Different models, different contours: are they comparable?

I will get contour lines of electromagnetic field strength around power lines. The contours will be calculated by different agencies using different models. We need to check whether the resulting zones (x meter from power line) around the power lines are similar between models/agencies. There is no 'gold standard' because it is not possible to actually measure the field strength on the ground. Furthermore, the zone is not simply a straight line because in some situations two power lines cross or approach each other and we are most interested in these deviating situations. Is there a way in GIS to compare the modelling results (polylines/contours) among each other?

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I have found a topic on averaging of polylines here: mathoverflow.net/questions/96415/polyline-averaging but am not able to find any practical implementations for polyline averaging in GIS. Any suggestions? – Oscar Breugelmans Sep 16 '13 at 15:17
Can you not request the original rasterized data from which the contour lines are extracted? If not, is there any assurance that the contour levels at least will be set to the same values in all the datasets? In any event, can you at least insist that the contours be given to you as polygons rather than polylines? (There is, in general, no unique way to impute the values from contours as polylines.) – whuber Sep 16 '13 at 17:01
We will get rasterized data as well, but that still leaves the question how to compare the model results. Any suggestions on finding the average of multiple rasters and finding the deviation between rasters? – Oscar Breugelmans Sep 20 '13 at 7:59
There are many good ways to compare rasters. Which one to use depends on your purpose. To give you a sense of why this is so important, contrast the following. (1) "Similar" means the two models agree on total power, even within local areas. You could integrate the absolute values of differences in squared raster values. (2) "Similar" means the models agree on where strength is below a regulatory threshold. You could measure the total area where one model exceeds and the other falls below that threshold. The results can be very different. What is your purpose? – whuber Sep 20 '13 at 15:43
Thanks @whuber. We are looking into the agreement of the models on the field strength below a regulatory threshold (your second option). I will start with some simulations to check whether we can construct an average (or median) raster based on the different model results. Then - as you suggest - I will look into ways to compare the areas where a model exceeds or falls below the average (or median). We also have to find some way to check whether a maximum absolute difference (in meters) between models is not exceeded. – Oscar Breugelmans Sep 23 '13 at 7:57

There are many ways. You could for example compare the ratios of the mutual area and the diffrence. Or you could check the Hausdorff distance of the polygons. Probably you should combine the two.

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A combination of Hausdorff distance and area ratios is useful, but gives me insight in 1 model against 1 other model only. I'm looking for a method to find something like the 'average' of all models and compare each model outcome to the average. – Oscar Breugelmans Sep 16 '13 at 14:14

I'm sure that smarter people that I will have better answers....

But an idea is to create raster surfaces from the contours, as this may afford easier comparisons between the different models, and the overlapping nature of the data.

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That's a good start: but please see gis.stackexchange.com/questions/61550/… for a cautionary note. The special circumstances here (namely, the possible availability of power line location data and the expectation that power falls with distance from the lines) might make this solution practicable. If so, the next part of the answer is to propose how the various rasters should be compared. – whuber Sep 16 '13 at 17:06
@whuber you were the entity I was alluding to when invoking persons smarter than I ;) – Stephen Lead Sep 17 '13 at 3:55
The contour lines are derived from raster surfaces, so I will have those available. Not sure whether the assumption that field strength will fall with distance from the line will be correct when power lines approach or cross each other, but that's something we have to check. If you can help me with a practical solution for comparing the rasters I will be most grateful. – Oscar Breugelmans Sep 17 '13 at 7:28