Updated 14 Oct 2010
variogramfit performs a least squares fit of various theoretical variograms to an experimental, isotropic variogram. The user can choose between various bounded (e.g. spherical) and unbounded (e.g. exponential) models. A nugget variance can be modelled as well, but higher nested models are not supported.
The function works best with the function fminsearchbnd available on the FEX. You should download it from the File Exchange (File ID: #8277). If you don't have fminsearchbnd, variogramfit uses fminsearch. The problem with fminsearch is, that it might return negative variances or ranges.
Supported bounded models:
'blinear' -- bounded linear
'circular' -- circular model
'spherical' -- spherical model, =default
'pentaspherical' -- pentaspherical model
Supported unbounded functions :
'exponential' -- exponential model
'gaussian' -- gaussian variogram
'whittle' -- Whittle's elementary correlation (involves a modified Bessel function of the second kind).
'stable' -- stable models sensu Wackernagel 1995). Same as gaussian, but with different exponents. Supply the exponent alpha (<2) as an additional pn,pv-pair 'stablealpha',alpha (default = 1.5).
'matern' -- Matern model. Requires an additional pn,pv pair. 'nu',nu (shape parameter > 0, default = 1). Note that for particular values of nu the matern model reduces to other authorized variogram models. (nu = 0.5 : exponential model, nu = 1 : Whittles model, nu -> inf : Gaussian model)
Wackernagel, H. (1995): Multivariate Geostatistics, Springer.
Webster, R., Oliver, M. (2001): Geostatistics for Environmental Scientists. Wiley & Sons.
Minsasny, B., McBratney, A. B. (2005): The Matérn function as general model for soil variograms. Geoderma, 3-4, 192-207.
Wolfgang Schwanghart (2023). variogramfit (https://www.mathworks.com/matlabcentral/fileexchange/25948-variogramfit), MATLAB Central File Exchange. Retrieved .
MATLAB Release Compatibility
Platform CompatibilityWindows macOS Linux
- Sciences > Earth, Ocean, and Atmospheric Sciences > Weather and Atmospheric Science >
- Engineering > Civil and Environmental Engineering > Environmental Engineering >
Inspired by: fminsearchbnd, fminsearchcon, Experimental (Semi-) Variogram, parseargs: Simplifies input processing for functions with multiple options
Inspired: Ordinary Kriging, Kriging and Inverse Distance Interpolation using GSTAT
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forth output argument now contains the anonymous function of the variogram model. This is needed for kriging (to come).
removed a bug concerning weight functions. So far the weight function (either Cressie85 or McBratney86) was not invoked when called.
Seems I forgot to include the m file in the previous update. Here it is.
The matern model was added as theoretical variogram.