The simulations were undertaken with the limited-area atmospheric prediction model COSMO (Consortium for Small-scale Modeling) version 4.23. We employed the COSMO-7 setup developed by the Swiss Federal Office for Meteorology and Climatology (MeteoSwiss) for the purpose of providing boundary conditions for the inner COSMO-2 grid used for forecasting the weather in Switzerland. The COSMO-7 setup has a grid spacing of 6.6 km and its domain covers central and southern Europe (35.16∘ N, 9.80∘ E (lower left) to 56.84∘ N, 23.02∘ E (upper right); see Fig. ).

The COSMO model is based on the primitive hydro-thermodynamical equations describing compressible nonhydrostatic flow in a moist atmosphere without any scale approximations. The model equations are solved numerically on a rotated latitude–longitude grid, with terrain-following coordinates in the vertical (60 vertical levels, and lowest level at 10 m), using an Eulerian finite difference method. Parameterization schemes are used to resolve the sub-grid-scale physical processes such as vertical diffusion (turbulence), convection, radiation and soil processes. A tracer transport module was recently added to the COSMO model, permitting the online transport of passive tracers in a manner that is fully consistent with the physics of the model . In our setup, advective transport was accomplished with a three-dimensional semi-Lagrangian scheme. The tracers are transported in the model as moist air mass mixing ratios qCO2. Values reported here are provided as dry air mole fractions χCO2, calculated as χCO2 = qCO2/(1 - qH2O) Mdry/MCO2, where qH2O is the specific humidity and Mdry and MCO2 are the molar masses of dry air and CO2, respectively. The column-averaged dry air mixing ratio is calculated as follows: XCO2=∑k=1K(p(k+1/2)-p(k-1/2))qCO2(k)/∑k=1K(p(k+1/2)-p(k-1/2))1-qH2O(k)⋅Mdry/MCO2, where k is the total number of vertical model levels (K = 60) and p is pressure. We refer to for more details.

The fossil-fuel emissions for CO2 were generated by merging a relatively coarse emission inventory for the regions outside Switzerland (EDGAR v4.2_FT2010, approx. 10 km; ) with a high-resolution (0.5 km) emission inventory for Switzerland. The latter was produced by the company MeteoTest specifically for the CarboCount CH project. The annual emissions from this merged product for the year 2008 amount to 2.54 Pg CO2 over the domain, representing about 10 % of the global emissions of that year . We merged the emission categories from the two inventories to five large emission categories: power generation, residential heating, road transportation, industrial processes, and others. Even though each of these different categories have a distinct emission pattern, many of them co-occur in the large metropolitan areas, leading to a very patchy emission pattern with strong emission hotspots and extensive regions with relatively low emission densities (Fig. ).

These emission inventories are given for each emission category as annual totals for each grid cell, i.e., Eann, requiring us to multiply them with time functions to generate hourly time series of the fossil-fuel emissions at each location . The time functions we employed were originally generated by the University of Stuttgart (Institute für Energiewirtschaft und Rationelle Energieanwendung, IER) for the GENEMIS project and have been used since in several air quality modeling studies. The time functions are comprised of diurnal, weekly and seasonal components and are specific to each of the main economic sectors (activities collected in the Selected Nomenclature for Air Pollution (SNAP) codes) . When constructing these time functions, it is ensured that their annual mean is equal to unity so that the annual totals remain unchanged. The scaled emission flux, E(t), is then computed by modifying the annual total fossil-fuel emission, i.e., Eann: E(t)=Eann⋅fdiurnal(t)⋅fweek(t)⋅fseason(t), where t is time (hour of the year) and fdiurnal, fweek and fseason are the diurnal, weekly and seasonal scaling factors, respectively. The time function factor fdiurnal depends on the hour of the day (local time (LT), thour = t modulo 24 h) and is different for weekdays and weekends to reflect the different level of activities on weekdays and weekends. The factor fweek depends on the day of the week, with one value for weekdays (Monday–Friday) and a lower one for Saturdays and Sundays. The factor fseason depends on the month, but in order to avoid discontinuities between subsequent months it is linearly interpolated to a given day between the centers (day 15) of 2 adjacent months. The time functions (except for the daily one) vary also by country and are locally adjusted to reflect local time. Some reassignments were necessary to align the categories used in EDGAR v4.2 and the CarboCount CH inventory (both following IPCC guidelines) with the SNAP categories as described in the Supplement.

The time functions differ greatly between the various categories, reflecting their very different time course of activities over the average day, week or year (see Fig. a and b). Among all diurnal time functions, road transportation has the largest diurnal variability and is characterized by two peaks during the day that reflect the rush hour periods (08:00–09:00 and 17:00–18:00 LT). Also residential and commercial combustion have a distinct diurnal cycle with two peaks. In contrast, the emissions from industrial processes and fossil-fuel-fired power plants vary less over the course of the day and also have only one peak. The time functions for the day-of-week reflect primarily the lower industrial activities and traffic during the weekend, while most other sectors continue to emit at only slightly smaller rates (see Fig. a). Combining all the sectors together, emissions during the weekend are 15–20 % lower than during the week. The seasonal time functions depend primarily on the local climatic conditions (see Fig. b and d), with northern, eastern and central European countries having a maximum in winter, likely due to their need for residential heating, while there is little seasonality in emissions in the southern European countries. The seasonality of the total emission (Fig. c) follows that of the northern, eastern and central European countries with a wintertime maximum, although somewhat less pronounced due to leveraging effect from the southern European countries.

In order to be able to trace the fossil-fuel signature in atmospheric CO2 back to the emitters, we consider separate fossil-fuel tracers for 10 different countries (or groups of countries) in our atmospheric transport model (see Fig. ). Each of these tracers receives only the emissions from its respective country or group of countries, while elsewhere the emissions are set to zero. Due to the linearity of atmospheric transport and the absence of any transformation of CO2 in the atmosphere, the individual country-based tracers can then be summed to obtain the total fossil-fuel CO2 signal. In addition, in order to determine the contribution of the different CO2 emission categories to the total fossil-fuel CO2, we also included five additional fossil-fuel tracers, one each for the five categories we consider: power generation, residential heating, road transportation, industrial processes, and others. For these five tracers, we used time-invariant emissions, permitting us to assess also the role of the time variations in emissions on the fossil-fuel CO2 signal. In total, we included 17 fossil-fuel tracers (10 countries, 5 sectors, total fossil-fuel CO2 with time-varying emission and total fossil-fuel CO2 with time-constant emission) in our high-resolution simulation study.

At the lateral boundaries, we employ a partial relaxation boundary condition for these 17 tracers. In such a partial relaxation, the tracer is relaxed to the boundary concentration only at the outermost grid cells of the domain and only when the wind is directed toward the inside of the domain (in COSMO, this option is provided by the switch “T_RELAX_INFLOW”). Since we are interested in the fossil-fuel signal emanating from emissions in Europe only, the lateral boundary concentration was set to zero. Through this option, we avoid creating a situation where the zero concentration boundary condition is propagated (erroneously) against the flow back into our domain.

In order to simulate the distribution of total atmospheric CO2, we also include in our model three other CO2 components, namely background CO2, the terrestrial biospheric CO2 and the oceanic CO2 components. The background CO2 represents that part of the atmospheric CO2 that enters the domain through its boundaries. These boundary concentrations are provided by the post-assimilation results of CarbonTracker Europe . For this tracer, we use a “full” relaxation boundary condition. This means that we are restoring the modeled mixing ratio toward the value provided by CarbonTracker across a transition zone consisting of 13 grid cells, with the relaxation increasing in strength from the inner to the outer border of this zone. In COSMO, this option is provided by the “T_RELAX_FULL” switch.

For the terrestrial biospheric CO2 component, we used the hourly terrestrial biospheric fluxes from the Vegetation Photosynthesis and Respiration Model (VPRM) . For the oceanic CO2 component, we combined the monthly air–sea CO2 flux estimates for the Atlantic from with the annual mean flux estimates for the Mediterranean by . As the oceanic flux contribution is small, no attempt was made to add higher-frequency variability. The lateral boundary conditions for these two tracers were handled the same way as those for the fossil-fuel signal, i.e., a partial relaxation toward a zero concentration at the boundary.

The hindcast simulation started on 1 March 2008, with the initial and boundary conditions for meteorology taken from the operational hourly COSMO-7 analyses of MeteoSwiss and the initial and boundary conditions for atmospheric CO2 provided by CarbonTracker Europe . The model was then run for 13 months until 26 April 2009. No assimilation of any meteorological data was performed. The lateral and surface boundary conditions for the total of 21 CO2 tracers considered (17 fossil fuel, 4 other components) were prescribed as described above. We consider the first 26 days as a spinup and use the subsequent 12 months for our analyses.

We evaluate our COSMO-based results for the total atmospheric CO2 concentration (computed by summing the fossil-fuel component with the three others) by comparing them to the measurements from four sites in central Europe, namely Mace Head (MHD; 3.33∘ N, 9.90∘ W; 5 m above ground, 15 m a.s.l.; coastal site), Cabauw (CBW; 51.97∘ N, 4.92∘ E; 20, 60, 200 m above ground, 0 m a.s.l.; flatland, near urban site), Hegyhatsal (HUN; 6.95∘ N, 16.65∘ E; 10, 48, and 115 m above ground, 248 m a.s.l.; continental site) and Puy de Dôme (PUY; 45.46∘ N, 2.58∘ E, 1480 m a.s.l.; mountain site).

The modeled daily mean atmospheric CO2 at these four sites agrees generally well with the corresponding observations, although the agreement deteriorates with proximity to the ground (see Table ). This deterioration is likely a consequence of the stronger influence of local processes closer to the ground, which are more difficult to capture by the model. At the highest measurement level, the correlation between the modeled and observed values exceed 0.6 at all sites and are statistically significant at the p < 0.05 level. The highest correlation is found at MHD (> 0.80). This is due to the relatively steady conditions that characterize this relatively clean coastal site. Influence from air pollution is only observed during episodes of transport from the UK and continental Europe, which are very well captured by the model. The correlations are somewhat lower at the more polluted or more continental sites, i.e., between 0.57 (lowest level) and 0.63 (highest level) at the coastal tall tower station CBW in the Netherlands and between 0.52 (lowest level) and 0.68 (highest level) at the continental tall tower station HUN in Hungary. The atmospheric CO2 variations at the mountain top site PUY in France are well captured (r = 0.72). COSMO tends to systematically underestimate the observed CO2 concentration at most of the stations and levels, except at the coast of Ireland (MHD), where it is overestimated by 0.3 ppm (Table ). The biases tend to get larger with increasing continentality of the sites and the associated higher complexity of the surrounding terrain and other influencing factors. At CBW, the biases amount to between -1.4 and -5.7 ppm, while in central Hungary (HUN) the biases exceed -4 ppm at even the highest vertical level.

The general underestimation of the total CO2 can stem from biases in any of the components that make up the total CO2 plus biases in atmospheric transport and mixing. The low and positive bias at MHD, where the contribution of the background CO2 component dominates, suggests that this component is overall well modeled and likely not responsible for the bias at the other sites. Since the contribution of the oceanic fluxes is very small, this component can be excluded as an explanation as well. Thus, the general underestimation is thus likely due to the superposition of biases in atmospheric transport and biases in the underlying boundary conditions for the fossil-fuel emissions and/or terrestrial fluxes. COSMO is known for ventilating the planetary boundary layer (PBL) too strongly, particularly in wintertime under weakly stratified conditions. This may be especially acute for the HUN site, because the air in the lowest atmospheric levels tends to get trapped at this site owing to the wintertime prevalence of anticyclonic conditions in the Carpathian Basin . An alternative explanation is that the biospheric sink simulated by VPRM is too strong, as discussed later. Unfortunately, we do not have observationally based estimates of the fossil-fuel or terrestrial biosphere components at the four sites discussed so far, requiring us to use data from other sites for further evaluation.

Even though COSMO exhibits some biases in the mean, it captures the observed variability generally well (Table ). In particular, COSMO reproduces the strong gradient in variability between the coastal site MHD (obs: ∼ 7 ppm; mod: ∼ 4 ppm) and the continental site in central Hungary (obs: ∼ 11 ppm; mod: ∼ 8 ppm), reflecting primarily differing contributions of synoptic variations on atmospheric CO2. However, the absolute magnitude of the variability is not well captured by our simulations, with COSMO consistently underestimating the observed variability. Overall, the evaluation of the total atmospheric CO2 concentration reveals an agreement with the observations at the four sites in terms of both mean and variability. The agreement is clearly better further away from the ground, i.e., at heights of at least 50 m above the ground.

Estimates of the fossil-fuel component in atmospheric CO2 are available for our model simulation period from Lutjewad in the Netherlands (LUT; 6.35∘ E, 53.4∘ N; 1 m a.s.l.) and from Heidelberg in Germany (HEI; 49.417∘ N, 8.675∘ E; 116 m a.s.l.) . Both estimates are based on a combination of concurrent CO and 14CO2 measurements and represent the fossil-fuel-induced offset relative to a regional background. They are thus comparable to our modeled fossil-fuel component, as this reflects the offset relative to the domain-wide background induced by the lateral boundary conditions. Lutjewad is located on the Wadden Sea dike in the north of the Netherlands, influenced by the highly populated and industrialized areas in the Netherlands and in northwestern Germany (Ruhr area). The Heidelberg station is located near an urban center with considerable fossil-fuel emissions.

At the Dutch site LUT, the daily-averaged fossil-fuel CO2 component simulated by our model compares well with the observations (r = 0.73, mean bias -4 ppm) (see Fig. a). Generally, the model reproduces the observed variability, especially in summer, when the fossil-fuel CO2 component is low due to the deep mixing in the atmosphere. But the model underestimates the estimated fossil-fuel CO2 component substantially in winter. This may be due to several reasons. First, the model may transport signals too quickly out of the PBL, which is a known problem of many atmospheric transport models under stratified conditions typical of wintertime (see also above) . Second, our wintertime emission inventory in the region might be too small due to, for example, our underestimating the strength of the seasonal signal in the time functions. Third, the observations might be biased high. One reason is that these reconstruction rely on a constant ratio between CO and 14CO2, which may lead to an underestimation of the 14C–CO ratio compared to real values at some time of the year and subsequent overestimation of the inferred fossil-fuel CO2 .

At Heidelberg, our model captures the fossil-fuel CO2 component even better, particularly since the model has a very small mean bias of 0.75 ppm. Also the day-to-day and the seasonal variations are well represented with a correlation coefficient of 0.72. The model's (small) overestimation of the fossil-fuel component may be due to our prescribing all emissions at the surface, while the fossil-fuel-fired power plants that contribute substantially to the fossil-fuel CO2 at this site tend to have an effective emission height quite some distance above the ground due to the height of the stacks and the additional rise of the buoyant plumes . Another reason might be an overestimation of the emissions in our emission inventory EDGAR – an explanation furthered by EDGAR's emission being higher than those of IER . Especially assuring, and particularly so in comparison to the situation at LUT, is the COSMO model's ability at HEI to capture most of the variability and amplitude of the fossil-fuel component in winter. An exception are the observations from late December and early January, where the data include a number of exceptionally high peaks. These peaks may be the result of very strong local trapping of the emitted fossil-fuel CO2 by, for example, a local inversion situation, i.e., a process that our model cannot properly resolve.

Despite these discrepancies, the evaluation results provide us with good confidence to use our COSMO-7-based system to investigate the spatiotemporal variability of the fossil-fuel CO2 in central and southern Europe. The presence of an overall negative bias in the total atmospheric CO2 in the absence of such a bias in the fossil-fuel component suggests that the bias comes from the terrestrial biospheric component. This could be due to our VPRM-based estimates of the net fluxes being too negative, as suggested by , i.e., suggesting a too strong sink for central and southern Europe, or for our model simulating a too small diurnal and/or seasonal rectification effect , i.e., a too small correlation between the time variations in the terrestrial exchange fluxes and atmospheric transport and mixing. This deficiency does not impact our results much, since our focus will be on the spatiotemporal variability of the fossil-fuel CO2 signal.

In the annual mean, the fossil-fuel component of atmospheric CO2 in the surface layer (∼ 10 m above ground) amounts to more than 10 ppm across wide swaths of central Europe (Fig. a). We computed this mean using data from all times of the day in order to fully reflect the annual mean. In large metropolitan areas, such as in western Germany (Ruhr region), Berlin, London, Paris and Milan, the annual mean fossil-fuel component exceeds even 30 ppm. To first order, the distribution of the surface fossil-fuel CO2 reflects the distribution of the emissions (see Fig. ), suggesting a somewhat limited effectiveness of atmospheric transport and mixing to disperse the signal aloft and in lateral directions. In mountainous regions this is clearly a consequence of topographic constraints; elsewhere this is largely a result of the strong spatial gradients in emissions, which remain conserved in the annual mean due to the overall diffusive nature of the dispersion. Nevertheless, a substantial amount of the emitted CO2 is being transported away, leading to a sizeable fossil-fuel CO2 signal extending far into the oceans surrounding Europe, especially the North Sea.

Despite this lateral transport, the relatively good conservation of the spatial gradients in emissions sets our results distinctly apart from previous studies, where the fossil-fuel CO2 signal was modeled to be very smooth in space and on average also substantially smaller. For example, compared to the results obtained with the medium-resolution (0.5∘) Regional Model (REMO) , one can detect in our simulations nearly all major metropolitan regions and other fine-scale features, such as individual fossil-fuel-fired power plants (e.g., in eastern Germany). This is primarily the result of the high horizontal and vertical resolution of COSMO permitting this model to conserve the spatial gradients well. This good conservation is particularly well illustrated when considering snapshot distributions of the fossil-fuel CO2 for individual seasons (Fig. ). This figure also shows the strong impact of the transport and dilution by the diurnal variations of the PBL, whose impact is particularly strong in summer.

For much of Europe, the fossil-fuel component is the dominant contributor to the spatial gradients in annual mean atmospheric CO2 (Fig. b–d). In many places it accounts for nearly all of the spatial gradients, with the contribution of the background and the terrestrial biospheric component being substantially smaller. The latter shows gradients up to 10 ppm (Fig. c), while the background signal does not exceed a few ppm (Fig. d). In the big cities, the fossil-fuel CO2 component represents even a sizeable fraction (10 %) of the total CO2 concentration. This dominance of the fossil-fuel component together with its highly patterned nature owing to the many point sources leads to a hotspot pattern in the near-surface map of total atmospheric CO2 over much of Europe (Fig. b). However, due to lower emissions in southwestern Europe, the fossil-fuel CO2 signal is less strikingly visible there compared to central Europe. At the same time, the sign of the biospheric signal changes in the south and becomes positive. This compensates for the smaller fossil-fuel signal there and results in a relatively uniform spatial pattern of atmospheric CO2 across Europe (Fig. b). Also the relatively low CO2 concentrations in the mountain regions, such as the Alps, Apennines, Pyrenees and central France, reflect the much lower contribution from the fossil-fuel component.

Naturally, when investigating the column-averaged dry air mole fractions (XCO2), i.e., the property typically measured by remote sensing from a satellite, the annual mean gradients of the fossil-fuel component are much smaller than those seen at the surface (see Fig. a). This is a consequence of the lateral gradients being much weaker aloft due to a more effective horizontal transport and mixing. An additional reason is a much stronger influence of the lateral boundary conditions, which results in a dilution of the fossil-fuel components. As a result, most of the hotspot nature seen in the surface concentration pattern is blurred in XCO2. Also the magnitude of the signal is much weaker. While the surface signal of the fossil-fuel CO2 signal amounted to more than 30 ppm in strong emissions regions, the signal in the column-averaged annual mean XCO2 hardly exceeds 2 ppm. The impact of the predominant westerly air flow becomes much more obvious in the column-averaged dry air mole fraction XCO2, with the fossil-fuel component revealing a clear eastward increase that is substantially stronger than the gradient in the underlying emissions.

The relative dominance of the fossil-fuel component over the other components of atmospheric CO2 is much weaker when considering the column-averaged dry air mole fraction of CO2 (see Fig. b–d). As a result, the total XCO2 is made up of three relatively equally sized contributions, with the fossil-fuel CO2 signal continuing to dominate the XCO2 variations in the major metropolitan areas. Contrary to the annual surface pattern, where CO2 tends to increase eastward, the highest XCO2 are found in southwestern Europe with a trend toward lower values going eastward. This is partly a consequence of the lateral boundary conditions for atmospheric CO2, which tend to lead to the advection of elevated background CO2 into the domain from the southwest. But the most important reason is the strong negative terrestrial biosphere signal over Europe, reflecting the sizeable carbon sink in European forests in the last decade . Interestingly, the relatively uniform negative distribution for XCO2 in Fig. c contrasts with a more patterned biospheric signal in the lowest layer of the atmosphere (Fig. c). There, the strong negative signal is restricted to central Europe, while much of southern Europe has a positive annual mean biospheric signal. The likely reason for this difference is the biospheric rectification effect , which tends to lead a vertical redistribution of CO2, i.e., positive values in the lower atmosphere and negative ones aloft. In most of Europe, this rectification signal is relatively small in comparison to the annual mean biospheric component, so that the latter determines the overall signal. But in southern Europe, where the biospheric fluxes tend to be smaller in magnitude and in the annual mean to be near zero, the rectifier effect can dominate, explaining the positive signals in the surface layer (Fig. c) and simultaneously the negative signals when the biospheric signal is integrated vertically (Fig. c).

The temporal variability of the fossil-fuel CO2 signal at the surface is very large, leading to a standard deviation around the annual mean of 30 ppm or more in the hotspot regions (Fig. a). These hotspots correspond largely to the regions of highest emissions (Fig. ). This high variability is a result not only of the temporal variability of the emissions but also of the interaction of variability in atmospheric transport and mixing with the strong lateral gradients seen in the snapshot figures (see Fig. ).

A similar pattern of variability is seen in surface atmospheric CO2 (Fig. b), suggesting that the fossil-fuel CO2 is a major determinant not only of the annual mean spatial distribution of atmospheric CO2 but also of its temporal variability. This is confirmed by Fig. a, which shows the relative contribution of the fossil-fuel CO2 signal to the temporal standard deviations of atmospheric CO2. In many places, particularly in Europe's major metropolitan areas but also in many urban areas across Europe, the fossil-fuel signal dominates the variability in atmospheric CO2. But the high fossil-fuel contribution is not limited to the urban areas. In fact, the region delineated by having a 50 % contribution or more extends over much of northern central Europe, including the North Sea (see Fig. a).

In order to better understand the origin of the strong variability, we decomposed the variability into seasonal, synoptic and diurnal contributions. The seasonal variation component was derived by averaging the data on a monthly basis and by subtracting the annual mean. The synoptic component was then computed by subtracting from the data the time series of the monthly means and then forming daily averages of these deseasonalized data. Finally, the diurnal variability was derived by subtracting the seasonal and synoptic components from the data. To determine the fractional contribution, we then computed the fractional variance of each component relative to the total variance. Since the different temporal components can compensate for each other, the sum of the fractional variance can actually exceed unity.

This decomposition reveals that the contribution of the fossil-fuel CO2 to the total variability of atmospheric CO2 varies greatly depending on the temporal scale considered (Fig. ). While the fossil-fuel contribution is comparably small on seasonal timescales (Fig. b), the contribution on synoptic and particularly on diurnal timescales is actually very large, exceeding 60 % across nearly the entire northern part of central Europe (Fig. c and d). The small contribution on the seasonal timescales is the result of the dominance of the seasonal cycle of the biospheric fluxes in most of Europe. An exception are a few places in northern Europe and in the very south of our European domain. We interpret this to be caused primarily by the relatively strong seasonality of the fossil-fuel emissions in these regions due to the strong summertime requirement for cooling in the south and the strong wintertime demand for heating in the north.

The pattern of the fossil-fuel contribution on synoptic timescales is very similar to that of the total contribution, meaning its contribution dominates the total temporal variability. This is consistent with synoptic variations also being among the strongest contributors to atmospheric variability due to baroclinic waves and frontal systems being formed out of the strong baroclinicity that characterize the mid-latitudes. These synoptic weather events transport the emitted CO2 also quite efficiently outside the main metropolitan areas, explaining the widespread signal of the fossil-fuel contribution to the total variance of atmospheric CO2. Even larger than the fossil contribution to synoptic variability is the contribution on the diurnal timescale, with the fossil-fuel CO2 contributing more than half of the variability over most of Europe. This high variability comes from the interaction of the diurnal variability of the fossil-fuel emissions, with the strong diurnal variability of atmospheric transport, particularly the diurnal mixing of the PBL. This covariability between fossil-fuel emissions and atmospheric transport exceeds that between the biospheric fluxes and atmospheric transport over the entire year due to the latter fluxes being large and relevant only during the spring–summer period, while the fossil-fuel emissions are relatively high during most of the months of the year, particularly close to the sources.

In order to elucidate the role of the temporal variations in fossil-fuel emissions on the fossil-fuel CO2, we contrast the results of our standard simulation with time-varying emissions with those where the fossil-fuel emissions were kept constant over time. The annual emissions are identical for the two cases, but the time-constant case has, on average, considerably higher emissions in summer and at night.

The contrast between these two cases shows only a small change in the high diurnal variability of atmospheric CO2 seen in Fig. 8d (results not shown). The largest changes are found around some of the large metropolitan areas (e.g., London, Paris, Milan), but they do not exceed 10%. Thus the majority of the diurnal variability in the fossil-fuel CO2 stems from the diurnal variations in atmospheric transport and mixing acting on the strong horizontal gradients in emissions.

While not contributing much to the diurnal variability in the fossil-fuel CO2, the consideration of the time-varying emission matters quite substantially for the annual mean distribution of the fossil CO2 signal. Figure a reveals that the annual mean fossil CO2 signal in the simulation with time-varying emissions is substantially lower over wide swaths of Spain, Italy, Benelux, (western) Germany and the UK compared to the simulation where fossil-fuel emissions were kept constant. The strongest negative signals are found close to the strongest emitters in these countries, with magnitudes exceeding several ppm. But the magnitude of the signal does not correspond to the magnitude of emissions, since regions with comparably low emissions such as Spain have signals that are as large as those in high emission regions of the Netherlands. The relatively large signals in southern Europe are likely due to the stronger PBL dynamics in these regions throughout the year in comparison to central and northern Europe. Some regions also have a positive signal from the time-varying emissions, such as parts of France and northeastern Germany. Thus the interaction between the variations in fossil-fuel emissions and the variations in atmospheric transport and mixing leads to a substantial net signal in atmospheric CO2, even though the total emissions in both cases are identical.

This net signal represents a fossil-fuel-driven rectification effect in analogy to the rectification effect associated with the terrestrial biosphere , i.e., a signal that is due to the covariance of emissions and atmospheric transport and mixing. Its (mostly) negative sign emerges from the fact that when the emissions are large, e.g., during the day, the transport and mixing away from the surface is strong, diluting the fossil-fuel signal in atmospheric CO2. In contrast, when the emissions are small, e.g., during the night, the transport and mixing tends to be weak. Taken together, this results in a more efficient dilution of the emissions in the time-varying emission case compared to the time-invariant case, thus explaining the mostly negative sign of the fossil-fuel rectification effect.

This explanation is supported by the mostly positive correlation between the height of the PBL and the fossil-fuel emissions, since the height of the PBL is a good proxy for the magnitude of the mixing and transport in the lowest levels of the atmosphere (Fig. b).

But there are a number of notable exceptions. For example, wide swaths of northeastern Germany and Poland and some places in central France have a positive rectification signal. Further, there are places where the covariation of fossil-fuel emission and the PBL is negative, yet the fossil-fuel rectification effect is still negative (e.g., the Ruhr valley region in western Germany), suggesting that our explanation does not cover all aspects. In response, one first needs to recognize that not only PBL but also other temporally varying phenomena, such as local atmospheric circulation patterns (e.g., mountain winds, sea breezes), can lead to covariability between emissions and transport/mixing, creating a rectification signal that can differ in sign. The contribution of the sea breeze can be identified quite clearly by the strong negative sign along most of the coastline between southern Europe and the Mediterranean. Second, the local timing between the growth and decay of the PBL and the emissions can be quite different due, in part, to the substantially different time functions for the different emission categories and their different local contributions (Fig. ). For example, in regions with a large contribution from road transportation, the local emissions have a strong peak in the early morning hours, when the PBL is still shallow, leading to a high signal there, while emissions are lower when the PBL is at its maximum in the early afternoon. This would create a positive rectification signal. Finally, in certain places, also the seasonal rectification appears to play a role, i.e., the seasonal covariations of the emissions with the PBL height. In fact, in many places the magnitude of the correlation between emission and PBL height on seasonal timescales exceeds that on diurnal timescales. This seasonal variation is particularly large for residential heating, which is maximum in winter when the PBL is low, leading to a positive seasonal rectification. This effect likely contributes to the negative correlations between emissions and PBL height in large urban centers such as Paris (Fig. b). We suspect that such seasonal effects are also the primary reason for the positive rectification signal in northeastern Germany and northern Poland. In southern Europe, these seasonal covariations tend to lead to a negative fossil-fuel rectification effect because the emissions peak in summer (Fig. b), when the PBL height is at its seasonal maximum.

The magnitude of the fossil-fuel rectification effect is smaller than the rectifier effect induced by the exchange fluxes with the terrestrial biosphere but still quite substantial. Thus, the fossil-fuel rectification effect clearly needs to be taken into consideration when modeling the atmospheric fossil-fuel CO2 signal, highlighting the need to use and apply accurate time functions. Our results thus clearly support the results of , who demonstrated the substantial impact of the consideration of time-varying emissions on atmospheric CO2. We extend their result by demonstrating an effect on the annual mean fossil-fuel CO2, suggesting that special attention needs to be given to the relative timing of variations in atmospheric transport and mixing and fossil-fuel emissions. Our results confirm the recent findings by , who demonstrated the fossil-fuel rectification effect for the first time in a global model. Their signal is locally smaller than ours due to their use of a much coarser-resolution model, but they also show that the sign of the fossil-fuel rectification effect tends to vary between timescales, with the diurnal being primarily negative, while the seasonal rectification effect being positive. This supports our explanation for the positive signals in northeastern Germany and northern Poland.

Near the surface, the fossil-fuel emissions from a particular region create a distribution that stays mostly within the region of origin (see Fig. a and b). The fossil-fuel CO2 is highly concentrated near the localized areas of high emissions and then drops off quickly by distance with an e-folding spatial scale of a few hundred kilometers. As a result, the fossil-fuel signal tends to be relatively small outside the region of origin, rarely exceeding 1 ppm in contrast to the > 20 ppm signal close to the sources. The different magnitudes of the fossil-fuel CO2 signals from different regions largely reflects the total emissions, but also the emission intensity, i.e., the emission per unit area. For example, with a total emission of 0.59 Pg CO2 yr-1, Germany is the biggest source of fossil-fuel CO2 within Europe, nearly double that of the second-biggest emitter (i.e., France), yet Germany is almost half the size of France, resulting in a considerably higher emission intensity over Germany.

A different picture emerges when considering XCO2, i.e., the column-averaged dry air mole fraction CO2. After having been transported aloft, where the fossil-fuel signal can be much more readily dispersed, the imprint of the emissions of any particular region to the fossil-fuel CO2 within another region is actually quite large (Fig. c and d). In a small country, such as Switzerland, only 20% of the fossil-fuel signature in XCO2 above its territory stems from emissions within, while the contribution of Germany alone is 21 % and that of France 18 % (Fig. ). A similar distribution of sources is found for other small countries, such as Austria. In contrast, the fraction of the territorial emissions to the total fossil-fuel signal is quite a bit larger for large countries and regions, such as France or Germany. In the latter case, more than 50 % of its total fossil-fuel CO2 signal stems from emissions within, with four countries contributing most of the remainder. The countries and regions with high overall emissions also contribute, of course, most strongly to the fossil-fuel CO2 signal in other countries, with Germany contributing 17 % to the signal in France, 11 % to that in Italy and 28% to that in the Netherlands. Owing to its lower total emissions, France just contributes 10 % to the signal in Germany and 9 % to that in Italy. Thus, as is the case with classical air pollution, the fossil-fuel CO2 does not stop at the national borders but extends to continental scales (see Fig. ).

Among all the processes, the CO2 emissions from power plants dominate the fossil-fuel distribution, with concentrations reaching up to 16 ppm in the northern part of the domain (see Fig. ). The point-source nature of this emission sector is clearly visible in the surface distribution, as is the spatially distinct distribution owing to the large differences in power production in the different countries of central Europe. While France has very few fossil-fuel-fired power plants as a result of its high reliance on nuclear and hydroelectric power plants, Germany, Italy, the Netherlands and Poland rely strongly on coal- and gas-fired power plants for their electricity production. This leads to a highly heterogeneous fossil-fuel CO2 signals of the power plant sector. In total, this sector contributes 32 % to the total fossil-fuel CO2 signal in central Europe, which is slightly smaller than its contribution to emissions (33 %). This small difference emerges from the somewhat stronger loss of the signal across the lateral boundaries from this sector relative to the signal from the other sectors.

The second-largest fossil-fuel CO2 signal is generated by the emissions from the road transportation sector (22 %) (Fig. d), with this share actually being somewhat larger than its share in total emissions (21 %). The transportation sector signal is very smooth due to the distributed nature of the emissions from this sector (see also Fig. ).

The CO2 signal from the industrial and residential sectors are more granular than that from the transportation sector but still not as distinct as the power plant sector, as there are less country-specific policies impacting the CO2 emissions from these sectors. The emissions and consequently the CO2 signal largely follow population density. The residential sector (mostly heating) contributes 18 % to the total fossil-fuel signal in atmospheric CO2, slightly larger than the emissions from the industrial sector (17 %). These two shares in the signal very nearly reflect their shares in total emissions. The emissions from the “other” sectors (e.g., shipping, waste incineration) is smaller, in comparison (11 %), but not negligible.

The relative contribution of the emissions from the different sectors to the fossil-fuel CO2 vary strongly by region (Fig. ). Clearly, close to major fossil-fuel-fired power plants, this sector dominates. Owing to the dominance of this mode of electricity production in northern Europe, this signal is particularly strong there. This is most evident over the North Sea, where the advection of the emitted CO2 from the power plants in the UK and the Netherlands creates a particularly visible plume over the ocean. But elsewhere, any of the four major sources can take the leading role. For example, in Switzerland, Paris, and London, the emissions from the residential sector dominate the signal, while over much of southern and western Europe, the transportation sector dominates. The industrial sector dominates the signal in a few hotspot areas, where its emissions are high but no major fossil-fuel-fired power plants are nearby.

These high spatial variations in the relative contribution puts the findings of into a spatial context, as they reported for the Heidelberg site a dominance for emissions from power plants (28 %), while the transportation sector contributed only 15%. This is a typical value for much of western Germany, reflecting the relative contribution of the different emission sectors (see also Fig. ). But the contributions are very different, for example, for the CarboCount CH sites in Switzerland . At Beromünster, the transportation sector dominates over the other sectors, with nearly 70 % stemming from this sector alone, while the contribution from power plant emissions is very low at this site, since Switzerland does not operate any fossil-fuel power plants.

These large differences in the relative contribution from the different emission sectors have major implications for the analysis of the fossil-fuel CO2 and how it may change in response to mitigation measures. For example, these large differences will lead to substantial spatial gradients in the CO to CO2 ratio in the fossil-fuel signal, as the different emission sectors have very different CO to CO2 emission ratios. Since CO is often used to identify the fossil-fuel component from atmospheric CO2 observations, these variations need to be carefully disentangled in order to properly diagnose the fossil-fuel component. The strong variations in the contributions from the different sectors thus add a substantial amount of uncertainty to the CO method . A second consequence concerns the detection of changes in emissions from the different sectors. Thus, with the transportation sector contributing little to the very large fossil-fuel signal in much of the northeastern part of our domain, reductions in this sector will be difficult to discern in that region. In contrast, the high relative contribution of the transportation sector to the total signal in southwestern Europe makes it actually quite feasible to detect mitigation measures in this sector in that part of Europe, even though the overall signal might not be that high.

An important caveat of our simulations is the fact that the effective height of the emissions above surface was not considered, but rather all CO2 was released into the lowest model level. As a consequence, the surface CO2 signals from elevated stack emissions from power plants and residential heating are likely biased high relative to those from the transportation sector. Given the large contribution from power plant emissions, it will be important to accurately consider the effective emission height (including plume rise) in future simulations, a point that was also raised by .

According to their intended nationally determined contributions filed with the United Nations Framework Convention on Climate Change (UNFCCC) in late 2015, the European Union and its member states have agreed to a binding target of a domestic reduction in greenhouse gas emissions of at least 40 % by 2030 compared to 1990 (http://www4.unfccc.int/Submissions/INDC/Published Documents/Latvia/1/LV-03-06-EU INDC.pdf). A major question driving international policy making is to what degree such a reduction can be verified through independent means, such as through the monitoring of atmospheric CO2 . To address this question, we conducted several sensitivity experiments to investigate how various reductions in the magnitude and types of emissions affect not only the annual mean fossil-fuel CO2 signal but also its variability. The goal is to determine whether reduced fossil-fuel emissions might be detectable by current and future observing systems, especially satellites. As the satellites have a typical overpass time of 13:00 UTC, we conducted all subsequent analyses using the model data only from this time slot.

Since CO2 is a conservative tracer in the atmosphere on the timescales considered here, a uniform reduction in the emissions leads to a uniform and directly proportional reduction of its current distribution; i.e., a 30 % reduction of total fossil-fuel emission would simply lead to a 30 % reduction of the fossil-fuel CO2 signal at the surface (Fig. a) and throughout the atmospheric column (Fig. a). Concretely, the fossil-fuel CO2 would be reduced by more than 4 ppm near the surface for vast stretches of central and northern Europe, with maximum reductions of 10 ppm or more in the emission hotspots (Fig. a). This contrasts with the reduction in the column-averaged annual mean XCO2, amounting to just over 0.2 ppm in the regions where the surface decreases by 4 ppm or more (Fig. b). A reduction of 0.5 ppm is reached in just a few isolated locations, generally characterized by a high density of point sources, primarily fossil-fuel-fired power plants. Thus, given current measurement accuracies of better than 0.1 ppm for a ground-based observing network , a 30 % reduction in the fossil-fuel emissions is fundamentally easily detectable for such a system, although one needs to bear in mind the nontrivial task of separating the signal from the background variability. In contrast, such a reduction in the fossil-fuel emissions is not trivial to detect by satellite observations for most regions (except around the big power plants) as it is very challenging to obtain and maintain accuracies better than 0.5 ppm by current space-based observing systems . Furthermore, such high accuracies are only achieved when the data are averaged over large scales, i.e., on the order of 1000 km or more. Nevertheless, taking 0.5 ppm as the threshold for detection within a single pixel, a 30 % reduction in fossil-fuel emissions thus appears to be beyond the detectability except for a few hotspot regions (Fig. b). Even a 50 % reduction would not be trivial to detect for a satellite-based system on the basis of changes in the column-averaged dry air mole fraction.

Given these challenges, a potentially attractive second avenue for determining changes in fossil-fuel emissions is the reduction in temporal variability of atmospheric CO2 that goes alongside the reduction in the mean signal. This is particularly promising given the very high contribution of the fossil-fuel CO2 signal to the variability in atmospheric CO2 (see Fig. ). As is the case for the mean, the conservative nature of atmospheric CO2 implies that a uniform reduction of the emissions will lead to a uniform and proportional reduction of the variability of the fossil-fuel signal as well. However, this is not the case for the variability in total atmospheric CO2, since covariations between the fossil-fuel signal and the signal from, for example, the terrestrial biosphere can lead to nonlinear effects. For example, a negative correlation between the two components would lead to a situation where the variability of atmospheric CO2 was smaller than that of the individual components. In such a case, a reduction of the fossil-fuel emission would lead to a smaller decrease in variability than expected. If the two components were positively correlated, the opposite would occur, i.e., the variability in atmospheric CO2 would decrease more than expected.

Near the surface, the reduction in the temporal standard deviation and in the mean have nearly the same amplitude for most places (Fig. c). This makes the analysis of changes in the temporal variability indeed an attractive option to enhance the detectability of changes in fossil-fuel emissions. This is much less the case for the annual mean XCO2, where the standard deviation changes are in general much smaller than the changes in the mean, with just a few isolated places revealing changes in the standard deviation of 0.5 ppm or more that might be discerned by the current generation of satellites.

But in these isolated places, the analysis of the temporal variability might be an interesting option even for satellite-based measurement systems (Fig. ). In those places, indicated by the green circles in (Fig. c), the changes in the temporal standard deviation are very large. Even for changes in emissions of around only 30 %, the changes would be detectable for current satellites (Fig. ). But the number of such sites is very low across Europe, making this a specialized, rather than general, option.

The detection challenge is not simpler for other potential emission reduction scenarios, as outlined, for example, in the EU road map (http://ec.europa.eu/clima/policies/strategies/2050/index_en.htm). A 50 % reduction in the emissions from power plants alone (representing a reduction of the overall emissions by 16 %) results in the mean surface concentration of atmospheric CO2 going down by more than 2 ppm over large parts of northwestern Europe, following the pattern of the surface signal of this sector (see Fig. a). In addition, we find a substantial reduction of the standard deviation of surface atmospheric CO2 by more than 2 ppm in these regions, with the hotspots of power plant emissions showing a reduction in the standard deviation of atmospheric CO2 of 5 ppm or more. The reduction of the average annual mean column XCO2 is much smaller than that of atmospheric CO2 at the surface, amounting to little more than 0.2 ppm over wide swaths of northern Europe. The maximum reductions are of the order of 0.5 ppm in the proximity of large clusters of fossil-fuel-fired power plants, i.e., generally too small to detect. But, in these regions, the changes in the variability in XCO2 is quite high, making this method again potentially attractive for detecting changes. In fact, in several regions, including some major cities, a 19 % reduction of the fossil-fuel emissions would result in a change of more than 0.5 ppm in the standard deviation, i.e., above detection level. This thus supports the findings of that changes in fossil-fuel emissions are fundamentally detectable over major cities or major point sources, but it also shows that this detection is very challenging.

The signals get even more difficult to discern if the emission reductions occur in individual sectors other than the power plants. For example, detectable signals by current generation satellites occur only if industrial emissions are cut by more than 80 % or if residential emissions are cut by more than 90 %. Also country-level emissions are not trivial to be clearly detected. A reduction in Germany by 50 % is potentially detectable by current satellites, with a maximum reduction of XCO2 by 0.95 ppm. For most other countries, however, a 50 % reduction in emissions is difficult to detect.

All the analyses here relied on using the model output on all available days; i.e., we assumed perfect temporal coverage. This is overly optimistic, since cloud cover and other complicating factors (e.g., aerosol layers) will cause the coverage to decrease considerably, complicating the detection. We assumed here also “perfect transport”, i.e., no errors in how the emission reductions manifest themselves in a change in the concentration field. In fact, errors in this transport are perhaps, besides the lack of observations, the largest impediment to detect changes in fossil-fuel emissions.

But regardless of this additional challenge, there is much additional information contained in high-frequency observations of atmospheric CO2. As we demonstrated above, the temporal variations are potentially highly useful for detecting fossil-fuel emissions changes from various sources, especially those with a strong spatial granularity such as power plants or individual cities. For a routine monitoring of strong point sources, therefore proposed a constellation of five satellites that combine imaging capability with a relatively wide swath . Such a constellation would offer daily global coverage, though the presence of clouds would reduce the effective coverage considerably. As the precision and accuracy of satellite retrieved XCO2 will improve in the future, that minimum change will go down as well.