Abstract. A sonic anemometer reports three-dimensional (3-D) wind and sonic temperature (Ts) by measuring the time of ultrasonic signals transmitting along each of its three sonic paths, whose geometry of lengths and angles in the anemometer coordinate system was precisely determined through production calibrations and the geometry data were embedded into the sonic anemometer operating system (OS) for internal computations. If this geometry is deformed, although correctly measuring the time, the sonic anemometer continues to use its embedded geometry data for internal computations, resulting in incorrect output of 3-D wind and Ts data. However, if the geometry is remeasured (i.e., recalibrated) and to update the OS, the sonic anemometer can resume outputting correct data. In some cases, where immediate recalibration is not possible, a deformed sonic anemometer can be used because the ultrasonic signal-transmitting time is still correctly measured and the correct time can be used to recover the data through post processing. For example, in 2015, a sonic anemometer was geometrically deformed during transportation to Antarctica. Immediate deployment was critical, so the deformed sonic anemometer was used until a replacement arrived in 2016. Equations and algorithms were developed and implemented into the post-processing software to recover wind data with and without transducer-shadow correction and Ts data with crosswind correction. Post-processing used two geometric datasets, production calibration and recalibration, to recover the wind and Ts data from May 2015 to January 2016. The recovery reduced the difference of 9.60 to 8.93 ∘C between measured and calculated Ts to 0.81 to −0.45 ∘C, which is within the expected range, due to normal measurement errors. The recovered data were further processed to derive fluxes. As data reacquisition is time-consuming and expensive, this data-recovery approach is a cost-effective and time-saving option for similar cases. The equation development can be a reference for related topics.

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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.

Abstract.A sonic anemometer (sonic) reports 3-dimensional wind and sonic temperature (T s ) by measuring the time of ultrasonic signals flying along each of its three sonic paths whose geometry of lengths and angles in the sonic coordinate system was precisely determined through production calibrations and was embedded into the sonic's firmware. If the sonic path geometry is deformed, although correctly measuring the time, the sonic continues to use its embedded geometry data for 20 internal computations, resulting in incorrect data. However, if the geometry is re-measured (i.e. recalibrated) to update sonic firmware, the sonic can resume reporting correct data. In some cases, where immediate recalibration is not possible, a deformed sonic can be used because ultrasonic signal-flying time is still correctly measured. For example, transportation of a sonic to Antarctica in 2015 resulted in a geometrically deformed sonic. Immediate deployment was critical, so the deformed sonic had been used until a replacement arrived in 2016. To recover data from this deformed sonic, equations and algorithms 25 were developed and implemented into the post-processing software to recover wind data with/without transducer shadow correction and T s data with crosswind correction. Using two geometric datasets, production calibration and recalibration, post-processing recovered the wind and T s data from May 2015 to January 2016. The recovery reduced the difference of 9.60 to 8.93 °C between measured and calculated T s to 0.81 to -0.45 °C, which is within the expected range due to normal measurement errors. The recovered data were further processed to derive fluxes. Since such data reacquisition is time-30 consuming and expensive, this data recovery approach is a cost-effective and time-saving option applicable to similar cases.The equation development can be a reference to the studies on related topics.

<p>Among various measurement techniques, eddy covariance (EC) is the most direct one for measuring evapotranspiration (ET) fluxes at field to ecosystem scales (Aubinet et al., 2000). In the past two decades, EC flux towers around the world, particularly those within the FLUXNET, have served as a worldwide network of calibration and validation for surface-atmosphere energy and ET flux data obtained from remote sensing-based models or hydrological process-based models (Wang and Dickinson, 2012). </p><p>One of the major challenges in model-data benchmarking is the spatial mismatch issue. For example, the grid cell size of around 10<sup>6</sup> – 10<sup>8</sup> m<sup>2</sup> in typical Earth system regional modeling cases is often several orders of magnitude larger than the EC flux footprints of around 10<sup>3</sup>–10<sup>7</sup> m<sup>2</sup>. Since most flux tower sites are located in more-or-less heterogeneous landscapes, multiple measurement units for spatially adequate sampling and representative fluxes are of interest for capturing the fine-scale spatial variation. However, the deployment of higher density sampling points was mainly limited by the costs of conventional analyzers. Therefore, there is increasing demand in the development of low-cost water vapor analyzers specifically for more spatial representative terrestrial ET flux footprints measurements based on EC methods.</p><p>In recent years, laser-based gas spectrometers have shown good reliability and effectiveness in the high-frequency and high-sensitivity measurement of various atmospheric trace gases. In this work, we have developed an open-path analyzer (HT1800, HealthyPhoton Co., Ltd.) for fast and sensitive measurements of atmospheric water vapor density. The analyzer employs a low-power vertical cavity surface emitting laser (VCSEL) and a near-infrared Indium Galinide Arsenide (InGaAs) photodetector. An open-path configuration with 0.5 m effective optical path length is used for selective and sensitive detection of the single spectral transition of H<sub>2</sub>O at 1392 nm, which has been extensively studied in the field of spectroscopic analysis. Using this spectral line to realize the single-component measurement of water vapor density can avoid the complex cross-calibration process due to the H<sub>2</sub>O-CO<sub>2</sub> spectral interference as happened in traditional nondispersive infrared (NDIR) analyzers. On the other hand, the semiconductor nature of lasers and detectors can borrow the mature optical communication industry fabrication process, so that the cost of the core optoelectronic devices is expected to be reduced in mass production.</p><p>The analyzer has a precision (1σ noise level) of 15 μmol mol−1 (ppmv) at a sampling frequency of 10 Hz. Due to its open-path configuration, there is no delay or high-frequency damping due to surface adsorption. The analyzer head has a weight of ~2.8 kg and dimensions of 46 cm (length) and 9.5 cm (diameter). It can be powered by solar cells, with a total power consumption of as low as 10 W under normal operations. With good performance in terms of response time and precision, this instrument is an ideal tool for ET flux measurements based on the EC technique. An EC flux tower was built based on the open-path analyzer, which also included an integrated CO<sub>2</sub> and H<sub>2</sub>O open-path gas analyzer and 3-D sonic anemometer (IRGASON, Campbell Scientific) for comparison of ET flux measurement.</p>