For those of you who use GAMV (Fortran 77 DOS version) of GSLIB (1998
version) to calculate indicator variograms it is worthwhile to know that
GAMV uses a different indicator coding from the one described in its
manual, as we recently realized.
In the manual, p. 11, Eq. II.6 defines the indicator I(u,z) = 1 if Z(u)
<= z else I(u,z) = 0, with z being the cutoff value in respect to which
the indicator is created. This is the most common definition of
indicator coding, see also Goovaerts, 1997, p. 285, Eq. 7.20.
However, GAMV is programmed to code the inverse way, but not exactly. On
lines 323-327of GAMV, it says :
if (vr(id,iv).lt.cut(ic)) then vr(id,jv) = 0.0 else vr(id,jv) = 1.0,
or : I(u,z) = 0 if Z(u) < z else I(u,z) = 1. An indicator variogram will
be the same regardless whether a 0 or a 1 is used to code values above
or below the cutoff. But a difference from the definition in the manual
occurs whenever an observation is equal to the cutoff, i.e. not the same
observations will be coded equally according to the definition in the
manual or according to GAMV. E.g. if the cutoff is 5, observations of
value 4 and 5 both will be coded as a 1 according to the definition but
they will be coded as 0 and 1 respectively in GAMV. Consequently the
resulting indicator variograms will be different.
GAMV is erroneous in the situation where one has a data set with a large
proportion of zero's, say 30 %. In this case, when one uses zero as a
cutoff, GAMV returns no indicator variogram (all indicator semivariances
are zero) because all observations are coded as one ! Whereas 30 %
should be coded as either one or zero and the remaining 70 % as the
opposite (zero or one, resp.), yielding indicator semivariances > 0.
In short, on line 323 of GAMV, the .lt. should be either .le. or .gt.,
the latter being the preferred modification since it results in a coding
identical to the definition given in the book.
I hope this is helpful.
Marc Van Meirvenne
Dept. Soil Management and Soil Care
Fac. of Agricultural and Applied Biological Sciences
Coupure 653, 9000 Gent, Belgium
Tel. + 32 (0)9 264 6056
Fax + 32 (0)9 264 6247
e-mail : Marc.Vanmeirvenne@...
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