Top–down estimates of the spatiotemporal variations in emissions and uptake
of CO

Quantification of surface fluxes of CO

The objective of our study is to quantify the ability of ASCENDS column
measurements to constrain CO

Global studies of the impact of satellite measurements on top–down estimates
of CO

We use a novel approach for our inversions that facilitates high-resolution
evaluation of satellite column measurements. The approach relies on a
Lagrangian, or air-mass-following, transport model (as opposed to an
Eulerian, or fixed-frame-of-reference, model), run backward in time from the
observation points (receptors) using ensembles of particles to generate
footprints describing the sensitivity of satellite CO

In this observing system simulation experiment (OSSE) we utilize the
Stochastic Time-Inverted Lagrangian Transport (STILT) particle dispersion
model (Lin et al., 2003), driven by meteorological fields from the Weather
Research and Forecasting (WRF) model (Skamarock and Klemp, 2008) in a domain
encompassing North America, in a Bayesian inversion. The WRF–STILT (Nehrkorn
et al., 2010) footprints are used to compute weekly flux uncertainties over
a 1

We use a Bayesian synthesis inversion method, which optimizes the agreement
between model and observed CO

We solve for flux uncertainties in each land cell on a

We solve Eq. (1) using the standard matrix inversion function in the Interactive Data Language (IDL) software package. We also verify the solution using the alternative singular value decomposition approach (Rayner et al., 1999) in IDL. Given the large dimensions of the matrices – more than 15 000 10 sec average observations each month and 13 205 weekly flux elements over each 5 week period – the procedure requires large amounts of computer memory but a modest amount of processing time: several hours per monthly inversion on the NASA Center for Climate Simulation high-performance computing system.

Vertical weighting functions per ppmv of CO

Examples of measurement locations (individual 10 sec averages)
and 10 sec uncertainties (1

We consider candidate lidar wavelengths near 1.57

Examples of the coverage of ASCENDS observations available for analysis and
their associated uncertainties (for a reference uncertainty at RRV of 0.5 ppm) are shown in Fig. 2
over 7-day periods in January and July for
the two candidate wavelengths. ASCENDS provides dense coverage over the
domain with few large gaps, especially in July. A large majority of the 10-second-average observations have uncertainties of < 2 ppm in all
four cases except for 2.05

We derived a priori flux uncertainties at

The a priori flux uncertainties were specifically derived from the standard
deviations of daily mean CASA-GFED NEE over each month in 2007 divided by

Spatiotemporal correlation parameters used.

Off-diagonal elements of the a priori flux error covariance matrix are
filled using spatial and temporal error correlations derived from an
isotropic exponential decay model with month-specific correlation lengths
(Table 1) estimated from ground-based and aircraft CO

A priori weekly flux uncertainty for

Our CASA-GFED-based a priori flux uncertainties, scaled to approximate the values used by Baker et al. (2010), are shown in Fig. 3. The largest uncertainties occur generally where the absolute value of NEE is highest, e.g., in the “Corn Belt” of the US in summer. The spatial and seasonal variations exhibit similarities to those of Baker et al. (2010).

The STILT Lagrangian model, driven by WRF meteorological fields, has
features (including a realistic treatment of convective fluxes and mass
conservation properties) that are important for accurate top–down estimates
of GHG fluxes that rely on small gradients in the measured concentrations (Nehrkorn et al., 2010). In the present application of STILT
(

A footprint quantitatively describes how much surface fluxes originating in
upwind regions contribute to the total mixing ratio at a particular
measurement location; it has units of mixing ratio per unit flux. This is to
be distinguished from a satellite footprint, which is the area of earth reflecting
the lidar signal. In the current application, footprints are computed for
each 5 km simulated observation that passes the cloud/aerosol filter in
January, April, July, and October 2007 at 3 h intervals back to 10 days
prior to the observation time. Separate footprint maps have been computed
for 15 receptor positions above ground level for the purpose of vertically
convolving with the lidar weighting functions and producing one
weighted-average footprint per measurement. The receptors are spaced 1 km
apart in the vertical from 0.5 to 14.5 km a.g.l. This procedure results in

It is important to note that although a footprint is defined for each of the
15 vertical levels, the footprint expresses the sensitivity of the mixing
ratio (measured at the receptor point located at that vertical level) to the
surface fluxes upwind, not to the fluxes upwind at the same level. Thus the footprints defined for receptor points located at high
altitudes (e.g., 12.5, 13.5, 14.5 km) are often zero, indicating that a
receptor at that upper level is not influenced by surface fluxes inside the
domain (within the 10-day span examined here). Conversely, receptor points
located at the lowest levels (e.g., 0.5, 1.5, 2.5 km) tend to have large
footprints (with values of the order of 10

Footprint maps for one simulated ASCENDS measurement location
(marked by black star) on 1 January 2007 at 18:00 UTC, integrated over 10 days
and convolved over the 500–14 500 m AGL range with two candidate ASCENDS
weighting functions: the CO

Figure 4 shows the vertically-weighted footprints of a selected column
measurement location (in southern Canada) over 10 days for the 1.57 and
2.05

To construct the Jacobians,

Jacobian values averaged over all observations and weekly
flux intervals for the
1.57

Figure 5 shows the overall influence of the surface fluxes on the observations during each month (i.e., the average weekly Jacobian values for
the 1.57

Footprint values are largest in summer due once again to horizontal and vertical motions. Winds during this season are relatively light and allow the fluxes to stay inside the domain for a long time, maximizing their integrated influence on observations in the domain; vertical mixing across the deep boundary layer brings particles over a large portion of the column into contact with the surface.

Although WRF–STILT provides the capability to generate and optimize boundary condition influences on observed concentrations, this was not available at the time of this study and, consequently, we neglect uncertainties in the influence of boundary conditions in our standard inversion (discussed further in Sect. 4.2). Similarly, we neglect uncertainties regarding the influence of North American fluxes occurring more than 10 days before a particular observation. Note that fluxes are often transported out of the domain within 10 days, so that these fluxes can only influence the observations via the boundary conditions.

In the following, we present results for four cases involving different
combinations of measurement wavelength and baseline error level: 1.57

A posteriori weekly flux uncertainty during

A posteriori uncertainties (Fig. 6) are smaller than the a priori values (Fig. 3), an expected result of the incorporation of observational information. The reduction in uncertainty is often larger in areas that have higher a priori uncertainties, as can be seen more clearly in the maps of percentage reduction in uncertainty in Fig. 7. Uncertainty reductions are relatively large year-round in places such as southern Mexico and the Pacific Northwest of the US; in April and October in the southeastern US; and in July in the US Midwest, areas with forest fire emissions in central Canada (appearing as hot spots of uncertainty reduction), and Alaska and western Canada. A priori uncertainties are relatively high in these areas so that there is more room for observations to tighten the constraint. In contrast, where a priori uncertainties are already small, observations are not able to provide a much tighter constraint.

Weekly fractional flux uncertainty reduction over

Of course, the uncertainty reductions are not dependent simply on the prior uncertainties. For example, the highest uncertainty reductions, up to 50 %, occur in southern Mexico in October, where a priori uncertainties are not especially large. The high uncertainty reductions here can be explained by the large Jacobian values (Fig. 5) combined with the low uncertainties of nearby observations (not shown). Although a priori uncertainties and Jacobian values in July in this area are similar to those in October, observation uncertainties are higher, resulting in lower uncertainty reductions. The tendency of uncertainty reductions to be higher where average Jacobian values are larger can also be seen in the similarity of the spatial patterns in the January maps in Figs. 5a and 7a, for example. As described in Sect. 2.4, fluxes in western and central areas of the continent are captured by more observations in the domain than fluxes in the east and close to the other edges; thus, the former can be better constrained in this inversion.

In July, the largest uncertainty reductions occur in northern Alaska and northwestern Canada, which have much smaller a priori uncertainties than places such as the Midwest. This is an effect of the smaller grid cells at higher latitudes: the a priori errors are correlated over larger numbers of cells at these latitudes given the spatially uniform correlation lengths we specify, so that the average flux over each cell is more tightly constrained than that for an otherwise comparable cell at lower latitudes. This is a less important issue when results are aggregated to the larger scales dealt with in later sections of this paper.

Uncertainty reductions are smallest in January, for the following reasons: (1) a
priori flux uncertainties are smallest during the dormant season, (2) observation errors are largest in winter due to the low reflectance of snow
and ice cover at the measurement wavelengths, and (3) there is fast
dispersion of fluxes in winter by strong winds, transporting fluxes out of
the domain and out of detection by observations in the domain and thus
reducing the average Jacobian values in January relative to the other months
(Fig. 5). The ratio of the averaged Jacobian elements for January to those for July is 0.51 for the 1.57

Weekly fractional flux uncertainty reduction (RMS over the 4
months) for

Inversions for the 2.05

Biomes used, taken from Olson et al. (2001) with modifications by Gourdji et al. (2012).

For assessing large-scale changes in carbon sources and sinks it is useful
to aggregate high-resolution results to biomes and the entire continent, and
to seasons and years. We use the biome definitions in Fig. 9 taken from
Olson et al. (2001) with modifications by Gourdji et al. (2012). To
aggregate the flux uncertainties we summed up the variances within each
biome and over each month and then the year, in units of (Pg C yr

We compare our results with those from two other inversion systems: a global
inversion using ASCENDS observations (a companion study to this one) and a
North American regional inversion using the same WRF–STILT Lagrangian model
as ours but with a network of ground-based observation sites (Gourdji et
al., 2012). The global OSSE uses the same ASCENDS data set sampling and
underlying observation error model as the regional OSSE. Among the primary
differences are the global domain of the analysis (and thus the use of
observations outside and inside the North American domain) and the
coarser spatial resolution of the transport and flux solution,
4.5

Results aggregated to biomes and continent and compared
with other studies.

Flux uncertainties aggregated to entire continent and month
or year (Pg C yr

Uncertainty reductions are largest in July and smallest in January at the
continental scale (Table 2). The uncertainty reductions for the 1.57

At the annual biome scale our uncertainty reductions range from 50 % for the desert biome (averaged across the cases) to 70 % for the temperate grassland/shrubland biome (Fig. 10c). The reductions scale, as before, with increasing a priori uncertainty (Fig. 10a), observation quality and density, and now with the biome area (Fig. 10d). We find a modest correlation between uncertainty reduction and area in the set of biomes, with a linear correlation coefficient of 0.5. In addition, the uncertainty reduction is higher on the continental scale than on the biome scale. The a posteriori uncertainty increases with increasing area more slowly than does the a priori uncertainty because many of the a posteriori error covariance terms summed in the aggregation to biome are negative, whereas all of the a priori error covariance terms are positive or zero. This explains why uncertainty reduction tends to increase with increasing area.

Our a posteriori uncertainties range from 0.12 to 0.33 Pg C yr

We now discuss the implications of our analysis for the ASCENDS design.
Hungershoefer et al. (2010) suggested levels of posterior flux uncertainty
on different spatiotemporal scales that global CO

Hungershoefer et al. suggested that to determine the location of the global
terrestrial C sink and whether C cycle feedbacks are occuring one
requires annual net carbon flux estimates with a precision better than 0.1 Pg C yr

A simplifying assumption in our standard inversion is the neglect of uncertainties in the boundary conditions (BCs). It is especially important in a regional inversion (Eulerian or Lagrangian) to accurately account for the influence of lateral boundary inflow on concentrations within the domain (Göckede et al., 2010b; Lauvaux et al., 2012; Gourdji et al., 2012). Because we neglect BC uncertainties, we essentially assume that all of the information in the ASCENDS observations can be applied to reducing regional flux uncertainties rather than the combination of BC and flux uncertainties. Thus the amount of flux uncertainty reduction reported for our standard inversion may be higher than it would be if we accounted for BC uncertainties.

We conducted a test inversion for July (1.57

In addition to containing random errors, BCs can also be a source of
systematic errors. For example, Gourdji et al. (2012) found that two
plausible sets of BC around North America generated inferred fluxes that
differed by 0.7–0.9 Pg C yr

Sparseness of observations has been a major cause of uncertainty in the
boundary influence in previous regional inversions. Lauvaux et al. (2012),
who conducted mesoscale inversions for the US Midwest using tower
measurements, found BC errors to be a significant source of uncertainty in
the C budget over 7 months. They estimated that a potential bias of 0.55 ppm
in their BCs translates into a flux error of 24 Tg C over 7 months in their
1000 km

Ratio of the posterior uncertainty for the 2

Posterior uncertainties are generally sensitive to the assumed prior uncertainties, although one might not expect the sensitivity to be so great in the case of a dense observational data set such as the one examined here. We test this hypothesis with an alternative prior uncertainty estimate, one that is uniformly larger than that of the standard inversion by a factor of 2. Figure 11a–d shows the ratio of the posterior uncertainty of the large-prior inversion to that of the standard inversion, normalized by a factor of 2. Large areas of the domain have ratios significantly less than 1, especially in July and October. Where the ratio is close to 1, the posterior uncertainty is sensitive to the prior, indicating that the observations have a relatively weak influence; where the ratio is significantly less than 1, the posterior uncertainty is not so sensitive to the prior. The test demonstrates that the posterior uncertainty in many areas is not highly sensitive to the prior uncertainty and is strongly influenced by the observations. However, the sensitivity is high in the tundra and the desert due to the tight (small) prior constraints in those regions (Fig. 3).

Although the posterior uncertainty is not highly sensitive to the prior in all areas, it still increases everywhere in the large-prior inversion relative to the standard inversion, implying that our findings regarding whether or not the observations meet the target requirement (Sect. 4.1) are dependent on the assumed priors. However, our standard priors are already enlarged uniformly by a factor of 4 relative to one set of prior uncertainty estimates, and they would have to be enlarged further over large areas to substantially increase biome-level posterior uncertainties. In addition, the larger the prior uncertainties are, the larger the uncertainty reductions are in general. Wherever the posterior uncertainty increases by a factor smaller than the prior uncertainty does (e.g., where the ratio is less than 1 in Fig. 11), the uncertainty reduction increases. Altogether, the results of this sensitivity test suggest that it is important to consider different measures of the impact of observations on flux estimates, such as posterior uncertainty and uncertainty reduction, as we have done in this OSSE, given that different measures can be affected differently by assumptions such as prior uncertainties.

The inversion results are potentially sensitive to the assumed a priori flux
error correlation lengths, with longer correlation lengths leading to smoother uncertainty reduction patterns and larger uncertainty reductions.
Rodgers (2000) shows that the inclusion of a priori error correlations can
result in more “degrees of freedom for signal,” i.e., more information
provided by the measurements on the unknowns. We carried out a test with
alternative values for the correlation lengths derived from the study by
Chevallier et al. (2012): a shorter spatial correlation length of 200 km
and a longer temporal correlation length of 35 days for all months (we
estimated these values from Fig. 5a and b of Chevallier et al. for the

This analysis did not evaluate the impact of potential systematic errors
(biases) in the observations or the transport model, which are not well
represented by the Gaussian errors assumed in traditional linear error
analysis (Baker et al., 2010). Chevallier et al. (2007) demonstrated that
potential biases in OCO satellite CO

The potential combined use of multiple wavelengths in the ASCENDS
measurements, e.g., various offsets from 1.57

Our comparison of the results for the 1.57 and 2.05

We have conducted an observing system simulation for North America using
projected ASCENDS observation uncertainty estimates and a novel approach
utilizing a portable footprint library generated from a high-resolution
Lagrangian transport model to quantify the surface CO

Based on the flux precision on an annual biome scale suggested by
Hungershoefer et al. (2010) for understanding the global carbon sink and
feedbacks, ASCENDS observations would meet a threshold requirement for all
biomes within the range of the measurement designs considered here. The
observations constrain a posteriori uncertainties to a level of 0.01–0.06 Pg C yr

The results we have presented may be optimistic, since potential systematic errors in the observations, boundary conditions, and transport model that we have neglected would degrade the flux estimates. However, modifications to the size and location of our regional domain (e.g., an eastward shift) could improve the constraints by satellite observations on North American fluxes. In addition, our consideration of different measures of the impact of observations on flux estimates, such as posterior uncertainty and uncertainty reduction, strengthens the study, given that different measures can be affected differently by assumptions such as prior uncertainties.

In future work, inversions in various regions (including, for example, South America) with a more comprehensive treatment of error sources could more definitively establish the usefulness of ASCENDS observations for constraining fluxes at fine and large scales and answering global carbon cycle science questions.

Work at NASA and AER has been supported by the NASA Atmospheric CO