The FFCO2 emissions data product, Fossil Fuel Data Assimilation System (FFDAS) version 2.0, is used as the flux boundary condition for the model simulations in this study (Asefi-Najafabady et al., 2014). The FFDAS FFCO2 emissions were estimated using a diagnostic model (the Kaya identity, Kaya and Yokoburi, 1997), constrained by a series of spatially explicit observational data sets, which decompose emissions into population, economics, energy, and carbon intensity terms (Rayner et al., 2010). The observational data sets used in the FFDAS include a remote sensing-based nighttime lights data product, the LandScan gridded population data product, national sector-based fossil fuel CO2 emissions from the International Energy Agency (IEA), and a recently constructed database of global power plant CO2 emissions (Elvidge et al., 2009; Asefi-Najafabady et al., 2014).

The FFDAS emissions are produced at 0.1∘ × 0.1∘ resolution for the years 1997 to 2010. The emissions for year 2002 are used in this study. Sub-annual temporal structure is imposed on these annual emissions based on two additional data sets. Diurnal and weekly cycles are derived from a global data product referred to as Temporal Improvements for Modeling Emissions by Scaling (TIMES hereafter) at 0.25∘ × 0.25∘ resolution (Nassar et al., 2013). The monthly temporal cycle is obtained from the global data product developed by Andres et al. (2011) at a resolution of 0.1∘ × 0.1∘ and similarly imposed on the FFDAS emissions. With these temporal structure data sets, five separate FFCO2 emission fields are created:

A global 0.1∘ × 0.1∘ FFCO2 emission field in which only the diurnal cycle is represented (“diurnal cycle emissions” – DCE). This is accomplished by distributing the annual emission total in each grid cell evenly for every day of the year (divided by 365), and then distributing the daily total to the 3 h model simulation resolution according to the diurnal fractions from TIMES.

The DCE FFCO2 emissions over the three LSRs show a diurnal cycle (Supplement, Fig. S1) that is characterized by smaller emissions at night and in the early morning vs. larger emissions starting at sunrise and remaining elevated until just after sunset. The DCE emissions typically reach a minimum value between midnight and 03:00 local time (LT) and a maximum value at ∼ 15:00 LT. This pattern is expected from the diurnal variations in human activity, such as waking vs. sleeping hours and work-related activity cycles (e.g., on-road vehicle “rush” hours, starting and ending most daily work cycles). We also show the diurnal cycle of PBL height used in this study (Fig. S1), which shows similar diurnal variation to the diurnal DCE FFCO2 emissions.

The WCE FFCO2 emissions reflect diminished economic activity on the weekends vs. the weekdays. For most of the planet, Saturday and Sunday are the designated weekend days, but in some Middle Eastern countries, Thursday and Friday constitute the weekend days (Fig. S2).

The MCE FFCO2 emissions reflect the different energy needs in winter vs. summer: for example, due to space heating of buildings (Fig. S3). However, the space/time patterns reflect different fossil-fuel-based energy use across the planet. For example, the FFCO2 emissions in western Europe are larger in December and January and smaller in July and August. The US also shows peak emissions in December–January, but with a second peak in July–August. The summer peak is due to electricity-driven air-conditioning prevalent in the United States (Gregg et al., 2009). China exhibits an unusual monthly variation, with the largest FFCO2 emissions in December followed by a sudden drop in January and February, and then an increasing trend to December. This has been attributed to uncertainty in the underlying energy consumption data, discussed in detail in Gregg et al. (2008).

To enable atmospheric transport simulation, the five FFDAS emission fields were regridded from their original 0.1∘ × 0.1∘ spatial resolution to the 1.25∘ × 1∘ atmospheric transport model (see Sect. 2.3) resolution (longitude × latitude). When regridding, emissions originally emanating from land are often allocated to water-covered grid cells – an artifact typically encountered along coastlines when regridding from a fine to coarse resolution. Such a mismatch can lead to a dynamical inconsistency between the emissions and atmospheric transport. To avoid this error, we apply the “shuffling” reallocation method described in Zhang et al. (2014) for all five emissions fields. For the purposes of atmospheric transport simulations, the emissions derived from FFDAS for the year 2002 are repeated across all the years in the atmospheric transport model runs.

In order to place the impact of the temporal variation in FFCO2 emissions within a larger context, an additional experiment is conducted driven by terrestrial biospheric carbon fluxes with diurnal and seasonal variations. The biospheric CO2 flux is a recent version of that used in the TransCom experiment: CASA model net ecosystem exchange estimates with “neutral” annual fluxes (e.g., Law, et al., 2008; Peylin et al., 2013; Randerson et al., 1997) at a 1∘ × 1∘ spatial resolution and 3-hourly temporal resolution (referred to as “CASA fluxes” hereafter). The terrestrial biospheric fluxes have a seasonal cycle, characterized by negative values (carbon uptake from the atmosphere to land) during the growing season (late spring and summer) vs. positive fluxes (carbon release from the land to the atmosphere) during the dormant season (winter and early spring) (Fig. S3). The biospheric fluxes also contain diurnal variation with typically negative values during the daytime (dominated by photosynthetic uptake) and positive values during the night (dominated by respiration) (Fig. S1).

The biospheric fluxes are regridded from the original 1∘ × 1∘ to the 1.25∘ × 1∘ transport model resolution with the same shuffling method used for the FFCO2 emission fields.

A global tracer transport model, the Parameterized Chemical Transport Model (PCTM), is used to simulate the FFCO2 concentrations resulting from each of the five FFCO2 emission fields (Kawa et al., 2004, 2010). The meteorological fields from the Goddard Earth Observing System Data Assimilation System Version 5 (GEOS-5) MERRA reanalysis products are used to drive the atmospheric transport (Reineker et al., 2008). The model uses a semi-Lagragian advection scheme (Lin and Rood, 1996); the sub-grid-scale transport includes convection and boundary layer turbulence processes (McGrath-Spangler and Molod, 2014). The model grid is run at 1.25∘ longitude × 1∘ latitude with 72 hybrid vertical levels, and produces CO2 concentration output every hour. The CO2 concentration output from PCTM has been widely used in comparison with in situ and satellite measurements (Parazoo et al., 2012). It has been shown that PCTM simulates the diurnal, synoptic, and seasonal variability in CO2 concentration well (e.g., Kawa et al., 2004, 2010; Law et al., 2008).

A total of six emission cases are run through the PCTM. The GEOS-5 meteorology has a 3 h time resolution and a constant 7.5 min time step is used in the model simulations.

In this study, all five FFCO2 simulations use the same meteorology and the same annual total FFCO2 emissions. The only difference between the FFCO2 simulations is the sub-annual temporal structure as described in Sect. 2.1. Hence, the resulting atmospheric FFCO2 concentration differences are due to the differences in the time structure of the FFCO2 emissions only. The atmospheric FFCO2 concentration is examined in two ways: (a) near the surface (at ∼ 998 hPa; in the bottom layer, which is ∼ 126 m or ∼ 15 hPa thick) and (b) as a pressure-weighted column integral. In order to understand how the different cyclic components of the FFCO2 emissions interact with the simulated atmospheric transport at multiple timescales, we present the simulated FFCO2 concentration results for the annual mean, and individual sub-annual cycles for both near-surface and column-integral (diurnal, weekly, monthly). In addition to global difference maps, concentration differences between the cyclic and flat FFCO2 emissions are examined at selected GLOBALVIEW-CO2 monitoring sites (http://www.esrl.noaa.gov/gmd/ccgg/globalview/co2/co2_intro.html) (Masarie and Tans, 1995).

The impact of the FFCO2 emissions' sub-annual temporal structure is defined as the simulated concentration difference between each sub-annually varying FFCO2 emission field and the FE emission field, when averaged over specific time cycles: ΔCit=1N∑k=1N1M∑j=1MCitj,k-1M∑j=1MCif(j,k), where ΔCit is the mean concentration difference at the ith grid cell for cyclic emissions, N is the total counts of cycles over the investigated period, Citj,k is the jth hourly concentration in the kth cycle at the ith grid cell for cyclic emissions, M is the total counts of hourly periods for each cyclic emissions, and Cif(j,k) is the jth hourly concentration in the kth cycle at the ith grid cell for flat emissions.

By utilizing Eq. (1), the impact on simulated CO2 concentration is examined for each individual sub-annual FFCO2 emissions cycle and their combination. Impacts include

the annual mean full-day concentration difference between each cyclic FFCO2 emission and the flat emission fields, in order to explore FFCO2 emissions rectification;

Camp,it=Cmax⁡,itΔCitj|j=1,M-Cmin⁡,itΔCitj|j=1,M, where Camp,it is the amplitude at the ith grid cell, Cmax⁡,it is the maximum of the concentration differences at the ith grid cell, Cmin⁡,it is the minimum of the concentration differences at the ith grid cell, ΔCitj is the mean concentration difference for the jth point of the sub-annual cycle at the ith grid cell that is defined as Eq. (1), and M is the total points of the sub-annual cycle.

Figure 1a shows the annual mean full-day surface FFCO2 concentration difference between the ACE and FE emission fields (ACE minus FE). Despite the same annually integrated emissions at each grid cell, the annual mean surface concentration difference shows nonzero values, suggesting rectification of the FFCO2 emissions. The largest negative surface FFCO2 concentration differences (up to -1.35 ppm) are found over the LSRs, coincident with the largest fossil-fuel-based industrial activity and energy consumption. Smaller positive surface FFCO2 concentration differences (up to 0.13 ppm) appear over north and northeastern Europe and western Siberia. The annual mean surface FFCO2 concentration differences between the DCE and FE and the MCE and FE are shown in Fig. 1b and c, respectively. The negative surface FFCO2 concentration differences in Fig. 1a are primarily driven by the DCE emissions (Fig. 1b) while the positive differences are primarily driven by the MCE emissions (Fig. 1c). Figure 1a includes the contribution from the WCE emissions, but no rectification results from this emission cycle at annual scales (Fig. S4).

Over the LSRs, the diurnal FFCO2 emissions are temporally correlated with the diurnal variation in the PBL (Fig. S1). The emissions are largest during daytime when the PBL is well mixed, so air with enriched CO2 tends to be transported aloft. By contrast, the smaller nighttime FFCO2 emissions are mixed into a typically shallower and stable PBL, so this lower-CO2 air is confined closer to the surface. This covariation, when compared to the same dynamic coupling in the FE field, leads to greater FFCO2 loss from the surface to the free troposphere in the ACE simulation, resulting in the negative annual mean surface FFCO2 concentration difference values over the LSRs. The negative DCE rectification is up to -1.44 ppm at the grid cell scale over the western US (Fig. 1b). Note that the diurnal FFCO2 rectifier effect shows little variation across the LSRs, due mainly to the similar diurnal amplitude of the diurnal emission fields.

The annual mean surface FFCO2 concentration differences between the MCE and flat FE emissions are largest over the LSRs during the local winter months and smallest during the local summer months (Fig. S3). This variation interacts with simultaneous variations in PBL variation. However, distinct from the diurnal FFCO2 rectification, the seasonal FFCO2 rectification shows positive values (up to 0.23 ppm) for north and northeastern Europe vs. negative values (up to -0.28 ppm) in East Asia, and a near-zero signal (no rectification) in the US (Fig. 1c). The positive rectification obtained in north and northeastern Europe to Siberia is associated with the coincidence of large wintertime FFCO2 emissions and weak wintertime atmospheric mixing, which tends to trap CO2-enriched air near the surface. Additionally, the greater vertical mixing in summertime interacts with the smaller summer FFCO2 emissions, thus distributing more of the CO2-depleted air to the free troposphere. The limited seasonal rectification in North America vs. the other LSRs is mainly due to the more complex FFCO2 emissions seasonality, with peak emissions in both the winter and summer months as shown previously. Finally, the negative rectification in East Asia is mainly ascribed to the previously mentioned anomalous monthly FFCO2 emissions in China (increasing trend from January to December) and their interaction with atmospheric transport. Hence, the CO2-depleted air is confined to the surface in East Asia by the very small FFCO2 emissions combined with the inactive atmospheric transport in January and February.

The rectification of the FFCO2 fluxes can be compared to the well-known biosphere flux rectifier. Surface concentration differences of up to 20.35 ppm at the grid cell scale for the biospheric flux simulation (Fig. S5) are centered over the tropical land and northern mid- to high latitudes with much greater spatial extent than found for either the diurnal or seasonal FFCO2 rectifier. Similar to the FFCO2 rectification, the biospheric rectifier is a combination of diurnal and seasonal rectifications (e.g., Denning et al., 1995, 1996; Yi et al., 2004; Chen and Chen, 2004; Chan et al., 2008; Williams et al., 2011). For the diurnal biospheric rectification, the daytime net negative CASA fluxes typically coincide with a well-mixed PBL and greater interaction with the free troposphere. At night, this flux is typically reversed and mixed into a shallow PBL, resulting in a positive full-day annual mean surface CO2 concentration due to the greater loss of CO2-depleted air during the day. In the case of the seasonal biospheric rectifier, the summer net negative CASA fluxes are mixed into a thicker PBL, resulting in a strong negative surface perturbation, whereas the winter net positive CASA fluxes are mixed into a thinner PBL, resulting in a weaker positive perturbation. The two interactions combine to give a positive annual mean surface CO2 concentration. The above analysis indicates that FFCO2 rectification is mechanistically similar to biospheric rectification, but the FFCO2 rectifier effect occurs mainly at local-to-regional scales, while the biosphere rectification is expressed at a larger spatial scale.

Atmospheric inversion studies of CO2 fluxes using flask and tall tower atmospheric CO2 measurements require consideration of CO2 concentration sampling times (e.g., Peters et al., 2007; Dang et al., 2011). Given the importance of the simulated CO2 concentration to the diurnal cycle of FFCO2 emissions, we sub-sample the DCE FFCO2 simulation output for local afternoon (noon–18:00 LT) conditions, a common sampling time for flask measurement and a chosen sampling time by inversions to avoid the difficulties associated with capturing nighttime PBL dynamics. Figure 2 presents the spatial distribution of the annual mean, afternoon-only surface FFCO2 concentration difference between the DCE and FE fields. Values vary from -0.21 to +1.13 ppm, with larger positive values centered over the LSRs. Negative values are present over regions with low emissions, which is mainly due to the interaction of small emissions and a stable PBL at nighttime and the early morning in the DCE experiment compared to the same dynamic in the FE experiment. The afternoon and 24 h mean signals (Fig. 1b) are of opposite signs but roughly the same magnitude over the LSRs. This is due to the afternoon signal being sampled at the time of the largest afternoon emissions but also contributing the weakest surface signal to the 24 h diurnal span. The afternoon mean signal indicates that a potential bias would be incurred by ignoring the diurnal variability in the FFCO2 emissions. It is noteworthy that the afternoon effect mainly occurs at the local scale, and has a much smaller spatial extent than the full-day diurnal rectification. This indicates that CO2 monitoring strategies could minimize the effect of the FFCO2 diurnal cycle when using afternoon measurements and the measurements can be taken close to large source regions for studies influenced by the diurnal cycle.

The continuous atmospheric CO2 measurements taken by many monitoring stations can see the complete 24 h coverage of atmospheric CO2 concentration, and can enable the estimate of sub-daily fluxes in inversion studies using these data (e.g., Law et al., 2008). This motivates the examination of the diurnal peak-to-peak amplitude of the simulated concentration, since this parameter includes the overall daily information of the diurnal FFCO2 concentration.

Figure 3a displays the amplitude of the annual mean diurnal surface concentration difference between the DCE and FE fields across the globe. The largest amplitude values are centered over the LSRs, with peak-to-peak values reaching 9.12 ppm in western US (-117∘ E, 34∘ N). Local sunrise is the point when the FFCO2 concentrations reach their greatest difference. At local sunrise, the FE emissions exceed the DCE emissions, which are small prior to the increase of daytime emitting activity (Fig. S1). When combined with the minimum in vertical mixing and a shallow nighttime PBL, the resulting FFCO2 concentration difference is negative (DCE minus FE). Local sunset, by contrast, is the point in the annual mean diurnal cycle where the differences between the DCE and FE fields are at their smallest (Fig. S1) and the DCE emissions exceed those of FE. This combines with the much greater vertical mixing and greater PBL height, and tends to ameliorate the resulting surface FFCO2 concentration difference. Hence, the amplitude difference is driven primarily by the concentration difference at the minima of the diurnal cycle (local sunrise).

To provide context for the magnitude of the FFCO2 diurnal amplitude, the surface FFCO2 DCE concentration amplitude can be compared to that resulting from biosphere fluxes. This is shown in Fig. 3b, where the ratio of FFCO2 amplitude to the total of the FFCO2 and biosphere amplitudes is presented. Averaged over the LSRs, the diurnal amplitude of the annual mean FFCO2 concentration accounts for more than 15 % of the total diurnal amplitude, and this ratio rises as high as 87 % at the grid cell scale over the LSRs (corresponding to a FFCO2 diurnal amplitude that is 5 ppm larger than the biospheric amplitude, Fig. 3b). The diurnal amplitude can be examined seasonally as well. The diurnal FFCO2 amplitude accounts for a larger portion (up to 5 ppm) of the total diurnal variation than the diurnal biospheric amplitude in winter, when the biosphere is relatively quiescent and vertical mixing is less vigorous (Fig. S6). Overall, this result indicates that studies of diurnal atmospheric CO2 should consider the contribution of diurnal FFCO2 emissions, especially over LSRs and in wintertime.

Figure 4 shows the amplitude of monthly CO2 concentration difference between the MCE and FE (MCE - FE) fluxes. The seasonal amplitude varies from 0.01 to 6.11 ppm, with large signals over the LSRs as seen in previous figures. Both the magnitude and spatial extent are larger than found in the diurnal case. The longer periodicity allows more time for an atmospheric signal to build up and to be advected further from the emission source regions. The seasonal maxima and minima contribute equally to the amplitude for all regions (Fig. S7). The seasonal maximum mainly occurs in December–January, driven by the larger FFCO2 emissions during winter (Fig. S8). The seasonal minimum exhibits variable timing across the LSRs, with January for China (up to -3.42 ppm), August/September for the US (-1.09 ppm) and June/July for western Europe (-2.55 ppm). This timing is consistent with the timing of the smallest FFCO2 emissions over each region (Fig. S8). The seasonal minimum in East Asia is, as has been mentioned, likely an artifact of the inventory statistics.

The FFCO2 seasonal amplitude can also be compared to the seasonal biospheric amplitude, for context (Fig. 4b). The biospheric amplitudes are much larger than the FFCO2 amplitudes at the global scale, except for specific industrialized source regions in the US, western Europe and East Asia, where the FFCO2 amplitude accounts for more than 25 % of the total seasonal amplitude. This result indicates a non-negligible local-to-regional FFCO2 effect on seasonal amplitude of atmospheric CO2 concentration.

The impact of the weekly cycle of FFCO2 emissions is demonstrated here by constructing a mean weekday and mean weekend surface FFCO2 concentration from the difference between the WCE and FE simulations (Fig. 5). As expected, the surface FFCO2 difference values are centered over LSRs, with predominantly positive FFCO2 concentration values for the weekdays and negative values on the weekends. The negative weekend values are a reflection of the reduced weekend FFCO2 emissions vs. weekday activity (Nassar et al., 2013). There are a few deviations from this regular weekday/weekend pattern. First, the different definition of what constitutes weekend activity is seen over the Middle East, where the weekend is typically Thursday–Friday vs. Saturday–Sunday in most of the rest of the world. In contrast to other weekdays, Monday shows positive values only in narrow portions of East Asia. The other large source regions show negative surface FFCO2 concentration difference values. This spatial pattern primarily reflects the residual effect of the lower weekend FFCO2 emissions. This coherent FFCO2 concentration difference dissipates after 24 h and is then dominated by the higher weekday FFCO2 emissions. The residual effect of the larger Friday FFCO2 emissions does not show up clearly in the simulated weekend FFCO2 concentration (Fig. 5d), due to the fact that the weekend mean is constructed from 2 days and the residual effect from effect from Friday is likely negated in the 2-day mean.

Atmospheric CO2 monitoring locations were originally situated away from fossil fuel source regions, but as FFCO2 emissions have risen dramatically over time, they are increasingly influenced by FFCO2 sources. A large number of monitoring stations are situated in strongly affected areas in temperate North America, western Europe and East Asia that show a strong diurnal concentration. Noteworthy are the coastal sites close to the large source regions in the US and western Europe – these show significant influence from the DCE flux component, despite the fact that these locations are assumed to represent upwind background CO2. Time series of daily afternoon-mean CO2 concentration differences demonstrate this influence (Fig. 6). For the sake of brevity, we focus on two stations: La Jolla, in the western US (32.9∘ N, 117.3∘ W; 10 m a.s.l.; referred to as LJO), and Lutjewad of the Netherlands (53.4∘ N, 6.35∘ E; 61 m a.s.l.; referred to as LUTDTA). The two sites were selected because they are close to LSRs (locations highlighted in the figure). A strong seasonality of up to 5 ppm for LUTDTA and up to 3 ppm for LJO is shown in the daily afternoon mean CO2 concentration difference from the ACE simulation. Synoptic variability with approximately the same magnitude is also evident (Fig. 6b). These seasonal and synoptic effects are very similar to those presented in Peylin et al. (2011) at the station scale. Finally, a slight weekly cycle can be seen in spring and summer at both stations.

The time series can be further understood through examination of the cyclic FFCO2 flux contributions (Fig. 6c–e). The MCE simulation shows the largest daily afternoon mean impact on CO2 concentrations (up to 5.5 ppm) vs. smaller values for the WCE (2.2 ppm) and DCE (1.6 ppm). Large seasonality is shown in the MCE that is caused by the interaction of the monthly FFCO2 emissions and atmospheric transport. The WCE and DCE display slight but evident seasonality that is driven mainly by the seasonal atmospheric transport. Synoptic variability is seen in the MCE (up to 4 ppm) and DCE (up to 1 ppm). The synoptic-scale effect is comparable to the results found in Peylin et al. (2011), where a ∼ 5 ppm effect was found. Also, a weekly cycle is illustrated for the WCE driven by the weekly FFCO2 emissions. These temporal patterns are common to the stations with significant response to the time cycle FFCO2 emissions, but the magnitude is dependent on the local dynamical conditions, transport patterns and proximity of the site to the FFCO2 sources. LJO shows a larger impact than LUTDTA in July and August, associated mainly with the large FFCO2 emissions in summer. Differences are found in the timing of the synoptic events between the two sites, and the amplitude of the synoptic variation in the CO2 concentration difference at LUTDTA is roughly twice that at LJO, which suggests that the synoptic events of atmospheric transport play an important role in distributing the FFCO2 at LUTDTA.

The analysis above indicates significant CO2 concentration response to sub-annual FFCO2 emission variability near the surface. With the advent of satellite measurements, as well as the surface-based spectrometers of the TCCON network, it is important to examine the response of vertically averaged CO2 concentrations to the FFCO2 emissions. How important is sub-annual FFCO2 emission variability to the CO2 concentration seen from space? And what impact do these FFCO2 emission cycles have on studies that use satellite measurements?

To answer these questions, the same analysis is performed for the simulated column-integral CO2 concentration for all the cyclic FFCO2 emissions as was performed for the surface. For generality, we have used simple pressure weighting to compute the column averages, rather than the vertical weighting appropriate for any particular satellite. Results indicate weak rectifier effects in the simulated column-integral FFCO2 concentration, with ACE having negative values from -0.02 to -0.06 ppm. The ACE rectification is centered over large source regions and the MCE component represents the largest contribution overall, varying from -0.02 to -0.06 ppm (Fig. S9). The DCE exhibits similar rectification magnitudes varying from -0.02 to -0.04 ppm, but with a response covering a smaller spatial extent. The MCE rectification reflects the larger vertical and spatial effect of the monthly FFCO2 emission variability as compared to the WCE and DCE. Compared to the surface effect, the column-integral rectification is almost an order of magnitude smaller. However, note the negative signal in western Europe from MCE, which is opposite to the positive signal at the surface (Fig. 1). Overall, the sub-annual FFCO2 emission variability has little effect on all aspects of the column-integral CO2 concentration.