# Investigating the Potential of Cosmic-Ray Neutron Sensing for Estimating Soil Water Content in Farmland and Mountainous Areas

^{1}

^{2}

^{3}

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## Abstract

**:**

^{2}) of 0.645 and a root mean square error (RMSE) of 0.046 cm

^{3}·cm

^{−3}for farmland, and reproduces the daily dynamics of SWC. The R

^{2}and RMSE in mountainous areas are 0.773 and 0.049 cm

^{3}·cm

^{−3}, respectively, and the estimation accuracy of CRNS cannot be improved by the weighting calculation. The estimation accuracy of CRNS is acceptable in both regions, but the mountainous terrain obstructs neutron transmission, causing a deviation between the actual and theoretical neutron footprints in mountainous areas. Thus, the accuracy of SWC estimation is limited in mountainous terrain. In conclusion, this study demonstrates that CRNS is suitable for use in farmland and mountainous areas and that further attention should be given to the effects of topography and vegetation when it is applied in mountainous environments.

## 1. Introduction

## 2. Experimental Site and Instrumentation

#### 2.1. Cosmic-Ray Neutron Sensing Probe and Meteorological Equipment

_{3,}which can detect neutrons in the fast energy range. The fast neutron is absorbed while passing through the tube and induces a pulse of electrical current that is sent to the pulse module. Then a counting module (CR300, Campbell Scientific, Logan, UT, USA) records an electrical pulse signal that is proportional to the neutron density (Figure 1 and Figure 2).

#### 2.2. Study Site 1

#### 2.3. Study Site 2

## 3. Methodology

#### 3.1. Calibration

_{p}is given by [25]:

^{−2}), which was determined to be 138 g·cm

^{−2}in this study; P is the pressure at the specific site; and P

_{0}is an arbitrary reference pressure (the long-term average pressure at the specific site, KPa).

_{w}is defined as [26]:

^{−3}) and ρ

_{0}is the absolute humidity at the reference time (g·m

^{−3}).

_{i}and can be expressed as [25]:

_{m}is the measured neutron intensity of the cosmic-ray neutron monitors, which are designed to detect high-energy secondary neutrons. I

_{0}is a specified baseline reference intensity at a given time. The neutron monitor at Yang-Ba-Jing, China was used in our study.

_{m}is the measured neutron count from CRNP.

#### 3.2. Estimation of SWC

^{3}·cm

^{−3}), ρ

_{bd}is the soil bulk density, ρ

_{w}is the water density, N is the neutron count calibrated with Equation (4), N

_{0}is the counting rate over dry soil under the same reference conditions, and a

_{i}is the fitting parameter. The parameters were defined as a

_{0}= 0.0808, a

_{1}= 0.372, and a

_{2}= 0.115 for water contents higher than 0.02 kg kg

^{−1}.

#### 3.3. Horizontal Weight

#### 3.4. Vertical Weight

#### 3.5. Estimation of Measurement Accuracy

^{2}) and root mean square error (RMSE). The R

^{2}and RMSE are given by:

## 4. Results and Discussion

#### 4.1. Footprint Estimation at Different Study Sites

#### 4.2. SWC Variation and Seasonal Characteristics at Different STUDY Sites

^{3}·cm

^{−3}to 0.40 cm

^{3}·cm

^{−3}at the Fengqiu station and from 0.05 cm

^{3}·cm

^{−3}to 0.30 cm

^{3}·cm

^{−3}at the Hemuqiao station (see Figure 3). As expected, the range of SWC and the footprint simulations in Section 4.1 consistently showed that Fengqiu stored a larger amount of SWC during the experimental periods. In general, in this study, Fengqiu provided more hydrogen with higher humidity than Hemuqiao despite the occurrence of more frequent precipitation and greater total precipitation at the Hemuqiao station. Differences in SWC storage between Fengqiu and Hemuqiao are most likely predominantly influenced by topography. Thin soil thickness and a large terrain gradient characterize Hemuqiao [28], while, in Fengqiu, flat farmland, which retains more soil water than the land in Hemuqiao, can provide abundant hydrogen resources.

#### 4.3. Spatial Characteristics of SWC at Different Study Sites

^{2}values were 0.487 and 0.798 for Fengqiu and Hemuqiao, respectively. The RMSE values were 0.054 and 0.049 cm

^{3}·cm

^{−3}for Fengqiu and Hemuqiao, respectively. The weighting calculation improved the accuracy of CRNS estimation in Fengqiu compared to the average calculation, indicating that the weighting simulation was consistent with the spatial characteristics of the CRNS footprint. Previous studies reported that the neutron density detected by CRNP is heterogeneously distributed within the CRNS footprint [30,31,32]. Despite this result, the weighting calculation did not significantly improve the CRNS estimation accuracy of Hemuqiao.

^{2}) and the RMSE. In the context of 6 samplings, the R

^{2}for Fengqiu was 0.645, while the RMSE was 0.049 cm

^{3}·cm

^{−3}; in the context of 7 samplings, the R

^{2}and RMSE for Hemuqiao were 0.773 and 0.049 cm

^{3}·cm

^{−3}, respectively (see Figure 4a,c). The estimation accuracy of CRNS increased as the sampling frequency increases, indicating that CRNS was well correlated with SWC [33,34]. Although the R

^{2}for Fengqiu was lower than that of Hemuqiao, the linear fitting curve for Fengqiu was closer to the 1:1 line than that of Hemuqiao, suggesting that CRNS estimated a more accurate SWC at the Fengqiu station.

^{3}·cm

^{−3}. However, no significant correlation between the daily variation in CRNS and FDR was observed at Hemuqiao. The time series of SWC measured by FDR represented a continuous change in SWC at the experimental site. Therefore, the determination coefficient of 0.059 indicated that CRNS could not accurately represent the diurnal variation in SWC at Hemuqiao. CRNS counts depend on the proximity of neutron density to the surface, and thus fluctuate within a certain range. Increasing the sampling interval can improve statistical stability, as previously reported in several studies [21,33]. This study assumed that the daily or 12 h variation in the CRNS could adequately describe the temporal variation in SWC without increasing the error due to long sampling intervals.

^{3}·cm

^{−3}of soil volumetric water content [20]. However, it is not possible to determine the dynamic changes in bamboo forest contributions to the hydrogen pool during wet conditions with high interception storage. Therefore, we recommend that calibration for forest vegetation be considered in further studies to obtain more accurate estimates.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Detection Radius (m) of Simulations at Different SWCs (cm^{3}·cm^{−3}) and air Humidities (g·cm^{−2})

**Table A1.**Detection radius obtained by simulations under different SWCs (cm

^{3}·cm

^{−3}) and air humidities (g·cm

^{−2}). The pattern of variations in the detection radius values indicates the impact of SWC and air humidity on detection radius.

SWC | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 |

Radius with the air humidity of 10 | 187 | 178 | 172 | 166 | 161 | 157 | 153 | 150 |

Air humidity | 5 | 10 | 15 | 20 | 25 | 30 | 33 | |

Radius with SWC of 0.15 | 184 | 178 | 173 | 168 | 164 | 160 | 158 |

^{2}was 0.976.

## Appendix B. Detection Depth (cm) of Simulations at Different SWCs (cm^{3}·cm^{−3}) and air Humidities (g·cm^{−2})

**Table A2.**Detection depth obtained by simulations under different SWCs (cm

^{3}·cm

^{−3}) and air humidities (g·cm

^{−2}). The pattern of variations in the detection depth values indicates the impact of SWC and air humidity on detection depth.

SWC | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 |

Depth with the air humidity of 10 | 35.3 | 29.2 | 24.8 | 21.6 | 19.1 | 16.9 | 15.2 | 13.7 |

Air humidity | 5 | 10 | 15 | 20 | 25 | 30 | 33 | |

Depth with SWC of 0.15 | 29.1 | 29.2 | 29.2 | 29.2 | 29.3 | 29.4 | 29.4 |

^{2}was 0.954. SWC had a significant impact on the detection depth (p < 0.001), but there was no significant impact observed on air humidity to the detection depth (p = 0.919).

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**Figure 1.**Location of the cosmic-ray neutron sensing probe and the experimental sampling design at Fengqiu station. (

**a**) Cosmic-ray neutron sensing probe. (

**b**) Frequency domain reflection (FDR) auto soil moisture monitor. (

**c**) Bird’s-eye view of the study site, I: cosmic-ray neutron sensing probe; II: meteorological instrument; III: FDR auto soil moisture monitors; IV: soil sampling points.

**Figure 2.**Location of the cosmic-ray neutron sensing probe and the experimental sampling design at Hemuqiao station. (

**a**) View of the study site. (

**b**) CRNP system. (

**c**) Meteorological instrument. (

**d**) Digital elevation map and sampling points of the study site, I: CRNP; II: Meteorological instrument; III: FDR auto soil moisture monitor; IV: Soil sampling points.

**Figure 3.**Comparison of SWC measured by the CRNS and the FDR at the Fengqiu station (

**a**) and the Hemuqiao station (

**b**). N

_{0}corresponds to the neutron count rate on 4 June 2020, at the Fengqiu station, while N

_{0}corresponds to the neutron count rate on 18 November 2019, at the Hemuqiao station.

**Figure 4.**The SWC correlation between CRNS and point sampling. (

**a**) The SWC correlation between CRNS and weighted point sampling in Fengqiu. (

**b**) The SWC correlation between CRNS and averaged point sampling in Fengqiu. (

**c**) The SWC correlation between CRNS and weighted point sampling in Hemuqiao. (

**d**) The SWC correlation between CRNS and averaged point sampling in Hemuqiao.

**Table 1.**The footprint of the CRNS simulated by URANOS at different study sites. The theoretical values of the detection radius and detection depth were obtained from simulation results under extremely dry and extremely humid conditions.

Study Site | Maxim Radius | Minimum Radius | Maxim Depth | Minimum Depth |
---|---|---|---|---|

Fengqiu | 139 m | 127 m | 31.2 cm | 16.9 cm |

Hemuqiao | 153 m | 125 m | 45.9 cm | 19.1 cm |

Theoretically | 218 m | 123 m | 65.9 cm | 13.8 cm |

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## Share and Cite

**MDPI and ACS Style**

Jiang, Y.; Xuan, K.; Gao, C.; Liu, Y.; Zhao, Y.; Deng, H.; Li, X.; Liu, J.
Investigating the Potential of Cosmic-Ray Neutron Sensing for Estimating Soil Water Content in Farmland and Mountainous Areas. *Water* **2023**, *15*, 1500.
https://doi.org/10.3390/w15081500

**AMA Style**

Jiang Y, Xuan K, Gao C, Liu Y, Zhao Y, Deng H, Li X, Liu J.
Investigating the Potential of Cosmic-Ray Neutron Sensing for Estimating Soil Water Content in Farmland and Mountainous Areas. *Water*. 2023; 15(8):1500.
https://doi.org/10.3390/w15081500

**Chicago/Turabian Style**

Jiang, Yifei, Kefan Xuan, Chen Gao, Yiren Liu, Yuan Zhao, Haodong Deng, Xiaopeng Li, and Jianli Liu.
2023. "Investigating the Potential of Cosmic-Ray Neutron Sensing for Estimating Soil Water Content in Farmland and Mountainous Areas" *Water* 15, no. 8: 1500.
https://doi.org/10.3390/w15081500