Modeling and prediction of sulfuric acid digestion analyses data from PXRF spectrometry in tropical soils

Sérgio Henrique Godinho Silva Elen Alvarenga Silva Giovana Clarice Poggere Alceu Linares Pádua Junior Mariana Gabriele Marcolino Gonçalves Luiz Roberto Guimarães Guilherme Nilton Curi About the authors

ABSTRACT

Sulfuric acid digestion analyses (SAD) provide useful information to environmental studies, in terms of the geochemical balance of nutrients, parent material uniformity, nutrient reserves for perennial crops, and mineralogical composition of the soil clay fraction. Yet, these analyses are costly, time consuming, and generate chemical waste. This work aimed at predicting SAD results from portable X-ray fluorescence (pXRF) spectrometry, which is proposed as a “green chemistry” alternative to the current SAD method. Soil samples developed from different parent materials were analyzed for soil texture and SAD, and scanned with pXRF. The SAD results were predicted from pXRF elemental analyses through simple linear regressions, stepwise multiple linear regressions, and random forest algorithm, with and without incorporation of soil texture data. The modeling was developed with 70 % of the data, while the remaining 30 % was used for validation through calculation of R2, adjusted R2, root mean square error, and mean error. Simple linear regression can accurately predict SAD results of Fe2O3 (R2 0.89), TiO2 (R2 0.96), and P2O5 (R2 0.89). Stepwise regressions provided accurate predictions for Al2O3 (R2 0.87) and Ki - molar weathering index (SiO2/Al2O3) (R2 0.74) by incorporating soil texture data, as well as for SiO2 (R2 0.61). Random forest also provided adequate predictions, especially for Fe2O3 (R2 0.95), and improved results of Kr - molar weathering index (SiO2/(Al2O3 + Fe2O3)) (R2 0.66), by incorporation of soil texture data. Our findings showed that the SAD results could be accurately predicted from pXRF data, decreasing costs, time and the production of laboratory waste.

soil clay fraction; weathering indices; random forest; proximal sensors; green chemistry

Introduction

Applied research using portable X-ray fluorescence (pXRF) spectrometry has increased dramatically over the last few years in different fields of Soil Science ( Duda et al., 2017Duda, B.M.; Weindorf, D.C.; Chakraborty, S.; Li, B.; Man, T.; Paulette, L.; Deb, S. 2017. Soil characterization across catenas via advanced proximal sensors. Geoderma 298: 78-91. ; Chakraborty et al., 2017Chakraborty, S.; Man, T.; Paulette, L.; Deb, S.; Li, B.; Weindorf, D.C.; Frazier, M. 2017. Rapid assessment of smelter/mining soil contamination via portable X-ray fluorescence spectrometry and indicator kriging. Geoderma 306: 108-119. ; Silva et al., 2017Silva, S.H.G.; Teixeira, A.F.S.; Menezes, M.D.; Guilherme, L.R.G.; Moreira, F.M.S.; Curi, N. 2017. Multiple linear regression and random forest to predict and map soil properties using data from portable X-ray fluorescence analyzer (pXRF). Ciência e Agrotecnologia 41: 648-664. ; Stockmann et al., 2016Stockmann, U.; Cattle, S.R.; Minasny, B.; McBratney, A.B. 2016. Utilizing portable X-ray fluorescence spectrometry for in-field investigation of pedogenesis. Catena 139: 220-231. ). Weindorf et al. (2014)Weindorf, D.C.; Bakr, N.; Zhu, Y. 2014. Advances in portable X-ray fluorescence (PXRF) for environmental, pedological, and agronomic application. Advances in Agronomy 128: 1-45. suggested that, in the future, great efforts will be made to establish correlations between pXRF data and results of conventional laboratorial analyses.

Recent studies have used pXRF data to predict various soil chemical and physical properties resulted from conventional laboratory analyses ( Aldabaa et al., 2015Aldabaa, A.A.A.; Weindorf, D.C.; Chakraborty, S.; Sharma, A.; Li, B. 2015. Combination of proximal and remote sensing methods for rapid soil salinity quantification. Geoderma 239: 34-46. ; Sharma et al., 2014Sharma, A.; Weindorf, D.C.; Man, T.; Aldabaa, A.A.A.; Chakraborty, S. 2014. Characterizing soils via portable X-ray fluorescence spectrometer. 3. Soil reaction (pH). Geoderma 232-234: 141-147. ; Sharma et al., 2015Sharma, A.; Weindorf, D.C.; Wang, D.; Chakraborty, S. 2015. Characterizing soils via portable X-ray fluorescence spectrometer. 4. Cation exchange capacity (CEC). Geoderma 239: 130-134. ; Silva et al., 2017Silva, S.H.G.; Teixeira, A.F.S.; Menezes, M.D.; Guilherme, L.R.G.; Moreira, F.M.S.; Curi, N. 2017. Multiple linear regression and random forest to predict and map soil properties using data from portable X-ray fluorescence analyzer (pXRF). Ciência e Agrotecnologia 41: 648-664. ; Zhu et al., 2011Zhu, Y.; Weindorf, D.C.; Zhang, W. 2011. Characterizing soils using a portable X-ray fluorescence spectrometer. 1. Soil texture. Geoderma 167–168: 167-177. ). This means that, analyses that are costly, difficult to be performed, time-consuming, and that generate chemical residues could be replaced or at least reduced, if accurate predictions of their results are achieved from pXRF data ( Rouillon and Taylor, 2016Rouillon, M.; Taylor, M.P. 2016. Can field portable X-ray fluorescence (pXRF) produce high quality data for application in environmental contamination research? Environmental Pollution 214: 255-264. ; McGladdery et al., 2018McGladdery, C.; Weindorf, D.C.; Chakraborty, S.; Li, B.; Paulette, L.; Podar, D.; Pearson, D.; Kusi, N.Y.O.; Duda, B. 2018. Elemental assessment of vegetation via portable X-ray fluorescence (PXRF) spectrometry. Journal of Environmental Management 210: 210-225. ).

In Brazil, sulfuric acid digestion analyses (SAD) are important for studies concerning geochemical balance of nutrients, parent material uniformity, nutrient reserves for perennial crops, as well as mineralogical composition of the soil clay fraction, among others ( Curi and Kämpf, 2012Curi, N.; Kämpf, N. 2012. Soil characterization = Caracterização do solo. p. 147-170. In: Ker, J.C.; Curi, N.; Schaefer, C.E.G.R.; Vidal-Torrado, P., eds. Pedology: fundamentals = Pedologia: fundamentos. SBCS, Viçosa, MG, Brazil (in Portuguese). ). These analyses provide contents of some elements expressed on the oxide basis (Al2O3, SiO2, Fe2O3, TiO2, and P2O5). Furthermore, this data allows calculating two indices used in the Brazilian Soil Classification System and in soil surveys to differentiate highly weathered soils, that is, Ki (SiO2/Al2O3) and Kr (SiO2/(Al2O3 + Fe2O3)). However, conventional SAD is expensive, time-consuming, and generates considerable amounts of chemical waste. In an attempt to overcome this issue, Silva et al. (2018)Silva, S.H.G.; Silva, E.A.; Poggere, G.C.; Guilherme, L.R.G.; Curi, N. 2018. Tropical soils characterization at low cost and time using portable X-ray fluorescence spectrometer (pXRF): effects of different sample preparation methods. Ciência e Agrotecnologia 42: 80-92. used pXRF to estimate SAD results applying simple linear regression, obtaining accurate predictions only for Fe2O3 and TiO2. Nevertheless, several more robust statistical models have been used in other studies, generating suitable results, such as multiple linear regressions ( Rourke et al., 2016Rourke, S.M.O.; Stockmann, U.; Holden, N.M.; Mcbratney, A.B.; Minasny, B. 2016. 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. ; Forkuor et al., 2017Forkuor, G.; Hounkpatin, O.K.L.; 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. ) and random forest algorithm ( Chagas et al., 2016Chagas, C.S.; Carvalho Junior, W.; Bhering, S.B.; 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. ; Souza et al., 2016Souza, E.; Inácio, E.; Filho, F.; Ernesto, C.; Reynaud, G.; Batjes, N.H. 2016. Pedotransfer functions to estimate bulk density from soil properties and environmental covariates: Rio Doce basin. Scientia Agricola 73: 525-534. ; Silva et al., 2017Silva, S.H.G.; Teixeira, A.F.S.; Menezes, M.D.; Guilherme, L.R.G.; Moreira, F.M.S.; Curi, N. 2017. Multiple linear regression and random forest to predict and map soil properties using data from portable X-ray fluorescence analyzer (pXRF). Ciência e Agrotecnologia 41: 648-664. ).

Considering that SAD determines the chemical composition of fine fractions (clay fraction mainly) and that pXRF determines the soil bulk chemical composition, we hypothesize that the results of soil bulk chemical composition determined by pXRF could be well correlated with SAD results in tropical soils, allowing the replacement of SAD by prediction models using pXRF data as input variables. In this sense, this study aimed at predicting the results of SAD from pXRF data, applying simple and multiple linear regressions as well as random forest algorithm. We expect not only to reduce cost, time and laboratory waste, but also to facilitate the use of SAD-derived information in studies on tropical soils.

Materials and Methods

Soil sampling and laboratory analyses

This study was conducted using 52 soil samples collected from the southern, southeastern, and northeastern regions of Brazil, encompassing four states, 19 soil classes according to Soil Taxonomy ( Soil Survey Staff, 2014Soil Survey Staff. 2014. Keys to Soil Taxonomy, 12ed. USDA-Natural Resources Conservation Service, Washington, DC, USA. ) and 14 parent materials ( Table 1 ).

Table 1
– Soils, parent material, location, number of samples (n), soil horizon, texture and results of sulfuric acid digestion analysis.

Soils were morphologically described, and samples from A and B horizons were collected for laboratory analyses. The soil texture analyses were performed according to Baver et al. (1972)Baver, L.D.; Gardner, W.H.; Gardner, W.R. 1972. Soil Physics. John Wiley, New York, NY, USA. and Gee and Bauder (1986)Gee, G.W.; Bauder, J.W. 1986. Particle-size analysis. p. 383-412. In: Klute, A., ed. Methods of soil analysis. American Society of Agronomy, Madison, WI, USA. . For SAD ( Embrapa, 1997Empresa Brasileira de Pesquisa Agropecuária [Embrapa]. 1997. Manual of soil analysis methods = Manual de métodos de análises de solos. Embrapa Solos, Rio de Janeiro, RJ, Brazil (in Portuguese). ), 1 g of soil was mixed with 500 mL of sulfuric acid and 500 mL of water. Then, the solution was boiled for 30 min followed by addition of 50 mL of water. This mixture was filtered and the Fe2O3 and Al2O3 contents were determined by titration, whereas TiO2 and P2O5 contents were determined by colorimetry, and SiO2, by gravimetry. From these results, weathering indices [Ki = SiO2/Al2O3 and Kr = SiO2/(Al2O3 + Fe2O3)] were calculated.

pXRF analyses

Soil samples from A and B horizons were air-dried, ground and sieved through a 2-mm mesh (air-dried fine earth, ADFE). Next, about 15 g of ADFE were analyzed by pXRF spectrometry, in the Trace (dual soil) mode, during 60 s, in triplicate, using the Geochem software, as recommended by Weindorf and Chakraborty (2016)Weindorf, D.C.; Chakraborty, S. 2016. Portable X-ray fluorescence spectrometry analysis of soils. Methods of Soil Analysis. DOI:10.2136/methods-soil.2015.0033. . This equipment has a Rh X-ray tube, 50 keV, 100 µA, and a silicon drift detector (SDD) with resolution of <145 eV, which allows detection of several chemical elements, from Mg to U ( Weindorf et al., 2014Weindorf, D.C.; Bakr, N.; Zhu, Y. 2014. Advances in portable X-ray fluorescence (PXRF) for environmental, pedological, and agronomic application. Advances in Agronomy 128: 1-45. ; Ribeiro et al., 2017)Ribeiro, B.T.; Silva, S.H.G.; Silva, E.A.; Guilherme, L.R.G. 2017. Portable X-ray fluorescence (pXRF) applications in tropical Soil Science. Ciência e Agrotecnologia 41: 245–254. . The pXRF performance was checked through scanning reference materials (CRM) certified by National Institute of Standards and Technology (NIST) (2710a and 2711a) and a sample certified by the equipment manufacturer for the elements detected in most samples. The values recovered (100 × pXRF results/certified results) for these elements in comparison to information from CRM 2710a and 2711a and the manufacturer’s sample, were Al2O3 (84/65/91), Fe (81/66/85), SiO2 (64/47/85), P2O5 (381/547/-), Ti (82/69/-), K2O (60/47/89), Cr (-/112/-), Mn (74/59/85), Ni (-/96/101), Ca (40/46/-), Cu (-/77/92), Zn (-/85/-), V (51/27/-), Zr (-/105/-), Rb (104/102/-), and Pb (107/108/104), respectively. Lack of recovery values indicates that either a certified concentration of that element was not available in the reference sample or the pXRF was not able to detect that element. It is worth mentioning that the results of pXRF may be influenced by particle size, moisture content, scanning time, interelemental interference, and atomic weight ( Peinado et al., 2010Peinado, F.M.; Ruano, S.M.; González, M.G.B.; Molina, C.E. 2010. A rapid field procedure for screening trace elements in polluted soil using portable X-ray fluorescence (PXRF). Geoderma 159: 76-82. ; Weindorf et al., 2014Weindorf, D.C.; Bakr, N.; Zhu, Y. 2014. Advances in portable X-ray fluorescence (PXRF) for environmental, pedological, and agronomic application. Advances in Agronomy 128: 1-45. ; Ribeiro et al., 2017)Ribeiro, B.T.; Silva, S.H.G.; Silva, E.A.; Guilherme, L.R.G. 2017. Portable X-ray fluorescence (pXRF) applications in tropical Soil Science. Ciência e Agrotecnologia 41: 245–254. , which may explain some low recovery values for some elements.

Statistical analyses

Simple linear regressions were generated between the pXRF elemental results and elemental results from SAD, such as pXRF Al2O3 to predict SAD Al2O3. Similarly, weathering indices were calculated from both SAD and pXRF results and simple linear regressions were adjusted between them.

Contrary to the procedure to adjust simple linear regression models, when only pXRF data equivalent to the elements provided by SAD (Al2O3, SiO2, Fe2O3, TiO2, and P2O5) were used, stepwise multiple linear regressions were created to predict SAD results based on all the elements detected by pXRF for all samples, that is, Al2O3, Fe, SiO2, P2O5, Ti, K2O, Cr, Mn, Ni, Cu, Zn, allowing the generation of more robust models. Furthermore, two regression models per element resulted from SAD were created varying the datasets, as follows: a) using only pXRF data; and, b) using pXRF data in addition to soil texture data of each sample (sand, silt, and clay contents). In this case, we adopted the backward stepwise method in which the least important variables for the model were removed. The addition of soil texture data may improve predictions, due to relationships found between the mineral composition of the soil and the particle size fraction in which each mineral is commonly found. Quartz (SiO2) is the main mineral found in the sand fraction of tropical soils, while most clay particles correspond to kaolinite and Fe- and Al-oxides ( Kämpf et al., 2012Kämpf, N.; Marques, J.J.; Curi, N. 2012. Mineralogy of brazilian soils = Mineralogia de Solos Brasileiros. p. 81-146. In: Pedology fundamentals = Pedologia fundamentos. SBCS, Viçosa, MG, Brazil (in Portuguese). ).

The random forest algorithm was applied to predict the SAD results as well as weathering indices through the same elements used in stepwise multiple linear regression. Random forest was performed in R software, through the random Forest package ( Liaw and Wiener, 2015Liaw, A.; Wiener, M. 2015. Package “randomForest”. R Development Core Team 2: 1-29. ). The number of trees grown by the model was 1000, the number of variables used per node was 5, and the number of variables inserted per tree was four, which is 1/3 of the total number of predictors, as suggested by Liaw and Wiener (2002)Liaw, A.; Wiener, M. 2002. Classification and regression by random forest. R News 2: 18–22. . The model provides the mean square of residuals OOB (out-of-bag), the percentage of variance explained by the model, and the importance of each variable for the model ( Breiman, 2001Breiman, L. 2001. Random forests. Machine Learning 45: 5-32. ; Liaw and Wiener, 2002Liaw, A.; Wiener, M. 2002. Classification and regression by random forest. R News 2: 18–22. ). Similar to stepwise multiple linear regressions, random forest models were created with different datasets: a) only pXRF data; and, b) pXRF data in association with sand, silt, and clay contents of each sample.

For the generation of models through linear regressions, stepwise multiple linear regressions, and random forest algorithm, the total database was separated into two datasets: 37 samples (70 %) for the creation of models, and 15 samples (30 %) for validation of the generated models to ensure that they provide accurate predictions of SAD results and weathering indices through pXRF data.

Validation

The predicted values resulted from the linear regressions, stepwise multiple linear regressions, and random forest models were compared with the observed values through calculations of R2, adjusted R2 (R2adj), root mean square error (RMSE) (Equation 1), and mean error (ME) (Equation 2). The greater the R2 and R2adj, and the lower the RMSE and ME, the more accurate the prediction models, considering the defined parameter. Then, the best method was determined to calculate the content of each element, as well as to predict weathering indices resulted from SAD.

R M S E = 1 n i = 1 n e i - m i 2 (1)
M E = 1 n i = 1 n e i - m i (2)

where n: number of observations; ei: values estimated by the model; and mi: values obtained through SAD.

Results and Discussion

Soil chemical attributes

The range of SAD values result from different factors of soil formation ( Tables 1 , 2 , and 3 ), similar to values found for other soils from other regions of Brazil ( Curi and Franzmeier, 1987Curi, N.; Franzmeier, D.P. 1987. Effect of parent rocks on chemical and mineralogical properties of some Oxisols in Brazil. Soil Science Society of American Journal 51: 153-158. ; Vasconcelos et al., 2013Vasconcelos, F.C.W.; Carvalho, S.A.; Silva, S.H.G., Silva, E. A., Guerreiro, M.C.; Curi, N. 2013. MACRO simulator (Version 5.0) for predicting atrazine herbicide behavior in Brazilian Latosols. Ciência e Agrotecnologia 37: 211-220. ; Santos et al., 2014Santos, W.J.R.; Curi, N.; Silva, S.H.G.; Fonseca, S.; Silva, E.; Marques, J.J. 2014. Detailed soil survey of an experimental watershed representative of the brazilian Coastal Plains and its practical application. Ciência e Agrotecnologia 38: 50-60. ; Carvalho Filho et al., 2015Carvalho Filho, A.; Inda, A.V.; Fink, J.R.; Curi, N. 2015. Iron oxides in soils of different lithological origins in Ferriferous quadrilateral (Minas Gerais, Brazil). Applied Clay Science 118: 1-7. ). Soils developed from itabirite, basalt, gabbro, and tuffite presented the highest Fe2O3 and TiO2 contents and the lowest SiO2 contents. Fe2O3 and TiO2 decrease and SiO2 increases as the parent material becomes felsic, with greater quartz amounts, such as soils derived from gneiss. The lowest Fe2O3 contents were found in the Typic Endoaquent, due to the reduction of Fe3 to Fe2 followed by solubilization of Fe-bearing minerals ( Schaetzl and Anderson, 2005Schaetzl, R.J.; Anderson, S. 2005. Soil: Genesis and Geomorphology. Cambridge University Press, New York, NY, USA. ) and Fe2 leaching.

Table 2
– Portable X-ray fluorescence (pXRF) spectrometry data for A- and B-horizon samples of the soils studied.

Table 3
– Maximum, minimum, and mean values of data from sulfuric acid digestion analyses (SAD) and elemental analyses by portable X-ray fluorescence (pXRF) spectrometry of A- and B-horizon samples of the soils studied.

Fe2O3, Al2O3, and P2O5 pXRF contents were lower or greater than those found for SAD according to soil mineralogy and, hence, soil texture, which presented a wide variation for the studied soils due to the diversity of parent materials and weathering degree of soils ( Table 4 ). For Al2O3 and P2O5, 75 and 77 % of the samples, respectively, presented SAD contents greater than those obtained by pXRF. The opposite trend was observed for SiO2, Fe2O3, and TiO2, which presented 73, 63, and 67 % of the samples with pXRF contents greater than SAD contents. The SAD analyses are more likely to provide the digestion of clay-sized particles ( Curi and Kämpf, 2012Curi, N.; Kämpf, N. 2012. Soil characterization = Caracterização do solo. p. 147-170. In: Ker, J.C.; Curi, N.; Schaefer, C.E.G.R.; Vidal-Torrado, P., eds. Pedology: fundamentals = Pedologia: fundamentos. SBCS, Viçosa, MG, Brazil (in Portuguese). ). Since Brazilian soils have large contents of SiO2 in the sand fraction, mainly as quartz ( Brinatti et al., 2010Brinatti, A.M.; Mascarenhas, Y.P.; Pereira, V.P.; Partiti, C.S.D.; Macedo, A. 2010. Mineralogical characterization of a highly-weathered soil by the Rietveld method. Scientia Agricola 67: 454-464. ; Kämpf et al., 2012Kämpf, N.; Marques, J.J.; Curi, N. 2012. Mineralogy of brazilian soils = Mineralogia de Solos Brasileiros. p. 81-146. In: Pedology fundamentals = Pedologia fundamentos. SBCS, Viçosa, MG, Brazil (in Portuguese). ), the SiO2 content is only accessed by pXRF, justifying its larger content than that found with SAD, similar to the results for Fe2O3 and TiO2, which are components of minerals also occurring in the sand fraction, such as magnetite, rutile, and ilmenite ( Kämpf et al., 2012Kämpf, N.; Marques, J.J.; Curi, N. 2012. Mineralogy of brazilian soils = Mineralogia de Solos Brasileiros. p. 81-146. In: Pedology fundamentals = Pedologia fundamentos. SBCS, Viçosa, MG, Brazil (in Portuguese). ). Since higher contents of Al and P are commonly found in the clay fraction ( Brinatti et al., 2010Brinatti, A.M.; Mascarenhas, Y.P.; Pereira, V.P.; Partiti, C.S.D.; Macedo, A. 2010. Mineralogical characterization of a highly-weathered soil by the Rietveld method. Scientia Agricola 67: 454-464. ), these contents obtained through SAD were higher than those obtained with pXRF.

Table 4
– Minimum, maximum, mean, and standard deviation values of soil texture for A- and B-horizon samples of the studied soils.

Simple linear regression modeling and predictions

Table 5 presents the values of R2, Radj and the equations obtained by simple linear regressions between SAD and pXRF data. For the predictions of Fe2O3, TiO2, and P2O5, R2 and Radj values were higher than 0.80, showing an adequate fit of these regressions for the prediction of these SAD results directly from pXRF data.

Table 5
– Equations, R2, and Radj for prediction of sulfuric acid digestion results from elemental characterization by portable X-ray fluorescence (pXRF) spectrometry (in ppm).

The prediction of Fe2O3 had the highest R2 and R2adj, followed by P2O5. It is noteworthy that SAD quantifies mostly the elemental contents in the clay fraction ( Resende et al., 1987Resende, M.; Bahia Filho, A.F.C.; Braga, J.M. 1987. Clay mineralogy of Latossols estimated by chemical allocation of total oxides contents by H2SO4digestion. Revista Brasileira de Ciência do Solo 23: 17-23 (in Portuguese, with abstract in English). ; Curi and Kämpf, 2012Curi, N.; Kämpf, N. 2012. Soil characterization = Caracterização do solo. p. 147-170. In: Ker, J.C.; Curi, N.; Schaefer, C.E.G.R.; Vidal-Torrado, P., eds. Pedology: fundamentals = Pedologia: fundamentos. SBCS, Viçosa, MG, Brazil (in Portuguese). ). Consequently, since Fe2O3 of tropical soils is concentrated in this fraction due to the high weathering degree of these soils, the contents obtained by pXRF should be well correlated to those from SAD. However, Fe2O3 is also present in the form of magnetite in the sand fraction ( Schaefer et al., 2008Schaefer, C.E.G.R.; Fabris, J.D.; Ker, J.C. 2008. Minerals in the clay fraction of brazilian Latosols (Oxisols): a review. Clay Minerals 43: 137-154. ). Thus, the presence of this mineral in this fraction may have prevented an even better adjustment.

For Al2O3 and SiO2, adequate adjustments were not possible. Conversely, the Ki and Kr indices had R2 of 0.59 and 0.53, respectively. Possible reasons for SAD Al2O3 and SiO2 predictions not to be viable include the frequent occurrence of quartz (SiO2) and some presence of phyllosilicates (containing both Al and Si, among other elements) in the sand fraction of Brazilian soils. Again, as SAD quantifies mainly the elemental content of the clay fraction ( Resende et al., 1987Resende, M.; Bahia Filho, A.F.C.; Braga, J.M. 1987. Clay mineralogy of Latossols estimated by chemical allocation of total oxides contents by H2SO4digestion. Revista Brasileira de Ciência do Solo 23: 17-23 (in Portuguese, with abstract in English). ), portions of Si and Al detected by pXRF were not quantified by SAD, hindering an adequate fit of linear regressions between these values. Another factor that may have influenced the adjustment of these prediction models is the low recovery values obtained for Si and Al, probably due to factors that influence the pXRF analysis, such as particle size, moisture, sample weight, sample preparation, data collection, and instrument alignment ( Weindorf et al., 2014Weindorf, D.C.; Bakr, N.; Zhu, Y. 2014. Advances in portable X-ray fluorescence (PXRF) for environmental, pedological, and agronomic application. Advances in Agronomy 128: 1-45. ; Silva et al., 2018Silva, S.H.G.; Silva, E.A.; Poggere, G.C.; Guilherme, L.R.G.; Curi, N. 2018. Tropical soils characterization at low cost and time using portable X-ray fluorescence spectrometer (pXRF): effects of different sample preparation methods. Ciência e Agrotecnologia 42: 80-92. ; Santana et al., 2018Santana, M.L.T.; Ribeiro, B.T.; Silva, S.H.G.; Poggere, G.C.; Guilherme, L.R.G.; Curi, N. 2018. Conditions affecting oxide quantification in unknown tropical soils via handheld X-ray fluorescence spectrometer. Soil Research 56: 648-655. ; Ribeiro et al., 2018Ribeiro, B.T.; Weindorf, D.C.; Silva, B.M.; Tassinari, D.; Amarante, L.C.; Curi, N.; Guilherme, L.R.G. 2018. The influence of soil moisture on oxide determination in tropical soils via portable X-ray fluorescence. Soil Science Society of America Journal 82: 632-644. ; Peinado et al., 2010Peinado, F.M.; Ruano, S.M.; González, M.G.B.; Molina, C.E. 2010. A rapid field procedure for screening trace elements in polluted soil using portable X-ray fluorescence (PXRF). Geoderma 159: 76-82. ), although the samples of this study were analyzed in similar conditions regarding these influencing factors. In fact, this may be a constraint to the pXRF analysis if such factors are not taken into account.

In contrast, the equations generated to predict SAD Fe2O3, TiO2, and P2O5 from the contents obtained by pXRF were validated ( Figure 1 ). TiO2 obtained R2 and Radj of 0.96 with very low values of RMSE and ME. P2O5 and Fe2O3 presented an R2 of 0.89. For P2O5, the ME and RMSE values were low, whereas for Fe2O3 the RMSE values were the highest among all elements ( Figure 1 ) due to the greater range of Fe2O3 contents.

Figure 1
– Validation of simple linear regressions to predict results of sulfuric acid digestion analyses from data obtained with portable X-ray fluorescence (pXRF) spectrometry. RMSE = root mean square error; ME = mean error.

These results confirm the possibility of using pXRF to predict Fe2O3, TiO2, and P2O5 contents of SAD. In a preliminary study, only Fe2O3 and TiO2 yielded adequate fit values for linear regressions ( Silva et al., 2018Silva, S.H.G.; Silva, E.A.; Poggere, G.C.; Guilherme, L.R.G.; Curi, N. 2018. Tropical soils characterization at low cost and time using portable X-ray fluorescence spectrometer (pXRF): effects of different sample preparation methods. Ciência e Agrotecnologia 42: 80-92. ). Santana et al. (2018)Santana, M.L.T.; Ribeiro, B.T.; Silva, S.H.G.; Poggere, G.C.; Guilherme, L.R.G.; Curi, N. 2018. Conditions affecting oxide quantification in unknown tropical soils via handheld X-ray fluorescence spectrometer. Soil Research 56: 648-655. found adequate results for predicting SAD Fe2O3 and TIO2 for Brazilian soils. In this study, this trend was confirmed in addition to an adequate adjustment for P2O5 contents, which has not been previously reported.

Stepwise modeling and predictions

The stepwise multiple linear regression method allowed the evaluation of these models to predict SAD chemical composition from pXRF values using additional predictors in relation to those used in the simple linear regression, that is, other pXRF elemental data and soil texture data. The generated models that used either pXRF data only or pXRF + texture data as predictor variables and their R2 and Radj values are shown in Table 6 .

Table 6
– Equations, R2, and Radj for stepwise multiple linear regressions to predict sulfuric acid digestion (SAD) results from data of portable X-ray fluorescence (pXRF) spectrometry, with and without incorporating soil texture data (in %) into the models.

In the stepwise regressions, the R2 values were all above 0.79 for models without incorporation of soil texture data and above 0.83, after incorporating texture data as predictor variables, including Al2O3 and SiO2, which did not yield adequate models through simple linear regression. A better adjustment of the equations when including texture data was observed for predictions of SAD Al2O3 and SiO2. For Fe2O3, TiO2, P2O5, Ki, and Kr, models with or without soil texture data presented basically the same R2 and R2adj values. This behavior indicates that not only texture, but also other elements provided by the pXRF analysis, in addition to Fe, Al, Si, P, and Ti, contributed to modeling SAD results.

Regarding the pXRF elemental data, the number (in parenthesis) of models in which each element was present is: Zr (12), Fe (12), Mn (9), Al (8), Ti (8), Rb (8), Ni (8), Cr (8), Si (7), V (6), Cu (6), P (6), Ca (6), Pb (5), K (4), Cl (3), Zn (3). This fact demonstrates that some elements that now are easily accessed with pXRF may be well correlated with soil properties, facilitating the development of prediction models. Rubidium (Rb), for instance, was found to be correlated with clay content in soils from the United States by Zhu et al. (2011)Zhu, Y.; Weindorf, D.C.; Zhang, W. 2011. Characterizing soils using a portable X-ray fluorescence spectrometer. 1. Soil texture. Geoderma 167–168: 167-177. . Regarding the texture variables in 7 models, sand, silt, and clay were present, respectively, in 3, 2, and 3 models. All the models incorporating texture data as predictor variables presented at least one size fraction in the equation, except for the Kr model, highlighting the expectations confirmed of sand presence in SAD SiO2 model, while clay was one of the variables of the SAD Fe2O3 and Al2O3 models, which reflects Brazilian soils mineralogy, as previously discussed.

Although the Al2O3 and SiO2 content did not present a good fit with simple linear regressions ( Table 5 ), in stepwise multiple linear regressions these two elements achieved high R2 and Radj, that is, 0.79 and 0.76 for Al2O3, and 0.79 and 0.71 for SiO2, with and without incorporating texture. When incorporating texture data as predictors, the model for SAD Al2O3 included clay and silt variables, which can be explained by the weathering process and formation of kaolinite and gibbsite in greater proportion in these size fractions.

In contrast, the SAD SiO2 model used sand as a variable. Quartz predominates in the sand fraction of tropical soils, which reinforces the importance of this particle size fraction for the prediction of SAD SiO2. The non-adjustment of the simple linear regression for SiO2 may be because SAD does not digest quartz, as this method is intended for minerals in the clay fraction ( Resende et al., 1987Resende, M.; Bahia Filho, A.F.C.; Braga, J.M. 1987. Clay mineralogy of Latossols estimated by chemical allocation of total oxides contents by H2SO4digestion. Revista Brasileira de Ciência do Solo 23: 17-23 (in Portuguese, with abstract in English). ). The SiO2 content could be underestimated in SAD, while in the pXRF analysis, all SiO2 is detected from soil bulk composition. In the stepwise regression, the use of the sand fraction in the model as a predictor variable corrected this effect leading to better model adjustments.

For the prediction of SAD Fe2O3, the clay fraction was one of the independent variables inserted into the model, reinforcing the concentration of the Fe-bearing minerals in the smallest particle fractions in soils as the weathering processes advance, mainly as hematite and goethite ( Kämpf et al., 2012Kämpf, N.; Marques, J.J.; Curi, N. 2012. Mineralogy of brazilian soils = Mineralogia de Solos Brasileiros. p. 81-146. In: Pedology fundamentals = Pedologia fundamentos. SBCS, Viçosa, MG, Brazil (in Portuguese). ). The sand fraction was included as predictor variable into the SAD TiO2 model, whereas both sand and silt fractions were present in the model for the SAD P2O5 prediction. This result indicates the presence of minerals containing P and Ti in the sand and silt fractions in the soils studied. The sand and silt fractions of soils developed from basalt, gabbro, tuffite, and amphibolite may present considerable amounts of minerals such as anatase, rutile, and titanomagnetite, which present Ti in their composition ( Fabris et al., 1997Fabris, J.D.; Jesus Filho, M.F.; Coey, J.M.D.; Mussel, W.N.; Goulart, A.T. 1997. Iron-rich spinels from Brazilian soils. Hyperfine Interactions 110: 23–32. ; Fabris et al., 1998Fabris, J.D.; Coey, J.M.D.; Mussel, W.N. 1998. Magnetic soils from mafic lithodomains in Brazil. Hyperfine Interactions 114: 249–258. ).

The Ki and Kr indices were also submitted to stepwise multiple linear regressions, yielding R2 values of 0.90 and 0.84, respectively. Models with and without soil texture data had similar R2 values. Most predictor variables were the same in models with and without incorporation of soil texture data, except for the prediction of Ki values. In this last case, by incorporating soil texture data into the model, the clay content was added to the model while Si was replaced by Rb.

The validation indices for prediction of SAD values and weathering indices from the formerly presented equations are shown in Figure 2 . Except for Kr, Fe2O3, and SiO2, validation indices were always better when incorporating soil texture into the models. P2O5, TiO2, Ki, and Kr presented RMSE and ME values close to zero for validation of models with and without incorporating soil texture data, which is in agreement with the low range of their values. R2 and R2adj for Fe2O3 validation without incorporating texture data were the same as those found with simple linear regressions, but RMSE and ME values were lower with the stepwise regression. These values were slightly better than those that incorporated texture data as predictors. P2O5 and TiO2 had a similar trend, with validation of models incorporating texture presenting better results. Predictions of these elements were also improved in comparison to simple regressions.

Figure 2
– Validation of stepwise multiple linear regressions to predict results of sulfuric acid digestion analyses from portable X-ray fluorescence (pXRF) spectrometry data without (a) and with (b) soil texture data. RMSE = root mean square error; ME = mean error.

A considerable improvement in the modeling and validations was achieved for Al2O3 and SiO2 values, whose models reached R2 and R2adj that were much higher than those obtained with simple regressions. Al2O3 validation indicated that texture improved validation indices and the opposite trend was found for SiO2. Ki and Kr also improved in modeling and prediction quality compared to simple regression, although their validation indices were lower than those obtained for the predictions of SAD elemental contents.

In general, when using multiple regressions, texture data and pXRF elemental data other than Fe, Ti, Al, Si, and P were fundamental to improve prediction of SAD results, although predictions of SAD Fe2O3, TiO2, and P2O5 also provided adequate results using simple linear regressions. This shows that besides soil texture, the mineralogical composition of different particle size fractions also influences the results and can be accessed by pXRF. Attention should be drawn to the fact that some of the elements used in the equations presented low recovery values, which is important since they tend to be present in small concentrations in the soils.

Random forest modeling and predictions

Random forest models for most SAD elemental contents as well as for Ki and Kr presented high percentage of variance explained and small errors ( Table 7 ), indicating good adjustments of the models. Little variation occurred by adding information on soil texture into the models, except for Al2O3, which showed an improvement of 13 % of variance explained in the presence of such data.

Table 7
– Modeling results to predict sulfuric acid digestion results from portable X-ray fluorescence (pXRF) spectrometry by random forest algorithm, with and without incorporating soil texture data into the models.

The most important variables for predicting SAD SiO2, Fe2O3, Ki and Kr were these elemental contents/weathering indices obtained from pXRF even in the presence of sand, silt, and clay data ( Table 8 ). For the SAD Al2O3 model, the clay content was the most important variable, followed by pXRF Rb and Al2O3 contents. In the model without soil texture variables, Rb was the most important, followed by Al2O3. This fact demonstrates the importance of variables provided by pXRF for these predictions. Zhu et al. (2011)Zhu, Y.; Weindorf, D.C.; Zhang, W. 2011. Characterizing soils using a portable X-ray fluorescence spectrometer. 1. Soil texture. Geoderma 167–168: 167-177. used pXRF data for predicting sand and clay contents in soils from Lousiana and New Mexico (USA) and found a correlation of 0.91 between Rb and clay contents. These findings may indicate a similar trend also for Brazilian soils, although these authors are aware of differences between those soils and the ones in our study.

Table 8
– Importance of the variables (Imp) for random forest models using only pXRF data or pXRF together with texture data to predict results from sulfuric acid digestion analyses.

For SAD SiO2 prediction, silt and sand were defined as the 4th and 8th most important variables, and clay was the least important. In both models for SAD TiO2, pXRF V was the most important variable, followed by pXRF TiO2. As expected, the indices Ki and Kr calculated using pXRF SiO2, Al2O3, and Fe2O3 results were the most important variables to predict SAD Ki and Kr, followed by pXRF SiO2, since the latter element is taken into account in the formulae used to calculate those indices.

The validation of the random forest models is presented in Figure 3 . The validation results, in general, were very similar with and without incorporation of soil texture data into the models. Thus, for random forest algorithms, soil texture data did not improve the predictions of SAD results and Ki and Kr values. However, random forest provided better results for SAD Al2O3 with texture data, and SAD Fe2O3 and Kr with and without this attribute data in comparison to stepwise regression. It demonstrates that, without information on soil texture, random forest algorithms can be used to deliver better predictions of SAD Fe2O3, and Kr than stepwise multiple linear regressions.

Figure 3
– Validation of random forest models to predict results of sulfuric acid digestion analyses from portable X-ray fluorescence data without (a) and with (b) soil texture data. RMSE = root mean square error; ME = mean error.

Influence of soil texture on the prediction of weathering indexes

The prediction of elemental contents (expressed on the oxide basis) and weathering indices from the pXRF analysis was substantially improved when texture was used, especially in the multiple regression analysis for Al2O3 and SiO2. The reasons for this occurrence are, first, due to the nature of the SAD and pXRF analyses: while the SAD is efficient in the dissolution of minerals of the clay fraction, the pXRF analysis provides results of the total chemical composition of the sample. Thus, such pXRF results may differ from those obtained from other analyses, including SAD, which explains the reason why the incorporation of soil texture into the models in addition to the contents of elements in the minerals was decisive for the improvement of the prediction models. Second, mineralogy of Brazilian soils is mostly dominated by kaolinite, Fe and Al oxides (hematite, goethite, and gibbsite) in the clay fraction and quartz in association with smaller contents of muscovite in the sand fraction ( Melo et al., 2001Melo, V.F.; Singh, B.; Schaefer, C.E.G.R.; Novais, R.F.; Fontes, M.P.F. 2001. Chemical and mineralogical properties of kaolinite-rich brazilian soils. Soil Science Society America Journal 65: 1324-1333. ; Inda et al., 2010Inda, A.V.; Torrent, J.; Barrón, V.; Bayer, C. 2010. Aluminum hydroxy-interlayered minerals and chemical properties of a subtropical brazilian Oxisol under no-tillage and conventional tillage. Revista Brasileira de Ciência do Solo 34: 33-41. ; Kämpf et al., 2012Kämpf, N.; Marques, J.J.; Curi, N. 2012. Mineralogy of brazilian soils = Mineralogia de Solos Brasileiros. p. 81-146. In: Pedology fundamentals = Pedologia fundamentos. SBCS, Viçosa, MG, Brazil (in Portuguese). ; Silva et al., 2012Silva, E.A.; Gomes, J.B.V.; Filho, J.C.A.; Vidal-Torrado, P.; Cooper, M.; Curi, N. 2012. Morphology, mineralogy and micromorphology of soils associated to summit depressions of the northeastern brazilian Coastal Plains. Ciência e Agrotecnologia 36: 507-517. ; Carvalho Filho et al., 2015Carvalho Filho, A.; Inda, A.V.; Fink, J.R.; Curi, N. 2015. Iron oxides in soils of different lithological origins in Ferriferous quadrilateral (Minas Gerais, Brazil). Applied Clay Science 118: 1-7. ). The dominance of either sand or clay fraction in most Brazilian soils reflects the soil parent material. The silt content is much lower due to the high weathering degree of these soils ( Tables 3 and 4 ) and represents the maximum instability fraction. Thus, the sand and clay contents as well as the mineralogical composition of these particle size fractions influenced primarily the predictions of SAD Al2O3 and SiO2 contents. Thus, considering the high validation indices for all the SAD results and weathering indices, pXRF could be adopted as an alternative method to provide such soil data. The creation of better models to predict SAD results is encouraged, mainly through incorporation of more soil data.

Conclusions

Accurate predictions of SAD Al2O3, Fe2O3, SiO2, P2O5, and TiO2 results as well as Ki and Kr weathering indices can be obtained using pXRF data with and without incorporation of soil texture data into the models, through simple linear regressions, stepwise multiple linear regressions, and random forest algorithm. The clay and sand contents were crucial to improve the models to predict SAD Al2O3 and SiO2, respectively. These findings demonstrate that it is possible to use pXRF to reduce costs, time, and the amount of chemical waste produced by the SAD analyses. In addition, these results contribute to speeding up not only soil chemical characterization, but also the assessment of information on soil weathering degree, geochemical balance of nutrients, parent material homogeneity, reserve of nutrients for perennial crops, mineralogy of the clay fraction, among others. Finally, the association of new tools and robust algorithms enhance soil characterization for varying purposes, while providing a fast, cost-effective, and “green chemistry” alternative for the SAD analyses.

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  • Edited by: Tiago Osório Ferreira

Publication Dates

  • Publication in this collection
    04 Nov 2019
  • Date of issue
    2020

History

  • Received
    26 Apr 2018
  • Accepted
    10 Jan 2019
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