[R-sig-Geo] Non-symmetric variogram map in gstat

[David Rossiter]

I've found a quite puzzling behaviour in gstat's variogram method, with
the map=T argument. I believe the result should be a symmetric map
because all the semivariances are squared differences. This is indeed
the case if I try an example from the Meuse set:

> library(gstat)
> data(meuse)
> coordinates(meuse) <- ~x + y
> class(meuse)
[1] "SpatialPointsDataFrame"
attr(,"package")
[1] "sp"
> v <- variogram(log(lead) ~ 1, meuse, cutoff=1000, width=200, map=T)
> plot(v)
> # symmetric plot as expected, confirm by looking at array
> v$map at data$var1
  [1] 0.241586 0.875118 1.329685 0.978228 0.877734 0.854946 0.628017
0.356488  0.323171 0.299103 0.389137
...
[111] 0.387982 0.302654 0.319343 0.356488 0.630622 0.862242 0.877734
0.978228  1.329685 0.875118 0.241586
> # and the number of pairs:
> v$map at data$np.var1
  [1]   2  10  13  36  44  63  86 137 141 122 123   3   7  26  53  60
92 123  150 156 123  87   4  12  41  61
 ...
[105]  92  61  53  26   7   3 122 122 143 137  87  64  44  36  13  10
2

BUT ... when I try with the Jura dataset I get non-symmetric results:

> data(jura)
> coordinates(jura.pred) <- ~Xloc + Yloc
> class(jura.pred)
[1] "SpatialPointsDataFrame"
attr(,"package")
[1] "sp"
> v <- variogram(Ni ~ 1, jura.pred, cutoff=1.2, width=0.18, map=T)
> plot(v)
# not symmetric! Confirm with array:
> v$map at data$var1
  [1]  89.5503  59.3319  88.4276  79.4282  75.1518 147.6931  55.4805
43.6888   70.5159  86.9107  59.5392
...
[188] 105.4008  48.2219  72.3849  35.7244  66.7842  62.4743  72.9742
72.6469   70.9808
> # and the number of pairs
> v$map at data$np.var1
  [1]  42  78  54  97 124  39 159  82  92  62  79  70  93  68 114  78
177  86   92  72  59  82 192  95 192  79
...
[183]  73 135  72  72  97 101  76 137  39 111 105 132  94  31

Clearly both the number of pairs and the resulting average semivariance
are not symmetric!

Both of the objects are converted to SpatialPointsDataFrames. I can see
no obvious reason for this discrepency.

D G Rossiter
Senior University Lecturer
Department of Earth Systems Analysis (DESA)
International Institute for Geo-Information Science and Earth
Observation (ITC)
mailto:rossiter at itc.nl,  Internet: http://www.itc.nl/personal/rossiter