Flux measurements of reactive nitrogen compounds are of increasing importance to assess the impact of unintended emissions on sensitive ecosystems and to evaluate the efficiency of mitigation strategies. Therefore, it is necessary to determine the exchange of reactive nitrogen gases with the highest possible accuracy. This study gives insight into the performance of flux correction methods and their usability for reactive nitrogen gases. The eddy-covariance (EC) technique is today widely used in experimental field studies to measure land surface–atmosphere exchange of a variety of trace gases. In recent years, applying the EC technique to reactive nitrogen compounds has become more important since atmospheric nitrogen deposition influences the productivity and biodiversity of (semi)natural ecosystems and their carbon dioxide (

The eddy-covariance (EC) method is widely applied for determining turbulent exchange of trace gases and energy between the biosphere and atmosphere

Application of the EC technique to

Evaluating fluxes with these closed-path EC systems leads to underestimation of fluxes due to damping in the high- and low-frequency ranges. An EC setup, like any measurement setup, is comparable with a filter which removes high- and low-frequency parts from measured signals. High-frequency losses are, for example, related to sensor separation

The magnitude of the high-frequency flux loss depends on the trace gas of interest, the experimental setup, wind speed, and atmospheric stability. In recent literature, different estimates of flux losses due to high-frequency damping have been reported. For example

In the past decades, several methods for calculating spectral correction factors have been proposed based on theoretical cospectra

We analyzed data from two measurement sites. At both sites we installed a custom-built

The first site (52

The TRANC and sonic anemometer were installed at 2.50 m above ground. The sampling inlet was designed after

Our second site (48

Physical parameters of the EC setups.

Important terms and corresponding shortcuts used in this study.

Data were collected with the software EddyMeas, included in the software EddySoft

The recorded datasets show a time lag between the measurements of the sonic anemometer and the gas analyzers due to sampling of air through the inlet system (converter, tube, analyzer cell), the processing of signals within the analyzers, and the distance between the two instruments. The time lag was estimated with the covariance maximization method

For the high-frequency damping analysis, we selected time series of vertical wind, temperature, and

For a quantitative evaluation of the high-frequency damping from the half-hourly flux (co)spectra, a quality flagging has to be applied. Flagging of (co)spectra is done automatically in EddyPro. However, the criteria are usually optimized for inert gases like

Another possibility for the characterization of the quality or influence of noise on power spectra and cospectra is the determination of the decline in the inertial subrange following the power law. Therefore, the slope of the decrease was evaluated on a double logarithmic scale by a linear regression. The theoretical slope for power spectra of temperature and inert trace gas concentrations is

We used four different cospectral approaches for the computation of high-frequency losses. The fifth approach of

The theoretical damping calculation (THEO) is the most commonly applied method

In order to prevent a misunderstanding between

Theoretical cospectra could deviate from site-specific characteristics of the turbulent transfer, while theoretical transfer functions could miss important chemical or microphysical processes, which are more important for

Comparison of observed normalized cospectra with modified Kaimal cospectra (green) for similar wind speed and stability and their theoretical and experimental transfer functions at BOG

Cospectra of FOR are shifted to the left due to the larger measurement height above canopy and the increased contribution of low-frequency, large-scale eddies with height

The in situ cospectra method (ICO) utilizes

Illustration of the calculation of

The iteration was started with

The semi-in-situ cospectra approach is similar to the one described in Sect.

The in situ ogive method (IOG) is based on

Application of the in situ power spectral method (IPS) after

Figure

Normalized cospectra and power spectra of

The shapes of the power spectra for

Distribution of spectral slopes in the high-frequency range (

The slopes of

In the following, we present the results of the damping correction methods introduced in Sect.

Boxplots of the flux damping factor (

Box plots of the flux damping factor (

Monthly

At both sites, the median

At FOR, the median

At BOG, the median

By subtracting

Averages of monthly medians and lower and upper quartiles of

For investigating deviations of the different methods more precisely, we computed correlation, bias, and precision as the standard deviation of the difference for each pair of methods. The results are summarized in Table

For investigating a trend in meteorological variables such as temperature, relative humidity, stability, and wind speed, we classified them into bins, calculated

Dependency of the flux damping factor (

A slight dependence on wind speed for BOG

Values of

At BOG, the linear decline in

After comparing

Statistical analysis of the response time (

It is obvious that medians of

We further determined the correlation between monthly averaged

Measured fluxes of

Some

Removing high-frequency variations which consist mainly of white noise is easier for

The findings indicate that using Ps for estimating correction factors of gases with low turbulent fluctuations, which are measured by a closed-path instrument, can be problematic. Therefore, we recommend using cospectra to estimate

White noise was observed in power spectra of

The number of good quality (co)spectra for

In general,

There could be other effects which superpose the wind speed and stability dependencies, for example, (chemical) damping processes occurring inside the TRANC–CLD system. Humidity and

Consequently, the strongest contributor to the overall damping has to be the TRANC.

The difference between the ICO and sICO method is the usage of Kaimal cospectra for determining

The main difference between ICO and the IOG method is that IOG utilizes the low-frequency part and (s)ICO the high-frequency part of the cospectrum. The low-frequency part is much more variable than the high-frequency one, especially on a half-hourly basis. As a consequence, the ratio between

A general or site-specific parameterization of the damping as a function of wind speed and stability was not possible for the entire wind speed and stability range. A parameterization would be possible only for certain wind speed and stability ranges. For example, a parameterization can be performed for unstable conditions and for wind speeds above 1.5 m s

For an aspired correction of the determined fluxes, half-hourly estimated

We investigated flux losses of total reactive nitrogen (

We found that

Differences in flux losses are related to measurement height and hence to the variable contribution of small- and large-scale eddies to the flux. No systematic or only partly significant dependencies of the empirical methods (ICO, sICO, and IOG) on parameters such as atmospheric stability and wind speed, which have an influence on the shape and position of cospectrum, were observed. In the case of the empirical methods, we found a wind speed dependency on damping factors (

The empirical methods perform well at both sites and median

Our investigation of different spectral correction methods showed that ICO is most suitable for capturing damping processes of

Transfer functions used for validation of

Transfer functions used for evaluation of the

The cospectrum for stable conditions after

Result of the comparison between different damping determination methods at the two measurement sites. Bias

Median

Dependency of the response time (

All data are available upon request from the first author of this study (pascal.wintjen@thuenen.de). Also, Python 3.7 code for damping factor calculation as well as the data analysis code can be requested from the first author. All necessary equations for determining the damping factors are given in this paper.

PW wrote the manuscript, carried out the measurements at the forest site, and performed data analysis and interpretation. CA gave scientific advice. FS helped with coding and evaluated meteorological measurements. CB conducted the measurements at the peatland site and gave scientific advice. All authors discussed the results, and FS, CA, and CB reviewed the manuscript.

The authors declare that they have no conflict of interest.

We thank Undine Zöll for scientific and logistical help; Jeremy Rüffer and Jean-Pierre Delorme for excellent technical support, particularly during the field campaigns; and the Bavarian Forest National Park Administration, namely Burkhard Beudert, Wilhelm Breit, and Ludwig Höcker, for technical and logistical support at the site. We further thank the two anonymous reviewers for valuable comments that helped improve the quality of the manuscript.

This research has been supported by the German Environment Agency (UBA) (FORESTFLUX project, support code FKZ 3715512110) and the German Federal Ministry of Education and Research (BMBF) (Junior Research Group NITROSPHERE, support code FKZ 01LN1308A).

This paper was edited by Thomas F. Hanisco and reviewed by two anonymous referees.