Fitting variograms
Overview
Fitting theoretical variograms to empirical observations is an important modeling step to ensure valid mathematical models of geospatial continuity. Given an empirical variogram, the fit
function can be used to perform the fit:
GeoStatsFunctions.fit
— Methodfit(V, g, algo=WeightedLeastSquares(); range=nothing, sill=nothing, nugget=nothing)
Fit theoretical variogram type V
to empirical variogram g
using algorithm algo
.
Optionally fix range
, sill
or nugget
by passing them as keyword arguments, or set their maximum value with maxrange
, maxsill
or maxnugget
.
Examples
julia> fit(SphericalVariogram, g)
julia> fit(ExponentialVariogram, g)
julia> fit(ExponentialVariogram, g, sill=1.0)
julia> fit(ExponentialVariogram, g, maxsill=1.0)
julia> fit(GaussianVariogram, g, WeightedLeastSquares())
fit(Vs, g, algo=WeightedLeastSquares(); kwargs...)
Fit theoretical variogram types Vs
to empirical variogram g
using algorithm algo
and return the one with minimum error.
Examples
julia> fit([SphericalVariogram, ExponentialVariogram], g)
fit(Variogram, g, algo=WeightedLeastSquares(); kwargs...)
Fit all "fittable" subtypes of Variogram
to empirical variogram g
using algorithm algo
and return the one with minimum error.
Examples
julia> fit(Variogram, g)
julia> fit(Variogram, g, WeightedLeastSquares())
See also GeoStatsFunctions.fittable()
.
Example
# sinusoidal data
𝒟 = georef((Z=[sin(i/2) + sin(j/2) for i in 1:50, j in 1:50],))
# empirical variogram
g = EmpiricalVariogram(𝒟, :Z, maxlag = 25u"m")
Mke.plot(g)
We can fit specific models to the empirical variogram:
γ = GeoStatsFunctions.fit(SineHoleVariogram, g)
Mke.plot(g)
Mke.plot!(γ, maxlag = 25u"m")
Mke.current_figure()
or let the framework find the model with minimum error:
γ = GeoStatsFunctions.fit(Variogram, g)
Mke.plot(g)
Mke.plot!(γ, maxlag = 25u"m")
Mke.current_figure()
which should be a SineHoleVariogram
given that the synthetic data of this example is sinusoidal.
Optionally, we can specify a weighting function to give different weights to the lags:
γ = GeoStatsFunctions.fit(SineHoleVariogram, g, h -> 1 / h^2)
Mke.plot(g)
Mke.plot!(γ, maxlag = 25u"m")
Mke.current_figure()
Methods
Weighted least squares
GeoStatsFunctions.WeightedLeastSquares
— TypeWeightedLeastSquares()
WeightedLeastSquares(w)
Fit theoretical variogram using weighted least squares with weighting function w
(e.g. h -> 1/h). If no weighting function is provided, bin counts of empirical variogram are normalized and used as weights.