Snow evolution simulation method and device, electronic equipment and storage medium
By explicitly tracking the snow cover life cycle using a Lagrange adaptive multilayer framework and the fourth-order Runge-Kutta method, the problem of insufficient accuracy in existing snow cover simulation methods is solved, and high-precision simulation of the hydrothermal coupling process of snow cover is achieved, supporting hydrological processes and water resource management in high-altitude and cold regions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TSINGHUA UNIVERSITY
- Filing Date
- 2026-04-16
- Publication Date
- 2026-07-14
Smart Images
Figure CN122389320A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of water resources management technology, specifically to a snow cover evolution simulation method and apparatus, electronic equipment, computer-readable storage medium, and computer program product. Background Technology
[0002] Currently, snow accumulation simulation methods in land surface process models and hydrological models are mainly divided into three categories: the day-degree factor method, the two-layer model, and the multi-layer model.
[0003] The day factor method (such as HBV and SRM models) estimates snowmelt amount from meteorological factors such as temperature and radiation using empirical coefficients. It is simple to calculate and has low parameter requirements, making it suitable for areas with scarce data. However, this method is an empirical statistical method and cannot explicitly simulate the dynamic evolution of state variables such as snow depth and snow water equivalent. It is also difficult to describe the hydrothermal processes inside the snow, thus limiting its applicability under climate change scenarios.
[0004] Two-layer models (such as VIC and DHSVM models) divide snow cover into upper and lower layers, with the upper layer handling surface energy exchange and the lower layer serving as a hydrothermal reservoir, providing a certain physical basis. However, their structural simplification is significant, making it difficult to accurately reflect the vertical heterogeneity within the snow cover, resulting in limited simulation accuracy. Studies have shown that the snow depth correlation coefficient is approximately 0.60–0.83, and the root mean square error of snow water equivalent can reach 55 mm, with the error being particularly pronounced in scenarios with significant snow layering and complex hydrothermal processes.
[0005] Multilayer models (such as Noah-MP and CLM models) divide snow cover into multiple layers and characterize temperature profiles and densification processes by solving one-dimensional heat conduction equations, which is currently the mainstream approach. However, these models are generally based on the Eulerian framework (fixed grid or preset number of layers). When new snow accumulates or old snow melts, layer reset or grid reconstruction is required, which can easily introduce numerical diffusion, leading to blurred snow layer interfaces and making it difficult to accurately track the complete life cycle of a single snow layer from deposition to melting. In addition, most models ignore the advectional heat changes carried by infiltrated water flow in the energy balance solution, and do not accurately characterize the hydrothermal coupling processes such as snowmelt water generation, retention, migration, and refreezing. Ultimately, this affects the simulation accuracy of snow depth, snowmelt equivalent, and snowmelt runoff, limiting the improvement of hydrological forecasting and mechanism understanding in high-altitude and cold regions.
[0006] Therefore, there is an urgent need to develop a snow simulation method that can avoid the inherent defects of the Euler framework, explicitly track the evolution of the snow layer, and refine the simulation of the hydrothermal coupling process. Summary of the Invention
[0007] This application provides a method and apparatus for simulating snow cover evolution, electronic equipment, and storage medium to address the problem of insufficient accuracy in existing snow cover simulation methods.
[0008] This application provides a method for simulating snow cover evolution, including: The snow layer structure was determined by simulating the snow accumulation and melting process; For each snow layer, a hydrothermal coupling equation is constructed, and the temperature of the snow layer at the second moment is obtained by using the first attribute parameter of the current snow layer at the first moment using the fourth-order Runge-Kutta method. Determine the freeze-thaw rate of the snow layer at the second moment based on the temperature of the snow layer at the second moment. Based on the first attribute parameters of the current snow layer at the first moment and the freeze-thaw rate of the current snow layer at the second moment, determine the second attribute parameters of the current snow layer at the second moment.
[0009] In one embodiment, determining the snow layer structure by simulating the snow accumulation and melting process includes: The density of new snowfall is determined based on near-surface temperature and near-surface wind speed. The thickness of the new snowfall is determined based on the density, amount, and water density of the new snowfall. The snow cover structure is determined based on the new snowfall thickness, the current top layer thickness, and the time interval between two snowfall events.
[0010] In one embodiment, the determination of the new snowfall thickness based on the new snowfall density, snowfall amount, and water density is performed using the following formula: in, Indicates the thickness of the new snowfall. Indicates the amount of snowfall. , This indicates the density of new snowfall.
[0011] In one embodiment, determining the snow layer structure based on the new snowfall thickness, the current top layer thickness, and the time interval between two snowfall events includes: If the following two conditions are met: (1) The current top layer thickness is less than the preset maximum thickness. (2) The time interval between two snowfall events is less than the preset time. The new snowfall thickness is incorporated into the current top layer thickness to obtain the updated snow surface thickness; If any condition is not met, the total number of snow layers is incremented by one, and the new snowfall thickness is taken as an independent surface snow layer thickness.
[0012] In one embodiment, the hydrothermal coupling equation is constructed for each snow layer as follows: in, It is the density of snow cover. It is the specific heat capacity of snow. It's the thickness of the snow layer. It is the center height of the snow layer. It is the temperature of the snow layer. It is the specific heat capacity of water. It is the density of water. It refers to the intensity of rainfall. It refers to the intensity of snowfall. It is the specific heat capacity of ice. Near-surface temperature, It is the flux of liquid water entering the snow layer. It's the freeze-thaw rate. It is the latent heat of fusion. It is the thermal conductivity of snow. It is shortwave radiation incident on the snow layer. It is the length of time that snow absorbs sunlight. It is the amount of liquid water that evaporates or condenses on the surface of snow. Latent heat of vaporization It refers to the amount of ice sublimation or deposition on the surface of the snow. To sublimate latent heat, It is the sensible heat flux between the snow surface and the atmosphere. It is the net longwave radiation of the snow surface; The first line applies to the surface layer of snow, and the second line applies to the inner layer. Only applicable to the surface of snow; The first attribute parameters of the current snow layer at the first moment include the snow density, snow layer thickness, freeze-thaw rate, and snow layer temperature at the first moment.
[0013] In one embodiment, the determination of the freeze-thaw rate of the snow layer at the second moment based on the temperature of the snow layer at the second moment is performed using the following formula. in, This indicates the amount of snow cover at the second moment. It is the snow density of the current snow layer at the first moment. It is the specific heat capacity of snow. It is the current snow layer thickness at the first moment. It is the temperature at which snow melts. It is the temperature of the snow layer at the second moment. It is the latent heat of fusion. It is the time interval between the first moment and the second moment.
[0014] In one embodiment, determining the second attribute parameter of the snow layer at the second time based on the first attribute parameter of the snow layer at the first time and the freeze-thaw rate of the snow layer at the second time includes: Based on the first attribute parameters of the snow layer at the first moment and the freeze-thaw rate of the snow layer at the second moment, determine the liquid water content and solid water content of the snow layer at the second moment.
[0015] In one embodiment, determining the second attribute parameter of the snow layer at the second time based on the first attribute parameter of the snow layer at the first time and the freeze-thaw rate of the snow layer at the second time includes: Determine the snow density of the snow layer at the second moment based on the first attribute parameter of the snow layer at the first moment. The snow layer thickness at the second moment is determined based on the snow layer density at the second moment.
[0016] In one embodiment, determining the snow layer structure by simulating the snow accumulation and melting process further includes: When the thickness of any snow layer is below the minimum thickness threshold When the snow layer is removed, the total number of layers is reduced accordingly.
[0017] Secondly, embodiments of this application also provide a snow cover evolution simulation device, comprising: The structure determination module is used to determine the snow layer structure by simulating the snow accumulation and melting process; The temperature determination module is used to construct a hydrothermal coupling equation for each snow layer and use the fourth-order Runge-Kutta method to solve for the temperature of the current snow layer at the second moment using the first attribute parameters of the current snow layer at the first moment. The freeze-thaw rate determination module is used to determine the freeze-thaw rate of the snow layer at the second moment based on the temperature of the snow layer at the second moment. The attribute update module is used to determine the second attribute parameter of the current snow layer at the second moment based on the first attribute parameter of the current snow layer at the first moment and the freeze-thaw rate of the current snow layer at the second moment.
[0018] Thirdly, embodiments of this application also provide an electronic device, including: Memory is used to store executable instructions for a computer; The processor, when executing computer-executable instructions stored in the memory, implements the snow cover evolution simulation method provided in the embodiments of this application.
[0019] Thirdly, embodiments of this application also provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the snow cover evolution simulation method provided in embodiments of this application.
[0020] Fourthly, embodiments of this application also provide a computer program product, which includes computer-executable instructions stored in a computer-readable storage medium; When the processor of the electronic device reads the computer-executable instructions from the computer-readable storage medium and executes the computer-executable instructions, it implements the snow accumulation evolution simulation method provided in the embodiments of this application.
[0021] The snow cover evolution simulation method, apparatus, electronic equipment, and storage medium provided in this application are based on a Lagrange adaptive multilayer framework. Compared with existing multilayer snow cover schemes using Eulerian grids, this method achieves the following significant technical advantages: First, by treating each snow layer as an independent unit and explicitly tracking its complete lifecycle from deposition to complete melting, it completely avoids the interface ambiguity and numerical diffusion problems caused by artificial layering or grid reconstruction, thus achieving high-fidelity and physically consistent simulation of the snow cover profile evolution process. Second, by constructing a hydrothermal coupling equation, it explicitly analyzes the continuous changes in temperature, freeze-thaw rate, thickness, density, and ice-water content of each layer, and fully considers the advection heat effect of infiltrating water flow, significantly improving the simulation accuracy of the hydrothermal coupling process inside the snow cover. Third, this method does not preset an upper limit on the number of snow layers; computationally, it only maintains existing snow layers and their adjacent relationships, avoiding redundant calculations caused by fixed number of layers or frequent grid reconstruction. Finally, since the evolution process of each snow layer can be explicitly obtained, the model output has clear physical interpretability, which is conducive to in-depth analysis of the intrinsic mechanism of snow cover change, improvement of parameterization scheme, and support for remote sensing verification and model application in areas with insufficient data. It provides a reliable technical tool for hydrological process simulation, snowmelt runoff forecasting and water resource management in high-altitude and cold regions. Attached Figure Description
[0022] Figure 1 This is a schematic flowchart of a snow cover evolution simulation method provided in an embodiment of this application; Figure 2 This is a schematic flowchart simulating the snow accumulation process provided in the embodiments of this application; Figure 3 This is a comparative diagram of the snow depth change process simulated at each station; Figure 4 This is a schematic diagram of the time-series changes in snow water equivalent obtained from simulations at various stations; Figure 5 This is a comparative diagram showing the evaluation results of snow water equivalent simulation performance of 26 energy balance-based snow cover models at the same site; Figure 6 This is a schematic diagram comparing the simulation results of the VIC land surface model with those of the method (LAMS) in this application; Figure 7This is a block diagram of a snow cover evolution simulation device provided in an embodiment of this application; Figure 8 This is a block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation
[0023] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this specification as detailed in the appended claims.
[0024] The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of this specification. The singular forms “a,” “the,” and “the” as used in this specification and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.
[0025] It should be understood that although the terms first, second, third, etc., may be used in this specification to describe various information, this information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this specification, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."
[0026] Figure 1 This is a schematic flowchart of a snow cover evolution simulation method provided in an embodiment of this application. Figure 1 As shown, the method includes steps S110-S140.
[0027] Step S110: Determine the snow layer structure by simulating the snow accumulation and melting process.
[0028] In one embodiment, such as Figure 2 The step S110 may include steps S111-S113.
[0029] Step S111: Determine the density of new snowfall based on near-surface temperature and near-surface wind speed.
[0030] The density of new snowfall can be calculated using the following formula (1). (1) In the formula, New snowfall density, Near-surface temperature, The temperature at which snow melts. Near-surface wind speed, It is the lowest density of fresh snow. , , These are empirical parameters.
[0031] Step S112: Determine the thickness of the new snowfall based on the new snow density, snowfall amount, and water density.
[0032] The thickness of the new snowfall can be calculated using the following formula (2): (2) in, Indicates the thickness of the new snowfall. Indicates the amount of snowfall. , This indicates the density of new snowfall. Snowfall amount can be obtained through meteorological observations.
[0033] Step S1113: Determine the snow layer structure based on the new snowfall thickness, the current top layer thickness, and the time interval between the two snowfall events.
[0034] Among them, if the following two conditions are met: (1) the current top layer thickness is less than the preset maximum thickness. (2) The time interval between two snowfall events is less than the preset time. The new snowfall thickness is incorporated into the current top layer thickness to obtain an updated snow surface thickness; if any condition is not met, the total number of snow layers is incremented by one, and the new snowfall thickness is taken as an independent snow surface thickness.
[0035] The current top layer thickness is the current thickness of the surface snow layer. If the current top layer thickness is not thick (less than...), then... Furthermore, the time interval between the two snowfall events was very short (less than the preset time). If the snowfall is below a certain threshold, then the new snowfall can be incorporated into the current snow cover. Conversely, if the snowfall is below a certain threshold, then the new snowfall is treated as a separate layer, meaning the new snowfall is the surface layer and the current top layer is the inner layer, thus increasing the total number of snow layers by one. Of course, this applies when the thickness of any snow layer is below the minimum thickness threshold. When this occurs, the snow layer is automatically removed, reducing the total number of snow layers accordingly. , and These three parameters enable the method to achieve a refined simulation of the dynamic process of snow accumulation (i.e., the snow accumulation and melting process), capturing key physical features while maintaining numerical stability.
[0036] Step S120: For each snow layer, construct a hydrothermal coupling equation and use the fourth-order Runge-Kutta method to solve for the temperature of the current snow layer at the second moment using the first attribute parameters of the current snow layer at the first moment.
[0037] Once the snow layer structure is determined, a hydrothermal coupling equation can be established for each snow layer to calculate its temperature and then deduce its other physical properties.
[0038] The hydrothermal coupling equations for each snow layer are as follows: (3) in, It is the density of snow cover. It is the specific heat capacity of snow. It's the thickness of the snow layer. It is the center height of the snow layer ( It is the difference in center height between adjacent snow layers. This represents the gradient of heat conduction flux in the snow layer. This represents the temperature gradient between two adjacent layers, calculated by dividing the temperature difference by the center height difference; taking the second snow layer as an example... This includes the temperature gradients between the second and third snow layers, as well as between the second and first snow layers. For the surface layer, then... (It only includes the temperature gradient between the surface and the second snow layer). It is the temperature of the snow layer. It is the specific heat capacity of water. It is the density of water. It refers to the intensity of rainfall. It refers to the intensity of snowfall. It is the specific heat capacity of ice. Near-surface temperature, It is the flux of liquid water entering the snow layer. It's the freeze-thaw rate. It is the latent heat of fusion. It is the thermal conductivity of snow. It is shortwave radiation incident on the snow layer. It is the length of time that snow absorbs sunlight. It is the amount of liquid water that evaporates or condenses on the surface of snow. Latent heat of vaporization It refers to the amount of ice sublimation or deposition on the surface of the snow. To sublimate latent heat, It is the sensible heat flux between the snow surface and the atmosphere. It is the net longwave radiation of the snow surface; The first line applies to the surface layer of snow, and the second line applies to the inner layer. This only applies to the surface layer of snow. In other words, the hydrothermal coupling equations for the surface and inner layers of snow are different.
[0039] The primary attribute parameters of the current snow layer at the first moment can include snow density, snow layer thickness, freeze-thaw rate, and snow layer temperature. The fourth-order Runge-Kutta method is used to solve for the temperature of the current snow layer at the second moment using these primary attribute parameters. The first and second moments are relative; subsequent moments can be used as the first moment to continuously update the state of the snow layer and simulate the evolution of snow cover.
[0040] The fourth-order Runge-Kutta method (RK4) is a classic numerical method for solving initial value problems of ordinary differential equations. It obtains a more accurate solution than the simple Euler method by calculating the slope (gradient) multiple times within a time step and performing a weighted average, while not requiring the calculation of higher-order derivatives, making it relatively simple to implement. The typical application steps of RK4 are as follows: (1) State vector: Define the state variables of all snow layers at the first moment, such as the temperature, density, and thickness of each snow layer. (2) Calculate the derivative (slope): Based on the current state of each layer, calculate the rate of change (i.e., derivative) of each state variable with time according to the conservation of energy and mass. Four-step recursion: RK4 uses this derivative to perform four "prediction-correction" steps to calculate the slope (k1, k2, k3, k4) at four different time points, and finally combines these four slopes with specific weights (1 / 6, 1 / 3, 1 / 3, 1 / 6) to obtain the high-precision average rate of change within the time step. State update: Using this weighted average rate of change, the state of the entire snow system is advanced from the current first time t to the second time t+Δt. Therefore, by using the fourth-order Runge-Kutta method and the first attribute parameters of the current snow layer at the first time (t), the temperature of the current snow layer at the second time (t+Δt) can be obtained. In other words, when calculating the temperature of the current snow layer at the second time (t+Δt), the variable values in formula (3) are the attribute parameters (i.e., the first attribute parameters) of the current snow layer at the first time (t), such as the snow layer temperature, snow layer density, snow layer thickness, freeze-thaw rate, and liquid water flux into the snow layer.
[0041] In one embodiment, the above-mentioned hydrothermal coupling equation can be constructed in the following manner.
[0042] It should be noted that the temperature and phase composition (ice and liquid water) of the snow layer are calculated using the laws of energy conservation and mass conservation. The energy conservation equation for each snow layer is as follows: (4) The terms on the left side of the equation represent the rate of change of heat in the snow layer per unit time. On the right side of the equation, the first row of the vectors within the square brackets applies to the surface layer, and the second row applies to the inner layer; the terms within the curly braces apply only to the surface layer of snow. The terms on the right side of equation (4) represent, in order: the advection heat brought by inflow / precipitation, the heat carried away by outflow, the absorbed solar shortwave radiation, the conduction heat flux, the latent heat effect of phase change (melting / refreezing), and the net longwave radiation of the snow surface layer (… The heat flux generated due to evaporation (condensation) or sublimation (deposition) or ), and the sensible heat flux between the snow surface and the atmosphere ( ).
[0043] in, It is the density of snow cover. It is the specific heat capacity of snow. It is the temperature of the snow layer. It is the center height of the snow layer. It's the thickness of the snow layer. and These are the rainfall and snowfall intensities, respectively. and These are the specific heat capacities of water and ice, respectively. and It refers to the water flux and temperature entering the snow layer from the upper layer. It is the water flux outflow from the snow layer. It is the shortwave radiation incident on the snow layer, for the surface of the snow, , It is the total incident solar shortwave radiation. It's albedo. Here we use a simple assumption: when the total snow layer thickness... Greater than 0.1m and At temperatures below 0°C, ,otherwise, . This refers to the absorption length of sunlight by the snow; the amount of shortwave radiation that passes through the current snow layer and enters the next snow layer is... . It is the thermal conductivity of snow. Gradient conduction, representing heat, It is the mass flux of snow melting or refreezing (i.e., freeze-thaw rate). It is the latent heat of fusion. , It is the amount of liquid water that evaporates or condenses on the surface of snow. It is the latent heat of vaporization; , It refers to the amount of ice sublimation or deposition on the surface of the snow. For latent heat of sublimation. If liquid water exists on the surface of the snow, then only consider... ,Right now If no liquid water is present, then consider ,Right now . and All are derived from formulas To calculate, where, and These are the specific humidity of the snow surface and the air near the ground, respectively. According to the input air pressure and water vapor pressure Calculated using formula (5): (5) and The calculation still uses the same formula, but the water vapor pressure in the formula... Replace it with the saturated vapor pressure obtained from the snow surface temperature using the Goff-Gratch equation (Goff, 1957).
[0044] Net longwave radiation of snow surface Use formula (6) to calculate: (6) in, The emissivity of snow. This is the Stefan–Boltzmann constant. The surface snow temperature, This represents the incident long-wave radiation. The sensible heat flux between the snow surface and the air. The calculation formula is: (7) in, air density, The specific heat capacity of air. This is the heat exchange coefficient.
[0045] The water balance of each snow layer can be expressed by the following formula: (8) (9) in, and These represent the volumetric ice content and volumetric water content in the snow layer, respectively. and These represent the mass content of ice and the mass content of water, respectively. According to and Ignoring the influence of air (air density is much smaller than that of ice and water), the specific heat capacity of the snow layer can be calculated: (10) By combining the above formulas (4), (8), (9), and (10), we can obtain the hydrothermal coupling equation shown in formula (3).
[0046] Step S130: Determine the freeze-thaw rate of the snow layer at the second moment based on the temperature of the snow layer at the second moment.
[0047] The formula for calculating the freeze-thaw rate of the snow layer at the second moment is as follows: (11) in, This indicates the amount of snow cover at the second moment. It is the snow density of the current snow layer at the first moment. It is the specific heat capacity of snow. It is the current snow layer thickness at the first moment. It is the temperature at which snow melts. It is the temperature of the snow layer at the second moment. It is the latent heat of fusion. It is the time interval between the first moment and the second moment.
[0048] The snow density of the snow layer at the first moment Snow layer thickness And the temperature of the snow layer at the second moment. Substituting into formula (11), the freeze-thaw rate of the snow layer at the second moment can be calculated. .
[0049] Step S140: Determine the second attribute parameter of the current snow layer at the second moment based on the first attribute parameter of the current snow layer at the first moment and the freeze-thaw rate of the current snow layer at the second moment.
[0050] The second attribute parameter refers to the attribute parameter of the snow layer at the second moment. It is called the second attribute parameter in order to distinguish it from the attribute parameter of the snow layer at the first moment. The second attribute parameter may also include the snow layer density, snow layer thickness, liquid water content, and solid water content (i.e., ice content) of the snow layer at the second moment.
[0051] In one embodiment, step S140 specifically includes: determining the liquid water content and solid water content of the current snow layer at the second moment based on the first attribute parameter of the current snow layer at the first moment and the freeze-thaw rate of the current snow layer at the second moment.
[0052] when hour, When the snow melts, the absolute value of the melt does not exceed the ice content in the snow layer; when , When water in the snow layer refreezes, its absolute value does not exceed the water content in the snow layer.
[0053] Assuming the water-holding capacity of the snow layer yes Functions: (12) Here are the parameters If we take 0.3, then the maximum water holding capacity of the snow layer is: (13) When the water content in the snow layer is greater than When excess water is present, it will flow to the lower layers under the influence of gravity. Otherwise, the liquid water remains within the layers. That is: (14) Infiltration flux of this layer That is, the inflow flux of the next snow layer The freeze-thaw rate of the snow layer at the second moment was obtained. Infiltration volume and the exchange of water between the snow surface and the atmosphere ( and ), and then the liquid water content and solid water content of the current snow layer at the second moment can be obtained according to formulas (8) and (9).
[0054] In one embodiment, step S140 further includes: determining the snow layer density of the current snow layer at the second time based on the first attribute parameter of the current snow layer at the first time; and determining the snow layer thickness of the current snow layer at the second time based on the snow layer density of the current snow layer at the second time.
[0055] It should be noted that the density of the snow layer is mainly affected by snow pressure and temperature, and the formula for its density change over time is as follows: (15) in, It is the sum of its own mass and the mass of the overlying snow. , , and It is an empirical coefficient. It is the viscosity coefficient, and its calculation formula is as follows: (16) in, , This is an empirical coefficient. Let be the initial viscosity coefficient. According to formula (15), the updated snow layer density is obtained explicitly by using the forward difference method. (i.e., the snow density at the second moment). Specifically, given the snow density, snow temperature, and the sum of the masses of the current snow layer and the upper snow layer at the first moment t (the mass of the current snow layer is the sum of the mass of ice content and the mass of water content, and the mass of the upper snow layer is the sum of the mass of ice content and the mass of water content), substitute these values into the above formulas (15) and (16) to calculate the snow density at the second moment t+Δt.
[0056] Furthermore, the snow layer thickness at the second moment can be calculated using the following formula (17): (17) in, This represents the current snow layer thickness at time t+1 (i.e., the second time). It is the snow density of the current snow layer at time t (i.e., the first time). It is the snow density of the current snow layer at time t+1 (i.e., the second time). It is the current snow layer thickness at time t (i.e., the first time).
[0057] Compared with the prior art, this application has the following beneficial effects: (1) Achieve explicit tracking of the snow cover life cycle and improve the simulation realism of snow profile evolution.
[0058] This application, based on a Lagrange adaptive multilayer framework, treats each snow layer as an independent unit, explicitly tracking its complete lifecycle from deposition to ablation. When new snow arrives, the model automatically generates new layers; when a layer completely melts, the model dynamically updates the vertical adjacency relationships between the remaining layers, without requiring manual layering or mesh reconstruction. This mechanism avoids the numerical diffusion problems caused by fixed meshes and manual layering in traditional Eulerian frameworks, ensuring clear snow layer interfaces and continuous material exchange, and more realistically reproducing the natural evolution of snow profiles. For hydrological simulation, this means a significant improvement in the accuracy of characterizing key hydrological properties such as snow's water storage capacity, interlayer hydraulic connections, and meltwater transport paths.
[0059] (2) Refine the analysis of the internal water-heat coupling process of snow accumulation to improve the simulation accuracy of the snow melting flow process.
[0060] This application explicitly analyzes the continuous changes in thickness, density, liquid water content, and ice content of each snow layer during accumulation, densification, melting, refreezing, and drainage processes by coupling water balance and energy balance equations. In particular, it fully considers the heat transfer effect during liquid water infiltration and the water retention and refreezing mechanisms within the snow layers. This enables the model to accurately simulate the vertical transport of meltwater within the snow layer, including key hydrological processes such as water-blocking effects and refreezing of meltwater at night or during cold periods. Compared to existing multilayer models, this application more realistically reflects the hysteresis effect and peak response of snowmelt runoff, providing a more reliable physical basis for snowmelt runoff forecasting.
[0061] (3) It takes into account both physical mechanisms and computational efficiency, and provides a highly applicable snow accumulation simulation tool for land surface processes and hydrological models.
[0062] This application employs an adaptive multilayer structure without pre-setting an upper limit on the number of snow layers, enabling flexible adaptation to simulation needs across different climate zones and snow depths. During calculations, the model only needs to maintain the currently existing snow layers and their adjacent relationships, avoiding redundant calculations caused by fixed layers or frequent grid reconstruction in traditional methods. Furthermore, this method is highly modular, easily coupled with existing land surface process models or hydrological models (such as VIC, Noah-MP, SWAT, etc.), and can directly output key hydrological variables such as snowmelt water equivalent, interlayer liquid water storage, and bottom outflow. Therefore, this invention is suitable for studying the mechanisms of hydrological processes in high-altitude watersheds and also has the potential for large-scale, long-term snowmelt runoff simulation, providing strong technical support for water resource management, spring flood warning, and climate change impact assessment.
[0063] (4) The simulation results are more interpretable and support the understanding of the process mechanism. Because this method explicitly tracks the evolution of each snow layer, the simulation results directly reflect the response of each layer to meteorological forcing, giving the model output clear physical meaning and facilitating researchers' analysis of the underlying mechanisms of snow cover changes. This high interpretability is of great significance for improving snow cover parameterization schemes, validating remote sensing observations, and enhancing the model's applicability in data-scarce regions.
[0064] It should be noted that existing multi-layer snow models (such as Noah-MP and CLM) are typically based on Eulerian meshes. When simulating the processes of snow accumulation, densification, and ablation, the snow layers need to be artificially relayered or the mesh reconstructed. This approach makes it difficult to explicitly track the complete lifecycle of each snow layer from deposition to ablation and easily introduces numerical diffusion, leading to blurred interfaces between snow layers and distorted material exchange, thereby reducing the simulation accuracy of snow profile evolution. This application introduces a Lagrangian adaptive multilayer framework, treating each snow layer as an independent unit with vertical adjacency. A new layer is generated at the top of the snow layer during snowfall, and the adjacency relationships between the remaining layers are dynamically updated when the layer completely ablates. This method eliminates the need for artificial relayering and does not limit the number of snow layers. It avoids the mesh reconstruction artifacts inherent in Eulerian frameworks and achieves physical consistency and high-fidelity tracking of snow profile evolution.
[0065] Existing multilayer models often neglect the advectional heat changes caused by infiltrating water flow when solving for energy balance, and their descriptions of the generation, retention, migration, and refreezing processes of liquid water inside snow are relatively simplified, making it difficult to realistically reflect the vertical migration patterns of snowmelt water and its impact on energy redistribution. This application constructs a dynamic control system composed of coupled water balance and energy balance equations to explicitly analyze the continuous changes in thickness, density, liquid water content, and ice content of each snow layer during accumulation / input, densification, melting / refreezing, and drainage / outflow processes. This enables a refined simulation of the hydrothermal processes inside snow, improving the physical realism of the snowmelt process simulation.
[0066] In existing snow cover models used in hydrological and land surface modeling applications, the accuracy of simulations of basic snow cover state variables—including snow depth and snow water equivalent—still needs improvement. Particularly under the influence of complex snow layer structures, existing models struggle to accurately characterize the accumulation, compaction, and ablation processes of multiple snow layers, leading to discrepancies between the dynamic evolution of snow depth and snow water equivalent and actual observations. Furthermore, due to insufficient descriptive capabilities for key hydrological processes such as ice layer water blocking, intralayer refreezing, and meltwater runoff delay, existing models cannot accurately reproduce the spatiotemporal dynamics of snowmelt runoff, thus affecting the reliability of snowmelt runoff forecasts and the understanding of mechanisms for responding to climate change. This application aims to provide a snow cover simulation tool with clearly defined physical mechanisms and strong adaptive capabilities, enabling high-precision simulation of snow cover state variables (snow depth, snow water equivalent) and their associated hydrothermal processes, providing reliable technical support for hydrological process simulation, snowmelt runoff forecasting, and water resource management in high-altitude and cold regions.
[0067] Furthermore, to verify the effectiveness of the method provided in this application, snow cover observation data (such as snow depth and snow water equivalent) from multiple global stations provided by SnowMIP and corresponding meteorological information were used to validate the proposed simulation method (Ménard et al., 2019). The input meteorological data included hourly snowfall, precipitation, air temperature, humidity, shortwave radiation, longwave radiation, air pressure, and wind speed. During the simulation, the observed surface soil temperature was used as a boundary condition. Station information is shown in Table 1 below: Table 1 Geographic Information of Each Site During the simulation, except for the minimum albedo value at each site... Aside from differentiating the parameters based on actual surface characteristics, all other model parameters remained consistent to verify the applicability of the method under different climatic and surface conditions. The snow depth variation process simulated at each station is as follows: Figure 3 As shown in Table 2, detailed evaluation indicators are presented. The results demonstrate that the method proposed in this invention can effectively capture the seasonal evolution characteristics of snow depth and accurately reproduce the peak snow depth and its occurrence time at each station. From a quantitative evaluation perspective, the closer the Nash-Sutcliffe efficiency coefficient (NSE) and Kling-Gupta efficiency coefficient (KGE) are to 1, the better the simulation performance. The average NSE for the four stations reached 0.85, and the average KGE reached 0.82, indicating that the method exhibits excellent simulation performance at most stations. Specifically, the performance of each station is as follows: CDP station (1995–2013) has an NSE of 0.67 and a KGE of 0.51, which are relatively low, but the correlation coefficient R reaches 0.94, indicating that the simulation of the dynamic trend of snow depth at this station is still relatively ideal; RME station (1989–2007) has an NSE and KGE as high as 0.95 and 0.88, respectively, an RMSE of 13.18 cm, and a MAE of 7.84 cm; WFJ station (1998–2015) has an NSE of 0.89, a KGE of 0.92, an RMSE of 26.49 cm, and a MAE of 19.19 cm, and the simulation results are reliable; SOD station (2008–2013) also performed well, with an NSE and KGE of 0.90 and 0.95, respectively, an RMSE of 8.04 cm, and a MAE of 6.18 cm, and the simulation accuracy is high. In summary, the method of this invention can stably obtain high-precision snow depth simulation results under different climatic conditions and snow cover characteristics, demonstrating good generalization ability and application potential.
[0068] Table 2 Simulated indicators of snow depth at different stations Table 2 Simulated indicators of snow depth at different stations Note: NSE is the Nash-Sutcliffe efficiency coefficient, KGE is the Kling-Gupta efficiency coefficient, R is the correlation coefficient, RMSE is the root mean square error, and MAE is the mean absolute error.
[0069] Snow water equivalent (SWE) is a key parameter for quantifying the total water storage within the snow cover, directly reflecting the water resource reserves of the snow layer, and is an important input variable for hydrological simulation and runoff forecasting. The time-series variations of snow water equivalent at various stations obtained from simulations are shown below. Figure 4 As shown, overall, the simulation results can reproduce the observed SWE accumulation and ablation process well, and the magnitude and temporal phase are in good agreement with the measured data. Quantitative evaluation indicators for the snow water equivalent simulation at each station are shown in Table 3. Overall, the Nash-Sutcliffe efficiency coefficient (NSE) at all four stations is above 0.80, and the Kling-Gupta efficiency coefficient (KGE) is above 0.75, indicating that the method of this invention has high accuracy in snow water equivalent simulation. Specifically, the CDP station showed a good simulation effect with an NSE of 0.85, a KGE of 0.75, an R-coefficient of 0.96, and RMSE and MAE of 6.11 cm and 3.68 cm, respectively. The RME station performed best, with an NSE of 0.93, a KGE of 0.85, a high R-coefficient of 0.97, and RMSE and MAE of only 5.37 cm and 3.06 cm, respectively. The WFJ station had an NSE of 0.80, a KGE of 0.88, an R-coefficient of 0.90, an RMSE of 12.34 cm, and a MAE of 8.81 cm. Considering the large variation in snow water equivalent at this station, the simulation results are still reliable. The SOD station had an NSE of 0.84, a KGE of 0.82, an R-coefficient of 0.95, an RMSE of 2.16 cm, and a MAE of 1.72 cm, with small simulation errors and high accuracy.
[0070] In summary, the method of the present invention can accurately simulate the snowmelt equivalent change process at multiple sites and under different climatic conditions, demonstrating good applicability and stability, and can provide reliable snowmelt equivalent data support for snowmelt runoff forecasting and water resource assessment.
[0071] Table 3. Simulation results of snow water equivalent at different stations In evaluating the performance of snowmelt equivalent simulations, Krinner et al. (2018) used the standardized root mean square error (NRMSE) as an evaluation metric. This metric is defined as the ratio of the root mean square error (RMSE) to the standard deviation of the observed values, and is used to measure the model's predictive ability relative to the observed climate mean. For the same site, this study systematically evaluated the snowmelt equivalent simulation performance of 26 energy balance-based snowmelt models. The evaluation results are as follows: Figure 5 As shown in the figure, the dashed line represents NRMSE = 1. If the model's NRMSE exceeds this threshold, it indicates that the simple method of using observed climate averages as predictions is superior to the model. The black squares represent the ensemble average results of 26 models in the study by Krinner et al. (2018). Krinner et al. (2018) pointed out that multi-model ensemble averaging usually exhibits the lowest error and has the best simulation effect in most cases. Based on this, the method of this invention was applied to four sites: CDP, RME, WFJ, and SOD. The calculated NRMSE values were 0.39, 0.28, 0.45, and 0.40, respectively. The comparison results show that the NRMSE values of the method of this invention at each site are comparable to the results of the multi-model ensemble averaging, indicating that this method surpasses most existing models in the simulation of snow cover water equivalent and has a simulation capability comparable to multi-model ensemble averaging, further verifying the effectiveness and superiority of the snow cover simulation method proposed in this invention.
[0072] To further evaluate the performance of the method (LAMS) in simulating snowmelt equivalent, its results were compared with those of several mainstream international snow cover models at the CDP site. The root mean square error (RMSE) was used as the evaluation index; a lower RMSE indicates higher simulation accuracy. The comparison results are shown in Table 4. The reference models included in the comparison were: the JIM model, the WEB-DHM-S model, the ISBA-FR / ES model, and the CROCUS model. These models are all internationally recognized snow cover schemes based on energy balance, and their simulation results are cited from relevant literature. From the RMSE of the snowmelt equivalent simulation, the JIM model's RMSE under different settings ranged from 23 to 77 kg / m², with the best performance being the uncalibrated JIM 849 version (RMSE = 23 kg / m²); the WEB-DHM-S model had an RMSE of 35 kg / m²; the ISBA-FR and ISBA-ES models had RMSEs of 69 kg / m² and 39 kg / m², respectively; and the CROCUS model had an RMSE of 71 kg / m². In comparison, the LAMS model of this invention achieves a snow water equivalent simulation RMSE of only 13 kg / m² at the same site, significantly lower than all reference models used in the comparison. These comparative results demonstrate that the method of this invention outperforms existing mainstream snow cover models in terms of snow water equivalent simulation accuracy at CDP sites, further validating the effectiveness and superiority of the proposed Lagrange adaptive multilayer framework in simulating snow cover hydrological processes.
[0073] Table 4. Comparison of RMSE of snow water equivalent and snow depth in CDP simulations of the LAMS model and reference models (JIM, WEB-DHM-S, ISBA-FR / ES, CROCUS) at the SnowMIP site; lower values indicate better performance. To further compare the snow cover simulation effects in existing hydrological models, using the same input data, the simulation results of the widely used VIC land surface model and the method of this invention (LAMS) are compared and analyzed. Figure 6 To ensure comparability of results, we bypassed the temperature-based precipitation phase partitioning scheme within the original VIC model and directly input precipitation and snowfall data provided by SnowMIP into both models. The VIC model employs a simplified two-layer snow cover scheme, comprising a thin top layer controlling flux and a thick bottom layer storing mass. As shown in Table 5, the simulation performance of the VIC model is significantly inferior to that of the method described in this invention. At the SOD site, the VIC model simulated snow depth with an NSE of 0.49 and a KGE of 0.54, while the method achieved 0.89 and 0.90, respectively. At the WFJ site, the VIC model simulated snow depth with an NSE of 0.85 and a KGE of 0.71, while the method achieved 0.93 and 0.86, respectively. Based on the snowmelt equivalent simulation, the NSE and KGE values for the SOD site VIC were 0.77 and 0.81, respectively, while those for LAMS were 0.86 and 0.85. For the WFJ site, the NSE and KGE values for VIC were 0.67 and 0.79, respectively, while our method achieved 0.92 and 0.92. Furthermore, our method significantly outperformed VIC in terms of NRMSE. At the SOD site, the snow depth NRMSE decreased from 0.71 to 0.33, and the snowmelt equivalent NRMSE decreased from 0.48 to 0.37. At the WFJ site, the snow depth NRMSE decreased from 0.39 to 0.26, and the snowmelt equivalent NRMSE decreased from 0.57 to 0.29. The snow depth simulated by VIC at multiple sites was significantly lower than the observed values. This systematic overestimation of snowmelt may stem from the inherent structural simplification of its two-layer scheme, leading to an overly sensitive and rapid response of the model to surface energy inputs (including radiation, sensible heat, and latent heat fluxes), resulting in an overly rapid snowmelt process. The Lagrange Adaptive Multilayer Framework (LAMS) proposed in this invention explicitly analyzes the vertical evolution of snow cover properties such as thickness, density, temperature, and liquid water content in each layer through a layer-tracking mechanism. This refined simulation capability makes the reproduction of snowmelt dynamics more gradual and physically accurate. Based on the above comparative results, the superior performance of LAMS strongly demonstrates that its layer-tracking method makes a significant contribution to improving the accuracy of snow cover simulation in land surface process models and hydrological models, and can provide more reliable technical support for the simulation of hydrological processes in cold regions and the forecasting of snowmelt runoff.
[0074] Table 5. Simulation performance of VIC and LAMS models on snow depth and snowmelt equivalent at SOD and WFJ sites. This invention can precisely characterize the hydrothermal processes within snow cover, accurately simulating the spatiotemporal dynamics of snow depth, snow water equivalent, and meltwater runoff. It can provide core technical support for spring snowmelt runoff forecasting in high-altitude and cold-climate river basins in my country, serving flood control, disaster reduction, and water resource allocation. This invention is highly modular and can be embedded into existing mainstream land surface process models (such as Noah-MP and CLM) and hydrological models (such as VIC and SWAT), enhancing their ability to simulate snow cover processes and supporting water resource assessment and land-atmosphere interaction research under the background of climate change. The simulation results of this invention (such as snow depth, snow water equivalent, and snow cover) can be directly compared and verified with satellite remote sensing observations, and can also serve as the background field for data assimilation systems, improving the accuracy and spatiotemporal continuity of remote sensing inversion products. This invention can provide medium- and long-term snowmelt runoff forecasts, providing decision-making basis for the optimized scheduling of reservoir groups mainly supplied by snowmelt, agricultural irrigation planning, and urban water supply security.
[0075] The above are merely preferred embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.
[0076] Figure 7 This is a block diagram of a snow cover evolution simulation device provided in an embodiment of this application, such as... Figure 7 As shown, the device includes: a structure determination module 610, a temperature determination module 620, a freeze-thaw rate determination module 630, and an attribute update module 640.
[0077] The structure determination module 610 is used to determine the snow layer structure by simulating the snow accumulation and melting process.
[0078] The temperature determination module 620 is used to construct a hydrothermal coupling equation for each snow layer and use the fourth-order Runge-Kutta method to solve for the temperature of the current snow layer at the second moment using the first attribute parameters of the current snow layer at the first moment.
[0079] The freeze-thaw rate determination module 630 is used to determine the freeze-thaw rate of the snow layer at the second moment based on the temperature of the snow layer at the second moment.
[0080] The attribute update module 640 is used to determine the second attribute parameter of the current snow layer at the second moment based on the first attribute parameter of the current snow layer at the first moment and the freeze-thaw rate of the current snow layer at the second moment.
[0081] The specific implementation process of the functions and roles of each module in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.
[0082] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. Each method step is implemented by a corresponding module, which will not be described in detail here. The device embodiments described above are merely illustrative. The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of the solution in this specification according to actual needs. Those skilled in the art can understand and implement this without creative effort.
[0083] Figure 8 This specification illustrates a hardware structure diagram of an electronic device housing a snow cover evolution simulation apparatus according to an exemplary embodiment. Figure 8 As shown, the device may include: a processor 301, a memory 302, an input / output interface 303, a communication interface 304, and a bus 305. The processor 301, memory 302, input / output interface 303, and communication interface 304 are interconnected within the device via the bus 305.
[0084] The processor 301 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the steps of the snow accumulation evolution simulation method provided in the embodiments of this specification.
[0085] The memory 302 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 302 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program code is stored in the memory 302 and is called and executed by the processor 301.
[0086] Input / output interface 303 is used to connect input / output modules to realize information input and output. Input / output modules can be configured as components in the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Input devices may include keyboards, mice, touch screens, microphones, various sensors, etc., and output devices may include displays, speakers, vibrators, indicator lights, etc.
[0087] Communication interface 304 is used to connect a communication module (not shown in the figure) to enable communication and interaction between this device and other devices. The communication module can communicate via wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).
[0088] Bus 305 includes a pathway for transmitting information between various components of the device (e.g., processor 301, memory 302, input / output interface 303, and communication interface 304).
[0089] It should be noted that although the above-described device only shows the processor 301, memory 302, input / output interface 303, communication interface 304, and bus 305, in specific implementations, the device may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the above-described device may only include the components necessary for implementing the embodiments of this specification, and not necessarily all the components shown in the figures.
[0090] This specification also provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the snow cover evolution simulation method provided in this specification.
[0091] This specification also provides a computer program product, which includes computer-executable instructions stored in a computer-readable storage medium; wherein, when the processor of an electronic device reads the computer-executable instructions from the computer-readable storage medium and executes the computer-executable instructions, it implements the steps of the snow cover evolution simulation method described in the above embodiments of this application.
[0092] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.
[0093] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0094] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.
Claims
1. A method for simulating snow cover evolution, characterized in that, include: The snow layer structure was determined by simulating the snow accumulation and melting process; For each snow layer, a hydrothermal coupling equation is constructed, and the temperature of the snow layer at the second moment is obtained by using the first attribute parameter of the current snow layer at the first moment using the fourth-order Runge-Kutta method. Determine the freeze-thaw rate of the snow layer at the second moment based on the temperature of the snow layer at the second moment. Based on the first attribute parameters of the current snow layer at the first moment and the freeze-thaw rate of the current snow layer at the second moment, determine the second attribute parameters of the current snow layer at the second moment.
2. The method according to claim 1, characterized in that, The process of determining the snow layer structure by simulating the snow accumulation and melting process includes: The density of new snowfall is determined based on near-surface temperature and near-surface wind speed. The thickness of the new snowfall is determined based on the density, amount, and water density of the new snowfall. The snow cover structure is determined based on the new snowfall thickness, the current top layer thickness, and the time interval between two snowfall events.
3. The method according to claim 2, characterized in that, The thickness of the new snowfall is determined based on the density, amount, and water density of the new snowfall using the following formula: in, Indicates the thickness of the new snowfall. Indicates the amount of snowfall. , This indicates the density of new snowfall.
4. The method according to claim 2, characterized in that, The process of determining the snow cover structure based on the new snowfall thickness, the current top layer thickness, and the time interval between two snowfall events includes: If the following two conditions are met: (1) The current top layer thickness is less than the preset maximum thickness. (2) The time interval between two snowfall events is less than the preset time. The new snowfall thickness is incorporated into the current top layer thickness to obtain the updated snow surface thickness; If any condition is not met, the total number of snow layers is incremented by one, and the new snowfall thickness is taken as an independent surface snow layer thickness.
5. The method according to claim 1, characterized in that, For each snow layer, the hydrothermal coupling equation is constructed as follows: in, It is the density of snow cover. It is the specific heat capacity of snow. It's the thickness of the snow layer. It is the center height of the snow layer. It is the temperature of the snow layer. It is the specific heat capacity of water. It is the density of water. It refers to the intensity of rainfall. It refers to the intensity of snowfall. It is the specific heat capacity of ice. Near-surface temperature, It is the flux of liquid water entering the snow layer. It's the freeze-thaw rate. It is the latent heat of fusion. It is the thermal conductivity of snow. It is shortwave radiation incident on the snow layer. It is the length of time that snow absorbs sunlight. It is the amount of liquid water that evaporates or condenses on the surface of snow. Latent heat of vaporization It refers to the amount of ice sublimation or deposition on the surface of the snow. To sublimate latent heat, It is the sensible heat flux between the snow surface and the atmosphere. It is the net longwave radiation of the snow surface; The first line applies to the surface layer of snow, and the second line applies to the inner layer. Only applicable to the surface of snow; The first attribute parameters of the current snow layer at the first moment include the snow density, snow layer thickness, freeze-thaw rate, and snow layer temperature at the first moment.
6. The method according to claim 1, characterized in that, The freeze-thaw rate of the snow layer at the second moment is determined based on the temperature of the snow layer at the second moment using the following formula. in, This indicates the amount of snow cover at the second moment. It is the snow density of the current snow layer at the first moment. It is the specific heat capacity of snow. It is the current snow layer thickness at the first moment. It is the temperature at which snow melts. It is the temperature of the snow layer at the second moment. It is the latent heat of fusion. It is the time interval between the first moment and the second moment.
7. The method according to claim 1, characterized in that, The step of determining the second attribute parameter of the snow layer at the second moment based on the first attribute parameter of the snow layer at the first moment and the freeze-thaw rate of the snow layer at the second moment includes: Based on the first attribute parameters of the snow layer at the first moment and the freeze-thaw rate of the snow layer at the second moment, determine the liquid water content and solid water content of the snow layer at the second moment.
8. The method according to claim 1, characterized in that, The step of determining the second attribute parameter of the snow layer at the second moment based on the first attribute parameter of the snow layer at the first moment and the freeze-thaw rate of the snow layer at the second moment includes: Determine the snow density of the snow layer at the second moment based on the first attribute parameter of the snow layer at the first moment. The snow layer thickness at the second moment is determined based on the snow layer density at the second moment.
9. The method according to claim 1, characterized in that, The method of determining the snow layer structure by simulating the snow accumulation and melting process also includes: When the thickness of any snow layer is below the minimum thickness threshold When the snow layer is removed, the total number of layers is reduced accordingly.
10. A snow cover evolution simulation device, characterized in that, include: The structure determination module is used to determine the snow layer structure by simulating the snow accumulation and melting process; The temperature determination module is used to construct a hydrothermal coupling equation for each snow layer and use the fourth-order Runge-Kutta method to solve for the temperature of the current snow layer at the second moment using the first attribute parameters of the current snow layer at the first moment. The freeze-thaw rate determination module is used to determine the freeze-thaw rate of the snow layer at the second moment based on the temperature of the snow layer at the second moment. The attribute update module is used to determine the second attribute parameter of the current snow layer at the second moment based on the first attribute parameter of the current snow layer at the first moment and the freeze-thaw rate of the current snow layer at the second moment.
11. An electronic device, characterized in that, include: Memory is used to store executable instructions for a computer; A processor, when executing computer-executable instructions stored in the memory, implements the snow cover evolution simulation method according to any one of claims 1 to 9.
12. A computer-readable storage medium, characterized in that, The device stores computer-executable instructions, which, when executed by a processor, implement the snow cover evolution simulation method according to any one of claims 1 to 9.
13. A computer program product, characterized in that, The computer program product includes computer-executable instructions stored in a computer-readable storage medium; When the processor of the electronic device reads the computer-executable instructions from the computer-readable storage medium and executes the computer-executable instructions, it implements the snow cover evolution simulation method according to any one of claims 1 to 9.