Pixel based Correlation for 2 Rasters

Question

I was working with Pollution data from OMI i.e. NO2 & O3.

I need to find the correlation between the two rasters.

I need pixel-based correlation, but in ArcGIS Pro, I could only find point-based correlation.

How do I do pixel-based correlation for the rasters?

Answer 1

Download and install latest QGIS with GRASS GIS. The tool is r.covar under the GRASS tools. It outputs the covariance/correlation matrix.

Answer 2

Please look at this post for some clarity on your problem and take note that, the way you are describing your analysis, the results would be nonsense. You cannot derive a correlation using two observations. However, you can use a moving window approach. I would also mention that, without evaluating the significance, a global correlation can be dubious. The rule of large numbers causes a distribution convergence in raster data and can easily cause spurious correlations. To support a global correlation between two rasters one should produce a p-value to indicate signifiance.

The Geomorphometry & Gradient Metrics toolbox has a correlation function that derives a moving window correlation raster. It should be compatible with ArcPro under Python 3 but, is not extensively tested and I am no longer supporting the toolbox. In theory, ESRI has take over maintenance so if you have any issues you can contact Shawn Walbridge at ESRI. You could also just grab the correlation.py file as it has everything you need to perform this analysis.

Here is the raster algebra, in ESRI parlance, to return a moving window correlation.

tmpXY = Times(rasterOne, rasterTwo)
  xBar = FocalStatistics(rasterOne, analysisWindow, "MEAN")
    yBar = FocalStatistics(rasterTwo, analysisWindow, "MEAN")
      xyBar = FocalStatistics(tmpXY, analysisWindow, "MEAN")
        coVar = Minus(xyBar, Times(xBar, yBar))
      xStd = FocalStatistics(rasterOne, analysisWindow, "STD")
    yStd = FocalStatistics(rasterTwo, analysisWindow, "STD")
  xyStd = Times(xStd, yStd)
corr = Divide(coVar, xyStd)