Abstract. 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 T=Ts1+0.51q-1, where q is
specific humidity, or T=Ts1+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
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 (χH2O) 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 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 a little (±0.02 K) from the
uncertainty in χH2O 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.
