Measurement and Analysis of Soil Temperature Field Based on Fiber Bragg Grating Sensor Array

Studying the soil temperature field and its variation law is of great significance to the real-time service of agricultural production. To solve the problems of low detection efficiency and difficulty of distributed detection, a distributed detection method of soil temperature field using wavelength division multiplexing and space division multiplexing technologies based on fiber Bragg grating (FBG) sensor is proposed. In this scheme, the stainless steel tube encapsulating the FBG string was vertically buried in the measured soil, and the tunable laser method and the peak-seeking algorithm were used to demodulate the wavelength of each sensor of the FBG string. The soil temperature field measurement experiments were carried out in the farmland environment. The experimental results show that the proposed method can detect the soil temperature field in real time. The internal temperature of soil changes periodically with the periodic change of surface environment temperature. With the increase of depth, the influence of surface temperature on soil temperature gradually decreases, and the amplitude of soil temperature oscillation gradually decreases, but the hysteresis effect of temperature peak becomes more and more obvious. The ambient wind speed can reduce the temperature of soil surface and shallow layer. Soil moisture affects the speed of temperature transfer from the surface layer to the deep layers, and the hysteresis effect of temperature peak is more significant in the soil with higher moisture. Solar radiation has a great influence on the temperature of soil surface and shallow layer.


I. INTRODUCTION
Soil temperature is an important environmental factor that directly or indirectly affects and reflects plant growth and development. On the one hand, soil temperature affects physiological processes such as plant seed germination, water and nutrient absorption, and root development [1], [2]. On the other hand, soil temperature affects chemical processes and life activities such as organic matter decomposition, nutrient transformation, and microbial activities. These activities are accompanied by the absorption and release of heat, which The associate editor coordinating the review of this manuscript and approving it for publication was Santosh Kumar . in turn affects the changes in soil temperature [3], [4], [5]. Soil temperature can help to forecast and understand soil ecosystem changes, and it is an important basis for determining normal crop growth. Therefore, monitoring soil temperature field and studying its variation laws are important for both real-time service and theoretical research of agricultural production.
The research of soil temperature field detection mainly includes surface temperature detection and subsurface temperature detection. Three main methods are commonly used to detect the soil temperature field: 1. The contact measurement method based on thermal resistance, thermocouples, and other electrical sensors.
In this method, electric sensors are usually placed on the surface of the soil or buried in the soil at different depths for real-time temperature measurement. Han et al. [6] designed a soil sensor suitable for wireless sensor network (WSN) application system. Thermistors were used to collect soil temperature and were connected in series and parallel for non-linear error compensation or linearization. Xue et al. [7] established a soil fire temperature field model. The temperature data of each layer of soil were collected by thermocouple, and the change of soil temperature field of each layer during the fire process was obtained. The digital integrated temperature sensor DS18B20 was a single bus device, which supported multi-point networking function and could realize multi-point temperature measurement. It was widely used in the field of soil temperature detection [8], [9], [10], [11].
2. The noncontact measurement method based on visible light and infrared imaging. This method is mainly used for the measurement of soil surface temperature. Li et al. [12] studied the temperature variation laws of soil covered with different plastic films at different instants based on infrared imaging technology. Xu et al. [13] used thermal infrared remote sensing techniques to monitor soil temperature in forested area. Nicolas et al. [14] used satellite infrared remote sensing to collect snow soil temperature in permafrost areas and perform temperature retrieval.
3. The simulation measurement method based on soil temperature field prediction model. In this method, a prediction model is established to simulate the soil temperature by analyzing the relationship between the soil temperature field and meteorological factors, environmental factors [15], [16], [17], and combining the observed and recorded historical data of soil temperature. Diniz et al. [18] reformulated the mathematical model of soil temperature by inserting a variable referring to cloud cover. Wang et al. [19] proposed an embedded network prediction model based on the gated recurrent unit (GRU) model, which was used to learn the local and global features of historical temperature for improving the prediction performance of soil temperature. Doro et al. [20] developed and implemented a new cosine model and a pseudo-heat-transfer model. These new models could better predict soil temperature for a wide range of pedoclimatic conditions. Xie et al. [21] calibrated and verified the SHAW model based on the soil temperature measurement data of the last two years.
Traditional electrical sensors such as thermal resistance and thermocouples have shortcomings such as being susceptible to electromagnetic radiation, poor long-term stability and short signal transmission distance. They are not suitable for distributed measurement. The noncontact measurement method based on visible light, infrared imaging is only suitable for measuring surface or shallow soil temperature, but not for real-time measurement of subsurface soil temperature. In addition, the noncontact measuremen method requires the acquisition and processing of a large number of images. This method has complex data processing, low measurement efficiency and poor real-time performance. The third method is suitable for temperature prediction and theoretical research, and it is difficult to realize real-time temperature measurement.
Compared with traditional sensors, the fiber Bragg grating (FBG) temperature sensor has many advantages, such as small volume, antielectromagnetic interference, corrosion resistance, easy remote operation, easy multiplexing, and so on. FBGs with different center wavelengths can be engraved at different positions of the fiber to form FBG strings. By cascading multiple FBG strings, a sensor array is formed. FBG sensor array is especially suitable for distributed multipoint measurement and structural health monitoring [22], [23]. In recent years, researchers have carried out a lot of research on the application of temperature and soil moimsture measurement with FBG sensor array [24], [25], [26], [27], [28], [29], [30].
To solve the above problems, a distributed detection method of soil temperature field based on FBG sensor array was proposed. FBG sensor array based on wavelength division multiplexing and space division multiplexing technologies is arranged at different depths of soil for multi-layer real-time temperature measurement. The distribution law, variation law of soil temperature field and its relationship with solar radiation power, soil moisture, wind speed and other factors were studied. This method improves the measurement efficiency of soil temperature, and also provides a reference for the measurement of space temperature field in other fields.

II. SOIL TEMPERATURE FIELD ANALYSIS
Soil temperature and its distribution depend on the heat exchange process of the soil. The sources of soil heat include solar radiation heat, heat generated in the earth's interior, and heat released by biological and chemical processes in the soil. Among them, solar radiation heat is the main source of soil heat. The soil heat is exported to the outside world in various ways, including radiation on the soil surface, convection, evaporation, plant transpiration, and conduction to the depths of the ground. The external factors affecting heat exchange include air density, temperature and moisture, ambient wind speed, terrain, ground cover, etc. The internal factors include soil composition, structure, moisture, color, etc.
Since solar radiation is the main source of soil heat, the soil temperature has daily and annual cycle variations due to the cyclical changes in solar radiation. This paper studies the daily variation of soil temperature.
The main form of heat transfer in soil is thermal conduction. It is assumed that the soil is a homogeneous isotropic medium. Its thermal properties do not change with depth, and there is no heat exchange along the horizontal direction. Therefore, the calculation of soil natural temperature field can be simplified as one-dimensional periodic heat conduction problem of semi-infinite body under the third boundary condition [31], [32]. The unsteady heat conduction equation of soil natural temperature field is: where τ is the time, x is the depth below the soil surface, t(x, τ ) is the soil temperature at time τ and at depth x, a is the soil thermal diffusivity. a is a physical quantity that expresses the speed of soil temperature change under the condition of certain heat gain and loss, which can be calculated by the following formula: where C g is soil volumetric heat capacity, γ is soil thermal conductivity, ρ is soil density, C p is soil specific heat. The relationship between soil thermal diffusivity and soil moisture is complex, because the soil moisture affects both soil thermal conductivity and volumetric heat capacity. According to experiments and observations, in the case of low soil moisture, the soil thermal diffusivity increases with the increase of soil moisture. However, when the soil moisture exceeds a certain value, the thermal conductivity of the soil does not increase significantly, and the heat capacity still increases linearly with the moisture, so the soil thermal diffusivity decreases instead. If the initial state temperature distribution of the soil is not considered, the boundary conditions of the above soil heat conduction equation are: where δ is the depth of the soil constant temperature layer, T a is the temperature of the soil constant temperature layer, which is approximately equal to the average soil surface temperature.
If the ambient temperature does not change suddenly, the temperature of the soil surface will not jump greatly. It is assumed that the diurnal variation of soil surface temperature is in the form of a simple harmonic function: where τ 0 is the fluctuation period, which is 24 hours for the daily variation, T m is the amplitude of soil surface temperature fluctuations above and below the average T a . According to Equations (1), (3) and (4), the theoretical calculation model of soil temperature field at different depths and at different times can be obtained by using the separation variable method: It can be seen from Equation (5) that the variation of soil temperature at the depth x is similar to the variation of surface temperature, and they are both cosine functions with the same period. However, the amplitude of soil temperature fluctuation below the surface decays rapidly and exponentially with depth. When reaching a certain depth, the fluctuation amplitude of soil temperature is very small. Below this depth, the soil temperature can be seen to remain constant, known as the isothermal layer. The time when the soil temperature at x depth reaches the peak value lags behind the time when the soil surface temperature reaches the peak value. The lag time can be calculated by equation x τ 0 πa/2.

III. SOIL TEMPERATURE MEASUREMENT MECHANISM BASED ON FBG SENSOR ARRAY A. FBG TEMPERATURE SENSING PRINCIPLE
FBG is a diffraction grating formed by periodically modulating the refractive index of the fiber core in the axial direction. It can reflect light of specific wavelength, which is the FBG Bragg wavelength λ B , shown in Fig. 1.
The Bragg wavelength λ B is related to the grating period and the effective refractive index n eff of the fiber core, shown in Equation (6): If the FBG temperature changes, the photothermal effect caused by the temperature change causes the effective refractive index to change and the thermal expansion coefficient causes the grating constant to change. The relative displacement of the Bragg wavelength caused by temperature change is: where α = 1 ∂ ∂T is the thermal expansion coefficient of optical fiber, ξ = 1 n eff ∂n eff ∂T is the thermal optical coefficient of optical fiber, K T is the temperature sensitivity coefficient of the relative wavelength.
If FBG is subjected to axial strain ε z , the photoelastic effect causes the refractive index to change, which causes the Bragg wavelength shift: where P e = n 2 eff [P 12 − υ(P 11 + P 12 )]/2, P 11 and P 12 are the elastic optic coefficient, υ is optical fiber Poisson's ratio, K ε is the relative wavelength strain sensitivity coefficient of the FBG.
According to Equations (7) and (8), the relationship between the change in the grating Bragg wavelength and the change in temperature and axial strain is: Therefore, if measures are taken to prevent FBG from being disturbed by stress, there is a linear relationship between λ B and T . The temperature change can be determined by detecting the displacement of the Bragg wavelength.

B. SOIL TEMPERATURE MEASUREMENT SYSTEM BASED ON FBG ARRAY
The structure of the distributed soil temperature measurement system based on FBG array was shown in Fig. 2. It was constructed by the wavelength division multiplexing and space division multiplexing technology.
Seven FBGs with different Bragg wavelengths were connected in series on one transmission fiber. FBG n1 and FBG n2 were used to measure the ambient air temperature and soil surface temperature respectively, and FBG n3 -FBG n7 were used to measure the temperature of multi-layer soil under the surface.
The FBG n3 -FBG n7 sensor string was coated with uncured diluted thermal conductive silicone grease and then placed into a stainless steel tube. This ensured the mechanical strength of the FBG sensor string. The thermal conductive silicone grease was used to fully fill the gap between the optical fiber and the stainless steel pipe wall to ensure the uniformity of FBGs temperature. This could also avoid the influence of soil moisture, water vapor and other factors on FBG temperature measurement. The thermal conductive silicone grease used can maintain the paste state at −50 • C-230 • C without solidifying or adhesive force, and it can avoid uneven heating of the FBG.
The upper end of the stainless pipe was filled with epoxy resin to seal the stainless steel gate and fix the optical fiber. The tail of FBG sensor string was kept free to avoid the interference of stress on FBGs during temperature measurement. FBG n1 and FBG n2 were also in a relaxed state.
The wavelength of the narrow-band light source output by the tunable laser could vary within a certain range. The laser scanning step size and frequency could be controlled by the driver. A narrow-band laser was emitted to an FBG array through a circulator. Different sensing channels could be selected through the optical switch. When the light source wavelength was consistent with the Bragg wavelength of an FBG, the reflected signal light intensity was maximum. The reflected light signal reached the photoelectric converter through the circulator, and it was converted into an electrical signal. The data processing computer collected the electrical signal, and the signal voltage peak was obtained by the peak-seeking algorithm. The measured temperature and FBG positioning could be determined by comparing the Bragg wavelength of each FBG and its variation.

IV. FBG CALIBRATION AND EXPERIMENTAL EQUIPMENT A. FBG CALIBRATION
Two FBG sensor strings were used in the experiment, and each string was engraved with 7 FBGs, a total of 14 FBGs. The length of the FBG grating area was 10 mm, the 3 dB bandwidth was 0.209 nm-0.232 nm, the reflectivity was greater than 92%, and the length of the transmission fiber was 15 m. In the experiment, the Bragg wavelengths of FBG 11  Before the experiment, it was necessary to recalibrate the temperature sensitivity coefficient of each FBG. The FBG sensor string to be calibrated was put into a temperature control chamber. The temperature of the control chamber was set from 10 • C-70 • C. The Bragg wavelengths of the FBGs were recorded every 10 • C, as shown in Fig. 3. Based on the measured Bragg wavelength and parameters of each FBG, the reflection spectrum of the FBG string could be plotted. Fig. 4 showed the reflection spectrum of FBG 11 -FBG 17 at 20 • C. The calibration curves were shown in Fig. 5. The calibration results showed that the temperature change of each FBG was basically linear with the Bragg wavelength displacement in the measured temperature range. The temperature sensitivity coefficient of each FBG sensor is greater than 10 pm/ • C.

B. EXPERIMENTAL MATERIALS AND EQUIPMENT
The experimental system was mainly composed of two FBG sensor strings, a FBG demodulator, two soil moisture meters, a solar power meter and an anemometer. The equipment models were shown in Table 1. The FBG demodulator was shown in Figure 3, and its wavelength band was 1525 nm-1565 nm, the scanning frequency was 100 Hz, and the wavelength resolution was 1 pm. Based on this demodulator, the FBG array was used to measure the surface temperature of photovoltaic module by the author, the measurement results were basically consistent with those of contact electrical sensor and infrared thermal imager [27]. The soil moisture meter was used to measure the moisture of each layer of soil, as shown in Fig. 6. In addition, the anemometer and solar power meter were used to measure wind speed and solar power, respectively.
Before the experiment, the stainless steel tubes packaged with FBG string were vertically embedded in the measured soil. FBG n3 -FBG n7 were used to measure soil temperature at 5 cm, 15 cm, 25 cm, 35 cm, and 45 cm below the surface, respectively. The moisture sensor probes were arranged near each FBG buried underground to measure the soil moisture at the corresponding position. The anemometer and solar power meter were placed on the surface of the measuring point.

V. EXPERIMENT AND RESULT ANALYSIS
The geographic location of the experiment was latitude 31 • 44'3'' N, longitude 118 • 49'51'' E, and altitude 6 m. The measuring object was farmland soil, and the soil type was red soil.

A. MEASUREMENT AND ANALYSIS OF DAILY VARIATION OF SOIL TEMPERATURE FIELD
The packaged FBG sensor string was buried in the soil 72 hours before the measurement. The measurement area was well watered so that the soil was in full contact with the sensor probe. The measurements were taken from July 24 at 8:50 to July 25 at 9:50, with data collected at 2-minute intervals. During the measurement, the weather was mainly sunny, occasionally cloudy, the maximum wind speed was 1.05 m/s, the average wind speed was 0.082 m/s. The wind speed had little effect on the soil temperature.
The measurement results were shown in Fig. 7. T05, T15, T25, T35, T45 were the soil temperatures at depths of 5 cm, 15 cm, 25 cm, 35 cm, and 45 cm, respectively. T00 was the surface temperature of the measurement point, and Ta was the air temperature.
The measurement results were analyzed as follows: (1) The daily curves of atmospheric temperature and shallow soil temperature were close to the cosine function model with a period of 24 h. The temperature of the deep soil layer (below 45 cm) is basically at a constant temperature.
(2) With the increase of depth, the influence of surface temperature on soil temperature decreased gradually, and the oscillation amplitude decreased gradually, but the hysteresis effect of temperature peak was more and more obvious.
(3) The daily variation of soil temperature showed the characteristics of alternating changes in the values of the upper and lower soil layers. During the daytime, the soil temperature gradually decreased from the surface layer to the deep layer, and the opposite was true at night.
The above experimental results are basically consistent with the results of the aforementioned theoretical analysis of soil temperature field. However, affected by solar radiation and air flow changes, the frequency and amplitude VOLUME 10, 2022  of atmospheric and surface temperature fluctuations in the daytime were higher, and the ripple of temperature curves at night were less.

B. INFLUENCE OF SOIL MOISTURE ON TEMPERATURE FIELD
The two packaged FBG sensor strings were buried in two areas to be measured, A and B. The two experimental areas were watered to different degrees so that the soil moisture was significantly different in the two areas. The measurement period was from 9:00 on August 19 to 9:00 on August 20, and the data were collected every 2 minutes. During the measurement, the weather was mainly sunny, the gust was level 2. The wind speed had little effect on the soil temperature. The measurement results were shown in Fig. 8 and Fig. 9.   By analyzing the measurement results in Figures 8 and 9, it could be seen that: (1) The higher the soil moisture, the more surface water evaporated, which was conducive to the heat dissipation of the surface and shallow soil. Within a certain moisture range, the higher the soil moisture, the lower the surface and shallow soil temperatures. Soil moisture had less effect on deep soil temperatures.
(2) Soil moisture affected the speed of heat transfer from the surface layer to the deep layer. In summer, compared with the soil with medium moisture, the hysteresis effect of temperature peak in the soil with high moisture was more significant.

C. INFLUENCE OF SOLAR RADIATION POWER ON TEMPERATURE FIELD
Before the experiment, two places A and B were irrigated to the same degree so that their soil moisture levels were VOLUME 10, 2022 essentially the same. 72 hours before the measurement, the B area was shielded from the sun by a sunshade net. The During the measurement, the weather was sunny and cloudy. The measurement results were shown in Fig. 10.
By analyzing the measurement results in Fig. 10, it could be seen that: (1) The solar radiation power fluctuated frequently due to the cloud cover. Affected by the fluctuation of solar radiation power, the soil surface temperature fluctuated significantly, and the fluctuation frequency of both fluctuations was basically the same.
(2) The shading of solar radiation by the sunshade net reduced the soil temperature, and had a great impact on the temperature of the soil surface and shallow layer.

D. INFLUENCE OF AMBIENT WIND SPEED ON TEMPERATURE FIELD
Before the experiment, two places A and B were irrigated to the same degree to make the soil moisture basically the same. A fan was used to circulate air in the B area to simulate natural wind. The fan started to run at 10:00 on August 26, and the soil temperature was measured from 10:20 on August 26 to 13:20 on August 26. During the experiment period, the weather was cloudy with gust of level 1. Natural wind had little effect on soil temperature. The measurement results were shown in Fig. 11.
Wind speed could accelerate convective heat exchange between soil and atmosphere, promote evaporation of water from the soil surface, accelerate heat dissipation, and lower soil temperature. The analysis of the measurement results in Fig. 11 showed that the wind speed had a greater effect on the surface and shallow soil temperature, but had little effect on the deeper soil.

VI. CONCLUSION
A soil temperature field detection system based on distributed FBG sensor array was designed by combining wavelength division multiplexing technology and space division multiplexing technology. The stainless steel tubes packaging the fiber grating string were vertically buried in the soil to be measured, and the tunable laser method and the peak-seeking algorithm were used to demodulate the wavelength displacement of each sensor in the FBG string. An experimental platform was built to carry out soil temperature measurement experiments in the farmland environment. The experimental results are as follows: 1. The temperature sensitivity coefficient of the FBG sensor of this detection method is greater than 10 pm/ • C, and the response time of the sensing probe is short. The detection system can obtain the multi-layer temperature distribution of soil in real time.
2. The temperature inside the soil changes periodically with the periodic change of surface environment temperature. With the increase of depth, the influence of surface temperature on soil temperature gradually decreases, the oscillation amplitude decays approximately exponentially and eventually tends to be constant, but the hysteresis effect of temperature peaks is becoming more and more obvious.
3. The daily variation of soil temperature shows the characteristics of alternating changes in the values of the upper and lower soil layers. The rate of change of surface soil temperature is much greater than that of deep soil temperature. In summer, the temperature of the surface and the shallow layer is significantly higher than that of the deep layer in the daytime, but the opposite is true at night. 4. Soil moisture affectes the speed of heat transfer from the surface layer to the deep layer. Within a certain moisture range, the higher the soil moisture, the lower the surface and shallow soil temperatures. Soil moisture has less effect on deep soil temperature values. The fluctuation of solar radiation has a great influence on the temperature of surface and shallow layer soil. Wind speed can reduce the temperature of surface and shallow soil, but has little effect on the temperature of deep soil.
Soil temperature is closely related to crop growth. In this paper, the FBG sensor array was used to realize the real-time detection of soil temperature, and the relationship between temperature field changes and environmental parameters was obtained. This laid a foundation for taking effective measures to control soil temperature and keeping it at a moderate value. The influence of environmental parameters on the soil temperature field is coupled and complex. How to obtain environmental parameter information from soil temperature field information through data analysis and data mining is one of the future research directions.
HENG ZHAO is currently pursuing the B.Eng. degree in electrical engineering and automation with the School of Mechanical and Electrical Engineering, Jinling Institute of Technology, with strong hands-on development ability. During the university, he actively participated in the research projects of his tutor, published two articles and obtained three software copyrights. His main research interests include optical fiber sensing technology and embedded control technology. He received many awards in the national robot related competitions.
FEI FENG is currently pursuing the B.Eng. degree in mechanical engineering and automation with the School of Mechanical and Electrical Engineering, Jinling Institute of Technology, with strong hands-on development ability. During the University, he actively participated in the research projects of his tutor, published four articles and obtained two software copyrights. His main research interests include optical fiber sensing technology and robotics. He received many awards in the national robot related competitions.
QIYUE WU is currently pursuing the B.Eng. degree in electrical engineering and automation with the School of Mechanical and Electrical Engineering, Jinling Institute of Technology, with strong hands-on development ability. During the University, he actively participated in the research projects of his tutor. His main research interests include robotics and embedded control technology. He received many awards in the national robot related competitions.
BO WEI received the B.Eng. degree in electronic information engineering from Hefei University, Hefei, China, in 2008, the M.Eng. degree in microelectronics and solid state electronics from the Yanshan University, Qinhangdao, China, in 2011. He is the General Manager of Wuxi Brillouin Electronic Technology Company Ltd., China. His current research interests include application of optical fiber sensing technology and application of intelligent control technology.