Tree sapwood xylem water-oxygen monitoring root zone soil oxygen environment analysis system and method
By using oxygen concentration-liquid flow rate composite sensors and tree root zone-trunk oxygen diffusion model in trees, the problem of difficulty in accurately monitoring the soil oxygen environment in the tree root zone in the prior art is solved, and non-destructive and real-time monitoring and evaluation are achieved, improving the efficiency of tree growth and ecological protection.
Patent Information
- Application Number
- CN202510091069.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-21
- Publication Date
- 2025-04-04
AI Technical Summary
The prior art is difficult to accurately and in real time to monitor the soil oxygen environment in the tree roots, and traditional buried sensors may interfere with soil structure and damage the root system.
The oxygen concentration-liquid flow rate composite sensor is used to combine the tree root zone-trunk oxygen diffusion model to realize the oxygen transmission model from the xylem of the trunk to the root zone, and conduct lossless and real-time monitoring.
Real-time, in-situ and accurate monitoring of the physiological status of trees is achieved, and the soil oxygen environment data in the root area is obtained. It is suitable for a variety of soil types and environmental conditions, improving the efficiency of tree growth and ecological environment protection.
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Figure CN119756486A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a water-oxygen monitoring technology for the xylem of tree sapwood, and more particularly to a system and method for analyzing the oxygen environment of the root zone soil. The system and method utilize an oxygen concentration-liquid flow rate composite sensor to implement an oxygen transmission model from the root zone to the xylem of the sapwood near the trunk, so as to realize water-oxygen monitoring of the xylem of the trunk, thereby obtaining the oxygen environment data of the root zone soil. Background Art
[0002] A continuous and stable supply of oxygen is a necessary condition for trees to maintain normal metabolism. However, due to factors such as insufficient precipitation, poor drainage, and hardened urban roads, the soil oxygen content is insufficient, affecting the normal growth and development of trees. Therefore, the analysis of the oxygen environment in the root zone soil is of great significance to agricultural and forestry production and ecological protection.
[0003] Oxygen transport in the root zone of trees is affected by many factors, including soil type, moisture, temperature, and root activity. By monitoring the changes in oxygen concentration and sap flow rate in real time, we can have a more comprehensive understanding of the oxygen transport process in the root zone. Current monitoring methods are insufficient in accuracy and coverage, and are difficult to meet the needs of practical applications.
[0004] At present, most soil oxygen sensors used for monitoring are buried sensors, but they need to be detected at fixed points, making it difficult to capture the oxygen concentration in the entire root zone. In addition, buried sensors may interfere with soil structure and damage the root system. Establishing a soil oxygen diffusion model is a simple method to quickly obtain oxygen concentration gradients based on the physical and chemical properties of the soil, but the input data of the model is uncertain, and the model structure and parameters are related to the physical and chemical properties of the soil, so its applicability is limited. In recent years, fluorescence imaging methods have become important in non-invasive measurements, which can intuitively display the oxygen distribution of soil in the root zone of plants, but they can only be carried out under laboratory conditions and cannot be used for in-situ monitoring in the field. Due to the wide and deep distribution of tree roots and the complexity of the spatial distribution of oxygen in the soil, direct measurement methods have great limitations. Therefore, it is of great scientific significance and application value to develop a soil oxygen analysis system and method with low loss, high applicability, and real-time in-situ indirect monitoring.
[0005] The present invention uses an oxygen concentration-liquid flow rate composite sensor combined with an oxygen transmission model from the root zone to the sapwood xylem near the trunk to monitor the water-oxygen in the sapwood xylem of trees. It can not only realize real-time, in-situ, and accurate monitoring of the physiological state of trees, but also obtain data without interfering with the soil and root system, and is applicable to a variety of soil types and environmental conditions. Through this system, the oxygen environment of the root zone soil can be effectively analyzed, and the efficiency and effect of tree growth and ecological environment protection can be improved. Summary of the invention
[0006] The purpose of the present invention is to provide a root zone soil oxygen environment analysis system and method for tree sapwood xylem water-oxygen monitoring, the system and method comprising an oxygen concentration-liquid flow rate composite sensor, a data processing module, and a tree root zone-trunk oxygen diffusion model;
[0007] The oxygen concentration-liquid flow rate composite sensor adopts a bifurcated optical fiber with a double-probe structure, including an upper and a lower probe, the upper probe is a heating probe of a thermal diffusion liquid flow sensor, which contains a heating element and a thermocouple, and the lower probe is an optical fiber oxygen probe and a reference probe of a thermal diffusion liquid flow sensor, which contains a thermocouple and an optical fiber, and the probe body is two hollow cylindrical steel needles, and a chromium alloy-copper-nickel alloy (E type) thermocouple is used inside the steel needle as a temperature probe to obtain temperature data;
[0008] The core of the data processing module is a PC equipped with Windows system, which is installed with DataLogger software;
[0009] The tree root zone-trunk oxygen diffusion model takes the oxygen concentration and sap flow rate of the xylem of the sapwood near the trunk as input, and the oxygen concentration gradient on the xylem sap flow transmission path as output, establishes an oxygen spatial distribution mapping chain, and realizes a quantitative description of the oxygen transmission process.
[0010] Further, the temperature probe of the composite sensor uses chromium alloy and copper-nickel alloy thermocouple wires with a diameter of 0.127 mm, which are welded to form a thermocouple joint and insulated from the inner wall of the probe;
[0011] Furthermore, the upper probe has a circle of heating resistance wire tightly wrapped around the outer layer of the stainless steel needle, and an aluminum tube is installed outside the resistance wire;
[0012] Furthermore, the lower reference probe has an optical fiber installed inside the hollow cylindrical steel needle, and the top of the optical fiber is coated with a layer of An oxygen sensitive film with a primary oxygen sensitive dye;
[0013] The oxygen sensitive membrane is prepared by using a sol-gel process, tetraethoxysilane (TEOS) and n-octyltriethoxysilane (Octyl-triEOS) as precursors, and porous organic modified silicate is used as a carrier matrix. Finally, As oxygen-sensitive dye;
[0014] Furthermore, the reference probe temperature data of the liquid flow detection unit can be used to perform temperature compensation on the oxygen detection unit and correct the detection result.
[0015] Furthermore, the DataLogger software can perform data preprocessing, set acquisition parameters for the data collector, and connect the PC to the data collector via USB or RS232 to complete text data export and conversion;
[0016] The data collector model is RR-1008, which includes 8 single-ended channels and 4 differential channels. It can efficiently obtain returned text data and calculate and analyze the text data through preset formulas.
[0017] Furthermore, the tree root zone-trunk oxygen diffusion model, based on the water transport model and the soil oxygen diffusion model, establishes an oxygen transfer model from the root zone to the xylem of the sapwood near the trunk, and uses the aboveground measurement data to non-destructively estimate the oxygen environment of the root zone soil;
[0018] The water transport model regards the tree root system as a whole, assuming that the roots at the same soil depth are evenly distributed, and closely connects the soil in the tree root zone with the xylem of the tree trunk through transpiration with water transfer as a link. The oxygen dissolved in the water is transported along with the water, and is transported from the root system to the trunk through the xylem vessels with water as a carrier.
[0019] The soil oxygen diffusion model takes into account the transport of oxygen to the tree roots, which first passes through the porous soil to reach the tree root zone, and then is absorbed by the tree through the boundary layer around the roots. Due to the non-uniformity of the pore size in the soil and the irregularity of the liquid boundary layer around the root zone, the present invention assumes that the liquid boundary layer around the root zone is circular for model construction.
[0020] The data processing flow of the present invention is as follows: the oxygen concentration and liquid flow rate data obtained by the composite sensor are imported into a PC equipped with a Windows system, and the data is pre-processed by DataLogger software. The pre-processed data is input into the large model verification system and compared with the standard data in the large model. The verification system verifies the accuracy of the sensor data through calculation and analysis, and evaluates the health of the oxygen environment in the root zone.
[0021] The verification method of the present invention comprises: comparing the actual monitoring data with the standard data in the large model, calculating the difference between the two. According to the degree of difference, evaluating whether the oxygen environment in the root zone is normal or not. If the difference is within the allowable range, it means that the oxygen environment in the root zone is normal; if the difference exceeds the range, it indicates that there may be an abnormality and further investigation is required.
[0022] The verification results of the present invention can be used to guide tree health management. By accurately monitoring and evaluating the root zone oxygen environment, potential problems can be discovered and dealt with in a timely manner, thereby improving the health and growth quality of trees. The present invention provides a reliable technical method and provides a scientific basis for the evaluation and management of the soil oxygen environment in the root zone of trees.
[0023] The dual-probe oxygen concentration-liquid flow rate composite sensor described in the embodiment of the present invention is combined with a tree root zone-trunk oxygen diffusion model to monitor the oxygen concentration and liquid flow rate in the xylem of the tree trunk at the same position in real time, thereby reducing the damage to the tree caused by using a single sensor to arrange multiple probes, and realizing non-destructive estimation of the soil oxygen environment in the root zone using the measurement data of the aboveground part. BRIEF DESCRIPTION OF THE DRAWINGS
[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.
[0025] Figure 1 It is a structural schematic diagram of a root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to the present invention. Among them, 101 is an oxygen concentration-liquid flow rate composite sensor, 102 is a data processing module, and 103 is a tree root zone-trunk oxygen diffusion model.
[0026] Figure 2 It is a schematic diagram of the probe structure of the oxygen concentration-liquid flow rate composite sensor in the present invention. Among them, 104-oxygen sensitive membrane, 105-thermocouple connector, 106-aluminum tube, 107-stainless steel needle, 108-plastic hub, 109-chrome alloy, 110-copper-nickel alloy, 111-heating wire, 112-positive electrode, 113-negative electrode.
[0027] Figure 3 It is a schematic diagram of the bifurcated optical fiber structure of the oxygen concentration-liquid flow rate composite sensor in the present invention. Among them, 114 is a heating probe and 115 is a reference probe.
[0028] Figure 4 This is a schematic diagram of a verification experiment of the tree root zone-trunk oxygen diffusion model in the present invention, using a galvanic cell type sensor for monitoring. Among them, 116-PVC pipe, 117-waterproof breathable membrane, 118-sealing ring, 119-galvanic cell type oxygen sensor. DETAILED DESCRIPTION
[0029] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in combination with the drawings and specific examples in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. The methods are conventional methods unless otherwise specified. Raw materials can be obtained from public commercial channels unless otherwise specified.
[0030] The research principle of the fiber optic oxygen probe in the composite sensor of the present invention is based on the oxygen measurement principle of photoluminescence and fluorescence quenching. When the excitation light source reaches the oxygen sensitive membrane, the ground state molecules of the fluorescent substance absorb the excitation light to reach the excited state, then deactivate and return to the ground state, and release energy to generate fluorescence. Under a certain oxygen environment, fluorescence quenching occurs between the excited state molecules of the fluorescent substance and the oxygen molecules, resulting in a decrease in fluorescence intensity and a shortened fluorescence lifetime. The generated fluorescence is transmitted back along the optical fiber, undergoes photoelectric conversion, and obtains oxygen concentration data.
[0031] The liquid flow probe in the composite sensor of the present invention adopts the thermal diffusion method based on the Granier principle. The calculation formula of the total liquid flow rate of the trunk is shown in Formula 1:
[0032] F=uA sapwood (1)
[0033] Where F is the total sap flow; u is the average sap flow rate of the trunk; A sapwood is the cross-sectional area of the sapwood at the height of the heating probe. The sap flow rate is calculated from the relationship between the temperature difference between the upper heating probe and the lower reference probe and the sap flow rate.
[0034] The tree root zone-trunk oxygen diffusion model is based on the macroscopic water absorption model and the root-soil oxygen diffusion model. Assuming that the plant root is a cylinder, the root water absorption model can be used to obtain the distribution function S(z) of the cylindrical root water absorption rate along the vertical gradient of the soil:
[0035]
[0036] Among them, L max is the maximum effective root length density; z is the soil depth; L r is the vertical extension depth of the root system; p is the soil water potential, α(p) is the water stress response function, Tr is the crop transpiration rate, S i is the xylem sap flow rate, A canopy is the canopy projection area, A sapwood is the sapwood area.
[0037] At the same time, the xylem sap flow rate Si and oxygen concentration Ci are obtained by using the near-ground oxygen concentration-sap flow rate composite sensor, and then the relationship between the root water absorption rate S(z) and the plant root oxygen concentration Cr(z) at the soil depth z is obtained. The principle formula of the tree root zone-trunk oxygen diffusion model can be further deduced as follows. After calculation, the soil gas phase oxygen concentration in the plant root zone can be obtained:
[0038]
[0039] Where C(z) is the gas-phase oxygen concentration in the soil at the root when the soil depth is z; z is the soil depth; R is the radius of the liquid boundary layer around the root plus the root radius; a is the root radius; C i is the oxygen concentration; S(z) is the root water absorption rate distribution function along the vertical gradient of the soil when the soil depth is z; D1 is the diffusion coefficient of oxygen in the soil liquid phase; α is the Bunsen absorption coefficient, which is equivalent to the gas solubility per unit volume of water under normal pressure (101.3 kPa); S i is the xylem sap flow rate; C w (Z) is the oxygen concentration in the liquid phase on the root surface at soil depth z.
[0040] The specific structure and working mode of the present invention are further explained below in conjunction with the accompanying drawings.
[0041] like Figure 1 As shown, a root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the sapwood xylem of a tree mainly includes an oxygen concentration-liquid flow rate composite sensor 101, a data processing module 102, and a tree root zone-trunk oxygen diffusion model 103. The oxygen concentration-liquid flow rate composite sensor 101 uses an optical fiber with a double-probe structure, which is used to measure the sap flow rate and oxygen content in the xylem of the trunk, and transmits the measured data to the data processing module 102. The PC of the data processing module 102 has Datalogger software for data processing, and transmits the processed data to the tree root zone-trunk oxygen diffusion model 103. The tree root zone-trunk oxygen diffusion model takes the oxygen concentration and sap flow rate of the xylem of the sapwood near the trunk as input, and finally outputs the oxygen concentration gradient on the transmission path, establishes an oxygen spatial distribution mapping chain, and realizes the estimation of soil oxygen concentration.
[0042] like Figure 2As shown in the figure, the double probe structure of the oxygen concentration-liquid flow rate composite sensor, the upper probe is the heating probe of the thermal diffusion liquid flow sensor, which contains a heating element and a thermocouple, and the lower probe is the fiber optic oxygen probe and the reference probe of the thermal diffusion liquid flow sensor, which contains a thermocouple and an optical fiber. The probe body is two hollow cylindrical steel needles, and a chromium alloy-copper nickel alloy (E type) thermocouple is used inside the steel needle as a temperature probe to obtain temperature data. Among them, the upper probe is tightly wrapped with a circle of heating resistance wire on the outer layer of the stainless steel needle, and the resistance wire is equipped with an aluminum tube outside. The top of the optical fiber of the lower probe is coated with a layer of Oxygen sensitive film with oxygen sensitive dye as the main component.
[0043] The present invention will be further described below in conjunction with specific examples, but the present invention is not limited to the following examples. Methods are conventional methods unless otherwise specified, and raw materials can be obtained from public commercial channels unless otherwise specified.
[0044] Example 1 Preparation of oxygen sensitive membrane
[0045] The preparation process of the oxygen sensitive film at the top of the optical fiber of the lower probe of the oxygen concentration-liquid flow rate composite sensor of the present invention is as follows: first, 4 ml of tetraethoxysilane (TEOS, Kaimart (Tianjin) Chemical Technology Co., Ltd., purity 98%) and 0.2 ml of n-octyltriethoxysilane (Octyl-triEOS, Tianjin Xiensiopude Technology Co., Ltd., purity 98%) are mixed into a precursor solution, 1.25 ml of ethanol and 0.4 ml of 0.1 mol·L -1 Hydrochloric acid was added to the sol solution, and the lid was sealed and magnetically stirred for 1 h. During the stirring process, 0.1 ml of Triton-X-100 (Beijing Haosai Technology Co., Ltd.) was added. (Shanghai Myrel Chemical Technology Co., Ltd.) was dissolved in 10 ml of ethanol to form an oxygen sensitive solution; 2 mg of coumarin (AFC, Tianjin Xiensiopude Technology Co., Ltd.) was dissolved in 5 ml of ethanol and 5 ml of (3-isocyanatopropyl) triethoxysilane (TESPIC, Tianjin Xiensiopude Technology Co., Ltd., purity 95%) to obtain a reference solution; 0.5 ml of the oxygen sensitive solution and 0.5 ml of the reference solution were mixed into 1 ml of the precursor solution to prepare a composite sensitive dye. The composite sensitive material was coated on the end face of the optical fiber and dried to form an oxygen sensing film.
[0046] Example 2: Galvanic cell sensor monitors soil oxygen concentration in the root zone of trees
[0047] A galvanic oxygen sensor is used to continuously monitor the soil oxygen concentration in the tree root zone. Figure 4As shown in the figure, a PVC pipe with an inner diameter of 23 mm was selected and cut into four sections of 0.5 m, 1 m, 1.5 m and 2 m in length. The oxygen sensor was installed in the PVC pipe, and the interfaces at both ends were sealed with sealing rings to prevent air from entering the soil along the PVC pipe and affecting the test results. After the sensor was installed, four holes with a diameter of 23 mm and a depth of 0.5 m, 1 m, 1.5 m and 2 m were dug out at a distance of 1 m from the tree trunk using a special soil shovel. The PVC pipe equipped with the oxygen sensor was inserted into the soil to measure the changes in oxygen concentration at different depth gradients near the root zone. Each oxygen sensor recorded the soil oxygen concentration in the root zone at intervals of 1 minute, and the average value was taken over an interval of 10 minutes using a data logger.
[0048] The oxygen concentration obtained by analyzing the oxygen diffusion model from the root zone to the trunk is compared with the soil oxygen concentration data measured by the galvanic oxygen sensor during the test. The present invention uses paper mulberry as the research object for the experiment. The results measured by the galvanic oxygen sensor are as follows: the average oxygen concentration of the soil gas phase at a depth of 0.5m is 19.38%, the average oxygen concentration of the soil gas phase at a depth of 1m is 17.92%, the average oxygen concentration of the soil gas phase at 1.5m is 16.51%, and the average oxygen concentration of the soil gas phase at a depth of 2.0m is 13.41%. The results estimated by the oxygen diffusion model from the root zone to the trunk are: the soil gas phase oxygen concentration at the root of 0.5m is 18.2649%, the soil gas phase oxygen concentration at the root of 1.0m is 16.2666%, the soil gas phase oxygen concentration at the root of 1.5m is 13.5826%, and the soil gas phase oxygen concentration at the root of 2.0m is 11.9549%. It can be seen from the above data that the four gradient estimation errors are all less than 3%, which further illustrates the effectiveness of the tree root zone-trunk oxygen diffusion model of the present invention.
[0049] Finally, it should be noted that the above embodiments are only used to illustrate the specific technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the above embodiments, a person skilled in the art should also understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features can be replaced by equivalents. Therefore, these modifications or improvements made without departing from the spirit of the present invention are within the scope of protection claimed by the present invention.
Claims
1. A root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood, characterized by: The system includes an oxygen concentration-liquid flow rate composite sensor, a data processing module, and a tree root zone-trunk oxygen diffusion model; The oxygen concentration-liquid flow rate composite sensor adopts a bifurcated optical fiber with a double-probe structure, including an upper and a lower probe; the upper probe is a heating probe of a thermal diffusion liquid flow sensor, which contains a heating element and a thermocouple, and the lower probe is an optical fiber oxygen probe and a reference probe of a thermal diffusion liquid flow sensor, which contains a thermocouple and an optical fiber; the probe body is two hollow cylindrical steel needles, and a chromium alloy-copper-nickel alloy (E type) thermocouple is used inside the steel needle as a temperature probe to obtain temperature data; The core of the data processing module is a PC equipped with Windows system; the PC equipped with Windows system is installed with DataLogger software; The tree root zone-trunk oxygen diffusion model takes the oxygen concentration and sap flow rate of the xylem of the sapwood near the trunk as input, and the oxygen concentration gradient on the xylem sap flow transmission path as output, establishes an oxygen spatial distribution mapping chain, and realizes a quantitative description of the oxygen transmission process.
2. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 1, characterized in that: The temperature probe of the composite sensor uses chromium alloy and copper-nickel alloy thermocouple wires with a diameter of 0.127 mm, forms a thermocouple joint by welding, and is insulated from the inner wall of the probe.
3. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 1, characterized in that: The upper probe has a circle of heating resistance wire tightly wound around the outer layer of the stainless steel needle, and an aluminum tube is arranged outside the resistance wire.
4. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 1, characterized in that: The lower reference probe has an optical fiber installed inside a hollow cylindrical steel needle, and the top of the optical fiber is coated with a layer of Oxygen sensitive film with oxygen sensitive dye as the main component.
5. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 4, characterized in that: The oxygen sensitive membrane is prepared by using a sol-gel process, tetraethoxysilane (TEOS) and n-octyltriethoxysilane (Octyl-triEOS) as precursors, and porous organic modified silicate is used as a carrier matrix. Finally, As oxygen sensitive dye.
6. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 1, characterized in that: The reference probe temperature data of the liquid flow detection unit can be used to perform temperature compensation on the oxygen detection unit and correct the detection result.
7. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 1, characterized in that: The DataLogger software can perform data preprocessing, set acquisition parameters for the data logger, and connect the PC to the data logger via USB or RS232 to complete text data export and conversion.
8. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 7, characterized in that: The data collector model is RR-1008, which includes 8 single-ended channels and 4 differential channels. It can efficiently obtain returned text data and calculate and analyze the text data through preset formulas.
9. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 1, characterized in that: The tree root zone-trunk oxygen diffusion model establishes an oxygen transfer model from the root zone to the xylem of the sapwood near the trunk based on the water transport model and the soil oxygen diffusion model, and non-destructively estimates the soil oxygen environment in the root zone based on the measurement data of the aboveground part.
10. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 9, characterized in that: The water transport model regards the tree root system as a whole, assuming that the roots at the same soil depth are evenly distributed, and uses transpiration to closely connect the soil in the tree root zone and the xylem of the trunk with water transfer. The oxygen dissolved in the water is transported along with water and is transported from the root system to the trunk through the xylem vessels with water as the carrier.
11. The root zone soil oxygen environment analysis system and method for monitoring water-oxygen in the xylem of tree sapwood according to claim 9, characterized in that: The soil oxygen diffusion model takes into account the transport of oxygen to the tree roots, which first passes through the porous soil to reach the tree root zone, and then is absorbed by the tree through the boundary layer around the roots. Due to the non-uniformity of the pore size in the soil and the irregularity of the liquid boundary layer around the root zone, the present invention assumes that the liquid boundary layer around the root zone is circular for model construction.