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RESEARCH ARTICLE

Rapid elemental prediction of heterogeneous tropical soils from pXRF data: a comparison of models via linear regressions and machine learning algorithms

Álvaro José Gomes de Faria https://orcid.org/0000-0002-2817-5908 A , Sérgio Henrique Godinho Silva https://orcid.org/0000-0003-2750-5976 A * , Luiza Carvalho Alvarenga Lima B , Renata Andrade A , Lívia Botelho A , Leônidas Carrijo Azevedo Melo https://orcid.org/0000-0002-4034-4209 A , Luiz Roberto Guimarães Guilherme A and Nilton Curi https://orcid.org/0000-0002-2604-0866 A
+ Author Affiliations
- Author Affiliations

A Department of Soil Science, Federal University of Lavras, P.O. Box 3037, Zip Code 37200-900, Lavras, Minas Gerais, Brazil.

B Department of Mechanical Engineering, Federal University of Lavras, P.O. Box 3037, Zip Code 37200-900, Lavras, Minas Gerais, Brazil.

* Correspondence to: sergio.silva@ufla.br

Handling Editor: Irshad Bibi

Soil Research 61(6) 598-615 https://doi.org/10.1071/SR22168
Submitted: 20 July 2022  Accepted: 1 March 2023   Published: 27 March 2023

© 2023 The Author(s) (or their employer(s)). Published by CSIRO Publishing

Abstract

Context: USEPA 3051a is a standard analytical methodology for the extraction of inorganic substances in soils. However, these analyses are expensive, time-consuming and produce chemical residues. Conversely, proximal sensors such as portable X-ray fluorescence (pXRF) spectrometry reduce analysis time, costs and consequently offer a valuable alternative to laboratory analyses.

Aim: We aimed to investigate the feasibility to predict the results of the USEPA 3051a method for 28 chemical elements from pXRF data.

Methods: Samples (n = 179) representing a large area from Brazil were analysed for elemental composition using the USEPA 3051a method and pXRF scanning (Al, Ca, Cr, Cu, Fe, K, Mn, Ni, P, Pb, Sr, Ti, V, Zn and Zr). Linear regressions (simple linear regression – SLR and stepwise multiple linear regressions – SMLR) and machine learning algorithms (support vector machine – SVM and random forest – RF) were tested and compared. Modelling was developed with 70% of the data, while the remaining 30% were used for validation.

Key results: Results demonstrated that SVM and RF performed better than SLR and SMLR for the prediction of Al, Ba, Bi, Ca, Cd, Ce, Co, Cr, Cu, Fe, Mg, Mn, Mo, P, Pb, Sn, Sr, Ti, Tl, V, Zn and Zr; R2 and RPD values ranged from 0.52 to 0.94 and 1.43 to 3.62, respectively, as well as the lowest values of RMSE and NRMSE values (0.28 to 0.70 mg kg−1).

Conclusions and implications: Most USEPA 3051a results can be accurately predicted from pXRF data saving cost, time, and ensuring large-scale routine geochemical characterisation of tropical soils in an environmentally friendly way.

Keywords: acid digestion, environmental modelling, pedology, proximal sensors, soil analysis, soil chemistry, soil variability, USEPA 3051a.


References

Alvares CA, Stape JL, Sentelhas PC, et al. (2013) Köppen’s climate classification map for Brazil. Meteorologische Zeitschrift 22, 711–728.
Köppen’s climate classification map for Brazil.Crossref | GoogleScholarGoogle Scholar |

Andrade R, Faria WM, Silva SHG, et al. (2020) Prediction of soil fertility via portable X-ray fluorescence (pXRF) spectrometry and soil texture in the Brazilian Coastal Plains. Geoderma 357, 113960
Prediction of soil fertility via portable X-ray fluorescence (pXRF) spectrometry and soil texture in the Brazilian Coastal Plains.Crossref | GoogleScholarGoogle Scholar |

Andrade R, Silva SHG, Weindorf DC, et al. (2021) Micronutrients prediction via pXRF spectrometry in Brazil: influence of weathering degree. Geoderma Regional 27, e00431
Micronutrients prediction via pXRF spectrometry in Brazil: influence of weathering degree.Crossref | GoogleScholarGoogle Scholar |

Araújo SR, Wetterlind J, Demattê JAM, Stenberg B (2014) Improving the prediction performance of a large tropical vis-NIR spectroscopic soil library from Brazil by clustering into smaller subsets or use of data mining calibration techniques. European Journal of Soil Science 65, 718–729.
Improving the prediction performance of a large tropical vis-NIR spectroscopic soil library from Brazil by clustering into smaller subsets or use of data mining calibration techniques.Crossref | GoogleScholarGoogle Scholar |

Barros e Souza AB, Demattê JAM, Bellinaso H, et al. (2021) A sensors-based profile heterogeneity index for soil characterization. Catena 207, 105670
A sensors-based profile heterogeneity index for soil characterization.Crossref | GoogleScholarGoogle Scholar |

Benedet L, Acuña-Guzman SF, Faria WM, et al. (2021) Rapid soil fertility prediction using X-ray fluorescence data and machine learning algorithms. Catena 197, 105003
Rapid soil fertility prediction using X-ray fluorescence data and machine learning algorithms.Crossref | GoogleScholarGoogle Scholar |

Bispo FHA, de Menezes MD, Fontana A, et al. (2021) Rare earth elements (REEs): geochemical patterns and contamination aspects in Brazilian benchmark soils. Environmental Pollution 289, 117972
Rare earth elements (REEs): geochemical patterns and contamination aspects in Brazilian benchmark soils.Crossref | GoogleScholarGoogle Scholar |

Bocardi JMB, Pletsch AL, Melo VF, Quinaia SP (2020) Quality reference values for heavy metals in soils developed from basic rocks under tropical conditions. Journal of Geochemical Exploration 217, 106591
Quality reference values for heavy metals in soils developed from basic rocks under tropical conditions.Crossref | GoogleScholarGoogle Scholar |

Borges CS, Weindorf DC, Nascimento DC, et al. (2020) Comparison of portable X-ray fluorescence spectrometry and laboratory-based methods to assess the soil elemental composition: applications for wetland soils. Environmental Technology & Innovation 19, 100826
Comparison of portable X-ray fluorescence spectrometry and laboratory-based methods to assess the soil elemental composition: applications for wetland soils.Crossref | GoogleScholarGoogle Scholar |

Brinatti AM, Mascarenhas YP, Pereira VP, et al. (2010) Mineralogical characterization of a highly-weathered soil by the rietveld method. Scientia Agricola 67, 454–464.
Mineralogical characterization of a highly-weathered soil by the rietveld method.Crossref | GoogleScholarGoogle Scholar |

CETESB (2014) Companhia de Tecnologia de Saneamento Ambiental. Decisão de Diretoria 045/2014/E/C/I, de 20-02-2014. Dispõe sobre a aprovação dos Valores Orientadores para Solos e Águas Subterrâneas no Estado de São Paulo - 2014, em substituição aos Valores Orientadores. (CETESB)

Chagas CS, Carvalho Junior W, Bhering SB, Calderano Filho B (2016) Spatial prediction of soil surface texture in a semiarid region using random forest and multiple linear regressions. Catena 139, 232–240.
Spatial prediction of soil surface texture in a semiarid region using random forest and multiple linear regressions.Crossref | GoogleScholarGoogle Scholar |

Chai T, Draxler RR (2014) Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature. Geoscientific Model Development 7, 1247–1250.
Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature.Crossref | GoogleScholarGoogle Scholar |

Chang CW, Laird DA, Mausbach MJ, Hurburgh CR (2001) Near-infrared reflectance spectroscopy–principal components regression analyses of soil properties. Soil Science Society of America Journal 65, 480–490.
Near-infrared reflectance spectroscopy–principal components regression analyses of soil properties.Crossref | GoogleScholarGoogle Scholar |

Chen M, Ma LQ (1998) Comparison of four USEPA digestion methods for trace metal analysis using certified and florida soils. Journal of Environmental Quality 27, 1294–1300.
Comparison of four USEPA digestion methods for trace metal analysis using certified and florida soils.Crossref | GoogleScholarGoogle Scholar |

CONAMA (2009) Conselho Nacional do Meio Ambiente. Resolução Conama no 420, de 28 de dezembro de 2009: Dispõe sobre critérios e valores orientadores de qualidade do solo quanto à presença de substâncias químicas e estabelece diretrizes para o gerenciamento ambiental de. (CONAMA)

COPAM (2011) Conselho Estadual de Política Ambiental, Deliberação Normativa Copam no 166, de 29 de junho de 2011. Altera o Anexo I da Deliberação Normativa Conjunta Copam CERH no 2 de 6 de setembro de 2010, estabelecendo os Valores de Referência de Qualidade dos Solos. (COPAM)

Coringa EAO, Couto EG, Torrado PV (2014) Geoquímica de solos do pantanal norte, Mato Grosso. Revista Brasileira de Ciência do Solo 38, 1784–1793.
Geoquímica de solos do pantanal norte, Mato Grosso.Crossref | GoogleScholarGoogle Scholar |

Costa YT, Ribeiro BT, Curi N, et al. (2019) Organic matter removal on oxide determination in oxisols via portable X-ray fluorescence. Communications in Soil Science and Plant Analysis 50, 673–681.
Organic matter removal on oxide determination in oxisols via portable X-ray fluorescence.Crossref | GoogleScholarGoogle Scholar |

Declercq Y, Delbecque N, De Grave J, et al. (2019) A comprehensive study of three different portable XRF scanners to assess the soil geochemistry of an extensive sample dataset. Remote Sensing 11, 2490
A comprehensive study of three different portable XRF scanners to assess the soil geochemistry of an extensive sample dataset.Crossref | GoogleScholarGoogle Scholar |

Dharumarajan S, Hegde R, Singh SK (2017) Spatial prediction of major soil properties using Random Forest techniques – a case study in semi-arid tropics of South India. Geoderma Regional 10, 154–162.
Spatial prediction of major soil properties using Random Forest techniques – a case study in semi-arid tropics of South India.Crossref | GoogleScholarGoogle Scholar |

Drouet T, Herbauts J, Gruber W, Demaiffe D (2007) Natural strontium isotope composition as a tracer of weathering patterns and of exchangeable calcium sources in acid leached soils developed on loess of central Belgium. European Journal of Soil Science 58, 302–319.
Natural strontium isotope composition as a tracer of weathering patterns and of exchangeable calcium sources in acid leached soils developed on loess of central Belgium.Crossref | GoogleScholarGoogle Scholar |

Faria ÁJG, Silva SHG, Melo LCA, et al. (2020) Soils of the Brazilian Coastal Plains biome: prediction of chemical attributes via portable X-ray fluorescence (pXRF) spectrometry and robust prediction models. Soil Research 58, 683–695.
Soils of the Brazilian Coastal Plains biome: prediction of chemical attributes via portable X-ray fluorescence (pXRF) spectrometry and robust prediction models.Crossref | GoogleScholarGoogle Scholar |

Faria AJG, Silva SHG, Andrade R, et al. (2022a) Prediction of soil organic matter content by combining data from Nix Pro™ color sensor and portable X-ray fluorescence spectrometry in tropical soils. Geoderma Regional 28, e00461
Prediction of soil organic matter content by combining data from Nix Pro™ color sensor and portable X-ray fluorescence spectrometry in tropical soils.Crossref | GoogleScholarGoogle Scholar |

Faria AJG, Silva SHG, Melo LCA, et al. (2022b) Relationship between elemental content determined via portable X-ray fluorescence and traditional acid_digestion-based methods in tropical soils. Soil Research 60, 661–677.
Relationship between elemental content determined via portable X-ray fluorescence and traditional acid_digestion-based methods in tropical soils.Crossref | GoogleScholarGoogle Scholar |

Forkuor G, Hounkpatin OKL, Welp G, Thiel M (2017) High resolution mapping of soil properties using remote sensing variables in south-western Burkina Faso: a comparison of machine learning and multiple linear regression models. PLoS ONE 12, e0170478
High resolution mapping of soil properties using remote sensing variables in south-western Burkina Faso: a comparison of machine learning and multiple linear regression models.Crossref | GoogleScholarGoogle Scholar |

González S, Herrera F, García S (2015) Monotonic random forest with an ensemble pruning mechanism based on the degree of monotonicity. New Generation Computing 33, 367–388.
Monotonic random forest with an ensemble pruning mechanism based on the degree of monotonicity.Crossref | GoogleScholarGoogle Scholar |

Gozukara G, Zhang Y, Hartemink AE (2021) Using vis-NIR and pXRF data to distinguish soil parent materials – an example using 136 pedons from Wisconsin, USA. Geoderma 396, 115091
Using vis-NIR and pXRF data to distinguish soil parent materials – an example using 136 pedons from Wisconsin, USA.Crossref | GoogleScholarGoogle Scholar |

Hornik K, Weingessel A, Leisch F, Davidmeyerr-Projectorg MDM (2015) Package ‘e1071’. Available at https://cran.r-project.org/web/packages/e1071/e1071.pdf

Hou H, Takamatsu T, Koshikawa MK, Hosomi M (2005) Migration of silver, indium, tin, antimony, and bismuth and variations in their chemical fractions on addition to uncontaminated soils. Soil Science 170, 624–639.
Migration of silver, indium, tin, antimony, and bismuth and variations in their chemical fractions on addition to uncontaminated soils.Crossref | GoogleScholarGoogle Scholar |

Hseu Z-Y, Chen Z-S, Tsai C-C, Jien S-H (2016) Portable X-Ray fluorescence (pXRF) for determining Cr and Ni contents of serpentine soils in the field. In ‘Digital soil morphometrics’. Progress in soil science. (Eds A Hartemink, B Minasny) pp. 37–50. (Springer: Cham)

Jalali SAS, Navidi MN, Mohammadi JS, et al. (2019) Prediction of soil cation exchange capacity using different soil parameters by intelligent models. Communications in Soil Science and Plant Analysis 50, 2123–2139.
Prediction of soil cation exchange capacity using different soil parameters by intelligent models.Crossref | GoogleScholarGoogle Scholar |

Javadi SH, Mouazen AM (2021) Data fusion of XRF and vis-NIR using outer product analysis, granger–ramanathan, and least squares for prediction of key soil attributes. Remote Sensing 13, 2023
Data fusion of XRF and vis-NIR using outer product analysis, granger–ramanathan, and least squares for prediction of key soil attributes.Crossref | GoogleScholarGoogle Scholar |

Kabata-Pendias A (2010) ‘Trace elements in soils and plants.’ 4th edn. (CRC Press)

Kabata-Pendias A, Mukherjee AB (2007) ‘Trace elements from soil to human.’ (Springer-Verlag: Berlin)

Kämpf N, Marques JJ, Curi N (2012) Mineralogia de Solos Brasileiros. In ‘Pedologia Fundamentos’: (Eds JC Ker, N. Curi, CEGR Schaefer, P Vidal-Torrado). p. 343. (SBCS: Viçosa, MG)

Liaw A, Wiener M (2002) Classification and regression by random forest. R News 2, 18–22.

Liaw A, Wiener M (2015) Package ‘randomForest’. R Dev. Core Team. Available at https://cran.r-project.org/web/packages/randomForest/randomForest.pdf

Lima TM, Weindorf DC, Curi N, et al. (2019) Elemental analysis of Cerrado agricultural soils via portable X-ray fluorescence spectrometry: inferences for soil fertility assessment. Geoderma 353, 264–272.
Elemental analysis of Cerrado agricultural soils via portable X-ray fluorescence spectrometry: inferences for soil fertility assessment.Crossref | GoogleScholarGoogle Scholar |

Liu Y, Wang C, Xiao C, et al. (2021) Prediction of multiple soil fertility parameters using VisNIR spectroscopy and PXRF spectrometry. Soil Science Society of America Journal 85, 591–605.
Prediction of multiple soil fertility parameters using VisNIR spectroscopy and PXRF spectrometry.Crossref | GoogleScholarGoogle Scholar |

Lopes AS, Guilherme LRG (2016) A career perspective on soil management in the Cerrado region of Brazil. Advances in Agronomy 137, 1–72.
A career perspective on soil management in the Cerrado region of Brazil.Crossref | GoogleScholarGoogle Scholar |

Lucà F, Conforti M, Castrignanò A, et al. (2017) Effect of calibration set size on prediction at local scale of soil carbon by Vis-NIR spectroscopy. Geoderma 288, 175–183.
Effect of calibration set size on prediction at local scale of soil carbon by Vis-NIR spectroscopy.Crossref | GoogleScholarGoogle Scholar |

Mancini M, Weindorf DC, Chakraborty S, et al. (2019a) Tracing tropical soil parent material analysis via portable X-ray fluorescence (pXRF) spectrometry in Brazilian Cerrado. Geoderma 337, 718–728.
Tracing tropical soil parent material analysis via portable X-ray fluorescence (pXRF) spectrometry in Brazilian Cerrado.Crossref | GoogleScholarGoogle Scholar |

Mancini M, Weindorf DC, Silva SHG, et al. (2019b) Parent material distribution mapping from tropical soils data via machine learning and portable X-ray fluorescence (pXRF) spectrometry in Brazil. Geoderma 354, 113885
Parent material distribution mapping from tropical soils data via machine learning and portable X-ray fluorescence (pXRF) spectrometry in Brazil.Crossref | GoogleScholarGoogle Scholar |

Mancini M, Weindorf DC, Monteiro MEC, et al. (2020) From sensor data to Munsell color system: Machine learning algorithm applied to tropical soil color classification via Nix™ Pro sensor. Geoderma 375, 114471
From sensor data to Munsell color system: Machine learning algorithm applied to tropical soil color classification via Nix™ Pro sensor.Crossref | GoogleScholarGoogle Scholar |

Marko M (2018) Coefficient-of-determination Fourier transform. Computation 6, 61
Coefficient-of-determination Fourier transform.Crossref | GoogleScholarGoogle Scholar |

Marques JJ, Schulze DG, Curi N, Mertzman SA (2004a) Trace element geochemistry in Brazilian Cerrado soils. Geoderma 121, 31–43.
Trace element geochemistry in Brazilian Cerrado soils.Crossref | GoogleScholarGoogle Scholar |

Marques JJ, Schulze DG, Curi N, Mertzman SA (2004b) Major element geochemistry and geomorphic relationships in Brazilian Cerrado soils. Geoderma 119, 179–195.
Major element geochemistry and geomorphic relationships in Brazilian Cerrado soils.Crossref | GoogleScholarGoogle Scholar |

Meier M, Souza E, Francelino MR, et al. (2018) Digital soil mapping using machine learning algorithms in a tropical mountainous area. Revista Brasileira de Ciencia do Solo 42, e0170421
Digital soil mapping using machine learning algorithms in a tropical mountainous area.Crossref | GoogleScholarGoogle Scholar |

Melo VF, Schaefer CEGR, Singh B, et al. (2002a) Propriedades químicas e cristalográficas da caulinita e dos óxidos de ferro em sedimentos do grupo barreiras no município de Aracruz, estado do Espírito Santo. Revista Brasileira Ciência do Solo 26, 53–64.
Propriedades químicas e cristalográficas da caulinita e dos óxidos de ferro em sedimentos do grupo barreiras no município de Aracruz, estado do Espírito Santo.Crossref | GoogleScholarGoogle Scholar |

Melo VF, Novais RF, Schaefer CEGR, et al. (2002b) Mineralogia das frações areia, silte e argila de sedimentos do grupo barreiras no município de Aracruz, estado do Espírito Santo. Revista Brasileira de Ciência do Solo 26, 29–41.
Mineralogia das frações areia, silte e argila de sedimentos do grupo barreiras no município de Aracruz, estado do Espírito Santo.Crossref | GoogleScholarGoogle Scholar |

Meurer EJ, Rheinheimer RD, Bissani CA (2010) Fenômeno de Sorção em Solos. In ‘Fundamentos de Química do Solo’. 4th edn. (EJ Meurer). (Evangraf: Porto Alege)

Murata T (2010) Bismuth solubility through binding by various organic compounds and naturally occurring soil organic matter. Journal of Environmental Science and Health - Part A Toxic/Hazardous Substances and Environmental Engineering 45, 746–753.
Bismuth solubility through binding by various organic compounds and naturally occurring soil organic matter.Crossref | GoogleScholarGoogle Scholar |

Nascimento ES, Tenuta Filho A (2010) Chemical waste risk reduction and environmental impact generated by laboratory activities in research and teaching institutions. Brazilian Journal of Pharmaceutical Sciences 46, 187–198.
Chemical waste risk reduction and environmental impact generated by laboratory activities in research and teaching institutions.Crossref | GoogleScholarGoogle Scholar |

Nawar S, Delbecque N, Declercq Y, et al. (2019) Can spectral analyses improve measurement of key soil fertility parameters with X-ray fluorescence spectrometry? Geoderma 350, 29–39.
Can spectral analyses improve measurement of key soil fertility parameters with X-ray fluorescence spectrometry?Crossref | GoogleScholarGoogle Scholar |

Nickerson CAE (1997) A note on “A concordance correlation coefficient to evaluate reproducibility”. Biometrics 53, 1503–1507.
A note on “A concordance correlation coefficient to evaluate reproducibility”.Crossref | GoogleScholarGoogle Scholar |

O’Rourke SM, Minasny B, Holden NM, McBratney AB (2016a) Synergistic use of Vis-NIR, MIR, and XRF spectroscopy for the determination of soil geochemistry. Soil Science Society of America Journal 80, 888–899.
Synergistic use of Vis-NIR, MIR, and XRF spectroscopy for the determination of soil geochemistry.Crossref | GoogleScholarGoogle Scholar |

O’Rourke SM, Stockmann U, Holden NM, et al. (2016b) An assessment of model averaging to improve predictive power of portable vis-NIR and XRF for the determination of agronomic soil properties. Geoderma 279, 31–44.
An assessment of model averaging to improve predictive power of portable vis-NIR and XRF for the determination of agronomic soil properties.Crossref | GoogleScholarGoogle Scholar |

Pelegrino MHP, Silva SHG, de Faria ÁJG, et al. (2022) Prediction of soil nutrient content via pXRF spectrometry and its spatial variation in a highly variable tropical area. Precision Agriculture 23, 18–34.
Prediction of soil nutrient content via pXRF spectrometry and its spatial variation in a highly variable tropical area.Crossref | GoogleScholarGoogle Scholar |

R Development Core Team (2019) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available at https://www.r-project.org/ [Accessed 17 July 2020]

Ravansari R, Wilson SC, Tighe M (2020) Portable X-ray fluorescence for environmental assessment of soils: not just a point and shoot method. Environment International 134, 105250
Portable X-ray fluorescence for environmental assessment of soils: not just a point and shoot method.Crossref | GoogleScholarGoogle Scholar |

Ravansari R, Wilson SC, Wilson BR, Tighe M (2021) Rapid PXRF soil organic carbon and organic matter assessment using novel modular radiation detector assembly. Geoderma 382, 114728
Rapid PXRF soil organic carbon and organic matter assessment using novel modular radiation detector assembly.Crossref | GoogleScholarGoogle Scholar |

Ribeiro BT, Nascimento DC, Curi N, et al. (2019) Assessment of trace element contents in soils and water from cerrado wetlands, triângulo mineiro region. Revista Brasileira de Ciencia do Solo 43, e0180059
Assessment of trace element contents in soils and water from cerrado wetlands, triângulo mineiro region.Crossref | GoogleScholarGoogle Scholar |

Rosolen V, De-Campos AB, Govone JS, Rocha C (2015) Contamination of wetland soils and floodplain sediments from agricultural activities in the Cerrado Biome (State of Minas Gerais, Brazil). Catena 128, 203–210.
Contamination of wetland soils and floodplain sediments from agricultural activities in the Cerrado Biome (State of Minas Gerais, Brazil).Crossref | GoogleScholarGoogle Scholar |

Santana MLT, Ribeiro BT, Silva SHG, et al. (2018) Conditions affecting oxide quantification in unknown tropical soils via handheld X-ray fluorescence spectrometer. Soil Research 56, 648–655.
Conditions affecting oxide quantification in unknown tropical soils via handheld X-ray fluorescence spectrometer.Crossref | GoogleScholarGoogle Scholar |

Santos RD, Santos HG, Ker JC, et al. (2015) ‘Manual de descrição e coleta de solos no campo.’ 7a revisad. (Sociedade Brasileira de Ciencia do solo: Viçosa, MG)

Santos HG, Jacomine PKT, Anjos LHC, et al. (2018) ‘Sistema Brasileiro de Classificação de Solos.’ 5th edn. (Embrapa: Brasília)

Shcherbakov MV, Brebels A, Shcherbakova NL (2013) A survey of forecast error measures. World Applied Sciences Journal 24, 171–176.
A survey of forecast error measures.Crossref | GoogleScholarGoogle Scholar |

Silva YJAB, Nascimento CWA, Biondi CM (2014) Comparison of USEPA digestion methods to heavy metals in soil samples. Environmental Monitoring and Assessment 186, 47–53.
Comparison of USEPA digestion methods to heavy metals in soil samples.Crossref | GoogleScholarGoogle Scholar |

Silva EA, Weindorf DC, Silva SHG, et al. (2019) Advances in tropical soil characterization via portable X-Ray fluorescence spectrometry. Pedosphere 29, 468–482.
Advances in tropical soil characterization via portable X-Ray fluorescence spectrometry.Crossref | GoogleScholarGoogle Scholar |

Silva SHG, Silva EA, Poggere GC, et al. (2020) Modeling and prediction of sulfuric acid digestion analyses data from PXRF spectrometry in tropical soils. Scientia Agricola 77, e20180132
Modeling and prediction of sulfuric acid digestion analyses data from PXRF spectrometry in tropical soils.Crossref | GoogleScholarGoogle Scholar |

Silva SHG, Ribeiro BT, Guerra MBB, et al. (2021) pXRF in tropical soils: methodology, applications, achievements and challenges. Advances in Agronomy 167, 1–62.
pXRF in tropical soils: methodology, applications, achievements and challenges.Crossref | GoogleScholarGoogle Scholar |

Soil Survey Staff (2014) Soil survey field and laboratory methods manual. Version 2. USDA-NRCS. Available at https://www.nrcs.usda.gov/Internet/FSE_DOCUMENTS/stelprdb1244466.pdf [Verified 15 February 2021]

Soltanpour PN, Johnson GW, Workman SM, et al. (1996) Inductively coupled plasma emission spectrometry and inductively coupled plasma-mass spectrometry. In ‘Methods of soil analysis. Part 3. Chemical methods’. (Eds DL Sparks, AL Page, PA Helmke, RH Loeppert, PN Soltanpour, MA Tabatabai, CT Johnston, ME Sumner) pp. 91–139. (John Wiley & Sons, Ltd)

Souza JJLL, Abrahão WAP, Mello JWV, et al. (2015) Geochemistry and spatial variability of metal(loid) concentrations in soils of the state of Minas Gerais, Brazil. Science of the Total Environment 505, 338–349.
Geochemistry and spatial variability of metal(loid) concentrations in soils of the state of Minas Gerais, Brazil.Crossref | GoogleScholarGoogle Scholar |

Stockmann U, Cattle SR, Minasny B, McBratney AB (2016) Utilizing portable X-ray fluorescence spectrometry for in-field investigation of pedogenesis. Catena 139, 220–231.
Utilizing portable X-ray fluorescence spectrometry for in-field investigation of pedogenesis.Crossref | GoogleScholarGoogle Scholar |

Taebi A, Mansy HA (2017) Time-frequency distribution of seismocardiographic signals: a comparative study. Bioengineering 4, 32
Time-frequency distribution of seismocardiographic signals: a comparative study.Crossref | GoogleScholarGoogle Scholar |

Tavares TR, Molin JP, Hamed Javadi S, et al. (2021) Combined use of vis-NIR and XRF sensors for tropical soil fertility analysis: assessing different data fusion approaches. Sensors 21, 148
Combined use of vis-NIR and XRF sensors for tropical soil fertility analysis: assessing different data fusion approaches.Crossref | GoogleScholarGoogle Scholar |

USEPA (2007a) Method 6200: Field portable X-ray fluorescence spectrometry for the determination of elemental concentrations in soil and sediment. US EPA. Available at https://www.epa.gov/sites/production/files/2015-12/documents/6200.pdf [Accessed 10 December 2019]

USEPA (2007b) Method 3051a (SW-846): Microwave assisted acid digestion of sediments, sludges, soils, and oils. US EPA. Available at https://www.epa.gov/sites/production/files/2015-12/documents/3051a.pdf [Accessed 27 January 2021]

Vasques GM, Rodrigues HM, Coelho MR, et al. (2020) Field proximal soil sensor fusion for improving high-resolution soil property maps. Soil Systems 4, 52
Field proximal soil sensor fusion for improving high-resolution soil property maps.Crossref | GoogleScholarGoogle Scholar |

Wan M, Qu M, Hu W, et al. (2019) Estimation of soil pH using PXRF spectrometry and Vis-NIR spectroscopy for rapid environmental risk assessment of soil heavy metals. Process Safety and Environmental Protection 132, 73–81.
Estimation of soil pH using PXRF spectrometry and Vis-NIR spectroscopy for rapid environmental risk assessment of soil heavy metals.Crossref | GoogleScholarGoogle Scholar |

Wan M, Hu W, Qu M, et al. (2020) Rapid estimation of soil cation exchange capacity through sensor data fusion of portable XRF spectrometry and Vis-NIR spectroscopy. Geoderma 363, 114163
Rapid estimation of soil cation exchange capacity through sensor data fusion of portable XRF spectrometry and Vis-NIR spectroscopy.Crossref | GoogleScholarGoogle Scholar |

Wang D, Chakraborty S, Weindorf DC, et al. (2015) Synthesized use of VisNIR DRS and PXRF for soil characterization: Total carbon and total nitrogen. Geoderma 243–244, 157–167.
Synthesized use of VisNIR DRS and PXRF for soil characterization: Total carbon and total nitrogen.Crossref | GoogleScholarGoogle Scholar |

Weindorf DC, Chakraborty S (2020) Portable X-ray fluorescence spectrometry analysis of soils. Soil Science Society of America Journal 84, 1384–1392.
Portable X-ray fluorescence spectrometry analysis of soils.Crossref | GoogleScholarGoogle Scholar |

Weindorf DC, Bakr N, Zhu Y (2014) ‘Advances in portable X-ray fluorescence (PXRF) for environmental, pedological, and agronomic applications.’ (Elsevier)

Willmott CJ, Ackleson SG, Davis RE (1985) Statistics for the evaluation and comparison of models. Journal of Geophysical Research 90, 8995–9005.
Statistics for the evaluation and comparison of models.Crossref | GoogleScholarGoogle Scholar |

Wu W, Li AD, He XH, et al. (2018) A comparison of support vector machines, artificial neural network and classification tree for identifying soil texture classes in southwest China. Computers and Electronics in Agriculture 144, 86–93.
A comparison of support vector machines, artificial neural network and classification tree for identifying soil texture classes in southwest China.Crossref | GoogleScholarGoogle Scholar |

Yang X, Post WM (2011) Phosphorus transformations as a function of pedogenesis: a synthesis of soil phosphorus data using Hedley fractionation method. Biogeosciences 8, 2907–2916.
Phosphorus transformations as a function of pedogenesis: a synthesis of soil phosphorus data using Hedley fractionation method.Crossref | GoogleScholarGoogle Scholar |