For many decades, the Canadian Meteorological Centre (CMC) has been producing operational weather forecasts for public dissemination. Since 24 February 1997, these forecasts have utilized the Global Environmental Multiscale (GEM) model (Côté et al., 1998a, b; Girard et al., 2014). GEM is a grid-point model which solves the hydrostatic (global domain) or nonhydrostatic (Yeh et al., 2002) (regional domain) primitive equations using a hybrid terrain-following vertical coordinate (Girard et al., 2014). As of February 2013, the grid spacing of the global model is roughly 25 km, originally using a regular lat–long grid and, since December 2015, a yin–yang grid (Qaddouri and Lee, 2011). There are 80 vertical levels spanning the surface to 0.1 hPa. The usual physical processes of radiation (Li and Barker, 2005), boundary layer mixing (Bélair et al., 1999), shallow (Bélair et al., 2005) and deep convection (Kain and Fritsch, 1990; Kain, 2004), orographic gravity wave drag (McFarlane, 1987) and nonorographic gravity wave drag (Hines, 1997a, b) are included in all model configurations. The land surface model and assimilation scheme are described in Bélair et al. (2003a, b). More details of the physics package are found in Mailhot et al. (1998).

Operational air quality forecasts have been produced by CMC since 2001 in order to provide real-time forecasts of the air quality health index on a limited area domain covering most of North America. As of 18 November 2009, these forecasts have utilized GEM-MACH (Modelling Air quality and CHemistry) (Moran et al., 2010; Robichaud and Ménard, 2014; Makar et al., 2015). GEM-MACH is a version of GEM in which complete tropospheric chemistry (involving over 100 chemical reactions) is modelled online, where “online” refers to the fact that the chemistry module is fully integrated into the meteorological model time step. The operational products involve an analysis of ground-level ozone, fine and coarse particulate matter (PM2.5 and PM10), NO2 and SO2 over a limited area domain covering North America (Robichaud and Ménard, 2014). The grid spacing currently used is 10 km horizontally, with 80 vertical levels from the surface to 0.1 hPa. The operational forecasts are driven by time evolving meteorological boundary conditions from the operational regional deterministic prediction system (Fillion et al., 2010; Caron et al., 2015), while the chemical boundary conditions are defined using predetermined seasonally-averaged states. A global version of GEM-MACH is also in development for the purpose of providing boundary conditions for the regional model and a parameterized stratospheric chemistry model (McLinden et al., 2000) is used for UV index forecasting.

Our primary interest is in global greenhouse gas distributions, and thus we chose to use the global GEM-MACH configuration. In the future, extensions of our system for regional greenhouse gas simulations could be based on the operational regional GEM-MACH configuration. By definition, an operational forecasting system is constantly changing. Since our period of interest commences in 2009 with the launch of GOSAT on 23 January and since the upper boundary of GEM was raised from 10 to 0.1 hPa on 22 June 2009 (Charron et al., 2012), this stratospheric model configuration was chosen. However, for computational expediency (especially during the model development phase) the grid spacing was coarsened to 0.9∘ (400 × 200 grid points), which is roughly twice the grid spacing used by CMC's global deterministic prediction system (800 × 600 grid points) in 2009. The model time step is 15 min.

Our primary focus in this work is global carbon dioxide simulation, but extensions for other greenhouse gases (methane and CO) are also being developed. For that we employ a simple parameterized climate chemistry involving a single OH reaction for the methane and CO simulations. This chemical module is activated from the GEM-MACH chemical interface, which is also used to handle emission inputs. This simplified model version, which only includes the treatment of greenhouse gas (chemistry and transport), will be called GEM-MACH-GHG hereafter.

The dry air mass of the atmosphere is known to be constant, since changes in trace gases are very small (Trenberth, 1981; Trenberth and Smith, 2005). However, as with many weather and climate prediction models, GEM does not conserve dry air mass. Specifically, GEM loses 0.1 hPa in global mean surface pressure during a 10-day forecast, which is precisely the same rate as that seen in the ECMWF model (Diamantakis and Flemming, 2014). This loss is only 0.01 % of the global mass and thus there is a negligible impact on medium-range weather forecasts. However, for longer simulations relevant for climate timescales, this error can accumulate. Thus GEM (as does the ECMWF and other models) has a parameter to allow the global mean surface pressure to be conserved by adding a spatially uniform adjustment to each grid cell. The constant is determined by the constraint that the air mass at the end of the dynamics step equal that at the start of the step. For our simulations of tracer transport, it is necessary to use this switch to enforce the conservation of dry air mass.

The advection scheme in GEM uses a semi-Lagrangian approach as it affords longer time steps and the computational efficiency desirable in an operational context. However, semi-Lagrangian schemes are well known to be non-conservative (Williamson, 1990; Staniforth and Côté, 1991). GEM is a grid point model, and the semi-Lagrangian approach involves first determining the upstream positions of the grid cells (using a 3-D trajectory in our case) and then interpolating the value of the advected field at these locations. During this first step, gradients in the wind field will limit the accuracy of advection and during the second step, errors associated with the interpolation of the advected field can deteriorate species mass conservation. By combining a finite volume approach with the semi-Lagrangian scheme, it is possible to devise inherently mass-conserving schemes such as SLICE (Semi-Lagrangian Inherently Conserving and Efficient) (Zerroukat and Allen, 2012). Indeed, this scheme is being investigated for implementation with GEM in the future. In the meantime, an interim solution is needed. The approach taken here, as in Diamantakis and Flemming (2014), is to adopt a global mass fixer. To be clear, the global mass is obtained by summing the individual masses of carbon in each grid box. The mass of carbon in a grid box is determined from the mixing ratio (mass of carbon divided by the mass of dry air) times the mass of dry air in the same box. A global mass fixer scheme computes the global mass of tracer at the beginning and end of the advection step and then distributes the change in global mass among various grid cells. There is no unique way of distributing the mass spatially, so different choices result in different mass fixer schemes. While a few approaches were tried and tested with a few different chemical species (ozone, CH4 and CO2), the one which produced the most physically desirable results was that by Bermejo and Conde (2002). In this scheme, the global mass is distributed according to the smoothness of the field. That is, mass is preferentially adjusted where gradients are larger (and interpolation error is known to be larger). The exact scheme used in GEM is precisely that selected by ECMWF and it is described in Diamantakis and Flemming (2014, Sect. 3.1). For greenhouse gas transport, the ECMWF forecast model also uses the Bermejo–Conde scheme (Agusti-Panareda et al., 2016).

For tracers, another issue with the interpolation step of the semi-Lagrangian advection scheme is the potential creation of spurious subgrid-scale structure due to Gibbs effects. To avoid this problem, GEM uses a quasi-monotonic interpolation scheme (Bermejo and Staniforth, 1992) which combines high-order and low-order interpolation schemes to prevent overshoots and undershoots, thereby preventing the formation of spurious extrema. However, just as Flemming and Huijnen (2011) noted, enforcing monotonicity was found to worsen the problem of mass non-conservation because it tends to diffuse gradients. Therefore, monotonicity was replaced by an iterative locally mass conserving (ILMC) scheme (Sørensen et al., 2013). The idea behind the ILMC scheme is to locally preserve the shape of the field and its gradients by distributing the excess (or deficit of) mass due to spurious extrema in the cubic interpolated field to ever increasing shells around the upstream departure point but in such a way that spurious extrema are avoided. By design, the use of ILMC does not impact our lack of global mass conservation, so it is used for preserving positive definiteness of tracer fields in place of a quasi-monotonic interpolation scheme. The ILMC is performed first, and then the Bermejo and Conde (2002) scheme is applied to the ILMC-corrected field. Details on the implementation of monotonic and mass-conservation schemes in GEM and their impact on species transport are found in de Grandpré et al. (2016).

The primitive equations solved by GEM are naturally written in terms of a moist density or pressure variable. However, when tracers are defined as mixing ratios with respect to moist air, tracers become coupled to the water vapour evolution. Thus one of two options must be taken. Either the tracer variable must be redefined every time the water vapour field is modified in the model or the tracers must be defined as mixing ratios with respect to dry air (e.g. Neale et al., 2010). The latter option has the advantage that measurements of CO2 are frequently made in terms of dry mole fraction and are thus more easily related to a mixing ratio with respect to dry air. Since the nominal tracer equation within GEM assumed a moist mixing ratio, for this work GEM was modified to permit tracers to be defined as mixing ratios with respect to dry air (DMR). This involved (1) modifying the global mean surface pressure adjustment to ensure global dry air mass conservation, (2) converting the mass fixer scheme (i.e. the Bermejo–Conde scheme) and the ILMC to deal with DMR, (3) modifying the vertical diffusion equation to handle DMR and (4) ensuring emissions are correctly inserted into GEM's bottom model layer. Once all of these changes had been made, the tracer mass change in a given time step was found to still display a coupling to the water vapour change in that same time step. The reason was found to be due to the fact that the continuity equation in GEM does not account for the change in surface pressure due to the change in water vapour which occurs as a result of mass flux at the Earth's surface (i.e. because of precipitation or evaporation). By adding a new adjustment to surface pressure field after the physics step to account for the change in global water vapour mass, and correspondingly redefining the tracer variable using a vertical regridding approach similar to Jöckel et al. (2001) except for the use of dry pressure coordinates, global mass conservation of CO2 was obtained during a model forecast. This deficiency in GEM's continuity equation is not unusual as it was also present in NASA GMAO's GEOS5 model (Takacs et al., 2015). The adjustment to the model dynamics done here to account for the modified continuity equation is rather similar to that described in Sect. 2a of Takacs et al. (2015) although our work was done independently. The main difference is that only water vapour mass is considered here whereas cloud liquid water and cloud ice mass are also considered in Takacs et al. (2015) (although the authors note that additional masses due to liquid and ice phases are negligible). As these authors demonstrate, without the correction to the model's continuity equation, dry air mass conservation is not assured. They also note that in the context of an assimilation cycle, further constraints on dry air mass are needed during the analysis and initialization steps. Furthermore, they show that the impact of the errors is evident in the mismatch of global water vapour tendency based on the water vapour field itself vs. that based on precipitation minus evaporation changes for reanalysis products such as MERRA (Rienecker et al., 2011) and ERA-Interim (Dee et al., 2011).

It is standard to apply an explicit high-order (typically ∇6) diffusion operator to the meteorological fields in applications involving the global GEM model. It is arguably consistent therefore to apply the same level of diffusion to the tracer fields. However, because the constituent variables are defined as mixing ratios, the operator is not mass conservative. Because of the effort involved in obtaining a careful accounting of tracer mass (described in Sect. 3.2), it was decided to not apply any horizontal diffusion to the tracers.

The parameterization of deep convection most frequently used by GEM and GEM-MACH is due to Kain and Fritsch (1990). The Kain and Fritsch (KF) scheme is based on a single column bulk mass flux approach. Entrainment of ambient air into the cloud environment associated with updrafts and downdrafts is proportional to the corresponding mass flux and inversely proportional to the cloud radius. So narrower convective towers experience more entrainment of lower-buoyancy ambient air and consequently have less intensity and lower cloud tops. The KF scheme is used in several forecast models (e.g. Japanese Meteorological Agency model, Saito, 2012; Bologna Limited-Area Model (BOLAM), Lagouvardos et al., 2003; High-Resolution Limited-Area Model (HIRLAM), Eerola, 2013; Weather Research and Forecasting Nonhydrostatic Mesoscale Model (WRF-NMM), Gallus Jr. and Bresch, 2006). With the KF scheme, GEM has a good representation of convectively coupled waves and is able to capture the Madden–Julian oscillation (Lin et al., 2008).

The version of the KF scheme used for global deterministic prediction, which was our starting point, had to be modified for the purpose of greenhouse gas transport. The original parameters resulted in too frequent penetration of convection into the stratosphere in the tropics. This is because the updraft core radius had been set to 1500 km globally. This is a reasonable value for extratropical convection over land, and since the target region of ECCC's forecasting systems is Canada, it is a valid choice. However, observations (Lucas et al., 1994, and references therein) show that the updraft core radius varies with latitude and from land to ocean. Thus over the oceans, a value of 900 km is used in the tropics with 1000 km in the extratropics. Over tropical land grid points, a value of 1200 km is used. With these settings, tropical convection overshoots fall in the correct range (below 80 hPa). However, the model climatology is altered. The parameter changes impact land–sea contrasts which influence stationary Rossby wave generation and the spin-up of the Brewer–Dobson circulation in the stratosphere. They also affect flow over topography, which impacts orographic wave drag and its associated transport circulations. An animation (Fig. S1 in the Supplement) shows a comparison of the impact of changing KF parameters vs. that of adding convective tracer transport on CO2 evolution. As expected, the change in parameters impacts the stratospheric distribution after a few months of simulation, whereas the introduction of tracer transport through deep convection impacts the tropical tropospheric CO2 distribution at all times as well as the Northern Hemisphere in summer. The zonal mean values are small but so too are zonal standard deviations (both are less than 0.3 ppm). Another animation which compares the impact of changing KF parameters to that of adding convective tracer transport on column mean or XCO2 (Fig. S2 in the Supplement) reveals that the magnitude of the impact is smaller for the change in parameters (maxima of 0.3 ppm) than for the introduction of tracer transport through deep convection (maxima of 0.8 ppm).

Turbulence in the PBL is important for the transport of heat, momentum, moisture and constituent fluxes from the surface to the atmosphere. The PBL scheme in GEM is described in Bélair et al. (1999), Benoit et al. (1989) and Mailhot and Benoit (1982). Since a summary of GEM's PBL scheme was recently presented in McTaggart-Cowan and Zadra (2015) and Aliabadi et al. (2016), we note here only the main differences between GEM's PBL parameterization and those of other models used for greenhouse transport or flux inversion.

Shallow convection also exerts a significant impact on the tracer distribution and vertical mixing in the lower troposphere (e.g. Dacre et al., 2007). The shallow convection scheme in GEM is a modified Kuo parameterization (Kuo, 1974) developed at ECCC (Bélair et al., 2005). As with the original Kuo scheme it does not address convective tracer transport. However, unlike the KF scheme it is not based on a mass flux formulation that can be easily adapted to handle tracers. For this reason the version of GEM used for this study does not include tracer transport by shallow convection.

The vertical transport of greenhouse gas fluxes follows that of other constituents and is described by ∂C∂t=-1ρ∂∂zρw′C‾=1ρ∂∂zρK∂C∂z-γ, where C is the constituent mixing ratio on resolved scales, ρ is air density, w′ is subgrid-scale vertical velocity and the product with an overbar is the vertical flux of constituent due to subgrid-scale turbulence. The first equality denotes the impact of subgrid-scale motions on the resolved constituent distribution. The subgrid-scale flux is parameterized through the second equality and is a function of the vertical gradient of the constituent. γ is a counter gradient flux relevant for an unstable PBL. K is the thermal eddy diffusivity and it depends on properties of the flow. Most models define K diagnostically in terms of an eddy length scale and local gradients of wind and virtual potential temperature. Such schemes are said to invoke a first-order closure. However, GEM's scheme specifies K through a prognostic equation for turbulent kinetic energy and is thus deemed a 1.5-order closure scheme (Holtslag, 2015). When K is determined diagnostically through local flow properties, the case of an unstable or strongly convective PBL is not well represented. Thus, an extension for non-local mixing due to large-scale eddies is often invoked in which the counter-gradient term represents large eddy flux and K permits eddy length scales comparable to the PBL height in the case of unstable boundary layers. CarbonTracker (Peters et al., 2004) and GEOS-Chem (Lin and McElroy, 2010) both use such a nonlocal scheme based on Holtslag and Boville (1993). ECMWF also uses a diagnostic nonlocal scheme (Köhler et al., 2011). In GEM's 1.5-order closure scheme, K can also represent nonlocal effects due to large eddies in an unstable PBL through a careful definition of eddy length scale (Bélair et al., 1999). One notable difference between GEM's prognostic nonlocal scheme and diagnostic nonlocal schemes is that the latter require PBL height as an input for determining K, whereas in GEM's scheme the PBL height is diagnosed from the turbulent kinetic energy profile (so K is not a direct function of PBL height).

A minimum value for eddy diffusivity of 0.1 m2 s-1 is imposed in the PBL in GEM-MACH for air quality applications. This value was empirically chosen to balance the impacts on the various tropospheric reactive species (P. Makar, personal communication, 2012). In this work, the minimum value was raised to 10 m2 s-1 because a value of 1 or 0.1 was found to occasionally lead to too little mixing. This was most evident in spuriously low CO2 concentrations in the daytime during summer when biospheric fluxes are large and negative. (Note that the eddy diffusivity is kept fully varying in space – it is only the minimum value that is slightly altered. This is in contrast to earlier versions of GEOS-Chem in which instantaneous full mixing of emissions and mixing ratios occurred in the PBL. See Lin and McElroy, 2010, for example.) A negative consequence of raising the minimum value to 10 is a reduced amplitude of the diurnal cycle of CO2 (as will be seen in Sect. 4). However, many models have difficulty in capturing the amplitude of the diurnal cycle (Law et al., 2008; Patra et al., 2008) so this consequence was considered tolerable at present. Moreover, the comparison of model results to measurements on sub-diurnal timescales is very difficult, leading Law et al. (2008) to recommend that “comparisons with observations should only be made for daily or longer time averages, and possibly for only part of the diurnal cycle”. Thus, many inversion systems assimilate only afternoon mean observations and do not attempt to capture sub-diurnal timescales (Peters et al., 2010).

To transport greenhouse gases, a simulation cycle is used. Meteorological analyses archived at the CMC are inserted periodically to constrain the transport to reality. While operational assimilation cycles use an update frequency of 6 h, model forecasts during such a short period will be contaminated by spurious gravity wave generation, as evident in surface pressure time series (as well as other fields) (see Daley, 1991, chap. 6). However, after 24 h, spurious gravity waves have generally dispersed so an update frequency of 24 h was chosen, just as in Agustí-Panareda et al. (2014). (Note that a 6 h update cycle had also been tested and the resulting CO2 evolution was very close to that obtained with a 24 h update cycle, but because the stratospheric circulation was poorer the 24 h update cycle is preferred.) A schematic diagram of the transport cycle is depicted in Fig. 1. The upper half of the figure depicts the operational system which collects meteorological observations over a 6 h window and uses these in a 4-D variational assimilation or 4D-Var (Gauthier et al., 2007) to generate an estimate of the meteorological state for a deterministic prediction. Although the operational deterministic prediction system now uses a hybrid approach to background error covariance estimation (Buehner et al., 2015), the analyses used here (from 2009 to 2010) were generated using the previously operational 4D-Var system (Charron et al., 2012). On the cycle's start date at 00:00 UTC, the meteorological analysis is combined with an initial state for greenhouse gases (here CO2 only) and a 24 h coupled meteorology and tracer forecast is produced. The 24 h tracer forecast is subsequently combined with the meteorological analysis for the next day at 00:00 UTC (blue boxes) to produce a new coupled initial state for the second day's forecast (red filled circles). Note that no additional “initialization” or filtering (see Daley, 1991, chap. 6, 9, 10) scheme such as a digital filter or incremental analysis updates (Bloom et al., 1996) is used, as the impact on the CO2 field was found negligible. Also note that in our simulation cycles, no assimilation of greenhouse gases is performed. An assimilation system is currently in development as discussed in Sect. 6.

In Fig. 1, every time a new analysis is inserted, a new surface pressure field informed by atmospheric observations is introduced. This surface pressure analysis will differ from the 24 h forecast of surface pressure because the model is not perfect, so the model forecast cycle will experience an abrupt shift in global mean surface pressure and, hence, global air mass. The change in global air mass will then impact the global tracer mass. To maintain global tracer mass conservation across this discontinuity, it is necessary to redefine the tracer mixing ratio for the change in air mass. The scheme adopted follows that used by GEM for the global surface pressure adjustment. Specifically, a spatially uniform increment in tracer mixing ratio is determined based on the constraint that the global tracer mass be preserved (see Appendix A for details). The adjustment so obtained is small, with a mean value of -8 × 10-5 ppm and a standard deviation of 0.015 ppm over a 1-year simulation. Since the surface pressure analyses are stored with only 16 bit precision (because the analysis uncertainty does not warrant more precision than this), this ultimately limits our knowledge of the tracer mixing ratio and the local tracer mass. With our global adjustment scheme, the adjustments are much smaller than 16 bit precision will allow, and thus the scheme is justifiable.

ECCC has been delivering operational weather forecasts for over 40 years and the products have been based on the GEM model for 19 years. As with many national weather forecast centres, ECCC participates in regular intercomparisons of operational forecasts following WMO standards. For the global configuration, forecasts on the medium (up to 10 days) range are compared every month and are available at http://web-cmoi.cmc.ec.gc.ca/verification/monthly/observations/obs_monthly_e.html. Thus the quality of GEM transport has been documented. However, since changes were made to the model that affect weather prediction (specifically, the change to the continuity equation, the implementation of conservation of the dry air contribution to the global mean surface pressure and the convective transport scheme parameters) it is necessary to demonstrate the quality of the meteorological fields for the purpose of greenhouse gas transport. Since offline transport models often use reanalyses such as ERA-Interim or MERRA to transport constituents, we compare our 24 h forecasts against these products. In general, analyses more closely match observations than do forecasts because models are imperfect, and reanalyses should be superior in quality to operational analyses because the former use a superset of observations and a single, recent model version. Thus, our 24 h forecasts cannot be expected to be superior to any of ERAI, MERRA or JRA-55 (Kobayashi et al., 2015) reanalyses. Nevertheless, because of the usage of a 24 h forecast cycle (Fig. 1), it is important to verify that transport on this forecast range is reasonable, and reanalyses serve as high-quality reference fields.

The initial meteorological fields used at the start of every cycle (Fig. 1) come from archived operational products interpolated to our lower-resolution grid and topography. Thus our transport can only drift from reality for 24 h before it is corrected so that, even with our modifications to GEM, significant transport errors are not expected. Nevertheless, since changes of several hPa in 3-day forecasts of surface pressure do arise from the adjustment to the continuity equation and these could impact synoptic-scale forecasts, it is worth verifying the quality of our modified transport. Figure 2 (left column) shows the monthly mean difference of temperature, zonal and meridional wind differences between GEM-MACH-GHG and ERAI fields for July 2009 based on 6-hourly difference fields. ERAI fields were obtained from http://reanalysis.org on pressure levels in GRIB format and interpolated to GEM's grid at 1.5∘ resolution. GEM fields were also output on the same pressure levels and resolution. The mean differences can be compared to those between other reanalyses: MERRA and ERAI (middle column) and JRA-55 and ERAI (right column). The latter difference fields were obtained from http://reanalysis.org using the Web-based Reanalysis Intercomparison Tools (WRIT; Smith et al., 2014) with the values saved in NetCDF format for plotting. It is evident that for all fields, GEM-MACH-GHG is as similar to ERAI as other reanalysis products although our products are 24 h forecasts (not analyses or reanalyses). For temperature (top row), the largest differences appear in the stratosphere for all models. In the stratosphere where models and observations are biased, assimilation can be challenging (Polavarapu and Pulido, 2016), so this result is not surprising. The extratropical zonal mean stratosphere is dominated by the slow Brewer–Dobson circulation, which is forced by waves propagating upward from the troposphere (Andrews et al., 1987; Vallis, 2006). The spectrum of waves from a given model depends on parameterizations such as convection and gravity wave drag which generate high-frequency subgrid-scale waves, as well as resolved waves. Therefore, different models can be expected to have rather different spectra and thus different forcing of the Brewer–Dobson circulation. For wind fields, the largest differences occur in the tropics. Zonal wind differences are greatest in the tropical stratosphere (middle row). The zonal mean tropical stratosphere is dominated by the quasi-biennial oscillation (QBO), which is driven by vertically propagating waves. Climate models have difficulty capturing the QBO as it depends on vertical resolution, gravity wave drag parameterizations and the spectrum of waves generated by tropical convection schemes (Baldwin et al., 2001; Campbell and Shepherd, 2005). Analyses can capture the QBO by assimilating the few radiosonde wind observations available in the tropics. However, the amplitude and phase of the QBO captured may depend on the underlying model and assimilation system characteristics. In general, since few direct measurements of winds are available to constrain analyses, and there are no simple dynamical balances available to infer winds from observations related to mass fields, model biases in the tropics are difficult to correct with data assimilation (Polavarapu and Pulido, 2016). In Fig. 2, the meridional winds (bottom row) differ most in the tropical troposphere where these issues of lack of measurements, and simple dynamical balances will prevail.

In summary, the meteorological fields used to transport CO2 in our system are similar in quality to those from reanalyses which have been used with offline transport models. Reanalyses are not perfect and their uncertainty can be quantified through the degree of disagreement with other reanalysis products. Thus, when offline transport models use reanalyses, this uncertainty impacts their transport quality. While we use a 24 h update cycle, this subsection has demonstrated that throughout the 24 h forecast the uncertainty is comparable to that of an individual reanalysis product. Thus results on the sensitivity of transport error to meteorological uncertainty obtained with our sequence of 24 h forecasts has direct relevance to transport errors obtained with a 6 h insertion of reanalysis products. While statistics for July 2009 were shown in Fig. 2, those for December 2009, July 2010 and December 2010 are found in the Supplement (Figs. S3–S5).

Having established that the meteorological fields that will transport constituents are sufficiently accurate, the CO2 evolution can be assessed. Since the goal is to assess GEM-MACH-GHG as a transport model, realistic surface-to-atmosphere fluxes are required. Without realistic sources and sinks of CO2, discrepancies with observations could be equally attributed to erroneous fluxes as to erroneous transport. Even with a good source of retrieved atmospheric fluxes, the evaluation of GEM-MACH-GHG transport requires care (as discussed below). For this purpose, posterior fluxes from CarbonTracker 2013B (hereafter referred to as CT2013B; Peters et al., 2007) were obtained and regridded in a mass conservative way to GEM's grid. CarbonTracker was chosen because it is generally recognized as a good product, is regularly monitored and updated and is readily available from http://carbontracker.noaa.gov. These fluxes were also used for a similar purpose in Houweling et al. (2010). CT2013B fluxes are available every 3 h, with fluxes inserted at every model timestep. With an initial condition from CarbonTracker for 1 January 2009 00:00 UTC and the CT2013B fluxes, GEM-MACH-GHG was run for all of 2009–2010. The resulting CO2 simulations are compared against observations assimilated by CT2013B (continuous observations), observations not assimilated by CT2013B (columns from Total Carbon Column Observing Network (TCCON) and aircraft profiles) and gridded 3-D concentration fields from CT2013B.

Figure 3 compares CO2 time series from GEM-MACH-GHG with CT2013B fluxes to surface observations from ECCC's greenhouse gas measurement network (Worthy et al., 2005) at Alert, East Trout Lake and Sable Island. Alert is a remote Arctic site far from CO2 sources, so it can be used to assess long-range transport. East Trout Lake is close to sources and will reflect diurnal variations in CO2 fluxes convolved with boundary layer mixing. Sable Island is downstream of sources on the eastern edge of the continent and effectively reveals synoptic-scale variability. The comparison at Alert (top panel) reveals general agreement between the model and measurements throughout the 2-year period, with the exception of low values during the autumn of both years. This departure can be explained by a discrepancy between CarbonTracker's transport and GEM-MACH-GHG's transport. CT2013B fluxes were obtained by minimizing the difference between observations and CarbonTracker's forecasts and thus reflect the amount of flux needed to bring CarbonTracker in line with measurements. Since CarbonTracker's transport is not perfect, the retrieved fluxes retain a signature of CarbonTracker's transport errors which may or may not match GEM-MACH-GHG's transport errors. To demonstrate this point, GEM-MACH-GHG was run with another set of retrieved fluxes, this time from GEOS-Chem (Deng et al., 2016), for July 2009–December 2010 and no such autumnal drift is seen (Fig. S6). Thus GEM-MACH-GHG is potentially able to capture long and seasonal timescales of CO2 transport. The time series at East Trout Lake (middle panel) shows that the smaller amplitude of the diurnal cycle in winter relative to summer is captured by the model. However, CarbonTracker's diurnal cycle amplitude in summer at this site appears too large. The amplitude of the diurnal cycle is further discussed in the context of Fig. 4. Finally, the bottom panel compares observed and modelled time series at Sable Island where synoptic-scale variations are more evident. It is clear that the model captures synoptic scales well, as expected from a weather forecast model. In particular, variations on the 1-month timescale are seen in August and September of 2009 and the model follows these variations well. The ability of GEM-MACH-GHG to capture synoptic scales is important, since the ground-based measurement network can resolve the global carbon budget and very large (continental) spatial scales (e.g. Peylin et al., 2013). Then in a data assimilation or flux inversion system, the model can supplement the large spatial scales observable with this network with realistic synoptic scales (e.g. Agustí-Panareda et al., 2014).

The mean diurnal cycle at individual stations can reveal more clearly the realism of a model's boundary layer variation. Here we choose two sites close to sources and sinks because the amplitude of the diurnal cycle at such sites should vary through the year. Figure 4 shows that the model's mean diurnal cycle at East Trout Lake with GEM-MACH-GHG with CT2013B (blue) fluxes compare well to measurements (black), whereas CT2013B (green) has a too-large amplitude in April and July 2009 (consistent with Fig. 3). However, the model's behaviour varies with location and time. At Fraserdale, GEM-MACH-GHG's diurnal cycle amplitude is clearly too low in all months whereas CarbonTracker fares better in July and October 2009. The fact that the diurnal variability from GEM-MACH-GHG is lower than that observed stems from the choice made for the minimum value of eddy diffusivity (Sect. 3.5). Lowering this value can increase the amplitude of the diurnal cycle, but with the increased risk of occasional spuriously low values of CO2 during summer daytime. As noted earlier, it is difficult to compare models to measurements on sub-diurnal timescales (Law et al., 2008; Patra et al., 2008) and most models have difficulty in capturing boundary layer evolution so flux inversions typically use only afternoon mean measurements.

GEM-MACH-GHG transport is directly compared to CarbonTracker's transport in Figs. 5 and 6. Figure 5 presents the column mean CO2 weighted by air mass on 1 July 2009 00:00 UTC and 31 December 2009 00:00 UTC from GEM-MACH-GHG with CT2013B fluxes (top panel), CT2013B (middle panel) and the difference between these two (bottom panel). The higher resolution of GEM-MACH-GHG is evident particularly in July, when the largest differences occur at small spatial scales. CT2013B has more CO2 than GEM-MACH-GHG in both the tropics and the Northern Hemisphere. However, in winter (right column) CT2013B has more CO2 mainly in the tropics. The tropical differences in both seasons are likely related to differences in convection schemes in the two models. The increased CO2 in the northern midlatitudes in boreal summer may be due to differing meridional transport or to differing rates of vertical mixing or a combination of both. Zonal mean fields also reveal that the greatest differences between the two GEM-MACH-GHG simulations and CT2013B are in the summer (Fig. 6, top panel). Throughout the troposphere and near the surface, CT2013B has more CO2. In winter, CT2013B has a slight deficit near the surface compared with GEM-MACH-GHG. Differences in the stratosphere between the two models are also evident in Fig. 6. Since GEM-MACH-GHG has better vertical resolution compared to CarbonTracker (80 vs. 25 levels) and GEM is designed to have a realistic stratosphere (Charron et al., 2012), differences in stratospheric and mesospheric flow are to be expected. However, the mass of CO2 in the stratosphere and mesosphere is very small, so the column mean or surface values would be insensitive to such differences. In summary, when GEM-MACH-GHG is run with CT2013B fluxes, differences in transport errors between CarbonTracker and GEM-MACH-GHG are evident. Differences are within 3 ppm in column mean and 4 ppm in zonal mean. Neither (any) model can be expected to have perfect transport, so the acceptability of transport is generally gauged through comparisons of model predictions to measurements.

To assess seasonal timescales, it is useful to compare to the TCCON measurements (Wunch et al., 2011). The data used for this study are from the GGG2014 release, available on the network's website http://tccon-wiki.caltech.edu. All sites with measurements in 2009 and 2010 are selected, as listed in Table 1. The details of how the model profiles were converted to column-averaged dry mole fraction (XCO2) and smoothed following Wunch et al. (2010) is provided in Appendix B along with the precise definitions of the statistics discussed here (bias, root mean square (RMS) and scatter). The statistics for 2009–2010 are shown in Table 2. The bias is below 1 ppm for every station except Eureka, which only had 49 h of measurements in 2010. No selection is applied when considering which sites are included in the “all”, “mean” or standard deviation (SD) statistics. At Eureka, the -2.66 ppm bias significantly impacts the station-to-station SD of the bias, it is 0.3 ppm without Eureka. (Note that an error in surface pressure was recently discovered at Eureka and preliminary results for a correction suggest a 0.5 ppm difference in XCO2, which would reduce the Eureka EC-CAS bias by a corresponding amount.) Except for Eureka and Park Falls, the station bias is positive and the overall standard deviation is 0.96 ppm with a high correlation coefficient of 0.95. Although we did not perform a data assimilation, the posterior fluxes from CarbonTracker contain information from the observations they used, so we can compare our Table 2 to Massart et al. (2016, Table 2). The biases of individual stations are mostly lower here, as is the overall averaged bias. This is because the surface observations assimilated by CarbonTracker with a long assimilation window are able to constrain the global atmospheric growth rate, whereas the system used by Massart et al. (2016) does not use long assimilation windows and thus does not constrain the global growth rate as effectively. The full time series for Park Falls (USA) and Wollongong (Australia) are shown in Fig. 7 and the seasonal bias as well as the seasonal statistics using data from all sites combined are shown in Table 3. Seasons are defined as DJF (December, January and February), MAM (March, April and May), JJA (June, July and August) and SON (September, October and November). The model is able to reproduce seasonal variations of XCO2 with biases ranging between -1 and +1 ppm (excluding Eureka) and scatter values consistently below 1 ppm. The large negative bias at Eureka in autumn is consistent with the time series shown in Fig. 3. Other northern stations (Sodankylä and Bialystok) have similar but smaller biases. As discussed earlier, the discrepancy of GEM-MACH-GHG transport with that of CarbonTracker (as imprinted in the posterior fluxes) may explain this behaviour since other posterior fluxes do not have this particular issue (Fig. S6).

The vertical structure of model CO2 is compared to NOAA aircraft profiles (Sweeney et al., 2015) over Canada and the USA in Fig. 8. Following Agustí-Panareda et al. (2014), mean model profiles at the nearest model grid point and timestep to the profile location were averaged over all profiles for a season. Both observed and model values were binned into 1 km layers. The observations are from ObsPack2013 (2013) (Masarie et al., 2014) and include only profiles from Canada or the contiguous USA. The annually averaged model profiles are shown in panel a. In the annual average, GEM-MACH-GHG has good agreement with these independent measurements while CT2013B has a very slight positive bias. Both models are quite good compared to the ensemble of models shown in Stephens et al. (2007, Fig. 2b). However, the other panels reveal that GEM-MACH-GHG's excellent annual result in the free troposphere is because of compensating errors in different seasons. The boreal winter season (DJF) is not shown because December 2008 was not simulated. However, the behaviour of the model in boreal winter 2009 (based on January–February) and 2010 is qualitatively similar to its behaviour in spring (panel b). Panels b–d reveal that GEM-MACH-GHG agrees quite well with observations from 3 to 6 km in all seasons. However, from 1 to 3 km, vertical gradients are too sharp but of opposing directions in boreal spring (panel b) and summer (panel c). In autumn (panel d) the gradient is slightly too large, while CT2013B is almost perfect. Thus, the vertical mixing just above the boundary layer is too weak, as with most models (see Yang et al., 2007). A possible reason for the overestimation of vertical gradient with GEM-MACH-GHG is the lack of tracer transport through shallow convection. These biases in vertical gradients will be relevant for regional flux inversions (see Stephens et al., 2007) that may use GEM-MACH-GHG results as boundary conditions.

Although flux inversion systems focus on retrieving relatively long timescale signals (than 2 weeks), it is useful to first consider CO2 predictability on weather timescales before considering errors o longer timescales (next subsection). Specifically, we isolate the impact of the loss of meteorological predictability on CO2 predictability. The meteorological predictability problem on weather timescales is related to forecast sensitivity to initial conditions, but the atmospheric variability of CO2 on diurnal (Law et al., 2008), synoptic (Chan et al., 2004; Agustí-Panareda et al., 2014) and seasonal and interannual (Gurney et al., 2002, 2004; Baker et al., 2006a; Le Quéré et al., 2015) timescales is largely governed by the terrestrial biospheric fluxes and hence is determined by sensitivity to boundary rather than initial conditions. Nevertheless, the CO2 predictability error arising from loss of meteorological predictability on weather timescales has not to our knowledge been identified, and it can be used to identify an upper limit on forecast errors. This may be relevant for operational data assimilation or forecasting systems such as those at ECMWF (Agustí-Panareda et al., 2014) and NASA Goddard (Ott et al., 2015), which use update cycles of 12 or 24 h and also examine the quality of short-term forecasts. It will also serve as an upper limit for transport error arising from the presence of uncertain meteorological analyses in Sect. 5.2.

Predictability of weather normally refers to the sensitivity of forecast errors to initial conditions such that any infinitesimal perturbation will lead to diverging forecasts in a finite length of time. This is the so-called butterfly effect and it occurs because of the underlying nonlinear chaotic dynamics of the governing equations (Palmer, 2006). To compute predictability error of meteorological variables on weather timescales, one can simply start with a reference simulation and perturb the initial conditions. Eventually, the forecasts will diverge, but the error will saturate at climatological levels. Once saturation has been reached, the statistics of this predictability error can be determined. However, with a transported tracer such as CO2, the model forecast requires regular insertion of wind fields. During our forecast cycle, the meteorology is constrained by analyses every 24 h and departure from reality will represent at most a 24 h forecast error. Thus for transported constituents, the definition of the predictability experiment is slightly different. The reference simulation will be taken as the GEM-MACH-GHG 2-year run with CT2013B fluxes. Then a comparable “climate cycle” is run in which the model, initial conditions, CO2 fluxes and surface forcing are identical to those used in the reference cycle. However, with the second and all subsequent cycles, the meteorological fields are not replaced by analyses but are instead copied from the 24 h forecast fields. Thus the meteorology fields used to transport the CO2 field in this “climate cycle” are never updated with observations (analyses) and will thus depart from those used in the reference cycle in the first 2 weeks. The divergence of the CO2 field in the “climate cycle” from that in the reference cycle, once the error has saturated, defines the CO2 predictability error arising from the loss of meteorological predictability.

Starting from 1 January 2009 00:00 UTC, the reference and climate cycles are run for 1 month with fields saved every 6 h. The differences between the corresponding fields from the two cycles are computed for temperature, zonal and meridional wind components, CO2 and surface pressure. Vorticity and divergence fields are computed from the wind difference fields. Then the global mean of the zonal standard deviation of each difference field is computed after first subtracting the zonal mean. The resulting global mean values are called predictability errors and they have the same units as the corresponding forecast field. In order to get a comparable scale for all variables, the errors were normalized by the global mean of the zonal standard deviation for a reference state. The choice of this state is arbitrary but has implications on the maximum values attained (as will be discussed below). The reference field was taken as the initial state used to launch both the control and climate cycles and corresponds to 1 January 2009 00:00 UTC. Figure 9 shows the time and height variation of the predictability error normalized by the variability of the reference state for all four variables. When the predictability error approaches the variability of the reference state, values approach 1. Thus predictability is expected only when the relative error is much less than 1. In Fig. 9, we see that temperature loses predictability within 10 days, as expected (i.e. the normalized error reaches 0.8). However, CO2 loses predictability in the troposphere within 2–3 days except very near the surface, where it reaches 5 days. The predictability of CO2 more closely resembles that of the wind (vorticity and divergence) fields which also lose predictability in fewer than 5 days in the troposphere. This makes sense because the wind fields are used to transport the CO2 field. The difference in evolution of the CO2 field in the reference and climate cycles (figures not shown) reveals largest values to be associated with gradients created by large fluxes (whether natural or anthropogenic). This ability of the uncertainty in wind analyses to act on CO2 gradients and to spread the uncertainty downstream was previously illustrated by Liu et al. (2011) using an ensemble of wind fields. CO2 is more predictable in the stratosphere, with the loss of predictability occurring after 5 days in the lower stratosphere. The extended predictability of CO2 in the lower stratosphere is similar to that seen in the vorticity field (bottom left panel). The reason that the vorticity field is more predictable than the divergence field (with a loss of predictability occurring after 3–4 days in the troposphere) is because the vorticity field is associated with slower rotational modes whereas the divergence field is often associated with higher-frequency waves. The atmospheric kinetic energy spectrum is dominated by rotational motions in the troposphere (Koshyk et al., 1999; Skamarock et al., 2014). In the stratosphere, the zonal mean flow in winter is driven by very large-scale vertically propagating planetary waves (Andrews et al., 1987; Vallis, 2006) so large-scale rotational modes dominate the energy spectrum and extended predictability in vorticity and CO2 results.

While predictability is considered lost when its normalized error approaches 1, sometimes the relative error is much greater than 1. This occurs because of the arbitrary choice taken for the normalization. In our case, the reference state corresponds to the initial state, which corresponds to a relatively quiescent synoptic situation since January 2009 marks the strongest and most prolonged stratospheric major warming on record (Manney et al., 2009). The criteria for a stratospheric sudden warming (SSW) were met on 24 January 2009 when zonal mean easterlies replaced the climatologically normal westerlies at 10 hPa. However, easterlies were noted in the mesosphere prior to this date (Manney et al., 2009). This pattern is consistent with the appearance of anomalously large predictability error in relative vorticity in the mesosphere prior to 24 January and the appearance of anomalously large errors in the stratosphere (layer 6) after 15 January. Although global mean values are shown, it is zonal standard deviation that is computed, and the departure from a zonal mean will be large during a wave 2 vortex splitting event such as occurred in 2009. Thus zonal standard deviations are anomalously large throughout much of the Northern Hemisphere because the climate cycle does not capture this event whereas the reference cycle does. The extent of the disturbance in the Northern Hemisphere is large enough to influence the global mean values. Anomalously large CO2 predictability error appears in the mid-stratosphere around 20 January 2009. The disturbance of CO2 due to the SSW is to be expected since the disturbance of CO in the mesosphere, N2O in the mid-stratosphere and H2O in the lower stratosphere as the vortex deformed and split was evident in MLS (Microwave Limb Sounder) observations (Manney et al., 2009).

Figure 10 compares the layer mean normalized predictability error for different variables for the layers indicated by the dashed lines in Fig. 9 and labelled in white text at the left edge of each panel. Near the surface, the normalized CO2 predictability error closely follows that of the specific humidity field (for about 3 days). Both moisture and CO2 fields are advected by the wind fields and are similarly affected by the predictability of the wind fields. In this bottom layer, CO2 and moisture are more predictable than the wind field presumably because of their dependence on surface fluxes, although the normalization, which is layer dependent, cannot be ruled out as a contributing factor. However, they are both less predictable than the temperature field (Fig. 10a). In the troposphere, the loss of CO2 predictability is similar to the loss of predictability in vorticity (panels b, c) for the first few days. After that, the loss of predictability for CO2 is faster than that for the vorticity and divergence fields. While the normalization may play a role in this result, it is also worth noting that the predictability of vorticity and divergence fields will differ from that of wind components because very smooth wind field errors generate little error in vorticity and divergence fields. Throughout the atmosphere, temperature loses predictability at a slower rate than CO2 does. While both moisture and CO2 are transported by wind fields, moisture is also a dynamic variable; thus the loss of predictability for specific humidity is not the same as that for CO2 in the lower to mid-troposphere (panels b, c) beyond day 5. Predictability error increases from day 1 to reach saturation levels in 10–15 days for all levels except the upper stratosphere (Fig. 10f), which is affected by the SSW. Thus in the next section, climatological levels of predictability error will be discussed for periods longer than 1 month in the troposphere.

Waves of 24 h in period are seen, particularly, in the vorticity and divergence plots in Fig. 10. This occurs because the forecasts in the reference cycle are abruptly corrected every 24 h with the insertion of a new analysis. When the predictability error of the 24 h forecast error is large compared to that of the analysis valid at the same time, we see stripes at the 24 h period. Thus we conclude that the normalized 24 h forecast error of the wind field is much larger than that of the temperature field. This makes sense because the global observing system is dominated by information about the mass field with relatively sparse direct observations of the wind field (Baker et al., 2014). In addition, the mass field (which is reflected in the temperature field) is a much smoother field and is thus more easily observable with a given network relative to fields which are dominated by smaller spatial scales (such as vorticity or divergence).

In summary, the global predictability of CO2 due to uncertain meteorological initial conditions is very short in the free troposphere and is associated with the predictability of wind fields. This predictability limit refers only to sensitivity to meteorological initial conditions and it will be counter balanced by the predictability coming from biospheric fluxes on diurnal and synoptic scales. It is important to note (and this is discussed more fully in Sect. 6) that the predictability diagnostic used here is dependent on an arbitrary normalization and an arbitrary threshold to define predictability so absolute results are not expected. Instead, the relative predictability between variables or between atmospheric layers is expected to be more reliable. To improve this type of predictability, more observations will be needed where the wind fields have finer spatial scales and where convection is occurring. The current global meteorological measurement network is relatively sparse in the tropics where convection is important, but new observations from space-borne lidars may be able to remedy this problem (Baker et al., 2014).

As noted earlier, CO2 observations contain information on seasonal to interannual timescales. Specifically, the global surface network used in flux inversions is able to constrain the global CO2 budget and capture seasonal and interannual variability of the global fluxes (e.g. Baker et al., 2006a; Peylin et al., 2013). The source of predictability on subseasonal to seasonal and longer timescales partially derives from climate predictability on those scales but also from long timescale information contained in terrestrial biospheric fluxes which are, in turn, influenced by climate variability (Patra et al., 2005). In this section, we explore the predictability of CO2 on longer timescales and compare these to CO2 simulation errors due to the use of uncertain meteorological analyses.

The predictability experiment in Sect. 5.1 represents an extreme case in which no information from observations is present in the wind fields after the initial time. In reality, in our CO2 transport cycle (Fig. 1), the wind fields are constrained to observations by the insertion of a meteorological analysis every 24 h. However, the analyses are not perfect and have a certain level of uncertainty. To simulate this uncertainty, we could perturb the analyses every 24 h with an analysis error. In a variational data assimilation system such as that used at ECCC, it is possible to estimate the analysis error covariance matrix but it is expensive to do so, and such estimates are not routinely made. In contrast, a simple perturbation such as random spatially uncorrelated errors will not be useful as they will primarily generate unbalanced motions. What is more relevant is a perturbation of the size and shape of the 6 h analysis error, given the use of a 6 h forecast cycle in operations. (Reanalyses are also available at 6 h intervals and these are sometimes used to constrain flux inversions.) Thus, in order to simulate a coherent 6 h analysis error, we simply insert the analysis state valid 6 h prior to the actual analysis time (i.e. the one from 18:00 UTC of the day before, instead of the correct one from 00:00 UTC), relabelling the date and time to the correct ones. In addition, because the shift in the diurnal cycle for the meteorology would impact the CO2 predictability, the diurnal cycle is removed from the perturbations by subtracting the monthly mean of each synoptic hour. Then, the deviation of the CO2 field from this perturbed analysis cycle from the reference cycle defines the error due to the use of uncertain meteorological analyses. This error should be much smaller than the predictability error arising from uncertain meteorological initial conditions. However, it should be larger than an actual analysis error because of the additional component corresponding to the evolution of the true state in 6 h. Thus it is an overestimate of analysis error.

Figure 11 shows the monthly mean spatial spectra of various difference fields averaged over several model levels for July (top row) and December (bottom row) of 2009. The spectra refer to the spherical harmonics (Boer, 1983) of a scalar field multiplied by its complex conjugate and summed over zonal wavenumbers. The x axis then defines a total wavenumber. While spectra were computed for each day at 00:00 UTC, these were averaged over the month to filter some noise and identify a robust signal. In addition, they were averaged over 12 model levels to get representative spectra for a few atmospheric layers, namely the bottom 4 layers shown in Fig. 9. The blue curves in Fig. 11 depict mean spectra of the CO2 state from the reference cycle similarly averaged in time and in the vertical dimension. The black curves represent the predictability error arising from uncertain meteorological initial conditions. This error is very small at the end of the first cycle (on 2 January 2009) but rapidly increases during the first 2 weeks to saturate at climatological levels (Sect. 5.1). Since we are interested in this saturated level of error, we do not consider the first month of errors. The 2 months chosen in Fig. 11 represent the variation seen in various months of the year. The predictability error is seen to be lower than the reference state itself for very large spatial scales but quickly equals (around wavenumber 10) and then surpasses the power in the reference state. The reason that the power in the predictability error can be larger than that in the state itself is that it involves the difference of two fields. In the limit where two fields become uncorrelated, the variance of the difference equals the sum of the variances. If the two fields have the same climatological variance, the variance of the difference is twice the climatological variance. Thus it is not surprising that the power in the predictability error should surpass that in the reference state for small spatial scales. What is more intriguing is that some information is still retained in the largest scales (wavenumbers less than 5) even after 6 or 12 months of simulation. The source of this predictability at very large scales is mainly due to surface fluxes of CO2 which are the same for both the reference and climate cycles. However, it might also be partially from the surface forcing of meteorological fields. Subseasonal to seasonal predictability is manifested in modes of variability such as the Madden–Julian oscillation (MJO), the Pacific North American (PNA) pattern, midlatitude blocking events and the North Atlantic Oscillation (NAO) (Waliser, 2006) and their predictability derives from atmospheric boundary conditions, namely sea surface temperature, soil moisture, snow cover, vegetation and sea ice (Shukla and Kinter III, 2006). These ocean and land surface conditions influence fluxes of moisture and sensible and latent heat into the atmosphere which may change low-level atmospheric convergence and lead to atmospheric heating anomalies, which influence the large-scale flow. To see if long timescales in the meteorological analyses play a role in the large-scale predictability seen in Fig. 11, an experiment was run in which the predictability experiment was repeated, but this time incorrect surface fields (from 3 months later) were used. With no information from atmospheric observations as well as a seasonally shifted error in the surface forcing, the predictability error is worsened at these largest scales, particularly in the summer (June, July and August) near the surface (Fig. S7) and in the lower troposphere (not shown). The differences in CO2 evolution in the two predictability experiments during boreal summer are largest in the northern extratropics (not shown). This confirms that the ocean and land surface are playing a role in predictability of the system at the largest scales in the lower troposphere in boreal summer. In the mid- and upper troposphere, smaller impacts are seen but the impact is largest in the spring (not shown). In Fig. S7, the remaining predictability seen at wavenumbers below 10 for all months is then attributed to the common CO2 fluxes used by the reference and predictability experiments. Thus Fig. S7 confirms that the dominant source of predictability at large scales seen in Fig. 11 is due to surface fluxes.

In summary, a direct impact of climate predictability on CO2 predictions through the ocean and land surface is seen through the worsened predictability in boreal summer months when biospheric CO2 fluxes are largest. Since CO2 fluxes were specified, and were the same in the reference and predictability experiments, this climate signal is retained and explains most of the CO2 predictability at large scales in Figs. 11 and S7. Finally, it is worth noting that a shift of 1 month in surface fields resulted in no real deterioration of the predictability error since there is still significant correlation among surface fields due to a 1-month lag.

The red curves in Fig. 11 depict the spectra due to analysis uncertainty. As expected, these spectra are reduced compared to predictability errors because meteorological analyses are used in this cycle, although they are 6 h out of date. In particular, significant error reduction at large scales is seen. However, the red curves also intersect the reference state spectra at increasingly smaller wavenumbers as height increases. Thus, if analysis uncertainty is considered, there is a gain of information over climatological error levels defined by the predictability error but only for the larger spatial scales. The analysis perturbations used here overestimate analysis error so we can expect that the spatial scales resolved are a conservative estimate. However, whatever the size of the error, there will be a limit to the spatial scales resolved because of meteorological analysis imperfections. At the very least, the meteorological observing system has a given spatial resolution and, moreover, meteorological assimilation systems (like ECCC's) may compute analysis increments at a coarser resolution than that of the model. Beyond the point where the red and blue curves intersect, there is no useful information in the CO2 field at these scales due to meteorological analysis uncertainty because the power in the CO2 prediction error is larger than that in the CO2 state. In fact, the CO2 predictions with analysis uncertainty (red curves) asymptote to the predictability error spectra for large wavenumbers. For these spatial scales, using the updated meteorological analysis is no better than having no updates at all. Near the surface, there is the greatest gain of information, but in the upper troposphere the spectra of CO2 errors due to analysis uncertainty are less than that of the reference state only for wavenumbers lower than 30. Thus the fact that the meteorological analysis has information on only certain spatial scales places limits on the spatial scales that can be retrieved in a transported field such as CO2.

Another view of the spectra can be obtained by summing over total wavenumber and plotting with respect to zonal wavenumber (Fig. 12) because zonal wavenumber spectra are more indicative of the tropical signal. In this figure, it is evident that there is almost no information retained in the predictability error (i.e. the black curve lies above the blue one). In other words, predictability error spectra surpass that of the reference state at all levels except near the surface for the first few zonal wavenumbers. When a 3-month shift in surface fields is included in the predictability experiment, all predictability is lost in July and August since the power in the predictability error (red curves) exceeds that of the reference state (black curves) for all wavenumbers (Fig. S8). Predictability is mostly lost in September as well. Thus using the correct land and ocean surface fields may be relevant for capturing predictability in July, August and September in the tropics. The dominant mode of tropical subseasonal variability is the MJO, which is characterized by very large scales (zonal wavenumbers 1 and 2 in wind and rainfall fields) in the tropics (Waliser, 2006); GEM can capture predictability associated with this mode (Lin et al., 2008), supporting the notion that GEM has predictive skill in the tropics on seasonal scales. However, since predictability was already close to lost even with the correct land and ocean surface (power in predictability error is same order of magnitude as that for reference state), the worsened predictability in July to September with incorrect land and ocean surface fields is not a clear indication of their influence in the tropics. Indeed, outside of these 3 months, shifting the land and ocean surface fields by 3 months has little impact (red and black curves are similar in Fig. S8). This suggests that most of the information retained at the largest scales (seen in Fig. 11) in the predictability experiment is coming from the extratropics or signals with latitudinal structure for these months. Indeed, the CO2 evolution (not shown) in the reference and predictability experiments differs the most in northern hemispheric extratropics. Thus the large-scale predictability seen in the northern extratropics is due to large CO2 variability during October to May associated with biospheric fluxes, but from June to September the ocean and land forcing of GEM's climate is also important. When analysis uncertainty is simulated (red curves), there is a gain of information over predictability error but fewer than 20 zonal waves are resolved in the mid-troposphere (Fig. 12, layers 2 and 3). In the lowest layer, about 40 waves are resolved. Compared to Fig. 11, there are significantly fewer waves being resolved. Thus structure in the meridional direction is better resolved in analyses than structure in the zonal direction is.

It is also useful to examine other sorts of model errors in terms of their impact on CO2 predictions. Figure 13 shows the spectra of errors due to the inclusion (or not) of convective tracer transport (cyan curves). The impact of adding convective tracer transport is primarily at large scales and exceeds CO2 errors due to imperfect wind analyses (red curves) only in the mid-troposphere for wavenumbers less than 5. Spectra for April 2009 were shown in Fig. 13 because the impact of adding convective tracer transport was largest in spring months. The impact is always less than that due to imperfect wind analyses if zonal wavenumber spectra are considered (bottom row). Thus, for our model, this type of model error is exceeded by transport error due to uncertain meteorological analyses for most spatial scales. This type of analysis in which components of transport error are compared may thus be useful in diagnosing the dominant sources of transport error for a given transport model.