Published as NIST SP 250-83 

NIST Special Publication 250-83

Calibration of Hygrometers with the 

Hybrid Humidity Generator

C.W. Meyer 

J.T. Hodges 

P.H. Huang 

W.W. Miller 

D.C. Ripple 

G.E. Scace 

Thermometry Group 

Process Measurements Division 

Chemical Science and Technology Laboratory

December 2008 

U.S. Department of Commerce 

Carlos M. Gutierrez, Secretary 

National Institute of Standards and Technology 

Patrick Gallagher, Deputy Director 
Page 2 of 48 

ABSTRACT 

We describe here the calibration of customer hygrometers using a new humidity generator that 

has been commissioned at the National Institute of Standards and Technology. The NIST 

Hybrid Humidity Generator (HHG) generates frost/dew points from –70 °C to +85 °C (mole 

fractions from 1×10−6

 to 0.57) using calibration gas flows up to 150 standard liters per minute. 

The HHG combines the two-pressure and divided-flow humidity generation techniques (hence 

the name “hybrid”). The centerpiece of the HHG is a heat exchanger/saturator that is immersed 

in a temperature-controlled bath stable to within 1 mK. For dew/frost point temperatures above 

–15 °C, the two-pressure principle is employed. For frost points at or below –15 °C, the watervapor/air mixture is produced by mixing metered streams of moist air produced by the twopressure method with purified, dry air. In this special publication, we describe the design of the 

generator. We also describe a series of performance and validation tests on the HHG and use the 

results of these to construct an uncertainty budget for the generator when used in two-pressure 

mode and when used in the divided-flow mode. These tests include measurements of 

temperature gradients and pressure stability in the generator under various operating conditions, 

and comparison of the humidity generated by the HHG to that generated or measured by the 

other NIST humidity standards. For dew/frost point temperatures, the uncertainty budget yields a 

total expanded uncertainty (k = 2) of less than 0.025 °C for dew/frost point temperatures above –

60 °C. For mole fraction, the budget yields a total expanded relative uncertainty of less than 

0.2 % for mole fractions above 2 ×10−5

. 

KEY WORDS: humidity; generator; standards; saturator; calibration; hygrometer; water vapor. 

Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. Such 

identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Special Publication 250-83 

Natl. Inst. Stand. Technol. Spec. Publ. 250-83, 48 pages (December 2008) 

CODEN: NSPUE2 
Page 3 of 48 

Calibration of Hygrometers with the Hybrid Humidity Generator 

Table of Contents 

1. Overview of the Calibration Service ........................................................................................................... 4

2. Principle of Operation .................................................................................................................................. 4

3. Humidity Definitions ................................................................................................................................... 5

4. Generator Design ......................................................................................................................................... 6

4.1. Gas Source ................................................................................................................................ 6

4.2. Saturation System ..................................................................................................................... 6

4.2.1. Pre-saturator ............................................................................................................. 7

4.2.2. Connecting tube ....................................................................................................... 8

4.2.3. Final Saturator .......................................................................................................... 9

4.3. Implementation of the Two-Pressure Method ........................................................................ 11

4.4. Implementation of the Divided-Flow Method ........................................................................ 11

5. Performance and Validation Tests ............................................................................................................. 13

5.1 Temperature Uniformity and Stability in Final Saturator ........................................................ 13

5.2 Pressure Stability in Final Saturator......................................................................................... 17

5.3 Self-consistency of the Generator in 2-P Mode ....................................................................... 17

6. Uncertainty Budget .................................................................................................................................... 18

6.2. Dew point temperature generated in 1-P or 2-P mode ........................................................... 19

6.3. Relative humidity generated in 1-P or 2-P mode ................................................................... 19

6.4. Water mole fraction generated in divided-flow mode ........................................................... 20

6.5. Frost-point temperature generated in divided-flow mode ...................................................... 20

6.6. Relative humidity generated in divided-flow mode ............................................................... 20

6.7. Uncertainty elements ............................................................................................................. 21

7. Comparisons with other NIST Humidity Standards .................................................................................. 29

7.1. Humidity Generators .............................................................................................................. 29

7.2. Gravimetric Hygrometer ........................................................................................................ 31

8. Calibration of Hygrometers ....................................................................................................................... 32

8.1 General Method. ...................................................................................................................... 32

8.2 Initial Procedures. .................................................................................................................... 33

8.3 Connecting the hygrometers to the hybrid generator. .............................................................. 33

8.4 Data Acquisition. ..................................................................................................................... 34

8.5 Quality Control. ....................................................................................................................... 34

9. Summary .................................................................................................................................................... 36

Appendix I−−Derivation of the Uncertainty Equations for the Hybrid Generator ....................................... 39

Appendix II—Uncertainty Element Subcomponents for the Hybrid Generator ........................................... 46

Sample Calibration Report ............................................................................................................................. 47
Page 4 of 48 

1. Overview of the Calibration Service 

The NIST Hybrid Humidity Generator [1,2] provides calibration services for a variety of 

humidity–measuring instruments. Calibrations are performed by subjecting the instrument under 

test to air with an accurately known moisture content produced by the generator. The calibration 

system described here does not currently include a test chamber (a chamber in which the humid 

air is directed and where the temperature and pressure are sufficiently constant and uniform). At 

this time, hygrometers requiring a test chamber for calibration must be calibrated using the NIST 

2-P Mark II Generator. The calibrations may be performed using humidity definitions of 

dew/frost point, relative humidity, mole fraction, or mass ratio. For the case of relative humidity 

calibrations, a separate calibration of the instrument’s external temperature probe is performed 

by means of comparison against a standard thermometer. The instruments and ranges of 

calibration include but are not restricted to: 

1. Chilled-Mirror Hygrometers, calibrated at customer-specified points over the dew/frost range 

of –70 °C to +85 °C, or alternatively over the relative-humidity range 5% to 100% for 

temperatures between −45 °C and 85 °. 

2. Aluminum-oxide Hygrometers, calibrated at customer-specified points over the dew/frost 

range of –70 °C to +85 °C. 

3. Electrolytic Hygrometers, calibrated at customer-specified points over a volume-ratio range of 

10–6 to the upper limit of the hygrometer. 

4. Cavity Ring-Down Hygrometers, calibrated at customer-specified points over a volume-ratio 

range of 10–6 to the upper limit of the hygrometer. 

Customers should consult the web addresses http://www.nist.gov/thermometry and 

http://ts.nist.gov/MeasurementServices/Calibrations/Humidity.cfm to find the most current 

information regarding calibration fees and technical contacts. The Thermometry Group follows 

the policies and procedures described in the NIST Calibration Services Users Guide, which can 

be found at these web addresses: http://ts.nist.gov/MeasurementServices/Calibrations/policy.cfm 

http://ts.nist.gov/MeasurementServices/Calibrations/domestic.cfm and 

http://ts.nist.gov/MeasurementServices/Calibrations/foreign.cfm. 

These web pages give instructions for ordering a calibration for domestic and foreign customers. 

They discuss: a) customer inquiries, b) pre-arrangements and scheduling, c) purchase orders, d) 

shipping, insurance, and risk of loss, and e) turnaround time. 

2. Principle of Operation 

Generation of gas with an accurately known moisture content starts with saturating the gas with 

water at a known temperature and pressure. Controlled saturation is accomplished by flowing a 

stream of the gas over a layer of water with a constant, uniform temperature until the gas is in 
Page 5 of 48 

thermodynamic equilibrium with the water. Ideally, the pressure of the gas is constant and 

pressure gradients within the gas are negligible. The mole fraction x of water vapor in the gas is 

then calculated using the equation 

 f (T ,P ) P

e (T ) x = s s

s

s 1)

Here, Ts and Ps are the temperature and pressure of the gas and water in the saturator, and e (Ts) 

is the water vapor pressure at Ts, as calculated by [3,4]. The enhancement factor f(Ts, Ps) reflects 

departures from ideal solution behaviour and non-ideal gas effects [5]. When Ps is 

approximately at ambient pressure, the generator is said to operate in one-pressure (1-P) mode. 

At a given value of Ts, two methods can be used to lower the humidity while still knowing its 

value accurately: the two-pressure (2-P) technique and the divided-flow method. The hybrid 

humidity generator (HHG) is capable of using these two methods separately or together (hence 

the name hybrid). The two-pressure technique [6] involves saturating the gas at an elevated 

pressure and afterwards expanding the gas down to ambient pressure. The divided-flow method 

[6] involves diluting the saturated gas with dry gas using precisely metered streams of gas. Such 

a technique allows generation of arbitrarily low humidity values while operating the saturator at 

convenient temperatures. When performing hygrometer calibrations, the HHG operates in 1-P or 

2-P mode for mole fractions greater than or equal to 1.6 × 10−3

 (a frost point of −15 °C). The 

HHG uses the divided flow method for mole fractions less than this value. 

3. Humidity Definitions 

The HHG generates humidity by the definition of mole fraction, but calibrations are also 

performed for other definitions, though they may require additional measurements. 

The dew point temperature TDP is defined as the temperature (for a given mole fraction x and gas 

pressure Pc) at which liquid water and water vapor are in equilibrium. Here, the subscript “c” in 

Pc refers to the chamber in which the dew point is being determined, (although the gas, if air, is 

often in an open environment). Experimentally, determination of TDP requires the additional 

measurement of Pc. Once Pc has been determined, TDP is obtained by iteratively solving the 

equation 

 f (T ,P ) P

e (T ) x = DP c

c

DP . 2) 

While Eq. 2 is structurally similar to Eq. 1, TDP = Ts only when Pc = Ps. Similarly, the frost point 

temperature TFP is given by 

 f (T ,P ) P

e (T ) x = FP c

c

i FP , 3) 

where ei is the saturated vapor pressure for ice, as calculated by [7,8]. 

Relative humidity is defined by 
Page 6 of 48 

( ) ( )( ) c c c

c

c

p

e T f T ,P

xP

e T

e

RH ≡ = 4) 

where ep is the partial pressure of the water vapor in the air and Tc is the air temperature in the 

chamber or location of interest. Experimentally, determination of RH requires the additional 

measurements of Pc and Tc. Chilled-mirror hygrometers that determine RH do so by directly 

measuring TDP using the chilled mirror, measuring Tc with an external thermometer, and 

calculating RH using Eqs. 2−3 while assuming f (T ,P ) f (T ,P ) DP c ≅ c c . 

The mass ratio r is equal to the ratio of water mass to air mass in a given volume of gas, and is 

related to the mole fraction by 

x

x

x

x

m

m

r − = − = 10.62196

1 a

w , 5) 

where mw = 18.015268 g/mol [9] and ma = 28.96546 g/mol [10] are the molar masses of water and 

air, respectively. 

4. Generator Design 

A schematic representation of the layout of the HHG is shown in Figure 1 for a) the 2-P mode 

and b) the divided-flow mode. The system involves a dry gas source, a two-pressure saturation 

system and (for divided-flow mode) a dilution system. The components of the HHG are 

described below. 

4.1. Gas Source

The gas used in the HHG comes from the in-house supply of compressed air at NIST that has a 

pressure head of 550 kPa. Before entering the generator, the gas passes through a large 

regenerating gas dryer and CO2 scrubber; this reduces the water mole fraction to 1 × 10-6 and 

removes 95 % of the CO2. The CO2 removal prevents a reaction between it and the saturator 

water that forms carbonic acid. After purification, the gas passes through a 240 L ballast tank 

which serves to minimize pressure pulses produced by the gas dryer. Computer-controlled mass 

flow controllers regulate the gas flow out from the tank; the maximum gas flow is 150 L/min. 

4.2. Saturation System

The saturation system of the HHG consists of a pre-saturator and final saturator with a heatable 

tube connecting them. These parts are described below. 
Page 7 of 48 

(a)

(b)

4.2.1. Pre-saturator 

The pre-saturator accomplishes virtually all of the saturation, and the final saturator performs 

small adjustments to ensure that the generated humidity is constant and determinable with 

minimal uncertainty. 

The purpose of the pre-saturator is to allow the HHG to generate high water mole fractions with 

low uncertainty. For a thermodynamic generator to accomplish this, the dry carrier gas must be 

humidified to a dew-point temperature nearly equal to the final saturator temperature before 

entering the saturator. Since water vapor mole fractions in the HHG approach 0.57, operation 

without a pre-saturator would cause excessive latent heat loading on the final saturation process. 

This would introduce large temperature gradients in the final saturator, resulting in large 

uncertainties in the mole fraction of water in the gas. 

A schematic diagram of the pre-saturator is shown in Fig. 2. It is a commercially made system 

that saturates the incoming gas by first passing the gas through its saturation chamber. In this 

chamber the gas is sprayed with water heated to about 10 °C above the desired saturation dewFigure 1. Schematic representation of the hybrid humidity generator (HHG) 

in a) two-pressure mode and b) divided-flow mode 
Page 8 of 48 

point. Afterwards the gas passes through the pre-saturator’s heat exchanger, which is controlled 

at approximately the desired dew-point temperature. The gas’s excess moisture condenses inside 

this heat exchanger and flows down to the pre-saturator’s water reservoir. 

4.2.2. Connecting tube 

The pre-saturator and final saturator are connected using 2.5 cm diameter stainless steel tubing. 

When dew points higher than the ambient temperature are to be generated, the tubing is 

temperature-controlled to be about 10 °C higher than the desired dew point in order to prevent 

water condensation in the tubing. To ensure a uniform temperature of the inner tube, with no 

cold spots where water could condense, the connecting tube is surrounded by an outer aluminum 

“shell” tube of inner diameter 7.3 cm and outer diameter 7.6 cm. Resistance heaters wound 

around this shell tube heat the shell tube to the desired temperature. Industrial process 

controllers with thermocouple sensors control the temperature of the shell tube. Heating of the 

Figure 2. Schematic diagram of the pre-saturator of the HHG. 
Page 9 of 48 

connecting tube is accomplished by heat transfer through air from the outer tube. Heating the 

connecting tube in this way generates less temperature non-uniformities on the tube than if the 

resistance heaters were directly attached to the tube. 

4.2.3. Final Saturator 

The final saturator is composed of a heat exchanger and saturation chamber. Both systems rest 

inside a commercially-made temperature-controlled bath of volume 167 L that is uniform to 

within 0.003 °C at 25 °C. The heat exchanger is located immediately above the saturation 

chamber in the bath. The gas first enters the heat exchanger, which conditions the gas to be at 

the temperature of the saturation chamber; this minimizes sensible heat loading on the chamber 

and also minimizes latent heat loading on it if the entering gas is oversaturated. In addition, the 

heat exchanger condenses out any moisture above the dew-point of the saturation chamber; this 

condensed water is then directed down into the saturation chamber. The heat exchanger is made 

of 316L stainless steel and is composed of two header tanks separated by an array of 116 parallel 

tubes with inner diameter 7.8 mm and length 48.5 cm. The parallel tube design minimizes the 

pressure drop across the heat exchanger. The diameter of the tubes is sufficiently large to 

prevent them from being blocked by condensed water droplets. With the tube dimensions 

described and with a gas flow of 150 L/min, the gas flows through the parallel tubes for a period 

of about ten thermal time constants. 

The gas exiting the heat exchanger flows into the saturation chamber below. The chamber is flat 

and roughly rectangular in shape. The saturation chamber is also made of 316L stainless steel 

and contains a 2.2-cm layer of water and a 2.2 cm layer of gas above it. The chamber has a 

horizontal area of 0.28 m2

, with total water and gas volumes of 6.16 L each. Stainless steel 

dividers inside the saturator partition the chamber into two channels of width 3.7 cm that follow 

a serpentine path, as shown in Fig. 3. Each channel covers half the area of the saturation 

chamber, as shown. The dividers are continuously welded along their lengths into the top plate 

of the chamber, allowing no gas flow over the dividers. Twisted vanes are welded to the dividers 

to improve mixing between the gas and water vapor while the gas is in the saturation chamber. 

Inside the saturation chamber, a rectangular cross section rather than a circular cross-section is 

used because the former exhibits less sensitivity to water height changes than would a circular 

cross-section design. For a given water level, the rectangular section contains more water 

volume and has a smaller rate of change in airway cross-sectional area with water level, relative 

to a circular cross section. Therefore, increases in water volume in the chamber (from water 

condensation in the heat exchanger) are less likely to restrict the airway; this allows the generator 

to produce very high dew-point temperatures for significant time periods. 

After the final saturator was constructed, the stainless steel inside of it was commercially 

passivated to insure that the saturator would not contaminate the water stored in it. Since then, 

samples of water kept in the saturator for several months have been analyzed and show no 

noticeable increase in the level of impurities. 
Page 10 of 48 

The temperature of the final saturator is determined using a standard platinum resistance 

thermometer (SPRT) immersed in the temperature-controlled bath. The SPRT has been 

calibrated on the International Temperature Scale of 1990 (ITS-90) by the NIST Thermometry 

Group. The resistance of the SPRT is measured using a computer-interfaced AC resistance 

bridge with a temperature-controlled 25 Ω standard resistor as the reference resistor. A pressure 

transducer based on a silicon strain gauge, interfaced to a computer, measures the pressure in the 

saturator; the gauge is connected to a point in the saturator near the gas outlet using 1⁄4 inch 

(0.635 cm) stainless-steel tubing. This tubing is at a sharp vertical slope in the region 

immediately above the saturator. Therefore, when the saturator is above the ambient 

temperature, any condensation occurring in the tubing is directed down to the saturator; this 

ensures that the transducer is never exposed to condensed water and always properly measures 

the pressure inside the saturator. Chamber pressure measurements (for dew point determination) 

are also made with a pressure transducer based on a silicon strain gauge. Both transducers have 

been calibrated against a piston gauge that has been calibrated by the NIST Pressure and 

Vacuum Group. 

The entire heat-exchanger/final-saturator system is shown in Fig. 4. A horizontal plate on top of 

the heat exchanger supports the system inside the temperature-controlled bath and also serves as 

the top cover to the bath. Two sets of water fill tubes and exit tubes can be seen in the figure, one 

for each channel. The fill tubes are used to fill the saturation chamber with water. The exit tubes 

are used to withdraw water that is above the fill level; this is accomplished by applying a vacuum 

to the tubes. When viewed from above, the saturator and heat exchanger nearly fill the bath 

chamber, and almost touch a baffle plate attached to the two bath stirrers (see figure). This 

configuration promotes optimal circulation of water within the bath, with minimal dead-zones. 

Such a design minimizes temperature-non-uniformity in the bath. 

Figure 3. Schematic diagram of the saturation chamber. 
Page 11 of 48 

4.3. Implementation of the Two-Pressure Method

The two pressure technique [6] involves saturating the gas at an elevated pressure and afterwards 

expanding the gas down to ambient pressure. The advantage of this technique is that a range of 

humidity values can be generated using one saturator temperature. This is useful for two 

reasons. First, it is much faster for an operator to change the saturator pressure than to change 

the saturator temperature. Secondly, the low humidity limit of the generator is lowered, since the 

molar fraction is inversely proportional to the saturator pressure. 

 

The HHG employs the two-pressure technique by first using the 550 kPa pressure head of the gas 

source to raise the pressure in the saturator. It then uses an expansion valve at the exit of the 

saturation chamber to control the pressure. The expansion valve consists of a throttle valve with 

a high-speed motor/gear assembly. A PID controller that senses the pressure using the strain 

gauge mentioned above sets the opening of the throttle. The valve is located immediately above 

the temperature-controlled bath and is connected to the gas outlet from the saturator. Figure 5 

shows a photograph of the laboratory layout of the pre-saturator, saturator, connector tube, and 

throttle valve. 

4.4. Implementation of the Divided-Flow Method

The divided-flow method [6] involves diluting the saturated gas with dry gas using preciselymetered streams of gas. The mole fraction after dilution is 

N

n x n x

x &

& & s s + p p = 6) 

Figure 4. The final saturator. Photograph of the saturator, showing 

the heat exchanger and saturation chamber (left), and schematic 

diagram of the saturator in the temperature-controlled bath, showing 

direction of water flow in the bath (right). 
Page 12 of 48 

where ns & and p n& are the molar flows of the saturated gas and pure gas, respectively, and N& is the 

total molar flow. Also, xs is the molar fraction of water in the saturated gas and xp is the residual 

molar fraction of water in the pure gas; the value of xp is determined both from the efficiency of 

the gas purifier and from water outgassing from the tube walls of the manifold. Such a technique 

allows generation of arbitrarily low humidity values while operating the saturator at convenient 

temperatures. When generating low humidity, this method has two principal advantages. First, 

the temperature-controlled bath may be operated with water, which is much safer and less 

expensive than liquids with lower freezing temperatures. Secondly, the technique avoids the 

large temperature gradients in the generator bath that often exist at low temperatures; these 

gradients add large uncertainties to the uncertainty of the generated humidity. 

The HHG employs the divided-flow method using a gas multiplexer. The multiplexer contains 

seven flow-metering banks. Each bank consists of a commercially-made mass-flow controller 

and a commercially-made flow meter (a laminar-flow element) that measures the standard 

volume flow. The metering ranges of the flow meters are 10 cm3

/min, 100 cm3/min, 1 L/min, 10 

L/min, 30 L/min, 100 L/min, and 100 L/min. The upstream side of each flow bank is connected 

in parallel to both the saturated gas supply and a purified gas supply. When the divided flow 

method is used, both the saturated gas supply (and hence the saturator) and the purified gas are 

kept at a pressure of approximately 300 kPa. The purified gas comes from the original gas source 

described in section 2.1, but it is additionally dried using a molecular sieve; the sieve is specified 

to reduce the water mole fraction of the gas to 1 × 10-9. The downstream side of each flow bank 

connects to a common outlet manifold. Pneumatic valves controlled by a computer select 

whether dry gas, wet gas, or no gas flows through each bank. For those banks with flow, the 

computer-controlled mass-flow controllers adjust the flow to provide the dilution nominally 

specified. The flow meters measure the flow of the saturated gas υs& and the flow of the dry gas 

υp& and provide this information to the computer. The two flows are added to obtain the total 

Figure 5. Laboratory configuration of several components of the HHG. 
Page 13 of 48 

flow V& . The flow meters have been calibrated for pure air by the NIST Fluid Metrology Group, 

using upstream pressures of 300 kPa to replicate the conditions under which they are used. 

When measuring the air flow of the saturated gas (with x = 0.0022), it is assumed that the change 

to the flow-meter calibration due to the saturation is negligible. It is also assumed that 

n N V& & & & / / s = υs and n N V& & & & / / p =υp . Combining the above assumptions has been shown to cause 

an error of less than 3.5 × 10−4

ns & , which is below the calibration uncertainties for the flow 

meters. Figure 6 shows a photograph of the multiplexer. 

5. Performance and Validation Tests 

Performance tests were made on the HHG in two-pressure mode to determine components of an 

uncertainty budget for the generator. Specifically, we measured temperature gradients and 

temperature stability in the saturator bath, and temperature gradients and pressure stability inside 

the saturation chamber. 

5.1. Temperature Uniformity and Stability in Final Saturator

We measured temperature non-uniformities in the bath with five type K thermocouples used in 

differential mode, measured with an 8 1⁄2 digit multimeter through a scanner with low thermal 

emfs. We attached the reference junction of each thermocouple to the exit point from the 

saturator chamber, and placed the measuring junction in thermal contact with the location of 

Figure 6. Photograph of the multiplexer, which is used when 

operating the HHG in divided-flow mode. 
Page 14 of 48 

interest. The locations examined were the entrance to the heat exchanger, the exit from the heat 

exchanger, the entrance to the saturation chamber, the bath below the saturation chamber, and 

the bath above the saturation chamber. 

Figure 7 shows the temperature non-uniformities measured. In a) they are shown as a function 

of bath temperature with no gas flow. Between 0 °C and 40 °C, the non-uniformities are within 

the resolution of the measurements. At 60 °C non-uniformities become observable and at 85 °C 

they reach 16 mK. However, the largest non-uniformities are vertical, with the top of the bath 

being cooler than the bottom, and it has been found that the largest temperature variation (at the 

top of the bath by the entrance to the heat-exchanger) is strongly dependent on the bath fill level. 

In b) they are shown at 84 °C as a function of gas flow when the pre-saturator temperature is 

85 °C. Here, the non-uniformities are plotted as a function of time; before 1800 s the flow is 

zero, and after 1800 s the flow is 150 L/min. No significant difference in the non-uniformities is 

seen for these two flows. Note that the non-uniformity at the entrance to the heat exchanger is 

noticeably smaller in b) than in a); we attribute this to a higher bath fill level in b). In b), the 

non-uniformity in the bath above the heat exchanger is not shown because the corresponding 

thermocouple was not functioning when the measurements were made. As a result of these 

studies, we have concluded that during humidity calibrations the fill level of the bath should 

always be approximately 2.5 cm below the top lid of the bath container. 

We also measured the thermal effects of pre-saturated gas flowing through the saturator. The 

measurements were made using two metal-sheathed, type T thermocouples that are mounted 

with measuring junctions near the saturator entrance. The junction of the first thermocouple is 

immersed in the water and that of the second is located in the gas stream. Figure 8 shows the 

temperature difference between the thermocouple junctions when gas flows through the 

generator and when no gas flows through (with no flow, we assume both thermocouples are at 

the bath temperature). For this plot, the bath temperature is 22 °C, the gas flow is 50 L/min and 

the differences are plotted as a function of pre-saturator dew point. When the pre-saturator dew 

point is considerably less than the bath temperature, temperature non-uniformities occur due to 

evaporative cooling of the water in the chamber. With a dew-point 8 °C below the bath 

temperature, the non-uniformity is over 0.1 °C. However, no non-uniformities are resolvable 

when the dew point is above the bath temperature; in this case the excess moisture condenses in 

the heat exchanger and the gas is at thermal equilibrium with the saturation chamber by the time 

it enters the chamber. These measurements demonstrate the importance of setting the presaturator to a dew point above rather than below the bath temperature. 

In addition, we measured the stability of the bath over 1200 s at a series of bath temperatures. 

Figure 9 shows the results. At 20 °C the standard deviation was at a minimum, at 0.2 mK. As 

the bath temperature was lowered, the standard deviation reached 0.9 mK at 0.5 °C and, as it was 

raised, the standard deviation reached 1.1 mK at 85 °C. 
Page 15 of 48 

Figure 7. Temperature non-uniformities in the bath containing the final saturator, 

as measured by differential type K thermocouples attached to the outside of the 

saturator. The plots display temperature differences between the designated 

location and the exit point from the saturation chamber. In a), the nonuniformities are shown as a function of bath temperature when no gas flows 

through the generator. In b), the effect of gas flow on the non-uniformities is 

shown for a temperature of 84 °C. The non-uniformities are shown as a function 

of time, with no flow before 1800 s and 150 L/min after 1800 s. Here, the 

saturator is at ambient pressure and the pre-saturator is generating a dew point of 

85 °C). 
Page 16 of 48 

Figure 9. Standard deviation of the temperature fluctuations in 

the bath containing the final saturator as a function of bath 

temperature, as measured by an SPRT. 

Figure 8. Temperature deviations from the bath temperature 

inside the saturation chamber at the entrance to the chamber when 

gas is flowing through it. The flow is 50 L/min and the bath 

temperature is 22 °C. The deviations are plotted as a function of 

pre-saturator dew point. The blue and red circles are from type T 

thermocouples (used in absolute mode) placed in the water and 

gas, respectively. Here, ΔT = Tflow –Tno flow, where Tflow and 

Tno flow are the measured temperatures with and without gas flow, 

respectively. Tno flow is assumed to be the bath temperature. 
Page 17 of 48 

5.2. Pressure Stability in the Final Saturator

For measuring pressure fluctuations in the saturation chamber, we first optimized the PID 

settings of the pressure controller. We then measured the pressure variations at the optimum 

settings. At a saturator temperature of 20 °C and with a variety of pressures and flows up to 

150 L/min, the standard deviation was less than 15 Pa. An example is shown in Fig. 10, where 

the flow was 100 L/min, and the standard deviation of the pressure fluctuations was 9 Pa. 

Unfortunately, since pressure is controlled by adjustments of gas flow out of the saturation 

chamber, optimal pressure control results in noticeable gas-flow fluctuations. Gas flow 

fluctuations can cause mirror-temperature instabilities for chilled-mirror hygrometers, preventing 

them from achieving optimal resolution. Therefore, less-than-optimal PID settings may be 

required to keep gas-flow fluctuations at acceptable levels. The level of fluctuations that is 

acceptable must be determined for each hygrometer. 

5.3. Self-consistency of the Generator in 2-P Mode

For the self-consistency tests, we generated dew points with eight different saturator 

temperatures and saturator pressures ranging from 500 kPa to ambient. By varying the degree of 

pressure expansion, the same dew point may be generated over a range of saturator temperatures. 

Self-consistency of the generator output was tested by using a chilled-mirror hygrometer as a 

transfer standard. We performed a 4-wire resistance measurement of the hygrometer’s platinum 

resistance thermometer (PRT), which is in thermal contact with its mirror. The hygrometer dewpoint temperature, as determined by the PRT, was then calculated with the Callendar-van Dusen 

equation [11], using 100 Ω as the assumed PRT resistance at 0 °C. The flow through the 

Figure 10. Pressure fluctuations in the saturator when the flow is 

150 L/min. The standard deviation of the fluctuations is 9 Pa. 
Page 18 of 48 

generator was 30 L/min, and 0.5 L/min of this flow was directed through the hygrometer. The 

difference between the hygrometer-measured dew point temperature and the generated dew point 

temperature, ΔTDP, was then plotted for each dew point of the set. Figure 11 shows ΔTDP as a 

function of dew point temperature. The overlap between the dew points generated at different 

saturator temperatures, indicated with different symbols, shows the degree of self-consistency of 

the HHG. The dew point values agree with each other to within 20 mK. 

6. Uncertainty Budget 

Based on these performance tests as well as measurement equipment specifications, we have 

constructed uncertainty budgets for the humidity generated by the HHG. There are budgets for 

the two expressions of humidity (mole fraction and dew/frost-point) under two conditions: twopressure generator without dilution and two pressure with dilution. The total uncertainties 

associated with these budgets are based on the ISO and NIST guidelines for the expression of 

uncertainty in measurement [12,13]. The equations relating the total uncertainties to the 

uncertainty components are listed below and derived in Appendix I. 

The total uncertainty for humidity generated by the hybrid generator is presented here for four 

different humidity definitions: water mole fraction, dew/frost-point temperature, relative 

humidity, and mass ratio. For each of these four definitions, we present the uncertainty for the 

cases of humidity generated in 1-P mode, 2-P mode, and divided-flow mode. In the equations 

below, u(X) is the standard uncertainty of the quantity X. 

Figure 11. Comparison of dew points generated by the HHG using different 

saturator temperatures. The comparisons were made using an uncalibrated 

chilled-mirror hygrometer as a transfer standard. Here ΔTDP is the measured 

dew point minus the generated dew point. Measurements with the saturator at 

different temperatures are plotted with different symbols. The hygrometer 

repeatability (k = 1) is shown as an error bar. 
Page 19 of 48 

6.1. Water Mole Fraction Generated in 1-P or 2-P Mode

Here, the total standard uncertainty for the water mole fraction, u(x), is expressed as 

( ) ( ) ( ) ( )2 calc

s

2

s

s 2 calc

s

2

s

2

s

2

2

s

2 s

s

2

s

s

s

2 1 1 ( ) u f P

e

u e

P

u P

P

e

u T

dT

de

P

u x ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = . 7) 

The four relevant uncertainties are u(Ts), u(Ps), ( ) calc

s u e and ( ) calcs u f . Here, ( ) calcs u e and ( ) calcs u f

are the uncertainties of the calculated values of e(Ts) and fs(Ts,Ps), respectively, due to the 

imperfect knowledge of these physical relations. 

6.2. Dew-point Temperature Generated in 1-P or 2-P Mode

For this case, the total standard uncertainty of the dew-point temperature TDP or frost-point 

temperature TFP of the gas in a test chamber with pressure Pc and temperature Tc = TDP or Tc =

TFP is expressed as 

( ) [ ] ( ) ( ) ( ) ( )( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ + + Δ + Δ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = 2 calc

r

2 calc

2

c

2

c

2

s

2

2 s

s

2

s

s

s

2

c DP

2 c

DP

1

/

u f u e

P

u P

P

u P

u T

dT

de

de dT e

e

u T 8) 

The five relevant uncertainties are u(Ts), u(Ps), u(Pc), ( ) calc u Δe and ( ) calc

u Δf . When the generator 

is used in 1-P mode (Ps ≅ Pc), 

( ) ( ) 0 calc calc

u Δer = u Δf = . 9) 

 When the generator is used in 2-P mode (Ps ≠ Pc), 

( ) ( ) ( )

2

c

2 calc

c

2

s

2 calc

s 2 calc

r

e

u e

e

u e

u Δe ≡ + , 10) 

( ) ( ) ( )

2 calc

c

2 calc

s

2 calc

u Δf ≡ u f + u f . 11) 

Here, ( ) calc

c u e and ( ) calcc u f are the uncertainties of the calculated values of e(Tc) and fc(Tc,Pc), 

respectively, due to the imperfect knowledge of these physical relations. In Eq. 10, note that the 

subscript “r” in calc

r Δe is used to show that it is a relative quantity and therefore dimensionless. 

6.3. Relative Humidity Generated in 1-P or 2-P Mode

The total standard uncertainty for relative humidity, u(RH), of the gas in the test chamber with 

temperature Tc and pressure Pc is expressed as 
Page 20 of 48 

( ) ( )

( ) ( ) ( )( )] 2 calc calc

c

c

2

c

2

c

c

c

2

s

s

2

s

2

s

s

s

2

s c

2 c s

1 1

1 1 ( )

u P u e u f Pu T

dT

de

e

u P

P

u T

dT

de

P e e

P e

u RH

+ + Δ + Δ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎢

⎢

⎣

⎡

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⎥

⎦

⎤ ⎢

⎣

⎡ =

 12) 

The six relevant uncertainties are u(Ts), u(Ps), u(Tc), u(Pc), ( ) calc u Δe and ( ) calc

u Δf . Here, 

( ) calc u Δe and ( ) calc u Δf are given by Eqs. 10−11. 

6.4. Water Mole Fraction Generated in Divided-flow Mode

For this case, u(x) is expressed as 

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

⎥

⎥

⎦

⎤

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ + ⎠

⎞ ⎜

⎝

⎛ + + −

+ ⎢

⎢

⎣

⎡

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

≅

2

2

s

2

s

2

p

2

s

2

2

p

2 calc

2 s

s

2 calc

s

2

s

2

2 s

s

2

s

s

s

2 2

1

1

N

u n

x

u x

x

x

N

u n

u f

e

u e

P

u P

u T

dT

de

e

u x x

&

&

&

&

 13) 

The seven relevant uncertainties are u(Ts), u(Ps), ( ) calc

s u e , ( ) calcs u f , u(xp), ( ) u ns & and ( ) u np & . 

6.5. Frost-point Temperature Generated in Divided-flow Mode

In the hybrid generator, the divided flow method will only be used for generating frost points. 

Here, the total standard uncertainty of the frost-point temperature TDP of the gas in the test 

chamber is 

( ) ( )

[ ] ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ⎥

⎥

⎦

⎤

+ + + + + Δ

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ +

⎠

⎞ ⎜

⎝

⎛ + + − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

2 calc

2

c

2 calc

c

2

s

2 calc

s

2

c

2

c

2

2

p

2

2

s

2

s

2

p

2

s

2

s

2

2 s

s

2

s

s

s

2

c c

2

2 c

FP 1 1

/

u f

xP

u e

e

u e

P

u P

N

u n

N

u n

x

u x

x

x

P

u P

u T

dT

de

de dT e

xP

u T

&

&

&

&

 14) 

The nine relevant uncertainty elements are u(Ts), u(Ps), u(xp), ( ) u ns & , ( ) u np & , u(Pc), ( ) calc

s u e , 

( ) calc

c u e and ( ) calc

u Δf . Here, ( ) calcu Δf is defined in Eq. 11. 

6.6. Relative Humidity Generated in Divided-flow Mode
Page 21 of 48 

Here, the total standard uncertainty of the relative humidity of the gas in the test chamber is 

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( )

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎥

⎥

⎦

⎤

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ + ⎠

⎞ ⎜

⎝

⎛ + + −

⎢

⎢

⎣

⎡

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⎥

⎦

⎤ ⎢

⎣

⎡ =

calc 2

2 c

c

calc 2

2 c

c

2

c

c

c

2

c

2

c

2

p

p

2

c

c

2

2

p

2

2

s

2

s

2

p

2

s 2 calc

s

2

s

2 calc

s

2

s

2

2 s

s

2

s

s

s

2

c

2 c

( ) ( ) ( ) 1

1

1

u f

e

u e

u T

dT

de

P e

u P

x

N

n

x

e

P

N

u n

N

u n

x

u x

x

x

u f

e

u e

P

u P

u T

dT

de

e e

xP

u RH

&

&

&

&

&

& 15) 

The eleven relevant uncertainty elements are u(Ts), u(Ps), u(xp), ( ) u ns & , ( ) u np & , u(Pc), u(Tc), 

( ) calc

s u e , ( ) calcc u e , ( ) calcs u f ,and ( ) calcc u f . 

6.7 Mass Ratio

The total standard uncertainty for mass ratio is related to that for the mole fraction by 

( ) ( ) ( ) 1

1 0.6220 2 u x

x

u r − = . 16) 

Here, u(x) is given by Eq. 7 when the generator is used in 1-P or 2-P mode, and by Eq. 13 when 

the generator is used in divided-flow mode. 

6.7. Uncertainty Elements

Shown in Table 1 is a list of all the relevant uncertainty elements mentioned above and their 

standard uncertainty values. The subcomponents of the uncertainty elements Ts, Ps, and Pc are 

given in Appendix II. The value for the uncertainty of Tc is based on the typical uncertainty for 

the calibration of external temperature probes at NIST. [14] The table does not contain all 

uncertainty elements for the calibration of hygrometers by the HHG, as the table does not include 

uncertainties from measurement repeatability of the particular hygrometer under calibration. In 

the calibration reports, however, the total uncertainty for the calibration of the hygrometer is 

reported, with the uncertainty due to hygrometer repeatability determined as described in 

section 8.4. In Table 1, the uncertainty for the calculation of e(T) is obtained from Table 2 of 

[15]. The uncertainties for the calculations of fs and fc are presented as a fit to the uncertainty 

data of Table 9 in [16]; because there is no data below −50 °C, we extrapolated the curve 

determined from the available data to obtain the uncertainty formula listed in Table 1. In 

obtaining the formula, the “maximum percentage uncertainties” from [17] were divided by 3 to 

obtain the standard uncertainty. The values for ( ) calc

s u f and ( ) calcc u f decrease with temperature 

and increase with pressure, and are quite significant for some operating conditions. By 

comparison, the uncertainties of calc

s e and calcc e are negligible. 
Page 22 of 48 

An additional uncertainty element is that due to moisture diffusion through the vertical pressure 

sensing tube of the final saturator. When the saturator temperature is above ambient, moisture 

will condense inside the tube in the ambient-temperature region and drip down to the saturator. 

As the air in that region dries from the condensation, additional moisture will diffuse through the 

tube from the saturator to the ambient-temperature region. This creates a diffusion-driven 

moisture flow which can lower the water mole fraction of the air exiting the saturator. We have 

calculated the depletion and determined it to be less than 0.002 % for the intended gas flows 

through the generator (over 20 L/min). This amount is negligible compared to other 

uncertainties, and as a result we are not including it in Table 1. 

X u(X) (k = 1) Condition Unit 

 

Ts 1.5 

0.16Ts/°C – 4.9 

(T ≤ 40 °C) 

(T > 40 °C) 

mK 

Ps 18 (Ps ≈ ambient pressure) Pa 

( ) 2 2 29 /10000 Pa + Ps (Ps > ambient pressure) Pa 

Tc 10 mK 

Pc 15 Pa 

calc

s e 44×10-6 calcs e Pa 

calc

s f Ps/(107

·Pa) (18.3 K/Ts – 0.047) -- 

calc

c e 44×10-6 calcc e Pa 

calc

c f Pc/(107

·Pa) (18.3 K/Tc – 0.047) -- 

xp 10 nmol mol−1

s n& 5×10-4s n& 

1×10-3

s n&

( s n& ≥ 7.5×10-6 mol s−1

) 

( s n& < 7.5×10-6 mol s−1

) 

mol s−1

mol s−1

p n& 5×10-4p n& mol s−1

Table 1. Uncertainty elements for the Hybrid Humidity Generator and their 

uncertainties. Here, u(X) is the standard uncertainty for element X. The 

elements with subscript “c” refer to the environment in which the humidity is 

to be determined. The element Tc is only relevant when the hygrometer uses 

an external thermometer for determination of relative humidity. 
Page 23 of 48 

Figure 12 shows the total expanded uncertainty for humidity generated by the HHG when the 

generator is operated in 1-P mode. The uncertainty is shown for the a) mole fraction (relative 

uncertainty) and b) dew point. Here, the total expanded uncertainty is given by U(x) = ku(x), 

where the coverage factor is k = 2. The expanded relative uncertainty is given by Ur(x) = U(x)/x. 

In the figure, the black curve represents the total uncertainty, while the other curves represent the 

contributions to the total uncertainty from individual uncertainty components. In Fig. 10(b), the 

uncertainty contributions from calc

s e and calcc e are zero, because these uncertainties cancel out 

when the generator is used in 1-P mode; the uncertainty contributions for calc

s f and calcc f are zero 

for the same reason. Also in this plot, the curve designated as “P” represents the contributions 

from both Ps and Pc. The figure shows that for the 1-P mode, the dominant uncertainty is from 

pressure measurement and stability, except for saturator temperatures above 60 °C; in this case 

uncertainties due to temperature non-uniformities in the bath dominate. Figures 13(a) and 13(b) 

show similar plots for the case when the generator is operated in 2-P mode with Ps = 500 kPa. In 

Fig. 13(b), the discontinuity at 0 °C is due to the assumption of frost-point generation below this 

temperature. This figure shows that when the saturator is operated in this way, the uncertainties 

in calc

s f and calcc f usually dominate. 

Figure 14 shows the expanded uncertainty generated by the HHG when it is used in divided-flow 

mode. The uncertainties plotted are (a) the water mole fraction (relative uncertainty) and (b) the 

frost-point temperature. For these plots, the saturator parameters are Ps = 300 kPa and 

Ts = 0.5 °C. In the plots, “n” refers to the combined contribution to the total from ns& and np& . In 

Fig 14(a), Ur(x) is relatively constant for x > 2×10−5

. At the highest value of x shown in the plot, 

np & = 0 and so Ur(x) is only due to the saturator. As x decreases to 2×10−5

, Ur(x) increases slightly 

due to the rising significance of ( ) u ns & and ( ) u np & . As x decreases below 2×10−5

, ( ) p u x /x

dominates Ur(x), increasing its value to nearly 1 % at x = 2×10−6

. In (b), the total expanded 

uncertainty is U(TFP) = ku(TFP). For −55 °C ≤ TFP ≤ −12 °C, U(TFP) ≈ 14 mK and is relatively 

constant over this entire range. As TFP decreases below −55 °C, U(TFP) rises rapidly up to 58 mK 

at −70 °C due to the increasing influence of ( ) p u x . 

Figure 15 shows the expanded relative uncertainty Ur(RH) = U (RH)/RH for relative humidity 

calibrations using humid gas generated by the HHG and flowing to an environment with 

temperature Tc = 20 °C and pressure 100 kPa. Here, Ur(RH) includes the uncertainty of the 

humidity produced by the generator and the uncertainty of the calibration of the hygrometer’s 

external temperature probe. In plots a) and b) the generator is operated in 2-P mode; the plots 

show the uncertainty for two saturator temperatures: a) Ts = 20 °C and b) Ts = 1 °C, which 

generate different relative humidity ranges. In plot c) the generator is operated in divided-flow 

mode.

Figure 16 shows the total expanded relative uncertainty for mass ratio, Ur(r) = U(r)/r, generated 

by the HHG when the generator is operated in a) 1-P mode and b) 2-P mode with Ps = 500 kPa. 

In the plots, the black curve represents the total uncertainty, while the other curves represent the 

contributions to the total uncertainty from individual uncertainty components. 
Page 24 of 48 

Figure 12. Total expanded uncertainty U for the (a) mole fraction and (b) dew-point 

temperature generated by the HHG saturator when used in 1-P mode. The black curve 

represents the total uncertainty, while the other curves show the contributions from 

individual uncertainty elements. In a), the expanded uncertainty is expressed as a 

relative uncertainty Ur(x) = U(x)/x = ku(x)/x, where k = 2 and u(x) is the standard 

uncertainty for x. In b), the total expanded uncertainty is U(TDP) = ku(TDP). In b), P

represents the combined contributions from both Ps and Pc.
Page 25 of 48 

Figure 13. Total expanded uncertainty U for the (a) mole fraction and (b) 

dew/frost-point temperature generated by the HHG saturator when used in 

2-P mode with Ps = 500 kPa. The black curve represents the total 

uncertainty, while the other curves show the contributions from individual 

uncertainty elements. In a), the expanded uncertainty is expressed as a 

relative uncertainty Ur(x) = U(x)/x = ku(x)/x, where k = 2 and u(x) is the 

standard uncertainty for x. In b), the total expanded uncertainty is 

U(TDP) = ku(TDP). In b), P , e

calc, and fcalc each represent the combined 

contributions of their quantity from both the saturator and chamber 

(hygrometer).
Page 26 of 48 

Figure 14. Total expanded uncertainty for the a) water mole fraction 

(relative uncertainty) and b) frost-point temperature generated by the 

HHG when it is used in divided flow mode with a saturator pressure of 

Ps = 300 kPa. ). Here, f

calc represents the combined uncertainty 

contributions from both the saturator and chamber (hygrometer), and 

n& represents the combined uncertainty contributions from the wet gas 

and dry gas. 
Page 27 of 48 

Figure 15. Total expanded relative uncertainty Ur(RH) for the relative humidity calibrations 

using humid gas generated by the HHG to an environment of temperature Tc = 20 °C and 

pressure Pc = 100 kPa; here, Ur(RH) includes the uncertainty for the calibration of the 

hygrometer’s external temperature probe. In plots a) and b), the generator is used in 2-P 

mode, and the saturator temperature is a) 20 °C and b) 1 °C; the relative humidity is varied 

by changing the saturator pressure. In c) the generator is used in divided-flow mode. 
Page 28 of 48 

Figure 16. Total expanded relative uncertainty Ur(r) 

for the mass ratio r generated by the HHG. In the 

plots the generator is used in a) 1-P mode, b) 2-P 

mode with Ps = 500 kPa, and c) in divided-flow mode. 
Page 29 of 48 

7. Comparisons with other NIST Humidity Standards 

7.1. Humidity Generators

To further validate the performance of the HHG and also determine the level of consistency 

between the NIST thermodynamic humidity generators, we made comparison measurements 

with the NIST 2-P generator Mark II [17] and the LFPG [18]. One set of comparisons was 

performed using the uncalibrated chilled-mirror hygrometer described in section 4 as a transfer 

standard. For the dew points generated, the expanded uncertainties (k=2) for the 2-P generator 

and LFPG are 40 mK [19] and 13 mK [18], respectively. In the LFPG, nitrogen was used as the 

gas source. Figure 17 shows the difference between the measured dew point and the expected 

dew point from the generator over the range −15 °C to 30 °C. The data from the HHG are those 

shown in Fig. 11. For measurements below 0 °C, the gas moisture was observed to condense on 

the mirror as dew rather than frost. The HHG and LFPG agree within 10 mK, which is within 

the combined expanded uncertainties of the two generators and the hygrometer. The HHG and 

2-P generator agree within 40 mK; the difference is also within their combined expanded 

uncertainties, though only marginally so. We made a second set of comparison measurements 

against the LFPG over the frost point range −50 °C to −20 °C using a second chilled-mirror 

hygrometer. The comparison values and respective expanded uncertainties are shown in 

Figure 18. Once again, the HHG and LFPG agree within the combined expanded uncertainties 

of the two generators and the hygrometer over this range. Finally, a third set of comparison 

measurements was made against the LFPG over the low-humidity range. This time a 

commercial cavity ring down spectrometer served as the transfer standard hygrometer, which 

measured humidity in units of water mole fraction. The measurements were made over the range 

1 μmol/mol to 5 μmol/mol (−76 °C to −65 °C frost point). To simplify the comparison, air was 

used as the gas source in the LFPG as well as in the HHG. The results, shown in Figure 19, 

agree to within the generators’ expanded uncertainties. The results of these comparisons validate 

the performance of the HHG, showing that it generates correct humidity values to within its 

uncertainties. 
Page 30 of 48 

Figure 18. Comparison of frost points generated by the HHG with those 

generated by the LFPG. The comparisons were made using a second 

chilled-mirror hygrometer as a transfer standard. Here, ΔTFP = TFP-g − TFP-h, 

where TFP-g is the frost point expected from the generator and TFP-h is the 

frost point measured by the hygrometer. 

Figure 17. Comparison of dew points generated by the HHG with 

those generated by the NIST Two-pressure (2-P) generator and the 

NIST Low Frost-point Generator (LFPG). The comparisons were 

made using an uncalibrated chilled-mirror hygrometer as a transfer 

standard. Here, ΔTDP = TDP-g – TDP-h, where TDP-g is the dew point 

expected from the generator and TDP-h is the dew point measured by 

the hygrometer. The uncertainty bars reflect the expanded (k=2) 

uncertainties of the generators and hygrometer. 
Page 31 of 48 

7.2. Gravimetric Hygrometer

In addition to the comparisons reported in the previous section, we performed comparisons 

between the humidity generated by the HHG and that measured by the NIST gravimetric 

hygrometer [21,22]. The gravimetric hygrometer is a primary standard for humidity 

measurement. It determines the mass ratio of water to air in a humid gas sample by separating 

out the water from the gas and subsequently determining the masses of the water and dry air. 

The results of the comparison are shown in Figure 20, which plots Δx/x, where Δx ≡ xGH − xHHG; 

here, xGH is the mole fraction measured by the gravimetric hygrometer and xHHG is that generated 

using the HHG. Here, the saturator pressure was ≈200 kPa for all points except for those where 

log10(x) = −2.7. In this case the saturator pressure was 300 kPa and the saturator temperature 

was 1 °C; these are the saturator parameters used when the HHG is operated in divided-flow 

mode. 

The expanded uncertainty (k = 2) of the mole fraction measurements by the gravimetric 

hygrometer is estimated to be 0.20 % over the range of humidity in the plot. For the hybrid 

generator using the above parameters, the expanded uncertainty is estimated to be less than 

0.08 %, so the combined expanded relative uncertainty of the HHG and gravimetric hygrometer 

is estimated to be Ur(x) ≈ 0.22%. 

Figure 19. Comparison of mole fraction x generated by the HHG with that 

generated by the NIST Low Frost-point Generator. The comparisons were 

made using a commercial cavity ring down spectrometer as a humidity 

transfer standard. Here, Δx = xg – xh, where xg is the mole fraction expected 

from the generator and xh is the mole fraction measured by the hygrometer. 

The uncertainty bars reflect the expanded (k = 2) uncertainties of the 

generators. 
Page 32 of 48 

The values of Δx/x are all within 0.2 % and the averages of the points taken at one value of x are 

all within 0.12 %. This is within the combined uncertainties of the HHG and gravimetric 

hygrometer, showing agreement between the two systems. 

8. Calibration of Hygrometers 

8.1. General Method.

The calibrations are done at specific humidity points as requested by the customer. The hybrid 

generator temperature/pressure parameters are set to generate the desired humidity. For each 

nominal humidity point, a data-acquisition application is used to measure the temperature and 

pressure of the saturator, the pressure inside the hygrometers, and the wet-gas and dry-gas flows 

(if the divided flow method is used); these measurements are used to calculate the humidity 

inside the hygrometers. The application also records the humidity measurement of the customer 

hygrometer and check standard hygrometer. All measurements are recorded in a spreadsheet. 

Once the data is acquired for all requested humidity points, the results are assembled into a 

workbook. The new check standard data is compared to previous check standard data to validate 

the performance of the generator during this set of measurements. The final results comparing 

the customer hygrometer humidity to the HHG humidity are placed in a calibration report. For 

calibrations of chilled-mirror hygrometers measuring relative-humidity, dew-point calibrations 

are made using the generator, and subsequently a comparison calibration is made of the 

temperature probe in a stirred bath [14]. 

Figure 20. Comparison of mole fraction x measured by the NIST 

gravimetric hygrometer with that generated by the HHG. Here, 

Δx ≡ xGH − xHHG, where xGH is the mole fraction measured by the 

gravimetric hygrometer and xHHG is that generated using the HHG. The 

combined expanded (k = 2) relative uncertainties of the gravimetric 

hygrometer and generator are Ur(x) ≈ 0.22 %. 
Page 33 of 48 

8.2. Initial Procedures. 

Before connecting the hygrometers to the hybrid generator, they are checked for cleanliness; any 

noticeable dirt inside a hygrometer or on its fittings is grounds for rejecting the instrument for 

calibration. For the case of chilled-mirror hygrometers, we clean the hygrometer mirrors with 

ethanol. Finally, tests are performed to ensure that calibration points requested for each 

hygrometer are within its measurement range. 

The pressure gauges of the hybrid generator are prepared for operation by correcting the zero 

offset for their readings. This is done by exposing the two gauges to a vacuum to measure their 

zero-offset values. The new values are entered into the data acquisition application to ensure 

accurate pressure measurements during the calibration. 

8.3. Connecting the hygrometers to the hybrid generator.

When connecting the hygrometers to the generator, a bypass tube (with an outlet into the room) 

is connected in parallel with the hygrometers (see Fig. 21). A valve on the bypass tube allows 

control of the proportion of output gas bypassing the hygrometers. As seen in the figure, a gauge 

located between the hygrometers and the bypass valve measures the hygrometer pressure. In this 

configuration, no gas flowing into the hygrometers passes through the line for the gauge. 

If the desired humidity values exceed a frost point of −15 °C (x = 1.6 × 10−3), the hygrometers 

are connected directly to the output of the 2-P generator, at a point downstream of the expansion 

valve, as shown in Figure 1a. If the desired dew point values are above ambient temperature, the 

tubes connecting the output of the generator to the hygrometers are wrapped with heater tape so 

that they can be heated to at least 10 °C above the generated dew point temperature. 

If the desired humidity values are below a frost point of −15 °C, we use the divided flow system, 

with the multiplexer attached to the saturator. The hygrometers are attached to the output of the 

multiplexer, as shown in Figure 1b. 

The tubing used for connecting the generator to the hygrometers is made of electropolished 

stainless steel. The valves and fittings used in the manifold are also made of stainless steel. 

Metal-gasket face-seal fittings may be used over the entire range of the HHG. Compression 

fittings may be used for frostpoints and dewpoints above −40 °C. 

Figure 21. Connections of customer hygrometer and check standard to hybrid generator. 
Page 34 of 48 

8.4. Data Acquisition. 

The order in which the data for the calibration points is acquired is at the discretion of the 

operator. However, for highest efficiency we plan the order so that as many points as possible 

can be taken at one saturator temperature. 

After setting the hybrid generator to generate the desired humidity, a computer application opens 

up a spreadsheet. The application then performs the data acquisition and records the 

measurements for the hybrid generator, check standard, and customer hygrometers in the 

spreadsheet at 30 s intervals for a total of 30 min. Finally, the application averages the 

measurements for the last 20 minutes to give the final values. If the data readings are not stable, 

the application is run again with the same generator parameters. If the readings are still not 

stable, efforts will be made to find and fix the source of the problem. The spreadsheet includes 

plots that monitor the saturator temperature and pressure, as well as the dew/frost point and 

molar fraction of the generator. It also includes plots that monitor the measurements of the check 

standard and customer hygrometers. 

For the calibration points with the highest and lowest humidity values, the computer application 

is run twice to check the repeatability of the hygrometer. If the repeat measurements agree with 

the first measurements to within the historical repeatability for that type of hygrometer, then this 

historical repeatability is assigned to the customer hygrometer. If the repeat measurements do not 

agree, additional uncertainty is added or the hygrometer is rejected, depending on the degree of 

disagreement. For the case of chilled-mirror hygrometers, the dew/frost layer is removed before 

the repeat measurements are made so that a new dew/frost layer will form for the next data set. 

After the first calibration point is completed and the hygrometer repeatability established, 

measurements at the subsequent calibration point are performed only once. An exception to this 

rule is made if the calibration measurement value is anomalous to the group of calibration points 

and appears suspect. 

8.5. Quality Control. 

If the stability and/or repeatability of the hygrometer are significantly worse than the values 

given by the hygrometer specifications and the sources of these problems cannot be corrected, 

the hygrometer is rejected for calibration and returned to the customer. 

As a check on the consistency of the HHG, a check standard (a chilled-mirror hygrometer) is 

attached to the output of the generator as shown in Fig. 21 when performing calibrations. A 

measurement history of the check standard exists for dew/frost points at available multiples of 

10 °C (i.e. −70 °C, −60 °C, ... 70 °C, 80 °C) as well as 84 °C. During the course of a 

hygrometer calibration, comparisons are made of at least two check-standard points. These 

points are preferably at the highest and lowest customer calibration points. If the highest/lowest 

customer calibration points have no check-standard history, additional data is taken at the checkstandard points closest to them. Data acquisition for the check standard is performed as 

described in section 8.4. After the check-standard data acquisition and evaluation is complete, 

the new check standard results are compared to earlier check standard results. If the new check 
Page 35 of 48 

standard measurements differ from the trend line set by the old measurements by more than the 

expanded total uncertainty (k=2) of the HHG and hygrometer, the new results are considered 

suspect, and further investigation must be made to determine the validity of these results. An 

example of a check-standard history plot is shown in Fig. 22. 

At a minimum of once every four months, cross checks are made on the pressure measurement 

and temperature measurement systems for the final saturator to ensure that their measurements 

are within the stated uncertainties. For the two pressure gauges, measurements are first 

performed on a vacuum to measure their zero-offset values and correct for them in the data 

acquisition application. Measurements are then made at ambient pressure to compare the gauges’ 

measured values with those from a calibrated aneroid barometer. If the comparison at ambient 

pressure yields results that are outside of the stated uncertainty, the gauges are recalibrated 

against a piston gauge with a NIST-traceable calibration. For the temperature measurement 

system, the bath temperature measured by the SPRT is compared with that displayed by the bath 

control when the bath is at 20 °C to test for consistency with previous comparisons. In addition, 

the resistance of a second calibrated standard resistor is measured with the SPRT’s resistancemeasurement system to test its integrity. 

Figure 22. Check Standard history plot for a dew point of 84 °C. Here, the 

saturator temperature is Ts = 84 °C. The plot shows the difference ΔTDP

between the dew point temperature measured by the check standard and 

that generated by the HHG as a function of date. The dashed lines 

represent the k = 2 uncertainty limits for the hygrometer repeatability. 
Page 36 of 48 

9. Summary 

We have described here the design and performance of the new hybrid generator at NIST, which 

generates dew/frost-points between −70 °C and 85 °C (mole fractions between 2.5 μmol/mol and 

0.57 mol/mol). This primary generator uses a novel design that incorporates both the twopressure method and divided-flow method; this provides an opportunity to perform validation 

tests on the conventional 2-P method in the low-frost-point range. Between −60 °C and 85 °C 

the dew/frost-point expanded uncertainty is always below 25 mK. Between −70 °C and −60 °C 

the uncertainty is between 25 mK and 60 mK. Over the low frost point range, this uncertainty is 

considerably lower than the uncertainty of most 2-P generators, including that of NIST. Over the 

range −70 °C to −60 °C, the uncertainty of the HHG is larger than the uncertainties for higher 

ranges due to the increasing influence of the uncertainty of xp, which we estimate to be u(xp) = 10 

nmol/mol. Comparison of the expected humidity generated by the HHG with that by other NIST 

generators shows agreement within the expanded uncertainties of the generators and transfer 

hygrometer. Comparison of the expected humidity generated by the HHG with that measured by 

the NIST gravimetric hygrometer also shows agreement within the combined expanded 

uncertainties of the generator and hygrometer. These comparisons provide a satisfactory 

validation of the performance of the HHG. 
Page 37 of 48 

References 

[1] G.E. Scace et al., An Overview of the NIST Hybrid Humidity Generator, in Proceedings 

of the 5th International Symposium on Humidity and Moisture (Rio de Janeiro, Brazil: 

INMETRO, 2007). 

[2] C.W. Meyer et al, Performance and Validation Tests on the NIST Hybrid Humidity 

Generator, in Proceedings of the 10th International Symposium on Temperature and 

Thermal Measurements in Industry and Science (TEMPMEKO 2007), Int. J. 

Thermophys., DOI 10.1007/s10765-007-0342-4. 

. 

[3] A. Saul and W. Wagner, International Equations for the Saturation Properties of Ordinary 

Water Substance, J. Phys. Chem. Ref. Data 16, 893−901 (1987). 

[4] W. Wagner and A. Pruss, International Equations for the Saturation Properties of 

Ordinary Water Substance--Revised According to the International Temperature Scale of 

1990, J. Phys. Chem. Ref. Data 22, 783−787 (1993). 

[5] R.W. Hyland and A. Wexler, Formulations for the Thermodynamic Properties of Dry Air 

from 173.15 K to 473.15 K, and of Saturated Moist Air from 173.15 K to 372.15 K, at 

Pressures to 5 MPa., ASHRAE Trans. 89-IIa, 520−535 (1983). 

[6] A. Wexler, Humidity Standards, Tappi 44 (6), 180A −191 A (1961). 

[7] International Association for the Properties of Water and Steam, Revised Release on the 

Pressure along the Melting and Sublimation Curves of Ordinary Water Substance (2008), 

available at www.iapws.org. 

[8] W. Wagner, R. Feistel, and T. Riethmann, New Equations for the Melting Pressure and 

Sublimation Pressure of H2O Ice Ih. To be submitted to J. Phys. Chem. Ref. Data. 

[9] International Association for the Properties of Water and Steam, Release on the 

Ionization Constant of H2O (2007), available at www.iapws.org. 

[10] A. Picard et al., Metrologia, 45, 149 (2008). 

[11] ASTM Standard E 1137/E 1137M - 04, Annual Book of ASTM Standards, vol. 14.03, 

ASTM International, Conshohocken, PA (2006), 473-479. 

[12] ISO, Guide to the Expression of Uncertainty in Measurement, International Organization 

for Standardization, Geneva (1993). 

[13] B.N. Taylor and C.E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty 

of NIST Measurement Results, NIST Technical Note 1297, National Institute of 

Standards and Technology, Gaithersburg (1994). 
Page 38 of 48 

[14] C.D. Vaughn and G.F. Strouse, The NIST Industrial Thermometer Calibration 

Laboratory, in Proceedings of TEMPMEKO 2001: the 8th International Symposium on 

Temperature and Thermal Measurements, B. Fellmuth, J. Seidel, G. Scholz, eds., VDE 

Verlag GMBH, Berlin (2002), 629-634. 

[15] A. Wexler, Vapor Pressure Formulation for Water in Range 0 to 100 °C, Jour. Res. NBS 

80A, 775−785 (1976). 

[16] R.W. Hyland, A Correlation for the Second Interaction Virial Coefficients and 

Enhancement Factors for Moist Air, Jour. Res. NBS 79A, 551−560 (1975). 

[17] S. Hasegawa and J.W. Little, The NBS Two-Pressure Humidity Generator, Mark 2, Jour. 

Res. NBS 81A, 81−88 (1977). 

[18] G.E. Scace and J.T. Hodges, Uncertainty of the NIST Low Frost-point Humidity 

Generator, in Proceedings of TEMPMEKO 2001: the 8th International Symposium on 

Temperature and Thermal Measurements, B. Fellmuth, J. Seidel, G. Scholz, eds., VDE 

Verlag GMBH, Berlin (2002), 597-602. 

[19] P.H. Huang, Determining Uncertainties of Relative Humidity, Dew/frost-point 

Temperature, and Mixing Ratio in a Humidity Standard Generator, in Papers and 

Abstracts from the Third International Symposium on Humidity and Moisture, National 

Physical Laboratory, Teddington, UK (1998), 149-158. 

[20] J.W. Lovell-Smith, On Correlation in the Water Vapour Pressure Formulation, 

Metrologia 43, 556-560 (2006). 

[21] C.W. Meyer et al., Automated Continuous-Flow Gravimetric Hygrometer as a Primary 

Humidity Standard, in Proceedings of the 5th International Symposium on Humidity and 

Moisture, (Rio de Janeiro, Brazil: INMETRO, 2007). 

[22] C.W. Meyer et al., A Second-Generation NIST Gravimetric Hygrometer, in preparation. 
Page 39 of 48 

Appendix I. Derivation of the Uncertainty Equations for the Hybrid Generator 

The total uncertainty of a quantity z is related to the n individual uncertainty components yi

through the general law of error propagation [12]: 

( ) ( ) ( ) i j

j

n

i

n

j i i

i j

n

i

i

i

u y u y

y

z

y

z

u y r

y

z

u z ∂

∂

∂

∂

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂ = ∑ ∑ ∑

−

= = + =

1

1 1

,

1

2 2 ( ) 2 A1) 

The relevant quantities and the derivatives ∂z/∂yi may be found by expanding the differential dz: 

∑= ∂

∂ =

n

i

i

i

dy

y

z dz

1

. A2) 

Below, the total uncertainty for humidity generated by the hybrid generator will be derived for 

four cases: 1) water mole fraction when the generator is used in 2-P mode or 1-P mode, 2) dewpoint temperature when the generator is used in 2-P mode or 1-P mode, 3) water mole fraction 

when the generator is used in divided-flow mode, and 4) frost-point temperature when the 

generator is used in divided-flow mode. 

1. Water Mole Fraction When the Generator is Used in 2-P Mode or 1-P Mode

The total uncertainty for this case is obtained by applying Eq. A2 to Eq. 1, which yields 

2 s

s

s s

s

s

s

s

s

s dP

P

e f df P

e de

P

f dx = + − . A3) 

where fs ≡ f(Ts,Ps) and es ≡ e (Ts,Ps). In des, we can separate out the differential relating to the 

uncertainty of its calculating equation calc des from that relating to the uncertainty of the 

temperature from which it is calculated: 

s

s

calc s

s s dT

dT

de de = de + . A4) 

Similarly, in dfs, we can separate out to the differential relating to the uncertainty of its 

calculating equation calc dfs from that relating to the uncertainty of the temperature and pressure 

from which it is calculated: 

s

s

s

s

s

calc s

s s dP

dP

df dT

dT

df df = df + + . A5) 

However, because fs ≈ 1, dfs/dTs and dfs/dPs are very small and so Eq. A5 may be approximated 

as calc dfs ≈ dfs . Using these two approximations while combining Eqs. A3−A4 gives 
Page 40 of 48 

calc

s

s

calc s

s

s

2 s

s

s

s

s

s

s

1 1 df P

e

de

P

dP

P

e

dT

dT

de

P

dx = − + + . A6) 

The uncertainty in the mole fraction may then be expressed as 

( ) ( ) ( ) ( )2 calc

s

2

s

s 2 calc

s

2

s

2

s

2

2

s

2 s

s

2

s

s

s

2 1 1 ( ) u f P

e

u e

P

u P

P

e

u T

dT

de

P

u x ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = . A7) 

2. Dew-point Temperature When the Generator is Used in 2-P Mode or 1-P Mode

Here we consider the total uncertainty for the dew point temperature TDP in a chamber with 

temperature Tc = TDP, pressure Pc, and water vapor pressure ec. This uncertainty may be 

determined by inverting Eq. A4 to solve for dTs and then substituting the saturator parameters 

with the chamber parameters (Ts with TDP, es with ec, and calc

s e with calcc e ): 

[ ]( ) calc

c c

c DP

DP c /

1 de de

de dT

dT = dT = − . A8) 

Letting fc ≡ f(Tc, Pc), we can express ec in terms of x and Pc: 

c

c

c f

xP

e = . A9) 

Differentiating Eq. A9 and inserting the resulting expression for dec in Eq. A8 gives 

[ ] ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ = + − − calc

2 c c

c

c

c

c c

c

c DP

DP /

1 df de

f

xP dP

f

x dx

f

P

de dT

dT . A10) 

Using the approximations fc ≅ 1 and calc df c ≅ df c in Eq. A10 and combining it with Eqs. 1 and 

A6 and yields 

[ ]

( ) ⎥

⎦

⎤

+ − +

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − + −

c

c

calc c

c

calc

c s

calc

c

calc

s

s

c

2 s

s

c s

s

s

s

s

c

c c

DP /

1

dP

P

e

e df df

de de

P

P dP

P

P e dT

dT

de

P

P

de dT

dT

. A11) 

Recognizing that x is the same in both the saturator and chamber, s s c c e / P ≅ e / P , and so A11 

may be written 
Page 41 of 48 

[ ]

( ) ⎥

⎦

⎤

+ − +

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − + −

c

calc c

c

calc

s

c

calc

c

s

calc

s

s

s

s

s

s

c DP s

c

DP

1

/

P

dP df df

e

de

e

de

P

dP dT

dT

de

de dT e

e dT

. A12) 

This equation can be simplified by defining the differentials 

c

calc

c

s

calc

calc s

e

de

e

de dΔe ≡ − and A13) 

calc

c

calc

s

calc dΔf ≡ df − df . A14) 

Then Eq. A12 becomes 

[ ] ⎥

⎦

⎤ ⎢ + Δ +

⎣

⎡ = − + Δ

c

calc calc c

s

s

s

s

s

c DP s

c

DP

1

/ P

dP d e d f P

dP dT

dT

de

de dT e

e dT . A15) 

And the uncertainty of the dew point temperature is 

( ) [ ] ( ) ( ) ( ) ( )( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ + + Δ + Δ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = 2 calc

r

2 calc

2

c

2

c

2

s

2

2 s

s

2

s

s

s

2

c DP

2 c

DP

1

/

u f u e

P

u P

P

u P

u T

dT

de

de dT e

e

u T A16) 

The uncertainties ( ) calc

u Δf and ( ) calc u Δe have not been resolved by the humidity community, 

and it is currently an area of active work [20]. Because of this, we use in this document the 

conventional analysis [20]. When the generator is used in 1-P mode (Ps ≅ Pc), this method 

assumes that ec ≅ es and fc ≅ fs, and therefore 

( ) ( ) 0 calc calc

u Δer = u Δf = A17) 

 For the 2-P mode (Ps ≠ Pc), the method assumes that there are no correlations between ( ) calc

s u e

and ( ) calc

c u e and between ( ) calcs u f and ( ) calcc u f ; therefore 

( ) ( ) ( )

2

c

2 calc

c

2

s

2 calc

s 2 calc

r

e

u e

e

u e

u Δe ≡ + and A18) 

( ) ( ) ( )

2 calc

c

2 calc

s

2 calc

u Δf ≡ u f + u f . A19) 
Page 42 of 48 

3. Relative Humidity When the Generator is Used in 2-P Mode or 1-P Mode

Here we consider the total uncertainty for the relative humidity RH in a chamber with 

temperature Tc, pressure Pc when the generator is used in 2-P or 1-P mode. The relative 

humidity is defined as 

c

p

e

e

RH ≡ , A20) 

where the partial water vapor pressure ep in the chamber is given by 

c

c

p f

xP

e = A21) 

and ec is the saturated water vapor pressure for the chamber at temperature Tc. Note that ec is a 

function of Tc, while ep is an independent variable. Placing Eq. A21 into Eq. A20, 

c c s

s s c

c c

c

e f P

e f P

e f

xP

RH ≡ = , A22) 

The total uncertainty for this case is obtained by applying Eq. A2 to Eq. A21, which yields 

c

c s

2

c

s s c

2 s

c c s

s s c

c

s

2

c c

s s c

c

c c s

s s

s

c c s

s c

s

c c s

s c ( ) de

e f P

e f P dP

e f P

e f P df

e f P

e f P dP

e f P

e f df

e f P

e P de

e f P

f P d RH = + + − − − . A23) 

Recognizing that 

dT

dT

de

de = de + calc A24) 

and by approximating fs = f c ≅ 1, A22 becomes 

⎥

⎦

⎤ ⎢

⎣

⎡ − − − +

⎥ + +

⎦

⎤ ⎢

⎣

⎡ = +

c

c

calc c

c

s

2

c

s c

2 s

c s

s c

c

c s

s c

c

s c

s

s

s c

s c

s

s

calc s

s

s c

c ( )

dT

dT

de de

e P

e P dP

e P

e P df

e P

e P

dP

P e

e df P ee P dT

dT

de de

P e

P d RH

. A25) 

Inserting Eqs. A13 and A14 yields: 
Page 43 of 48 

⎥

⎦

⎤ ⎢

⎣

⎡ = + − − + Δ + Δ

= + − − + Δ + Δ

dT d e d f dT

de

P e

dP

P

dP dT

dT

de

P e e

P e

d f

e P

e P d e

dT

de

e P

e P dT

dT

de

e P

e P dP

e P

e P dP

P e

e dT

dT

de

P e

P d RH

calc

c

c

c

s c

s

c

c

s

s

s

s c s

c s

c s

calc s c

c

c

c s

s c

c

c

c

s

2

c

s c

2 s

c s

s c

c

s c

s

s

s

s

s c

c

1 1

( )

. A26) 

Remembering s s c c e / P ≅ e / P , the uncertainty for the relative humidity is then 

 

( ) ( ) ( )

( ) ( )( ) ⎥

⎥

⎦

⎤

+ Δ + Δ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎢

⎢

⎣

⎡

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

2 calc 2 2 calc

c

2

c

c

c

2

2 s

s

2

2 c

c

2

s

2

s

s

s

2

1

1 1 1 ( )

u T u e u f dT

de

e

u P

P

u P

P

u T

dT

de

e

u RH

 A27) 

Once again, the values of ( ) calc u Δe and ( ) calc u Δf are best estimated by Eq. A16 when the 

generator is used in 1-P mode and by Eq. A17 and Eq. A18 when the generator is used in 2-P 

mode. 

4. Water Mole Fraction When the Generator is Used in Divided-flow Mode

For the generator used with the divided-flow method, the differential for the mole fraction may 

be expanded as 

( ) ( )

2 p

s s p

2 s

s s p p p s p dn

N

n x x

dn

N

n x x

N

n dx n dx

dx & &

& & &&

&

& & − − − +

+ = A28) 

Since xp « xs, this reduces to 

2 p

s s

2 s

p s

p

p

s

s dn

N

n x dn

N

n x

dx

N

n

dx

N

n dx & &

& & &

&

&

&

&

& ≅ + + − A29) 

Using the result of Eq. A6 as dxs, and noting xs ≅ es / Ps , this becomes 

p

s

2

s s

s

s

2

p s

p

calc p

s

s

calc s s

s

s

s

2 s

s

s s

s

s

s

s

s dn

N P

n e dn

N P

n e

dx

N

n

df NP

n e de

NP

n dP

NP

n e dT

dT

de

NP

n dx & &

& & &

&

&

&

&

&

&

&

&

&

&

& ≅ − + + + + − A30) 

Noting that s s NPs x n e & ≅ & and s s Ps x ≅ e , the mole fraction uncertainty is then 
Page 44 of 48 

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

⎥

⎥

⎦

⎤

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ + ⎠

⎞ ⎜

⎝

⎛ + + −

+ ⎢

⎢

⎣

⎡

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

≅

2

2

s

2

s

2

p

2

s

2

2

p

2 calc

2 s

s

2 calc

s

2

s

2

2 s

s

2

s

s

s

2 2

1

1

N

u n

x

u x

x

x

N

u n

u f

e

u e

P

u P

u T

dT

de

e

u x x

&

&

&

&

 A31) 

5. Frost-point Temperature When the Generator is Used in Divided-flow Mode

In the hybrid generator, the divided flow method will only be used for generating frost points. 

We expand the frost-point temperature differential by combining Eqs. A10 and A30, which 

yields 

[ ]

⎥

⎦

⎤

+ + + + − −

⎢

⎢

⎣

⎡ = − + +

calc

c

c

calc

p c

s

2

s s

s

s

2

p s

p

p

calc

s

s

calc s s

s

s

s

2 s

s

s s

s

s

s

s

s

c c

c

FP

1

/

de

P

dn xd xdf N P

n e dn

N P

n e

dx

N

n

df NP

n e de

NP

n dP

NP

n e dT

dT

de

NP

n

de dT

P dT

& &

& & &

&

&

&

&

&

&

&

&

&

&

&

 . A32) 

Here ec is the saturated vapor pressure for ice. Because of this, we assume no correlation 

between the uncertainties of calc

c e and calcs e , since calcs e is the calculation of the saturated vapor 

pressure for water and is different for that of ice. Using the definition for calc Δf in Eq. A14, and 

noting that s s NPs x n e & ≅ & and s s Ps x ≅ e , Eq. A32 becomes 

[ ]

⎥

⎦

⎤

+ + + − + Δ

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ +

⎠

⎞ ⎜

⎝

⎛ = − + −

calc

c

calc

c

s

calc

s

c

p c

s

s

s p

s

s

s

s

s

c c s

c

FP 1 1

/

d f xP

de

e

de

P

dP

N

dn

N

dn

x

dx

x

x

P

dP dT

dT

de

de dT e

xP dT

&

&

&

&

 A33) 

The frost-point temperature uncertainty then becomes 

( ) ( )

[ ] ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ⎥

⎥

⎦

⎤

+ + + + + Δ

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ +

⎠

⎞ ⎜

⎝

⎛ + + − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

2 calc

2

c

2 calc

c

2

s

2 calc

s

2

c

2

c

2

2

p

2

2

s

2

s

2

p

2

s

2

s

2

2 s

s

2

s

s

s

2

c c

2

2 c

FP 1 1

/

u f

xP

u e

e

u e

P

u P

N

u n

N

u n

x

u x

x

x

P

u P

u T

dT

de

de dT e

xP

u T

&

&

&

&

 A34) 

Here, we once again use the conventional method for estimating ( )

2 calc u Δf , which employs 

Eq. A18. 
Page 45 of 48 

6. Relative Humidity When the Generator is Used in Divided-flow Mode

Here we consider the total uncertainty for the relative humidity RH in a chamber with 

temperature Tc and pressure Pc when the generator is used in divided-flow mode. From Eqs. 

A20-A22, the relative humidity is 

c c

c

e f

xP

RH ≡ , A35) 

and so 

( ) 2 c

c c

c

c

c

2

c

c

c

c c c c

c df

e f

xP de

e f

xP dP

e f

x dx

e f

P d RH = + − − A36) 

Inserting Eq. 6, Eq. A24, and Eq. A30 and into Eq. A36 yields:

( )

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − − − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ −⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ +

⎠

⎞ ⎜

⎝

⎛ = − + + + −

c

calc

c

c

c

c

c

c c

c

p

p

c

c

s p

s

calc s p

s

s

calc

s

s

s

s

s

s

c s

c

1 1

1 1

de df

e

dT

dT

de

P e

dP

x

N

n

x

e

P

N

dn

N

dn

x

dx

x

x df

e

de

P

dP dT

dT

de

e e

xP d RH

&

&

&

&

&

&

 A37) 

The uncertainty for relative humidity is then: 

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( )

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎥

⎥

⎦

⎤

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ + ⎠

⎞ ⎜

⎝

⎛ + + −

⎢

⎢

⎣

⎡

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⎥

⎦

⎤ ⎢

⎣

⎡ =

calc 2

2 c

c

calc 2

2 c

c

2

c

c

c

2

c

2

c

2

p

p

2

c

c

2

2

p

2

2

s

2

s

2

p

2

s 2 calc

s

2

s

2 calc

s

2

s

2

2 s

s

2

s

s

s

2

c

2 c

( ) ( ) ( ) 1

1

1

u f

e

u e

u T

dT

de

P e

u P

x

N

n

x

e

P

N

u n

N

u n

x

u x

x

x

u f

e

u e

P

u P

u T

dT

de

e e

xP

u RH

&

&

&

&

&

& 38) 
Page 46 of 48 

Appendix II. Uncertainty Element Subcomponents for the Hybrid Generator 

 Source of uncertainty Standard Uncertainty Unit 

Saturation efficiency 0.5 mK 

Saturator

Bath 

gradients 

1 (T ≤ 40 °C) 

0.16T/°C – 5.4 (T > 40 °C) mK 

 Air contamination < 0.2 mK 

Saturator Water contamination < 0.2 mK 

Temperature Stability 1 mK 

Ts Calibration 0.5 mK 

SPRT Drift 0.3 mK 

 Self-heating 0.1 mK 

 Bridge Calibration 0.1 mK 

 Resolution 0.1 mK 

Calibration 7 Pa 

 Drift 10 + 0.0001 Ps/Pa Pa

Saturator Pressure Resolution 7 Pa

Pressure gauge Hydrostatic head 1 Pa

Ps Flow effect 2 Pa

 Repeatability 7 Pa 

Throttle 

Valve 

Ps 

stability 

7 (Ps ≈ ambient pressure) 

20 (Ps > ambient pressure) Pa 

 Calibration 7 Pa

 Drift 5 Pa

Chamber Pressure Resolution 7 Pa

Pressure gauge Hydrostatic head 1 Pa

Pc Flow effect 2 Pa

 Repeatability 7 Pa

 Pc stability 7 Pa 

Table 2. Subcomponents for the uncertainty elements Ts, Ps, and Pc
Page 47 of 48 

Sample Calibration Report 

UNITED STATES DEPARTMENT OF COMMERCE 

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY 

GAITHERSBURG, MARYLAND 

REPORT OF CALIBRATION 

DEW-POINT HYGROMETER 

DPH Systems S/N 28637 

Submitted by 

Humidity Measurement Instruments 

Peoria, IL 61615 

The dew-point hygrometer was calibrated by comparison against air of known moisture content, generated by the NIST 

Hybrid Humidity Generator. The hygrometer mirror was cleaned using ethanol before the calibration. Subsequently, 

the outlet from the generator was connected to the inlet of the hygrometer using a 1/4-inch (0.635) diameter stainless 

steel tube. The dew points generated during the calibration ranged from −70 °C to 20 °C. For each calibration point, 

the following procedure was used. The generator was set to produce humidified air with a flow of 30 standard liters per 

minute (SLM), and 0.5 SLM of this air was set to pass through the hygrometer. Once the flow started, humidity 

measurements were made with the hygrometer to determine when the readings reached a steady state. Once a steady 

state was reached, the determined values of the generated humidity were averaged over a period of 20 minutes, as were 

the values of the humidity on the hygrometer display. These average values are presented below in Table 1 for all 

calibration points. A minimum of six calibration data sets was taken for the first calibration point for the determination 

of the repeatability of the hygrometer. The standard uncertainty due to repeatability, as represented by the standard 

deviation of the final values of these data sets, was determined to be 0.02 °C. The generator and the complete 

calibration procedure are described in NIST SP250-xx, entitled “Calibration of Hygrometers with the Hybrid Humidity 

Generator”, which may be found at http://ts.nist.gov/MeasurementServices/Calibrations/upload/SP250-xx.pdf. 

The uncertainty of the calibration includes the uncertainty of the moisture content of the gas generated by the Hybrid 

Humidity Generator and that due to the measurement repeatability of the hygrometer. The uncertainty is expressed as 

an expanded relative uncertainty U = kuc , with U determined from a combined standard uncertainty uc and a coverage 

factor k = 2. The values of U are dependent on the individual calibration parameters. A discussion of the uncertainty 

components for the calibration and a presentation of the total uncertainties as a function of the calibration parameters is 

provided in NIST SP250-xx. Values of U are provided in Table 1 for each calibration point. 

Measurements and analysis performed by: For the Director 

Peter Huang National Institute of Standards and Technology 

 Dr. Dean Ripple 

 Leader, Thermometry Group 

 Process Measurements Division 

Test No. 274-999 

Measurements performed on September 20, 2007 

Service ID: 36070S 

Report Date: September 21, 2007 
Page 48 of 48 

Table 1 

Humidity Measurement Instruments Dew-point Hygrometer 

DPH Systems S/N 28637 

 Dew/frost-point S/N 28637 U 

 Temperature Reading (k = 2)

 [°C] [°C] [°C] 

 20.05 19.87 0.02 

 10.02 10.12 0.02 

 0.03 0.03 0.02 

−10.01 −10.11 0.03 

−20.02 −20.00 0.03 

−29.96 −30.01 0.03 

−39.99 −40.12 0.04 

−49.95 −50.14 0.04 

−59.95 −60.09 0.04 

−70.00 −70.14 0.05