Dear all,
I have two datasets, each covering single raster images from monthly gridded environmental data over a period of 20 years. Now, I would like to compute Pearson's correlation between the two raster datasets using QGIS or R. Any idea?
Looking forward to the discussion!
Best wishes
Michael
There is no problem, if the bidimensional data sets have corresponding cells (discrete values) the condition is identical to that of a two monodimensional ordered vectors that is the usual case for Pearson r. It is sufficient you put in a line the cells acoording to their coordinates (Position), I will insert the corresponding values of the two rasters as Image1 and Image2 with fictitious values:
Position Image1 Image2
(1,2) 2.4 3.1
(1,3) 2.5 2.9
(1,4) 3.4 4.1
............
(n,n) 3.7 5.3
Then you will compute Pearson r between Image1 and Image2 values
Dear Michael
You could make a systematic point dataset, and extract the values from each raster into separate columns. If rasters are not that big then you could calculate the correlation coefficient between the separate rasters in MsExcel (=PEARSON(array1; array2)). In case you have large raster datasets then it is better to do it in MsAccess.
In Ms Access (No NULL values are allowed):
Create Table MyData and several colums (y2001, y2002, y2003 etc.). Then create new query (SQL view) for year 2001-2002, paste the following code and run it.
SELECT Count(*) AS N, Sum([y2001]) AS SumOfX, Sum([y2002]) AS SumOfY, Sum([y2001]^2) AS SumOfX2, Sum([y2002]^2) AS SumOfY2, Sum([y2001]*[y2002]) AS SumOfXY, [SumOfX2]-([SumOfX])^2/[N] AS SXX, [SumOfY2]-[SumOfY]^2/[N] AS SYY, [SumOfXY]-[SumOfX]*[SumOfY]/[N] AS SXY, [SXY]/Sqr([SXX]*[SYY]) AS CORREL
FROM MyData;
The answer (r) is provided in the column CORREL. You have to run it multiple times for every pair of years (2002-2003, 2003-2004 etc.) in order to get annual correlation indexes. In case you want to do it on monthly basis, you have to tune the query accordingly.
It would be faster to do it within ArcGIS:
https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-analyst/how-band-collection-statistics-works.htm
Another tool for ArcGIS:
http://www.sdmtoolbox.org/technical-info#Uni4b
I hope it helps.
Caro Alessandro, dear Andrius,
many thanks for your answers! the first seems to be more difficult to understand (at least for me!) and the second includes Microsoft software and ArcGIS. I am basically working with R and QGIS, so my approach so far was:
1) creating raster datasets from netcdf files or hdf using the reproject/warp tool from the toolbox
2) create random point dataset, which covers my case study area
3) using the point sampling tool plugin from QGIS to extract the values from the raster
4) calculating the meanvalue for each month (in this case: 228 month from 2000 - 2018)
5) plot them using R and the packages library(ggplot2); library(reshape2) and this code:
library(plotly)
library(ggplot2)
library(reshape2)
##read the csv with MW = meanvalue of each month from 1000 random points
s
Dear Michael, the important issue is that you forget or the non-essential and ancillary aspects and go the the heart of each problem. If you want to compute a correlation (any kind of correlation) between two X and y variables, you need to have some statistical units (in your case cells of the map) each one described by their respective X and Y values.
If this is the case, you can put down your information as a file having three variables:
1. an ID variable uniquely identifying each stattistical unit
2. X value correspondent to each unit
3. Y value correspondent to each unit
At this point you can calculate Pearson r with the usual formula:
r = covariance(x,y) /( sqrt(variance (x) )*( sqrt (variance (y))
That's all, you can make the computations with the software you prefer but this is the bare fact and it is independent of any software (think of the fact Pearson correlation was developed at the end of XIX century many decades before the first computer appeared)
Dear Alessandro,
many thanks for your quick response! I will prepare my data according to your instructions and then try to perform the test in R. As soon as I got the first results (or issues...) I will upload them here to this discussion.
Best wishes
Michael
Dear Alessandro, dear all,
I extracted my monthly data now and performed a Pearson correlation test with this code:
###library("ggpubr")
ggscatter(data, x = "Data1", y = "P", add = "reg.line", conf.int = TRUE, col="black", cor.coef = TRUE, cor.method = "pearson", xlab = "Data1", ylab = "Precipitation")
which tests precipitation against a second variable (here called Data1).
I attach the plot and it looks like there is strong correlation between both.
The colums I used were monthly mean values (1000 random points) over the period 2000-2018.
I will now try to perform this with single values from each month for each of the 1000 points or directly from the cells of the raster (after resampling to the same grid size).
Cheers!
Michael
Dear Michael Kempf
I have different raster which include geographic variables (Dem, slope, Aspect, Hillshade, Curvature, surface roughness, and topographic wetnees index ), also i have meteorological variables (relative humidity and wind speed) , so I need to generate linear equation with Bias correction and meteorological and geographic variables in R, could you help me to fixed it
Dear all,
Ihave asked this question a couple of months ago and I would like to share the development with you to enable other scientists to follow up. Here is what I have done so far to perform correlation between raster time series data:
I used some packages
library(raster)
library(ncdf4)
library(sp)
library(rgdal)
library(st)
library(sf)
library(maptools)
library(gtools)
#create a raster stack from a set of rasters, e.g. tif files. Watch out that they are #in the correct order
dd = list.files(pattern='.tif')
dd
I suggest you t use crossrecurrence (CRQA) after having linearized the two matrixes according to i,j coordinates so that each i,j distinct couple has an Y1 value for iamge 1 and an Y2 value for image 2. The use of CRQA solves the problem of exact phase see:
https://www.frontiersin.org/articles/10.3389/fpsyg.2014.00510/full
Article Multidimensional Cross-Recurrence Quantification Analysis (M...
Article Cross Recurrence Plot Based Synchronization of Time Series
https://www.sciencedirect.com/science/article/abs/pii/S0370157306004066
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