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I have downloaded the UK Ordinance Survey's 1km grids in shapefile format for ArcMap.

If you need to download them to have a look first you can find them here look for link in the first Answer to the Question Ordnance Survey grids - download or generate?.

They 'supposedly' represent 1km grids however here is where the first problem begins. If I calculate their dimensions and areas in ArcMap their size differ from one another. How is this possible are they not supposed to be regularly spaced every 1km?

The second problem I encounter is - of course as a result of the first problem - that if I try to divide the areas into smaller sections they grid would now shift slightly to one side.

Can you please advise if there is a way to solve this problem and/or if you get the same results?

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2 Answers 2

After calculating areas of the 1km grid shapefile rectangles, I can confirm that the single cells are not precisely 1km². The error is small, though. If your errors are larger, it is possible that your problem is related to a different issue (possible reprojection errors).

Small errors in the source dataset

Most of the calculated areas are less than 10m² off. (Mean value is 1km², standard deviation is 7m²; there are some outliers (corresponding to E-W-oriented lines in the far north): 210 out of 286000 rectangles have errors >100m², the largest errors being about 130m².)

Given the fact that on a 1km² rectangle, a 1mm increase in width propagates to a 1m² area increase, I am not sure if these shapefiles were designed to have a sub-meter precision. I have checked the coordinates of one of the most inaccurate grid cells: x error was 2 mm, y error 134 mm.

The error seems to be systematical, maybe due to inaccuracies during the initial generation of the grid coordinates: (See detail picture, blue/green shows "too small" areas, orange/red shows "too large" ones)

1km BNG shapefile, showing calculated area for each grid cell. Colors highlight errors from ideal 1km² area

Although the error is pretty small, it seems unnecessary as grid cells are precisely defined. If you need more precise grid cells, either re-create them (inherit the naming scheme from the provided shapefile), or alter the coordinates of the individual shapes by rounding to the closest integer number. (This works because all errors are smaller than 0.5m, and linear unit is meter as the coordinates are given in OSGB 1936 projected coordinate system.) In fact, all Northing / Easting coordinates of the OSGB 1km grid should be multiples of 1000.)

However, with the grid lines being misaligned by a maximum of 13cm (less then 1cm for most grid lines), I would consider this a rather minor issue, which can most likely be neglected for many scenarios.

Possible coordinate transformation issue

Note that the British national grid uses the OSGB 1936 datum. This is based on the Airy 1860 ellipsoid. (See the OSNG wikipedia article for an overview information about datum shifts.)

In general, no transformation is without error, especially in the sub-meter scale. Do not perform transformations if you do not have to use them; for best precision, stay in original OSGB36 as long as possible and reproject in a final step, after calculations.

For reference, I projected the shapefile to PCS UTM30N (WGS84) and calculated areas afterwards. The error was much higher, most cells were about 140m² off from 1km².
Calculating areas after projection to GCS WGS84 produced an even larger error (approx. 650m² for most cells)

If you for some reason cannot use the original coordinate system for your project, eventually based on a different ellipsoid (e.g. UTM 30N with WGS84ellipsoid), check if coordinate transformations have been applied correctly.

For on-the-fly transformation, go to "Layer Properties" -> "coordinate system" -> "Transformations..." . Choose "GCS_OSGB_1936" in the "Convert from" box. The "Into" field should be your destination projection (e.g. GCS_WGS_84). Select one of the methods. (There is an overview article about transformations at ESRI blogs, the knowledge base article #21327 for a detailed list of transformations, and also a GIS.SE question that deals with transformations and OSGB).
For a permanent transformation of the shapefile, use "Arc Toolbox" -> "Data management Tools" -> "Projections and Transformations" -> "Feature" -> "Project".

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lavarider - thanks very much for checking. The problem I have at the moment is that I need to use/create a grid (100m - 200m - 1000m etc) over parts of the UK which will be extremely accurate and where all grids will be integers. Ultimately I will be requiring the data in lat/lon format using the WGS_1984 projection however most of the data I have to start with is in BNG. What is your advice in this case. I need to make sure that the data can be transformed from BNG to WGS_1984 back and forth multiple times without losing precision. Is this something possible or errors will always be produced? –  user26450 Feb 2 at 15:06
    
If the cited shapefile is too defective for your case, you could create your own. But maybe it is an option to do your task without a specific, heavy-weight "grid shapefile", but calculate your custom grid coordinates directly from OSGB Northing and Easting coordinates? Do you really need a shapefile? - For precision issues (and loss) of back and forth-transformation I suggest you could ask a new question, providing more details about the specific workflow. –  lavarider Feb 2 at 18:11
    
Hi, new question created –  user26450 Feb 2 at 18:50
    
Hi lavarider, I have tried to open a new question as you have suggested but unfortunately has been flagged as 'duplicate' which is not at all. Could you please have a look at my question? Many thanks –  user26450 Feb 2 at 22:21
    
Please refer to the high-quality comments in cffk's answer, which are dealing with the projection issues in more detail (especially: try to stay on Airy ellipsoid). I was able to contribute to the initial shp-accuracy question - to the detailed difficulties of projection issues, with the precision you seem to look for, my contributions will probably stay minor. However, try to ask well written questions - in particular, it would be helpful if you are more clear about a well defined level of precision that you require. –  lavarider Feb 3 at 9:51

Let's stick with the UK ellipsoid + datum (to avoid datum transformation issues). You will inevitably have the "problem" is that the Ordnance Survey grids are defined on the OS projection which is a transverse Mercator projection with central longitude 2°W and central scale 0.9996012717. The scale variation over Britain is roughly 0.9996 to 1.0002 (more in the Hebrides). On the central meridian a "1km x 1km" grid is actually 1000.4m x 1000.4m (on the Airy ellipsoid) and so its area is about 800 m2 more than 1 km2.

The normal way to deal with this discrepancy is to do all your analysis in the OSGB coordinate system (essentially converting the ellipsoid to a plane). However, you always need to be aware that the actual distances and areas will need to be adjusted according to the local scale.

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The main issue that I have here is that the grids will have to be regular in WGS_1984. If I want to avoid discrepancies with regards to a grid created using WGS_1984, but some of the data is projected and gridded using BNG, how can I go about and do this? Let me know if this is not clear and I'll explain differently. –  user26450 Feb 2 at 17:52
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You could transform the data to WGS84 (carefully!). However, I think you are assuming that 1km x 1km grids for the national grid must measure exactly 1km by 1km. They don't (see my answer) and they can't (because you can't flatten the earth onto a plane -- which is what the national grid does -- without distorting lengths). –  cffk Feb 2 at 17:58
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Your goal -- a grid of (200m)^2 squares on WGS84 -- is an impossible one. You can't put such a grid on the WGS84 ellipsoid without some distortion. So you'll need to modify your goal before I can offer any meaningful help. –  cffk Feb 2 at 19:12
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I still don't understand what you're up to. Your statement that only Lambert conformal can be used at mid-latitudes is false. The UK (and much of the US and Europe) uses transverse Mercator. I still think it's a mistake to transform the UK coordinates to WGS84, if you can avoid doing so. You say that they "have to be in WGS84", but I wonder what this is based on. What's the matter with just transforming the UK 1km (or 200m) grid to lat/long on the Airy ellipsoid. This transformation is accurately reversible (round trip error is around 10^-8 m). –  cffk Feb 3 at 1:05
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There's a variant of Mercator called "transverse Mercator". It may be the most commonly used conformal projection for large scale mapping. Look it up in Wikipedia. It's well suited for any area with an E-W extent of 1000km or less (for example the British Isles). (Larger areas are dealt with by dividing them into N-S strips.) –  cffk Feb 3 at 12:10

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