I want to measure biomass on a coastal mudflat. I can only access points inside the polygon. Are there any methods available that would allow me to estimate values of the points outside of the polygon, based on the values of points inside the polygon?

x <- rnorm(50, -1.841, 0.01)
y <- rnorm(50, 55.663, 0.01)
xy <- data.frame(x,y, values=rnorm(50))
coordinates(xy) <- c("x", "y")
proj4string(xy) <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84")

makePolygons <- function(coordsx, coordsy){

  coords <- matrix(c(c(coordsx, coordsy)), ncol=2)
  p <- Polygon(coords)
  p <- Polygons(list(p), ID = "p")
  myPoly <- SpatialPolygons(list(p))
  spdf = SpatialPolygonsDataFrame(myPoly, data.frame(variable1 = c(2),
                                                     variable2 = c(3), row.names = c("p")))
  proj4string(spdf) <- CRS("+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0")

  print("polygon is in longlat!!!")



myPoly <- makePolygons(coordsx=c(-1.841960, -1.843464, -1.888623, -1.841960), 
                      coordsy=c(55.633696, 55.68178, 55.63841, 55.633696))

plot(myPoly, add=T)

enter image description here

  • Vegetation is on mudflats in an intertidal zone - some areas are too dangerous to get to. Vegetation biomass is a predictor variable
    – luciano
    Commented Jun 13, 2013 at 14:02
  • 9
    You have a significant problem, because it is very likely that inaccessibility and biomass are related. That makes it invalid to extrapolate data obtained from accessible places to all places. For a valid approach, you must find some way--even if only a surrogate way--to measure some representative part of the inaccessible areas. Kriging (and most other contouring procedures) will paper over the problem beautifully and the software will happily give you highly detailed, incredibly wrong results.
    – whuber
    Commented Jun 13, 2013 at 15:18
  • 2
    My approach would be to relate ground-based biomass estimates to NDVI values, perhaps based off Landsat data. Use regression to predict biomass from NDVI within the danger zones.
    – Aaron
    Commented Jun 13, 2013 at 15:37
  • @whuber although areas within red polygons are accessible, they are never used by people.
    – luciano
    Commented Jun 14, 2013 at 5:23
  • 1
    What does that matter? How does that change the nature of your study or the sampling procedure?
    – whuber
    Commented Jun 14, 2013 at 12:15

1 Answer 1


My best guess is to transform the polygons into a point grid and estimate the value in each point that isn't overlapping the points containing data. There's a pretty neat tutorial on this here.

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