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 (T_s) 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 = T_s (1 + 0.51q)⁻¹, where q is specific humidity, or T = T_s (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 T_s 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 T_s and water vapor molar mixing ratio (χ_H2O) 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 T_s and χ_H2O. Based on current specifications for T_s and χ_H2O 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 T_s measurements and little (±0.03 K) from the uncertainty in χ_H2O measurements. Apparently, the improvement on measurement technologies particularly for T_s 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 T_s 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.

中文翻译：

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通过封闭路径涡流协方差通量系统采样的空气流的声波温度和水汽混合比导出的空气温度方程

摘要。空气温度（T）在大气和生态系统之间通量交换的许多方面起着基础性作用。此外，了解在何处（相对于其他基本测量）和在什么频率上测量T以准确描述此类交换至关重要。在闭合路径涡协方差（CPEC）通量系统，Ť可以从声波温度（计算Ť_小号由三维超声风速仪和红外气体分析仪的快速响应senosrs测量）和水蒸汽的混合比例，分别。Ť然后通过使用任一的计算Ť  =  Ť_小号（1个+ 0.51 q) ^-1，其中q是比湿度，或T  =  T _s (1 + 0.32 e  /  P ) ^-1，其中e是水蒸气压，P是大气压。将q和e  /  P转换为相同的水蒸气混合比，分析揭示了这两个方程之间的差异。CPEC 系统中的这种差异可能达到 ±0.18 K，从而给T的精度带来不确定性从两个方程，并提出了哪个方程更好的问题。为了澄清不确定性并回答这个问题，彻底研究了根据T _s和 H ₂ O 相关变量的T方程的推导。上面的两个方程是用近似值开发的。因此，既没有评估它们的准确性，也没有回答问题。基于第一性原理，本研究根据T _s和水蒸气摩尔混合比 (χ _{H 2 O} )推导出T方程，无需任何假设和近似。因此，这个方程本身没有任何误差，T 中的精度从这个方程（方程计算的T）完全取决于T _s和 χ _{H 2 O}的测量精度。根据CPEC300 系列中T _s和 χ _{H 2 O 的}当前规格并考虑到它们的最大测量不确定度，方程计算的T的精度规定在 ±1.01 K 范围内。该精度不确定度主要 (±1.00 K) T _s测量的不确定性和很少 (±0.03 K) χ _{H 2 O}的不确定性测量。显然，改进测量技术尤其是T _s将是缩小该精度范围的关键。在正常的传感器和天气条件下，指定精度被高估，实际精度更好。方程计算的T具有与高频T _s等效的频率响应，并且在测量过程中对太阳污染不敏感。由于在测量频率的时间尺度上同步并在测量体积的空间尺度上与所有空气动力学和热力学变量相匹配，该T在边界层气象学和应用气象学中具有其先进的优点。