Introduction
The Ozone Monitoring Instrument (OMI) was launched in
2004 on board the Aura satellite, in a polar, sun-synchronous orbit at
approximately 705 km altitude, with a local Equator-crossing time
of 13:45 (ascending node). Its main objective is to monitor trace
gases in the Earth's atmosphere, especially ozone. It was built as the
successor to the ESA instruments Global Ozone Monitoring Experiment (GOME)
and Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY)
, and NASA's Total Ozone Mapping Spectrometer (TOMS) instruments
e.g.. GOME and SCIAMACHY were the first
space-borne hyperspectral instruments, measuring the complete spectrum
from the ultraviolet (UV) to shortwave infrared (SWIR) wavelength
range with a relatively high spectral resolution (typically
0.2–1.5 nm), from which multiple trace gases, clouds, and aerosol
parameters can be retrieved simultaneously. TOMS instruments have been
monitoring the ozone column at a relatively high spatial resolution
(50 × 50 km2) with daily global coverage since 1978. OMI was
designed to combine those functions and measure the complete spectrum
from the UV to the visible wavelength range (up to 500 nm) with a high
spatial resolution and daily global coverage. To this end, the imaging
optics were completely redesigned.
Instead of a rotating mirror, in OMI a two-dimensional CCD (charge-coupled device) detector
array (780 × 576 pixels) is used to map the incoming radiation
in the across-track and wavelength dimensions simultaneously. A swath
of about 2600 km in the across-track direction is imaged along one
dimension of the detector array. Spectrally, the radiation is split
into two UV channels and a visible (VIS) channel and imaged along the
wavelength dimension of the detector array. The spectral
resolution of the VIS channel is 0.63 nm. The along-track direction
is scanned due to the movement of the satellite. In default “Global”
operation mode, five consecutive CCD images, each with a nominal
exposure time of 0.4 s, are electronically co-added during a 2 s
interval. The subsatellite point moves about 13 km during this
time interval . The consequence of this
design is that the spatial response function of the OMI footprints is
not box-shaped but has a peak at the centre of the footprint. This
new design, avoiding moving parts, was used in OMI for the first time
and is now being used in several new, upcoming satellite missions.
The point spread function (PSF) is defined as the response of the
imaging system to a point source, while the telescope field of view (FoV)
is defined by the projection of the OMI spectrograph slit on the
Earth's surface from the point of view of a CCD pixel. This projection
is affected by Fraunhofer diffraction of the imaging optics, which,
for a circular aperture, can be modelled using an Airy function. For a
rectangular slit, used in OMI, the solution can be approximated by a
Gaussian function in two dimensions. The FoV has been determined
pre-flight by measuring the intensity response to a star stimulus for
all pixels. The response function was measured by exposing the pixels
to a point source and rotating the instrument. The sensitivity curve
found in this way was fitted to a Gaussian curve, of which the full
width at half maximum (FWHM) was reported. This is proprietary
information, but the results are summarised here. In the swath
(across-track) direction the average peak position for each pixel was
determined and fitted to a linear curve to determine the spatial
sampling distance for the three channels, which gives the
instantaneous FoVs in the across-track direction for individual
pixels. For the VIS channel the FoV for the entire swath is
115.1∘. The PSF in the across-track direction was not
determined (or reported). However, a memo from the OMI Science Support
Team from 2005 shows an across-track pixel size estimation from these
measurements, where the sizes have been determined by assuming no
overlap between adjacent pixels and computing the distances between
the peak positions when imaged on the Earth. This yields sizes in the
across-track direction of 23.5 km at nadir and 126 km for far
off-nadir (56∘) pixels.
In the along-track direction the FoV was characterised by tilting the
instrument to simulate the movement in the flight direction. The
measurements were fitted to a Gaussian curve with variable width for
different across-track angles and wavelengths. This width is reported
as the FWHM in degrees, which is about 0.95 at nadir and 1.60 at 56∘ for
the VIS channel. This corresponds to a nadir pixel size in
the along-track direction of about 15 km and a far off-nadir pixel
size of about 42 km when the Gaussian is convolved with a boxcar
function whose width is the 13 km movement of the subsatellite point
during the 2 s exposure.
The instantaneous FoV (iFoV) of the OMI instrument is influenced by a
polarisation scrambler, which transforms the incoming radiation from
one polarisation state into a continuum of polarisation states (as
opposed to unpolarised light). The incoming beam is split into four
beams of equal intensity, scrambled, and projected onto the CCD. Since
the projections of the four beams are slightly shifted with respect to
each other, the polarisation state of the incoming radiation still
slightly determines the intensity distribution of the four beams and
therefore the iFoV in the flight direction. The only property which is
not dependent on the polarisation state of the incoming radiation is
the centre of weight of the four beams. This corresponds to the centre
of the ground pixels, which is therefore the only geolocation
coordinate that can be determined unambiguously .
Therefore, centre coordinates are provided in the Level 1b data
product, but corner coordinates are not. However, for mapping
purposes, ground pixel area computations (e.g. for emission estimates
per unit area), and collocation, an OMI corner coordinate product was
developed, called OMPIXCOR, which is provided online via the OMI data
portal . Two sets of quadrangular corner coordinates
are provided. One set contains tiled pixel coordinates, which
are essentially the midpoints between adjacent centre coordinates,
mainly useful for visualisation purposes, as no overlap between pixels
is imposed. The other set contains so-called 75FoV pixel coordinates,
which, according to , correspond to 75 % of the
energy in the along-track FoV. The authors assumed a 1∘ FWHM
for the iFoV to fix a Gaussian distribution and convolved it with a
boxcar to model the satellite movement. The area under a Gaussian
curve corresponds to about 76 % at FWHM for a normal distribution
(exponent of 2); however, the authors claim to have used a
super-Gaussian distribution with exponent of 4 for this. In this case the energy
contained within the FWHM has increased to about 89 %. When this iFoV
is convolved with the boxcar function, the energy within the FWHM will
have increased even more. The 75FoV pixels generally overlap in the
along-track direction, since radiation emanating from successive scans
enter the FoV. The coordinates in the across-track direction, however,
are still the half-way points between adjacent pixels.
The application of quadrangular pixel shapes for OMI can become
problematic when pixel values are aggregated onto a regular grid
(e.g. Level 3 products that are reported on a regular lat.–long. grid).
If pixels overlap, which might occur when several orbits are averaged
or in the case of 75FoV pixels, extreme values may be smoothed and reduced
due to averaging. A more realistic distribution that preserves mean values
can be reconstructed using a parabolic spline surface on the
quadrangular grid, resulting in a much better visualisation
. In cases where values from OMI are compared with
those of another instrument, especially one with a higher spatial
resolution, the approximate true shape of an OMI pixel is desired.
For example, we intend to combine spectral measurements from OMI and
MODIS to determine the aerosol direct effect over clouds
. To this end, an optimal characterisation of the FoV
of the OMI footprint is desired, to optimise the accuracy of the
retrieval.
In this paper, the OMI FoV for the VIS channel is investigated by
testing various predefined shapes and sizes under various
circumstances and determining the maximal correlation between OMI and
MODIS reflectances. In Sect. ,
the consistency between overlapping OMI and MODIS reflectances is
investigated. A cloud-free scene from 2008 is used to study the FoV
under the most optimal circumstances. In Sect. , a two
dimensional super-Gaussian function with a varying exponent is
introduced, which can change shape from a near-quadrangular to a
sharp-peaked distribution. Furthermore, the sizes in both along- and
across-track directions can be varied. This function is used to
define various FoVs, which are investigated for various scenes. The
change in FoV is further investigated by looking into the effect of
scene and geometry changes during the (varying) overpass times of OMI
and MODIS. The conclusions from this study are reported in
Sect. . The geolocations of the pixels in the UV channels
are slightly different from those in the VIS channel. However, the FoV
cannot be determined in the same way for the UV, since MODIS measurements
do not overlap with these channels spectrally.
Data
The Aura satellite flies in formation
with the Aqua satellite in the afternoon constellation (A-train). Aqua was
launched in 2002, to lead Aura in the A-train by about 15 min. The time
difference between the instruments within the A-train is controlled by
keeping the various satellites within control boxes, which are defined as the
maximum distances to which the satellites are allowed to drift before
correcting manoeuvres are executed. Therefore, the time difference between
OMI and MODIS is variable by up to a few minutes. A major orbital manoeuvre
in 2008 of Aqua decreased the distance between the Aura and Aqua control
boxes to about 8 min.
MODIS RGB image of the reference scene on 4 November 2008 at
14:00 UTC (start of the central MODIS granule). The yellow lines
indicate the MODIS data granules, and the red lines the considered OMI
swath, which was confined to rows 2–57, with the exception of pixels in
the row anomaly (see text). The green pixels indicate the
darkest (vegetated) and the brightest (cloud-covered) areas in the
scene. The OMI reflectance spectra of these pixels are shown in
Fig. . The blue OMI pixels correspond to the blue-marked points in Fig. .
To investigate the correlation between OMI and MODIS observed
reflectances, several scenes were selected. One reference scene will
be discussed here in detail. It was an almost cloud-free scene over
the Sahara on 4 November 2008, around 14:00 UTC (start of the
first MODIS granule). At this point in time, the time difference
between OMI and MODIS was reduced to 8 min and around 20–30 s, depending on the pixel row. The differences between the
pixel times arise from the fact that MODIS has a scanning mirror,
while OMI has no scanning optics but exposes the CCD to different
scenes while moving in the flight direction. The scene is visualised
in Fig. , using MODIS channels 2, 1, and 3 to create
an RGB picture at 1 km2 resolution. The MODIS granules are outlined
in yellow, while the considered OMI scene is outlined in red. From
June 2007 onward, OMI suffered from a degradation of the observed
signal in an increasing number of rows, called the row anomaly
. In November 2008 the anomaly was limited to
only rows 53 and 54 for scenes near the Equator. These rows were
disregarded in the comparison. In order to stay within the MODIS swath,
the OMI swath was further reduced to rows 2 to 57. A total of
7335
OMI pixels are left in the scene.
To compare reflectances from OMI and MODIS, the reflectance measured
by OMI is convolved with the MODIS spectral response function. MODIS
channel 3 at 469 nm overlaps with the OMI VIS channel (350–500 nm).
This is illustrated in Fig. , where two OMI
reflectance spectra from the VIS channel are plotted, together with
the normalised MODIS response function of channel 3 (red curve). The
reflectance spectra correspond to the darkest and brightest pixels (at
469 nm) in Fig. , indicated by the green boxes. The
darkest pixel is a vegetated area with an OMI reflectance of 0.0935,
and the brightest pixel is a cloud-covered scene with an OMI
reflectance of 0.5040, both at 469 nm.
OMI top-of-atmosphere reflectance spectra on 4 November 2008 at
14:09:19 UTC and 14:12:43 UTC of the green pixels in
Fig. (black/green), and the
normalised MODIS response function of channel 3 (red).
All the 7335 OMI pixels in the scene in Fig.
were compared to collocated MODIS pixels; see Fig. a. Here, all the MODIS pixels that fall (partly)
within an OMI quadrangular pixel, as defined by the OMPIXCOR 75FoV
corner coordinates, are averaged with equal weight, which is the
easiest and quickest averaging strategy. The MODIS reflectances are
somewhat lower than the OMI reflectances; a linear fit through the
points shows a slope of 0.959 and an offset of 0.0023. The MODIS
reflectances show a Pearson's correlation coefficient r of 0.998
with the OMI reflectances and a standard deviation (SD) of 0.0039.
The SD refers to the rms deviation of the measurements to the model
fit.
Scatter plot of OMI and MODIS collocated reflectances for the scene
in Fig. using quadrangular OMI pixels (a) and
optimised super-Gaussian (n=2, m=4) pixels (b). The red dashed
line is the linear least-squares fit to the measurements, given by the linear
function y = a0+a1x in the plot. r is Pearson's correlation
coefficient, and σ the standard deviation of the points to the fitted line. The
blue-marked points have the largest σ and correspond to the blue OMI
pixels in Fig. . N is the number of points, and max
ROMI and min ROMI the maximum and minimum value in the
plot, respectively.
One-dimensional normalised super-Gaussian distribution
functions with varying exponents n. The normal distribution (n=2)
is plotted in blue.
OMI 75FoV corner coordinates (dark-blue-filled circles), with the
OMI centre coordinate (dark blue diamond) and collocated MODIS centre
coordinates (black and coloured squares). The colours of the squares indicate
the weighting of the MODIS pixels as indicated by the colour bar.
(a) Quadrangular weighting, with all MODIS pixels within the corner
coordinates having equal weights, everything else disregarded; (b) a
2-D flat-top super-Gaussian distribution with exponents n=m=8, resembling the
quadrangular shape with smoothed edges; (c) a 2-D super-Gaussian
distribution with n=2 and m=4; (d) a 2-D point-hat
super-Gaussian distribution with exponents n=1 and m=2; (e) a 2-D
super-Gaussian distribution (n=2, m=4) with twice the width in the
across-track direction; (f) a 2-D super-Gaussian distribution
(n=2, m=4) with twice the width in the along-track direction. Different
OMI row numbers are shown (see panel captions) to show the change in
orientation and number of MODIS pixels for different rows.
Pearson's correlation coefficient r for OMI and MODIS collocated
reflectances in the scene of Fig. as a function of
super-Gaussian shape and size of the assumed FoV. The blue line indicates the
correlation as a function of exponent n (a) and m (b)
for fixed 75FoV corner coordinates. The point marked “Quadr.” marks the
correlation for a quadrangular FoV. The red lines are the relationships for
varying pixel sizes when the optimal Gaussian exponents n=2 and m=4 are
chosen. Note that the scales are logarithmic on both x axes.
(a) MODIS RGB scene on on 7 October 2008 at 10:20 UTC over
the the Middle East. Yellow and red lines as in Fig. , while
the individual red OMI pixels are cloud pixels that were manually discarded.
(b) Dependence of Pearson's correlation coefficient r between the
OMI and MODIS observed reflectance for the scene in the left panel as a
function of super-Gaussian shape and size, as in Fig. . The
optimum in this case was found for Gaussian exponents n=2 and m=4, and
1 × 75FoV corner coordinates in both directions.
Same as Fig. but on 11 October 2008 at 04:45 UTC over
Australia. The optimum in this case was found for Gaussian exponents n=1.5
and m=2, and 1 × 75FoV corner coordinates in both directions. A fit of
Gaussian exponents n=2 and m=4 is best for slightly larger pixels
(1.25 × 75FoV, red line).
OMI point spread function
The true FoV of an OMI pixel is expected to resemble a flat-top
Gaussian shape. To investigate the OMI FoV, the response at 469 nm is
compared to the MODIS channel 3 signals, weighted using different
super-Gaussian functions in two dimensions and checking the change in
the correlation and SD between the OMI and MODIS reflectances. A 2-D
super-Gaussian distribution is defined by
g(x,y)=exp-(xwx)n-(ywy)m,
where x and y are the along- and across-track
directions,
and wx,y are the weights in either direction, defined by
wx=FWHMx2(log2)1/n;wy=FWHMy2(log2)1/m.
FWHMx and FWHMy are the full widths at half maximum in the
along- and across-track directions, respectively, defined in this paper
by the 75FoV pixel corner coordinates. The size of the FoV model can
be varied to include more or fewer MODIS pixels from neighbouring
pixels in the along- and across-track directions by varying wx and
wy. All size changes are reported relative to FWHMx and FWHMy.
The shape of the FoV model is determined by the Gaussian exponents n and
m, which define the “pointedness” of the distribution. In one dimension,
n=2 corresponds to a normal distribution, n<2 results in a point-hat
distribution, and n>2 results in a flat-top distribution; see the
illustration in Fig. . Various FoV models are illustrated in
Fig. . The colours of the square MODIS pixels indicate the
relative contribution of that pixel. The different panels show OMI pixels at
different rows, to illustrate the change in orientation and number of MODIS
pixels that fall inside an OMI pixel when the viewing zenith angle (VZA) changes.
Fig. a shows the quadrangular OMI pixel, with all MODIS pixels
within the OMI corner coordinates having equal weight, while all pixels
outside the footprint have zero weight. Figure b shows a 2-D
flat-top super-Gaussian (n=m=8) shape using the 75FoV corner coordinates to
constrain the FWHM, resembling the quadrangular shape but with smoother
edges. Fig. c shows a 2-D super-Gaussian distribution, with
n=2 and m=4, which represents the optimal representation of the FoV using a
super-Gaussian function. Fig. d shows a 2-D point-hat
super-Gaussian (n=1, m=1.5) distribution, which is the optimal fit of
this function when broken clouds are in the scene.
Figure e and f show the weights for pixels which are assumed
to be twice as wide or long as the 75FoV pixels and using a 2-D
super-Gaussian distribution with n=2 and m=4.
The size and shape of the FoV model were varied by changing n from
0.5 to 16, m from 1 to 16, and the FWHM from 0.5 to 3 times the
75FoV corner coordinates. For each configuration the correlation
between the OMI and MODIS reflectances and the SD were determined,
using all pixels from the scene in Fig. . The
correlation change is shown in Fig. . The blue
solid curve shows the change in correlation for a changing
Gaussian exponent and 1⋅ FWHM, i.e. the change in FoV model
shape and 75FoV corner coordinates to constrain the FWHM. In the top
panel the change in correlation coefficient r is shown for a
changing Gaussian exponent n using the optimal Gaussian exponent
found for the across-track direction m=4. For this function the
optimal Gaussian exponent in the along-track direction is n=2. The
blue dotted curve shows the goodness of fit q corresponding to each
of the correlation coefficients r (the blue solid line). It
indicates the probability of a non-random Chi-square fit, which was
determined using a constant error for OMI measurements, and a constant
error for MODIS measurements but weighted by the number of MODIS
pixels in each OMI pixel. It shows a reasonably good fit at the
optimum n=2.
The red line shows the change in correlation when the along-track width is
varied. The shown curve is for the optimal Gaussian parameters, n=2 and m=4,
and peaks at 1.0, meaning that the 75FoV corner coordinates are the optimal
sizes to constrain the FWHM when a super-Gaussian model is used. The lower
panel shows the same dependencies in the across-track direction. The change
of r is shown for changing m (the shown blue solid line is for the optimal
Gaussian exponent n=2) and the red curve is the width in the across-track
direction for n=2 and m=4. The red curve also peaks at 1, again confirming
the 75FoV corner coordinates, while m peaks at 4. However, the change for
larger m is minimal, meaning that the softness of the edges in the
across-track direction make very little difference. Only the goodness of fit
q decreases significantly for larger m, so m=4 can be used as the
optimal parameter. These four optimal parameters are also the absolute
maximum in the entire parameter space, with r=0.998. This is noticeably
higher than the correlation when quadrangular pixels are used.
Super-Gaussian exponents m and n as a function of OMI pixel row,
averaged over all scenes introduced in this paper. The FWHM was
fixed to the 75FoV pixel sizes, shown in the lower panel,
to determine the optimal exponent. The fat lines are boxcar
averages using five points.
Same as Fig. but on 7 January 2008 at 13:45 UTC over
the Sahara. The optimum in this case was found for Gaussian
exponents n=1.5 and m=2, and 1 × 75FoV corner coordinates,
or n=2 and m=4, and 1.25 × 75FoV corner coordinates in both
directions.
MODIS RGB image on 13 August 2006, around
13:33 UTC (lower part of the image). The yellow lines
indicate the MODIS data granules, and the red lines the considered OMI
swath, which was from rows 10–50. The optimal correlation between
OMI and MODIS for this scene was found for Gaussian exponents n=1, m=1.5
and 75FoV corner coordinates. The correlation for this pixel
shape is shown in the right panel.
(a) Simulated clear-sky reflectances for the
reference scene in Fig. using OMI scattering
geometries (x axis) and MODIS geometries (y axis). The colours
indicate the OMI viewing zenith angle of each simulated pixel. The
reflectances were simulated at 469 nm, for a standard atmosphere
reaching to sea level and an ozone column of 334 DU. The surface
albedo was varied according to a database (see text). The underlying
red dashed line shows the linear fit to the simulations. (b) Same
data as in the left panel but plotted as the relative difference
between the OMI and MODIS reflectances.
The correlation between the OMI and MODIS reflectances and the SD,
when the optimal FoV model for this scene is used, is shown in the
Fig. b. The SD for the optimal FoV is
0.0036. The change in SD for different shapes and sizes is not shown,
because it is consistent with the change of the reciprocal of the
correlation, in the sense that it is minimal when the correlation
peaks and can be equally used to find the optimal FoV characterisation
in this way.
FoV sensitivity
When a super-Gaussian form is assumed, the optimal super-Gaussian
model parameters for the reference scene are n=2 and m=4, and the
75FoV corner coordinates for the Gaussian FWHM. However, the
correlation between OMI and MODIS reflectances is not a constant. A
number of scenes were investigated to show the change in correlation
between OMI and MODIS reflectances in time and space.
First, another cloud-free scene was found over the Middle East on 7
October 2008, starting at 10:20 UTC; see Fig. . The time
difference between OMI and MODIS is about 8 min and 34–45 s. This
scene is entirely cloud-free over land, and the reflectance ranges
from 0.12 over the ocean to 0.41 over the desert. The correlation
between the OMI and MODIS reflectances is depicted in Fig. b, which displays the same dependencies as in
Fig. . The highest correlation (r=0.9977) was
found for the same super-Gaussian parameters as before, confirming the
optimal OMI FoV model. Only the goodness of fit was slightly lower
than before, indicating a lower confidence in the correlation.
Viewing angle dependence
Next, a scene over Australia was selected on 11 October 2008 starting
at 04:45 UTC; see Fig. . The time difference between OMI
and MODIS is about 8 min and 35–43 s. This scene has a
large cloud-free part, as well as a large cloudy part. Most cloud
pixels, indicated by the red rectangles, were not used in the
analysis. The correlation between OMI and MODIS for various shapes and
sizes is again displayed in the right panel. The maximum correlation
for this scene was lower than before, r=0.9927, and obtained for a
point-hat super-Gaussian distribution with exponents n=1.5 and
m=2, and FWHM corner coordinates. The goodness of fit is
significantly lower than before.
One reason for the lower Gaussian exponents of the 2008 Australian
scene in the across-track direction is the removal of the pixels at
the end of the swath, which were filtered because of the clouds in
those pixels. The OMI FoV is dependent on the pixel row, or viewing
angle, with wider FoVs at the swath ends. Since most of the cloud
pixels are at the swath ends, removing these pixels removes the larger
exponents. The viewing angle dependence of the FoV is treated here.
Since the OMI FoV is dependent on the polarisation of the scene, the
FoV should also be dependent on the scattering geometry. Furthermore,
the diffraction at the edges of the FoV can be distinctly different
for FoVs at nadir compared to those with a large VZA. To
investigate this effect, the OMI FoV was characterised using
a super-Gaussian function dependent on VZA. For all the scenes
described in this paper, the optimal super-Gaussian shape was
determined per OMI pixel row, by varying the Gaussian exponent and
determining the maximum correlation between OMI and MODIS pixels for
each pixel row. Then the optimal exponents were averaged and plotted
as a function of pixel row. In this analysis, the 75FoV pixel sizes
were used to reduce the number of variables and because the above
analysis showed that the 75FoV corner coordinates are good indicators
of the pixel sizes for Gaussian shapes. The result is shown in
Fig. . The super-Gaussian exponents are rather wildly
fluctuating, because they have a limited sensitivity near the optimum,
especially m. Averaging over the scenes reduces this but is
somewhat arbitrary. In Fig. a boxcar average over five
neighbouring points is shown as well.
Still, some change in Gaussian exponents can be observed as a function
of VZA. The Gaussian exponent in the across-track direction m
changes from around 3–4 at nadir to about 7 at far off-nadir.
Also n is VZA dependent, changing from about 1.5 at nadir to more
than 2 at the swath edges. The reason for the increasing exponents
towards the swath edges is the pixel size increase towards the swath
edges. The pixel sizes are shown for reference. FoVs at larger VZA are
much wider, changing the optimal super-Gaussian that fit the FoV.
Furthermore, as observed before, the diffraction at the edges of the
FoV will be different at larger viewing angle.
Scene dependencies
The smaller Gaussian exponents for the 2008 Australian scene
(Fig. ) are only partly explained by the VZA dependence. The
Gaussian exponent n<2 indicates a point-hat super-Gaussian
distribution in the along-track direction, which is, as
Fig. e shows, a distribution that is physically
unlikely. For this scene, the super-Gaussian function is apparently
not a good representation of the OMI FoV. The reason for
this mismatch is broken cloud fields in the scene, which change the
scene reflectance between overpasses of Aqua and Aura. Scene
dependencies will be investigated below.
The overpass time between Aqua and Aura changed in 2008, when a
correcting manoeuvre brought OMI closer to MODIS. To illustrate the
effect, another Sahara cloud-free scene in the beginning of 2008 was
selected, when the manoeuvre had not yet been performed; see
Fig. . The time difference between the instruments for
this scene is as large as around 14 min, up to 16 min and
26 s. In this case, the highest correlation is found for a
super-Gaussian distribution with exponents n=1.5 and m=2, which is
again a point-hat super-Gaussian distribution. Similarly, when the
shape is fixed to the optimal Gaussian exponents, the highest
correlation is found for pixel sizes that are wider than the 75FoV
corner coordinates; see the red curves in Fig. . This is
different from the reference scene in Fig. . The
maximum correlation for this scene is r=0.982, which is lower than
for the reference scene, in December 2008. The goodness of fit q
shows much lower values, showing the difficulty with the used FoV
model to correlate the OMI and MODIS reflectances. Apparently, the
time difference between Aqua and Aura of 15 min makes a
comparison between the two instruments much more challenging, even for
almost-cloud-free scenes. It is unlikely that the OMI FoV has changed
much between January and December 2008. Furthermore, a cloud-free
Sahara scene in 2006 (31 January 2006, around 13:55 UTC, not shown)
showed the same lower correlation, peaking for the same Gaussian
exponents.
The effect of changing scenes between overpasses can be illustrated by
looking at the pixels with the highest SD between the OMI reflectances
and the average collocated MODIS reflectances. Even for a scene after
2008, when the overpass time difference is reduced to about
8 min, the retrieved top-of-atmosphere (TOA) reflectance can change significantly
during this time in the case of broken clouds. The pixels with the
highest SD for the reference scene were marked blue in Fig. b. The marked points correspond to the blue
coloured OMI pixels in Fig. , which are the areas
where the scene contains broken cloud fields. In the few minutes
between Aqua and Aura overpasses these clouds change shape and
position, changing the average reflectance in a pixel when the cloud
fraction is changed.
This is the main reason for the small optimal super-Gaussian exponent
for the 2008 Sahara scene (Fig. ) and the Australian scene
(Fig. ): due to scene changes during the different overpass
times, the observed overlap function deviates from the true FoV, which
closely resembles a Gaussian or flat-topped Gaussian. Instead a more
point-hat distribution with wider wings is found. The centre
coordinates have the relative highest correlation, albeit lower than
before, while the correlation becomes smoothed over a larger area,
giving the tails of the function a higher correlation than for the
true FoV.
Accuracy of combining OMI and MODIS
The optimal overlap function for MODIS pixels within an OMI FoV can
now be determined for practical purposes, i.e. mixed scenes with
ocean, land, and clouds. This is needed to determine the accuracy that
can be expected when OMI and MODIS measurements are combined to
reconstruct the reflectance spectrum for the entire shortwave
spectrum. To determine the accuracy, the correlation between
collocated OMI and MODIS reflectances and the SD was determined by
comparing the instruments for the scene shown in Fig. .
This scene was taken on 13 June 2006, starting on 13:33 UTC, when the
time difference between the instruments was about 15 min. The
scene contains a mixture of land and ocean scenes, with and without
clouds, and also smoke from biomass burning on the African continent.
Only OMI rows 10–50 were processed, which will often be the case to
avoid problems with large pixels or extreme viewing angles. The
optimal correlation was found for super-Gaussian exponents n=1 and m=1.5,
and 75FoV corner coordinates (not shown). The low Gaussian
exponents can again be explained from the presence of clouds that
change the scene between the overpasses, and the exclusion of wide
pixels at the swath edges. The correlation between the OMI and MODIS
reflectances using this shape is shown in the right panel of
Fig. . Obviously, the correlation is a lot lower than
for cloud-free scenes (r=0.964). The SD is 0.0371, which must be
taken into account when OMI and MODIS reflectances are compared or
combined. Furthermore, the slope of a linear fit between the OMI and
MODIS reflectance is 0.941, which is smaller than that for cloud-free
scenes, which showed about 4 % difference. This larger range in
reflectances for cloud scenes apparently offsets the difference
between the instruments even further.
Geometry differences
The 4–5 % difference between OMI and aggregated MODIS reflectances at
469 nm (Fig. ) can be governed by changes in viewing
and solar conditions between OMI and MODIS. Since the optics and
subsatellite points differ for both instruments, the viewing angles
are slightly different, even if the satellites roughly follow the same
orbit. More importantly, since Aura is always behind Aqua, the solar
zenith angle for OMI is always different from that of MODIS.
To investigate the effect of the differences in scattering geometry on the
measured TOA reflectance, a cloud-free Rayleigh reflectance was modelled for
each OMI pixel in the reference scene in Fig. . Each pixel
was simulated twice, once using the OMI scattering geometry and once using an
average MODIS scattering geometry. In this way the expected reflectance
difference can be determined due to the difference in overpass time, keeping
all else the same. To determine the average MODIS reflectance, the simulated
radiances were averaged over the OMI footprint using the optimal flat-top
Gaussian distribution with n=2 and m=4, as was determined for this scene
(Fig. ). The average radiance was then divided by the cosine
of the solar zenith angle of the MODIS pixel which is closest to the centre
of the OMI pixel. In this way, the most representative solar zenith angle is
used to normalise the radiances. A realistic surface albedo was taken for
each pixel, in order to make the model results comparable to the
observations. The surface albedo database used was the Terra/MODIS spatially
completed snow-free diffuse bihemispherical land surface albedo database
. The monochromatic calculations were performed at 469 nm,
using a standard Rayleigh atmosphere reaching to sea level
and an ozone column of 334 DU. The results are shown in Fig. .
The reflectance ranges from about 0.085 to 0.28, depending on the
surface albedo, which is smaller than the observed reflectances (cf.
Fig. b). This is mainly due to the clouds
in the scene which are not simulated. The simulated OMI reflectances
are larger than the simulated MODIS reflectances due to different
geometries, like the observations. There is a small dependence on VZA,
as shown in Fig. b, where the
relative differences between the OMI and MODIS reflectances are
plotted as a function of either reflectance, to highlight the change
for changing VZA (in colours). However, the difference between the
simulated OMI and MODIS reflectances, with a slope of 0.9965 and an
offset of -0.001, is much smaller than between the observations.
Therefore, we conclude that geometry differences between OMI and MODIS
introduce differences of less than 1 % and cannot explain the observed
slope between OMI and MODIS reflectances. Most likely, calibration
differences are causing the difference between the observed
reflectances. The simulated correlation and SD are also notably better
than for the observed scene. As noted before, clouds have the largest
impact on the correlation between the observed reflectances of a
scene.
Conclusions
The correlation between OMI and collocated MODIS reflectances was
determined, to intercompare the performance of the instruments and to
find the FoV of the OMI footprint. MODIS channel 3 at 469 nm
overlaps with OMI's visible channel, and the signals can be compared
when the reflectance signal of OMI is multiplied with the MODIS
spectral response function, and MODIS reflectances are aggregated over
the OMI footprint.
Due to the design of the OMI CCD detector array and the optical path,
the footprint of OMI is not quadrangular and light from successive
scans enters the OMI FoV. The shape and size of the FoV was
determined for a cloud-free scene, to eliminate, as much as possible,
scene changes due to the different overpass times of Aura and Aqua.
Assuming a super-Gaussian shape with variable exponents and FWHM, the
best characterisation of the OMI FoV was found for exponents n=2 and
m=4, and 1 × 75FoV corner coordinates to constrain the FWHM.
The OMI FoV changes as a function of viewing angle. When the FWHM are
fixed, the Gaussian exponent ranges from about 1.5 at nadir to more
than 2 at the swath edges, while m ranges from about 3 to 7. This is
mainly due to the increase in pixel size for off-nadir angles.
Furthermore, the diffraction at the FoV edges is viewing angle
dependent, and the OMI FoV is dependent on polarisation, due to the
presence of a polarisation scrambler in the OMI optical path.
The OMI-MODIS overlap function is scene dependent. In particular, for
larger time differences between the Aqua and Aura overpasses, the
optimal overlap function shape is found for smaller Gaussian exponents
and wider overlaps. When the scene changes between overpasses, the
signal is spread over a larger area, centred around the centre
coordinate. Therefore, a more optimal overlap function is found for a
point-hat distribution with wider wings. This is especially true for
cloud scenes, which are most frequent. The correlation decreases and
the SD increases when clouds are in the scene, and this can be used as
an indication of the expected accuracy of a comparison between OMI and
MODIS reflectances. For a scene with broken clouds over both land and
ocean in 2006, optimal Gaussian exponents of n=1 and m=1.5 were found.
In general, the changes in correlation coefficient are small for small
changes of the Gaussian exponents (much smaller than e.g. changes due
to time differences). The true OMI FoV is approximated by a
super-Gaussian distribution with exponent n=2 and m=4, and 75FoV
corner coordinates.
The use of non-scanning optics like those of OMI will be continued
in new instruments, in particular TROPOspheric Monitoring Instrument
(TropOMI) on Sentinel-5 , to be launched in 2016. For TropOMI, a cloud
masking feature is anticipated from Visible Infrared Imaging Radiometer Suite
(VIIRS) on Suomi-NPP . Sentinel-5P will fly in “loose formation” with
Suomi-NPP, with expected overpass time differences of about 5 min.
The results from this study are relevant for that mission, since such
an overpass time difference will significantly change the overlap
function between TropOMI and VIIRS, and affect the accuracy of a
cloud mask from VIIRS. High-resolution VIIRS measurements can be used
in the way presented in this paper to study and characterise
the TropOMI FoV and the accuracy of the cloud mask.