
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

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71381
10.1038/s41598-024-71381-8
Article
Assessment of portable X-ray fluorescence (pXRF) for plant-available nutrient prediction in biochar-amended soils
Antonangelo Joao joao.antonangelo@wsu.edu

1
Zhang Hailin 2
1 https://ror.org/05dk0ce17 grid.30064.31 0000 0001 2157 6568 Department of Crop and Soil Sciences, Washington State University, Pullman, WA USA
2 https://ror.org/01g9vbr38 grid.65519.3e 0000 0001 0721 7331 Plant and Soil Sciences Department, Oklahoma State University, Stillwater, OK USA
2 9 2024
2 9 2024
2024
14 203778 3 2024
27 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Portable X-ray Fluorescence probe (pXRF) is a tool used to measure many elements quickly and efficiently in soil with minimal sample preparation. Although this sensing technique has been widely used to determine total elemental concentrations, it has not been calibrated for plant-available nutrient predictions. We evaluated the potential of using pXRF for fast plant-available nutrient quantification. Two experiments were conducted in soils treated with two types of biochars to obtain a practical range of soil pH (5.5 − 8.0) and organic carbon (2.0 − 5.5%). Biochars applied were derived from switchgrass (SGB) and poultry litter (PLB). The first experiment received biochars at application rates up to 8% (w/w) and had no plants. The second experiment had up to 4% of SGB or PLB planted with ryegrass (Lolium perenne). Linear regression (LR), polynomial regression (PolR), power regression (PowR), and stepwise multiple linear regression (SMLR) were the models tested. Regardless of the extraction method, phosphorus (P) showed a strong relationship between pXRF and several laboratory extraction methods; however, K prediction via pXRF was sensitive to the plant factor. The optimum soil available-P corresponding to the maximum P uptake in plant tissues can be assessed with pXRF. The LR was inconsistent for calcium (Ca), sulfur (S), and copper (Cu) and non-significant for magnesium (Mg), iron (Fe), and zinc (Zn). Our results showed that pXRF is applicable to estimate P availability in soils receiving organic amendments. More evaluations are needed with diverse soil types to confirm the findings before using pXRF for fertilizer recommendation.

Keywords

Portable x-ray fluorescence
Soil nutrients extraction
Traditional methods
Wet chemistry
Biochar
Subject terms

Sensors and probes
Environmental chemistry
http://dx.doi.org/10.13039/100007593 College of Agricultural, Human and Natural Resource Sciences, Washington State University http://dx.doi.org/10.13039/100009496 Oklahoma Agricultural Experiment Station issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Plant available nutrient concentration in the soil is one of the important factors for fertilizer recommendations and it is obtained through traditional time consuming and costly laboratory methods using wet chemistry (WC). As a proximal sensor, portable X-ray fluorescence (pXRF) spectrometry can be a potential tool in precision agriculture to quantify several elements in a matter of seconds to minutes1,2. Disadvantageously, the elemental concentrations obtained by such a technique are total amount, which includes free ions in soil solution, elements in the structure of soil minerals and organic matter, and nutrients strongly adsorbed or fixed to clay-sized particles3. Fortunately, with the assistance of mathematical and statistical techniques, the total concentrations of elements determined by pXRF can be used to predict the soil exchangeable/available nutrient concentrations4. For this, the development of prediction models can be explored and validated to reduce the cost and time required by traditional WC laboratory analyses of nutrient concentrations3,5. Hence, it becomes important to evaluate the precision of measurements and the accuracy of prediction models using pXRF1,6.

Some of the current literature is inconsistent with respect to the prediction of soil nutrient availability using pXRF. To exemplify, the XRF analysis of dry spectra can reliably predict exchangeable-K7. XRF has also been reported to accurately predict exchangeable Ca and available P3, but the study also reported that available K was not successfully predicted. To date, the amount of research on the prediction of soil micronutrients (Cu, Fe, Mn, Zn, etc.) availability using a pXRF is nearly non-existent. In that scenario, more efficient methods for soil analysis using a pXRF are needed to complement precision nutrient management via more accurate and fast fertilizer recommendations.

One of the reasons behind the lack of good relationships between pXRF measurements and plant available nutrients from WC might be due to the traditional extraction method used by some laboratories. Therefore, it also becomes essential to explore more than one conventional method for a single nutrient to assess different relationships between those available/exchangeable amounts with total amounts from pXRF. This can identify which method is better predicted by pXRF to determine the soil nutrient availability. Among the traditional methods used to assess soil nutrients availability in soils are (1) Mehlich-3 (M3), to determine phosphorus (P), potassium (K), calcium (Ca), magnesium (Mg), sulfur (S), copper (Cu), iron (Fe), manganese (Mn), and zinc (Zn); (2) monocalcium phosphate (MCP) for S; (3) ammonium acetate for exchangeable-Ca, -Mg, and -K, (4) DTPA for most of the micronutrients; and (5) other methods developed just for soil available P such as Olsen, Bray, and Water Extraction.

Hence, various methods are employed to extract available phosphorus (P), potassium (K), calcium (Ca), magnesium (Mg), and micronutrients from soil, each with its specific principles and applications. The Mehlich-3 (M3) extraction method is widely used for its effectiveness in extracting P, K, Ca, Mg, and micronutrients simultaneously, making it suitable for multi-nutrient analysis. Bray and Olsen's methods are specific to P extraction, with Bray suitable for acidic soils and Olsen for alkaline soils. Water-extractable phosphorus (WEP) offers a rapid assessment of soluble P but may not capture all plant-available forms. DTPA extraction is common for assessing micronutrient availability, while ammonium acetate is used for K, Ca, and Mg in soils with low cation exchange capacity (CEC). Selection depends on soil type, pH, nutrient of interest, and analysis goals, emphasizing the need for method choice based on soil characteristics for accurate nutrient management.

Biochar's application as a soil amendment proves invaluable when assessing the reliability of pXRF measurements in predicting nutrient availability. This is primarily because the incorporation of biochar into the soil provides a diverse range of soil pH levels and organic carbon (OC) content, mirroring the natural conditions of many agricultural soils8. Moreover, broad literature investigating biochar’s positive effects on soil properties has commonly found that increased soil nutrient levels are one of the main benefits9. As an example, the application of poultry-based biochars has been shown to increase both total and plant available P and K concentrations in amended soils10,11.

We undertook two comprehensive studies to assess the viability of utilizing X-ray Fluorescence (XRF) as a predictive tool for plant-available nutrient estimation. In one of these studies, we introduced ryegrass cultivation to validate potential alterations in nutrient dynamics that could influence the accuracy of portable XRF measurements. We evaluated the prediction of exchangeable P, K, Ca, Mg, S, Cu, Fe, and Zn from pXRF elemental data by identifying the best possible regression model. To the best of the authors' knowledge, no work has compared the prediction of soil available nutrients by pXRF with several traditional methods, such as those previously mentioned, by evaluating relationships with and without plants grown in the trials. Furthermore, the utilization of distinct biochars tailored to suit a practical range of soil OC and pH levels exemplifies the uniqueness of this research and justifies the assessment of several extraction methods for comparison goals. Finally, the biochar application promotes an exhaustive evaluation of the pXRF technique since the soil is amended with organic material, making the analyzed matrix even more heterogeneous, which makes this work unique. We hypothesize that there is predictive accuracy of X-ray Fluorescence (XRF) for estimating plant-available nutrients in soil when compared to traditional soil testing methods, regardless of the presence of plants or the application of distinct biochars.

Material and methods

Biochar production and characterization

The biochars were produced from two feedstocks, switchgrass (Panicum virgatum) and poultry litter using high-temperature slow pyrolysis (700 °C). The details of switchgrass-derived biochar (SGB) and poultry litter-derived biochar (PLB) were described in Antonangelo and Zhang12. The coarse biochar materials were evenly and gently ground with a mortar and pestle before being sieved through 1- and 0.25-mm sieve for physicochemical analyses and experimentation, respectively13. The SGB and PLB characterization including major physicochemical properties can be found in Table 1 and in Antonangelo et al.14. In the experiments, the two distinct biochars were applied separately at elevated rates, as will be elaborated upon later.Table 1 Biochar properties analyzed by several methods.

Biochar	P a	K	Ca	Mg	S	Fe	Zn	Cu	
–––––––––––-Total (EPA 3050B), mg kg–1–––––––––––-	
SGB	2000 ± 200	4000 ± 400	8000 ± 1000	3000 ± 300	400 ± 100	111 ± 20	54 ± 5.8	23 ± 2.7	
PLB	40,000 ± 800	80,000 ± 600	50,000 ± 2000	20,000 ± 100	10,000 ± 600	6903 ± 1295	1477 ± 43	253 ± 4.0	
	–––––––––––-Total (pXRF), mg kg–1–––––––––––-	
SGB	1705 ± 352	18,905 ± 1767	28,766 ± 5608	20,118 ± 5740	1064 ± 127	558 ± 189	145 ± 26	52 ± 23	
PLB	34,324 ± 5204	210,335 ± 4757	19,816 ± 3648	ND	ND	5559 ± 1092	ND	ND	
	–––––––––––-Available (Mehlich 3), mg kg–1–––––––––––-	
SGB	237.4 ± 4.6	616	1575	541	‒	‒	‒	‒	
PLB	14,238 ± 276	54,504	5690	6869	‒	‒	‒	‒	
	–––––––––––-Available (NH4Ac), mg kg–1–––––––––––-	
SGB	‒	125 ± 4.0	329 ± 64	79.1 ± 18	‒	‒	‒	‒	
PLB	‒	42,900 ± 1121	1522 ± 80.8	1096 ± 38.3	‒	‒	‒	‒	
	–––––––––––-Available (DTPA), mg kg–1–––––––––––-	
SGB	‒	‒	‒	‒	‒	2.7	3.8	1.2	
PLB	‒	‒	‒	‒	‒	122.4	29.8	9.8	
Values after ± are the standard deviation (n = 3) of triplicates.

“‒”: not analyzed. When values lack a preceding ± , it indicates that the samples were not determined in triplicates due to insufficient biochar material.

ND non-detected.

aPhosphorus availability from biochars assessed by Bray, Olsen, and Water Extractable Phosphorus (WEP) are, respectively, 203.8 ± 3.7, 52.6 ± 1.2, and 42.5 ± 3.5 mg kg−1 for switchgrass-derived biochar (SGB); and 4716 ± 37, 1631 ± 28, and 912 ± 55.9 mg kg−1 for poultry litter-derived biochar (PLB).

Soil sampling and experiments

The soil chosen for our experiment constituted a composite sample derived from the merging of three individual subsamples (equal volumes) to reduce heterogeneity, all obtained from a depth range of 0–15 cm. These subsamples were collected from locations proximate to chat piles (debris from milling operations), once used for agriculture purposes, and soil yards within the Tar Creek region, situated in Picher, Ottawa County, Oklahoma—a site characterized by significant metal contamination. However, the contaminated sites have undergone various remediation measures and have been repurposed for feed and food production or recreational use, provided they meet appropriate guidelines set forth by the EPA under the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) and the Resource Conservation and Recovery Act (RCRA). The initial characteristics of both the subsamples and the resulting composite sample can be found in Supplementary Table S1. Notably, our study leveraged the same portable X-ray fluorescence (pXRF) instrument, which had been previously validated and calibrated for measuring heavy metal concentrations15. This approach allowed us to broaden the scope of analysis to encompass soil nutrient availability, thereby serving a dual purpose: the assessment of metal contaminants and the prediction of nutrient accessibility within the soil. This information holds particular relevance for potential land use scenarios, such as phytoremediation initiatives or agricultural cultivation in these areas.

In the first experiment (no plants), 200 g of 2 mm sieved soils were mixed with 0.0 (control), 1.0, 2.0, 4.0, and 8.0% (w/w) of 0.25-mm sieved SGB, and PLB in plastic containers. The mixture was then incubated and monitored for 10 weeks, while keeping the experiment units at 75% of field capacity before sampling and analyses. The pots were arranged in a laboratory environment using the completely randomized design (CRD) with 3 replications (n = 3).

In a second trial, ryegrass was cultivated in a pot experiment. 1.2 kg of the dried and sieved soils were mixed with 0.0 (control), 0.5, 1.0, 2.0, and 4.0% (w/w) of the same 0.25-mm sieved SGB and PLB in plastic pots. The 8.0% treatment used in the 1st experiment was excluded since preliminary experiment show ryegrass growth was negatively impacted at this rate of biochar application12. Each pot was supplied with a uniform quantity of nitrogen (N) determined based on the soil test specifically for grass production, with the N contribution from biochars being subtracted. Given those biochars already offered sufficient phosphorus (P) and potassium (K), only the control group received extra P and K supplementation. The soil + biochar mixture was incubated for 30 days at 75% of field capacity before ryegrass sowing (each pot was sown at a rate of 30 kg ha−1 as estimated from the pot surface area). Ryegrass growth was monitored for 75 days in an environmentally controlled growth chamber. The pots were arranged in a CRD with 3 replications (n = 3). Plots were rotated once a week to eliminate spatial variability in the growth chamber. Procedures for the pot experiment were detailed in Antonangelo and Zhang12.

Across experiments, biochars added the following amounts of major macro- and micro-nutrients (in kg ha‒1) for SGB (0.5‒8%): P (20‒320), K (40‒640), Ca (80‒1280), Mg (30‒480), S (4‒64), Cu (0.23‒3.68), Fe (1.11‒17.8), and Zn (0.54‒8.64); and for PLB (0.5‒8%): P (400‒6400), K (80‒12,800), Ca (500‒8000), Mg (200‒3200), S (100‒1600), Cu (2.53‒40.5), Fe (69‒1104), and Zn (14.8‒236).

Soil analysis by traditional methods

Soil analysis at the Soil, Water, and Forage Analytical Laboratory (SWFAL) at Oklahoma State University was conducted using conventional WC techniques, following well-established procedures documented in the scientific literature. Laboratory results were maintained through standards, blank samples, and internal and external checks. Blank samples were used to verify each analysis, while internal reference samples were employed every 10 to 20 samples. If a check failed, the entire batch was reanalyzed. All results were double-checked for accuracy and reviewed for issues.

Drying and grinding can chemically and physically homogenize soil samples and affect the accuracy of prediction models; however, we used the same procedures of sample preparation in the two experiments to ensure the same conditions for comparison purposes between pXRF and traditional WC methods. The "traditional methods" refer to well-established and conventional techniques that have been commonly used and accepted in the field of soil science. These methods are typically recognized for their reliability and have a history of being employed as standard practices for nutrient extraction and analysis.

In the 1st experiment (no plants), soil samples were dried, sieved to a 2mm size, and analyzed for pH, soil OC, and extractable P, K, Ca, Mg, S, Fe, Cu, and Zn. The soil pH was determined in deionized water (DI) with a 1:1 soil-to-water ratio16. The OC was determined with dry combustion17 using a LECO 828 carbon and nitrogen analyzer (St. Joseph, MI). Plant-available P, K, Ca, and Mg were extracted by shaking 2 g of soil in 20 mL of Mehlich 3 (M3) solution (0.001 M EDTA, 0.015 M NH4F, 0.2 M CH3COOH, 0.25 M NH4NO3, 0.013 M HNO3; pH buffered to 2.5) for 5 min18 and quantified by inductively coupled plasma atomic emission spectroscopy (ICP-AES). Plant-available S was extracted by shaking 10 g of soil in 25 mL of 0.008 M MCP ([Ca(H2PO4)2.H2O]) for 30 min19 and determined with an ICP-AES. Phytoavailable micronutrients (Fe, Cu, and Zn) were analyzed by adding 20 mL of DTPA (0.005 M DTPA, 0.01 M CaCl2.2H2O, 0.2 M Sorbitol, 0.11 M triethanolamine, 0.05 M HCl; pH buffered to 7.3) to 10 g of soil, shaken for 2 h20, and quantified with ICP-AES.

In the second experiment, we employed a variety of traditional methods to enhance the global relevance of our study. It must be emphasized that, on a global scale, soil nutrient extraction methods carry inherent uncertainty, influenced by various factors. Within a lab, precision can be improved through standardization, calibration, and skilled technicians, but slight variations may still occur due to sample homogenization and instrument precision. Between labs, uncertainty grows due to equipment differences, calibration variations, and technician expertise. To reduce inter-laboratory disparities and enhance soil nutrient analysis accuracy, standardized protocols, and reference materials are essential.

Additionally, we introduced a plant factor to investigate its potential influence on pXRF measurements, as well as to assess the correlation between soil nutrient levels obtained via pXRF and those acquired through various extraction methods, concerning nutrient concentrations in plant tissues. In both experiments, we treated the soils with elevated doses of biochar, thereby creating a practical range of soil pH and organic carbon (OC) levels suitable for agricultural applications, as illustrated in Fig. 1.Fig. 1 Boxplot of soil pH and organic carbon (OC) after switchgrass- and poultry litter-derived biochar application rates. The squared symbols denote the average. Boxes span the 25th to 75th data percentile, whiskers represent 1.5 × the interquartile range, and horizontal lines denote the median.

At the end of the pot experiment, the dried and sieved soil samples were analyzed by the same methods described above. In addition, plant available P was also determined by Bray-1, Olsen, and Water Extractable Phosphorus (WEP); Ca, Mg, and K by ammonium acetate (NH4Ac); and S, Zn, Cu, and Fe by M3 (determined in the same filtrate used for M3-P, -K, -Ca, and -Mg determination). The Olsen-P and Bray-P consist of the phosphate (PO4-P) extraction using a 0.5 N NaHCO3 solution adjusted to pH 8.521 and a dilute acid solution of hydrochloric acid containing ammonium fluoride22, respectively. Ammonium molybdate and antimony potassium tartrate were added so that the orthophosphate ion reacted to form a complex. The complex was reduced with ascorbic acid to form a blue-colored complex that absorbs light at 880 nm in a spectrometer, instrument used for Olsen-P and Bray-P colorimetric determination. The absorbance is proportional to the concentration of orthophosphate in the sample. For the WEP extraction, DI water was used23: 2.0 g of soil was weighed and placed in 50 mL centrifuge tubes, then 20 mL of DI water was added to create soil-to-water extraction ratios of 1:10 (w:v). After the addition of DI water, tubes were shaken on an end-over-end shaker for 1-h, centrifuged at 5000 rpm for 5 min, and filtered through a 0.45 µm glass filter paper before determination by an ICP-AES. For K, Ca, and Mg extracted with ammonium acetate, the NH4Ac solution was buffered at pH 7.0, and 20 mL was added to a 2 g of dried soil into a 50 mL container, then the mixture was slowly shaken in a reciprocating shaker for 1 h, filtered and analyzed24 by an ICP-AES.

Soil analysis by pXRF

All X-ray fluorescence (XRF) measurements were performed with a portable XRF (pXRF) using the TRACER 5i Portable/Handheld XRF Spectrometer (Bruker, Kennewick, WA, USA). A full description of the instrument can be found in Zhang et al.15. The ‘Soil Nutrient and Metal’ calibration provided by the manufacturer was used for all measurements. As shown in Fig. 2, the pXRF was mounted upside down on a stand and samples were packed in a sample holder and then placed on the window, then readings were taken in duplicates at 50 kV, and 39 µA15. Samples were analyzed using 2 phase scans of 30 s each phase, totalizing 60 s per reading.Fig. 2 (a) The sample is carefully positioned to ensure it fully occupies the portable X-ray Fluorescence (pXRF) sample holder, specifically designed for 32mm XRF Sample Cups. (b) Subsequently, the sample holder, housing the specimen earmarked for analysis, is securely inserted into the inverted mount of the pXRF device. Within this configuration, pXRF measurements are conducted and automatically recorded on a connected computer system. This graphical representation has been adapted from the research conducted by Zhang et al. (2021).

A certified reference material (CRM), ‘Metal-rich reference sediment’ (SdAR-M2, International Association of Geoanalysts, Keyworth, Nottingham, UK), was included in the determination of the total elemental concentrations by pXRF. Before analysis, the accuracy of the equipment was checked using the CRM. The average ± standard deviation (SD) for the concentrations of the elements of interest (P, K, Ca, Mg, S, Fe, Cu, and Zn) of both actual samples and CRM were calculated along with the difference between reported values of the CRM and CRM measurements (Supplementary Table S2). For multivariate modeling, the elements selected were those obtained for all samples by pXRF: P, K, S, Ca, Mg, Fe, Cu, Zn, Al, Si, Ti, V, Cr, Mn, Ni, As, Rb, Sr, Zr, Ba, Pb. Descriptive statistics of all other elements (excluding the elements of interest) are presented in Supplementary Table S3, and their accuracy is in Supplementary Table S4.

The K-edge absorption energies and the pXRF limit of detection (LOD) for the elements of interest are summarized in Table 2. Ranges in soil nutrient concentrations determined by the traditional methods and pXRF are shown in Table 3.Table 2 Summary of elemental K-edge absorption energies that were scanned under 50 keV pXRF analysis settings, the pXRF limit of detection (LOD), and the maximum limit for the calibration provided by the manufacturer.

Element	K‒edge (keV)	_______ pXRF (mg kg‒1) _______	
LOD	Maximum limit a	
P	2.1	30	1900	
K	3.6	40	50,000	
S	2.5	35	133,000	
Ca	4.0	25	10,000	
Mg	1.3	600	252,000	
Fe	7.1	15	248,000	
Cu	9.0	 < 5	30,800	
Zn	9.7	 < 5	99,000	
a: Maximum value of the calibration method used.

Table 3 The ranges of soil nutrient concentrations from lowest to highest as determined by several methods.

Method	P	K	S	Ca	Mg	Fe	Cu	Zn	
___________________ mg kg–1 ___________________	
1st experiment–––––-	
DTPA	—	—	—	—	—	11–24	0.8–2.6	97–188	
MCP	—	—	25–610	—	—	—	—	—	
M3	25–1318	113–3304	—	1606–2859	149–875	—	—	—	
pXRF	107–1584	5976–15,226	253–2269	2912–9775	4411–10,751	13,935–20,741	18–62	967–7169	
	2nd experiment–––––-	
DTPA	—	—	—	—	—	16–38	1.3–2.9	93–208	
MCP	—	—	14–529	—	—	—	—	—	
M3	25–1015	39–1483	37–915	1648–2717	123–529	111–146	1.8–4.6	244–369	
NH4Ac	—	47–1920	—	1716–2942	147–518	—	—	—	
Bray	25–1041	—	—	—	—	—	—	—	
Olsen	7.7–273	—	—	—	—	—	—	—	
WEP	1.1–40.3	—	—	—	—	—	—	—	
pXRF	75–1195	3643–8582	372–2198	2285–8673	7149–13,535	11,831–22,819	17–46	1011–2815	
Results displayed for each element comprise the whole dataset of measurements (n = 27).

The results from soils treated with two biochars, separately, (switchgrass- and poultry litter-derived biochars) were combined to exhibit the full range of values.

“—”: not applicable.

Nutrient concentrations in ryegrass

Ryegrass shoots were harvested, washed with DI water, and oven-dried at 105° C until constant weight. Dried plant materials were ground using a mechanical grinder to pass through a 1mm screen and then analyzed for P, K, Ca, Mg, S, Fe, Cu, and Zn using EPA method 3050B25 ‒ digestion by concentrated HNO3 and H2O2. To determine nutrient concentrations in plant tissues, 0.5 g of ground plant materials were predigested for 1 h with 10 mL of trace metal grade HNO3 in the HotBlock™ Environmental Express block digester (Environmental Express, 2345A Charleston Regional Parkway, Charleston, South Carolina 29,492, SC, United States), and the digests were then heated to 115 °C for 2 h and diluted with DI water to 50 mL26. Finally, the digested samples were filtered, and P, K, Ca, Mg, S, Fe, Cu, and Zn were determined by ICP-AES.

Data analysis

Data analysis was conducted by following established procedures from the existing literature, drawing from studies that have previously calibrated and modeled predictions for soil nutrient availability using portable X-ray fluorescence (pXRF) technology.

Regression models

Linear regression (LR), 2nd-degree polynomial regression (PolR), power regression (PowR), and stepwise multiple linear regression (SMLR) were applied for the predictions of soil nutrient concentrations. LR, PolR, and PowR were generated considering the elemental concentrations obtained by pXRF as independent variables and the available concentrations as dependent variables3. For the assessment of the best model, the coefficient of determination (R2), root mean square error (RMSE), and Akaike Information Criterion (AICc) were evaluated.

For the 1st experiment, the rates of both biochars were tested separately and their results were combined to verify the relationship between increased rates of biochar application and soil nutrient increment (Supplementary Table S5). Since the results did not exhibit a clear trend, analyses of covariance (ANCOVA) between independent and dependent variables were performed for both experiments in JMP 15. According to the results (Table 4), it was reasonable to combine the data from soils treated with either SGB or PLB to evaluate the regression models. Although multiple regression models were tested, we plotted graphs showing the significant linear relationship (LR) graphics since it is easier to use.Table 4 Analysis of covariance (ANCOVA) between analytical methods‒pXRF and chemical extraction‒for soils treated with increased rates of biochars derived from two feedstocks, switchgrass (SGB) and poultry-litter (PLB).

Method	P	K	S	Ca	Mg	Fe	Cu	Zn	
___________________ p-value (SGB × PLB interaction) ___________________	
1st experiment–––––-	
DTPA	—	—	—	—	—	0.7564	0.1577	0.5749	
MCP	—	—	 < .0001*	—	—	—	—	—	
M3	0.1067	 < .0001*	-	0.105	0.1955	—	—	—	
	2nd experiment–––––-	
DTPA	—	—	—	—	—	0.2347	0.2855	0.2447	
MCP	—	—	0.0002*	—	—	—	—	—	
M3	0.1482	0.0002*	 < .0001*	0.8534	0.1344	0.7659	0.8507	0.6374	
NH4Ac	—	0.0002*	—	0.612	0.1146	—	—	—	
Bray	0.1266	—	—	—	—	—	—	—	
Olsen	0.1262	—	—	—	—	—	—	—	
WEP	0.2676	—	—	—	—	—	—	—	
p ≥ .05 means that slopes are not different for SGB and PLB rates increment thus results can be combined. Results displayed for each element comprise the whole dataset of measurements (n = 27).

*: Although slopes are significantly different they were combined since SGB regression was not significant (p > .05) or was inversely related. “—”: not applicable.

Pearson, Spearman, and Kendall correlation coefficients were calculated between biochar rates and results from pXRF with traditional WC methods when appropriate.

Stepwise multiple linear regression (SMLR)

For the Stepwise Multiple Linear Regression (SMLR), all 21 soil elements provided by pXRF measurements were used as independent variables to predict the soil nutrient availability. This was to account for any elemental interference that can occur due to overlapping spectra. The SMLR was generated with the whole dataset of measurements in JMP Pro 15 using the backward method27 as described in Pelegrino et al.3. Initially, the model contains all variables. Then, the least statistically significant ones are removed. The remaining variables comprise the final SLR model. In this study variable removal was based on the AICc because it is more appropriate for finding the best model for predicting future observations28.

The stepwise regression process used statistical criteria to automatically select variables, indicating that multicollinearity, if present, did not significantly affect the model's performance. Post-modeling diagnostics, such as correlation assessments and variance inflation factor calculations, confirmed the independence of these variables, supporting the conclusion that multicollinearity was not a substantial concern. Therefore, the simultaneous inclusion of nutrients and XRF-derived elements in the SMLR model is scientifically justified, considering their distinct contributions and the absence of multicollinearity issues.

Non-linear segmented regressions

Non-linear segmented models were performed only for nutrients that provided a meaningful relationship between pXRF and traditional methods in the 2nd experiment. As in Stammer and Mallarino29, the maximum responsive soil test P&K and pXRF-P&K to P&K concentrations in ryegrass shoots were determined by fitting the segmented polynomial linear–plateau (LP) response models using the NLIN (non-linear) procedure of SAS version 9.4. The models were accepted only when the NLIN convergence criterion method successfully converged, and the model was significant at least at p < 0.05.

All data analysis was performed using the whole dataset of measurements (n = 27) and graphs were created using Excel.

Results and discussion

Relationships in biochar amended soils without plants (1st experiment)

A strong linear relationship was obtained between pXRF and traditional WC methods for P, K, S, Ca, and Cu (Fig. 3). The LR was better for those nutrients when compared to the power regression (PowR, Table 5). Although PolR was slightly better in terms of AICc and RMSE, the differences were negligible, which makes adopting LR reliable and better in practice. Furthermore, exercising caution when applying the PolR model to data is crucial as it must be determined if there is empirical or theoretical support for a non-linear relationship between plant-available nutrient concentration and total element levels. Specifically, it must be established whether nutrients increase with total elements up to a certain point and then decline as total elements rise. This is vital for accurate model predictions in the context of nutrient-plant interactions. Unfortunately, no relationships were found for Mg, Fe, and Zn when evaluating LR, PolR, and Pow (Table 5). On the other hand, the SMLR provided better results for all nutrients and significant results for Mg, Fe, and Zn given the drastic change in all statistical parameters evaluated (AICc, RMSE, and R2) (Table 5 and Supplementary Fig. S1). However, embracing SMLR throughout might not be feasible in practice if different commercial pXRF instruments containing their respective (and specific) calibration methods, LOD, and elements analyzed30 are used unless a clear and unique trend is globally observed. In our experiment, the variables impacting the prediction of soil available nutrients via pXRF are presented in Table 6. This will be further discussed for comparison and to elucidate similar trends between the two experiments.Fig. 3 Linear relationship between soil nutrients determined by pXRF and traditional methods (1st experiment). ***: p < .001. RMSE: root mean square error.

Table 5 Evaluation of the regression models for predicting soil nutrient concentrations from pXRF.

Element	Method	______ LR a______	______ PolR ______	______ PowR ______	______ SMLR ______	
AICc b	RMSE	R2	AICc	RMSE	R2	AICc	RMSE	R2	AICc	RMSE	R2	
		1st experiment ––––––––-	
P	M3	305	62.5	0.98	292	47.7	0.99	352	151	0.87	273	26.5	0.99	
K	M3	385	277	0.93	378	235	0.95	397	348	0.88	316	65.9	0.99	
S	MCP	284	42.6	0.94	274	34.3	0.96	290	48	0.93	233	15.9	0.99	
Ca	M3	361	177	0.74	363	177	0.75	362	181	0.73	340	107	0.92	
Mg	M3	373	223	0.04	376	227	0.04	372	223	0.04	250	17.7	0.99	
Fe	DPTA	147	3.33	0.01	149	3.38	0.02	147	3.33	0.01	106	1.29	0.88	
Cu	DTPA	‒13.9	0.17	0.89	‒11.8	0.17	0.89	‒5.49	0.2	0.85	‒37.4	0.10	0.96	
Zn	DTPA	243	19.8	0.01	245	20.1	0.02	243	19.8	0.01	239	15.9	0.46	
		2nd experiment ––––––––-	
P	M3	322	86.2	0.92	323	85	0.93	346	134	0.81	310	52.5	0.98	
	Olsen	254	24.1	0.92	253	23.1	0.93	276	36.8	0.81	236	14.3	0.98	
	Bray	328	96.1	0.91	327	91.3	0.93	352	149	0.80	304	40.9	0.99	
	WEP	145	3.24	0.93	148	3.30	0.93	166	4.80	0.84	140	2.67	0.96	
K	M3	394	327	0.48	375	224	0.77	371	213	0.78	322	70.7	0.98	
	NH4Ac	406	408	0.47	386	272	0.78	381	254	0.80	330	89.1	0.98	
S	MCP	343	128	0.41	336	108	0.60	347	139	0.31	303	39.8	0.96	
	M3	372	217	0.41	363	177	0.62	376	235	0.31	338	77.2	0.95	
Ca	M3	391	309	0.12	394	314	0.13	391	308	0.12	376	211	0.64	
	NH4Ac	385	273	0.29	387	279	0.29	385	274	0.29	365	126	0.90	
Mg	M3	339	118	0.05	342	119	0.06	339	118	0.05	262	24.4	0.97	
	NH4Ac	334	107	0.08	337	109	0.08	334	107	0.08	252	16.9	0.98	
Fe	DTPA	176	5.77	0.03	178	5.76	0.07	176	5.76	0.03	127	2.01	0.90	
	M3	200	79.6	0.01	202	8.95	0.05	200	79.6	0.01	172	4.08	0.84	
Cu	DTPA	21.4	0.33	0.35	24.1	0.33	0.35	21.4	0.33	0.35	23	0.34	0.32	
	M3	63.8	0.72	0.27	66.2	0.73	0.27	63.5	0.72	0.28	54	0.49	0.73	
Zn	DTPA	272	34.3	0.02	275	34.8	0.03	272	34.2	0.02	224	11.4	0.91	
	M3	279	38.8	0.06	282	39.4	0.07	279	38.8	0.06	252	20.0	0.79	
aLR linear regression, PolR polynomial regression, PowR power regression, SMLR stepwise multiple linear regression.

bAICc Akaike information criterion (sample-size adjusted formula), RMSE root mean square error (mg kg−1).

R2: coefficient of determination.

Table 6 Equations from stepwise multiple linear regression models (SMLR) based on the lowest adjusted Akaike information criterion (AICc).

Element	Method	SMLR equation	p-value	
		1st experiment ––––––––-	
P	M3	640.4 + 0.15 K + 0.13S ‒ 0.01Zn ‒ 0.02Al ‒ 0.20Ti + 9.05Ni ‒ 7.44Rb	***	
K	M3	11,010 + 0.39 K + 0.31S ‒ 0.03Al ‒ 0.03Si ‒ 28 V	***	
S	MCP	‒166.6 + 0.402P + 0.275Zr	***	
Ca	M3	‒1754 + 0.55S ‒ 0.03Al + 0.01Si + 38 V	***	
Mg	M3	442 + 0.08 K + 0.08S ‒ 0.01Zn ‒ 0.01Al ‒ 0.10Ti + 6.25Ni ‒ 4.03Rb	***	
Fe	DPTA	29 ‒ 0.0001Ca ‒ 0.001 Mg ‒ 0.0004Al + 0.1 V + 0.03Zr ‒ 0.02Ba	***	
Cu	DTPA	0.16 + 0.0002 K ‒ 0.00004Al + 0.017Ni	***	
Zn	DTPA	289.5 + 0.09S ‒ 0.025Ca ‒ 0.011 Mg ‒ 0.003Al + 0.319Pb	*	
		2nd experiment ––––––––-	
P	M3	2656 + 0.943P ‒ 0.01Al ‒ 0.01Si + 0.289Ti ‒ 11.7 V + 1.21Zr + 0.607Ba	***	
	Olsen	205.9 + 0.259P ‒ 0.01Al ‒ 0.001Si ‒ 1.14 V + 0.377Zr + 0.196Ba	***	
	Bray	2814 + 1.04P ‒ 0.02Al ‒ 0.01Si + 0.34Ti ‒ 14.6 V + 2.1Cr ‒ 7.4Ni + 2.1Zr + 0.81Ba	***	
	WEP	20.58 + 0.037P ‒ 0.0005Fe ‒ 0.0001Si + 0.576As	***	
K	M3	3763 + 1.12P + 0.239 K ‒ 0.08Ca ‒ 0.01Al ‒ 0.01Si ‒ 8.51 V	***	
	NH4Ac	1915 + 2.05P + 0.177 K ‒ 0.15Ca ‒ 0.009Si	***	
S	MCP	129 ‒ 0.89P + 0.3 K + 0.27S ‒ 0.05Ca ‒ 0.02 Mg ‒ 0.02Al ‒ 0.4Ti + 10.6 V ‒ 1.1Pb	***	
	M3	452 ‒ 1.51P + 0.5 K + 0.42S ‒ 0.08Ca ‒ 0.03 Mg ‒ 0.04Al ‒ 0.7Ti + 16.5 V ‒ 2.0Pb	***	
Ca	M3	189 + 0.208 K ‒ 0.06 Mg ‒ 0.04Al + 5.58Zr	***	
	NH4Ac	724 ‒ 1.7P + 0.46 K + 0.21S ‒ 0.06 Mg ‒ 17.9Cu ‒ 0.67Ti + 18.6 V + 20.2Sr ‒ 1.5Ba	***	
Mg	M3	‒201.9 + 0.29P + 0.06S ‒ 0.007Al + 0.88Zr + 0.317Ba	***	
	NH4Ac	190 + 0.10P + 0.05 K + 0.06S ‒ 0.03Zn ‒ 0.01Al ‒ 0.11Ti + 0.74Zr + 0.248Ba	***	
Fe	DTPA	1.14 + 0.007S ‒ 0.003Ca + 0.0097Ti + 0.058Cr ‒ 0.53Ni	***	
	M3	202.8 ‒ 0.01 K + 0.0026 Mg + 0.001Al + 0.02Ti ‒ 0.74 V ‒ 0.109Zr ‒ 0.092Pb	***	
Cu	DTPA	1.634 + 0.00076P	**	
	M3	7.98 + 0.00031 Mg + 0.0002Al ‒ 0.057 V ‒ 0.0118Zr ‒ 0.00528Ba ‒ 0.00825Pb	***	
Zn	DTPA	50.74 + 0.017 K + 0.04S ‒ 0.0189Ca + 0.0038Fe ‒ 0.004Al + 0.0289Ti	***	
	M3	75.3 + 0.015 K + 0.037S + 0.0046Fe ‒ 3.01Cu + 0.0354Ti	***	
***: p < .001. **: p < .01. *: p < .05.

In contrast to the work reported by Andrade et al.31, the soil Zn availability was not predicted by pXRF in our experiment, although the positive Cu prediction agreed with the results demonstrated by those authors. The work of Pierangeli et al.32 also achieved successful prediction of available-Cu (R2 = 0.80) when using pXRF although those authors compared pXRF results with those from Mehlich-1 extraction. Also, the inability to predict available Fe was observed by Andrade et al.31. The area from where soils were collected in our experiment exhibited a parent material rich in Zn8, such as sphalerite, smithsonite33, and hemimorphite34, which might have confounded the relationship between available Zn from DTPA and total Zn from pXRF. The results on the prediction of available micronutrients using a pXRF were further investigated in experiment 2 to verify the consistency of the results.

Overall, our results were like those obtained by Pelegrino et al.3 for P, K, and Ca, even considering that those authors performed their experiment in acidic tropical soils, which is not the case for our experiment. Although our exchangeable-K predictions were consistent and reliable in our first trial, which disagrees with the observations of Pelegrino et al.3, those authors used agricultural lands where several crops were cultivated over the years, which might have influenced their results. The consistency of results in our soil incubation study was further evaluated in the second experiment, where plants were grown.

Relationships in biochar amended soils with plants (2nd experiment)

Soil nutrient availability

Overall, the LR models could be established only for P and K regardless of the extraction method used to determine their availability with traditional WC methods. However, the LR model was not significant for S, Ca, Cu, Mg, Fe, and Zn (Fig. 4). In the case of P and K, the r-values (Pearson) ranged from 0.87 to 0.98 and 0.69 to 0.96 (data not shown), respectively for both experiments (p < 0.001) when comparing the several traditional methods and pXRF measurements. As in the 1st experiment, the differences observed in the statistical parameters of the LR, PolR, and PowR models tested in this study were negligible (except for K in some cases), which makes adopting LR models more advantageous, mainly to predict soil P availability (Table 5 and Fig. 4).Fig. 4 Linear relationship between soil nutrients determined by pXRF and several traditional methods (2nd experiment). ***: p < .001. RMSE: root mean square error. Please note that as the control sample has a P concentration of 25 mg kg−1, which is lower than the critical threshold, it is below the LOD of the XRF analysis. Approximately two-thirds of the samples are closely clustered around the control sample. Despite the overall range spanning up to 200 mg kg−1, many of these samples exhibit P concentrations that are above the LOD, indicating detectable variations in P content among them.

In the 2nd experiment the LR relationship between P-pXRF and available-P from several extraction methods was as strong as in the 1st experiment (Figs. 3 and 4). The reason results comparing pXRF-P and acidic extraction methods, such as M3 and Bray, offering a close 1:1 relationship (given the slopes in Figs. 3 and 4) is likely a consequence of the strong acidity of such extraction solutions overestimating available P by dissolving precipitated complexes of calcium and magnesium phosphates at higher pHs. This can be justified by the highly positive correlation (r-value) among P, Ca, and Mg in both experiments (Supplementary Fig. S2).

Oppositely, the work of Pelegrino et al.3 revealed that soil available-P prediction with pXRF was poor although significant; however, the authors attributed such finding to the presence of iron (Fe) and aluminum (Al) oxides in the acidic tropical soils where their study was carried out35, which is not the case of our experiment. Those fixed forms of P in the soil are not available and not detected from conventional extraction methods although are detected by the XRF technique. However, it is important to note that soil has a finite capacity to absorb P into clay complexes. Upon reaching saturation, this condition facilitates more accurate comparisons between total and available P. On the other hand, similar results to those obtained by Pelegrino et al.3 regarding soil K availability were observed in our 2nd experiment most likely due to the same reasons. The lack of regression models' ability to establish good relations between total K concentrations determined by pXRF and soil available-K from traditional WC is attributed to the fact that total K concentrations include several forms of K in the soil. In addition to the available concentrations, fixed-K associated to hydroxy-interlayered vermiculite and structural-K36 associated mainly with the crystalline structure of muscovite37, microcline, orthoclase, and biotite (Supplementary Table S6) also exist in soils. Those non-available K forms might become available in the presence of plants37. However, such availability is not detected with conventional extraction methods. This will be further discussed in the next subsection.

The prediction of soil available-Ca, -S, and -Cu was inconsistent and results varied from one experiment to another. In the 2nd experiment, none of the common regression models (LR, PolR, PowR) exhibited a significant fit as observed in the 1st trial (Table 5), and it varied to a higher extent for S and Cu when compared to Ca. However, SMLR was successful for those nutrients, and a common variable, Al, affecting the prediction of soil available-Ca was observed in both experiments when using M3 (Tables 5 and 6). Hornblende, Augite, and Anorthite are primary minerals containing Ca, Al, and Si and are relatively resistant to weathering (Supplementary Table S6), thus not providing readily available Ca in the soil, although are easily measured with a pXRF.

As in the 1st experiment, SMLR succeeded in predicting the availability of Mg, Fe, and Zn (Supplementary Fig. S3), nutrients unsuccessfully fitted in the common regression models (LR, PolR, and PowR) (Tables 5 and 6). It is assumed that those elements are mostly found in non-available fractions in the soil measured by pXRF, and Mg and Fe are omnipresent components of those mineral fractions. It is further evidenced by evaluating the variables most affecting Mg and Fe prediction from both experiments. When comparing the same solution used for extraction, Al, Si, and Ca are elements commonly affecting the prediction of available Mg and Fe (Table 6) and are components of Mg/Fe-bearing minerals such as biotite, hornblende, augite, olivine (Supplementary Table S6), and dolomite, this last particularly an Mg-based mineral found in the area of study34.

In the work of Dasgupta et al.38, the agroclimatic zone also appeared influential in predicting available K, Mg, Zn, and Fe with a pXRF. The work of Mancini et al.39, oppositely, has found good predictions of exchangeable/available Ca and Mg; however, those authors used a combined/fused application of pXRF + Vis–NIR + NixPro™. The available Fe prediction was also successfully achieved only when using a combined application of pXRF and magnetic susceptibility32. On the other hand, the exchangeable-K prediction of Dasgupta et al.38 was as poor as ours in the second experiment, with R2 values less than 0.5 (Fig. 4).

Soil available Mg could not be predicted with pXRF in either experiment, which might be a consequence of the complex and heterogenous soil matrix making Mg-pXRF measurements very sensitive. Portable XRF faces limitations when it comes to light elements such as Mg40. This is due to the challenges linked to Mg's low atomic number (Z = 12), resulting in reduced sensitivity and detectability in pXRF instruments. It's important to note that the detection limit in pXRF is affected by the atomic number, with lower values yielding weaker X-ray signals. Additionally, matrix effects, caused by complex sample compositions or the presence of other elements, can hinder accurate Mg quantification by influencing X-ray absorption and scattering. Furthermore, the X-ray properties of light elements like Mg are less favorable for pXRF, leading to weaker emissions and potential difficulties in detection and quantification. Spectral interferences from neighboring elements in the X-ray spectrum can further complicate Mg analysis by hindering accurate differentiation and quantification.

The inconsistency with exchangeable-Ca from one experiment to another is also attributed to the heterogeneity of the soil matrix mainly because the plant factor was added. This is further confirmed by the work of Benedet et al.6 who provided a reliable relationship between Ca/Mg as determined by traditional laboratory methods based on WC and pXRF; however, they evaluated limestone and lime-based materials which offered a more homogeneous matrix for pXRF measurements.

Portable X-ray fluorescence spectrometry is a valuable analytical technique for elemental analysis in soil and environmental science. When assessing biochar and soil matrices separately, as well as in combination, several factors can influence XRF measurements. Biochar, a carbonaceous material resulting from organic matter pyrolysis, may exhibit low mineral content, potentially resulting in weaker XRF signals for mineral elements such as Si, Ca, and Fe. Soil, on the other hand, is a complex matrix containing diverse mineral compositions, depending on type and location, often with high concentrations of elements like Si, Al, Fe, and Ca. Elemental interference can occur due to overlapping spectra in the matrices, and variations in density, homogeneity, particle size, and sample preparation can impact measurement accuracy. When biochar and soil are combined, mixing ratios, homogenization, sample heterogeneity, and the need for specialized calibration standards become crucial considerations. In conclusion, successful XRF analysis of biochar, soil, or their mixtures necessitates careful attention to these factors, meticulous sample preparation, and calibration to mitigate matrix effects and ensure the reliability of results in diverse environmental contexts.

It is crucial to highlight that in our experiment, SGB contains a notably high carbon (C) content when compared to PLB, which, conversely, exhibits a significantly higher ash content. Consequently, the enrichment of soil nutrients stemming from the latter biochar aligns more effectively with the escalating rates of biochar application. In this context, it is essential to underscore the substantial influence of carbon presence within a sample matrix on pXRF spectroscopy outcomes. Carbon's X-ray absorption and scattering can attenuate signal intensity and result in spectral overlap with other elements, potentially leading to calibration discrepancies. This underscores the need for specialized procedures to ensure accurate analysis of carbon-rich samples. Employing proper sample preparation techniques becomes imperative in mitigating these challenges and guaranteeing dependable XRF results when dealing with samples bearing significant carbon content.

Plant mineral concentrations

Given that P was the nutrient presenting consistent results in both experiments, it was chosen as the primary factor for predicting the maximum responsive concentration in the soil. In contrast, K showed some promise compared to other nutrients, albeit not as consistently as P. This selection was based on establishing a relationship between P&K-pXRF measurements in the soil and the P&K contents in plant tissues, as depicted in Figs. 5 and 6.Fig. 5 The trends of phosphorus (P) uptake in ryegrass shoots (PTissue) as a function of pXRF‒P and available‒P in the soil from several extraction methods. Significant fits to the linear-with-upper-plateau statistical model were obtained. ***: p < .001. Values followed by ± are the standard deviation. WEP: water extractable phosphorus.

Fig. 6 The trends of potassium (K) uptake in ryegrass shoots (KTissue) as a function of pXRF‒K and soil available‒K from two extraction methods. Significant fits to the linear-with-upper-plateau statistical model were obtained. ***: p < .001. Values followed by ± are the standard deviation. NS: non-significant (p > .05).

The segmented model was able to predict the maximum responsive P concentration in the soil to the P uptake by plants while using a pXRF, and so did the conventional extraction methods since their relationships to pXRF measurements were equally successful (Figs. 4 and 5). Concentrations of P from pXRF were also highly correlated (p < 0.001) with their concentrations in ryegrass tissues (r = 0.74) (data not shown). Therefore, in the case of P, not only does the utilization of a pXRF device allow us to confidently determine 100% sufficiency for ryegrass cultivation, but the robust linear regression constructed (Fig. 4), comparing results from traditional methods with pXRF measurements, demonstrates its effectiveness even at elevated levels of P concentration. This highlights the pXRF technology extends its applicability beyond the 100% sufficiency threshold for cash crops. Consequently, pXRF can play a vital role in interpreting the dynamics of P buildup and accumulation in soil, which holds significant environmental implications.

Table 7 presents the STP values calculated from the equations of LR, PolR, and PowR models when using the joint point (njoint) obtained by XRF and vice-versa. When comparing the ‘njoint (pXRF)’ and the ‘predicted value (pXRF)’ it is noticed that LR gives the closest values obtained by pXRF in the segmented model, except for the WEP (Table 7). This reinforces the reliability of using LR to predict soil available P with pXRF for fertilizer recommendation. Interestingly, the opposite is observed when comparing 'predicted value (TM)' and 'njoint (TM)' since PowR exhibited the closest values to the joint point obtained with traditional methods (Table 7). This also makes sense since segmented models are non-linear models and so are PowR models.Table 7 Comparison of measured and predicted soil nutrient sufficiency levels as derived by the different soil analysis methods and plant tissue analysis.

Method	Regression model	Equation	njoint (pXRF)	Predicted value (TM)	njoint (TM)	Predicted value (pXRF)	
		P, mg kg−1 –––––––––––-	
M3	LR	‒72 + 0.97x	285	203	114	193	
PolR	‒118 + 1.3x‒0.0003x2		229		186	
PowR	86.3e(0.002x)		160		129	
Olsen	LR	‒14 + 0.27x		62	45	222	
PolR	‒31.7 + 0.39x‒0.0001x2		72		207	
PowR	27.5e(0.002x)		49		240	
Bray	LR	‒70 + 1.04x		226	136	198	
PolR	‒143 + 1.6x‒0.0004x2		267		188	
PowR	98.5e(0.002x)		180		153	
WEP	LR	‒3.44 + 0.038x		7	5	221	
PolR	‒3.01 + 0.04x‒0.0000x2		7		225	
PowR	2.90e(0.002x)		6		236	
		K mg kg‒1 –––––––––––-	
M3	LR	‒1377 + 0.27x	—	—	119	5476	
PolR	3667‒1.4x + 0.0001x2		—		6078	
PowR	0.41e(0.001x)		—		5875	
NH4Ac	LR	‒1689 + 0.34x		—	150	5476	
PolR	4750‒1.8x‒0.0002x2		—		6112	
PowR	0.41e(0.001x)		—		5949	
LR linear regression, PolR polynomial regression, PowR power regression, njoint joint point obtained from the linear-with-upper-plateau model, TM traditional method (based on wet chemistry).

The non-linear segmented model did not fit for pXRF‒K vs KTissue as it fitted for pXRF‒P vs PTissue. It might be a consequence of the weak linear relationship between pXRF‒K × M3‒K and NH4Ac‒K in the 2nd experiment (Fig. 4). However, the pXRF‒K × M3‒K relationship in the 1st experiment was good (Fig. 3). Thus, the plant factor (2nd experiment) seems to influence the soil available‒K. The total K from pXRF includes other K fractions such as non-exchangeable, which might be extractable by M3 and NH4Ac. Those fractions may become available in the presence of plants37. Although there is no trend in pXRF-K × KTissue relationship (Fig. 6), it is possible to visually observe a gradual increase, especially for PLB, not a plateau point (njoint) since it was not significant. On the other hand, a njoint point is observed for the traditional methods (Fig. 6) since they are designed to extract only exchangeable or other readily available forms of K to plants.

The significant influence of silicon (Si) and aluminum (Al), the primary components in K-containing minerals, on predicting available K through pXRF measurements is evident in both experiments (Supplementary Table S6 and Table 6). It is important to note that K fractions associated with mineral forms, as measured by pXRF, exhibit different dynamics in terms of plant availability compared to readily available forms. This explains the lack of correlation between pXRF‒K × KTissue and the weak linear relationship between pXRF‒K × M3‒K and NH4Ac‒K in the second experiment. Consequently, statistical parameters RMSE and R12 from PolR and PowR respectively show more significant improvements over LR (Table 5) in the second experiment when plant factors are considered, reinforcing the earlier discussion.

In conclusion, the values for a potential joint point (njoint) derived from pXRF measurements range from 5875 to 6112 mg K kg−1, depending on the extraction method employed (Table 7). These values exceed those calculated using LR (5476 mg K kg−1), demonstrating that the availability of previously unavailable K does not adhere to a linear relationship during plant cultivation because K forms can be indiscriminately measured by pXRF.

Conclusion and final considerations

This work evaluated the applicability of a pXRF instrument to predict the available concentrations of macro- and micro-nutrients in a soil amended with various rates of biochars derived from two different feedstocks. The soils studied with and without plants encompassed wide ranges of pH and OC and well represented common agricultural fields. Overall, XRF sensing results are highly correlated with plant-available P from conventional WC methods, but it failed to predict secondaries or micronutrients accurately. More research is needed before XRF can be recommended as a routine tool for nutrient management. In this study, P showed a strong relationship between the total amounts by pXRF and plant available forms of several different extraction methods. Distinguished biochar outcomes were integrated into regression models, with SGB serving as a link between P levels observed in the control and the higher P levels achieved with PLB. Nevertheless, special consideration should be given to very low to low P levels in alternative agricultural scenarios to accurately evaluate XRF as a test for available P.

Potassium prediction could be affected by the presence of plants grown in the soil. It is imperative to acknowledge that, despite rigorous analysis and attempts at data transformation, the K dataset cannot be conformed to exhibit the same robustness observed in the P dataset, which consistently demonstrated efficacy across all experimental conditions explored in this study. The linear relationship was inconsistent for Ca, S and Cu when comparing the two experiments. Therefore, predictions for those nutrients with pXRF might be influenced by some effect originating from ryegrass cultivation. The pXRF did not work to linearly predict the availability of Mg, Fe, and Zn.

It is pertinent to note that the limited accuracy in predicting the presence of various soil nutrients, including Mg, S, Zn, and Cu, could be attributed to the inability of a portable X-ray fluorescence spectrometer (pXRF) to detect these elements when analyzing PLB, as outlined in Table 1. The difference in the ability of a pXRF to detect certain elements in PLB compared to SGB could be attributed to the distinct elemental compositions of these two biochars, not their quantities since PLB exhibited a much higher content of those elements in comparison to SGB (Table 1). We assume that PLB, being derived from a different source, may have a different elemental profile, possibly containing elements in forms or concentrations that are less conducive to pXRF analysis, including the chemical matrix in which elements are bound and their oxidation states. Differences in the organic and inorganic constituents of these biochars can lead to varying detection capabilities by the instrument, resulting in differential accuracy in predicting the presence of Mg, S, Zn, and Cu. Further investigation is necessary to precisely determine the specific reasons behind the variability in pXRF detection performance between contrasting biochars.

Several studies have attempted to assess the predictive capabilities of portable X-ray fluorescence (pXRF) in soil nutrient analysis, yielding somewhat inconsistent results. However, there has been a limited exploration of pXRF utility in quantifying elemental concentrations in biochars for assessing their potential as fertilizers. Our research represents a pioneering effort in bridging these two contrasting matrices—biochar and soil. Notably, our study focused on evaluating two distinct biochars with unique properties. This innovative approach opens avenues for future research endeavors that could involve broader scale pXRF measurements, encompassing a wider array of soils and a more extensive range of biochars. It also paves the way for investigations involving various matrix combinations in agricultural soils subjected to organic amendments. It is highly encouraged to further evaluate the efficacy of a portable XRF in situ to speed up the process of fertilizer recommendation and the accuracy of nutrient management.

Legislative compliance

All research studies on cultivated plants, including the collection of plant material, is in comply with relevant institutional, national, and international guidelines and legislation.

Supplementary Information

Supplementary Information.

Abbreviations

LR Linear regression

PLB Poultry litter biochar

PolR Polynomial regression

PowR Power regression

pXRF Portable x-ray fluorescence

SGB Switchgrass biochar

SMLR Stepwise multiple linear regression

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-71381-8.

Acknowledgements

This study was funded by the Oklahoma Agricultural Experiment Station and Washington State University CAHNRS.

Author contributions

JA and HZ contributed to the conception and design of the study. JA organized the database. JA performed the statistical analysis. JA and HZ wrote the first draft of the manuscript. JA and HZ wrote sections of the manuscript. JA contributed to the methodology. JA contributed to visualization. JA contributed to the data validation and data curation. HZ contributed to the resources. JA and HZ contributed to writing the first draft, reviewing, and editing. HZ contributed to supervision, project administration, and funding acquisition. JA and HZ contributed to the manuscript revision, and read, and approved the submitted version.

Data availability

Authors can make raw data available upon proper request after consulting the corresponding author.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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References

1. Faria ÁJ Rapid elemental prediction of heterogeneous tropical soils from PXRF DATA: A comparison of models via linear regressions and machine learning algorithms Soil Res. 2023 61 598 615 10.1071/SR22168
Faria, Á. J. et al. Rapid elemental prediction of heterogeneous tropical soils from PXRF DATA: A comparison of models via linear regressions and machine learning algorithms. Soil Res. 61, 598–615 (2023).10.1071/SR22168
2. Silva SH PXRF in tropical soils: Methodology, applications, achievements and challenges Adv. Agron. 2021 10.1016/bs.agron.2020.12.001
Silva, S. H. et al. PXRF in tropical soils: Methodology, applications, achievements and challenges. Adv. Agron.10.1016/bs.agron.2020.12.001 (2021).10.1016/bs.agron.2020.12.001
3. Pelegrino MH Prediction of soil nutrient content via pXRF spectrometry and its spatial variation in a highly variable tropical area Precision Agricult. 2021 23 18 34 10.1007/s11119-021-09825-8
Pelegrino, M. H. et al. Prediction of soil nutrient content via pXRF spectrometry and its spatial variation in a highly variable tropical area. Precision Agricult. 23, 18–34 (2021).10.1007/s11119-021-09825-8
4. Rawal A Determination of base saturation percentage in agricultural soils via portable X-ray fluorescence spectrometer Geoderma 2019 338 375 382 10.1016/j.geoderma.2018.12.032
Rawal, A. et al. Determination of base saturation percentage in agricultural soils via portable X-ray fluorescence spectrometer. Geoderma 338, 375–382 (2019).10.1016/j.geoderma.2018.12.032
5. Benedet L Rapid soil fertility prediction using X-ray fluorescence data and machine learning algorithms CATENA 2021 197 105003 10.1016/j.catena.2020.105003
Benedet, L. et al. Rapid soil fertility prediction using X-ray fluorescence data and machine learning algorithms. CATENA 197, 105003 (2021).10.1016/j.catena.2020.105003
6. Benedet L Clean quality control of agricultural and non-agricultural lime by rapid and accurate assessment of calcium and magnesium contents via proximal sensors Environ. Rese. 2023 221 115300 10.1016/j.envres.2023.115300
Benedet, L. et al. Clean quality control of agricultural and non-agricultural lime by rapid and accurate assessment of calcium and magnesium contents via proximal sensors. Environ. Rese. 221, 115300 (2023).10.1016/j.envres.2023.115300
7. Nawar S Richard F Kassim AM Tekin Y Mouazen AM Fusion of gamma-rays and portable X-ray fluorescence spectral data to measure extractable potassium in soils Soil Tillage Res. 2022 223 105472 10.1016/j.still.2022.105472
Nawar, S., Richard, F., Kassim, A. M., Tekin, Y. & Mouazen, A. M. Fusion of gamma-rays and portable X-ray fluorescence spectral data to measure extractable potassium in soils. Soil Tillage Res. 223, 105472 (2022).10.1016/j.still.2022.105472
8. Antonangelo JA Zhang H Sitienei I Biochar amendment of a metal contaminated soil partially immobilized Zn, pb, and CD and reduced ryegrass uptake Frontiers in Environ. Sci. 2023 10.3389/fenvs.2023.1170427
Antonangelo, J. A., Zhang, H. & Sitienei, I. Biochar amendment of a metal contaminated soil partially immobilized Zn, pb, and CD and reduced ryegrass uptake. Frontiers in Environ. Sci.10.3389/fenvs.2023.1170427 (2023).10.3389/fenvs.2023.1170427
9. Borges BMMN Chemical and spectroscopic evaluations supporting superior P availability after biochar-P fertilizer application Soil Tillage Res. 2022 223 105487 10.1016/j.still.2022.105487
Borges, B. M. M. N. et al. Chemical and spectroscopic evaluations supporting superior P availability after biochar-P fertilizer application. Soil Tillage Res. 223, 105487 (2022).10.1016/j.still.2022.105487
10. Hass A Chicken manure biochar as liming and nutrient source for acid Appalachian soil J. Environ. Q. 2012 41 1096 1106 10.2134/jeq2011.0124
Hass, A. et al. Chicken manure biochar as liming and nutrient source for acid Appalachian soil. J. Environ. Q. 41, 1096–1106 (2012).10.2134/jeq2011.0124
11. Novak, J. M., Johnson, M. G. & Spokas, K. A. Concentration and release of phosphorus and potassium from lignocellulosic- and manure-based Biochars for fertilizer reuse. Frontiers in Sustainable Food Systems 2, 1–9 (2018).
12. Antonangelo JA Zhang H Heavy Metal phytoavailability in a contaminated soil of northeastern Oklahoma as affected by Biochar Amendment Environ. Sci. Pollut. Res. 2019 26 33582 33593 10.1007/s11356-019-06497-w
Antonangelo, J. A. & Zhang, H. Heavy Metal phytoavailability in a contaminated soil of northeastern Oklahoma as affected by Biochar Amendment. Environ. Sci. Pollut. Res. 26, 33582–33593 (2019).10.1007/s11356-019-06497-w
13. Antonangelo JA Zhang H Sun X Kumar A Physicochemical properties and morphology of biochars as affected by feedstock sources and pyrolysis temperatures Biochar 2019 1 325 336 10.1007/s42773-019-00028-z
Antonangelo, J. A., Zhang, H., Sun, X. & Kumar, A. Physicochemical properties and morphology of biochars as affected by feedstock sources and pyrolysis temperatures. Biochar 1, 325–336 (2019).10.1007/s42773-019-00028-z
14. Antonangelo JA Souza JL Whitaker A Arnall B Zhang H Evaluation of mehlich-3 as a multi-element extractant of micronutrients and sulfur in a soil–ryegrass system amended with varying biochar rates from two feedstocks Land 2022 11 1979 10.3390/land11111979
Antonangelo, J. A., Souza, J. L., Whitaker, A., Arnall, B. & Zhang, H. Evaluation of mehlich-3 as a multi-element extractant of micronutrients and sulfur in a soil–ryegrass system amended with varying biochar rates from two feedstocks. Land 11, 1979 (2022).10.3390/land11111979
15. Zhang H Antonangelo J Penn C Development of a rapid field testing method for metals in horizontal directional drilling residuals with XRF sensor Sci. Rep. 2021 10.1038/s41598-021-83584-4 34963697
Zhang, H., Antonangelo, J. & Penn, C. Development of a rapid field testing method for metals in horizontal directional drilling residuals with XRF sensor. Sci. Rep.10.1038/s41598-021-83584-4 (2021).34963697 10.1038/s41598-021-83584-4
16. Burt R Soil Survey Laboratory methods manual 2004 Scientific Publishers
Burt, R. Soil Survey Laboratory methods manual (Scientific Publishers, 2004).
17. Nelson DW Sommers LE Total carbon, organic carbon, and organic matter SSSA Book Series 2018 10.2136/sssabookser5.3.c34
Nelson, D. W. & Sommers, L. E. Total carbon, organic carbon, and organic matter. SSSA Book Series10.2136/sssabookser5.3.c34 (2018).10.2136/sssabookser5.3.c34
18. Mehlich A Mehlich 3 soil test extractant: A modification of Mehlich 2 extractant Commun. Soil Sci. Plant Anal. 1984 15 1409 1416 10.1080/00103628409367568
Mehlich, A. Mehlich 3 soil test extractant: A modification of Mehlich 2 extractant. Commun. Soil Sci. Plant Anal. 15, 1409–1416 (1984).10.1080/00103628409367568
19. Brown JR Recommended chemical soil test procedures for the North Central Region 1998 University of Missouri-Columbia
Brown, J. R. Recommended chemical soil test procedures for the North Central Region (University of Missouri-Columbia, 1998).
20. Lindsay WL Norvell WA Development of a DTPA soil test for zinc, iron, manganese, and copper Soil Sci. Soc. Am. J. 1978 42 421 428 10.2136/sssaj1978.03615995004200030009x
Lindsay, W. L. & Norvell, W. A. Development of a DTPA soil test for zinc, iron, manganese, and copper. Soil Sci. Soc. Am. J. 42, 421–428 (1978).10.2136/sssaj1978.03615995004200030009x
21. Olsen SR Watanabe FS Cole CV Effect of sodium bicarbonate on the solubility of phosphorus in calcareous soils Soil Sci. 1960 89 288 291 10.1097/00010694-196005000-00010
Olsen, S. R., Watanabe, F. S. & Cole, C. V. Effect of sodium bicarbonate on the solubility of phosphorus in calcareous soils. Soil Sci. 89, 288–291 (1960).10.1097/00010694-196005000-00010
22. Bray RH Kurtz LT Determination of total, organic, and available forms of phosphorus in soils Soil Sci. 1945 59 39 46 10.1097/00010694-194501000-00006
Bray, R. H. & Kurtz, L. T. Determination of total, organic, and available forms of phosphorus in soils. Soil Sci. 59, 39–46 (1945).10.1097/00010694-194501000-00006
23. Roswall T Hotspots of legacy phosphorus in agricultural landscapes: Revisiting water-extractable phosphorus pools in soils Water 2021 13 1006 10.3390/w13081006
Roswall, T. et al. Hotspots of legacy phosphorus in agricultural landscapes: Revisiting water-extractable phosphorus pools in soils. Water 13, 1006 (2021).10.3390/w13081006
24. Normandin V Kotuby-Amacher J Miller RO Modification of the ammonium acetate extractant for the determination of exchangeable cations in calcareous soils Commun. Soil Sci. Plant Anal. 1998 29 1785 1791 10.1080/00103629809370069
Normandin, V., Kotuby-Amacher, J. & Miller, R. O. Modification of the ammonium acetate extractant for the determination of exchangeable cations in calcareous soils. Commun. Soil Sci. Plant Anal. 29, 1785–1791 (1998).10.1080/00103629809370069
25. Church C Spargo J Fishel S Strong acid extraction methods for “total phosphorus” in soils: EPA method 3050B and EPA method 3051 Agricult. Environ. Lett. 2017 2 160037 10.2134/ael2016.09.0037
Church, C., Spargo, J. & Fishel, S. Strong acid extraction methods for “total phosphorus” in soils: EPA method 3050B and EPA method 3051. Agricult. Environ. Lett. 2, 160037 (2017).10.2134/ael2016.09.0037
26. Jones JB Case VW Sampling, handling, and analyzing plant tissue samples SSSA Book Series 2018 10.2136/sssabookser3.3ed.c15
Jones, J. B. & Case, V. W. Sampling, handling, and analyzing plant tissue samples. SSSA Book Series10.2136/sssabookser3.3ed.c15 (2018).10.2136/sssabookser3.3ed.c15
27. Wang Q Koval JJ Mills CA Lee K-ID Determination of the selection statistics and best significance level in backward stepwise logistic regression Commun. Stat. Simul. Comput. 2007 37 62 72 10.1080/03610910701723625
Wang, Q., Koval, J. J., Mills, C. A. & Lee, K.-I.D. Determination of the selection statistics and best significance level in backward stepwise logistic regression. Commun. Stat. Simul. Comput. 37, 62–72 (2007).10.1080/03610910701723625
28. Brewer MJ Butler A Cooksley SL The relative performance of AIC, AICc and BIC in the presence of unobserved heterogeneity Methods Ecol. Evol. 2016 7 679 692 10.1111/2041-210X.12541
Brewer, M. J., Butler, A. & Cooksley, S. L. The relative performance of AIC, AICc and BIC in the presence of unobserved heterogeneity. Methods Ecol. Evol. 7, 679–692 (2016).10.1111/2041-210X.12541
29. Stammer AJ Mallarino AP Plant tissue analysis to assess phosphorus and potassium nutritional status of corn and soybean Soil Sci. Soc. Am. J. 2018 82 260 270 10.2136/sssaj2017.06.0179
Stammer, A. J. & Mallarino, A. P. Plant tissue analysis to assess phosphorus and potassium nutritional status of corn and soybean. Soil Sci. Soc. Am. J. 82, 260–270 (2018).10.2136/sssaj2017.06.0179
30. Weindorf DC Chakraborty S Portable x-ray fluorescence spectrometry analysis of Soils Soil Sci. Soc. Am. J. 2020 84 1384 1392 10.1002/saj2.20151
Weindorf, D. C. & Chakraborty, S. Portable x-ray fluorescence spectrometry analysis of Soils. Soil Sci. Soc. Am. J. 84, 1384–1392 (2020).10.1002/saj2.20151
31. Andrade R Micronutrients prediction via PXRF Spectrometry in Brazil: Influence of weathering degree Geoderma Reg. 2021 27 e00431 10.1016/j.geodrs.2021.e00431
Andrade, R. et al. Micronutrients prediction via PXRF Spectrometry in Brazil: Influence of weathering degree. Geoderma Reg. 27, e00431 (2021).10.1016/j.geodrs.2021.e00431
32. Pierangeli LM Combining proximal and remote sensors in spatial prediction of five micronutrients and soil texture in a case study at farmland scale in southeastern Brazil Agronomy 2022 12 2699 10.3390/agronomy12112699
Pierangeli, L. M. et al. Combining proximal and remote sensors in spatial prediction of five micronutrients and soil texture in a case study at farmland scale in southeastern Brazil. Agronomy 12, 2699 (2022).10.3390/agronomy12112699
33. Beattie RE Quantitative analysis of the extent of heavy-metal contamination in soils near Picher, Oklahoma, within the Tar Creek Superfund Site Chemosphere 2017 172 89 95 10.1016/j.chemosphere.2016.12.141 28063319
Beattie, R. E. et al. Quantitative analysis of the extent of heavy-metal contamination in soils near Picher, Oklahoma, within the Tar Creek Superfund Site. Chemosphere 172, 89–95 (2017).28063319 10.1016/j.chemosphere.2016.12.141
34. Schaider LA Senn DB Brabander DJ McCarthy KD Shine JP Characterization of zinc, lead, and cadmium in mine waste: Implications for transport, exposure, and bioavailability Environ. Sci. Technol. 2007 41 4164 4171 10.1021/es0626943 17612206
Schaider, L. A., Senn, D. B., Brabander, D. J., McCarthy, K. D. & Shine, J. P. Characterization of zinc, lead, and cadmium in mine waste: Implications for transport, exposure, and bioavailability. Environ. Sci. Technol. 41, 4164–4171 (2007).17612206 10.1021/es0626943
35. Resende M Mineralogia de Solos Brasileiros interpretação E APLICAÇÕES 2005 UFLA
Resende, M. Mineralogia de Solos Brasileiros interpretação E APLICAÇÕES (UFLA, 2005).
36. Meena VS Maurya BR Verma JP Does a rhizospheric microorganism enhance K+ availability in agricultural soils? Microbiol. Res. 2014 169 337 347 10.1016/j.micres.2013.09.003 24315210
Meena, V. S., Maurya, B. R. & Verma, J. P. Does a rhizospheric microorganism enhance K+ availability in agricultural soils?. Microbiol. Res. 169, 337–347 (2014).24315210 10.1016/j.micres.2013.09.003
37. Firmano RF Potassium reserves in the clay fraction of a tropical soil fertilized for three decades Clays Clay Min. 2020 68 237 249 10.1007/s42860-020-00078-6
Firmano, R. F. et al. Potassium reserves in the clay fraction of a tropical soil fertilized for three decades. Clays Clay Min. 68, 237–249 (2020).10.1007/s42860-020-00078-6
38. Dasgupta S Influence of auxiliary soil variables to improve PXRF-based soil fertility evaluation in India Geoderma Reg. 2022 30 e00557 10.1016/j.geodrs.2022.e00557
Dasgupta, S. et al. Influence of auxiliary soil variables to improve PXRF-based soil fertility evaluation in India. Geoderma Reg. 30, e00557 (2022).10.1016/j.geodrs.2022.e00557
39. Mancini, M. et al. Proximal sensor data fusion for Brazilian soil properties prediction: Exchangeable/available macronutrients, aluminum, and potential acidity. Geoderma Regional 30, (2022).
40. Marguí E Queralt I de Almeida E X-ray fluorescence spectrometry for Environmental Analysis: Basic principles, instrumentation, applications and recent trends Chemosphere 2022 303 135006 10.1016/j.chemosphere.2022.135006 35605725
Marguí, E., Queralt, I. & de Almeida, E. X-ray fluorescence spectrometry for Environmental Analysis: Basic principles, instrumentation, applications and recent trends. Chemosphere 303, 135006 (2022).35605725 10.1016/j.chemosphere.2022.135006
