Optimal designs for variogram estimation

✍ Scribed by Werner G. Müller; Dale L. Zimmerman

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 170 KB
• Volume: 10
• Category: Article
• ISSN: 1180-4009
• DOI: 10.1002/(sici)1099-095x(199901/02)10:1<23::aid-env333>3.0.co;2-p

✦ Synopsis

The variogram plays a central role in the analysis of geostatistical data. A valid variogram model is selected and the parameters of that model are estimated before kriging (spatial prediction) is performed. These inference procedures are generally based upon examination of the empirical variogram, which consists of average squared dierences of data taken at sites lagged the same distance apart in the same direction. The ability of the analyst to estimate variogram parameters eciently is aected signi®cantly by the sampling design, i.e. the spatial con®guration of sites where measurements are taken. In this paper, we propose design criteria that, in contrast to some previously proposed criteria oriented towards kriging with a known variogram, emphasize the accurate estimation of the variogram. These criteria are modi®cations of design criteria that are popular in the context of (nonlinear) regression models. The two main distinguishing features of the present context are that the addition of a single site to the design produces as many new lags as there are existing sites and hence also produces many new squared dierences from which the variogram is estimated. Secondly, those squared dierences are generally correlated, which inhibits the use of many standard design methods that rest upon the assumption of uncorrelated errors. Several approaches to design construction which account for these features are described and illustrated with two examples. We compare their eciency to simple random sampling and regular and space-®lling designs and ®nd considerable improvements.