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Porosity distribution by computed tomography and its importance to characterize soil clod samples
Applied Radiation and Isotopes 92 (2014) 37–45
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Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Porosity distribution by computed tomography and its importance to characterize soil clod samples Luiz F. Pires n, André M. Brinatti, Sérgio C. Saab, Fabio A.M. Cássaro Laboratory of Soil Physics and Environmental Sciences, Department of Physics, State University of Ponta Grossa (UEPG), Av. Carlos Cavalcanti, 4748, CEP. 84.030-900, Ponta Grossa, PR, Brazil
H I G H L I G H T S
2D detailed analysis of porosity distribution was carried out. 2D images permitted to evaluate the size of macropores inside clod samples. Samples with volumes varying from 50 to 100 cm3 were studied with millimetric resolution. The investigation allowed a new insight about the variability of soil clod structure.
art ic l e i nf o
a b s t r a c t
Article history: Received 3 January 2014 Received in revised form 15 May 2014 Accepted 11 June 2014 Available online 19 June 2014
Gamma-ray computed tomography (CT) was employed to study the soil quality of clod samples used to investigate porosity (ϕ). Samples with volumes varying from 50 to 100 cm3 were collected from the soil surface. 2D CT images were obtained with millimetric resolution. Porosity distribution analyses were carried out to infer the soil clod structure. Results obtained provided a new insight on the variability of internal clod structure due to the large amount of data analyzed, information that is not provided by traditional methods used in physics applied to soil. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Gamma-ray attenuation Soil variability 241 Am Soil structure FWHM
1. Introduction Soil porosity (ϕ) represents an index of the relative pore space. This physical property indicated by the volume fraction of pores should be equal to the areal porosity, which is related to a crosssection area. The fraction of a bulk soil sample occupied by water and air ranges, on average, from 0.3 to 0.6 (Jury and Horton, 2004; Hillel, 2004). Traditionally ϕ is determined from the relationship between the soil bulk density (ds) and particle density (dp). Another method proposes the use of saturation water content; however, this is avoided due to the entrapped air during soil saturation (Hillel, 2004). The structure of aggregated soils cannot be quantitatively determined without information about its ϕ. In agriculture, ϕ has been frequently used as an indicator of soil quality (Gupta et al., 1989). Thus, representative evaluations of ϕ can avoid biased
n
Corresponding author. Tel.: þ 55 42 32203044; fax: þ 55 42 32203042. E-mail addresses: [email protected], [email protected] (L.F. Pires).
http://dx.doi.org/10.1016/j.apradiso.2014.06.010 0969-8043/& 2014 Elsevier Ltd. All rights reserved.
soil physical characterizations, mainly those related to soil water transport studies. Therefore, the interior characterization, of the structure of clod samples, in a non-invasive way, could be interesting to infer the representativeness of the samples used (Borges et al., 2014; Borges and Pires, 2012; Timm et al., 2005). Non-destructive inspection techniques, such as computed tomography (CT), can represent a useful tool to previously select more representative soil clods, to be used in ϕ measurements. CT is a non-invasive method for mapping the linear attenuation coefficient m (x,y) (cm 1) in a determined internal cross-section of some material. Relating different colors or different shades of gray to distinct values of m makes it possible to visualize a 2-D image of the selected cut or plane (Kak and Slaney, 2001). CT images are extremely useful to obtain detailed analysis of porous media structures as well as their modifications due to any external agent. Detailed profiles of ϕ distributions can be easily obtained in cross-section images of a sample. Typically, CT image resolutions extend from some millimeters to few micrometers (Zhou et al., 2013; Vaz et al., 2011; Císlerová and Votrubová, 2002), which allow a soil structure analysis with a high level of details.
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The aim of this study was to characterize the distribution of soil porosity within clod samples. To achieve this aim, a first generation low cost CT scanner (US$ 50,000) exclusively used for soil science studies (Cruvinel et al., 1990) was utilized. Cross-sectional images (2-D) of clod samples were analyzed in a non-invasive way. Traditional and CT based methods were used to evaluate ϕ, being the former utilized to verify the quality of data obtained via the nuclear method.
2. Material and methods Twenty-four clod samples of a soil characterized as EutricNitosol (FAO, 1998) (24% sand, 33% silt, 43% clay, 1.62 g cm 3 dry bulk density and 2.68 g cm 3 particle density) were collected in a coffee field plot located in Piracicaba, SP, Brazil (221400 S; 471380 W; 580 m a.s.l.). The sampling area was considered homogeneous in relation to mechanical analysis, fertility and agricultural production potential. In order to determine ϕ and to analyze the soil quality by the CT method, soil clods with volumes varying from 50 to 100 cm3 were collected from the 0–15 cm soil layer of the referred plot field. Details about the sampling methodology can be found in Grossman and Reinsch (2002). A first generation CT scanner (Fig. 1) was used to obtain 2-D soil clod section images. The equipment was designed and built by the Brazilian Agricultural Research Corporation (São Carlos, SP, Brazil) for exclusive applications in soil science. The CT scanner employs a radioactive source of 241Am (59.54 keV; E3.7 GBq) and a NaI(Tl) detector (7.62 7.62 cm2) lead (Pb) shielded from external radiation. The description of a similar scanner can be found in Cruvinel et al. (1990). Circular lead collimators (1–4.5 mm) were employed to collimate the radiation beam. The 2-D images were obtained with angular steps of 2.251 up to a rotation of 1801 (80 rotation steps) and linear displacements of 0.11 cm (80 linear steps) resulting in 80 projections. The rotation steps occurred only after a full set of 80 linear displacements. An algorithm based on the filtered back projection method was used to reconstruct the CT images (Macedo et al., 2000). Each image obtained (bmp file format; 8 bits) consisted of 6400 (matrix of 80 80 points) data of about 0.012 cm2 (0.11 cm by 0.11 cm) spatial resolution each one. The total measuring time for each tomography was around 24 h. The total counts were taken for
Fig. 1. Scheme of the first generation γ-ray computed tomography (CT) scanner to evaluate the soil physical quality of clod samples. CT image of a clod sample and the tomographic unit (TU) matrix used to obtain the soil porosity (ϕ) matrix. The TU matrix represents the region selected inside the clod image. LT-12 (line 12 of matrix) and VT-15 (column 15 of matrix) are the selected line and column/vertical transects used to measure ϕ.
sufficient time periods (15 s) to obtain statistical accuracy better than 1% without any absorber and around 3% with absorber (Turner et al., 2012; Knoll, 2010). Samples were fixed on the measurement table with the help of adhesive tape in order to avoid any movements during scanning. The calibration of the system was obtained following the procedures described in Crestana et al. (1985) and Vaz et al. (1989). A 25 30 matrix (750 ϕ values), which corresponds to a rectangular area of 9.08 cm2 located close to the center of the clod sectional images, was selected for ϕ analyses (Fig. 1). This matrix is located inside the 80 80 matrix, which represents the whole area scanned during CT scanning. Also, one horizontal (LT) and one column/vertical (VT) transect were selected, at the center of the each data matrix (line 12 (LT-12) and column 15 (VT-15)), to investigate the spatial variability of ϕ inside the soil clod samples. Soil porosity was calculated using
ϕ ¼ ½1 ðds =dp Þ
ð1Þ
where dp is the soil particle density. Details about the method used to determine dp can be found in Flint and Flint (2002). Soil bulk density was calculated by relating the water and soil mass attenuation coefficients, residual soil water content (θ), water density (dw), and the tomographic unit (TU): ds ¼ ½ðTU=0:955Þ ð0:199θdw Þ=0:339 (Pedrotti et al., 2005). TU takes the air as the medium with the minimum possible m value. It is related to the Hounsfield Unit (HU) that takes the water as a reference medium for which HU¼0 (Macedo et al., 2000). The differences in TU associated with each point of the soil matrix can be associated with differences in gray scales in the reconstructed images. The percent relative deviation (RD) between the values of ϕ for the traditional (TM) and CT methods was calculated according to RDð%Þ ¼
X ðTMÞ X ðCTÞ :100 X ðTMÞ
ð2Þ
In summary, data analysis was carried out based on the following steps: i) Reconstruction of the 2D images for qualitative analysis; ii) Elaboration of graphs of frequency (histograms) of ϕ values of 24 clod samples. These graphs were constructed by using the function plot/statistical graphs/histogram in the program Origin 8.0 (Origin, 2007); iii) Elaboration of graphs of frequency of ϕ values and the respective Gaussian adjustments for ϕ distributions. The parameters: area (A) below the curve and full width at halfmaximum (FWHM) of ϕ distributions were obtained based on the mathematical adjustment. The step size selected for the analysis of ϕ frequency between the maximum and minimum values of ϕ, for each sample, was 0.03 cm3 cm 3. The porosity interval selected was from 0.10 to 0.70 cm3 cm 3. These analyses were carried out to find similarities among ϕ distributions in order to classify the clod samples based on homogeneities/heterogeneities in their structures. FWHM intervals (A–F) were defined according to the following criterion: the parameter w (Origin, 2007) obtained from the Gaussian adjustment for sample 2 (the smallest value among samples) was used to normalize all the other w parameters (24 samples). Samples with similar wN (normalized) were grouped together. The average values of wN for the groups (B–F) were as follows: 0.79 (0.7%), 0.70 (2.3%), 0.65 (2.1%), 0.59 (4.0%) and 0.52 (1.2%). Numbers between parenthesis represent the coefficient of variation (CV); iv) Elaboration of FWHM variation graph for the 24 soil clod samples set and graph of ϕ distribution variation by using the ϕ interval of item (iii). For the last graph the ϕ distribution was normalized for each sample considering the most frequent ϕ
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
value for each distribution. This first graph was built to analyze the FWHM tendency among clod samples and the second one to show the heterogeneities of ϕ distributions;
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v) Elaboration of box plot graphs of variations of ϕ for the line (LT-12) and vertical (VT-15) transects (Fig. 1) selected inside the data matrix (25 30). These graphs were built in order to
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Fig. 2. 2-D tomographic images of clod samples.
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Fig. 3. Distribution of soil porosity (ϕ) values for an area of 9.08 cm2 (750 TU values) selected inside the whole clod sample.
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
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Fig. 4. Distribution of soil porosity (ϕ) values for an area of 9.08 cm2 (750 TU values) selected inside the whole clod sample and the respective Gaussian adjustments for each ϕ distribution. The terms R2, A and FWHM represent the coefficient of determination, the area below the curve and the full width at a half-maximum of the curve, respectively.
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analyze the variability of ϕ among clod samples. Each box corresponds to a distribution of 30 ϕ values for LT-12 and 25 ϕ values for VT-15.
3. Results and discussion Very good correlation (r ¼ 0.99) between TU and m during CT calibration was obtained. Mass attenuation coefficients for soil and water were 0.339 70.002 cm2 g 1 and 0.19970.003 cm2 g 1, respectively. These values are in good agreement with those found in the literature for the same type of soil and water (Ferraz and Mansell, 1979). CT image cross-sections of the twenty-four soil clod samples investigated in this study are presented in Fig. 2. The planes of image acquisition were located at the center of the samples, and the data available allowed a continuous 2-D analysis of TU distribution inside the soil clods. The black regions observed in some samples (e.g. S3, S6, S24) indicate the presence of very dense materials (E 2.99 g cm 3). On the other hand, the white regions (e.g. S4, S19, S21) are related to
Table 1 Intervals of FWHM used to analyze the soil porosity (ϕ) distributions. Group
FWHM range
Samples
A B C D E F
o 0.0849 0.0850–0.0949 0.0950–0.1049 0.1050–0.1149 0.1150–0.1249 0.1250 40.1030
S2 S8/S10/S11/S14/S20/S22 S3/S4/S12/S13/S15/S17/S19/S23 S1/S5/S9/S16/S21 S7/S24 S6/S18
macropores. The larger macropores inside some clods can be associated with dead roots, wormholes or soil cracks (Rogasik et al., 2014). According to Hamblin (1985) biological pores can be originated, for example, from wormholes (500–11,000 μm in size), tap roots of dicotyledons (300–10,000 μm in size), nodal (500– 10,000 μm in size), seminal (100–1000 μm in size) and lateral (50– 100 μm in size) roots of cereals, and so on. The areas associated with the holes found in S19 and S21 (Fig. 2s and u) were approximately 45.2 and 12.9 mm2 in size, respectively. Other samples with small holes were S4, S7, S9 and S17 (Fig. 2d, g, i and q). Macropores for these samples presented areas of about 3.4 mm2. This is one of the advantages of CT analysis over traditional techniques, that is, the possibility of observing qualitatively the heterogeneity of the clod interior. Distribution histograms of ϕ found in the investigated clod samples are presented in Fig. 3. The analysis presented in Fig. 3 can be used as an indicator of soil clod heterogeneity at the millimetric scale (Mooney et al., 2007). In order to complement the conclusions obtained based on the histogram analysis, Gaussian adjustments of the ϕ distributions were also carried out (Fig. 4). The results of the Gaussian adjustments (Allmaras and Kempthorne, 2002) made it possible to classify the distributions of clod sample ϕ in different groups (Table 1). According to these distributions samples such as 10, 14, and 22 (Figs. 3j, n, v and 4j, n, v) and 12, 13, and 23 (Figs. 3l, m, w and 4l, m, w) were classified as presenting similar ϕ distributions. The average ϕ (Table 2) evaluated by CT for samples 10, 14 and 22 was exactly the same (0.40 cm3 cm 3). Coincidently samples 12, 13 and 23 also presented the same values of average ϕ (0.37 cm3 cm 3). This result is an indication that clod samples with similar values of the macroscopic parameter ϕ tend to have most of the time close distributions of ϕ. Taken into account the 24 clod samples (Table 2), the average ϕ obtained via TM was 0.37 70.02 (CV ¼5.7%). When the CT method
Table 2 Soil porosity (ϕ) values obtained via traditional (TM) and computed tomography (CT) methods. Sample
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24
ϕ (cm3 cm 3)
CT TM
LT-12
VT-15
25 30M
RDTM LT-12
RDTM VT-15
RDTM 25 30M
0.40 0.38 0.42 0.35 0.36 0.36 0.35 0.36 0.36 0.39 0.33 0.38 0.37 0.36 0.38 0.35 0.37 0.38 0.42 0.37 0.37 0.37 0.37 0.36
0.45 0.40 0.43 0.41 0.38 0.36 0.42 0.41 0.45 0.40 0.42 0.38 0.38 0.42 0.39 0.35 0.39 0.40 0.41 0.40 0.35 0.43 0.39 0.37
0.48 0.41 0.45 0.39 0.39 0.38 0.39 0.39 0.40 0.38 0.40 0.43 0.35 0.41 0.40 0.36 0.39 0.35 0.42 0.37 0.29 0.43 0.39 0.37
0.45 0.39 0.44 0.39 0.37 0.35 0.39 0.38 0.39 0.40 0.40 0.37 0.37 0.40 0.39 0.34 0.38 0.36 0.39 0.38 0.37 0.40 0.37 0.36
11.7 4.1 2.9 18.2 6.1 0.5 18.5 14.5 24.3 2.1 26.5 0.2 3.9 16.0 3.5 0.9 5.6 4.1 1.9 8.3 5.3 15.2 4.5 3.3
19.1 6.7 7.7 12.4 8.9 6.1 10.0 8.9 10.5 3.0 20.4 13.0 4.3 13.3 6.1 3.7 5.6 8.9 0.5 0.2 21.5 15.2 4.5 3.3
11.7 1.5 5.3 12.4 3.3 2.3 10.0 6.1 7.8 2.1 20.4 2.8 1.2 10.5 3.5 2.0 2.9 6.3 6.7 2.9 0.2 7.2 0.8 0.5
(8.6) (5.5) (11.6) (14.9) (9.1) (10.1) (9.0) (6.8) (21.1) (11.3) (11.5) (7.9) (7.6) (13.9) (18.0) (14.5) (8.3) (12.8) (9.5) (9.9) (11.5) (9.8) (9.8) (16.1)
(6.7) (7.0) (13.2) (9.8) (9.9) (11.3) (11.3) (8.8) (10.9) (12.7) (6.6) (9.4) (9.8) (9.6) (11.4) (9.6) (14.6) (15.8) (8.7) (14.1) (16.4) (10.7) (14.0) (9.5)
(8.9) (9.0) (12.1) (17.1) (14.1) (18.7) (14.5) (11.5) (15.4) (13.8) (13.9) (11.6) (13.3) (13.7) (14.1) (14.3) (17.8) (17.3) (16.2) (15.2) (41.8) (12.7) (12.3) (16.1)
LT-12 and VT-15 mean the line (n¼ 30) and column/vertical (n¼ 25) transects (Fig. 1); values between parenthesis represent the coefficient of variation (CV); RD is the relative deviation considering the traditional method as reference; 25 30M is the complete data matrix (n ¼750) selected for image analysis by CT.
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
is considered, the average ϕ values determined for the LT-12, VT15 (Fig. 1) and whole data matrix (25 30) were 0.40 70.03 (CV ¼6.9%), 0.39 70.04 (CV ¼9.5%) and 0.38 70.02 (CV ¼ 6.4%). The relative deviations considering TM as standard were 7.6%, 5.7% and 3.5%, respectively. The last result means that the best way to evaluate ϕ via CT is to consider the whole data matrix. This result is closely related to concepts such as the representative elementary measurements (Constanza-Robinson et al., 2011; Bear, 1972). The largest CVs found for S6, S17 and S21 (Fig. 2f, q and u) are related to the heterogeneities of the soil clods and also to the difficulty to select the data matrix due to the sample shape. The scientific literature reports that ϕ for clay to silt textural classes should range from 0.62 to 0.47 cm3 cm 3 (Libardi, 2004). Therefore, the values found in this study are different from the common ones in the literature. One explanation to this result is that the clod samples were collected at the inter-rows of the experimental field, which are frequently subjected to human and vehicles traffic for crop management. In order to better analyze the similarities among clod samples, analyses of correlation of the normalized distributions of ϕ (Fig. 4), between samples of the same FWHM group (Fig. 5a), were carried out (Table 3). For samples grouped as B strong correlations were found (R40.85) between the normalized ϕ distributions, which could be an indication of the similarity among the soil structure of this group. The most frequent value of ϕ for samples of this group was observed around 0.42 cm3 cm 3, being an exception S8 (Fig. 5b). The graph shown in Fig. 5b represents a 2-D analysis of the normalized ϕ distribution. Through this graph, it is also possible to verify possible
heterogeneities among samples. If all the soil samples were considered homogeneous, the distribution should present well-defined inferior and superior limits of ϕ distribution and the most common (frequent) value located at the same place for all samples. The samples grouped as C, S3 presented average to weak correlations (0.43 o Ro0.69) in comparison to the other samples of the group (Table 3). This occurred due to an asymmetric distribution of ϕ for S3. This result is corroborated by the analysis in Fig. 5b, in which the darker regions for S3 tends to be more frequent in the superior part of the distribution (increase in ϕ). On the other hand, the other samples of this group were characterized with strong correlations (R40.90). Considering samples in group D (Table 3), only average to weak or null correlations among samples were observed. Two explanations can be given to this result i) the asymmetry among ϕ distributions and ii) the most frequent ϕ value is different among samples (S1: E0.48 cm3 cm 3, S5: E0.39 cm3 cm 3, S9: E0.42 cm3 cm 3,S16: E0.36 cm3 cm 3, S21: E 0.33 cm3 cm 3). Although these samples are characterized by similar values of FWHM (Fig. 5a), the average ϕ measured by CT is also different among samples (Table 2). Samples of the other groups were characterized by presenting more homogeneous average ϕ values among samples. Finally, samples of groups E and F (Table 3) presented strong correlations. Similar to the other samples with correlations over 0.90, this occurred mainly due to the similarity between the normalized ϕ distributions (Fig. 5b). In conclusion, the results of this last analysis of correlation (Table 3) together with the distributions of ϕ (Figs. 3 and 4) can be
0.685
F
F E
FWHM
0.12
D
D
C
0.10
D C
0.06
BB
B
0.08
D
C
C
D C
E
C
C C
B
B
B
A 2
4
6
8
Distribution
0.14
2
4
6
1.0
0.565
0.9
0.505
0.505
0.445
0.445
0.385
0.385
0.5
0.325
0.325
0.4
0.265
0.265
0.205
0.205
0.145
0.145 2
4
6
0.75
0.75
0.60
0.60
0.45
0.45
0.15 0.00
CC
C B C
2
4
6
8
D
FCBD
B
C
0.30
E
10 12 14 16 18 20 22 24
Sample Number
8
0.8 0.7 0.6
0.3 0.2 0.1 0.0
10 12 14 16 18 20 22 24
Sample Number 0.90
BB
0.685 0.625
10 12 14 16 18 20 22 24
EB D
10 12 14 16 18 20 22 24
0.565
0.90
C CD F
8
0.625
Sample Number
0.30 D A
43
D
A
C CD F E B D B
0.15 0.00
2
4
6
8
BC
C
BC
C DC
F
B BD
CE
10 12 14 16 18 20 22 24
Sample Number
Fig. 5. (a) Distribution of FWHM among clod samples. (b) Map of normalized soil porosity (ϕ) distribution among clod samples. The black color indicates the most frequent value of ϕ. (c) Box plot graphic of ϕ variations along the line (LT-12) transect selected inside the clod CT images. (d) Box plot graphic of ϕ variations along the column/vertical (VT-15) transect selected inside the clod CT images. Letters from A to F represent the FWHM groups presented in Table 1.
44
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
Table 3 Linear adjustment equations obtained for the correlations between clod samples of the same FWHM group. Group
Adjustment equation
A B
S2 S8 S10 0.02 þ 0.84x (0.96) S10 S11 0.02 þ 0.88x (0.97) S11 S14 0.01 þ1.01x (0.99) S14 S20 0.01 þ1.05x (0.97) S20 S22 0.01þ 0.90x (0.97) S3 S4 0.06þ 0.61x (0.64) S4 S12 0.01 þ1.03x (0.95) S12 S13 0.01 þ0.96x (0.99) S13 S15 0.02 þ 0.80x (0.93) S15 S17 0.02 þ 1.00x (0.91) S17 S19 2E 3þ0.91x (0.93) S19 S23 8E 4þ1.06x (0.98) S1 S5 0.15þ 0.27x (0.27) S5 S9 0.01 þ0.71x (0.81) S9 S16 0.07þ 0.75x (0.63) S16 S21 0.04þ 0.87x (0.87) S7 S24 1E 3þ1.08x (0.92) S6 S18 0.01þ 0.98x (0.99)
C
D
E F
– S8 S11 0.04þ 0.69x (0.86) S10 S14 0.02 þ 0.89x (0.97) S11 S20 0.02 þ 1.05x (0.96) S14 S22 0.01þ 0.99x (0.99) –
– S8 S14 0.04 þ0.72x (0.89) S10 S20 0.02 þ 0.98x (0.99) S11 S22 0.01 þ1.00x (0.99) –
– S8 S20 0.04þ0.83x (0.95) S10 S22 0.01þ 0.90x (0.98) –
– S8 S22 0.03 þ 0.73x (0.90) –
– –
– –
–
–
–
–
–
–
–
–
–
–
–
–
–
–
S3 S12 0.10þ 0.45x (0.44) S4 S13 0.01 þ0.99x (0.95) S12 S15 0.03 þ 0.76x (0.91) S13 S17 0.02 þ 0.94x (0.99) S15 S19 0.01þ 1.06x (0.99) S17 S23 0.01þ 1.01x (0.95) –
S3 S13 0.10 þ0.44x (0.44) S4 S15 0.02 þ 0.88x (0.99) S12 S17 0.02 þ 0.90x (0.99) S13 S19 0.01 þ0.87x (0.95) S15 S23 0.01 þ1.13x (0.97) -
S3 S15 0.06þ0.58x (0.68) S4 S17 0.03 þ0.93x (0.94) S12 S19 0.02 þ0.84x (0.94) S13 S23 3E 3þ 0.99x (0.98) –
S3 S17 0.11 þ0.43x (0.46) S4 S19 2E 6þ 0.96x (0.99) S12 S23 0.01 þ0.94x (0.97) –
S3 S19 0.06þ 0.60x (0.66) S4 S23 9E 4þ1.02x (0.98) –
S3 S23 0.08 þ 0.52x (0.53) –
–
–
–
–
–
–
–
–
–
–
–
–
–
–
S1 S9 0.07þ 0.48x (0.58) S5 S16 0.02 þ 0.87x (0.89) S9 S21 0.14þ 0.39x (0.33) –
S1 S16 0.19 0.002x ( 0.002) S5 S21 0.08 þ 0.60x (0.61) –
S1 S21 0.22 0.13x ( 0.13) –
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
S S represents the correlation between samples of the same FWHM group (Table 1). Values between parenthesis are related to the coefficient of correlation (R) of the linear adjustment.
an interesting way to help the definition of representative measurements of soil physical properties such as those presented by Vandenbygaart and Protz, (1999), Baveye et al. (2002) and Borges et al. (2012). Analyzing the ϕ distribution from the transects (Fig. 1) it is possible to observe that there were no substantial changes at the median and its asymmetry among samples (Fig. 5c and d). The differences in the interquartile range give an idea of the variability of ϕ. The use of the line or vertical transects demonstrate practically the same tendencies of changes of average ϕ (n ¼30 – LT-12 and n ¼25 – VT-15) for the majority of samples. This result is interesting and means that both transects can be chosen to infer about the variations of ϕ. The alterations observed in average ϕ along transects can be associated with the presence of small stones and holes inside the investigated samples as observed in the 2D soil images (Fig. 2). This type of analysis emphasizes the relevance of the present approach to guide studies involving ϕ determinations with noinvasive techniques. The large amount of data obtained is quite interesting for the variability analysis of soil properties (Beckett and Webster, 1971). It is important to emphasize the difficulty to obtain such type of analyses through traditional techniques.
By using CT, it was possible to identify the presence of very dense objects inside the clod samples and to evaluate the macropores areas. It was also possible to obtain important information about the quality of the clod samples and their structure variability through the analysis of ϕ distribution, something that traditional methods used in soil science cannot provide. The use of statistical tools allowed to group the clod samples according to their FWHM values. Samples within the same group were analyzed based on their ϕ distributions and average values of ϕ in order to try to find similarities among clod structures. It was observed that in most of the cases samples belonging to the same group presented similar distributions of ϕ and average values of this soil physical property almost equal when evaluated by CT.
Acknowledgments To CNPq (304310/2011-5) for research grants and to Dr. Osny O. S. Bacchi from CENA/USP, Piracicaba, Brazil, for the infrastructure used to obtain the tomographic images.
References 4. Concluding remarks CT allowed a detailed 2-D study of the internal structure of clods used for ϕ measurements with millimetric spatial resolution.
Allmaras, R.R., Kempthorne, O., 2002. Errors, variability, and precision (Soil Science Society American Book Series. 5). In: Dane, J.H., Topp, G.C. (Eds.), Methods of Soil Analysis. Part 4. Physical Methods. Soil Sci. Soc. Am., Inc., Madison, WI, pp. 15–44.
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Baveye, P., Rogasik, H., Wendroth, O., Onasch, I., Crawford, J.W., 2002. Effect of sampling volume on the measurement of soil physical properties: simulation with X-ray tomography data. Meas. Sci. Technol. 13, 775–784. Bear, J., 1972. Dynamics of Fluids in Porous Media. American Elsevier Pub. Co., USA. Beckett, P.H.T., Webster, R., 1971. Soil variability: a review. Soil Fertil. 34, 1–15. Borges, J.A.R., Pires, L.F., 2012. Representative elementary area (REA) in soil bulk density measurements through gamma ray computed tomography. Soil Tillage Res. 123, 43–49. Borges, J.A.R., Pires, L.F., Pereira, A.B., 2012. Computed tomography to estimate the representative elementary area for soil porosity measurements. Sci. World J. 2012, 526380. Borges, J.A.R., Pires, L.F., Costa, J.C., 2014. Representative elementary length (REL) to measure soil mass attenuation coefficient. Sci. World J. 2014, 584871. Císlerová, M., Votrubová, J., 2002. CT derived porosity distribution and flow domains. J. Hydrol. 267, 186–200. Constanza-Robinson, M.S., Estabrook, B.D., Fouhey, D.F., 2011. Representative elementary volume estimation for porosity, moisture saturation, and air–water interfacial areas in unsaturated porous media: data quality implications. Water Resour. Res. 47, 1–12. Crestana, S., Mascarenhas, S., Pozzi-Mucelli, R.S., 1985. Static and dynamic three dimensional studies of water in soil using computed tomographic scanning. Soil Sci. 140, 326–332. Cruvinel, P.E., Cesareo, R., Crestana, S., Mascarenhas, S., 1990. X- and gamma-rays computerized minitomograph scanner for soil science. IEEE Trans. Instrum. Meas. 39, 745–750. FAO, 1998. World reference base for soil resources. FAO ISRIC and ISSS, Italy. Ferraz, E.S.B., Mansell, R.S., 1979. Determining water content and bulk density of soil by gamma-ray attenuation methods, (No. 807, IFAS, Flórida). Tech. Bull. 807, 51. Flint, A.L., Flint, L.E., 2002. Particle density (Soil Science Society American Book Series. 5). In: Dane, J.H., Topp, G.C. (Eds.), Methods of Soil Analysis. Part 4. Physical Methods. Soil Sci. Soc. Am., Inc., Madison, WI, pp. 229–240. Grossman, R.B., Reinsch, T.G., 2002. The solid phase: bulk density and linear extensibility (Soil Science Society American Book Series. 5). In: Dane, J.H., Topp, G.C. (Eds.), Methods of Soil Analysis. Part 4. Physical Methods. Soil Sci. Soc. Am., Inc., Madison, WI, pp. 201–228. Gupta, S.C., Sharma, P.P., De Franchi, S.A., 1989. Compaction effects on soil structure. Adv. Agron. 42, 311–338. Hamblin, A., 1985. The influence of soil structure on water movement, crop root growth, and water uptake. Adv. Agron. 38, 95–158.
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Hillel, D., 2004. Introduction to Environmental Soil Physics. Elsevier Academic Press, USA. Jury, W.A., Horton, R., 2004. Soil Physics. Wiley, USA. Kak, A.C., Slaney, M., 2001. Principles of Computerized Tomographyc Imaging. IEE Press, USA. Knoll, G.F., 2010. Radiation Detection and Measurement. Wiley, USA. Libardi, P.L., 2004. Dinâmica da água no solo. EDUSP, Brazil. Macedo, A., Jorge, L.A.C., Crestana, S., 2000. Microvis: Program Manual for Reconstruction and Visualization of Tomographic Images, Embrapa - CNPDIA, Brazil. Mooney, S., Morris, C., Craigon, J., Berry, P., 2007. Quantification of soil structural changes induced by cereal anchorage failure: image analysis of thin sections. J. Plant Nutr. Soil Sci. 170, 363–372. Origin 8, 2007. User Guide, 1st edition OriginLab Corporation, Northampton, UK. Pedrotti, A., Pauletto, E.A., Crestana, S., Holanda, F.S.R., Cruvinel, P.E., Vaz, C.M.P., 2005. Evaluation of bulk density of Albaqualf soil under different tillage systems using the volumetric ring and computerized tomography methods. Soil Tillage Res. 80, 115–123. Rogasik, H., Schrader, S., Onasch, I., Kiesel, J., Gerke, H.H., 2014. Micro-scale dry bulk density variation around earthworm (Lumbricusterrestris L.) burrows based on X-ray computed tomography. Geoderma 213, 471–477. Timm, L.C., Pires, L.F., Reichardt, K., Roveratti, R., Oliveira, J.C.M., Bacchi, O.O.S., 2005. Soil bulk density evaluation by conventional and nuclear methods. Aust. J. Soil Res. 43, 97–103. Turner, J.E., Downing, D.J., Bogard, J.S., 2012. Statistical Methods in Radiation Physics. Wiley-VCH, Germany. Vandenbygaart, A.J., Protz, R., 1999. The representative elementary area (REA) in studies of quantitative soil micromorphology. Geoderma 89, 333–346. Vaz, C.M.P., Crestana, S., Mascarenhas, S., Cruvinel, P.E., Reichardt, K., Stolf, R., 1989. Using a computed tomography miniscanner for studying tillage induced soil compaction. Soil Technol. 2, 313–321. Vaz, C.M.P., de Maria, I.C., Lasso, P.O., Tuller, M., 2011. Evaluation of an advanced bench top micro-computed tomography system for quantifying porosities and pore-size distributions of two Brazilian Oxisols, Soil Sci. Soc. Am. J. 75, 832–841 Zhou, H., Peng, X., Perfect, E., Xiao, T., Peng, G., 2013. Effects of organic and inorganic fertilization on soil aggregation in an Ultisol as characterized by synchrotron based X-ray micro-computed tomography. Geoderma 195/196, 23–30.
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Porosity distribution by computed tomography and its importance to characterize soil clod samples Luiz F. Pires n, André M. Brinatti, Sérgio C. Saab, Fabio A.M. Cássaro Laboratory of Soil Physics and Environmental Sciences, Department of Physics, State University of Ponta Grossa (UEPG), Av. Carlos Cavalcanti, 4748, CEP. 84.030-900, Ponta Grossa, PR, Brazil
H I G H L I G H T S
2D detailed analysis of porosity distribution was carried out. 2D images permitted to evaluate the size of macropores inside clod samples. Samples with volumes varying from 50 to 100 cm3 were studied with millimetric resolution. The investigation allowed a new insight about the variability of soil clod structure.
art ic l e i nf o
a b s t r a c t
Article history: Received 3 January 2014 Received in revised form 15 May 2014 Accepted 11 June 2014 Available online 19 June 2014
Gamma-ray computed tomography (CT) was employed to study the soil quality of clod samples used to investigate porosity (ϕ). Samples with volumes varying from 50 to 100 cm3 were collected from the soil surface. 2D CT images were obtained with millimetric resolution. Porosity distribution analyses were carried out to infer the soil clod structure. Results obtained provided a new insight on the variability of internal clod structure due to the large amount of data analyzed, information that is not provided by traditional methods used in physics applied to soil. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Gamma-ray attenuation Soil variability 241 Am Soil structure FWHM
1. Introduction Soil porosity (ϕ) represents an index of the relative pore space. This physical property indicated by the volume fraction of pores should be equal to the areal porosity, which is related to a crosssection area. The fraction of a bulk soil sample occupied by water and air ranges, on average, from 0.3 to 0.6 (Jury and Horton, 2004; Hillel, 2004). Traditionally ϕ is determined from the relationship between the soil bulk density (ds) and particle density (dp). Another method proposes the use of saturation water content; however, this is avoided due to the entrapped air during soil saturation (Hillel, 2004). The structure of aggregated soils cannot be quantitatively determined without information about its ϕ. In agriculture, ϕ has been frequently used as an indicator of soil quality (Gupta et al., 1989). Thus, representative evaluations of ϕ can avoid biased
n
Corresponding author. Tel.: þ 55 42 32203044; fax: þ 55 42 32203042. E-mail addresses: [email protected], [email protected] (L.F. Pires).
http://dx.doi.org/10.1016/j.apradiso.2014.06.010 0969-8043/& 2014 Elsevier Ltd. All rights reserved.
soil physical characterizations, mainly those related to soil water transport studies. Therefore, the interior characterization, of the structure of clod samples, in a non-invasive way, could be interesting to infer the representativeness of the samples used (Borges et al., 2014; Borges and Pires, 2012; Timm et al., 2005). Non-destructive inspection techniques, such as computed tomography (CT), can represent a useful tool to previously select more representative soil clods, to be used in ϕ measurements. CT is a non-invasive method for mapping the linear attenuation coefficient m (x,y) (cm 1) in a determined internal cross-section of some material. Relating different colors or different shades of gray to distinct values of m makes it possible to visualize a 2-D image of the selected cut or plane (Kak and Slaney, 2001). CT images are extremely useful to obtain detailed analysis of porous media structures as well as their modifications due to any external agent. Detailed profiles of ϕ distributions can be easily obtained in cross-section images of a sample. Typically, CT image resolutions extend from some millimeters to few micrometers (Zhou et al., 2013; Vaz et al., 2011; Císlerová and Votrubová, 2002), which allow a soil structure analysis with a high level of details.
38
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
The aim of this study was to characterize the distribution of soil porosity within clod samples. To achieve this aim, a first generation low cost CT scanner (US$ 50,000) exclusively used for soil science studies (Cruvinel et al., 1990) was utilized. Cross-sectional images (2-D) of clod samples were analyzed in a non-invasive way. Traditional and CT based methods were used to evaluate ϕ, being the former utilized to verify the quality of data obtained via the nuclear method.
2. Material and methods Twenty-four clod samples of a soil characterized as EutricNitosol (FAO, 1998) (24% sand, 33% silt, 43% clay, 1.62 g cm 3 dry bulk density and 2.68 g cm 3 particle density) were collected in a coffee field plot located in Piracicaba, SP, Brazil (221400 S; 471380 W; 580 m a.s.l.). The sampling area was considered homogeneous in relation to mechanical analysis, fertility and agricultural production potential. In order to determine ϕ and to analyze the soil quality by the CT method, soil clods with volumes varying from 50 to 100 cm3 were collected from the 0–15 cm soil layer of the referred plot field. Details about the sampling methodology can be found in Grossman and Reinsch (2002). A first generation CT scanner (Fig. 1) was used to obtain 2-D soil clod section images. The equipment was designed and built by the Brazilian Agricultural Research Corporation (São Carlos, SP, Brazil) for exclusive applications in soil science. The CT scanner employs a radioactive source of 241Am (59.54 keV; E3.7 GBq) and a NaI(Tl) detector (7.62 7.62 cm2) lead (Pb) shielded from external radiation. The description of a similar scanner can be found in Cruvinel et al. (1990). Circular lead collimators (1–4.5 mm) were employed to collimate the radiation beam. The 2-D images were obtained with angular steps of 2.251 up to a rotation of 1801 (80 rotation steps) and linear displacements of 0.11 cm (80 linear steps) resulting in 80 projections. The rotation steps occurred only after a full set of 80 linear displacements. An algorithm based on the filtered back projection method was used to reconstruct the CT images (Macedo et al., 2000). Each image obtained (bmp file format; 8 bits) consisted of 6400 (matrix of 80 80 points) data of about 0.012 cm2 (0.11 cm by 0.11 cm) spatial resolution each one. The total measuring time for each tomography was around 24 h. The total counts were taken for
Fig. 1. Scheme of the first generation γ-ray computed tomography (CT) scanner to evaluate the soil physical quality of clod samples. CT image of a clod sample and the tomographic unit (TU) matrix used to obtain the soil porosity (ϕ) matrix. The TU matrix represents the region selected inside the clod image. LT-12 (line 12 of matrix) and VT-15 (column 15 of matrix) are the selected line and column/vertical transects used to measure ϕ.
sufficient time periods (15 s) to obtain statistical accuracy better than 1% without any absorber and around 3% with absorber (Turner et al., 2012; Knoll, 2010). Samples were fixed on the measurement table with the help of adhesive tape in order to avoid any movements during scanning. The calibration of the system was obtained following the procedures described in Crestana et al. (1985) and Vaz et al. (1989). A 25 30 matrix (750 ϕ values), which corresponds to a rectangular area of 9.08 cm2 located close to the center of the clod sectional images, was selected for ϕ analyses (Fig. 1). This matrix is located inside the 80 80 matrix, which represents the whole area scanned during CT scanning. Also, one horizontal (LT) and one column/vertical (VT) transect were selected, at the center of the each data matrix (line 12 (LT-12) and column 15 (VT-15)), to investigate the spatial variability of ϕ inside the soil clod samples. Soil porosity was calculated using
ϕ ¼ ½1 ðds =dp Þ
ð1Þ
where dp is the soil particle density. Details about the method used to determine dp can be found in Flint and Flint (2002). Soil bulk density was calculated by relating the water and soil mass attenuation coefficients, residual soil water content (θ), water density (dw), and the tomographic unit (TU): ds ¼ ½ðTU=0:955Þ ð0:199θdw Þ=0:339 (Pedrotti et al., 2005). TU takes the air as the medium with the minimum possible m value. It is related to the Hounsfield Unit (HU) that takes the water as a reference medium for which HU¼0 (Macedo et al., 2000). The differences in TU associated with each point of the soil matrix can be associated with differences in gray scales in the reconstructed images. The percent relative deviation (RD) between the values of ϕ for the traditional (TM) and CT methods was calculated according to RDð%Þ ¼
X ðTMÞ X ðCTÞ :100 X ðTMÞ
ð2Þ
In summary, data analysis was carried out based on the following steps: i) Reconstruction of the 2D images for qualitative analysis; ii) Elaboration of graphs of frequency (histograms) of ϕ values of 24 clod samples. These graphs were constructed by using the function plot/statistical graphs/histogram in the program Origin 8.0 (Origin, 2007); iii) Elaboration of graphs of frequency of ϕ values and the respective Gaussian adjustments for ϕ distributions. The parameters: area (A) below the curve and full width at halfmaximum (FWHM) of ϕ distributions were obtained based on the mathematical adjustment. The step size selected for the analysis of ϕ frequency between the maximum and minimum values of ϕ, for each sample, was 0.03 cm3 cm 3. The porosity interval selected was from 0.10 to 0.70 cm3 cm 3. These analyses were carried out to find similarities among ϕ distributions in order to classify the clod samples based on homogeneities/heterogeneities in their structures. FWHM intervals (A–F) were defined according to the following criterion: the parameter w (Origin, 2007) obtained from the Gaussian adjustment for sample 2 (the smallest value among samples) was used to normalize all the other w parameters (24 samples). Samples with similar wN (normalized) were grouped together. The average values of wN for the groups (B–F) were as follows: 0.79 (0.7%), 0.70 (2.3%), 0.65 (2.1%), 0.59 (4.0%) and 0.52 (1.2%). Numbers between parenthesis represent the coefficient of variation (CV); iv) Elaboration of FWHM variation graph for the 24 soil clod samples set and graph of ϕ distribution variation by using the ϕ interval of item (iii). For the last graph the ϕ distribution was normalized for each sample considering the most frequent ϕ
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
value for each distribution. This first graph was built to analyze the FWHM tendency among clod samples and the second one to show the heterogeneities of ϕ distributions;
39
v) Elaboration of box plot graphs of variations of ϕ for the line (LT-12) and vertical (VT-15) transects (Fig. 1) selected inside the data matrix (25 30). These graphs were built in order to
S2
S3
S4
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
S18
S19
S20
S22
S23
S24
S1
S5
S17
S21
r
Fig. 2. 2-D tomographic images of clod samples.
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L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
S1
320
240
240
240
240
160
160
160
160
80
80
80
80
0
0
0
0.3
0.5
0.6
0.2
0.3
0.4
0.5
0.6
S6
480
0.2
0.3
0.4
0.5
0
0.6
S7
480
400
320
320
240
240
240
240
F
400
320
F
400
320 160
160
160
160
80
80
80
80
0
0
0
0.2
0.3
0.4
0.5
0.6
S9
0.2
0.3
0.4
0.5
0.6
S10
480
0.2
0.3
0.4
0.5
0
0.6
S11
480
320
240
240
240
240
160
160
80
80
80
0
0
80 0
0.2
0.3
0.4
0.5
0.6
S13
F
400
320
F
400
320
F
400
320
160
0.2
0.3
0.4
0.5
0.6
S14
480
0.2
0.3
0.4
0.5
0
0.6
S15
480
320
240
240
240
240
F
400
320
F
400
320
F
400
320 160
160
160
160
80
80
80
80
0
0
0
0.3
0.4
0.5
0.6
S17
480
0.2
0.3
0.4
0.5
0.6
S18
480
0.2
0.3
0.4
0.5
0
0.6
S19
480
320
320
320
320
240
240
240
240
160
80
80
0 0.2
0.3
0.4
0.5
0
0.6
S21
480
0.2
0.3
0.4
0.5
160
160
80
80
0 0.2
0.6
S22
480
F
400
F
400
F
400
160
0.3
0.4
0.5
320
320
320
320
240
240
240
240
160
160
80
80
80
0
0
0
0.2
0.3
0.4
0.5
0.6
0.2
0.3
0.4
0.5
0.6
F
400
F
400
F
400
160
0.3
0.2
0.3
0.6
0.4
0.5
0.6
0.4
0.5
0.6
0.5
0.6
0.5
0.6
0.5
0.6
S16
0.2
0.3
0.4
S20
0.3
0.4
S24
480
400
0.5
S12
0 0.2
0.6
S23
480
0.2
480
400
0.4
S8
480
400
0.2
0.3
480
400
160
0.2
480
400
F
F F
0.4
S5
480
F
F
400
320
F
400
320
0.2
S4
480
400
480
F
S3
480
320
480
F
S2
480
400
F
F
480
160 80
0.2
0.3
0.4
0.5
0.6
0
0.2
0.3
0.4
Fig. 3. Distribution of soil porosity (ϕ) values for an area of 9.08 cm2 (750 TU values) selected inside the whole clod sample.
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
S1
320
320
320
240
240
240
240
160
160
160
160
80
80
80
80
0.3
0.6
0.3
0.4
0.5
0.6
S6
480
0.3
0.4
0.5
0 0.2
0.6
S7
480
400
320
320
240
240
240
240
F
400
320
F
400
160
160
160
160
80
80
80
80
0.3
0.4
0.5
0 0.2
0.6
S9
0.3
0.4
0.5
0 0.2
0.6
S10
480
0.3
0.4
0.5
0 0.2
0.6
S11
480
320
320
320
320
240
240
240
240
F
400
F
400
F
400
160
160
160
160
80
80
80
80
0.3
0.4
0.5
0 0.2
0.6
S13
480
0.3
0.4
0.5
0.6
0.3
o
S14
480
0 0.2
0.4
0.5
0 0.2
0.6
S15
480
320
240
240
240
240
F
400
320
F
400
320
F
400
320 160
160
160
160
80
80
80
80
0 0.2
0.3
0.4
0.5
0 0.2
0.6
S17
480
0.3
0.4
0.5
0.6
s
S18
480
0 0.2
0.3
0.4
0.5
0 0.2
0.6
S19
480
320
240
240
240
240
F
400
320
F
400
320
F
400
320 160
160
160
160
80
80
80
80
0.3
0.4
0.5
0 0.2
0.6
S21
480
0.3
0.4
0.5
0 0.2
0.6
S22
480
0.3
0.4
0.5
0 0.2
0.6
S23
480
320
240
240
240
240
F
400
320
F
400
320
F
400
320 160
160
160
160
80
80
80
80
0 0.2
0.3
0.4
0.5
0.6
0 0.2
0.3
0.4
0.5
0.6
0 0.2
0.3
0.4
0.3
0.5
0.6
0 0.2
0.6
0.4
0.5
0.6
0.4
0.5
0.6
0.5
0.6
0.5
0.6
0.5
0.6
S16
0.3
0.4
S20
0.3
0.4
S24
480
400
0.5
S12
480
400
0 0.2
0.3
480
400
0.4
S8
480
400
0 0.2
0.3
480
320
F
F
0.5
S5
480
F
0.4
0 0.2
400
0 0.2
F
F
320
F
400
0 0.2
S4
480
400
480
F
S3
480
400
0 0.2
F
S2
480
400
F
F
480
41
0.3
0.4
Fig. 4. Distribution of soil porosity (ϕ) values for an area of 9.08 cm2 (750 TU values) selected inside the whole clod sample and the respective Gaussian adjustments for each ϕ distribution. The terms R2, A and FWHM represent the coefficient of determination, the area below the curve and the full width at a half-maximum of the curve, respectively.
42
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
analyze the variability of ϕ among clod samples. Each box corresponds to a distribution of 30 ϕ values for LT-12 and 25 ϕ values for VT-15.
3. Results and discussion Very good correlation (r ¼ 0.99) between TU and m during CT calibration was obtained. Mass attenuation coefficients for soil and water were 0.339 70.002 cm2 g 1 and 0.19970.003 cm2 g 1, respectively. These values are in good agreement with those found in the literature for the same type of soil and water (Ferraz and Mansell, 1979). CT image cross-sections of the twenty-four soil clod samples investigated in this study are presented in Fig. 2. The planes of image acquisition were located at the center of the samples, and the data available allowed a continuous 2-D analysis of TU distribution inside the soil clods. The black regions observed in some samples (e.g. S3, S6, S24) indicate the presence of very dense materials (E 2.99 g cm 3). On the other hand, the white regions (e.g. S4, S19, S21) are related to
Table 1 Intervals of FWHM used to analyze the soil porosity (ϕ) distributions. Group
FWHM range
Samples
A B C D E F
o 0.0849 0.0850–0.0949 0.0950–0.1049 0.1050–0.1149 0.1150–0.1249 0.1250 40.1030
S2 S8/S10/S11/S14/S20/S22 S3/S4/S12/S13/S15/S17/S19/S23 S1/S5/S9/S16/S21 S7/S24 S6/S18
macropores. The larger macropores inside some clods can be associated with dead roots, wormholes or soil cracks (Rogasik et al., 2014). According to Hamblin (1985) biological pores can be originated, for example, from wormholes (500–11,000 μm in size), tap roots of dicotyledons (300–10,000 μm in size), nodal (500– 10,000 μm in size), seminal (100–1000 μm in size) and lateral (50– 100 μm in size) roots of cereals, and so on. The areas associated with the holes found in S19 and S21 (Fig. 2s and u) were approximately 45.2 and 12.9 mm2 in size, respectively. Other samples with small holes were S4, S7, S9 and S17 (Fig. 2d, g, i and q). Macropores for these samples presented areas of about 3.4 mm2. This is one of the advantages of CT analysis over traditional techniques, that is, the possibility of observing qualitatively the heterogeneity of the clod interior. Distribution histograms of ϕ found in the investigated clod samples are presented in Fig. 3. The analysis presented in Fig. 3 can be used as an indicator of soil clod heterogeneity at the millimetric scale (Mooney et al., 2007). In order to complement the conclusions obtained based on the histogram analysis, Gaussian adjustments of the ϕ distributions were also carried out (Fig. 4). The results of the Gaussian adjustments (Allmaras and Kempthorne, 2002) made it possible to classify the distributions of clod sample ϕ in different groups (Table 1). According to these distributions samples such as 10, 14, and 22 (Figs. 3j, n, v and 4j, n, v) and 12, 13, and 23 (Figs. 3l, m, w and 4l, m, w) were classified as presenting similar ϕ distributions. The average ϕ (Table 2) evaluated by CT for samples 10, 14 and 22 was exactly the same (0.40 cm3 cm 3). Coincidently samples 12, 13 and 23 also presented the same values of average ϕ (0.37 cm3 cm 3). This result is an indication that clod samples with similar values of the macroscopic parameter ϕ tend to have most of the time close distributions of ϕ. Taken into account the 24 clod samples (Table 2), the average ϕ obtained via TM was 0.37 70.02 (CV ¼5.7%). When the CT method
Table 2 Soil porosity (ϕ) values obtained via traditional (TM) and computed tomography (CT) methods. Sample
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24
ϕ (cm3 cm 3)
CT TM
LT-12
VT-15
25 30M
RDTM LT-12
RDTM VT-15
RDTM 25 30M
0.40 0.38 0.42 0.35 0.36 0.36 0.35 0.36 0.36 0.39 0.33 0.38 0.37 0.36 0.38 0.35 0.37 0.38 0.42 0.37 0.37 0.37 0.37 0.36
0.45 0.40 0.43 0.41 0.38 0.36 0.42 0.41 0.45 0.40 0.42 0.38 0.38 0.42 0.39 0.35 0.39 0.40 0.41 0.40 0.35 0.43 0.39 0.37
0.48 0.41 0.45 0.39 0.39 0.38 0.39 0.39 0.40 0.38 0.40 0.43 0.35 0.41 0.40 0.36 0.39 0.35 0.42 0.37 0.29 0.43 0.39 0.37
0.45 0.39 0.44 0.39 0.37 0.35 0.39 0.38 0.39 0.40 0.40 0.37 0.37 0.40 0.39 0.34 0.38 0.36 0.39 0.38 0.37 0.40 0.37 0.36
11.7 4.1 2.9 18.2 6.1 0.5 18.5 14.5 24.3 2.1 26.5 0.2 3.9 16.0 3.5 0.9 5.6 4.1 1.9 8.3 5.3 15.2 4.5 3.3
19.1 6.7 7.7 12.4 8.9 6.1 10.0 8.9 10.5 3.0 20.4 13.0 4.3 13.3 6.1 3.7 5.6 8.9 0.5 0.2 21.5 15.2 4.5 3.3
11.7 1.5 5.3 12.4 3.3 2.3 10.0 6.1 7.8 2.1 20.4 2.8 1.2 10.5 3.5 2.0 2.9 6.3 6.7 2.9 0.2 7.2 0.8 0.5
(8.6) (5.5) (11.6) (14.9) (9.1) (10.1) (9.0) (6.8) (21.1) (11.3) (11.5) (7.9) (7.6) (13.9) (18.0) (14.5) (8.3) (12.8) (9.5) (9.9) (11.5) (9.8) (9.8) (16.1)
(6.7) (7.0) (13.2) (9.8) (9.9) (11.3) (11.3) (8.8) (10.9) (12.7) (6.6) (9.4) (9.8) (9.6) (11.4) (9.6) (14.6) (15.8) (8.7) (14.1) (16.4) (10.7) (14.0) (9.5)
(8.9) (9.0) (12.1) (17.1) (14.1) (18.7) (14.5) (11.5) (15.4) (13.8) (13.9) (11.6) (13.3) (13.7) (14.1) (14.3) (17.8) (17.3) (16.2) (15.2) (41.8) (12.7) (12.3) (16.1)
LT-12 and VT-15 mean the line (n¼ 30) and column/vertical (n¼ 25) transects (Fig. 1); values between parenthesis represent the coefficient of variation (CV); RD is the relative deviation considering the traditional method as reference; 25 30M is the complete data matrix (n ¼750) selected for image analysis by CT.
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
is considered, the average ϕ values determined for the LT-12, VT15 (Fig. 1) and whole data matrix (25 30) were 0.40 70.03 (CV ¼6.9%), 0.39 70.04 (CV ¼9.5%) and 0.38 70.02 (CV ¼ 6.4%). The relative deviations considering TM as standard were 7.6%, 5.7% and 3.5%, respectively. The last result means that the best way to evaluate ϕ via CT is to consider the whole data matrix. This result is closely related to concepts such as the representative elementary measurements (Constanza-Robinson et al., 2011; Bear, 1972). The largest CVs found for S6, S17 and S21 (Fig. 2f, q and u) are related to the heterogeneities of the soil clods and also to the difficulty to select the data matrix due to the sample shape. The scientific literature reports that ϕ for clay to silt textural classes should range from 0.62 to 0.47 cm3 cm 3 (Libardi, 2004). Therefore, the values found in this study are different from the common ones in the literature. One explanation to this result is that the clod samples were collected at the inter-rows of the experimental field, which are frequently subjected to human and vehicles traffic for crop management. In order to better analyze the similarities among clod samples, analyses of correlation of the normalized distributions of ϕ (Fig. 4), between samples of the same FWHM group (Fig. 5a), were carried out (Table 3). For samples grouped as B strong correlations were found (R40.85) between the normalized ϕ distributions, which could be an indication of the similarity among the soil structure of this group. The most frequent value of ϕ for samples of this group was observed around 0.42 cm3 cm 3, being an exception S8 (Fig. 5b). The graph shown in Fig. 5b represents a 2-D analysis of the normalized ϕ distribution. Through this graph, it is also possible to verify possible
heterogeneities among samples. If all the soil samples were considered homogeneous, the distribution should present well-defined inferior and superior limits of ϕ distribution and the most common (frequent) value located at the same place for all samples. The samples grouped as C, S3 presented average to weak correlations (0.43 o Ro0.69) in comparison to the other samples of the group (Table 3). This occurred due to an asymmetric distribution of ϕ for S3. This result is corroborated by the analysis in Fig. 5b, in which the darker regions for S3 tends to be more frequent in the superior part of the distribution (increase in ϕ). On the other hand, the other samples of this group were characterized with strong correlations (R40.90). Considering samples in group D (Table 3), only average to weak or null correlations among samples were observed. Two explanations can be given to this result i) the asymmetry among ϕ distributions and ii) the most frequent ϕ value is different among samples (S1: E0.48 cm3 cm 3, S5: E0.39 cm3 cm 3, S9: E0.42 cm3 cm 3,S16: E0.36 cm3 cm 3, S21: E 0.33 cm3 cm 3). Although these samples are characterized by similar values of FWHM (Fig. 5a), the average ϕ measured by CT is also different among samples (Table 2). Samples of the other groups were characterized by presenting more homogeneous average ϕ values among samples. Finally, samples of groups E and F (Table 3) presented strong correlations. Similar to the other samples with correlations over 0.90, this occurred mainly due to the similarity between the normalized ϕ distributions (Fig. 5b). In conclusion, the results of this last analysis of correlation (Table 3) together with the distributions of ϕ (Figs. 3 and 4) can be
0.685
F
F E
FWHM
0.12
D
D
C
0.10
D C
0.06
BB
B
0.08
D
C
C
D C
E
C
C C
B
B
B
A 2
4
6
8
Distribution
0.14
2
4
6
1.0
0.565
0.9
0.505
0.505
0.445
0.445
0.385
0.385
0.5
0.325
0.325
0.4
0.265
0.265
0.205
0.205
0.145
0.145 2
4
6
0.75
0.75
0.60
0.60
0.45
0.45
0.15 0.00
CC
C B C
2
4
6
8
D
FCBD
B
C
0.30
E
10 12 14 16 18 20 22 24
Sample Number
8
0.8 0.7 0.6
0.3 0.2 0.1 0.0
10 12 14 16 18 20 22 24
Sample Number 0.90
BB
0.685 0.625
10 12 14 16 18 20 22 24
EB D
10 12 14 16 18 20 22 24
0.565
0.90
C CD F
8
0.625
Sample Number
0.30 D A
43
D
A
C CD F E B D B
0.15 0.00
2
4
6
8
BC
C
BC
C DC
F
B BD
CE
10 12 14 16 18 20 22 24
Sample Number
Fig. 5. (a) Distribution of FWHM among clod samples. (b) Map of normalized soil porosity (ϕ) distribution among clod samples. The black color indicates the most frequent value of ϕ. (c) Box plot graphic of ϕ variations along the line (LT-12) transect selected inside the clod CT images. (d) Box plot graphic of ϕ variations along the column/vertical (VT-15) transect selected inside the clod CT images. Letters from A to F represent the FWHM groups presented in Table 1.
44
L.F. Pires et al. / Applied Radiation and Isotopes 92 (2014) 37–45
Table 3 Linear adjustment equations obtained for the correlations between clod samples of the same FWHM group. Group
Adjustment equation
A B
S2 S8 S10 0.02 þ 0.84x (0.96) S10 S11 0.02 þ 0.88x (0.97) S11 S14 0.01 þ1.01x (0.99) S14 S20 0.01 þ1.05x (0.97) S20 S22 0.01þ 0.90x (0.97) S3 S4 0.06þ 0.61x (0.64) S4 S12 0.01 þ1.03x (0.95) S12 S13 0.01 þ0.96x (0.99) S13 S15 0.02 þ 0.80x (0.93) S15 S17 0.02 þ 1.00x (0.91) S17 S19 2E 3þ0.91x (0.93) S19 S23 8E 4þ1.06x (0.98) S1 S5 0.15þ 0.27x (0.27) S5 S9 0.01 þ0.71x (0.81) S9 S16 0.07þ 0.75x (0.63) S16 S21 0.04þ 0.87x (0.87) S7 S24 1E 3þ1.08x (0.92) S6 S18 0.01þ 0.98x (0.99)
C
D
E F
– S8 S11 0.04þ 0.69x (0.86) S10 S14 0.02 þ 0.89x (0.97) S11 S20 0.02 þ 1.05x (0.96) S14 S22 0.01þ 0.99x (0.99) –
– S8 S14 0.04 þ0.72x (0.89) S10 S20 0.02 þ 0.98x (0.99) S11 S22 0.01 þ1.00x (0.99) –
– S8 S20 0.04þ0.83x (0.95) S10 S22 0.01þ 0.90x (0.98) –
– S8 S22 0.03 þ 0.73x (0.90) –
– –
– –
–
–
–
–
–
–
–
–
–
–
–
–
–
–
S3 S12 0.10þ 0.45x (0.44) S4 S13 0.01 þ0.99x (0.95) S12 S15 0.03 þ 0.76x (0.91) S13 S17 0.02 þ 0.94x (0.99) S15 S19 0.01þ 1.06x (0.99) S17 S23 0.01þ 1.01x (0.95) –
S3 S13 0.10 þ0.44x (0.44) S4 S15 0.02 þ 0.88x (0.99) S12 S17 0.02 þ 0.90x (0.99) S13 S19 0.01 þ0.87x (0.95) S15 S23 0.01 þ1.13x (0.97) -
S3 S15 0.06þ0.58x (0.68) S4 S17 0.03 þ0.93x (0.94) S12 S19 0.02 þ0.84x (0.94) S13 S23 3E 3þ 0.99x (0.98) –
S3 S17 0.11 þ0.43x (0.46) S4 S19 2E 6þ 0.96x (0.99) S12 S23 0.01 þ0.94x (0.97) –
S3 S19 0.06þ 0.60x (0.66) S4 S23 9E 4þ1.02x (0.98) –
S3 S23 0.08 þ 0.52x (0.53) –
–
–
–
–
–
–
–
–
–
–
–
–
–
–
S1 S9 0.07þ 0.48x (0.58) S5 S16 0.02 þ 0.87x (0.89) S9 S21 0.14þ 0.39x (0.33) –
S1 S16 0.19 0.002x ( 0.002) S5 S21 0.08 þ 0.60x (0.61) –
S1 S21 0.22 0.13x ( 0.13) –
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
S S represents the correlation between samples of the same FWHM group (Table 1). Values between parenthesis are related to the coefficient of correlation (R) of the linear adjustment.
an interesting way to help the definition of representative measurements of soil physical properties such as those presented by Vandenbygaart and Protz, (1999), Baveye et al. (2002) and Borges et al. (2012). Analyzing the ϕ distribution from the transects (Fig. 1) it is possible to observe that there were no substantial changes at the median and its asymmetry among samples (Fig. 5c and d). The differences in the interquartile range give an idea of the variability of ϕ. The use of the line or vertical transects demonstrate practically the same tendencies of changes of average ϕ (n ¼30 – LT-12 and n ¼25 – VT-15) for the majority of samples. This result is interesting and means that both transects can be chosen to infer about the variations of ϕ. The alterations observed in average ϕ along transects can be associated with the presence of small stones and holes inside the investigated samples as observed in the 2D soil images (Fig. 2). This type of analysis emphasizes the relevance of the present approach to guide studies involving ϕ determinations with noinvasive techniques. The large amount of data obtained is quite interesting for the variability analysis of soil properties (Beckett and Webster, 1971). It is important to emphasize the difficulty to obtain such type of analyses through traditional techniques.
By using CT, it was possible to identify the presence of very dense objects inside the clod samples and to evaluate the macropores areas. It was also possible to obtain important information about the quality of the clod samples and their structure variability through the analysis of ϕ distribution, something that traditional methods used in soil science cannot provide. The use of statistical tools allowed to group the clod samples according to their FWHM values. Samples within the same group were analyzed based on their ϕ distributions and average values of ϕ in order to try to find similarities among clod structures. It was observed that in most of the cases samples belonging to the same group presented similar distributions of ϕ and average values of this soil physical property almost equal when evaluated by CT.
Acknowledgments To CNPq (304310/2011-5) for research grants and to Dr. Osny O. S. Bacchi from CENA/USP, Piracicaba, Brazil, for the infrastructure used to obtain the tomographic images.
References 4. Concluding remarks CT allowed a detailed 2-D study of the internal structure of clods used for ϕ measurements with millimetric spatial resolution.
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