Statistical assessment of some errors in thermocouple hygrometric water potential measurement

Abstract

A model is presented for the calculation of some errors in the measurement of water potential for individual thermocouple hygrometers used in the dewpoint or psychrometric mode. The model is based on calculation of the relative standard error in measured thermocouple psychrometric water potential as a function of temperature. Sources of error in the psychrometric mode were found in the calibration of the instrument as a function of water potential and temperature and in voltage (due to electronic noise and zero offsets) and temperature measurement in the field. Total error increased as temperature decreased, approaching a value usually determined by the shape of the thermocouple junction, electronic noise (at low voltages < 1 μV) and errors in temperature measurement. At higher temperatures, error was a combination of calibration errors, electronic noise and zero offset voltages. For a measured water potential of — 1250 kPa, field calibration data for a number of leaf psychrometers contained total errors that ranged between 6 (at 0°C) and 2% (at 45°C) for the better psychrometers and between 11 (at 0°C) and 5% (at 45°C) for the worst, assuming zero offsets were 0.5 μV. Zero offsets were < 0.7 μV at all times. The dewpoint errors arose from calibration of the dewpoint hygrometer as a function of water potential, not temperature correcting the calibration slope to other temperatures, setting the dewpoint coefficient incorrectly and errors in voltage and temperature measurement. The total error also increased as temperature decreased, because of the differences in temperature sensitivity between dewpoint and psychrometric calibration constants. Consequently, the major source of error in the dewpoint mode arose from the difficulty in determining the dewpoint coefficient. This error, which is temperature dependent, contains three subcomponent errors; the temperature dependence, random variation associated with determining the temperature dependence and error in setting the correct value of the dewpoint coefficient. Calibration and extrapolation errors were smaller than those of the psychrometric technique. Typically, the error in a dewpoint measurement varied between ∼ 6 and 2% for the best leaf hygrometer and between 10 and 3% for the worst for temperatures beween 0 and 45°C, respectively. At low temperatures, the dewpoint technique often has no advantage over the psychrometric technique, in terms of measurement errors.