Optimal network design for spatial prediction of soil redistribution (137Cs) based on a minimax approach

Abstract

Measuring ¹³⁷Cs is considered an effective method to study soil redistribution rate and hence needs sampling at a number of sites. The spatial configuration of the network of sites to be sampled has a substantial effect on the soil redistribution assessment. Here, motivated by sampling ¹³⁷Cs, we adopted a model-based approach. For this, we chose the average kriging variance (AKV) as a design criterion. In fact, by minimizing the AKV of soil ¹³⁷Cs prediction in the paired sub-catchments of Iran's Golestan province, we determined the optimal sampling design in the case that no directly measured prior information of the primary variable of interest (¹³⁷Cs) is available. However, the AKV depends on some unknown parameters and preliminary estimates of model parameters are not available. To overcome this problem, we apply the minimax approach which minimizes the maximum value of design criterionover the misspecification of parameters. The method is illustrated taking into account the ancillary information (slope%) from representative Sub-catchments (Sample and Testifier, each around 190 ha in size). A simulated annealing algorithm is used to search for an optimal design from among all possible designs. Since, the number of sampling points is often limited by time and budgetary constraints, we use a sequential-based method for selecting the sample size. It is shown that 60 sites are sufficient for the proposed Sample and Testifier sub-catchments.

Keywords

• 137Cs, Golestan province, minimax approach, simulated annealing, spatial sampling

References

1. Bachhuber, H., Bunzl, K., Schimmack, W., 1987. Spatial variability of fallout-Cs-137 in the soil of a cultivated field, Environmental Monitoring and Assessment 43, 93-101.
2. Banerjee S., Carlin B.P., Gelfand A.E., 2004. Hierarchical modeling and analysis for spatial data. Chapman and Hall/ CRC. 452p.
3. Brus D.J., De Gruijter, J.J., Walvoort D.J., De Vries F., Bronswijk J.J., Römkens P.F., De Vries W., 2002. Mapping the probability of exceeding critical thresholds for cadmium concentrations in soils in the Netherlands, Journal of Environmental Quality 31, 1875-1884.
4. Brus D.J., De Gruijter, J.J., 1997. Random sampling or geostatistical modelling? Choosing between design-based and model-based sampling strategies for soil (with discussion), Geoderma 80, 1-44.
5. Higgitt D.L., 1995. Quantifying erosion rates from cesium-137 measurements-a comment, Australian Journal of Soil Research 33, 709-714.
6. Lettner, H.P., Bossew, P., Hubmer, A.K., 2000. Spatial variability of fallout caesium-137 in Austrian alpine regions, Journal of Environmental Radioactivity 47, 71-82.
7. Li, Y., 2010. Can the spatial prediction of soil organic matter contents at various sampling scales be improved by using regression kriging with auxiliary information? Geoderma 159, 63-75.
8. Lobb, D.A., Kachanoski, R.G., Miller, M.H., 1999. Tillage translocation and tillage erosion in the complex upland landscapes of southwestern Ontario, Canada. Soil & Tillage Research 51, 189-209.

9. Lu, X.X., Higgitt, D.L., 1999. Sediment yield variability in the Upper Yangtze, China. Earth Surface Processes and Landforms 24, 1077-1093.
10. Mabit, L., Bernard, C., Laverdiere, M.R., 2002. Quantification of soil redistribution and sediment budget in a Canadian watershed from fallout caesium-137 (Cs-137) data, Canadian Journal of Soil Science 82, 423-431.
11. Mabit, L., Bernard, C., Laverdiere, M.R., 2007, Assessment of erosion in the Boyer River watershed (Canada) using a GIS oriented sampling strategy and Cs-137 measurements, Catena 71, 242-249.
12. Mabit, L., Bernard, C., Makhlouf, M., Laverdiere, M.R., 2008. Spatial variability of erosion and soil organic matter content estimated from Cs-131 measurements and geostatistics, Geoderma 145, 245-251.
13. Montgomery, J.A., Busacca, A.J., Frazier, B.E., Mc Cool, D.K., 1997. Evaluating soil movement using Cesium-137 and the revised universal soil loss equation, Soil Science Society of America Journal 61, 571-579.
14. Ritchie, J.C., Ritchie, C.A., 2008. Bibliography of publications of 137Cs studies related to erosion and sediment deposition. Available at http://www.ars.usda.gov/Main/docs.htm?docid=17939.
15. Schuller, P., Walling, D.E., Sepulveda, A., Castillo, A., Pino, I., 2007. Changes in soil erosion associated with the shift from conventional tillage to a no-tillage system, documented using 137Cs measurements, Soil & Tillage Research 94, 183-192.
16. Spöck, G., Pilz, J., 2010, Spatial sampling design and covariance-robust minimax prediction based on convex design ideas, Stochastic Environmental Research and Risk Assessment 24, 463-482.
17. Sutherland, R.A., 1994, Spatial variability of 137Cs and the influence of sampling on estimates of sediment redistribution, Catena 21, 57-71.
18. Van Groenigen, J.W., Stein, A., 1998, Constrained optimization of spatial sampling using continuous simulated annealing, Journal of Environmental Quality 27, 1078-1086.
19. Wallbrink, P.J., Croke, J., 2002, A combined rainfall simulator and tracer approach to assess the role of best management practices in minimising sediment redistribution and loss in forests after harvesting, Forest Ecology and Management 170, 217-232.
20. Webster, R., Oliver, M.A., 1992, Sample adequately to estimate variograms of soil properties, Journal of Soil Science 43, 177-192.
21. Yang, M.Y., Tian, J.L., Liu, P.L., 2006, Investigating the spatial distribution of soil erosion and deposition in a small catchment on the Loess Plateau of China, using Cs-137. Soil & Tillage Research 87, 186-193.
22. Zapata, F., 2002, Handbook for the assessment of soil erosion and sedimentation using environmental radionuclides, The Netherlands, Kluwer Academic Publishers.