Ocean Color Forum

Topic Frequently Asked Questions / Data Products & Algorithms FAQ / How do I estimate actual pixel area? (locked)

**How do I estimate actual pixel area?**

The reported nominal resolution for a sensor is only valid for pixels near

the center of the scan. The following equations explain how one would

estimate the area for any pixel given it's position in the scan.

The following equations ONLY provide an estimation, as they do not

account for orbit height variation, oblateness of the Earth, etc...

**For MODIS**(or any nadir sensor) :

`Compute the scan angle, S (in radians), given pixel number:`

S = (I-hp)/H

where:

I is the zero-based pixel index

hp is 1/2 the total number of pixels (zero-based) (for MODIS each scan is 1354 "1km" pixels, 1353 zero-based, so hp = 676.5)

H is the sensor altitude divided by the pixel size (for MODIS altitude is approximately 700km, so for "1km" pixels, H = 700/1)

For 500m pixels, hp = 1353, H = 1400 (700/0.5)

For 250m pixels, hp = 2706, H = 2800 (700/0.25)

`Compute the zenith angle:`

Z = asin(1.111*sin(S))

where Z is the zenith angle.

`Compute the Along-track pixel size:`

Pt = Pn*9*sin(Z-S)/sin(S)

where Pn is the nadir pixel size (e.g. 1km, 0.5km, 0.25km)

`Compute the Along-scan pixel size:`

Ps = Pt/cos(Z)

Thus, area is ~ Pt * Ps

**For SeaWiFS:**

the equations are the same but the constants are different

(

*20 degree tilt, slightly larger pixels, and LAC vs. GAC*)

For SeaWiFS LAC (1285 pixels), hp = 642 and H = 630 (700/1.111)

For SeaWiFS GAC (248 pixels), hp = 123.5 and H = 157.5 (700/4.444)

For both cases, at 20 degrees tilt,

Z = asin(1.125*sin(S))

Pt = Pn*8*sin(Z-S)/sin(S)

where Pn for SeaWiFS is ~1.2 km at 20 degrees tilt,

and Ps is computed as for MODIS.

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