Although sonic anemometers have been used extensively for several decades in micrometeorological and ecological research, there is still some scientific debate about the measurement uncertainty of these instruments. This is due to the fact that an absolute reference for the measurement of turbulent wind fluctuations in the free atmosphere does not exist. Traditionally, two approaches have been applied to evaluate the performance of sonic anemometers, either by placing them in a wind tunnel and testing them for different flow angles or by putting different instruments next to each other in the field over a homogeneous surface, so that all of them can be expected to measure the same wind velocities and turbulence statistics. The first approach has the advantage that the true flow characteristics are well known; however, the characteristics of the flow deviate far from those in the turbulent atmospheric surface layer where sonic anemometers are typically deployed. Reynolds numbers in a wind tunnel, for instance, are several orders of magnitude smaller than under natural conditions. In contrast, the second intercomparison approach has the disadvantage that it lacks an uncontested reference; however, such field experiments allow the simultaneous evaluation of several instruments under real-world conditions. In other words, the first approach has a high internal validity while the second approach has a high external validity.

Wind-tunnel experiments have been an important milestone towards revealing and quantifying probe-induced flow distortion effects. One of the first wind-tunnel tests including a correction equation for flow distortion effects is reported by Kaimal (1979). Considering the results of another wind-tunnel study about a three-dimensional hot-wire anemometer, Högström (1982) stressed the importance of such test for all turbulence sensors, and wind-tunnel experiments soon became a standard method for optimizing and calibrating sonic anemometers. Subsequently, Zhang et al. (1986) developed a new sonic anemometer based on measurements from the wind tunnel, which inspired the design of the Campbell CSAT3. A further wind-tunnel calibration for the Gill Solent R2 sonic anemometer is presented by Grelle and Lindroth (1994).

However, researchers soon realized that the transferability of wind-tunnel experiments to field conditions is limited. A very interesting comparative wind-tunnel study about several sonic anemometers (Gill Solent, METEK USA-1, Kaijo Denki TR-61A, TR-61B, and TR-61C) is conducted by Wieser et al. (2001). They evaluate flow distortion correction algorithms provided by the respective manufacturers and come to the following conclusion: “Because of the very low level of turbulence in the wind tunnel (no fences or trip devices have been used), the size and stability of vortices set up behind struts may be increased in comparison with field measurements” (Wieser et al., 2001). Moreover, Högström and Smedman (2004) present a critical assessment of laminar wind-tunnel calibrations by using a hot-film instrument as reference during a field experiment over a flat and level coastal area with very low vegetation. Their results indicate that wind-tunnel-based corrections might be overcorrecting, or at least do not improve the comparison with the reference measurement of turbulence statistics.

Despite these known limitations, more extensive wind-tunnel calibration studies were conducted, which led to the publication of the so-called angle-of-attack correction for Gill Solent R2 and R3 (van der Molen et al., 2004; Nakai et al., 2006). However, it is often overlooked that angle-of-attack-dependent errors might partially be an artefact of wind-tunnel experiments, because in quasi-laminar wind-tunnel flows the angle-of-attack remains constant. In contrast, the flow distortion caused by the same geometrical structure is much smaller under turbulent conditions, when the three-dimensional wind vector and the corresponding flow angles fluctuate constantly (Huq et al., 2017).

In order to address concerns about the validity of these wind-tunnel-based calibrations, the angle-of-attack-based flow distortion concept was investigated in the field under natural turbulent conditions. Nakai and Shimoyama (2012) mounted several Gill WindMaster instruments at different angles next to each other above a short grass canopy, and Kochendorfer et al. (2012) conducted a very similar field experiment focusing on RM Young Model 81000 anemometers, while the Campbell CSAT3 was only briefly examined. It has to be noted that the results of these two studies were interpreted under the false assumption that the instantaneous wind vector remains unchanged between different instruments that are mounted more than 1 m apart, which contradicts the concept of a fluctuating turbulent flow with a certain decay of the spatial autocorrelation function (Kochendorfer et al., 2013; Mauder, 2013).

However, such side-by-side comparisons with different alignment of the same instrument can be quite instructive, as long as only turbulence statistics are analysed, which can indeed be considered to be similar across several metres over homogeneous surfaces. Although their study site is less than ideal for a field intercomparison (over a sloped forest canopy within the roughness sublayer), Frank et al. (2013) found that non-orthogonally positioned transducers can underestimate vertical wind velocity (w) and sensible heat flux (H), by comparing the output of two pairs of CSAT3 anemometers while one pair was rotated by 90∘. This finding was substantiated in a follow-up study (Frank et al., 2016), which also covers a side-by-side comparison of two CSAT3 mounted at different alignment angles plus two sonic anemometers with an orthogonal transducer array and a CSAT3 with one vertical path. An elaborate statistical analysis leads them to the following conclusion: “Though we do not know the exact functional form of the shadow correction, we determined that the magnitude of the correction is probably somewhere between the Kaimal and double-Kaimal correction” (Frank et al., 2016), referring to the original work of Kaimal (1979).

In a parallel chain of events, international turbulence comparison experiments (ITCEs) have been carried out at different places around the world since the early days of sonic anemometry used for micrometeorological field campaigns (Dyer et al., 1982; Miyake et al., 1971; Tsvang et al., 1973, 1985), mostly with the aim of investigating the comparability of different instrumental designs. Typically, relative differences were analysed based on those comparative datasets, which generally suffer from the lack of a “true” reference measurement or etalon, but those experiments have the advantage that many anemometer models can be tested at once under real-world conditions. Nevertheless, absolute biases were also sometimes detected, such as the flow distortion from supporting structures, which from the 1976 ITCE was deduced from a non-zero mean vertical wind speed, especially for geometries with a supporting rod directly underneath the measurement volume (Dyer, 1981).

In those early ITCEs, mostly custom-made instruments were tested. However, since the beginning of the 1990s, a growing number of commercial sonic anemometer models have become available from a number of manufacturers. Based on their field intercomparison experiments, Foken and Oncley (1995) classified all instruments commonly used at the time according to their expected errors into those that are suitable for fundamental turbulence research and those that are sufficient for general flux measurements. About one decade later, several then-popular models were compared in a thorough and comprehensive study by Loescher et al. (2005). They tested eight different probes for the accuracy of their temperature measurement in a climate chamber; they investigated biases of the w measurement in a low-speed wind tunnel, and investigated differences in the turbulence statistics measured in the field. At about the same time, Mauder et al. (2007) conducted a field intercomparison of seven different sonic anemometers as part of the international energy balance closure experiment EBEX-2000 above a cotton field in California. Both studies more or less confirmed the classification of Foken and Oncley (1995), who concluded that only the directional probes without supporting structure directly underneath the measurement volume meet the highest requirements of turbulence research, while no significant deviations between those top-class instruments were detected.

The persisting lack of energy balance closure at many sites around the world (Stoy et al., 2013) and the emerging indications of a general flux underestimation of non-orthogonal sonic arrays (Frank et al., 2013) were the primary motivation of a special field experiment by Horst et al. (2015). They conducted an intercomparison at an almost ideal site, which was flat, even and with a homogeneous fetch. Two CSAT3 representing a typical non-orthogonal sensor were compared against two different orthogonal probes manufactured by Applied Technologies Inc. and one custom-made CSAT3 with one vertical path. Under the assumption that the flow-distortion correction of Kaimal (1979) is correct, they state that the CSAT3 requires a correction of 3 to 5 %. This is in quite good agreement with the conclusion of Frank et al. (2016), who suggest a correction of the magnitude between Kaimal and double Kaimal, and the numerical study of Huq et al. (2017), which found an underestimation of 3 to 7 %. Thus, at least for the CSAT3, some consensus is emerging about the magnitude of the correction required under turbulent conditions in the field.

Although the results on measurement error are converging for the CSAT3 model, less is known about the comparability between different sonic anemometer models available today. As the last comprehensive intercomparison experiments were conducted more than 10 years ago, and some new models have emerged on the market since then and some others have received firmware upgrades, we believed that it was time for another field intercomparison covering commonly used sonic anemometers. We deployed six different models from four different manufacturers next to each other over a short grass canopy. Furthermore, two CSAT3 were tested simultaneously in order to compare the influence of transducer rain guards. An orthogonal regression analysis is applied to the turbulence statistics obtained from the different instruments, and quantitative measures of uncertainty, such as bias and comparability (RMSE), are derived.

In theory, the overall agreement between sonic anemometers cannot be better than the random error, if the seven different measurement systems collect independent samples of an homogeneous turbulence field (Richardson et al., 2012). The stochastic error due to limited sampling of the turbulent ensemble (Finkelstein and Sims, 2001) is 17 % or 0.03 m s-1 on average for u* and 14 % or 5 W m-2 for Hs, based on data from CSAT3_1. The comparability values that we found between different instruments for these two quantities are only slightly larger. This means that a better agreement is hardly physically possible, and the remaining small discrepancies can be explained by slight surface heterogeneities within the footprint area of the different systems and by a very small instrumental error. The agreement between the two CSAT3 is as good as the agreement with other sonic anemometer models.

We found a much better agreement between different sonic anemometers, especially for u* and Hs, in comparison to previous intercomparison experiments (Loescher et al., 2005; Mauder et al., 2007). All tested instruments were within the limits that Mauder et al. (2006) classified as type A, i.e. sonic anemometers suitable for fundamental turbulence research. Perhaps this can partially be explained by a consistent digital data acquisition, implemented here with a very high precision clock and event-driven communication using Python programming language. Probably, the implementation of a more efficient spike removal algorithm for the high-frequency data and other additional quality tests in the post-processing scheme of Mauder (2013) also helped to improve the data quality of the resulting fluxes and consequently improved the agreement.

On top of that, the filtering for obstructed wind direction sectors and for rain, as described in Sect. 2.2, was crucial to remove poor-quality data. Both additional steps improved the agreement between instruments considerably. For σw, regression slopes ranged between 1.00 and 1.24 and intercepts were between -0.05 and 0.00 m s-1 after processing according to Mauder (2013). After filtering for obstructed wind direction, slopes ranged between 0.98 and 1.22 and intercepts remained between -0.05 and 0.00 m s-1. As can be seen from the results (Table 4), the overall agreement further improved after the filtering for rainy periods. Especially, some outliers of the CSAT3_2, which did not have the rain-guard meshes at the transducer heads, were rejected after this step. The effect of the data filtering on other quantities, such as Hs, was smaller. Here, the slopes ranged already only between 0.97 and 1.00 after processing according to Mauder (2013), which did not change much further after filtering for obstructed wind directions and for rainy periods (Table 7). This can be explained by the fact that the scheme of Mauder (2013) is designed for quality control of fluxes and not necessarily standard deviations. It is therefore much stricter for Hs than for σw.

Considering flow distortion errors of the order of 5 % or more that are reported in the literature (Frank et al., 2016; Horst et al., 2015; Huq et al., 2017), the very good agreement between all sonic anemometers in this field experiment is nevertheless somewhat surprising. A contribution by changes in the firmware of the different sonic anemometers over the last 10 years is likely but not fully documented. According to the manufacturer, the two CSAT3 sonic anemometers have no flow distortion correction at all, while all the other five instruments probably do apply some sort of correction – although the exact details are not publicly available for all of them. This could mean that flow distortion errors are indeed significant for our experiment but perhaps all instruments are afflicted with an error of almost the exact same magnitude and consequently underestimate σw and vertical scalar fluxes similarly, despite the obvious differences in sensor geometry and internal data processing.

Alternatively, one might also suppose that the flow distortion errors were generally small for our experimental setup due to the occurred distribution of instantaneous flow angles, since flow-distortion effects tend to be smaller for smaller angles of attack, as indicated by the studies of Grelle and Lindroth (1994) and Gash and Dolman (2003). However, the standard deviation of the angles of attack was about 15∘, which is comparable to other field experiments. For comparison, Gash and Dolman (2003) report about 90 % of their data to be within ±20∘ for the Horstermeer peat bog site, and Grare et al. (2016) report their data to be in a range of ±15∘, most of times even within ±10∘, measuring at 10 m above shrubland. Horst et al. (2015) report their angles of attack to be mostly within ±8∘ for measurements above low weeds and crop stubble with an aerodynamic roughness length of 0.02 m. Since the spread of angles of attack is at the upper end of the values reported in the literature, our comparison results can be considered as a conservative estimate for the random instrument-related uncertainty of typical applications of eddy covariance measurements over vegetation canopies. A common significant systematic error of all tested instruments is quite possible, as suggested by Frank et al. (2016).

One exception to the overall very good agreement is the sonic temperature measurement by both Gill sonic anemometers, the HS and the R3. This error appears not only as an offset but also as deviation of a linear functional relationship and increased scatter. A similar behaviour of other Gill anemometers has been reported before, and a possible explanation has also been provided in the past (Mauder et al., 2007; Vogt, 1995). Obviously, the sonic temperature measurement of Gill anemometers is compromised by a temperature dependence of the transducer delay, i.e. the time delay between the arrival of a sound pulse at the transducer and the registration by the electronics board.

Generally, biases and regression intercepts were very small for all sensors and all computed variables, except for the temperature measurements of the two Gill sonic anemometers (HS and R3), which are known to have a transducer-temperature dependence of the sonic temperature measurement (Mauder et al., 2007). Nevertheless, the Gill anemometers show an equally good agreement for other turbulence statistics. The comparability (RMSE) of the instruments is not always as good as the bias, indicating a random error that is slightly larger than any systematic discrepancies. The best overall agreement between the different instruments was found for the quantities U, σw, and Hs, which suggests that the sensors' physical structure and internal signal processing are designed for measuring wind speed and vertical scalar fluxes as accurately as possible. However, the relative random uncertainty of u* measurements is still large, pointing to the particular challenge in measuring the covariance of horizontal and vertical wind components due to the rather small spectral overlap.

The uncertainty estimate of Mauder et al. (2006) for the buoyancy flux measurement of 5 % or 10 W m-2 was confirmed, not only for those instruments that were classified in that study as “type A” (CSAT3 and Gill HS) but also for those that were labelled “type B” (Gill R3) back then and all other tested instruments (METEK uSonic3-omni, RM Young 81000 and 81000RE). Hence, from our results we cannot derive a classification of the tested sonic anemometers in different quality levels, which means that the evolution of anemometers by all major manufacturers has converged over the last decade.

For applications aiming at measuring vertical scalar fluxes, all tested instruments can be considered equally suitable, as long as digital data acquisition is implemented to avoid additional uncertainty and a stringent data quality control procedure is applied to detect malfunction of the eddy covariance system. Moreover, the deviations between instruments of different manufacturers are not larger than between different serial numbers of the same model. Therefore, we do not consider it to be necessary to agree on one single anemometer model to ensure comparability, e.g. for intensive field campaigns or for networks of ecosystem observatories. Instead, other criteria should be taken into account for the selection of a sonic anemometer, such as climatic conditions of a measurement site (e.g. frost, fog, heat), the distribution of wind directions (omnidirectional or not), the measurement height (path length), the compatibility with an existing data acquisition system or a certain scientific objective. In principle, this conclusion is not in contradiction with the classification Foken and Oncley (1995) and Mauder et al. (2006), because they also concluded that all instruments under investigation were suitable for general flux measurements. Only for specific questions of fundamental turbulence research was it advised to use certain types of instruments.

Although a good agreement between six different sonic anemometer models indicates a high precision of these type of instruments in general, a field intercomparison study can only provide limited insight into the absolute accuracy of these measurements. Particularly, a systematic error that is common to all tested instruments can inherently never be detected in this way. In the past, wind-tunnel experiments were conducted for this purpose, although their transferability to real-world conditions was always debated. Numerical simulations of probe-induced flow distortion (Huq et al., 2017) may provide a better way to characterize the suitability of sonic anemometers for turbulence measurements in the future. If systematic errors for one certain instrument are known from these computationally very expensive simulations, then classical field intercomparisons can be used to test models against such a well-characterized sensor. Moreover, a comparison with a remote sensing based system that is free of flow distortion, such as lidar, would be very helpful if it is able to sample a similarly small volume of air at a similar measurement rate as a sonic anemometer.