Evaluation of 4 years of continuous δ 13 C ( CO 2 ) data using a moving Keeling plot method

Different carbon dioxide (CO2) emitters can be distinguished by their carbon isotope ratios. Therefore measurements of atmospheric δC(CO2) and CO2 concentration contain information on the CO2 source mix in the catchment area of an atmospheric measurement site. This information may be illustratively presented as the mean isotopic source signature. Recently an increasing number of continuous measurements of δC(CO2) and CO2 have become available, opening the door to the quantification of CO2 shares from different sources at high temporal resolution. Here, we present a method to compute the CO2 source signature (δS) continuously and evaluate our result using model data from the Stochastic Time-Inverted Lagrangian Transport model. Only when we restrict the analysis to situations which fulfill the basic assumptions of the Keeling plot method does our approach provide correct results with minimal biases in δS. On average, this bias is 0.2 ‰ with an interquartile range of about 1.2 ‰ for hourly model data. As a consequence of applying the required strict filter criteria, 85 % of the data points – mainly daytime values – need to be discarded. Applying the method to a 4-year dataset of CO2 and δC(CO2) measured in Heidelberg, Germany, yields a distinct seasonal cycle of δS. Disentangling this seasonal source signature into shares of source components is, however, only possible if the isotopic end members of these sources – i.e., the biosphere, δbio, and the fuel mix, δF – are known. From the mean source signature record in 2012, δbio could be reliably estimated only for summer to (−25.0± 1.0) ‰ and δF only for winter to (−32.5± 2.5) ‰. As the isotopic end members δbio and δF were shown to change over the season, no year-round estimation of the fossil fuel or biosphere share is possible from the measured mean source signature record without additional information from emission inventories or other tracer measurements.


Introduction
A profound understanding of the carbon cycle requires closing the atmospheric CO 2 budget at a regional and global scale.For this purpose it is necessary to distinguish between CO 2 contributions from oceanic, biospheric and anthropogenic sources and sinks.Monitoring these CO 2 contributions separately is desirable to improve process understanding, to investigate climatic feedbacks on the carbon cycle and also to verify emission reductions and design CO 2 mitigation strategies (Marland et al., 2003;Gurney et al., 2009;Ballantyne et al., 2010).
A possibility to distinguish between different CO 2 sources and sinks utilizes concurrent 12 CO 2 and 13 CO 2 observations in the atmosphere.The carbon isotope ratio can be used to identify and even quantify different CO 2 emitters if every emitter has its specific known δ 13 CO 2 signature.For example, the CO 2 fluxes from land and ocean can be distinguished using the ratio of stable carbon isotopologue 13 CO 2 / 12 CO 2 in addition to CO 2 concentration measurements (Mook et al., 1983;Ciais et al., 1995;Alden et al., 2010).In other studies, measurements of 13 CO 2 have been used to distinguish between different fuel types (Pataki, 2003;Lopez et al. 2013;Newman et al., 2016) or to evaluate ecosystem behavior (Torn et al., 2011), to mention but a few examples of the many published in the literature.
In the last decade, new optical instrumentation has been developed, simplifying continuous isotopologue measure-Published by Copernicus Publications on behalf of the European Geosciences Union.These situations can be usually identified by a large error of the intercept, δ S (we choose an error > 2 ‰ to reject these results).(c) Sources and sinks with different isotopic signatures or sink fractionation occur at the same time and lead to a wrong apparent source signature.Strong biases are prevented by choosing a minimum net CO 2 concentration range of 5 ppm and demanding a monotonous increase of CO 2 during the 5 h (see text for more details).Note that the background value is displayed for illustration, but it is not used in the moving Keeling plot method.ments.This has led to an increasing deployment of these instruments, thereby increasing the temporal and spatial resolution of 13 C(CO 2 ) and CO 2 data (Bowling et al., 2003;Tuzson et al., 2008;McManus et al., 2010;Griffith et al., 2012;Vogel et al., 2013;Vardag et al., 2015a;Eyer et al., 2016).These data records may lead to an improved understanding of regional CO 2 fluxes, allowing estimates of mean δ 13 C source signatures at high temporal resolution.Estimating mean source signatures from concurrent δ 13 C(CO 2 ) and CO 2 records over time provides, e.g., insight into temporal changes in the signatures of two different CO 2 sources such as fossil fuels and the biosphere if their relative share to the CO 2 offset is known.This may be used to study biospheric responses to climatic variations like drought, heat, floods, vapor pressure deficit etc. (Ballantyne et al., 2010;2011;Bastos et al., 2016).Likewise, the mean source signature can be used to separate between different source CO 2 contributions if the isotopic end members of these sources are known at all times (Pataki, 2003;Torn et al., 2011;Lopez et al. 2013;Moore and Jacobson, 2015;Newman et al., 2016).
Many studies have successfully used the Keeling or Miller-Tans plot method (Keeling, 1958;1961;Miller and Tans, 2003) to determine source signatures in specific settings (e.g., Pataki, 2003;Ogée et al., 2004;Lai et al., 2004;Knohl et al., 2005;Karlsson et al., 2007;Ballantyne et al., 2010).However, the situations in which Keeling and Miller-Tans plots yield correct results need to be selected carefully (Miller and Tans, 2003).Only if all possible pitfalls are precluded can the Keeling intercept (or the Miller-Tans slope) be interpreted as the gross flux-weighted mean isotopic signature of all CO 2 sources and sinks in the catchment area of the measurement site.Especially in polluted areas with variable source-sink distribution, estimation of isotopic sig-nature using a Keeling or Miller-Tans plot requires a solid procedure, e.g., accounting for wind direction changes or simultaneously occurring CO 2 sinks and sources.
In this study, we discuss the possible pitfalls of CO 2 source signature determination from a continuous dataset using the Keeling plot method and follow a specific modification of this method for automatic retrieval of mean source signature with minimal biases.We test this method with modelsimulated CO 2 mole fraction and δ 13 C(CO 2 ) data.Using a modeled dataset where all source signatures are known enables us to test if the calculated source signature is correct, which is vital when evaluating measured data with an automated routine.Having found a method to determine the isotopic signature of the mean source correctly from measured CO 2 and δ 13 C(CO 2 ) data, we discuss which information can be reliably extracted from these results.

Methods
2.1 Keeling and Miller-Tans plot method Keeling (1958Keeling ( , 1961) ) showed that the mean isotopic signature of a source mix can be calculated by re-arranging the mass balance of total CO 2 , and of δ 13 C of total CO 2 , i.e., δ tot , to where CO 2bg and δ bg are the concentration and δ 13 C(CO 2 ) of the background component and CO 2S and δ S are the concentration and δ 13 C(CO 2 ) of the mean source, respectively.Plotting δ tot vs. 1 / CO 2tot yields a y intercept of δ S (cf.Fig. 1a).Miller and Tans (2003) have suggested an alternative approach to determine the mean isotopic signature by rearranging Eqs. ( 1) and ( 2) such that δ S is the regression slope when plotting CO 2tot • δ tot vs. CO 2tot : They argue that this approach might be advantageous since the isotopic signature does not need to be determined from extrapolation to 1 / CO 2 = 0, which could introduce large errors in the δ S estimate.Zobitz et al. (2006) have compared the Keeling and the Miller-Tans plot method (Eqs.3 and 4) and found no significant differences between both approaches when applied to typical ambient CO 2 variations.We were able to reproduce this result with our modelsimulated dataset (cf.Sect. 3.1).Differences between both approaches were (0.00 ± 0.04) ‰ when applying certain criteria (standard deviation of intercept < 2 ‰, CO 2 range within 5 h > 5 ppm), which will be explained in Sect.2.3.The choice of fitting algorithm has also been discussed in the literature.Pataki (2003), Miller and Tans (2003) and Zobitz et al. (2006) compared different fitting algorithms for the regression and came up with different recommendations.Orthogonal distance regression (ODR) and weighted total leastsquares (WTLS) fits (model 2 fits) take into account errors on x and y, whereas ordinary least-squares (OLS) minimization (model 1 fit) only takes into account y errors.Zobitz et al. (2006) have found differences between both fitting algorithms especially at small CO 2 ranges.We have also applied a model 1 (OLS) and model 2 (WTLS) fit to our simulated data and have not found any significant differences ((0.00 ± 0.01) ‰) between them when applying certain criteria (error of intercept < 2 ‰, CO 2 range within 5 h > 5 ppm; see Sect.2.3).In our study, we use a WTLS fit (Krystek and Anton, 2007) as a stable algorithm for fitting a straight line to a dataset with uncertainty in x and y direction in a Keeling plot method.Note that the isotopic signature of the mean source δ S can be determined from linear regression without requiring a background CO 2 and δ 13 C(CO 2 ) value.However, the Keeling and Miller-Tans plot methods are only valid if the background and the isotopic signature of the source mix δ S are constant during the period investigated (Keeling, 1958;Miller and Tans, 2003).Further, the approaches are only valid when sources and sinks do not occur simultaneously.Miller and Tans (2003) gave an example which showed that as soon as sources and sinks of different isotopic signature/fractionation occur simultaneously, the determination of isotopic signature of the source-sink mix may introduce biases.In these cases, the results cannot be interpreted as mean flux-weighted source signature anymore.This has very unfortunate consequences, since in principle we are interested in determining the isotopic signature of the source mix of a region during all times, i.e., also during the day, when photosynthesis cannot be neglected.

Moving Keeling plot method
For a continuous long-term dataset, we suggest an automatic routine to determine the mean isotopic signature of the source mix.It is similar to the moving Keeling plot for CH 4 currently suggested by Röckmann et al. (2016).In our case of CO 2 , we also have to take into account the possibility of simultaneously occurring sinks and sources, which is not important in the case of CH 4 .Our moving Keeling plot method is a specific case of the classical Keeling plot method (Eq. 3) (Keeling, 1961) as it uses only five hourly-averaged measurement points of CO 2 and δ 13 C(CO 2 ), fitting a regression line through these five data points (cf.Fig. 1a, illustrated only for three data points for clarity of inspection).We choose 5 h as a compromise between number of data points, and thus of robust regression, and of source mix constancy.This compromise also manifests itself in such a manner that a window size of 5 h leads to maximum coverage.No background value is included in the regression.The moving Keeling plot method works such that, e.g., for the determination of the mean source signature at 15:00, we use the hourly CO 2 and δ 13 C(CO 2 ) measurements from 13:00 to 17:00 and fit a regression line.Next, for the determination of the source signature at 16:00, we use the CO 2 and δ 13 C(CO 2 ) measurements from 14:00 to 18:00 and so on.Note that this approach leads to a strong autocorrelation of neighboring source signature values.

Filter criteria of the moving Keeling plot method
In order to prevent pitfalls in the regression-based determination of mean isotopic signature, we set a few criteria for the moving Keeling plots to "filter" out situations in which a Keeling plot cannot be performed.These filter criteria are also similar in type to the ones introduced by Röckmann et al. (2016).We here explain why these filter criteria are needed for CO 2 and how they are set.
A prerequisite for the Keeling plot is that the source mix and the background need to stay constant during the investigated period (see Fig. 1a).Varying source mixes may occur when, e.g., the wind direction and therewith the footprint of the measurement site change, or if the emission patterns themselves change over time.This may lead to strong biases of the regression-based mean isotopic source signature (illustrated in Fig. 1b).We eliminate these cases by inspecting the error of the determined intercept δ S .If the source mix or the background significantly change within 5 h, the data points will not fall on a straight line and the error of the intercept will increase.We here set an error of 2 ‰ (in a WTLS fit) as a threshold between an acceptable and a "bad" fit, after having inspected many Keeling plots individually.Also, we demand a monotonous increase of CO 2 within 5 h, as a de-S.N. Vardag et al.: Continuous δ 13 C(CO 2 ) source signature using a moving Keeling plot method crease would be due to either a sink of CO 2 or a breakdown of the boundary layer inversion potentially associated with a change of catchment area of the measurement, both biasing the resulting mean source signature.
As mentioned before, the determination of a mean isotopic signature is not per se possible during the day when CO 2 sinks and sources are likely to occur simultaneously (Miller and Tans, 2003).This can be explained in the Keeling plot by the vector addition of CO 2 source and sink mixing lines with different isotopic signatures, resulting in a vector with an intercept different from the expected one, leading to an isotopic signature which can even lie outside the expected range of the isotopic source end members (see Fig. 1c).This potential bias is stronger the smaller the net CO 2 signal is.Therefore, e.g., for evaluation of the Heidelberg data, we demand an increase in CO 2 during the 5 h period of at least 5 ppm to exclude periods where the photosynthetic sink is similarly strong to total CO 2 sources.This normally leads to an exclusion of daytime periods, when the boundary layer inversion typically breaks up and the photosynthetic sink is most pronounced.Therefore, we are mainly rejecting periods in which isotopic discrimination during photosynthesis dominates the mean isotopic source signature.During winter, it may happen that the inversion does not break up due to the cold surface temperatures, but in this season photosynthetic activity is typically much smaller than fossil fuel emissions, and therefore biases of the regression-based mean source signature are only small.
In the next section, we show that with these filter criteria -i.e., (i) error of the Keeling plot intercept < 2 ‰, (ii) monotonous increase during 5 h and (iii) increase of > 5 ppm during 5 h, which we chose empirically -we are able to successfully reject those source signatures where the underlying assumptions for the Keeling plot method are not met.In Sect.3.1, we will also briefly discuss how sensitive the result is to the choice of filter criteria.Note that the filter criteria may differ for different measurement sites depending on the source heterogeneity and footprint of the catchment areas.Therefore, respective filter criteria need to be designed individually for each measurement station.

Evaluation of the moving Keeling plot method
We apply the moving Keeling plot method to a modeled CO 2 and δ 13 C(CO 2 ) dataset.As also pointed out by Röckmann et al. (2016) in their CH 4 study, this has the advantage that we can test and evaluate our filter criteria as we know exactly the individual isotopic source signatures that created the modeled dataset and, thus, the contribution-weighted mean isotopic source signature at every point in time.Details on the Stochastic Time-Inverted Lagrangian Transport (STILT) model (Lin et al., 2003) and on the computation of the mod-eled CO 2 and δ 13 C(CO 2 ) record as well as of the resulting mean source signature, δ STILT S , are given in Appendix A. We apply the same filter criteria to the calculated mean source signature of the STILT-modeled dataset δ STILT S as to the regression-based mean source signature (Sect.2.3).The "unfiltered" source signatures (black in Fig. 2a) are 0-2 ‰ more enriched than the "filtered" source signatures (blue).This offset is mainly caused by the daytime source signatures, which are on average more enriched than nighttime source signatures (Fig. 2b) but more likely to be filtered out based on the criteria of Sect.2.3.
We have now evaluated the moving Keeling plot method and the used filter criteria based on the model data and tested whether they allow a bias-free retrieval of the mean source signature.In Fig. 3a, we compare the regressionbased source signatures to the filtered reference source signature of Fig. 2a, which we have extracted from the model.We compare not only the mean difference of the mean source signature but also the hourly differences of the mean source signature as well as the smoothed difference.This enables us to clearly state how well we are able to determine the hourly mean source signature and its long-term trend.
Figure 3a displays the filtered seasonal changes of the source signature exemplary for the year 2012.The moving Keeling plot method is able to extract the seasonal variability of the mean isotopic signature correctly.The median difference (and interquartile range) between the smoothed regression-based (red) and smoothed modeled (blue) approach (both smoothed with 50th-percentile filter with window size of 100 h, no smoothing 50 points in front of large data gaps) is 0.0 ± 0.4 ‰.A smoothing window size of 100 h (ca. 4 days) was chosen, so that synoptical and seasonal variations of δ S can be seen while diurnal variations are suppressed.On a shorter diurnal timescale, we compare individual hourly results for the source signature (stars in Fig. 3b,  c).The interquartile range of the filtered hourly difference between the reference δ STILT S and the moving Keeling plot signature is about 1.2 ‰ throughout the year, but the median difference is small (0.2 ‰).The source signature of the model reference and moving Keeling plot source signature show the same temporal pattern both in summer and in winter.Further, we find that, if we do not apply all of the criteria described in Sect.2.3 (unfiltered data in Fig. 3b, c), we see larger differences between regression-based source signature (from the moving Keeling plot) and the STILT reference values.
Note that with the criteria established in Sect.2.3 we have to reject about 85 % of all estimated source signatures.This seems to be an intrinsic problem for an urban setting with many different sources and sinks.Obviously, in many situations the prerequisites of the Keeling plot method are not fulfilled, and, if not filtered out, these data would introduce biases in the retrieved mean source signature.Depending on the application, it may be worthwhile to loosen the filter criteria to increase the data coverage.For example, if one sets  no criteria for the minimal CO 2 range, but only for the error of the intercept (< 2 ‰), about 60 % of all data remain for the estimated source signature, but the median difference between model-and Keeling-based results increases to 0.3 ‰, and the interquartile range increases to 2.4 ‰ (hourly data), which is about twice what we found before.Withdrawing all filter criteria and using only nighttime values leads to a coverage of about 35 % (nighttime) and an interquartile range of 3.5 ‰.The filter criteria which we use here (Sect.2.3) are, thus, rather strict, but we are confident to precisely extract the correct source signature from the δ 13 C(CO 2 ) and CO 2 record at the highest temporal resolution.

The measured source signature record in Heidelberg
We now apply this approach to real measured Heidelberg data.We use the CO 2 and δ 13 C(CO 2 ) record at hourly time resolution (Fig. B1) to compute the isotopic source signature via regression (Fig. 4).The quality of the CO 2 and δ 13 C(CO 2 ) record is assessed in Appendix B. The measurement site and its surrounding catchment area are described by Vogel et al. (2010).We observe a distinct seasonal cycle of the mean isotopic source signature in Heidelberg.Smoothed minimum values of about −32 ‰ are reached in winter.Maximum values of about −26 ‰ occur in summer.This annual pattern is reproduced every year and is similar to annual patterns observed by, e.g., Schmidt (1999) for Schauinsland, Germany, or by Sturm et al. (2006) for Bern, Switzerland.Additionally, the first year shows a more enriched summer maximum source signature.A number of data points (fewer than 0.5 %) lie outside the range of realistic end members between −20 and −45 ‰ of any source in the catchment area (see Table A1).These outliers are not unusual in an urban setting, as the interquartile range of the modeled δ S for the Heidelberg catchment area is about 1.2 ‰ for hourly (nonsmoothed) data, which is only about 30 % higher than the interquartile range of the measured data (see Fig. 4 (1.8 ‰)).
The slightly lower variability in the model may be due to a lower variability in the coarse-resolution emission inventory used in STILT (0.1 • × 0.1 • ).Our 4-year record of the mean source signature in Heidelberg (see Fig. 4) provides a first insight into the source characteristics at the measurement station.It reaches its minimum in winter, when we expect residential heating (mainly isotopically depleted natural gas; see Table A1) to contribute significantly to the source mix.The source signature reaches its maximum in summer, when more enriched biospheric fluxes are expected to dominate the CO 2 signal.This observed seasonal cycle in Heidelberg is very similar to the filtered modeled source signature in amplitude as well as in phase (blue line in Fig. 4).

Information content derived from δ S
We now want to elaborate what quantitative information can be drawn from the mean source signature record in Heidelberg about its components.For an urban continental measurement site, we have to assume that there are at least two main source types of CO 2 in the catchment area: fuel CO 2 and CO 2 from the biosphere.In this simplest case, we essentially have one equation for δ S (Eq. 6) with three unknown variables (δ bio , δ F and the fuel (or biosphere) share f F ); only if two of these variables are known can the third variable be quantified from the measurements: Which of the variables is the one to be estimated depends, of course, on the research question.If the fossil fuel share and end members are well known from inventories, one could be especially interested in determining the isotopic end member δ bio in order to study biospheric processes and their feedback to climatic parameters (Ciais et al., 2005;Ballantyne et al., 2010;Salmon et al., 2011).Contrarily, one may be interested in determining the relative share of fossil fuel CO 2 in the catchment area (with known δ bio and δ F ) to monitor emission changes independently from emission inventories.
As noted, a quantification of the relative shares of fossil fuel and the biospheric CO 2 at continental stations is only possible if information on the isotopic end members of both source categories is available.For example, Vardag et al. (2015b) used the isotopic signatures of δ bio (assumed to be known within a fixed uncertainty) and δ F (obtained by calibration with 14 C(CO 2 )) to calculate the fossil fuel CO 2 contribution from the (continuously) measured CO 2 and δ 13 C(CO 2 ) signal.However, knowing the isotopic signatures δ bio and δ F over the entire course of the year requires an extensive number of measurements at the relevant sources throughout the year and further assumptions of how to scale up these point measurements to a mean source signature of all relevant sources.Therefore, the question, which we address here, is whether it is possible to obtain information on these end members from our measured source signature record, despite the fact that we have three unknown variables and only one equation.In the following, we discuss this question exemplary for the year 2012, for which we have modeled data, inventory information and the mean measured isotope signature.We restrict the discussion to a single year as we focus on discussing which information can principally be obtained from a year-round mean source signature record.
We have noted that, in order to obtain information from δ S on δ bio (δ F ), we require information on the fuel CO 2 share and δ F (on the fuel CO 2 share and δ bio ).However, in cases where the relative share of the biosphere (fossil fuels) is negligible, the isotopic signature of δ F (δ bio ) would equal the mean measured isotopic signature.In these cases, the number of unknown variables would be reduced to one, as the fossil fuel (biospheric) share is ≈ 100 % and δ bio (δ F ) does not contribute to the mean source signature.In a typical catchment area, the relative share of fossil fuels and of the biosphere will not be negligible throughout the year; however in winter, fossil fuel CO 2 will dominate, while in summer the biospheric CO 2 will dominate the CO 2 offset compared to the background.For example, from the STILT model results for Heidelberg (Sect.3.1 and Appendix A), we perceive that on cold winter days in Heidelberg the fossil fuel share can be about 90 to 95 % of the total CO 2 offset.In summer, it reaches a minimum of about 20 %.We may, thus, be able to obtain information about the isotopic end members of δ F in winter (δ bio in summer), when the mean source signature is dominated by the fossil fuel (biospheric) share.

Evaluation of δ S in Heidelberg
To calculate the isotopic end members of δ i from the measured source signature in Heidelberg (and with that to solve Eq. 6), we require the fossil fuel CO 2 share, which we take here from STILT and the bottom-up emission inventory Emissions Database for Global Atmospheric Research (EDGARv4.3;EC-JCR/PBL, 2015).However, as we only require the share and not the absolute concentration, we are largely independent from potentially large model transport errors.We thus assume an absolute uncertainty of 10 % of the fossil fuel share (and of the biospheric share).
To determine δ F in addition to the fuel CO 2 share, we require a value for δ bio .Here we use a typical mean value of the isotopic end member of δ bio = −25.0‰ and assume a seasonal cycle as determined for Europe by Ballantyne et al. (2011) (see Figs. 2 and3 in Ballantyne et al., 2011) displayed in Fig. 5a as a solid green line.We show δ bio with two possible uncertainties of 0.5 and 2.0 ‰.As expected, the uncertainty of the unknown δ F is only acceptably small when the relative share of the biosphere becomes negligible, which is the case in winter (Fig. 5a).The isotopic end member of δ F in winter is about (−31.0 ± 2.5) ‰ in January to March 2012 and decreases to (−32.5 ± 2.5) ‰ in November to December 2012.Further, Fig. 5a shows that the best estimate of the resulting isotopic signature δ F is more depleted in summer than in winter.This curvature is the opposite of what we would expect from EDGAR transported by STILT (see assumed δ F in Fig. 5b).Only when assuming an uncertainty of the biospheric end member of ±2 ‰ or more, the uncertainty range of the estimated δ F allows a more enriched δ F signature in summer than in winter.This suggests that the isotopic source signature of the biosphere in summer is most probably more depleted (by about 2 ‰) than the previously assumed δ bio value based on Ballantyne et al. (2011).
To estimate δ bio (Fig. 5b), we require (besides the fossil fuel share) the isotopic source signature δ F .Here we use δ F calculated with the STILT model on the basis of EDGAR emissions and source signatures according to Table A1.Its annual mean value is −31.0 ‰, and it shows a seasonal cycle with more enriched signatures in summer than in winter.We show the results for δ bio for two possible δ F uncertainties of 1.0 and 3.0 ‰ (see Fig. 5b).The best estimate of the isotopic end member of δ bio in summer is about −25.0 ± 1.0 ‰ in June to August 2012.This reinforces the presumption that δ bio is more depleted than the assumed δ bio value based on Ballantyne et al. (2011) during summer.
The uncertainty of the isotopic end members in Fig. 5a  and b has three components: (1) the uncertainty of the fossil fuel CO 2 share estimated from STILT, which we assume to be about 10 % (absolute) in our case; (2) the uncertainty of the other known isotopic end member (0.5 and 2 ‰ for δ bio or 1.0 and 3.0 ‰ for δ F ); and (3) the uncertainty of the measured mean source signature itself (ca.0.4 ‰; see Sect.3.1 for interquartile range of difference between smoothed regressionbased and smoothed modeled source signature).Note that an uncertainty of 10 % of the fossil fuel share is at the low end of uncertainties.However, an uncertainty of 20 % of the fossil fuel share would increase the uncertainty in the unknown isotopic end members by only 0.2-0.4‰ for δ bio in summer and δ F in winter.
The derived uncertainty of δ F is about 2.5 ‰ in winter, and that of δ bio is about 1.0 ‰ in summer.An uncertainty of ±2.5 ‰ for δ F is rather large if we want to use this observation-based top-down result for further quantitative source apportionment.Vardag et al. (2015b) showed that a misassignment of 2.5 ‰ in δ F leads to a bias in the continuous fuel CO 2 estimate of about 15 % for an urban measurement site like Heidelberg.The observation-based biospheric end member δ bio has an uncertainty of only about 1.0 ‰ in Figure 5. (a) A fixed isotopic end member of the biosphere (green, ±uncertainty of 0.5 ‰ (light green area) and 2 ‰ (crosshatched green)) together with the measured source signature (black) results in δ F (red, ±its uncertainty).(b) A fixed isotopic end member of the fuel mix (red, ±uncertainty of 1.0 ‰ (salmon pink) and 2.0 ‰ (crosshatched gray-pink)) together with the measured source signature (black) results in δ bio (green, ±its uncertainty).In both cases, also the fuel CO 2 share (or biospheric CO 2 share) is required.We here use the share calculated with STILT on the basis of EDGAR v4.3 and assume an absolute uncertainty of 10 %.June to August 2012, which is a very well constrained value for this period.
We cannot assume that the isotopic end members δ bio and δ F remain constant over the course of the year: δ bio typically shows a seasonal cycle possibly due to seasonal changes in the fraction of respiration from C3/C4 plants as well as due to influences of meteorological conditions on biospheric respiration.Likewise, δ F typically shows more enriched values in summer, when the contribution of residential heating (and therewith of depleted natural gas) is much smaller than in winter.Therefore, no year-round estimation of fuel CO 2 share is possible from only CO 2 and δ 13 C(CO 2 ) either.

Summary and conclusions
Many measurement stations are currently being equipped with new optical instruments which measure δ 13 C(CO 2 ), aiming at an improved quantitative understanding of the carbon fluxes in their catchment area.If this additional δ 13 C(CO 2 ) data stream is not directly digested in regional model calculations, the mean isotopic source signature is often computed from the δ 13 C(CO 2 ) and CO 2 records for a potential partitioning of source contributions.A bias-free determination of source signature, however, requires carefully selecting the data for situations in which determination of source signature with a Keeling plot method can pro-vide reliable results.This excludes periods (1) when sinks and sources occur simultaneously, (2) when the source mix changes or (3) when the signal-to-noise ratio is too low (Keeling, 1958;1961;Miller and Tans, 2003).
We therefore developed filter criteria and show that the routine and accurate determination of δ 13 C(CO 2 ) source signature is possible if the introduced filter criteria are applied.As suggested by Röckmann et al. (2016), we use a modeled dataset for validation of the approach.We find that for a station like Heidelberg the bias introduced by our analysis is only (0.2 ± 1.2) ‰ for hourly data.The uncertainty decreases in the long-term to (0.0 ± 0.4) ‰.We are, therefore, able to estimate the source signature correctly, but 85 % of the data are rejected by the filter criteria.Further, as the filter criteria are such that the source signatures are more likely to be filtered out during the day than during the night, the longterm source signature is not representative of real daily averages, but only of periods where the data were not filtered out (mainly nighttime).As a consequence, the isotopic end members δ bio and δ F can also only be estimated for these periods.This problem does not occur for CH 4 , which has only weak daytime sinks.
By applying the moving Keeling plot method to a real dataset measured in Heidelberg, we were able to determine the source signature over the course of 4 years.We find a distinct seasonal cycle of the mean source signature with val-ues of about −26 ‰ in summer and about −32 ‰ in winter.This general behavior was expected due to the larger relative contribution of more depleted fossil fuel CO 2 in winter.For a unique interpretation of the mean source signature, possible sources in the catchment area need to be identified.As soon as there is more than one source, the source signature is a function of the isotopic end members of all sources, as well as of their relative shares.Therefore, to study the seasonal and diurnal changes of fossil fuel shares at a continental station, information on the isotopic end members of the fossil fuel mix as well as of the biosphere is required at the same time resolution.Unfortunately, the isotopic end members are often not known with high accuracy.The uncertainty of the isotopic end members often impedes or even prevents a unique straightforward determination of the source contribution in the catchment area (e.g., Pataki, 2003;Torn et al., 2011, Lopez et al. 2013;Röckmann et al., 2016) and calls for elaborated statistical models based on Bayesian statistics.This important fact is sometimes mentioned, but the consequences for quantitative evaluations are rarely emphasized, preserving the high expectations associated with isotope measurements.
We showed that for the urban site of Heidelberg we can use the observation-based mean source signature record to estimate the isotopic end member δ F in winter and the isotopic end member δ bio in summer within the uncertainties of ±2.5 and ±1.0 ‰, respectively.Here we assumed an uncertainty of ±10 % for the fossil fuel and the biospheric CO 2 share and an uncertainty of the other isotopic end member δ F of ±3.0 ‰ and δ bio of ±2.0 ‰.However, in the winter season we cannot obtain any reliable information on δ bio , and in summer we cannot study δ F .For a year-round determination of fossil fuel share, δ bio and δ F are required throughout the year.As no reliable determination of δ bio and δ F is possible during the entire year based only on atmospheric observations, there is a need for either very good bottomup information for the catchment area of interest or frequent measurement campaigns close to the sources.However, the disadvantage of using such a bottom-up approach is that usually only information from a few specific sites are available, which need then to be upscaled correctly such that they are representative of the entire catchment area.For a determination of δ F during the entire year, one can possibly utilize 14 C(CO 2 ) and CO/CO 2 measurements (following Vardag et al. (2015b)) or O 2 /N 2 measurements (e.g., Sturm et al. 2006;Steinbach et al., 2011), all of which exhibit their own deficiencies, which are discussed elsewhere (e.g., Ciais et al., 2015;Vardag et al., 2015b).
Finally, we could show that, even though it is not possible to determine the isotopic end members throughout the year, it is possible to refute certain literature values.For example, a respiration signature of −23 ‰ in August and September 2012 as reported by Ballantyne et al. (2011) is most likely too enriched as this would lead to more depleted δ F values in summer than in winter.This is in contrast to what we would expect based on emission inventories.

Data availability
The CO 2 and δ 13 C(CO 2 ) records from the measurement site Heidelberg are available at http://www.iup.uni-heidelberg.de/institut/forschung/groups/kk/Data/Hourly_FTIR.txt.In future, this dataset will also be accessible via the ICOS Carbon portal.CO 2 flask data from Mace Head (Dlugokencky et al., 2015) can be downloaded at ftp://aftp.cmdl.noaa.gov/data/trace_gases/co2/flask/surface/.The δ 13 C(CO 2 ) flask data from Mace Head (White et al., 2015) (Mook, 2000) www.biogeosciences.net/13/4237/2016/Biogeosciences, 13, 4237-4251, 2016 the biospheric CO 2 sink, dominating in summer, discriminates against δ 13 C(CO 2 ), leaving the atmosphere enriched in 13 C(CO 2 ), while CO 2 decreases.On top of the seasonal cycle, CO 2 in Heidelberg (Fig. B1) slightly increases over the course of 4 years by about 2 ppm yr −1 .At the same time δ 13 C(CO 2 ) decreases by about 0.04 ‰ yr −1 .These rates are similar to the CO 2 increase and δ 13 C(CO 2 ) decrease rates in Mauna Loa, Hawaii, USA (Dlugokencky et al., 2015;White et al., 2015), and therefore reflect the global increase of CO 2 from 13 C-depleted sources moderated by air-sea gas exchange.It is not visible to the eye how the degree of depletion in δ 13 C(CO 2 ) varies over the course of the year (see Fig. B1).To analyze this behavior, the mean source signature must be computed (see Sect. 2.2 and Fig. 4).

Figure 1 .
Figure 1.Regression-based determination of source signature using a Keeling plot.For clarity of illustration, we only draw three data points instead of five, which we use for our computation.(a) Constant source mix during the time of source signature determination leads to the correct flux-weighted mean isotopic signature (following Eq.A1), δ S .(b) Change of source mix during the period of determination of a Keeling plot due to either a temporal change of emission characteristics or a wind direction change (transportation) leads to a biased result.These situations can be usually identified by a large error of the intercept, δ S (we choose an error > 2 ‰ to reject these results).(c) Sources and sinks with different isotopic signatures or sink fractionation occur at the same time and lead to a wrong apparent source signature.Strong biases are prevented by choosing a minimum net CO 2 concentration range of 5 ppm and demanding a monotonous increase of CO 2 during the 5 h (see text for more details).Note that the background value is displayed for illustration, but it is not used in the moving Keeling plot method.

Figure 2 .
Figure 2. Source signature as calculated with the STILT model following Eq.(A1).(a) Unfiltered in black and filtered (for monotonous increase and minimal range) in blue.Only about 15 % of all data points fulfill our strict criteria.However, they are distributed approximately evenly throughout the year.(b) Diurnal cycle of modeled mean source signature due to diurnally varying mean source mix.Gray areas denote times when source signature is usually filtered out.

Figure 3 .
Figure 3.Comparison between modeled reference source signature (blue) and the moving Keeling plot intercept (red), which is regressionbased using the modeled CO 2 and δ 13 C(CO 2 ) records.(a) Long-term comparison for the year 2012.The smoothed lines of window size 100 are also shown in the respective colors.(b) Summer excerpt and (c) winter excerpt (gray areas in a) of both reference and regressionbased source signature.The crosses denote unfiltered data, and bold stars denote filtered data.The green lines in panels (b) and (c) give the measured CO 2 concentration during the summer and winter periods, respectively.

Figure 4 .
Figure 4. Moving Keeling plot method-based source signature in Heidelberg from 2011 until mid-2015.The black line is the smoothed measured source signature, and the blue line gives the smoothed modeled source signature (both 50th-percentile filter with window size = 100 h).Half a window size before the beginning of a large data gap the data are not further smoothed to prevent smoothing artifacts.

Figure B1 .
Figure B1.Continuous Heidelberg hourly FTIR record of (a) CO 2 and (b) δ 13 C(CO 2 ) from April 2011 to June 2015.Data gaps occur when the instrument was away during a measurement campaign or when instrumental problems occurred.

Table A1 .
δ 13 C(CO 2 ) source signature of fuel types and biosphere as used in the model and the range of literature values.Note that for a specified region the range of possible isotopic signature can often be narrowed down if the origin and/or production process of the fuel type is known.