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פותח על ידי קלירמאש פתרונות בע"מ -
Optimal spatial sampling design for the estimation of the variogram based on a least squares approach
Year:
1999
Source of publication :
Water Resources Research
Authors :
רוסו, דוד
;
.
Volume :
35
Co-Authors:
Bogaert, P., Division of Soil Physics, Agricultural Research Organization, Volcani Center, Bet-Dagan, Israel
Russo, D., Division of Soil Physics, Agricultural Research Organization, Volcani Center, Bet-Dagan, Israel
Facilitators :
From page:
1275
To page:
1289
(
Total pages:
15
)
Abstract:
A methodology for the choice of optimal spatial sampling designs is proposed. The problem is to find an optimal finite set of space locations where a random field has to be sampled, in order to minimize the variability of the parametric variogram estimator. Under the hypothesis that the random field is Gaussian second-order stationary and using a first-order approximation for the linearization of the parametric variogram with respect to its parameters, we are able to express the covariance matrix of the parameter estimators as a function of the sampling design. An optimization algorithm based on a generalized least squares approach is proposed in order to reduce the variability of these estimators through the minimization of the determinant of their covariance matrix. In order to validate this approach, a practical case study is conducted for two different variogram models. It shows that compared to random sampling designs, the benefit of the optimization procedure is somewhat limited for a variogram model without nugget effect. For a variogram model with nugget effect, random sampling designs are associated with much higher variability on the parameter estimators than optimized designs because of the typical lack of information offered by random sampling designs for small distances between locations. The performance of random sampling designs compared tO optimized or alternative regular designs is shown to be poor with respect to parameter estimation, especially when a nugget effect is included in the variogram model. The parameters that benefit the most from the optimization procedure are the variance and the nugget effect, whereas the improvement for the range parameter estimation is limited. The optimization algorithm provides yardstick results, yielding reference values for the selection of an alternative regular design. The applicability of the algorithm is very wide, and it can greatly help the user to understand the way the parameters are influenced by the choice of a set of sampling locations instead of another.
Note:
Related Files :
estimation method
least squares method
Sampling
variogram
עוד תגיות
תוכן קשור
More details
DOI :
10.1029/1998WR900078
Article number:
Affiliations:
Database:
סקופוס
Publication Type:
מאמר
;
.
Language:
אנגלית
Editors' remarks:
ID:
20261
Last updated date:
02/03/2022 17:27
Creation date:
16/04/2018 23:35
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Scientific Publication
Optimal spatial sampling design for the estimation of the variogram based on a least squares approach
35
Bogaert, P., Division of Soil Physics, Agricultural Research Organization, Volcani Center, Bet-Dagan, Israel
Russo, D., Division of Soil Physics, Agricultural Research Organization, Volcani Center, Bet-Dagan, Israel
Optimal spatial sampling design for the estimation of the variogram based on a least squares approach
A methodology for the choice of optimal spatial sampling designs is proposed. The problem is to find an optimal finite set of space locations where a random field has to be sampled, in order to minimize the variability of the parametric variogram estimator. Under the hypothesis that the random field is Gaussian second-order stationary and using a first-order approximation for the linearization of the parametric variogram with respect to its parameters, we are able to express the covariance matrix of the parameter estimators as a function of the sampling design. An optimization algorithm based on a generalized least squares approach is proposed in order to reduce the variability of these estimators through the minimization of the determinant of their covariance matrix. In order to validate this approach, a practical case study is conducted for two different variogram models. It shows that compared to random sampling designs, the benefit of the optimization procedure is somewhat limited for a variogram model without nugget effect. For a variogram model with nugget effect, random sampling designs are associated with much higher variability on the parameter estimators than optimized designs because of the typical lack of information offered by random sampling designs for small distances between locations. The performance of random sampling designs compared tO optimized or alternative regular designs is shown to be poor with respect to parameter estimation, especially when a nugget effect is included in the variogram model. The parameters that benefit the most from the optimization procedure are the variance and the nugget effect, whereas the improvement for the range parameter estimation is limited. The optimization algorithm provides yardstick results, yielding reference values for the selection of an alternative regular design. The applicability of the algorithm is very wide, and it can greatly help the user to understand the way the parameters are influenced by the choice of a set of sampling locations instead of another.
Scientific Publication
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