Crop Science 40:709-712 (2000)
© 2000 Crop Science Society of America
CROP ECOLOGY, MANAGEMENT & QUALITY
Correction of Thermocouple Psychrometer Readings for the Interaction of Temperature and Actual Water Potential
J.P. Comstock
Boyce Thompson Institute for Plant Research, Tower Road, Ithaca, NY 14853 USA
jpc8{at}cornell.edu
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ABSTRACT
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The standard method of temperature correction for a thermocouple psychrometer only yields satisfactory results for a limited range of water potential and temperature. Contrary to assumptions in standard practices, there is an interaction between the actual water potential under measurement and the temperature correction. Fortunately, the errors associated with ignoring this interaction are often small, and data are presented here that permit an assessment of whether the error is within acceptable limits under specific experimental conditions. More elaborate algorithms are given that can be used more robustly across a wide range of measurement conditions if needed. The temperature responses of two commonly used commercial psychrometers were examined, and it was found that this interaction resulted in model-specific correction algorithms. More specifically, it was found that the frequently made assumption of a correction factor that changes linearly with temperature is a satisfactory approximation across a range of at least 15 to 35°C. However, it was also found that the slope describing how this correction factor changes with temperature itself changes as a function of the actual water potential being measured. The details and magnitude of this effect were model specific.
Abbreviations: RH, relative humidity • µV, microvolt
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INTRODUCTION
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THERMOCOUPLE PSYCHROMETERS are widely used for measuring water potentials of soils and plants. At equilibrium, when a water-containing sample (e.g., leaf, soil, expressed sap, saline solution) is enclosed in a small, isothermal chamber, the relative humidity (RH) of the vapor phase in contact with the liquid fraction will be less than 100% whenever the liquid has a water potential below 0 MPa. The reduction in RH can be measured via the temperature depression from evaporation of a wet thermocouple junction (psychrometric mode of measurement). The commonly employed "Spanner" psychrometer measures this evaporative cooling after water has first been condensed on the thermocouple junction via the Peltier effect (Spanner, 1951). It is fundamentally a measurement of temperature depression, but it is common to relate psychrometer microvolt (µV) signals directly to water potentials without first converting them to temperatures. No evaporation should occur at 100% RH, and the signal increases as water potential and RH decline. At constant temperature, the µV signal measuring evaporative cooling of the psychrometric thermocouple junction is almost linearly related to the water potential of the sample.
Theoretically, RH has a fairly constant relationship to water potential, which is only minimally affected by changes in background temperature (Lang, 1967). However, the measured signal is one of evaporative cooling, and the same RH depression at a higher temperature will create a larger diffusion gradient for evaporation, and hence it will produce a larger µV signal from the psychrometer. For such reasons, it is often a standard practice to convert initial readings, which may have been made under variable temperature conditions, to equivalent readings expected if measured at 25°C. Considerable effort has been made to evaluate the theoretical aspects of how temperature and psychrometer geometry interact to affect psychrometer readings (Dalton, 1968; Peck, 1968; Scotter, 1972). The observed temperature depression of the junction is the result of a complex energy budget including heat conduction along the wires, radiative heat transfer, and latent heat loss. Temperature enters into many of these terms, with several minor as well as a few major effects on the observed signal. In many current applications, these multiple effects of temperature are simplified into a single temperature correction factor used to convert the measured signal to the expected signal for the same water potential measured at 25°C (Wiebe et al., 1971). The value of the correction factor needed to correct data from a range of temperatures back to 25°C is often calculated in accordance with a simple algorithm that assumes a linear relationship between the signal ratio, observed µV/expected µV corrected to 25°C (Ø), and temperature (T) (Brown, 1970; Wiebe et al., 1970).
| (1) |
This practice is encouraged in some manufacturer's recommendations (e.g., Plant Water Status Instruments in situ stem hygrometer manual, Wescor C-52 sample chamber manual), and subsequent technical reports have also presented the characterization of new instruments as a fixed linear relationship (Wullschleger et al., 1988). However, it is also known that the simple relationship of Eq. [1] can be affected by actual water potential (Kauraw and Gupta, 1985; Meyn and White, 1972) and that details of psychrometer construction and design can affect these interactions. It was observed in our lab that changing psychrometer temperature while measuring the water potential of salt solution standards often produced small but consistent discrepancies with expected values (Lang, 1967) and that these discrepancies were greater at some molalities than others. More detailed calibration procedures were undertaken to check the accuracy of Eq. [1] across a wide range of water potentials and to specifically test for water potential x temperature interactions in the psychrometer response.
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Methods
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Two commercially available models of psychrometer were examined: (i) the C-52 sample chamber (Wescor, Logan, UT), which is designed primarily for evaluating leaf-punches or other small samples in the laboratory, and (ii) an in situ stem psychrometer (Plant Water Status Instruments, 7 Elmhurst Crescent, Guelph, ON Canada N1H 6C8).
Sodium chloride calibration solutions were used throughout as water potential standards, and the combined effect of temperature and molality on water potential was taken from the tables by Lang (1967).
Both types of psychrometer were read in psychrometric mode (wet-bulb depression) by an automated datalogger (model CR7, Campbell Scientific, Logan UT). Cooling time to initiate condensation on the psychrometric junction was 10 s at -2.81 V excitation, and the temperature depression from evaporative cooling was measured 6 s after active cooling ceased. This measurement protocol was used consistently for all readings and produced sensitivities at 25°C ranging from 4.0 to 5.0 µV MPa-1 for different individual instruments. Psychrometers were allowed to equilibrate under each set of conditions until fully stable. This ranged from 30 min to several hours depending on psychrometer model, molality, and measurement conditions (e.g., waiting for full thermal stability after a large temperature change). Once fully stable conditions were reached, a minimum of six replicate readings were taken and averaged. The standard deviation of such replicates ranged from ± 0.02 to ± 0.05 µV.
Psychrometers were maintained in a temperature controlled, insulated box. It was found that extremely stable and isothermal conditions could be maintained when the calibration box was kept just 2 or 3° above room temperature. For large temperature changes, the box was placed inside a darkened growth chamber so that it was always just a few degrees above ambient air temperature throughout the temperature calibration. The following two procedures were used to determine the temperature dependency of the psychrometric readings.
Continuous Readings across Temperatures
The simplest procedure was to put salt solution standards into the psychrometers and repeatedly change the temperature to take readings at 15, 25, and 35°C. Three reps of each of four salt solutions were used in a total of 12 psychrometers (of each model). Molalities ranged from 0.1 to 1.0 for a water potential range at 25°C of 0.462 to 4.64 MPa. Data reduction was somewhat complicated by having to factor out the actual change in water potential of a given molality as temperature changed before calculating Ø. Psychrometers were repeatedly read at 25°C throughout the calibration to evaluate any drift in readings independent of temperature.
Reloaded Salts at Each Temperature Change
The purpose of this second approach was largely to check if pressure changes caused by changing temperature in the enclosed vapor chambers could be affecting the results. The operator entered the growth chamber after temperature equilibration to repeatedly change the calibration salts such that a full calibration was performed at each temperature.
Second-order polynomial fits were made to the data relating µV signal to water potential at each fixed temperature (minimum r2 of 0.99, usually 0.999 or higher). These regressions were used to interpolate µV signals at 15, 25, and 35° to allow repeated estimates of Ø while holding water potential constant. Salt solution holders but not psychrometric junctions were thoroughly cleaned and dried between each calibration solution. Calibration at 25°C was performed at both the beginning and end of the entire procedure, and instruments showing measurable calibration drift were excluded from analysis. Sample sizes were six and nine instruments for C-52 and in situ stem instruments, respectively.
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Results
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Both approaches listed above gave essentially identical results (Fig. 1A and 1B)
. While data from the continuous reading approach was somewhat more cumbersome to deal with in data reduction, it tended to give less variable results because it avoided the experimental noise inherent in reloading samples.
The utility of a linear correction for background temperature as presented in Eq. [1] was supported for both types of psychrometer. For data measured at 15, 25, and 35°C, a linear fit of Ø on temperature consistently gave r2 values of 0.999. Nonetheless, the slopes of these regressions were not all equal, but increased with decreasing water potential in both psychrometer models (Fig. 1A and 1B). While these qualitative interactions between water potential and temperature were similar for all psychrometers, quantitatively there was some variability observed among responses by individual instruments and strong differences in the mean response by different psychrometer models. The C-52 generally showed greater temperature sensitivity (i.e., y axis of Fig. 1), but showed an abrupt decrease in temperature sensitivity at very high water potentials. The in situ stem psychrometer showed a mean temperature sensitivity closer to that of Eq. [1], but it too showed a marked decrease in slope at higher water potentials. The water potentials at which the mean value of the temperature sensitivity slope actually equaled 0.027 (as commonly used), were about -1.6 and -0.4 MPa for in situ stem and C-52 psychrometers, respectively.
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Discussion
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These data confirm previous observations that use of a single fixed slope in Eq. [1] is not fully justified (Kauraw and Gupta, 1985; Meyn and White, 1972). Substantial errors are possible if the interactions between temperature sensitivity and water potential are ignored (Fig. 2)
. The error analysis presented here assumes that the psychrometers were correctly calibrated for 25°C. Simulated µV readings taken at other temperatures were assumed to conform exactly to the relationships given in Fig. 1. Normal data analysis was then simulated by "incorrectly" correcting the µV signal back to 25°C by use of Eq. [1] with a fixed slope of 0.027. The errors given in Fig. 2 reflect the difference between finally calculated water potential and the original defined value. This analysis predicted large error percentages at high water potentials near 0 MPa, but larger absolute errors at low water potentials. The greatest potential for error occurs when low water potential measurements are taken at low temperatures.
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Fig. 2 The expected error from using a fixed slope of 0.027 in Eq. [1] for a wide range of temperature and water potential assuming the interactions between temperature sensitivity and water potential given in Fig. 1 are the correct ones. (A) in situ stem and (B) C-52 sample chamber psychrometers. In both panels, a negative percentage of error indicates that the water potential calculated according to Eq. [1] was closer to 0 MPa than the actual water potential
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Although the C-52 sample chamber showed greater variation in slope as water potential changed, and therefore a greater potential for error, this instrument is most commonly used under laboratory conditions of stable temperature such that the errors would actually be rather trivial. If used in the field or at field stations with uncontrolled environments, users should be aware of this added effect. If a fixed slope is used for convenience, 0.027 is probably too low, but the optimal choice depends on the range of water potentials expected.
The in situ stem psychrometer is designed to be used under field conditions, where temperature may change 10 to 15°C on a diurnal basis and even larger temperature fluctuations might occur over longer periods, or for use in laboratory experiments, where large temperature fluctuations may be imposed as deliberate treatments. Happily, the change in temperature sensitivity of this instrument was more gradual than in the Wescor model (Fig. 1A vs. 1B), and the slope of 0.027, which is standardly used in Eq. [1], was correct for a water potential that was in the middle of the water potential range of many data sets. Consequently, errors in past data ignoring the dependence of the slope of Ø on water potential may not always have been large. If consideration of Fig. 2 indicates that the expected error under a given set of experimental conditions is unacceptable, the curve in Fig. 1A can be described by:
 | (2) |
where m is the variable slope given as a constant (0.027) in Eq. [1] and 
is water potential. To make the more robust correction, an analogue of Eq. [1] must be determined using the output of Eq. [2] to replace 0.027. The intercept too must be adjusted. Equation [1] is meant to convert a reading at any temperature to the expected µV value that would have been observed at 25°C. If a reading was actually taken at 25°C, Eq. [1] must output a correction factor of 1.0. The needed y intercepts to go with slopes from Eq. [2] are therefore calculated as 1 - 25m. Since is not initially known, use of Eq. [2] requires an iterative solution. Using 0.027 as a first guess of m in Eq. [1], an estimate of must first be calculated by standard procedures. Then, this first estimate of is used to recalculate m. Repetition of this process leads to correct values of both m and within three iterations. An equation analogous to Eq. [2], but specific for the Wescor model, is given in the caption of Fig. 1. Models other than those discussed here would require empirical measurement of how m and were related.
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ACKNOWLEDGMENTS
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This work was supported by NSF grant IBN 94-96093. My thanks go out for the flawless psychrometric technique of Adam Levin and Rick Willhite. I wish to thank Mikaîlou Sy for helpful comments on the manuscript, and Mary Alyce for a convincing portrayal of interest in psychrometers, even sometimes at dinner.
Received for publication July 8, 1999.
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REFERENCES
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- Brown, R.W. 1970. Measurement of water potential with thermocouple psychrometers: Construction and applications. USDA Forest Service Research Paper INT-80.
- Dalton F.N. Design criteria for Peltier-effect thermocouple psychrometers. Soil Sci. 1968;105:12-17.
- Kauraw D.L., Gupta R.K. Thermocouple psychrometer probe. II. Calibration of thermocouple psychrometer: A rapid technique. Z. Pflanzenernaehr. Bodenk. 1985;148:574-583.
- Lang A.R.G. Osmotic coefficients and water potentials of sodium chloride solutions from 0 to 40°C. Aust. J. Chem. 1967;20:2017-2023.
- Meyn R.L., White R.S. Calibration of thermocouple psychrometers: a suggested procedure for development of a reliable predictive model. In: Brown R.W., Van Haveren B.P., eds. Psychrometry in water relations research. Logan: Utah Agric. Exp. Stn, 1972:55-64.
- Peck A.J. Theory of the Spanner psychrometer, 1. The thermocouple. Agric. Meteorol. 1968;5:433-447.
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- Wullschleger S.D., Dixon M.A., Oosterhuis D.M. Field measurement of leaf water potential with a temperature-corrected in situ thermocouple psychrometer. Plant Cell Environ. 1988;11:199-203.
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ABSTRACT
INTRODUCTION
