Neutron-Gamma Analysis of Soil for Digital Agriculture

Abstract

This chapter describes technical aspects of neutron stimulated gamma ray analysis of soil carbon. The introduction covers general principles, different modifications of neutron gamma analysis, measurement system configurations, and advantages of this method for soil carbon analysis. Problems with neutron-gamma technology for soil carbon analysis and investigation methods including Monte-Carlo simulation of neutron interaction with soil elements are discussed. Based on investigation results, a method to extract the “soil carbon net peak” from raw acquired data was developed. A direct proportional dependency between the carbon net peak area and average carbon weight percent in the upper 10 cm soil layer for any carbon depth profile was demonstrated. Calibration of the measurement system using sand-carbon pits and field measurements of soil carbon are described. Compared to traditional chemical analysis (dry combustion) data, measurement results demonstrated good agreement between methods. Thus, neutron stimulated gamma ray analysis can be used for in situ determination of near surface soil carbon content and is applicable for precision geospatial mapping of soil carbon.

1. Introduction

Agricultural operations play important roles in productivity and profitability of soil resources, and can influence aspects of climate change and the ability of soil to sequester carbon which has relevance to when quantifying carbon storage for credits. Development of sustainable land use practices requires understanding and evaluating impacts of these practices on soil resources. Exact knowledge of soil chemical composition can improve modern precision agricultural practices. For these reasons, large-scale measuring and mapping of soil elements (primarily carbon) on agricultural lands has become important today.

The current “gold standard” method of “dry combustion” for soil carbon determinations is based on extensive analysis of laboratory processed field samples. This method is labor intensive and time consuming. Other techniques (i.e., laser-induced breakdown spectroscopy, near- and mid-infrared spectroscopy, diffuse reflectance infrared Fourier transform spectroscopy, and pyrolysis molecular beam mass spectrometry) yield carbon values for small soil volumes (0.01–10 cm³) near the soil surface [1], which may not be representative of large field areas.

Neutron-gamma analysis (NGA) can overcome these disadvantages and can be used to create soil carbon distribution maps of large field areas. Soil carbon content, expressed in average carbon weight percent in the upper 10 cm soil layer (Cw%), can be derived directly from in-situ neutron-gamma analysis results. Knowledge of soil density allows for calculating carbon content in mass units. The ratio of carbon in the 10–30 cm topsoil layer of various soil types can be used for estimating soil carbon to a 30 cm depth. This 0–30 topsoil layer is used for estimating carbon sequestered in soil [2].

Modified NGA, particularly Pulse Fast Thermal Neutron Analysis (PFTNA as classified by [3]), can be used for determining soil elemental (C, H, Si, etc.) contents. This can be accomplished by analyzing soil gamma spectra induced by 14.1 MeV neutron pulses. This includes gamma spectra acquired during neutron pulses (i.e., from gamma rays appearing due to inelastic neutron scattering, INS spectra) and between pulses (i.e., from gamma rays appearing due to thermal neutron capture, TNC spectra). Details concerning this methodology have been previously described [4, 5, 6, 7].

A custom mobile PFTNA system was developed and constructed for measuring soil carbon in agricultural fields in the scanning regime [4, 6]. A GPS device and specially developed software were added to the mobile system for simultaneous acquisition of gamma signals and geographical positions. Maps of surface soil carbon distribution were constructed utilizing this system in conjunction with IGOR software [8] and ArcMap [9]. Technical aspects of neutron stimulated gamma ray analysis of soil carbon, developed algorithms, methodology and software for data acquisition, data processing, and mapping will be described in this chapter. In addition, factors that affect measurement error and required measurement times will be discussed.

2. Materials and methods

2.1 Physical basis of PFTNA

NGA is based on registration of gamma rays that appear in soil under neutron irradiation. A neutron generator is used as a neutron flux source. Each soil element issues gamma rays with predefined energies during certain nuclear reactions of that element with neutrons. Detectors register gamma rays as a spectrum that is the dependency of the registered gamma rays vs. their energy. In general, this gamma spectrum consists of many gamma peaks produced by various elements due to different processes of neutron-nuclear interactions and the continuous background. Since some peaks overlap, extraction of gamma peaks that correspond to particular soil elements is difficult. PFTNA can be used to overcome this problem. This method uses the difference in duration of INS (pico- and femto-second intervals) and TNC (dozens microsecond intervals) nuclear reactions to divide the spectra that appear due to these processes. With PFTNA, the neutron generator works in the pulse regime, and the single spectrum acquired is divided into two spectra in two separate memory locations. The INS spectrum, which is the gamma ray spectrum that appears due to inelastic neutron scattering of soil nuclei, is acquired during neutron pulses. The TNC spectrum, which appears due to thermal neutron capture, is acquired between pulses. Examples of these spectra are shown in Figure 1.

Figure 1.

Example of INS and TNC gamma spectra showing some peaks of interest.

In the INS spectrum, the gamma peak used for determining soil carbon (centroid at 4.44 MeV) is still a complicated peak. This peak consists of the gamma response from soil carbon, carbon in measurement system construction materials, and the cascade transition peak of silicon-28. A system background measurement should be conducted to define the gamma response corresponding to carbon in system components. This measurement is conducted under conditions where the effect of soil on the spectra is negligible (i.e., system is lifted to a height of more than 4–6 m above the ground). The silicon-28 cascade transition peak can be defined from determining values of the silicon-28 peak (centroid at 1.78 MeV in the spectra) and the cascade transition coefficient. The net carbon peak area can be computed by removing the background and silicon portions from the carbon peak. The net carbon peak area is directly associated with the average carbon content in the upper 10 cm soil layer expressed in weight percent [5]. This is true for any soil type regardless of carbon distribution shape. To relate net carbon peak area with average soil carbon content, corresponding calibration measurements (PFTNA measurements of model soil samples with well-known carbon contents) should be performed. Such measurements are needed to develop an equation for calculating soil carbon content from measured net carbon peak areas.

2.2 Carbon content returned by PFTNA

Since carbon distribution in soil is not uniform or known, several carbon content parameters can directly affect PFTNA measurements. Since soil carbon can sometimes be characterized as carbon surface density in the 30 cm soil layer, it was assumed that the PFTNA system acquired gammas from ∼30 cm soil layer from irradiation by 14 MeV neutrons [1]. However, Monte-Carlo simulations did not confirm this assumption for unpredictable soil carbon distributions and soil densities [5].

Carbon content can be expressed as the average carbon weight percent in a given soil layer. Previous work showed [5] that soil carbon (expressed in weight percent in 10 cm upper soil layer) can be directly estimated from PFTNA gamma spectra measurements and corresponding peak area calculations. This can be done by applying previously defined calibration dependency using homogeneous reference samples. Workability of this expression for any type of soil with any soil carbon distribution shape with depth was confirmed using Monte-Carlo (Geant4, [10]) simulations. In addition, experimental measurements in agricultural fields were confirmed by comparison to traditional soil chemical analysis results.

2.3 PFTNA system design

To conduct soil carbon field measurements, a mobile PFTNA system was constructed on a platform (75 cm × 23 cm × 95 cm; ∼300 kg) for towing by all-terrain vehicles over agricultural fields. The PFTNA system consisted of a MP320 pulsed neutron generator (NG; Thermo Fisher Scientific, Colorado Springs, CO), three 12.7 cm × 12.7 cm × 15.2 cm NaI(Tl) scintillation detectors (Scionix USA, Orlando, FL) with corresponding electronics (XIA LLC, Hayward, CA), a R2D-410 neutron detector (Bridgeport Instruments, LLC, Austin, TX), a power system (four 12 V 105 Ah DC105–12 batteries; a CGL 600 W-series DC-AC Inverter, Nova Electric, Bergenfield, NJ; and a PS4Quad Pro Charger, Pro Charging Systems, LLC, LaVergne, TN), a GPS device, an operational laptop, and an Android tablet. Iron and boric acid shielding is placed between the NG and gamma detectors to reduce irradiation of gamma detectors by fast neutrons (Figure 2).

Figure 2.

Scheme of the PFTNA system.

The power system supplies all electronic equipment with 110 V AC voltage. Uninterrupted working time is ∼20 h.

The neutron generator produces a pulsed output of 10⁷–10⁸ n s⁻¹ depending on parameter settings; neutron energy is 14 MeV.

Specially developed software allows spectral acquisition and defines the time interval for saving spectra to the laptop hard drive. This software also reads and saves GPS coordinates of the PFTNA system during scanning.

The tablet is mounted in the towing vehicle and is used for GPS set up and tracking system movement.

2.4 Data acquisition procedure

2.4.1 Gamma spectra acquisition

As mentioned above, the gamma peak with a centroid at 4.44 MeV is used to define soil carbon content. Gamma spectra containing peaks of interest with centroids at 4.44 and 1.78 MeV (used to correct silicon-28 interference in the carbon peak) are measured by gamma detectors. Gamma spectra measurements are the accumulation of gamma detector response in corresponding memory cells. Each memory cell accumulates the response (in counts) corresponding to a specific gamma ray energy interval. Gamma rays produced by 14 MeV neutrons have an energy less than this value. The studied energy interval is divided into 1024 cells (or channels) with channel widths of ∼10 keV. Gamma ray production under neutron irradiation is a statistical process. Thus, spectra acquisition should continue for some time to achieve required accuracy. The average count rate (counts per second, cps) depends on neutron flux intensity, number of nuclei of interest in the sample (soil), efficiency of neutron-nuclei interactions, and detector(s) volume and efficiency of gamma ray registration. From a radiation safety viewpoint, total neutron yields exceeding 2 × 10⁷ neutrons per second should not be used in a field system. In general, soil carbon content is no more than 5–10 w%, and agricultural soil density varies from ∼1200 to 1600 kg/m³. Under these conditions, gamma detectors with relatively large volumes should be used to achieve suitable count rates in channels of interest. In the described mobile PFTNA system, three gamma detectors with a total volume of ∼7.5 dm³ were used. To achieve a soil carbon content accuracy no worse than ±0.5 w%, the accuracy of carbon peak area determinations should be no worse than ±10 cps. The carbon peak area is around 200 cps when soil carbon content is ∼2–3 w%. To reach the desired accuracy for the described equipment, measurement time should be no less than 15 min [11]. For elements having a soil content greater than carbon, determinations with this same accuracy require shorter spectra acquisition time. For example, the higher soil content of silicon (∼30 w%) requires a spectra acquisition time of ∼1 min or less.

2.4.2 Data acquisition modes

Soil carbon measurements using the PFTNA mobile system can be done in both static and scanning modes. In static mode, the system is moved to a particular position in the field, and measurements are performed for at least 15 min. Acquired data can be recorded at the end of measurement or periodically at desired time intervals. In scanning mode, the measurement system is continuously moved over the surveyed field, and acquired data are recorded every 30 s (or other previously defined time interval) during certain scanning time (see Section 2.4.4. for detail). Scanning mode is preferable for soil carbon measurement using the PFTNA mobile system since error associated with uneven soil carbon distribution at this scale (1–10 m) is practically negligible. Along with gamma spectra records, associated geographical coordinates defined by the GPS device are saved as well.

2.4.3 System background measurement and calibration

After construction, the PFTNA system should be calibrated prior to measuring soil elements. The calibration process consists of 2 parts: system background measurements and determining the dependency of the peak area of interest vs. elemental content in reference samples. This can be done for any soil element, but calibration for soil carbon content measurements are described herein.

System background is defined by peak areas of interest in the gamma spectra when the mobile system is lifted above the ground and away from any large objects. In this case, only system construction materials contribute to the gamma spectra. System background is part of the measured soil spectra and should be subtracted to attain the net soil spectra.

Reference samples for defining calibration dependency should be relatively large. For testing our PFTNA system, four 150 cm × 150 cm × 60 cm pits with sand-coconut shell mixtures of known carbon content (0, 2.5, 5 and 10 w% of carbon) were used. Calibration measurements should be performed such that errors are negligible compare to field measurements [4].

2.4.4 PFTNA field surveying methodology

To create soil elemental distribution maps, a number of evenly distributed points should be measured over the surveyed field. These can be represented in soil contour maps with elemental content isolines. Isolines can be created using Deterministic methods (Inverse Distance Weighting, Global polynomial interpolation, Local polynomial interpolation, Radial Basis Functions) or Geospatial methods (Kriging, Areal interpolation, Empirical Bayesian Kriging). Using these methods for surveying a field, there is a consensus that the required number of evenly distributed points (i.e., geographical coordinates and soil elemental content) needed for acceptable analysis is ∼30, with 20 being the accepted minimum [12]. To attain this set of points, the surveyed field should be virtually divided into approximately equal site areas. Measurements can be done in static or scanning modes. If the field is believed to contain areas with sharp changes in soil elemental content (e.g., an asphalt road passing through the field), the number of sites (and therefore site area) should be adjusted accordingly.

To perform static mode measurements, the PFTNA system should be positioned at the center of each site for at least 15 min. In total, this mode would require a minimum of 5 h of measurement time excluding time required for moving the system between sites.

As previously mentioned, scanning mode measurements are preferable. In this mode, the system is towed within each site for ∼15 min. The total measurement time is no different than static mode, but the error associated with unevenly distributed soil carbon is absent. To provide the required scanning time per site, the operator should select a suitable speed and path length. To aid the operator, the Android tablet installed in the cabin of towing vehicle traces the scanning path and displays the time spent at each site.

2.4.5 Soil density measurement

Results from PFTNA soil measurements is the average carbon weight percent in the upper 10 cm soil layer. To express soil carbon in mass units, soil density should also be concurrently measured to a depth of 10 cm (a Troxler 3440 Moisture Density Gauge aids in these measurements). Soil density is measured at five points in each site by the envelope scheme. The central point coincides with the geometric site center, and distance between points is ∼40 m. Soil density for the site is assumed to be the average of the 5 points.

2.5 Data processing

2.5.1 Primary processing of spectra

The current FPTNA system has three gamma detectors. From a statistical point of view, processing each spectrum separately (peak areas calculation) and summarizing results of the three detectors is a common way of performing calculations. However, peak area determination from the spectrum of one detector yields relatively large statistical error since the soil carbon signal is relatively small. For this reason, spectra from the three detectors are summed prior to analysis.

During runtime, spectra acquired by each detector and corresponding geographic coordinates are saved at set time intervals. Each record (r) of raw data (for the ith detector, i = 1, 2, 3 detector number) consists of the following: measured INS and TNC gamma spectra $S_{\mathit{INS},r,i}\left({\mathit{Ch}}_{\mathit{\text{meas}}}\right)$, $S_{\mathit{TNC},r,i}\left({\mathit{Ch}}_{\mathit{\text{meas}}}\right)$, which are the number of counts in the channel (cnt/ch) versus channel number (${\mathit{Ch}}_{\mathit{\text{meas}}}$) in the multichannel analyzer; real time of spectra acquisition (RT_INS,r,i, RT_TNC,r,i, s); input (absorbed by detector) and output (recorded in spectra) gamma ray count rates (ICR_INS,r,i, ICR_TNC.r,i, OCR_INS,r,i and OCR_TNC.r,i, cps); clock time of recording of the INS and TNC spectra; and GPS coordinates. Due to each detector having its own energy calibration (correlation between photon energy and channel number), which can vary from day-to-day due to changing environmental conditions (primarily temperature), positions of peak centroids in spectra do not coincide (Figure 3).

Figure 3.

Example of raw and shifted INS spectra of 3 detectors around the 6.13 MeV oxygen peak received during field scanning (559, 561, and 564 identify individual detectors in the PFTNA system).

Spectra of each detector must be brought to one energy calibration to be summarized. To achieve identical energy calibration, the energy calibration for a reference detector of the same type was established under laboratory conditions. To accomplish this by using several known gamma lines, the neutron stimulated gamma spectra (due to both inelastic neutron scattering and thermal neutron capture) of wet and dry soil, and soil-carbon mixes were acquired (see [4]). This resulted in several well-identified gamma peaks in the created spectra (e.g., 0.847 MeV iron peak, 1.779 MeV silicon peak, 2.223 MeV hydrogen peak, 4.438 MeV carbon peak, and 6.129 MeV oxygen peak, 7.63 MeV iron peak). These peak positions (in channel number) were used to create an energy calibration curve for the reference detector; this was a straight line in the range of interest. Spectra measured by other detectors (of the same type) under different conditions can be brought to this calibration line utilizing a shifting procedure (using Igor Pro software [8]).

With this procedure, channel numbers of two well identified peaks, Ch_1,meas and Ch_2,meas, in each measured $S\left({\mathit{Ch}}_{\mathit{\text{meas}}}\right)$ spectrum are defined. Peaks with centroids at ε₁ = 1.78 MeV of ²⁸Si, and ε₂ = 6.13 MeV of ¹⁶O (see Figure 1) are used. Next, channels of acquired spectra (Ch_meas) are shifted to a new position (Ch_new) (for all INS and TNC spectra) according to the following equations:

$${\mathit{Ch}}_{\mathit{new}}=\mathrm{Int}\left[X\left({\mathit{Ch}}_{\mathit{\text{meas}}}\right)\right],$$E1

where

$$X\left({\mathit{Ch}}_{\mathit{\text{meas}}}\right)=\frac{d_{\mathit{ref}}-d_{\mathit{\text{meas}}}+b_{\mathit{ref}}·{\mathit{Ch}}_{\mathit{\text{meas}}}}{b_{\mathit{\text{meas}}}},$$E2

$$d_{\mathit{ref}}={\epsilon }_1-b_{\mathit{ref}}·{\mathit{Ch}}_{1,\mathit{ref}},$$E3

$$d_{\mathit{\text{meas}}}={\epsilon }_1-b_{\mathit{\text{meas}}}·{\mathit{Ch}}_{1,\mathit{\text{meas}}},$$E4

$$b_{\mathit{ref}}=\frac{{\epsilon }_2-{\epsilon }_1}{{\mathit{Ch}}_{2,\mathit{ref}}-{\mathit{Ch}}_{1,\mathit{ref}}},$$E5

$$b_{\mathit{\text{meas}}}=\frac{{\epsilon }_2-{\epsilon }_1}{{\mathit{Ch}}_{2,\mathit{\text{meas}}}-{\mathit{Ch}}_{1,\mathit{\text{meas}}}},$$E6

${\mathit{Ch}}_{1,\mathit{ref}}$ and ${\mathit{Ch}}_{2,\mathit{ref}}$ are the channel numbers for energy ε₁ and ε₂ in the reference calibration line. Count numbers in the channel with the new channel number $S\left({\mathit{Ch}}_{\mathit{new}}\right)$ are calculated as

$$\begin{array}{rcl}S\left({\mathit{Ch}}_{\mathit{new}}\right)& =& S\left({\mathit{Ch}}_{\mathit{\text{meas}}}\right)-S\left({\mathit{Ch}}_{\mathit{\text{meas}}}\right)·\left\{X\left({\mathit{Ch}}_{\mathit{\text{meas}}}-1\right)-\mathrm{Int}\left[X\left({\mathit{Ch}}_{\mathit{\text{meas}}}-1\right)\right]\right\}\\ & & +S\left({\mathit{Ch}}_{\mathit{\text{meas}}}+1\right)\left\{X\left({\mathit{Ch}}_{\mathit{\text{meas}}}\right)-\mathrm{Int}\left[X\left({\mathit{Ch}}_{\mathit{\text{meas}}}\right)\right]\right\},\hfill \end{array}$$E7

Shifted spectra of the detectors (Figure 3) can be summarized. The shifted spectra are used in the next data processing steps.

2.5.2 Data processing static mode measurements

For static measurements, the PFTNA system is placed on a particular site where the carbon content must be defined. The required value for spectra acquisition time will depend on the desired statistical error. After spectra acquisition, the gamma spectra are shifted according to procedures described in Section 2.5.1. The net INS spectrum is found as the difference of summarized INS spectra (3 detectors) and summarized TNC spectra (3 detectors). The net INS spectrum (Figure 4a) is used for determining silicon (1.78 MeV) and carbon (4.44 MeV) peak areas. Peak areas are calculated by their Gaussian fitting using IGOR software [8]. The 1.78 MeV peak is approximated by one Gaussian (Figure 4b), while the 4.44 MeV peak uses two Gaussians (Figure 4c) since it contains a silicon transition component.

Figure 4.

Example of the net INS spectrum (a), and 1.78 MeV and 4.44 MeV peak fittings by one (b) and two Gaussians (c), respectively.

Received values of silicon (PA1.78_soil) and carbon (PA4.44_soil) peaks areas are used in the next steps of data processing for calculating of soil carbon content.

2.5.3 Data processing scanning mode measurements

When surveying in scanning mode, the PFTNA system is towed across the field while simultaneously measuring the gamma spectra. Acquired gamma spectra and geographical coordinates of the PFTNA system position are saved every 30 s (∼50 m of travel). To ensure even coverage, the surveyed field is virtually divided into sites of approximately equal area. During scanning, the system should be present within each site for at least 15 min; this is required time ensures that error from the combined soil carbon spectrum attributed to each site (see further) not exceed 0.5 w% as explained in Section 2.4.2.

As previously mentioned, creating a map of soil carbon distribution requires a dataset consisting of no less than 20 points of defined elemental contents and corresponding geographical coordinates. To attain this dataset, the field should be virtually divided into the same number of sites. During data processing, the difference between two sequentially recorded spectra and geographical coordinate midpoints are determined, and the differential spectra (midpoints spectra) are assigned to these midpoints. All midpoint spectra having coordinates within a given site will be attributed to this site and after primary processing (as described in Section 2.5.1) will be averaged. The soil carbon content will be determined from this averaged spectrum. The dataset consisting of soil carbon content values and geographical coordinates of corresponding site centers will be used for creating maps.

All acquired spectra are processed on the data processing computer as follows. After spectra shifting procedures, gamma peaks at positions of interest become coincident in each spectrum. The differential spectra between two shifted sequentially recorded spectra for the ith detector, ${\mathrm{\Delta }S}_{\mathit{INS},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)$, ${\mathit{\Delta S}}_{\mathit{TNC},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)$, are calculated (channel by channel) as:

$$\begin{array}{c}{\mathrm{\Delta }S}_{\mathit{INS},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)=S_{\mathit{INS},r+1,i}\left({\mathit{Ch}}_{\mathit{new}}\right)-S_{\mathit{INS},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)\\ {\mathrm{\Delta }S}_{\mathit{TNC},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)=S_{\mathit{TNC},r+1,i}\left({\mathit{Ch}}_{\mathit{new}}\right)-S_{\mathit{TNC},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right),\end{array}$$E8

where S_{INS,r + 1,i}(Ch_new), S_{TNC,r + 1,i}(Ch_new) and S_INS,r,i(Ch_new), S_TNC,r,i(Ch_new) are the shifted measured gamma spectra for r + 1th and rth record (in counts per channel) for ith detector and INS and TNC spectra, respectively. (Here and hereafter, all actions with spectra are done channel by channel).

The differential spectra in cps/ch (counts per second per channel), $\mathrm{\Delta }S{\prime }_{\mathit{INS},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)$ and $\mathrm{\Delta }S{\prime }_{\mathit{TNC},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)$ are calculated as:

$$\begin{array}{c}\mathrm{\Delta }S{\prime }_{\mathit{INS},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)=\frac{{\mathrm{\Delta }S}_{\mathit{INS},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)}{{\mathit{LT}}_{\mathit{INS},r+1,i}-{\mathit{LT}}_{\mathit{INS},r,i}},\\ \mathrm{\Delta }S{\prime }_{\mathit{TNC},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)=\frac{{\mathrm{\Delta }S}_{\mathit{TNC},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)}{{\mathit{LT}}_{\mathit{TNC},r+1,i}-{\mathit{LT}}_{r,i}},\end{array}$$E9

where LT_{INS,r + 1,i}, LT_{TNC,r + 1,i} and LT_INS,r,i, LT_TNC,r,i are the live time (in s) for the r + 1th and rth record for the ith detector, and INS and TNC spectra, respectively. Live time for each spectrum is calculated as [4]:

$$\begin{array}{c}{\mathit{LT}}_{\mathit{INS},r,i}={\mathit{RT}}_{\mathit{INS},r,i}·\frac{{\mathit{OCR}}_{\mathit{INS},r,i}}{{\mathit{ICR}}_{\mathit{INS},r,i}},\\ {\mathit{LT}}_{\mathit{TNC},r,i}={\mathit{RT}}_{\mathit{TNC},r,i}·\frac{{\mathit{OCR}}_{\mathit{TNC},r,i}}{{\mathit{ICR}}_{\mathit{TNC},r,i}}\end{array}$$E10

The two sums of the three differential spectra for each rth record, $\mathrm{\Delta }S{\prime }_{\mathit{INS},r}\left({\mathit{Ch}}_{\mathit{new}}\right)$ and $\mathrm{\Delta }S{\prime }_{\mathit{TNC},r}\left({\mathit{Ch}}_{\mathit{new}}\right)$, were then calculated as:

$$\begin{array}{c}\mathrm{\Delta }S{\prime }_{\mathit{INS},r}\left({\mathit{Ch}}_{\mathit{new}}\right)=\sum _{i=1}^3\mathrm{\Delta }S{\prime }_{\mathit{INS},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right),\\ \mathrm{\Delta }S{\prime }_{\mathit{TNC},r}\left({\mathit{Ch}}_{\mathit{new}}\right)=\sum _{i=1}^3\mathrm{\Delta }S{\prime }_{\mathit{TNC},r,i}\left({\mathit{Ch}}_{\mathit{new}}\right)\end{array}$$E11

The net INS spectrum for each rth record $\mathrm{\Delta }S{\prime }_{\mathit{Net},\mathit{INS},r}\left({\mathit{Ch}}_{\mathit{new}}\right)$ was then calculated as the difference between INS and TNC spectra as:

$$\mathrm{\Delta }S{\prime }_{\mathit{Net},\mathit{INS},r}\left({\mathit{Ch}}_{\mathit{new}}\right)=\mathrm{\Delta }S{\prime }_{\mathit{INS},r}\left({\mathit{Ch}}_{\mathit{new}}\right)-\mathrm{\Delta }S{\prime }_{\mathit{TNC},r}\left({\mathit{Ch}}_{\mathit{new}}\right)$$E12

The net INS spectra found in this manner will have geographical coordinates of corresponding midpoints. After sorting by site, the average spectra of all net INS midpoint spectra attributed to each site are found. Finally, these average spectra are used for determining soil carbon content for each site. This dataset consisting of soil carbon content and geographical coordinates of corresponding site centers will be used for creating maps.

2.5.4 Calculating soil carbon content

After primary processing of spectra (Section 2.5.1) and finding the summarized (3 detectors) INS and TNC spectra in counts rate (cps) and net INS spectra (Section 2.5.3), the peak areas of silicon (centroid at 1.78 MeV) and carbon (centroid at 4.44 MeV) can be found using Gaussian fitting procedures (in cps; Section 2.5.2). The background portions of these peaks were found as described in Section 2.4.3.

Carbon content (Cw%) is calculated by Eq. (13):

$${\mathit{\text{Cont}}}_{\text{soil}}=\frac{\left(\mathrm{PA}{4.44}_{\mathit{\text{soil}}}-\mathrm{PA}{4.44}_{\mathit{bkg}}\right)-k_1·\left(\mathrm{PA}{1.78}_{\mathit{\text{soil}}}-\mathrm{PA}{1.78}_{\mathit{bkg}}\right)}{k_2},$$E13

where PA4.44_soil, PA1.78_soil and PA4.44_bkg, PA1.78_bkg are the carbon and silicon peak areas in the soil and system background spectra, respectively, while k₁ is a silicon transition coefficient and k₂ is the calibration coefficient. These coefficients are defined during system calibration (see Section 2.4.3).

The total carbon content in the upper 10 or 30 cm soil layer of a surveyed field can be defined from PFTNA measurement results. In addition to PFTNA carbon content (in w%) data, field soil density (d in kg/m³) is required. Determination of field soil density was described in Section 2.4.5.

Total field soil carbon in the 10 cm layer (TC10, ton) can be determined according to following equation:

$$\mathit{TC}10=\sum _{i=1}^n\frac{{\mathit{\text{Cont}}}_{\text{soil}i}}{100}·d_i·S_i·\frac{0.1}{1000},$$E14

where n is the number of sites in a divided field for PFTNA measurements, ${\mathit{\text{Cont}}}_{\text{soil}i}$, and $d_i,S_i$are soil carbon content (w%), soil density (kg/m³), and area (m²) of the ith site, respectively. Area can be taken from the computer software used to divide the field into sites. Given that the PFTNA measurement result is an average soil carbon content for the field, $\overline{{\mathit{\text{Cont}}}_{\text{soil}}}$, then.

$$\mathit{TC}10=\frac{\overline{{\mathit{\text{Cont}}}_{\text{soil}}}}{100}·\overline{d_{\text{field}}}·S_{\mathit{\text{field}}}·\frac{0.1}{1000},$$E15

where $\overline{d_{\text{field}}},S_{\text{field}}$ are average field soil density (kg/m³) and field area (m²), respectively.

Total carbon content in the upper 30-cm soil layer of the surveyed field (TC30, ton) can be defined as:

$$\mathit{TC}30=\frac{\mathit{TC}10}{0.55},$$E16

where the coefficient 0.55 is the ratio of the carbon surface density (g/cm²) in the 10-cm layer to the carbon surface density in the 30-cm layer with an error of ±0.10. This coefficient was found to be the average value for different carbon depth profiles for several agricultural fields in Alabama.

2.6 Measurement and data processing software

The system is supported by three software applications: Scanning App, Navigator App, and Computing App. The data flow within software applications is presented in Figure 5.

Figure 5.

Data flow within software applications.

2.6.1 Scanning App

The mobile system is managed by the Scanning App. This Windows desktop application was developed in-house using the C# programming language and .Net WPF (Windows Presentation Foundation) technology [13]; this app can run on a consumer-grade computer. The Scanning App runs on the mobile system laptop; application features are presented in Table 1.

Feature name	Feature description
1. Gamma detector control	The current version of the Scanning App supports communication with system electronics. This app is not only capable of acquiring current spectra data from the gamma detector, but also provides an interface to access and edit all electronics settings required to tune the spectra acquisition process
2. GPS connectivity	The current version of the Scanning App supports any GPS device that can communicate with NMEA 0183 (National Marine Electronics Association) standard GLL (Geographic Position—Latitude/Longitude) or GGA (Global Positioning System Fix Data) protocols over a Bluetooth or USB port [14, 15]. The Scanning App can scan and automatically find the GPS device. GPS data is acquired in one second intervals
3. Spectra plot	The Scanning App features a plot that allows spectral zooming (in and out), adding guidelines, and loading spectra from saved files to allow the operator to visually analyze spectra
4. Adjustable time intervals	The time interval between spectra acquisitions can be customized. The time interval can also be set to increase logarithmically
5. Failure handling	The Scanning App pauses the measurement, alerts the operator via a detailed error message, and sounds an alarm in the event of the following scenarios: Neutron generator failure was inferred from the nature of the acquired spectra. The current version of the Scanning App cannot manage the neutron generator directly. Connection with the GPS device was lost. In this case, the Scanning App also constantly attempts to re-establish the connection. Connection with any of the detectors was lost. Due to the nature of the current detectors, the Scanning App must be terminated and manually restarted.

Table 1.

Scanning App features.

2.6.2 Navigator App

The map managing process is mainly performed through the Navigator App. The Navigator App is an Android application developed in-house with Kotlin programming language [16] and can run on a consumer-grade Android tablet or smartphone. Navigator App features are presented in Table 2.

Feature name	Feature description
1. Creating field maps	The Navigator App allows the operator to create field maps consisting of multiple individual pieces (zones). For each zone, the number of sites in that zone can be defined, and the Navigator App will automatically generate the site polygons. For visual purposes, the operator can also adjust the color of the polygon boundaries
2. Editing field maps	The Navigator App allows editing of existing field map zone boundaries, adding or deleting zones, changing the number of sites in each zone, and color preferences
3. Scanning navigation	During the field scan, the Navigator App tracks the path of the mobile system, the time spent scanning, and the time spent at each individual site. Sites are also color-coded via a red-green-blue gradient scheme, with blue indicating that the site was scanned for the required time. Required time for sites can be set before scanning begins
4. Exporting and importing field maps	The Navigator App can export any field map or scanning map into a KML file. It also exports field boundary maps into a special file that can be imported into the Computing software or another Navigator App

Table 2.

Navigator App features.

2.6.3 Computing App

After measurement, the spectra from the Scanning App and the field boundary file from the Navigator App must be processed by the Computing App. The Computing App is a Windows desktop application developed in-house using the C# programming language and .Net WPF technology [13]; this app can run on a consumer-grade computer. The Computing App implements the algorithms in Section 2.5.1–2.5.4 to process static and scanning mode spectra and produce carbon content results. For some mathematical operations on spectra, the Computing App automatically communicates with Igor Pro, which is a scientific data analysis software by WaveMetrics [8]. Additionally, the Computing App contains features presented in Table 3.

Feature name	Feature description
1. Map management	The Computing App allows for modifying and exporting maps imported from the Navigator App
2. Troxler data support	Troxler Data can be imported and will be automatically distributed by sites and applied during computations. The Computing App outputs the weight of carbon (metric tons) for the upper 10 or 30 cm of soil
3. Additional data support	Additional data consisting of geolocation-value pairs can be imported and automatically distributed by sites
4. Neutron yield support	Neutron yield data can be imported for spectra correction
5. Additional analysis support	Apart from results data, the Computing App exports data corresponding to intermediary steps of the computing process, and outputs specially computed and formatted additional spectra data for further spectra analysis

Table 3.

Computing App features.

3. Results and discussion

Example soil carbon measurements conducted using the technology described in this chapter are presented in Figures 6 and 7 and Table 4. These measurements were performed on a field in Iowa using the PFTNA mobile system. The field size was 53 ha. Scanning time was ∼5.5 h.

Figure 6.

Map showing field and site borders, scanning path, carbon content values, and site soil densities.

Figure 7.

Carbon distribution map.

Site #	Latitude; Longitude	Carbon peak area ± err, cps	Avg. carbon content in 10 cm ± err, w%	# of mid-; points	Scanning time, m:s	Site area, ha	Avg. soil density in 10 cm layer, g/cm^3	Carbon content in 10 cm ± err, ton	Carbon content in 30 cm ± err, ton
1	41.2728; −92.0303	200 ± 6	2.96 ± 0.33	28	14:01	2.67	1.30	103 ± 12	187 ± 41
2	41.2731; −92.0275	218 ± 5	3.80 ± 0.28	38	19:00	2.61	1.22	121 ± 12	220 ± 46
3	41.2718; −92.0276	220 ± 5	3.99 ± 0.28	35	17:30	2.73	1.26	137 ± 10	249 ± 49
4	41.2747; −92.0295	217 ± 7	3.77 ± 0.37	31	15:30	2.91	1.27	139 ± 17	253 ± 56
5	41.2739; −92.0304	205 ± 7	3.13 ± 0.36	32	16:01	2.43	1.31	99 ± 12	181 ± 39
6	41.2761; −92.0318	216 ± 7	3.80 ± 0.35	31	15:32	2.67	1.16	118 ± 15	215 ± 47
7	41.2738; −92.0333	208 ± 6	3.20 ± 0.32	31	15:30	2.67	1.39	119 ± 21	216 ± 54
8	41.2746; −92.0321	208 ± 8	3.27 ± 0.41	30	15:01	2.67	1.27	111 ± 15	201 ± 46
9	41.2721; −92.0336	206 ± 6	3.21 ± 0.31	35	17:31	2.67	1.38	118 ± 15	214 ± 47
10	41.2722; −92.0350	203 ± 7	3.14 ± 0.37	31	15:30	2.67	1.29	108 ± 14	196 ± 44
11	41.2786; −92.0302	209 ± 6	3.37 ± 0.32	32	16:01	2.67	1.37	123 ± 13	223 ± 47
12	41.2796; −92.0285	187 ± 8	2.30 ± 0.41	31	15:30	2.75	1.30	82 ± 15	150 ± 38
13	41.2793; −92.0265	209 ± 9	3.43 ± 0.46	32	16:00	2.75	1.31	124 ± 18	226 ± 52
14	41.2783; −92.0279	220 ± 8	4.03 ± 0.44	31	15:31	2.58	1.33	138 ± 16	251 ± 54
15	41.2774; −92.0296	206 ± 6	3.33 ± 0.29	30	15:00	2.58	1.29	111 ± 12	202 ± 43
16	41.2760; −92.0290	201 ± 6	3.03 ± 0.33	32	16:00	2.67	1.14	93 ± 16	168 ± 42
17	41.2765; −92.0274	215 ± 7	3.70 ± 0.36	32	16:01	2.67	1.34	132 ± 16	240 ± 52
18	41.2766; −92.0259	213 ± 7	3.67 ± 0.38	28	14:00	2.67	1.46	143 ± 16	260 ± 55
19	41.2748; −92.0257	221 ± 6	4.12 ± 0.32	33	16:31	2.67	1.31	144 ± 15	261 ± 55
20	41.2748; −92.0276	216 ± 5	3.74 ± 0.29	34	17:01	2.67	1.44	143 ± 12	260 ± 52
Avg ± STD			3.45 ± 0.44
			In 10 cm layer:			In 30 cm layer:
Total field carbon content ± error, ton			2406 ± 66			4374 ± 216
Specific field carbon content ± error, ton/ha			45 ± 1			82 ± 4

Table 4.

Results of calculating the carbon content of an Iowa field (confidence level of errors is 0.68).

Sites of equal area and the PFTNA scanning path are shown in Figure 6. Soil density measurement points and site centers are also shown. Geographical coordinates of site centers, values of carbon gamma peak areas, calculated values of soil carbon weight percent, and soil carbon content in the 10 and 30 cm layers for each site are presented in Table 4. The total carbon weight in the 10 and 30 cm layers of this field and the average carbon weight per ha are also shown in this table. The average carbon weight percent for this field was 3.45 w% with a variation (STD) of 0.44 w%. This variation is larger than the average error of soil carbon weight percent in each site, indicating that changes of carbon weight percent are present within the field. The carbon distribution map for this field was created using Local Polynomial Interpolation (Deterministic methods) in ArcMap based on Cw% site data (Figure 7). The insignificant change in carbon content from ∼4 (east border) to ∼3 w% (west border) can be seen on this field map. Knowledge of average values and carbon content changes across a field can be very useful in modern agricultural practices. Data regarding total carbon content in the 10 and 30 cm layers of this field can be useful for agricultural practice and ecological assessments.

Based on the discussed example and previous experiments, the equipment for implementing Pulsed Fast/Thermal Neutron Analysis of soil carbon content under field conditions was demonstrated to be reliable. Such measurements return soil carbon contents within a relatively short time for large fields (53 ha for ∼5.5 h), and accuracy of measurements were no worse than traditional chemical analysis.

4. Conclusion

Application of neutron gamma analysis for soil elemental determinations can be an alternative to traditional chemical analysis. This technology has advantages over other methods since it is a nondestructive in-situ method that requires no soil sampling and associated laboratory processing.

The presented PFTNA methodology can be used for determination and mapping of soil carbon content. The accuracy of soil carbon analysis by PFTNA is no worse than traditional chemical analysis. Acquiring more experience and refining the described technology for large-scale soil carbon content determination under diverse field environments is the future direction of this research.

The equipment and methodology described in this chapter can also be applied to measure field content of elements such as Fe, Si, Al, H (water content) and Cl (soil contamination by chlorinated compounds). In addition, this mobile system can be used for measuring and mapping natural soil radioactivity, particularly potassium-40; in this case, the neutron generator is turned off since only gamma detectors are required. The application of the PFTNA technology for such assessments are other future topics of investigation.

Acknowledgments

This research was supported by U.S. Department of Agriculture-Agricultural Research Service National Soil Dynamics Laboratory and the authors are indebted to Mr. Barry G. Dorman and Mr. Robert A. Icenogle for technical assistance in experimental measurements, and to Mr. Dexter LaGrand for assistance with software installation. We thank XIA LLC for their electronics and detectors in this project.