Air temperature equation derived from sonic temperature and water vapor mixing ratio for turbulent airflow sampled through closed-path eddy-covariance flux systems

Zhou, Xinhua
Gao, Tian
Zhen, Xiaojie
Suyker, Andrew
Awada, Tala
Okalebo, Jane
Zhu, Jiaojun
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© Author(s) 2021
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Air temperature (T) plays a fundamental role in many aspects of the flux exchanges between the atmosphere and ecosystems. Additionally, knowing where (in relation to other essential measurements) and at what frequency T must be measured is critical to accurately describing such exchanges. In closed-path eddy-covariance (CPEC) flux systems, T can be computed from the sonic temperature (Ts) and water vapor mixing ratio that are measured by the fast-response sensors of a three-dimensional sonic anemometer and infrared CO2–H2O analyzer, respectively. T is then computed by use of either , where q is specific humidity, or , where e is water vapor pressure and P is atmospheric pressure. Converting q and into the same water vapor mixing ratio analytically reveals the difference between these two equations. This difference in a CPEC system could reach ±0.18 K, bringing an uncertainty into the accuracy of T from both equations and raising the question of which equation is better. To clarify the uncertainty and to answer this question, the derivation of T equations in terms of Ts and H2O-related variables is thoroughly studied. The two equations above were developed with approximations; therefore, neither of their accuracies was evaluated, nor was the question answered. Based on first principles, this study derives the T equation in terms of Ts and the water vapor molar mixing ratio () without any assumption and approximation. Thus, this equation inherently lacks error, and the accuracy in T from this equation (equation-computed T) depends solely on the measurement accuracies of Ts and . Based on current specifications for Ts and in the CPEC300 series, and given their maximized measurement uncertainties, the accuracy in equation-computed T is specified within ±1.01 K. This accuracy uncertainty is propagated mainly (±1.00 K) from the uncertainty in Ts measurements and a little (±0.02 K) from the uncertainty in measurements. An improvement in measurement technologies, particularly for Ts, would be a key to narrowing this accuracy range. Under normal sensor and weather conditions, the specified accuracy range is overestimated, and actual accuracy is better. Equation-computed T has a frequency response equivalent to high-frequency Ts and is insensitive to solar contamination during measurements. Synchronized at a temporal scale of the measurement frequency and matched at a spatial scale of measurement volume with all aerodynamic and thermodynamic variables, this T has advanced merits in boundary-layer meteorology and applied meteorology.
This article is published as Zhou, X., Gao, T., Takle, E. S., Zhen, X., Suyker, A. E., Awada, T., Okalebo, J., and Zhu, J.: Air temperature equation derived from sonic temperature and water vapor mixing ratio for turbulent airflow sampled through closed-path eddy-covariance flux systems, Atmos. Meas. Tech., 15, 95–115,, 2022. This work is distributed under the Creative Commons Attribution 4.0 License.