2.6.1.1.5.3 Calculate Solar Angles
Solar and viewing angles
required for cloud clearing
are also determined at this
stage. The angles are
calculated at a series of tie
points across the scan
at increments of 25 km in the
acrosstrack coordinate
x; these values are
required for internal
use within the processor,
although only values at
50 km intervals are output
to the product.
The following angles are
calculated:
 The azimuth of the
sun at the pixel;
 The elevation of the
sun as seen from the
pixel;
 The azimuth of the
subsatellite point
measured at the pixel.
 The elevation of the
satellite as seen from
the pixel.
These quantities are
required for use by the 1.6
micron cloud clearing test,
to identify situations
in which sunglint might be present,
while the solar
elevation is also used to
distinguish day and night
measurements in cloud clearing and
level 2 processing. The
satellite azimuth and
elevation are also used in the
calculation of the
topographic correction.
The solar and viewing angles
are calculated at the
centres and edges of the
acrosstrack bands defined
in Section 2.3.1. .
These correspond to a
series of acrosstrack positions
separated by 25 km. Thus
if we define an index k,
the solar angles are
calculated for nominal
acrosstrack coordinates
x = 25(k –
10) km
for k = 0, 20. In
this formulation even
values of k
correspond to the band edges,
and odd values of k to the
bandcentres. Internally
within the processor values are
calculated for both band
centres and band edges and for every
instrument scan, but
only the band edge values on the
granule rows are output
to the product ADS.
Although defined at the
nominal positions in the
equation above, in practice
the angles are
calculated for specific instrument
pixels. For each
view and for every tenth instrument
scan, and for each value
of k, the
instrument pixel whose
acrosstrack coordinate is
closest to the nominal
value given by equation (3.1) is
identified, and its
line of sight azimuth and elevation
(measured at the
satellite) are derived using
the same algebra as in
Section 2.6.1.1.5.1.1. . The
calculation of the
angles is then carried out using the
standard ENVISAT mission
CFI subroutine
pp_target
(Reference: Document
POISGMVGS0559, PPF_POINTING
Software User Manual) with the
scan time and the line
of sight azimuth and elevation as
parameters.
Results for intermediate
instrument scans are
calculated by linear
interpolation with respect to
scan number for each acrosstrack
distance, and the
results are regridded to the image
rows in a similar way to
the pixel data.
2.6.1.1.5.4 Calculate Topographic Corrections
For those scan pixels that
coincide with tie points for
which topographic corrections
are required, and that
are over land, the topographic
height is determined
from a digital terrain model and
topographic corrections to
the latitude and longitude are
calculated.
2.6.1.1.5.4.1 Theoretical Basis
The pixel geolocation
described in
Section 2.6.1.1.5.1. finds the
intersection of the line of
sight from the instrument with
the reference ellipsoid.
If the land surface is
elevated by an amount
H above the reference
surface, the intersection of the
line of sight with
the land surface, which is the
true pixel position, is
displaced towards the satellite
in the direction of the
projected line of sight
by an amount that is
proportional to the elevation
H.
Let the unit vector from
the pixel to the satellite
be k =
(kx, ky,
kz). If the
azimuth and elevation of the
line of sight at the pixel are
a, e respectively,
then the components of the unit
vector k are
  eq 2.128 
  eq 2.129 
  eq 2.130 
expressed in a local
coordinate system in which the
x axis is
directed to the east, the
y axis is directed to
the north parallel to
the local meridian, and the
z axis is vertical.
The pixel position is
displaced by linear amounts
  eq 2.131 
  eq 2.132 
The corrections in
latitude dφ and
longitude
dλ are the
corresponding
angular displacements:
  eq 2.133 
,
  eq 2.134 
,
where φ
is the latitude of the pixel.
Here R and
N are the two
orthogonal radii of curvature of
the Earth at
latitude φ;
N and R are
the radii of
curvature in prime vertical and
in the meridian
respectively, given by
  eq 2.135 
,
  eq 2.136 
,
  eq 2.137 
,
where e is the
eccentricity of the
reference ellipsoid, and
the geodetic constant
  eq 2.138 
.
The quantity N
cos φ is the
radius of the parallel of
latitude at
φ.
2.6.1.1.5.4.2 Algorithm Description
The topographic
corrections are computed for the
same tie points as the
image pixel latitude and
longitude. This method makes use
of the satellite
viewing angles for the
appropriate view and tie point
previously computed. The
topographic height is determined
from a digital elevation
model.
The nominal tie points
are at acrosstrack distances
x = {275, 250, 225,
... 275} km, corresponding to
an acrosstrack index k
through x =
25(k – 11) km,
k = (0, ...
22). However, if k = 0
or k = 22, no
viewing angles will be
available from the solar and
viewing angles calculation, and
so these cases are
omitted.
The algorithm is applied
to both nadir and forward
view instrument scans.
For each scan, the algorithm
steps are as follows.
 For each
acrosstrack distance for
which a
correction is required,
the index p
of the instrument pixel is
found whose
acrosstrack coordinate is
closest to the required
acrosstrack
distance. The latitude
φ and
longitude λ
of this
pixel are found.
 The local
altitude (over land) or
bathymetry
(over sea), H,
at latitude
φ and
longitude λ
is extracted
from the digital
elevation model.
 The pixel is
regridded to the appropriate
image row. Steps 4 and 5
are performed only if
the pixel regrids to a tie
row.
 If H
< 0 (note this includes
the case
that the pixel is
over sea), the latitude
and longitude corrections
are set to zero and
Step 5 is omitted.
 If H
³ 0 the satellite
azimuth and
elevation
corresponding to the pixel,
calculated in the solar and
viewing angles
module (Section
2.6.1.1.5.3), are extracted
and
converted to
radians, and the latitude
and
longitude corrections d
φ, d
λ are
calculated using
equations (
eq.
2.131 ) to
(
eq.
2.138 ) in Section
2.6.1.1.5.4.1. above.
Note that the
corrections are the quantities
to be added to the
nominal latitude and
longitude to give
the topographically corrected
values.
