Page 263 - Modern Spatiotemporal Geostatistics

244 Modern Spatiotemporal Geostatistics — Chapter 12

Figure 12.11. Maps of standard deviation error of the SK estimates for the
water-level elevations (in ft) for the years 1975 and 1998. Triangles
denote observation wells where hard data were available in space/time.

Lognormal kriging

One of the best-known non-Gaussian geostatistical estimators is the lognormal
SK. An interesting situation is presented in the following proposition, which
was proven by Lee and Ellis (1997b).
PROPOSITION 12.4: Assume that the specificatory knowledge consists
of hard data x hard at points p t (i = 1, ..., m). Let X(p) be a lognormal
field with known mean and (centered) covariance functions. The log-
normal simple kriging (LSK) estimate and the lognormal BME (LBME)
estimate of X(p k) at point p k (k £ i) are given, respectively, by

and

where V^ vW and a'g K are the SK estimate and estimation variance of
the log-transformed field Y(p) = togX(p).
Some interesting applications of Proposition 12.4 in the context of spatial
sampling, etc., may be found in Lee and Ellis (1997b)

Nonhomogeneous/nonstationary kriging

The analysis of this section is a special case of Proposition 10.4 (p. 211).
Consider only hard data at points p i (i = 1, 2, ..., m) and assume that the
generalized spatiotemporal covariance of the underlying S/TRF-f/M X(p] is