# Determining the distributions of soil carbon and nitrogen in particle size fractions using near-infrared reflectance spectrum of bulk soil samples

Bernard G. Barthès, Didier Brunet, Edmond Hien, Frank Enjalric, Sofian

Conche, Grégoire T. Freschet, Rémi d'Annunzio, Joële Toucet-Louri

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Bernard G. Barthès, Didier Brunet, Edmond Hien, Frank Enjalric, Sofian Conche, et al. Determining the distributions of soil carbon and nitrogen in particle size fractions using near-infrared reflectance spectrum of bulk soil samples. Soil Biology and Biochemistry, 2008, 40 (6), pp.1533-1537. 10.1016/j.soilbio.2007.12.023. hal-01195059

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<figure><img src="image_2.png" /></figure>
# Determining the distributions of soil carbon and nitrogen in particle size fractions using near infrared reflectance spectrum of bulk soil samples

Bernard G. Barthès<fnref n="1" />, Didier Brunet<fnref n="1" />, Edmond Hien<fnref n="2" />, Frank Enjalric<fnref n="3" />, Sofian Conche<fnref n="1" />,
Grégoire T. Freschet<fnref n="1" />,<fnref n="4" />, Rémi d'Annunzio<fnref n="5" />, Joële Toucet-Louri<fnref n="1" />

## Abstract

This study aimed at assessing the potential of near infrared reflectance spectroscopy (NIRS) for determining the distribution of soil organic matter (SOM) in particle size fractions, which has rarely been attempted. This was done on sandy soils from Burkina Faso (three sites) and Congo-Brazzaville (one site). Over the total sample set, NIRS accurately predicted carbon (C) and nitrogen (N) concentrations (g kg⁻<fnref n="1" /> fraction) in the fraction < 20 µm. When considering Burkina Faso only, predictions were improved in general; those of C and N amounts (g kg⁻<fnref n="1" />) became accurate for the fraction < 20 µm but not for the coarser fractions, probably due to heterogeneous SOM repartition. However, most SOM being < 20 µm in general, NIRS could be considered promising for determining SOM size distribution.

**Keywords:** Soil organic matter; Particle size fractions; Near infrared reflectance spectroscopy (NIRS)

## Introduction

Near infrared reflectance spectroscopy is a rapid and low-cost approach that uses regression methods to express a property as a function of sample reflectance. It has been applied for determining different SOM pools, such as mineralizable or microbial SOM (Chang et al., 2001; Ludwig et al., 2002). However, though the distribution of SOM in particle size fractions

<footnote n="1">¹ IRD-SeqBio, Montpellier SupAgro, bât. 12, 2 pl. Viala, 34060 Montpellier cedex 1, France.</footnote>

<footnote n="2">² Université de Ouagadougou, UFR SVT, 03 BP 7021 Ouagadougou 03, Burkina Faso.</footnote>

<footnote n="3">³ UMR System, CIRAD, Département PERSYST, Montpellier SupAgro, bât. 27, 2 pl. Viala, 34060 Montpellier cedex 1, France.</footnote>

<footnote n="4">⁴ Present address: Department of Systems Ecology, Faculty of Earth and Life Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands.</footnote>

<footnote n="5">⁵ UMR LERFOB, INRA, route d'Amance, 54280 Champenoux, France; CIRAD, UPR Ecosystèmes de plantations, Campus de Baillarguet, 34398 Montpellier cedex 5, France.</footnote>
provides useful information, due to the different composition and dynamics of SOM size
fractions (Christensen, 1992; Feller et al., 2001), very few studies have attempted
characterizing it using NIRS (Móron and Cozzolino, 2004; Cozzolino and Móron, 2006). Yet,
this would be relevant because usual fractionation procedures are tedious, while measuring
soil reflectance requires ca. one minute per sample. The present work aimed at assessing
whether NIRS could facilitate characterizing the particle size distribution of SOM, by
studying the accuracy of NIRS determinations based on bulk soil spectra.

**Materials and methods**

The 193 studied soil samples originated from three sites in Burkina Faso and one site in Congo-Brazzaville (Table 1). The particle size fractionation of SOM (reference method) was carried out on 2-mm sieved air-dried soil samples of 20 g, following Gavinelli et al. (1995). The procedure involved chemical dispersion; shaking; wet-sieving at 200 then 50 µm; ultrasonication of the suspension < 50 µm when dispersion seemed incomplete; wet-sieving at 20 µm; withdrawing of an aliquot of the suspension < 20 µm; fraction oven-drying (40°C) then weighing; C and N analyses by dry combustion. Four samples from Saria were fractionated in triplicate and four samples from Pointe-Noire in duplicate.

Reflectance was measured between 1100 and 2500 nm at 8 nm intervals with a Foss NIRSystems 5000 spectrometer (Silver Spring, MD, USA), on two 5-g subsamples per sample (2-mm sieved, oven-dried at 40°C). Each spectrum, averaged from 32 scans, was recorded as absorbance (log [1/reflectance]). Data analyses were conducted using the WinISI III-v.1.61 software (Infrasoft International, LCC, State College, PA, USA). According to preliminary results, spectra were mean centred and variance-scaled, then a first derivate was applied. A principal component analysis was carried out on spectral data for calculating the Mahalanobis distance H, and samples with H > 3 were eliminated; then the sample set was divided into a calibration subset including the 100 most representative samples, and a remaining validation subset (Shenk and Westerhaus, 1991a). Calibration models were derived from spectra and reference values using modified partial least square regression (Shenk and Westerhaus, 1991b). Cross validation was performed on the calibration subset and the number of factors giving the smallest standard error of cross validation (SECV) determined the optimal number of factors of the model. The calibration performance was assessed using coefficient of determination (R²cal), SECV (as absolute value or as % of the mean), and RPD (ratio of standard deviation to SECV). The prediction accuracy was evaluated on the validation subset, using validation R² (R²val) and relative standard error of prediction (SEP).
## Results and discussion

The cumulative yields of fraction masses, C and N averaged 100, 89 and 96%, respectively, rather low recoveries being attributed to soluble SOM (Christensen, 1992). Most samples were sandy, but the fraction < 20 µm generally included the highest proportion of SOM (Table 2). Coefficients of variation of fraction C and N were 2-3% for the fraction < 20 µm and 12-21% for the other fractions in Saria, and 22-32% in Pointe-Noire.

The NIRS analysis was first carried out over the complete sample set (Table 3). Calibration and prediction were accurate for all fraction masses and for C and N concentrations (g kg⁻¹ fraction) in the fraction < 20 µm, but not for fraction C and N amounts (g kg⁻¹ soil). They were reasonably accurate for C/N in the fractions < 50 µm but not in the coarser ones. Moreover, they were rather accurate for total soil C (Ct) and N (Nt), and very accurate for Ct/Nt. Calibrations and predictions were more accurate in general when considering only the 159 samples from Burkina Faso. This was clear for the fraction < 20 µm as regarded C and N concentrations (R²val = 0.94-0.97, SEP = 12%), C amount (R²val = 0.87, SEP = 24%), N amount (R²val = 0.71, SEP = 19%), and C/N (R²val = 0.82, SEP = 11%), and also for Ct and Nt (R²val = 0.84-0.94, SEP = 17%).

Accurate NIRS determinations of Ct and Nt have been extensively reported, especially for rather homogeneous textural sets (Dalal and Henry, 1986; Morra et al., 1991; Brunet et al., 2007). Several studies have also reported NIRS determination of Ct/Nt (Chang and Laird, 2002; Ludwig et al., 2002). Here Ct/Nt was more accurately predicted than Ct and Nt, suggesting that spectra include precise information on SOM quality. The prediction accuracy of fraction masses was similar in the present study and in those involving comparably homogeneous sets (Chang et al., 2001; Chang et al., 2005; Madari et al., 2006). Here fraction mass was less accurately predicted for the fraction < 20 µm than for the others, probably due to less precise reference determination (aliquot withdrawing).

For the fraction < 20 µm, which included most SOM in general, NIRS predictions of C and N were accurate, especially when considering Burkina Faso only. By contrast, C and N were poorly predicted in the fractions > 20 µm, probably due to heterogeneous SOM repartition. Indeed, due to its low SOM content, every fraction > 20 µm included a limited number of organic particles. Depending on the subsample, a couple of organic particles more or less could thus affect fraction SOM content, leading to discrepancies between replicates, or between reference and NIRS analyses. This underlined that the apparent imprecision of NIRS predictions might actually reflect imprecise reference determinations, and that more attention
should be paid to using the same subsample for spectral then conventional analyses, NIRS being non-destructive. Fraction C/N was reasonably predicted for fine fractions, confirming that spectra include relevant information on SOM quality, but predictions were poor for coarse fractions, probably due to heterogeneous SOM repartition. Very few studies have attempted predicting the size distribution of SOM using NIRS. Móron and Cozzolino (2004) and Cozzolino and Móron (2006) used visible and near infrared reflectance spectra to study topsoil samples representing different Uruguayan soils. Texture was not described precisely but SOM data suggest that most samples were rather clayey. On the whole, predictions regarding the fractions < 50 µm or N were more accurate in these studies than in the present one, but those regarding the fractions > 50 µm or C/N were more accurate in the present one, whereas no clear difference between studies could be found for C.

In conclusion, due to the accurate prediction of C and N in the fine fraction, which contribution to total SOM was dominant in general, NIRS could be considered promising for facilitating the determination of SOM distribution in particle size fractions.

## Acknowledgements

The authors thank Moussa Barry, Damien Landais, Raphaël Manlay, Dominique Masse, Laurent Saint-André and Sansan Youl for sample collection, and two anonymous reviewers for their recommendations. This work received financial support from the French Ministry of Higher Education and Research (Project MIROT founded by the Action Concertée Incitative "Ecologie quantitative").

## References

- Brunet, D., Barthès, B.G., Chotte, J.L., Feller, C., 2007. Determination of carbon and nitrogen contents in Alfisols, Oxisols and Ultisols from Africa and Brazil using NIRS analysis: Effects of sample grinding and set heterogeneity. Geoderma 139, 106–117.

- Chang, C.W., Laird, D.A., Mausbach, M.J., Hurburgh, C.R.J., 2001. Near-infrared reflectance spectroscopy - Principal components regression analyses of soil properties. Soil Science Society of America Journal 65, 480–490.

- Chang, C.W., Laird, D.A., 2002. Near-infrared reflectance spectroscopic analysis of soil C and N. Soil Science 167, 110–116.

- Chang, C.W., Laird, D.A., Hurburgh, C.R.J., 2005. Influence of soil moisture on near-infrared reflectance spectroscopic measurements of soil properties. Soil Science 170, 244–255.

- Christensen, B.T., 1992. Physical fractionation of soil and organic matter in primary particle size and density separates. In: Stewart, B.A. (Ed.), Advances in Soil Science, vol. 20, Springer, New York, pp. 1–90.
Cozzolino, D., Móron, A., 2006. Potential of near-infrared reflectance spectroscopy and chemometrics to predict soil organic carbon fractions. Soil & Tillage Research 85, 78–85.

Dalal, R.C., Henry, R.J. 1986. Simultaneous determination of moisture, organic carbon and total nitrogen by near infrared reflectance spectrophotometry. Soil Science Society of America Journal 50, 120–123.

FAO-ISRIC-ISSS (Food and Agriculture Organization of the United Nations, International Soil Reference and Information Centre, International Society for Soil Science), 1998. World Reference Base for Soil Resources. FAO, Rome.

Feller, C., Balesdent, J., Nicolardot, B., Cerri, C., 2001. Approaching “functional” soil organic matter pools through particle-size fractionation: Examples for tropical soils. In: Lal, R., Kimble, J.M., Follett, R.F., Stewart, B.A. (Eds.), Assessment Methods for Soil Carbon. Lewis Publishers, CRC Press, Boca Raton, FL, pp. 53–67.

Gavinelli, E., Feller, C., Larré-Larrouy, M.C., Bacye, B., Djegui, N., Nzila, J.D.D., 1995. A routine method to study soil organic matter by particle-size fractionation: Examples for tropical soils. Communications in Soil Science and Plant Analysis 26, 1749–1760.

Ludwig, B., Khanna, P.K., Bauhus, J., Hopmans, P., 2002. Near infrared spectroscopy of forest soils to determine chemical and biological properties related to soil sustainability. Forest Ecology and Management 171, 121–132.

Madari, B.E., Reeves, J.B., III, Machado, P.L.O.A., Guimarães, C.M., Torres, E., McCarty, G.W., 2006. Mid- and near-infrared spectroscopic assessment of soil compositional parameters and structural indices in two Ferralsols. Geoderma 136, 245–259.

Móron, A., Cozzolino, D., 2004. Determination of potentially mineralizable nitrogen and nitrogen in particulate organic matter fractions in soil by visible and near-infrared reflectance spectroscopy. Journal of Agricultural Science 142, 335–343.

Morra, M.J., Hall, M.H., Freeborn, L.L., 1991. Carbon and nitrogen analysis of soil fractions using near-infrared reflectance spectroscopy. Soil Science Society of America Journal 55, 288–291.

Shenk, J.S., Westerhaus, M.O., 1991a. Population definition, sample selection and calibration procedures for near infrared reflectance spectroscopy. Crop Science 31, 469–474.

Shenk, J.S., Westerhaus, M.O., 1991b. Population structuring of near infrared spectra and modified partial least square regression. Crop Science 31, 1548–1555.
<table><caption>**Table 1.** Presentation of the studied sites, soils and samples.</caption><thead><tr><th>Location</th><th>Soil type<sup>a</sup><br>(and % sand<sup>b</sup>)</th><th>Mean annual<br>rainfall and<br>temperature</th><th>Land use</th><th>Number<br>of<br>samples</th><th>Sample<br>depth<br>(cm)</th></tr></thead><tbody><tr><td>Banh<br>(northern Burkina)<br>14°04'N, 02°26'W</td><td>Ferralic<br>Arenosol<br>(48-94%)</td><td>600 mm<br>29°C</td><td>Millet with<br>or without<br>manure addition<br>(corralling)</td><td>56</td><td>0-10<br>to<br>80-100</td></tr><tr><td>Saria<br>(central Burkina)<br>12°16'N, 02°09'W</td><td>Ferric<br>Acrisol<br>(59-66%)</td><td>800 mm<br>28°C</td><td>Sorghum with<br>or without<br>manure and/or<br>fertilizers</td><td>51</td><td>0-10<br>and<br>10-20</td></tr><tr><td>Torokoro<br>(southern Burkina)<br>10°03'N, 04°25'W</td><td>Lixisol<br>(68-86%)</td><td>1100 mm<br>27°C</td><td>Crops (cotton,<br>yam, sorghum),<br>fallow, orchard,<br>forest</td><td>52</td><td>0-10</td></tr><tr><td>Vicinity of Pointe-Noire<br>(Congo-Brazzaville)<br>04°S, 12°E</td><td>Ferralic<br>Arenosol<br>(91-96%)</td><td>1200 mm<br>25°C</td><td>Eucalyptus<br>plantations<br>and savanna</td><td>34</td><td>0-10</td></tr></tbody></table>

<footnote><sup>a</sup> FAO-ISRIC-ISSS (1998).</footnote>

<footnote><sup>b</sup> 50-2000 µm.</footnote>
<table><caption>**Table 2.** Reference data regarding the mass, C and N concentrations (g kg⁻¹ fraction) and amounts (g kg⁻¹ soil), and C/N ratio of particle size fractions and total soil for the total sample set and each site separately.</caption><thead><tr><th rowspan="2">Variable</th><th>Fraction</th><th colspan="4">Total set</th><th colspan="4">Banh (Burkina)</th><th colspan="4">Saria (Burkina)</th><th colspan="4">Torokoro (Burkina)</th><th colspan="4">Pointe-Noire (Congo)</th></tr><tr><th>(µm)</th><th>Mean</th><th>SD</th><th>Min</th><th>Max</th><th>Mean</th><th>SD</th><th>Min</th><th>Max</th><th>Mean</th><th>SD</th><th>Min</th><th>Max</th><th>Mean</th><th>SD</th><th>Min</th><th>Max</th><th>Mean</th><th>SD</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td rowspan="4">Mass<br>(g 100 g⁻¹)</td><td>&gt; 200</td><td>37.0</td><td>13.8</td><td>14.5</td><td>78.9</td><td>22.5</td><td>3.5</td><td>14.5</td><td>35.2</td><td>31.8</td><td>1.9</td><td>23.7</td><td>35.0</td><td>49.0</td><td>9.2</td><td>28.4</td><td>65.2</td><td>50.2</td><td>11.8</td><td>26.7</td><td>78.9</td></tr><tr><td>50-200</td><td>38.5</td><td>12.2</td><td>17.6</td><td>66.8</td><td>51.1</td><td>9.1</td><td>33.7</td><td>66.2</td><td>30.1</td><td>2.2</td><td>25.1</td><td>36.1</td><td>30.2</td><td>7.0</td><td>17.7</td><td>48.1</td><td>43.4</td><td>11.5</td><td>17.6</td><td>66.8</td></tr><tr><td>20-50</td><td>8.4</td><td>6.9</td><td>0.6</td><td>22.6</td><td>5.4</td><td>1.9</td><td>0.6</td><td>9.9</td><td>19.2</td><td>1.1</td><td>16.6</td><td>22.6</td><td>5.4</td><td>1.8</td><td>2.8</td><td>11.1</td><td>1.5</td><td>0.5</td><td>0.8</td><td>2.8</td></tr><tr><td>&lt; 20</td><td>16.3</td><td>7.8</td><td>2.7</td><td>43.7</td><td>22.1</td><td>9.0</td><td>5.1</td><td>43.7</td><td>18.7</td><td>2.2</td><td>14.8</td><td>22.9</td><td>14.9</td><td>3.3</td><td>9.5</td><td>26.3</td><td>5.1</td><td>1.3</td><td>2.7</td><td>8.1</td></tr><tr><td rowspan="4">C concentration<br>(g kg⁻¹ fr.)</td><td>&gt; 200</td><td>1.9</td><td>2.3</td><td>0.2</td><td>24.8</td><td>1.3</td><td>3.3</td><td>0.2</td><td>24.8</td><td>1.4</td><td>1.6</td><td>0.2</td><td>7.9</td><td>2.5</td><td>1.4</td><td>0.9</td><td>8.5</td><td>2.9</td><td>2.1</td><td>0.6</td><td>9.3</td></tr><tr><td>50-200</td><td>2.9</td><td>3.1</td><td>0.2</td><td>20.4</td><td>0.8</td><td>1.2</td><td>0.2</td><td>9.1</td><td>1.3</td><td>1.3</td><td>0.2</td><td>6.8</td><td>4.4</td><td>2.3</td><td>1.4</td><td>14.1</td><td>6.3</td><td>4.2</td><td>1.6</td><td>20.4</td></tr><tr><td>20-50</td><td>11.5</td><td>19.4</td><td>0.2</td><td>84.6</td><td>2.1</td><td>2.5</td><td>0.7</td><td>18.8</td><td>1.1</td><td>0.7</td><td>0.2</td><td>4.0</td><td>6.4</td><td>4.0</td><td>2.4</td><td>20.9</td><td>50.4</td><td>15.5</td><td>22.2</td><td>84.6</td></tr><tr><td>&lt; 20</td><td>21.0</td><td>16.1</td><td>2.8</td><td>65.4</td><td>9.5</td><td>7.1</td><td>2.8</td><td>47.5</td><td>10.6</td><td>3.9</td><td>6.3</td><td>19.7</td><td>24.9</td><td>6.0</td><td>17.1</td><td>45.4</td><td>49.7</td><td>8.8</td><td>32.3</td><td>65.4</td></tr><tr><td rowspan="4">C amount<br>(g kg⁻¹ soil)</td><td>&gt; 200</td><td>0.8</td><td>0.9</td><td>ε₁</td><td>6.6</td><td>0.3</td><td>0.9</td><td>ε₁</td><td>6.6</td><td>0.5</td><td>0.5</td><td>0.1</td><td>2.5</td><td>1.2</td><td>0.6</td><td>0.5</td><td>3.8</td><td>1.5</td><td>1.2</td><td>0.3</td><td>5.7</td></tr><tr><td>50-200</td><td>1.0</td><td>1.2</td><td>0.1</td><td>7.2</td><td>0.4</td><td>0.8</td><td>0.1</td><td>6.0</td><td>0.4</td><td>0.4</td><td>0.1</td><td>2.1</td><td>1.3</td><td>0.6</td><td>0.6</td><td>4.0</td><td>2.6</td><td>1.5</td><td>0.6</td><td>7.2</td></tr><tr><td>20-50</td><td>0.3</td><td>0.3</td><td>ε₁</td><td>1.6</td><td>0.1</td><td>0.1</td><td>ε₁</td><td>0.6</td><td>0.2</td><td>0.1</td><td>ε₁</td><td>0.8</td><td>0.3</td><td>0.2</td><td>0.1</td><td>1.4</td><td>0.8</td><td>0.4</td><td>0.2</td><td>1.6</td></tr><tr><td>&lt; 20</td><td>2.5</td><td>1.4</td><td>0.8</td><td>11.8</td><td>1.7</td><td>0.5</td><td>0.8</td><td>3.1</td><td>2.0</td><td>0.7</td><td>1.0</td><td>3.7</td><td>3.8</td><td>1.9</td><td>2.0</td><td>11.8</td><td>2.5</td><td>0.8</td><td>1.2</td><td>4.7</td></tr><tr><td></td><td>total soil</td><td>5.2</td><td>3.5</td><td>1.2</td><td>21.3</td><td>2.5</td><td>2.2</td><td>1.2</td><td>18.0</td><td>3.8</td><td>1.8</td><td>1.9</td><td>10.1</td><td>7.5</td><td>3.2</td><td>3.8</td><td>21.3</td><td>8.1</td><td>3.4</td><td>4.2</td><td>17.7</td></tr><tr><td rowspan="4">N concentration<br>(g kg⁻¹ fr.)</td><td>&gt; 200</td><td>0.11</td><td>0.17</td><td>0.01</td><td>2.15</td><td>0.09</td><td>0.29</td><td>0.01</td><td>2.15</td><td>0.10</td><td>0.11</td><td>0.02</td><td>0.57</td><td>0.12</td><td>0.07</td><td>0.06</td><td>0.45</td><td>0.12</td><td>0.08</td><td>0.03</td><td>0.39</td></tr><tr><td>50-200</td><td>0.17</td><td>0.17</td><td>ε₂</td><td>0.90</td><td>0.06</td><td>0.12</td><td>ε₂</td><td>0.90</td><td>0.10</td><td>0.10</td><td>0.02</td><td>0.53</td><td>0.27</td><td>0.13</td><td>0.10</td><td>0.80</td><td>0.31</td><td>0.17</td><td>0.07</td><td>0.81</td></tr><tr><td>20-50</td><td>0.70</td><td>1.14</td><td>0.01</td><td>4.69</td><td>0.19</td><td>0.24</td><td>0.05</td><td>1.83</td><td>0.09</td><td>0.06</td><td>0.01</td><td>0.34</td><td>0.34</td><td>0.20</td><td>0.13</td><td>1.17</td><td>3.01</td><td>0.77</td><td>1.08</td><td>4.69</td></tr><tr><td>&lt; 20</td><td>1.88</td><td>1.28</td><td>0.40</td><td>6.40</td><td>1.13</td><td>0.85</td><td>0.40</td><td>6.21</td><td>1.15</td><td>0.40</td><td>0.69</td><td>2.23</td><td>1.89</td><td>0.38</td><td>1.44</td><td>3.17</td><td>4.19</td><td>0.81</td><td>2.80</td><td>6.40</td></tr><tr><td rowspan="4">N amount<br>(g kg⁻¹ soil)</td><td>&gt; 200</td><td>0.04</td><td>0.05</td><td>ε₂</td><td>0.57</td><td>0.02</td><td>0.08</td><td>ε₂</td><td>0.57</td><td>0.03</td><td>0.04</td><td>ε₂</td><td>0.19</td><td>0.06</td><td>0.03</td><td>0.02</td><td>0.18</td><td>0.06</td><td>0.05</td><td>0.02</td><td>0.19</td></tr><tr><td>50-200</td><td>0.06</td><td>0.07</td><td>ε₂</td><td>0.59</td><td>0.03</td><td>0.08</td><td>ε₂</td><td>0.59</td><td>0.03</td><td>0.03</td><td>0.01</td><td>0.16</td><td>0.08</td><td>0.04</td><td>0.03</td><td>0.23</td><td>0.13</td><td>0.06</td><td>0.03</td><td>0.33</td></tr><tr><td>20-50</td><td>0.02</td><td>0.02</td><td>ε₂</td><td>0.10</td><td>0.01</td><td>0.01</td><td>ε₂</td><td>0.05</td><td>0.02</td><td>0.01</td><td>ε₂</td><td>0.07</td><td>0.02</td><td>0.01</td><td>0.01</td><td>0.08</td><td>0.05</td><td>0.02</td><td>0.01</td><td>0.10</td></tr><tr><td>&lt; 20</td><td>0.23</td><td>0.09</td><td>0.11</td><td>0.83</td><td>0.20</td><td>0.06</td><td>0.11</td><td>0.41</td><td>0.21</td><td>0.07</td><td>0.12</td><td>0.39</td><td>0.29</td><td>0.12</td><td>0.15</td><td>0.83</td><td>0.21</td><td>0.06</td><td>0.12</td><td>0.34</td></tr><tr><td></td><td>total soil</td><td>0.37</td><td>0.20</td><td>0.14</td><td>1.73</td><td>0.27</td><td>0.21</td><td>0.14</td><td>1.73</td><td>0.35</td><td>0.15</td><td>0.16</td><td>0.93</td><td>0.48</td><td>0.20</td><td>0.26</td><td>1.45</td><td>0.39</td><td>0.11</td><td>0.21</td><td>0.75</td></tr><tr><td rowspan="4">C/N</td><td>&gt; 200</td><td>18.4</td><td>4.7</td><td>10.8</td><td>37.3</td><td>17.5</td><td>4.2</td><td>10.8</td><td>27.3</td><td>14.5</td><td>1.2</td><td>11.8</td><td>17.5</td><td>20.2</td><td>3.6</td><td>13.9</td><td>31.7</td><td>22.9</td><td>5.2</td><td>14.7</td><td>37.3</td></tr><tr><td>50-200</td><td>15.5</td><td>3.4</td><td>7.7</td><td>27.7</td><td>13.9</td><td>2.8</td><td>7.7</td><td>20.5</td><td>13.5</td><td>1.1</td><td>10.6</td><td>15.9</td><td>16.4</td><td>2.1</td><td>12.1</td><td>23.8</td><td>19.5</td><td>4.3</td><td>11.9</td><td>27.7</td></tr><tr><td>20-50</td><td>14.4</td><td>3.5</td><td>6.8</td><td>23.6</td><td>11.4</td><td>1.8</td><td>6.8</td><td>14.9</td><td>12.3</td><td>1.1</td><td>10.4</td><td>14.6</td><td>18.2</td><td>2.4</td><td>12.5</td><td>23.6</td><td>16.7</td><td>2.5</td><td>13.2</td><td>22.5</td></tr><tr><td>&lt; 20</td><td>10.5</td><td>2.5</td><td>5.4</td><td>19.4</td><td>8.2</td><td>1.4</td><td>5.4</td><td>10.9</td><td>9.2</td><td>0.6</td><td>8.0</td><td>10.5</td><td>13.2</td><td>1.6</td><td>10.8</td><td>19.4</td><td>12.0</td><td>1.5</td><td>8.9</td><td>16.3</td></tr><tr><td></td><td>total soil</td><td>13.3</td><td>4.5</td><td>5.6</td><td>32.7</td><td>9.6</td><td>1.4</td><td>5.6</td><td>12.0</td><td>10.9</td><td>1.2</td><td>7.5</td><td>13.9</td><td>15.3</td><td>1.2</td><td>13.3</td><td>18.4</td><td>20.5</td><td>4.2</td><td>15.4</td><td>32.7</td></tr></tbody></table>

SD is the standard deviation.

ε₁ < 0.1 g kg⁻¹; ε₂ < 0.01 g kg⁻¹.
<table><caption>**Table 3.** Calibration and validation results for the mass, C and N concentrations (g kg⁻¹ fraction) and amounts (g kg⁻¹ soil), and C/N ratio of particle size fractions and total soil for the total sample set.</caption><thead><tr><th rowspan="2">Variable</th><th rowspan="2">Fraction</th><th colspan="4">Calibration</th><th colspan="4">Validation</th></tr><tr><th>n<sub>1</sub></th><th>R<sup>2</sup>cal</th><th>SECV<br>(absol.<br>value)</th><th>SECV<br>(%)</th><th>RPD</th><th>n<sub>2</sub></th><th>R<sup>2</sup>val</th><th>SEP<br>(absol.<br>value)</th><th>SEP<br>(%)</th></tr></thead><tbody><tr><td rowspan="4">Mass</td><td>&gt; 200 µm</td><td>93</td><td>0.783</td><td>6.3</td><td>16.1</td><td>2.2</td><td>86</td><td>0.819</td><td>5.3</td><td>15.7</td></tr><tr><td>50-200 µm</td><td>96</td><td>0.787</td><td>6.1</td><td>15.8</td><td>2.2</td><td>86</td><td>0.798</td><td>5.4</td><td>14.0</td></tr><tr><td>20-50 µm</td><td>93</td><td>0.948</td><td>1.5</td><td>19.8</td><td>4.4</td><td>86</td><td>0.961</td><td>1.4</td><td>14.4</td></tr><tr><td>&lt; 20 µm</td><td>95</td><td>0.813</td><td>3.0</td><td>20.2</td><td>2.3</td><td>86</td><td>0.891</td><td>2.7</td><td>14.4</td></tr><tr><td rowspan="4">C concentration</td><td>&gt; 200 µm</td><td>84</td><td>0.801</td><td>0.5</td><td>24.4</td><td>2.2</td><td>86</td><td>0.533</td><td>0.9</td><td>66.7</td></tr><tr><td>50-200 µm</td><td>97</td><td>0.797</td><td>1.1</td><td>33.8</td><td>2.2</td><td>86</td><td>0.699</td><td>1.2</td><td>63.0</td></tr><tr><td>20-50 µm</td><td>88</td><td>0.914</td><td>4.0</td><td>30.3</td><td>3.4</td><td>86</td><td>0.915</td><td>4.5</td><td>60.1</td></tr><tr><td>&lt; 20 µm</td><td>90</td><td>0.945</td><td>3.4</td><td>14.4</td><td>4.2</td><td>86</td><td>0.953</td><td>3.4</td><td>20.3</td></tr><tr><td rowspan="4">N concentration</td><td>&gt; 200 µm</td><td>88</td><td>0.833</td><td>0.03</td><td>24.9</td><td>2.4</td><td>86</td><td>0.515</td><td>0.06</td><td>81.4</td></tr><tr><td>50-200 µm</td><td>91</td><td>0.825</td><td>0.05</td><td>25.6</td><td>2.4</td><td>86</td><td>0.776</td><td>0.06</td><td>47.5</td></tr><tr><td>20-50 µm</td><td>88</td><td>0.908</td><td>0.25</td><td>30.5</td><td>3.3</td><td>86</td><td>0.907</td><td>0.29</td><td>59.6</td></tr><tr><td>&lt; 20 µm</td><td>93</td><td>0.869</td><td>0.39</td><td>18.7</td><td>2.8</td><td>86</td><td>0.929</td><td>0.30</td><td>20.1</td></tr><tr><td rowspan="4">C amount</td><td>&gt; 200 µm</td><td>89</td><td>0.765</td><td>0.3</td><td>29.6</td><td>2.1</td><td>86</td><td>0.649</td><td>0.3</td><td>64.2</td></tr><tr><td>50-200 µm</td><td>90</td><td>0.857</td><td>0.3</td><td>26.7</td><td>2.7</td><td>86</td><td>0.775</td><td>0.4</td><td>60.0</td></tr><tr><td>20-50 µm</td><td>91</td><td>0.668</td><td>0.1</td><td>41.3</td><td>1.7</td><td>86</td><td>0.690</td><td>0.1</td><td>57.1</td></tr><tr><td>&lt; 20 µm</td><td>93</td><td>0.742</td><td>0.5</td><td>17.6</td><td>2.0</td><td>86</td><td>0.700</td><td>0.8</td><td>34.6</td></tr><tr><td rowspan="4">N amount</td><td>total soil</td><td>88</td><td>0.810</td><td>1.1</td><td>18.9</td><td>2.3</td><td>86</td><td>0.831</td><td>1.2</td><td>28.2</td></tr><tr><td>&gt; 200 µm</td><td>86</td><td>0.832</td><td>0.01</td><td>23.4</td><td>2.4</td><td>86</td><td>0.657</td><td>0.02</td><td>56.7</td></tr><tr><td>50-200 µm</td><td>87</td><td>0.804</td><td>0.02</td><td>27.7</td><td>2.2</td><td>86</td><td>0.674</td><td>0.03</td><td>62.5</td></tr><tr><td>20-50 µm</td><td>93</td><td>0.671</td><td>0.01</td><td>48.5</td><td>1.7</td><td>86</td><td>0.647</td><td>0.01</td><td>45.0</td></tr><tr><td rowspan="4">C/N ratio</td><td>&lt; 20 µm</td><td>92</td><td>0.617</td><td>0.04</td><td>16.1</td><td>1.6</td><td>86</td><td>0.518</td><td>0.06</td><td>25.5</td></tr><tr><td>total soil</td><td>94</td><td>0.771</td><td>0.06</td><td>16.2</td><td>2.1</td><td>86</td><td>0.776</td><td>0.07</td><td>22.5</td></tr><tr><td>&gt; 200 µm</td><td>91</td><td>0.604</td><td>2.7</td><td>14.5</td><td>1.6</td><td>86</td><td>0.348</td><td>3.7</td><td>21.0</td></tr><tr><td>50-200 µm</td><td>94</td><td>0.461</td><td>2.1</td><td>13.2</td><td>1.4</td><td>86</td><td>0.345</td><td>2.7</td><td>17.5</td></tr><tr><td rowspan="4"></td><td>20-50 µm</td><td>96</td><td>0.775</td><td>1.6</td><td>10.8</td><td>2.1</td><td>86</td><td>0.683</td><td>1.9</td><td>13.9</td></tr><tr><td>&lt; 20 µm</td><td>97</td><td>0.748</td><td>1.1</td><td>10.4</td><td>2.0</td><td>86</td><td>0.764</td><td>1.3</td><td>13.4</td></tr><tr><td>total soil</td><td>94</td><td>0.874</td><td>1.3</td><td>9.2</td><td>2.8</td><td>86</td><td>0.878</td><td>1.3</td><td>10.6</td></tr></tbody></table>

n₁ is number of samples in the calibration set after the elimination of calibration outliers.

n₂ is the number of samples in the validation test.

SECV and SEP are standard error of cross-validation and of prediction, respectively, and are expressed as absolute values or as proportions of the mean.

RPD is the ratio of standard deviation to SECV.