# What's the best projection for rasterization of random latitude and longitude data in the northern Atlantic?

I have a dataset in the WGS84 geographic coordinate system that I would like to interpolate along a grid using Python.

It appears `gdal_grid` is not available through the Python bindings, so I plan to use another 2D interpolation method after rasterizing the data.

To rasterize the data, I plan to re-project it using pyproj, then write it to a raster using the gdal python bindings. The UTM projection coordinate system seems like it would be the best projection, but my data spans the North Atlantic (i.e. multiple UTM zones).

Update:
I'm open to suggestion on the interpolation method, but I had planned to use an inverse distance interpolation (as shown here). These are presence absence sightings data from ship cruise tracks, which do not necessarily follow lines of latitude. They span from latitudes in the mid 70's to mid 50's. Thanks!

## What projection would be best to use?

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The answer might depend on the nature of the data and the interpolation method you choose. For instance, if your data follow correlation patterns that track along lines of latitude and you want to krige the data, you would likely favor a projection in which those lines of latitude are roughly straight and parallel, even though there might be a lot of distortion. Could you share some relevant information about the data and how you plan to interpolate them? – whuber Feb 12 '13 at 17:55
requested information added to post. Thanks! – ryanjdillon Feb 13 '13 at 9:25

## 2 Answers

Sightings constitute a (non-random) sample of some process or population. Accordingly, interpolation (especially) IDW is not a good idea: it solves a different problem altogether.

Consider making a density map. When doing so, it's probably better to favor equal-area projections over conformal projections (because changes of area bias the density, whereas non-conformality does not, even though it might change the qualitative appearance of the map).

There are many equal-area projections of the world. (Unfortunately, popular projections, including Mercator, Transverse Mercator, and Stereographic, are not among them.) Most of them are cylindrical. This is nice in one way--lines of latitude and longitude form an orthogonal grid on the map--but it's bad near the poles, because the scale distortion is all focused in one (vertical) direction where it can become extreme.

These considerations suggest a compromise: just about any projection suitable for a largish area (like a large country), when shifted to the center of the North Atlantic, would likely do a good job, simply because its overall relative distortion should be limited. For instance, the Albers equal-area conic projection is popular for the conterminous US. Changing its central meridian to -30 degrees, its reference parallel to 55 degrees north, and its standard parallels to 45 and 65 degrees, re-points it at the North Atlantic:

The Tissot indicatrices show how little distortion actually occurs within this region: scale errors are less than 1.5% in any direction throughout; that's much more accuracy than needed for interpolation or kernel density estimates.

In contrast--to see what really has been accomplished by this choice compared to others that might suggest themselves--consider the Mercator projection:

The huge discrepancies between the inner and outer circles of the Tissot indicatrices testify to the large changes in scale from south to north in this map. In effect, any interpolation or density calculation based on these map coordinates would use neighborhoods near the top that are approximately half the size of the neighborhoods near the bottom (in reality, not on the map). That's appreciable distortion; there's no sense introducing it into the calculations when it's simple enough to choose a better projection.

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This is excellent. Thanks whuber. I now realize I should have rather said that I am attempting to interpolate the sighting effort data, which I think maybe should be handled differently - kind of like a catch per unit effort (CPUE) value. The plan is to ultimately make ESRI ACII grid files of my environmental covarients and sighting (i.e. presence) data to run in the MaxEnt model. I hope to use the effort in determining my study area (what data to include for the model). – ryanjdillon Feb 13 '13 at 15:50
Yes, it does make sense to interpolate catch per unit effort data: they can be considered samples of a theoretical "harvestability" function. I suspect IDW will do a terrible job. One reason is that you do not want an interpolator that strictly "honors" the data, because there must be considerable measurement error. (If you return to the same location after some time, it's unlikely you'll get the same catch per unit effort there.) Some statistical smoothing method would likely be better for your purposes. – whuber Feb 13 '13 at 17:14
Just saw that I didn't select an answer, my apologies. As for your last comment whuber, would you suggest any particular statistical method(s) for interpolation? – ryanjdillon Feb 28 '13 at 11:09
GDAL's grid_data offers only inverse distance to a power, moving average, and the nearest neighbor algorithms. – ryanjdillon Feb 28 '13 at 11:21

Google Mercator (EPSG:3857) should be the best solution. It covers the whole world up to 85° North/south.

So if your data is not near the arctic, it should work.

And you can use Openlayers plugin for a background map, if you want to vizualize the data in QGIS.

But keep in mind that lengths are not real metres.

EDIT

If you don't like that, you can try lambert conformal conical. EPSG:3034 is defined for pan-european mapping. Parallels are 35° and 65° North; giving you this map layout:

You might change lon_0 from 10° East to something more western if you don't like the perspective.

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For many purposes this has to be one of the worst possible choices in a region close to a pole, because that is where the distortions in Mercator become arbitrarily large. With caution it might be applicable to an extended part of the North Atlantic, but before recommending such a solution we should ascertain whether the planned interpolation is robust to such distortions. – whuber Feb 12 '13 at 17:53