An application of a spatial simulated annealing sampling optimization algorithm to support digital soil mapping
Abstract
Spatial simulated annealing (SSA) was applied to optimize the sampling configuration for soil organic matter mapping through various sampling scenarios in a Hungarian study site. Prediction-error variance of regression kriging was applied as quality measure in the optimization procedures. Requisites of SSA come from a legacy soil dataset and from spatial auxiliary information. Four scenarios were set to represent the major capabilities of SSA. Scenario 1 and 2 represented completely new sampling designs to optimize with predefined constraints. In scenario 1, number of new observations was the constraint, whilst in scenario 2, it was the value of the quality measure. In both scenarios, areas inaccessible for sampling (roads, farms etc.) were also taken into account. Scenario 3 and 4 represented complementary sampling configurations to optimize taking the previously collected samples into consideration. In scenario 3, the constraint was the number of new observations, whilst in scenario 4, it was the value of the quality measure. In both cases, two types of previously collected sampling design were simulated, a regular and a clustered configuration. The resulted designs were evaluated by Kolmogorov-Smirnov test, nearest neighbour distribution function and empty space function. In cases of scenario 1 and 3, the results showed that, all of the optimized sampling configurations cover properly both geographic and feature space, respectively. In cases of scenario 2 and 4, the resulted calibration curves can be used to determine the sample size for a given quality measure value. Furthermore, we could determine the minimal sample size for a given scenario, which has to be collected to represent properly both geographic and feature space. In conclusion, SSA is a valuable tool to optimize the sampling design considering a lot of constraints.
References
Baume, O.P., Gebhardt, A., Gebhardt, C., Heuvelink, G.B.M. and Pilz, J. 2011. Network optimization algorithms and scenarios in the context of automatic mapping. Computers and Geosciences 37. 289-294. https://doi.org/10.1016/j.cageo.2010.04.014
Bárdossy, Gy. 1997. Geomatematikai kérdések geológus szemmel (Questions of Geomathematics from the point of view of a geologist). Magyar Geofizika 38. (2): 124-141.
Bivand, R.S., Pebesma, E.J. and Gómez-Rubio, V. 2008. Applied Spatial Data Analysis with R. New York, Springer, 375 p.
Brus, D.J. and Heuvelink, G.B.M. 2007. Optimization of sample patterns for universal kriging of environmental variables. Geoderma 138. 86-95. https://doi.org/10.1016/j.geoderma.2006.10.016
Deutsch, C.V. and Journel, A.G. 1998. GSLIB: Geostatistical Soft ware Library and User's Guide (2nd Ed.). New York, Oxford University Press, 369 p.
Dobos, E., Michéli, E. and Montanarella, L. 2007. The population of a 500-m resolution soil organic matter spatial information system for Hungary. In Developments in Soil Science, Vol. 31. Eds.: Lagacherie, P., McBratney, A.B. and Voltz, M. Amsterdam, Elsevier B.V. 487-495. https://doi.org/10.1016/S0166-2481(06)31036-7
Geiger, J. 2006. Geostatisztika (Geostatistics). Szeged, University of Szeged, 77 p.
Goovaerts, P. 1999. Geostatistics in soil science: stateof-the-art and perspectives. Geoderma 89. 1-45. https://doi.org/10.1016/S0016-7061(98)00078-0
Hengl, T. 2009. A Practical Guide to Geostatistical Mapping. 2nd Ed. Amsterdam, University of Amsterdam, 291 p.
Hengl, T., Heuvelink, G.B.M. and Rossiter, D.G. 2007. About regression-kriging: from equations to case studies. Computers and Geosciences 33. 1301-1315. https://doi.org/10.1016/j.cageo.2007.05.001
Hengl, T., Heuvelink, G.B.M. and Stein, A. 2004. A generic framework for spatial prediction of soil variables based on regression-kriging. Geoderma 122., 75-93. https://doi.org/10.1016/j.geoderma.2003.08.018
Hengl, T., Rossiter, D.G. and Stein, A. 2003. Soil sampling strategies for spatial prediction by correlation with auxiliary maps. Australian Journal of Soil Research 41. 1403-1422. https://doi.org/10.1071/SR03005
Heuvelink, G.B.M., Brus, D.J. and de Gru?ter, J.J. 2007. Optimization of sample configurations for digital mapping of soil properties with universal kriging. In Developments in Soil Science, Vol. 31. Eds.: Lagacherie, P., McBratney, A.B. and Voltz, M. Amsterdam, Elsevier B.V. 137-151. https://doi.org/10.1016/S0166-2481(06)31011-2
Illés, G., Kovács, G. and Heil, B. 2011. Nagyfelbontású digitális talajtérképezés a Vaskereszt erdőrezervátumban (High resolution digital soil mapping in the Vaskereszt forest reserve). Erdészettudományi Közlemények 1. 29-43.
McBratney, A.B., Mendonca Santos, M.L. and Minasny, B. 2003. On digital soil mapping. Geoderma 117. 3-52. https://doi.org/10.1016/S0016-7061(03)00223-4
Melles, S.J., Heuvelink, G.B.M., Twenhöfel, C.J.W., van Dijk, A., Hiemstra, P.H., Baume, O. and Stöhlker, U. 2011. Optimizing the spatial pattern of networks for monitoring radioactive releases. Computer and Geosciences 37. 280-288. https://doi.org/10.1016/j.cageo.2010.04.007
Minasny, B. and McBratney, A.B. 2007. Spatial prediction of soil properties using EBLUP with the Matérn covariance function. Geoderma 140. 324-336. https://doi.org/10.1016/j.geoderma.2007.04.028
Pásztor, L., Szabó, J., Bakacsi, Zs., Laborczi, A., Dobos, E., Illés, G. and Szatmári, G. 2014. Elaboration of novel, countrywide maps for the satisfaction of recent demands on spatial, soil related information in Hungary. In Global Soil Map: Basis of the Global Spatial Soil Information System. Eds.: Arrouays, D. et al. London, Taylor &Francis Group, 207-212. https://doi.org/10.1201/b16500-40
Szatmári, G. 2014. Optimization of sampling configuration by spatial simulated annealing for mapping soil variables. In 6th Croatian-Hungarian and 17th Hungarian Geomathematical Congress: "Geomathematics - from theory to practice". Eds.: Cvetković, M., Novak Zelenika, K. and Geiger, J., Zagreb. Croatian Geological Society, 105-111.
Szatmári, G. and Barta, K. 2012. Az erózió, az erózió-veszélyeztetett ség és a területhasznosítás kapcsolata mezőföldi területen (Relationship between water erosion, potential erosion and land use on an area in the Mezőföld region). Agrokémia és Talajtan 61.(1): 41-56. https://doi.org/10.1556/Agrokem.60.2012.1.4
Szatmári, G. and Barta, K. 2013. Csernozjom talajok szervesanyag-tartalmának digitális térképezése erózióval veszélyeztetett mezőföldi területen (Digital mapping of the organic matter content of
chernozem soils on an area endangered by erosion in the Mezőföld region). Agrokémia és Talajtan 62. (1): 47-60. https://doi.org/10.1556/Agrokem.62.2013.1.4
van Groenigen, J.W. and Stein, A. 1998. Constrained optimization of spatial sampling using continuous simulated annealing. Journal of Environmental Quality 27. 1078-1086. https://doi.org/10.2134/jeq1998.00472425002700050013x
van Groenigen, J.W., Siderius, W. and Stein, A. 1999. Constrained optimisation of soil sampling for minimisation of the kriging variance. Geoderma 87. 239-259. https://doi.org/10.1016/S0016-7061(98)00056-1
Wang, J.-F., Stein, A., Gao, B.-B. and Ge, Y. 2012. A review of spatial sampling. Spatial Statistics 2. 1-14. https://doi.org/10.1016/j.spasta.2012.08.001
Webster, R. and Oliver, M.A. 2007. Geostatistics for Environmental Scientists 2nd Ed. Chichester, Wiley, 330 p. https://doi.org/10.1002/9780470517277
Wischmeier, W.H. and Smith, D.D. 1978. Predicting rainfall erosion losses: A guide to conservation planning. Washington D.C., U.S. Government Printing Office, 58 p.
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