We estimate the overall

About 43 % of global anthropogenic carbon dioxide (

Bottom-up (BU) inventories (e.g., of

Tracking emissions from a TD perspective requires observations. Various
networks, such as the Total Carbon Column Observing Network (TCCON) and the
National Oceanic and Atmospheric Administration (NOAA) Earth System Research
Laboratory (ESRL) in situ

Within the past 10 years, two satellites have been shown to have high-precision (better than 1 ppm) small-footprint (

We test trajectory-based inversion schemes to see if they can reproduce known
emissions (from inventories and previous studies) from the California South
Coast Air Basin (SoCAB). Our goal is not to apportion spatially, but rather
to come up with a single number for the total flux and an estimate of
uncertainty. Fluxes from this urban area (pop.

We use observations of column-averaged dry-air mole fraction (denoted

Data are obtained from the TCCON and OCO-2. We use TCCON data from the
California Institute of Technology (Caltech) site in Pasadena, California

OCO-2 data are available starting September 2014 when the instrument began
its nominal operational mission

In Appendix

Our flux estimate involves scaling the a priori spatial inventory, or
subregions of the prior up or down to reduce the measurement–model mismatch.
More important than the total prior absolute flux is the distribution of
sources. EDGAR (Emissions Database for Global Atmospheric Research;

This same prior is used for CO, but total emissions are 1 % of

A priori flux maps for

A detailed

For our methane prior we first distribute emissions from landfills as point
sources (available 2010–2015,

We use various publicly available statistics to get a sense of annual

Statistics for the SoCAB.

Most of these values are approximations.

A dynamical model is needed in conjunction with the a priori flux estimates
to generate forward model

We use the North American Mesoscale Forecast System (NAM) at 12 km
resolution (3 h temporal) from the NOAA data archive as the primary model
source. NAM is run with a non-hydrostatic version of the WRF at its core with
a Mellor–Yamada–Janjić planetary boundary layer (PBL) scheme

We use HYSPLIT-4

Figure

HYSPLIT 400 m a.g.l. back trajectories for NAM 12 km for 2015.
For each day trajectories are shown ending at the two different TCCON receptor
sites at 14:00 (UTC

Others interested in undertaking similar studies may also consider using the
recently developed X-STILT (X-Stochastic Time-Inverted Lagrangian Transport)
model to obtain footprints for column observations

Different schemes can be applied to reduce the measured–model mismatch. One
of the simplest is to find the ratio between the average enhancements in the
observations and the forward model and then to scale the prior
based on this ratio. Bayesian inversions are more complex, but can also
improve information on the spatial distribution and intensity of fluxes

In summary, we have four sets of observations of

Several previous studies have discussed the SoCAB

Histograms of

Table

SoCAB

Models that assimilate only global in situ (i.e., no total column)

Our flux estimate of

Most of the estimates from previous studies include only emissions from
fossil fuel use. We have not separately accounted for biospheric uptake
(emissions) in the model, and if it is significant, the anthropogenic flux
would be larger (smaller) than our net estimate. In the GEOS-Chem model
described by

Estimates of SoCAB

OCO-2 provides better spatial coverage than TCCON
(Fig.

A visualization of OCO-2 observations and the forward model used in
the flux inversion on 20 June 2015. The nadir track is shown in red starting
at the bottom and

Using the same methodology we estimate a

SoCAB

We also estimate a CO flux of

For a single estimate of the SoCAB flux, we have a sufficiently large sample
that random uncertainty is small. This is supported by a bootstrap analysis
in which we select a random subset of data equal in size to the original

Several variables (

Assessment of sensitivity to initial values for

We next test the sensitivity to different inversion and modeling schemes
(Table

Fluxes from various methods.

For a given gas, all the inversions use the same observed

There is some uncertainty due to the accuracy and resolution of the emission
inventories.

Finally we consider the observation uncertainty.

In summary, we estimate 5 % random uncertainty from the bootstrap
analysis, 10 % from our choice of initial values, 5 % from the prior
flux, 10 % from observations and the boundary condition, and 20 %
from model winds (Appendix

Emission ratios can help us evaluate the inversion for the SoCAB. In previous
studies it was noted that the Pasadena area is a good receptor site for the
basin, so tracer–tracer ratios observed there should approximately correlate
with emission ratios

We estimate emission ratios using the solar zenith angle (SZA) anomaly method
described by

Emission ratios compared with previous studies. Numbers shown are
central values from the different methods and studies. Overall fits are shown
as dashed lines. The ratio from the gradients of Pasadena (Caltech) to Lancaster (AFRC)
is based on the difference between the two TCCON sites. Values
from

In November 2015, the large

Weekday : weekend emission ratios.

The weekday-to-weekend (WD : WE) flux ratios are listed in
Table

This study demonstrates a method to readily obtain estimates of net

This study is one of only a few in which satellite observations were used to
help infer the net flux of

The overall uncertainty is 25 %, with the dynamical model contributing
the most. X-STILT

TCCON data used in
this study (GGG2014: Iraci, et al., 2014; Wennberg et al., 2014) are hosted at the TCCON data archive
(

GOSAT–ACOS v2.9

Compared with the TCCON, OCO-2 spectra have a lower resolution. OCO-2
observations are also sensitive to surface albedo and are more sensitive to
aerosol scattering than solar-viewing instruments. These sensitivities can
cause spurious results, which need to be filtered out. Included in the OCO-2
data is a binary flag as well as warn levels (WLs) for quality filtering. WLs are a global metric of data quality, for which WLs less than or equal to
(0, 1, 2, 3, 4, 5) correspond to about (50 %, 60 %, 70 %,
80 %, 90 %, 100 %) of data passing in v8r, and larger WLs
generally correspond to less reliable data. WL definitions are different for
v7 and v8, but here we use the binary

For TCCON observations we use the public data, which already have some static within-range filters applied. We also exclude data that differ from the model by a factor of 10 or greater, leaving 4872 observations.

To eliminate the ambient

Because we expect most of the difference in

Even in the absence of local anthropogenic emissions, the

Histogram of wind speed errors (HYSPLIT minus measured) compared to
surface observations at the San Gabriel airport. The mean error is

Dynamical models can have errors in the PBL height estimation as well as in
the wind speed and direction. In a case study for spring 2011 and 2012
primarily over the Midwestern US, a NAM temperature-derived PBL height had a
mean bias of about

Trajectory speed and direction are estimated based on when and where
trajectories ending at 50 m a.g.l. enter a 5 km radius circle around the
receptor site. Results are shown in Fig.

HYSPLIT mean trajectories are air parcel locations at different heights for
select times (in our case, every 20 min). These are aggregated and
normalized for each

Maps of monthly averaged residence times in the mixing layer per pixel for
trajectories ending at 21:00 UTC, shown for all times leading up to the
observation. Pixels are

The Kalman filter used to estimate SoCAB

We initialize the iterations with an arbitrary scaling factor

We iterate over the

Some single scale factor inversions can be written in the form

Effects of scaling a random subset of model data compared to no scaling. When fewer points are scaled, they are scaled by a larger amount. The Kalman filter and nonlinear inversion are more affected by a few strong outliers than the linear inversion.

This is demonstrated in a sensitivity test, in which we scale a subset of points
(Fig.

The Bayesian approach to solving atmospheric inverse problems has been
described in more detail by

Extent of the eight spatial subregions. C: center; Q1–Q4: SoCAB quadrants; O: ocean; CV: Central Valley, D: all other areas, mostly the Mojave Desert to the northeast.

The generalized forward model can be written as

Here,

We also use a similar linear model of the form

For the linear forward model (Eq.

For a nonlinear forward model (e.g., Eq.

We define values for

For simplicity,

JKH, JuL, and POW were involved in the overall conceptualization, investigation, and methodology development. JKH carried out the formal analysis and visualization and wrote the original draft. POW secured funding and computational resources and provided supervision. TO and SM developed the ODIAC FF inventory and provided instructions on its use. KG and JiL developed the Hestia-LA FF inventory and provided instructions on its use. CMR, LTI, JRP, PWH, DW, and POW provided TCCON data, which involved funding acquisition, site management, data processing, and QA/QC. JKH, JuL, TO, LTI, DW, and POW were involved in revising the paper.

The authors declare that they have no conflict of interest.

The authors wish to acknowledge providers of data. OCO-2 lite files were
produced by the OCO-2 project at the Jet Propulsion Laboratory, California
Institute of Technology. Resources supporting OCO-2 retrievals were provided
by the NASA High-End Computing (HEC) Program through the NASA Advanced
Supercomputing (NAS) Division at Ames Research Center. Nightlight products
were obtained from the Earth Observation Group, NOAA National Geophysical
Data Center and are based on Suomi NPP satellite observations. The
0.1

We thank Ron Cohen, Nick Parazoo, Anna Karion, and Taylor Jones for helpful discussions. We thank Nasrin Pak for discussions on landfills.

This work was financially supported by NASA's OCO-2 project (grant no. NNN12AA01C) and NASA's carbon cycle and ecosystems research program (grant no. NNX14AI60G and NNX17AE15G). Tomohiro Oda is supported by the NASA Carbon Cycle Science program (grant no. NNX14AM76G). The Hestia data product was made possible through support from Purdue University Showalter Trust, the National Aeronautics and Space Administration grant 1491755, and the National Institute of Standards and Technology grants 70NANB14H321 and 70NANB16H264. The authors thank the referees for their comments. Edited by: Robert McLaren Reviewed by:two anonymous referees