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| Titel |
Influence of parameter estimation uncertainty in Kriging: Part 2 - Test and case study applications |
| VerfasserIn |
E. Todini, F. Pellegrini, C. Mazzetti |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1027-5606
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| Digitales Dokument |
URL |
| Erschienen |
In: Hydrology and Earth System Sciences ; 5, no. 2 ; Nr. 5, no. 2, S.225-232 |
| Datensatznummer |
250002410
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| Publikation (Nr.) |
 copernicus.org/hess-5-225-2001.pdf |
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| Zusammenfassung |
| The theoretical
approach introduced in Part 1 is applied to a numerical example and to the case
of yearly average precipitation estimation over the Veneto
Region in Italy. The proposed methodology was used to assess the effects of
parameter estimation uncertainty on Kriging estimates and
on their estimated error variance. The Maximum Likelihood (ML) estimator
proposed in Part 1, was applied to the zero mean deviations
from yearly average precipitation over the Veneto Region in Italy, obtained
after the elimination of a non-linear drift with elevation. Three
different semi-variogram models were used, namely the exponential, the Gaussian
and the modified spherical, and the relevant biases as
well as the increases in variance have been assessed. A numerical example was
also conducted to demonstrate how the procedure leads to unbiased
estimates of the random functions. One hundred sets of 82 observations were
generated by means of the exponential model on the basis
of the parameter values identified for the Veneto Region rainfall problem and
taken as characterising the true underlining process. The values
of parameter and the consequent cross-validation errors, were estimated from
each sample. The cross-validation errors were first computed
in the classical way and then corrected with the procedure derived in Part 1.
Both sets, original and corrected, were then tested, by means
of the Likelihood ratio test, against the null hypothesis of deriving from a
zero mean process with unknown covariance. The results of the
experiment clearly show the effectiveness of the proposed approach.
Keywords: yearly rainfall, maximum likelihood, Kriging, parameter
estimation uncertainty |
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