Iterative methods, devices, equipment, media, and programs for unsaturated soil water movement equations

Abstract

This invention discloses an iterative method, apparatus, equipment, medium, and program product for unsaturated soil water movement equations, relating to the field of soil water movement simulation technology. The method includes: during the iterative solution of the unsaturated soil water movement equation using the Newton-Raphson iteration method, detecting whether a grid cell is in an extreme moisture content region based on the previous soil water negative pressure value and the previous soil volumetric water content; when the grid cell is an anomalous grid cell, comparing the current soil water negative pressure value, the previous soil water negative pressure value, and a reference soil water negative pressure value; performing a consistency check on the current comparison result and the previous comparison result to determine the local iterative instability detection result of the anomalous grid cell; and correcting the current soil water negative pressure value based on the reference soil water negative pressure value when local iterative instability exists in the anomalous grid cell. The technical solution of this invention can improve the computational efficiency and stability of soil water numerical simulation under complex conditions.

Description

Technical Field

[0001] This invention relates to the field of soil water movement simulation technology, and in particular to an iterative method, apparatus, equipment, medium, and program product for unsaturated soil water movement equations. Background Technology

[0002] The vadose zone is a crucial transitional area connecting surface water and groundwater, determining the distribution of precipitation and irrigation water among infiltration, surface runoff, groundwater recharge, and evapotranspiration. Especially in thick vadose zones, soil moisture dynamics directly impact groundwater recharge estimations and surface-groundwater coupling simulation results. Therefore, accurately simulating unsaturated zone water transport processes is of great significance for refined water resource management and regulation.

[0003] Currently, research on soil moisture transport processes mainly relies on numerical simulation methods. Among these, the Richards equation (the equation for unsaturated soil water movement) is the most commonly used governing equation to describe unsaturated water flow. However, since both soil moisture content and unsaturated hydraulic conductivity exhibit highly nonlinear variations with pressure head, the Richards equation (the equation for unsaturated soil water movement) usually forms a highly nonlinear algebraic equation system after discretization. Its solution efficiency and stability are highly dependent on nonlinear iterative methods.

[0004] Most existing mainstream soil water models employ Picard-type iterative methods (Picard successive approximation methods) for solution. While these methods are relatively simple to compute and generally exhibit good overall stability, they often require a large number of iterations under strongly nonlinear conditions due to their linear convergence characteristics, leading to a significant decrease in computational efficiency. Therefore, a locally stable correction method that balances computational efficiency and solution stability is urgently needed to improve the computational efficiency and stability of numerical simulations of soil water under complex conditions. Summary of the Invention

[0005] This invention provides an iterative method, apparatus, equipment, medium, and program product for unsaturated soil water movement equations, which can improve the computational efficiency and stability of soil water numerical simulation under complex conditions.

[0006] According to one aspect of the present invention, an iterative method for unsaturated soil water movement equations is provided, the method comprising: In the process of iteratively solving the equation of unsaturated soil water movement using the Newton iteration method, the current soil water negative pressure value of each grid cell in the current iteration layer, the previous soil water negative pressure value of each grid cell in the previous iteration layer, and the previous soil volume water content are obtained. For a single grid cell, based on the previous soil water negative pressure value and the previous soil volume moisture content of the previous iteration layer, it is detected whether the grid cell is an abnormal grid cell in the extreme moisture content region. For a single grid cell, when the grid cell is an abnormal grid cell, the current soil water negative pressure value and the previous soil water negative pressure value are compared with the reference soil water negative pressure value to obtain the current comparison result and the previous comparison result. For a single anomalous grid cell, a consistency check is performed on the current comparison result and the previous comparison result to determine the local iterative instability detection result of the anomalous grid cell; For a single abnormal grid cell, when the abnormal grid cell exhibits local iterative instability, the current soil water negative pressure value is corrected based on the reference soil water negative pressure value.

[0007] According to another aspect of the present invention, an iterative apparatus for unsaturated soil water movement equations is provided, the apparatus comprising: The iterative data acquisition module is used to acquire the current soil water negative pressure value of each grid cell in the current iteration layer, the previous soil water negative pressure value of each grid cell in the previous iteration layer, and the previous soil volume water content during the iterative solution of the unsaturated soil water movement equation using the Newton iteration method. An abnormal grid cell detection module is used to detect, for a single grid cell, whether the grid cell is an abnormal grid cell in an extreme moisture content region, based on the previous soil water negative pressure value and the previous soil volume moisture content of the previous iteration layer. The soil water negative pressure value comparison module is used to compare the current soil water negative pressure value and the previous soil water negative pressure value with the reference soil water negative pressure value when the grid cell is an abnormal grid cell, for a single grid cell, to obtain the current comparison result and the previous comparison result. The local iterative instability detection module is used to perform consistency detection on the current comparison result and the previous comparison result for a single abnormal grid cell, and determine the local iterative instability detection result of the abnormal grid cell; The current soil water negative pressure value correction module is used to correct the current soil water negative pressure value based on the reference soil water negative pressure value when a single abnormal grid cell exhibits local iterative instability.

[0008] According to another aspect of the present invention, an electronic device is provided, the electronic device comprising: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor, which enables the at least one processor to perform the iterative method for unsaturated soil water movement equations according to any embodiment of the present invention.

[0009] According to another aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to execute and implement the iterative method for the unsaturated soil water movement equations according to any embodiment of the present invention.

[0010] According to another aspect of the present invention, a computer program product is provided, the computer program product comprising a computer program that, when executed by a processor, implements the iterative method for unsaturated soil water movement equations according to any embodiment of the present invention.

[0011] The technical solution of this invention involves obtaining the current soil water negative pressure value, the previous soil water negative pressure value, and the previous soil volumetric water content of each grid cell in the current iteration layer during the iterative solution of the unsaturated soil water movement equation using the Newton-Raphson iteration method. For a single grid cell, based on the previous soil water negative pressure value and the previous soil volumetric water content, it detects whether the grid cell is an abnormal grid cell in an extreme water content region. When the grid cell is an abnormal grid cell, the current soil water negative pressure value and the previous soil water negative pressure value are compared with a reference soil water negative pressure value to obtain the current comparison result and the previous comparison result. The results are compared, and consistency checks are performed between the current comparison results and the previous comparison results to determine the local iterative instability detection results of abnormal grid cells. When local iterative instability exists in abnormal grid cells, the current soil water negative pressure value is corrected according to the reference soil water negative pressure value. A local cell stabilization correction mechanism is introduced. By detecting whether the current soil water negative pressure value and the previous soil water negative pressure value cross the reference soil water negative pressure value, local stabilization correction is performed on abnormal grid cells, thereby reducing the instability risk of Newton iteration under strong nonlinear conditions. While maintaining the high solution efficiency of the Newton iteration method, the stability and robustness of the numerical solution of the unsaturated soil water motion equation are improved.

[0012] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1This is a flowchart of an iterative method for the equation of motion of unsaturated soil water according to Embodiment 1 of the present invention; Figure 2 This is a flowchart of an iterative method for the equation of motion of unsaturated soil water according to Embodiment 2 of the present invention; Figure 3 This is a flowchart of an iterative method for the equation of motion of unsaturated soil water according to Embodiment 3 of the present invention; Figure 4 This is a schematic diagram illustrating the relationship between the previous soil water holding capacity and the current soil water negative pressure value, the previous soil water negative pressure value, and the reference soil water negative pressure value when the soil is near saturation, according to Embodiment 3 of the present invention. Figure 5 This is a schematic diagram illustrating the relationship between the previous soil water content and the current soil water negative pressure value, the previous soil water negative pressure value, and the reference soil water negative pressure value at near residual moisture content, according to Embodiment 3 of the present invention. Figure 6 This is a schematic diagram of the structure of an iterative device for the equation of motion of unsaturated soil water according to Embodiment 4 of the present invention; Figure 7 This is a schematic diagram of the structure of an electronic device that implements the iterative method for the unsaturated soil water movement equation in this embodiment of the invention. Detailed Implementation

[0015] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0016] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0017] Example 1 Figure 1This is a flowchart illustrating an iterative method for unsaturated soil water movement equations according to Embodiment 1 of the present invention. This embodiment is applicable to iterating unsaturated soil water movement equations. The method can be executed by an unsaturated soil water movement equation iterative device, which can be implemented in hardware and / or software. This device can be configured in an electronic device that performs the unsaturated soil water movement equation iterative function.

[0018] See Figure 1 The iterative method for the unsaturated soil water movement equations shown includes: S101. In the process of iteratively solving the equation of unsaturated soil water movement using the Newton-Raphson iteration method, the current soil water negative pressure value of each grid cell in the current iteration layer, the previous soil water negative pressure value of each grid cell in the previous iteration layer, and the previous soil volumetric water content are obtained.

[0019] The equation for unsaturated soil water movement is a parabolic partial differential equation that describes the unsteady flow of water in unsaturated porous media (such as soil).

[0020] The core idea of ​​Newton's iteration method is to approximate the root of the equation step by step using a tangent to approximate the curve. Newton's iteration method utilizes the construction of the Jacobian matrix, which typically exhibits faster local convergence speed when approaching the convergent solution, thus offering a significant advantage in improving the efficiency of soil water numerical simulation. However, in regions with extreme water content, the derivative of the soil hydraulic function changes rapidly, leading to a significant increase in the risk of Jacobian matrix linearization mismatch. This can also cause problems such as abnormally large update amounts, local numerical oscillations, and even iteration divergence in Newton's iteration method.

[0021] For example, the basic form of Newton's iteration method can be represented by the following formula: ; In the formula, This is the current iteration value; This is the value from the previous iteration; The function value of the equation; denoted as the derivative of the equation. The equation can be an equation governing the movement of unsaturated soil water.

[0022] A grid cell is the smallest spatial control volume that carries the soil water negative pressure value and soil volumetric water content after discretizing the continuous soil space. The unknowns include either the soil water negative pressure value or the soil volumetric water content.

[0023] The previous iteration layer is used to linearize the unsaturated soil water movement equation. The previous iteration layer includes the previous soil water negative pressure values ​​for all grid cells calculated in the previous round of Newton iterations within the current time step. The previous soil water negative pressure value is the soil water negative pressure value at the start of the current round of Newton iterations. The previous soil volumetric water content is obtained by substituting the previous soil water negative pressure value into the soil moisture characteristic curve.

[0024] The current iteration layer is the target of this Newton iteration. The current iteration layer contains the current negative soil water pressure values ​​for all grid cells being solved in this round of Newton iterations. The current negative soil water pressure value is the negative soil water pressure value at the end of this round of Newton iterations.

[0025] Specifically, in the process of iteratively solving the equation for unsaturated soil water movement using the Newton-Raphson iteration method, the current soil water negative pressure value of each grid cell in the current iteration layer and the previous soil water negative pressure value of each grid cell in the previous iteration layer are obtained. The soil volumetric water content is obtained by substituting the previous soil water negative pressure value into the soil moisture characteristic curve.

[0026] S102. For a single grid cell, based on the previous soil water negative pressure value and the previous soil volumetric water content of the previous iteration layer, detect whether the grid cell is an abnormal grid cell in the extreme water content region.

[0027] Extreme moisture content regions represent the extreme states of the soil moisture characteristic curve. These regions are also where linearization is prone to failure when using the Newton-Raphson iteration method to solve the unsaturated soil water movement equation. Extreme moisture content regions include near-saturated or near-residual moisture content regions. These regions describe the extreme states at both ends of the soil moisture characteristic curve. The near-saturated region is where the soil volumetric moisture content is close to saturation, and the soil water negative pressure is close to 0. The near-residual moisture content region is where the soil volumetric moisture content is close to residual moisture content, and the soil water negative pressure tends towards negative infinity. In solving the unsaturated soil water movement equation using the Newton-Raphson iteration method, the near-saturated region converges slowly or not at all, while the near-residual moisture content region is prone to divergence. Anomaly grid cells are grid cells located in extreme moisture content regions.

[0028] Specifically, for a single grid cell, the previous soil volumetric moisture content is compared with the saturated moisture content and residual moisture content. If the previous soil volumetric moisture content is close to the saturated moisture content, the negative pressure value of the previous soil water in the previous iteration layer is compared with 0. If the negative pressure value of the previous soil water in the previous iteration layer is close to 0, the grid cell is determined to be in the near-saturated region within the extreme moisture content region. Grid cells in the near-saturated region within the extreme moisture content region are identified as anomalous grid cells. If the previous soil volumetric moisture content is close to the residual moisture content, it is checked whether the negative pressure value of the previous soil water in the previous iteration layer tends to negative infinity. If so, the grid cell is determined to be in the near-residual moisture content region within the extreme moisture content region. Grid cells in the near-residual moisture content region within the extreme moisture content region are identified as anomalous grid cells.

[0029] In an optional embodiment of the present invention, for a single grid cell, detecting whether the grid cell is an abnormal grid cell in an extreme moisture content region based on the previous soil water negative pressure value and the previous soil volumetric moisture content of the previous iteration layer includes: for a single grid cell, calculating the previous soil water holding capacity based on the previous soil water negative pressure value and the previous soil volumetric moisture content of the previous iteration layer; for a single grid cell, comparing the previous soil water holding capacity with the reference soil water holding capacity to detect whether the grid cell is an abnormal grid cell in an extreme moisture content region.

[0030] The previous soil water capacity is used to characterize the change in soil volumetric water content with soil water negative pressure under the current suction state. The previous soil water capacity measures the soil's sensitivity to changes in soil water negative pressure. It is calculated based on the upper soil water negative pressure and the previous soil volumetric water content from the previous iteration layer. The previous soil water capacity is the coefficient of the time term in the unsaturated soil water movement equation. It is an important parameter in Newton's iteration method.

[0031] The reference soil water capacity is used to measure whether a grid cell is located in an extreme moisture content zone. Optionally, the reference soil water capacity can be set and adjusted by technicians based on experience. For example, the range of values ​​for the reference soil water capacity is... .

[0032] Specifically, for a single grid cell, the soil water content calculation formula is used to calculate the derivative of the previous soil volumetric water content with respect to the previous soil water negative pressure value, and thus obtain the previous soil water content.

[0033] For example, the following formula can be used to represent the formula for calculating soil water content: ; in, The negative soil water pressure value of the i-th grid cell in the previous iteration layer. The corresponding previous soil water holding capacity; θ is the derivative of soil volumetric moisture content with respect to soil water negative pressure; h is the previous soil volumetric moisture content; This represents the negative soil water pressure value of the i-th grid cell during the k-th iteration, i.e., the previous negative soil water pressure value.

[0034] Specifically, for a single grid cell, the previous soil water holding capacity is compared with the reference soil water holding capacity. If the previous soil water holding capacity is less than the reference soil water holding capacity, then the grid cell is determined to be an anomalous grid cell located in an extreme moisture content zone.

[0035] This scheme introduces anomaly grid cells to determine whether the previous soil water holding capacity grid cell is located in an extreme moisture content zone. It employs parameters that directly reflect the numerical properties of the unsaturated soil water movement equation, directly detecting the divergence state of the unsaturated soil water movement equation itself in the Newton iteration process, thus screening outomaly grid cells and improving their accuracy. By comparing the previous soil water holding capacity with the reference soil water holding capacity, it detects whether the grid cell is anomaly grid cell located in an extreme moisture content zone, thereby improving the screening efficiency of outomaly grid cells.

[0036] S103. For a single grid cell, when the grid cell is an abnormal grid cell, the current soil water negative pressure value and the previous soil water negative pressure value are compared with the reference soil water negative pressure value to obtain the current comparison result and the previous comparison result.

[0037] The reference soil water negative pressure value is the soil water negative pressure value corresponding to the maximum value of the derivative of the soil hydraulic function. The reference soil water negative pressure value is determined based on the characteristics of the derivative of the soil hydraulic function. The soil hydraulic function is a set of functions describing the nonlinear relationship between soil volumetric water content, unsaturated hydraulic conductivity, and soil water negative pressure. The soil hydraulic function includes soil moisture characteristic curves, hydraulic conductivity functions, and water diffusivity functions, etc. The soil hydraulic function is the core input for solving the equations of motion of unsaturated soil water.

[0038] The current comparison result is the comparison between the current soil water negative pressure value and the reference soil water negative pressure value. For example, the current comparison result includes the current soil water negative pressure value being greater than the reference soil water negative pressure value and the current soil water negative pressure value being less than the reference soil water negative pressure value.

[0039] The previous comparison result is the comparison between the previous soil water negative pressure value and the reference soil water negative pressure value. For example, the previous comparison result includes a previous soil water negative pressure value being greater than the reference soil water negative pressure value and a previous soil water negative pressure value being less than the reference soil water negative pressure value.

[0040] Specifically, for a single grid cell, when the grid cell is an anomalous grid cell, the current soil water negative pressure value is compared with the reference soil water negative pressure value. If the current soil water negative pressure value is greater than the reference soil water negative pressure value, then the current comparison result is determined to be that the current soil water negative pressure value is greater than the reference soil water negative pressure value. If the current soil water negative pressure value is less than the reference soil water negative pressure value, then the current comparison result is determined to be that the current soil water negative pressure value is less than the reference soil water negative pressure value. The previous soil water negative pressure value is then compared with the reference soil water negative pressure value. If the previous soil water negative pressure value is greater than the reference soil water negative pressure value, then the previous comparison result is determined to be that the previous soil water negative pressure value is less than the reference soil water negative pressure value.

[0041] S104. For a single abnormal grid cell, perform a consistency check between the current comparison result and the previous comparison result to determine the local iterative instability detection result of the abnormal grid cell.

[0042] The results of local iterative instability detection are used to characterize whether anomalous grid cells exhibit local iterative instability. For example, the results may include the presence or absence of local iterative instability in anomalous grid cells.

[0043] Specifically, for a single anomalous grid cell, a consistency check is performed between the current comparison result and the previous comparison result. If the current comparison result is consistent with the previous comparison result, then the local iterative instability detection result of the anomalous grid cell is determined to be that the anomalous grid cell does not have local iterative instability. If the current comparison result is inconsistent with the previous comparison result, then the local iterative instability detection result of the anomalous grid cell is determined to be that the anomalous grid cell has local iterative instability.

[0044] In an optional embodiment of the present invention, for a single abnormal grid cell, a consistency check is performed on the current comparison result and the previous comparison result to determine the local iterative instability detection result of the abnormal grid cell, including: for a single abnormal grid cell, if the current comparison result and the previous comparison result are consistent, it is determined that the abnormal grid cell does not have local iterative instability; for a single abnormal grid cell, if the current comparison result and the previous comparison result are inconsistent, it is determined that the abnormal grid cell has local iterative instability.

[0045] If the current comparison result is consistent with the previous comparison result, it can be understood that both the current and previous soil water negative pressure values ​​are located on the same side of the reference soil water negative pressure value. If the current comparison result is inconsistent with the previous comparison result, it can be understood that both the current and previous soil water negative pressure values ​​are located on different sides of the reference soil water negative pressure value, that is, the current and previous soil water negative pressure values ​​cross the reference soil water negative pressure value. In this case, the Newton linearization assumption fails, the soil state undergoes a qualitative change in one iteration (e.g., from "with water" to "without water"), and the residuals and Jacobian matrix change drastically within one iteration. Therefore, it is determined that the abnormal grid cell exhibits local iterative instability.

[0046] Specifically, for a single anomalous grid cell, if the current comparison result is consistent with the previous comparison result, the anomalous grid cell is determined to have no local iterative instability. If the current comparison result is inconsistent with the previous comparison result, the anomalous grid cell is determined to have local iterative instability.

[0047] This scheme improves the efficiency of detecting local iterative instability in anomalous grid cells by determining that the anomalous grid cell does not have local iterative instability when the current comparison result is consistent with the previous comparison result, and determines that the anomalous grid cell has local iterative instability when the current comparison result is inconsistent with the previous comparison result.

[0048] S105. For a single abnormal grid cell, when the abnormal grid cell has local iterative instability, the current soil water negative pressure value is corrected according to the reference soil water negative pressure value.

[0049] When there is local iterative instability in abnormal grid cells, the current soil water negative pressure value is unreliable, so it is necessary to correct the current soil water negative pressure value.

[0050] Specifically, for a single abnormal grid cell, when the abnormal grid cell exhibits local iterative instability, the current soil water negative pressure value is abandoned, and the current soil water negative pressure value is corrected to the reference soil water negative pressure value.

[0051] In an optional embodiment of the present invention, after performing consistency detection on the current comparison result and the previous comparison result for a single abnormal grid cell to determine the local iterative instability detection result of the abnormal grid cell, the method further includes: for a single abnormal grid cell, when there is no local iterative instability in the abnormal grid cell, maintaining the current negative soil water pressure value.

[0052] When there is no local iterative instability in the abnormal grid cells, the current soil water negative pressure value is reliable, so there is no need to correct the current soil water negative pressure value.

[0053] Specifically, for a single anomalous grid cell, if there is no local iteration instability in the anomalous grid cell, the current negative soil water pressure value is retained, and the next iteration continues.

[0054] This scheme maintains the current negative soil water pressure value when there is no local iterative instability in the abnormal grid cells, thus ensuring the continuation of the Newton-Raphson iteration process of the unsaturated soil water motion equation and guaranteeing the iteration efficiency of the unsaturated soil water motion equation.

[0055] The technical solution of this invention involves obtaining the current soil water negative pressure value, the previous soil water negative pressure value, and the previous soil volumetric water content of each grid cell in the current iteration layer during the iterative solution of the unsaturated soil water movement equation using the Newton-Raphson iteration method. For a single grid cell, based on the previous soil water negative pressure value and the previous soil volumetric water content, it detects whether the grid cell is an abnormal grid cell in an extreme water content region. When the grid cell is an abnormal grid cell, the current soil water negative pressure value and the previous soil water negative pressure value are compared with a reference soil water negative pressure value to obtain the current comparison result and the previous comparison result. The results are compared, and consistency checks are performed between the current comparison results and the previous comparison results to determine the local iterative instability detection results of abnormal grid cells. When local iterative instability exists in abnormal grid cells, the current soil water negative pressure value is corrected according to the reference soil water negative pressure value. A local cell stabilization correction mechanism is introduced. By detecting whether the current soil water negative pressure value and the previous soil water negative pressure value cross the reference soil water negative pressure value, local stabilization correction is performed on abnormal grid cells, thereby reducing the instability risk of Newton iteration under strong nonlinear conditions. While maintaining the high solution efficiency of the Newton iteration method, the stability and robustness of the numerical solution of the unsaturated soil water motion equation are improved.

[0056] Example 2 Figure 2 This is a flowchart of an iterative method for the unsaturated soil water movement equation provided in Embodiment 2 of the present invention. Based on the above embodiments, this embodiment further adds the step of "obtaining the scale parameters and empirical parameters of the soil moisture characteristic curve; determining the reference soil water negative pressure value based on the scale parameters and empirical parameters of the soil moisture characteristic curve" before "for a single grid cell, when the grid cell is an abnormal grid cell." This improves the accuracy of the reference soil water negative pressure value. It should be noted that parts not detailed in this embodiment can be found in the descriptions of other embodiments.

[0057] See Figure 2 The iterative method for the unsaturated soil water movement equations shown includes: S201. In the process of iteratively solving the equation of unsaturated soil water movement using the Newton-Raphson iteration method, the current soil water negative pressure value of each grid cell in the current iteration layer, the previous soil water negative pressure value of each grid cell in the previous iteration layer, and the previous soil volumetric water content are obtained.

[0058] S202. For a single grid cell, based on the previous soil water negative pressure value and the previous soil volumetric water content of the previous iteration layer, detect whether the grid cell is an abnormal grid cell in the extreme water content region.

[0059] S203. Obtain the scale parameters and empirical parameters of the soil moisture characteristic curve.

[0060] The soil moisture characteristic curve is a curve used to describe the relationship between soil volumetric water content and soil water negative pressure. The scale parameter describes the soil water negative pressure value at which significant water loss begins. The scale parameter determines the position and range of the soil moisture characteristic curve. The scale parameter controls the position of the soil moisture characteristic curve on the horizontal axis. Empirical parameters describe the uniformity of soil pore size. Empirical parameters determine the steepness of the soil moisture characteristic curve.

[0061] Specifically, the soil moisture characteristic curve can be fitted to obtain the scale parameters and empirical parameters of the soil moisture characteristic curve.

[0062] In an optional embodiment of the present invention, obtaining the scale parameters and empirical parameters of the soil moisture characteristic curve includes: determining the scale parameters and empirical parameters of the soil moisture characteristic curve based on the soil properties.

[0063] Soil texture (also known as soil quality) refers to the percentage by mass of sand, silt, and clay particles in the soil. Soil texture determines how soil water is retained and how it flows. The mapping relationship between soil texture and the scale parameters and empirical parameters of the soil moisture characteristic curve can be pre-stored in scale parameter and empirical parameter data tables.

[0064] Specifically, based on the mass percentages of the three particle sizes (sand, silt, and clay) corresponding to the soil type, the scale parameters and empirical parameters of the soil moisture characteristic curve are determined by consulting the scale parameter and empirical parameter data tables.

[0065] This scheme incorporates soil properties, which can quickly determine the scale parameters and empirical parameters of the soil moisture characteristic curve, thereby improving the efficiency of determining the scale parameters and empirical parameters of the soil moisture characteristic curve, and thus improving the iterative efficiency of the unsaturated soil water movement equation.

[0066] S204. Determine the reference soil water negative pressure value based on the scale parameters and empirical parameters of the soil moisture characteristic curve.

[0067] Specifically, the reference soil water negative pressure value can be determined by using the calculation formula of the reference soil water negative pressure value, based on the scale parameters and empirical parameters of the soil moisture characteristic curve.

[0068] For example, the following formula can be used to represent the formula for calculating the negative pressure value of reference soil water: ; In the formula, The reference soil water negative pressure value; α is the scale parameter in the soil moisture characteristic curve; n is the empirical parameter in the soil moisture characteristic curve.

[0069] S205. For a single grid cell, when the grid cell is an abnormal grid cell, the current soil water negative pressure value and the previous soil water negative pressure value are compared with the reference soil water negative pressure value to obtain the current comparison result and the previous comparison result.

[0070] S206. For a single abnormal grid cell, perform a consistency check between the current comparison result and the previous comparison result to determine the local iterative instability detection result of the abnormal grid cell.

[0071] S207. For a single abnormal grid cell, when the abnormal grid cell has local iterative instability, the current soil water negative pressure value is corrected according to the reference soil water negative pressure value.

[0072] The technical solution of this invention obtains the scale parameters and empirical parameters of the soil moisture characteristic curve, and determines the reference soil water negative pressure value based on the scale parameters and empirical parameters of the soil moisture characteristic curve. This introduces and improves the scale parameters and empirical parameters of the soil moisture characteristic curve, further determining the reference soil water negative pressure value and improving the accuracy of the reference soil water negative pressure value.

[0073] Example 3 Figure 3 This is a flowchart illustrating an iterative method for the unsaturated soil water movement equation provided in Embodiment 3 of the present invention. Based on the above embodiments, Figure 3 This is a preferred embodiment of the present invention. See also: Figure 3 The iterative method for the unsaturated soil water movement equations shown includes: S301. The Richards equation is solved iteratively using the Newton iteration method.

[0074] The basic form of Newton's iterative method can be represented by the following formula: ; In the formula, This is the current iteration value; This is the value from the previous iteration; The function value of the Richards equation (the equation for the movement of unsaturated soil water); This is the derivative of the Richards equation (the equation for the movement of unsaturated soil water).

[0075] S302. Solve for the current negative soil water pressure value of each grid cell in the current iteration layer.

[0076] Specifically, assume that the current negative soil water pressure of the i-th grid cell in the current iteration is [value missing]. The previous soil water negative pressure value of the i-th grid cell in each grid cell to be determined in the previous iteration was... Where i is the grid cell number; k is the previous iteration layer number; and k+1 is the current iteration layer number.

[0077] S303. Detect whether the negative pressure value of soil water on the grid cell is in the near-saturation zone or near the residual moisture content zone.

[0078] Specifically, check the previous soil water content corresponding to each grid cell in the last iteration: ; in, The negative soil water pressure value of the i-th grid cell in the previous iteration layer. The corresponding previous soil water holding capacity; θ is the derivative of soil volumetric moisture content with respect to soil water negative pressure; h is the previous soil volumetric moisture content; It represents the negative soil water pressure value of the i-th grid cell in the k-th iteration, which is the negative soil water pressure value of the previous iteration layer.

[0079] Specifically, the previous soil water holding capacity is further compared with the reference soil water holding capacity to determine whether the grid cell is in the near-saturation zone or the near residual moisture content zone.

[0080] Among them, when At this time, it is determined that the grid cell is in the near-saturation region or the near-residual moisture content region. For example Figure 4 As shown, the soil water content of the previous grid cell in the near-saturation zone approaches 0. Figure 5 As shown, the soil water content of the grid cell in the near residual moisture zone approaches 0. Here, soil water negative pressure is the soil water negative pressure value; soil moisture content is the soil volumetric water content.

[0081] In the formula, The negative soil water pressure value of the i-th grid cell in the previous iteration layer. The corresponding previous soil water holding capacity; ε is the reference soil water holding capacity, and the recommended value range for ε is... .

[0082] S304. Determine whether the previous soil water negative pressure value and the current soil water negative pressure value are on the same side as the reference soil water negative pressure value.

[0083] Specifically, if and So, if Figure 4 As shown, the water content of the grid cells was close to the saturation water content in the previous iteration.

[0084] Specifically, if and So, if Figure 5 As shown, the water content of the grid cells was close to the residual water content in the previous iteration.

[0085] Among them, the reference soil water negative pressure value This represents the negative soil water pressure value corresponding to the maximum value of the derivative of the soil hydraulic function. The reference negative soil water pressure value is determined based on the characteristics of the derivative of the soil hydraulic function.

[0086] Preferably, the following formula can be used to calculate the reference soil water negative pressure value: ; In the formula, The reference soil water negative pressure value; α is the scale parameter in the soil moisture characteristic curve; n is the empirical parameter in the soil moisture characteristic curve.

[0087] S305. If the local cell iteration becomes unstable, the current iteration value is discarded, and the current soil water negative pressure value of the grid cell is corrected to the reference soil water negative pressure value.

[0088] The current iteration value is the current soil water negative pressure value.

[0089] Specifically, when the i-th grid cell experiences local iteration instability, the current soil water negative pressure value is constrained to the reference soil water negative pressure value.

[0090] For example, let In the formula, This represents the current negative soil water pressure value. For reference soil water negative pressure value.

[0091] S306. Repeat the iterative calculation until the convergence condition is met.

[0092] This invention improves the numerical stability of the Richards equation under strongly nonlinear conditions through a local grid point stabilization correction mechanism, while maintaining the high solution efficiency of the Newton iteration method.

[0093] For example, a one-dimensional vertical homogeneous soil column is used as the computational object. The Richards equation is used to describe the water transport process in the unsaturated zone, and the Newton iteration method is used for nonlinear iterative solution. In each Newton iteration, a local element stability correction mechanism is used to detect whether abnormal grid elements have experienced local iterative instability. If instability occurs, the pressure head of the grid element is locally stabilized and corrected, and the nonlinear iterative calculation for the current time step is repeated, thereby improving the numerical stability of the model under strongly nonlinear conditions.

[0094] In a specific example, the computational domain is a one-dimensional vertical homogeneous soil column with a depth of 100m and a spatially discrete grid of 1000 layers. The total simulation duration is 100 days. The soil hydraulic parameters are implemented using the Van Genuchten model (VG model). The soil hydraulic parameters are shown in Table 1. The top boundary uses a variable flux boundary, and the bottom boundary uses a free drainage boundary. The flux conditions given for the top boundary are shown in Table 2. After each Newton iteration, local stability is checked for all grid cells.

[0095] First, calculate the previous soil water content corresponding to each grid cell in the previous iteration layer: ; in, The negative soil water pressure value of the i-th grid cell in the previous iteration layer. The corresponding previous soil water holding capacity; θ is the derivative of soil volumetric moisture content with respect to soil water negative pressure; h is the previous soil volumetric moisture content; It represents the negative soil water pressure value of the i-th grid cell in the k-th iteration, which is the negative soil water pressure value of the previous iteration layer.

[0096] Secondly, when the soil water content is lower than the reference soil water content, that is... When the grid cell is in the near-saturation region or near the residual moisture content region, it is determined that the grid cell is in the near-saturation region or near the residual moisture content region.

[0097] Subsequently, the judgment and Is it located on the same side as the reference soil water negative pressure value? a. If and Therefore, in the previous iteration, the water content of the grid cells was close to the saturation water content.

[0098] b. If and Therefore, in the previous iteration, the water content of the grid cells was close to the residual water content.

[0099] If any of the above conditions are met, then the current iteration value is... Or the value of the previous iteration Exceeding the reference soil water negative pressure value The grid cell is determined to have experienced local iterative instability.

[0100] Among them, soil water negative pressure reference value The preferred option is expressed as: ; In the formula, The reference soil water negative pressure value; α is the scale parameter in the soil moisture characteristic curve; n is the empirical parameter in the soil moisture characteristic curve.

[0101] Then, when the reference soil water negative pressure value is crossed, the current iteration value is discarded and the current soil water negative pressure value of the grid cell is corrected to the reference soil water negative pressure value.

[0102] Immediately In the formula, This represents the current negative soil water pressure value. For reference soil water negative pressure value.

[0103] Finally, the Jacobian matrix for the current time step is reconstructed, and Newton iteration is performed again until the convergence condition is met.

[0104] To verify the stability and efficiency of this invention, the CSOILWAT (Crop-Soil-Water) model based on this invention was compared with VS2DT (Variably Saturated Two-Dimensional Flow and Transport), HYDRUS-1D (HYDRUS One-Dimensional, a software package for simulating water-heat-solute transport in a variable-saturated one-dimensional medium), and SWAP (Soil-Water-Atmosphere-Plant) models. All models were computed using the same computational domain, boundary conditions, time step, and mesh generation conditions. The comparison results of the number of iterations and running speed of the different models are shown in Table 3. The results show that under strong infiltration conditions, this invention can stably complete the entire simulation process and effectively reduce the total number of iterations and running time. Regarding the total number of iterations, under the same simulation conditions, the COILWAT model has the fewest iterations, which is 0.07-0.42 times that of other models. In terms of running speed, the COILWAT model has the fastest running speed, which is 0.08-0.11 times that of other successful simulation models. In the near-saturation and near-residual water content regions, the local element stabilization correction mechanism effectively avoids abnormal increases in the update amount of the Newton iteration method, thus significantly reducing the risk of local numerical oscillations and iteration divergence. Compared with traditional methods, this invention only corrects abnormal grid cells that experience local iteration instability, thus improving stability while maintaining the high computational efficiency of the Newton iteration method.

[0105] The vadose zone is a crucial transitional area connecting surface water and groundwater, determining the distribution of precipitation and irrigation water among infiltration, surface runoff, groundwater recharge, and evapotranspiration. Especially in thick vadose zones, soil moisture dynamics directly impact groundwater recharge estimations and surface-groundwater coupling simulation results. Therefore, accurately simulating unsaturated zone water transport processes is of great significance for refined water resource management and regulation.

[0106] Currently, research on soil moisture transport processes mainly relies on numerical simulation methods. Among these, the Richards equation (the equation for unsaturated soil water movement) is the most commonly used governing equation to describe unsaturated water flow. However, since both soil moisture content and unsaturated hydraulic conductivity exhibit highly nonlinear variations with pressure head, the Richards equation (the equation for unsaturated soil water movement) usually forms a highly nonlinear algebraic equation system after discretization. Its solution efficiency and stability are highly dependent on nonlinear iterative methods.

[0107] Most existing mainstream soil water models use Picard-type iterative methods (Picard successive approximation methods) for solving. This method has a relatively simple computational form and usually has good overall stability. However, since it only has linear convergence characteristics, it often requires a large number of iterations under strong nonlinear conditions, which leads to a significant decrease in computational efficiency.

[0108] In contrast, the Newton iteration method, by constructing the Jacobian matrix, typically exhibits faster local convergence near the convergent solution, thus demonstrating a significant advantage in improving the efficiency of soil water numerical simulation. However, in the near-saturation or near-residual water content region, the derivative of the soil hydraulic function changes rapidly, leading to a significant increase in the risk of Jacobian matrix linearization mismatch. This may also cause problems such as abnormally large update amounts, local numerical oscillations, or even iteration divergence in the Newton iteration method.

[0109] Therefore, there is an urgent need for a local stability correction method that can balance computational efficiency and solution stability in order to improve the computational efficiency and stability of soil water numerical simulation under complex conditions.

[0110] The local element stabilization correction mechanism proposed in this invention corrects abnormal grid cells by detecting whether the current iteration value crosses the reference pressure head (i.e., the reference soil water negative pressure value) with the previous iteration value. This reduces the risk of iterative instability under strong nonlinear conditions, improving the stability and robustness of the numerical solution of the Richards equation while maintaining the high solution efficiency of the Newton iteration method. Compared with existing technologies, this invention has the following advantages: First, by detecting the state of local elements and adjusting the soil water negative pressure value, it can effectively reduce the simulation divergence risk caused by the non-differentiability of derivatives in the near-saturated and near-residual water content regions, improving the solution stability of the Richards equation under strong nonlinear conditions. Second, it only corrects abnormal local elements, without requiring overall correction of the entire nonlinear equation system or reduction of the time step, thus improving stability while maintaining the high convergence efficiency of the Newton iteration method. Third, this invention is applicable to the simulation of unsaturated water flow under conditions of strong infiltration, frequent saturation-unsaturation transition, and thick vadose zone, and has good engineering application value.

[0111] Example 4 Figure 6 This is a schematic diagram of an iterative device for the unsaturated soil water movement equation provided in Embodiment 4 of the present invention. This embodiment of the invention is applicable to the iterative application of the unsaturated soil water movement equation. The device can execute the iterative method for the unsaturated soil water movement equation and can be implemented in hardware and / or software. The device can be configured in an electronic device that carries the function of iterating the unsaturated soil water movement equation.

[0112] See Figure 6The unsaturated soil water movement equation iterative device shown includes: an iterative data acquisition module 601, an abnormal grid cell detection module 602, a soil water negative pressure value comparison module 603, a local iterative instability detection module 604, and a current soil water negative pressure value correction module 605. Specifically, the iterative data acquisition module 601 is used to acquire the current soil water negative pressure value of each grid cell in the current iteration layer, the previous soil water negative pressure value of each grid cell in the previous iteration layer, and the previous soil volumetric water content during the iterative solution of the unsaturated soil water movement equation using the Newton-Raphson iteration method; the abnormal grid cell detection module 602 is used to detect whether a grid cell is an abnormal grid cell in an extreme water content region based on the previous soil water negative pressure value and the previous soil volumetric water content of the previous iteration layer; and the soil water negative pressure value comparison module 603 is used to, for a single grid cell, in the grid... When a point cell is an abnormal grid cell, the current soil water negative pressure value and the previous soil water negative pressure value are compared with the reference soil water negative pressure value to obtain the current comparison result and the previous comparison result; the local iterative instability detection module 604 is used to perform consistency detection on the current comparison result and the previous comparison result for a single abnormal grid cell to determine the local iterative instability detection result of the abnormal grid cell; the current soil water negative pressure value correction module 605 is used to correct the current soil water negative pressure value based on the reference soil water negative pressure value when a local iterative instability exists in a single abnormal grid cell.

[0113] The technical solution of this invention involves obtaining the current soil water negative pressure value, the previous soil water negative pressure value, and the previous soil volumetric water content of each grid cell in the current iteration layer during the iterative solution of the unsaturated soil water movement equation using the Newton-Raphson iteration method. For a single grid cell, based on the previous soil water negative pressure value and the previous soil volumetric water content, it detects whether the grid cell is an abnormal grid cell in an extreme water content region. When the grid cell is an abnormal grid cell, the current soil water negative pressure value and the previous soil water negative pressure value are compared with a reference soil water negative pressure value to obtain the current comparison result and the previous comparison result. The results are compared, and consistency checks are performed between the current comparison results and the previous comparison results to determine the local iterative instability detection results of abnormal grid cells. When local iterative instability exists in abnormal grid cells, the current soil water negative pressure value is corrected according to the reference soil water negative pressure value. A local cell stabilization correction mechanism is introduced. By detecting whether the current soil water negative pressure value and the previous soil water negative pressure value cross the reference soil water negative pressure value, local stabilization correction is performed on abnormal grid cells, thereby reducing the instability risk of Newton iteration under strong nonlinear conditions. While maintaining the high solution efficiency of the Newton iteration method, the stability and robustness of the numerical solution of the unsaturated soil water motion equation are improved.

[0114] In an optional embodiment of the present invention, the abnormal grid cell detection module 602 includes: a previous soil water capacity calculation unit, used to calculate the previous soil water capacity for a single grid cell based on the previous soil water negative pressure value and the previous soil volumetric water content of the previous iteration layer; and an abnormal grid cell detection unit, used to compare the previous soil water capacity with the reference soil water capacity for a single grid cell, and detect whether the grid cell is an abnormal grid cell in an extreme water content region.

[0115] In an optional embodiment of the present invention, the local iterative instability detection module 604 includes: a first local iterative instability detection unit, configured to determine that the abnormal grid cell does not have local iterative instability when the current comparison result is consistent with the previous comparison result for a single abnormal grid cell; and a second local iterative instability detection unit, configured to determine that the abnormal grid cell has local iterative instability when the current comparison result is inconsistent with the previous comparison result for a single abnormal grid cell.

[0116] In an optional embodiment of the present invention, the device further includes: a soil parameter acquisition module, configured to, for a single grid cell, when the grid cell is an abnormal grid cell, compare the current soil water negative pressure value of each grid cell in the current iteration layer and the previous soil water negative pressure value of each grid cell in the previous iteration layer with a reference soil water negative pressure value, and before obtaining the current comparison result and the previous comparison result, acquire the scale parameters and empirical parameters of the soil moisture characteristic curve; and a reference soil water negative pressure value determination module, configured to determine the reference soil water negative pressure value based on the scale parameters and empirical parameters of the soil moisture characteristic curve.

[0117] In an optional embodiment of the present invention, the soil parameter acquisition module includes: a soil parameter determination unit, used to determine the scale parameters and empirical parameters of the soil moisture characteristic curve based on the soil properties.

[0118] In an optional embodiment of the present invention, the device includes: a current soil water negative pressure value maintenance module, which is used to maintain the current soil water negative pressure value for a single abnormal grid cell when there is no local iterative instability in the abnormal grid cell after performing consistency detection on the current comparison result and the previous comparison result for the single abnormal grid cell.

[0119] The unsaturated soil water movement equation iteration device provided in the embodiments of the present invention can execute the unsaturated soil water movement equation iteration method provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method.

[0120] In the technical solutions of this invention, the acquisition, storage, and application of the current soil water negative pressure value of each grid unit in the current iteration layer, the previous soil water negative pressure value of each grid unit in the previous iteration layer, the previous soil volumetric water content, the scale parameters and empirical parameters of the soil moisture characteristic curve, etc., all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0121] Example 5 Figure 7 A schematic diagram of an electronic device 700 that can be used to implement embodiments of the present invention is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0122] like Figure 7 As shown, the electronic device 700 includes at least one processor 701 and a memory, such as a read-only memory (ROM) 702 and a random access memory (RAM) 703, communicatively connected to the at least one processor 701. The memory stores computer programs executable by the at least one processor. The processor 701 can perform various appropriate actions and processes based on the computer program stored in the ROM 702 or loaded into the RAM 703 from storage unit 708. The RAM 703 can also store various programs and data required for the operation of the electronic device 700. The processor 701, ROM 702, and RAM 703 are interconnected via a bus 704. An input / output (I / O) interface 705 is also connected to the bus 704.

[0123] Multiple components in electronic device 700 are connected to I / O interface 705, including: input unit 706, such as keyboard, mouse, etc.; output unit 707, such as various types of displays, speakers, etc.; storage unit 708, such as disk, optical disk, etc.; and communication unit 709, such as network card, modem, wireless transceiver, etc. Communication unit 709 allows electronic device 700 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0124] Processor 701 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 701 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, digital signal processors (DSPs), and any suitable processor, controller, microcontroller, etc. Processor 701 performs the various methods and processes described above, such as the iterative method for the equation of motion of unsaturated soil water.

[0125] In some embodiments, the iterative method for unsaturated soil water movement equations can be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 708. In some embodiments, part or all of the computer program can be loaded and / or installed on electronic device 700 via ROM 702 and / or communication unit 709. When the computer program is loaded into RAM 703 and executed by processor 701, one or more steps of the iterative method for unsaturated soil water movement equations described above can be performed. Alternatively, in other embodiments, processor 701 can be configured to perform the iterative method for unsaturated soil water movement equations by any other suitable means (e.g., by means of firmware).

[0126] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0127] Computer programs used to implement the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0128] In the context of this invention, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0129] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0130] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or middleware components (e.g., application servers), or frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0131] A computing system can include clients and servers. Clients and servers are generally geographically separated and typically interact via communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system. It addresses the shortcomings of traditional physical hosts and VPS (Virtual Private Server) services, such as high management difficulty and weak business scalability.

[0132] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0133] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. An iterative method for unsaturated soil water movement equations, characterized in that, The method includes: In the process of iteratively solving the equation of unsaturated soil water movement using the Newton iteration method, the current soil water negative pressure value of each grid cell in the current iteration layer, the previous soil water negative pressure value of each grid cell in the previous iteration layer, and the previous soil volume water content are obtained. For a single grid cell, based on the previous soil water negative pressure value and the previous soil volumetric water content of the previous iteration layer, it is detected whether the grid cell is an abnormal grid cell in the extreme water content region. For a single grid cell, when the grid cell is an abnormal grid cell, the current soil water negative pressure value and the previous soil water negative pressure value are compared with the reference soil water negative pressure value to obtain the current comparison result and the previous comparison result. For a single anomalous grid cell, a consistency check is performed on the current comparison result and the previous comparison result to determine the local iterative instability detection result of the anomalous grid cell; For a single abnormal grid cell, when the abnormal grid cell exhibits local iterative instability, the current soil water negative pressure value is corrected based on the reference soil water negative pressure value.

2. The method according to claim 1, characterized in that, The step of detecting whether a single grid cell is an abnormal grid cell in an extreme moisture content region, based on the previous soil water negative pressure value and the previous soil volumetric water content of the previous iteration layer, includes: For a single grid cell, the soil water holding capacity is calculated based on the previous soil water negative pressure value and the previous soil volume water content of the previous iteration layer. For a single grid cell, the previous soil water holding capacity is compared with the reference soil water holding capacity to detect whether the grid cell is an abnormal grid cell in an extreme water content zone.

3. The method according to claim 1, characterized in that, The step of performing a consistency check on the current comparison result and the previous comparison result for a single anomalous grid cell to determine the local iterative instability detection result of the anomalous grid cell includes: For a single anomalous grid cell, if the current comparison result is consistent with the previous comparison result, it is determined that the anomalous grid cell does not have local iterative instability. For a single anomalous grid cell, if the current comparison result is inconsistent with the previous comparison result, it is determined that the anomalous grid cell has local iterative instability.

4. The method according to claim 1, characterized in that, Before comparing the current soil water negative pressure value of each grid cell in the current iteration layer and the previous soil water negative pressure value of each grid cell in the previous iteration layer with the reference soil water negative pressure value for a single grid cell, when the grid cell is an abnormal grid cell, to obtain the current comparison result and the previous comparison result, the method further includes: Obtain the scale parameters and empirical parameters of the soil moisture characteristic curve; The reference soil water negative pressure value is determined based on the scale parameters and empirical parameters of the soil moisture characteristic curve.

5. The method according to claim 4, characterized in that, The scale parameters and empirical parameters for obtaining the soil moisture characteristic curve include: Based on the soil properties, determine the scale parameters and empirical parameters of the soil moisture characteristic curve.

6. The method according to claim 1, characterized in that, After performing a consistency check on the current comparison result and the previous comparison result for a single anomalous grid cell to determine the local iterative instability detection result of the anomalous grid cell, the method further includes: For a single anomalous grid cell, the current negative soil water pressure value is maintained when there is no local iterative instability in the anomalous grid cell.

7. An iterative device for the equation of motion of unsaturated soil water, characterized in that, The device includes: The iterative data acquisition module is used to acquire the current soil water negative pressure value of each grid cell in the current iteration layer, the previous soil water negative pressure value of each grid cell in the previous iteration layer, and the previous soil volume water content during the iterative solution of the unsaturated soil water movement equation using the Newton iteration method. An abnormal grid cell detection module is used to detect, for a single grid cell, whether the grid cell is an abnormal grid cell in an extreme moisture content region, based on the previous soil water negative pressure value and the previous soil volume moisture content of the previous iteration layer. The soil water negative pressure value comparison module is used to compare the current soil water negative pressure value and the previous soil water negative pressure value with the reference soil water negative pressure value when the grid cell is an abnormal grid cell, for a single grid cell, to obtain the current comparison result and the previous comparison result. The local iterative instability detection module is used to perform consistency detection on the current comparison result and the previous comparison result for a single abnormal grid cell, and determine the local iterative instability detection result of the abnormal grid cell; The current soil water negative pressure value correction module is used to correct the current soil water negative pressure value based on the reference soil water negative pressure value when a single abnormal grid cell exhibits local iterative instability.

8. An electronic device, characterized in that, The electronic device includes: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the iterative method for the unsaturated soil water movement equation as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute the iterative method for the unsaturated soil water movement equation as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the iterative method for the unsaturated soil water movement equation according to any one of claims 1-6.

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