HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text Free Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in ISI Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via ISI Web of Science (4) Citing Articles via Google Scholar Google Scholar Articles by Skøien, J. O. Articles by Blöschl, G. Search for Related Content PubMed Articles by Skøien, J. O. Articles by Blöschl, G. GeoRef GeoRef Citation Agricola Articles by Skøien, J. O. Articles by Blöschl, G. Related Collections Watershed and Landscape Processes Scaling

Scale Effects in Estimating the Variogram and Implications for Soil Hydrology

Institute for Hydraulic and Water Resources Engineering, Vienna Univ. of Technology, Karlsplatz 13, A-1040 Vienna, Austria

View larger version (11K): [in a new window]   Fig. 1. The sampling scale triplet—spacing LS, extent LE, and support LA—for the two-dimensional case.

View larger version (17K): [in a new window]   Fig. 2. Sample variograms obtained from 100 samples with extent LE* = 5.6 and support LA* = 0 from 10 realizations of the random field. Horizontal bars represent estimates of the integral scale (solid) and the correlation length (dashed) from a two-parameter model, and the vertical bars represent the variance (solid) and sill from a two-parameter model (median with 25 and 75% quantiles as error bars).

View larger version (15K): [in a new window]   Fig. 3. Effect of spacing LS* and extent LE* on the estimated correlation length *, by the weighted least squares (WLS, green) and maximum likelihood (ML, blue) methods, and integral scale * (red lines) for gridded sampling (median with 25 and 75% quantiles as error bars), for the one-parameter model.

View larger version (15K): [in a new window]   Fig. 4. Effect of spacing LS* and extent LE* on the estimated correlation length, by the weighted least squares (WLS, green) and maximum likelihood (ML, blue) methods, and integral scale * (red lines) for random sampling (median with 25 and 75% quantiles as error bars), for the one-parameter model.

View larger version (22K): [in a new window]   Fig. 5. (Top) Effect of spacing LS* and extent LE* on the estimated sill s*, by the weighted least squares (WLS, green) and maximum likelihood (ML, blue) methods, and the sample variance s2* (red). (Bottom) Effect of spacing LS* and extent LE* on the estimated correlation length * (WLS green, ML blue) and the integral scale * (red). Gridded sampling (median with 25 and 75% quantiles as error bars). All are for the two-parameter model.

View larger version (21K): [in a new window]   Fig. 6. (Top) Effect of spacing LS* and extent LE* on the estimated sill s*, by the weighted least squares (WLS, green) and maximum likelihood (ML, blue) methods, and the sample variance s2* (red). (Bottom) Effect of spacing LS* and extent LE* on the estimated correlation length * (WLS green, ML blue) and the integral scale * (red). Random sampling (median with 25 and 75% quantiles as error bars). All are for the two-parameter model.

View larger version (29K): [in a new window]   Fig. 7. (Top) Effect of spacing LS* and extent LE* on the estimated nugget 0*, by the weighted least squares (WLS, green) and maximum likelihood (ML, blue) methods. (Middle) Effect of spacing LS* and extent LE* on the estimated sill s* (WLS green, ML blue) and the sample variance s2* (red). (Bottom) Effect of spacing LS* and extent LE* on the estimated correlation length * (WLS green, ML blue) and the integral scale * (red). Gridded sampling (median with 25 and 75% quantiles as error bars). All are for the three-parameter model.

View larger version (26K): [in a new window]   Fig. 8. (Top) Effect of spacing LS* and extent LE* on the estimated nugget 0*, by the weighted least squares (WLS, green) and maximum likelihood (ML, blue) methods. (Middle) Effect of spacing LS* and extent LE* on the estimated sill s* (WLS green, ML blue) and the sample variance s2* (red). (Bottom) Effect of spacing LS* and extent LE* on the estimated correlation length * (WLS green, ML blue) and the integral scale * (red). Random sampling (median with 25 and 75% quantiles as error bars). All are for the three-parameter model.

View larger version (12K): [in a new window]   Fig. 9. Effect of support LA* on the estimated correlation length *, by the weighted least squares (WLS, green) and maximum likelihood (ML, blue) methods, and integral scale * (red) for gridded sampling (median with 25 and 75% quantiles as error bars), for the one-parameter model. Vertical line in each panel shows LS* = LA*. LE* = 10, spacing LS* according to Eq. [8].

View larger version (21K): [in a new window]   Fig. 10. (Top) Effect of support LA* on the estimated sill s*, by the weighted least squares (WLS, green) and maximum likelihood (ML, blue) methods, and the sample variance s2* (red). (Bottom) Effect of support LA* on the estimated correlation length * (WLS green, ML blue) and the integral scale * (red). Gridded sampling (median with 25 and 75% quantiles as error bars). All are for the two-parameter model. LE* = 10, spacing LS* according to Eq. [8].

View larger version (28K): [in a new window]   Fig. 11. (Top) Effect of support LA* on the estimated nugget 0*, by the weighted least squares (WLS, green) and maximum likelihood (ML, blue) methods. (Middle) Effect of support LA* on the estimated sill s* (WLS green, ML blue) and the sample variance s2* (red). (Bottom) Effect of support LA* on the estimated correlation length * (WLS green, ML blue) and the integral scale * (red). Gridded sampling (median with 25 and 75% quantiles as error bars). All are for the three-parameter model. LE* = 10, spacing LS* according to Eq. [8].

View larger version (23K): [in a new window]   Fig. 12. Estimated sill and correlation length from (a) the weighted least squares (WLS) method (green) and (b) the maximum likelihood (ML) method (blue), together with variance and integral scale (red). The thin black lines correspond to the analytical expectations. All are for the two-parameter model, with 100 gridded samples.