Sensitivity of atmospheric CO2 inversions to seasonal and interannual variations in fossil fuel emissions



[1] Estimates of fossil fuel CO2 are a critical component in atmospheric CO2 inversions. Rather than solving for this portion of the atmospheric CO2 budget, inversions typically include estimates of fossil fuel CO2 as a known quantity. However, this assumption may not be appropriate, particularly as inversions continue to solve for fluxes at reduced space and timescales. In this study, two different alterations are made to widely used fossil fuel CO2 emissions estimates, and these altered emissions are run through a series of atmospheric inversion experiments. The first alteration is the inclusion of a seasonal cycle which depends upon both season and latitude. The other alteration is the inclusion of year-by-year changes in the spatial distribution of fossil fuel CO2 emissions. All but the interannual inversion experiments are run with three models from the TransCom 3 atmospheric inversion intercomparison. These three models span the key components of atmospheric transport and hence can be expected to capture the range of potential bias caused by assumed fossil fuel CO2 emission estimates when interacting with transport processes. Key findings include the lack of seasonal rectification of the seasonally varying fossil fuel CO2 emissions in the annual mean. Examination of monthly fluxes in the seasonal inversion, however, indicates that significant bias is likely occurring and may be as large as 50% of the residual flux during certain times of the year. In this study, interannual variations were little effected by shifts in the spatial pattern of fossil fuel CO2 emissions. However, as the spatial scale of inversions is reduced, potential bias will likely increase.

1. Introduction

[2] The emission of fossil fuel CO2 forms a key component of atmospheric CO2 inversions aimed at characterizing sources and sinks of CO2 to the Earth's atmosphere. In recent inversion studies, including those of the TransCom 3 experiment, the fossil fuel emissions are designated as a “background” or “presubtracted” flux [Gurney et al., 2002, 2003, 2004]. Fossil fuel emissions are not the only background fluxes specified; other fluxes are often included in this fashion such as a global oceanic flux and an estimate of biospheric exchange.

[3] Once these background emissions are specified in space and time, the fluxes that are estimated in the inversion process, the “residual” fluxes, represent adjustments to the background fluxes such that the resulting CO2 concentration best matches atmospheric CO2 concentrations observed at particular times and locations. This may be expressed as

equation image

where Cobs represents observed CO2 at a particular points in space and time, Cff represents the contribution to the observed CO2 due to global fossil fuel emissions, Coc, the contribution due to a chosen global oceanic flux, Cnbio, the contribution due to a neutral biosphere flux, and Cres, the contribution of the residual fluxes from the chosen N discretized regions [see Gurney et al., 2000]. An additional term, the oxidation of CO is considered small and is neglected here. This expression is valid for every location in the atmosphere. Rearrangement of this basic budget makes clear the motivation behind the term “presubtracted”; the residual CO2 can be defined as the difference between the observed CO2 and the sum of the first three terms on the right-hand side of equation (1). Hence the contribution of the background fluxes are subtracted from the observations leaving the residual CO2 concentration as the observational constraint in the inversion.

[4] An atmospheric inversion therefore is composed of two distinct steps. First, a series of forward model runs are completed in which the fixed background fluxes and adjustable unit regional fluxes (e.g., 1 Gt C yr−1) are input into the model atmosphere. The inverse step adjusts the regional fluxes such that a best match is achieved between the summation of the simulated CO2 concentrations and the observed.

[5] In practice, the fossil fuel, neutral biosphere, and oceanic fluxes can be adjusted in the inversion process in the same way that the discretized residual fluxes are. However, this is typically not performed in atmospheric CO2 inversions and these fluxes are provided to the inversion with small uncertainty and hence nearly fixed at the values provided. There are two reasons for this convention.

[6] First, the three background fluxes are considered well known. For the fossil fuel background flux, the emissions are considered reliable at the 1° × 1° scale and as annual means. The neutral biosphere portion of the background fluxes is considered a subset of the total net biome production (NBP), by definition, while the oceanic fluxes are generally considered a good first guess and represent a combination of model and data products. The second reason for fixing the values of the background fluxes relates to the first reason; the background fluxes are not considered as scientifically interesting as the residual fluxes primarily because the latter constitute the portion of the global carbon budget that is poorly understood.

[7] The problem with this approach arises if the assumed background fluxes are sufficiently different from their true values. This is exacerbated when the spatial and temporal scale of the background fluxes are different from those solved for. In this case, bias in the background fluxes will be directly transferred to the residual fluxes and hence constitute a bias to the regional flux estimates [Kaminski et al., 2001; Engelen et al., 2002]. For the case of the fossil fuel background flux this arises primarily because the prescribed emissions data may not contain the true dynamics in space and time of the fossil emissions in the real world.

[8] In this paper we test how much impact more realistic fossil fuel carbon fluxes might have on the series of TransCom 3 results completed in the last few years. Because the TransCom 3 methodology associated with the inclusion of fossil background fluxes is widely found in inverse studies of atmospheric CO2, the results presented here have wide applicability to atmospheric CO2 inversions in general.

2. Methods

[9] Figure 1 shows widely available global gridded maps of fossil fuel emissions for the years 1990 and 1995. The 1990 annual mean fossil emissions (1° × 1°) are from Andres et al. [1996] and total 5.812 Gt C yr−1. The 1995 annual mean fossil source (1° × 1°) is derived from the data prepared by Brenkert [1998] and totals 6.173 Gt C yr−1. The 1990 emissions were constructed from country level emissions of CO2 due to fossil fuel burning and cement manufacturing which in turn were derived from United Nations energy statistics [Marland and Rotty, 1984; Marland et al., 2003]. The country emissions were allocated to clusters of grid cells (and subclusters for nine countries) based on geopolitical data [Lerner et al., 1988]. The emissions within these grid cell clusters were allocated according to 1984 population density. A number of adjustments were made to account for border issues, land/sea masking, and the emissions of very small countries. The 1995 fossil fuel emissions were constructed similarly to the 1990 emissions. The primary difference was the use of 1990 population density estimates rather than 1984 [Li et al., 1996].

Figure 1.

Fossil fuel emissions for (a) 1990 and (b) 1995. Grid cells dimensions are 1° × 1°.

[10] These two gridded emissions data sets (or their immediate predecessors) are widely used as background fluxes in atmospheric CO2 inversions [e.g., Rödenbeck et al., 2003; Peylin et al., 2002; Bousquet et al., 2000; Rayner et al., 1999; Fan et al., 1998]. In the TransCom 3 experiment, a combination of the 1990 and 1995 emissions were used to capture some of the temporal shifts that are known to have occurred in fossil fuel CO2 emissions during the 1990s. As mentioned in section 1, any differences between these emissions data sets and real values would be aliased into the residual fluxes. Such errors could come in two forms: (1) errors in the total emissions data themselves and (2) mismatches between the spatiotemporal resolution of the fossil fuel emissions and the residual fluxes.

[11] In the first instance, much care has been taken to accurately account for the fossil fuel emissions totals for the globe and errors at this scale have been estimated as 6% to 10% [Marland and Rotty, 1984]. At the regional or country level scale, such errors are considered to be much larger though comprehensive error estimates have not been quantified. A recent study in which Asian emissions were quantified arrived at ±95% confidence intervals in CO2 emissions that ranged from a low of 7% in Japan to 91% in Southeast Asia [Streets et al., 2003]. Though such errors are not insignificant, the more error prone aspect of the emissions data is the way in which emissions are allocated at scales smaller than a country. Emissions do not covary with population density in all cases. For example, roughly one quarter of California's electricity production occurs outside the state ( The emissions associated with the in-state consumption occurs at the power generating facilities which may be hundreds to thousands of miles away from the direct consumption of electricity. Highways are another example of potentially low population locations that may have inordinately large emissions.

[12] The second form of error has the potential to be more serious. The two commonly used fossil fuel data sets reflect annual mean emissions and represent only the stated years. Temporal variability at scales smaller (seasonal, diurnal) and larger (interannual) than the annual mean are therefore not represented. Variations at scales smaller than 1° × 1° are also not captured, though characterizing such variability has not been routinely attempted by atmospheric inversions to date.

[13] A number of atmospheric CO2 inversions have estimated fluxes at monthly scales (seasonal inversions) and multiyear scales (interannual inversions) and have relied on one or both of the fields introduced above [Enting et al., 1995; Kaminski et al., 1999; Gurney et al., 2004; Rayner et al., 1999; Bousquet et al., 2000; Rödenbeck et al., 2003]. Furthermore, should fossil fuel emissions exhibit seasonal or diurnal variations that covary with vertical transport in the planetary boundary layer, rectification may occur [Denning et al., 1995]. Recent fossil emissions data for the United States and Europe indicate that fossil fuel emissions do exhibit seasonality with greater emissions during winter months and less during summer months [Blasing et al., 2003; Levin et al., 2001]. These data suggest that the peak-to-peak amplitude varies from 20% to 30% and has exhibited a steady decline over the last 20 years. The decline in the seasonal amplitude is due to the rise of coal combustion in summer months in order to produce greater electricity. This is likely due to the expansion of air conditioning during the summer [Blasing et al., 2002; Gregg and Andres, 2003]. European researchers have suggested that the equivalent peak-to-peak amplitude for Europe is approximately 40%, slightly higher than that shown for the United States [Levin et al., 2001].

[14] Country tabulations of fossil fuel emissions over the last two decades indicate that the interannual variation in the spatial pattern of emissions has been changing. These are most likely due to geopolitical and economic events [see Nakicenovic et al., 2000]. Examples include the demise of the centrally planned economies of central Europe at the beginning of the 1990s, the dramatic growth in the east Asian economy, and the fuel shifts that have occurred recently in western Europe countries such as substitution of natural gas for coal some sectors in the UK.

[15] In the current experiment, we test the sensitivity of the annual, seasonal, and interannual TransCom 3 inversion results to two potential variations in fossil emissions not captured in the standard experiment. We test the impact of seasonally varying fossil fuel emissions and emissions that vary in space and time over multiyear timescales. In order to fully explore the possible inverse results to more realistic fossil fuel emissions, three different transport models have been used that span key transport characteristics of the TransCom 3 experiment [Gurney et al., 2003].

[16] Figure 2a shows the simulated annual/zonal mean surface CO2 concentration of the TransCom 3 models in response to 1990 fossil fuel emissions. All the participating models ran the provided fossil fuel CO2 emissions field forward for 4 years starting with a 350 ppm initial condition. Figure 2 presents the CO2 concentration in the final year of the forward runs. The three models chosen for this study are represented by bold lines: MATCH:NCEP, JMA, and PCTM (Kawa et al. [2004] (PCTM); Chen [2003] (MATCH); and Sasaki et al. [2003] (JMA)). MATCH:NCEP has the largest concentration maximum over the source regions of the northern hemisphere while JMA has the smallest. The PCTM model exhibits a CO2 concentration maximum that is toward the larger of the 18 models shown though not as large as the MATCH:NCEP model. The magnitude of the interhemispheric gradient provides a useful index of how vigorously the various models transport CO2 horizontally and vertically. [Denning et al., 1999].

Figure 2.

TransCom 3 annual/zonal mean surface CO2 concentration (ppm) resulting from 4 years constant emissions of (a) 1990 fossil fuel CO2 and (b) neutral biosphere exchange. The models used in the current study are denoted in bold.

[17] Figure 2b shows the simulated annual/zonal mean surface CO2 concentration in response to the neutral biosphere flux generated from the Carnegie Ames Stanford Approach model [Randerson et al., 1997]. As with the fossil fuel CO2 presented in Figure 2a, Figure 2b presents the last year of 4 in which each model ran the biospheric exchange forward in time. Unlike the fossil fuel emissions, however, the neutral biosphere exchange contains no net flux when averaged over an entire year. It does contain both positive and negative exchange with the surface reflecting times in which photosynthesis or respiration dominate, respectively.

[18] As with the fossil fuel emissions, MATCH:NCEP has one of the larger CO2 concentration maxima while JMA is among the models with the smallest. In contrast to the fossil fuel emissions, PCTM has a concentration maximum toward the smaller of the models shown. The relative magnitude of the northern extratropical CO2 maximum (coincident with the strongly seasonal biosphere exchange) provides a reasonable indication of how strongly the models exhibit seasonal rectification. For a model to exhibit strong seasonal rectification, it must have vertical exchange of biospheric CO2 with the planetary boundary layer (PBL) and a PBL mixing depth that has seasonal variation anticorrelated with the biosphere flux at the surface [Heimann et al., 1986; Keeling et al., 1989; Denning et al., 1995]. The combination of these two processes results in a vertical redistribution of mixing ratio in the annual mean. Strongly rectifying models move CO2 aloft, concentrating it near the surface and vice versa.

[19] All three models have similar vertical resolutions (28 sigma, 25 hybrid, and 32 hybrid layers for MATCH:NCEP, PCTM, and JMA respectively). However, the lowest layer in the JMA model (0.97 sigma) is larger than either MATCH:NCEP (0.99 sigma) or PCTM (0.985 sigma) thereby providing a larger volume of air within which to mix the surface emissions. Furthermore, the JMA model as it was used in this study contains a simple diffusion scheme for cumulus convection and a fixed PBL. The MATCH:NCEP model utilizes a combination of vertical diffusion, a penetrative convective parameterization and local convective transport to simulate subgrid vertical transport. The PBL height in MATCH:NCEP is diagnosed from the bulk Richardson number. The PCTM model uses a combination of vertical diffusion and pairwise convective parameterization for subgrid vertical transport. The PBL height is determined from the magnitude of the vertical diffusion, itself varying in time and space.

[20] These subgrid-scale vertical transport characterizations are consistent with the results in Figure 2. The utilization of a fixed PBL for the JMA model results in no seasonality in PBL height and hence limited seasonal rectification of the biosphere exchange exhibited in Figure 2b. The relatively large surface layer compared to either the MATCH:NCEP or PCTM models combined with purely diffusion in the vertical results in lower mixing ratios in response to the aseasonal fossil fuel emissions evident in Figure 2a. The MATCH:NCEP model, constructed with both a relatively small surface layer and a seasonally varying PBL with limited but strongly seasonal convective vertical exchange, results in both trapping of the aseasonal fossil emissions and a strong rectifier. PCTM has a surface only slightly larger than MATCH:NCEP and convective parameterization resulting in a response similar to MATCH:NCEP in Figure 2a. However, PCTM also exhibits a relatively weak rectifier. Though the seasonal phasing of the vertical exchange produces realistic seasonal CO2 concentrations near the surface, the magnitude of the seasonal mass exchange in the PBL is likely much weaker than that exhibited by the MATCH:NCEP model. Hence the PCTM model exhibits strong “trapping” of the aseasonal fossil fuel emissions (Figure 2a), but relatively weak rectification (Figure 2b).

[21] Given the importance of these two responses to diagnosing the overall transport characteristics of tracer transport models, the three models chosen do a good job at spanning the spread available to the TransCom 3 experiment.

2.1. Constructing Seasonally Varying Fossil Fuel Emissions

[22] In order to test the impact that seasonal fossil fuel emissions might have on inverse results, a series of hypothesized seasonal fossil fuel emissions maps were generated. These emissions were created by taking the existing TransCom 3 fossil fuel emissions and adding seasonal variation. This was done at every grid cell according to

equation image

where Fi,j,mn is the new flux at grid cell with longitude index i, latitude index j, and month index m. Fi,j,mo is the original flux. Ak is the amplitude factor (AF) that represents the percent increase in the original fossil emissions. Nine different AFs were chosen creating nine different seasonal fossil fuel emission maps. These included AFs of 0% (the aseasonal “base case”), 10%, 20%, etc. up to 80%. This AF is modified by both a latitude and time (month) dependence. The former is represented by θj which is the latitude in radians. The latter is represented by the expression within the cosine term and causes a maxima to occur in January and a minima to occur in July.

[23] Figure 3 shows an example with an AF of 20% and a base emission level of 100. This shows that the emissions reach a maximum at 90° north, decreasing as the latitude decreases, and ultimately changing sign in the southern hemisphere. In the 80% amplitude modification case, the January emissions are roughly three times larger than the July emissions at 40° north. For the 50% amplitude modification case, this gives a January/July ratio of roughly 2. As indicated previously, limited data for the United States and Europe indicate peak to peak amplitudes at roughly 40° N are on the order of 20% to 30% (or AFs of 10% to 15%). In this formulation, that would correspond most closely to an AF of 30%.

Figure 3.

Seasonal fossil fuel emissions example with an amplitude factor of 20% and a base level of 100 units.

2.2. Constructing Interannually Varying Fossil Fuel Emissions

[24] In order to capture realistic interannual variations in fossil fuel emissions at the scale of the basis function regions (see Figure 1, supplementary information of Gurney et al. [2002] for a basis function map), annual tabulations of fossil fuel emissions at the country level have been utilized [Marland et al., 2003]. Because the gridded fossil fuel emissions introduced earlier are only available for the years 1990 and 1995, country level data is necessary to capture the spatiotemporal changes in emissions over many years.

[25] Country level data is incorporated by assigning each country in the country level fossil fuel emission tabulation to one of the 11 TransCom 3 land regions. For each TransCom 3 region and year (1979 to 2000) a fraction of the annual global total emissions was calculated from this tabular data (αi(t)). The global 1990 fossil fuel emissions map shown in Figure 1 was similarly regionalized into the 11 TransCom land regions. These 11 regional fossil fuel emissions maps were run though the PCTM model as individual components of the background fossil fuel flux. In this way, CO2 concentration resulting from this flux at all the observing stations were generated from each of the regions, independently. The CO2 concentration associated with a given regional fossil fuel emissions pattern were then scaled for each year to reflect the spatiotemporal changes evident in the country level data. This can be seen by redrafting equation (1):

equation image

where αi represents the fraction for a given region, i, in a given year, t, and Cffi represents the fossil fuel emissions for a given region and year. This model run will be referred to as the “perturbed” interannual run.

[26] A base case run for this interannual experiment was constructed by running (through PCTM) the global 1990 emissions map (no regionalization) for each year but allowing the global total emissions to change according to the global sum of the country level emissions. The global total increases by 24% from 1980 to 2000. This model run will be referred to as the “base” interannual run.

[27] Two important caveats must be mentioned. First, the forward simulations were run with the PCTM model only. This was done because of the three models employed, PCTM tended toward the middle of the distribution in Figure 2a. Second, the spatial distribution within the individual TransCom 3 regions remains fixed at that provided by the 1990 emissions map. Therefore the results only address changes that cause fossil fuel emissions to shift from one region to another but do not reflect changes that occur within regions. The implications of this will be discussed later.

[28] The time series of the regional fractions are shown in Figure 4. Europe and temperate Asia show the greatest changes over this time period. Europe experienced declines of over 35% in the late 1980s and early 1990s. Temperate Asia shows increasing emissions throughout the period with some leveling off starting in the mid-1990s. Absolute emissions in temperate North America grew at a rate nearly comparable to the global total hence its fractional share remained fairly constant.

Figure 4.

Regional fossil fuel emissions as a fraction of the yearly global total.

3. Results

3.1. Annual Mean Inversion

[29] Nine seasonal fossil emissions maps were constructed following the procedure described in the last section and run forward through the three models. Figure 5a shows the annual/zonal mean CO2 concentration for four of the nine AF cases. Figure 5b shows a difference plot of the 80% and base AF and the 30% and base AF cases for each of the models. The model with the largest rectifier (MATCH:NCEP) exhibits the greatest sensitivity to the fossil seasonality. PCTM has the next largest CO2 concentration difference followed by the JMA model.

Figure 5.

(a) Annual/zonal mean surface CO2 concentration resulting from seasonal fossil fuel emissions for four of the nine AFs (including the base case). (b) CO2 concentration difference between the 80% and base AF cases.

[30] The other feature to note is the absolute magnitude of the increase in northern extratropical concentration as the fossil seasonality is increased. For the MATCH:NCEP model, the maximum concentration difference in the northern extratropics of Figure 5b is roughly 0.4 ppm. If one considers the more realistic AF case of 30%, the maximum concentration difference is about 0.15 ppm.

[31] This suggests very small amounts of rectification when one compares this to the CO2 concentration maximum from the neutral biosphere exchange of over 3.7 ppm (Figure 2b). This suggests that the residual fluxes will be little influenced by the annual mean rectification of the seasonal fossil fuel emissions.

[32] Table 1 shows the residual fluxes for all 22 TransCom 3 land and ocean regions that result from the inverse operation. The CO2 observing stations used, their associated uncertainty and the prior flux information was all identical to that used in the control TransCom 3 annual mean inversion [Gurney et al., 2002]. The only difference was that the current inversion used only the 1990 fossil fuel emissions rather than a mixture of 1990 and 1995. This was done for simplicity since the focus here is on the difference when seasonality is included in the emissions.

Table 1. Annual Mean, Regional Inverse Flux Estimates for the Base AF Case and the Change in Flux for an Inversion Run With the 30% AFa
  • a

    Regional inverse flux estimates and the change in flux are in units of Gt C yr−1. Results are shown for all three models.

Boreal North America0.24−0.01−0.080.01−0.080.02
Temperate North America−0.920.04−0.68−0.01−0.920.01
Trop America0.54−0.010.40−0.010.06−0.02
South America0.210.00−1.040.00−0.430.03
Northern Africa−0.590.000.530.070.04−0.08
Southern Africa−0.170.01−1.160.00−0.080.01
Boreal Asia−0.65−0.03−1.39−0.070.25−0.03
Temperate Asia0.460.01−0.130.05−0.480.08
Tropical Asia0.51−0.021.430.040.04−0.02
North Pacific0.310.000.700.010.53−0.01
West Pacific−0.25−0.01−0.090.00−0.260.01
East Pacific0.09−0.010.09−
South Pacific0.470.000.330.010.850.00
Northern ocean0.
North Atlantic−−
Tropical Atlantic−0.130.00−
South Atlantic0.
Southern Ocean0.160.000.740.000.39−0.01
Tropical Indian Ocean−0.51−0.010.00−0.02−0.680.01
South Indian Ocean−

[33] The table provides the base case and the flux difference for the 30% AF case. As expected the changes are very small compared to the magnitude of the residual fluxes in the base case run. This result leads to the first important conclusion concerning the impact of seasonal fossil fuel emissions on the annual mean: Fossil fuel rectification does not produce significant bias in the flux.

3.2. Seasonal Inversion

[34] Though the influence of seasonally varying fossil fuel emissions on the annual mean inversion is small, the impact may be larger when solving for each month in an individual year, a process often referred to as a “seasonal inversion.” The concern for the seasonal inversion is not rectification, but straightforward bias in the monthly mean residual fluxes.

[35] An initial glimpse at how the monthly estimated fluxes from the inversion might respond to a seasonal fossil emissions field is shown in Figure 6a. This shows the monthly mean CO2 concentration response (CO2 concentration minus the initial condition of 350 ppm) at three northern stations; Hungary (HUN, 46.95°N, 16.65°E), Mauna Loa (MLO, 19.53°N, 155.58°W), and North Carolina (ITN, 35.35°N, 77.38°W). Hungary has the largest response due to its proximity to fossil fuel sources. North Carolina had the largest response of the North American stations while Mauna Loa was typical of background, oceanic stations. Figure 6b shows the same three stations but reflects the difference between the base AF case and the 30% and 80% AF cases, respectively.

Figure 6.

(a) CO2 concentration response at three stations reflecting seasonal fossil fuel emissions. Five AFs for each of the three models are shown. (b) CO2 concentration response difference between the 80% AF and the base case and the 30% AF and the base case.

[36] Both the underlying transport and the seasonality of the fossil fuel emissions itself contribute to the total seasonality of the response. The seasonality of the base AF case, in which no fossil fuel seasonality exists, combined with previous TransCom 3 results suggests that the MATCH:NCEP model has less vertical and horizontal mixing in winter compared to either the PCTM or JMA models with the JMA model exhibiting the greatest amount of winter mixing. This is indicated by the increased Winter concentrations for both the continental sites in Figure 6a. For the Hungary location, the MATCH:NCEP model exhibits winter/summer differences of 5 ppmv for the base AF case. For the PCTM and JMA models this difference is approximately 2 ppmv and less than 1 ppmv, respectively.

[37] Examination of the difference plots of Figure 6b indicates that the contributions due to the seasonality of mixing versus the seasonality of the emissions are comparable for the MATCH:NCEP and PCTM models. This is evidenced by the fact that the seasonal change in the 30–0% case of Figure 6b (the blue lines) is similar in magnitude to the seasonal change in the aseasonal fossil response in Figure 6a for each of these models. This suggests that for the most realistic 30% AF case, the underlying transport seasonality is an equal contributor to the total fossil fuel response as is the seasonality forced by the emissions at the surface. In contrast, the emissions seasonality dominates for the JMA model due to the fact that the JMA model has little transport seasonality evidenced by the lack of a seasonal response for all cases in Figure 6a.

[38] Finally, the contribution to the total response due to the seasonally varying emissions can be seen by examining the relative magnitudes of the winter response difference in Figure 6b across the models. In either the 80–0% or the 30–0% differences, MATCH:NCEP has the greatest response followed next by PCTM and finally JMA.

[39] So, in summation, while MATCH:NCEP and PCTM receive equal contributions to the total fossil fuel response from their underlying transport seasonality and seasonally varying fossil fuel emissions, the magnitudes of those contributions are greatest for the MATCH:NCEP model. The JMA model by contrast, has little underlying transport seasonality, receiving all of the total response from the seasonal emissions at the surface.

[40] Figure 7 shows similar information but for the entire global surface and for the months of February and August. The MATCH:NCEP and PCTM models exhibit much greater sensitivity to the seasonal emission at all times of the year than JMA. However, MATCH:NCEP has a much more vigorous response in the winter compared to PCTM but PCTM appears to have a somewhat more vigorous summer response, particularly in Eurasia. This suggests that PCTM is mixing more in the winter than MATCH:NCEP but mixing less in the summer. This may partly explain why PCTM traps nonseasonal fossil to the same extent as MATCH:NCEP but has a relatively weak rectifier (see Figures 2a and 2b).

Figure 7.

Global surface CO2 concentration response (ppm) for the months of February and August. Maps represent the difference between the 30% and base AF fossil fuel emissions cases.

[41] Examination of the February and August response relative to the base case at all the stations included in the inversion is shown in Figure 8. Since the station locations are where the observations influence the residual fluxes, these differences will give a good indication of how the regional residual fluxes will likely turn out. In February, the ordering of the response is similar to what is seen in Figure 7, MATCH:NCEP and PCTM respond most vigorously in continental regions to the seasonal emissions with JMA showing a weak response. However, August shows all three models responding similarly to the emissions suggesting that at the stations, summertime mixing is comparable. This is somewhat different from the interpretation of Figure 7 and reflects that fact that the station locations are able to witness the larger wintertime differences among the models than the summer. This highlights the importance of examining responses at the stations rather than at every surface model grid cell as the station observations are the locations used in the inversion to optimize the residual fluxes.

Figure 8.

CO2 concentration response difference at all of the observation stations for the month of (a) February and (b) August. The values represent the difference between the 30% and base AF fossil fuel emissions cases.

[42] As with the annual mean inversion, all nine fossil fuel emission cases were included in a series of seasonal inversions. Details on the inversion methodology and the construction of the regional response functions are given by Gurney et al. [2004].

[43] Figure 9 shows results for the temperate North American and European regions for all three of the models and for base, 30% and 80% AF cases. Note that the results are deseasonalized by subtracting the neutral biosphere. Both the MATCH:NCEP and PCTM models require lessened respiration outside of the growing season while the JMA model requires little adjustment during the winter months. All models require greater uptake during the growing season in Europe while only JMA requires greater uptake in temperate North America. Figure 10 shows the difference in residual seasonal fluxes between the 30% and base AF cases for all northern extratropical land regions.

Figure 9.

Monthly mean inverse flux estimates for the temperate North American and European land regions. Inverse flux estimates are shown for three fossil fuel AF cases (base, 30%, and 80%) and all three transport models.

Figure 10.

Estimated regional fluxes for each month and each model represented as the difference between the 30% and the base AF cases. All northern extratropical regions are shown.

[44] All three models exhibit the same overall behavior. During the winter months, respiration fluxes are lessened due the greater amount of fossil CO2 generated during these months near the surface. During the summer months, less uptake is required to counter the lessened fossil fuel CO2.

[45] It is somewhat surprising that the seasonal fossil emissions require changes to the northern land fluxes that are of very similar magnitude for all three models. The response differences in Figure 8 would have suggested that JMA would require the smallest flux adjustment as the fossil fuel seasonality increases, particularly in the winter. The likely explanation for this is that the stations where the response differences are the greatest in Figure 8 are stations for which the “data uncertainty” is very large and hence have a proportionately smaller influence on the inversion results. For example, the three stations exhibiting the largest response difference for the MATCH:NCEP model in Figure 8a are HUN, BAL, and ITN. These stations also have the three largest uncertainty values. To illustrate this, we weight the response differences in Figure 8 by the associated station uncertainty (1/σ2) as shown in Figure 11.

Figure 11.

As in Figure 8 except the response values have been weighted by the inverse square of the “data uncertainty.”

[46] Unlike the annual mean inversion, fossil fuel seasonality has profound implications for the seasonal inversion. The residual fluxes estimated for the northern extratropical land regions are substantially altered when fossil fuel seasonality is included in the background flux. The residual fluxes estimated for these land regions are typically interpreted as alterations of regional biosphere exchange, either through land use change or regional-scale fluctuations of temperature or precipitation [Gurney et al., 2003]. From Figures 9 and 10, it is clear that the potential bias to the residual fluxes caused by the misspecification of the fossil fuel background flux can be as large as 50% at the height of the growing season, seriously complicating interpretation of seasonal inverse results. A more accurate portrayal of fossil fuel seasonality is required in order to interpret seasonal atmospheric CO2 inversions.

3.3. Interannual Inversion

[47] Methodological details regarding the interannual inversion are given by D. F. Baker et al. (TransCom 3 inversion intercomparison: Impact of transport model errors on the interannual variability of regional CO2 fluxes, 1988–2003, submitted to Global Biogeochemical Cycles, 2005) and K. R. Gurney et al. (manuscript in preparation, 2004). The important differences to note when comparing the interannual inversion to the seasonal or annual mean inversion relate to the CO2 observational station network chosen. The annual mean and the seasonal inversion utilized an average of CO2 observations for the years 1992 to 1996. Given the criteria detailed by Gurney et al. [2002], this led to a network composed of 75 CO2 observing stations.

[48] For the interannual case, a number of different networks have been used that span different time periods. Because inversion results are sensitive to the particular stations chosen and because adding stations to the inversion at the time they began data collection can create spurious features, inverse studies rely on discrete station networks when presenting results. The longest time period for which stations meet the TransCom criteria, spans 1980 to 2000. Over this time period, 23 stations qualify as continuously operating. The shortest qualifying network is composed of 114 stations and spans the 1995 to 2000 time period. These two networks and time periods will be used to test the interannual fossil fuel CO2 sensitivity.

[49] In Figure 12, CO2 fluxes estimated with interannual inversions that include large-scale regional shifts in fossil fuel emissions are presented for two regions. These are the two regions most affected by the inclusion of interannual shifts. Overall, the interannual variability is little changed owing to the smooth nature of the regional shifts (see Figure 4). The primary impact is a shift in the long-term mean values.

Figure 12.

Impact of spatiotemporal changes on residual fluxes for two regions. The base interannual inversion results (solid) and the perturbed interannual inversion results (dashed) are shown for (a) the European region and (b) the northern ocean region. The heavy lines denote the 23 station network, while the light lines denote the 114 station network.

[50] Both the European and the northern ocean regions are affected by the shifting fossil fuel spatial pattern. Both the 23 and 114 station networks show lessened European uptake during the 1990s owing to the fact that the global share of European fossil fuel emissions declines (see Figure 4).

[51] The northern ocean region shows a similar feature though the adjustment is less dramatic. This is due to the fact that the model response for the northern ocean and the European region are not completely orthogonal. Hence only some of the impact of the changing European fossil fuel emissions are attributed to the northern ocean region.

[52] Figure 13 shows difference plots for these two regions and the two different stations networks used. The increasing number of CO2 observational stations available later in the time period were added primarily in the northern extratropical land regions. This appears to cause a shift in the adjustment between the two regions shown. As the number of European stations increase, the residual flux is more correctly attributed to the European region and less to the northern ocean region. This is seen by the increase in the difference flux for the European region utilizing 114 stations and a decrease in the difference flux over the northern ocean.

Figure 13.

Deseasonalized flux difference (Gt C yr−1) between the base interannual run and the perturbation run for (a) Europe and (b) the northern ocean. Both the 23 and 114 station network results are shown.

[53] It is important to note that these interannual sensitivity results influence interpretation of the annual mean estimates. For example, the 1995 to 1999 mean difference for the European region (114 station network) is roughly 0.5 Gt C yr−1. This represents an approximate 40% change in the calculated 5 year average for this region relative to the base case.

4. Discussion and Conclusions

[54] Overall, the greatest impact of more realistic fossil fuel emissions within the TransCom 3 atmospheric CO2 inversions is on the interpretation of the seasonal fluxes. Recent data of fossil fuel consumption in both the United States and Europe indicate that fossil fuel emissions, do indeed, have a seasonal cycle with peak to peak amplitudes that range from 20% to 30%. It is likely that fossil fuel use in the remainder of the industrial and industrializing countries also varies over the year though subtropical latitudes may be less likely to exhibit such variations.

[55] The combination of atmospheric transport trapping the greater fossil fuel emissions in the winter months and the fact that CO2 observations are primarily at the surface results in significant changes to the estimated regional fluxes. The simple seasonal inversions performed here suggest that the lack of fossil fuel seasonality in recent inverse studies may produce biased flux estimates of up to 50% at the height of the growing season in regions where fossil fuel emissions are a large.

[56] The potential bias found here is not dependent upon model transport as the three models used in this study represent transport end-members in the TransCom 3 atmospheric inversion intercomparison. This is primarily due to the fact that the stations near the seasonal fossil source regions have been assigned large data uncertainty in the TransCom 3 inversion setup. Such stations leverage much less influence on the inverse minimization than those with relatively small data uncertainty. When, in the future, models are run at higher resolution with analyzed winds (and therefore able to simulate point locations better) the sensitivity of the residual fluxes to transport differences will likely increase.

[57] A couple of important caveats should be mentioned regarding the hypothesized seasonal fossil fuel emissions. First, real fossil fuel emissions are very likely not as smooth as those hypothesized here. The U.S. emissions data exhibit structure not captured by equation (2). The phasing may also be somewhat shifted in general and as a function of latitude or region. Finally, the real emissions appear to have an amplitude that exhibits interannual variability in addition to the broad amplitude decline over time.

[58] It is possible that fossil fuel emissions exhibit a diurnal cycle owing to the fact that transportation, lighting, heating and some industrial/commercial processes vary between night and day. This will vary somewhat by latitude but also by longitude. Though purely speculative, this may have an added impact when inversion move to solving for residual fluxes at subdaily temporal resolution.

[59] Fossil fuel seasonality appears to have little impact on the annual mean inversion. This is consistent with what one might expect from a basic numerical argument. If one considers the temperate North American region, the peak to peak span of the total biospheric flux is roughly 7 Gt C yr−1. This should be compared to a peak to peak span of roughly 0.5 Gt C yr−1 for fossil fuel emissions, assuming a 30% AF. On the basis of the span of emissions alone, one would not expect significant rectification. However, this comparison of flux extremes represents a regional integral. Given the strong heterogeneity of fossil fuel emissions, one might expect that areas proximal to fossil fuel source regions could have flux spans that rival locations with active biospheric exchange. Were station locations also proximal to these intense fossil fuel emitting locations, fossil fuel rectification may occur and be observed. This is where the results of the annual mean experiment performed here are useful. One important caveat to the annual mean results is the fact that the basis function regions are very large relative to the extent of fossil fuel source regions. Inversions that attempt to resolve basis functions at much finer scales may contain grid cells for which the seasonality of fossil emissions are on par with biospheric exchange.

[60] Annual mean inverse results are sensitive to more realistic spatiotemporal shifts in fossil fuel emissions. As demonstrated in section 3.3, consideration of the shifting fossil fuel emissions in Europe throughout the late 1990s led to a reduction in the 5 year average net uptake of roughly 40% compared to an inversion run with a fixed fossil fuel spatial pattern.

[61] The year-to-year variability of residual fluxes in a time-dependent inversion appear little affected by the inclusion of realistic shifts in the fossil fuel spatial pattern. An important caveat to this conclusion is the limited way the spatiotemporal changes were accounted for in the current study. Spatiotemporal changes at scales smaller than the large basis function regions of the TransCom 3 project may alter the interannual variability of residual fluxes. This may not only pertain to between country emission shifts but within country shifts.

[62] As atmospheric CO2 inversions solve for fluxes at smaller and smaller spatial and temporal scales, realistic spatiotemporal fossil fuel emissions are required. Furthermore, the problem of displaced energy consumption and production vis a vis CO2 emissions will be critical.

[63] Fortunately, there is no need to completely reinvent the wheel. A large community of researchers work on detailed energy production and consumption though the focus is not on CO2 emissions. Oftentimes, the emphasis is on emissions of other more short-lived but directly hazardous pollutants. There is an extremely useful collaboration to be made between the inverse modeling community and the energy modeling community, particularly as the inverse approach further reduces the spatiotemporal scale of their estimated carbon fluxes.


[64] This work was made possible through support from the National Science Foundation (OCE-9900310), NOAA (NA67RJ0152, Amend 30), the International Geosphere Biosphere Program/Global Analysis, Interpretation, and Modeling Project and, NASA Carbon Cycle Science.