Evaluating and attributing uncertainties in total column
atmospheric CO

Here we test the reported uncertainties of version 7 OCO-2 XCO

Variations of total column CO

The OCO-2 instrument measures radiances in the molecular oxygen (O

Nadir observations usually return useful measurements only over land. Glint observations return useful data over both land and ocean. Here, we discriminate land-glint and ocean-glint observations because they have different error statistics. We do not evaluate Target data in this analysis due to spurious statistics that are observed with the Target data.

As discussed in Boesch et al. (2006), Connor et al. (2008), and O'Dell et al. (2012 and
references therein), total column estimates of XCO

We use version 7 of the OCO-2 data, the first OCO-2 product distributed for
general users. These data, like those described for GOSAT data in Wunch et al. (2011), are bias-corrected using a fit to retrieved aerosol optical depth
and the retrieved vertical CO

We find empirically that use of data with warn levels less than 10 improves the comparison between the calculated uncertainties and observed variance as discussed in the Appendix.

We evaluate the uncertainties of the XCO

As discussed in O'Dell et al. (2012), a CO

For the next three sections, we test the following hypotheses regarding the
observed distributions within the collection of “small neighborhoods” and
their calculated uncertainties:

H1: observed variability in small neighborhood is due to natural XCO

H2: observed variability in small neighborhood is due to measurement noise.

H3: observed variability is correlated.

H4: observed variability within a small neighborhood is described by a
slowly varying bias that is not explained by natural XCO

To evaluate whether measurement noise in the radiances is the primary factor
driving variability within a small neighborhood we first assume that the
terms

In order to test whether natural variability, or

The calculated, observed, and modeled uncertainties for land-nadir observations. The black circles are the observed
distributions and red circles are modeled distributions.

Observed and modeled distributions for land-glint data.

We next compare observed variability across all the neighborhoods to the
calculated uncertainties using two approaches. In the first approach we
gather all observations that have approximately the same calculated
measurement uncertainty due to noise,

Calculate the

Collect all of the

Compare the standard deviation of the collection of

We next test whether the calculated measurement noise is a useful value for
predicting the expected distribution of observations within a neighborhood.
Because each

We next test whether the observed variance, versus that due to measurement
noise or sampling, explains the upper right panel of Figs. 1, 2, and 3. To
perform this test, we perform the following steps:

Within each neighborhood, replace the calculated measurement error with the “actual” measurement error as shown by the solid red line in the upper left panel of Figs. 1, 2, and 3, for each observation.

Create a simulated distribution of observations based on this new uncertainty.

Randomly sample (or take) one of these observations

Repeat steps 1–3 for all observations in the neighborhood.

Calculate the variance of this “modeled” set of observations for each neighborhood.

Observed and modeled distributions for sea-glint data.

Distribution of XCO

The red dots in Figs. 1b, 2b, and 3b show the modeled distributions using the steps discussed above. The modeled distribution is more consistent with the mean of the observed distribution relative to the one-to-one line. However, it is clear from this simulation that errors due to random noise and sampling do not explain the observed variance for each neighborhood although the distribution of variances for the ocean show much better agreement relative to the land distributions.

We next test whether observed correlations in the data could explain the
distributions of the data within a neighborhood. Figure 4 shows the joint
distribution of the XCO

In order to test whether these observed correlations could explain the
distributions shown in Figs. 1, 2, and 3, we conservatively use a
correlation coefficient of 0.7 for all observations (an extreme case). We
then use the following procedure, building on the steps described in the
previous section.

Within each neighborhood replace the calculated measurement error with the “actual” measurement error as shown in the upper left panels of Figs. 1, 2, and 3 for an observation.

Starting with the first observation (in time) within a neighborhood for Footprint #1, sample a value for the observation from the distribution of “actual” measurement errors. Label this the “modeled” observation.

For all subsequent observations in time for Footprint #1, sample each “modeled” observation from a distribution that is correlated with the modeled observation at the previous time step and has a variance corresponding to the “actual” measurement error.

For observations in Footprints #2–8, sample each modeled observation from a distribution correlated with the modeled observation at the same time step in the previous (adjacent) footprint, again with a variance corresponding to the “actual” error.

Calculate variance of this “modeled” set of observations, for each neighborhood.

As can be seen in the lower left panels of Figs. 1, 2, and 3, adding correlations to the data makes the comparison worse because the modeled distributions become much narrower relative to the modeled distributions in the upper right panels of these figures. Our conservative choice of a 0.7 correlation between observations at adjacent times and footprints illustrates this effect clearly. We therefore conclude that while correlations are empirically observed in the data, they cannot completely explain the observed distributions within the small neighborhoods.

We next examine whether “non-random” uncertainties could explain the
observed distributions in the upper right panels of Figs. 1, 2, and 3. For
example, as shown in Eq. (1), the jointly retrieved parameters (

The difference between XCO

Figure 6 shows the variation of XCO

For land-nadir, land-glint, and ocean-glint data the variance of the slopes
is given by 1.28 ppm 100 km

To test whether these slowly varying changes explain the distribution of
XCO

Within each neighborhood replace the calculated measurement error with the “actual” measurement error as shown in the upper left panels of Figs. 1, 2, and 3 for an observation.

Starting with the first observation (in time) within a neighborhood for Footprint #1, sample a value for the observation from the distribution of “actual” measurement errors. Label this the “modeled” observation.

For all subsequent observations in time for Footprint #1, sample each “modeled” observation from a distribution that is correlated with the modeled observation at the previous time step and has a variance corresponding to the “actual” measurement error.

For observations in Footprints #2–8, sample each modeled observation from a distribution correlated with the modeled observation at the same time step in the previous (adjacent) footprint, again with a variance corresponding to the “actual” error.

Adjust each modeled observation with a linear function where the slope of the linear function is randomly chosen from the fitted Laplace distribution to the slopes (e.g., the Laplace function shown in Fig. 7).

Calculate variance of this “modeled” set of observations, for each neighborhood.

Each typical observation has a random error related to noise and a
systematic error that is in principle bounded by the calculated interference
error (e.g., Boxe et al., 2010) and is approximately 0.2 ppm. Within a typical
grid box an OCO-2 observed measurement over land is within

In contrast, the observed distributions of slopes for the ocean data is 0.48 ppm 100 km

We find no relationship between the distribution of slopes for a
neighborhood and the corresponding mean of the calculated interference error,
suggesting that the calculated interference error does not explain the
observed slope within a neighborhood, in contrast to the measurement error.
However, there is a correlation between the slope and the estimated
magnitude of interferences, such as aerosol optical depth, surface albedo,
and surface pressure. For example, the correlation between the slopes of
land-glint data with the mean uncertainty in the interferences is 0.06
whereas the correlation between the observed slopes in XCO

We compare XCO

This 0.65 ppm estimate for the accuracy of the land data is likely a lower bound because it is based on observed gradients across a region with the bias removed.

For example Wunch et al. (2017) shows that the root-mean-square difference between the land nadir and glint data is 1.36 ppm, which is twice the value that we obtain for the accuracy. However, both ours and that of Wunch et al. (2017) suggest a relationship between these larger than expected uncertainties in the OCO-2 data and interferences due to surface properties or aerosols.

This analysis sheds further light on the sources of uncertainty of the
observed XCO

The data used in this paper are publicly accessible at the following web page:

This appendix provides supporting analysis for the results discussed in the
main text by comparing the distribution of synoptic variability of XCO

Distribution of all data used in this analysis for sea glint with
no data quality flags used (all warn levels are used).

Same as Fig. A1 but using only data with “warn levels” < 10.

Figures A1–A6 show comparisons of the expected distribution for all
data used in this analysis (black line) with the actual distribution (red
line). The components due to natural variability, noise, and interferences
are shown on the bottom of each figure. Note that the

Same as Fig. A1 but for land glint.

Same as Fig. A2 but for land glint.

Same as Fig. A1 but for land-nadir scenes.

Same as Fig. A2 but for land-nadir scenes.

The authors declare that they have no conflict of interest.

Part of this research was carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration. Funding for Susan Kulawik provided by
NASA Roses NMO710771/NNN13D771T, “Assessing OCO-2 predicted sensitivity and
errors”.