We investigate different methods for estimating anthropogenic CO

Earth's carbon budget is strongly influenced by anthropogenic CO

Second, a complication of applying

Turnbull et al. (2015) showed that for an urban study area in the middle
of the North American continent, the local CO

Since CO is often co-emitted during (incomplete) combustion and since CO can
be measured continuously, the CO offset relative to clean air,

One of these tracers may be

In many settings, we will exhibit neither a constant ratio

In the present study, we investigate how continuous CO

We discuss the model results for three typical European sites, which differ in their annual mean fuel
CO

For the study's purpose of theoretically assessing precision and accuracy of
different tracer configurations for fuel CO

We used the Stochastic Time-Inverted Lagrangian Transport (STILT) model
(Lin et al., 2003) as well as preset source and sink distributions (see
below). To simulate the atmospheric transport we used meteorological fields
from the European Centre for Medium-Range Weather Forecast with 3-hourly
temporal resolution and 25 km

For the biospheric CO

Anthropogenic emissions of CO

The STILT model calculates the total trace gas mole fraction of CO

The total CO mole fraction (

The

Tracer or tracer combinations, required parameters and formula for
estimation of targeted fuel CO

In the following, we use six different tracers or tracer combinations to
derive continuous fuel CO

We investigated how well the different tracer combinations perform at a
typical urban, rural and polluted measurement site. First, we will discuss
the upper limit of precision and accuracy of fuel CO

The integrated footprint-weighted parameters (e.g.,

In contrast to methods using CO and/or

As

Histograms showing the differences between the modeled fuel
CO

Same as Fig. 1 but for Gartow. In Gartow, mean fuel CO

Same as Fig. 1 but for Berlin. In Berlin, mean fuel CO

Normally it is not be
possible to determine parameters such as

Sensitivity analysis: median difference between the modeled fuel
CO

The mean difference between the modeled and tracer-based fuel CO

All methods using

Generally, the absolute standard deviation of the different tracer
distributions is larger at the polluted station than at urban and rural
stations. At the same time, we found that the variation in the
footprint-weighted parameters such as

We have found that only small median differences occur when using

We have investigated how well we are able to estimate fuel CO

The error bars given at

We confirm that the CO

Critical parameters/variables of the CO method (orange in Fig. 4) are the CO
offset

The sensitivities of fuel CO

Figure 4m–p display the sensitivity of the

Magnitude, physical reason and reference of parameter variation (included in Figs. 5–7).

Same as Fig. 1 but now also including measurement imprecision.

Same as Fig. 2 but now also including measurement imprecision.

Same as Fig. 3 but now also including measurement imprecision.

In Sects. 3.3.1–3.3.4, we have seen how sensitive the fuel CO

Comparison of median diurnal cycle of fuel CO

The random vectors which were used in this study in this study are summarized and explained in Table 3. The distributions of the difference
between estimated (including measurement and parameter uncertainties and
sub-monthly variations) and modeled fuel CO

When including the measurement uncertainties and (input and
footprint-weighted) parameter variability in the considerations, the mean
bias remains unaltered, since the included uncertainty is random. However,
the distributions of the CO and

For urban sites, CO and

As the diurnal cycle of CO

One can see that the

One could consider implementing a diurnal correction into the fuel CO

In inverse model studies, often only afternoon hours are used to derive
fluxes, as the atmospheric mixing can be better simulated by the models
during conditions with a well-developed mixed layer (Gerbig et al., 2008).
Therefore, it is especially important to check the afternoon values of fuel
CO

Absolute mean difference of tracer-based estimate and modeled (assumed as correct) fuel CO

In order to estimate fuel CO

Since

Previous radiocarbon calibration approaches have suggested integrated (e.g.,
monthly) sampling of

Integrated sample calibration: take

Annual grab sample calibration: randomly select a number of
samples

Seasonal grab sample calibration: randomly select a number of
samples

Seasonal event calibration: Randomly select an “event day”
each season. On this day, select

Comparing these sampling strategies to each other using one model run is
difficult, since the result changes from random realization to random
realization, depending on the selection of calibration samples in sampling
strategy 2–4. We have therefore performed a Monte Carlo simulation (with 500
runs) and used the root median square difference between the obtained and
originally modeled reference values

Table 4 shows the absolute mean difference and standard deviation (as determined from
a Gaussian fit to the difference histogram of modeled and tracer-based fuel
CO

We further find that, since

The accuracy of the seasonal event calibration is slightly worse than the accuracy of the seasonal calibration (see Table 4) due to non-representativeness of a single event for the entire season.

In this work, we analyzed the advantages and disadvantages of different
tracers for estimating continuous fuel CO

The results of our model study suggest that, with our current measurement
precision of continuous tracers such as CO or

We find that CO

In contrast to CO

The precision of CO- and

We have found that hypothetical future

We have compared the diurnal cycle of the tracer-based fuel CO

In order to better study the biospheric carbon fluxes on all relevant
scales, it is important to improve fuel CO

We formally introduce six different tracers or tracer combinations, which we
use to estimate fuel CO

Annual or half-yearly (summer: S; winter: W) averaged

When using CO

This simple approach is valid if (nearly) all CO

The CO offset (

We now include

Total fuel CO

This method of fuel CO

When using

Following Levin et al. (2008), we can derive fossil fuel CO

The background values

Further, in order to solve Eqs. (A2)–(A11), we need the input parameters

Solving Eqs. (A3), (A8), (A9) and (A11) for fuel CO

Re-arranging Eqs. (1) and (2) for

We have argued that we only require a realistic set of input parameters,
rather than an absolutely correct set of parameters to estimate
uncertainties of the different tracer methods. However, the results
presented so far are to some degree dependent on the emission
characteristics used in our model (see Table A1). When using CO as a tracer
for fuel CO

Figure B1 shows that fuel CO

We thank Ute Karstens and Thomas Koch for valuable modeling
lessons and help with setting up the model. We are also grateful for
valuable discussions on fossil fuel CO