R gstat krige() - Covariance matrix singular at location [5.88,47.4,0]: skipping

Question

When I want to perform the kriging it only works sometimes, depending on what values I use in my datatable. As a result of the krige function I get for var1.pred: NA NA NA ... and var1.var: NA NA NA ... (but only when I use the "wrong" values in my datatable.)

For example:

• it works always (so far) when I only use 10 values
• it works when I use 50 values, but only with certain ones
• it works not when I use 50 values and the "wrong" values
• it works when I use 25 values and the before mentioned "wrong" values

I don't get it why it's sometimes working and sometimes not. The strange thing is that when I add Zwiesel;49.02999878;13.22999954;2.2 to the datatable it works when I use less then ~20 values, but it doesn't work when I use more then 50 values ...

Where is my mistake?

myWeatherTable.csv:

Place;Latitude;Longitude;Temperature
Aachen;50.77999878;6.09999990;3
Abbikenhausen;53.52999878;8.00000000;7.9
Adelbach;49.04000092;9.76000023;3.1
Adendorf;51.61999893;11.69999981;1.9
Alberzell;48.45999908;11.34000015;4.6
...
...

My code to perform kriging interpolation

WeatherData <- read.csv(file="myWeatherTable", header = TRUE, sep ";")

coordinates(WeatherData) = ~Longitude + Latitude

vario <-  variogram(log(Temperature) ~1, WeatherData)
vario.fit <- fit.variogram(vario, vgm("Sph"))

min_lon <- min(WeatherData$Longitude)
max_lon <- max(WeatherData$Longitude)
min_lat <- min(WeatherData$Latitude)
max_lat <- max(WeatherData$Latitude)
Longitude.range <- as.numeric(c(min_lon,max_lon))
Latitude.range <- as.numeric(c(min_lat,max_lat))
grd <- expand.grid(Longitude = seq(from = Longitude.range[1], to = Longitude.range[2], by = 0.1),
  Latitude = seq(from = Latitude.range[1],to = Latitude.range[2], by = 0.1))
coordinates(grd) <- ~Longitude + Latitude
gridded(grd) <- TRUE

plot1 <- WU_data_spatial %>% as.data.frame %>%
  ggplot(aes(Longitude, Latitude)) + geom_point(size=1) + coord_equal() + 
  ggtitle("Points with measurements")

plot2 <- grd %>% as.data.frame %>%
  ggplot(aes(Longitude, Latitude)) + geom_point(size=1) + coord_equal() + 
  ggtitle("Points at which to estimate")

grid.arrange(plot1, plot2, ncol = 2)

kriged <- krige(Temperature~ 1, WeatherData, grd, model=variogram_fit)

Warnings:

1: In predict.gstat(g, newdata = newdata, block = block,  ... :
Covariance matrix singular at location [5.88,47.4,0]: skipping...
2: In predict.gstat(g, newdata = newdata, block = block,  ... :
Covariance matrix singular at location [5.98,47.4,0]: skipping...
3: In predict.gstat(g, newdata = newdata, block = block,  ... :
Covariance matrix singular at location [6.08,47.4,0]: skipping...
4: In predict.gstat(g, newdata = newdata, block = block,  ... :
Covariance matrix singular at location [6.18,47.4,0]: skipping...
...
...

Answer 1

This error is commonly returned because you have duplicate locations. You can check this using the sp::zerodist function.

To remove duplicate locations you call sp::zerodist within a bracket index.

WeatherData <- WeatherData[-zerodist(WeatherData)[,1],] 

Answer 2

because your sampling point（eg.soil point）have duplicate locations. try to delete the same location points