What unit is the distance in when using cKDTree?

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I am trying to calculate the distance between the closest points in two geodataframes.

I used the function created by jHUW here. The function is as follows:

def ckdnearest(gdA, gdB):
    nA = np.array(list(gdA.geometry.apply(lambda x: (x.x, x.y))))
    nB = np.array(list(gdB.geometry.apply(lambda x: (x.x, x.y))))
    btree = cKDTree(nB)
    dist, idx = btree.query(nA, k=1)
    gdB_nearest = gdB.iloc[idx].drop(columns="geometry").reset_index(drop=True)
    gdf = pd.concat(
        [
            gdA.reset_index(drop=True),
            gdB_nearest,
            pd.Series(dist, name='dist')
        ], 
        axis=1)

    return gdf

It's working fine between my datasets, but I was wondering what unit the returned distance is in. I did some research and found that the unit will be the same as the unit of the array used. I used an array of lat-lons, like so:


    array([[-122.3295182,   47.6202074],
           [-122.296276 ,   37.8789939],
           [-122.6857603,   45.5289172],
           [-118.3804073,   33.9017057],
           [ -93.2911788,   44.860997 ]])

I tried to find out what the units of lat-lons would be, but was unsuccessful. I also checked the distance between some of the point pairs on GoogleMaps to get some insight, but couldn't make sense of them. For instance, Googlemaps show a distance of 1.5 miles for my first pair, but the distance returned by the function is 0.0087466. I understand that ckDTree calculates the Euclidean distance but even then, the difference seems quite large. Please provide some insight if you have them.

scipy distance python
1 Answers

The result of Scipy is indeed a L2 norm (aka Euclidean distance). The meaning of this distance is dependent of the chosen coordinate system. In your case, you appear to use a geographic coordinate system (which is a spherical coordinate system). As a result, coordinates are are based on angles and cannot be linearly transformed to meters (for example in Antarctica changing the angle does not impact much the distance in meter). Additionally, one need to consider the distortion of the space while computing the distance: a straight line for use on earth is a geodesic in your geographic space. The L2 norm computed by Scipy does not consider this. In fact, using this metric probably results in wrong results: the L2 norm computed over-estimate the actual distance (of the geodesic, both in meter or radian) in Antarctica compared to the equator. This means two point near to the north pole can be considered as close as two points located each in Japan and Europe... Thus, you certainly need to use a better metric. As for the unit of the distance, it does nor make much sense mainly because of this issue. On relatively good metric would be the length of the geodesic (possibly in meters) or the angle between two point. Unfortunately, AFAIK this is not possible with Scipy... Using a GIS library (like GDAL) may help.

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