vgm                  package:gstat                  R Documentation

_G_e_n_e_r_a_t_e, _o_r _A_d_d _t_o _V_a_r_i_o_g_r_a_m _M_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

     Generates a variogram model, or adds to an existing model. 
     'print.variogramModel' prints the essence of a variogram  model.

_U_s_a_g_e:

     vgm(psill, model, range, nugget, add.to, anis, kappa = 0.5)
     print.variogramModel(x, ...)

_A_r_g_u_m_e_n_t_s:

   psill: (partial) sill of the variogram model component 

   model: model type, e.g. "Exp", "Sph", "Gau", "Mat". Calling vgm()
          without a model argument returns the list with available
          models. 

   range: range of the variogram model component 

   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) 

  add.to: a variogram model to which we want to add a component 

    anis: anisotropy parameters: see notes below 

       x: a variogram model to print 

     ...: arguments that will be passed to 'print', e.g. 'digits' (see
          examples) 

_V_a_l_u_e:

     an object of class 'variogramModel', which extends data.frame
     Called without a model argument returns a character list with
     available models.

_N_o_t_e:

     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(45, 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,
     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 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. 

     (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 (en
     then also in gstat) is in error, but I have not corrected anything
     afterwards.

_A_u_t_h_o_r(_s):

     Edzer J. Pebesma

_R_e_f_e_r_e_n_c_e_s:

     Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat
     package. Computers & Geosciences, 30: 683-691.

_S_e_e _A_l_s_o:

     show.vgms to view the available models, fit.variogram,
     variogram.line, variogram for the sample variogram.

_E_x_a_m_p_l_e_s:

     vgm(10, "Exp", 300)
     x <- vgm(10, "Exp", 300)
     vgm(10, "Nug", 0)
     vgm(10, "Exp", 300, 4.5)
     vgm(10, "Mat", 300, 4.5, kappa = 0.7)
     vgm( 5, "Exp", 300, add.to = vgm(5, "Exp", 60, nugget = 2.5))
     vgm(10, "Exp", 300, anis = c(30, 0.5))
     vgm(10, "Exp", 300, anis = c(30, 10, 0, 0.5, 0.3))
     # Matern variogram model:
     vgm(1, "Mat", 1, kappa=.3)
     x <- vgm(0.39527463, "Sph", 953.8942, nugget = 0.06105141)
     x
     print(x, digits = 3);
     # to see all components, do
     print.data.frame(x)

