A modeling method for granular snow compaction considering liquid water seepage and phase change mechanism

Abstract

This invention discloses a snow compaction modeling method that considers the mechanisms of liquid water seepage and phase change. This method simulates a snow column as a three-component porous medium composed of a solid phase (snow grains), a liquid phase (water), and a gaseous phase (air) to explain the influence of liquid water generated by processes such as rainfall and surface snow melting on snow compaction. Compared to traditional snow compaction models that only consider temperature and the pressure of the overlying snow grains, this invention, from the perspective of revealing the mechanisms of liquid water seepage and phase change, considers the impact of refreezing on the snow layer mass and the impact of the latent heat of phase change released during refreezing on the snow layer temperature. The latent heat of phase change released by the refreezing of liquid water can accelerate the snow compaction rate. When there is a large amount of liquid water on the surface of the snow column, this invention can more accurately simulate the snow compaction process. By comprehensively considering multiple influencing factors, this invention improves the simulation accuracy of the snow compaction process and can be more widely applied to different scenarios and environments.

Description

Technical Field

[0001] This invention belongs to the technical fields of glacier mass balance monitoring, ice core paleoclimate environment analysis, glacier ice reserve estimation, snow and ice disaster prediction, snow and ice engineering, and snow and ice physics research. More specifically, it relates to a granular snow densification modeling method that takes into account the seepage and phase change mechanism of liquid water. Background Technology

[0002] Glaciers are flowing solids formed from snow crystals, a transformation process that is lengthy and complex. Snow crystals are formed by the sublimation of water vapor in the atmosphere at low temperatures. Due to the constantly changing conditions during sublimation, such as temperature, water vapor saturation, and airflow disturbances, newly fallen snow crystals exhibit a variety of shapes. According to thermodynamic principles, the lower the free energy of a system, the more stable the system. For the same volume, a sphere has the smallest surface area, and reducing the surface area reduces the system's free energy. Therefore, snow crystals of various shapes automatically transform into spherical particles; this process is called autosphericization. After autosphericization, snow crystals form spherical snow particles (simply called granules). Under the pressure of their own weight and the overlying snow, these particles are compressed and tightly interlocked, causing the pores between them to continuously shrink. The brightness and transparency of the snow layer gradually decrease, eventually forming glacial ice. The process of new snow—granules—glacial ice is called the compaction process of granules or glacial formation. Glacial ice, under the influence of gravity, slowly flows along the mountain slope, eventually forming a glacier.

[0003] Frost compaction is an intermediate process in the transformation of new snow into glacial ice. Studying frost compaction plays a crucial role in glaciology, including glacial mass balance monitoring and paleoclimate analysis using ice cores. For example, frost compaction models can simulate the depth-density profile of frost, improving the accuracy of glacial mass balance monitoring; they can also predict the age of ice at the time of bubble closure, helping to infer the time series of past climate changes and predict future climate conditions. Due to the lack of suitable technology to observe the evolution of frost columns across the entire glacier, models are often used to simulate the frost compaction process.

[0004] Most current frit compaction models are empirical models established in polar ice sheets. These models only consider the effects of temperature and the pressure of the overlying frit on the compaction process. Their advantages are relatively simple modeling and strong adaptability to the modeling region; their disadvantages are a lack of sufficient understanding of the physical mechanisms, incomplete theoretical foundation, and lack of universality. Due to the porosity and permeability of frit, if liquid water is present on the surface of the frit column, it will permeate into the pore spaces within the frit column. When there is sufficient pore space and the freezing temperature is met, the liquid water can refreeze into solid ice, forming a thick or thin ice layer depending on the amount of refreezing. The latent heat of phase change released in this process will significantly accelerate the frit compaction rate to a certain extent. Therefore, it is essential to design a frit compaction model that considers the role of liquid water, based on the mechanism of liquid water permeation and phase change. Summary of the Invention

[0005] In response to the shortcomings and improvement needs of existing technologies, this invention provides a granular snow compaction modeling method that takes into account the seepage and phase change mechanisms of liquid water. It aims to solve the technical problems that existing granular snow compaction models lack sufficient understanding of physical mechanisms, have incomplete theoretical foundations, and lack universality.

[0006] To achieve the above objectives, this invention provides a granular snow compaction modeling method that takes into account the seepage and phase change mechanisms of liquid water, comprising the following steps:

[0007] The snow column is divided into a finite number of snow layers, each with a thickness of dz. The time required for snowfall to accumulate to dz is called the time step dt.

[0008] Obtain daily surface temperature, snowfall, precipitation, temperature of precipitation, net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux in the glacier study area;

[0009] Based on the daily rainfall temperature, net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux, the daily meltwater volume is calculated; then, the sum of the daily meltwater volume and the rainfall volume is taken as the daily total liquid water volume; according to the time step, the daily surface temperature, snowfall, and liquid water volume are resampled to obtain the surface temperature, snowfall, and total liquid water volume for each time step;

[0010] The relationship between the temperature T of snow grains and the density ρ of snow grains in each snow grain layer is established using the one-dimensional heat conduction equation.

[0011] Based on the aforementioned relationship and combined with the surface temperature and snowfall at each time step, the grain compaction rate of each grain layer in the grain column corresponding to that time step is obtained. Then according to The snow density ρ of each snow layer was obtained without considering the effect of liquid water.dry , where ρ origin The initial snow density for each snow layer;

[0012] Combining the total liquid water volume at each time step and the saturated water volume V of each snow layer wm and bound water volume V wi Determine the amount of liquid water V in each snow layer at this time step. w Among them, saturated water volume V wm It is a function of snow density ρ, and bound water volume V wi =V w *S wi S wi The water storage capacity of each snow layer;

[0013] by With V w -V wi The smaller value in Q is taken as the actual refreeze amount within each snow grain layer, where Q cold The cold content of each snow layer, For the latent heat of melting of snow grains, ρ w The density of water;

[0014] The calculated snow density ρ = ρ_snow in each snow layer considering the effect of liquid water is obtained. dry +Δρ, where Δρ=(refreeze*ρ w ) / dz.

[0015] Further, the calculation of daily meltwater volume based on the temperature, net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux of the daily rainfall includes:

[0016] Based on the daily rainfall temperature and critical temperature, the surface heat flux caused by rainfall is calculated; the sum of the net longwave radiation flux, net shortwave radiation flux, sensible heat flux, latent heat flux, and surface heat flux is taken as the net energy flux; the net energy flux is divided by the latent heat of melting of the snow grains. The daily amount of melted water is obtained.

[0017] Furthermore, when T rain Less than T m At that time, the surface heat flux Q rain It is zero;

[0018] When T rain Greater than or equal to T m At that time, the surface heat flux Q rain Represented as:

[0019] Q rain =c w *mrain *(T rain -T m )

[0020] Among them, c w m is the specific heat capacity of water. rain For rainfall, T rain The temperature of the rainfall, T m This is the critical temperature.

[0021] Furthermore, the relationship between the snow temperature T and the snow density ρ within each snow layer is as follows:

[0022]

[0023] Among them, c f ρ is the specific heat capacity of the snow pellets, which is related to the snow pellet temperature T; K is the thermal conductivity of the snow pellet layer, which is a function of the snow pellet density ρ and the snow pellet temperature T. Gradient operator under one-dimensional conditions Q L The latent heat of phase change released by the refreezing of liquid water, and

[0024] Furthermore, the snow grain densification rate Represented as:

[0025]

[0026]

[0027]

[0028]

[0029] Where c is the proportionality coefficient, ρ i T is the density of ice. c =T-273.15, Snowfall amount at each time step.

[0030] Furthermore, the initial snow density ρ of each snow layer origin Obtained through the following methods:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] Where, ρ i ρ is the density of ice. s Let R be the surface density, R be the Boltzmann constant, and z be the depth of the snow layer. 550 550 kg·m -3 The density corresponding to the depth, T mean A is the average surface temperature over the days. mean This represents the average annual snowfall.

[0038] Furthermore, the water storage capacity S of each snow pellet layer wi Represented as:

[0039]

[0040]

[0041] Where, ρ i This is the density of ice.

[0042] Furthermore, the total liquid water volume at each time step and the saturated water volume V of each snowflake layer are combined. wm and bound water volume V wi Determine the amount of liquid water V in each snow layer at this time step. w ,include:

[0043] Calculate the effective saturation Θ within each snow layer:

[0044]

[0045] θ w =V w / dz

[0046] θ s =V Wm / dz

[0047] θ i =V wi / dz

[0048] The quantity of liquid water is then determined by the following formulas:

[0049]

[0050] K w =K s *K r

[0051]

[0052]

[0053]

[0054] V w =min[u w dτ,LW in ]+V′ w

[0055] Among them, u w K represents the seepage velocity of liquid water between snow grains. w Let h be the hydraulic conductivity of the snow layer, h be the pressure head, g be the gravitational acceleration caused by gravity, and v be the velocity of the snow layer. w It is the dynamic viscosity coefficient of water, d g The diameter of the snow crystal is given by parameters α, n, and m, where α = 7.3d. g +1.9, n=15.68exp(-0.46d g )+1, dτ is the time required for liquid water to seep through a snowpack; LW in V′ represents the amount of liquid water entering a specific snow layer, calculated as the difference between the total liquid water volume at that time step and the liquid water volume in the layers above that snow layer. w V′ represents the amount of unfrozen liquid water in each snow layer at the previous time step, where V′ represents the amount of unfrozen liquid water in the first snow layer. w It is zero.

[0056] Furthermore, the cold content Q of each snow grain layer cold Represented as:

[0057] Q cold =c f *m f *(T m -T)

[0058] Among them, c f The specific heat capacity of the snow pellet is related to its temperature T, m f Let m be the mass of the snow grains within this snow layer. f =ρ dry *dz.

[0059] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0060] (1) It more realistically reflects the physical properties of snow pellets: Traditional snow pellet compaction models only consider the effects of factors such as temperature and the pressure of overlying snow pellets on snow pellet compaction, while the action of liquid water generated by processes such as rainfall and surface snow melting is another important factor affecting snow pellet compaction. This invention elucidates the influence of liquid water on the compaction process from the perspective of revealing the mechanism of liquid water seepage and phase change, such as considering the influence of the latent heat of phase change released by the refreezing of liquid water on the temperature of snow pellets, and considering the influence of the ice layer generated by the refreezing of liquid water on the quality of the snow pellet layer, which can more accurately reflect the physical properties of snow pellets;

[0061] (2) Improved accuracy of the snow compaction model: This invention considers the influence of liquid water on the snow compaction process, which is closer to the actual ice formation process of glaciers. It can more accurately predict the snow compaction rate and change trend, thereby improving the accuracy of the model.

[0062] (3) The applicability of the model has been enhanced: As the temperature of glaciers gradually increases, the glacier area affected by seasonal surface meltwater continues to increase. Therefore, the granular snow densification model constructed considering the action of liquid water can be more widely applied to different scenarios and environments. Attached Figure Description

[0063] Figure 1 A technical roadmap for a granular snow compaction modeling method that takes into account the seepage and phase change mechanism of liquid water, provided in an embodiment of the present invention;

[0064] Figure 2 (a) and (b) are schematic diagrams of the snow compaction process and geometric model during modeling, respectively, of a snow compaction modeling method that takes into account the seepage and phase change mechanism of liquid water provided in an embodiment of the present invention. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0066] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0067] See Figure 1 , combined Figure 2 This embodiment provides a granular snow compaction modeling method that takes into account the seepage and phase change mechanisms of liquid water, including the following steps:

[0068] S1. Divide the snow column into a finite number of snow layers, each with a thickness of dz. The time required for snowfall to accumulate to dz is called the time step dt.

[0069] Specifically, such as Figure 2 As shown in (a), after fresh snow falls to the ground, it undergoes a densification process under its own weight and the pressure of the overlying snow layer. Liquid water caused by the melting of the surface snow layer and rainfall seeps downwards along the porous snow grains, forming a snow column (assuming an area of ​​1m²). 2 Storage, refreezing, and runoff occur within the snow column (from the surface to the granular-glacier ice interface). Refreezing forms an ice layer that increases the mass of the snow column; the latent heat of phase change released during refreezing increases the temperature of the snow column, thereby accelerating the densification rate; runoff reduces the mass of the snow column, but since runoff does not affect snow density, it will not be described in detail in this invention.

[0070] like Figure 2 As shown in (b), with the vertically downward direction as positive, a geometric model is established by combining the geometric characteristics of granular snow and the macroscopic manifestations of the granular snow densification process. The granular snow column is divided into a finite number of granular snow layers, each with a thickness of dz and a granular snow-glacier ice interface depth of z. i In subsequent processing, it is assumed that each snow grain layer has specific physical properties and states, such as density and thermal conductivity.

[0071] Furthermore, when snowfall accumulates to the thickness dz of the frit layer, a new frit column is formed. This snowfall is considered the first frit layer of the new frit column, and a frit layer is removed from the bottom of the frit column to ensure that the number of frit layers within each frit column remains constant. The time required for snowfall to accumulate to dz is called the time step dt between two frit columns.

[0072] S2. Obtain daily surface temperature, snowfall, precipitation, temperature of precipitation, net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux in the glacier study area.

[0073] Specifically, daily surface temperature, snowfall, precipitation, precipitation temperature, net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux of the glacier study area are obtained from meteorological datasets. The air temperature at a depth of 2 meters above the ground surface can be used as the precipitation temperature.

[0074] S3. Calculate the daily meltwater volume based on the temperature, net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux of the daily rainfall; then sum the daily meltwater volume with the rainfall to obtain the daily total liquid water volume; resample the daily surface temperature, snowfall, and liquid water volume according to the time step to obtain the surface temperature, snowfall, and total liquid water volume for each time step.

[0075] Specifically, the daily meltwater volume (m) melt Calculations were performed using the surface energy balance model.

[0076] 1) Calculate the surface heat flux Q caused by rainfall based on the temperature of daily rainfall and the critical temperature. rain When the temperature T during rainfall rain Less than the critical temperature T for melting and refreezing m At (273.15K), the surface heat flux Q caused by rainfall rain If the value is zero, then the heat flux value is calculated using the following formula:

[0077] Q rain =c w *m rain *(T rain -T m )

[0078] Among them, c w It is the specific heat capacity of water (4200 J·kg) -1 ·℃ -1 ), m rain This refers to rainfall.

[0079] 2) Calculate the net energy flux by combining the surface heat flux calculated in step 1) with the net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux obtained from the meteorological dataset. The formula is:

[0080] Q net =SW+LW+H+LE+Q rain

[0081] Among them, Q net Net energy flux (W·m) -2 ), SW, LW, H, LE, Q tain These represent the net longwave radiation flux, net shortwave radiation flux, sensible heat flux, latent heat flux, and surface heat flux caused by rainfall, respectively. The unit of each flux is W·m. -2 .

[0082] 3) Calculate meltwater volume based on net energy flux: in The latent heat of melting of granular snow (333500 J·kg) -1 ).

[0083] After calculating the daily meltwater volume, the sum of the daily meltwater volume and rainfall is used as the daily liquid water volume. Simultaneously, based on the time step, the daily surface temperature, snowfall, and liquid water volume are resampled to obtain the surface temperature, snowfall, and total liquid water volume for each time step. During resampling, the surface temperature is averaged, while the other variables are cumulative. The resampled data is used as the driving data for the snow compaction model.

[0084] In addition, when driving the grainy snow compaction model, initial conditions and boundary conditions also need to be set. The specific steps are as follows:

[0085] 1) Temperature boundary conditions: Let the temperature of the uppermost layer of the snow column be the input surface temperature, the temperature of the lowermost layer be the temperature of the layer above it, and the temperature of the remaining snow layers be simulated using the snow temperature equation (which will be described in detail in step S4).

[0086] 2) Initial conditions: The surface density ρ of snow grains is usually assumed in the snow grain densification model. s The surface density is a constant, but different locations have different surface temperatures, leading to different surface densities. In 2018, Fausto et al. proposed a relationship between surface temperature and near-surface temperature (usually taken as air temperature at 2m) based on snow density at 0.1m in front of 200 locations:

[0087] ρ s =362.1 + 2.78T a

[0088] Among them, T a The surface density is the average near-surface temperature (°C) of the previous year. This embodiment uses an empirical parameterized equation to calculate the surface density.

[0089] S4. Establish the relationship between the snow temperature T and snow density ρ in each snow layer using the one-dimensional heat conduction equation.

[0090] Specifically, the frit temperature equation reflects the relationship between the frit temperature T and the frit density ρ within each frit layer:

[0091]

[0092] Among them, c f The specific heat capacity of the snow pellets is related to the snow pellet temperature T. In this invention, c is taken as... f =152.5 + 7.122 * T; K is the thermal conductivity of the snow layer, which is a function of snow density ρ and snow temperature T. Since we are currently considering the one-dimensional case, the gradient operator Q L It is the latent heat of phase change released by the refreezing of liquid water, Q in the first time step. L The Q value of subsequent time steps is negligible.L The value represents the latent heat of phase transition released in the previous time step. K can be obtained from the thermal conductivity formula proposed by Calonne et al., which applies to the entire compaction process:

[0093]

[0094] θ = 1 / (1 + exp(-0.04(ρ-450)))

[0095]

[0096]

[0097] k i (T)=9.828exp(-5.7×10 -3 T)

[0098]

[0099] Where, k i (T) and k a (T) represent the thermal conductivity of ice and air at temperature T, respectively. and These are the reference temperatures T ref = Thermal conductivity of ice and air at -3℃.

[0100] S5. Based on the aforementioned relationship and the surface temperature and snowfall corresponding to each time step, obtain the snow compaction rate of each snow layer in the snow column corresponding to that time step. Then according to The snow density ρ of each snow layer was obtained without considering the effect of liquid water. dry , where ρ origin The initial snow density for each snow layer.

[0101] Specifically, S5 includes the following sub-steps:

[0102] 1) In 2011, Li et al., building on previous research, considered the effects of temperature sensitivity and vapor flow on the granulation process of the Greenland ice sheet. This invention focuses on considering liquid water seepage and phase change mechanisms, taking into account the impact of refreezing on granulation mass and the effect of latent heat of phase change released during refreezing on granulation temperature. Therefore, the LZ-2011 model, which considers temperature sensitivity, is used as the granulation evolution model. The proportionality coefficient c of this model is expressed as:

[0103]

[0104]

[0105]

[0106] Where c is the proportionality coefficient, T c =T-273.15, Snowfall amount at each time step.

[0107] 2) According to the LZ-2011 model, the snow compaction rate can be expressed as the proportionality coefficient c and the snow density ρ and ice density ρ. i (917kg·m -3 The functional relationship of ) is:

[0108]

[0109] 3) First, based on the long-term average temperature (the average daily surface temperature) T mean And long-term average snowfall (the average annual snowfall) A mean Obtain the initial snow density ρ for each snow layer origin Then, the snow density ρ of each snow layer without considering the effect of liquid water is obtained based on the following formula. dry :

[0110]

[0111] Wherein, the initial snow density ρ of each snow layer origin The analytical solution obtained from the model of Herron et al. yielded the following:

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118] Where R is the Boltzmann constant, z is the depth of the snow layer, and z 550 550 kg·m -3 The density corresponds to the depth.

[0119] S6, Combining the total liquid water volume at each time step and the saturated water volume V of each snow layer. wm and bound water volume V wi Determine the amount of liquid water V in each snow layer at this time step. w Among them, saturated water volume V wmIt is a function of snow density ρ, and bound water volume V wi =V w *S wi S wi The water storage capacity of each snow layer.

[0120] Specifically, S6 includes the following sub-steps:

[0121] 1) The snow column is simulated as a three-component porous medium composed of a solid phase (snow particles), a liquid phase (water), and a gaseous phase (air). Let P represent the porosity of the snow layer with thickness dz, that is, the proportion of the volume of the pore space within the snow layer to the total volume of the snow layer, expressed as: P = 1 - ρ / ρ i Then the pore space corresponding to this snow layer is The volume occupied by snowflakes is

[0122] 2) As liquid water seeps into the snow pellet column, the pore spaces within each snow pellet layer will contain both air and liquid water. The maximum pore space that liquid water can occupy is called the saturation volume. Considering the volume of expansion if all the liquid water in the pore space were to refreeze into ice, the saturation volume is expressed as: The saturated water content is θ s =V wm / dz. Assume the amount of liquid water in the snow layer is V. w The volumetric water content of this layer is θ. w =V w / dz. The capillary action of snow crystals causes a portion of liquid water to be stored within the snow layer, preventing refreezing or runoff. This portion of liquid water is called bound water. According to Coleou et al., the water storage capacity of the snow layer is expressed as:

[0123]

[0124]

[0125] The amount of bound water in each snow grain layer is V. wi =V w *S wi The bound water content is θ i =V wi / dz. Where, ρ w =1000kg·m -3 This is the density of water.

[0126] Therefore, the effective saturation within each snow grain layer is:

[0127]

[0128] 3) During the seepage process of granular snow, liquid water is a non-Newtonian fluid, and its viscosity is not constant. To simplify the model, this invention assumes that liquid water is affected by gravity and capillary attraction during the seepage process, treating it as a Newtonian fluid with constant viscosity, and its flow within the granular snow column follows Newton's law of viscosity. Darcy's law, which describes the seepage process of liquid water in a granular snow column, states:

[0129]

[0130] Among them, u w It is the seepage velocity of liquid water between snow grains (m·s) -1 ), K w It is the hydraulic conductivity of the snow layer (m·s) -1 h is the pressure head (m). The vertical gradient of capillary suction is represented by the +1 term, which represents the effect of gravity.

[0131] According to Shimizu et al., saturated hydraulic conductivity K s for:

[0132]

[0133] Where g is the gravitational acceleration caused by gravity, and v w (1.787×10 -6 m 2 ·s -1 ) is the dynamic viscosity coefficient of water, d g (m) is the diameter of the snow crystal.

[0134] According to van et al., the unsaturated hydraulic conductivity K r for:

[0135]

[0136] According to Hirashima et al., the pressure head h is:

[0137]

[0138] Where the parameter α = 7.3d g +1.9, n=15.68exp(-0.46d g )+1,

[0139] Let the hydraulic conductivity K of the snow layer be... w =K s *K r The water transport within the Darcy time step dτ can then be calculated, and its value is u. wdτ. Here, the initial value of dτ is assumed to be 60s, and this value is iteratively adjusted to approximately the time required for liquid water to seep through a snowpack. The amount of liquid water entering a snowpack is LW. in V is the difference between the liquid water volume at this time step (i.e., the liquid water volume entering the first frit layer of the frit column) and the liquid water volume of each layer above that frit layer. The liquid water volume V of each frit layer is... w Take u w dτ、LW in The minimum value is related to the amount of unfrozen liquid water V′ in each snow layer at the previous time step. w The sum of, i.e., V w =min[u w dτ,LW in ]+V′ w V′ of the first snow layer w It is zero.

[0140] S7, with With V w -V wi The smaller value in Q is taken as the actual refreeze amount within each snow grain layer, where Q cold The cold content of each snow layer, For the latent heat of melting of snow grains, ρ w This is the density of water.

[0141] Specifically, when liquid water (excluding bound water) exists in the pore space and the refreezing temperature is met, a phase transition occurs, causing the liquid water to freeze into ice. This process releases latent heat of phase transition, increasing the energy of the granular snow column. Simultaneously, the formed ice increases the mass of the granular snow layer, further affecting its density.

[0142] The cold content of each snow layer is equal to the temperature T of that snow layer rising to the critical temperature Tc. m The amount of heat required to be absorbed:

[0143] Q cold =c f *m f *ΔT=c f *m f *(T m -T)

[0144] Where, m f Let m be the mass of the snow grains within this snow layer. f =ρ dry *dz. The refreezing capacity that this cold content may cause is:

[0145]

[0146] The actual refreezing amount within each snow pellet layer is the smaller of the refreezing capacity (refreeze_cap) and the amount of liquid water available for refreezing within the snow pellet layer, i.e., refreeze = min(refreeze_cap). cap V w -V wi Therefore, the latent heat of phase transition caused by refreezing is:

[0147] S8. Calculate the snow density ρ = ρ_snow for each snow layer considering the effect of liquid water. dry +Δρ, where Δρ=(refreeze*ρ w ) / dz.

[0148] Specifically, the refreezing of ice layers increases the mass of the snow pellet by m. re =refreeze*ρ w Therefore, the density of the snow column increases by Δρ = m re / dz, the final snow density for each snow layer considering the effect of liquid water is: ρ=ρ dry +Δρ.

[0149] In practical applications, the model obtained in steps S1 to S8 is used to simulate the snow depth-density data of the glaciers in the study area. The simulation results are compared with the measured snow depth-density data of the study area, and the model is calibrated based on the comparison results.

[0150] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for compacting granular snowflakes that takes into account the mechanisms of liquid water seepage and phase change, characterized in that, Includes the following steps: The snow column is divided into a finite number of snow layers, each with a thickness of dz. The time required for snowfall to accumulate to dz is called the time step dt. Obtain daily surface temperature, snowfall, precipitation, temperature of precipitation, net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux in the glacier study area; Based on the daily rainfall temperature, net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux, the daily meltwater volume is calculated; then, the sum of the daily meltwater volume and the rainfall volume is taken as the daily total liquid water volume; according to the time step, the daily surface temperature, snowfall, and liquid water volume are resampled to obtain the surface temperature, snowfall, and total liquid water volume for each time step; The relationship between the temperature T of snow grains and the density ρ of snow grains in each snow grain layer is established using the one-dimensional heat conduction equation. Based on the aforementioned relationship and combined with the surface temperature and snowfall at each time step, the grain compaction rate of each grain layer in the grain column corresponding to that time step is obtained. Then according to The snow density ρ of each snow layer was obtained without considering the effect of liquid water. dry , where ρ origin The initial snow density for each snow layer; Combining the total liquid water volume at each time step and the saturated water volume V of each snow layer wm and bound water volume V wi Determine the amount of liquid water V in each snow layer at this time step. w Among them, saturated water volume V wm It is a function of snow density ρ, and bound water volume V wi =V w *S wi S wi The water storage capacity of each snow layer; by With V w -V wi The smaller value in Q is taken as the actual refreeze amount within each snow grain layer, where Q cold The cold content of each snow layer, For the latent heat of melting of snow grains, ρ w The density of water; The calculated snow density ρ = ρ_snow in each snow layer considering the effect of liquid water is obtained. dry +Δρ, where Δρ=(refreeze*ρ w ) / dz.

2. The granular snow densification modeling method considering liquid water seepage and phase change mechanisms according to claim 1, characterized in that, The calculation of daily meltwater volume based on the temperature, net longwave radiation flux, net shortwave radiation flux, sensible heat flux, and latent heat flux of the daily rainfall includes: Based on the daily rainfall temperature and critical temperature, the surface heat flux caused by rainfall is calculated; the sum of the net longwave radiation flux, net shortwave radiation flux, sensible heat flux, latent heat flux, and surface heat flux is taken as the net energy flux; the net energy flux is divided by the latent heat of melting of the snow grains. The daily amount of melted water is obtained.

3. The granular snow densification modeling method considering liquid water seepage and phase change mechanisms according to claim 2, characterized in that, When T rain Less than T m At that time, the surface heat flux Q rain It is zero; When T rain Greater than or equal to T m At that time, the surface heat flux Q rain Represented as: Q rain =c w *m rain *(T rain -T m ) Among them, c w m is the specific heat capacity of water. rain For rainfall, T rain The temperature of the rainfall, T m This is the critical temperature.

4. The granular snow densification modeling method considering liquid water seepage and phase change mechanisms according to claim 1, characterized in that, The relationship between the snow temperature T and snow density ρ within each snow layer is as follows: Among them, c f ρ is the specific heat capacity of the snow pellets, which is related to the snow pellet temperature T; K is the thermal conductivity of the snow pellet layer, which is a function of the snow pellet density ρ and the snow pellet temperature T. Gradient operator under one-dimensional conditions Q L The latent heat of phase change released by the refreezing of liquid water, and 5. The granular snow densification modeling method considering liquid water seepage and phase change mechanisms according to claim 1, characterized in that, The snow grain densification rate Represented as: Where c is the proportionality coefficient, ρ i T is the density of ice. c =T-273.15, Snowfall amount at each time step.

6. The granular snow densification modeling method considering liquid water seepage and phase change mechanisms according to claim 1, characterized in that, The initial snow density ρ of each snow layer origin Obtained through the following methods: Where, ρ i ρ is the density of ice. s Let R be the surface density, R be the Boltzmann constant, and z be the depth of the snow layer. 550 550 kg·m -3 The density corresponding to the depth, T mean A is the average surface temperature over the days. mean This represents the average annual snowfall.

7. The granular snow densification modeling method considering liquid water seepage and phase change mechanisms according to claim 1, characterized in that, The water storage capacity S of each snow layer wi Represented as: Where, ρ i This is the density of ice.

8. The granular snow densification modeling method considering the seepage and phase change mechanism of liquid water according to claim 7, characterized in that, The total liquid water volume at each time step and the saturated water volume V of each snow layer are combined. wm and bound water volume V wi Determine the amount of liquid water V in each snow layer at this time step. w ,include: Calculate the effective saturation Θ within each snow layer: θ w =V w / d θ s =V wm / d θ i =V wi / d The quantity of liquid water is then determined by the following formulas: K w =K s *K r V w =min[u w dτ,LW in ]+V′ w Among them, u w K represents the seepage velocity of liquid water between snow grains. w Let h be the hydraulic conductivity of the snow layer, h be the pressure head, g be the gravitational acceleration caused by gravity, and v be the velocity of the snow layer. w It is the dynamic viscosity coefficient of water, d g The diameter of the snow crystal is given by parameters α, n, and m, where α = 7.3d. g +1.9, n=15.68exp(-0.46d g )+1, dτ is the time required for liquid water to seep through a snowpack; LW in V′ represents the amount of liquid water entering a specific snow layer, calculated as the difference between the total liquid water volume at that time step and the liquid water volume in the layers above that snow layer. w V′ represents the amount of unfrozen liquid water in each snow layer at the previous time step, where V′ is the amount of unfrozen liquid water in the first snow layer. w It is zero.

9. The granular snow densification modeling method considering the seepage and phase change mechanism of liquid water according to claim 1, characterized in that, The cold content Q of each snow layer cold Represented as: Q cold =c f *m f *(T m -T) Among them, c f The specific heat capacity of the snow pellet is related to its temperature T, m f Let m be the mass of the snow grains within this snow layer. f =ρ dry *dz.

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