Variograms

TK

using SpeciesDistributionToolkit
const SDT = SpeciesDistributionToolkit
using PrettyTables
using CairoMakie
using Statistics

Get some info on temperature

polygon = getpolygon(PolygonData(NaturalEarth, Countries))["Austria"]
temperature = SDMLayer(RasterData(CHELSA2, AverageTemperature); SDT.boundingbox(polygon)...)
mask!(temperature, polygon);

Code for the figure

f = Figure()
ax = Axis(f[1,1]; aspect=DataAspect())
hm = heatmap!(ax, temperature, colormap=:thermal)
lines!(ax, polygon, color=:black)
hidespines!(ax)
hidedecorations!(ax)
Colorbar(f[1,2], hm)

get variogram

x, y, n = variogram(temperature; width=10., shift=5.);

Code for the figure

f = Figure()
ax = Axis(f[1,1]; xlabel="Distance", ylabel="Variogram")
scatter!(ax, x, y, markersize=n ./ maximum(n) .* 8 .+ 4, color=:grey50)
ylims!(ax, quantile(y, [0.0, 0.9])...)

can fit a model

Not exported

in progress

these are also convenience functions

G = SDT.fitvariogram(x, y, n; family=:gaussian);
E = SDT.fitvariogram(x, y, n; family=:exponential);
S = SDT.fitvariogram(x, y, n; family=:spherical);

Code for the figure

scatter!(ax, x, y, markersize=n ./ maximum(n) .* 8 .+ 4, color=:grey50)
vx = LinRange(extrema(x)..., 100)
lines!(ax, vx, G.model.(vx), label="Gaussian")
lines!(ax, vx, E.model.(vx), label="Exponential", linestyle=:dash)
lines!(ax, vx, S.model.(vx), label="Spherical", linestyle=:dot)
ylims!(ax, quantile(y, [0.0, 0.9])...)
axislegend(ax, position=:lt)

check which are better

M = permutedims(hcat([[m.range, m.sill, m.nugget, m.error] for m in [G, E, S]]...));
M = hcat(["Gaussian", "Exponential", "Spherical"], M);

pretty_table(
    M;
    alignment = [:l, :c, :c, :c, :c],
    backend = :markdown,
    column_labels = ["Model", "Range", "Sill", "Nugget", "Error"],
    formatters = [fmt__printf("%3.3f", [2, 3, 4, 5])],
)

Model	Range	Sill	Nugget	Error
Gaussian	503.149	28.222	3.171	4.150
Exponential	461.813	19.117	0.161	5.368
Spherical	498.146	23.522	0.183	4.479

Related documentation

SpeciesDistributionToolkit.variogram Function

variogram(L::SDMLayer; samples::Integer=2000, bins::Integer=100; kwargs...)

Generates the raw data to look at an empirical semivariogram from a layer. This method will draw samples pairs of points at random, then aggregate them in bins bins.

This returns three vectors: the empirical center of the bin, the semivariance within this bin, and the number of samples that compose this bin.

source

SpeciesDistributionToolkit.fitvariogram Function

fitvariogram(x, y, n; family = :gaussian)

Fits a variogram of the given family based on data representing the central bin distance x, the semivariogram y, and the sample size n. The data are returned as a named tuple containing the range, the sill, the nugget, the error, and the model. The model is a function that can be called on a given distance to obtained the best fit variogram.

Possible values of family are :gaussian (default), :spherical, and :exponential.

Values are optimized using the Nelder-Mead algorithm with samples samples and maxiter iterations.

source

fitvariogram(L::SDMLayer; family::Symbol=:gaussian, kwargs...)

Fits the variogram based on a layer. The kwargs... are passed to variogram.

source