I am trying to get population densities for world metropolitan areas (e.g., # of residents per square kilometer or square mile) and if possible comparison figures for previously points in time (e.g., the latest available estimate versus 1 year ago, 5 years ago, etc.).  Can I use the GRUMP data ?

The population densities for the GRUMP urban extents could work.  However,  please note that the GRUMP urban extents represent contiguous built up areas and so in many places multiple cities are combined into one large urban are, for example, New York and Philadelphia are part of the same urban extent. Also, for the changes in density over time, we only have one estimate of spatial extent, so comparing densities between years is not recommended as it would assume no spatial growth, only population growth.

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