OMI and MODIS data
We use several data sets from the OMI and Moderate resolution Imaging Spectroradiometer (MODIS) instruments
flying on the NASA Aqua and Terra satellites.
OMI is a spectrometer that acquires Earth and solar spectra at UV–vis
wavelengths from 270 to 500 nm with a spectral resolution of approximately
0.5 nm. The OMI ground footprint varies; near the nadir, it is approximately
12 km along the satellite track and 24 km across the 2600 km track. The
footprint size increases towards the swath edge. We use TOA radiance and
solar irradiance in the OMI vis channel to retrieve cloud parameters and
NO2 amounts.
The MODIS-derived BRDF kernel coefficients
from the 16-day MCD43GF data set are used to compute GLERs
over land for the OMI swath .
The kernel coefficients are provided for snow-free land and permanent ice
at a high spatial resolution. Over transient snow-covered regions, we
retain the standard
climatological LER of that was routinely used for the previous cloud retrievals.
GLER computation
The BRDF kernel coefficients
are averaged over an OMI FOV and used to calculate the TOA
radiance for a given observational geometry assuming pure Rayleigh scattering
in the atmosphere.
For radiative transfer (RT) calculations, we use
the vector linearized discrete ordinate radiative transfer (VLIDORT) code . VLIDORT
computes the Stokes vector in a plane-parallel
atmosphere with a Lambertian or non-Lambertian underlying surface.
It has the ability to deal with attenuation of
solar and line-of-sight paths in a spherical atmosphere, which is important for
large solar zenith angles (SZAs) and viewing zenith angles (VZAs).
VLIDORT accounts for polarization at the ocean surface using a full Fresnel reflection matrix.
The TOA radiance computed by VLIDORT is then inverted to derive GLER using
the following exact equation:
ITOA=I0+RT1-RSb,
where I0 is the TOA radiance calculated for a black surface, R is the
GLER, T is the total (direct+diffuse) solar irradiance reaching the
surface converted to the ideal Lambertian-reflected radiance (by dividing by
π) and then multiplied by the transmittance of the reflected radiation
between the surface and TOA in the direction of a satellite instrument, and
Sb is the diffuse flux reflectivity of the atmosphere for the case of its
isotropic illumination from below . All quantities, I0, T,
and Sb are calculated using a known surface pressure.
We use a monthly climatology of surface pressure taken from the Global
Modeling Initiative (GMI) chemistry transport model driven by the NASA Global Modeling and Assimilation Office
(GMAO)
GEOS-5 global data assimilation system with a spatial resolution
of 1∘ latitude by 1.25∘ longitude. Surface pressure for each
OMI pixel Ps is calculated as follows:
Ps=Ps(GMI)exp(-Δz/H),
where Ps(GMI) is the GMI surface pressure at a resolution of
1∘×1.25∘, Δz=z-z(GMI), z is
the terrain height of the OMI pixel from a digital elevation model,
z(GMI) is the terrain height at resolution of 1∘×1.25∘, H=(kT)/(Mg) is the scale height, where k is the Boltzmann
constant, T is the GMI air temperature at the surface, M is the mean
molecular weight of air, and g is the acceleration due to gravity.
To calculate TOA radiance over water surfaces, we account for both light specularly reflected
from a rough water surface and also for diffuse light backscattered by water bulk and transmitted through
the water surface.
Reflection from the water surface is described by the Cox–Munk slope distribution function
as implemented in .
Diffuse light from the ocean is calculated using a Case 1 water model that has chlorophyll concentration as a single input parameter.
Bidirectionality of the underwater diffuse light is accounted for following .
More details about the GLER computation can be found in .
An important update of our ocean surface model is the use of a variable wind
speed instead of a single climatological wind speed of
5 m s-1 as in .
Retrievals of wind speed are taken from the Advanced Microwave Scanning Radiometer for
the Earth Observing System (AMSR-E) that flies on NASA's Aqua satellite (with Aura-OMI closely following Aqua).
The use of wind speed
from the AMSR-E measurements improves in the GLER over ocean.
Thanks to the higher spatial resolution of AMSR-E, it is possible to match fine structure
of the wind field to the TOA radiances
and GLERs over the sun-glint-affected areas.
The O2-O2 slant column density fitting algorithm
The operational OMI O2-O2 SCD retrieval
uses the differential optical absorption
spectroscopy (DOAS) approach, simultaneously retrieving SCDs of
O2-O2 and O3 in the 460–490 nm wavelength interval
and using single-temperature O2-O2 cross sections
and a first-degree polynomial approximating the wavelength dependence
of reflectances in the fitting window.
Here, we generally follow the approach developed by for the
NO2 SCD estimates. Instead of simultaneous retrieval of coefficients
of multiple parameters as takes place in the classical DOAS formalism, we
divide the problem into a series of sequential steps
(Fig. ).
Flow
diagram of the O2-O2 SCD retrieval algorithm. The algorithm
input comprises the OMI monthly mean solar irradiances; the radiances
(dependent on wavelength, line of sight (row), and position (along orbit));
the laboratory cross sections of O3, NO2, and H2O (X
sections); the atmospheric (RS air) and liquid-water (RS water) Raman
scattering spectra (all X sections convolved with the row- and
wavelength-dependent OMI instrument line-shape functions); and the OMI
cloud-fraction (CF) estimates provided by an independent retrieval. RS
denotes the amplitudes of the combined air and water Raman scattering
spectrum.
Step 1 involves the removal of interfering trace-gas absorption. The spectral
range chosen for the O2-O2 SCD retrievals is affected by
relatively strong O3 absorption that, in most cases, distorts the
O2-O2 profiles (Fig. ). The same applies to
NO2 absorption over polluted regions (e.g., the Beijing area; see
Fig. ) and, to a far lesser extent, the mainly equatorial
regions over the open-water Pacific, where the H2O absorption may
distort the flanks of the broad O2-O2 profiles
(Fig. ). Note the clear presence of the ozone
feature around λ∼462 nm, as well as the large distortion of the
O2-O2 profile caused by the broad ozone absorption around
λ∼482 nm. In this particular example, the only easily
recognizable Ring spectrum feature is seen at λ∼486.5 nm. The
gradual ∼13 % change in reflectances between 450 and 500 nm comes
from a combination of comparable strength signals: the ozone absorption and
the Rayleigh-scattering component. For better guidance, in
Figs. – we show scaled absorption spectra of
the main trace gases that may contribute to the general appearance of a
reflectance spectrum. We keep the same plotting style for
Figs. –, though noting that in each
particular example one may see quite a different impact from the same absorption
constituent. For example, while the NO2-related signal barely registers in
Fig. (practically unpolluted region), the heavily
contaminated Beijing area (Fig. ) shows a clear presence of
the NO2 absorption at λ∼457–466 nm (three features),
λ∼475 and 480 nm (these two are superposed on the broad
O2-O2 absorption), and the well-defined NO2
absorption at λ∼489 nm that rivals the strength of the
retrieved O2-O2 feature. In this particular case of the
heavily NO2-polluted region, the omnipresent O3 absorption
plays a far less important role compared to the spectrum shown in
Fig. . In addition, though to a far lesser extent (when
compared to ozone, Ring, and NO2), the H2O absorption may
distort the flanks of the broad O2-O2 profiles, mainly in the
equatorial regions over the open-water Pacific.
(a) Reflectance normalized at λ=464 nm (bold black
line) for the OMI orbit 7921 from 10 January 2006, with row 14 and orbital
exposure 1550 at 65.37∘ N and 88.58∘ E (high slant
column ozone values). For reference, the arbitrarily shifted and scaled
absorption spectra of H2O (thin blue line), NO2 (green),
O2-O2 (red), and O3 (cyan) are plotted in the upper
portion of the panel. The arbitrarily scaled and shifted Ring patterns (as
seen in reflectances) are shown in black. (b) The rectified
O2-O2 absorption profile (i.e., the ratio of the data denoted
by the red and blue lines in a, with additional adjustments to the
blue-line data – see text for more details). The dashed black line shows the
1.0 reference level. In panel (b), the vertical dotted lines denote the
wavelength range used in the SCD fits of the O2-O2 absorption
profile.
The spectral domain chosen for the O2-O2 retrieval is not
optimal for simultaneous O3, NO2, or H2O estimates.
Optimal fitting windows are the ∼290–340, 400–465, and 435–450 nm
intervals for O3, NO2, and H2O, respectively.
Hence, to minimize the biases that may be introduced by the sub-optimal DOAS
estimates of the interfering trace-gas species, we use the SCDs provided by
independent OMI products: NO2 and H2O
from OMNO2SCD and O3 from OMDOAO3
, and we remove the corresponding absorption features from the
observed radiances. We find that, as expected, at large SZAs
the corrections based on the UV O3 SCD retrievals result in large
spectral residuals pointing to systematic underestimates of O3
absorption strength. This stems from the notion that the relatively (to the
visual range) higher Rayleigh optical depth effectively masks the
lower-atmosphere O3 absorption. Hence, at SZA>80∘ we adjust the UV SCDs by a constant 1.25 coefficient. This helps
to reduce the spectral residuals related to the underestimated O3
absorption to a manageable (on average <0.1 %) level.
Step 2 closely follows the approach from , comprising the simultaneous,
iterative wavelength adjustment and Ring spectrum removal.
At each FOV (row, 60 in total) the reflectances are produced from the
individual, prefiltered earthshine radiances (from Step 1) normalized by the
monthly-averaged OMI irradiances. These irradiances are iteratively adjusted
to accommodate slight relative (radiances vs. irradiances) wavelength shifts.
For estimates of the line-filling factors (i.e., the Raman scattering
amplitudes), we use an appropriate combination of the air and water Raman
scattering spectra . We split the retrieval region into two
“micro-windows”, 451–469 and 483–496 nm, and iteratively evaluate the
wavelength shifts and the Raman-spectrum amplitudes in each window. For the
final removal of the Raman scattering patterns, we use an average of the two
micro-window estimates. The individual micro-window wavelength shifts
are used for wavelength adjustments of irradiances in each micro-window,
interpolating these estimates in the 469–483 nm domain occupied by the main
O2-O2 absorption.
Similar to Fig. but for
row 44 and orbital scan number
iTime=1315 pointing to the Beijing area.
In (a), the thick blue line follows the reflectances
after removal of the trace-gas (O3 and H2O)
absorption,
however with the Ring spectrum features remaining intact.
This is to be compared to the adjacent black line that follows the
original reflectances. Panel (b) shows the normalized O2-O2
profile as used in the SCD retrieval.
Similar to Fig. but for the open-water nearly cloud-free (f<0.05) region of the Indian Ocean (54.02∘ S, 106.91∘ E, OMI
orbit 7791, 1 January 2006). The thick blue line follows these reflectances
after removal of the Ring patterns and the trace-gas (O3, NO2, and H2O)
absorption. The red line shows the piecewise fit to the blue line.
Similar to Fig. but for the
Sahara desert (OMI orbit 8013,
16 January 2006, row 20, orbital exposure 1180).
Panel (b) shows the rectified O2-O2 absorption profile,
i.e., the ratio of the data denoted by the red and blue lines in (a),
with additional adjustments to the blue-line data – see text for more
details.
Step 3 involves normalizing the O2-O2 profile in preparation
for SCD evaluations. We deem this step to be the most important procedure; it
may change the outcome by as much as ∼20 % in extreme cases such as
the open-water scenes (Fig. ) and Sahara desert
(Fig. ) representing two extremes and the remaining cases
falling in between. Figures a and a show the observed
reflectances before (black lines) and after (blue lines) the removal of
trace-gas absorption and the Raman line-filling patterns, and the red lines
follow the adopted continuum fits. Note the profound difference among the
wavelength dependencies of the reflectances in these extreme cases. While
the cloud-free, open-water case (Fig. ) is predominantly
Rayleigh controlled, leading to a steep decline in reflectances, the much
brighter Sahara surface controls the appearance of the radiances at long OMI
wavelengths, leading to the gradual increase in reflectances
(Fig. ). Figures b and b show normalized
O2-O2 profiles. In a case-by-case study of the presumably
cloud-free areas, we have found that various combinations of linear functions
fitting the flanks of the O2-O2 profile lead to gross
underestimates (mainly over open-water areas) or overestimates (deserts and
semideserts) of the retrieved scene pressures that are directly linked to
the biases in the SCD evaluations. Hence, we have implemented a more flexible
approach, defining two broad categories of the surface reflectances and
applying different fitting approaches to each of them.
The reflectances from Step 2 are averaged in 2 nm intervals, providing a set
of estimates at λ=463 and 495 nm that are partitioned into two
general categories. The first broad category comprises all the relatively
cloud-free low-reflectance scenes, with r(463)r(495)>1.05 and r(463)<0.25. The second class includes the remaining
scenes. For both categories, the fitting starts from applying the third-degree
polynomial to the 459–466 and 484–494 nm regions, identifying and
eliminating large (∼5σ, i.e., ±0.5 %) deviations and
then repeating the procedure, ultimately normalizing the reflectances in the
450–500 nm range by the fit. The normalized reflectances in the 459–465
and 484–490 nm intervals are refitted with a first-degree polynomial and,
again, all reflectances in the 450–500 nm range are renormalized by this
fit. This concludes the fitting for the second category of scenes. However, at
this point the fitting proceeds for the first class of the relatively
cloud-free, low-reflectance scenes. Yet again, the normalized radiances in
the 465–470 and 482–487 nm intervals are iteratively (rejecting the large
±1 % deviations) refitted with a second-degree polynomial; then this
fit is applied exclusively to the region occupied by the
O2-O2 profile, 465–491 nm. The line edges are further
refined by applying piecewise fits (first- or second-degree polynomials) to the
relatively narrow windows, 459–465 and 486–491 nm, thus concluding this
rather involved procedure for the first category of the low-reflectance
scenes.
Step 4, the SCD retrieval, follows the approach described in . Here,
preliminary SCD values are obtained from two algorithms, the Nelder–Mead minimization method
and the least-squares Levenberg–Marquardt fit , taking the latter as a default
and fitting the normalized (Step 3) O2-O2 profile in the 465–487 nm interval.
These evaluations are repeated for each temperature-dependent O2-O2 cross section;
there are five of them measured by .
Each cross section is fitted to the data, providing an individual root mean square (RMS)
value of the fitting residuals. These five RMS values are approximated by
a parabolic function. The minimum of the function is used
to construct via linear interpolation a synthetic O2-O2 profile that is removed
from the normalized reflectances, thus leaving us with the residuals that are presumably
dominated by instrumental noise. The noise is reduced by an iterative procedure similar to one
described in . The final SCD evaluation is performed over a slightly
broadened wavelength range, 463–488 nm.
As implemented, the algorithm relies on optimal SCD retrievals of the
O3, NO2, and H2O trace gases, as well as preliminary
cloud-fraction estimates. The latter is used exclusively over deep-water
areas during the wavelength calibration and the Raman scattering removal. If
needed, such cloud fractions can be substituted for appropriately adjusted
reflectances, thus vying for self-sufficiency. The use of independent
O3, NO2, and H2O SCDs is an essential part of the
algorithm that, especially for the scenes with heavy O3 and
NO2 loads, leads to more accurate O2-O2 SCDs. The use
of the trace-gas SCDs does not create any paradox when the NO2 values
are used in order to retrieve cloud properties that should be
incorporated into the NO2 estimates. Note that in the implemented
algorithm we use the NO2 SCD estimates that can be obtained without
any relevance to cloud properties. These cloud properties are used later,
during the conversion of the NO2 slant columns to the NO2
vertical columns. Opting for a complete self-reliance of the cloud algorithm,
one may substitute the required O3, NO2, and H2O
SCDs for SCD estimates provided by the appropriate trace-gas climatologies.
ECFs retrieved with our algorithm versus those retrieved from
OMCLDO2. Results are provided as 2-D densities in ECF bins of 0.01. The color
scale represents the number of OMI pixels falling within a given bin. Data
for 13 November 2006, 30∘ S–30∘ N. (a) Land; (b) ocean.
Similar to Fig. but for OCP.
Comparison of scene pressures from our algorithm (black curve) and
OMCLDO2 v2 (red) with surface pressures (blue) along cross-track position 20
of OMI orbit 4415 (14 May 2005). The green curve shows cloud fractions for
this cross-track position.
Cloud algorithm
The O2-O2 cloud algorithm described here is based on the O2-O2
absorption band at 477 nm. This algorithm is broadly similar
to the operational O2-O2
cloud algorithm developed at the Royal Netherlands Meteorological Institute (KNMI)
known as OMCLDO2 . However, our approach differs in a number of aspects.
First, we use normalized radiance at 466 nm to compute f with
Eq. () in a separate step. This wavelength was selected because it
is not significantly affected by gaseous absorption and rotational Raman
scattering and it is still sufficiently close to the O2-O2
absorption band center at 477 nm. f is calculated using linear
interpolation of lookup tables (LUTs) of Ig and Ic.
The tables were generated for 23 different surface and cloud pressures, 20
surface reflectivities, 30 SZAs, 20 VZAs, and 20 relative azimuth angles.
Nodes and their locations were selected on the basis of the analysis of
interpolation errors.
A threshold for acceptable interpolation error was set at 0.2 %. It
should be noted that aerosols are implicitly accounted for in the
determination of f, as they are treated (like clouds) as particulate
scatters.
Difference between the scene pressure and the surface pressure,
Psc-Ps, for our algorithm (a) and OMCLDO2 v2 (b).
Data are for 13 November 2006.
Two-dimensional histograms comparing effective cloud fraction (ECF) retrieved
with GLER (y axes) and climatological LER (x axes) for land (a) and
ocean (b). The color scale shows numbers of data points. OMI data
are for 13 November 2006.
Differences between ECFs retrieved with GLER and those retrieved
with climatological LER, f(GLER)-f(ClimLER). OMI data are
for 13 November 2006. No snow-/ice-covered areas are included in the comparison.
Cross-track dependence of ECF zonal means retrieved with GLER (black) and
climatological LER (red) for different latitude bins. Data are for
13 November 2006; effective cloud fractions are between 0.05 and
0.25.
Our
algorithm retrieves cloud OCP from the OMI-derived oxygen dimer SCD at 477 nm.
The OCP, here also denoted as Pc, is estimated using the MLER
method to compute the appropriate air mass factors (AMFs) . To
solve for OCP, we invert the following equation:
SCD=AMFg(Ps,Rg)VCD(Ps)(1-fr)+AMFc(Pc,Rc)VCD(Pc)fr,
where VCD is the vertical column density of O2-O2
(VCD=SCD/AMF), AMFg and AMFc are the
precomputed (at 477 nm) clear-sky (subscript g) and overcast (cloudy,
subscript c) subpixel AMFs, Ps is the surface pressure, and
fr is the cloud radiance fraction (CRF) given by fr=fIc/Im. Equation () is similar to that
frequently used for retrieval of trace-gas VCDs with the MLER model provided
Pc and Rc are known (see, e.g., ). Here we
use this equation for retrieval of Pc assuming that the
O2-O2 VCD is known. The CRF is calculated at 466 nm. CRF
defines a fraction of TOA radiance reflected by the cloud. It should be noted
that CRF is wavelength dependent (see discussion in Sect. ).
The CRF retrievals at different wavelengths are included in our output.
Lookup tables of the TOA radiances and AMFs were generated using VLIDORT.
Temperature profiles needed for estimation of VCD and AMF are taken from
the NASA GMAO GEOS-5 global data assimilation system .
In addition to OCP, we retrieve the so-called scene pressure,
Psc. The scene pressure is derived from Eq. ()
assuming that fr=1 and Rc is equal to the scene LER,
Rsc:
SCD=AMFc(Psc,Rsc)VCD(Psc).
Rsc is determined from the measured TOA radiance using
Eq. () for a known surface pressure. In the absence of clouds
and aerosols, the Psc should be equal to Ps.
Psc is therefore an important diagnostic tool for evaluation of
the performance of cloud pressure algorithms.
Two-dimensional histogram similar to Fig. but comparing OCPs
retrieved with GLER with those retrieved with climatological LER.
Differences between OCPs retrieved with GLER and climatological LER
for 13 November 2006. Data are shown for ECF>0.05 only.
Cross-track dependence of OCPs retrieved with GLER (black) and those retrieved with climatological LER (red) for
13 November 2006.