Generate, or Add to Variogram Model
vgm.RdGenerates a variogram model, or adds to an existing model.
print.variogramModel prints the essence of a variogram model.
Arguments
- psill
(partial) sill of the variogram model component, or model: see Details
- model
model type, e.g. "Exp", "Sph", "Gau", or "Mat". Can be a character vector of model types combined with c(), e.g. c("Exp", "Sph"), in which case the best fitting is returned. Calling vgm() without a model argument returns a data.frame with available models.
- range
range parameter of the variogram model component; in case of anisotropy: major range
- kappa
smoothness parameter for the Matern class of variogram models
- nugget
nugget component of the variogram (this basically adds a nugget compontent to the model); if missing, nugget component is omitted
- add.to
the variogram model to which we want to add a component (structure)
- anis
anisotropy parameters: see notes below
- x
a variogram model to print or plot
- ...
arguments that will be passed to
print, e.g.digits(see examples), or tovariogramLinefor the plot method- covtable
if model is
Tab, instead of model parameters a one-dimensional covariance table can be passed here. See covtable.R in tests directory, and example below.- Err
numeric; if larger than zero, the measurement error variance component that will not be included to the kriging equations, i.e. kriging will now smooth the process Y instead of predict the measured Z, where Z=Y+e, and Err is the variance of e
- m
object of class
variomodel, see geoR- cutoff
maximum distance up to which variogram values are computed
- type
plot type
Value
If a single model is passed, an object of class variogramModel
extending data.frame.
In case a vector ofmodels is passed, an object of class
variogramModelList which is a list of variogramModel
objects.
When called without a model argument, a data.frame with available models is returned, having two columns: short (abbreviated names, to be used as model argument: "Exp", "Sph" etc) and long (with some description).
as.vgm.variomodel tries to convert an object of class variomodel (geoR) to vgm.
Details
If only the first argument (psill) is given a
character value/vector indicating one or more models, as in vgm("Sph"),
then this taken as a shorthand form of vgm(NA,"Sph",NA,NA),
i.e. a spherical variogram with nugget and unknown parameter values;
see examples below. Read fit.variogram to find out how
NA variogram parameters are given initial values for a fitting
a model, based on the sample variogram. Package automap
gives further options for automated variogram modelling.
Note
Geometric anisotropy can be modelled for each individual simple model by giving two or five anisotropy parameters, two for two-dimensional and five for three-dimensional data. In any case, the range defined is the range in the direction of the strongest correlation, or the major range. Anisotropy parameters define which direction this is (the main axis), and how much shorter the range is in (the) direction(s) perpendicular to this main axis.
In two dimensions, two parameters define an anisotropy ellipse, say
anis = c(30, 0.5). The first parameter, 30, refers to
the main axis direction: it is the angle for the principal direction
of continuity (measured in degrees, clockwise from positive Y, i.e. North).
The second parameter, 0.5, is the anisotropy ratio, the ratio
of the minor range to the major range (a value between 0 and 1). So,
in our example, if the range in the major direction (North-East) is 100,
the range in the minor direction (South-East) is 0.5 x 100 = 50.
In three dimensions, five values should be given in the form anis
= c(p,q,r,s,t). Now, $p$ is the angle for the principal direction of
continuity (measured in degrees, clockwise from Y, in direction of X),
$q$ is the dip angle for the principal direction of continuity (measured
in positive degrees up from horizontal), $r$ is the third rotation angle
to rotate the two minor directions around the principal direction defined
by $p$ and $q$. A positive angle acts counter-clockwise while looking
in the principal direction. Anisotropy ratios $s$ and $t$ are the ratios
between the major range and each of the two minor ranges. The anisotropy code
was taken from GSLIB. Note that in http://www.gslib.com/sec_gb.html
it is reported that this code has a bug. Quoting from this
site: “The third angle in all GSLIB programs operates in the opposite
direction than specified in the GSLIB book. Explanation - The books
says (pp27) the angle is measured clockwise when looking toward
the origin (from the postive principal direction), but it should be
counter-clockwise. This is a documentation error. Although rarely used,
the correct specification of the third angle is critical if used.”
(Note that anis = c(p,s) is equivalent to anis = c(p,0,0,s,1).)
The implementation in gstat for 2D and 3D anisotropy was taken from the gslib (probably 1992) code. I have seen a paper where it is argued that the 3D anisotropy code implemented in gslib (and so in gstat) is in error, but I have not corrected anything afterwards.
References
Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers and Geosciences, 30: 683-691.
Deutsch, C.V. and Journel, A.G., 1998. GSLIB: Geostatistical software library and user's guide, second edition, Oxford University Press.
For the validity of variogram models on the sphere, see Huang, Chunfeng, Haimeng Zhang, and Scott M. Robeson. On the validity of commonly used covariance and variogram functions on the sphere. Mathematical Geosciences 43.6 (2011): 721-733.
See also
show.vgms to view the available models, fit.variogram, variogramLine, variogram for the sample variogram.
Examples
vgm()
#> short long
#> 1 Nug Nug (nugget)
#> 2 Exp Exp (exponential)
#> 3 Sph Sph (spherical)
#> 4 Gau Gau (gaussian)
#> 5 Exc Exclass (Exponential class/stable)
#> 6 Mat Mat (Matern)
#> 7 Ste Mat (Matern, M. Stein's parameterization)
#> 8 Cir Cir (circular)
#> 9 Lin Lin (linear)
#> 10 Bes Bes (bessel)
#> 11 Pen Pen (pentaspherical)
#> 12 Per Per (periodic)
#> 13 Wav Wav (wave)
#> 14 Hol Hol (hole)
#> 15 Log Log (logarithmic)
#> 16 Pow Pow (power)
#> 17 Spl Spl (spline)
#> 18 Leg Leg (Legendre)
#> 19 Err Err (Measurement error)
#> 20 Int Int (Intercept)
vgm("Sph")
#> model psill range
#> 1 Nug NA 0
#> 2 Sph NA NA
vgm(NA, "Sph", NA, NA)
#> model psill range
#> 1 Nug NA 0
#> 2 Sph NA NA
vgm(, "Sph") # "Sph" is second argument: NO nugget in this case
#> model psill range
#> 1 Sph NA NA
vgm(10, "Exp", 300)
#> model psill range
#> 1 Exp 10 300
x <- vgm(10, "Exp", 300)
vgm(10, "Nug", 0)
#> model psill range
#> 1 Nug 10 0
vgm(10, "Exp", 300, 4.5)
#> model psill range
#> 1 Nug 4.5 0
#> 2 Exp 10.0 300
vgm(10, "Mat", 300, 4.5, kappa = 0.7)
#> model psill range kappa
#> 1 Nug 4.5 0 0.0
#> 2 Mat 10.0 300 0.7
vgm( 5, "Exp", 300, add.to = vgm(5, "Exp", 60, nugget = 2.5))
#> model psill range
#> 1 Nug 2.5 0
#> 2 Exp 5.0 60
#> 3 Exp 5.0 300
vgm(10, "Exp", 300, anis = c(30, 0.5))
#> model psill range ang1 anis1
#> 1 Exp 10 300 30 0.5
vgm(10, "Exp", 300, anis = c(30, 10, 0, 0.5, 0.3))
#> model psill range ang1 ang2 ang3 anis1 anis2
#> 1 Exp 10 300 30 10 0 0.5 0.3
# Matern variogram model:
vgm(1, "Mat", 1, kappa=.3)
#> model psill range kappa
#> 1 Mat 1 1 0.3
x <- vgm(0.39527463, "Sph", 953.8942, nugget = 0.06105141)
x
#> model psill range
#> 1 Nug 0.06105141 0.0000
#> 2 Sph 0.39527463 953.8942
print(x, digits = 3);
#> model psill range
#> 1 Nug 0.0611 0
#> 2 Sph 0.3953 954
# to see all components, do
print.data.frame(x)
#> model psill range kappa ang1 ang2 ang3 anis1 anis2
#> 1 Nug 0.06105141 0.0000 0.0 0 0 0 1 1
#> 2 Sph 0.39527463 953.8942 0.5 0 0 0 1 1
vv=vgm(model = "Tab", covtable =
variogramLine(vgm(1, "Sph", 1), 1, n=1e4, min = 0, covariance = TRUE))
vgm(c("Mat", "Sph"))
#> [[1]]
#> model psill range kappa
#> 1 Nug NA 0 0.0
#> 2 Mat NA NA 0.5
#>
#> [[2]]
#> model psill range
#> 1 Nug NA 0
#> 2 Sph NA NA
#>
#> attr(,"class")
#> [1] "variogramModelList" "list"
vgm(, c("Mat", "Sph")) # no nugget
#> [[1]]
#> model psill range kappa
#> 1 Mat NA NA 0.5
#>
#> [[2]]
#> model psill range
#> 1 Sph NA NA
#>
#> attr(,"class")
#> [1] "variogramModelList" "list"