A regional CO2 observing system simulation experiment for the ASCENDS Satellite Mission

Introduction Conclusions References

(ASCENDS) satellite mission will provide greater coverage in cloudy regions, at high latitudes, and at night than passive satellite systems, as well as high precision and accuracy. In a novel approach to quantifying the ability of satellite column measurements to constrain CO 2 fluxes, we use a portable library of footprints (surface influence functions) generated by the WRF-STILT Lagrangian transport model in a regional Bayesian 10 synthesis inversion. The regional Lagrangian framework is well suited to make use of ASCENDS observations to constrain fluxes at high resolution, in this case at 1 • latitude × 1 • longitude and weekly for North America. We consider random measurement errors only, modeled as a function of mission and instrument design specifications along with realistic atmospheric and surface conditions. We find that the ASCENDS 15 observations could potentially reduce flux uncertainties substantially at biome and finer scales. At the 1 • × 1 • , weekly scale, the largest uncertainty reductions, on the order of 50 %, occur where and when there is good coverage by observations with low measurement errors and the a priori uncertainties are large. Uncertainty reductions are smaller for a 1.57 μm candidate wavelength than for a 2.05 μm wavelength, and are Earth Networks Greenhouse Gas Network, http://ghg.earthnetworks.com/), and satellite missions dedicated to measurement of CO 2 column amounts. The last include the Greenhouse gases Observing SATellite (GOSAT) launched in January 2009 (Yokota et al., 2009), the Orbiting Carbon Observatory 2 (OCO-2) to be launched in 2014 (Crisp et al., 2008;Eldering et al., 2012), and the planned Active Sensing of CO 2 Emissions 25 over Nights, Days, and Seasons (ASCENDS) mission recommended by the US National Academy of Sciences Decadal Survey (NRC, 2007). 12821 approaches estimate the reduction of flux uncertainties stemming from the availability of satellite data using an inverse solution for relatively coarse grid boxes or regions at weekly to monthly resolution (e.g. Houweling et al., 2004;Chevallier et al., 2007;Feng et al., 2009;Baker et al., 2010;Kaminski et al., 2010;Hungershoefer et al., 2010;Basu et al., 2013). The present study extends these global studies to the regional 20 scale using simulated ASCENDS data. Regional trace gas inversions are well-suited for making use of high-density satellite observations to constrain fluxes at fine scales. Regional transport models are less computationally expensive to run than global transport models for a given resolution, so it is more tractable to run a regional model at high resolution. The more precise determination of source-receptor relationships al-25 lows one to solve for fluxes at a finer resolution. This reduces potential "aggregation error" resulting from assuming fixed fine-scale flux patterns when optimizing scaling factors on a coarser scale (Kaminski et al., 2001;Engelen et al., 2002;Gerbig et al., 2003). We use a novel approach for our inversions that facilitates high-resolution evaluation of satellite column measurements. The approach relies on a Lagrangian (airmassfollowing) transport model, run backward in time from the observation points (receptors) using ensembles of particles, to generate footprints describing the sensitivity of satellite CO 2 measurements to surface fluxes in upwind regions. This approach en-5 ables more precise simulation of transport in the near field than running source pulses through an Eulerian (with fixed frame of reference) transport model, since, in the former, meteorological fields are interpolated to the subgrid-scale locations of particles. Thus, filamentation processes, for example, can be resolved (Lin et al., 2003), and representation errors (Pillai et al., 2010) are minimized. The Lagrangian approach, implemented 10 in the backward (receptor-oriented) mode, offers a natural way of calculating the adjoint of the atmospheric transport model. The utility of Lagrangian particle dispersion models is well established for regional trace gas flux inversions involving in situ observations (e.g. Gerbig et al., 2003;Lin et al., 2004;Kort et al., 2008Kort et al., , 2010Zhao et al., 2009;Schuh et al., 2010;Göckede et al., 2010a;Gourdji et al., 2012;Miller et al., 2012, 15 2013; McKain et al., 2012;Lauvaux et al., 2012). A convenient feature of Lagrangian footprints is their portability -they can be shared with other groups and readily applied to different flux models, inversion approaches, and molecular species, thus enabling comparisons based on a common modeling component. In addition, footprints for different measurement platforms can be merged easily in an inversion. 20 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 25 compute weekly flux uncertainties over a 1 • latitude × 1 • longitude grid. This study focuses on land-based biospheric fluxes. We report results based on realistic sampling and observation errors for ASCENDS and other input data fields for year 2007. Section 2 provides details on our inputs and inversion methods, and presents examples of Introduction observation uncertainties, a priori flux uncertainties, and WRF-STILT footprint maps. Section 3 presents posterior flux uncertainty results at various spatial and temporal scales, as well as comparisons with other studies, including preliminary results from a companion global ASCENDS OSSE. Section 4 discusses target and threshold requirements for instrument design parameters with respect to addressing key scien-5 tific questions. It also discusses additional sources of uncertainty and limitations of our analysis, as well as other considerations regarding ASCENDS. Section 5 contains concluding remarks. 10 We use a Bayesian synthesis inversion method, which optimizes the agreement between model and observed CO 2 concentrations and a priori and a posteriori flux estimates in a least-squares manner (e.g. Enting et al., 1995). Since we focus on uncertainty levels in estimating the constraint on fluxes that ASCENDS observations will provide, we did not perform a full inversion and computed only the a posteriori flux error 15 covariance associated with the inversion solution. The a posteriori flux error covariance matrix is given bŷ the week preceding each of those months). We focus on weekly flux resolution in this study, rather than daily or higher resolution, for computational efficiency. In addition, the Decadal Survey called for a satellite mission that can constrain carbon cycle fluxes at weekly resolution on 1 • grids (NRC, 2007). The ASCENDS observations would likely also provide significant constraints on fluxes at higher resolutions such as daily, as 10 suggested by test inversions not reported here. We solve Eq. (1) using the standard matrix inversion function in the Interactive Data Language (IDL) software package. We verified the solution using the alternative singular value decomposition approach (Rayner et al., 1999), again in IDL. Given the large dimensions of the matrices-more than 15 000 10 s average observations each month 15 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. 20 We consider candidate lidar wavelengths near 1.57 μm and 2.05 μm (Caron and Durand, 2009). These have peak sensitivities in the mid-and lower troposphere, respectively ( Fig. 1). Other candidate wavelengths with different vertical sensitivities and error characteristics are possible and could be assessed with the same inversion methodology. We derive the temporal/spatial sampling and random error characteristics for 25 ASCENDS pseudo-data based on real cloud/aerosol and surface backscatter conditions for year 2007 in a method similar to that of Kawa et al. (2010) (Fig. 2). The error calculations use CALIPSO optical depth (OD) data, 5 together with surface backscatter calculated from Moderate Resolution Imaging Spectroradiometer (MODIS) satellite reflectance over land or glint backscatter, calculated using 10 m analyzed wind speeds (Hu et al., 2008) interpolated to the sample locations, over ocean. Samples with total column cloud plus aerosol OD > 0.7 are rejected. For each wavelength case, the measurement errors at each location are scaled to across the 10 s span. Such a 10 s, conditionally-sampled measurement is expected to represent the basic ASCENDS CO 2 data granule. The uncertainties in the series of 10 s pseudo-data are assumed to be uncorrelated, i.e. the observation error covariance matrix S ε is diagonal. Examples of the coverage of ASCENDS observations available for analysis and their 20 associated uncertainties (for a reference uncertainty at RRV of 0.5 ppm) are shown in Fig. 2 over seven-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 s-average observations have uncertainties of < 2 ppm in all four cases except for 2.05 μm in January. The uncertainties are especially small 25 over land areas, which is helpful for constraining terrestrial fluxes. The uncertainties are generally larger for 2.05 μm than for 1.57 μm (by a factor of 1-1.6 over snow-free Introduction land and a factor of 1.6-1.8 over snow-/ice-covered areas) except in ice-free oceanic areas, where the uncertainties are similar ( Fig. 2e and f).

A priori flux uncertainties
We derived a priori flux uncertainties at 1 • × 1 • resolution from the variability of net ecosystem exchange (NEE) in the Carnegie-Ames-Stanford-Approach (CASA) bio-5 geochemical model coupled to version 3 of the Global Fire Emissions Database (GFED3) (Randerson et al., 1996;van der Werf et al., 2006van der Werf et al., , 2010. In the version of CASA used here, a sink of ∼ 100 Tg C yr −1 is induced by crop harvest in the US Midwest that is prescribed based on National Agriculture Statistics Service data on crop area and harvest. We neglected uncertainties in fossil fuel emissions, assuming 10 like most previous inversion studies that those emissions are relatively well known. We ignored oceanic fluxes as well for this study, since their uncertainties are also relatively small (e.g. Baker et al., 2010). 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 √ 7 to scale 15 approximately to weekly uncertainties. This approach assumes that the more variable the model fluxes are in a particular grid cell and month, the larger the errors tend to be; the same reasoning has been applied in previous inversion studies to the estimation of model-data mismatch errors (e.g. Wang et al., 2008). We enlarged the resulting uncertainties uniformly by a factor of 4 to approximate the magnitude of those used 20 in the global ASCENDS OSSE described in this paper; these are, in turn, essentially the same as the standard ones of Baker et al. (2010), based on differences between two sets of bottom-up flux estimates. In addition to allowing for better comparison of the two OSSEs, the enlargement by a factor of 4 is consistent with suggestions by biospheric model intercomparisons that the true flux uncertainty is greater than that 25 based on a single model's variability (Huntzinger et al., 2012).
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 12827 Introduction with month-specific correlation lengths (Table 1) estimated from ground-based and aircraft CO 2 data in a North America regional inversion by Gourdji et al. (2012). Although these correlation lengths are not strictly applicable to our study, which has a different setup from that in the geostatistical inverse modeling system of Gourdji et al., they are nonetheless reasonable estimates in general for the purposes of this study. Note 5 that Gourdji et al. used a 3 hourly flux resolution, so the temporal correlation lengths may be too short for the coarser weekly resolution of our study. Chevallier et al. (2012) show that aggregation of fluxes to coarser scales increases the error correlation length. The analysis by Chevallier et al. (2012) using global flux tower data found a weeklyscale temporal error correlation length of 36 days, longer than the values we use. They 10 found a spatial correlation length of less than 100 km at the site scale (∼ 1 km), increasing to 500 km at a 300 km-grid scale; our correlation lengths (100 km-grid) mostly fall within that range. In a test, we used alternative values for the spatiotemporal correlation lengths derived from the Chevallier et al. study, and found that the inversion results are moderately sensitive (Sect. 3.1).
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).

WRF-STILT Model, Footprints, and Jacobians
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 ap-25 plication of STILT (www.stilt-model.org, revision 640), hourly output from WRF version 2.2 is used to provide the transport fields at a horizontal resolution of 40 km with 31 eta levels in the vertical, over a North American domain (Fig. 2a) from the North American Regional Reanalysis (NARR) at 32 km resolution are used to provide initial and boundary conditions for the WRF runs. To prevent drift of the WRF simulations from the analyses, the meteorological fields (horizontal winds, temperature, and water vapor at all levels) are nudged to the NARR analysis every 3 h with a 1 h relaxation time and are reinitialized every 24 h (at 00:00 UTC). Simulations are run out for 30 h, but only hours 7-30 from each simulation are used to avoid spin-up effects during the first 6 h. The WRF physics options used here are the same as those described by Nehrkorn et al. (2010). 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 10 units of mixing ratio per unit flux. This is to be distinguished from a satellite footprint, 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 posi-15 tions a.g.l. 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 ∼ 90 000 footprint calculations per day, placing stringent demands on our computational approach. In this study, STILT simulates the release of an ensemble of 500 particles at 20 each receptor in the column.
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 the fluxes upwind at the same level. So intuitively, the footprints defined for receptor points lo-25 cated 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 ACPD 14, 12819-12862, 2014 A regional CO 2 observing system simulation experiment levels (e.g. 0.5, 1.5, 2.5 km) tend to have large footprints (with values of the order of 10 −3 ppm (μmol m −2 s −1 ) −1 or higher), being most influenced by nearby surface fluxes. 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 μm wavelengths. Nonzero footprints occur wherever air observed at the receptor site has been in contact with 5 the surface within the past 10 days. Patterns of vertical and horizontal atmospheric motion explain the somewhat unexpected spatial patterns of the footprints in this particular example, with very high values occurring at a significant distance upwind of the receptor (in the vicinity of Texas and Oklahoma) as well as immediately upwind. Vertical mixing lifts the signature of surface fluxes to higher levels, so that it can be detected by receptors at multiple levels, resulting in a higher value for the vertically-convolved footprint, while slower winds in a particular area, such as Texas and Oklahoma, can result in a larger time-integrated impact of fluxes on the observation. The footprint values are larger for 2.05 μm due to the higher sensitivity of that measurement near the surface, as previously discussed.

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To construct the Jacobians, K, that enter Eq. (1), we averaged the footprints of all the 5 km receptor locations within a given 10 s interval, including only the land cells. We arranged the averaged footprints in a two-dimensional Jacobian, running across flux time intervals and grid cells in one direction and across observations in the other. (The 3 h flux intervals associated with each transport run are defined relative to fixed 20 UTC times and not relative to the observation times.) We then aggregated the Jacobian elements to the final flux resolution, e.g., weekly. For any particular month, we solved only for fluxes occurring in the week prior to the beginning of the month and in the first 4 weeks of that month. Figure 5 shows the overall influence of the surface fluxes on the observations during 25 each month (i.e. the average weekly Jacobian values for the 1.57 μm weighting function). Values tend to decrease from west to east, reflecting the general westerly wind direction, which transports CO 2 influences out of the domain more quickly for fluxes occurring closer to the eastern edge than for those farther west. Values also tend to ACPD 14, 12819-12862, 2014 A regional CO 2 observing system simulation experiment decrease towards the north and northwest and in the southernmost part of the continent: these areas lie close to the edges of the domain shown in Fig. 2a. Areas with smaller average footprint values are generally not as well constrained by the observations, as will be discussed later in this paper; thus, our domain boundaries artificially limit flux constraints in certain parts of the continent. Previous regional inversion stud-5 ies may not have highlighted this issue because they used ground-based observations, whose sensitivities are more confined to near-field fluxes than those of satellite column measurements. We will quantify the impact of the boundaries on average footprint gradients in future work, providing guidance for future studies on optimal sizes and shapes of domains (e.g. shifted eastward) for avoiding large gradients while controlling computational cost. Footprint values are largest in summer, again due 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, and vertical mixing across the deep boundary layer brings particles over 15 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 this analysis (discussed further in Sect. 4.2). Similarly, we neglect uncertainties 20 due to 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.

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In the following, we present results for four cases involving different combinations of measurement wavelength and baseline error level: 1.57 μm and 0.5 ppm RRV error

A posteriori flux uncertainties at the grid level
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 uncer-5 tainty 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 east and close to the other edges; thus, the former can be better constrained in this inversion.
Another feature is that 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: 5 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. and thus reducing the average Jacobian values in January relative to the other months (Fig. 5). The ratio of the average of the Jacobian elements over the domain for January to that for July is 0.51 for the 1.57 μm wavelength.
Inversions for the 2.05 μm wavelength, with its higher sensitivity near the surface, result in greater uncertainty reduction, despite the larger observation errors over land 20 (Fig. 8c vs. a, and d vs. b). Inversions assuming 1.0 ppm instead of 0.5 ppm error at RRV result in less uncertainty reduction (Fig. 8b vs. a, and d vs. c) as expected, with maximum uncertainty reduction of ∼ 30 % vs. ∼ 40 %, for 1.57 μm. These cases are compared further in the section below on biome-aggregated results.
The inversion results are sensitive to the assumed a priori error correlation lengths, 25 with longer correlation lengths leading to more smooth uncertainty reduction patterns and larger uncertainty reductions. The reason for this is that longer a priori error correlation lengths result in fewer "unknowns" to be constrained by the observations. Rodgers (2000) shows that the inclusion of a priori correlations can result in more "degrees of . Apparently, the decrease in the spatial correlation length relative to the standard inversion has a larger effect than the increase in the temporal correlation length.

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We conclude that our inversion results vary moderately given two reasonable sets of estimates for the a priori spatiotemporal error correlation lengths.

Comparison with global inversion
We compare our regional OSSE results with those from a companion global OSSE to assess effects of methodological differences. The global OSSE uses the same 15 ASCENDS dataset sampling and underlying observation error model as the regional OSSE. Among the primary differences are the global domain of the analysis and the coarser spatial resolution of the transport and flux solution, 4.5 • latitude × 6 • longitude.
Other differences include the mathematical technique of the inversion (variational data assimilation, as in an earlier study, Baker et al., 2010), the Eulerian transport model, 20 the spatial patterns of the a priori flux uncertainties (the overall magnitudes are not different, as described in Sect. 2.3), and the assumption of zero a priori correlation among fluxes (which can be justified by the coarser spatial scale). Comparison of our inversion results with results from the global study yields insight into the effect of inversion resolution on estimated flux uncertainties.

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To aggregate our flux uncertainties to 4.5 • × 6 • resolution (in units of μmol m −2 s −1 ) for comparison with the global inversion, we computed the variance of the average of the between the fine-scale cells and accounting for fractional overlap of some of the 1 • × 1 • cells with a 4.5 • × 6 • cell. Aggregating our a priori and a posteriori uncertainties in this manner, we find that our fractional uncertainty reductions over the 4 months are substantially smaller overall than those of the global inversion (Fig. 9). The differences in spatial distribution can be attributed in part to the different a priori uncertainty patterns.

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Reductions greater than 55 % cover large areas of North America in the global inversion, reaching values of over 75 %, whereas only a few 4.5 • × 6 • cells exhibit values greater than 55 % in the regional inversion. Note that we are not comparing exactly the same quantity, as the variational inversion method does not directly compute a full a posteriori error covariance matrix; rather, it uses (estimate -truth) statistics as a proxy 10 for uncertainty, which is accurate for a sufficiently large sample . One possible reason for the difference in results is that information from the observations is used to optimize the fine-scale patterns in addition to the coarse-scale magnitudes in our inversion, in contrast to the global inversion in which a flat spatial distribution of flux is assumed inside each coarse grid box, providing an additional constraint on the 15 fluxes. Thus, in our inversion, less information is available to reduce the uncertainties of the coarse-scale magnitudes, causing our uncertainty reductions to be smaller than those of the global inversion when compared at the same scale. (Note however that our imposing of a priori flux error correlations provides an additional constraint on fluxes and reduces the difference in effective flux resolution between the two studies.) On the 20 other hand, the coarser global inversion is affected by larger aggregation errors (Kaminski et al., 2001;Engelen et al., 2002;Gerbig et al., 2003), which are not accounted for in the uncertainty reduction values. Another factor that likely contributes to the larger uncertainty reductions in the global inversion is that it allows fluxes to be constrained by observations both outside and inside a particular region. This can be especially important for fluxes close to the regional edges, as was discussed in Sect. 3.1. We do not attempt to quantify the individual impacts of the two main methodological differences or the various other differences.

Results aggregated to biomes and continent
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. 10 taken from Olson et al. (2001) with modifications by Gourdji et al. (2012). We used a similar approach for aggregating our 5 results here to the one we used to aggregate results to a coarser grid (Sect. 3.2). In addition, we aggregated the global inversion results to the same biomes for comparison, summing the (estimate -truth) values and accounting for fractional biome coverage in each of the coarse grid cells. Uncertainty reductions are largest in July and smallest in January, at the continental scale ( Table 2). The uncertainty reductions for the 1.57 μm wavelength are on average 8 % smaller than those for 2.05 μm. The uncertainty reductions for the 1.57 μm wavelength with 0.5 ppm error are larger than those for 2.05 μm with 1.0 ppm error. The uncertainty reductions for 0.5 ppm error are on average 16 % larger than those for 1.0 ppm error. (Note that there is no reason to expect direct proportionality between measure-15 ment uncertainties and a posteriori flux uncertainties (Eq. 1), nor is there reason to expect proportionality between uncertainty reduction and a posteriori uncertainty.) The uncertainty reduction for the inversion with alternative a priori error correlation lengths, aggregated to the continent and month, is less than that for the standard inversion for all months except July, for which the uncertainty reduction is marginally larger. For 20 July, the impact of the much longer temporal correlation length relative to the standard inversion on the aggregated result more than offsets that of the slightly shorter spatial correlation length. The annual uncertainty reduction for the alternative inversion is slightly larger than that for the standard inversion, because of the disproportionate influence of July, with its large a priori uncertainty.

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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. 11c). The reductions scale with increasing a priori uncertainty (Fig. 11a)

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | and observation quality and density, as before, and now also with biome area (Fig. 11d). We find a modest correlation between uncertainty reduction and area in the set of biomes here, 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 uncer-5 tainty since many of the a posteriori error covariance terms that are 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 −1 at the monthly, con-10 tinental scale across all four cases (Table 2), from 0.04 to 0.08 Pg C yr −1 at the annual, continental scale (Fig. 11a), and from 0.01 to 0.06 Pg C yr −1 at the annual, biome scale (Fig. 11a). To put these numbers into perspective, the estimated current global terrestrial sink is roughly 2.5 Pg C yr −1 (Le Quéré et al., 2012). Our uncertainties are generally similar to those from the North American regional inversion of Gourdji et al. (2012) 15 (Fig. 11a) and the global inversion (Fig. 11b) coverage of ASCENDS as compared to the in situ network; some of the biomes are not well constrained by the in situ network (i.e. the ones for which Gourdji et al. did not report aggregated results). Note that the comparison is not a precise one, given the methodological differences. The global inversion's method for estimating uncertainties based on (estimate -truth) statistics cannot provide an annual uncertainty estimate 25 for the one-year inversion and produces somewhat noisy results for individual months. Therefore, to compare the regional and global inversions, we took the RMS of the four monthly uncertainties. Our uncertainty reduction is smaller than that of the global inversion across all biomes for Case 1 (Fig. 11c) of similar magnitude on average (Fig. 11b). However, the continent-level uncertainty reductions are similar, at 78 % and 83 %, respectively, suggesting that there are larger negative correlations in the posterior errors among biomes in our analysis. 5 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 2 measurement missions should strive for to allow for answering key carbon cycle science questions. In the following, we evaluate our results relative to those requirements, the only such specific guidelines for CO 2 satellite 10 missions in the scientific literature. Hungershoefer et al. suggested that to determine where the global terrestrial C sink is occurring and whether C cycle feedbacks are occurring requires annual net carbon flux estimates with a precision better than 0.1 Pg C yr −1 (threshold) or 0.02 Pg C yr −1 (target) at a scale of 2000 km × 2000 km, similar to the biomes we consider. These pre-15 cision levels are based on the range of estimated fluxes across various biomes. The proposed A-SCOPE active CO 2 measurement mission defined a similar target requirement -0.02 Pg C yr −1 at a scale of 1000 km×1000 km (Ingmann et al., 2008). According to our results (Fig. 11a), all tested ASCENDS cases would meet the minimum threshold requirement across all biomes easily, with a posteriori uncertainties ranging from 0.01 20 to 0.06 Pg C yr −1 . In addition, the two cases with 0.5 ppm error would meet the more stringent target requirement for a majority of biomes, while the two cases with 1.0 ppm error would meet it for 3 out of 7 biomes. The meeting of the target requirement is a consequence of the information provided by the observations and not merely an effect of the specified a priori uncertainty, given that the a priori uncertainty is higher than the target level for all of the biomes with the exception of desert, the prior uncertainty for which is already at the target level.

Boundary condition uncertainties
A simplifying assumption in this analysis is the neglect of uncertainties in the boundary conditions (b.c.). It is especially important in a regional inversion (Eulerian or La-5 grangian) 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 b.c. 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 b.c. and flux uncertainties. Thus, the 10 amount of flux uncertainty reduction reported here is likely higher than it would be if we accounted for b.c. uncertainties. The magnitude of b.c. errors can be substantial. In addition to containing random errors, b.c. can also be a source of systematic errors. For example, Gourdji et al. (2012) found that two plausible sets of b.c. around North America generated inferred fluxes 15 that differed by 0.7-0.9 Pg C yr −1 on the annual, continental scale (which is a very large amount compared to the annual a posteriori uncertainties for North America of 0.04-0.08 Pg C yr −1 that we estimated in our OSSE, Fig. 11a). They concluded that b.c.
errors may be the primary control on flux errors at this coarse scale, while other factors such as flux resolution, priors, and model transport are more important at sub-domain 20 scales. 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 b.c. errors to be a significant source of uncertainty in the C budget over 7 months. They 25 estimated that a potential bias of 0.55 ppm in their b.c. translates into a flux error of 24 Tg C over 7 months in their 1000 km × 1000 km domain. Although they applied corrections to the model-derived b.c. using weekly aircraft profiles at four locations near 12839 Introduction their domain boundaries, they stated that the b.c. uncertainties were still large given the limited duration (a few hours per week) and spatial extent of the airborne observations, and concluded that additional observations would be necessary to reduce the uncertainties. ASCENDS is promising in this respect, as it (along with other satellites) will provide more frequent and widespread observations of concentrations at regional 5 boundaries, possibly lowering the role of b.c. in the overall C budget uncertainty to a minor one. ASCENDS observations could specifically be used in a global CO 2 data assimilation system to provide accurate b.c. for the regional flux inversion.

Other sources of error
This analysis did not evaluate the impact of potential systematic errors (biases) in 10 the observations or the transport model, which are not well represented by the Gaussian errors assumed in traditional linear error analysis . Chevallier et al. (2007) demonstrated that potential biases in OCO satellite CO 2 measurements related to the presence of aerosols can completely negate the improvements to prior uncertainties provided by the measurements for the most polluted land regions and for 15 ocean regions. In another OCO OSSE, Baker et al. (2010) found that a combination of systematic errors from aerosols, model transport, and incorrectly-assumed statistics could degrade both the magnitude and spatial extent of uncertainty improvements by about a factor of two over land, and even more over the ocean. Thus, it will be important to control systematic errors in ASCENDS observations and the transport model 20 as well as minimizing random errors. Note that systematic observation errors can be expected to decrease over the course of the mission as adjustments are made to the measurement system and to the retrieval algorithms in calibration/validation activities.

Other considerations in evaluating ASCENDS
The potential combined use of multiple wavelengths in the ASCENDS measurements, Introduction fluxes given the sensitivities to concentrations at different levels of the atmosphere. Furthermore, other CO 2 datasets will certainly be available alongside the ASCENDS data (e.g. from in situ networks), and the combination of datasets will provide stronger constraints on fluxes than any individual dataset (Hungershoefer et al., 2010). Our comparison of the results for the 1.57 and 2.05 μm wavelengths over North

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America may be less applicable to other parts of the world. The global OSSE study by Hungershoefer et al. (2010), which compared various observing systems, including a satellite lidar system similar to ASCENDS, A-SCOPE, found that the 1.6 μm wavelength results in larger uncertainty reductions over South America while performing less well than 2.0 μm over temperate and cold regions. They attribute the better perfor-10 mance of 1.6 μm over South America to the strong vertical mixing of air there, which lessens the disadvantage of that wavelength's having weaker sensitivity to the lower troposphere. (However, they used a simpler error formulation.) On the other hand, in our global inversion, 2.05 μm results in larger uncertainty reductions than 1.57 μm throughout the world, by 8 % on average (for RRV error of 0.5-1.0 ppm).

Conclusions
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 2 flux constraints provided by the future observations. We consider 20 four possible configurations for the active optical remote sensing instrument covering two weighting functions and two random error levels. We find that the ASCENDS observations potentially reduce flux uncertainties substantially at fine and biome scales. across the biomes, and for 0.5 ppm RRV reference error are on average ∼ 25 % larger than those for 1.0 ppm error. Our uncertainty reductions are substantially smaller than those of a global AS-CENDS inversion at the 4.5 • × 6 • scale of the latter's model grid and at the biome scale. The global inversion benefits from the use of observations located around the 10 world rather than in a limited region, and it has fewer unknowns to be solved for within North America. On the other hand, inversions at higher resolution enable investigation of biospheric and other processes at the finer scales that are needed to understand the mechanisms for inferred CO 2 flux variability and trends. In addition, by reducing aggregation error, higher-resolution inversions can produce flux estimates with less system-15 atic error than those of lower-resolution inversions when aggregated to the same scale. 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 measurement designs considered here. The observations constrain a posteriori uncer-20 tainties to a level of 0.01-0.06 Pg C yr −1 , and could thus help pin down the location and magnitude of long-term C sinks. With regards to the more stringent target requirement, a subset of the instrument designs would meet the target for a majority of biomes.
The results we have presented may be optimistic, as uncertainties in boundary conditions and potential systematic errors in the observations and transport model that we 25 have neglected would degrade the flux estimates. On the other hand, 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 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.

ACPD
Acknowledgements. Work at NASA and AER has been supported by the NASA Atmospheric 5 CO 2 Observations from Space program element and NASA ASCENDS Pre-Phase A activity funding. We are grateful to the NASA Ames HEC facility staff for assistance in executing the WRF-STILT runs on the Pleiades supercomputer, and to the NASA HEC Program for granting use of the Dali system at the NASA Center for Climate Simulation. We also thank J. Abshire, E. Browell, and R. Menzies for contributions to ASCENDS data characterization, G. J. Collatz 10 for making available the CASA-GFED fluxes that we used to construct the a priori uncertainties, R. Aschbrenner for help with the footprint calculations, S. Gourdji for providing correlation parameters and the biome map, P.