The SimplifiedMapping
Equation of VISSR Image
Data
from the Geostationary Meteorological Satellite(GMS)
Abstract
This
paper aims
information
to develop
values of space-craft, which
The
popular
the image
but it is difficultto maintain
accuracy.
An
matrix
a
considerable
for more sophisticated image
source.
concern
ducts
image
The
are
display
the
potential
products that
media
VISSR
data
Resolution
present
with
using actual data set.
frame)
to geocentric
is essential. In
to map
data
without
FAX
coordinate
general, it may
any
procedure
information
on
orbital elements and specifications of space
pro-
craft. The
displays (so
Facsimile,
The
a mapping
turn out to be an impracticable
of principal
image
for mapping
projection plane (for examples,
system
data as the basic data
for computer-processed
called, High
to perform
or VISSR
exists
equation
a sufficient accuracy.
from
use mapped
the satellite data producer.
error analysis is also investigated
Introduction
on the limited
display format and specific
is a linear interpolation
equation is defined as a transformation
reasonable
There
equation based
are easily obtained from
transformation
data,
mapping
a simplified mapping
like a set of longitude-latitude values, VISSR
present
model
is reduced
to
simplest forms on the condition of limited
Low
information
which
the user can be known.
Resolution Facsimile) rebroadcast via GMS
Chan (1978) investigated the transformation
and
procedure
(FAX)
recorded
on
either
photo-facsimile
or other facsimile recorder.
problem
Coastlines, latitude-longitude lines and
other physiographic
in the FAX's.
These
are helpful for posimost
1. Input
cases there
but in some
tions, such as in time-compositing
image
data, planimetered
measure
tness contours, displacement
this
Data
Inputs to mapping
technique include the
line and pixel coordinates (/, /) of the FAX
applica-
elements
mapped
form
of brigh-
plus information
these
coordinates
needed to transinto
The information
is cri-
rived from
tically important.
the FAX
on
transformation
In these applications, the transformation
ber
KATO
13
―
which
are
de-
are;
1) a pair of scan line number,
Kazuyasu
geocentric
coordinates (<p,2).
measurement
of clouds, the precision of mapping
Taichi TAKAHASHI,
calculated
and its specifications.
in dealing with linear in-
terpolation scheme,
detail, and
features are implanted
tioning the targets. In
is an advantage
in
exactly based on satellitedynamics
corresponded
pixel numto the sub-
Table 1
VISSR Original Image Data
High-Resolution FAX
Full Disc
Partial Disc
(19°S,140°E)
(35°S,140°E)
Average
Earth
Radius:
Distance between
Parameters for mapping
69. 9081
39.05299
-318
4945
69.55504
39.05299
-910
4945
69.55504
39.05299
0.637028949 x 107 m.
Space-Craft
and Earth
Center:
0.422702899 x 108 m
equivalent to about
latitude-longitude lines which
orbital motion.
are melded
values may
for solving
the mapping
are needed
equation.
are defined as specific values which
on the characteristics of the GMS
craft, and on the FAX
These
These
The
depend
the change
space-
of
nominal
to represent
the
systems
related to the
discussion are defined.
1) Satellite Coordinate
formats.
The
with justifiableaccuracy.
coordinate
subsequent
This system
are;
System
(X, Y, Z)
is defined such that the X-
axis is in the direction of the earth center-
3) stepping angle (radians per line).
4) sampling
then be used
orbital elements
of
of this, it is per-
orbital elements are ignored.
values.
constants
5° or 0.1 radians
In view
missible to consider that
and their (/, /) coordinates
In addition, some
23. 9748
4945
2) data set of intersection points of the
the FAX,
34.98618
2177
satellite point (SSP).
with
model.
space craft center, the F-axis is perpendi-
angle (radians per pixel).
5) average
earth radius.
6) nominal
distance between
cular to the X-axis and lies in
obtained from
earth and
the plane
rotating X-axis with space-
craft, and the Z-axis given by Z
satellite.
This
system
=XxY.
is illustrated in Fig. 1 (left
side).
The
actual data related to the GMS
summarized
in Table. 1 except for 2). Line,
pixel number
depending
are
2) Earth Coordinate
associated with SSP are fixed,
on a type of FAX
(gray
System
This is defined such
scale,
(x, y, z)
that the
minus
scale mark, annotation and back porch data
position of the GMS)
which
torial plane, the z-axis is perpendicular
are inserted to the FAX
x-
axis is in the direction of 140°E (nominal
data format
are not considered).
and lies in the equato
this plane (in the direction of the north
pole), and the ^-axis is given by y =zXx.
2.
2. 1
The
VISSR
Mapping
Model
Definition of Coordinate
System
present picture-taking process of the
takes about
25 minutes.
This is well-known
as the inertial coor-
dinate system when
the direction of x-axis
is in the vernal
This is
equinox, as illustrated in
Fig. 1 (right side).
u
―
Meteorological
Satellite Center
Technical
Note
No. 1, March
1979
Satellite
Fig. 1
2) VISSR
Frame
Coordinate
This is defined such that
this system
frame,
is in
the
of / and
line number
tively when
shape of earth is a perfect sphere.
Following
of VISSR
vectors,
Vse,
Vsp,
Vep
are
defined.
the direction of
and the /-axis is in the
/-axis is perpendicular
4) The
the origin of
stepping direction,as shown
values
System (/, /)
center
the /-axis is in
scanning
Illustration of various coordinate system.
1
Xs
VISSR
in Fig. 1. The
Ys
Vse=
to the /-axis. The
0
= Rse
(1)
0
Zs
/ are generally called a
and
a
pixel number
Xp
respec-
the origin is positioned at the
upper left corner of the VISSR
Vsp=
Yp =
frame.
cos q(Jo―JP)-cos p(I0―Ip)
R
cos q(J0―Jp)-sin
Zp,
p(I0―Ip)
sin q(Jo-JP)
(2)
2. 2
Mapping
Equation
―cos(p-cos(X0―X)
xe
Throughout
this report, the abbreviation
s, e, p are used
position
located
The
of the point
space-craft,
of interest
Vep=
earth,
which
following
1) The
assumptions
constant
during
and
then
to an
2) The
3) The
VISSR
Rse:
system
and
those
distance between
a nominal
Re:
period,
R: distance between
atti-
averaged
space-craft and
earth radius.
between
during
interest point on the earth.
VISSR
p: sampling
scan line, pixel
the VISSR
expressed
space-craft and
q: stepping angle.
angle.
Jo: line number
from
system
sin <p
nearly
period.
defined
(3)
where,
in
attitude.
difference
coordinate
is
observation
be assinged
actual
number
COS (p ･ COS (^o ―^)
earth.
of space-craft
spin rate is constant
observation
made
Re
ze
model.
attitude
may
are
ye
is
on the earth, as illustrated in Fig. 1.
the present
tude
to denote
Io: pixel number
coordinate
associated to the SSP.
associated to the SSP.
^o: direction of the minus
in the satellite
Jp: line number
is negligible.
interest.
xo
X-axis (140°E).
associated to the point of
MMtWlM.^'y*-
SM^
Ip: pixel number associated to the point
mi^r
1979^3 H
following
result.
of interest.
xex
xe2
xes
xe4
yel
ye2
ye3
ye4
ze3
ze4
<p:latitude of the point interest.
CM] X
X: longitude of the point of interest.
The
transformation matrix [M]
from
earth coordinate system to satellitec oor=
dinate system is defined by the following
equation
lM]xVep=Vsp-Vse
The
transformation
function
matrix
of orbital elements,
specifications etc.
[M]
(4)
from
Instead
[M]
space-craft
may
then
data
des-
limitted input
to increased
mapping
[M]
The
Consider a small quadrangle
can
trarily on the earth.
Vepi=
Re
yet =
zet -
cos
Re-sin
x IVe}
=
[7s]
(8)
arbi-
matrix [M]
can be
equation, from
equation
X IVeJ
X l[Ve＼ X [Fe]J] (9)
matrix.
R
which
R
can be
expressed simply by the trigonometry
mula, applying to the triangle SEP
Re2=Rs2+R2-2Rs-R-cosg
(10)
where,
cosg=(Vse,
(5)
=cos
<pi
2, 3, 4)
Vsp)/＼Vse＼-＼Vsp＼
q(Jo-Jp)-cos p(Io-Ip)
(11)
Then, it is obvious that
R=Rs
･ cos g± VW27c^oTig
^R^2
:::Re2Y
(12)
Y'pt
The
equation (12) yields two solutions, it
follows that the desired solution is
'R･ cos q(Jo-Jpi)･ cos p(I0-Ipi)-Rs
R
R ･ cos q(J0―JPi)sin P(h―I Pi)
Rs-cosg―
g-(Rs*-Re*)
I-cos
(13)
■R-sin q(Jo-Jpi)
(i=l, 2, 3, 4)
Consequently, it may
above
foras il-
lustrated in Fig. 1.
Z'Pi
=
equation is sym-
to obtain
X'Pi
Vspi-Vse^
Z'Pt
vectors related
<pi･ sin (^0―^f)
(i=l,
Z'pt
Finally, it remains
<pi■cos (A0―Ai)
■cos
Y'p2
= [7s]
to these points are given by
― Re･
Z'pt
(7)
appears in the equation (2),(6).
to be map-
designated
The
Y'Pt
where, t denotes the inverse
by four points Pj,
be
Y'p%
transformation
[M]
simplifications
curacy.
P2, P3, P4. they
Y'p2
(8).
affecting the ac-
ped which is surrounded
Y'px
derived following
efficiency of the
process without
X'pA
of estimating
be derived from
will lead
X'pa
bollically written as
is a
sible that, for simplifications,[M]
Section 1. Such
X'p2
For convenience, above
these factors exactly, it is pos-
cribed in
'Xfp1
be shown
that the
equations (4), (5) and (6) yield the
―
2. 3
Mapping
The
transformation
dinate system
16 ―
Procedure
to VISSR
from
frame
earth
coor-
coordinate
Meteorological SatelliteCenter Technical Note No. 1, March 1979
system, and its inverse transformation
described.
Both
quently
occured
handle
the image
image
data
image
data.
are fre-
to the user who
plans to
data
using
the
displays or the raw
to four points, the following
equations are derived
xe
[M]-1
ye
digital
x
ze
viously defined in Section 2.2. The
from
corresponding
VISSR
Let considers the small quadrangle
formation
are
transformation
matrix
[M]
can
R-cosq(J0-Jp)-cosp(I0-Ip)-Rs
pretrans-
R･ cos q(Jo-JP)･sinp{h
be estimated
(18)
Ip)
R･ sin q(Jo-JP)
equation (9) based on the locations of
where,
four corners related to small quadrangle.
1) Transformation
System
The
to VISSR
Coordinate
System
(19)
Rs2-cos g― Rs2-Re
R―Rs- cos g―
from Earth Coordinate
(20)
cosg=cosq(J0-Jp)-cosp(I0-Ip)
point of interest located on the earth
Finally, the longitude-latitude values cor-
is expressed by a pair of longitude-latitude
values (1, <p).Those
quadrangle
frame
points within the small
are transformed
coordinate
to the VISSR
system.
tions for accomplishing
The
computa-
this are given by
―Re-cos
Y'p
= [M]X
Re-cos
<p=sm-＼ze/Re')
(21)
X=Xo-ye/Re'-cos(sin-＼ze/Re'))
(22)
Re'=Vxe2+ye2+zez
<p-cos(A0―X)
(p-s'm (Xo―X)
(23)
(14)
3.
Z'p
to / and / are given by
where,
equation (4),it is obvious that
X'p
responding
Verification
Re-sincp
The
Knowing
Xp', Yp', Zp', the pair of line
number (7≫/pixelnumber (Jp) correspond-
exact
mapping
a general
derivation
has been
developed
at the Meteorological
equation
An
Ip^h-iYp'/iR-cosisin-'Zp'/R'V/p
Jp=U-($m-＼Zp'/R'))Iq
(15)
(16)
model
model
where,
2) Transformation from
Coordinate System
(17)
VISSR
to Earth
Frame
Coordinate
those
pixel
Throughout
servation
time
purposes
between
mapping
the present
model.
expressed
are shown
in
in Tables
in these
Tables,
previously
defined
con-
are
It may be preferableto apply the trans-
at the
top of tables.
location
formation to selected data set of fairly
gnated
well-known points which are expressed by
transformation
the VISSR frame coordinate system (/,/).
in the middle of table. The
Knowing
ing in upper
the values of line-pixelnumber
―
17 ―
points
matrix
The
for
[Ml
2, 3 and
ob-
Ia, Jo, Re, Rs, q, p
four
visible
VISSR
stants
System
present
the exact
from
and
the
a difference
from
differences
channel
4.
to validate
derived
and
The
R'=^(Xp'+Rsy+Yp'2+Zp/2
way
with
Satellite Center(MSC).
is to calculate
estimates
concerned
for operational
ing to {X, <p) are derived from following
effective
model
of (<p, X)―(I, J) relation
summarized
of desi-
calculating
is also
the
shown
figures appear-
portion of table indicate the
Table 2
Differencesbetween the present model and the exact mapping model. The
quadrangle
for estimating the transformation matrix is located at a high latitude region (northern
hemisphere).
VISSR
TIME
USED
197 8
･
CONSTANT
FOUR
100.0
2199
2268
2337
240b
2*75
254*
2613
2682
2751
Table
VlSSK
USED
/
0.2
0.0
0,2-0.1
0.2
0.0
0.2-0.0
0.1
0.1
0.1-0,0
0.0
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.0
-0.0
-0.1
-0.2
-0.3
-0.3
-0.*
*0.0
30.0
3
5.0
7.0
6.0
5.0
*.O
3.0
2.0
1.0
0.0
FOuR
Same
≪
33
:
0,0
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0,0
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C
140,0
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1
1
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POINTS
2
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c
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LAMBDA)
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:
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0
4284
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4988
5076
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0.0
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2.5-6.6
1.2-3.6
0.2-1.5
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0.1
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1.3
-1.5
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CONSTANT
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23
0.3-0,1
0,2-0,1
0.2-0.1
0.2-0.1
0.1-0.1
0.1-0.1
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-0.2-0.1
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0.0
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POINTS
TIME
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version (<p,X) into (/, /).
curacy.
differences
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0.2
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0.0
-0.3-0.1
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-0.4-0.2
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0.7
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0.5
1.0
0.3
0.
8
0.2
0.
5
"<J.0
3928
1.7
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3
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-0.3-0.2
PHAI
DEGKEE
LAMBDA)
process.
discussion, itis seen
model
model
If the
the model
portion illustrates the
result shows
0.0
every lOdeg.
frame
approximates
the
with justifiable ac-
satellite data
defined
producer
six constants
longitude/latitude intervals,
allows
the user to perform
coordinate transformation
area to be converted.
The
0.*
1.3
and a table involving (<p,A)―(I,J) relation
the point of interest is
appearing in lower
0.6
0.1
provides previously
―9.8 are replaced to 99.9.
―9.9 is set where
0.2
0.3
-0.2
From
portion are the
located at the deep space area.
0.4
that the present
exact
9.9 from
0.6
0.1
1.5
0.9
increased efficiency of the mapping
both
difference of estimates in the case of con-
ranging
0.3
1.2
1.0
3807
1.1
-0
models, applying the conversion from (/, /)
The
0.8
(UNIT
difference of estimates obtained from
into {<p,1). Those in lower
O.t
-0.0
3686
0.9 1.3
0.7 1.1
0.5
1.0
0.*
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0.1-0.*
0.1-0,5
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-0.0-0.2
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AND
PIXEL
FOR
VIS.)
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0.2-0.3
0.1-0.3
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(
is located at a high latitude region
PaRa"ETE*S
JO
RE
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for the quadrangle
hemisphere).
TIME
CONSTANT
1, except
information
that the difference is
without
the
detailed
on orbital elements, misalign-
ments, etc.
less than 0.6 pixel (or line) unit within the
area of interest and its vicinity. 0.6 pixel
References
is equivalent to 0.2 infrared pixel.
F.K.
4.
Conclusion
The
mapping
much
forms.
and
equations
as possible
Such
Remarks
and
are optimized
reduced
simplifications
Chan
VISSR
lead
Distortion-Free
Data
from
Mapping
Service, Under
to
19
―
Contract
of
Geosynchronous
Satellites. National Environmental
as
to simplest
will
(1978) :
Imagery
Satellite
No. 01-3-M01-1864.
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