Confusion about grid registration concepts and their relevance in modelling I'm trying to make use of the ETOPO1 dataset as the bathymetry input of a wave model. I came upon this discussion of grid registration: Registration of Structured Square-Cell Grids.

I read this material several times and I'm still confused about some things. From what I understand of the diagram on that page: the blue dots represent the data values. We know from the dataset what the latitude and longitude of each of the blue dots is. And for each blue dot, it is always in the center of the cell, which is the area it represents. If I'm right so far, what is the difference or significance of these two schemes? What is the purpose of the red lines? Why might there be an ambiguity, since we already know the locations of the blue dots and the data values at those locations? Does it affect how we interpret the data? 

If anyone can help me with this, or point me to relevant resources, it would be much appreciated.
Yes, it makes a difference. In this case the grid-registered dataset is higher fidelity. However, the cell-registered is easier to handle.

As you see, both types of data are available on the dataset's page. The page states:


  The grid-registered is the authoritative registration.


The page also points out:


  The cell-registered is derived from the grid-registered,
  and the conversion produces slightly flattened relief.


So what's the difference? The grid-registered version puts the data points at the grid corners (the red lines, not the grey squares, define the grid boundaries. You have to imagine the grid cells in the left-hand image). So if there are $n \times m$ grid cells, there are $(n+1) \times (m+1)$ data points in the grid-registered data.

Since there are fewer data points in the cell-registered version, making it involves some smoothing (averaging) of the values in the grid-registered version. There's an illustration of this effect on the other page you linked to; notice how the centre cell of value 90 ends up being smoothed away:



So if accuracy is paramount, you should use the grid-registered version.

But...

You might find cell-registered data more convenient to work with (for me at least it's more intuitively analogous to an image).

The catch is that if you have grid-registered but accidentally treat it as cell-registered, then the data will shift by half a cell. So you should keep careful track of what kind of data you have. As the NOAA page states:


  Most grid applications recognize both types and avoid [the grid shift]
  problem but care should be taken.


Indeed, one popular open source GIS tool, GRASS, apparently only handles cell-registered data, as explained in the GRASS wiki. So after loading (to wherever) you should check where the pixels of the raster actually end up.