A method for in-situ rapid acquisition of soil hydraulic parameters based on moisture infiltration process

Abstract

The application discloses a method for in-situ rapid acquisition of soil hydraulic parameters based on water infiltration process, adopts a brand-new derivation method, derives an analytical solution which can accurately describe one-dimensional water infiltration of homogeneous soil under constant water head boundary conditions based on Richards water flow control equation and Brooks-Corey model, first depicts the important infiltration characteristics that the saturation zone grows with time, and can more accurately simulate the soil water infiltration process. Based on the inverse process of the analytical solution, a parameter optimization estimation method is provided. The method only needs to measure the change data of cumulative infiltration and wetting zone length with time in the water infiltration process through a time domain reflectometer (TDR), and can rapidly acquire the soil hydraulic characteristics in-situ in a field. The calculation method is low in cost, stable in inversion process, avoids problems such as multiple solutions of parameters and non-convergence, and provides a powerful acquisition means for parameters required by large-area watershed hydrological simulation.

Description

Technical Field

[0001] This invention relates to a method for rapidly obtaining soil hydraulic parameters in situ based on the water infiltration process, belonging to the field of farmland irrigation and soil hydrological measurement technology. Background Technology

[0002] Soil hydraulic properties (soil moisture characteristic curves, saturated / unsaturated hydraulic conductivity) are fundamental input parameters for simulating soil moisture movement in the vadose zone. Due to the relatively large spatiotemporal variability of soil hydraulic properties, determining representative and accurate values ​​for soil hydraulic parameters within a region or watershed is a massive and time-consuming task. Therefore, developing simple, low-cost, and time-saving methods is crucial for studying soil hydraulic properties within a region or watershed.

[0003] Traditional methods for obtaining soil hydraulic parameters typically rely on ring sampling and laboratory analysis. This method requires expensive equipment (such as sandboxes, suction plate apparatus, pressure membrane apparatus, and centrifuges) and acquires parameters through a slow drainage process. Furthermore, saturated hydraulic conductivity needs to be measured separately using an additional constant or variable head method, which is time-consuming, labor-intensive, and costly. Vertical infiltration or horizontal adsorption tests represent relatively rapid soil moisture movement processes and are often used to indirectly and quickly obtain soil hydraulic parameters. These methods often employ numerical inversion to obtain parameters, which suffers from problems such as non-convergence and multiple solutions. Inversion based on approximate solutions is currently the most promising development direction. Many approximate solutions exist for infiltration problems, but their accuracy is insufficient to support the need for inversion and prediction of soil hydraulic parameters. One important reason is that current infiltration formulas do not consider the important characteristic of the saturation zone increasing over time during infiltration. In addition, soil structure is particularly important for hydraulic properties, but using ring sampling to collect undisturbed soil samples for laboratory measurement inevitably damages the undisturbed soil structure during sampling and transportation, leading to distorted measurement results. Therefore, there is an urgent need to develop a method for rapidly obtaining soil hydraulic properties parameters that can be directly applied in situ in the field. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for rapidly obtaining soil hydraulic parameters in situ based on the water infiltration process.

[0005] The technical solution adopted in this invention is as follows:

[0006] A method for rapidly obtaining soil hydraulic parameters in situ based on the water infiltration process, comprising the following steps:

[0007] (4) Measure the saturated water content θ of the soil. s Initial water content θ i Retention water content θ r ;

[0008] (5) For the in-situ one-dimensional water infiltration process in the field under waterlogged conditions, the cumulative infiltration amount I and the length of the wetted zone z were measured and obtained. f Relationship with the infiltration time t;

[0009] (6) Optimize and calculate the parameters n and h to be determined based on the objective function (9). d and K s

[0010]

[0011] In the above formula: I i and These are the observed values ​​and the predicted values ​​from the analytical model for cumulative infiltration, respectively; z f,i and These are the observed value and the predicted value of the wet zone length, respectively; N is the total number of observations.

[0012] Preferably, in step (3), the Levenberg-Marquardt algorithm is used to optimize the objective function (9). The algorithm's idea is to estimate the correct parameters n and h to be determined. d and K s This minimizes the objective function (9), where the estimated value is... and Obtained through the following methods:

[0013] For a given set of estimated parameters n e h d,e and K s,e For any infiltration time t, the saturation zone length z is obtained from formula (5) using the Newton-Simpson method. s The estimated value

[0014]

[0015] Based on the above method, the obtained The estimated value of the cumulative infiltration I is obtained by formula (6).

[0016]

[0017] The length z of the wetted area is calculated using formula (7). f The estimated value

[0018]

[0019] The unknown parameter in the above formula is defined as follows:

[0020]

[0021] Preferably, the method for obtaining the parameters in steps (1) and (2) is as follows:

[0022] Before infiltration, the TDR probe is inserted into the soil to be tested, and the water head height is h. p In the water infiltration test, the time-domain reflectometry signal of the TDR probe was collected starting before infiltration to calculate the initial soil moisture content θ. i and saturated water content θ s The soil was sampled using a ring sampler to measure its retained water content θ. r Because of the retained water content θ r Determined solely by soil texture, in-situ destructive sampling can be conducted after infiltration is complete. Indoor drainage tests at 15 bar are performed using a pressure membrane apparatus, and θ is determined by gravimetric analysis. r ;

[0023] During the infiltration of accumulated water, the time series data of the wetting front is obtained in real time by interpreting the waveform of the time-domain TDR. f ~t, and the time series data of cumulative infiltration I~t.

[0024] Preferably, the method for obtaining the parameters in steps (1) and (2) is more specifically as follows:

[0025] A. Before water infiltration, insert a TDR probe of length L vertically and completely into the soil to be tested until the tip of the probe is flush with the soil. Before water infiltration begins, use a time domain reflectometer to measure and collect the TDR probe reflection signal at a certain frequency. Continue collecting until the wetting front exceeds the probe length and the probe monitoring soil layer reaches saturation.

[0026] B. No wetting front was observed in the TDR measurement area before and at the end of infiltration. The apparent positions of the probe head and tail before infiltration were extracted from the TDR reflected signal waveform, and then the apparent length L of the soil layer monitored by the initial TDR probe was obtained. ad The apparent positions of the probe head and tail at the end of infiltration are also obtained, thus acquiring the apparent length L of the soil layer monitored by the TDR probe at saturation. as The initial average dielectric constant K of the monitored soil layer was calculated using electromagnetic wave propagation theory. ad =(L ad / L) 2 and the average dielectric constant K at saturation as =(L as / L) 2 Then, using the relationship between soil moisture content and dielectric constant, K ad and K as Converted to initial soil moisture content θ iand saturated water content θ s ;

[0027] C. After infiltration begins, the TDR reflected signal waveform at each moment in the TDR-measured interval, from the wetting front to the probe tail, shows the apparent length L of the soil layer monitored by the TDR probe. a and the apparent length L of the wetted area aw According to L a The average dielectric constant K of the monitored soil layer was calculated. a =(L a / L) 2 The average dielectric constant K of the soil layer was monitored using a TDR probe by utilizing the relationship between soil moisture content and dielectric constant. a Converting this to real-time average moisture content θ, and then calculating the cumulative soil infiltration I = L*(θ - θ) i The time series data I-t of the cumulative infiltration amount and the length z of the wetted zone were obtained. f =L*(L ad -L a +L aw ) / L ad Time series data z of the length of the wet region was obtained. f ~t.

[0028] Preferably, in step (C), the apparent positions of the wetting front and the probe tail in the TDR waveform are extracted using the second derivative method, specifically as follows: The first and second derivatives of the waveform data are calculated respectively. After the location where the maximum value of the first derivative occurs, the first zero point of the first derivative of the waveform data is determined as the apparent position X corresponding to the TDR probe head. h The second derivative in X h The locations where the second and third local maxima occur are respectively the apparent locations X corresponding to the wetting front. f The apparent position X corresponding to the tail of the TDR probe e Monitoring the apparent length L of the soil layer a X is the distance X between the apparent positions of the probe head and tail. e -X h ; Apparent length L of the wetted region aw X is the distance X between the apparent positions of the probe head and tail. f -X h .

[0029] The beneficial effects of this invention are as follows:

[0030] Compared with existing technologies, this invention employs a novel derivation method, utilizing the Richards flow control equation and the Brooks-Corey model to derive an analytical solution to the one-dimensional water infiltration problem in homogeneous soil under constant head boundary conditions. This provides the first detailed characterization of the important infiltration characteristic of the saturated zone increasing over time, enabling a more accurate description of the soil water infiltration process. Furthermore, this invention develops a method for obtaining soil hydraulic parameters by reversing the analytical solution of one-dimensional water infiltration in homogeneous soil under waterlogged conditions. Combined with Time Domain Reflectometer (TDR) technology, it only requires real-time recording of reflection waveforms during in-situ waterlogging infiltration experiments in the field to interpret the changes in cumulative infiltration and wetted zone length over time, thus obtaining complete soil hydraulic parameters. This method offers stable parameter inversion, low computational cost, and avoids problems such as multiple solutions and non-convergence, providing a powerful tool for efficiently obtaining parameters required for large-scale watershed or regional hydrogeochemical cycle process modeling. Attached Figure Description

[0031] Figure 1 This is a flowchart of the calculation process of the present invention;

[0032] Figure 2 This is a comparison chart of the changes in the length of the wetted zone observed by the TDR method and conventional methods;

[0033] Figure 3 This is a comparison chart of the cumulative infiltration changes between analytical simulation and experimental observation;

[0034] Figure 4 This is a comparison between the soil moisture characteristic curve predicted by the method of this invention and the measured results of the pressure membrane method. Detailed Implementation

[0035] The following description, in conjunction with the accompanying drawings, further illustrates the content of the present invention, but should not be construed as limiting the invention. Modifications and substitutions made to the methods, steps, or conditions of the present invention without departing from the spirit and essence of the invention are all within the scope of the invention. Unless otherwise specified, the technical means used in the following embodiments are conventional means well known to those skilled in the art. Figure 1 The calculation process of this invention is explained.

[0036] Example 1

[0037] Technical Principle: Based on Richard's flow control equations and the Brooks-Corey model, the flux assumption, and the integral mean value theorem, a profile equation describing soil water infiltration is obtained. Then, based on the principle of mass conservation and the profile equation, a complete analytical model describing one-dimensional water infiltration in homogeneous soil under constant head boundary conditions is derived. Among them:

[0038] Richard's flow control equations and their initial and boundary condition expressions are as follows:

[0039]

[0040] In the formula: θ and θ i Soil moisture content and initial soil moisture content (cm) 3 cm -3 ), t is the infiltration time, z is the vertical coordinate, and K is the soil hydraulic conductivity (cm / min). -1 h is the soil matrix suction (cm), h p It is the depth of water accumulation in the soil surface layer (cm).

[0041] The Brooks-Corey model used to describe the relationship between soil unsaturated hydraulic conductivity, soil matric potential, and soil water content are expressed as follows:

[0042]

[0043]

[0044] In the formula: θ s and θ r These are soil saturated water content and retained water content (cm). 3 cm -3 ), K s Soil saturated hydraulic conductivity (cm min) -1 ), where n is the soil pore size distribution index, h d It is the soil air intake suction value (cm), m=3n+2.

[0045] Equation (4) describes the relationship between effective soil water saturation S and soil depth z (cm) in a one-dimensional water infiltration profile. In equation (4), z f z is the length of the wetted area (cm). s The length of the saturation region (cm)

[0046]

[0047] Formula (5) describes the length z of the saturated zone in the soil moisture profile during infiltration. s Quantitative relationship with infiltration time t (min)

[0048]

[0049] Formula (6) describes the length z of the saturated zone in the soil moisture profile during infiltration. s (cm) and the length of the wetted area z f Quantitative relationship of (cm)

[0050]

[0051] Formula (7) describes the length z of the saturated zone in the soil moisture profile during infiltration. s The quantitative relationship between (cm) and cumulative infiltration I (cm)

[0052]

[0053] In the formula: θ i It is the initial water content, K i Hydraulic conductivity (cm min) at initial soil moisture content -1 The remaining unknown parameters are defined as follows:

[0054]

[0055] By reversing the above analytical model, a method for obtaining soil hydraulic parameters (n, h) is obtained. d and K s The optimization calculation method is as follows:

[0056] Step 1, for constant head conditions (h) p The in-situ one-dimensional water infiltration process in the field was measured to obtain the cumulative infiltration volume I and the length of the wetted zone z. f Data on changes over infiltration time t;

[0057] Step 2: Measure the saturated water content θ of the soil. s Initial water content θ i Retention water content θ r Based on the above parameters and the datasets I~t and z obtained from the measurements... f ~t, the parameters n and h to be determined are calculated by optimizing the objective function (9). d and K s :

[0058]

[0059] In the formula: and I i These are the observed values ​​and the predicted values ​​from the analytical model for the cumulative infiltration, respectively. and z f,i These are the observed value and the predicted value of the wet zone length, respectively; N is the total number of observations.

[0060] The objective function (9) is optimized using the Levenberg-Marquardt algorithm, whose core idea is to estimate the correct parameters (n, h) to obtain the desired result. d and K s This makes the objective function (9) reach its minimum value, and the estimated value in the formula is... and The parameters are obtained as follows: for a given set of estimated parameters (n) e h d,e and K s,e For any infiltration time t, the saturation zone length z can be calculated using the Newton-Simpson method according to formula (5). s The estimated value

[0061]

[0062] Based on the above The estimated value of the cumulative infiltration I can be calculated using formula (7).

[0063]

[0064] The length z of the moist front can be calculated using formula (6). f The estimated value

[0065]

[0066] In the formula: the parameters are defined as above.

[0067] Example 2

[0068] Step 1: Collect red soil from Yingtan, Jiangxi Province (28.202942°N, 116.948483°E, sand 20.9%, silt 34.9%, clay 44.2%), air-dry, crush, and pass through a 2mm sieve, according to 1.29g cm⁻¹. -3 The bulk density of the soil was measured and placed into an acrylic glass column with an inner diameter of 19 cm and a length of 30 cm. Before the infiltration test, a 30 cm long time-domain TDR probe was first inserted into the soil surface, and the initial water content θ of the soil to be tested was obtained by time-domain TDR measurement. i =0.058cm cm -3 Since the initial moisture content is relatively low, the retained moisture content is temporarily approximated by the initial moisture content, i.e., θ. r =0.058cm cm -3 In practical applications, if a more accurate value of retained moisture content is required, a ring sample can be taken within 0.5m of the study area and brought back to the laboratory to be measured using a pressure membrane analyzer.

[0069] Step 2: Subsequently, a constant pressure water supply is provided using an industry-standard Marshall bottle, with a water head height of h. pA water infiltration test with a depth of 1 cm was conducted, equipped with an automatic water level monitoring and acquisition system. During the water infiltration process, real-time reflected waveform signals of the tested soil were acquired using time-domain TDR. Waveform analysis and interpretation were used to obtain data sequences I~t and z of the cumulative infiltration amount and the length of the wetted zone over time. f ~t( Figure 2 and 3 (Observed values). After the infiltration test, water was supplied until the soil column was saturated, and then the soil saturation water content θ was measured using a TDR. s =0.513cm cm -3 .

[0070] Step 3, based on the known parameter θ i θ s θ r and h p The time series data I-t of the measured cumulative infiltration and the time series data z of the wetting front. f ~t, using the Levenberg-Marquardt algorithm to optimize formula (9), and then simultaneously estimate the parameters n and h. d and K s The estimated results are compared with the measured values ​​from the standard pressure diaphragm method and the constant head method, as shown in Table 1 and... Figure 4 As shown in the table, it can be seen that the method for estimating soil hydraulic parameters using the present invention is an accurate method.

[0071] Table 1. Comparison between soil hydraulic parameters estimated based on this invention and measured soil hydraulic parameters.

[0072] n <![CDATA[h d (cm)]]> <![CDATA[K s (cm min. -1 )]]> Measured value 0.17 1.2 0.079 estimated value 0.1965 2.588 0.081 .

[0073] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for rapidly obtaining soil hydraulic parameters in situ based on the water infiltration process, characterized in that... The steps include: (1) Measure the saturated water content θ of the soil. s Initial water content θ i Retention water content θ r ; (2) For the one-dimensional in-situ water infiltration process in the field under waterlogged conditions, after the infiltration begins, the apparent length L of the soil layer monitored by the TDR probe is extracted from the TDR reflection signal waveform before the wetting front reaches the tail of the TDR probe at each time point in the interval measured by the TDR probe. a and the apparent length L of the wetted area aw According to L a The average dielectric constant K of the monitored soil layer was calculated. a =(L a / L) 2 The average dielectric constant K of the soil layer was monitored using a TDR probe by utilizing the relationship between soil moisture content and dielectric constant. a Converting this to real-time average moisture content θ, and then calculating the cumulative soil infiltration I = L*(θ - θ) i The time series data I-t of the cumulative infiltration amount and the length z of the wetted zone were obtained. f =L*(L ad -L a +L aw ) / L ad Time series data z of the length of the wet region was obtained. f ~t, where L is the length of the TDR probe, L ad To monitor the apparent length of the soil layer using an initial TDR probe; (3) Optimize and calculate the parameters n and h to be determined based on the objective function (9). d and K s In the above formula: I i and These are the observed values ​​and the predicted values ​​from the analytical model for cumulative infiltration, respectively; z f,i and These represent the observed length of the wet region and the predicted length from the analytical model, respectively; N is the total number of observations, and K... s Where is the soil saturated hydraulic conductivity, n is the soil pore size distribution index, and h is the soil saturated hydraulic conductivity. d It is the soil air intake suction value; In step (3), the Levenberg-Marquardt algorithm is used to optimize the objective function (9) by estimating the correct parameters n and h. d and K s This minimizes the objective function (9), where the predicted value is... and Obtained through the following methods: For a given set of estimated parameters n e h d,e and K s,e For any infiltration time t, the saturation zone length z is obtained from formula (5) using the Newton-Simpson method. s Predicted value Based on the above method, the obtained The predicted value of cumulative infiltration I is calculated using formula (6). K i The hydraulic conductivity at the initial soil moisture content is used to calculate the length z of the moist zone using formula (7). f Predicted value The unknown parameter in the above formula is defined as follows: h p This refers to the water head height.

2. The method for rapidly obtaining soil hydraulic parameters in situ based on the water infiltration process according to claim 1, characterized in that... The specific methods for obtaining the parameters in steps (1) and (2) are as follows: Before infiltration, the TDR probe is inserted into the soil to be tested, and the water head height is h. p In the water infiltration test, the time-domain reflectometry signal of the TDR probe was collected starting before infiltration to calculate the initial soil moisture content θ. i and saturated water content θ s The soil was sampled using a ring sampler to measure its retained water content θ. r ; Time-series data of the wetted zone length were obtained in real time by interpreting the reflection waveform of the TDR during the water infiltration process. f ~t, and the time series data of cumulative infiltration I~t.

3. The method for rapidly obtaining soil hydraulic parameters in situ based on the water infiltration process according to claim 2, characterized in that... The method for obtaining the parameters in step (1) is more specifically as follows: A. Before water infiltration, insert a TDR probe of length L vertically and completely into the soil to be tested until the tip of the probe is flush with the soil. Before water infiltration begins, use a time domain reflectometer to measure and collect the TDR probe reflection signal at a certain frequency. Continue collecting until the wetting front exceeds the probe length and the probe monitoring soil layer reaches saturation. B. No wetting front was observed in the TDR measurement area before and at the end of infiltration. The apparent positions of the probe head and tail before infiltration were extracted from the TDR reflected signal waveform, and then the apparent length L of the soil layer monitored by the initial TDR probe was obtained. ad The apparent positions of the probe head and tail at the end of infiltration are also obtained, thus acquiring the apparent length L of the soil layer monitored by the TDR probe at saturation. as The initial average dielectric constant K of the monitored soil layer was calculated using electromagnetic wave propagation theory. ad =(L ad / L) 2 and the average dielectric constant K at saturation as =(L as / L) 2 Then, using the relationship between soil moisture content and dielectric constant, K ad and K as Converted to initial soil moisture content θ i and saturated water content θ s .

4. The method for rapidly obtaining soil hydraulic parameters in situ based on the water infiltration process according to claim 3, characterized in that: In step (2), the apparent positions of the wetting front and the probe tail in the TDR waveform are extracted using the second derivative method, as follows: The first and second derivatives of the waveform data are calculated respectively. After the location where the maximum value of the first derivative occurs, the first zero point of the first derivative of the waveform data is determined to be the apparent position X corresponding to the head of the TDR probe. h The second derivative in X h The locations where the second and third local maxima occur are respectively the apparent locations X corresponding to the wetting front. f The apparent position X corresponding to the tail of the TDR probe e ; Monitoring the apparent length L of the soil layer a X is the distance X between the apparent positions of the probe head and tail. e -X h ; Apparent length L of the wetted region aw X is the distance X between the apparent positions of the probe head and tail. f -X h .

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