Accurately measuring the turbulent transport of reactive and conservative greenhouse gases, heat, and organic compounds between the surface and the atmosphere is critical for understanding trace gas exchange and its response to changes in climate and anthropogenic activities. The relaxed eddy accumulation (REA) method enables measuring the land surface exchange when fast-response sensors are not available, broadening the suite of trace gases that can be investigated. The

This study evaluates a variety of different REA approaches with the goal of formulating recommendations applicable over a wide range of surfaces and meteorological conditions for an optimal choice of the

With respect to overall REA performance, we found that the

For REA applications without deeper site-specific knowledge of the turbulent transport and degree of scalar similarity, we recommend using either the

Trace gases play a significant role in the atmosphere because of their relationship to human-induced climate change, their wide variety of natural and anthropogenic sources, and their impact on human and ecosystem health. Understanding their source and transport behavior is needed to better quantify, predict, and mitigate anthropogenic effects on the environment. The exchange of trace gases between the Earth's surface and the atmosphere is often the result of a combination of several biophysical processes and mechanisms. Observing the net turbulent exchange, i.e., the flux density of such gases can help identify their sources and sinks, which in turn can help identify their forcings. Micrometeorological techniques can measure area-integrated fluxes at the ecosystem level and are therefore suitable for computing atmospheric budgets of trace gases and aerosol species.

The most direct method to measure flux density, hereafter referred to as “flux”, between the surface and the atmosphere is the eddy covariance (EC) technique, which requires fast (

For the REA technique, the concentration difference between the two sample reservoirs,

Since the choice of the

The large number of potential combinations for the critical REA parameters and varying site conditions may often seem overwhelming either to the first-time user focusing on investigating the dynamics of a certain trace gas species or even to the advanced user lacking a detailed understanding of the site-specific turbulent flow conditions. To provide some science-based guidance, our study aims at giving a comprehensive overview covering the most common parameterizations of the

The most commonly employed REA variant is based upon scalar–scalar similarity: observations of a scalar

The

An alternative REA method was originally derived by

The requirements for this parameterization are (i) a linear relationship between

The statistical moments of the

Deadbands are widely used in REA applications. The use of a deadband can provide improved resolution of concentration differences by selectively sampling eddies with a larger contribution to the trace gas exchange. The turbulence characteristics can differ greatly across different ecosystems, therefore, an optimal deadband size must be chosen carefully. In the

Schematic quadrant plots to visualize the application of linear

When applying a linear deadband to

This approach offers the advantage of the deadband being proportional to the integral strength of the turbulent diffusive process transporting the trace gas of interest. During field sampling, the size of the deadband is dynamically adjusted by applying a back-looking running time window of fixed length to compute

Hyperbolic deadbands are specifically designed to exclude eddies with little flux contribution and maximize the concentration difference between the two sampling reservoirs. The exclusion of up- or downdrafts is in this case not only based on vertical wind velocity but also on the fluctuations of a proxy scalar. Hyperbolic deadbands are defined by the dimensionless factor

The use of large deadbands must be done with caution because they exclude a significant fraction of the data from being sampled. As a result, the random sampling error, which is related to

In this study, we compare

In the next steps, we proceed as follows: each of the above models is first optimized with respect to the deadband size. To do so, the accuracy of each

We selected three sites with strongly contrasting vegetation cover and surface roughness, vegetation architecture, and biogeochemical processes governing the vertical exchange of CO

Description of the three data sets used in this study: numbers from quality-screened data, aggregated to 30 min temporal resolution. IQR signifies interquartile range.

The grassland data

Finally, we use a data set acquired at a spruce forest site in the German Fichtelgebirge

Ensemble-averaged diurnal fluxes of kinematic heat flux

The comparison of the kinematic heat, moisture, and CO

The turbulence observations consisted of the three-dimensional wind vector and sonic temperature collected by a sonic anemometer (Lindenberg: CSAT3, Campbell Scientific Ltd., Logan, UT, USA; Dry Valleys: 81000 VRE, R.M. Young Company, Traverse City, Michigan, USA; Waldstein forest: USA 1-FHN, Metek, Elmshorn, Germany) and water vapor and carbon dioxide molar densities measured by an open path analyzer (LI-7500, LI-COR Inc., Lincoln, NE, USA) both recorded by a data logger (CR3000, Campbell Scientific Ltd., Logan, UT, USA). The sampling rate was 20 Hz. Spikes and outliers in raw turbulence time series were discarded according to

Raw velocities were rotated using the first two steps in the common three-dimensional rotation method ensuring that the mean crosswind and vertical wind components equal zero. A spectral correction was applied to EC fluxes following

Since simulating REA sampling requires selecting individual high-frequency data from a continuous time series and computing density-corrected scalar higher-order moments, an ad hoc density correction was applied to the water vapor and carbon dioxide molar densities

Diurnal course of scalar–scalar correlation coefficients

For the REA flux estimation, hyperbolic and linear deadbands of varying sizes were tested. The linear deadband size was scaled by increasing fractions of

This study evaluates estimates of the latent heat flux

We structured this section as follows. First, scalar correlation coefficients for the different ecosystems are presented in Sect. 4.1. In Sect. 4.2, we describe the choice of an optimal deadband size for each REA model based on both

Scalar similarity is an important assumption for the

To assess whether a scalar can serve as a viable proxy

Effect of deadband size on the concentration difference and measures of the random error. Panels

Figure

In the next step, we evaluate each REA model individually and select an optimal deadband size with respect to selected uncertainty metrics of the

Errors as a function of dynamic linear deadband width. The

The results for the

Interestingly, the observed underestimation of the latent heat flux is lessened for the forest and gravel sites when hyperbolic deadbands are applied, whereas it becomes larger for the meadow site. For the gravel site, the bias even changes sign for large hyperbolic deadbands. The RMSE shows no significant improvement when the small-scale eddies with small flux contributions are excluded irrespective of ecosystem. Based on Fig.

Errors as a function of dynamic hyperbolic deadband size. The

When applying a linear deadband to model 3 using

Errors as a function of dynamic linear deadband width. The

The performance of the constant

Errors as a function of dynamic linear deadband width. The

Table

Median

After choosing an optimal deadband size for each REA model, we now proceed to analyzing the effects of the diurnal light variability and atmospheric stability on flux estimates.

Flux RMSE as a function of the hour of day (local time) for each of the optimized

Data were binned according to the hour of day, and the RMSE was computed for each hour. Each panel in Fig.

So far, only one proxy–scalar combination was investigated in this study. However, showing that the presented results are also valid for other scalars is critical for their applicability. The data sets allow for including CO

The observed relationship between the

Dependence of the

It was pointed out in previous REA studies that

This figure only presents results from REA model 3 (

Summary of the REA models compared in this study, along with main findings.

The relationship between the

Kurtosis is in turn expected to be related to dynamic stability when changes in turbulence statistics and diabatic conditions lead to a non-Gaussian distribution of

At first sight, it is puzzling why the

This study has compared the performance of four different conditional sampling models to compute the water vapor flux. The tested REA models included the following methods: two approaches relying on the sensible heat

The dynamic scalar proxy (

For the

The dependence on atmospheric stability conditions was evaluated for each method and deadband size. No universal behavior of any stability-dependent (

Based on the findings obtained in this study, we attempt to formulate the following general recommendations. We overall recommend using either the

Figure

Same as Fig.

Data sets used are available at Zenodo:

CKT led the field experiments and performed the REA flux computations. TV and AH performed the data analysis and visualization. TV, AH, and CKT wrote the manuscript.

The authors declare that they have no conflict of interest.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Christoph K. Thomas acknowledges funding from the National Science Foundation Career Award in Physical and Dynamical Meteorology, award AGS 0955444.

We would like to thank the German Meteorological Service (DWD) for granting access to their Falkenberg site at the Lindenberg observatory. We further express our gratitude to Wolfgang Babel and Johannes Olesch for their assistance in collecting the observations at the Lindenberg and Waldstein sites in Germany and Joseph Levy for the opportunity of and assistance in collecting observation in the Dry Valleys of Antarctica. Teresa Vogl would like to thank the R project

This open-access publication was funded by the University of Bayreuth.

This paper was edited by Ivonne Trebs and reviewed by two anonymous referees.