# How to describe a MODIS Tile's distortion

When looking at the MODIS grid [1] and compare it to how the sinusoidal projection is distorted, I wonder how to both practically and formally describe the distortion factor for each MODIS grid tile.

By practically I mean, what's a center tile's (e.g. `row 8, col 18`) width and height in meters on ground compared to a tile of a region that is rather distorted on the sinusoidal projected map, like `row 2, col 14`?

My understanding is that, by example on the grid shown at [1] which should be a 1km resolution MODIS grid, each tile should be approximately `1200km * 1200km`, but is that approximation nearly the same for mentioned tile regions?

And by formally I mean, how to mathematically describe the distortion factor for MODIS tiles?

[1] http://modis-land.gsfc.nasa.gov/MODLAND_grid.html
[2] https://en.wikipedia.org/wiki/Sinusoidal_projection#/media/File:Tissot_indicatrix_world_map_sinusoidal_proj.svg

• The Tissot Indicatrix displays the infinitesimal distortion. Even for huge tiles, as in the MODIS grid, this will be a reasonable description of distortion throughout each tile (it is the complete first-order approximation thereof). Since you link to a Wikipedia image of a Tissot Indicatrix, what exactly are you looking for beyond that? Jan 21, 2016 at 21:25

## 1 Answer

The distortion in MODIS imagery people mostly worry about is the well known Bowtie effect due to whiskbroom scanning.

The Sinusoidal projection, or Sanson-Flamsteed, is an equal area projection and thusly both tiles you mentioned cover roughly the same area and have identical pixel sizes.

• This does not seem to be correct. Indeed, for a projection to be equal area it must obviously distort shapes. Jan 21, 2016 at 21:22
• You're correct @whuber. I mixed that up and removed this part from my answer. Jan 22, 2016 at 7:46