Let's say I have 4 raster layers with the same extend with data of 4 different years: 2006,2008,2010 and 2012:
library(raster)
r2006<-raster(ncol=3, nrow=3)
values(r2006)<-1:9
r2008<-raster(ncol=3, nrow=3)
values(r2008)<-3:11
r2010<-raster(ncol=3, nrow=3)
values(r2010)<-5:13
r2012<-raster(ncol=3, nrow=3)
values(r2012)<-7:15
Now I want to create raster layers for every year between 2006 and 2013 (or even longer) by inter-/extrapolating (a linear method should be a good start) the values of the 4 raster layers. The result should look like this:
r2006<-raster(ncol=3, nrow=3)
values(r2006)<-1:9
r2007<-raster(ncol=3, nrow=3)
values(r2007)<-2:10
r2008<-raster(ncol=3, nrow=3)
values(r2008)<-3:11
r2009<-raster(ncol=3, nrow=3)
values(r2009)<-4:12
r2010<-raster(ncol=3, nrow=3)
values(r2010)<-5:13
r2011<-raster(ncol=3, nrow=3)
values(r2011)<-6:14
r2012<-raster(ncol=3, nrow=3)
values(r2012)<-7:15
r2013<-raster(ncol=3, nrow=3)
values(r2013)<-8:16
Using lm() or approxExtrap don't seem to help a lot.
One way to do this is to separate your problem into two parts: 1. First, perform the numerical interpolation on the raster values, 2. and apply the interpolated values to the appropriate intermediate raster layers.
Idea: Build a data frame of the values() of the raster layers, time index that data frame, and then apply Linear Interpolation to those numbers. For linear interpolation I use approxTime from the simecol package.
For your example above,
library(raster)
library(simecol)
df <- data.frame("2006" = 1:9, "2008" = 3:11, "2010" = 5:13, "2012"=7:15)
#transpose since we want time to be the first col, and the values to be columns
new <- data.frame(t(df))
times <- seq(2006, 2012, by=2)
new <- cbind(times, new)
# Now, apply Linear Interpolate for each layer of the raster
approxTime(new, 2006:2012, rule = 2)
This gives:
# times X1 X2 X3 X4 X5 X6 X7 X8 X9
#1 2006 1 2 3 4 5 6 7 8 9
#2 2007 2 3 4 5 6 7 8 9 10
#3 2008 3 4 5 6 7 8 9 10 11
#4 2009 4 5 6 7 8 9 10 11 12
#5 2010 5 6 7 8 9 10 11 12 13
#6 2011 6 7 8 9 10 11 12 13 14
#7 2012 7 8 9 10 11 12 13 14 15
You can then store this, and take each row and apply to the values of that year's raster object.
Note: approxTime does not do linear extrapolation. It simply takes the closest value, so you need to account for that.