repeatability, resolution, short-termstability, hysteresis, temperatureeffects



Sources of uncertainty in RH calibration

Relative humidity generators:•Uncertainty form a standard generator•Uncertainty from a secondary standard (e.g., climatic chamber)

Relative humidity sensor:•Repeatability•Resolution•Short-term stability (in acalibration cycle)

•Long-term drift (of thecalibration curve)

•Flow measurement/stability•Non-linearity

•Hysteresis•Temperature dependence (built-in compensation)

•Stem temperature effects•Contamination (from ambient)•Self heating•Ambient effect on instrument



Climatic chamber calibration layout



A reference air temperature thermometer

Bonding

StainlessSteel Sheath

Aspiration

PRTconnection (4-w)

PRT

Flow

Airtemperature

Gold-coatedsurfaces



Calculation of reference RH

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ssssPP

tePtftePtf

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Reference dew point temperature � ts u(ts)Reference gas temperature � tc u(tc)Vapour pressure formulation � es(t) u[es(t)] Enhancement factor formulation � f(t, P) u[f(t, P)] Pressure (drop) measurement � P u(P)

Note: contributions in grey are comparatively small in a 2-T generator



Sensitivity coefficients

Effect of a temperature change of 1 °Cat various levels of temperature and relative humidity

TemperatureRelativehumidity 10 °C 20 °C 30 °C 50 °C

10 %rh50 %rh90 %rh

0.7 %rh

3.5 %rh

6.3 %rh

0.6 %rh

3.2 %rh

5.7 %rh

0.6 %rh

3.0 %rh

5.4 %rh

0.5 %rh

2.6 %rh

4.6 %rh



Do not simplify too much !Magnus-vs-Sonntag sat. vapour pressure difference

Temperature / °C-40 -20 0 20 40 60 80 100

% d

iffer

ence

(Mag

nus-

Sonn

tag

eq.)

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

+0.31%

-0.31%



Temperature dependence

RHread / %0 10 20 30 40 50 60 70 80 90 100

RH

ref -

RH

read

/ %

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

T = 25 °CT = 60 °C



Temperature dependence, non-linearity, hysteresis

RHread / %0 10 20 30 40 50 60 70 80 90 100

RH

ref -

RH

read

/ %

-6

-5

-4

-3

-2

-1

0

1

2

T = 10 °CT = 40 °CT = 65 °C



Temperature coefficient (of capacitive polymeric sensors)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 20 40 60 80 100

RH [%]

dRH/dT [%rh/°C]

(Buonanno et al., ISHM 2002)



Polynomial correction

� which order ?� extrapolation is allowed ?

RHread / %

0 10 20 30 40 50 60 70 80 90 100

RH

ref -

RH

read

/ %

-2

-1

0

1

2

3

4

T = 25 °C

2nd order

1st order

3rd order



Temperature effect on the electronics(e.g. partially-immersed probe)

Measurement chamber Ambient



Stem temperature effects

(Lovell-Smith et al., ISHM 2002)



Immersion errors

(Lovell-Smith et al., ISHM 2002)



Contamination (chemical interference)

(Leppanen et al., ISHM 2002)



Long-term drift of the calibration curve

RHread / %0 10 20 30 40 50 60 70 80 90 100

RH

ref -

RH

read

/ %

-6

-5

-4

-3

-2

-1

0

1

yr. 1998yr. 2001

yr. 2002 yr. 2004



Estimation of reference RH uncertainty

- by using relative uncertainty propagation equation:

NpN

pp XXXY ��21

21

1)()(

)(2

1

22 ��

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i

N

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ii

cr pwith

xxu

py

yuyu

)()()]([()]([)( 2222 Pufuteuteu

urrcsrssr

c��

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Uncertainty estimate for a RH hygrometer

Quantity Estimate[%rh]

Std. uncert.[%rh]

PDF Sens.coeff.

Contribution[%rh]

Reference relative humidity 50.0 0.21 N 1 0.21Readings of HUC 50.8 0.03 N 1 0.03Resolution of HUC 0 0.029 R 1 0.029Reproducibility of HUC 0 0.29 R 1 0.29

Combined std. uncertainty 0.36Expanded uncertainty (k=2) 0.72

Example of calibration of a RH hygrometer with 0.1-digit resolution at 50 %rh and 21 °C air temperature



Expression of the uncertainty for a RH hygrometer

Air temperature / °C%rh 5 10 20 30 40 50 60 7010 0.60 0.59 0.59 0.59 0.59 0.59

20 0.66 0.66 0.61 0.60 0.60 0.60 0.60 0.60

30 0.74 0.73 0.64 0.63 0.62 0.63 0.62 0.66

40 0.83 0.69 0.67 0.66 0.65 0.66 0.72 0.70

50 0.75 0.74 0.72 0.70 0.69 0.69 0.77 0.75

60 0.81 0.79 0.76 0.74 0.72 0.87 0.84 0.81

70 0.87 0.85 0.82 0.79 0.76 0.94 0.90 0.87

80 0.93 0.91 0.87 0.84 0.81 1.02 0.97

90 1.00 0.97 0.93 0.89 0.85 1.09 1.04

Example of a calibration of a RH hygrometer with 0.1-digit resolution at 50 %rh with 21 °C air temperature.

Note: each cell represents the expanded uncertainty in %rh

workshop rh hygrometer fernicola

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