# Coordinates in WDSS-II

There seems to be some confusion about the geolocation of WDSS-II’s grids.  First of all, most of the grids produced by WDSS-II algorithms are in Plate Carree (or equirectangular) projection for the reasons ably set forth in this cartoon.

Suppose you were to ask w2merger to make you a grid from radar data and you specify the top (northwest) corner with -t and bottom (southeast) corner with -b and spacing with -s as (35,-97), (34.97, -96.97) and (0.01,0.01) respectively.  You would then get this 3×3 grid:

I have found that if you consider that all pixels occupy a definite area of the earth, the above representation becomes very logical. It is also intuitive in that there are 3 pixels between 35 degrees and 34.97 degrees at a spacing of 0.01 degrees.

In the netcdf files output by WDSS-II, you will find that the northwest corner and the grid spacing for the above grid would be encoded as (35,-97) and (0.01,0.01).

So, are the pixels in WDSS-II defined by their north-west corners? Unfortunately, no. For that, you have to take into account that while a pixel occupies a certain area, it has only one value. Which location within the pixel does that value correspond to? The value of a bin is the average value within the region covered by that bin.

The answer to the second question leads to some tricky semantics. Before we get to those, let’s move on from the world geographic system to the projected coordinate system of the grid itself (see ArcGIS for an explanation of the difference).  Because the projection in question is Platee Carree, the transformation is a simple linear one between pixel coordinates and latitude-longitude, but such a transformation exists. For this coordinate system, the (0,0) point is the center of the northwest grid point.  This is needed so that we can think of a pixel’s value as being the average value within the bin if we had somehow had infinite resolution. The grid’s coordinate system, to put a picture to it, is like this: