We have implemented a regional carbon dioxide data assimilation system based
on the CarbonTracker Data Assimilation Shell (CTDAS) and a high-resolution
Lagrangian transport model, the Stochastic Time-Inverted Lagrangian
Transport model driven by the Weather Forecast and Research meteorological
fields (WRF-STILT). With this system, named CTDAS-Lagrange, we
simultaneously optimize terrestrial biosphere fluxes and four parameters
that adjust the lateral boundary conditions (BCs) against

To estimate the uncertainties in the optimized fluxes from the system, we performed sensitivity tests with various a priori biosphere fluxes (SiBCASA, SiB3, CT2013B) and BCs (optimized mole fraction fields from CT2013B and CTE2014, and an empirical dataset derived from aircraft observations), as well as with a variety of choices on the ways that fluxes are adjusted (additive or multiplicative), covariance length scales, biosphere flux covariances, BC parameter uncertainties, and model–data mismatches. In pseudo-data experiments, we show that in our implementation the additive flux adjustment method is more flexible in optimizing net ecosystem exchange (NEE) than the multiplicative flux adjustment method, and our sensitivity tests with real observations show that the CTDAS-Lagrange system has the ability to correct for the potential biases in the lateral BCs and to resolve large biases in the prior biosphere fluxes.

Using real observations, we have derived a range of estimates for the
optimized carbon fluxes from a series of sensitivity tests, which places the
North American carbon sink for the year 2010 in a range from

In the past decade, much attention has been given to estimating carbon fluxes at global scales (e.g., Rödenbeck et al., 2003; Peters et al., 2007; Chevallier et al., 2010; Peylin et al., 2013), while regional inversion studies with high spatial resolution for carbon fluxes are only gaining ground more recently (e.g., Rödenbeck et al., 2019; Göckede et al., 2010; Schuh et al., 2010; Tolk et al., 2011; Lauvaux et al., 2012; Gourdji et al., 2012; Broquet et al., 2013; Shiga et al., 2014; Alden et al., 2016; Kountouris et al., 2018). Such regional inversion studies contribute to a better understanding of the mechanism through which carbon fluxes react to environmental variations at a fine scale. But to link carbon fluxes and environmental drivers to atmospheric measurements, a high-resolution transport model is typically needed. In the framework for global inversions, typically, ensemble-based methods (Peters et al., 2007) are based on Eulerian models, and analytical methods (Rödenbeck et al., 2003; Chevallier et al., 2010) are with a linearized adjoint model of such Eulerian models. In terms of computational efficiency, Lagrangian models are superior to these traditional Eulerian models for high-resolution applications, which makes them suitable for computation-intensive regional atmospheric inversions. The computation cost of Lagrangian models increases with the increasing number of observations; however, it remains an advantage that offline Lagrangian transport results, i.e., footprints need to be computed only once, can be stored for future use.

However, both global and regional inversion studies suffer from various
uncertainties, including transport and representation errors, possible
observational biases when data from different laboratories are combined, and
uncertainties in a priori fluxes. For regional inversions, errors in lateral
boundary conditions (BCs) become another critical issue (Alden et al., 2016;
Gerbig et al., 2003; Schuh et al., 2010; Lauvaux et al., 2013), and can
bias flux estimates, particularly for smaller areas (Göckede et al.,
2010) and for shorter periods (Andersson et al., 2015). Several methods to
create lateral BCs have been employed, including deriving
them from mole fraction fields of global inversions (Kountouris et al.,
2018) and in situ mole fraction observations, e.g., aircraft profiles or
satellite observations (Jiang et al., 2015). Embedding a regional inversion
inside a global model domain has been widely applied for

To better understand regional carbon fluxes, we developed a data
assimilation system that employs a high-resolution Lagrangian atmospheric
transport model, the WRF-STILT model. Our assimilation system, the
CarbonTracker Data Assimilation Shell – Lagrange, (referred to as
“CTDAS-Lagrange”), is based on the CarbonTracker Europe system, which is a
widely applied global inversion system (Peters et al., 2010; van der
Laan-Luijkx et al., 2015, 2017). In our new
system, we optimize BCs using independent information from aircraft
profiles. We use a priori biosphere fluxes from the SiBCASA biosphere model
(Schaefer et al., 2008), and the other a priori fluxes for the components
ocean, fossil fuels, and fires are from CT2013B (accessible from the
archived release

The purpose of this paper is to describe and demonstrate the CTDAS-Lagrange
data assimilation system. We have performed preliminary inversions using a
subset of the available

Our system assimilates atmospheric

The model domain is shown together with the

Summary of assimilated PFP data from the NOAA ESRL North American tall tower and aircraft sampling program in 2010. We have selected 12 aircraft sites for this study. Observations (after data filtering, see Sect. 2.1.3) are flagged when the difference between simulated and observed values is larger than 3 times the prescribed model–data mismatch for each site. The bias indicates the mean difference between model forecast and observations.

Detailed site and sampling information of the tall tower observations
is listed in Table 1. Andrews et
al. (2014) used flask versus in situ comparisons for quality control and
pointed out such comparisons suffer from quasi-continuous in situ data (due
to, for example, switching of sampling lines among different heights,
calibrations), difference in sampling time, and atmospheric variability. The
mean differences between PFP and in situ

The NOAA ESRL aircraft

We use daytime data from the tall towers that are collected between 10:00
and 18:00 local time to constrain surface fluxes. Aircraft observations made
at altitudes higher than 3000 m above ground at all hours are used to
constrain BCs. In CTDAS-Lagrange, we use fossil fuel
emissions based on inventory estimates and do not attempt to optimize them.
We remove

The CTDAS-Lagrange system aims to improve the estimates of regional carbon
fluxes by combining a high spatial resolution Lagrangian modeling framework
with the existing CarbonTracker Data Assimilation Shell (van der Laan-Luijkx
et al., 2017). Transport of atmospheric

The Stochastic Time-Inverted Lagrangian Transport model coupled with the Weather Forecast and Research (WRF-STILT) is employed in our system (Lin et al., 2003; Nehrkorn et al., 2010). The STILT model is a receptor-oriented framework that links surface fluxes of trace gases with atmospheric mole fractions. During a WRF-STILT run, an ensemble of particles is released at the observation location (receptor) at a certain time, and particles are transported backward driven by the WRF wind fields. The influence function, i.e., footprint, for that particular receptor and time can be computed based on the density of the particles in the surface layer defined in STILT as the lower half of the well-mixed boundary layer (Gerbig et al., 2003).

We leverage a footprint library created for the NOAA CarbonTracker Lagrange
regional inversion framework
(

In the CTDAS-Lagrange system, we extended the existing ensemble Kalman smoother method as is implemented in CarbonTracker and CarbonTracker Europe (Peters et al., 2005, 2007, 2010; van der Laan-Luijkx et al., 2017) to simultaneously optimize biosphere fluxes and BC parameters.

We use two alternative ways of adjusting the total surface fluxes (additive
and multiplicative), while simultaneously optimizing the lateral BCs
by optimizing four parameters that are implemented as follows:

The state variables therefore include the gridded adjusting parameters for
the biosphere fluxes (3078 land grids with

The system aims to optimize (non-fire) net ecosystem exchange (NEE) of

We use biosphere fluxes simulated by the combined Simple Biosphere and
Carnegie-Ames-Stanford Approach (SiBCASA) model (Schaefer et al., 2008) as a prior
and fixed fossil fuel burning, ocean, and fire fluxes from CT2013B
(Peters et al., 2007, with updates documented at

We estimate the additive flux adjustments for each grid box in our domain, but a covariance structure is used to reduce the number of degrees of freedom in the state vector, and to balance it with the number of available observations. The covariance is calculated as an exponential function that decreases with distance between grid boxes, using a decorrelation length scale of 750 km. This covariance is only used between grid boxes that have the same dominant plant-functional type, as specified though the ecoregion maps that are also used in CT2013B. These in turn are based on TransCom regions, as well as the Olson ecosystem classification (Olson et al., 2002). Where CT2013B uses single scaling factors for each ecoregion, our gridded approach has approximately 122 degrees of freedom within its 3078 additive adjustment parameters as compared to an average of 112 independent observations per assimilation time step.

The time stepping flow of the ensemble Kalman
smoother filter used in CTDAS-Lagrange. The Xp

We have adapted the fixed lag ensemble Kalman smoother method from
Peters et al. (2005) to estimate fluxes and BC per 10-day time step. Because the
footprint of each receptor can go back in time up to 10 days, we need a
total assimilation window of 20 days to account for the backward
trajectories that overlap two time steps. Therefore, the total state vector
contains flux and BC parameters for two 10-day time steps (

A comparison of the setup between the base case and sensitivity runs (described in the Sect. 2.3) is given in Table 2.

Summary of the base and sensitivity runs using CTDAS-Lagrange.

The prior biosphere fluxes are simulated by the SiBCASA model, a diagnostic
biosphere model, which combines photosynthesis and biophysical processes
from the Simple Biosphere (SiB) model version 3 with carbon biogeochemical
processes from the Carnegie-Ames-Stanford Approach model (Schaefer et al.,
2008). Meteorological driver data are provided by the European Centre for
Medium-Range Weather Forecasts (ECMWF). SiBCASA calculates the surface
energy, water, and

CT2013B offers a number of flux estimates (ocean, fossil fuels, etc.) from
multiple models, which includes two different flux datasets for ocean and
fossil fuels, respectively. The fire fluxes are based on the Global Fire
Emissions Database (GFED) 3.1, which are calculated with the CASA model
(Giglio et al., 2006; van der Werf et al., 2006). The fire fluxes are not
optimized in CT2013B. The two different prior ocean fluxes for CT2013B
include a long-term mean of ocean fluxes that is derived from the ocean
interior inversions (Jacobson et al., 2007) and a climatology dataset that
is created from direct observations of seawater around the world and was
interpolated onto a regular grid map using a modeled surface current field
(Takahashi et al., 2009). We use the optimized ocean fluxes of CT2013B that
are calculated as the mean of an ensemble of run results. The two different
fossil fuel fluxes for CT2013B are the “Miller” emissions dataset and the
“ODIAC” emissions datasets (Oda and Maksyutov, 2011). The difference
between the two datasets is the processing schemes on the totals and
the spatial and temporal distributions of fossil fuel
emissions.
The fossil fuel fluxes are not optimized in CT2013B. We use the fixed fossil fuel data
of CT2013B, which is an average of “Miller” and “ODIAC”. The final
product of these fluxes is provided on 1

The lateral BCs could be constructed either from interpolated measurements or from the output of a global tracer model. The base case uses CT2013B optimized mole fraction fields.

To study the impact of different lateral BCs on flux
optimization, we have tested optimized mole fraction fields with the spatial
resolution of 1

We also assign different prior uncertainties other than 2 ppm for the
BC parameters. Experiments are designed as follows:

BC1: using CTE2014 mole fraction fields as lateral BCs;

BC2: using EMP as lateral BCs;

Pbc1: set the uncertainty in the BC parameter to 1 ppm;

Pbc2: set the uncertainty in the BC parameter to 3 ppm.

Gurney et al. (2004) point out that inversion results can be sensitive to
a priori fluxes for regions with sparse observations while the fluxes can be
well constrained by areas with dense observations. To investigate the impact
of different a priori fluxes on the optimized fluxes, we have designed two
sensitivity runs that incorporate two alternative biosphere fluxes as
a priori fluxes as follows:

B1: SiB3 biosphere fluxes;

B2: CT2013B optimized biosphere fluxes.

For further analysis of the sensitivity of the CTDAS-Lagrange system to the
annual mean and the seasonal magnitude of a priori fluxes, we have designed
a series of runs with modified SiBCASA fluxes. We scaled the respiration of
the SiBCASA fluxes while maintaining the gross primary production (GPP) estimate to obtain a priori
North American annual mean fluxes ranging from

The multiplicative flux adjustment of NEE relates the uncertainties to the
magnitude of the fluxes. As NEE is the difference between two gross fluxes,
gross primary production and ecosystem respiration, 10-day mean NEE can be
very small or even close to zero when GPP and respiration are close to each
other, e.g., in the so-called shoulder seasons (see Fig. 8), which limits the
ability of using multiplicative flux adjustment to scale the mean fluxes due
to low uncertainties in the inversion system (note that the large diurnal
cycle of the net flux will still be scaled though). Scaling both GPP and
respiration has been shown to circumvent this in deriving optimized mean
fluxes (Tolk et al., 2011). Here, we have instead implemented both
multiplicative and additive flux adjustment methods. For the multiplicative
method, we set the biosphere scaling parameter variance as 80 %, following
Peters et al. (2010); for the additive method, the variance is prescribed as
1.6

Simulated

For a better assessment of the adjusting ability of the two methods, we further perform experimental inversions using pseudo-data, i.e., Observing System Simulation Experiments (OSSEs). The primary aim of our OSSEs is to investigate the ability of our system to retrieve surface fluxes given the observational network. In particular, we test the implementation of the additive flux parameter vs. multiplicative flux parameter, and the ability to recover large biases in lateral BCs and prior fluxes. We run the CTDAS-Lagrange in a forward mode with the SiBCASA fluxes as prior to generate simulated mole fractions, and then try to recover the “truth” in an inversion using SiB3 fluxes as a priori.

The covariance length scale determines the rate at which the correlation between the fluxes of two grids within the same ecoregions decreases exponentially with increasing distance. The prescribed covariance effectively reduces the number of unknowns to be solved for, and improves the ability of the inversion system to retrieve optimized fluxes when data are limited (Rödenbeck et al., 2003; Gourdji et al., 2012). The choice of appropriate correlation length scale depends also on the observation density. For example, CarbonTracker Europe, which includes more observations than those used in this work, uses a correlation length scale of 300 km for North America. In addition, Alden (2013) found 700 km to be the best length scale to recover true fluxes over North America with a pseudo-data inversion experiment. To investigate the impact of covariance length scales on optimized fluxes, we performed sensitivity runs with a series of spatial correlation lengths: 300, 500, 750 km (base case), 1000, and 1250 km, labeled as CL1 to CL4, respectively.

Flux covariance determines the range in which prior biosphere fluxes can be
adjusted. It should ideally reflect the uncertainty in prior biosphere
fluxes, but information about prior flux errors is not readily available for
the priors used here or for terrestrial ecosystem models more generally. To
evaluate the possible influence of prior covariances on the optimized fluxes,
we modified the additive uncertainty by

Q1: decrease the magnitude of additive uncertainty by 50 %, which means the covariance is 25 % of the default;

Q2: increase the magnitude of additive uncertainty by 50 %, which means the covariance is 225 % of the default;

R1: set the MDM to 2 ppm for tower sites;

R2: set the MDM to 4 ppm for tower sites.

As a sensitivity test, we exclude observations at two tower sites (STR and WGC), which are characterized with larger prior and posterior residuals (simulated minus observed, both mean and standard deviation) than other sites. We have defined one sensitivity run as follows:

Obs: excluding STR and WGC, and the rest of the model setup is the same as the base case run.

This section covers the following topics:

As an example, a time series of simulated and observed

The seasonal cycle (10-day resolution) of the net

Figure 4 shows the seasonal cycle (10-day averages) of NEE
of

The seasonal cycle of the posterior fluxes shows a similar magnitude as the prior. In addition, the optimized fluxes generally show more fluctuations than prior fluxes over the year, which could be explained by effective constraints from atmospheric observations and possibly in some cases as artifacts that are caused by the sparseness of the observations. It should be noted that it does not mean that the actual errors in these fluxes are really reduced, as this can only be assessed using independent observations of these fluxes. With monthly averaging, the fluctuations in the derived posterior fluxes could be significantly reduced (see Fig. 4). Interestingly, the temperate crops/agriculture show double troughs in the uptake in May and July–August or a sudden drop in the uptake in June, which could be attributed to early-summer crops/agriculture harvests, temperature anomaly, or drought.

The mean prior and optimized fluxes for the summer months June–August are given in Fig. 5. The optimized fluxes show a similar spatial pattern as the prior fluxes, but display more spatial details. The optimized results place more carbon uptake in the agricultural US Midwest and the forests/wooded in the northeast of the US, as well as in the boreal forests/wooded and tundra/taiga of Canada; In contrast, less carbon uptake (or carbon emissions) is placed in the western US, especially in south Utah, north Arizona, and Louisiana.

Mean prior

Contribution of lateral transport to simulated

A comparison of the mole fraction contribution from three lateral BCs
for the eight tower sites is summarized in Table 3. The annual
means of the CTE2014 are consistently

Comparison of the optimized annual net biosphere fluxes (PgC yr

The optimized annual mean fluxes and the adjustment of the BC
parameters for the model runs with different prior lateral
BCs are shown in Table 4. When both biosphere fluxes and BC
parameters are optimized, i.e., “Flux

The residuals of the model runs with and without BC optimization (not shown), in almost all cases, are significantly reduced after optimization. The reduction in the residuals after optimization for aircraft sites is primarily due to the adjustment of the BC parameters. We notice that the residuals (means and standard deviations) of the model runs with optimized biosphere fluxes and BC parameters for the two sites STR and WGC are larger than those for other sites. Possible reasons are that the two sites are still significantly influenced by regional fossil fuel signals after the data filtering presented in Sect. 2.1.3, and are less sensitive to biosphere fluxes (due to their proximity to the west coast of North America there is less sensitivity to land flux than for other sites). We will investigate the impact of the two observation sites on optimized fluxes in the following section.

The time series of optimized North American averaged biosphere fluxes from the model runs with different prior lateral BCs are shown in Fig. 6. The differences among the optimized fluxes with additional BC optimization (Fig. 6b) become smaller than those from the “Flux only” runs (Fig. 6a). This can also be observed when averaged over major ecoregions (Fig. 6c and d), especially for the boreal forests and temperate forests. The differences in the optimized biosphere fluxes caused by different prior lateral BCs are mostly small, except that the deviation of the EMP optimized fluxes from the other two is slightly larger for the period July–September.

Mean optimized net biosphere fluxes (PgC yr

Optimized annual net biosphere fluxes (PgC yr

The optimized annual mean biosphere fluxes and associated BC parameter
adjustments from the runs with different prior biosphere fluxes are shown in
Table 5. The flux adjustments are in general large, resulting in
significantly larger annual mean uptake over North America than the prior;
however, the optimized annual mean fluxes from the runs using three
different prior biosphere products converge, except for the run using the
original CT2013B optimized fluxes. A further check indicates that the
residuals of the run are reasonable, but more observations have been
rejected compared with the other runs. The rejection takes place in the
period from June to August, which is caused by large fluctuations of the
a priori fluxes. Note that the a priori CT2013B fluxes are optimized using
weekly scaling factors in an assimilation window of 5 weeks long and incur
substantial variability (or noise) that averages out over larger scales in
CT2013B. But the forward simulations of the CTDAS-Lagrange system are
sensitive to the fluxes and their diurnal cycle is only in a 10-day window and
therefore more sensitive to this variability (or noise). Therefore, we have
made an additional sensitivity test (B2

Figure 7a shows the time series of the North American averaged biosphere fluxes of the model runs with different prior biosphere fluxes. It is noticeable that the difference in the seasonal amplitude between the SiB3 prior biosphere fluxes and the other two prior biosphere fluxes is diminished after optimization. Furthermore, the significant difference among the three prior products for the period August–October is largely reconciled by the inversion. Annual mean fluxes per ecoregion (Fig. 7c) indicate that the largest adjustment in the fluxes takes place for temperate forests and temperate grass, with fluxes from temperate grass changed from uptake to emissions. Note that the optimized fluxes per ecoregion do not always agree on their magnitudes, which is likely caused by insufficient constraints by observations, especially for the boreal region.

Prior and optimized annual net biosphere fluxes (PgC yr

To further investigate the sensitivity of the CTDAS-Lagrange system to the
seasonal magnitude and the annual mean of a priori fluxes, we scale the
respiration of the SiBCASA fluxes to obtain a variety of a priori fluxes
with the annual mean NEE ranging from

Sensitivity runs with a variety of prior biosphere fluxes
ranging from

Finally, we note that tests of CTDAS-Lagrange in so-called OSSEs (Fig. 9a)
confirm that a near-perfect truth can be estimated with the system if
pseudo-observations are created from known fluxes. In our experiments,
transport errors and systematic structural differences between truth and
prior flux

Comparison between two flux optimization methods: the
additive method

The prior/optimized fluxes using both additive and multiplicative flux
adjustment methods are shown in Fig. 8. We found that major differences
occur in the so-called shoulder seasons, where the flux adjustment is
significant for the run with the additive method but is negligible for the
run with the multiplicative method. The multiplicative method fails to
adjust the fluxes in this case because the NEE is small or even close to
zero around the shoulder seasons. Larger variations in the optimized fluxes
for the additive flux adjustment method are observed compared to those for
the multiplicative method, due to the flexibility of the additive flux
adjustment method and higher prior flux uncertainties. Note that both
methods reproduce observed

Figure 9 shows the inversion results of model runs with pseudo-data, further confirming the advantage of the additive method over the multiplicative method in the CTDAS-Lagrange system. The additive method recovers the seasonality better than the multiplicative method, noticeable mainly for the period June–July. It is also clearly shown that the multiplicative method fails to derive the “truth” fluxes around the shoulder season in the fall (no difference between the prior and the truth in the spring). Besides this, the estimate of the annual net biosphere fluxes derived from the additive method is also closer to the truth than that from the multiplicative method, although the associated uncertainties are rather large.

Comparison of the performance of inversions with pseudo-data using the two flux optimization methods:

Sensitivity of the optimized annual net biosphere fluxes
(PgC yr

The sensitivity of the CTDAS-Lagrange to the covariance length scale is shown in Fig. 10. The optimized fluxes tend to reach a robust value when the covariance length scale is larger than 750–1000 km, and we note that the difference between 750 and 1000 km is relatively small. We have tested whether including aircraft sites can reduce this length scale dependence below 1000 km, and find it can slightly alleviate the dependence but does not fully resolve that. The optimized fluxes for the temperate North America are relatively insensitive to the covariance length scale, as this region is relatively well sampled by the dataset. We have only used some of the available observations, and different results may be found when additional data are included, e.g., from Environment Canada tower sites.

From the above-described sensitivity runs, we derive an ensemble of estimates of optimized North American annual net biosphere fluxes in 2010 (see Fig. 11). The optimized biosphere fluxes of all the runs are larger (i.e., more uptake) than their corresponding prior fluxes. Compared to other factors, the prior biosphere fluxes have the largest impact on the optimization result. The selection of model–data mismatch with 3 ppm is reasonable, judging from the observed small differences between the model runs BASE and R2 (4 ppm). We notice the R1 (2 ppm) run makes a significant difference, as it rejects much more observations than the other two cases, especially during summertime when usually larger mismatches between observations and simulations occurred (not shown).

Comparing BASE, Q1 (decrease the magnitude of additive uncertainty by
50 %), and Q2 (increase the magnitude of additive uncertainty by 50 %),
we find the prior uncertainty magnitude ascribed to biosphere fluxes impacts
the result only a little, with small reductions in the optimized flux when the
uncertainty gets larger. In addition, we find that our system is sensitive
to the uncertainty in the BC parameter Pbc1 (1 ppm uncertainty) and
Pbc2 (3 ppm uncertainty), which results in the difference of flux estimates by
slightly more than 0.1 PgC yr

Excluding results from B2 that we consider unrealistic due to the high data
rejection rate (replaced by the B2

We have implemented a regional carbon assimilation system based on the CarbonTracker Data Assimilation Shell framework and a high-resolution Lagrangian transport model WRF-STILT. The new system, named CTDAS-Lagrange, optimizes both biosphere fluxes and four boundary condition (BC) parameters and is computationally efficient (1 year of optimization can be performed serially within 14 h with eight threads on a 12-core Intel Xeon processor E5 v2 family computer with a processor base frequency of 2.7 GHz, once footprints are calculated and stored offline). Furthermore, we have demonstrated that the additive flux adjustment method is more flexible in optimizing NEE than the multiplicative flux adjustment method, especially in the shoulder seasons of the year.

The sensitivity test results with three different lateral BCs
(CT2013B, CTE2014, and an empirical curtain) indicate that
CTDAS-Lagrange has the ability to largely correct for the potential biases
in the lateral BCs, with the BC optimization
absorbing up to 0.23 PgC yr

We derive an ensemble of estimates of the optimized annual net biosphere
carbon fluxes based on a series of sensitivity tests, which places the North
American Carbon sink for the year 2010 at

In addition, the estimate of net

Although we have accounted for the impact of possible biases in the prior lateral BCs on optimized fluxes, we find that there remains room to further reduce the biases at surface sites (shown in Table 1 as posterior residuals). This could be partially because aircraft observations are sparse, and are temporally insufficient for sampling the inflows of the continent. Also, the limited number of parameters used for BC adjustments could be a bottleneck; an alternative scheme with more extensive parameterization to offer more flexibility for BC adjustments could help.

North American 2010 annual net biosphere fluxes (PgC yr

Moreover, the optimization results of the CTDAS-Lagrange system depend on
the quality of the forward simulations, i.e., fixed a priori fluxes and
transport models. The optimization of biosphere fluxes may be influenced by
observations affected by local fossil fuel signals, which can be addressed
by using high-resolution fossil fuel emissions or filtering out the
observations. CO has long been studied and used as a tracer for fossil fuel
emissions, and its use as a quantitative tracer suffers mainly from varying
emission ratios of different sources and production by oxidation of
hydrocarbons. We have used CO as a fossil fuel tracer to filter out
observations that are considerably affected by fossil fuel emissions, which
is expected to serve our purpose reasonably well in wintertime; however,
this may not be appropriate on the occasions when production of CO by oxidation
of hydrocarbons can be significant in summertime. Thus the CO filtering may
have been overly conservative, reducing the number of observations by up to

We highlight that the use of aircraft data in this study suggests a very important constraint from free tropospheric measurements to the lateral BCs, which enables simultaneous optimization of BCs and biosphere fluxes. Our system is an open framework for regional atmospheric inversions that could be extended to use different atmospheric transport models, to study other trace gases, and for alternative geographic regions.

The codes can be downloaded from

The supplement related to this article is available online at:

WH and HC prepared the manuscript with contributions from all co-authors. WH, HC, IRvdV, and WP developed CTDAS-Lagrange, with contributions from the other authors. AEA, TH, and MM prepared the WRF-STILT footprints.

The authors declare that they have no conflict of interest.

This research is funded by the NOAA Climate Program Office's AC4 program (award number NA13OAR4310082 and additional support for production of the NOAA CarbonTracker Lagrange footprint library), and by the National Key R&D Program of China (2016YFA0600202). Wouter Peters was partially funded from European Research Council grant 649087 (ASICA). Ingrid T. van der Laan-Luijkx is funded by a NWO Veni grant (016.Veni.171.095). Data collection at Walnut Grove and Sutro towers was partially supported by the California Energy Commissions's Natural Gas Research Program and the California Air Resources Board at Lawrence Berkeley National Laboratory under US Department of Energy contract no. DE-AC02-05CH11231. We are grateful to Ian Baker for providing the SiB3 fluxes, to Andy Jacobson for his useful comments on the manuscript, and for the IT support at the Centre for Isotope Research of the University of Groningen.Edited by: Philippe Peylin Reviewed by: two anonymous referees