Hello All,
I've made a diagram of the geometry to try to get my understanding of these rotations clearer:
http://bit.ly/geosr_scan_geometry
The blue point in the sketch results from rotating the viewing vector through an angle y about the axis S_x, which is the tangent to the satellite orbit, and then through an angle x about S*_y, which is an axis formed by taking the axis S_y and rotating it through angle x.
The above sentence describes the angles in a way which is related to the functioning of the instrument, and I agree with Daniel that this is not an ideal approach for the standard.
To respond to Jim's question about parametric coordinates: I think it would be a shame to describe two components of a spherical polar coordinate system as "parametric" ... they are spherical angles which are very widely used. The challenge is to come up with a definition which is accurate and concise.
For the GEOS-R geometry we can define the angles in terms of a coordinate axis (the tangent to the orbit, S_x) and a reference plane (the plane defined by the Earth's polar axis and the vector from the centre of the Earth to the satellite). Once the axis and reference plane are defined, y is the azimuthal angle relative to the line from the satellite to the Earth's centre, and x is pi/2 minus the polar angle. i.e. x is pi/2 minus the angle between the line of sight and S_x. y is the angle between the line from the satellite to the Earth's centre and the perpendicular projection of the line of sight onto the reference plane.
For the alternative gimbal geometry a similar definition applies except that the coordinate axis (S_y) is parallel to the Earth's axis and the reference plane is the Earth's equatorial plane. Now y is pi/2 minus the angle between the line of sight and S_y. x is the angle between the line from the satellite to the Earth's centre and the perpendicular projection of the line of sight onto the reference plane.
regards,
Martin
________________________________
From: CF-metadata <cf-metadata-bounces at cgd.ucar.edu> on behalf of Martin Juckes - UKRI STFC <martin.juckes at stfc.ac.uk>
Sent: 20 April 2018 17:07
To: Randy Horne; Daniel Lee
Cc: cf-metadata at cgd.ucar.edu
Subject: Re: [CF-metadata] Fix Geostationary projection, including proposal for two new standard names
Hello Randy,
the sweep_angle_axis parameter appears to be used to distinguish between the two axis configurations, with a value of "x" to indicate that the GEOS series have the sweep axis aligned with "x", which here means East/West.
You've answered my questions now, thanks for your patience.
Given that the angles are components of the well known spherical coordinate system, which is, I believe defined in ISO 80000-2:2009, I feel it would be a mistake to omit reference to that in the definition. I appreciate that the complexity of the formulae (which I've attempted to work out from first principles, with results below) means that, for practical applications, you want to work with existing tools and procedures rather than starting from a fundamental definition. On the other hand, we are trying to set up a standard using universal language.
regards,
Martin
Working from first principles, the relationship between latitude and relative longitude on the Earth and the projection coordinates are (for the case of coordinate axis orientated E/W):
cos(lat) * sin(lon) = r1 * sin( y );
sin(lat) = r1 * cos(y) * sin(x);
where r1 is a solution of the quadratic:
r1*r1 - 2*Rs*r1*cos(x)*cos(y) + Rs*Rs -1 = 0.
________________________________
From: Randy Horne <rhorne at excaliburlabs.com>
Sent: 20 April 2018 15:15
To: Daniel Lee
Cc: Juckes, Martin (STFC,RAL,RALSP); cf-metadata at cgd.ucar.edu
Subject: Re: [CF-metadata] Fix Geostationary projection, including proposal for two new standard names
Dear Martin:
Note that the CF ?geostationary projection? has been design to accommodate both GOES-R and Meteosat (and Himawari, etc.), The ways the different imagers do their scans is different causing the same (x.y) angular coordinates to resolve to a different earth location. A projection parameter ?sweep angle? is included to allow the same projection to work for both imager designs.
A GOES-R writeup on this projection is located at:
https://www.goes-r.gov/users/docs/PUG-L1b-vol3.pdf, paragraph 5.1.2 ABI Fixed Grid.
v/r
randy
> On Apr 20, 2018, at 10:06 AM, Daniel Lee <Daniel.Lee at eumetsat.int> wrote:
>
> Hi Martin,
>
> Yes, you need both coordinates in order to find the position viewed on the Earth's surface - it's not a simple distance measurement.
>
> I'm a bit confused about your use of azimuth vs. polar - do you mean meridional and zonal?
>
> I'd be cautious about bringing in too much information about how geostationary satellites function into the grid mapping. Not all satellites use the same scanning principals - technology changes and there have already been a number of different geostationary satellites deployed with different scanning characteristics, so that the geostationary constellation currently contains satellites with different scanning methods. This will surely continue to change in the future.
>
> At the end of the day, describing geostationary satellite data with the method NOAA is currently using is well-established and has worked well for decades in several data formats, so I don't think we'll benefit much from changing anything except for maybe the name of the variables. The methodology should clearly remain the same.
>
> Cheers,
> Daniel
>
>> -----Original Message-----
>> From: CF-metadata [mailto:cf-metadata-bounces at cgd.ucar.edu] On Behalf
>> Of Martin Juckes - UKRI STFC
>> Sent: 20 April 2018 15:41
>> To: Randy Horne <rhorne at excaliburlabs.com>
>> Cc: cf-metadata at cgd.ucar.edu
>> Subject: Re: [CF-metadata] Fix Geostationary projection, including proposal
>> for two new standard names
>>
>> Hello Randy,
>>
>>
>> thanks, that clears up a lot of my confusion.
>>
>>
>> Since the coordinates are N/S and E/W aligned, at least at the origin, it may
>> be better to include this in the names. "x" and "y" are generally used for
>> coordinates which have an arbitrary orientation relative to the Earth's axis
>> which then needs to be specified in additional attribute values.
>>
>>
>> Your answer does not completely define the angles for me. If we consider a
>> point (A) which is, for example, at 45N at the same longitude, then it angular
>> distance in the N/S direction is uniquely defined, but if we take another point
>> (B) 45degrees to the east, then we have two angles and their values will
>> depend on the definition of the coordinate system.
>>
>>
>> I've found some documentation on geostationary satellites which suggests
>> that the viewing angles are related to the gimbal system, with an outer
>> "sweep" axis and an inner "fixed-angle" axis (this is from
>> proj4.org/projections/geos.html). Relating this back to the mathematical
>> terminology of spherical coordinates that I'm familiar with, I believe the angle
>> of rotation around the sweep axis is the azimuthal angle and the rotation
>> around the fixed axis is the polar angle. I.e. we have a spherical coordinate
>> system relative to the sweep axis.
>>
>>
>> The proj4.org document also states that the GEOS series have the sweep axis
>> aligned E/W, which would imply that projection_y_angular is an azimuthal
>> angle and projection_x_angular is a polar angle. With this information (and
>> the height of the satellite) I would be able to calculate the two angles for
>> point B. I'll get a different answer if projection_y_angular is the polar angle
>> and projection_x_angular is azimuthal, so it is important to know which is
>> which. Perhaps projection_polar_angle, projection_azimuthal_angle would
>> be better?
>>
>>
>> The calculation would indeed be complicated, as has already been
>> emphasized below, but I think it is worth going back to the fundamentals
>> here, and stating the underlying assumptions behind the coordinate system.
>> E.g. the fact that it is defined relative to a fixed point above the Earth's
>> surface which corresponds to an ideal satellite position.
>>
>>
>> regards,
>>
>> Martin
>>
>>
>>
>> ________________________________
>> From: Randy Horne <rhorne at excaliburlabs.com>
>> Sent: 20 April 2018 13:56
>> To: Juckes, Martin (STFC,RAL,RALSP)
>> Cc: cf-metadata at cgd.ucar.edu
>> Subject: Re: [CF-metadata] Fix Geostationary projection, including proposal
>> for two new standard names
>>
>> Hi Martin:
>>
>> RE: I agree with Jim that a little more basic information is needed about what
>> the angles are. I may be misinterpreting the discussion, but I had imagined
>> that the angles as components of a spherical coordinate system centred on
>> the satellite, with the nadir at (0,0) ... is that correct?
>>
>> The projection_x_angular_coordinate and projection_y_angular coordinates
>> are the angular distances from the satellite?s nadir in the E/W an N/S
>> direction, respectively, from the ideal location of the imaging instrument in
>> geostationary orbit.
>>
>>
>> v/r
>>
>> randy
>>
>>
>>
>>> On Apr 20, 2018, at 4:06 AM, Martin Juckes - UKRI STFC
>> <martin.juckes at stfc.ac.uk> wrote:
>>>
>>> I agree with Jim that a little more basic information is needed about what
>> the angles are. I may be misinterpreting the discussion, but I had imagined
>> that the angles as components of a spherical coordinate system centred on
>> the satellite, with the nadir at (0,0) ... is that correct?
>>
>> _____________________________________
>>
>> Randy C Horne (rhorne at excaliburlabs.com) Principal Engineer, Excalibur
>> Laboratories Inc.
>> voice & fax: (321) 952.5100
>> cell: (321) 693.1074
>> url: http://www.excaliburlabs.com
>>
>>
>>
>>
>> _______________________________________________
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>> CF-metadata at cgd.ucar.edu
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Received on Mon Apr 30 2018 - 03:59:19 BST
