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> # DOI 10.1007/s11004-011-9344-7
> # http://mypage.iu.edu/~srobeson/Pubs/variogram_sphere_mathgeo_2011.pdf
> 
> suppressPackageStartupMessages(library(sp))
> library(gstat)
> 
> if (require(sp, quietly = TRUE) && 
+ 	suppressPackageStartupMessages(require(fields, quietly = TRUE)) && 
+ 	suppressPackageStartupMessages(require(sf, quietly = TRUE))) {
+ data(meuse)
+ coordinates(meuse) = ~x+y
+ proj4string(meuse) = CRS("+init=epsg:28992")
+ ll = "+proj=longlat +ellps=WGS84"
+ # meuse.ll = spTransform(meuse, CRS("+proj=longlat +ellps=WGS84"))
+ meuse.ll = as(st_transform(sf::st_as_sf(meuse), sf::st_crs(ll)), "Spatial")
+ meuse.ll[1:10,]
+ variogram(log(zinc)~1, meuse.ll)
+ 
+ cloud1 = variogram(log(zinc)~1, meuse, cloud=T, cutoff=6000)
+ cloud2 = variogram(log(zinc)~1, meuse.ll, cloud=T, cutoff=6)
+ 
+ plot(cloud1$dist/1000, cloud2$dist, xlab="Amersfoort, km", ylab = "Long/lat")
+ abline(0,1)
+ 
+   data(ozone2)
+   oz = SpatialPointsDataFrame(ozone2$lon.lat, 
+ 		  data.frame(t(ozone2$y)), 
+ 		  proj4string=CRS("+proj=longlat +ellps=WGS84"))
+   variogram(X870731~1,oz[!is.na(oz$X870731),])
+   utm16 = "+proj=utm +zone=16"
+   # oz.utm = spTransform(oz, utm16)
+   oz.utm = as(sf::st_transform(sf::st_as_sf(oz), utm16) , "Spatial")
+   variogram(X870731~1,oz.utm[!is.na(oz$X870731),])
+ 
+ # Timothy Hilton, r-sig-geo, Sept 14, 2008:
+ 
+ foo <-
+ structure(list(z = c(-1.95824831109744, -1.9158901643563, 4.22211761150161,
+ 3.23356929459598, 1.12038389231868, 0.34613850821113, 1.12589932643631,
+ 23.517912251617, 3.0519158690268, 3.20261431141517, -2.10947106854739
+ ), lon = c(-125.29228, -82.1556, -98.524722, -99.948333, -104.691741,
+ -79.420833, -105.100533, -88.291867, -72.171478, -121.556944,
+ -89.34765), lat = c(49.87217, 48.2167, 55.905833, 56.635833,
+ 53.916264, 39.063333, 48.307883, 40.0061, 42.537756, 44.448889,
+ 46.242017)), .Names = c("z", "lon", "lat"), row.names = c(NA,
+ -11L), class = "data.frame")
+ 
+ coordinates(foo) <- ~lon+lat
+ 
+ proj4string(foo) <- CRS('+proj=longlat +ellps=WGS84')
+ 
+ vg.foo <- variogram(z~1, foo, cloud=TRUE, cutoff=1e10)
+ 
+ cat('==========\nvariogram:\n')
+ print(head(vg.foo))
+ 
+ cat('==========\nspDistsN1 Distances:\n')
+ print(spDistsN1(coordinates(foo), coordinates(foo)[1,], longlat=TRUE))
+ }
==========
variogram:
       dist        gamma dir.hor dir.ver   id left right
1 3115.1190 8.971063e-04       0       0 var1    2     1
2 1908.0468 1.909846e+01       0       0 var1    3     1
3 1405.6211 1.883757e+01       0       0 var1    3     2
4 1837.5667 1.347749e+01       0       0 var1    4     1
5 1522.8765 1.325847e+01       0       0 var1    4     2
6  119.9386 4.886139e-01       0       0 var1    4     3
==========
spDistsN1 Distances:
 [1]    0.0000 3115.1190 1908.0468 1837.5667 1481.6293 3775.6751 1480.4477
 [8] 3081.7541 4090.4022  665.9348 2683.1516
Warning message:
In CPL_crs_from_input(x) :
  GDAL Message 1: +init=epsg:XXXX syntax is deprecated. It might return a CRS with a non-EPSG compliant axis order.
> 
> proc.time()
   user  system elapsed 
   2.64    0.45    3.06