2.7.1 Level 2 Algorithms
The AATSR Level 2 processing steps are summarised
in figure2.12 . The main steps are
also outlined below.

Figure 2.12 Overview of the Level 2 processing. 
2.7.1.1 Prepare Inputs
Before averaged BTs and reflectances can be
derived from the input GBTR product, the
relevant measurement and annotation data
must be extracted from the L1B product
as follows.
2.7.1.1.1 Input Annotation Data Sets
The Annotation Data Sets of the GBTR
product that are required for Level 2
Processing are read in and converted
into appropriate units where necessary.
2.7.1.1.2 Assemble Regridded Brightness
Temperature Arrays
Grid coordinates and channel brightness
temperatures / reflectances for forward
and nadir views are read in from the
appropriate MDS of the GBTR product
and arranged in the required memory configuration.
2.7.1.1.3 Interpolate Solar Angles
The solar azimuth and elevation and
satellite azimuth and elevation, all
measured at the pixel, are available for
a series of uniformly spaced tie
point pixels in ADS #5 of the GBTR
product for the nadir view and in ADS #6
for the forward view images. This step
derives those angles that are
required for level 2 processing at every
scan, and at the bound edges of the
bands, by linear interpolation, between
these tie points. Only the solar
elevation is required for Level 2
processing as presently defined.
2.7.1.1.4 Interpolate Image Pixel position
The (geodetic) latitudes and longitudes
of a series of uniformly space tie point
pixels are available in ADS #3 of the
GBTR. This module derives the
latitude and longitude of each image
pixel by linear interpolation, in two
dimensions, between these tie points.
2.7.1.2 Derive Gridded Product
This step derives the contents of the GST
product at 1 km resolution from
the infrared brightness temperatures. It
derives the sea surface temperature
(SST) or, over land, the
vegetation index (NDVI), at 1 km resolution,
using cloud free data.
The derivation of SSTs uses the 11 and 12
µm channels for day time
data and for night time data the 11, 12 and
3.7 µm channels. For
each 1 km resolution element two
results are obtained, one using the combined
nadir and forward views and the
other using the nadir view alone.
The SSTs are calculated using preset
retrieval coefficients. These
coefficients are provided for both nadir
only and combined view SSTs
and are a function of latitude and
viewing angle. Smoothing is applied by
smoothing the difference between
the calculated SST and the 11 µm
brightness temperature. The effect is to
smooth the atmospheric correction.
Details of the SST retrieval algorithm are
contained in the following section:
The NDVIs are calculated using the nadir 0.67
and 0.87 µm channels and
the results are returned in the
combined image land pixels.
In order to provide completely filled images
the 11 µm brightness
temperature is returned in the nadir image
field when over land. In
cloudy conditions the cloud top
temperature is returned in the nadir image
field and the cloud top height
in the combined view image field (see
section 2.12.1.5. concerning placeholders).
2.7.1.2.1 SST Retrieval
2.7.1.2.1.1 Physical Justification
2.7.1.2.1.1.1 Introduction
Infrared radiation
emitted by the surface is
modified by its passage
through the atmosphere as a
result of absorption by
atmospheric gases and
absorption and scattering by
liquid and solid particles.
Accurate measurements of
SST from space are only
possible when the particle
effects are small, when
clouds and fog are absent, and
when the
reflected/scattered solar
component of the signal is
negligible (i.e., 3.7
µm night). In these
conditions the total upwelling
infrared radiance L
total(ν) observed
at a given
wavenumber ν by the
satellite at an altitude
Z is the sum of
three components:
 the radiation
emitted by the surface L
_{s}
(ν);
 the radiation
emitted by the atmosphere L
a(ν); and
 the atmospheric
radiation L
ar(ν)
reflected from the
surface back to space.
Thus
  eq 2.165 
The three terms in
Equation (1.1) are as follows;
  eq 2.166 
  eq 2.167 
  eq 2.168 
where εs
is the surface emissivity, T
s the surface
temperature, τ(ν,
0, Z) is the
transmission of the
atmosphere from the
surface to the satellite at
height Z,
ea is the emissivity of
the atmosphere at height
z,
τ(ν, z,
Z) is the
transmission of the atmosphere
from height
z to the satellite, and
τ(ν,
z, 0) is the
transmission of the atmosphere
from the height z to
the surface.
B(ν, T)
is the Planck Function,
given by the expression
  eq 2.169 
where C1 and
C2 are the first and
second radiation
constants, respectively.
The observed radiance in
the channel of width
Dν can be expressed in
terms of the brightness
temperature of the scene
T:
  eq 2.170 
This equation can be
solved to give the brightness
temperature T
corresponding to the observed
radiance.
In the absence of the
atmosphere the brightness
temperature is a direct
measurement of the radiating
surface temperature of the
Earth. Therefore, in a
world without atmosphere,
accurate SST could be
obtained from a single
brightness temperature, provided
the surface
emissivity were known. However,
the presence of the
real atmosphere
complicates the retrieval of
SST, and it is necessary to make
measurements at a
number of different of
wavelengths in parts of the
spectrum where the effects of
the atmosphere differ; this is
known as the
multichannel or multispectral
approach to atmospheric
correction.
The most commonly used
multichannel method is the
'split window'
method, in which the 10 
13 µm atmospheric window is
divided into two
spectral bands in which the
atmospheric effects are
markedly different. The two
split window channels are at 11
µm and 12 µm
respectively; the atmospheric
effect in this part of the
spectrum is mainly due
to water vapour and
is much stronger at 12 µmm
than at the shorter
wavelength. Thus, by using the
two split window
brightness temperatures
it is possible to provide a
correction for the effects of
the atmospheric water
vapour and therefore to retrieve
a more accurate SST.
AATSR uses the 11/12
µm split window, and has a
further channel at 3.7
µm. This improves the
retrieval, as it provides an
additional atmospheric
measurement and a more accurate
determination of
temperature because of the
stronger temperature dependence
of the Planck function
at the shorter wavelength.
The SST is retrieved using
an algorithm that
combines the brightness
temperatures T
_{i}
from each channel in the
following way:
  eq 2.171 
In addition to the
multichannel approach, AATSR
employs along track
scanning to provide a further
improvement in the atmospheric
correction. The dual
angle data are used in the
retrieval in the same
way as the other
brightness temperatures.
  eq 2.172 
where the subscript
i is the spectral
channel identifier, and
the superscripts n
and f are the nadir and
forward view
brightness temperature data from
each channel, respectively.
The coefficients in
and represent an
optimum linear
relationship between true sea
surface temperature and
the measured channel
brightness temperatures.
2.7.1.2.1.1.2 Channel selection
The objective of the
algorithm is to use the
measured infrared
brightness temperature values to
determine, for each cloudfree
pixel over sea, the
best estimate of the Sea Surface
Temperature (SST) of the
pixel, to form an SST image at 1
km resolution.
In practice the
derivation of SST makes use of
either 2 infrared
channels (11 micron and 12
micron), or of all three
infrared channels (3.7
micron, 11 micron and 12
micron), and may use either one
or both
views. The selection of the set
of channels to be
used depends on the
availability of the data.
Whenever possible, both
the nadir view and forward
view pixels are used.
Cloud contamination for the
forward view pixels is more
likely than for the
nadir view owing to the larger
sampling area in the
former, so the possibility of
using the brightness
temperatures from the
nadir view only is also
catered for. (It would be
possible in theory to
derive retrieval coefficients
for the case of a forward view
image only, but this is not done
in practice.)
From
eq.
2.171 , the algorithms
using the nadir view only
are given by
  eq 2.173 
or
  eq 2.174 
When both views are used
(
eq.
2.172 ), the
corresponding equations
are
  eq 2.175 
or
  eq 2.176 
respectively.
The coefficients
a, b,
c,
d for use in
the above equations are
predetermined by means of a
radiative transfer
modelling calculation. A
radiative transfer model (RTM)
is used to derive
the expected brightness
temperatures,
essentially by
evaluating
eq.
2.165 to
eq.
2.170 for each of a
representative
ensemble of atmospheric states
and SST values. From the
results the coefficients
of the linear regression
between SST and the measured
brightness temperatures
are derived. The RTM, and the
method of deriving the
coefficients, is described in
Zavody et al,
1995 1.3. in the context
of the ATSR instrument. The
derivation of the AATSR
coefficients proceeded along
similar lines, but
with the following differences;
 The version of
the RTM used incorporated
certain improvements;
 Aerosol robust
coefficients for the dual
view
retrieval were derived
using the method
described by Merchant
et al, 1999 1.3. ;
 A modified
acrosstrack banding scheme
was used, as
described below.
Preset coefficients are
specified for each of three
geographical regions:
tropical, midlatitude and
polar (note that in practice the
aerosolrobust dual
view coefficients for AATSR are
global: that is the
same coefficients are defined
for each of the three latitude
zones). The coefficients
also depend on the viewing
geometry, and so the
acrosstrack distance of the
pixel determines the set of
coefficients to be used
for a given pixel in a given
region. In total, 38 different
sets of coefficients are given
for each geographical region;
these represent 38
different acrosstrack distances
and correspond to 38
approximately equally spaced
air masses across the instrument
swath. These issues
are discussed in 2.7.1.1.3. and 2.7.1.1.4.
following.
2.7.1.2.1.1.3 Latitude zones
The latitude of the
pixel governs whether the
coefficients for the
tropical, temperate, or polar
regions are to be used. Three
zonal limits are
defined, TROPICAL_INDEX,
TEMPERATE_INDEX, and
POLAR_INDEX.
Numerical values are given in .

Table 2.29 Latitude Limits

Index

Value

TROPICAL_INDEX

12.5°

TEMPERATE_INDEX

37.0°

POLAR_INDEX

70.0°

The latitude and
acrosstrack band number of the
pixel determine the
usage of the retrieval
coefficients as follows. If the
absolute value of
the latitude is less than
TROPICAL_INDEX, the retrieval
coefficients for the
tropical zone and for the
appropriate acrosstrack
distance are used.
Similarly if the absolute value
of the latitude is greater
than or equal to
POLAR_INDEX the retrieval
coefficients for the polar or
highlatitude region
and for the appropriate
acrosstrack distance are
used.
If the pixel lies in the
midlatitude zone, a
slightly more complex
calculation is undertaken to
ensure that the retrieval varies
smoothly with
latitude. In these cases two
retrievals are computed, and
the final SST is
obtained by linear interpolation
between them with respect
to latitude. If the
absolute value of the latitude
is less than
TEMPERATE_INDEX but is not less
than TROPICAL_INDEX, two
retrievals are made
using the retrieval coefficients
for both the tropical and
midlatitude zones. If
these two retrievals are
T _{tropical}
and T _{temperate}
respectively, the
final value for the
retrieved SST is given by
  eq 2.177 
where
  eq 2.178 
and latitude is
the latitude of the pixel.
Similarly if the
absolute value of the latitude
is less than
POLAR_INDEX but not less than
TEMPERATE_INDEX, two retrievals
are made using the
retrieval coefficients for the
highlatitude and
midlatitude regions. If
these two retrievals are
T_{ polar}
and T_{ temperate}
respectively, the final
value for the
retrieved SST is given by
  eq 2.179 
where
  eq 2.180 
In each of the above
cases of course the relevant
retrieval coefficients
appropriate for the
acrosstrack distance of the
pixel are used.
This approach ensures
that the retrievals do not
show discontinuities at
latitudes equal to one of
the values
TROPICAL_INDEX,
TEMPERATE_INDEX, or
POLAR_INDEX. Note that
because the retrieval
equations are themselves
linear, the method of linear
interpolation described
above is equivalent to assuming
that the individual
retrieval coefficients vary
linearly with latitude in the
ranges TROPICAL_INDEX
< latitude <
TEMPERATE_INDEX and
TEMPERATE_INDEX <
latitude <
POLAR_INDEX.
2.7.1.2.1.1.4 AcrossTrack Bands
In the first instance,
coefficients are derived
offline for two
acrosstrack positions,
corresponding to the swath
centre and swath edge.
To derive retrieval
coefficients for intermediate
acrosstrack
positions, it is assumed that
the coefficients should be
proportional to the air
mass through which the pixel
is viewed, and the coefficients
for intermediate
positions are derived by linear
interpolation with
respect to nadir air mass
between the centre and edge
values.
Interpolated
coefficients are derived for a
set of 38 equally
spaced air mass values,
which correspond to
the centres of 38 bands parallel
to the swath on each
side of the ground track. The
same coefficients
are used for all pixels that
fall within a band, and the
separation between the
bands is sufficiently small
that perceptible
discontinuities are not
introduced at the
band edges.
The air mass is
proportional to secθ,
where θis the
angle of incidence of the line
of sight to the
pixel. 2.13 shows
the relationship between the
normalized air mass
secθand the
acrosstrack coordinate
x for the nadir view,
and for the nominal
scan geometry.

Figure 2.13 Normalized air mass versus acrosstrack position (km) 
Suppose the pixels are
indexed in an acrosstrack
direction by j
(0 ≤ j <
512). The acrosstrack
coordinate x,
measured from the centre of the
swath, of the midpoint of
pixel j is then given
by
  eq 2.181 
Let k (0
≤ k < 38) be
an index to the
acrosstrack bands. The bands
are defined so that
pixel j falls
in band k
where
  eq 2.182 
for general k,
or
  eq 2.183 
in the special case
k = 0. Here θ_{j}
is the angle of
incidence at pixel j,
and Δ is the selected air
mass increment
(strictly the increment in
secθ), which defines the
width of the bands. The adopted
value of the increment
Δ is 0.00207186.
2.14 shows the
relationship between band and
pixel number. Note that
band 0 is centred on the
ground track and that the bands
are arranged
symmetrically about the ground
track. The precise mapping
between band and pixel numbers
is defined in the auxiliary
Acrosstrack Band
Mapping Lookup Table, which is
contained in the SST Retrieval
Coefficient Data
File (ATS_SST_AX) 6.5.8. .
2.7.1.2.1.1.5 Smoothing
Finally, in the case of
the full resolution
(gridded) product smoothing
is applied to the
derived temperature images. This
step is required
because, although the derived
temperatures are valid
estimates of the true
SST, they are affected by
noise to a greater degree than
the measured
brightness temperatures
themselves, because the
coefficients
multiplying the brightness
temperatures in equations (
eq.
2.173 
eq.
2.176 )
may exceed unity, and combine
to yield a net increase in
variance.
The smoothing technique
adopted uses the difference
between the derived SST
image and the nadirview 11
micron brightness temperature
image. If there were
no atmosphere, the 11 micron
brightness temperature at near
normal incidence would be a very
good approximation to the
SST (differing only
because the emissivity of the
sea surface viewed at
normal incidence differs
slightly from unity). Thus the
difference between
the retrieved SST and the
nadirview 11 micron brightness
temperature is a good measure of
the atmospheric attenuation
in the 11 micron
channel, and might be expected
to show only small
spatial variations over
distances of a few
kilometres. Thus if this
difference is
smoothed, the result may be
added to the nadirview 11
micron brightness
temperature to give the smoothed
SST.

Figure 2.14 The acrosstrack band number as a function of pixel index 
The difference is
averaged over square blocks of
n by n
pixels, the pixels
corresponding to valid
retrievals being
included in the
average with equal weight. The
size n of the
smoothing block is defined by a
parameter in the auxiliary
file of Processor
Configuration Data (ATS_PC2_AX 6.5.7. ).
The nominal value of
n is 3, so that up to 9
pixels contribute to
each average. The smoothed
difference is then
added to the nadirview 11
micron brightness temperature to
give the final retrieved
SST value. If no valid
pixels contribute to the
average, or if there is no
valid nadir view SST, a
corrected SST is not
calculated and the smoothed SST
value is set to  1. (Note
that this overrides the
setting to the 11 micron
temperature for invalid SST
retrievals noted above.)
The smoothing is carried out
separately for the
nadir and dual view images.
The smoothing takes
account of cloud flagging; that
is, pixels flagged as
cloudy are not included in the
average, or an increased
variance of the smoothed
SST in cloudy areas would
result.
The smoothing step is
not required in the case of
the averaged (AST)
product.
2.7.1.2.1.2 Algorithm Description
2.7.1.2.1.2.1 Full resolution (gridded)
Surface Temperature Image Product
The AATSR full
resolution geophysical product
(ATS_NR__2P) contains a
single Measurement Data Set
(MDS), the contents of which are
switchable; that is
to say, the content of each
pixel field depends on
the surface type. Specifically,
the content of each data
field depends on the
setting of the forward and
nadir cloud flags and the land
flag. Thus the
processor must check the flag
settings for each pixel before
selecting the appropriate
procedure for the surface type.
These checks are
integral to the logical
structure of the
algorithm, and so are
shown in the algorithm
description that follows,
although the emphasis is
on the detailed derivation of
SST for clear sea pixels.
In the following, a
pixel value is invalid if it
does not represent a
valid brightness temperature.
This is indicated when the
numerical value
corresponds to an exception
value; otherwise the pixel is
valid.
The appropriate
acrosstrack band index
corresponding to an image pixel
is obtained by
entering the auxiliary
Acrosstrack Band Mapping
Lookup Table (from
the auxiliary file ATS_SST_AX 6.5.8. )
with the acrosstrack
index of the pixel. This value
is used to index the
set of coefficients to extract
the set corresponding to the
correct air mass value.
The logic of the
procedure used for deriving the
GSST product at 1 km
resolution is as follows.
Initially, the GSST confidence
word flags
nadir_image_valid and
combined_image_valid associated
with each image
pixel are initialised to the
value
FALSE. The nadir image
field is also set to
the 11 micron brightness
temperature; this is the
default if a valid retrieval is
not achieved.
Steps 1 to 3 below are
executed for each image scan,
then Step 4 is executed
to smooth the SST image.
1) Calculate the
nadirview image. For each pixel
in the scan, the
procedure is as follows:
The surface type flags
(cloud flag and land/sea
flag) associated with
each pixel are inspected.
If the pixel is over
land, a land surface
temperature (LST) retrieval
is attempted (see later
section). If this is successful,
the nadir image
valid flag in the confidence
word is set to TRUE.
If the pixel is cloudy,
the nadir view field is set
to the 11 micron
brightness temperature, as an
estimate of the cloud top
temperature, and the
nadir image valid
flag in the confidence word is
set to TRUE.
Otherwise the pixel is a
clear sea pixel, and an SST
retrieval is attempted.
The nadirview 11 and 12
micron brightness
temperatures are inspected
to ensure that both are
valid. If either is invalid, an
SST cannot be
retrieved and processing
continues at the next pixel.
If both are valid, an
SST retrieval is attempted
using either a 2channel
algorithm or a 3 channel
algorithm. If the solar
elevation is negative
(indicating a nighttime pixel)
and the 3.7 micron
brightness temperature
is valid, a 3 channel
algorithm (Equation)
is used, otherwise a
twochannel retrieval (Equation)
is used. If the 3.7
µm brightness temperature
is valid, the corresponding flag
of the confidence
word is set accordingly. In
either case the retrieval is
performed using the coefficients
for the appropriate
acrosstrack band index
and taking account of the
geographic zone as described
below.
1.1) If the pixel lies
within the tropical region
(latitude <
TROPICAL_INDEX) or if the
pixel lies within the polar
region (pixel latitude =
POLAR INDEX), then the SST is
calculated using the
retrieval coefficients for that
region and for the for the
appropriate acrosstrack
band index. Equation
is used if a twochannel
retrieval was specified, or
Equation
is used if a threechannel
retrieval was specified.
1.2) If the pixel lies
within the temperate region,
then the SST value is
calculated using the
coefficients for the temperate
region, and a second
SST value is calculated using
the coefficients for the polar
or tropical region. The
coefficients for the
tropical region are used if
the pixel latitude is
less than TEMPERATE_INDEX,
otherwise the
coefficients for the polar
region are used. In either case
the retrieval
coefficients for the appropriate
acrosstrack band index are
used, with Equation
if a twochannel retrieval was
specified, or Equation
if a threechannel retrieval was
specified. A linear
interpolation with latitude is
used to obtain the SST value
from those calculated
for the two regions, using Equation
or Equation
as appropriate.
1.3) In either case the
'nadironly SST is
valid flag' of the
confidence word is set.
2) Calculate the
dualview image. For each pixel
in the scan the
dualview SST is calculated as
follows:
The surface type flags
(cloud flag and land/sea
flag) associated with
the pixel in each view are
inspected.
If the pixel is over
land, and the 0.87 and 0.67
micron channel
reflectances are valid, the NDVI
is computed and
assigned to the combined
image field, and the
combined image valid flag in the
confidence word is
set to TRUE.
If the pixel is cloudy,
the combined image field is
set to zero, and the
combined image valid flag in
the confidence word is set to
FALSE. (The combined
image field is reserved for the
cloud top height value in
a future revision of the
processor.)
Otherwise the pixel is a
clear sea pixel, and an SST
retrieval is attempted.
If the 11 or 12 micron
brightness temperature values
of the pixel for either
view are invalid, an SST
cannot be retrieved and
processing continues at
the next pixel.
If all are valid, an SST
retrieval is attempted
using either a 4channel
algorithm or a 6channel
algorithm. If the solar
elevation is negative
(indicating a nighttime pixel)
and the 3.7 micron
brightness temperature
is valid in both views, a
6channel algorithm (Equation)
is used, otherwise a
fourchannel retrieval (Equation)
is used. If the 3.7
µm data is valid, the
corresponding flag of the
confidence word is set
accordingly. In either case the
retrieval is
performed using the coefficients
for the appropriate
acrosstrack band index
and taking account of the
geographic zone as described
below.
2.1) If the pixel lies
within the tropical region
(latitude <
TROPICAL_INDEX) or if the
pixel lies within the polar
region
(latitude =
POLAR_INDEX), then the SST is
calculated using the
retrieval coefficients for that
region and for the appropriate
acrosstrack band
index. Equation
is used if a fourchannel
retrieval was specified,
or Equation
if a sixchannel retrieval
was specified.
2.2) If the pixel lies
within the temperate region,
then the SST value is calculated
using the
coefficients for the temperate
region, and a second
SST value is calculated using
the coefficients for the polar
or tropical region. The
coefficients for the
tropical region are used if
the pixel latitude is
less than TEMPERATE_INDEX,
otherwise the
coefficients for the polar
region are used. In each case
the retrieval
coefficients for the appropriate
acrosstrack band index are to
be used, with Equation
if a fourchannel retrieval was
specified, or Equation
if a sixchannel retrieval was
specified. A linear
interpolation with latitude is
used to obtain the SST value
from those calculated
for the two regions, using Equation
or Equation
as appropriate.
2.3) In each case the
combined image valid flag of
the confidence word is
set.
3) The confidence word
flags that relate to cloud,
blanking pulses, and
cosmetic fill are set
appropriately.
4) Finally, the SST
image is smoothed as described
in section 2.7.1.2.1.1.5. above
2.7.1.2.2 Land Surface Temperature Retrieval
2.7.1.2.2.1 Physical Justification
The definition [3] of the LST
algorithm selected for AATSR
is based on work by Prata [1, 2] to
develop algorithms to
retrieve land surface temperature
(LST) from ATSR and AVHRR
data. These algorithms are based on
radiative transfer
theory applied to the exchange of
radiation between the
surface and atmosphere, and have
been subjected to extensive
validation using a network of
groundtruth sites across
Australia.
The algorithm for LST retrieval is
based on a splitwindow
algorithm similar to that used for
twochannel nadironly
SST retrieval:
  eq 2.184 
where a_{0}
, b_{0}
and c_{0}
are coefficients that depend
on the land surface
characteristics, viewing angle, and
atmospheric water
vapour, and T_{11}
and T_{12}
represent the brightness
temperatures in the 11 and
12 micron channels respectively.
In order to permit an
additional tuning of the algorithm,
a weak nonlinearity
is introduced by replacing Equation
eq.
2.184 by
  eq 2.185 
where the index n depends on
the incidence angle
θ as follows:
  eq 2.186 
Here m is an empirical
constant. Currently, the
value m = 5 is adopted. Equation
eq.
2.185
reduces to Equation
eq.
2.184 when
n = 1. If T _{11}
 T_{12}
is negative, then the term (T_{11}
 T_{12}
) n in Equation
eq.
2.185 is
in general complex. This
case can certainly arise in
practice, and the solution
adopted is to set n = 1
if T_{11}
< T_{12}
; in other words, to revert
to Equation
eq.
2.184 in
this case. The value
n = 1 is also adopted in
the case of inland
lakes.
2.7.1.2.2.1.1 Retrieval Coefficients
The essence of the
algorithm is to apply Equation
eq.
2.184
above to the 11 and
12 micron brightness
temperatures in the nadir view.
The retrieval
coefficients a
_{0}, b
_{0}, c
_{0}, depend on surface
characteristics and
atmospheric water vapour. Their
values must reflect the
complex variability of
the surface, and this is
achieved by means of lookup
tables read from the
auxiliary files. These define
the local
characteristics of the surface,
and the local climatology,
at a resolution of
0.5° in latitude by
0.5° in longitude.
Let the latitude and
longitude of the pixel indexed
by [i,
j] be represented by
φ(i, j),
λ(i, j)
respectively, with the
conventions that
  eq 2.187 
, and
  eq 2.188 
It is convenient to
redefine the origin of latitude
and longitude so that
both are positive. We thus
define the shifted coordinates
  eq 2.189 
The auxiliary files
define the surface class and
vegetation fraction in
cells of dimension 0.5°
in latitude by 0.5° in
longitude. Suppose that
each cell is identified by the
coordinates of its origin,
defined to be its lower
lefthand (i.e. southwest)
corner. The cells
form a two dimensional array
indexed by latitude
and longitude indices
lat_index
and lon_index, such
that the origin of the
cell indexed by
lat_index and
lon_index is
  eq 2.190 
where Δj,
Δl are the
cell dimensions in latitude and
longitude
respectively. In the present
case
  eq 2.191 
,
and so the indices of
the cell containing the point
(φ,
λ) are
  eq 2.192 
For each cell, entries
in a lookup table [LUT]
define the following
quantities:
 The surface type
classification within the
cell. The cell is assigned
to one of 14
surface types represented by
an integer in the range 1
to 14. The surface types
adopted comprise 13 land
cover
classes or biomes
together with an additional
class representing inland
lakes, and are
listed in Table 1. In the
following the surface type
classification will be
represented by the symbol
class.
 The vegetation
fraction f (0 <
f < 1)
representative of the cell.
This quantity has a seasonal
variation that is
represented in the tables by
defining 12 values of
f, one for each
calendar month. The basis of
the definition of
this variation is defined in
[3].
 The monthly mean
precipitable water at the
centre of the cell. Again
12 values are given,
one for each month, to
represent the seasonal
variation.
A further table defines
four sets of regression
coefficients a,
b and c
for each surface type,
corresponding to vegetation
and bare soil, and to day and
night conditions.

Table 2.30 The land type classification used by the AATSR LST algorithm.

Type

Description

Type

Description

1

Broadleaf
evergreen
trees

8

Broadleaf
shrubs with
groundcover

2

Broadleaf
deciduous
trees

9

Broadleaf
shrubs with
bare
soil

3

Broadleaf
and
needleleaf
trees

10

Dwarf trees,
shrubs with
groundcover

4

Needleleaf
evergreen
trees

11

Bare soil

5

Needleleaf
deciduous
trees

12

Broadleaf
deciduous
trees
with winter
wheat

6

Broadleaf
trees with
groundcover

13

Perennial
land ice

7

Groundcover

14

Permanent
inland lakes

Thus for a given pixel,
its latitude and longitude
define the 0.5°
´ 0.5° cell within
which the pixel falls according
to the equations
eq.
2.192 . The
surface type for
this cell, and the
vegetation fraction for
the current month and for the
same cell, are
extracted from the lookup
tables.
The vegetation fraction
is used to take account of
the seasonal variation
of vegetation cover, and the
consequent effect on the
retrieved surface
temperature. For each surface
type, and for day and
night conditions separately, two
sets of regression
coefficients are
provided, representing bare soil
and vegetated surfaces. The
coefficients used for
the retrieval are derived as a
linear combination of
these with the relative weights
determined by the vegetation
fraction.
Thus given the surface
type, the table of
coefficients is entered to
extract the two sets of
regression coefficients
a, b
and c for
this surface class for both
vegetation and bare
soil. The day or nighttime
coefficients, as
appropriate, are
extracted, and the following
linear combinations
are derived from the
mean of the
vegetation and bare soil values,
weighted by f, (1
 f) respectively. Thus
we have
  eq 2.193 
  eq 2.194 
  eq 2.195 
In these equations the
indices v,
s designate
vegetation and bare soil
respectively, so that for
example
a(class,
v) represents the
coefficient a
applicable to a vegetated
surface of surface type
class, and so on.
Finally, before
eq.
2.184 is
evaluated, a correction is
applied to the
coefficient a
_{0} that
depends on the precipitable
water.
  eq 2.196 
In this equation
sat_elev represents the
satellite elevation as
seem from the pixel, in
degrees,, and pw
represents the total
precipitable water (in units of
cm) at the position of the
pixel. This is derived
from the tabulated values
using a bilinear
interpolation. The lookup table
of precipitable
water values is valid
everywhere; that is,
it includes a value for each
cell, including sea
and coastal cells as well as
land cells; there are no
invalid values. The
coefficients a
_{0}, b
_{0} and c
_{0} given by equations
,
and
are the required
retrieval coefficients.
In the case of the
inland lake surface type,
class = 14, the
two sets of coefficients
for vegetation and bare soil are
identical, so the
coefficients are independent of
vegetation fraction, and the
precipitable water correction of
equation
is not applied,
equivalent to setting d
= 0.
In the above we have not
specified the units in
which temperature is
expressed, but the retrieval
coefficients have been developed
with all
temperatures expressed in
degrees Celsius. If temperatures
are expressed in Kelvin,
then in place of Equation
eq.
2.184
we have the
following equation for the LST
in K:
  eq 2.197 
This is the equation
actually used for the LST
retrieval. In it, T
_{0} is the temperature
in Kelvin at 0°C.
The LST is stored in the
product as a 16bit short
integer in units of
0.01K, and it is possible that
the retrieval will give a result
that exceeds the
maximum value that can be
represented in this way. In this
case, if the retrieved LST (in
units of 0.01K) exceeds
32767.5, then the output
LST is set to 32767 and the
nadir image valid flag is set to
false, to indicate
an outofrange value. Otherwise
the LST is rounded
to the nearest integer and the
nadir image valid flag is set
to true.
As well as the
quantities described above, a
topographic variance flag
field is defined for each
cell in a further LUT. This is a
twobit field that
is not used by the processing,
but is passed to the product
confidence word as a guide to
the quality of the retrieved
LST. The topographic
variance field indicates the
surface height range within
the cell; a low
topographic variance is likely
to be associated with
greater homogeneity of the
surface type within the cell,
and so a
better quality LST. Reference
[3] defines the
meaning of the
topographic variance field
values as follows.
Value

Meaning

0

Extremely flat
ground (very
high
confidence)

1

Some topographic
variation (good
confidence)

2

Significant
topographic
variation (low
confidence)

3

Extreme
topographic
variation
(no confidence)

The topographic variance
flag values have been
derived from a digital
elevation model.
2.7.1.2.2.1.2 Interpolation of
precipitable water
The water vapour sample
indexed by
lat_index,
lon_index and
corresponding to the cell whose
origin is at _{
} is taken to refer to the
point at the centre of the
halfdegree cell, whose
(shifted) coordinates are _{
}, and so the water vapour
samples form a grid whose
origin is at the point Δ
φ/2, Δ
λ/2.
For example, the cell at
58N, 7E extends over the
latitude range 58.0 to
58.5 and the longitude range
7.0 to 7.5, and is indexed by
lat_index =
296, lon_index = 374,
and the surface class
and vegetation fraction
associated with this cell are
taken to
apply to all pixels within the
specified range.
However, the
precipitable water value is
taken to refer to
the centre of the cell.
Thus the
precipitable water value
associated with the cell
[296][374] refers to
the point at latitude 58.25 N,
longitude 7.25 E.
This must be taken into
account in the interpolation
of precipitable water. The
centre points of the
cells are the grid points for
the interpolation of
the precipitable water
pw.
The precipitable water
is interpolated to the
position of the pixel
using a bilinear interpolation
between the four points of this
grid that surround
the pixel. These are the corner
points of a quadrilateral
enclosing the pixel.
The origin of this
quadrilateral is not necessarily
the sample point
corresponding to the cell in
which the pixel
falls. The grid defined by
the water vapour
sample points divides the cell
at (φ
_{0}, λ
_{0}) into four
quadrants, each of which
falls in a different
interpolation quadrilateral. The
quadrant into which the pixel
(φ,
λ) falls defines
the interpolation
quadrilateral, and its origin is
calculated as
follows.
The pixel (φ,
λ) falls within the cell
(φ_{0},
λ_{0}), as
given by the
equations
and
above. The nearest water
vapour sample to the pixel
is that which falls within the
same cell, at
coordinates (Δ
φ/2, Δ
λ/2) relative to
the origin of the cell, and
this sample is one of
the corner points of the
interpolation quadrilateral.
The coordinates of the
pixel relative to the cell
origin are
  eq 2.198 
  eq 2.199 
and relative to the
centre point (the precipitable
water sample) its
position is
  eq 2.200 
  eq 2.201 
with 0.5 ≤
ε,
η < 0.5.
The relative indices of
the origin of the
interpolation quadrilateral
are given by the
fractional parts, algebraically
defined, of the
displacements e,
h.
Thus
  eq 2.202 
  eq 2.203 
The indices of the cell
containing the origin of the
interpolation
quadrilateral are
lat_index +
iy, lon_index
+ ix. If
the array of precipitable water
samples for the
current month is
pw_table(lat_index,
lon_index), we then
have
  eq 2.204 
  eq 2.205 
  eq 2.206 
  eq 2.207 
Note the table must wrap
round when the longitude
index exceeds 719, so
that lon
_{index} = 720 is
interpreted as lon
_{index} = 0
(i.e. the longitude index is
interpreted modulo 720).
The fractional
displacements of the pixel
relative to the
origin of the
interpolation quadrilateral are
The interpolated
precipitable water value at the
pixel is then given by
  eq 2.208 
2.7.1.2.2.2 Algorithm Description
The following steps are
carried out for each pixel for
which the 11 and 12 micron
nadir view brightness
temperatures (T
_{11} and T
_{12}) are both valid. If
either of these brightness
temperatures in the nadir view is
invalid, no retrieval is
attempted for that pixel, and
the nadir image valid
flag remains FALSE.
Otherwise the calculation
proceeds as follows.
 Latitude and longitude
indices are derived from
the pixel latitude and
longitude according to
the equations (
eq.
2.192 ).
 The solar elevation at
the centre of the
acrosstrack band in which the
pixel falls is
inspected. If it is positive, a
day/night flag is set to
indicate daytime observations,
otherwise the flag is
set to indicate night.
 A linear interpolation
is used to determine the
satellite elevation at
the pixel from the band
edge satellite elevation values.
If T
_{11} > T
_{12} the nonlinear
exponent n
is calculated using equation
(
eq.
2.186 ), otherwise
n is set to
1.
 The retrieval
coefficients to be used for this
pixel are determined,
using the latitude and
longitude indices determined at
Step 1 to
extract the vegetation fraction
f and surface
classification
class appropriate for
this cell from the lookup
tables. The
precipitable water pw
is calculated by linear
interpolation as in ( 2.7.1.2.2.1.2. ). If
class < 1 or
class >
NCLASS (the number
of valid surface types) then the
class index is
out of range; the calculation
for this pixel is
abandoned and the
nadir_image_valid
flag remains false. Otherwise
the retrieval
coefficients are calculated
using equations (
eq.
2.193 ,
eq.
2.194 ,
eq.
2.195 ,
eq.
2.196 ). If
class = 14,
n = 1.
 The land surface
temperature is calculated
using Equation (),
trapping the condition that
the resulting LST is out of
range.
 The topographic
variance flag for the pixel is
set to the value
appropriate to the halfdegree
cell, taken from the table. Note
that this is a
twobit flag.
2.7.1.3 Derive Averaged Product (HalfDegree cells)
Averaged BTs and reflectances, and then
averaged SST and NDVI are derived for the
halfdegree cells via the following steps.
2.7.1.3.1 Spatial Averaging
For the averaged products in halfdegree
cells, the globe is imagined as divided
into cells 0.5° in latitude by
0.5° in longitude, and these
cells are further subdivided into 9
subcells extending 10 arcmin in
latitude by 10 arcmin in longitude. For
each channel, the average brightness
temperature (for the infrared channels)
or reflectance (for the visible
channels) is averaged over all
pixels of each type that fall within
each subcell, to give distributions of
a brightness temperature and radiance at
10 arc minute resolution. Averages
are performed for the forward and nadir
views separately, and a separate average
is performed for each surface type
(land and sea) and cloud state (clear or
cloudy). There are thus 4 averages per
channel per view. The mean acrosstrack
pixel number in each cell is also
derived, for use by the averaged SST algorithm.
2.7.1.3.2 Averaged SST Retrieval
The Averaged Surface Temperature
(AST) Product ATS_AR_2P
contains averaged geophysical
quantities at two different
resolutions, and with respect to
two different averaging schemes.
Measurement Data Sets at
resolutions of 0.5° by
0.5° and 10 by 10 arc
minutes with respect
to a latitude / longitude grid
provide continuity with existing
ATSR2 products. Other data
sets contain data averaged over equal
area cells of 50 by 50 km
and 17 by 17 km aligned with the
satellite ground track.
In the first averaging scheme,
the globe is imagined to be
divided into cells 0.5° in
latitude by 0.5° in
longitude, and each of these
cells is further subdivided
into 9 subcells extending 10 arcmin
in latitude by 10 arcmin in longitude.
Averaged brightness
temperatures and reflectances
are derived, for cloudfree
and cloudy pixels separately, by
averaging the data over these cells and
subcells. For those
subcells containing clear sea pixels,
an averaged sea surface
temperature is derived from the averaged
brightness temperature as
described below. Finally the
averaged SST for each 0.5° cell is
derived by averaging the
valid SST values for the component
subcells.
The subcells within each cell
are identified by an index
in the 0 to 8 as follows:
Further notes on AST product
structure are given in
Section 2.7.2.2. below.
The derivation of averaged SST
is in principle the same as
that described above for gridded
SST, but with the following
practical differences:
 The retrieval is based on
the average
brightness temperature for
clear sea pixels
within a subcell;
 Appropriate new criteria
for the validity of
brighness temperatures are
introduced;
 Different retrieval
coefficients are used.
In the following, the notation M(
ch
, v) is used to denote
the number of valid clear
sea pixels for channel
ch and view
v (v = nadir
¦ forward)
that fall within the 10 arc minute
subcell under consideration.
The appropriate acrosstrack
band index corresponding to
a subcell is obtained by
entering the auxiliary Acrosstrack Band
Mapping Lookup
Table 6.5.8. with the mean acrosstrack
pixel number for the
subcell. This value is used to index
the table of coefficients to
extract those corresponding to the
correct air mass
value.
The logic of the procedure used
for deriving the averaged
SST for the AST product is as
follows. Steps 1 and 2 below
are executed for each subcell
in a halfdegree cell, then Step 3 is
executed to determine
averaged quantities for the whole cell.
1) Calculate the nadirview
retrieval.
The minimum number of pixels
required for the cell in the
nadir view is determined;
minpn= 340 *
NADIR_PIXELS_THRESH * cos
((π/180)x
latitude) + 1,
where latitude is the
latitude of the subcell, in
degrees. The value
NADIR_PIXELS_THRESH is taken
from the auxiliary file
of Level 2 Processor
Configuration
Data(ATS_PC2_AX) 6.5.7. .
The number of pixels that have
contributed to the average
clear sea nadir brightness
temperature in each of the
11 and 12 micron channels is
inspected. If this is less
that minpn for either channel,
an SST cannot be retrieved, and the AST
field is set to an exception
value of –1.
Otherwise, if M(
ir12, n) ≥
minpn and
M(ir11, n) ≥
minpn, an SST
retrieval is attempted, using
either a 2 channel
algorithm or a 3 channel
algorithm. If the solar
elevation associated with the parent
cell (not the subcell) is
negative (indicating a nighttime
measurement) and a valid 3.7
micron brightness
temperature average is available, a 3
channel algorithm (Equation)
is used, otherwise a twochannel
retrieval (Equation)
is used.
For nighttime data the 3.7
micron brightness
temperature average is
considered to be valid if the
ratio of the number of contributing
pixels at 3.7 microns to the
number at 11 microns,
float{M(ir37, n)} /
float{M(ir11, n)}
≥ IR37_THRESH.
If the ratio is less than
IR37_THRESH the
twochannel algorithm is used.
The twochannel algorithm is
always used for daytime data.
The parameter
IR37_THRESH is taken from the
auxiliary file of Level 2 Processor
Configuration Data 6.5.7. .
If a threechannel retrieval is
possible, the corresponding
flag of the confidence word is
set accordingly. In either
case the retrieval is
performed using the coefficients for the
appropriate acrosstrack
band index and taking account of
the geographic zone as
described below.
1.1) If the subcell falls in
the tropical region
(latitude <
TROPICAL_INDEX) or if it
falls in the polar region
(latitude = POLAR
INDEX), then the SST is calculated using
the retrieval coefficients
for that region and for the
appropriate acrosstrack band
index. Equation
is used if a twochannel
retrieval is required, or
Equation
is used for a threechannel
retrieval.
1.2) Otherwise the subcell lies
within the temperate region.
Two SST values are calculated,
one using the coefficients
for the temperate region, and
the second using the coefficients for
the polar or tropical
region. The coefficients for the
tropical region are used if
the subcell latitude is less
than TEMPERATE_INDEX,
otherwise the coefficients for
the polar region are used.
In each case the retrieval
coefficients for the
appropriate acrosstrack band index are
used, with Equation
if a twochannel retrieval is required,
or Equation
if a threechannel retrieval is
required. A linear
interpolation with respect to latitude
is then used to obtain the
final SST value from the two
regional values, using Equation
or Equation
as appropriate.
2) Calculate the dualview
retrieval.
The minimum number of pixels
required for the cell in the
forward view is determined;
minpf= 340 *
FRWRD_PIXELS_THRESH * cos
((π/180) x
latitude) + 1,
where latitude is the
latitude of the subcell, in
degrees. The value
FRWRD_PIXELS_THRESH is taken
from the auxiliary file
of Level 2 Processor
Configuration Data
(ATS_PC2_AX) 6.5.7. .
For each view, and for each of
the 11 and 12 micron
channels, the number of pixels
that have contributed to the
corresponding average clear sea
brightness temperature in
the subcell is inspected. If this
is less than minpn
or minpf, as appropriate,
for either channel in either
view, an SST cannot be
retrieved, and the AST field is
set to an exception value of
–1.
Otherwise, if
M(
ir12, n) ≥
minpnand M(ir11,
n) ≥ minpn
and
M(
ir12, f) ≥
minpfand M(ir11,
f) ≥ minpf
an SST retrieval is attempted,
using either a 4channel
algorithm or a 6channel
algorithm. If the solar
elevation associated with the parent
cell (again not the
subcell) is negative (indicating a
nighttime measurement) in each
view, and if valid 3.7
micron brightness temperature
averages are available for
both the nadir and the forward
views, a 6channel algorithm
(Equation)
is used, otherwise a 4channel
retrieval (Equation)
is used.
For nighttime data the 3.7
micron brightness
temperature average is
considered to be valid if the
ratio of the total number of
contributing pixels in
the two views at 3.7 microns to that at
11 microns,
float{M(ir37, n) +
M(ir37, f)} /
float{M(ir11, n) +
M(ir11, f)}
≥ IR37_THRESH.
If the ratio is less than
IR37_THRESH the
twochannel algorithm is used.
The twochannel algorithm is
always used for daytime data.
If a 3 channel retrieval is
possible, the corresponding
flag of the confidence word is
set accordingly. In either
case the retrieval is
performed using the coefficients for the
appropriate acrosstrack
band index and taking account of
the geographic zone as
described below.
2.1 If the subcell falls in the
tropical region
(latitude <
TROPICAL_INDEX) or
if it falls in the polar region (pixel
latitude = POLAR
INDEX), then the SST is calculated
using the retrieval
coefficients for that region and for
the for the appropriate
acrosstrack band index. Equation
is used if a 4channel retrieval
was specified, or Equation
if a 6channel retrieval was
specified.
2.2) Otherwise the subcell lies
within the temperate region.
Two SST values are calculated,
one using the coefficients
for the temperate region, and
the second using the coefficients for
the polar or tropical
region. The coefficients for the
tropical region are used if
the subcell latitude is less
than
TEMPERATE_INDEX, otherwise the
coefficients for the polar
region are used. In each case the
retrieval coefficients for
the appropriate acrosstrack band index
are used, with Equation
if a 4channel retrieval is required, or
Equation
if a 6channel retrieval is required. A
linear interpolation with
latitude is then used to obtain the
final SST value from the two
regional values, using Equation
or Equation
as appropriate.
3) Calculate cell averages.
When the nadir and dual view SST
values have been calculated
for each of the subcells that
contribute to a cell,
average nadir and dual view SST
values are calculated for
the cell.
For up to nine 10arcmin cells
within the halfdegree cell,
the mean nadir view SST for the
halfdegree cell is derived.
This is repeated for the
dualview retrieval.
where k∈{0
≤ k ≤
8} is an index to the subcells and in
each case the sum is over
all values of k for
which the respective subcell
temperature is valid (i.e. has
a positive value), and where
μ_{1} and
μ_{2} are the numbers of
such valid temperatures in
the nadir and forward views,
respectively. If either of the values
μ_{1} or
μ_{2} is zero, the
corresponding temperature is set to 1.
The standard deviations of the 10arcmin
SST values are also
calculated, as is the mean acrosstrack
pixel number to be associated with the
30 arc minute SST:
sst_mean_pixel
(
cell) = _{
} if μ_{1} > 0
sst_mean_pixel
(
cell) = 1 if
μ_{1} = 0
where the sum is over all
k ∈ {0
≤ k ≤ 8}
for which corresponding SST T
nadir(k,
cell) is valid
(≠1.)
2.7.1.3.3 Averaged NDVI and LST Retrieval
The NDVI is calculated for each subcell
for which average
reflectances over land have been
calculated. The averaged
NDVI over all the subcells, and its
standard deviation, are
also computed.
The algorithm for Averaged LST retrieval
is essentially the same as
that described in Section 2.7.1.2.2. above,
but applied to the averaged
brightness temperature values for
clear pixels within the cell
in place of the pixel brightness
temperatures.
2.7.1.3.4 Spatially Averaged Cloud Parameters
This step provides physical information
on the cloud state additional to the
results of the cloud flagging provided
by the cloud clearing algorithms.
The product is based on the same
halfdegree cells defined above. The
frequency distribution of brightness
temperature for the cloudy pixels
within the cell is given together with
representative parameters and an
estimate of the cloudtop temperature.
The latter is interpreted as the
mean brightness temperature of the
coldest 25% of the cloudy pixels in the cell.
For each halfdegree cell, information is
given for the nadir and forward views
separately. The information consists of
the number of cloudy and cloudfree
pixels falling within the cell, a
histogram of the 11 µm brightness
temperatures of the cloudy pixels, and
various statistical parameters derived
from the histogram. The 11 µm
channel is used as the basis of the
product following the practice of
ATSR and ATSR2.
The product is generated as follows. Two
histograms are generated of the
frequency distribution of 11 µm
brightness temperature, for cloudy
pixels over sea and land respectively.
The histograms represent the brightness
temperature at 0.1 K resolution between
190 K and 290 K. Thus each contains
1000 bins where the first bin contains
the number of pixels with temperatures
in the range 190.0 to 190.1 K, and
the last bin contains the number of
pixels with temperatures in the range
289.9 to 290.0 K. The cloud state of
each filled pixel falling within the
cell is inspected. If it is clear, a
count of the number of clear pixels is
incremented; if it is cloudy, the 11
µm channel BT is inspected and
the count in the appropriate histogram
bin is incremented. Note that cosmetic
fill pixels are included in the processing.
As each pixel is inspected, a test is
made to determine whether its 11 µm
BT is lower than the lowest value
previously encountered, and if so to
store the location of the pixel. Then
when the histogram is complete the
identity of the minimum pixel will be
known, and can be used to extract
its channel values.
Once the histogram is complete for a
given cell, that is once all the pixels
falling within the cell have been
inspected, the cloud temperature and
coverage results are derived from it.
Firstly the total number of cloudy
pixels detected is computed by summing
the histogram samples. If this total
is less than 20 no further derivations
are performed. If 20 or more cloudy
pixels have been identified and
included in the histogram, the mean 11
µm brightness temperature and its
standard deviation are calculated from
the histogram.
The histogram is searched for the lowest
temperature represented by the
histogram. This is the temperature
corresponding to the first nonzero
bin of the histogram. Next, the
cloudtop temperature is estimated. The
histogram bin containing the 25th
percentile is identified; this is
the first bin (as the histogram is
searched in the direction of ascending
temperature) for which the cumulative
total of the bins up to and
including itself exceeds 25% of the
total number of cloudy pixels. The mean
temperature represented by the bins up
to and including this bin is calculated.
[Note that the cloud top temperature so
derived may represent the mean of
slightly more than 25% of the cloudy
pixels, since the cumulative total
including the 25th percentile bin may
exceed 25%.]
Finally the percentage cloud cover is
calculated from the ratio of cloudy
pixels to total pixels.
2.7.1.4 Derive Averaged Product (50 km cells)
For this part of the product, averaged BTs,
reflectances, SST and NDVI are
derived using the same method as in section 2.7.1.3.1. to section 2.7.1.3.4. , but averaged over
cells and subcells of
nominal dimensions 50 km x 50 km and 17 x
17 km respectively.
The SST retrieval algorithm used for 50 / 17
km resolution is essentially the
same as that for the halfdegree cells
described in Section 2.7.1.3. except that
the latitude dependence is
omitted from the calculation of the
validity thresholds minpn etc.,
because the cell and
subcell areas are independent of latitude
in this case.
