The Psychrometric Constant Is Not Constant - American ...

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The Psychrometric Constant Is Not Constant: A Novel Approach to Enhance the Accuracy and Precision of Latent Energy Fluxes through Automated Water Vapor Calibrations H. W. LOESCHER Science Office, National Ecological Observatory Network, and Institute of Alpine and Arctic Research, University of Colorado at Boulder, Boulder, Colorado

C. V. HANSON College of Forestry, Forest Science, Oregon State University, Corvallis, Oregon

T. W. OCHELTREE Stable Isotope Mass Spectrometry Laboratory, Division of Biology, Kansas State University, Manhattan, Kansas (Manuscript received 15 January 2009, in final form 14 April 2009) ABSTRACT Numerous agencies, programs, and national networks are focused on improving understanding of water and energy fluxes across temporal and spatial scales and on enhancing confidence to synthesize data across multiple sites. Enhancing the accuracy and precision in the surface energy balance and the latent energy (lE) flux lies, in part, with being able to uniformly calibrate water vapor measurements at and among sites to traceable standards. This paper examines (i) the traceable physical controls on field applications of chilledmirror hygrometers and (ii) an automated means to accurately and precisely calibrate infrared gas analyzers for water vapor concentrations and eddy covariance (lE) data. The environmental physics and gas handling were examined in a theoretical and applied manner that found that chilled-mirror technologies can be a robust measure of dewpoint temperatures and ambient water vapor only if the unit conversions are accounted for between inlet and body temperatures. Psychrometers were also examined and a functional relationship (exponential) was developed for the psychrometric constant against the wet-bulb temperature depression (Tdb 2 Twb), g 5 (5.71 3 105 ) 1 (5.48 3 104 )(1 0.66T dbT wb ) across a wider range of temperature depressions than previously reported. These empirical estimates of the psychrometer constant for small temperature depressions are much lower than other reported values—that is, ;0.000 52 K21 for a wet-bulb temperature depression (Tdb 2 Twb) of 4.3 K.

1. Introduction Ever since Empedocles described the four basic elements in the fifth century BCE, scientists have studied water vapor in the atmosphere and how it is transported throughout terrestrial and aquatic ecosystems (Wright 1981; Waterfield 2000). Eddy covariance (EC) is a direct, robust, nondestructive micrometeorological approach derived through the simplification of the conservation equation (Loescher et al. 2006; Baldocchi 2003; Shen

Corresponding author address: Hank Loescher, Science Office, National Ecological Observatory Network, 5340 Airport Blvd., Boulder, CO 80301. E-mail: [email protected] DOI: 10.1175/2009JHM1148.1 Ó 2009 American Meteorological Society

and Leclerc 1997; Kaimal and Wyngaard 1990) and is often used to estimate the net ecosystem exchange of water vapor—that is, latent energy (lE) fluxes (cf. Montieth and Unsworth 1990)—through the addition of above-canopy turbulent exchange and the change in H2O storage in the canopy air space [i.e., the temporal change in water vapor concentration integrated from ground level to the point of measured turbulent exchange; cf. Loescher et al. (2006), term I Eq. (1a) therein]. Comparisons of lE fluxes between the AmeriFlux Portable Eddy Covariance System (PECS; Ocheltree and Loescher 2007) and those at respective AmeriFlux sites show a large range of difference with a nonnormal distribution and a large amount of outliers (Fig. 1), suggesting that it is possible to enhance the

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FIG. 1. Frequency distribution depicting the percent deviation of (a) water vapor and (b) lE flux. Water vapor and lE flux estimates were normalized for comparison purposes at 20 (mmol H2O) mol21 and 500 W m22, respectively. Data are from AmeriFlux site comparisons using the PECS as the transfer standard (Ocheltree and Loescher 2007). Open bars indicate data from sites with apparent calibration or operating error from site instrumentation that was resolved after the comparison. Estimates are reported as median (61 SD). Note the nonnormal distributions.

accuracy and precision in lE flux by uniformly calibrating traceable water vapor measurements across the entire network. This has large implications in our ability to manage the accuracy and precision in lE fluxes among temporal and spatial scales required for other networks and programs, for example, the National Oceanic and Atmospheric Administration (NOAA)– Global Energy and Water Cycle Experiment (GEWEX), the National Science Foundation (NSF)–National Ecological Observatory Network (NEON), the NSF–Water and Environmental Research Systems (WATERS), and the Consortium of Universities for the Advancement of Hydrologic Science, Inc. (CUAHSI; Loescher et al. 2007; Sarmiento et al. 1999; Wofsy and Harriss 2002; Bolin et al. 1995; Houghton et al. 2001). Large coefficients of variation among short-term, 30-min flux aver-

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ages and among longer-term, interannual studies (Sierra et al. 2009) challenges our ability to detect trends—and have confidence in the processes that control lE flux. For both process level and decadal-scale studies, all sources of error (including sampling error and analytical error) for annual measurements must not exceed 10%. This sets an upper limit for calibration and validation in the sum of measurements that ensemble into lE estimates. Open- and closed-path infrared gas analyzers (IRGAs) are used to measure concentrations of water vapor because they operate at $10 Hz, the speed at which lE is transported by turbulence and required by the EC technique. IRGAs are subject to zero and span drift. Drift in closed-path IRGAs can occur on the order of hours to days, whereas precision of open-path IRGAs may be more stable over long periods (e.g., for several weeks) but they subject to significant inaccuracies in the span drift on the daily time scale. Manufacturers recommend field calibration approximately every three days; however, in practice, this is often not done at field sites because it requires significant technician time. IRGA calibrations require a zero (reference) gas, typically N2 or H2O-free air and (at least) two known standards of H2O (span) vapor, commonly provided by a precision dewpoint generator. Estimates of EC are less sensitive to calibration offsets in the zero calibration compared to changes in the span calibration—that is, gain function (cf. Ocheltree and Loescher 2007). Field calibrations are hampered by several issues: (i) researchers do not have the human resources to make the calibrations at the recommended intervals; (ii) researchers do not have a precision dewpoint generator; and (iii) calibration with the zero air needs to be made prior to the span that results in difficulty in maintaining a stable supply of H2O span gas because adsorption of water to tubing walls can take hours to equilibrate. Closed-path IRGAs also need to be calibrated at the same cell pressures as experienced during normal field operation; however, dewpoint generators have physical limitations, making this requirement difficult to achieve consistently. Open-path lE fluxes also need to be corrected for density fluctuations (Webb et al. 1980; Leuning 2004), which rely on accurate water vapor estimates. The objectives of this study were to determine (i) the traceable physical controls on field applications of chilledmirror hygrometers and (ii) an automated means to accurately and precisely calibrate IRGAs for water vapor concentrations, to provide more robust lE estimates. A few types and models of instrumentation were examined to test these objectives; however, this study is not an endorsement for any particular sensor or manufacturer.

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2. Methods To examine the stability, accuracy, and precision of water vapor concentrations, we used a loggable psychrometer, two models of field deployable chilled mirrors, and a laboratory-quality chilled-mirror hygrometer, which were then used to develop a new technique to automate IRGA H2O calibrations. The portable nature of the loggable psychrometer and field deployable chilled mirrors informed, in part, the choice of sensors—for example, no extra field building was needed when using a tunable diode laser.

a. Theoretical considerations There have been numerous derivations combining equations of state, ideal gas law, and the Van der Waals equation to estimate the maximum amount of water vapor held in air as a function of air temperature and pressure. Results from these equations typically vary ;1%, and here we use a commonly accepted formulation for the range of ambient air temperature, from 08 to 1008C (Buck 1981; Jones 1991),

bT x , es 5 f a exp Tx 1 c

(1)

where es is the saturated (or maximal) vapor pressure in air (kPa) at a given aspirated temperature Tx (8C); a, b, and c are derived coefficients 0.611 21, 17.502, and 240.97, respectively; f is the ‘‘enhancement factor’’ 5 1.0007 1 P(3.46 3 1025); and P is atmospheric pressure (kPa). The subscript x designates whether aspirated air temperature was from dry-bulb (db), wet-bulb (wb), or dewpoint (dp) temperatures. Ambient vapor pressure from the psychrometer was calculated using (rf. Campbell and Norman 1998) ea 5 es (wb) gt P(T db T wb ),

(2)

where ea is ambient vapor pressure (kPa), es(wb) is the saturation vapor pressure at wet-bulb temperature (kPa), and gt is the theoretical psychrometric constant (K21) gt 5

Cp «l

,

(3)

where Cp is the heat capacity of air (1005 J kg21 K21), l the latent heat of vaporization calculated by (2500.8 2 2.3668 Tdb) 3 103 (J kg21; List 1951), and « is the ratio of molecular weights of water to air (0.622) at constant pressure. There are, however, studies that challenge this formulation (Schurer 1981; Fan 1987; Visscher 1995),

and empirical estimates of g (ge) ranging from 0.00054 to 0.0007 K21 were found using a fixed, steady-state Tdb and Twb of 308 and 138C, respectively (Visscher 1995). We alternatively estimated ge by rearranging the psychrometric equation ge 5

es (wb) es (dp) , P(T db T wb )

(4)

where es(dp) is the saturation vapor pressure at dewpoint temperature (kPa) measured by a chilled mirror (see below). Equation (2) was rearranged to estimate dewpoint, Tdp (8C) from dry- and wet-bulb measurements (Campbell and Norman 1998), as follows: T dp 5

c ln(ea /a) . b ln(ea /a)

(5)

Field applications are inherently non–steady state. To assure robust comparisons between the chilled-mirror hygrometers and psychrometers, we had to account for differences (in Tdb) between that found in the ambient environment (i.e., what we wish to estimate) and the hygrometer body temperature (i.e., where the Tdp is measured by the hygrometer). Some models of hygrometers account for this by measuring both body and ambient (not necessarily inlet) temperatures and incorporate a similar correction to what is presented here, but this still remains a source of systematic error for other models. By definition es 5 ea at Tdp and by using was calculated by substituting T chamber Eq. (1), echamber a dp for Tx. In other words, we first calculated the ea at the chilled-mirror’s dewpoint temperature, Eq. (1). Next, the number of moles of water vapor in the chilled mirror were derived by rearranging the ideal gas law and using for the vapor pressure term and chilled-mirror echamber a body temperature (Tchamber) for the temperature term, such that n5

PV , RT x

nchamber 5

echamber V a , RT chamber

(6)

where n is the number of molecules in a mole, R is the ideal gas constant (8.314 47 J K21 mol21), and V is the fixed volume of the chamber (m3). Then, ambient vapor pressure from the chilled mirror was calculated by substituting nchamber from Eq. (6), causing nchamber to cancel and making the correction eair a 5

nchamber RT inlet dp V

5 echamber a

T inlet dp T chamber

,

(7)

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where T inlet dp is the ambient temperature measured at the inlet to the chilled mirror. Finally, we use eair a as the source of vapor pressure in Eq. (5) to estimate a corrected T corrected from the chilled-mirror hygrometers. IRGAs most often estimate water vapor in units of density or mole fraction, both subject to small changes in the molar volume of air. Here, we convert vapor pressures to mole fraction n/V by rearranging the ideal gas law to yield and apply the law of partial pressures: ea nH2 O V a : , P V a na

(8)

where the subscripts H2O and a are for water vapor and ambient air (which includes water vapor), respectively. Water vapor is calculated by IRGAs (models LI-7000 and LI-7500, LI-COR Inc.) from a raw absorptance value (cf. LI-COR manuals), H2O 5 T c cc x

A Sc , cc Pc

(9)

where H2O is in units of (mmol H2O) mol21, Tc is cell temperature (K), cc is the correction for water vapor (dimensionless), Pc is cell pressure (kPa), Sc is the span value for H2O (mV), A is the absorptance in the sample cell for H2O (number density mV21), and x is a polynomial applied to the normalized absorptance value. LI-COR Inc. determines LI-7000 H2O with a thirdorder polynomial using a range of water vapor supplied by a dewpoint generator. This assumes that any systematic error in the switching and plumbing is minimal and ignored, and no other source or sink of H2O exists in the measurement system. The polynomials are constrained to the range of ambient H2O and maximize the mV (mmol H2O)21 mol21. After H2O is calculated internally by the polynomial, its value is linearized and outputted by the IRGA using a digital–analog converter (DAC) such that H2O 5 V dc

Xf Xz V max

1 X z 5 cV 1 d,

(10)

where Vdc is the DAC signal (mV), Vmax is the full-scale millivolt output, and Xf and Xz are the H2O values associated with Vmax and the minimum output (e.g., 0 mV for unipolar output), respectively. Once the DAC is configured, the conversion can be expressed as a firstorder regression [right-hand term in Eq. (8)], where c and d represent a coefficient and offset, respectively. The precision of the closed-path IRGA to measure zero and span in the sample cell (zero and span drift, respectively) changes with temperature [,0.1 (mmol H2O)

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mol21 K21 and ,0.4% of the reading (K21), rf. LI-7000 manual]. Similarly, the zero and span drift in the openpath sensor are ,0.01 (mmol H2O) mol21 K21 and ,0.1–2% of the reading (rf. LI-7500 manual) when pressure is constant with internal chemicals at full efficacy. The symbol q is generic, indicating water vapor [(mmol H2O) mol21], either estimated by Eq. (8) or through unit conversions from the loggable psychrometer using Eq. (2) or from the chilled mirrors using Eq. (7). Even though LI-COR Inc. estimates the internal response of the IRGA x with a third-order polynomial, x is recalculated for each IRGA associated with the AmeriFlux PECS (Ocheltree and Loescher 2007) using a dewpoint generator as a source of water vapor at known temperatures and the D2 chilled mirror as the etalon (defined here as a transfer standard) every two weeks using Eq. (7). Once either IRGA was field deployed and equilibrated to the new environment, then they were initially field calibrated using a dewpoint generator to internally set the gain/zero (offset) and span (slope) that is applied to the linearized voltage measurement that is used in Eq. (8). In most IRGA deployments, factory calibrations of x are made once every 1–2 years and field calibrations every 2–16 weeks. Calibration drift in each type of IRGA appears daily [temperature dependence, e.g., ,0.2% of displayed value (refer to LI-7000 manual)] and longer term 2–7-day drift implies effects from lowfrequency changes to the physical or electronic environment. In this study, every effort was made to minimize short- and long-term drift.

b. Loggable psychrometers Two (model 3010, Theodor Friedrichs and Co.) loggable psychrometers with axially aspirated flow rates (;3 m s21) and triple-distilled water were used for this study. Each temperature measurement was made with a platinum resistance thermometer (PRT; Theodor Friedrichs and Co) and calibrated according to recommended National Institute of Standards and Technology (NIST) triple-point procedures (available online at http:// public.ornl.gov/ameriflux/sop.shtml). Accuracy and precision of the PRTs were both 60.03 K. Extreme care was used to assure no contamination occurs to the wetbulb wick, but we cannot rule out that contamination during field experiments can occur over long deployments. Psychrometry is considered the first principle measurement because it directly measures both dry- and wet-bulb temperatures. However, there are some physical limitations that affect the accuracy and precision of both temperatures: (i) adequate radiation shielding and aspiration is needed to couple temperature measurement to the true environment (Campbell and Norman 1998);

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(ii) wet bulbs cannot measure Tdp below 08C; (iii) when the evaporative demand exceeds the water supply to the wet bulb in desert environments; (iv) contaminants on the wet-bulb wick can alter its ability to measure true dewpoint; and (v) variances among instrument designs, for example, axial verses transverse flows. Moreover, there is additional uncertainty in ambient vapor pressure estimates on whether the psychrometric constant holds true over a wide range of wet-bulb temperature depressions.

c. Chilled-mirror hygrometers These optical-based sensors detect dew formation through the change in refracted light on the mirror surface (Ritsche 2005; Richardson et al. 2000; Richardson et al. 1999; Tarbell and Weller 1991; Katsaros 1991). Our transfer standard (etalon) was a laboratory hygrometer (model D2 with Optiplex monitor, General Eastern Inc.) calibrated at NIST using their primary standard mark 2 (M2) two-pressure humidity generator (Hasewaga and Little 1977) and traceable to the World Meteorological Organization’s reference psychrometer. Two models of field hygrometers were tested: DewTrak 200M (EdgeTech Inc.) and OEM 2010 (Yankee Environmental Systems Inc.). The response time of chilled mirrors is slower than aspirated psychrometers (on the order of .30 s) and is partially influenced by their ability to heat and cool the mirror with changing ambient temperatures. In the field, the DewTrak maintains environmental similarity through extensive shielding, an aspirated flow rate of 2.5 L min21 (;3.3 m s21; note that is not the flow rate through the sampling volume, which is not reported and may have implications for its response time), and a shaded inlet directly below the sensor housing (cf. DewTrak manual). The OEM 2010 was mounted inside a meteorological box, air was pulled through 1.2 m of 0.48 cm internal diameter (ID) tubing (Bev-A-Line, Thermoplastic Processes) and kept at the same horizontal height between the inlet and measurement location, and the flow rate was 0.75 L min21 (;1.6 m s21, as per manufacturer’s recommendations), with copper Constantine thermocouples monitoring inlet and tubing temperatures and the temperatures before and after the flow through the chilled mirror. Chilled mirrors are also limited by fouling and require regular mirror cleaning to avoid false readings; servicing the mirrors in the field is possible. Because these field-deployable chilled mirrors are relatively new, long-term stability in the field (over years of operation) has not been explored, and they may be subject to optical sensor degradation. On the basis of the past performance of laboratory-quality chilled mirrors and the manufacturer’s specifications, however, the accuracy and precision do not vary over the range of expected environmental conditions. This is particularly

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important when calculating near-saturated conditions and the significance of small Tdb 2 Twb depressions.

d. Laboratory tests The Allan variance was used to determine the optimal averaging time that minimizes effects due to electronic noise and changes in the physical environment (Ocheltree and Loescher 2007; Loescher et al. 2006; Allan 1966) in a custom chamber. This chamber measured 28 cm 3 17 cm 3 15 cm (length 3 width 3 depth) and was made of steel (painted such that it would not react with the water vapor and oxide), with an internal fan to ensure homogeneous, well-mixed conditions. Water vapor in the chamber was made by using a dewpoint generator (LI-610, LI-COR Inc.). Both the OEM 2010 and the DewTrak chilled mirrors were placed inside the chamber, with the DewTrak’s sensor block removed from its protective housing and inserted into the chamber through a sealed pass-through, mimicking its factoryaspirated flow rate. Water vapor leaving the chamber was plumbed to the Optica D2 as our traceable measurement. Steady-state conditions where achieved when the standard deviation (SD) in the dewpoint measured by the Optica D2 was ,60.18C. Chamber temperature (in this case, Tdb), pressure, flow rates through the sensors, and the respective dewpoints were recorded on a data logger (CR23X, Campbell Scientific Inc.) at 1 Hz. Because the loggable psychrometers could not be effectively controlled in this chamber, a second, larger chamber was constructed, consisting of 50 cm 3 78 cm 3 86 cm plastic-coated panels (with assumed low water absorption), and was used to determine the Allan variance for the loggable psychrometers, stability tests, and ge. Water vapor was made using an adjustable humidifier, and the air inside the chamber was mixed with dry air to achieve different dewpoints. Again, our etalon was the Optica D2 chilled mirror, which drew air from an inlet within 3 cm of the psychrometer inlet, and all the data were collected in the same manner. Accuracy of the loggable psychrometer was determined by the calibration of the PRTs. There are additional issues that can affect the accuracy of the psychrometers that could not be assessed, such as potential contamination of the wetbulb wick. Care was taken to assure no contamination occurred. Precision in both psychrometers and chilledmirrors hygrometers was estimated by short-term drift under steady-state conditions in the laboratory’s environmental chambers.

e. Field tests The loggable psychrometer, OEM 2010, and the DewTrak were tested at two sites with contrasting

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environmental conditions. The Oregon State University Hyslop experimental field site in Corvallis, Oregon (448389N, 1238129W), was tested from 8 to 21 May 2007; the Hyslop site is 68.6 m MSL and is a field of grasses and forbs. The second site, Appleton-Whittell Audubon Research Ranch in Elgin, Arizona (31835926.6280N, 110830937.3680W), was tested from 19 to 25 August 2007 and compared to IRGA data from the PECS. The Appleton-Whittell Audubon Ranch is at 989 m MSL in a natural regenerated desert, with the plant (grass) canopy height at 20 cm and with large and adequate fetch. Annual average ambient temperatures were ;15.78C, with daily average temperatures of ;22.58C in August (available online at http://www.audubon.org/local/ sanctuary/appleton/files/ARRmonannavg2mt.xls). At Appleton-Whittell, seasonal monsoon rains start in late July and typically persist for 4–6 weeks, making these grasslands productive, lowering sensible heat flux relative to the latent heat flux, and establishing ideal conditions for testing humidity sensor performance over a range of temperature depressions. Both sites had very short stature plant canopies, and therefore were appropriate for turbulent exchange measurements. It was assumed the storage term for net ecosystem exchange of water was ;0 for any specific averaging time. The Hyslop site is a Department of Energy (DOE)– AmeriFlux quality assurance/quality control field test facility; the Appleton-Whittell site is also a DOE– AmeriFlux site and a NOAA site/National Data Climate Center/U.S. Climate Reference Network (USCRN) site. Tower-based measurements at Appleton-Whittell were ;50 m west of the NOAA/USCRN site and ;3 m north of the AmeriFlux site. At both sites, the 3D sonic anemometer, the openpath IRGA, and the inlet for the closed-path IRGA were mounted 4 m above ground level (AGL) on an antennae-style tower (model 25G, Rohn Inc.). All established standard mounting and eddy covariance (turbulent exchange only) processing protocols for the AmeriFlux PECS system were used and can be found in Ocheltree and Loescher (2007), which included (i) corrections for high-frequency loss using Massman transfer function for closed-path data (Massman 2000; Massman and Clement 2004), (ii) corrections for density fluctuations in all open-path data (Webb et al. 1980; Massman 2004), (iii) removal of data during rain, and (iv) removal of data that did not meet diagnostics based on data quality flags from each IRGA and CSAT-3, and three other data quality flags (based on w9 integral turbulent statistics) supported by the Spoleto Agreement 2004 for CarboEurope-IP. Water vapor was manually calibrated in both of the IRGAs at the beginning of the field tests using the dewpoint generator (LI-610) according to the

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FIG. 2. The Allan variance was used to determine optimal averaging times (Allan 1966; Loescher et al. 2006; Ocheltree and Loescher 2007). The D2 etalon was placed in our environmental chamber with steady-state dewpoint conditions for more than 24-h prior to sampling. Variance units are in 8C; data were collected at 1 Hz. The other chilled-mirror hygrometers behaved similarly. Dotted line shows a 240-s averaging time.

manufacturers’ recommendations. Additional shielding from incident radiation was applied to the enclosure housing the closed-path IRGA on 22 August 2007. The DewTrak, loggable psychrometer, and the inlet for the OEM 2010, were all mounted at 1.8 m AGL and collocated together without interference of the flow around each of the sensor on a meteorological tripod approximately 2.3 m from the PECS. Sample air for the OEM 2010 was pulled from adjacent to the DewTrak inlet through 1 m of tubing (BEV-A-LINE, 0.48-cm ID) with a flow rate of 0.75 L min21 into the sensor mounted in a white meteorological box. Copper Constantine thermocouples were installed to monitor inlet and tubing temperatures and the temperatures before and after the flow through each of the two chilled mirrors. Also collocated on the same tripod at the same height was a longwave and shortwave broadband-component radiometer (model CNR-1, Kipp and Zonen B.V.).

3. Results and discussion a. Laboratory tests An averaging time of 240 s from the D2 was chosen to minimize instrument noise and to foster robust laboratory comparisons among sensors (Fig. 2). In the D2 data, and for chilled mirrors in general, there were small oscillations in the output as the instrument cycles above and below the actual dewpoint temperature to assure an accurate reading. As a result of this systematic sampling noise, the ideal averaging time is longer than that used to minimize electronic noise alone. The threshold determined by the Allan variance for the DewTrak 200M and

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TABLE 1. Comparison of measurements from our field instrumentation compared to a NIST-calibrated General Eastern Optica D2 chilled mirror in laboratory tests. Instrument

Range in dewpoint temperatures (8C)

Air temperature (8C)

Offset

Slope

R2

Psychrometer OEM 2010 DewTrak 200M

218–168 08–208 08–208

21.228–22.468 24.248–25.78 24.248–25.78

0.031 20.43 0.20

1.00 0.98 1.00

0.99 1.00 1.00

Yankee OEM 2010 were nearly identical. Using a 240-s averaging time, 61 SD were ;0.01 and 0.0048C from the DewTrak 200M and Yankee OEM 2010, respectively, and all three instruments compared well, Table 1. Instrument stability (short-term drift) in our specific D2 etalon was reported as nondetectable (i.e., 608C) over a 30-min period (P. Huang 2007, personal communication about NIST calibration). Instrument stability of the other sensors used in this study was determined by placing all the chilled mirrors and pyschrometers in our controlled environment at a Tdp of 16.28C. The short-term drift in the psychrometer was of the same magnitude as that found by the OEM 2010, 61 SD ;0.078C in Tdp (from the D2) 2 Tdp (from the psychrometer; Fig. 3a). Measured Tdp from both the DewTrak 200M and Yankee OEM 2010 had positive offsets from the D2 (Fig. 3b). The large error bars (.618C) evident in the OEM 2010 time series are due to the internal cycling of the sensor to appropriately range and find the dewpoint; once these averaging periods were identified (.3 SD), they were removed from subsequent analyses. The DewTrak 200M drifted downward (toward the D2 values) by ;0.18C during this sampling period (Fig. 3b). The internal electronics and mirror were removed from the DewTrak 200M and placed into the smaller chamber for the Allen variance analyses. To determine instrument precision and drift, the DewTrak 200M was placed into its shielding/housing used for outside applications. Hence, the internal volume of the DewTrak 200M shielding/housing was much larger than the D2 and Yankee OEM 2010. The air sample is not directly pulled through the sample chamber, but it relies on the exchange of air actively pulled through a radiation shield that surrounds the sample volume. Drift in the DewTrak 200M (Fig. 3b) is interpreted as resulting from slower flushing time (time constants by the movement of air through the sensor) due to the instrument design than from either the D2 or OEM 2010.

b. Psychrometric constant Using Eq. (4) in steady-state conditions, the psychrometer constant varied with the temperature depression (Tdb 2 Twb) (Fig. 4a). For large temperature depressions (drier air), our values agree well with other

reported values for similar experimental conditions (cf. citations in Fig. 4b). There are not any published values for small temperature depression—that is, values approaching saturation for any given air temperature. Under these conditions, the empirical estimates of the psychrometer constant derived here are much lower than reported values (Visscher 1995; Wylie and Lalas 1981). This experiment was repeated to assure the results were valid. The dewpoints derived from the psychrometer and the D2 compared better when the psychrometer constant from regressions found in Fig. 4a was used (Fig. 4b), showing that the subsequent

FIG. 3. Short-term drift in the (a) D2 and (b) DewTrak and OEM 2010 as determined against the D2 standard under steady-state chamber conditions; averaging time was 240 s and error bars are 61 SD. Note the large error bars in the OEM 2010 dataset, indicating the range the sensor cycles to assess and find Tdp is large. These data were identified and removed from subsequent analyses.

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decreases—that is, Tdb 2 Twb becomes smaller—the heat capacity of air has less relative influence than latent heat of vaporization per unit of water added to the atmosphere. There may be some additional uncertainty as a result of applying atmospheric pressure for unit conversions; however, the 60.5-kPa uncertainty associated with the accuracy in measuring atmospheric pressure only attributes 63 3 1026 K21 to our estimate of ge and is therefore discounted.

c. Field tests, psychrometers, and hygrometers

FIG. 4. (a) The relationship between the temperature depression (Tdb 2 Twb) as measured by the loggable psychrometers and the psychrometric coefficient (g e) calculated by Eq. (4) over a range of known water vapor concentrations (humidities). Data (open circles) are mean 61 SD averaged over 240-s; other symbols (upwardfacing triangles) are published data from several different models of psychrometers (Visscher 1995) using algorithms from Wylie and Lalas (1981) at a fixed, steady-state Tdb and Twb of 308 and 138C, respectively. (b) The relationship between the Optica D2 dewpoint and the calculated dewpoint using g t (uncorrected) and g e (corrected) coefficients.

(autocorrelated) polynomial also performed well for the field testing. Because these results show that the partial pressure of water vapor decreases with smaller temperature depression, g t 6¼ ge suggests that modeled and measured latent energy fluxes may be underestimated when conditions with high humidity prevail; that is, the psychrometric constant is present when applying either the Penman–Monteith or Priestly–Talyor equations. The American Meteorological Society defines the psychrometric constant as g 5 Cp/l ’ 0.4 (rwater/rair) (Tx)21, similar to Eq. (3) (available online at http://amsglossary. allenpress.com/glossary/ psychrometric1constant), where the density of water vapor is in grams and air is in kilograms, stating theoretically that it is not constant; however, no study to date has demonstrated this empirically. Data here show that as the temperature depression

In interpreting the field data, several issues emerged. First, the three instruments tracked similarly (Fig. 5a), but data from the DewTrak 200M were constantly higher than those from the OEM 2010 (Fig. 5b). We wished to compare factory-ready instruments; thus, the offsets are likely sensor specific (not model specific) and due to how they were initially factory calibrated. There was error associated with compensating for the difference between inlet air temperature and the body temperature where the air was sampled; this temperature difference was consistently larger in the OEM 2010. We considered the DewTrak data more robust than the OEM 2010 for our results because (i) the differences between air outlet temperature and sensor body temperature ranged 28–10.28C in the OEM 2010 (Fig. 6), likely the result of being in an unventilated enclosure; (ii) even though the OEM 2010 was adjusted for the calibration offset (from Fig. 3b), additional uncertainty remained in the OEM 2010 estimates as a result of its previous calibration history; (iii) the flow rate past the DewTrak chilled mirror was almost 2 times that of the OEM 2010, and (iv) data from the DewTrak agreed better to those from the D2. It is also important to note that even though the aspirated flow rate of the DewTrak was 2 times that of the Yankee, the flow rate across the chilled mirror was larger in the Yankee. The aspirated airflow through the Dewtrak did not directly pass over the mirror, but it had to mix with the chamber air through several holes in the chamber housing and could account, in part, for the more smoothed response in the time series; that is, the design of flow rates act like a high-pass filter. We are not advocating one model over the other but rather bringing to light different design features that may be key for specific applications. Second, the dewpoints from the DewTrak 200M were constantly higher than those from the psychrometer during the day when ambient temperatures and radiation loads increased .150 W m22 (Fig. 7). Because we have accounted for the difference between inlet and body temperature in the DewTrak-based estimates and it agreed best with the D2, we have focused on errors associated with the loggable psychrometer as the cause

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FIG. 6. Time series showing the difference between ambient air temperature (Ta) and the outlet air temperature of the chilledmirror air sample (Tx), where x is the representative chilled-mirror sensor. Data from the Appleton-Whittell Research Ranch from 21 to 25 Aug 2007.

FIG. 5. The 30-min averaged dewpoint temperatures measured at the Appleton-Whittell Research Ranch from 21 to 25 Aug 2007, where (a) is the time series data collected from each sensor, and (b) OEM 2010 data were 10% lower than those from the DewTrak 200M, with an offset of 0.378C.

for the observed difference with the two chilled mirrors. In this case, a smaller temperature depression can lead to higher dewpoint values, which can be caused by inaccuracies in either dry- or wet-bulb temperatures. Comparison of dry-bulb temperature (aspirated) measurements from the psychrometer and those found in the PECS and at the USCRN site differed ,0.18C over the length of the experiment (data not shown). Hence, we discount the error due to insufficient aspiration with high radiation loading like others have found, for example, Wylie and Lalas (1981). Insufficient aspiration may cause a residual increase of water vapor surrounding the wet bulb in humid or wet environments, causing a reduction in evaporative cooling. Operating in arid environments with high radiation loads and low ambient water vapor values (high vapor pressure deficit), even modest aspiration does not change the degree to which evaporative cooling has on true wet-bulb temperature; however, insufficient deliv-

ery of water to the wet bulb will increase Twb, reduce the temperature depression, and increase the dewpoint estimate (Visscher 1995). Consider a simple thought experiment: for conditions similar to those at AppletonWhippell with Tdb 5 308C and if Twb was 18C higher, then the true wet-bulb temperature at 218C would account for an approximate 1.798C increase in dewpoint (from 16.518 to 18.308C; rf. Fig. 5). Overall chilled-mirror hygrometers can be used for accurate and precise ea and Tdp measurements across the range of environmental conditions, from close to saturation to extreme arid environs with high radiation loading, particularly when (i) the flow rates are higher than those used in the psychrometer (.3 m s21); (ii) there is additional radiation shielding that can provide more thermal inertia than manufacturers’ specifications; and (iii) one accounts for unit conversions due to differences between inlet temperatures and chilled-mirror body temperatures. It is unclear what the maintenance and cleaning requirements for the optical components would be for long-term operation. On the basis of these observations (Figs. 6b, 7), we considered data from the DewTrak 200M more robust and used the data to estimate molar fraction of water and to test the IRGA calibrations. But it also should be noted that this is a technology that is rapidly advancing, and new, possibly more stable, models of field-deployable chilled-mirror hygrometers or water vapor lasers should be considered for future studies.

d. Field tests, calibrating IRGAs Both IRGAs were field calibrated (refer to section 2) and allowed to operate for three days in the field before

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(a)

(b)

FIG. 7. A comparison of Tdp between the DewTrak 200M and the loggable psychrometer, (a) for conditions when net radiation was .150 W m22, and (b) when net radiation was ,150 W m22. The Tdp from the psychrometer was calculated using Eq. (5); all data were averaged over 30 min from the Appleton-Whittell Research Ranch for the period from 21 to 25 Aug 2007.

the field experiment with the psychrometers and chilled mirrors was initiated. Descriptive statistics were made for water vapor measurements for each 1-min period from both of the IRGAs and the DewTrak 200M. The maximum and minimum 1-min values within a 30-min averaging period were used to estimate a new offset and slope (zero and gain) as a first-order regression, y 5 ax 1 b. If the a and b coefficients from the IRGAs were statistically different from the chilled mirror, then both coefficients were adjusted to the new value and the water vapor concentration was estimated [Eq. (9), Fig. 8]. During AmeriFlux comparisons, it is common to find drift in the H2O IRGA signal of 10%–20% (rf. Figs. 1a, 8a,b). Overall, offsets, slope, and residuals were improved (Figs. 8c,d). These H2O estimates were used for concentration estimates and used, in turn, for the Webb–Pearman–Leuning (WPL; Webb et al. 1980) corrections in EC estimates. This is a simple approach, and it is likely that other more site-specific approaches may be more appropriate.

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The protocol used here to calibrate IRGAs worked for our conditions, but there may be conditions when different averaging times for the minimum and maximum values should be considered. Chilled-mirror hygrometers have inherently slower response times than IRGAs as a result of (i) thermal inertia of the mirror (although all manufacturers work to minimize this); (ii) the algorithms used to find the dewpoint temperature require the mirror temperature cycle above and below the dewpoint, which lengthens its internal time constant; and (iii) large sample chambers coupled with low flow rates (compared to IRGAs). The slower response time needs to be considered when determining the optimal averaging time for calibrating the IRGAs. This becomes particularly important during the times of day when there are rapid changes in the mean water vapor concentration. In our data, there were times of the day when the minimum and maximum 1-min averages were not synchronous between the chilled mirror and IRGAs, and they may need to be removed for some applications. The same algorithm used here can be applied to longer averaging times—for example, estimating the minimum and maximum 30-min averages throughout a 24-h period could be used to calibrate the IRGAs just once a day, rather than for every 30-min averaging period. We were not able to test the longer averaging times because of the short duration of field sampling at both sites. Because EC estimates are based on variances and are somewhat insensitive to absolute offset, the EC calculations were only corrected for slope (gain) using the same criteria above. Verification of EC–derived lE fluxes is difficult because there are no other independent means of validation. Most have relied on well-calibrated instrumentation, statistical tests (e.g., plausibility, drift algorithms, integral turbulent statistics, stationarity; rf. Foken and Wichura 1996; Loescher et al. 2006; Ocheltree and Loescher 2007), and some redundancy of measurements. Data quality assurance has relied on these well-described tests, and knowing, minimizing, estimating, and reporting the sources of systematic and random error. Agreement among redundancy tests can be right for the wrong reasons, and rigorous examination is often needed. H2O-corrected lE estimates from both open- and closed-path IRGAs at the Hyslop site agreed better once the chilled-mirror corrections were applied (Figs. 9a,b). Examination of the cospectra from each IRGA also agreed well, indicating both instruments measured the same turbulent structure and all corrections converged (rf. Massman 2004; data not shown). At the Appleton-Whittell site, however, both IRGAs agreed well prior to applying the chilled-mirror correction (Fig. 9c), and after the corrections, the open-path

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FIG. 8. Comparison of the 30-min averaged molar water vapor estimates (q) between those estimated from the DewTrak 200M and the open- and closed-path IRGAs. Corrected values represent the mean q from the open- and closed-path IRGAs corrected to the DewTrak 200M for each 30-min averaging period, as described in the text. (a),(b) Uncorrected values do not compare well with the DewTrak 200M, with unexplained variability. (c),(d) Corrected values compare well. Data are from the AppletonWhittell Research Ranch from 21 to 25 Aug 2007; similar data were collected and corrected from the Hyslop site (data not shown).

IRGA lE estimates were ;3% larger than the closedpath estimates. The turbulent structure is often shifted toward higher frequencies in low stature, such as arid environments like that found at Appleton-Whittell, which open-path IRGAs measures in situ. Examining the cospectra for the two IRGAs, the open-path measures the high-frequency turbulence to 10 Hz, whereas the closed-path is attenuated at 6 Hz (rf. Fig. 10). Integrating the area under each curve and taking the difference amounts to ;3% of total flux. This implies that the high-frequency attenuation corrections for the closed-path sensor did not fully account for the loss in flux and is apparent in the chilled-mirror correction

values of lE (Fig. 9d). This result confirms the need for rigorous data analyses and minimizing all the sources of systematic error.

4. Conclusions d

d

Integrated variances under steady-state conditions can be used to determine statistically appropriate averaging times for instruments. Chilled mirrors cycle the heating and cooling of the mirror to continually update its’ dewpoint measurement. This cycling can be significant, and it needs to be identified and removed from the dataset.

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FIG. 9. Field results showing the correction of calibration drift (water vapor, q) in the open- and closed-path IRGA lE fluxes using DewTrak 200M. Here thirty 1-min statistics were used to estimate the maximum and minimum q values (and 61 SD) for each 30-min averaging period. The maximum and minimum q values were then used to determine the true gain function from psychrometer data compared to the IRGA gain function, and they were applied only when the maximum and/or minimum true gain function values were .1 SD from the IRGA gain function. The newly applied gain function of the IRGA was used to calculate new values of q, EC (w9q9), and subsequently lE. Data are 30-min average fluxes collected at the OSU Hyslop experimental field site from 8 to 21 May 2007, and the Appleton-Whittell Research Ranch from 21 to 25 Aug 2007. All closed-path data were corrected for high-frequency loss using Massman transfer function (Massman 2000; Massman and Clement 2004). All open-path data were corrected for density fluctuations (Webb et al. 1980; Massman 2004), and the lE estimates corrected for span drift also used span drift–corrected q estimates. Note the nonheteroscedastic nature of these data.

d

d

d

A functional relationship (exponential) was developed for the psychrometric constant. For small temperature depressions—that is, values approaching saturation for any given air temperature—these empirical estimates of the psychrometer constant are much lower than reported values, ;0.000528C21 for a Tdb 2 Twb depression of 4.38C. All other reported values used a Tdb 2 Twb of 178C. Chilled-mirror technologies can be a robust measure of dewpoint temperatures and ea only if the unit conversions are accounted for between inlet and body temperatures [Eqs. (6)–(8)]. Even though psychrometric measurements are based on first principles, it is very difficult to make wet-bulb psychrometric measurements in dry environments; it is difficult to deliver water to the wet bulb in psy-

d

chrometers in arid environments and this is a source of systematic error. Network-level strategic planning should take this result into account. Chilled-mirror technologies can be used to automate field calibrations of both closed- and open-path IRGAs, and they can enhance the accuracy and precision of estimates in both water vapor concentrations and EC-derived lE fluxes.

Acknowledgments. This research was supported by the Office of Science (BER), U.S. Department of Energy, Grant DE FG02-06ER64307 as part of the Terrestrial Carbon Program. The authors wish to thank the reviewers for their careful and thoughtful comments; B. Tanner, E. Swiatek, and Campbell Scientific Inc. for use of their equipment; R. Taylor at Edgetech Inc.; P. Huang at NIST;

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FIG. 10. Variance normalized cospectra of both the open- and closed-path IRGA covariances, w9q9, for notation and derivation (rf. Loescher et al. 2006). These data are for unstable atmospheres only, with a stability parameter ,20.1 (rf. Campbell and Norman 1998). Data are from the Appleton-Whittell Research Ranch from 21 to 25 Aug 2007. Cospectra were calculated with 2048 bytes per spectral size and output into 100 bins. Sensor separation between the close-path IRGA and the sample inlet was ;2 m; sensor separation between the open-path IRGA and the sample inlet was ;0.1 m.

H. Luo for field support; H. Gholz and Don Julio for inspiring many a late-night scientific discussion; the OSU Department of Forest Science; and the Audubon Appleton-Whittell Ranch for logistical support.

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