1388 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME II NOTES AND CORRESPONDENCEA Method for Rescaling Humidity Sensors at Temperatures Well below Freezing P. S. ANDERSON British Antarctic Survey, Cambridge, United Kingdom 20 December 1993 and 3 March 1994 ABSTRACT A method for extending the calibrated temperature range of a solid-state capacitive humidity sensor is presented. This technique is applicable to relative humidity instruments that are based around solid-state sensors.1. Introduction During 1991, the second field phase of the StableAntarctic Boundary Layer Experiment (STABLE 1I)was run at the British Antarctic Survey's Halley station(75-36'S, 26-42'W) on the Brunt Ice Shelf. VaisalaHMP35A humidity instruments were used during theexperiment to measure relative humidity (RH) andtemperature within the lowest 8 m of the boundarylayer. The instruments were mounted in naturallyventilated rad/afion shields (Vaisala type 2212). Halleyexperiences temperatures from +5- to -50-C and at~though these instruments are capable of operating overthis range, they are only within the manufacturer's calibration between -20- and +65-C. This paper presentsa technique for improving the calibration of theHMP35A at low temperatures. This technique shouldbe applicable go other solid-state humidity sensors.2. Properties of the HMP35A sensor The HMP35A humidity sensors axe based on theVaisala Humicap, ~ a capacitive device that is sensitiveto RH (Mesi~i 1993 ). The instrument incorporates theHumicap in a capacitance bridge followed by bothtemperature compensation and linearization circuitsto give a final voltage output proportional to RH overa specified temperature range. A 100f~ platinum resistance thermometer (PRT) is incorporated alongsidethe Humicap in the sensor head but is electhcally sel>arate from the rest of the instrument.t Humicap is a registered trademark of Vaisala, Oy, Finland. Corresponding author address.' Dr. P. $. Anderson, mi~h AntarcticSurvey, High Cross, Madinglcy Road, Cambridge, CB30ET UnitedKingdom. Relative humidity ~s the ratio of water vapor pressureto the vapor pressure for saturated air, expressed as apercentage: = x 1oo%. (l)Above 0-C the saturated vapor pressure P~t is the pressure exerted by water vapor in equilibrium with a planesurface of pure water. Below 0-C two definitions ofsaturated vapor pressure are possible depending onwhether the vapor is in equilibrium with liquid wateror ice. Since ice supports a lower Psat tharl water at thesame temperature, RH values below 0-C must be deofined as being measured with respect to water (RHw)or with respect to ice (RHt). In general RHw < RH~at the same temperature. The -aisala instruments are calibrated to measureRH with respect to water at all temperatures in accordance with the World Meteorological Office standardfor recording RIt. Saturated vapor pressure curves forvapor over water and ice are shown in Fig. 1.3. Method o~adjustraent The Vaisala HMP35A is factory calibrated to giveRHw and can be converted to give RH~ by multiplyingthe measurements by the ratio of the two saturatedvapor pressures. This ratio is a function of temperatureas shown in Fig. 1. Figure 2 shows the raw data from one HM?35Aplotted against temperature, with Fig. 3 showing thesame data corrected ~o give RH~. Each record shownis an hourly average o- RI-I with a total of around 3500records available for the analysis. The Humicap sensoremployed by the HMP35A instrument does not per-fectly mimic the evaporative properties of water overall temperatures, so the capacitance of the sensor is ac 1994 American Meteorological SocietyOCTOBER 1994 NOTES AND CORRESPONDENCE 1389900800 700~ 600~ 500r.~~ 400m~ 300 2001000 tri,lepoint (/ ~waV.-50 -40 -30 -20 -10 0 temperature (oc)FIG, 1. Pressures of saturated water vapor with respect to water and ice, and their ratio.1.6 1001.5 901.4 801.3~. 701.2 ~ 60 1.1' 110weak function of temperature as well as RH. TheHMP35A incorporates a quadratic temperature correction to ensure accurate output from the instrumentfrom -20- to +65-C, the correction being applied byan active filter within the instrument. The Humicaptemperature correction required over the extendedtemperature range from -60- to 180-C is shown in1009080~ 70~.' 60 504030 -5( -45 -40 -35 -30 -25 -20 -15 -10 -5 temperature (oc) FIG. 2. Relative humidity from the HMP35A humidity sensor. Inpr/nciple, this sensor should be closest to linearity in RH with respectto water.504030 -50 -45 -40 -35 -30 -25 -20 -15 -10 temperature (oc) FIG. 3. Values for RH with respect to ice, recalculated from the values of Fig. 2 using data of Fig. 1.Fig. 4 as a sixth-order polynomial [data supplied byVaisala (U.K.) Ltd.] However, within the calibratedrange of the HMP35A, this correction is adequatelyapproximated by a quadratic, as shown by the dashedcurve in the same figure. The higher-order polynomial correction can be applied to the uncorrected instrument to increase its cal1.60.8-100 -50 0 50 100 150temperature (oc) FIG. 4. Humicap correction curve together with the quadratic fit between -20- and +65-C. quadratic fit :' 1: ~ c-~2recti-n ~ calibrated range o~ ~he HMP35A, , , , I , , , , I , , , ~ I , , , , I , , , , I , , , , 2001390 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME llibrated temperature range. However, the exact correc- 110tion already applied to the HMP35A is needed beforethe raw output can be calculated and the new correction 100applied. Since this information was not available, analternative method was developed to extend the cali- 90brated operating temperature range of the partiallycorrected HMP35A.Figures 2 and 3 clearly show that at all temperatures .~ 80there is a maximum value of RH that can be measured, qA lack ofnudeation sites or the presence of supercooled ~ 70water fogs may cause air below 0-C to be supersatu- ~rated with respect to ice; such conditions often occur ~ 60at Halley (Anderson 1993). However, solid objects,including humidity sensors, act as nucleation sites for 50moisture and hence acquire a porous ice coating. Airdiffusing through this coating to the surface of the sen- 40sor will be saturated with respect to ice at the probetemperature, and thus the probe will be at !00% RH~;hence, the HMP35A will never experience supersatu- 30rated humidities. -5(The second temperature correction can be calculatedfrom this upper cutoff in RH~ and can then be used torescale all the RH values over the whole temperaturerange of the data. The first step involves finding a function of temperature, RHmax (T), that mimics the behavior of the maximum of RH~. To estimate the maxima, the data were sorted by temperature and thengrouped into sets of 100 readings. The 95th percentileof each group was found; this gives the RH~ value ineach group, which splits the readings into 5% aboveand 95% below the split point. With the highly skewed100 80 75 70 ~ I ,,~ I ,,,'~,,,~,,,,,~,~ .... ' .... -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 temperature (oc) FiG. 5. The RH~(T) for two of the five STABLE HMP35Ainstruments along with the quadratic approximations fitted by leastsquares. Results for the other three HMP35As lie between these curves. ,,, I ,,,,I,~ t,l,,,, I*,,,l ~,~ I ,,,, I,,, , I, !_~. -45 -40 -35 -30 -25 -20 -15 -10 -5 temperature (0C)F1G. 6. The relative humidities of Fig. 3 after rescaling by the quadratic fit of Fig. 5.scatter of the data within each group, this method foundthe RHt value dose to the maximum within each groupbut was not biased by occasional (possibly spurious)high readings. There are comparatively few records fortemperatures below -40-C, where the required temperature correction will be largest. Figure 3 implies thatthe instrument sensor was ice coated whenever temperatures were below -35-C, which is borne out byobservation; the low temperatures .were usually accompanied by rime deposition. All the individualreadings below -45 -C were assumed to be 100% RH~and were included in the rescaling. Any averaging: ofthese few points would have spread over an unacceptable temperature range and hence increased the errorin the 100% RH point. Figure 5 shows the resultingdata points from two of the STABLE instruments andthe quadratic approximation to RHmax(T) fitted byleast-squares method. The two datasets demonstratethe sensor-to-sensor variation seen in RHm~x (T); eachinstrument therefore requires an individual correctioncurve. The large number of initial records availablespread over a wide temperature range produces aclosely packed series of RHm~x(T) values by thismethod. If fewer initial data were available then ~Lhenumber of bins would be reduced. I suggest that the100-record-per-bin criterion is near optimal and shouldnot be reduced to increase the number of RHm~x(T)values. In Fig. 5 the scatter of RH~ax(T) values awayfrom the quadratic fit is small, and I expect that withsimilar data this technique would work acceptably withas few as 10 bins, thus requiring 1000 initial records.OCTOBER 1994 NOTES AND CORRESPONDENCE 1391 As the technique only determines the error inRHma~(T), the rescaling procedure to correct all RHdata is somewhat arbitrary. For instance, 100%RHm~(T) could be added to each RH value, whichassumes the error was an offset. It is most likely thatthe error is in the gain of the instrument (Lars Stormbom, Vaisala Oy, personal communication), as this isthe case for the original correction shown in Fig. 4,and so the data were multiplied by 1/RHm~(T) torescale the maximum observed humidity to 100%. Figure 6 shows the rescaled data with an excellentagreement of maximum RHz = 100% down to -45-C.Correction curves resulting from fitting a higher-orderpolynomial to RHm~x(T) gave a poorer agreementnear 0-C.4. Conclusions The useful working range of the ItMP35A sensorcan be extended to -40-C by application of a simpleprocedure based only on the instrument response tosaturated conditions. Since the correction procedure issomewhat arbitrary, its performance should be verifiedby intercomparing the corrected HMP35A with an absolute instrument such as a frost-point hygrometer.REFERENCESAnderson, P. S., 1993: Evidence for an Antarctic winter coastal po lynya. Antarctic Sci., 5, 221-226.Mesiii, H., 1993:Humicap--20 years of excellence. Vaisala News, 129,