I am trying to calculate population-weighted exposure level (PWEL) of particulate matter. I have raster layer of both particulate matter and population. The equation to calculate PWEL is:

equation to calculate PWEL

Pi is population in grid i and Ci is average particulate matter concentration. I have tried raster calculator but it is giving me PWEL = Ci.

Do you have any suggestions?

  • 1
    What formula are you using in raster calculator?
    – Bera
    Commented Oct 11, 2021 at 5:21
  • I cannot do the summation, so I use (Pi x Ci)/Pi. Mathematically Pi is canceling with the denominator. Commented Oct 11, 2021 at 6:52
  • 1
    Cell-wise it has to drop out. The formula makes sense only if it aggregates over a number of cells. Sum up \Sigma{Pi} separately over each aggregation into a population for that aggregation, and divide the \sigma{CiPi} for each aggregation by the aggregation's total population. Maybe think of it as PWEL_j = \Sigma{CiPi}/Pj
    – Dave X
    Commented Oct 12, 2021 at 2:09
  • Thank you for the answer Dave X. Could you please elaborate the answer, I couldn't get it? Commented Oct 12, 2021 at 6:33
  • If you have 30 cells 'i' in county 'k' then you add up the 30 Ci*Pi and divide by the population in county 'k' = sum(Pi) to get a PWEL for county 'k'.
    – Dave X
    Commented Oct 12, 2021 at 12:05

1 Answer 1


Thank you @Dave X for the suggestions. I haven't slept over this problem and based on your suggestion I found the solution. What I did is I convert the PM10 and Population data into vector (point). Then I match PM10 value closer to the population count. Finally, I perform the calculation over the district shapefile.

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