A genetic algorithm for resizing and sampling reduction of non-stationary soil chemical attributes optimizing spatial prediction
Abstract
Aim of study: To evaluate the influence of the parameters of the geostatistical model and the initial sample configuration used in the optimization process; and to propose and evaluate the resizing of a sample configuration, reducing its sample size, for simulated data and for the study of the spatial variability of soil chemical attributes under a non-stationary with drift process from a commercial soybean cultivation area.
Area of study: Cascavel, Brazil
Material and methods: For both, the simulated data and the soil chemical attributes, the Genetic Algorithm was used for sample resizing, maximizing the overall accuracy measure.
Main results: The results obtained from the simulated data showed that the practical range did not influence in a relevant way the optimization process. Moreover, the local variations, such as variance or sampling errors (nugget effect), had a direct relationship with the reduction of the sample size, mainly for the smaller nugget effect. For the soil chemical attributes, the Genetic Algorithm was efficient in resizing the sampling configuration, since it generated sampling configurations with 30 to 35 points, corresponding to 29.41% to 34.31% of the initial configuration, respectively. In addition, comparing the optimized and initial configurations, similarities were obtained regarding spatial dependence structure and characterization of spatial variability of soil chemical attributes in the study area.
Research highlights: The optimization process showed that it is possible to reduce the sample size, allowing for lesser financial investments with data collection and laboratory analysis of soil samples in future experiments.
Downloads
References
Alencar NM, dos Santos AC, de Paula Neto JJ, Rodrigues MOD, de Oliveira LBT, 2019. Variabilidade das perdas de solo em Neossolo Quartzarênico sob diferentes coberturas no ecótono Cerrado-Amazônia. Agrarian 12 (43): 71-78. https://doi.org/10.30612/agrarian.v12i43.8081
Alloway BJ, 1995. Heavy metals in soils, 2nd ed. Blackie A & P, Glasgow. https://doi.org/10.1007/978-94-011-1344-1
Anderson JR, Hardy EE, Roach JT, Witmer RE, 2001. A land use and land cover classification system for use with remote sensor data. U.S. Government Print Office. Washington DC. 41 pp.
Arruda MR, Moreira A, Pereira JCR, 2014. Amostragem e cuidados na coleta de solo para fins de fertilidade. Embrapa Amazônia Ocidental Manaus.
Atkinson PM, Lloyd CD, 2007. Non-stationary variogram models for geostatistical sampling optimisation: An empirical investigation using elevation data. Comput Geosci 33 (10): 1285-1300. https://doi.org/10.1016/j.cageo.2007.05.011
Bowman AW, Azzalini A, 2015. R package sm: nonparametric smoothing methods (vers 2.2-5.4). University of Glasgow, UK, & Università di Padova, Italy.
Callegari-Jacques SM, 2003. Bioestatística: princípios e aplicações. Artemed, Porto Alegre.
Cambardella CA, Moorman T, Parkin T, Karlen D, Novak J, Turco R, Konopka A, 1994. Field-scale variability of soil properties in central Iowa soils. Soil Sci Soc Am J 58: 1501-1511. https://doi.org/10.2136/sssaj1994.03615995005800050033x
Catapatti TR, Goncalves MC, Silva Neto MR, Sobroza R, 2008. Sample size and number of replications for assessment of agronomic characters in popcorn. Ciênc Agrotec 32 (3): 855-862. https://doi.org/10.1590/S1413-70542008000300023
Cherubin MR, Santi AL, Eitelwein MT, Menegol DR, Ros COD, Pias OHC, Bergjetti J, 2014. Eficiência de malhas amostrais utilizadas na caracterização da variabilidade espacial de fósforo e potássio. Ciênc Rural 44 (3): 425-432. https://doi.org/10.1590/S0103-84782014000300007
Chipeta MG, Terlouw DJ, Phiri KS, Diggle PJ, 2017. Inhibitory geostatistical designs for spatial prediction taking account of uncertain covariance structure. Environmetrics 28 (1): e2425. https://doi.org/10.1002/env.2425
Cressie NAC, 2015. Statistics for spatial data, rev. ed. John Wiley & Sons, NY. 928 pp.
Dal Canton LE, Guedes LPC, Uribe-Opazo MA, 2021. Reduction of sample size in the soil physical-chemical attributes using the multivariate effective sample size. J Agr Stud 9 (1): 357-376. https://doi.org/10.5296/jas.v9i1.17473
Dalmago GA, da Cunha GR, Pires JLF, Santi A, Fochesatto E, 2014. Potencial de aplicação da agrometeorologia em agricultura de precisão para produção de grãos. In: Agricultura de precisão: resultados de um novo olhar; Bernardi AC de C, Naime J de M, de Rezende AV, Bassoi LH, Inamasu RY (eds.). pp. 331-337. Embrapa, Brasília.
De Bastiani F, Cysneiros AFJ, Cysneiros AHM, Uribe-Opazo MA, Galea M, 2015. Influence diagnostics in elliptical spatial linear models. Test 24 (2): 322-340. https://doi.org/10.1007/s11749-014-0409-z
Di HJ, Kemp RA, Trangmar BB, 1989. Use of geoestatistics in designing sampling strategies for soil survey. Soil Sci Soc Am J 53 (4): 1163-1167. https://doi.org/10.2136/sssaj1989.03615995005300040028x
Domenech MB, Castro-Franco M, Costa JL, Amiotti NM, 2017. Sampling scheme optimization to map soil depth to petrocalcic horizon at field scale. Geoderma 290: 75-82. https://doi.org/10.1016/j.geoderma.2016.12.012
Embrapa, 2013. Sistema brasileiro de classificação de solos, 3ed. Empresa Brasileira de Pesquisa Agropecuária, Centro Nacional de Pesquisa de Solos, Brasília. 306 pp.
Faraco MA, Uribe-Opazo MA, Silva EA, Johann JA, Borssoi JA, 2008. Seleção de modelos de variabilidade espacial para elaboração de mapas temáticos de atributos físicos do solo e produtividade da soja. Rev Bras Cienc Solo 32 (2): 463-476. https://doi.org/10.1590/S0100-06832008000200001
Fattorini L, Corona P, Chirici G, Pagliarella MC, 2015. Design-based strategies for sampling spatial units from regular grids with applications to forest surveys, land use, and land cover estimation. Environmetrics 26 (3): 216-228. https://doi.org/10.1002/env.2332
Ferreyra RA, Apezteguía HP, Sereno R, Jones JW, 2002. Reduction of soil water spatial sampling density using scaled semivariograms and simulated annealing. Geoderma 110 (3-4): 265-289. https://doi.org/10.1016/S0016-7061(02)00234-3
Filizola HF, Gomes MAF, Souza MD, 2006. Manual de procedimentos de coleta de amostras em áreas agrícolas para análise da qualidade ambiental: solo, água e sedimentos. Embrapa Meio Ambiente, Jaguariúna - SP.
Gallardo A, Paramá R, 2007. Spatial variability of soil elements in two plant communities of NW Spain. Geoderma 139: 199-208. https://doi.org/10.1016/j.geoderma.2007.01.022
Grego CR, Oliveira RP, Vieira SR, 2014. Geoestatística aplicada a agricultura de precisão. In: Agricultura de precisão: resultados de um novo olhar; Bernardi AC de C, Naime J de M, de Rezende AV, Bassoi LH, Inamasu RY (Eds.). pp. 350-360. Embrapa, Brasília.
Griffith DA, 2005. Effective geographic sample size in the presence of spatial autocorrelation. Ann Assoc Am Geogr 95 (4): 740-760. https://doi.org/10.1111/j.1467-8306.2005.00484.x
Grzegozewski DM, Uribe-Opazo MA, De Bastiani F, Galea M, 2013. Influencia local a modelos espaciales lineales Gaussianos: Aplicación a la agricultura. Cienc Inv Agr 40 (3): 537-545. https://doi.org/10.4067/S0718-16202013000300006
Guedes LPC, Ribeiro Jr PJ, Piedade SMS, Uribe-Opazo MA, 2011. Optimization of spatial sample configurations using hybrid genetic algorithm and simulated annealing. Chil J Stat 2 (2): 39-50.
Guedes LPC, Uribe-Opazo MA, Ribeiro Jr PJ, 2014. Optimization of sample design sizes and shapes for regionalized variables using simulated annealing. Cienc Inv Agr 41 (1): 33-48. https://doi.org/10.4067/S0718-16202014000100004
Inamasu RY, Bernardi ADC, Vaz CMP, Naime JDM, Queiros LR, Resende AV, et al., 2011. Agricultura de precisão para a sustentabilidade de sistemas produtivos do agronegócio brasileiro. Embrapa Instrumentação, 2011. p. 14-26.
Johnson ME, Moore LM, Ylvisaker D, 1990. Minimax and maximin distance designs. J Stat Plan Inference 26 (2): 131-148. https://doi.org/10.1016/0378-3758(90)90122-B
Kestring F, Guedes LPC, De Bastiani F, Uribe-Opazo MA, 2015. Thematic maps comparison of different sampling grids for soybean productivity. Eng Agr 35: 733-743. https://doi.org/10.1590/1809-4430-Eng.Agric.v35n4p733-743/2015
Kravchenko AN, 2003. Influence of spatial structure on accuracy of interpolation methods. Soil Sci Soc Am J 67 (5): 1564-1571. https://doi.org/10.2136/sssaj2003.1564
Krippendorff K, 2013. Content analysis an introduction to its methodology, 2nd ed. Sage Publ Ltd, California. 412 pp.
Linden R, 2012. Algoritmos genéticos. Ciência Moderna Ltd, Rio de Janeiro. 496 pp.
Machuca-Mory DF, Deutsch CV, 2013. Non-stationary geostatistical modeling based on distance weighted statistics and distributions. Math Geosci 45 (1): 31-48. https://doi.org/10.1007/s11004-012-9428-z
Maity A, Sherman M, 2012. Testing for spatial isotropy under general designs. J Stat Plan Inf 142 (5): 1081-1091. https://doi.org/10.1016/j.jspi.2011.11.013
Maltauro TC, Guedes LPC, Uribe-Opazo MA, 2019. Reduction of sample size in the analysis of spatial variability of non-stationary soil chemical attributes. Eng Agr 39 (s): 56-65. https://doi.org/10.1590/1809-4430-eng.agric.v39nep56-65/2019
Manchuk JG, Deutsch CV, 2012. Note on working with trends in geostatistics. CCG Annual Report 14: 128-1/128-8.
Mardia KV, Marshall RJ, 1984. Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 71 (1): 135-146. https://doi.org/10.1093/biomet/71.1.135
Min L, Cheng, W, 1999. A genetic algorithm for minimizing the makespan in the case of scheduling identical parallel machines. Artif Intell Eng 13 (4): 399-403. https://doi.org/10.1016/S0954-1810(99)00021-7
Montanari R, Souza GSA, Pereira GT, Marques Jr. J, Siqueira DS, Siqueira GM, 2012. The use of scaled semivariograms to plan soil sampling in sugarcane fields. Precis Agric 13:1-11. https://doi.org/10.1007/s11119-012-9265-6
Nanni MR, Povh FP, Demattê JAM, Oliveira R.B, Chicati ML, Cezar E, 2011. Optimum size in grid soil sampling for variable rate application in site-specific management. Sci Agric 68 (3): 386-392. https://doi.org/10.1590/S0103-90162011000300017
Nunes LM, Caiero S, Cunha MC, Ribeiro L, 2006. Optimal estuarine sediment monitoring network design with simulated annealing. J Environ Manage 78 (3): 294-304. https://doi.org/10.1016/j.jenvman.2005.04.024
Pimentel Gomes F, 1985. Curso de estatística experimental, 12th. ed. Nobel, São Paulo. 451 pp.
Pronzato L, 2017. Minimax and maximin space-filling designs: some properties and methods for construction. J Soc Fr Statistique 158: 7-36.
R Development Core Team, 2021. R: A language and environment for statistical computing, vers 4.0.0. R Foundation for Statistical Computing, Vienna, Austria.
Ribeiro Jr PJ, Diggle PJ, 2001. geoR: a package for geostatistical analysis. R-NEWS1. 15-18.
Ribeiro GG dos S, Tachibana VM, Galo MDLBT, 2016. Influência do delineamento amostral na inferência espacial por geoestatística aplicada a dados de clorofila-a adquiridos em transectos. Rev Bras Cartogr 68 (4): 745-758.
Santos PCD, Santana ACD, Barros PLCD, Queiroz JCB, Vieira TDO, 2011. O emprego da geoestatística na determinação do tamanho "ótimo" de amostras aleatórias com vistas à obtenção de estimativas dos volumes dos fustes de espécies florestais em Paragominas, estado do Pará. Acta Amazon 41 (2): 213-222. https://doi.org/10.1590/S0044-59672011000200005
Sexton RS, Dorsey RE, Johnson JD, 1999. Optimization of neural networks: A comparative analysis of the genetic algorithm and simulated annealing. Eur J Oper Res 114 (3): 589-601. https://doi.org/10.1016/S0377-2217(98)00114-3
Shiflet AB, Shiflet GW, 2014. Introduction to computational science: modeling and simulation for the sciences, 2nd ed. Princeton Univ Press. 857 pp.
Siqueira DS, Marques Jr J, Pereira GT, Barbosa RS, Teixeira DB, Peluco RG, 2014. Sampling density and proportion for the characterization of the variability of Oxisol attributes on different materials. Geoderma 232 (234): 172-182. https://doi.org/10.1016/j.geoderma.2014.04.037
Szatmári G, László P, Takács K, Szabó J, Bakacsi Z, Koós S, Pásztor L, 2018. Optimization of second-phase sampling for multivariate soil mapping purposes: Case study from a wine region, Hungary. Geoderma 352: 373-384. https://doi.org/10.1016/j.geoderma.2018.02.030
Taiz L, Zeiger E, Møller IM, Murphy A, 2017. Fisiologia e desenvolvimento vegetal, 6th ed. Artmed Editora. 888 pp.
Uribe-Opazo MA, Borssoi JA, Galea M, 2012. Influence diagnostics in Gaussian spatial linear models. J Appl Stat 39 (3): 615-630. https://doi.org/10.1080/02664763.2011.607802
Vallejos R, Osorio F, 2014. Effective sample size of spatial process models. Spat Stat 9: 66-92. https://doi.org/10.1016/j.spasta.2014.03.003
Wang JF, Stein A, Gao BB, Ge Y, 2012. A review of spatial sampling. Spat Stat 2: 1-14. https://doi.org/10.1016/j.spasta.2012.08.001
Yang CT, Sung TC, Weng WC, 2006. An improved tabu search approach with mixed objective function for one-dimensional cutting stock problems. Adv Eng Soft 37 (8): 502-513. https://doi.org/10.1016/j.advengsoft.2006.01.005
Zhu Z, Stein ML, 2005. Spatial sampling for design for parameter estimation of the covariance function. J Stat Plan Infer 134 (2) 583-603. https://doi.org/10.1016/j.jspi.2004.04.017
© CSIC. Manuscripts published in both the printed and online versions of this Journal are the property of Consejo Superior de Investigaciones Científicas, and quoting this source is a requirement for any partial or full reproduction.
All contents of this electronic edition, except where otherwise noted, are distributed under a “Creative Commons Attribution 4.0 International” (CC BY 4.0) License. You may read here the basic information and the legal text of the license. The indication of the CC BY 4.0 License must be expressly stated in this way when necessary.
Self-archiving in repositories, personal webpages or similar, of any version other than the published by the Editor, is not allowed.
