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

Abstract. Air temperar (T) plays a fundamental role in many aspects of the flux exchanges between the atmosphere and ecosystems. Additionally, it is critical to know where (in relation to other essential measurements) and at what frequency T must be measured to accurately describe 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 senosrs of three-dimensional sonic anemometer and infrared gas analyzer, respectively. T then is computed by use of either T = Ts (1 + 0.51q)−1, where q is specific humidity, or T = Ts (1 + 0.32e / P)−1, where e is water vapor pressure and P is atmospheric pressure. Converting q and e / P 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 raises 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 were evaluated, nor was the question answered. Based on the first principles, this study derives the T equation in terms of Ts and water vapor molar mixing ratio (χH2O) without any assumption and approximation. Thus, this equation itself does not have any error and the accuracy in T from this equation (equation-computed T) depends solely on the measurement accuracies of Ts and χH2O. Based on current specifications for Ts and χH2O 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 little (±0.03 K) from the uncertainty in χH2O measurements. Apparently, the improvement on measurement technologies particularly for Ts would be a key to narrow this accuracy range. Under normal sensor and weather conditions, the specified accuracy is overestimated and actual accuracy is better. Equation-computed T has frequency response equivalent to high-frequency Ts and is insensitive to solar contamination during measurements. As synchronized at a temporal scale of measurement frequency and matched at a spatial scale of measurement volume with all aerodynamic and thermodynamic variables, this T has its advanced merits in boundary-layer meteorology and applied meteorology.