The simulations for TM5 and GEOS-Chem were run from the start of 2000 through the end of 2018, and the methodology closely follows what was performed in with minor updates to transport model versions and common CO2 fluxes.

We conduct CO2 forward runs in both models from 1 January 2000 through 31 December 2018, similar to those in but with updated CarbonTracker fluxes. Initial CO2 concentrations and surface fluxes throughout the simulation come from the CarbonTracker CT2017 release (, with updates documented at http://carbontracker.noaa.gov, last access: 12 May 2023) for the period 1 January 2000 to 31 December 2016 and then CT-NRT.v2019-2 for 1 January 2017 to 31 December 2018. The initial condition field used by both models on 1 January 2000 was created by averaging together 15 years of CO2 mole fraction fields from CT2016, each sampled on 1 January of the years 2001–2015 and then scaled to the year 2000. The scaling was performed by sampling the marine boundary layer from these mole fraction fields and then comparing them to the NOAA marine-boundary-layer reference surface (https://www.gml.noaa.gov/ccgg/mbl, last access: 12 May 2023) for the target date. For use in GEOS-Chem, the CarbonTracker initial condition was interpolated vertically in pressure and horizontally in space to the GEOS-Chem grid as described in .

CT2017 and CT-NRT.v2019-2 CO2 optimized fluxes are partitioned into four flux terms: the imposed fossil-fuel term, the optimized biological flux, the imposed fire-emission flux, and the optimized oceanic flux. Each of these terms is tracked independently as a tagged tracer along with a background tracer representing the initial condition. As a result of the optimization procedure, these fluxes are generally consistent with observed atmospheric CO2 mole fractions. They were created with an inverse-modeling system based on TM5 and may have artifacts and inaccuracies associated with that model's atmospheric transport and with assumptions used in the CarbonTracker data-assimilation system. However, in the analyses conducted here, we do not require that these fluxes be completely correct, only that they are reasonably representative of actual atmospheric CO2 exchange with the surface. While there is certainly large uncertainty in CT2017 fluxes, important aspects of the flux signals, such as seasonal terrestrial net ecosystem exchange at northern latitudes, placement of fossil-fuel emissions, and estimates of biomass burning, are generally consistent with the results from other inversion systems that assimilate surface in situ CO2 data . We found a small non-conservation of tracer mass in GEOS-Chem, with a monotonic loss of about 0.25 % in fossil-fuel CO2 over the period 2000–2018. Non-conservation of natural fluxes was about half as small. The global mass differences for these tracers were removed from the concentration data before analysis.

We ran three perturbation experiments on each transport model, with each simulation extending from 1 January 2016 to 31 December 2018. Control runs use the standard vertical transport in the models, unmodified from their stock configurations. The first experiment involved turning off convection in both CTMs. These will be called the “no-convection” or “NC” runs. The second experiment involved leaving convection on but turning off diffusive mixing in the models. These will be termed “no-diffusion” (“ND”) runs. It should be noted that vertical advection as part of the resolved wind fields in each model still remains in both perturbation and control runs for both models. We introduce the notion of a “convective effect”, which we are defining as control – NC – and a “diffusive effect” as control – ND. The diffusive and convective transport effects are not independent. The two processes have significant interactions such that total parameterized vertical transport is greater than the sum of the convective and diffusive effects. Exploring this nonlinear interaction, while intriguing, is beyond the scope of this paper. As a result, experiments in which both convection and diffusion are turned off will not be discussed.

Zonal-average “curtains” (latitude by vertical dimension) of CO2 from the control and NC simulations in the two models are presented in Fig. . These curtains are shown for typical Northern Hemisphere winter (February) and summer (August) conditions. The expected buildup of CO2 from fossil emissions and terrestrial biospheric respiration in boreal winter is evident at the northern midlatitudes to high latitudes in both models' control simulations (panels a and b). The overall differences between the GEOS-Chem and TM5 control runs are shown in panel c. The convective effects in the two models for February and the GEOS-Chem minus TM5 difference in convective effects are portrayed in the second row (panels d–f). The difference in convective effects (panels f and l) bears a remarkable similarity to the control simulation difference (panels c and i). This suggests visually that the GEOS-Chem minus TM5 difference in zonal-mean CO2 is strongly driven by the convective effect. Indeed, the fields are strongly correlated (February: panels a and c, r=0.72, p<0.0001; August: panels d and f, r=0.83, p<0.0001). This will be further discussed in Sect.  below. The diffusive effect (not shown here) is about 3 times larger in magnitude but is strongly concentrated near the surface. The diffusive effects are shown in Figs. S2 and S3.

The last two rows of Fig.  show the same quantities as the first two but for Northern Hemisphere summer (August). Terrestrial biosphere uptake results in a deficit of CO2 in the troposphere poleward of the northern midlatitudes. Again, the difference in the convective effect (panel l) is visually similar to the control simulation differences (panel i).

Zonal averages of the GEOS-Chem minus TM5 difference in XCO2 as a function of latitude and time are shown in the middle two columns of Fig. . Three-year averages of the differences are shown in the side panels and present a possible proxy or metric for the transport error effect on annual source/sink estimates of CO2 from inversions. As in the previous vertical curtain plots, the convective effect differences shown in the middle row of Fig.  bear a strong resemblance to the total difference between the control runs shown in the top row of Fig. . Vertical diffusivity effects as a column average (bottom row of Fig. ) are of a much smaller magnitude. It is also worth pointing out that, despite the strong seasonal patterns of differences seen in total CO2 (Fig. c and g), the annual mean differences in total CO2 (Fig. d and h) and fossil CO2 (Fig. a and e) are quite similar and thus likely driven by differences arising from fossil fuels.

Figure  shows the 2016–2018 spatially resolved time mean XCO2 difference between GEOS-Chem and TM5. This figure illustrates the zonal variability of the XCO2 differences, which was not shown in Figs.  and . The large band of negative differences evidenced by the blue band at the lower northern latitudes is driven in large part by differences aloft shown in Fig.  and not by differences near the surface. There is an anomalously high difference over China, which is not due to a deviation of the difference pattern aloft but a combination of weaker mixing in GEOS-Chem and anomalously strong fossil-fuel emissions over eastern China. Reproducing Fig. c only over the area of enhancement in Fig. , approximately 105 to 120∘ E longitude, results in PBL concentrations that are enhanced by 1–2 ppm CO2 over the majority of the lower 20 %–25 % of the atmosphere and is the strongest contributor to the column-average results in the spatial anomaly seen in Fig. .

Seasonal summaries of the XCO2 (Fig. ) subsetted into 45∘ latitude bands are shown in Fig. S4. There is excellent agreement between the differences in the convective effect and the differences in the control simulations, suggesting that convection differences between GEOS-Chem and TM5 are the predominant control on seasonal XCO2 transport differences.

In the planetary boundary layer near intense surface sources and sinks of CO2, the monthly average differences in the diffusive effect between the models are on the order of 10 ppm (Fig. ). This is an order of magnitude larger than the model differences in the column seen in Fig. . There is a marked seasonality to the difference of the CO2 mole fraction at this level (leftmost column, panels a, d, and g), and the convective and diffusive effect patterns in both seasons (topmost two rows, panels a–f) appear anti-correlated at large scales. We will return to discuss this in Sect. .

Exploratory analysis of the location of long-term carbon sinks is commonly performed by considering large zonal bands in order to contrast the tropics, extratropics, and high latitudes , each of which has different mechanistic reasons to develop sources or sinks of carbon in a warming climate. The difference in the convection effect across CTMs, as seen in the right-hand column of Fig. , generates a significant first-order bias on these important annual zonal scales.

An examination in Fig. c and f shows that while the convective effect difference largely explains the control simulation differences between the two models away from the surface, it does not extend to the same altitude as the control simulation differences. This remaining difference bears some similarity to the difference in ND runs (Figs. S2 and S3), indicating that while convection may be the main driver of the vertical differences in the model, it is likely that low-level PBL diffusivity differences also play a role.

Agreement on the seasonal cycle of XCO2 appears quite good between the GEOS-Chem and TM5 control runs, with the amplitude of the average zonal seasonal differences on the order of 1 ppm or less at 45∘ N and poleward. GEOS-Chem minus TM5 differences in modeled seasonal cycles at TCCON locations are 10 %–15 % of the amplitudes reported by . While this difference is small, it is likely still significant to science hypotheses attempting to explain observed decadal-scale changes in seasonal amplitude . Accounting for differences in convection reduces that difference by another order of magnitude, resulting in great agreement in XCO2 on seasonal-cycle amplitudes. Hence a focus on improving the modeling of convective mixing of trace gases could have a significant impact on the ability to constrain high-latitude seasonality.

The effect of uncertainty in the parameterized modeling of vertical mixing, and convection in particular, drives systematic differences in XCO2. These concentration differences then manifest themselves as the first-order source of flux bias across large zonal bands amongst satellite CO2-constrained flux-inversion models . However, in some regions there are notable exceptions to the zonal mean of transport differences. One of these is over eastern Asia in the general area of China (Fig. ). This anomaly to the zonal average largely arises from model differences in the spatially varying convection field acting on large regional sources of CO2 fossil-fuel consumption . While total CO2 is plotted in Fig. , one can see that the signal comes largely from the fossil-fuel-related portion of the CO2 budget (cf. Figs. S5, S6, and S7). Similar patterns emerge across areas of critical biological importance, such as the Amazon and equatorial Africa (Fig. S7), and even emerge at the national scales there (Fig. S8). These could result in regional flux anomalies that are dependent on the particular CTM being used in a flux inversion.

While parameterized diffusion and convection cause mixing in different parts of the column, they both act to move signals of surface exchange up, away from the PBL, and into the free troposphere. Historically, measurements of active and passive chemical species have been made more commonly within the PBL or at the surface than in the free troposphere. The availability of measurements near the surface without a correspondingly strong constraint on upper-atmospheric abundances means that those measurements speak strongly to the overall rate of ventilation of the PBL and not necessarily which process is responsible for the needed mixing. We speculate that CTMs may meet this constraint by using a different overall balance of convection and diffusion. The combination of remotely sensed total-column abundance with in situ measurements concentrated in the PBL may help to provide the needed constraint on vertical distribution to identify a correct balance of these mixing processes. In particular, this is an area where aircraft observations, campaign data (e.g., Atmospheric Tomography Mission (ATOM), ACT-America), and more operational data (e.g., In-Service Aircraft for a Global Observing System (IAGOS), NOAA light aircraft profiles) could provide a useful constraint.

The parent models for GEOS-Chem and TM5 simulate convection differently. Some of the vertical movement associated with convection is explicitly resolved, depending on the model grid resolution. Non-resolved movement is parameterized using significantly different schemes. NASA's GEOS-5 MERRA2 reanalysis uses the relaxed Arakawa–Schubert convection scheme , an updraft-only detraining plume cloud model , to provide driving convective mass fluxes used for GEOS-Chem. Version Cy31r2 of the IFS model was used to create the ERA-Interim reanalysis used to drive the present TM5 simulations. The IFS uses the Tiedtke convection scheme to provide upward and downward plume entrainment and detrainment mass fluxes at each model level and as a means to represent shallow, intermediate, and deep convection. Both GEOS-Chem and TM5 (based on the TM3 model from ) interpret convective mass fluxes from their parent models to drive relatively simple mixing schemes. This mixing can be represented by a matrix specifying exchange among the layers in the column of a given grid cell.

While the RAS and Tiedtke convective parameterizations are different, we can still perform qualitative comparisons of the upward convective mass fluxes from the parent models under investigation here. While the downdraft component from TM5 is important, it is an order of magnitude weaker than the updraft component, as can be seen in Fig. S9. The comparison (Fig. S9) shows convective activity that is significantly different between the two models and highlights shallow convection features driving lower-tropospheric mixing in TM5 that do not appear in GEOS-Chem. This would appear to support past research highlighting differences between shallow convection features in MERRA and ERA-Interim . This would suggest that the differences in CTM convective transport reported here result largely from differences in convection in the parent models as opposed to variations in how convective mixing is implemented in the CTMs. This confirms the findings of , , and . Comparisons to long-lived trace gases like SF6 might allow more definitive conclusions about how differences in parent-model convection and differences in their re-implementations in CTMs drive the large-scale differences seen in this paper . Other metrics such as the stratospheric age of air could provide insight into the differences seen here.

Recent analyses suggest that vertical transport in GEOS-Chem may be responsible for systematic biases in model performance against comparisons to CH4 and SF6 observations . Part of this suspected vertical mixing issue may be due to imperfect reproduction of parent GEOS5 model transport . In preliminary analysis of meridional gradients of trace gases, the GEOS5 parent model does not appear to exhibit the same systematic biases as the GEOS-Chem CTM (personal communication: Brad Weir, NASA-GMAO). When using offline parent convective mass flux fields, in theory, convective mixing of trace gases via resolved vertical velocity should be damped with increased averaging in time and space and decreased horizontal model resolution . Furthermore, the coarse temporal nature, e.g., 3 h or more, of the convective mass-flux averaging leads to an information loss because the higher time-resolution covariance between tracer fields and vertical motion is lost. The resolved vertical velocity in 0.5∘ by 0.667∘ MERRA2 is similar in location and magnitude to that from the approximately 80 km ERA-Interim (Sourish Basu, NASA-GMAO, personal communication, 9 August 2022). This should not be surprising due to the similar horizontal resolutions of the model fields and suggests that the averaging of resolved vertical velocity fields to the coarser-resolution CTM grids is likely not the reason for the differences shown in this paper.

Ideally, one would desire a CTM's transport to asymptotically converge to the parent model's transport as model spatial and temporal resolution increases to the native resolution of the parent model, but this has not been demonstrated. It is worth noting that past work utilizing two CTMs acting on the same parent meteorology has demonstrated the difficulty in characterizing this convergence. Tests are currently underway with high time- and space-resolution GEOS5 meteorology via the GEOS-Chem High Performance model to gauge this convergence. These tests will help to determine whether results such as are sufficient to explain all deficiencies in CTM vertical transport.

It is also worth noting that despite the clear patterns of difference in the large-scale convective mass fluxes from parent models used as inputs into GEOS-Chem and TM5 (see Fig. S9), there are likely other factors at play which could cause differences in vertical transport. For its advection scheme, TM5 uses parent-model mass fluxes and a corresponding flux-form advection scheme, whereas GEOS-Chem explicitly uses interpolated parent-model winds to diagnose mass fluxes for advection. The use of winds to drive advection, as opposed to mass fluxes, has been shown to be a likely source of error and bias . As a result of this, tests are also currently underway using the GEOS-Chem High Performance model to investigate the magnitude of this bias and to what degree those model errors and related errors in horizontal divergence might be related to vertical transport in GEOS-Chem (Sebastian Eastham, personal communication, 10 June 2022).