Skip to main content
Log in

Multi-lag cluster designs for estimating the semivariogram for sediments affected by effluent discharges offshore in San Diego

Environmental and Ecological Statistics Aims and scope Submit manuscript

Abstract

Maps are useful tools for understanding, managing, and protecting the marine environment, yet few useful and statistically defensible maps of environmental quality and aquatic resources have been developed in near-coastal regions. Current environmental management efforts, such as ocean monitoring by sewage dischargers, routinely sample areas of potential impact using sparse sampling grids. Heterogeneous oceanic conditions often make extrapolation from these grids to non-sampled locations questionable. Although rarely applied in coastal monitoring, kriging offers a more rigorous statistical approach to mapping and allows confidence intervals to be calculated for predictions. Its usefulness relies on accurate models of the spatial variability through estimating the semivariogram. Many optimal designs for estimating the semivariogram have been proposed, but these designs are often difficult to implement in practice. In this paper, we present simple design strategies for augmenting existing monitoring designs with the goal of estimating the semivariogram. In particular, we investigate a multi-lag cluster design strategy, where clusters of sites, spaced at various lag distances, are placed around fixed stations on an existing sampling grid. We find that these multi-lag cluster designs provide improved accuracy in estimating the parameters of the semivariogram. Based on simulation study findings, we apply a multi-lag cluster enhancement to the monitoring grid for the City of San Diego’s Point Loma Wastewater Treatment Plant as part of a special study to map chemical contaminants in sediments around its sewage outfall.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Burgess TM, Webster R, McBratney AB (1981) Optimal interpolation and isarithmic mapping of soil properties, VI. Sampling strategy. J Soil Sci 31:643–659

    Article  Google Scholar 

  • Cressie N (1985) Fitting variogram models by weighted least squares. Math Geol 17:563–586

    Article  Google Scholar 

  • Cressie N (1993) Statistics for spatial data. Wiley, New York

    Google Scholar 

  • Kaluzny SP, Vega SC, Cardoso TP, Shelly AA (1998) S+ Spatial stats user’s manual for windows and unix. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Lark RM (2002) Optimized spatial sampling of soil of estimation of the variogram by maximum likelihood. Geoderma 105:49–80

    Article  Google Scholar 

  • McBratney AB, Webster R, Burgess TM (1981) The design of optimal sampling schemes for local estimation and mapping of regionalized variables. Comput Geosci 7:331–334

    Article  Google Scholar 

  • Morris MD (1991) On counting the number of data pairs for semivariogram estimation. Math Geol 23:929–943

    Article  Google Scholar 

  • Muller WG, Zimmerman DL (1999) Optimal designs for variogram estimation. Environmetrics 10:23–37

    Article  Google Scholar 

  • Russo D (1984) Design of optimal sampling network for estimation the variogram. Soil Sci Soci Am J 48:708–716

    Google Scholar 

  • Stein ML (1990) Uniform asumptotic optimality of linear predictions of a random field using an incorrect second-order structure. Ann Stat 18:850–872

    Google Scholar 

  • Warrick AW, Myers DE (1987) Optimization of sampling locations for variogram calculations. Water Res Res 23:496–500

    Google Scholar 

  • Webster R, Oliver MA (2001) Geostatistics for environmental scientists. Wiley, Chichester

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kerry J. Ritter.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ritter, K.J., Leecaster, M.K. Multi-lag cluster designs for estimating the semivariogram for sediments affected by effluent discharges offshore in San Diego. Environ Ecol Stat 14, 41–53 (2007). https://doi.org/10.1007/PL00021845

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/PL00021845

Keywords

Navigation