The potential for regional-scale bias in top-down CO 2 flux estimates due to atmospheric transport errors

The potential for regional-scale bias in top-down CO2 flux estimates due to atmospheric transport errors S. M. Miller, I. Fung, J. Liu, M. N. Hayek, and A. E. Andrews Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA Department of Earth and Planetary Sciences, University of California–Berkeley, Berkeley, CA, USA Earth Science Division, Jet Propulsion Laboratory, NASA, Pasadena, CA, USA Global Monitoring Division, Earth Systems Research Laboratory, National Oceanic and Atmospheric Administration, Boulder, CO, USA Received: 18 August 2014 – Accepted: 19 August 2014 – Published: 15 September 2014 Correspondence to: S. M. Miller (scot.m.miller@gmail.com) Published by Copernicus Publications on behalf of the European Geosciences Union. 23681

velop two case studies.In the first case study, we examine the extent to which CO 2 transport uncertainties can bias CO 2 flux estimates.In particular, we use a common flux estimate known as CarbonTracker to discover the minimum hypothetical bias that can be detected above the CO 2 transport uncertainties.In the second case study, we then investigate which meteorological conditions may contribute to month-long biases in modeled atmospheric transport.
We estimate 6 hourly CO 2 transport uncertainties in the model surface layer that range from 0.15 to 9.6 ppm (standard deviation), depending on location, and we estimate an average error decorrelation time of 2.3 days at existing CO 2 observation sites.As a consequence of these uncertainties, we find that CarbonTracker CO 2 fluxes would need to be biased by at least 29 %, on average, before that bias were detectable at existing non-marine atmospheric CO 2 observation sites.Furthermore, we find that persistent, bias-type errors in atmospheric transport are associated with consistent low net radiation, low energy boundary layer conditions.The meteorological model is not necessarily more uncertain in these conditions.Rather, the extent to which meteorological uncertainties manifest as persistent atmospheric transport biases appears to depend, at least in part, on the energy and stability of the boundary layer.Existing

Introduction
Scientists increasingly use atmospheric CO 2 observations to estimate CO 2 fluxes at the Earth's surface (e.g., Gurney et al., 2002;Michalak et al., 2004;Peters et al., 2007;Gourdji et al., 2012).This "top-down" approach contrasts with "bottom-up" studies that rely primarily on expert knowledge of biological processes (e.g., Huntzinger et al., 2012;Raczka et al., 2013).In order to estimate the fluxes, top-down studies typically require a meteorology model to link fluxes at the surface with measurements taken downwind.Using this link, one can estimate the fluxes even if the atmospheric measurements do not themselves directly measure the fluxes.
However, both the accuracy and e ective resolution of the flux estimate hinge upon the accuracy of the meteorological model.Errors in the meteorological model may (or may not) translate into errors in CO 2 transport from the location(s) of surface fluxes to the atmospheric measurement site(s).Subsequently, errors in CO 2 transport may (or may not) bias estimated CO 2 fluxes depending upon the error characteristics and the space/time scales of interest.This cascading chain of cause and e ect defines the three types of errors or uncertainties that are of primary interest in this paper: (1) errors in modeled meteorological variables, (2) errors in atmospheric CO 2 transport, as they manifest in modeled atmospheric CO 2 concentrations, and (3) errors in the fluxes that result from problems in estimated transport.This study is particularly concerned with how CO 2 transport errors may propagate into the estimated fluxes.
More specifically, the e ect of CO 2 transport errors on the estimated fluxes depends upon two important factors.First, the flux estimate becomes more uncertain as the CO 2 transport error variance (or standard deviation) increases.Top-down studies that use Bayesian statistics will explicitly account for these variances when estimating fluxes (e.g., Enting, 2002;Tarantola, 2005) estimates the total variance due to an array of model or data errors -due to imperfect atmospheric transport or imperfect measurements, among many other sources of error (e.g.Gerbig et al., 2003;Michalak et al., 2005;Ciais et al., 2011).
Second, the flux estimate becomes more uncertain as the temporal and/or spatial covariance in the errors increases.As the covariances increase, each CO 2 measurement e ectively provides less and less independent information to constrain the surface fluxes.Error correlations, however, are often di cult to characterize (e.g.Lin and Gerbig, 2005;Lauvaux et al., 2009) and are omitted from most existing top-down studies.These di culties aside, correlated transport errors can have a number of impacts on the estimated greenhouse gas fluxes.First, a top-down study that does not account for these errors will typically underestimate the uncertainties in the flux estimate.Second, correlated errors can bias the flux estimate over a region or over the entire geographic area of interest (e.g., Stephens et al., 2007).
Quantification of this complex cause-and-e ect between meteorological errors and errors in estimated CO 2 fluxes represents an ongoing research challenge, and a number of existing studies have partly characterized these uncertainties.For example, a series of studies known as "TRANSCOM" represents one of the first coordinated projects on CO 2 transport uncertainties (Gurney et al., 2002;Baker et al., 2006).These early studies used 13 di erent global atmospheric models and compared di erences in topdown CO 2 budgets due to atmospheric model di erences.These models gave an uncertainty in the Northern Hemisphere CO 2 budget of ±1.1 Pg Cyr 1 (standard deviation; mean budget of 2.4 Pg Cyr 1 ) (Stephens et al., 2007).Subsequent to the TRANSCOM project, a number of studies have focused on the e ects of changing vertical mixing and/or planetary boundary layer height (PBLH) (Gerbig et al., 2008;Kretschmer et al., 2012Kretschmer et al., , 2014;;Parazoo et al., 2012;Pino et al., 2012).In general, these papers found that uncertainties in PBLH can lead to errors of up to 3 ppm in modeled CO 2 .Another paper examined the e ect of uncertain horizontal winds (Lin and Gerbig, 2005).The authors applied a particle-trajectory model at a measurement site in Wisconsin and found that uncertainties in the horizontal winds contributed 6 ppm (standard de- viation) to the overall CO 2 transport uncertainty.In summary, a number of previous studies have either perturbed individual meteorological parameters or, in the case of TRANSCOM, sampled a subset of transport uncertainties using 13 pre-selected atmospheric models.
Numerous questions still remain, however.For example, if one could carefully utilize all available meteorological observations, what meteorological and CO 2 transport uncertainties would remain?Furthermore, what is the combined e ect of meteorological errors from multiple parameters (e.g., wind, boundary layer, etc.) on CO 2 transport and subsequently on CO 2 fluxes?In addition, which meteorological errors are most likely to bias regional-scale CO 2 flux estimates on month-long time scales?
In the present study, we explore several facets of these questions using a global meteorology model ensemble and a meteorology data assimilation system -the Community Atmosphere Model (CAM) and an assimilation framework known as a Local Ensemble Transform Kalman Filter (LETKF) (Hunt et al., 2007;Liu et al., 2011).CAM-LETKF systematically estimates meteorology and CO 2 transport uncertainties to an extent not previously possible; this framework explicitly represents the CO 2 transport uncertainties that remain after assimilating several hundred thousand meteorology observations at each 6 h model time step.To accomplish this task, CAM-LETKF uses an ensemble of weather forecasts and optimizes the ensemble to match available meteorological observations.Furthermore, CAM-LETKF adjusts the variance of the weather ensemble at each time step to match the modeling uncertainties implied by the meteorological observations.
Using this toolkit, we construct two case studies to understand both the possible magnitude and potential drivers of bias in top-down CO 2 flux budgets.Previous studies by Liu et al. (2011) and Liu et al. (2012) used CAM-LETKF to estimate CO 2 transport uncertainties, and this study investigates connections with top-down CO 2 flux estimation.First, we construct a case study with a commonly-used estimate of CO 2 fluxes known as CarbonTracker (CT): how biased would regional CO 2 fluxes need to be before that bias were detectable above the meteorological uncertainties estimated by CAM-LETKF?We test this hypothesis at a number of atmospheric CO 2 monitoring sites in the US, Canada, Europe, and East Asia.Second, we construct a case study using a synthetic atmospheric tracer.This synthetic experiment serves as a lens to explore the possible meteorological factors associated with persistent, month-long deviations in atmospheric transport.

The meteorology and CO 2 model
The first component of CAM-LETKF is the meteorological model.We simulate global meteorology using the Community Atmosphere Model (CAM) and Community Land Model (CLM, version 3.5), run in weather forecast mode (not climate mode) (Collins et al., 2006;Oleson et al., 2008;Chen et al., 2010).Model simulations in this study have a spatial resolution of 2.5 longitude by 1.9 latitude with 26 vertical model levels.We save the global model output at 6 h time increments.Furthermore, we run the model for two time periods: January-February 2009 and May-July 2009.The first month of each run serves as an initial spin-up for the model-data assimilation system.The next section describes this assimilation in greater detail.

The meteorological model-data assimilation framework
The second component of CAM-LETKF is the data assimilation and model optimization framework.This framework serves two purposes.First, the LETKF optimizes modeled meteorology (CAM-CLM) to match available observations.Second, the LETKF uses an ensemble of model forecasts to represent model uncertainties that remain after data assimilation (Hunt et al., 2004(Hunt et al., , 2007)).We define each ensemble member and the mean of the entire ensemble as follows: where x i (m 1 1) is a single model ensemble member, x (m 1 1) is the mean of the model ensemble, and X i (m 1 k) refers to the i th column of the matrix that defines the ensemble spread.In this paper, the variable m 1 refers to the total number of model parameters -the model estimate for a variety of meteorological variables, concatenated across the globe and across all 6 hourly time steps in a given model run.Furthermore, we use k = 64 total ensemble members in this setup, as was done in Liu et al. (2011) and Liu et al. (2012).
Using this ensemble, CAM-LETKF steps through time in sequential 6 h intervals.First, the model ensemble at time t is optimized to match meteorological data.To this end, we assimilate the same meteorological observations used in the National Centers for Environmental Prediction-Department of Energy reanalysis 2 (Kanamitsu et al., 2002): temperature (in situ and satellite), zonal wind (in situ and satellite), meridional wind (in situ and satellite), surface pressure (in situ), and specific humidity (in situ).At each 6 h model time step, we assimilate between 180 000 to 330 000 observations globally.At that juncture, the ensemble mean associated with time t, x(t), represents the model best guess and the ensemble members, x(t) + X(t), collectively represent the posterior variances and covariances in the modeled meteorology.For the remainder of this paper, we define the 6 hourly meteorological uncertainties as the standard deviation (or alternately, the range) of each row in X.Second, we run 6 h CAM-CLM forecasts using these realizations as initial conditions -a total of 64 model forecasts.
This ensemble of global forecasts then becomes the prior (and prior variances and covariances) for the next LETKF assimilation cycle (Hunt et al., 2007).The 6 h cycle of data assimilation and model forecast then begins again.
This model ensemble, by design, is guaranteed to reflect actual uncertainties in modeled meteorology; at each 6 h model time step, we adjust the ensemble variance such that this variance matches against the model-data residuals (Li et al., 2009;Miyoshi, 2011).The Supplement describes this procedure, known as adaptive covariance inflation.For further technical detail on the LETKF and adaptive covariance inflation, refer to the Supplement, Hunt et al. (2004), Hunt et al. (2007), Li et al. (2009), Liu et al. (2011), or Miyoshi (2011).

CO 2 transport error variances and covariances
The CAM-LETKF system described above estimates not only meteorological uncertainties but also uncertainties in CO 2 transport.In this study, CO 2 is a passive tracer and is not part of the data assimilation.Instead, we use biospheric, oceanic, biomass burning, and fossil fuel CO 2 fluxes from CT (version "CT2011_oi", Fig. 1) (Peters et al., 2007, http://carbontracker.noaa.gov).Furthermore, we use CT as the initial condition for global atmospheric CO 2 mixing ratios on 1 January and 1 May 2009.Each CAM ensemble member uses the same initial condition for atmospheric CO 2 , so any subsequent di erences in CO 2 among the model realizations are due entirely to meteorological uncertainties.
We estimate 6 hourly CO 2 transport uncertainties using the standard deviation of CO 2 concentrations across the 64 model realizations (e.g., Fig. 2).To make this estimate, we calculate the standard deviation of each row in X [CO 2 ] , where the subscript "[CO 2 ]" refers to the atmospheric CO 2 concentrations estimated by the ensemble.In addition, we characterize temporal covariance or correlation in transport errors (i.e., in X [CO 2 ] ).To estimate an error decorrelation time, we use a variogram analysis.In specific, we fit an exponential variogram model to afternoon-only model output (1-7 p.m. LT) associated with a number of existing, global atmospheric CO 2 observation sites.Both Kitanidis (1997) and the Supplement describe variograms in greater detail.The remainder of the methods section applies this CO 2 and meteorology modeling framework to two case studies.In this case study, we construct a hypothesis test to determine whether biases in CT CO 2 fluxes would be detectable above atmospheric transport uncertainties.CT is a commonly-used global CO 2 flux estimate created by the US National Oceanic and Atmospheric Administration (NOAA).To create CT, NOAA scientists use atmospheric CO 2 data from observations towers and surface sites around the world and estimate regional scaling factors that optimize an initial CO 2 flux model (Peters et al., 2007).We test whether a hypothetical bias in regional scaling factors, like those estimated by CT, would be detectable at atmospheric CO 2 observation sites across the globe.We build this test using the CO 2 sum of squared residuals (SSR) from the CAM-LETKF model ensemble.A number of previous statistical and/or greenhouse gas studies construct hypothesis tests using squared residuals (e.g., Sheskin, 2003;Huntzinger et al., 2011).
In this setup, we construct the test as follows.First, compute the SSR associated with the transport uncertainties: This equation interpolates the model residuals (X [CO 2 ] ) to the observation sites, squares these residuals, and sums them over the entire time period of interest.More specifically, the variable n 2 refers to the number of hourly CO 2 observations at an observation site over the time span of the hypothesis test.In addition, H [CO 2 ] (n 2 m 2 ) is the matrix that interpolates or maps the ensemble deviations (X [CO 2 ] , dimensions m 2 k) to the CO 2 observations.Lastly, SSR (1 k) are the sum of squared residuals from each of the k CAM-LETKF model ensemble members.Note that some of the ensemble members will be closer than others to the ensemble mean or best estimate ( x[CO 2 ] ).Therefore, the k SSRs from the k ensemble members will not be identical and will instead form a distribution.23689 Second, we compute the SSR associated with a hypothetical bias ( ) in the fluxes: The output of this equation, FSSR, is a scalar that estimates the squared residuals due to a biased flux estimate, summed over all observations at a given CO 2 measurement site.The variable represents a hypothetical bias in CT fluxes.In this study, we conduct the hypothesis test at each measurement site individually, so the variable is specific to the site being considered.In addition, the variables in parentheses ( x[CO 2 ,surface] x[CO 2 ,600 hPa] ) quantify the contribution of regional-scale fluxes to CO 2 at the atmospheric observation site.Many top-down studies pre-subtract free troposphere or marine "clean air" concentrations from the CO 2 measurements or model output at the observation sites (e.g., Gerbig et al., 2003;Gourdji et al., 2012).These top-down studies then optimize regional fluxes to match the pre-subtracted CO 2 observations.In this study, we similarly subtract modeled concentrations at 600 hPa in the free troposphere ( x[CO 2 ,600 hPa] ) from those at the CO 2 observation sites ( x[CO 2 ,surface] ).The concentrations at 600 hPa are not necessarily a perfect measure of "clean air" concentrations.Rather, this approach is an approximation similar to that used in the existing literature.This di erence in concentrations is then used to estimate how a regional bias in CT fluxes would manifest at a given observation site ( CO 2 , in ppm).
Finally, we test the hypothesis.If the FSSR is larger than most of the k SSR associated with the meteorological uncertainties, then we can distinguish the flux bias ( ) above the meteorological noise.This statement can be formalized into a hypothesis test as follows: where A is the set of SSR that are greater than FSSR, and the expression |A| indicates the number of elements in A. If the p value is less than 0.05, we have disproven the null hypothesis -that the hypothetical bias ( ) in CO 2 fluxes is indistinguishable above the transport uncertainties.
Note that this hypothesis test accounts for both variance and temporal covariance in the CO 2 transport uncertainties, a concept discussed in detail in the Supplement.In addition, note that FSSR will almost never be zero due to diurnal or daily changes in NEP, even if the monthly-averaged NEP at a given site is zero.We conduct the hypothesis test above for both February and July 2009 at a variety of di erent observation sites in North America, Asia, and Europe.We report the results of this hypothesis test for a representative selection of global CO 2 observation sites -di erent types of observation towers located on di erent continents and in di erent biomes.Furthermore, we test this hypothesis using month-long modeled time series corresponding to afternoon data only (1-7 p.m. LT).We use this month-long window because CO 2 budgets are often reported in month-long increments.
In summary, case study 1 quantifies the extent to which atmospheric CO 2 transport errors can obscure any regional biases in estimated CO 2 fluxes.The next case study, in contrast, explores the meteorological conditions under which sustained CO 2 transport errors may be more likely to occur.

Case study 2: which meteorological factors may be associated with sustained, month-long transport biases?
We create a relatively simple, synthetic experiment to explore the meteorological conditions under which month-long model biases in atmospheric transport may occur.The spatial patterns in the CO 2 transport uncertainties are heavily influenced by spatial patterns in the CO 2 fluxes (Fig. 2).In other words, regions with large fluxes or large diurnal flux variability also show higher CO 2 transport uncertainties.As a result, it is di cult to disentangle the e ect of di erent meteorological parameters on CO 2 transport uncertainties.Instead, we create a synthetic tracer with constant global emissions in both 23691 space and time.This experiment serves as a lens to explore the possible e ects of di erent meteorological parameters independent of the spatial variability in CO 2 fluxes.
To this end, we initialize CAM-LETKF runs with zero atmospheric concentration of this synthetic tracer and then run CAM-LETKF forward for one month using constant global emissions (e.g., for both February and July 2009).Any uncertainties in the atmospheric distribution of this tracer are solely due to meteorological parameters, not due to the spatial distribution of the underlying fluxes.
Next, we calculate the coe cient of variation (CV) associated with the monthlyaveraged surface concentrations.The CV is an inverted signal-to-noise ratio; it measures the uncertainty in modeled surface concentrations relative to the average surface concentration ( µ ).For example, an uncertainty of 1 ppm in modeled concentrations is most problematic if the signal from surface fluxes is weak, and a 1 ppm uncertainty is less problematic if the signal from surface sources is strong.
For this setup, the CV equals the standard deviation in the monthly-averaged surface concentrations divided by the monthly surface concentration averaged across all 64-realizations.We then plot the tracer CV against monthly-averaged meteorological parameters and their associated uncertainties from CAM-LETKF.These relationships give insight into the meteorological conditions or meteorological uncertainties that are associated with month-long biases in the modeled synthetic tracer.

Uncertainties in the 6 hourly modeled CO 2 concentrations
Before examining the two case studies in detail, we first provide context on the CO 2 transport uncertainties estimated with CT fluxes and CAM-LETKF.Figure 2a and b visually summarize the average 6 hourly CO 2 transport uncertainties (standard deviations) in the model surface layer; these figures show how CO 2 transport uncertainties vary across the globe -from 0.15 to 9.6 ppm (standard deviation), depending on loca-tion.Furthermore, the transport uncertainties in Fig. 2a and b show several distinctive features.The largest uncertainties are localized to regions where either the magnitude or the diurnal cycle of the CT fluxes is largest (e.g., the US Eastern Seaboard and southern Siberia during summertime, the Amazon, the Congo, and eastern China).CO 2 transport uncertainties in the Eastern US and East Asia bleed, to a smaller degree, over the adjacent ocean where surface fluxes are small.These transport uncertainties are in the range of the uncertainties estimated in a number of previous studies.For example, the spatial patterns in the 6 hourly uncertainties are similar to those modeled by Liu et al. (2011) using CAM-LETKF and temperature-scaled CO 2 fluxes from TRANSCOM 3. In addition, a number of previous studies focused on the e ects of perturbing individual meteorological parameters at specific observation sites or for individual aircraft campaigns (e.g., Gerbig et al., 2003Gerbig et al., , 2008;;Lin and Gerbig, 2005;Kretschmer et al., 2012).Our 6 hourly transport uncertainties, though very di erent in both scope and scale, are comparable in magnitude to the individual parameter uncertainties estimated by Gerbig et al. (2003), Gerbig et al. (2008), and Kretschmer et al. (2012) but are less than the uncertainties in Lin and Gerbig (2005).Furthermore, our estimated 6 hourly transport uncertainties also appear similar to or slightly smaller than the model-data mismatch errors estimated at individual observation sites in several inversion studies (e.g., Peters et al., 2007;Schuh et al., 2010;Gourdji et al., 2012).Model-data mismatch includes not only transport errors but also any model or data errors unrelated to an imperfect initial flux estimate.This result may reflect the fact that atmospheric transport often dominates model-data mismatch errors.
Figure 3 places these transport uncertainties in context of CO 2 data measured at two observation sites in the United States.These time series plots validate the model's capacity to simulate daily variations in CO 2 concentrations.Furthermore, the comparison illustrates the magnitude of the CO 2 transport uncertainties relative to the diurnal cycle in CO 2 concentrations.For example, the uncertainties at AMT in July are 30 % of the diurnal range in the CO 2 measurements.Overall, the model ensemble depicted in these plots usually encapsulates the hourly-averaged measurements.CT fluxes are estimated using these CO 2 observations and the TM5 transport model (Tracer Model, version 5) (Peters et al., 2007), so one might expect the CAM model to fit the CO 2 observations relatively well.In the instances when the model ensemble does not encapsulate the hourly-averaged CO 2 measurements, one of the many other non-transport error types could be to blame; the ensemble spread only encompasses transport error and does not include measurement error, error due to finite model resolution, or errors in the fluxes.The Supplement provides more example CO 2 model-data comparisons, meteorology model validation, and data assimilation diagnostics.

CO 2 transport uncertainties at longer time scales
The uncertainty in monthly-averaged CO 2 concentrations provides one measure of how transport errors persist over time.In other words, these uncertainties provide a metric of error correlations in CO 2 transport.Uncorrelated transport errors will average out, to a large degree, over many model time steps, but temporal correlations prevent the errors from averaging down over time.As a result, large uncertainties in monthly-averaged concentrations indicate the potential for persistent bias in CO 2 fluxes estimated using atmospheric observations.Such bias could lead to under-or over-estimation of regional-scale CO 2 budgets.
To this end, Fig. 2c and d displays uncertainties in the month-long average surface concentrations for February and July 2009.In contrast to the 6 hourly uncertainties, these uncertainties are far more spatially-distributed; the largest uncertainties are not just associated with regions that have large fluxes.This result implies that CO 2 transport errors are correlated over longer periods of time in remote regions, compared to regions with large anthropogenic or biospheric fluxes.Furthermore, month-long transport uncertainties are large across the entire Northern Hemisphere during February even though biospheric fluxes are weak during that time period.A subsequent Sect.3.4 explores possible reasons why these month-long biases occur.In particular, the case study discussed in that section provides insight into why the month-long uncertainties may be large across the Northern Hemisphere during winter.
A variogram analysis provides an additional measure of the error correlations in CO 2 transport (see Sect. 2.3 and the Supplement).Based upon this analysis, we estimate CO 2 transport error decorrelation times of 2.2 and 2.3 days at global atmospheric CO 2 observation sites during February and July, respectively (see Table S1).The error decorrelation times are generally longer at marine sites (average of 2.9 and 2.7 days in February and July, respectively) or at sites that are far from large CO 2 fluxes.For example, the longest error decorrelation times occur at coastal sites in Japan, Korea and the Canary Islands.In contrast, decorrelation times are usually shorter than average for observation sites on the European mainland.
This level of temporal correlation in the CO 2 transport errors implies several largescale conclusions for estimating CO 2 fluxes.First, observation sites that are far from large fluxes are more likely to produce a biased CO 2 budget than sites near to large surface fluxes.These "remote" sites see a lower CO 2 signal from surface fluxes, and the transport errors at these locations are generally correlated over longer periods of time.Second, most existing top-down studies will underestimate the uncertainties in estimated CO 2 fluxes.Existing inversions rarely account for error correlations in CO 2 transport and most likely underestimate the posterior uncertainties as a direct result.The next Sect.3.3 quantifies the impact of the transport uncertainties discussed above on surface flux estimation.

3.3
Case study 1: how biased would CT fluxes need to be before that bias were detectable above the CO 2 transport uncertainties?
We use a case study from CT to understand how transport errors translate into uncertainty in a top-down, CO 2 flux estimate.In specific, if the flux scaling factors estimated by CT were incorrect, how wrong would those scaling factors need to be before the problem were detectable above atmospheric transport errors? Figure 4 shows the results of this case study (described in Sect.2.4) at a selection of global CO 2 observation sites.The y-axis of each bar plot shows the minimum bias that would be detectable using hourly-averaged CO 2 observations collected over an entire month.The mean minimum detectable bias across all non-marine sites is 29 % (at a month-long time scale).The results are not substantially di erent at short versus tall non-marine tower sites: 27 % and 31 %, respectively.In other words, the tall towers examined in this analysis are neither more or less sensitive to biased CO 2 fluxes in comparison to the set of short towers in Fig. 4. At marine sites, in contrast, the minimum detectable bias is far larger: 76 % on average.
These results show a number of additional trends across the di erent observation sites.In general, towers that are near large sources are better able to detect bias in the modeled fluxes.These include observation sites in the central and eastern US or in Germany and Eastern Europe -sites that are strongly influence by terrestrial (versus marine) airflow relative to other locations.Most of these towers see large signals from biospheric fluxes during summer (Figs.S9-S14).Other towers, in contrast, are less sensitive to detecting bias during the summertime (e.g., the marine towers and towers in the western US).The western US towers, for example, are surrounded by weak biosphere uptake that is diluted into a larger mixed layer during summer.But during summer, transport uncertainties increase due to large seasonal fluxes in adjacent regions.The sensitivity of the marine Japanese and Korean sites also declines in the summer.At these sites, the signal from surface fluxes is largest in winter.During summer, biosphere uptake somewhat cancels the signal from large anthropogenic emissions in China.
Note that this analysis only considers uncertainties due to meteorology.The capabilities of the atmospheric observations would deteriorate if other errors were included (e.g., measurement errors or errors due to model resolution).We now examine the results of the synthetic tracer experiment (Sect.2.5) to uncover possible drivers of atmospheric transport biases.Figure 5 displays the coe cient of variation (CV) for monthly-averaged surface concentrations of the synthetic tracer.The CV, a unitless quantity, does not just indicate where the uncertainties are largest.Rather, the CV indicates the magnitude of these uncertainties relative to the mean modeled tracer concentration.Arguably, this noiseto-signal ratio measures the influence of transport uncertainties more e ectively than a simple standard deviation.The remainder of this section focuses only on land regions because most existing top-down studies focus on land fluxes.This coe cient shows a number of distinctive seasonal and spatial patterns.Like the uncertainties in monthly-averaged CO 2 (Fig. 2c and d), the CV in Fig. 5 is highest in boreal and arctic regions of the Northern Hemisphere during winter.The CV is lowest over Europe, Australia, and the Amazon during all seasons.
We plot the synthetic tracer CV against numerous modeled meteorological parameters to understand the possible drivers behind the transport uncertainties.Of the 60 variables tested (Table S2), seven of the variables showed correlations (R 2 ) with the tracer CV that are greater or equal to 0.3 (Fig. 6).Meteorological conditions that lead to high atmospheric stability and low energy are most closely associated with persistent tracer uncertainties (relative to mean surface concentrations higher in regions with consistent low energy, limited vertical mixing, and/or high albedo.These biases are unlikely to be represented by most existing inversion uncertainty calculations, as explained in the previous sections.Furthermore, the meteorological model ensemble is not necessarily more uncertain these regions (see Figs. S16 and  S17).Note that month-long CO 2 transport biases did not correlate as strongly with meteorology uncertainties.Rather, the extent to which meteorological uncertainties translate into tracer transport uncertainties appears to depend, at least in part, on the stability and net energy input associated with the boundary layer.

Conclusions
In this paper, we use two case studies to investigate the potential for bias in top-down CO 2 flux estimates due to errors in modeled atmospheric CO 2 transport.The first case study examines the ability of in situ atmospheric observations to detect bias in estimated CO 2 fluxes.Among other results, we find that CT would need to be biased by 29 %, on average, before that bias were detectable above CO 2 transport uncertainties at terrestrial, atmospheric observation sites.These results are strongly influenced by temporal correlations in the transport uncertainties.In other words, atmospheric CO 2 measurements contain less information about the fluxes than is usually assumed by top-down studies that overlook transport error covariances.As a result, most existing inversions are likely to underestimate the uncertainties in estimated CO 2 fluxes and/or may be vulnerable to unforeseen biases in the estimated fluxes.Accounting for these correlated errors can be as simple as modifying one of the covariance matrix inputs in a Bayesian inversion.Accordingly, this study provides information to improve the setup of future top-down inverse modeling studies -an improvement that will widen the confidence interval on the estimated fluxes.
In a subsequent case study, we investigate the factors associated with month-long biases in atmospheric transport.The largest short-term CO 2 transport errors correlate strongly with the location of the largest surface fluxes, but month-long biases in at- mospheric transport are not only localized to regions with large fluxes.Rather, these biases may be more likely to occur at observation sites that are far from large fluxes and in regions with high atmospheric stability and low net radiation.Existing top-down flux studies may be more likely to estimate inaccurate regional fluxes under those conditions.
The Supplement related to this article is available online at doi:10.5194/acpd-14-23681-2014-supplement.Each panel shows the correlation between the synthetic tracer CV (Fig. 5) and various monthly-averaged meteorological parameters estimated by CAM-LETKF.We test the correlation with 60 di erent parameters (Table S2) and plot the relationships for which R 2 0.3.In all cases, we fit both a standard major axis regression and nonlinear least squares ( 1 [ 1 parameter+ 2 ] ) and plot the regression with the higher correlation coe cient.
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Figure 2 .Figure 3 .
Figure 2. The top panels display average 6 hourly CO 2 transport uncertainties estimated by CAM-LETKF.The uncertainties (standard deviations) are for the surface model layer for (a) February and (b) July 2009.To create these plots, we calculate the ensemble variance at each time step and subsequently average the variances across all time steps.These standard deviations are the square root these meaned 6 hourly variances.Furthermore, these plots include model output from all 24 h of each day.The Supplement provides analogous figures for daytimeor nighttime-only model output.The bottom-panels (c and d), in contrast, display the standard deviation in month-long averaged surface CO 2 concentrations.23705

Figure 4 .Figure 5 .
Figure 4. Results of the hypothesis test (Sects.2.4 and 3.3) at a selection of global CO 2 observation sites.Panel (a) shows the location, name, and type of each observation site examined in the hypothesis test.At sites with multiple measurement or inlet heights, we model the top inlet.Panels (b) and (c) show the test results for February and July 2009.The test asks the following question: how biased would CT fluxes need to be before CO 2 observation sites would detect that bias above the estimated CO 2 transport uncertainties?

Figure 6 .
Figure6.Each panel shows the correlation between the synthetic tracer CV (Fig.5) and various monthly-averaged meteorological parameters estimated by CAM-LETKF.We test the correlation with 60 di erent parameters (TableS2) and plot the relationships for which R ).For example, a high tracer CV is associated with low temperatures, low net radiative flux, low net solar flux, low planetary boundary layer height, and low vertical di usion di usivity.Furthermore, many of the meteorological variables exhibit a nonlinear relationship with the tracer CV; the CV increases more quickly when net radiation and planetary boundary heights are low.The results of this synthetic tracer experiment hold a number of potential applications to top-down CO 2 flux estimation.The danger of obtaining a biased CO 2 budget is likely 23697