Retrieval Algorithm

Generally, the following description of the MOPITT retrieval algorithm
applies to both the Version 3 (V3) and Version 4 (V4) products. 
Differences between the V3 and V4 retrieval algorithms are described in
detail in the V4 User's Guide available here
A paper describing the V3 CO retrieval algorithm was
published previously (Deeter
et al., JGR, 2003)
.  The mathematical
basis of the MOPITT retrieval algorithm is
also contained in (Pan
et al., JGR, 1998).

An optimal estimation-based retrieval algorithm and a fast radiative
transfer model are used to invert
the measured A and D signals to determine the tropospheric CO
profile. In principle, retrievals of CO may involve up to twelve
measured signals (calibrated radiances) in
two distinct bands: a near-infrared (NIR) band near 2.3 microns, and a
thermal-infrared (TIR) band near 4.7 microns. The TIR radiances are
sensitive to thermal emission from the earth's surface as well as
atmospheric absorption and emission. The NIR radiances are
sensitive to atmospheric CO solely through absorption of solar
radiation.
(However, the NIR radiances are not actually in either V3 or V4
products.) Currently, only clear-sky radiances (i.e., radiances
uncontaminated by
clouds) are fed to the retrieval algorithm. A detailed description of
the MOPITT cloud-detection algorithm can be found in (Warner
et al., Appl. Opt., 2001).

In atmospheric remote sensing, the common problem of inverting a set
of measured radiances to determine aspects of the atmospheric state
(temperature profile, trace gas mixing ratio profiles, etc.) is often
ill-conditioned, meaning that no unique solution exists without added
constraints. Thus, additional information of some type is usually
required to constrain the retrieval to fall within physically
reasonable limits. The CO retrieval algorithm used for MOPITT exploits
an optimal estimation technique. More precisely, MOPITT exploits the
technique referred to by Rodgers as "Maximum A Posteriori", or
"MAP" [C. D. Rodgers, Inverse Methods for Atmospheric Sounding:
Theory and Practice
, World Scientific, 2000]. The general strategy
of such techniques is to seek the solution most statistically
consistent with both the measured radiances and the typical observed
patterns of CO profile variability (as described quantitatively by
both the a priori mean profile and the a priori covariance matrix).

The TIR and NIR radiances depend not only on the vertical
distribution of tropospheric CO but also on various other atmospheric
quantities (such as
the atmospheric temperature and water vapor mixing ratio profiles) and
surface parameters (surface temperature and emissivity).  Reasonably
accurate values for all of these geophysical parameters
must be obtained to produce accurate retrievals. Atmospheric
temperature and water vapor profiles are obtained by spatially and
temporally interpolating reanalysis profiles from NCEP to the location
and time of each MOPITT pixel. However, sources of geophysical data
such as NCEP are unable to provide accurate values of surface
temperature and emissivity (both of which are highly variable) at the
temporal and spatial resolution demanded by the MOPITT
retrievals. Fortunately, information contained in the TIR radiances
allows retrieval of the surface temperature and
emissivity along with the CO profile, and makes external data sources
for these quantities necessary only for providing a priori values.
Thus, rather than assuming fixed values for the surface
temperature and emissivity, these two parameters are included in the
retrieval state vector (along with the elements of the CO profile).
(A closer inspection of the roles of surface temperature and
emissivity reveals that their effects on the TIR radiances are similar
but not identical. Thus, to first order, surface temperature and
emissivity together represent a single degree of freedom with respect
to
variability in the TIR radiances.)

The MAP technique combines two independent estimates of the same
vector quantity (i.e., the state vector determined solely from the
measurement vector and the "virtual" measurement represented by the
a priori state vector) with generally unequal covariances. Retrievals
of the CO profile consist of a "floating" surface-level retrieval
(tied to the pixel-dependent surface pressure value) and retrievals on
a set of fixed pressure levels.  V3 retrievals exploited a
seven-level grid with levels at the surface,
850, 700, 500, 350, 250, and 150 hPa. V4 retrievals exploit a ten-level
grid with levels at the surface, 900, 800, 700, 600, 500, 400, 300,
200, and 100 hPa.  The retrieved CO total column
value is obtained as a byproduct of the retrieved profile and is
obtained simply by integrating the retrieved profile from the surface
to the top of the atmosphere. The MOPITT CO Level 2 Product
therefore consists of retrieved values and estimated uncertainties of
the CO profile, CO total column, surface temperature, and surface
emissivity. The V4 Level 2 Product also includes the retrieval
averaging kernel matrix (an important diagnostic) for each retrieval. 
In the earlier V3 product, the retrieved error covariance matrix was
provided to facilitate calculations of retrieval averaging kernels (as
described here).

"Phase-I" CO Retrievals (March, 2000 - May, 2001)

For both the V3 and V4 Products, the radiances used for the Phase I
period include the A signal for Channel 7, and the D signals for
Channels 1, 3, and 7.

"Phase-II" CO Retrievals (August, 2001 - present)

In May, 2001, one of MOPITT's two coolers failed, effectively disabling
channels 1 - 4. After extensive diagnostics and some minor
reconfiguration of the Channel 7 PMC, MOPITT resumed operations
in August, 2001 with channels 5 - 8 fully functional.  No MOPITT
products are available for the period between May 7 and August 24,
2001.  For both the V3 and V4 Products, the radiances used for the
Phase II period include the A signal for Channel 5, and the D signals
for
Channels 5 and 7. As documented in (Deeter
et al., GRL, 2004)
, Phase I and Phase II CO retrievals are similar
(but not identical) in terms of vertical resolution and information
content.

MOPITT Forward Modeling

Forward modeling of the MOPITT channel radiances must combine accuracy
and precision while providing for variations in target and
contaminating gases, temperature, viewing geometry and surface
properties. To achieve this, a set of radiation models has been
developed. The following is a very brief overview of this work. An
expanded, though simplified, discussion can be found in "Channel
radiance calculations for MOPITT forward modeling and operational
retrievals" (Francis
et al., SPIE, 1999)
. A detailed discussion of the MOPITT forward
model is presented in (Edwards
et al., JGR, 1999)
.

Line-by-line Calculations

Gas correlation spectroscopy introduces a high resolution spectral
filter into the measurement process, having line widths of order 0.1
cm-1. In addition, calculations with spectral resolutions
as fine as 0.0025 cm-1 are required to construct the
databases which are key components of the higher-level MOPITT
radiation codes MOPABS and MOPFAS discussed below. Line-by-line (LBL)
calculations must therefore be performed to provide these filters and
databases. These are provided by the general purpose radiance and
transmittance model GENLN2. Although too cumbersome for operational
use, top-of-atmosphere radiances provided by GENLN2 also give
benchmarks against which faster MOPITT codes can be assessed.

MOPABS: An optical-depth lookup table model

An intermediate step in the MOPITT radiation code hierarchy, MOPABS
computes channel radiances through a monochromatic absorption
coefficient fitting scheme. This technique explicitly mirrors much of
the underlying physics of the radiative transfer. It yields
transmittance and radiance spectra across each channel passband, which
are integrated to give the MOPITT channel signals. The method has
essentially LBL accuracy and is considerably faster. Channel radiance
calculations for a given test atmosphere can typically be completed in
a few minutes. While this is still too slow for operational
retrievals, MOPABS is an important tool for the development of a truly
fast forward model. In addition, MOPABS has broad applications to
other MOPITT work.

MOPFAS: The MOPITT operational fast forward model

MOPFAS achieves faster performance than MOPABS by reformulating the
calculation so that time-consuming spectral integrations are
avoided. A regression scheme based on the OPTRAN technique is applied
to establish a correspondence between channel-integrated
transmittances and atmospheric state profiles, such that the former
can be inferred accurately and quickly given the latter. The
regression maps a set of predictors, obtained from the state profiles,
onto corresponding values of channel transmittance obtained from
MOPABS. The predictors are functions of absorber amount, pressure,
temperature and viewing geometry. The regression coefficients are
pre-computed through a least-squares fit over a representative
atmospheric ensemble. MOPFAS channel radiances are in good agreement
with MOPABS. Typically, MOPFAS and MOPABS have mean differences of
0.05 - 0.1% , with maximum differences of 0.4 - 0.7% depending on
channel and band. In addition, a MOPFAS calculation is about
105 times faster than GENLN2 LBL calculations. This is fast
enough for MOPFAS to be used in operational retrievals.

MOPITT Cloud Detection

The cloud detection algorithm described below applies to both V3 and V4
products.

The MOPITT cloud detection algorithm detects and removes measurements
contaminated by clouds before they reach the retrieval algorithm. 
MOPITT cloud detection exploits both MOPITT
radiances and the MODIS (MODerate-resolution Imaging
Spectroradiometer) cloud mask product to achieve maximum coverage and
accuracy. The cloud detection technique using only MOPITT radiances
(MOPCLD) is described in (Warner
et al., Appl. Opt., 2001)
.

The MOPCLD threshold method compares the observed radiances with
calculated clear sky radiances, and currently uses only one MOPITT
thermal channel at 4.7 µm. The threshold, based on observed
channel radiance and forward model calculated clear column radiance,
is: Robserved/Rcalculated

< 0.955. Only latitudes within 65° North and South are included
in this threshold test to avoid complications due to temperature
inversions. MOPITT solar channels are not currently used in the L2
cloud detection processing.

The MOPITT and Terra/MODIS instruments produce nearly simultaneous
measurements overlapping a large geographical area close to
nadir. MOPITT sensors scan across the track to a maximum satellite
zenith angle of 27° on both sides of nadir, pausing for
approximately 0.45 seconds to take measurements of an array of four
22 km by 22 km pixels.  The MODIS swaths are more than
twice as wide as those of MOPITT and provide complete overlap for
MOPITT measurements. The spatial resolution of the MODIS cloud mask
is 1x1 km.
Therefore, each MOPITT pixel is collocated to approximately 484 MODIS
1x1 km pixels.

To maximize accuracy and global coverage, MODIS cloud mask and MOPCLD
are combined in the MOPITT cloud detection algorithm. A MOPITT
pixel is considered clear when both methods agree it is clear and when
there is only low cloud in the field of view (FOV). Note that there
is a 5% cloud allowance (as determined by MODIS) in each MOPITT pixel
for it to be considered as clear. Cloud description flags are included
in MOPITT Level 2 files to indicate the cloud decisions made for each
pixel (see table below). Additional MODIS flags are used to locate
low level clouds when the MODIS cloud mask classifies a pixel as
cloudy and MOPCLD classifies it as clear (flag=4). In all other
cases, when MODIS cloud mask classifies a pixel as cloudy and MOPCLD
classifies it as clear, this pixel is considered cloudy (no retrieval
performed). The final decision is clear when MODIS says clear and
MOPCLD says cloudy (flag=3). In areas where MODIS cloud mask is not
available only MOPCLD is used (flag=1). Only MODIS cloud mask is used
in the polar-regions (above 65°N and below 65°S) (flag=5).

Currently, only our best estimates of cloud-free pixels are included
in the Level 2; retrievals are not performed on cloudy
pixels. Therefore, users should not need to filter the data
according to the cloud flags included in the Level 2 files. For
reference, the cloud flags used in both V3 and V4 products are listed
below.

Cloud Description Flags used in V3 and V4

Flag Description
1 MOPCLD only clear, thermal only
2 MOPCLD and MODIS cloud mask agree on clear
3 MODIS cloud mask only clear (when MOPCLD cloudy)
4 MOPCLD overriding MODIS cloud mask over low clouds (MODIS
test flags used)
5 MODIS cloud mask only, clear over polar regions

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