We used the eddy covariance (EC) technique to determine half-hourly gas and energy fluxes. The EC method requires high-frequency (typically >10 Hz) raw gas concentration and three-dimensional wind velocity measurements. A comprehensive description of the EC approach is given, for example, by . We recorded carbon dioxide (CO2) and water vapor concentrations as well as three-dimensional wind velocity with changing instrumentation on three different tower structures, all located on the central river terrace of Samoylov Island between 2002 and 2017 (see Fig. ). We deployed open-path (OP) as well as closed-path (CP) gas analyzers, at times simultaneously. Models, manufacturers and years of deployment are given in Table . Between the different setups, CP intake tube lengths varied from 5 to 8 m. OP analyzers were always installed inclined by about 10∘ from the vertical, as suggested in the analyzer manuals. Raw data were recorded at 20 Hz except for the periods 22 August 2009 to 19 July 2010 (10 Hz) and 31 August 2012 to 17 May 2013 (5 Hz). Until 29 April 2014, all raw data were recorded on a CR3000 data logger (Campbell Scientific, UK). From then on, CP analyzer and anemometer data were logged on a CR3000, whereas OP analyzer and anemometer data were recorded on a LI-7550 data logger (LI-COR Biosciences, USA). Although data coverage is biased towards the growing season, the data set contains considerably more shoulder season and winter fluxes in its second half from 2010 to 2017 (see Table ). The availability of year-round ancillary meteorological data, also increasing, resulted in gap-filled flux time series covering each half hour of the two years 2010 and 2016 (see Fig. ).

We set EddyPro to calculate quality flags according to that represent flux quality in three classes (0, 1 and 2), with 0 denoting the highest- and 2 denoting the lowest-quality class. This quality evaluation is based on tests for stationarity and developed turbulence and thereby indicates whether general EC assumptions about atmospheric conditions were met during a flux calculation period. Flux quality assessment was largely based on the scheme of . In the data set available for download, we included one column for each analyzer type containing this quality flag. Additionally, we applied six further screening steps and flagged fluxes of low quality. If a flagged flux was not already assigned to class 2 according to Mauder and Foken (2004), we set the quality flag to 2. In our opinion, fluxes of quality class 2 should be omitted from further analysis. They are included in the reported data set for the sake of completeness. We performed the six additional flagging steps in the following sequence. An overview of these filtering steps including the number of flagged values is given in Table .

In step 1, skewness and kurtosis were computed with EddyPro for the half-hourly high-frequency raw data time series of CO2 concentration, vertical wind speed and sonic temperature. If any of these statistics was outside certain intervals (skewness: [-2,2]; kurtosis: [1,8]; equivalent to the hard flag defined by ), CO2 flux values were flagged.

In step 2, OP fluxes were additionally filtered for an instrument signal strength indication (AGC) recorded from the LI-7500 sensor. Along with a software upgrade, this diagnostic value was renamed RSSI, and its definition was changed. We therefore recalculated the AGC values for sensors not running on firmware version 6.6 and above (before July 2013). According to the old AGC definition in the LI-7500 manual, typical clean window values range between 55 % and 65 %. As dirt accumulates on the windows (or anywhere in the optical path), the AGC value will increase up to 100 %. The new RSSI value takes 100 % for clean windows and decreases as windows get dirtier. In order to obtain one consistent diagnostic variable for the cleanness of the optical path, AGC was converted to the RSSI range. AGC values smaller than 44 were set to 44, then AGC values were mapped to the RSSI range as follows. RSSI(AGC)=188-2⋅AGC. We flagged OP CO2 flux values when RSSI≤60.

As quality control of the half-hourly time lag detection results was not applied during OP flux processing in EddyPro, we additionally screened OP time lags to identify low-quality flux values in step 3. We divided the time lag data set into subsets of different instrumental setup and binned the time lags of these subsets in 36 10∘ wind direction sectors. We used the 25th and 75th percentiles per class as filter thresholds. We flagged OP flux values with associated time lags outside the range spanned by these thresholds. Because we computed CP fluxes in EddyPro considering and compensating for low time lag detection quality, we did not perform this type of filtering step on CP fluxes.

In step 4, we flagged CP as well as OP fluxes when 30 min average concentration measurements were larger than 450 ppm or smaller than 300 ppm. CO2 concentrations outside this range indicate dirty OP gas analyzer optics or technical problems of the CP air sampling system (sudden pump speed changes due to brownouts, blocked filters, etc.).

To filter dubious, large OP fluxes that coincided with reasonable CP fluxes, we selected all OP fluxes when simultaneously measured CP values ranged between -2 and 2 µmol m-2 s-1. Step 5 only affected OP data from this subset. We calculated the 99th and 1st percentile of this group and flagged fluxes from it when they lay outside this percentile range.

In step 6, we flagged remaining outliers in both the CP and OP data sets by using the 0.1st and 99.9th percentile (-3.5423 and 3.3473 µmol m-2 s-1) of the CP time series after the concentration limits filter as absolute limits to define an acceptable range of OP and CP flux values.

To account for self-heating errors induced by the LI-7500 sensor electronics, we corrected OP fluxes as described by . The authors use WPL-corrected fluxes and add a correction term that accounts for self-heating effects of vertically installed instruments. In their approach, use a scaling factor ξ, taking values between 0 and 1, to trim the correction for inclined analyzer setups. With simultaneously available CP fluxes, we were able to estimate this scaling factor specifically for our site and periods of unique instrumental setups. As suggested by , we optimized this parameter with a nonlinear least squares method in Matlab (v. 9.2). We determined ξ for periods of different instrumental setups and separately for night (incoming shortwave radiation <20 Wm-2) and day (incoming shortwave radiation ≥20 Wm-2) conditions using the following equation:

Fc=Fc,WPL+ξ(Ts-Ta)ρcraTa, where Fc (kgm-2s-1) is the true CO2 flux, Fc,WPL (kgm-2s-1) is the WPL-corrected OP CO2 flux, Ts (K) is the instrument surface temperature, Ta (K) the ambient air temperature, ra (sm-1) the aerodynamic resistance and ρc (kgm-3) the ambient CO2 density. Prior to ξ optimization, we also estimated the instrument surface temperature Ts following the parameterization of separately for nighttime and daytime:

Ts,day=0.93(Ta-T0)+3.17+T0andTs,night=1.05(Ta-T0)+1.52+T0, with Ts,day (K) and Ts,night (K) as instrument surface temperature estimates and T0 set to 273.15 K. We determined the scaling factor as a parameter of Eq. (2), being the modified approach from . For function fitting, we assumed CP fluxes of quality classes 0 and 1 as true fluxes. We used WPL-corrected OP quality class 0 fluxes and the surface temperature estimates described above as independent variables. Before parameter optimization, we quality-screened the correction term (expression to the right-hand side of ξ in Eq. 2) and removed spikes ranging within the uppermost or lowest percent of its distribution. Throughout all years, ξ is larger during the daytime than at nighttime but generally small, adding mostly below 1 % of the full correction term to the uncorrected flux (see Table ). In four of the seven available years with simultaneous CP and OP fluxes, nighttime ξ optimization converged to values below zero. Before applying the correction models to these periods, we set nighttime ξ estimates to the median of the years yielding parameter values that, including their 95 % confidence bounds, ranged above zero. We used this value and the median of all daytime model optimizations to calculate corrected OP fluxes at times without parallel CP measurements. We did not correct OP fluxes when radiation measurements or correction term estimates were not available. Correlation between CP and OP fluxes improved throughout all quality classes by applying the self-heating correction (see Table ), while fluxes indicating net CO2 uptake were affected more strongly than fluxes above zero (see Fig. ).

We used the CP and the corrected OP fluxes (see Fig. ) to compile a CO2 flux time series. We aimed at keeping as many measured data points as possible, while omitting records with large uncertainty. We accepted all CP values of quality classes 0 and 1. At time steps where no CP fluxes were available, we selected OP values of the same quality classes. The resulting time series contains 75 921 data points. Additionally, we filled the remaining gaps in the time series using the marginal distribution sampling (MDS) method as first presented by . This method employs two types of model value calculations. The environmental variables global radiation, air temperature and water vapor pressure deficit are binned in classes and combined in a lookup table (LUT). In the case of a gap, flux values related to similar environmental conditions can be looked up and used for averaging and gap filling. The setup of different LUTs for fixed time periods was first described by . This process can be refined by the use of moving time windows around gaps, as applied by . The second model type implemented in the MDS algorithm exploits the commonly high autocorrelation of gas flux time series. The mean diurnal variation (MDV) technique was also first described by and uses the average of available gas flux measurements from adjacent days at the same hour of day to fill a flux gap. The MDS method has found wide application, as it has, for example, been the standard technique within the processing pipeline of the FLUXNET2015 data set, which includes over 1500 site years of data. The algorithm of combines a screening procedure of the available data for similar environmental conditions (lookup table steps) and the use of an MDV method (diurnal cycle steps) if a gap could not be filled within the lookup table steps. Both techniques include moving windows with variable sizes that are increased until a solution can be found. Large gaps are skipped. To run the gap-filling algorithm, we used the REddyProc routine that is accessible through a web-based service hosted by the Department of Biogeochemical Integration at Max Planck Institute Jena. The R routine that is executed on this server is a further-developed and extended version of the approach and is described by . We did not use the friction velocity filter or the flux partitioning capabilities of the REddyProc online tool. Gap filling resulted in 131 908 data points. The provided data set includes quality flags for each gap-filled value that depend on the method used and time window size, as defined by . These flags take values between 0 and 3, with 0 denoting measurement data, 1 indicating the most reliable and three least reliable gap-filled fluxes. To assess the overall quality of the gap-filling result, the MDS algorithm, in a stepwise manner, treats single available values as gaps and fills them according to the described scheme. Pearson's correlation coefficient between our compiled CO2 flux time series and the MDS quality assessment run, where these values were treated as artificial gaps, is 0.92, with a root mean squared error of 0.31 µmol m-2 s-1.

Flux uncertainty can be regarded as a combination of a systematic and a random part. While the attempt should be made to remove systematic biases, random errors cannot be corrected for . However, statistical methods exist to estimate the uncertainty in a flux measurement due to random errors. We used three different approaches from the literature to quantify random uncertainty and addressed fluxes with a suspected large bias by correcting for it during processing or by filtering in the course of quality assessment.

Most importantly, systematic errors are introduced when underlying EC assumptions are not met. Using the method of that combines an assessment of well-developed turbulence and steady-state conditions, we identified biased fluxes and flagged them. Other sources of systematic errors that we addressed include, for example, the angle of attack correction of faulty sonic anemometer readings, filtering for low instrument signal strength, the OP self-heating correction, and compensations for high-frequency loss and air density fluctuations (see Sect. 3.2.2, 3.3 and 3.4). Although we are confident that we applied corrections for systematic errors both rigorously and carefully enough, biases were certainly not always removed efficiently. The quality flags included in the data set, reflect a level of confidence based on the assessment of general EC assumptions and our six additional quality filtering steps (see Sect. 3.3).

To be able to include a random uncertainty estimate for each individual OP and CP flux in the provided data set, we set EddyPro to calculate random uncertainty estimates following . The authors developed a method that aims at quantifying flux uncertainty associated with turbulence sampling errors. These errors can contribute largely to the total random error as they refer to the insufficient sampling of large eddies with high spectral energy. Due to the stochastic nature of turbulence, this type of error is random. To estimate its magnitude, the so-called integral turbulence timescale (ITS) is first determined by expressing the covariance of vertical wind velocity and gas concentration as a function of a lag time between these two time series. The ITS is then given by integrating the cross-correlation function theoretically from 0 to infinity, in practice, however, until an upper lag time limit is reached. The upper limit can be defined in three different ways in EddyPro. We used the definition of the normalized cross-correlation function reaching a value of 1/e=0.369 to determine an upper lag time limit used for integration. While the normalized cross correlation should reach zero with increasing lag time in theory, in practice it sometimes does not. The setting we used on the one hand provides the least conservative estimate of the ITS but on the other hand offers computational efficiency and makes sure that an upper limit for integration can be reliably found. With the ITS, a flux uncertainty can be determined by calculating the variance of an EC flux or, as put it, by calculating the variance of the covariance. This ensemble variance would approach zero with the averaging time approaching infinity. In the data set available for download, a random uncertainty estimate calculated with the method of is given for each OP and CP flux (see Table ). Random uncertainties based on ITS estimation observations increase with absolute fluxes with mean values of 0.16 and 0.05 µmol m-2 s-1 for OP and CP fluxes (see Fig. ). OP random uncertainty estimates are generally larger and more scattered with respect to the corresponding flux values.

As the random uncertainty estimate described above specifically addresses the turbulence sampling error, other sources of random flux errors such as the noise introduced by the different components of the measurement system are neglected. With simultaneous measurements from two sensors, we could additionally estimate random errors for the measurement system as a whole during times when the data sets from both sensors overlapped. We followed the paired-observations approach as presented by and calculated a random error estimate ϵ as ϵ=12⋅(FCP-FOP), with the closed-path and open-path CO2 fluxes FCP and FOP of quality classes 0 and 1 in µmol m-2 s-1. The distribution of ϵ estimates is shown in Fig. . The ϵ values calculated with OP fluxes corrected for the self-heating error have a mean close to zero and are distributed more symmetrically than the ϵ values calculated with uncorrected OP fluxes. The mean of this distribution is shifted from its mode as well as from zero, indicating a much stronger systematic component within the measurement error. This result increases our confidence that the OP self-heating correction we applied was successful in removing a systematic bias from the data. Further following , we used the ϵ system error data set from the overlap period to generate flux uncertainty estimates for bins of increasing OP flux ranges. We sorted the ϵ values into 20 corresponding flux bins between -2 and 2 µmol m-2 s-1 and calculated an uncertainty estimate for each bin σ(ϵ)i as σ(ϵ)i=21Nj∑j=0Nj|ϵi,j-ϵ‾i|. Results show (see Fig. ) a similar data range and pattern of uncertainty estimates in relation to associated fluxes like the half-hourly values calculated following .

As a third method of random uncertainty estimation, we simplified the successive-observations approach from by using results of the quality run performed during MDS gap filling (see Sect. 3.5). We selected the time steps when a flux observation and an MDS value that was estimated using a 1-day window and the MDV technique were available. We used the standard deviation of the fluxes measured at the same hour of day within a 1-day window, as an uncertainty estimate of the observed flux. Results are shown in Fig.  and also increase with rising absolute fluxes in the same ranges as random uncertainties due to turbulence sampling error or measurement system error do.

We included the results obtained with ITS estimation in the uploaded data set considering the similarity between the uncertainty–flux relations calculated with independent methods as well as due to the advantage of a distinct uncertainty estimate for each sensor and time step.

In order to quantify the cumulative contribution of distinct surface classes to the EC source area, we evaluated the two-dimensional analytical footprint formulation described by in combination with a 0.14 m ×0.14 m resolution surface classification of Samoylov Island's central river terrace provided by . The authors divide the surface into four classes based on hydrology and vegetation communities, as illustrated in Fig. . presented an analytical solution to the crosswind-distributed advection–diffusion equation described by and . Using the analytical model of , the authors solved the power-law profiles of horizontal wind speed and eddy diffusivity by relating them to the Monin–Obukhov similarity theory, including the stability dependence of the exponents in the power laws at a certain height. We implemented the equations given in as a Matlab (v. 9.2) function and added a quality filter, omitting calculations when friction velocity was larger than 0.9 ms-1 or smaller than 0 ms-1, wind speed was below zero or above 20 ms-1, the crosswind standard deviation was below zero or above 3 ms-1, or Monin–Obukhov length was smaller than 10-3 m or larger than 104 m. Prior to half-hourly footprint calculations, we additionally determined roughness length statistics for annual subsets of data and binned them in 2 ∘ wind direction classes. The medians of these classes were used in the subsequent half-hourly footprint estimation, depending on the mean wind direction during these 30 min. We evaluated the footprint model at the same resolution that was used by to classify the surface (i.e., 0.14 m ×0.14 m). We could thereafter assign a probability of being the EC source area to each classified pixel and sum up the probabilities of all pixels belonging to the same surface class to estimate the contribution of each class. This process of combining an EC source area estimation with a land cover classification is similar to what has been applied and described in more detail by .