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\begin{document}

\title{Calculating an error correlation length scale from MFLL-OCO-2
column-average CO2 differences and using it to average OCO-2 data}



\author[1]{David F Baker}%
\author[1]{Emily Bell}%
\author[2]{Kenneth J Davis}%
\author[3]{Joel F Campbell}%
\author[3]{Bing Lin}%
\author[4]{Jeremy Dobler}%
\affil[1]{Cooperative Institute for Research in the Atmosphere / Colorado State University}%
\affil[2]{Earth and Environmental Systems Institute}%
\affil[3]{NASA Langley Research Center}%
\affil[4]{Spectral Sensor Solutions LLC}%


\vspace{-1em}



  
  \date{May 29, 2024}


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\begin{abstract}
To check the accuracy of column-average dry air CO2 mole fractions
(``XCO2'') retrieved from Orbiting Carbon Overvatory (OCO-2) data, a
similar quantity has been measured from the Multi-functional Fiber Laser
Lidar (MFLL) aboard aircraft flying underneath OCO-2 as part of the
Atmospheric Carbon and Transport (ACT)-America flight campaigns. Here we
do a lagged correlation analysis of these MFLL-OCO-2 column CO2
differences and find that their correlation spectrum falls off rapidly
at along-track separation distances of under 10 km, with a correlation
length scale of about 10 km, and less rapidly at longer separation
distances, with a correlation length scale of about 20 km. The OCO-2
satellite takes many CO2 measurements with small (~3 km\^{}2) fields of
view (FOVs) in a thin (\textasciitilde{}10 km wide) swath running
parallel to its orbit: up to 24 separate FOVs may be obtained per second
(across a ~6.75 km distance on the ground), though clouds, aerosols, and
other factors cause considerable data dropout. Errors in the CO2
retrieval method have long been thought to be correlated at these fine
scales, and methods to account for these when assimilating these data
into 10 top-down atmospheric CO2 flux inversions have been developed. A
common approach has been to average the data at coarser scales (e.g., in
10-second-long bins) along-track, then assign an uncertainty to the
averaged value that accounts for the error correlations. Here we outline
the methods used up to now for computing these 10-second averages and
their uncertainties, including the constant-correlation-with-distance
error model currently being used to summarize the OCO-2 version 9 XCO2
retrievals as part of the OCO-2 flux inversion model intercomparison
project. We then derive a new one-dimensional error model using
correlations that decay exponentially with separation distance, apply
this model to the OCO-2 data using the correlation length scales derived
from the MFLL-OCO-2 differences, and compare the results (for both the
average and its uncertainty) to those given by the current
constant-correlation error model. To implement this new model, the data
are averaged first across 2-second spans, to collapse the cross-track
distribution of the real data onto the 1-D path assumed by the new
model. A small percentage of the data that cause non-physical negative
averaging weights in the model are thrown out. The correlation lengths
over the ocean, which the land-based MFLL data do not clarify, are
assumed to be twice those over the land. The new correlation model gives
10-second XCO2 averages that are only a few tenths of a ppm different
from the constant-correlation model. {[}\ldots{}{]} Finally, we show how
our 1-D exponential error correlation model may be used to account for
correlations in those inversion methods that choose to assimilate each
XCO2 retrieval individually, and to account for correlations between
separate 10-second averages when these are assimilated instead.%
\end{abstract}%



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