The CUP_NEE is the period when the NEE flux is negative, and the downward and upward zero-crossing dates represent the onset and termination of the CUP_NEE, respectively. Hence, we shift the NEE zero-crossing dates to have a change Δ (where Δ is measured in days) in the CUP_NEE duration (ΔCUP_NEE). The NEE flux is characterized by daily temporal resolution, showing relatively gradual variations along the y-axis compared to the x-axis. For all the experiments performed, the NEE values (i.e., y-axis) are modified to achieve the desired timing adjustments (Δ) in CUP_NEE without altering the time axis itself. This adjustment ensures the creation of a smooth curve that closely mirrors the actual flux while achieving the intended change in CUP_NEE. For each value of ΔCUP_NEE, we modify the downward and upward zero-crossing dates of NEE separately to evaluate the effect of changes in the early and late CUP_NEE phases, respectively. This is achieved by adding or subtracting a continuous curve to the period extending from the peak in spring to the NEE minimum for early phase changes and the period from the NEE minimum to peak in winter for late phase changes. The curve is created by combining two distinct half-Gaussian curves (Fig. , red and blue curves): the first curve has its peak at the new onset/termination and a standard deviation (σ1) equal to one-third of the distance between the NEE peak in spring/winter and the new onset/termination. The second curve, also with its peak at the new onset/termination, has a different standard deviation (σ2) equal to one-third of the distance between the new onset/termination and the date corresponding to the NEE minimum value. This configuration (i.e., Gaussian peaks and σ) ensures that the Gaussian tail minimizes any shift around the NEE peak and trough while realizing the Δ shift at the onset or termination of the CUP_NEE.

Some pixels exhibit a distinct seasonal pattern without a well-defined peak in spring or winter. In those cases, the period for manipulating the early and late CUP phases then extends from the beginning of the year to the day of minimum NEE and from the day of minimum NEE to the end of the year, respectively. The portions of the first and second curves corresponding to the range from “μ-3σ1” to “μ” and from “μ” to “μ+3σ2”, respectively, are then combined and smoothed using a spline function (Fig. , purple curves).

We note that the annual flux is not conserved in the manipulation. However, we detrend the simulated CO₂ mixing ratio prior to CUP_MR analysis, which would remove any trend in the CO₂ mixing ratio caused by repetition of the manipulated years. Further, when evaluating the simulated CO₂ time series, we found that the change in the total annual flux only changes the peak-to-peak amplitude and does not influence the timing and duration of the simulated time series, except at times corresponding to periods of manipulation in the CUP_NEE. This happens, for instance, when the downward zero crossing of the NEE flux is manipulated: it changes only the CUP onset and has minimal influence on the CUP termination in the CO₂ mixing ratios. The different cases of manipulation are described below.

Δxd: In these simulations, every year has the same discrete change in CUP_NEE. In the different experiments, the magnitude of the shift (denoted by x) ranges from -10 to 10 d in intervals of 2 d.

The flux alteration is complicated to apply in some cases, as described below.

When a local maximum is observed between the downward or upward zero-crossing points and the minimum NEE. In such cases, adding the Gaussian curve shifts these peaks above the zero-crossing line, creating an additional downward or upward zero-crossing point. This complicates the assessment of CUP_NEE following the manipulation, and results in ΔCUP_NEE being different from the prescribed value. The Δ is kept at zero in this case.

We use a three-dimensional global atmospheric transport model, TM3 , to simulate CO₂ mixing ratios at the specified sites based on manipulated NEE fluxes. The model is run at a spatial resolution of 5° in longitude and 4° in latitude with 19 vertical levels, using 6-hourly NCEP reanalysis meteorological fields from 1995 to 2017 and daily surface fluxes from the Jena CarboScope CO₂ Inversion (version ID: sEXTocNEET_v2021) , with the NEE fluxes manipulated as previously described. The forward runs are carried out with (1) fixed transport (meteorology from a random year, here we used the year 2008 and repeated it in time such that there is no IAV) and (2) interannually varying transport for the period 1995 to 2017 to study the contribution of atmospheric transport to the IAV in CUP_MR. The first five years are excluded from the CUP_MR analysis to account for the model's spin-up time, and ΔCUP_NEE is held at zero during this period.

The forward transport runs simulate CO₂ mixing ratios at discrete time steps, which we sample at the frequency corresponding to the flask measurements (approximately bi-weekly) at the studied sites. This sampling interval sufficiently captures the larger-scale trends and seasonal variations critical to our analysis and allows for consistent comparison with previous studies that looked into long-term trends using flask measurements. We apply the EFD method described in to the output data and estimate the CUP_MR. Here, the CUP_MR is estimated using a threshold derived from the first derivative of the detrended and smoothed CO₂ mixing ratio seasonal cycle curves. A threshold of 15 % and 0 % of the first-derivative minimum was used as a threshold to determine the onset and termination of the CUP_MR, respectively, as in . The calculation is applied to an ensemble of the detrended time series, which allows for an uncertainty range on the CUP estimate to be calculated.

The calculated ΔCUP_MR consistently shows lower absolute values than the prescribed ΔCUP_NEE. For example, at BRW, ΔCUP_MR is 0.43 times the prescribed early phase ΔCUP_NEE as illustrated in Fig. a. This reduction in ΔCUP_MR is found across all the studied sites with varying degrees of intensity, as illustrated in Fig. d, when Δ is prescribed to either the early or late phases of CUP_NEE. This shows how atmospheric observations respond differently to CUP perturbations compared to local NEE measurements, and a one-on-one translation might lead to an incorrect interpretation of at least the magnitude of CUP changes. The persistent difference in the magnitude of ΔCUP_MR from the imposed ΔCUP_NEE results from the integration of signals from various regions with different CUP_NEE timings as detailed in Sect. .

At most studied sites, the Δ assigned to the early phase of CUP_NEE predominantly affects the onset of CUP_MR (Fig. b and e). The ΔCUP_MR then corresponds to the changes in onset of CUP_MR as indicated by the similar variation in the red bars in Fig. d and e. Similarly, Δ applied to the late phase of CUP_NEE primarily influences the termination of CUP_MR (Fig. c and f) which then drives ΔCUP_MR in experiment LNV00 (Fig. d and f, cyan bars). This suggests that the changes in the early and late phases of CUP at the surface can be analysed separately by examining the onset and termination of CUP inferred from CO₂ mole fraction observations. Contrary to the direct but dampened relationship between ΔCUP_NEE and ΔCUP_MR, we find an opposite response at some sites: a lengthening (shortening) imposed on CUP_NEE leads to shortening (lengthening) of the CUP_MR. This is seen to occur at sites ZEP and WIS, as indicated by the negative slopes at these sites (Fig. d).

At ZEP, the late phase ΔCUP_NEE leads to unintended changes in CUP_MR onset. For Δ prescribed to the late CUP_NEE phase, the change in CUP_MR termination is only 0.4 times the Δ, while that in the onset is 0.6 times the Δ. Thus, the changes intended for CUP_MR termination extend to CUP_MR onset in the following year. For example, a 10 d delay prescribed to the CUP_NEE termination results in a 4 d delay in CUP_MR termination and a 6 d delay in the onset. This results in a 2 d shorter CUP_MR, establishing an inverse relation between ΔCUP_MR and ΔCUP_NEE at ZEP (slope of -0.22 in the experiment LNV00). Likewise, at WIS, in experiment ENV00, the change in CUP_MR onset is only -0.2 times the applied early phase ΔCUP_NEE, while the change in termination is -0.3 times the perturbation imposed. This offsets the ΔCUP_MR and leads to a significant (p < 0.001) inverse relation between ΔCUP_MR and ΔCUP_NEE at WIS (slope of -0.06, in the ENV00 experiment).

Even when interannual variations from atmospheric transport are included, changes imposed in ΔCUP_NEE are reflected in ΔCUP_MR. The varying atmospheric transport leads to year-to-year variations in signal integration and changes that were not captured in the experiment with transport from single-year meteorology can be seen in the experiment with interannually varying transport. This is illustrated for different sites in Fig. . An inverse relation between ΔCUP_MR and ΔCUP_NEE was calculated at WIS and ZEP in experiments ENV00 and LNV00, respectively, as described in Sect. . However, in experiments with varying transport, slope values of 0.83 at WIS (experiment ENV0T) and 0.47 at ZEP (experiment LNV0T) are found, compared to -0.06 and -0.22 in the experiment with fixed transport. This suggests that anomalies observed in specific years may be predominantly attributed to the meteorological conditions of those particular years.

Out of all the evaluated sites, only SHM and BRW partially captured CUP_MR trends corresponding to the imposed trends in CUP_NEE as shown in Fig.  (results for other sites are shown in Table ). In experiment ENV0T, the largest trend in CUP_MR is derived at SHM, with values of 0.5 and -0.3 d yr⁻¹ for the imposed increasing (1.11 d yr⁻¹) and decreasing (-1.11 d yr⁻¹) trend, respectively. Similarly, in experiment LNV0T, the largest trend in CUP_MR is observed at BRW (0.5 and -0.2 d yr⁻¹ for the imposed increasing and decreasing trend, respectively). Nevertheless, part of the observed trend can be attributed to the IAV in atmospheric transport, thereby showing that the IAV in transport can influence our understanding of the actual long-term changes in CUP_NEE trends. This can be seen in Fig. , green bars (Δ0l), corresponding to experiments ENV0T and LNV0T. Note that in these experiments, there is no IAV in the CUP_NEE flux as indicated by the subscript “0”, and Δ0l indicates that no trend is prescribed to the CUP_NEE. Then any derived CUP_MR trend can be attributed solely to the IAV in transport. The trend from the IAV in transport contributes to the asymmetry between the red and blue bars. At BRW, experiment LNV0T, indicates that a CUP_MR trend of 0.1 d yr⁻¹ can arise from variability in transport alone, and accounts for about 20 % of the derived CUP_MR trend (blue bar showing 0.5 d yr⁻¹).

Furthermore, we observe that the actual IAV in the CUP_NEE fluxes contribute to the derived CUP_MR trends; however, as the IAV in the flux becomes larger, it imposes noise that makes the trends harder to detect. This is shown in experiments ENV1T and ENV2T (Fig. ), where the actual IAV in CUP_NEE is retained and doubled, respectively. In experiment ENV1T, the CUP_MR trend in response to the prescribed opposite trends, Δpl and Δnl are distinct in sign. Even though the magnitude of the prescribed trend is the same, a large difference in magnitude can be seen between results for Δpl (red bar, 0.6 d yr⁻¹) and Δpl (blue bar, -0.03 d yr⁻¹), for example, at BRW. This can be attributed to the increasing trend from both IAV in the actual flux and transport, as indicated by the green bar for ENV1T. The green bars in experiment ENV1T (0.3 d yr⁻¹) and ENV0T (0.1 d yr⁻¹) are distinct, and their difference (0.2 d yr⁻¹) is the contribution from the actual IAV in CUP_NEE alone. In the experiment where the IAV in CUP_NEE per pixel was doubled, it becomes evident that the imposed alterations in CUP_NEE are not accurately reflected in CUP_MR, even at sites like BRW, which exhibited pronounced responses in other experiments (ENV1T and LNV1T).

The various Transcom3 regions of the Northern Hemisphere contribute in various degrees to the CUP_MR changes observed at the studied sites. The changes in the Boreal regions are partially captured at both the higher and lower latitudes (e.g., ALT, BRW, SHM, MID, and MLO). Considering both the early and late ΔCUP_NEE phases, the contribution from the Eurasian Boreal region is largely seen at SHM (-3 d in the early and -7 d in the late CUP_NEE phase), followed by MID with (-3 in both the days early and late CUP_NEE phase), showing an eastward transport from the Eurasian Boreal region. Similarly, considering both the CUP_NEE phases, the contribution from the North American Boreal region is seen at all sites except ASK, WIS, and ZEP. In response to delayed onset, prescribed to the CUP_NEE in Eurasian Boreal region, a longer CUP_MR is calculated at ASK, WIS, and AZR (Fig. a), suggesting that the inverse slope relation between ΔCUP_MR and ΔCUP_NEE in Sect.  might largely be from changes in the Eurasian Boreal region. In the Eurasian Temperate region, the Δ prescribed to both the early and late CUP_NEE phases integrates at the lower latitude site (e.g., MID, MLO, NWR, and, SHM), whereas higher-latitude sites (e.g., ALT, BRW, and ZEP) only capture perturbations imposed during the early phase of CUP_NEE. The contribution from the North American Temperate region is strong during the early phase of CUP_NEE, while late phase changes are captured only by MID and AZR. Signals from the European region integrate well at most of the studied sites. At ZEP, a significant regional contribution from any of the studied TransCom3 regions can only be seen in the early CUP_NEE phase. This explains to some extent the direct relation between ΔCUP_MR and ΔCUP_NEE found only in the early phase (Sect. ).

The long-term trend in the CUP_MR could not be accurately attributed to different regions even for sites like BRW that showed a predominant response to the prescribed long-term trend in CUP_NEE (Sect. ). This can be seen from Fig. . At BRW, the CUP_MR trends partially reflect the CUP_NEE trends prescribed to the Eurasian Boreal region. For example, in the early CUP_NEE phase, we find a change of 0.32 and -0.06 d yr⁻¹ in response to the prescribed Δpl (1.1 d yr⁻¹) and Δnl (-1.1 d yr⁻¹), respectively. However, the large error bars show that the uncertainty in trend estimation is large when changes are prescribed to only a given TransCom3 region.

We have shown the significant role of interannually varying atmospheric transport in the evaluation of metrics derived from CO₂ mole fraction data. At certain sites such as ZEP and WIS, the CUP_MR from simulations with fixed transport failed to capture the CUP_NEE changes, whereas in simulations with varying transport, the prescribed CUP_NEE changes could be partially derived from CUP_MR. This indicates that in a given year of meteorology used in the fixed transport simulation, the atmospheric transport is unlikely to originate from the areas where the ΔCUP_NEE was prescribed, while in simulations with transport variability, the meteorology in other years might have originated from these regions. Thus, the anomalies observed in CUP_MR in a particular year could stem from transport variability rather than anomalies in CUP_NEE itself, rendering mixing ratio time-series less useful for studying interannual variations in CUP_NEE.

Finally, we show that due to the atmospheric transport, the source areas for a given station during the early and late CUP_NEE phases can be substantially different, influencing the expression of CUP_MR in the different CUP_NEE phases. For instance, our analysis (Fig. ) shows that WIS mainly receives signals from the Northern Hemisphere land pixels only in the late CUP_NEE phase. Consequently, at WIS, the CUP_MR is directly proportional solely to changes prescribed to late CUP_NEE phase (slope of 0.5 in LNV00). Similarly, at ZEP, the contribution of the Northern Hemisphere landmass to ΔCUP_MR occurs only in the early CUP_NEE phase. The atmospheric transport to ZEP is dominated by the regions Eurasian Boreal and Europe during March–May; in the following months (June–August), the air mass transport is largely confined to the Arctic and does not extend equatorward into the continents in some years . Our observations imply that at ZEP/WIS, changes in the onset/termination of CUP_NEE are more effectively reflected as changes in CUP_MR.

The long-term trends prescribed to the CUP_NEE could be partially derived from CUP_MR at BRW and SHM, even under IAV in atmospheric transport and CUP_NEE. However, when IAV in CUP_NEE was doubled, the prescribed trends were not captured. This suggests that the long-term trends in the observations may be compromised when there is a higher IAV in CUP_NEE. The contribution from atmospheric transport exhibited a CUP_MR trend of 0.11 d yr⁻¹ at BRW. This finding aligns with a study by where the IAV in transport alone caused a change of 0.16 d yr⁻¹ in the downward zero-crossing date at BRW for their analysis period between 1979 and 1999.

With warming, a longer growing season is observed in the high latitudes (e.g., , 2.6 d per decade). A longer growing season does not necessarily mean an increase in CUP_NEE or CUP_MR as they are determined by both photosynthesis and respiration. The existing literature on the CUP_NEE changes in the Northern Hemisphere based on CUP_MR varies from increasing to neutral to decreasing . The complications in interpreting CUP_NEE changes arise mostly when directly assessing the CUP from CO₂ mixing ratio. Therefore, CO₂ observations should preferably be interpreted following a formal inverse estimate of the corresponding surface NEE. It is then possible to account for the interannual variability, trends, and delays imposed by the slow atmospheric mixing. Nevertheless, the ability of such inversions to constrain regional changes in NEE can only be improved with an expanded observation network.

The regions contributing to the integrated signal at various observation sites are influenced by atmospheric transport to these locations. From the idealized simulations with no IAV in transport or CUP_NEE it turned out that at sites like ALT, BRW, SHM, and MLO, a significant contribution from Boreal and Temperate regions could be calculated, indicating that these remote sites receive well-mixed signals from higher- and mid-latitude regions in the Northern Hemisphere with strong seasonality. We calculate that the contribution from mid-latitude is significant at the sites in the Boreal region (e.g., ALT and BRW in the early CUP_NEE phase) in line with . They found that the seasonal cycle observed at higher latitude sites is most sensitive to changes in the seasonality of mid-latitude surface emissions; however, we do not find that the mid-latitude influence is more than the Boreal region influences at higher-latitude sites. At ZEP, strong signals from both Eurasian and North American regions dominate during the early CUP_NEE phase (Fig. ), and an amplification of the CUP_MR signal is found. Further, a significant change in the regional contribution is found between the early and late CUP_NEE phases, shifting from continental in the early CUP_NEE phase to ocean signals in parts of the late CUP_NEE phase (Sect. ). This change explains the significant difference in ΔCUP_MR to ΔCUP_NEE during different phases, as shown in Fig. . At WIS, ASK, and AZR, when a delayed onset is imposed on the CUP_NEE from Eurasian Boreal regions, a positive ΔCUP_MR (i.e., an extension in CUP_MR) is calculated. These sites are located in the temperate regions. The CO₂ 2D mixing ratio fields (Fig. ) reveal that changes imposed on the Boreal region propagate partially to the lower latitudes (around 30° N) later in the CUP_NEE phase. Thereby the delay imposed on the CUP_NEE of the Eurasian Boreal region in May integrates at the lower latitude region (near to the location of WIS, ASK, and AZR) only later in July, delaying and extending the CUP_MR.

When the long-term trends were applied to specific regions, the slope estimated from CUP_MR had large uncertainty due to the influence of IAV in transport and CUP_NEE. Furthermore, the flux manipulation strictly within the boundaries of the TransCom3 region in our experiments may have substantially limited the regions from which the signals reach the sites. In the real world, regional boundaries are more diffuse, and the footprint of the site provides a more accurate estimate of the regions contributing to the observed signals. Nonetheless, this aspect falls outside the scope of the present study.

The changes in the CO₂ mixing ratio time series from the Northern Hemisphere give a larger spatial perspective of the CUP_NEE changes. However, results from idealized simulations suggest that they are influenced by atmospheric transport IAV, seasonal changes in atmospheric transport, and IAV in the biospheric fluxes. We find a significant damping of the changes that were imposed on the CUP_NEE from the integration of signals from different regions that have varied timing and suggest a more intense change in the local spatial scales. With the constraints in NEE flux manipulation, imposed by the presence of local maxima and insufficient data points for Δ changes in the early and late CUP_NEE (Sect. ), the simulations in this study do not accurately represent the real-world scenarios. In the real world, the changes in CUP_NEE are asynchronous across space. Although we broadly examined the influence of different TransCom3 regions, conducting more dedicated footprint analyses of the studied sites may offer further insights into the signals studied here.