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I have estimates of fish density along transects from a lake and would like to extrapolate these estimates for the entire lake surface, using kriging methods. Based on information from here, here and here I have put together some code, but am somewhat underwhelmed by the result.

Data (reduced example)

 points <- new("SpatialPointsDataFrame", data = structure(list(fish_ha = c("0", 
                                                                   "0", "312", "227", "0", "455", "603", "112", "247", "265", "249", 
                                                                   "770", "357", "236", "69", "220", "137", "284", "762", "1675", 
                                                                   "522", "458", "345", "352", "245", "155", "156", "273", "349", 
                                                                   "159", "0", "0", "0", "24", "122", "329", "220", "233", "393", 
                                                                   "280", "360", "258", "389", "218", "897", "621", "96", "0"), 
                                                       kg_ha = c("0", "0", "4", "13", "0", "8", "11", "1", "16", 
                                                                 "3", "6", "10", "11", "12", "0", "0", "8", "8", "9", "49", 
                                                                 "4", "9", "13", "10", "4", "0", "3", "2", "4", "11", "0", 
                                                                 "0", "0", "0", "0", "5", "1", "7", "5", "4", "5", "3", "10", 
                                                                 "8", "12", "12", "16", "0")), row.names = c(NA, 48L), class = "data.frame"), 
       coords.nrs = numeric(0), coords = structure(c(4433881.1568807, 
                                                     4434063.60990585, 4434248.52978213, 4434424.85550047, 4434609.13424212, 
                                                     4434789.09718599, 4434961.90436403, 4435144.06069923, 4435319.2348634, 
                                                     4435491.86377727, 4435664.21278297, 4435844.41156398, 4436020.02906396, 
                                                     4436199.23270384, 4436369.11069566, 4436425.38302424, 4436251.93393992, 
                                                     4436074.63414255, 4435895.64721142, 4435713.93015789, 4435534.31261496, 
                                                     4435355.02277154, 4435169.23010039, 4435008.18551482, 4434822.16338571, 
                                                     4434612.63799854, 4434497.14610166, 4434310.76818349, 4434130.32709306, 
                                                     4433952.87071154, 4433770.4969528, 4433676.2458604, 4433761.22108147, 
                                                     4433828.82289591, 4434003.57719308, 4434193.63055075, 4434375.25860433, 
                                                     4434564.25516186, 4434749.01519503, 4434931.19940932, 4435117.92409774, 
                                                     4435298.99069721, 4435496.73990189, 4435669.74828463, 4435865.15000385, 
                                                     4436040.60330774, 4436224.66669998, 4436403.18795118, 5312861.836658, 
                                                     5312933.63486221, 5313011.00222572, 5313100.98546289, 5313184.76380388, 
                                                     5313276.55707233, 5313376.06518777, 5313463.36494439, 5313561.31118271, 
                                                     5313664.51767385, 5313766.74450944, 5313855.76146538, 5313952.32434893, 
                                                     5314046.71579149, 5314128.40161701, 5314201.72910295, 5314225.99569893, 
                                                     5314222.97125282, 5314227.9850289, 5314223.04148194, 5314222.10196228, 
                                                     5314224.20389437, 5314229.84305795, 5314218.85634075, 5314214.47324543, 
                                                     5314196.85755598, 5314203.17314432, 5314223.90908531, 5314212.71235654, 
                                                     5314194.7295721, 5314176.3936568, 5314079.49237766, 5314185.62832972, 
                                                     5314208.02911493, 5314292.57740121, 5314373.63466771, 5314456.73837339, 
                                                     5314542.36976885, 5314632.61275978, 5314724.6514073, 5314807.60929174, 
                                                     5314901.69214647, 5314997.06141053, 5315067.37271931, 5315161.91513888, 
                                                     5315241.88662221, 5315333.11425499, 5315433.52566703), .Dim = c(48L, 
                                                                                                                     2L), .Dimnames = list(NULL, c("coords.x1", "coords.x2"))), 
       bbox = structure(c(4433676.2458604, 5312861.836658, 4436425.38302424, 
                          5315433.52566703), .Dim = c(2L, 2L), .Dimnames = list(c("coords.x1", 
                                                                                  "coords.x2"), c("min", "max"))), proj4string = new("CRS", 
                                                                                                                                     projargs = "+proj=tmerc +lat_0=0 +lon_0=12 +k=1 +x_0=4500000 +y_0=0 +ellps=bessel +units=m +no_defs"))

Code

slot(points, "proj4string") <- CRS(SRS_string = "EPSG:31468")

grid <- as.data.frame(spsample(points, "regular", n = 1000)) %>% 
  rename(x = x1, y = x2)
coordinates(grid) <- c("x", "y")
gridded(grid) <- TRUE
fullgrid(grid) <- TRUE
slot(grid, "proj4string") <- CRS(SRS_string = "EPSG:31468")

kriging_result <- autoKrige(kg_ha ~ 1, points, grid)
plot(kriging_result)

enter image description here

Question

It looks to me like there hasn't been a lot of extrapolation outside of the actual transects. Is there any way to get predictions for a larger area?

N.B.: I have not clipped the grid to match the outline of the lake. I've had some issues there too, but for simplicity let's just look at the kriging for the time being.

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1 Answer 1

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This is simply how kriging works. It takes your data, looks at the correlation with distance, and then it can estimate with errors the values in a space according to its model.

If the variogram is flat after a certain distance, which in your case is about 200 units, then all the information from correlation is gone, and all it can do is say "my best guess is the mean of your data, and my uncertainty is this big, because that's the overall variation in all your data".

I don't think there's anything else you can do, there's no information 200 units away from the transect to say anything more about what the surface might be there. Clipping the output to a 200m buffer might make a better picture though, and put "here be dragons" in the rest of the lake!

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  • Hahaha, I'm not entirely sure, whether the project leaders are going to be happy with dragons in their waters, but I guess they will have to live with it. That said, the sonar data can be partitioned into larger segments, i.e. >200m, so that we could theoretically make predictions for larger intervals. In any case, thanks for clearing this up!
    – M.Teich
    Commented Jul 12, 2023 at 9:01

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