Ocean Color Forum
By Leon Majewski Date 2004-08-13 00:06
Hi
Is there a way to obtain an estimate of the area covered by a pixel from an unreprojected data set (eg a seawifs or modis L2 or L1A pixel off nadir)?

I'm currently using an estimate from the distance to neighbouring pixels; is there a way to use the sensor geometry?

Thanks
Leon Majewski
By fred Date 2004-08-13 10:00
Hi Leon,

This question is easier to address for MODIS than SeaWiFS, because of the effect of tilting on SeaWiFS.

It is certainly possible to use an analytical approximation for the pixel size vs. scan angle, based on a nominal orbit altitude and spherical Earth.  This calculation will be accurate to several percent.

For MODIS, a more accurate calculation can be performed using the geolocation product (MOD03), specifically the data objects Range and SenzorZenith.  The along-track pixel size in meters is the Range divided by 700.  The along-scan size is equal to the along-track size divided by the cosine of the SensorZenith.

As stated above, this is harder for SeaWiFS because of the sensor tilt (20 degrees forward or aft).  This has two effects:  it increases the path length and sensor zenith angle for a given scan angle, and it distorts the pixel shapes at larger scan angles, making them parallelograms instead of rectangles.  Another complication is that the SeaWiFS platform (OV-2) has looser attitude control than Terra and Aqua, with roll angles between 1 and 2 degrees.  This offsets the true nadir pixel from the nominal scan center by the same amount, making the scan slightly asymmetric.

However, I should also mention that the SeaWiFS along-track pixel size is not equal to the pixel-center spacing (again, unlike MODIS).  The reason is that the pixel size depends on the path length, while the center spacing results from the ground track speed and scan interval.  On the other hand, in the along-scan direction the pixel size and center spacing are equal.

If you are interested in analytic approximations for the pixel size for MODIS or SeaWiFS, please let me know (probably easier just to E-mail me at fred@seawifs.gsfc.nasa.gov).

Regards,
Fred Patt
By fred Date 2004-08-26 12:45
Hi Leon,

Sorry to take so long getting back to you with this.

The approximation of pixel size vs. scan angle is based on the Law of Sines:

sin(s)        sin(z)        sin(a)
------   =    ------   =    ------
Re            Ro            D

where s is the scan angle, z is the sensor zenith angle at the observed
location, a is the arc length on the Earth surface from the scan-center pixel,
Re is the Earth radius, Ro is the spacecraft orbit radius and D is the
spacecraft-to-location distance.

Also, from basic geometry, z = s + a

My approach is to first calculate z and a:

z = asin(Ro*sin(s)/Re)
a = z - s

The distance is then:

D = Re*sin(a)/sin(s)

The along-track pixel size is:

Pt = Pn*D/700

where Pn is the nadir pixel size; and the along-scan size is

Ps = Pt/cos(z)

For MODIS:

Ro = 7077 km
Re = 6371 km (mean Earth radius)
Pn = 1000 meters

For SeaWiFS, the values have to be corrected for the tilt as follows, and the pixel size is slightly larger:

Ro' = Ro*cos(20)                (tilt angle)
Re' = Re*cos(22.3)              (zenith angle at nadir)
Pn = 1120 meters

These values are then used in the above equations.