The method of detects a plateau in the relationship of nighttime NEE versus u* among all records within a temperature subset by a moving point test of records binned into different u* bins.

The nighttime data (default: Rg<10 Wm-2) are split into different times of year, here called seasons, to account for differing surface roughness. Then the data of each season are split into default six temperature subsets of equal size (according to quantiles). Within each temperature subset, data are split into 20 about equally sized u* bins. The default moving point method, called Forward2, determines the threshold based on these u* bins. It checks for each bin if the mean NEE is higher than 0.95 times the mean of the following 10 bins. If this also holds true for the next bin, the mean u* of the bin is reported as the threshold. There are often subsets of data in which no clear threshold can be detected. Hence, there are quality criteria for whether the estimate of a given subset is used in subsequent aggregation. One quality criterion specifies that temperature and u* should not be correlated within the temperature subset; another requires a minimum number of valid records within a subset. Next, the u* estimates for different temperature classes and seasons (details in Sect. ) are aggregated to derive a robust u* estimate. Within one season, the median is taken across the estimates of different temperature subsets. Within 1 year, the maximum is taken across the associated seasons.

Records during the nighttime with u* smaller than the estimated threshold are flagged as invalid and are replaced in the subsequent gap-filling processing step. In addition, each half hour after records with u* smaller than the threshold is flagged to be invalid.

Alternatively, breakpoint detection can be applied to the unbinned data, which avoids the sensitivity of the moving point method to the specifics of the binning schemes . REddyProc provides this method by estimating the breakpoint based on unbinned records within the seasons/temperature subsets using the segmented R-package . However, REddyProc differs from by keeping the same aggregating scheme of seasonal/temperature estimates to annual thresholds as with the moving point method.

Estimates of the u* threshold are often sensitive to the specifics of the combination of methods and the data, e.g., the binning, minimum number of records within a season or temperature subset, and criteria in aggregation. Therefore, a bootstrap (resampling with replacement) is applied to generate 200 artificial replicates of the dataset, and for each replicate the threshold is estimated . The 5th, 50th, and 95th percentile of the estimates are reported as a range of threshold estimates. The subsequent post-processing steps of gap filling and partitioning are then repeated using those different thresholds to propagate the uncertainty of u* threshold estimation to derived quantities such as annual NEE, GPP, and Reco.

In the look-up table (LUT) approach, the fluxes are binned by the meteorological conditions within a certain time window. Within the chosen time window and respective bin, each meteorological variable deviates less than a fixed margin to ensure similar meteorological conditions. The missing value of the flux is then calculated as the average value of the binned records and its uncertainty estimated from their standard deviation.

The original LUT of consisted of fixed periods over a year, while in REddyProc the meteorological conditions are sampled with a moving window around the gap to be filled.

NEE fluxes have a mean diurnal course (MDC) that follows the course of the sun with only respiration during nighttime and a combination of respiration and photosynthesis during daytime. This autocorrelation of the fluxes is exploited by taking the average value at the same time of day within a moving time window of adjacent days (Falge et al., 2001). In REddyProc the same time of day also includes the fluxes of the adjacent hour (±1 h).

Though the MDC method only showed a medium performance in the gap-filling comparison for net carbon fluxes by , it has the advantage that this approach can be used even if no meteorological information is available.

The so-called marginal distribution sampling (MDS) by exploits the covariation of the fluxes with the meteorological variables and their temporal autocorrelation based on the two methods LUT and MDC described above.

The filling of each half-hourly NEE with the MDS algorithm depends on the availability of the meteorological data of Rg, Tair, and VPD. (1) If all three meteorological variables are available, LUT will be used with default margins of 50 Wm-2, 2.5 ∘C, and 5.0 hPa, respectively. (2) If Tair or VPD are missing, only the variable Rg will be used. (3) If no meteorology is available, the gaps are filled with MDC. Following a specific sampling procedure, the MDS algorithm increases the number of days in the vicinity of the gap until there are enough data points (at least two) for gap filling. A more detailed description with a flow diagram is provided in the Supplement.

The MDS algorithm is optimized for carbon dioxide and water fluxes and can also be used to estimate the uncertainty of the half-hourly fluxes. In the comparison of gap-filling methods by , the MDS algorithm performed well for different artificial gap scenarios ranging from single half-hours to several days. Due to its flexibility in dealing with missing meteorological input data and its fast and highly automated routines available as an online tool (BGC16, Sect. ), the MDS gap-filling method has been widely used.

The method of estimates a temporally varying respiration–temperature relationship from nighttime data. First nighttime data are selected by a threshold of Rg<10 Wm-2, which is congruent with the BGC online tool (BGC16, Sect. ), but differs from the 20 Wm-2 reported in . Additionally, nighttime data are constrained between computed sunset and sunrise.

Next, temperature sensitivity, E0, of the relationship (Eq. ) is estimated by fitting the model to successive 15-day periods of nighttime data, and the resulting E0 series is aggregated to an annual estimate.

Reco(T)=RRefexpE01TRef-T0-1T-T0, where T0 is kept constant at -46.02 ∘C and where the reference temperature TRef is 15 ∘C, which is congruent with the BGC online tool (BGC16, Sect. ), but differs from the 10 ∘C reported in . For robustness each fit is repeated on a trimmed dataset excluding records with residuals outside the 5 %–95 % residual distribution. The annual aggregate is the mean across the three valid estimates with the lowest uncertainty in the fit. Single estimates of E0 are considered valid if there were a minimum of six records, temperature ranged across at least 5 ∘C, and estimates were inside the range of 30 to 450 K.

Subsequently, the respiration at reference temperature, RRef, is re-estimated from nighttime data using the annual E0 temperature sensitivity estimate for 7-day windows shifted consecutively for 4 days. The estimated value is then assigned to the central time point of the 4-day period and linearly interpolated between periods. Hence, the obtained respiration–temperature relationship varies across time.

Finally, Reco is estimated for both day- and nighttime from the temporarily varying Reco–temperature relationship, and daytime GPP is computed as Reco–NEE.

The method of models NEE using the common rectangular hyperbolic light-response curve (LRC) :

NEE=αβRgαRg+β+γ, where α (µmolCO2J-1) is the canopy light utilization efficiency and represents the initial slope of the light-response curve, β (µmolCO2m-2s-1) is the maximum CO2 uptake rate of the canopy at infinite Rg, and γ (µmolCO2m-2s-1) is a term accounting for ecosystem respiration. The hyperbolic light-response curve is modified to account for the temperature dependency of respiration after by setting respiration γ to the Lloyd and Taylor respiration model (Eq. ). Further, the constant parameter β in Eq. () is replaced by an exponential decreasing function at higher VPD values (Eq. ).

β=β0exp-k(VPD-VPD0) if VPD>10hPaβ0 otherwise, where the VPD0 threshold is 10 hPa in accordance with earlier findings at the leaf level , ignoring potential vegetation specific differences.

Parameter T0 in Eq. () was fixed as in the nighttime partitioning (Sect. ). Parameter TRef was fixed in each window to the median temperature within the window. The other parameters (E0,RRef,α,β0,k) of the model are estimated by the following steps. (1) A time-varying temperature sensitivity E0 is estimated from nighttime data for a window shifted by 2 days. (2) The E0 estimates are smoothed across successive windows by fitting a Gaussian process using the mlegp R-package that also estimates uncertainty of the smoothed E0. Next, a prior respiration, RRef, for reference temperature TRef=15 ∘C is re-estimated from nighttime data for each window with smoothed E0. (3) Parameters of the rectangular hyperbolic light-response curve (RRef, α, β0, k) are fitted using only daytime data and the previously determined temperature sensitivity (E0) for each window. (4) Finally, for each NEE record, GPP and Reco are estimated with the parameter set of the previous valid window and the parameters of the next valid window, and the two results are interpolated linearly by the time difference to the window centers. The Supplement reports necessary technical details about these steps.

Note, that contrary to the nighttime-based flux partitioning, both GPP and Reco are model predictions and do not add up exactly to observed NEE.

The biggest difference of REddyProc compared to DP06 is that REddyProc by default employs seasons that can span across years. With the within a year classification option, which is also employed by DP06, records of December are associated with the same season as January and February of the same year. With the default continuous classification, seasons start the same as in DP06 by default in March, June, September, and December. However, December is treated in the same season as January and February of the next year to avoid discontinuities at year boundaries. The annual u* threshold is then applied according to those continuous seasons spanning year boundaries. For example, the processing of 2014 data would by default use data from winter 2014 (starting in December 2013) to autumn 2014 (ending in November 2014). REddyProc also allows more flexibility with the user-specified classification into seasons as explained below.

There are further slight differences between REddyProc and DP06. Both methods bin in a way such that the number of records in each bin is similar. If there are numerically equal u* values, they are sorted into the same bin, resulting in bins with unequal record numbers. In DP06 sometimes no records are sorted into the subsequent bins, hampering the moving point detection. Conversely, the binning with REddyProc ensures that there are a minimum number of records in all bins. This often results in fewer bins. Moreover, differing from DP06, REddyProc employs several more quality criteria. First, when comparing the threshold bin to NEE in the following bins, it makes sure that there are least three bins to infer a plateau in NEE. Next, when aggregating the thresholds of different temperature classes to season, it ensures that a threshold was found in at least 20 % of the temperature classes. For those seasons during which no threshold could be determined, the annual estimate is used. When there are too few records within a year, a single season comprising all records is used for threshold estimation.

Differently to DP06, REddyProc only resamples data within seasons instead of across the entire year during the bootstrap, in order to protect periods of a similar u*–NEE relationship and to avoid seasonal biases in resampling.

The general relationship in the estimation of the u* threshold was retained between the two methods (Fig. ), although individual threshold estimates differed. The exceptionally high threshold value of >0.6 ms-1 for site FR-Pue was very probably an overestimate by DP06. However, one has to remember that each estimate has a high uncertainty, and the differences between the two methods were in the range of this uncertainty (Supplement). The estimate of the uncertainty of the u* thresholds with REddyProc was, however, only half of the uncertainty range estimated by DP06 (Supplement). This increased precision was mainly due to the modified bootstrapping scheme, which respects the u* seasons.

When propagating the differences in u* to differences in annual NEE, there was no bias and decreased scatter across sites between all the methods (Fig. ), despite the differences in u* threshold. The absolute differences in annual NEE between the methods were small (mostly <20 gCm-2yr-1), and mostly lower than half of the uncertainty range estimated from the bootstrap (Supplement). REddyProc  estimates u* thresholds with roughly double the precision compared to DP06, due to its protecting of seasons during bootstrap (Supplement).

The agreement between NEE based on u* estimates of REddyProc moving point implementation and current FLUXNET standard post-processing (DP06) (Fig. ) indicates that the sensitivity of NEE to the u* threshold estimate in the inferred ranges is low, which also explains the large uncertainty of the u* threshold estimate. One reason for the missing effect could be site selection of this study without many sites affected by advection, which show limited saturation of the NEE–u* dependence. Since in such cases the filtering does not work properly anyway, it should not change the conclusions for NEE. Hence, we infer that u* estimates of both DP06 and REddyProc are appropriate due to the negligible effect on NEE sums. The agreement implies that both methods can be interchanged in studies that are based on aggregated values, such as annual carbon budgets or for upscaling, without the need to reprocess data.

However, the increase in estimated precision, i.e., lower standard deviation, of the u* threshold estimate also yields an increase in estimated precision of the annual NEE by 50 % (Supplement). This will lead to improved accuracy and usability of EC measurements and any downstream, post-processed data products in model–data integration studies.

While the default seasons and their aggregation are in line with previous approaches, REddyProc allows site-specific knowledge to be used to derive better threshold estimates. For example, if there is a disturbance such as harvest, the u* threshold is expected to change and a different threshold should be applied for filtering before and after the disturbance. In this case the user can define a season change at the harvest date and use season-specific threshold estimates instead of the annually aggregated estimate (Sect.  in Appendix B).

Compared to the BGC16, the new implementation of the MDS algorithm in REddyProc was not limited to single years, but it filled the gaps with a window moving continuously over all years in the input data. This had the advantage of smoother gap filling over the end of the year, and this will especially be of interest for sites in which vegetation is not dormant during this time. This new feature led to different, probably more realistic gap-filled NEE values at the beginning and end of the year.

There were also slight differences in the sequence of window sizes between REddyProc and BGC16. For MDC, the window size with BGC16 had a few more intermediate day steps than REddyProc, which affected longer gaps with missing meteorology. The default meteorological variables and margins for LUT (see Sect. 4.2.2 above) were the same in both implementations.

While REddyProc restricts gap filling to the interpolation of gaps, BGC16 also restricted missing records in periods without measurements.

In the benchmark, REddyProc gap filling was run using the same measured NEE as input that passed the QA/QC routines and u* filtering. The annually aggregated values comprised both filled gaps and originally valid records.

REddyProc gap-filling results agreed with the results of BGC16. A few discrepancies at a half-hourly timescale were found mostly during longer gaps due to the usage of fewer window sizes, as shown for the DE-Tha case (Fig. a). At an annually aggregated timescale, the agreement between methods was strong (R2=0.99) (Fig. b). The outlier of site RU-Cok is due to the availability of only a few months of data for the whole year. While REddyProc filled gaps in the time period with available data, BGC16 extrapolated into the time before and after this period. The seasonal cycle was well reproduced at each site (Supplement).

The good agreement between NEE based on gap filling by REddyProc and gap filling by BGC16 (Fig. ) implies that both gap-filling tools can be used interchangeably without the need to reprocess data.

The main features of the REddyProc implementation of the nighttime-based partitioning algorithm were very similar to BGC16, using a reference temperature of 15 ∘C and trimming the estimates of temperature sensitivity E0 before aggregating them (Sect. ). REddyProc differed from BGC16 in computing the potential radiation that is used in subsetting the nighttime data to derive E0 and RRef (). While REddyProc used the exact solar time for the calculation of the potential radiation, where the sun culminates exactly at noon, BGC16 used the local winter time, which differs from the solar time depending on the location within the time zone.

Annual aggregated values of Reco predicted by REddyProc were in very good agreement (R2=0.99; slope ≈1) with BGC16 as shown in Fig.  and in the Supplement.

In order to evaluate the effects of the differences introduced in the code described above, we also computed Reco by prescribing either E0, or a selection of nighttime data, or both from BGC16 output in REddyProc. Results are reported in the Supplement and showed that the most important factor affecting the Reco computed with REddyProc was the different selection of nighttime data, though the differences were almost negligible at an annual timescale.

The two implementations agreed very well for most sites at an annual timescale. Because of no systematic deviations across sites, the spatial upscaling of fluxes should not be affected by REddyProc implementation. However, for some sites, such as IT-Amp, the relative errors that are quite large indicate problems related to the selection of nighttime data and problems due to large gaps in the dataset.

BGC16 differed from REddyProc (Sect. ), mainly in aspects of separation of nighttime data, estimation of temperature sensitivity from nighttime data, uncertainty estimation, treatment of missing values, and optimization library code.

While for separating nighttime data REddyProc used the exact solar time, where the sun culminates exactly at noon, BGC16 used the local winter time.

For the estimation of temperature sensitivity E0 from nighttime data, BGC16 used a reference temperature of 15 ∘C, instead of the median temperature inside the window. Hence, it estimated stronger correlations between parameters for windows with a different temperature range. Moreover, it omitted smoothing of the estimated E0 across time, often leading to large fluctuations of the E0 estimates across a few days (Supplement), larger estimates of its uncertainty, and differences in subsequent estimation of LRC parameters.

For uncertainty estimation, BGC16 relied on the curvature of the LRC fit's optimum instead of a bootstrap procedure. Hence, it could not take into account the uncertainty of E0 estimated from nighttime data before the daytime LRC fit. Moreover, during interpolation of fluxes based on previous and subsequent valid estimates, the distance weights differed. While REddyProc assigned the estimates to the time of the mean of valid record in a window, BGC16 assigned it to the start of the third day, also if there were only valid data for the first day in the window.

For weighting the records in the LRC fit, BGC16 used the raw estimated NEE uncertainty of each record. It did not check for high leverage of spurious low NEE uncertainty estimates. Its estimates, therefore, were in some windows very strongly influenced by a few records, and failed if a NEE uncertainty estimate of zero was provided. Moreover, when there were missing values or values below zero in a given NEE uncertainty, it set all uncertainty to 1, while REddyProc filled the gaps by setting the missing uncertainty to the maximum of 20 % of respective NEE but at least 0.7 µmolCO2m-2s-1.

Treatment of missing values was not considered by BGC16 and assumed to be handled prior to the processing. Hence, it did not handle missing VPD values and did not retry the LRC fit without the VPD effect in order to also use records with missing VPD. Moreover, as described above, when there were missing values of NEE uncertainty, weighting records in the LRC fit were omitted.

For compatibility with BGC16, the above code differences can be disabled in REddyProc. But differences in optimization library code and specifically the conditions of non-convergence on scattered data could not be eliminated, which led to differences in results as shown in the following section.

Annually GPP predictions of both implementations showed no significant bias across the test sites (Fig. ), although there was some scatter among individual predictions. Similar scatter was observed when comparing the predictions of the default REddyProc options to the predictions with compatibility options. Most of the differences were caused by decreasing the unreasonable high influence of NEE records with small NEE uncertainty (Supplement).

The largest differences in aggregated fluxes between implementations were due to the extrapolation of fitted parameters to periods where no parameter fits were obtained. In many of these cases, there were fits at the boundaries of these periods, whose validity was questionable. Whether these fits passed the quality check or not had a large influence on the extrapolation and hence on the aggregated values. For example, at RU-Cok parameter estimates for valid periods agreed between implementations. However, no valid parameters could be obtained for winter months. While REddyProc reported missing values, BGC16 also reported GPP values based on summer parameterizations for periods further away from summer, which in turn led to higher annual GPP estimates.

Uncertainty estimates of gross fluxes approximately doubled with REddyProc due to the accounting for uncertainty in temperature sensitivity estimates from nighttime data (Supplement).

Agreement between aggregated fluxes predicted by the daytime method and absence of bias for the test sites (Fig. ) suggest that the methods can be used interchangeably for upscaling, although differences in results of influential sites can potentially propagate to differences in upscaled estimates. REddyProc provides a quality flag for the results of the daytime partitioning, which allows less reliable data to be excluded in upscaling studies. For the results associated with good quality flags, we have greater confidence in the REddyProc-based estimates.

The daytime flux partitioning is quite sensitive to the details of the LRC fit. Small changes in treatment of extreme or missing NEE uncertainty estimates or changes in pre-processing and treatment of missing values cause different estimates of LRC parameters and propagate to predicted fluxes of GPP and Reco. Although we put much effort in trying to reproduce the results of BGC16, we were not able to eliminate all differences, especially in the subtle details in the parameter optimization library codes. The differences in predicted half-hourly fluxes, however, average out across sites and across time (Supplement), making this issue less severe at larger scales.

The estimated uncertainties are even more sensitive. Both implementations occasionally produce unreasonably high outliers that affect the aggregated values. REddyProc, in general, estimates higher uncertainties of predicted fluxes because it accounts for uncertainty in temperature sensitivity. Note that the uncertainty introduced to annually aggregated fluxes due to flux partitioning is smaller than uncertainty due to an uncertain u* threshold estimate. Hence, differences or difficulties in uncertainty estimation caused by flux partitioning do affect conclusions of the overall uncertainty estimates to a lesser extent.