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Ever wonder how ArcMap calculates proportional symbol sizes? The key is that the area of the symbols is proportional to the data values; i.e., the size in points is proportional to the square root of the data values (see below for the special case of Flannery Appearance Compensation).
Here ya go! No more trial and error!
Normal case:
Pj = (Valj/ValMin)^0.5 * Pmin
Flannery Appearance Compensation case:
Pj = 1.0083 * (Valj/ValMin)^0.5716 * Pmin
Where:
Pj = point size of the j'th feature
Valj = value of the j'th feature
ValMin = minimum value
Pmin = minimum point size
^0.5 is to the power of 0.5 (square root)
^0.5716 is to the power of 0.5716
Based on these equations, you can also determine the minimum point size needed to standardize the symbol sizes for two layers that have different minimums for the symbolized field:
Normal case:
PminB = (VminB/VminA)^0.5 * PminA
Flannery Appearance Compensation case:
PminB = 1.0083 * (VminB/VminA)^0.5716 * PminA
Where:
PminB = minimum point size for layer B
VminB = minimum data value for layer B
VminA = minimum data value for layer A
PminA = minimum point size for layer A
For example, given layer A has a minimum pt size of 2 and a minimum value of 10; if layer B has a minimum value of 20 then the minimum point size for layer B should be:
Normal case: (20/10)^0.5 * 2 = 2.83
Flannery: 1.0083 * (20/10)^0.5716 * 2 = 3.0
With these minimum point sizes the values in layer A will be symbolized in the same proportion as those in layer B.
Hope this helps someone!
Tim
NOAA Fisheries
Silver Spring, MD
References:
Flannery J (1971). “The Relative Effectiveness of Some Common Graduated Point Symbols in the Presentation of Quantitative Data.” Canadian Cartographer, 8(2), 96–109.
Tanimura S (2006). “Proportional Symbol Mapping in R.” Journal of Statistical Software, 15(5), 1-5. http://www.jstatsoft.org/v15/i05/v15i05.pdf |