The data used in this study came from 38 ICOS Class 1 and 2 stations measuring CO2 and H2O fluxes (Table ). The analysis was based on the 2024 data, the latest dataset available when most of the analyses for this paper were performed. The EC setup is standard at all ICOS sites and it is composed of a LI-7200(RS) (LI-COR Biosciences Inc., Lincoln, NE, USA) infrared gas analyser (IRGA) and one Gill HS-50 or HS-100 (Gill Instruments Ltd., Lymington, UK) 3-D sonic anemometer . All sites were equipped with a standard LI-COR heated 0.73 m-long sampling line of 5.33 mm of inner diameter, a LI-COR rain cap and a 2 µm inlet filter (Swagelok Company, Solon, OH, USA). The flow rate was fixed at each site, at a value between 10 and 16 Lmin-1 according to site specifications. The only exception was FR-Gri that switched several times between 12 and 15 Lmin-1 until the end of April, after which the flow rate was fixed at 12 Lmin-1. The acquisition rate was 20 Hz for 29 sites and 10 Hz for the remaining 9. According to ICOS instructions , the horizontal and vertical distances between the center of the anemometer sensing volume and the center of the sphere that encloses the IRGA raincap should be in the range 23.5/31 and 0/-0.05 cm, respectively. In practice, few exceptions to this rule are encountered (Fig. ).

The measurement heights across the 38 sites varied over a wide range, reflecting the diversity of ecosystems measured, from peatlands and shrublands to croplands and grasslands, and up to forests (Fig.  and Table ). Stations were classified into two categories, according to their height above the displacement plane (z-d). After visual inspection of z-d values and cross-checking with the characterisation of the ecosystem type, a clear distinction emerged between forests, with z-d above 7 m, and other ecosystems, where z-d was below 7 m (maximum 4 m). Those two categories were defined as high- and low-measurement-height sites, respectively (HMH and LMH).

The half-hourly fluxes uncorrected for frequency losses, data quality tests, as well as binned spectra and co-spectra used throughout this study, were computed by the ICOS Ecosystem Thematic Center (ETC), through the standard ICOS pipeline , using EddyPro (version 7.0.9), leading to the 2025 archive product . To compute the fluxes, the following main processing steps were performed: block average to compute the fluctuations around the mean and covariance maximisation to correct for time-lag. Spectra and co-spectra were computed for each half-hour using the Fourier transform and smoothed using fifty exponentially spaced frequency bins.

The frequency losses were corrected for using either our own implementation, described in the following section, or the standard ICOS pipeline that relies on correction of high-pass attenuations according to and correction for low-pass attenuations according to , including cross-wind and vertical sensor separation by and correction for the anemometer path averaging and time response .

The general principles of an experimental spectral correction procedure are presented in Fig. . They are generally well established, and follow for both spectral and co-spectral approaches the same steps. The main gas- and method-specific options and parametrizations, which are user-defined, are also highlighted (orange, blue and magenta elements in Fig. ).

Only high-frequency spectral losses were considered here. The analysis was performed in the frequency domain, using the (co-)spectra to assess the high-frequency attenuation and compute the flux correction factors. The approach used in this work relied on the use of meteorological data classes and average values. Based on the theorised dependencies found in the literature , wind speed classes were used for both gases and computation steps, namely cut-off frequency (cof) and correction factor (CF) estimation. For H2O only, an additional classification based on relative humidity (RH) was applied, as spectral attenuations of water fluxes have been shown to be driven by the adsorption and desorption processes of water molecules in the sampling tube of the IRGA that varies with RH . Finally, for the specific purpose of investigating the theorised dependence of sensor separation CFs to wind direction and for CO2 only, an additional assessment by wind direction classes was performed. In all three cases, a fixed number of classes containing an equal number of data points was used.

As an initial filtering step common to both cut-off frequency and correction factor computations, only data for which wind speed (WS), wind direction (WD), dimensionless stability parameter (zL), sensible heat flux (H), tracer flux (CO2 or H2O accordingly) and, for H2O only, RH were available were retained. In addition, considering the horizontal geometry of the sonic anemometer used in ICOS, an additional site-specific wind direction filter was applied to remove data affected by flow distortion caused by the horizontal boom supporting the sonic transducers.

Both normalised average temperature and CO2 concentration spectra and normalised average co-spectra of sensible heat flux and CO2 flux for all sites were generally well defined, matched quite well in the medium frequencies and showed the expected behaviour in the high frequencies (Figs.  and ). For some sites, especially of the HMH group (black titles in Fig. ), the presence of white noise on the average gas spectra was observed at a very high frequency, requiring the application of the denoising procedure (Appendix ). This procedure was performed for at least one class of WS at 21 sites (3 out of the 14 LMH, and 18 out of the 23 HMH). Overall, the spectra and co-spectra were of high quality, allowing a robust determination of TFs and associated cofs.

Normalised average spectra and co-spectra for H2O are generally well-defined and not noisy (Figs.  and ). However, H2O spectra show an unexpected behaviour at low frequencies, where they are systematically higher than the ideal ones. The two curves then cross, with the real spectra decreasing faster than the ideal in higher frequencies. It results in a TF that continuously decreases with increasing frequency, without having the typical plateau that precedes the fall linked to spectral losses (not shown). This behaviour is present for all sites for spectra and sometimes for co-spectra as well. It generally worsens with increasing RH values and makes it more challenging to perform a robust fitting procedure, as the Lorentzian equation expects a no-filter zone before the fall with the increasing frequency. This behaviour is acknowledged here, although the Lorentzian formulation is still used for fitting, as it represents the most widely adopted approach, consistent with the CO2 case. Moreover, similar deviations from the idealised TF have been reported in a range of atmospheric conditions and are not specific to the ICOS sites and set-up considered here. A more detailed discussion on this aspect is provided in Sect. .

Moreover, as it was the case for CO2, several occurrences of white noise are visible on real spectra at high frequency, which implies that the denoising procedure was necessary before cof computation. Indeed it was found that denoising was activated for at least one RH class in 32 sites (10 out of 15 and 22 out of 23 LMH and HMH respectively), with more occurrences observed for high RH and WS classes.

The impact of the sensor separation term has been highlighted in the gas-specific CF results (Sect.  and ). This factor is identical for any gas for a given setup and atmospheric condition. Therefore, its relative contribution depends on the importance of other sources of spectral loss, which are minimal for CO2 but more substantial for H2O, making the sensor separation term the main contribution to the total CF for CO2 (Fig. ).

The wind direction effect is proper to the sensor separation term, as no other source of spectral loss depends on it, and its impact on CFs is therefore further assessed for both methods. The focus is on CO2 results, as for H2O the RH effect was found to dominate over any other dependency.

To isolate the wind direction effect, 8 classes of WD were used to compute cofs and CFs for both approaches, selecting unstable conditions and data with WSs between 2 and 3 ms-1 (Fig. ). Because of this additional data filtering, some station datasets had not enough data for a robust computation and were excluded from the analysis. In these conditions, the directional effect dominates the full spectral CF, as expected. Interestingly, a trend with wind direction is observed in the co-spectral results as well, experimentally confirming the model assumption. The magnitude of co-spectral CF is systematically smaller than the theoretical one, but generally in phase with the expected minimum and maximum zones (Fig. ).

Finally, a systematic pattern of WSs with wind direction is observed across sites (not shown), which results in a cross-dependence that makes it harder to determine which term is the main driver of the CF dependence.

The comparison of spectral and co-spectral approaches has been presented through the impact on cut-off frequencies, correction factors, half-hourly fluxes and, finally, cumulative fluxes (not gap-filled). The results show that the differences between the methods for CO2 fluxes are systematic, the spectral method having higher CFs and thus amplifying the fluxes. The difference is always very low for HMH due to limited high-frequency signal content and therefore overall very low CFs. It is higher, but still limited, for LMH sites, the worst case being only 0.04 µmolm-2s-1 for mean median negative fluxes (Table ) and the impact on cumulative fluxes is only on average of 1.3 %. It can, however, reach higher values for specific stations (e.g. up to 0.56 µmolm-2s-1 for IT-BCi, and 4.8 % on cumulative fluxes).

The differences get worse for LE, with the spectral correction overestimating the co-spectral one by 2.48 Wm-2 on average for LMH half-hourly fluxes and by 4.5 % on cumulated fluxes. The overestimation is even reaching 5 %–10 % for 9 out of 38 sites (Fig. ).

The same order of magnitude for differences was found by in their single site study and here the differences are investigated in terms of dependencies, magnitude and causes, and placed in the larger framework of spectral correction approaches assumptions and limitations.

There are fundamental differences in the theory underlying the spectral and co-spectral methods to be considered and discussed.

The results across all sites confirm a strong dependence of the CF on the cof, which stresses the importance of correctly characterising the system attenuation behaviour, before combining it with the spectral content to get the CFs. Its computation depends on the quality of the (co-)spectra used to derive the empirical TF, as well as on the choice of the TF to be fitted to the data.

The use of Eqs. () and () to derive the TF relies on the assumption of spectral similarity in the low frequencies. This hypothesis is generally accepted and widely used in similar correction procedures, in particular when the half-hourly variability that could undermine its validity is levelled out by the use of averages over very specific atmospheric conditions . While well observed for CO2, including in this work, multiple works have highlighted an apparent lack of spectral similarity between H2O and temperature spectra . The observed shapes of the H2O spectral averages used in our work follow those findings (Fig. ), with a lack of spectral similarity in the lower frequencies that appears to worsen with increasing RH (and thus attenuation, not shown), and is more marked for spectra than co-spectra (Appendix ). Such dissimilarity has been investigated in various studies and was found to be systematic for water vapour fluxes at low frequencies due to different transport processes affecting the two variables . Besides, in their work, link a similar behaviour of gas spectra in the low frequencies to the presence of red noise (i.e., noise dominated by slow, correlated variations at low frequencies). In either case, this result challenges the validity of using spectra for the correction of water vapour attenuation, and the results should be interpreted keeping this limitation in mind.

The attenuation is approximated by a first-order filter in the shape of a Lorentzian (Eq. ). Although widely used in the literature , many argue that this simple response function does not reflect the complexity of the EC system, and therefore cannot correctly describe its whole damping behaviour . This is particularly true for H2O, for which other shapes of TFs (e.g. Gaussian) have been suggested . Similarly, the inclusion of a square root in the TF definition is still debated , and in particular is included in the co-spectral approach based on work relying on a Lorentzian TF shape . The choice of TF shapes and the impact it can have on the spectral-co-spectral comparison is hard to predict and should therefore be tested systematically for both methods and gases.

In addition to these general considerations, there are method-specific effects that should be acknowledged. Firstly, the co-spectral approach requires a proper time-lag estimation, the recognition of the low-pass-filtering-induced time lag and consequent phase-shift, and the inclusion of this effect in both the cof and CF estimations. It is included in this work through the use of TF (in both Eqs.  and ), which is however an approximation that could fail under very strong attenuations . Co-spectral data are also generally considered noisier and more sensitive to contamination from bad measurements than spectral data, since they depend on two variables . We observed that thanks to very selective high-quality filtering of the data, this risk can be minimised, resulting in good quality, noise-free co-spectra (Figs.  and ). In rare instances where lower-quality data pass all screenings, the impact generally depends on total attenuation. In our analysis, it resulted in co-spectral outputs being more impacted than spectral ones for CO2. This is because the spectral cofs, not including the sensor separation effect, are so high that a lower resolution of the TF has little to no impact, whereas this is not the case for co-spectra.

On the other hand, the presence of noise is observed for spectra, mostly in the highest frequencies when the real signal is low (Figs.  and ). Using an automatic procedure (described in Appendix ), noise was found and removed at 58 % and 84 % of sites for CO2 and H2O, respectively. In line with similar observations , these results confirm that denoising plays a central role in the spectral method, and that addressing the limitations of the current procedure (e.g. assumption of white noise) and stabilising a robust approach are necessary .

Finally, we showed that CO2 attenuation is dominated by the sensor separation effect, the theoretical term that corrects for this effect constituting on average 89 % of the total spectral CF (across sites and for unstable conditions) (Fig. ). For the spectral approach, this means that the final CF rely heavily on the theoretical equation defining this specific term. This is questionable for an approach that is initially intended to be mainly experimental. In these conditions, the applicability of the chosen theoretical approach to define the sensor separation CF should be addressed. The method developed by uses an exponential model to estimate the attenuation as a function of the co-spectral peak frequency (parameterised according to stability) and the distance between the sensors (depending on wind direction). If the modelled peak frequency does not reflect the turbulent characteristics of the site, the estimated attenuation could be biased . Here, a comparison with the co-spectra results revealed that CF_HL09 are far more sensitive to atmospheric stability than the experimental CF, reaching unrealistically high values under stable conditions (Fig. ). This is consistent with findings from other studies , and whilst the consequences on the fluxes surviving the traditional flux filtering are minimised (the u* filtering removes most stable conditions), it is considered methodologically questionable. Moreover, a dependence of co-spectral CF on wind direction was found, generally in phase but with a smaller amplitude than the modelled behaviour (Fig. ). This result experimentally confirms the theoretical framework, though only partially its application, and validates the co-spectral method in its ability to account for all sources of attenuation. It further suggests that explicitly including the directional effect in the co-spectral approach could improve CF computation. However, in practice, this is not always feasible: the additional classification, combined with site-specific wind roses, would further fragment the dataset, potentially leaving insufficient data to reliably apply the procedure. Given this limitation – and considering that a dependence between WD and WS is also observed (Fig. ), and that WS distribution at a given site is typically broader and more uniform than that of wind direction – WS classification alone is deemed sufficient for the co-spectral approach.

Common to the two approaches is the choice of the reference co-spectrum. Here, the fully empirical method is used, and therefore the measured sensible heat co-spectrum is considered ideal. However, it should be noted that what to use as an unattenuated reference is an ongoing discussion in the literature, with works suggesting that the empirical choice is not the wisest and that theory-based parametrisations of ideal co-spectra should be used .

All the limitations presented above can lead to uncertainties at different levels of the correction procedure. The errors linked to this effect are systematic, and an estimation of the sources and magnitude of those uncertainties at each step of the correction procedure is therefore necessary to assess the significance of the differences found.

Overall, our results show spectra characterised by a lack of spectral similarity in the low frequencies for H2O, increasing with RH, and by the presence of (assumed) white noise in the high frequencies, also for strong attenuations mostly. Even if the latter is accounted for with an ad hoc procedure, both contribute to increase the uncertainty in the TF definition and cof computation. On the other hand, concerns related to the quality of the co-spectral data are minimised, leading to stable results across sites. In this context, and for the very specific ICOS standard setup measuring CO2 and H2O, we recommend using the co-spectral approach.

Differences between methods were found to be more important for H2O than for CO2, at least on cumulative fluxes (Table  and Figs.  and ). In this specific metric, the absence of positive/negative offset effects compared to CO2 can play a role. But more important differences between methods can already be found on CFs (Figs.  and ). This is also due to higher CFs for H2O. While CO2 flux attenuation is dominated by the sensor separation effect, adsorption and desorption of water molecules on the sampling tube seem to dominate the high-frequency losses for H2O (Fig. ). This phenomenon results in a strong dependence to atmospheric RH and overall larger attenuations than for CO2, both observations in line with the existing literature . For the spectral approach, these effects translate in a decreased relative dependence of the final spectral-computed CF to sensor separation (Fig. ).

For both gases, differences between methods increase with stability and WS, and decrease with measurement height (Figs.  and ). It is known that these variables are linked to a shift of the reference co-spectrum peak towards the higher frequencies (for an increase in zL and WS and a decrease in z-d) , which yields greater CFs for the same cof and therefore an amplification of the differences between methods.

Atmospheric stability, and in particular the occurrences of stable conditions, play an important role through a double effect. Firstly, the shift of the reference co-spectrum and its consequences mentioned above are observed on both methods and gases, but the level of the impact on the CFs and then fluxes depends on the cof value – the smaller the cof, the larger the impact of a shift towards the high-frequency range. Secondly, for the spectral approach only, a direct effect arises from the theoretical sensor separation term, which is highly sensitive to zL under stable conditions. This leads to systematically large final CFs at low WSs, typically associated with stable episodes (Figs.  and ) and that cannot be reproduced by the fully experimental co-spectral approach.

The analysis of the impact of spectral corrections on fluxes is performed on u*-filtered fluxes. The filtering is applied to reflect the standard EC-flux post-processing pipeline that requires the removal of non-representative fluxes prior to their gapfilling . In practice, the removal of conditions considered as not fully turbulent largely filters stable conditions . Therefore, one major source of differences is removed, and, in the end, the impact of stable conditions on the final fluxes is minor (Figs.  and ).

In line with the work by , higher measurement heights above displacement level (z-d) yield lower CFs, which is again attributed to the shift of the reference co-spectrum towards higher frequencies. This effect is so important that, for stations that were categorised as “high-measurement-height sites” (23 out of 38), and that in practice cover all forest stations, CFs are so low that the high-frequency loss correction could probably be simply skipped and differences between methods for CO2 are so low that they cannot be appreciated (Fig. ). The situation is slightly different for H2O, where if the impact of z-d is clear on CF results (Fig. ), it is less so on (cumulative) fluxes (Figs.  and ), where differences between methods are enhanced by the larger magnitude of the CFs, including for HMH. These results highlight the importance of installing EC systems at the highest possible position, subject to considerations on the extension of the footprint in the target surface , and at the same time stresses the importance of an accurate correction procedure for towers measuring close to the canopy.

In this work, a WS classification is applied at the cof level to account for the dependence of cof on WS induced by sensor separation, as theorised by . Although this expected dependence is typically not accounted for in the literature, it is systematically observed for CO2 in our dataset, where the co-spectral cof increases with WS (Fig. ). This behaviour is consistent with the dominance of the sensor separation term in the overall correction. The resulting dependence of CFs on WS reflects the interplay of two competing effects. On the one hand, the sensor separation contribution is not expected to introduce a strong WS dependence, as the shift of the reference co-spectrum peak to higher frequencies is offset by the corresponding adjustment in cof. On the other hand, other sources of spectral losses, associated with a constant cof, should lead to a positive relationship between CF and WS. In the co-spectral approach, these two effects are accounted for simultaneously, yielding the observed trend. For the spectral approach, the separation of these contributions would suggest a stronger dependence of the non-sensor-separation term on WS (red lines in Fig. ), which is not observed. However, this apparent discrepancy can be explained by the very high cof values characterising the spectral method. Such high cofs result in CFs close to unity, making any dependence on WS difficult to detect. Unlike for cofs, this dependence of CFs on WS is consistent with standard practices in the literature, where explicit parameterisations are commonly implemented in flux correction approaches .

In contrast, for H2O, the application of a WS classification proves unnecessary. No clear relationship between cof and WS is observed for either method (Fig. ). Instead, spectral losses are dominated by the effect of RH, even when using an enclosed-path analyser with a relatively short tube.

One important finding emerging from the analysis is the efficiency of the ICOS setup in terms of limiting high-frequency losses. Regardless of the method, CFs of half-hourly fluxes are overall below 1.2 and mostly below 1.1 for unstable conditions (20 % to 10 % correction respectively) for CO2 (Fig. ), and reach a maximum of 2 for H2O for conditions with high RH and strong winds (Fig. , and more in detail in Fig. ). These results are in line with other values reported in the literature for the LI-7200 . They also confirm the superior performance of the enclosed-path analyser compared to closed-path systems for CO2 in terms of spectral losses. The improvement is less obvious for H2O, comparison of obtained cofs for H2O between our study and closed-path studies on DK-Sor, FI-Hyy and BE-Lon respectively showing no major differences. Moreover, high-frequency attenuations are shown to be overall coherent across sites (Figs.  and ), which highlights the effectiveness of the ICOS standardisation. This is particularly relevant in the context of an expanding network of stations whose main objective is delivering very high-quality data, as the choice of standard instruments for the EC systems facilitates inter-site comparisons and the consequent generalisation of potential findings at the network level directly. However, despite the technical improvements, the spectral correction is still a necessary step in the computation of final fluxes, as its inclusion can have an impact on the discussion around major unsolved topics concerning EC fluxes such as energy balance un-closure and reliability of long-term carbon budgets .

While relying on the ICOS-ETC products for input data, the frequency-loss correction procedure performed in this work is independent from the ICOS processing pipeline . This allowed us to build a customisable approach, not bounded to the options selected at the network level, where we could choose, based on an extensive literature review, some of the most up-to-date approaches to correct for high-frequency losses. Nevertheless, it remains interesting to compare our results with a recent ICOS network data release , considered a benchmark of high quality and standardisation and as such widely used around the world (10.18160/S6HM-CP8Q for download statistics of the multi-sites archive, > 1000 on 1 May 2026).

It was shown that differences in cumulative fluxes between our spectral approach and ICOS results are present, mostly higher than the differences between the two correction methods, and systematically leaning towards greater values (in absolute terms) for ICOS-ETC fluxes. For cumulative CO2 fluxes, they are significant at LMH, with 6 sites out of 14 showing differences higher than 4 % and smaller for HMH (5 out of 23 sites with differences higher than 4 %) (Fig. ). For cumulative H2O fluxes, differences are larger, with 11 out of 15 LMH and 9 out of 23 HMH showing differences higher than 10 %, with a total of 6 cases of very large differences (higher than 20 %) (Figs.  and ).

The impact on the fluxes is a direct consequence of the divergences between the CFs from the two approaches (not shown). These differences reflect differences between the spectral correction approaches: first an additional theoretical equation is applied to ICOS data to correct for low-frequency losses . Another equation is then applied in the high-frequency losses procedure to account for the anemometer losses for path averaging and time response . Then, for the sensor separation term, the Eq. (13) from the reference paper of is used instead of Eq. (16) in the present paper. All of this results in higher CF values. Then, thresholds for flux filtering and TF fitting range are different, and the denoising procedure is applied using a fixed frequency threshold. Moreover, the use of the TF to describe the attenuation of sensible heat co-spectra and compute CFs (Eq. ) in the spectral procedure is supported by the latest works , but in contradiction with the ICOS pipeline and EddyPro latest version see. This choice has a direct effect on the CF values, and has been shown to cause a bias of up to 10 % on fluxes by . A more detailed investigation was considered beyond the scope of our work. However, these results highlight the need for further investigation of the causes and the assessment of the impact of the different minor choices on the results.

In this context, it is important to point out that one major challenge faced by networks is the need for a procedure as automated and standard as possible, minimising manual processing and its associated subjectivity and workload. Thanks to the standardisation of the experimental set-up across sites, visual inspection and manual checks nevertheless made it possible to define consistent choices that could be applied uniformly to all sites. However, these steps still rely on user-defined decisions and therefore remain a source of subjectivity, whereas they should ideally be replaced by robust automated procedures. Moreover, performing the analysis on a multi-site dataset spanning a wide range of meteorological conditions and ecosystems made it possible to highlight both the difficulties and the limitations of a fully automated approach, as well as the key areas requiring further development. In particular, additional efforts should be made: to improve the filtering procedure by replacing the current uniform flux thresholds with criteria based on the signal-to-noise ratio, thereby allowing the inclusion of sites exhibiting small but well-resolved gas exchanges; to further develop the denoising procedure, for which the method by should be tested and validated on a multi-site dataset; and to develop a robust method for fitting threshold selection.

This study was limited to enclosed-path gas analysers, and therefore its conclusions are limited to this configuration. Other set-ups do exist, involving open-path or closed-path gas analysers, the latter being often used for other gases than CO2, in particular CH4 and N2O where also H2O is measured. For EC systems based on open-path analysers, high-frequency attenuation are intrinsically small, limiting the importance of the specific correction method. For closed-path systems, however, especially when long sampling tubes and limited flow rates are involved, the potential differences between spectral and co-spectral approaches to correcting high-frequency losses could be important and have not been addressed here. Differences related to sensor separation are expected to be more limited, even for non H2O, because the increasing importance of tube effects may overwhelm the sensor-separation effect, as observed for H2O in the present study. On the other hand, noise removal, which is already potentially problematic with enclosed-path analysers and is specific to the spectral approach, could become more critical as stronger tube-related attenuation increases the likelihood of noise at the high-frequency end of the spectra. A similar multi-site study, facilitated by the availability of a standardised dataset based on such analyser configurations, would therefore be valuable.