[R-sig-Geo] IDW + irregular blocks: Different results for different approaches ?

[Mauricio Zambrano]

Dear list,

Trying to find out a solution for obtaining the mean of interpolated
values within several polygons I found 2 ways for solving it, but the
results are slightly different:

Using the meuse dataset and a gstat example:

r1 = cbind(c(180114, 180553, 181127, 181477, 181294, 181007, 180409,
180162, 180114), c(332349, 332057, 332342, 333250, 333558, 333676,
332618, 332413, 332349))
r2 = cbind(c(180042, 180545, 180553, 180314, 179955, 179142, 179437,
179524, 179979, 180042), c(332373, 332026, 331426, 330889, 330683,
331133, 331623, 332152, 332357, 332373))
r3 = cbind(c(179110, 179907, 180433, 180712, 180752, 180329, 179875,
179668, 179572, 179269, 178879, 178600, 178544, 179046, 179110),
c(331086, 330620, 330494, 330265, 330075, 330233, 330336, 330004,
329783, 329665, 329720, 329933, 330478, 331062, 331086))

sr1=Polygons(list(Polygon(r1)),"r1")
sr2=Polygons(list(Polygon(r2)),"r2")
sr3=Polygons(list(Polygon(r3)),"r3")
sr=SpatialPolygons(list(sr1,sr2,sr3))
srdf=SpatialPolygonsDataFrame(sr, data.frame(cbind(1:3,5:3),
row.names=c("r1","r2","r3")))

data(meuse)
coordinates(meuse) = ~x+y
data(meuse.grid)
coordinates(meuse.grid) = ~x+y
gridded(meuse.grid) = TRUE


# 1st Approach: Interpolating with IDW using the 'mueuse.grid' as
'newdata' and then 'overlay'

x.idw <- krige(log(zinc)~1, locations=meuse, newdata=meuse.grid)
# Getting the mean values in each polygon
overlay(x.idw["var1.pred"], srdf, fn = mean)

# var1.pred
#X1    5.8697
#X2    5.6525
#X3    5.8536

# 2nd Approach: Interpolating with IDW using the 3 polygons as 'newdata'

x.idw.block <- krige(log(zinc)~1, locations=meuse, newdata=srdf )
# Getting the mean values in each polygon
x.idw.block["var1.pred"]@data

#var1.pred
#r1    5.9090
#r2    5.6700
#r3    5.8564


I would really appreciate if you can give some hint about why the
results are different for each polygon.

Thanks in advance,

Mauricio

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