Freeze-thaw Assessment of Plants Based on Envelope Analysis of Stem Volume Water Content Sequence


 Background: Frost stress is an abiotic stressor for plant growth that impacts the health and the regional distribution of plants. The freeze-thaw characteristics of plants during the overwintering period help to understand relevant issues in plant physiology, including plant cold resistance and cold acclimation. Therefore, we aimed to develop a non-invasive instrument and method for accurate in situ detection of changes in stem freeze-thaw characteristics during the overwintering period. Results: A sensor was designed based on standing wave ratio method (SWR) to measure stem volume water content (StVWC). We were able to measure stem volume ice content (StVIC) and stem freeze-thaw rate of ice (StFTRI) during the overwintering period. The resolution of the StVWC sensor is less than 0.05 %, the mean absolute error and root mean square error are less than 1 %, and the dynamic response time is 0.296 s. The peak point of the daily change rate of the lower envelope of the StVWC sequence occurs when the plant enters and exits the overwintering period. The peak point can be used to determine the moment of freeze-thaw occurrence, whereas the time point corresponding to the moment of freeze-thaw coincides with the rapid transition between high and low ambient temperatures. In the field, the StVIC and StFTRI of Juniperus virginiana L., Lagerstroemia indica L. and Populus alba L. gradually increased at the beginning, fluctuated steadily during, and then gradually decreased by the end of the overwintering period. The StVIC and StFTRI also showed significant variability due to differences among the tree species and latitude.Conclusions: The StVWC sensor has good resolution, accuracy, stability, and sensitivity. The envelope changes of the StVWC sequence and the correspondence between the freeze-thaw moment and the ambient temperature indicate that the determination of the freeze-thaw moment based on the peak point of the daily change rate of the lower envelope is reliable. The results show that the sensor is able to monitor changes in the freeze-thaw characteristics of plants and effectively characterize freeze-thaw differences and cold resistance of different tree species. Furthermore, this is a cost-effective tool for monitoring freeze-thaw conditions during the overwintering period.


Background
Frost is an atypical biological stress to woody plants in temperate and cold climates. It affects plant growth and distribution [1,2] by affecting mechanisms related to the diffusion of ice crystals, changes in cell membrane uidity, and osmoregulation of ion migration. However, freezing and thawing of plants is a process of mutual transformation of liquid water and solid ice. During the overwintering period, when the plant temperature is lower than the freezing point, the water in liquid state is frozen and turned into solid ice crystals in plants. When the plant temperature is higher than the freezing point, these solid ice crystals melt again and turn into liquid water in the tissues [3]. Plants undergo a cyclic process of alternating liquid water and solid ice in their bodies. However, this freeze-thaw cycle can damage tissues or organs of the tree and even lead to death [4][5][6].
The freeze-thaw characterization of plants can be assessed by their morphology, the half-lethal temperature (LT50) and the subcooling point [7,8]. The improvement of technology and instrumentation allowed the analysis of several biochemical metabolic indicators (e.g., enzyme activity, soluble proteins, respiration, etc.) in plant tissues. These indicators can also provide a more accurate assessment of the current state of the plant, providing a reference for the analysis of freeze-thaw characteristics of the plant [9]. However, these methods are not feasible on a large scale because of expensive equipment and high requirements for the operator. In recent years, with the development of image analysis technology, some scholars have detected the freezing and thawing of plants with nuclear magnetic resonance (NMR) by scanning the frozen and thawed parts of plants [10,11]. Some researchers have also used infrared imaging equipment to observe the temperature changes on the plant surface during freezing and thawing [12]. However, these devices are expensive and have strict limitations in their use, making it di cult to apply them in a practical context of agriculture and forestry.
Online nondestructive monitoring of freeze-thaw change information in plants in a practical context, has been proposed by Raschi et al. [13], with the use of ultrasound to detect freeze-thaw changes in plants and study the relationship between freeze related gas bursts in plants and ultrasound emission. Later, Charrier et al. used ultrasonic emission analysis to investigate ice nucleation and propagation processes in plant xylem, and the freezing dynamics of plants during freeze-thaw. They found that cavitation near the ice surface after freezing was closely related to ultrasonic emission [14]. Sparks et al. used a time domain re ectometry (TDR) sensor to detect the ice content in winter stems of Pinus contorta and found values between 0% and 75% [4,15]. TDR and ultrasound emission methods have the advantage of being nondestructive or minimally destructive, but high cost is a drawback that limits their use. Therefore, this study proposes a freeze-thaw detection method for plants based on the envelope analysis of StVWC sequence. The main subjects of this paper are: (1) the development of a low-cost StVWC sensor, (2) the establishment of a freeze-thaw description model based on envelope analysis of StVWC sequence, and (3) the monitoring of freeze-thaw changes and performing freeze-thaw decoding during the overwintering period of plants.

StVWC measurement principle and sensor
The principle of measuring the StVWC based on the standing wave ratio (SWR) and the dielectric properties of plant tissues is shown in Fig. 8. When 100 MHz electromagnetic wave generated by the signal source is transmitted along a coaxial transmission line, the impedance of the ring probe installed at the stem does not match the impedance of the transmission line. The electromagnetic wave will be re ected when transmitted to the probe; and then the incident and the re ected waves on the transmission line will be superimposed to form a standing wave [28,29]. The peak and trough values of the standing wave signal are measured at both ends of the transmission line and the difference between the peak and trough values is calculated (Eq. 1).
where β is the ampli cation of the ampli er; A is the amplitude of the electromagnetic wave output from the signal source; the coaxial transmission line impedance (Z 0 ) is 50 Ω; β and A are deterministic values, so that the voltage difference ΔU across the transmission line is only linearly related to the probe impedance (Z l ). Thus, a change in the StVWC will cause a change in the stem dielectric constant, which will lead to a subsequent change in the impedance at the probe. The StVWC can be calculated by establishing the relationship equation between ΔU and the StVWC (Eq. 2), with a and b as calibration coe cients.
The StVWC sensor designed in this study is shown in Fig. 9. It consists of two ring electrodes: American Society of Testing Materials (ASTM) 304 stainless steel with 12.6 mm of width and 0.65 mm of thickness with the adjustment knob on the electrode. The diameter of the ring electrode can be adjusted to different trunk diameters within the range of 30-80 mm (Fig. 9a). The hardware system is shown in Fig. 9b; it converts stem water information into electrical signals and the outputs are sent to the data processing unit. Then the temperature measurement module (DS18B20, Risym, China, range: -45°C-85°C, accuracy: ±0.5°C) synchronizes the acquired ambient temperature information. Subsequently, the data processing unit calculates the stem freeze-thaw information (StVIC, StFTRI) and transmits the data to the database via general packet radio service (GPRS) unit for real-time measurements. The StVWC sensor enclosure is made of white resin (DSM-IMAGE8000, Royal DSM, Netherlands), as shown in Fig. 9c, which has a dielectric constant (< 4) that does not affect the measuring performance of the sensor. The screw on the ring electrode has to pass through the hole and then the electrode interface can be connected. When the three main components are connected together, the assembled stem freeze-thaw sensor is ready as shown in Fig. 9d.
The relationship between the output voltage values of the StVWC sensor circuit and the true values of StVWC was obtained with calibration relationship coe cients to ensure the accuracy of the measurements. Fresh stem segments of Juniperus virginiana L., Lagerstroemia indica L., and Populus alba L. were selected as calibration samples. The stem segments were all 6 cm in length and the volume of the samples was measured by the over ow method after soaking in water. Afterwards, the sensor was mounted on the stem and placed in a drying oven set to 45°C (DHG-9037A, HASUC, China, range: 10 200°C, accuracy: ±1°C). The mass of the stems was weighed every 6 h and the corresponding voltage values were recorded until the stems were completely dry. Finally, the true values of StVWC were calculated with the variation in stem volume and stem mass; and a linear t was applied to the voltage values and the true values of StVWC to obtain the calibration coe cients.

( )
Concomitantly, the response characteristics of the sensor to the time-varying input quantity was measured with the sensor probe placed in the air. When the sensor output stabilized, a 500 ml beaker was lled with water, and the sensor probe was quickly immersed into the water. This is the input signal, the time of the input is a rst-order step signal. The dynamic characteristics were obtained by measuring the variation of the output voltage signal of the sensor with the input using an oscilloscope (TBS1052C, TEKTRONIX, American).

Freeze-thaw Model Of Plant Stem
Many trees or shrubs enter the overwintering period with essentially zero transpiration and minimal root water uptake [30]; therefore, StVWC can be a stable value during the overwintering period (Sun et al., 2019). In addition, the dielectric constant of water is 81 (25°C) and the dielectric constant of ice is approximately 3 (similar to the dielectric constant of dry matter in the stem of a plant) [20]. That means when the water in the stem is converted to ice, the StVIC can be calculated by the reduction in the StVWC before and after freezing and thawing. The key to the calculation is nding the moment when the freezing and thawing of the stem occurs [15,17].
Envelope analysis is a common method for the time series signal processing [31]. This study proposes and establishes a stem freeze-thaw detection method based on the envelope analysis of the StVWC sequence, to address the characteristics of its regular uctuation over time during the overwintering period. The schematic diagram for calculating the StVIC is shown in Fig. 10. StVWC uctuated in time, and the peak values (maximum and minimum) in each cycle of StVWC were connected to obtain the upper and lower curves with time, which are the upper envelope (δ a ) and lower envelope (δ b ). As the water in the stem is converted to ice during the overwintering period, the StVWC and the lower envelope ( δ b ) decrease signi cantly before leveling off, and the daily change rate of δ b is expressed by Δδ b (Eq. 3), where δ b t2 and δ b t1 are the δ b corresponding to the adjacent moments t2 and t1 respectively. When the peak point of Δδ b appears, the stem is considered to be in the freeze-thaw state. Then the moment t1 and the corresponding value of the upper envelope δ a t1 are recorded; and the StVIC after moment t1 is calculated using Eq. 4, where, StVIC tx is the volume of ice in the stem at moment tx; V ice tx is the volume of ice in the stem at moment tx; V is the volume of the stem; δ w tx is the volume of water in the stem at moment tx during freeze-thaw; ρ w is the density of water; and ρ ice is the density of ice.
Excessive freezing of plants during freeze-thaw will result in massive cell death, that causes irreversible damage to the plant [4,6]. Therefore, StFTRI is another important indicator of the freeze-thaw characteristics of plants, calculated by Eq. 5, where StFTRI tx is the freeze-thaw rate of ice in the stem at moment tx; and StVIC tx ' is the volume of ice in the stem corresponding to tx ' at an adjacent moment after tx.

Plant Materials
The plant materials were Juniperus virginiana L., Lagerstroemia indica L. and Populus alba L.. Juniperus virginiana L. was 5 years old with a height of 2.65 m and a stem diameter of 5.98 cm (Fig. 11a). Lagerstroemia indica L. was 3 years old with a height of 2.7 m and a stem diameter of 3.2 cm (Fig. 11b). Populus alba L. was 8 years old with a height of 7.5 m and a stem diameter of 8.2 cm (Fig. 11c). Stems were cut from these trees for sensor calibration and testing during non-freeze-thaw periods. The StVWC sensor was installed at 1 m of height above the ground of all trees. for Populus alba L.. Juniperus virginiana L. is located in Hohhot, Inner Mongolia, China (111º50 28 E, 40º32 34 N), which has a mid-temperate continental climate, and a regional average temperature of 24.0°C in July (hottest) and -10.0°C in January (coldest). Lagerstroemia indica L. is located at the Bajia Nurseries in Beijing, China (116º21 14 E, 40º0 55 N), the area has a warm temperate semi-humid semiarid monsoon climate, and the average temperature in the region is 26.0°C in July (hottest) and -5.0°C in The relationship between the true values of the StVWC and the output voltage of StVWC detected by the sensor circuit is shown in Fig. 1. The tted equation was obtained by linear tting ( Table 1). The tted coe cients of determination (R 2 ) of the linear ts were 0.9845, 0.9803, and 0.9892 for each tree species. Values a and b of the tted equations were used as calibration coe cients to the corresponding tree. The curve of the output dynamics captured by the oscilloscope is shown in Fig. 2 with the dynamic response time being 296 ms. Envelope characteristics of StVWC sequence with freeze-thaw moments The StVWC of Juniperus virginiana L., Lagerstroemia indica L., and Populus alba L. during the overwintering period was analyzed, and the lower envelope of the StVWC ( ) was calculated, as shown in Fig. 3., where uctuates at a high level at rst, then with the onset of winter, decreases rapidly. After entering the overwintering period, stays at a lower level. When spring comes, the plant starts to recover, and the lope rises rapidly again. After the overwintering period, continues to uctuate at a higher level. The accurate moment when plants enter and leave the freeze-thaw process is determined by the daily change rate of the lower envelope ( ), which is shown in Fig. 3.
As the phases of rapidly decrease and increase, two peaks appear in the daily change rate of the curve. Temperature variation of stem freeze-thaw moments The daily average temperature (T-Mean) of the plant growth environment was also recorded (Fig. 4). ranged from -1.0℃ 0.5℃, -7.0℃ 1.0℃, -3.5℃ 0.5℃,for melting points B 1 , B 2 , and B 3 , respectively. Once again, as the water in the plant reaches the zero temperature boundary of solid-liquid transition, the ice in the plant begins to melt, resulting in a rapid increase of water content in the plant, further causing a rapid rise in and in creating a peak.

Changes of StVIC during the overwintering period
The changes in the StVIC of Juniperus virginiana L., Lagerstroemia indica L., and Populus alba L. during the overwintering period are shown in Fig. 5. Before the overwintering period, the temperature is high, the plant does not freeze and thaw, and the StVIC is zero. As winter begins, the temperature decreases, the liquid water in the plant is transformed into ice, and the StVIC gradually rises. In the late winter, the temperature is low, and the StVIC further increases and uctuates within a certain range. When spring starts, the temperature increases, the StVIC starts to decrease, the ice melts into liquid water, and the StVIC gradually decreases until the overwintering period is over.
The uctuations in StVIC of Juniperus virginiana L., Lagerstroemia indica L., and Populus alba L. during the overwintering period were signi cantly different. The box plot of StVIC changes are shown in Fig. 6. The size of the boxes describes the magnitude of data volatility, showing that Juniperus virginiana L. is the least volatile and Populus alba L. is the most volatile.

Changes of StFTRI during the overwintering period
The stem freeze-thaw rate of ice (StFTRI) is closely related to the freeze-thaw process in the plant. When plants go through the overwintering period, the freeze-thaw process is so fast that it causes massive cell death, resulting in irreversible damage to the plant. The changes in StFTRI of Juniperus virginiana L., Lagerstroemia indica L., and Populus alba L. during the overwintering period are shown in Fig. 7. Table 2 shows the results of statistical analysis of the StFTRI volatility.  can be calculated, which is less than 0.05 %, indicating that the sensor has good resolution and can effectively measure the change in StVWC. The mean absolute error and root mean square error are less than 1%, indicating that the sensor has high accuracy and stability with respect to measurements. Concurrently, the dynamic response time of the sensor is 296 ms (Fig. 2), that meets the actual measurement requirements, indicating that the sensor has good sensitivity.

Determination of the freeze-thaw moment
The conversion of liquid and solid states of water is the basis for calculating the StVIC, which can be obtained by calculating the change in water content in the stem before and after freezing and thawing [4,15,16]. The key to calculate StVIC is to track the freeze-thaw moment [17]. In this study, we propose a method to determine the freeze-thaw moment based on the lower envelope and its daily change rate by analyzing the envelope of the StVWC sequence. The peak point of the daily change rate of the lower envelope (Fig. 3) provides a basis for the determination of the freeze-thaw moment. Previous studies have also shown that freezing of plant tissues occurs when temperature drops below the freezing point, followed by the production of ice crystals in the plant [6,13,18]. The rapid decrease (or increase) of ambient temperature near the solid-liquid transition boundary, indicates the formation (or disappearance) of ice crystals in plant tissues (Fig. 4). The peak of daily change rate of the lower envelope occurs at this time, allowing the determination of the freeze-thaw moment.
Freeze-thaw changes of plants during the overwintering period The changes in StVIC (Fig. 5) and StFTRI (Fig. 7) of Juniperus virginiana L., Lagerstroemia indica L., and Populus alba L. can be observed during the overwintering period. The StVIC rises continuously from autumn to winter as the plant enters dormancy and vitality decreases. The StVIC decreases in accordance with the general rule of plant growth process as the plant starts to grow back and vitality increases from winter to spring [19]. Some periodic uctuations of StVIC were observed during the overwintering period, with a decrease of ice in the stems when the temperature increased during the day; and an increase of ice in the stems when the temperature decreased during the night, con rming the periodic uctuations of StVIC in previous studies [4,20,21].
Freeze-thaw characteristics of deciduous broadleaf species and evergreen coniferous species The variation in StVIC of Lagerstroemia indica L. (a deciduous broadleaf species) and Juniperus virginiana L. (an evergreen coniferous species) can be compared in Fig. 6. The box height of Lagerstroemia indica L. was approximately three times the box height of Juniperus virginiana L., indicating that the StVIC of Juniperus virginiana L. is less volatile during the overwintering period. The StFTRI corresponding to Juniperus virginiana L. in Fig. 7 is also small, and the standard deviation of the StFTRI is only 0.00405 ( Table 2), indicating that evergreen coniferous species are more capable of regulating themselves during the overwintering period than the deciduous broadleaf species [5,22]. Therefore, Juniperus virginiana L. (evergreen coniferous species) is more resistant to cold because of its ability to regulate the ice-water content e ciently and adapt to the overwintering conditions [23,24].

Freeze-thaw characteristics of trees in different latitudes
The higher the latitude, the lower the winter temperature and the colder the overwintering period [25]. The latitude of Beijing is lower than Heilongjiang, therefore, the ambient temperature of Beijing is not as cold as that of Heilongjiang. The StVIC uctuation of Lagerstroemia indica L. in the warm temperate zone of Beijing (Haidian District) ranged from 0 % to 15% (Fig. 5b), and the overwintering StVIC uctuation of Populus alba L. in the middle temperate zone of Heilongjiang (Cap Hill, Harbin) ranged from 0 % to 60% (Fig. 5c). This indicates that Populus alba L. was subjected to intense stress by low temperature. However, the uctuation of StFTRI (Fig. 7c) was less drastic as compared to that of Populus alba L. (Fig. 7b