AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus GmbHGöttingen, Germany10.5194/amt-8-1641-2015Estimating bias in the OCO-2 retrieval algorithm
caused by 3-D radiation scattering from unresolved boundary layer cloudsMerrelliA.aronne.merrelli@ssec.wisc.eduBennartzR.https://orcid.org/0000-0001-7133-9659O'DellC. W.TaylorT. E.https://orcid.org/0000-0002-1650-4882Space Science and Engineering Center, University of
Wisconsin–Madison, Madison, Wisconsin, USADept. of Earth and Environmental Science,
Vanderbilt University, Nashville, Tennessee, USADept. of Atmospheric Science,
Colorado State University, Fort Collins, Colorado, USAA. Merrelli (aronne.merrelli@ssec.wisc.edu)1April2015841641165624September201421November201411March201511March2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/8/1641/2015/amt-8-1641-2015.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/8/1641/2015/amt-8-1641-2015.pdf
Due to the complexity of the multiple scattering problem for
shortwave radiative transfer in Earth's atmosphere, operational
physical retrieval algorithms commonly use a plane parallel
radiative transfer model (RTM). This so-called one-dimensional (1-D)
assumption allows practical retrieval algorithms to be
implemented. In order to understand the impacts of this assumption
for low altitude, unresolved clouds observed by OCO-2, the
three-dimensional (3-D) radiative transfer model SHDOM is used to
generate synthetic observations which are then processed by the
operational retrieval algorithm based on a 1-D RTM. Simulations are
performed over three realistic surface spectral albedos,
corresponding to snow, vegetation, and bare soil. The results show
that the existing cloud screening algorithm has difficulty
identifying sub-field of view (FOV), unresolved clouds that fill
less than half of the FOV. The unresolved clouds introduce a bias in
the retrieved CO2 concentration, as quantified by the dry
air mole fraction (XCO2). The biases are relatively small
(less than 1 ppm) when the albedo at 2.1 µm is
high, which is common over bare land surfaces. For cases with low
2.1 µm albedo, such as snow, the bias becomes much
larger, up to 5 ppm. These results indicate that the
XCO2 retrieval appears robust to 3-D scattering effects
from unresolved low level clouds when the short wave infrared
surface albedo is large, but for darker surfaces these clouds can
introduce significant biases.
Introduction
Constraining carbon dioxide fluxes on regional scales has been an
important goal of the earth science community for many
years. Increased knowledge in this area will improve our current
understanding of the different sources and sinks in the global carbon
cycle, as well as improve projections in future climate change
scenarios. Recently, efforts have been focused on accurate
measurements of carbon dioxide concentration from satellite platforms,
in order to obtain global data sets to constrain flux inversion
models. Measuring carbon dioxide in the shortwave region, by observing
reflected solar radiation in near infrared carbon dioxide absorption
bands, has the advantage of sensitivity to the full atmospheric
column. Relying on the thermal emission bands reduces sensitivity to
boundary layer carbon dioxide, where most of the concentration
variations reside.
Several satellite sensors have used this technique, including the past
sensor SCanning Imaging Absorption spectroMeter of Atmospheric CHartographY
(SCIAMACHY) on the European Space Agency's ENVIronmental SATellite (ENVISAT) , the current
Thermal and Near Infrared Sensor for Carbon Observation
Fourier-Transform Spectrometer (TANSO-FTS) on the Greenhouse gases
Observing SATellite (GOSAT) , and the Orbiting
Carbon Observatory-2 (OCO-2)
, and the planned
mission CarbonSat . The current state of
the art retrieval technique uses a combined observation of the oxygen
A-band at 0.76 µm, and CO2 absorption bands at 1.6
and 2.1 µm, in order to estimate the column-averaged dry
air mole fraction of CO2, termed XCO2. This
definition of XCO2 is consistent with the OCO-2 retrieval
algorithms and the Total Carbon Column
Observing Network TCCON,. Each absorption
band is observed at high spectral resolution (O(103) points per
band), to increase the measurement's information content.
In clear air columns, this technique is relatively straightforward,
and can be used for various trace gas concentration retrievals by
observing their associated molecular absorption bands. For carbon
dioxide, the measurement is especially challenging, since the desired
measurement uncertainty is very small.
estimates an absolute accuracy of 1–2 ppm is required for
XCO2 (a relative accuracy of approximately 0.25–0.5 %)
in order to substantially reduce surface flux uncertainties. Any
retrievals must account for variations in other geophysical variables
that can alter the signal (aerosols, surface albedo, and clouds, for
example), or detect their presence in order to appropriately flag the
data as contaminated.
The retrieval problem is an especially challenging one due to
a combination of high complexity of the radiative transfer problem and
high dimensional spectral data. The radiative transfer model must deal
with multiple scattering, and for OCO-2, polarization. The high
spectral resolution measurement covers regions with many isolated
absorption lines where the individual absorption line shapes and the
instrument spectral response become extremely important. All practical
retrieval methods make the plane parallel assumption to simplify the
radiative transfer problem to one dimension (1-D). By making this assumption,
the atmosphere is assumed to be horizontally homogeneous. The impact of this
1-D assumption has not been well explored in the context of trace gas
retrievals, although it has been studied in other contexts, such as
retrieval of aerosol near cloud or
cloud properties in inhomogeneous cloud fields
.
In this study, we investigate how the 1-D radiative transfer
assumption affects XCO2 retrieval in a specific case:
observations of isolated low clouds with simulated OCO-2
observations. By using a three-dimensional (3-D) radiative transfer
model, we generate realistic spectra for this particular case where
the sensor's view contains strong 3-D effects such as cloud shadowing
and lateral photon transport.
The paper is organized as follows: in Sect.
the radiative transfer models and input data sets are described in
detail. This includes a validation analysis to show the new simulation
framework is equivalent to an existing OCO-2 simulation
program. Important characteristics of the OCO-2 instrument are
reviewed. In Sect. , the operational OCO-2
retrieval algorithm is reviewed, with emphasis on the cloud screening
methods. Section describes the
specific simulated scenarios, and the results of processing the
synthetic spectra with the retrieval algorithm are presented in
Sect. . Finally, the results are discussed
and summarized in Sect. .
The OCO-2 sensor measures radiance spectra in three narrow spectral
bands: the oxygen A-band in the near infrared (NIR) at 0.76 µm wavelength, and the CO2 bands in the short wave infrared (SWIR)
at 1.6 and 2.1 µm. These are referred to as the O2A, WCO2
(“weak” CO2) and SCO2 (“strong” CO2) bands, for
brevity. Each of the three bands is a 1016 point spectrum covering the
absorption feature. This produces spectral channel spacings of
approximately 0.015, 0.03, and 0.04 nm in the middle of the
three bands. The instrument contains a linearly polarized filter that
will be oriented perpendicularly to the principal plane throughout the
orbit, so that the sensor measures the combination of Stokes vector
components (I-Q)/2. The sensor will be operated in three modes:
“nadir”, “glint”, and “target”. In nadir mode, the sensor will
point toward the subsatellite point (rotating to keep the polarizer
orientation as described above)
Due to a design error,
the instrument's polarization response is rotated 90 degrees
with respect to the original specification. The instrument
will orbit in the originally specified orientation for nadir
mode, implying the polarized measurement is (I+Q)/2.
In glint node, the spacecraft will be rotated 60 degrees
from the originally specified orientation, yielding a
polarized measurement of (I+1/2Q-3/2U)/2.
.
This is the primary mode for
over-land retrievals. In glint mode, the sensor will point near the
sun glint point, with the exact angular separation from the glint
point to be determined during on-orbit tests. This is the primary mode
for over-ocean retrievals, as the ocean surface is very dark in the
SWIR spectral range, only reflecting sufficient solar radiation near
the glint point. In target mode, the sensor will repoint through the
orbit to keep a particular point on Earth's surface in view. Note that
the instrument pointing is achieved through precise control of the
satellite bus yaw, pitch and roll axes via onboard reaction wheels; i.e., there are no moving fore-optics components. This study focuses on
the nadir mode, so the glint and target mode are not discussed
further.
Lab measurements of the OCO-2 instrument line shape (ILS) are used to
compute the simulated sensor radiance from monochromatic
calculations. The measured ILS shapes have full width at half maximum
(FWHM) of 0.04, 0.08, and 0.1 nm, in the three bands, implying
a spectral resolution (R∼λ/Δλ) of 20 000. No
measurements of the spatial response function (SRF) were available for
use in this study, so an approximation was used as a surrogate for the
real SRF. The surrogate SRF first combines the rectangular slit field
of view with the spacecraft motion through the 1/3 s collection
time. When the slit is oriented perpendicularly with respect to the
spacecraft motion, the resulting convolution of the slit field of view (FOV) and
spacecraft motion is a rectangle of about 1.3km×2.3km on the Earth surface. For other orientations, the
convolution will yield a parallelogram shape. Since the slit is
oriented according to the scattering principal plane, the relative
orientation changes through the orbit. For simplicity, the
perpendicular slit orientation, and rectangular IFOV (Instantaneous Field Of View), is used for all
simulations. This rectangular SRF is then convolved with a circular
2-D Gaussian function with σ width of 0.6 km for
the nadir view, to approximate the optical blur of the sensor. The
result is an oval shaped SRF, with widths at half-maximum of
1.7km×2.3km. This surrogate SRF ignores
some additional detailed information about the shape of the SRF due to
focal plane readout timing, but these further details are likely not
important for this study, as long as the SRF size and profiles are
approximately accurate.
Radiative transfer models
During algorithm development support for the original OCO mission, an OCO
simulator was developed at Colorado State University to produce full
orbit simulations . Development on the
simulator has continued through the NASA Atmospheric CO2 Observations
from Space (ACOS) program, and it has been updated to support
OCO-2. The simulator uses a highly optimized plane-parallel radiative
transfer model to compute radiance in scattering atmospheric profiles,
including cloud and aerosol layers. The overall simulator processing
pipeline was used as a template while implementing the 3-D version
used in this study. In short, the 3-D version replicates the same
steps as the 1-D model but replaces the 1-D plane parallel radiative
transfer model with the spherical harmonic discrete ordinate method
(SHDOM) developed by . For brevity, the two
methods will be called the 1-D OCO-2 and 3-D OCO-2 simulators.
Inputs to 3-D OCO-2 simulator
Important advances in spectroscopy have been made to effectively model
the OCO-2 bands. The OCO-2 science team supports development of
advanced absorption line models including broadening and line mixing
effects . The gas
absorption models are used to produce look up tables across the OCO-2
bands at a frequency resolution of 0.01 cm-1 wave number,
for a representative range of atmospheric pressures and
temperatures. The frequency dimension is thinned with an optimal
subset that uses coarse spacing (up to 2 cm-1) in the outer
line wings, and the full 0.01 cm-1 spacing at line
centers. This optimal subset defines the monochromatic frequency
set for individual radiative transfer model runs.
At these monochromatic frequencies, the scattering properties are
computed from a Mie algorithm (using the support programs supplied
with SHDOM) for cloud liquid water and dust aerosol. For cloud liquid
water, a gamma distribution particle size distribution (PSD) is used:
n(r)=arαexp(-br).
The α parameter is set to 7, which is equivalent to an
effective variance of 0.1 . The effective
radius is set to 10 µm. The aerosol is defined by the dust
type within the 1-D OCO-2 simulator, which uses the dust aerosol data
from from Solar Village, Saudi
Arabia. This is a scattering aerosol (ω∼0.96), with
effective radii of 0.1 and 1.9 µm in the fine and coarse
modes, respectively.
SHDOM is run at each of the monochromatic frequencies in the optimal
sampling subset, and computes normalized reflectance. Since the
optimal sampling list is a sparse subset of the 0.01 cm-1
monochromatic grid, the SHDOM simulations are linearly interpolated to
get continuous sampling. These reflectances are multiplied by the
solar irradiance and then convolved with the per-channel measured ILS,
where the irradiance and ILS are both defined on the continuous
0.01 cm-1 grid. The result is a spectral data array with 3
dimensions (X, Y, and spectral frequency), where the X and Y grid
is defined by the 100 m 3-D grid defining the liquid water
content (LWC) and aerosol field for SHDOM. One such spectral data
array is simulated for each of the OCO-2 bands.
Comparing simulated radiance spectra for a clear atmosphere
column using the 1-D OCO-2 simulator and the 3-D SHDOM-based OCO-2
simulator. The left column shows the simulated radiance for each
band, and the right column shows the radiance differences (1-D minus
3-D simulated spectra), with the ±1σ sensor noise level
envelope overplotted with red lines. Note the y axis units for the
plots in the left column are a factor of 103 larger than the
units on the right column.
Validation with 1-D OCO-2 simulator
In order to validate the radiance spectra produced by the 3-D OCO-2
simulator, a simple test was performed where the input grid to both
simulators was an identical clear atmosphere column. In this case the
SHDOM will essentially reproduce a 1-D radiative transfer
calculation. The differences between the spectra from each simulator
were very small. Figure shows an
example OCO-2 observation, with the difference spectra between the
OCO-2 simulator and the 3-D simulation from SHDOM. Note the y axis
range on the difference plot is 3 orders of magnitude smaller than
the y axis range on the radiance spectra, and the red lines show the
±1σ lines from the sensor noise model.
ACOS retrieval algorithm
The XCO2 retrieval for OCO-2 was developed by the NASA ACOS
team. The algorithm uses an optimal estimation physical retrieval,
with screening algorithms applied to identify the subset of the full
observation set that will produce high quality XCO2
retrievals. It has been applied to GOSAT NIR and SWIR spectral
measurements, which have similar spectral characteristics to the OCO-2
measurements.
Physical optimal estimation retrieval
The overall design of the optimal estimation (OE) retrieval is
described in , and
. For this study, the B3.4 version of the
algorithm is used, which has significant differences compared to the B2.9
algorithm documented in . The newer algorithm
retrieves two state variables related to fluorescence and uses
a different aerosol parameterization. No fluorescence was included in
the 3-D OCO2 simulator, so this part of the retrieval is disabled and
the fluorescence variable values within the prior and first guess state
vector are set to zero.
In both the B2.9 and B3.4 versions, four atmospheric scatterers
are used: water cloud, ice cloud, and “Kahn 2b” and “Kahn 3b”
aerosols. The Kahn aerosol types are defined in
. In the B3.4 version, the scattering
particles use a parameterized profile shape instead of allowing the
profile to vary independently across pressure levels. For each of the
four scatterer types, the profile is parameterized with a vertical
Gaussian profile in optical depth, with three free parameters: the
amplitude (the total optical depth), thickness, and height. The
thickness and height are expressed in terms of pressure normalized by
the surface pressure. The Gaussian profile is truncated when the
vertical offset is near or below the surface, in which case the
profile is renormalized such that the integral is equal to the total
optical depth. Figure shows the prior
profiles used in the retrieval along with the 1-σ perturbations
to the total optical depth and height from the a priori
covariance. The assumed prior values and variances are listed in
Table . All covariances are assumed to be
zero. Note that the thickness is tightly constrained by the prior
variance and is effectively a fixed parameter. This parameterization
results in a maximum number of degrees of freedom of 8 for the
scattering particles.
A priori values and SDs for aerosol and cloud profiles. Note that the state
vector contains the logarithm of the optical depth, so the σ range is a multiplicative
scaling. The pressure heights and thicknesses are expressed as unitless ratios with the surface
pressure.
Prior optical depth profiles. The thick solid line with
square markers shows the per-layer optical depth prior profile; the
solid lines show the ±σ range applied to the optical
depths; the dot-dashed lines show the ±σ range applied to
the pressure heights.
Pre-screening algorithm
The radiative transfer algorithm at the heart of the OE retrieval is
a plane parallel code similar to the 1-D OCO-2 simulator, but further
simplified and optimized. On a standard workstation at the University of
Wisconsin (AMD OpteronTM 4180 CPU),
this simplified model takes on the
order of 30 s to compute one iteration of the OE algorithm (e.g.,
computing the forward model result and Jacobians at the state vector
update). Compared to the data collection rate (24 observations per
second), this implies that only a small fraction of the observations
will be processed with the physical OE retrieval. The target for
initial operating capability is to apply the physical retrieval to
6 % of the total observations. Thus, careful prescreening methods
must be applied to the observations to select the subset most likely
to produce accurate XCO2 retrievals. The precise form of
the screening method is itself a subject of research within the ACOS
effort . In this study, the focus
will be on the “A-band preprocessor” (ABP), described in
. This prescreening algorithm uses
a highly simplified, single-step retrieval of surface pressure and
surface albedo, assuming a clear sky profile with only Rayleigh
scattering. It uses a subset of the full A-band spectrum. Tests with
this algorithm showed that the difference between the retrieved surface
pressure and the interpolated ECMWF analysis surface pressure is an
effective cloud screen. The pressure difference is especially
sensitive to higher altitude clouds that
introduce large photon path modification. Observations that yield
retrieved surface pressures much different than the forecast value (>±10 hPa) indicate significant cloud and/or aerosol
contamination in the observed radiance . In
effect, a thick cloud layer can act as a surface, so that the
retrieved surface pressure is related to the cloud top pressure
(CTP). This approach has been proposed as a retrieved cloud product
for previous missions (for example, a CTP measurement for the
O2 A-band was originally planned for CloudSat, see
). For OCO-2, however, the retrieved
surface pressure will be primarily used to remove cloud-contaminated
observations via the ABP.
At this time is not possible to retrieve XCO2 to the required
accuracy from the cloud-contaminated observations.
Following and simulation tests with the
B3.4 algorithm, a surface pressure threshold of 10 hPa is used
for the ABP. In addition, a χ2 threshold is computed by the ABP,
based on the noise level predicted by the sensor noise model
and the radiance level of the
observation. If the computed χ2 is larger than the threshold,
the observation will be screened.
Cloud and aerosol contamination need not be directly in the sensor's
field of view, and may be produced by significant multiple scattered
radiation from clouds near the field of view. Such scattered radiation
could cause either threshold (surface pressure or χ2) to be
exceeded. In this more general sense, the ABP could be viewed as
detecting “photon path modification” in the radiance observation,
and thus the 1-D retrieval algorithm will not produce an accurate
XCO2 retrieval.
Post-screening algorithm
In cases where the prescreening method does not correctly detect
a cloud or aerosol contaminated spectrum, the retrieval may converge
to an inaccurate XCO2 result. Therefore, additional
post-screening is performed on the retrieved state vector in an
attempt to eliminate poor quality retrievals. These post screens are
generally made by performing threshold tests on the retrieved surface
pressure, surface albedos, retrieved aerosol or cloud optical depths,
and reduced χ2 values for each band. The reduced χ2
is the calculated χ2 value divided by the number of degrees
of freedom, which is expected to be close to 1 if the modeled
and measured spectra differ only by random sensor noise.
The first two post screen
threshold tests are very similar to those used by the ABP, but use
tighter threshold values. The latter two thresholds are motivated from
simulation tests .
The values of the various post screening thresholds are continually
adjusted for the ACOS products by analysis and comparisons of GOSAT
and TCCON retrievals, in order to minimize the bias in the final
retrieved XCO2. Thus the particular values prescribed in
the B3.4 release documentation are not necessarily relevant to these
simulation experiments, especially for the reduced χ2 thresholds
for the spectral residuals. The residuals will include various model
deficiencies (such as inaccurate absorption line spectroscopy) when
compared with real data. No such effects are included in this
simulation and retrieval framework, so the reduced χ2 values
will be close to the theoretical values. To derive χ2 thresholds
for these tests, an ensemble of simulated clear sky spectra (with
aerosols but no cloud liquid water) was processed with the L2
algorithm. A threshold of 1.25 was selected for all three bands, which
is 3.6 SDs above the mean reduced χ2 values over all
retrievals. Approximately 0.1 % of all the clear retrievals exceed
this threshold in one of the bands.
Screening thresholds on the retrieved scattering optical depths are
also important for high accuracy retrievals. The values used in B3.4
applied to GOSAT high-gain observations over land are 0.15 for the sum
of all four scatterers (cloud water, cloud ice, and both Kahn aerosol
types), 0.07 for cloud water, and 0.045 for cloud ice. For the GOSAT
medium-gain observations over land, these thresholds are 0.1, 0.07, and
0.03, for the total, cloud water, and cloud ice optical depths,
respectively. Since these thresholds were empirically determined for
the GOSAT data as processed with the B3.4 algorithm, they are not
necessarily the best choice for this analysis. Tests with the clear
sky retrievals show that these thresholds were somewhat too
restrictive, and the selected thresholds in this analysis are 0.175,
0.1, and 0.03 for the total, cloud water, and cloud ice optical
depths, respectively. These threshold values are consistent with the
values selected for simulation-based tests ,
and are still more restrictive than the initially reported threshold
of 0.3 in aerosol optical depth for performing XCO2
retrievals .
Retrieval test setup
The specific tests are designed to explore potential retrieval biases
caused by low level clouds. Even without considering 3-D scattering
effects, low level layer clouds can be challenging to identify
. A low level layer cloud can introduce both
photon path shortening and lengthening
, which can tend to cancel and
mask the cloud's effect on the radiance measurement. The work
presented here can be viewed as an extension of these previous 1-D
simulation efforts to broken or isolated low clouds, which have strong
3-D scattering effects.
Scenarios
A single spheroidal liquid water cloud was created in the center of a
3.5 km (horizontal) × 2.5 km (vertical) domain.
The grid spacing is 100 m in all three dimensions.
Dust aerosol is evenly distributed within the domain, with
a total aerosol optical depth (AOD) of 0.05 in the vertical dimension.
The cloud has an altitude of 1.6 km, and a fixed thickness of
0.6 km in the z axis. Three cloud sizes are simulated, with the
cloud diameter in the horizontal axes set to 0.6, 0.8 and 1.2 km.
Therefore the smallest cloud is spherical, while the 0.8 and 1.2 km
clouds are oblate spheroids. The liquid water content (LWC) has a quadratic
profile in all three dimensions.
The cloud fraction within the blurred SRF (see
Sect. ) is not well defined, but it covers
roughly 10, 20, and 40 % of the unblurred, rectangular
nadir FOV for the three cloud sizes. The maximum
LWC, in the center of the cloud, is 0.125 gm-3, yielding
a maximum liquid water path (LWP) through the cloud center of
50 gm-2. The maximum visible optical depth along this
same path is approximately 8. Two solar zenith angles (SZAs) are used:
35, and 60∘. The surface is assumed to be Lambertian,
with realistic albedo values in regions classified as snow, vegetated,
and soil. Table lists the selected values.
Lambertian surface albedos, in each of the three OCO-2 spectral bands, for the three surface types.
The SHDOM has the option to run with open or periodic boundary conditions.
The periodic boundary condition is used for all cases. SHDOM is used
to simulated a nadir view
using these LWC and aerosol fields. The cloud field is then a grid of
identical clouds with a 3.5 km horizontal spacing, rather than
a single isolated cloud. In Fig. , the nadir
sensor view is shown for the three selected surface albedos for
a single OCO-2 spectral channel in each of the three bands. The single
channel is chosen at a wavelength between absorption lines so there is
little extinction of the solar radiation. The views are shown for the
35∘ solar zenith angle.
Creating OCO-2 spectra
Using the spectral data array described in Sect. ,
a synthetic OCO-2 observation is generated by applying the surrogate
SRF (see Sect. ). The 2-D nadir radiance array at
each channel frequency is multiplied by the SRF and summed to produce
the OCO-2 channel radiance. Figure shows
examples of the SRF applied to a low absorption O2A band channel. The
SRF is applied at various positions, by scanning left-to-right over
the cloud in the scene. A total of 25 SRF centered positions are used,
where the SRF is shifted by a single 100 m grid cell, and the
10th position is centered in the 3.5 km domain.
Positions 0, 5, 10, 15 and 20 (i.e., the center of the SRF falls at
positions 0.75, 1.25, 1.75, 2.25 and 2.75 km along the x axis
in the 100 m grid) are shown in Fig. .
The SRF positions move between regions dominated by clear, cloudy
or shadowed high resolution grid cells, depending on the cloud size
and solar zenith angle. For brevity, the positions will be referred
to as clear, cloudy and shadow, depending on which type of high
resolution pixel is dominant at that location, but it is
apparent that in all cases the SRF will contain a mixture
of all three types.
The process described in the previous section yields a total of 25
spectra, one per SRF positions for each scenario (a selected solar
zenith angle and surface albedo). For each spectrum, an ensemble of 37
simulated OCO-2 observations is generated with independent sensor
noise realizations for each observation. The sensor noise is drawn
from a Gaussian Probability Distribution Function, scaled by the
sensor noise model from . Each of these
ensembles are processed with the ABP algorithm and the B3.4 L2
retrieval code, and the relevant quantities are averaged over the
ensemble members. The ABP uses a subset of the O2A band
(759.18–760.75 nm), while the L2 retrieval runs on the full
3-band spectra. The L2 retrieval uses an input meteorology data set (in
operations, this is taken from a numerical weather forecast), which is
set to the truth values. In other words, the meteorology sent to the
L2 retrieval is the same meteorology data used to simulate the spectra
with the 3-D OCO-2 simulator.
Retrieval test resultsScreening rates
In normal operations, the results of the ABP would be applied before
performing L2 retrievals. In cases where 3-D effects are important, it
is possible that the ABP could preferentially identify cloudy
observations in cases where the full L2 algorithm can produce accurate
retrievals. This behavior would not have been captured in the
development of the ABP, since all radiative transfer models used in
the earlier studies were plane parallel. Therefore, in these
experiments, the L2 algorithm is applied to all simulated
observations, regardless of the output from the ABP. This allows full
characterization of the ABP performance, to verify that it is removing
the cloud-contaminated observations that the L2 algorithm cannot
accurately process.
Overhead views of the scene reflectance as simulated by
SHDOM, for a channel within each OCO-2 band that has relatively low
gas absorption. Each of the three columns shows the reflectance for
one of the three OCO-2 bands, and each of the three rows shows
reflectance from one surface type. All images are shown with the
same display scale, to highlight the differences in contrast between
the cloud and surface for the different spectral bands and surface
types.
ABP prescreening
Recall that at each SRF position, an ensemble of 37 spectra were
generated with independent sensor noise. The ensemble allows for
a screening fraction to be computed at each
position. Figure shows these fractions as
a function of SRF position, for the various scenarios. The ABP's
performance appears directly correlated to the O2A band albedo and the
cloud size, as expected. Recall that the ABP retrieves just the
surface pressure from the O2A band (see
Sect. ). Over snow, since the surface is much
more reflective, a larger proportion of the observed radiance is due
to the single scattering off the surface, which will tend to pull the
retrieved pressure to the surface value. The ABP also detects a cloud
mainly when the SRF is centered on the cloud, but not in the primarily
“clear” or “shadow” positions. A single screening rate for each
scenario can be computed by averaging over the SRF
positions. Table shows these results.
Postscreener
Figure shows the postscreening fractions,
with the same layout as Fig. showing the
prescreening fractions. The postscreening fractions are defined with
respect to the total number of simulated observations, since the L2
retrieval was run on all observations, not just the ones that were not
identified as cloudy by the ABP. Ideally, the postscreened fractions
should be equal or higher than the prescreened fractions from the
ABP. This would imply that the ABP correctly identified an observation
that would not have produced an accurate L2 retrieval. A higher
postscreening fraction is also expected, since the L2 retrieval has
access to more information (since it retrieves from all 3 OCO-2
bands), and uses a more complicated state vector.
For the vegetation and soil surfaces with 60∘ solar zenith
angle, the postscreening fractions as a function of the SRF position
are extremely similar to the prescreening fractions. For the remaining
cases, except for the soil surface at 35∘ solar zenith
angle, the post screening method tends to identify a much larger
fraction of cloudy observations. This is especially true over snow
where the fraction reaches nearly 100 % for the 0.8 km
cloud. The outlier scenario here is the soil surface at 35∘
solar zenith angle, where the ABP identifies a much higher rate of
cloud contamination than the postscreener. This behavior could be
described in two ways: either the ABP could be improperly identifying
these observations, (if these retrievals produce accurate
XCO2 retrievals) or the postscreener could be failing (if
the retrieved XCO2 is not accurate). This behavior will be
discussed below in the context of the state variable biases.
Percentage of simulated observations identified as cloudy by prescreener algorithm.
A summary of the postscreen fractions is shown in
Table . Note that although the postscreen
identifies the highest fraction of the cloud contaminated
observations, it also screens almost 30 % of the clear column test
spectra. This suggests that the postscreen could be improved with
scene dependent thresholds.
State variable bias
In order to quantify the impact of 3-D radiative transfer effects on
the retrieved state variables, the retrieval outputs will be compared
both to the known truth values as well as the results from the
cloud-free simulations. Since the ACOS XCO2 retrieval is known to
have biases even for clear sky retrievals
, the cloud-free simulations
help to separate the bias caused by 3-D radiative transfer effects
from the clear sky bias already present in the retrieval. In any
particular scenario, the bias due to 3-D effects will be the
difference between the bias computed in the cloudy retrievals
and the bias computed in the clear sky retrievals.
Overhead view of the scene reflectance multiplied by the SRF
at positions 0, 5, 10, 15, and 20, for the 0.6 km cloud in
the O2 A-band over the soil surface. The SRF moves from left
to right over the high spatial resolution grid. The top row shows
the SRF sequence for the 35∘ solar zenith angle (SZA), and the
bottom row shows the sequence for the 60∘ SZA. In the top row,
the SRF starts at a position where the FOV is primarily filled with
a “clear” surface view, to a “cloudy” position, and ends at a
“shadowed” position. In the bottom row, the periodic boundary
condition used in SHDOM causes the shadow to wrap around to the
other side of the high spatial resolution scene for the larger
SZA. For this case, the SRF starts in the “shadowed” position,
followed by “cloudy” and then “clear”.
As an initial example, the previous case noted in the screening
discussion above is revisited. For the 0.8 km cloud, over the
soil surface with solar zenith of 35∘, the ABP identified all
spectra with the SRF centered above the cloud as cloud
contaminated. However, the postscreen only found about 20 % of
these observations to be cloud
contaminated. Figure shows the bias in the
retrieved XCO2 as a function of the SRF position for this
scenario. The bias is defined as the retrieved values, minus the known
truth XCO2 value. The left subplot shows all converged
retrievals; the middle plot shows the screened retrievals (both
prescreen and postscreen are applied). The set of retrievals shown in
the middle plot would be the actual set retrieved by the full
end-to-end L2 processing algorithm. The gap in observations around SRF
position 10 is due to the ABP. The solid horizontal line shows the mean
retrieved XCO2 from the clear sky retrievals performed for
this scenario; the bold error bar marker centered on zero bias shows
the 1-σ range predicted by the posterior covariance from the
optimal estimation algorithm. Finally, to summarize the scatter plots,
the distribution of points is condensed down to a single box plot in
the right subplot, and the number of points in each is marked along
the bottom axis. The remaining bias distribution plots will match this
layout, with the results condensed into the pair of box plots. The
XCO2 biases shown here indicate that the L2 retrieval is
able to compute an accurate value XCO2 for all cases in this
scenario. This suggests that the ABP may be too aggressive in identifying cloud
contamination in this scenario.
Fraction of simulated spectra identified as cloudy by the
prescreening algorithm.
XCO2
Figure contains the XCO2
retrieval bias summary for all scenarios including the 0.6 and
0.8 km clouds. The 1.2 km cloud scenarios are not
included here, since the screening rates are high for these cases. The
different surface albedos are organized by row, with the snow,
vegetated and soil surfaces in the top, middle, and bottom rows,
respectively.
For the snow surface, the XCO2 biases are large, especially
for the 60∘ solar zenith angle. The 0.6 km cloud case
shows a consistent -5 ppm bias, which is 4 ppm lower
than the clear sky bias. In this case only 12.5 % of the
observations would be screened. For the 0.8 km cloud case, the
screening does reduce the bias magnitude, from -9 to
-6 ppm. This is the only case where the screening algorithms
substantially reduce the bias magnitude. Over the vegetated surface,
the absolute biases are much smaller. The mean biases are within
2 ppm of truth, and within 3 ppm of the clear sky
value. Finally, over soil, the biases are well represented by the
clear sky values. All biases are within approximately 0.3 ppm
of the clear sky bias.
Overall, the magnitude of the biases seem to be most strongly related
to the SCO2 surface albedo. In practice, an additional postscreen
filter on the retrieved SCO2 is used, which was not used in these
tests. A simple cutoff of about 0.05 albedo in the SCO2 band would
essentially remove all the snow observations. The results here suggest
the retrievals over snow are the most sensitive to 3-D radiative
transfer effects, further supporting the use of a screening threshold
in the SCO2 band.
Fraction of simulated spectra identified as cloudy by the
post screening algorithm.
Surface albedo
A key state variable in the optimal estimation retrieval is the
surface albedo in each band. The retrieved values are strongly
influenced by the 3-D radiative transfer effects. In
Fig. the biases for the retrieved
SCO2 albedo are shown for the same case as
Fig. . The bias is clearly correlated to
the SRF position, and thus to the influence of 3-D radiative transfer
effects. This scenario uses the soil surface, which has an albedo of
0.31. The range in bias is about 0.03, which is a relative bias
of 10 %. The other retrieved surface albedos show similar
relationships to the SRF position. Also note that the screening
algorithms remove retrievals mostly around SRF position 10 (the
position centered on the cloud), which is also where the retrieved
SCO2 albedo is the most accurate. The result is that the bias range,
shown by the box plot, is not reduced.
Bias in retrieved XCO2, showing the scatter plot
of all retrievals (left panel) and screened retrievals (middle
panel), compared to the single box plot summarizing the bias (right
panel). The error bar drawn with a thick black line, centered on
zero bias, is the predicted posterior error (1σ) from the
optimal estimation algorithm. The thin horizontal line marks the
mean bias for retrievals from a cloud-free simulation. Finally, the
number of retrievals in each box plot is indicated at the bottom of the
x axis in the right panel.
The summary of SCO2 albedo biases is shown in
Fig. . Although the albedo bias is
within the range 0.01–0.02 in all cases, the bias relative to the
SCO2 albedo is substantial. A 0.01 albedo bias relative to the 0.02,
0.10, and 0.31 albedo values, for the snow, vegetated, and
soil surfaces, respectively, is a relative bias of approximately 50, 10
and 3 %.
Surface pressure
The final retrieved variable for CO2 concentration is the dry
air mole fraction (the XCO2), which is equivalent to the
ratio of CO2 molecules and O2 molecules in the
column. The latter value is represented by the surface pressure, since
the O2 concentration varies much less than the CO2
concentration. This implies that any bias in the retrieved surface
pressure will directly cause bias in the retrieved
XCO2. Plots for surface pressure bias are shown in
Figs. and ,
matching the bias plots in the previous sections for XCO2
and SCO2 surface albedo.
Summary of XCO2 retrieval bias for all scenarios
with 0.6 and 0.8 km clouds. See
Fig. for details.
Since surface pressure is used in the ABP and for postscreening, large
surface pressure bias will cause the observation to be screened. In
Fig. , the maximum absolute surface
pressure bias is in the cloud-centered SRF positions. These are the
most likely to be screened, so in this case the overall surface
pressure bias is reduced somewhat by the screening algorithms. The
summary plot, in Fig. , shows that the
overall reduction in bias only occurs in a few scenarios (both SZA for
cloud size 0.8 km over the soil surface). The general patterns
in the surface pressure bias are different than those seen in
XCO2. For XCO2, the soil surface retrievals show
bias very similar to the clear sky bias, and then the bias increased
as the SCO2 albedo decreased, resulting in very large bias over the
snow surface. The results for surface pressure are more related to the
O2A albedo, since most of the sensitivity to surface pressure comes
from the O2A band measurement. Thus, the surface pressure bias for the
retrievals over the snow surface is quite different than the
vegetation and soil surface albedos. The absolute bias for the
retrievals over the snow surface albedo is about 1.5 hPa for
the 35∘ SZA and less than 0.3 hPa for the 60∘
SZA. The bias for the retrievals over the vegetation and soil surfaces
are similar, with nearly zero bias for the 0.6 km cloud and
35∘ SZA, and larger absolute bias for the larger cloud size
and SZA.
Bias in retrieved SCO2 albedo, with the same layout as
Fig. .
XCO2 and surface pressure
Since the XCO2 is directly related to the surface pressure,
the joint distribution of bias between these two variables is worth
examining. Figure shows scatter plots of
the biases for these two variables. Each panel corresponds to a single
scenario, matching the layout seen earlier in
Fig. . The black points show the biases for
the individual screened retrievals, and the large cyan cross shows the
clear sky retrieval bias. The overplotted ellipse in the lower left
corner is an example posterior covariance from the optimal estimation
algorithm. The covariance is computed for each retrieval, but within
each scenario the covariance does not change significantly between
each retrieval. Note that the display scales in both the x and
y axes are different in each row of plot panels (corresponding to
a single surface albedo). The “flattened” appearance of the
covariance ellipses for the snow surface albedo scenarios is largely
due to the large y-range for the XCO2 bias display. The
ellipse orientation describes the degree of covariance between the two
variables, as calculated by the optimal estimation algorithm. It is
clear that there is no consistent strong covariance,
but rather a weak covariance that is scenario dependent.
The retrieval biases also show correlation that is
dependent on the scenario. The correlation is highest in the
60∘ SZA, vegetation scenario, and very low in all
scenarios using the soil albedo.
Percentage of simulated observations identified as cloudy by postscreener algorithm.
Summary of SCO2 surface albedo retrieval bias for all
scenarios with 0.6 and 0.8 km clouds, with the same layout
as Fig. .
Profiles of atmospheric scatterers
The optimal estimation retrieval has parameterized profiles of four
atmospheric scatterers (see
Sect. ). Figure shows
the retrieved profiles of cloud water (top row), cloud ice (middle
row) and aerosol (bottom row) optical depth. Since the two aerosol
types were typically strongly correlated, the profiles were summed and
the combined profile is shown in Fig. . The
optical depths per layer are represented by the color scale, ranging
from 0 to 0.003. Vertical pressure levels are given on the y axis,
and the SRF positions are given on the x axis. Each column
represents the average retrieved optical depth profile for that SRF
position and simulation scenario. The four cloud and SZA scenarios
using the soil surface are shown. Note that the retrieval estimates
a significant amount of cloud ice optical depth at high altitudes,
even though the simulation did not include any cloud ice at any level,
and no scatterers above the 700 hPa level other than molecular
scattering. The gap in the middle of the second column (the
0.8 km cloud size, and 35∘ SZA) is due to the complete
screening of these retrievals.
Bias in retrieved surface pressure, with the same layout as
Fig. .
Discussion
The overall purpose of the prescreening algorithm is to quickly
identify observations that are sufficiently contaminated by cloud to
preclude accurate Level 2 XCO2 retrievals. Characterizing
its performance for the scenarios here must involve a discussion of
the prescreening rate as well as the XCO2 bias with and
without applying the prescreening.
Summary of surface pressure retrieval bias for all scenarios
with 0.6 and 0.8 km clouds, with the same layout as
Fig. .
In general, the ABP cannot detect the smallest sub-FOV cloud
(0.6 km diameter), and has limited ability to detect the
larger clouds (0.8 and 1.2 km diameter). It is important to
note however that the reasonable accuracy of the ABP algorithm in
identifying homogeneous cloudy scenes, i.e, 100 % FOV
contamination, has been shown on simulated data
. Furthermore, comparisons were favorable
against the MODIS cloud mask for select GOSAT soundings
. The screening fraction is related to
the albedo in the O2A band, as the screening rates are highest for the
soil surface, and zero for the snow surface (see
Table and
Fig. ). Likely this is due to poor contrast
between the surface and cloud when the surface is bright (for example,
in Fig. the cloud is barely discernible over
the snow surface in the O2A band). For the snow surface, the
XCO2 biases are often quite large, up to 5–10 ppm,
so the ABP is not effective within the scenarios over snow. Screening
out retrievals over snow surfaces could easily be achieved by other
simple tests. For example, filtering could be done seasonally by
latitude to exclude retrievals over likely snow covered regions, or by
requiring a minimum signal level in the SCO2 band. Operationally, the
ACOS retrieval algorithm has taken similar steps to avoid retrievals
over snow and ice surfaces, by using thresholds on the retrieved
albedos to exclude likely snow or ice covered surfaces. These
thresholds remove retrievals with very low SCO2 albedo, or retrievals
with a combination of very high O2A albedo and low SCO2 albedo. Over
the vegetated surface, the biases are smaller, but still significant,
up to 2 ppm to the known truth value and up to 3 ppm
relative to the clear sky bias value. These scenarios are the most
concerning for the ABP. The soil surface, in contrast, yields very
accurate XCO2 retrievals, with bias less than
1.5 ppm relative to the known truth value and within
0.3 ppm relative to the clear sky bias value. In fact, the L2
retrieval yields accurate XCO2 retrievals even for the
prescreened observations, indicating the ABP is too restrictive in
some cases.
Summary of surface pressure and XCO2 retrieval
bias and covariance for all scenarios with 0.6 and 0.8 km
clouds. Plot panels are arranged in the same order as
Fig. . In each panel, the screened
retrievals are shown (black points) along with the mean clear sky
retrieval (large cyan cross). The ellipse shows the 1σ
posterior covariance for these two retrieved variables, offset by an
arbitrary amount for display clarity.
Retrieved optical depth profiles of atmospheric scatterers
for four scenarios (cloud sizes 0.6 and 0.8 km for both SZA)
with the soil surface albedo. Each panel shows the profile in
a vertical column, with the y axis indicating profile pressure,
and the x axis indicating the SRF position. Top, middle and bottom
rows show the cloud water, cloud ice, and aerosol (sum of the Khan
2b and 3b) profiles, respectively. The far right column shows the
prior optical depth profiles used by the optimal estimation retrieval.
The postscreen filters applied after the L2 retrieval are much more
effective at identifying the cloud contamination. In nearly all
surface and SZA scenarios the 0.8 km cloud is identified in
more than half of the observations. The vegetated and soil surfaces
for 60∘ solar zenith angle are the exception, but the majority
of cases are screened at the 1.2 km cloud size.
The XCO2 biases on the final screened retrievals are
generally equivalent to the bias from the set of all converged
retrievals. This is illustrated with the box plots in
Fig. . If the screening methods were
preferentially identifying high XCO2 bias retrievals, then
the box plot for the screened retrieval set should be narrower and
closer to the clear sky bias. However, in all cases the two box plots
are equivalent.
For other retrieved state variables, the bias is more significant. The
SCO2 albedo bias results shown in
Figs. and
show similar behaviors as the
XCO2 bias. Specifically, the bias is largest for snow, and
smallest for soil, and the screening does not reduce the mean absolute
bias. The latter effect can be clearly seen in
Fig. , since the screening tends to
remove observations at SRF position 10 (centered on the cloud), where
the retrieved SCO2 albedo is close to the truth value.
The retrieved optical depth profiles for the scattering particles also
exhibit large biases. Figure shows the results
for four soil surface cases (0.6 and 0.8 km clouds at both
solar zenith angles). The profiles show complicated relationships to
the SRF positions, with both the total optical depths and the profile
altitudes changing as the SRF scans over the scene. Note that from the
screening rate results (Tables and
) most of these retrievals are passed by both
screening algorithms. Since the reduced χ2 was used as part of
the postscreen algorithm, the spectral residuals are small. Thus the
1-D radiative transfer model is able to recreate the spectra simulated
with the 3-D radiative transfer code well enough to produce low
χ2 values and pass the screening algorithm. Thus the patterns in
the optical depth profiles represent different 1-D plane parallel
representations of the 3-D scattering field in the simulations. These
scatterer profiles are very different from the true 3-D
distributions. Recall from Sect. that
the aerosol layer in the model is evenly distributed in the lower
2.5 km, which is the approximately the pressure layer for P>700hPa, while the cloud is located at an altitude of
1.6 km (approximately 800 hPa). The retrieved
scatterer profiles are displaced vertically as the SRF position moves
across the cloud, but the actual scatterers are at fixed
altitudes. Only the results for the retrievals over the soil surface
are shown here. The retrievals over other surfaces show qualitatively
similar behavior, in that the scatterer vertical profiles change
significantly with the SRF position.
Conclusions
By processing simulated OCO-2 observations created with a 3-D
radiative transfer model, the impact of 3-D scattering effects has
been estimated for the scenario of low altitude, sub-FOV liquid water
clouds. Tests were done for two solar zenith angles (35 and
60∘), and three surface types (snow, vegetation, and
soil). Overall, the retrieved XCO2 shows biases that are
strongly dependent on the SCO2 surface albedo. After screening, the
worst case mean bias over snow is roughly 5 ppm relative to
clear sky retrievals, for the 0.8 km cloud and 60∘ solar
zenith angle. At the other extreme, the mean retrieved XCO2
bias is less than 0.5 ppm relative to the clear sky retrieval
in all cases. The performance of the screening algorithms is highly
scene dependent, and no clear general trend is evident in the
data. The ABP has difficulty identifying these sub-FOV clouds, but in
many cases the L2 retrieval is still able to retrieve an accurate
XCO2. Neither screening method reduces the mean bias within
a single test case. From the overall perspective of the entire group
of tests, the screening methods do reduce bias by screening higher
fractions of the larger clouds sizes which do have larger
XCO2 bias. Both screening methods primarily detect the
cloud-centered SRF positions, so the shadow-contaminated observations
are detected less often.
While the analysis presented here does indicate potentially large
biases in the OCO-2 XCO2 retrievals, at present we do
not know the potential impact on the global XCO2 data set.
A future study is needed to connect these results to measured spatial
and temporal distribution of clouds. The resulting bias in a global
XCO2 data set will depend on the occurrence of cloudy scenes
similar to the presented synthetic scenarios. The biases could be
especially problematic if they are regionally correlated.
During this study, development has continued on the operational
retrieval algorithm past version B3.4. The treatment of aerosols is
quite different in more recent versions. A geographically dependent
aerosol climatology is used to select the pair of aerosols used for
each retrieval from a set of six aerosol types. Clearly the retrieval
biases among the albedo and aerosol profiles are highly correlated, so
the quantitative behavior may be very different in the new
algorithm. However the general behavior of the retrieved aerosol
profile – where it is highly dependent on the unresolved 3-D cloud
field – should remain unchanged.
Finally, one important caveat on these results is the reliance on an
unpolarized forward model. Since the actual OCO-2 measurement is
polarized, these results should be repeated with the same framework
using a fully polarized 3-D radiative transfer model. It is unknown
how the retrieval will behave differently when working with the
(I-Q)/2 radiance instead of the unpolarized radiance. In addition,
it would be important to extend these analyses to the glint mode
observation. Polarized radiative transfer is even more important for
simulating glint mode observation, since the glint mode relies on the
strongly polarized specular reflection from the ocean surface. Since
this project began, the SHDOM model has been improved and now can
perform the polarized radiative transfer .
Acknowledgements
This research project was supported by the NASA OCO-2 Science Team,
under contract NNX13AB97G. The authors thank the Space Science and
Engineering Center Technical Computing group for providing cluster
computing resources used for the simulations.
Edited by: H. Worden
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