Construction method of grain snow density profile model and acquisition method of grain snow density

Abstract

The invention discloses a construction method of a grain snow density profile model and an acquisition method of grain snow density, and belongs to the technical field of grain snow density simulation. The method comprises the following steps: acquiring related prior information based on characteristics and mechanisms of grain snow densification and utilizing the related prior information, specifically acquiring and calculating grain snow physical property parameters of different places and different depths through a grain snow densification model, and further obtaining grain snow characteristics of the corresponding places and different depths; on the basis, in consideration that deposition of the grain snow is gradually changed in time sequence, the depth-density profile of the grain snow is different responses to deposition characteristics of different stratums, and the whole has a certain time sequence characteristic, the complex mapping relation between the grain snow characteristics and the grain snow density is learned by adopting a recurrent neural network; according to the method, the complex mapping relation between each grain snow feature and the grain snow density can be utilized and excavated to the maximum extent, the dependence of a grain snow densification model on idealized hypothesis is reduced, the grain snow densities of different depths can be accurately obtained, and the universality is high.

Description

Technical Field

[0001] The present invention belongs to the technical field of particle snow density simulation, and more specifically, relates to a method for constructing a particle snow density profile model and a method for obtaining the particle snow density. Background Art

[0002] Snow compaction is the intermediate process of new snow transforming into glacier ice. In this process, snow is continuously compacted under its own gravity and the stress of the overlying snow layer, causing the growth and deformation of the grains, and its density increases with the depth. In the process of snow compaction, obtaining the depth-density profile of snow and establishing a snow density profile model are important in glaciology fields such as glacier material balance monitoring, ice core paleoclimate environment analysis, and glacier ice reserve estimation.

[0003] The construction methods of the particle snow density profile model are mainly divided into two methods: direct measurement and indirect interpretation. The direct measurement method is to obtain the particle snow density at a certain depth through ice core measurement. The particle snow density obtained by this method is the most accurate, but the cost of sampling and testing is high, and as the depth of the ice core increases, the difficulty of obtaining the particle snow density also increases. Therefore, the direct measurement method is limited to certain layers and certain areas, and it is difficult to obtain the complete particle snow density of multiple layers in multiple areas. The indirect interpretation method is to obtain the particle snow density at a certain depth through empirical / semi-empirical / physical model simulation based on known meteorological information. This method can achieve good results for the simulation of particle snow density under the modeling background at that time. However, due to the complex and strong heterogeneity of the underground conditions, the many factors affecting the particle snow density and the complex relationship, strong assumptions are often required when constructing the model, that is, the model is extremely simplified, so that this method cannot well dig out the complex nonlinear relationship between the particle snow density and various parameters and the continuity of space. At the same time, different models need to be selected for different meteorological information, and the selection process is easily dominated by people. It can be seen that the particle snow density profile models constructed by the above methods cannot accurately obtain the particle snow density at different depths. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present invention provides a method for constructing a grain snow density profile model and a method for obtaining the grain snow density, so as to solve the technical problem that the grain snow density profile models constructed by the prior art cannot accurately obtain the grain snow density at different depths.

[0005] In order to achieve the above object, in a first aspect, the present invention provides a method for constructing a snow particle density profile model, comprising:

[0006] Obtaining snow density profile data and corresponding meteorological data at different locations; the snow density profile data includes: actual measurement results of snow density at different depths;

[0007] Each meteorological data is input into the snow particle compaction model to calculate the snow particle physical parameters at different depths at the corresponding location, and then obtain the snow particle characteristics at different depths at the corresponding location;

[0008] Each snow particle feature is input into the recurrent neural network to obtain the snow particle density detection result at the corresponding depth; by minimizing the difference loss between each snow particle density detection result and the corresponding measured result, the recurrent neural network is trained to obtain the snow particle density profile model.

[0009] Further preferably, the granular snow characteristics include: one or more categories of data in the granular snow physical parameters; the granular snow physical parameters include the following categories of data: the temperature of the snow layer, the pressure of the overlying snow layer, the amount of liquid water in the snow layer, the porosity of the snow layer, the thermal conductivity of the snow layer and the hydraulic conductivity of the snow layer.

[0010] Further preferably, the method for obtaining the characteristics of snow particles at different depths at any location A includes:

[0011] Calculate X i Correlation coefficient between X and Y; i is the vector composed of the i-th type of data in the particle snow physical parameters at different depths at location A; Y is the vector composed of the measured results of particle snow density at different depths at location A; i=1,2,…,M; M is the number of data categories in the particle snow physical parameters;

[0012] The N categories with the largest correlation coefficients are taken as N candidate categories; 1≤N <M;

[0013] For each depth, a particle snow feature is constructed including data under N candidate categories of the particle snow physical property parameters at the depth.

[0014] More preferably, X i The correlation coefficient between X and Y is i The weighted average of the Kendall rank correlation coefficient, Spearman rank correlation coefficient, and Pearson linear correlation coefficient between it and Y.

[0015] Further preferably, the above-mentioned particle snow density profile data is pre-processed particle snow density profile data;

[0016] Among them, the preprocessing methods include:

[0017] For any measured snow density in the snow density profile data, ρ m , when ρ m When the density is higher than that of pure ice, ρ m Set to the density of pure ice; when ρ m The snow layer is the surface snow layer, and ρ m When it is lower than the preset threshold, ρm Set to the density of the next snow layer in the snow layer; when ρ m The snow layer is the bottom snow layer, and ρ m When it is lower than the preset threshold, ρ m Set to the density of the snow layer above the snow layer where it is located; when ρ m The snow layer is the middle snow layer, and ρ m When it is lower than the preset threshold, ρ m Set to the average density of the snow layer above and below it.

[0018] Further preferably, the preset threshold is Among them, 0<α<1 is the preset ratio; The ρ is obtained by inputting the meteorological data corresponding to the particle snow density profile data into the particle snow densification model without considering the effect of liquid water. m The density of snow particles in the snow layer.

[0019] Further preferably, the method for constructing the above-mentioned particle snow density profile model further includes: normalizing the obtained particle snow characteristics;

[0020] The above-mentioned inputting each snow particle feature into the recurrent neural network specifically includes: inputting each normalized snow particle feature into the recurrent neural network.

[0021] Further preferably, the method for constructing the above-mentioned particle snow density profile model further includes: normalizing the actual measurement results of the particle snow density;

[0022] The above-mentioned minimizing the difference loss between each snow particle density detection result and the corresponding measured result specifically includes: minimizing the difference loss between each snow particle density detection result and the corresponding normalized measured result.

[0023] In a second aspect, the present invention provides a method for obtaining snow particle density, comprising:

[0024] Obtaining meteorological data of the test location and inputting it into the particle snow compaction model, calculating the particle snow physical parameters at different depths of the test location, and then obtaining the particle snow characteristics at different depths of the test location;

[0025] The snow grain characteristics at different depths of the test site are respectively input into the snow grain density profile model to obtain the snow grain density at different depths of the test site;

[0026] The particle snow density profile model is constructed by using the method for constructing the particle snow density profile model provided in the first aspect of the present invention.

[0027] In a third aspect, the present invention further provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the method provided in the first aspect and / or the second aspect of the present invention.

[0028] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0029] 1. The present invention provides a method for constructing a grain snow density profile model, which utilizes the prior information related to the characteristics and mechanism of grain snow compaction itself, and specifically obtains and calculates the physical parameters of grain snow at different depths at different locations through the grain snow compaction model, and then obtains the grain snow characteristics at different depths at the corresponding locations; on this basis, considering that the deposition of grain snow is a temporal gradual change, the grain snow depth-density profile is a different response to the deposition characteristics of different strata, and has a certain temporal characteristic as a whole. The present invention adopts a recurrent neural network to learn the complex mapping relationship between grain snow characteristics and grain snow density, which can maximize the utilization and mining of the complex mapping relationship between grain snow characteristics at different depths and grain snow density at the corresponding depth, reduce the dependence of the grain snow compaction model on idealized assumptions, and can achieve accurate acquisition of grain snow density at different depths, and has strong universality.

[0030] 2. Furthermore, the method for constructing the particle snow density profile model provided by the present invention constructs the particle snow characteristics by analyzing the correlation between different data categories in the particle snow physical property parameters and the particle snow density, and selects category data in the particle snow physical property parameters that are more sensitive to the particle snow density, thereby further improving the accuracy of obtaining the particle snow density. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A flow chart of a method for constructing a snow particle density profile model provided by an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of the location and depth of a density profile of snow particles collected on an ice sheet provided by an embodiment of the present invention;

[0033] Figure 3 A unit structure diagram of the LSTM provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0035] In order to achieve the above-mentioned object, in the first aspect, the present invention provides a method for constructing a snow particle density profile model, such as Figure 1 As shown, including:

[0036] Obtaining snow density profile data and corresponding meteorological data at different locations; the snow density profile data includes: actual measurement results of snow density at different depths;

[0037] Each meteorological data is input into the snow particle compaction model to calculate the snow particle physical parameters at different depths at the corresponding location, and then obtain the snow particle characteristics at different depths at the corresponding location;

[0038] Each snow particle feature is input into the recurrent neural network to obtain the snow particle density detection result at the corresponding depth; the recurrent neural network is trained by minimizing the difference loss between each snow particle density detection result and the corresponding measured result to obtain the snow particle density profile model. The recurrent neural network can be RNN, LSTM, Bi-LSTM, GRU, etc., which are not limited here.

[0039] In an optional embodiment, the granular snow characteristics include: one or more categories of data in the granular snow physical parameters; the granular snow physical parameters include the following categories of data: the temperature of the snow layer, the pressure of the overlying snow layer, the amount of liquid water in the snow layer, the porosity of the snow layer, the thermal conductivity of the snow layer and the hydraulic conductivity of the snow layer.

[0040] Preferably, the method for obtaining the characteristics of snow particles at different depths at any location A includes:

[0041] Calculate X i Correlation coefficient between X and Y; i is the vector composed of the i-th type of data in the particle snow physical parameters at different depths at location A; Y is the vector composed of the measured results of particle snow density at different depths at location A; i=1,2,…,M; M is the number of data categories in the particle snow physical parameters;

[0042] The N categories with the largest correlation coefficients are taken as N candidate categories; 1≤N <M;

[0043] For each depth, a particle snow feature is constructed including data under N candidate categories of the particle snow physical property parameters at the depth.

[0044] It should be noted that the Kendall rank correlation coefficient calculation formula, Spearman rank correlation coefficient calculation formula, Pearson linear correlation coefficient calculation formula and other correlation coefficient calculation formulas can be used to calculate X i The correlation coefficient between X and Y. Preferably, X iThe correlation coefficient between X and Y is i The weighted average of the Kendall rank correlation coefficient, Spearman rank correlation coefficient, and Pearson linear correlation coefficient between it and Y.

[0045] In an optional implementation manner, the above-mentioned particle snow density profile data is pre-processed particle snow density profile data;

[0046] Among them, the preprocessing methods include:

[0047] For any measured snow density in the snow density profile data, ρ m , when ρ m When the density is higher than that of pure ice, ρ m Set to the density of pure ice; when ρ m The snow layer is the surface snow layer, and ρ m When it is lower than the preset threshold, ρ m Set to the density of the next snow layer in the snow layer; when ρ m The snow layer is the bottom snow layer, and ρ m When it is lower than the preset threshold, ρ m Set to the density of the snow layer above the snow layer where it is located; when ρ m The snow layer is the middle snow layer, and ρ m When it is lower than the preset threshold, ρ m Set to the average density of the snow layer above and below it.

[0048] Preferably, the preset threshold is Wherein, 0<α<1 is a preset ratio, and in an optional implementation manner, the value is 0.7; The meteorological data corresponding to the particle snow density profile data is input into the classic dry particle snow compaction model to simulate the ρ m The density of the snow particles in the snow layer. Among them, the classic dry snow particle compaction model is a snow particle compaction model that does not consider the effect of liquid water.

[0049] In an optional implementation, the method for constructing the above-mentioned particle snow density profile model further includes: normalizing the obtained particle snow characteristics;

[0050] The above-mentioned inputting each snow particle feature into the recurrent neural network specifically includes: inputting each normalized snow particle feature into the recurrent neural network.

[0051] In an optional implementation, the method for constructing the snow particle density profile model further includes: normalizing the measured results of the snow particle density;

[0052] The above-mentioned minimizing the difference loss between each snow particle density detection result and the corresponding measured result specifically includes: minimizing the difference loss between each snow particle density detection result and the corresponding normalized measured result.

[0053] It should be noted that the existing grain snow densification model often requires strong assumptions when building the model due to the lack of sufficient understanding of the physical mechanism, that is, the model is extremely simplified, so that the simulated grain snow density is quite different from the measured density. In complex problems where the variable relationship cannot be determined, the data-driven deep learning strategy is the best means to build its mapping relationship model at this stage. It is very suitable for problems with complex mapping relationships but lack of accurate physical models or empirical models. The problem now faced is this: the intrinsic relationship between each parameter and the grain snow density is quite complex, and is affected by factors such as depth, longitude and latitude, and temperature, showing strong nonlinear and temporal characteristics (the deposition of grain snow is a time-series gradient, and the grain snow depth-density profile is a different response to the sedimentary characteristics of different strata, and the whole has certain temporal characteristics). Considering that the sampling interval of the grain snow density profile is small, and the thickness can often reach tens of meters, that is, the length of the sequence that affects each other contains hundreds of data points, the present invention chooses to use a recurrent neural network as a data-driven model.

[0054] However, since the particle snow density profile is often multi-source and complex, and there are few measured particle snow density profiles, the simple and direct use of recurrent neural networks cannot guarantee the prediction effect of the model. The present invention considers the data-driven characteristics of combined deep learning and the physical constraints of the particle snow densification process itself to simulate the particle snow density profile. On the one hand, the data-driven model is used to maximize the use and mining of the complex mapping relationship between each parameter and the particle snow density, reducing the dependence of the particle snow densification model on idealized assumptions; on the other hand, the characteristics and mechanisms of the particle snow densification itself are used to feed back the algorithm and model, and it is converted into the constraints of the model or prior information for use. It can achieve accurate acquisition of the particle snow density at different depths, and has strong universality.

[0055] The present invention combines the understanding of the compaction process of the particle snow compaction model with the powerful data-driven prediction ability. While taking the physical mechanism into consideration, it can partially reduce the uncertainty of the particle snow density simulation that may be caused by the complex physical mechanism. While improving the accuracy of the particle snow density acquisition, it also has good generalization ability and robustness.

[0056] In order to further illustrate the method for constructing the snow particle density profile model provided by the present invention, a specific embodiment is described in detail below:

[0057] The method for constructing the particle snow density profile model provided in this embodiment includes the following steps:

[0058] 1) Obtain the measured snow particle density profile data and process outliers and blank values.

[0059] Specifically, the snow density data obtained from ice core drilling measurements and their corresponding depth, time, longitude and latitude are collected. The data covers various depth ranges and areas with no liquid water, areas with less liquid water, and areas with more liquid water, so as to conduct sample training under different scenarios and make the model have certain generalization and robustness. Figure 2 is the latitude and longitude corresponding to the particle snow density profile collected on a certain ice sheet and the range of its maximum depth. Due to the influence of measurement methods, formation factors, instrument limitations, etc., there may be certain abnormal values ​​and blank values ​​in the collected particle snow depth-density profile. These values ​​need to be processed to reduce their impact on the particle snow density prediction results in the later stage. The abnormal value in this embodiment refers to the density higher than pure ice (917kg m -3 ) or a measured snow density lower than 70% of the snow density simulated by the snow compaction model. For overestimated outliers, this embodiment sets them to the density of pure ice. For underestimated outliers and blank values, they are set to the average density of the upper and lower adjacent snow segments.

[0060] 2) Obtaining meteorological data of corresponding locations according to the latitude and longitude information of each snow density profile.

[0061] Meteorological data include: daily surface temperature, snowfall, total liquid water, snowmelt and sublimation at each location over a period of time. Daily precipitation is the difference between daily total precipitation and snowfall; daily total liquid water entering the snow column is the sum of daily snowmelt and precipitation.

[0062] 3) Input each meteorological data into the snow particle compaction model, calculate the snow particle physical parameters at different depths at the corresponding location, and then obtain the snow particle characteristics at different depths at the corresponding location;

[0063] The characteristics of granular snow include: one or more types of data in the physical parameters of granular snow; the physical parameters of granular snow include the following types of data: the temperature of the snow layer, the pressure of the overlying snow layer, the amount of liquid water in the snow layer, the porosity of the snow layer, the thermal conductivity of the snow layer and the hydraulic conductivity of the snow layer.

[0064] In this embodiment, the method for obtaining the characteristics of snow particles at different depths at any location A includes:

[0065] Calculate X i Correlation coefficient between X and Y; i is the vector composed of the i-th type of data in the particle snow physical parameters at different depths at location A; Y is the vector composed of the measured results of particle snow density at different depths at location A; i=1,2,…,M; M is the number of data categories in the particle snow physical parameters;

[0066] The N categories with the largest correlation coefficients are taken as N candidate categories; 1≤N <M;

[0067] For each depth, a particle snow feature is constructed including data under N candidate categories of the particle snow physical property parameters at the depth.

[0068] Among them, X i The correlation coefficient between X and Y is i The weighted average of the Kendall rank correlation coefficient, Spearman rank correlation coefficient and Pearson linear correlation coefficient between X and Y; the weight values ​​corresponding to the Kendall rank correlation coefficient, Spearman rank correlation coefficient and Pearson linear correlation coefficient can be set according to experience. Considering that the particle snow physical property parameters and particle snow density are generally non-normally distributed, the Kendall rank correlation coefficient and the Spearman rank correlation coefficient are given a larger weight, which can be adjusted according to the test results. In this embodiment, X i The weight values ​​corresponding to the Kendall rank correlation coefficient, Spearman rank correlation coefficient, and Pearson linear correlation coefficient between y and Y are 0.4, 0.4, and 0.2, respectively.

[0069] It should be noted that N is the number of preset categories, which can be selected based on experience in an optional implementation. Generally, categories with strong correlation are selected. Specifically, when calculating the correlation coefficient R s After that, the correlation strength is determined according to the following value range: 0.8≤|R s |≤1.0 indicates a very strong correlation; 0.6≤|R s |≤0.79 indicates strong correlation; 0.4≤|R s |≤0.59 indicates moderate correlation; 0.2≤|R s |≤0.39 indicates weak correlation; 0.0≤|R s |≤0.19 indicates no correlation.

[0070] In another optional implementation, according to the correlation analysis results, in accordance with the degree of correlation of each data category in the particle snow physical property parameters with the particle snow density, data categories are added in sequence to form different particle snow feature selections, such as particle snow feature selection 1 is the category data most relevant to the particle snow density, particle snow feature selection 2 is the first two categories of data with the highest degree of correlation with the particle snow density, and so on. The particle snow features under different particle snow feature selections are respectively input into the recurrent neural network for training to obtain different particle snow density profile models; each particle snow density profile model is respectively used to perform particle snow density detection in the test set, and the data category used in the particle snow feature corresponding to the particle snow density profile model with the highest accuracy is used as the optimal data category.

[0071] In this embodiment, in order to eliminate the influence of the differences in magnitude and dimension of each parameter on the model without affecting the data characteristics, reduce the training error, accelerate convergence and improve the accuracy of the model, after calculating the particle snow physical parameters at different depths in different locations, all types of data in the particle snow physical parameters are normalized by category. The particle snow feature is a vector of size 1×M, and each column corresponds to a data category in the particle snow physical parameters; the column values ​​corresponding to the N candidate categories in the particle snow feature at a certain depth are the corresponding normalized category data, and the values ​​of the remaining columns are 0.

[0072] It should be noted that the normalization process for a certain category of data in the particle snow physical property parameters can be: normalizing the data of this category at different locations and different depths together; or: normalizing the data of this category at different locations separately, and normalizing the data of this category at different depths at the same location together. This is not limited here.

[0073] There are many normalization methods. In this embodiment, the maximum and minimum normalization method is used to normalize each component data to between 0 and 1:

[0074]

[0075] Among them, y is the input or output component of the model, y * is the normalized input or output component, y max and min are the maximum and minimum values ​​of the model input or output, respectively.

[0076] It should be noted that there are many granular snow densification models, such as the granular snow densification model in patent CN202311200948.7, the granular snow densification model in Liquid water flow and retention on the Greenland ice sheet in the regional climate model, and the granular snow densification model in Development of physically based liquid water schemes for Greenland firn-densification models.

[0077] In this embodiment, the snow particle compaction model in patent CN202311200948.7 is used as an example for detailed description. The process of obtaining the snow particle physical parameters at different depths at a certain location through the snow particle compaction model includes:

[0078] A31, the snow column (assuming the area is 1m 2 , the height is from the surface to the grain snow-glacier ice interface) is divided into a finite number of grain snow layers, and the thickness of each grain snow layer is dz. The time required for the snow accumulation (snowfall minus sublimation) to reach 0.01m we (meters of water equivalent) is called the time step dt. The snow accumulation of each time step is regarded as the first grain snow layer of the grain snow column corresponding to the time step. At the same time, a grain snow layer is removed from the bottom of the grain snow column to ensure that the number of grain snow layers in each grain snow column remains unchanged. Therefore, the thickness of the grain snow layer dz is related to the snow accumulation, and changes slightly with the change of the mass of the grain snow layer during the subsequent compaction process.

[0079] A32. The relationship between the temperature T of each snow particle layer and the density ρ of the snow particles is established by the one-dimensional heat conduction equation:

[0080]

[0081] Among them, c f is the specific heat capacity of the granular snow, which is assumed to be equal to the specific heat capacity of ice in the present invention. K is the thermal conductivity of the granular snow layer, which is a function of the density of the granular snow and the temperature of the granular snow. Since we are currently considering a one-dimensional case, the gradient operator Considering the influence of the latent heat of phase change released during the refreezing of liquid water on the temperature of the snow particles, the temperature of the snow particles will be updated after refreezing.

[0082] A33. According to the relationship, combined with the surface temperature and snow accumulation corresponding to each time step, the dry snow density corresponding to each snow layer in the snow column corresponding to the time step is obtained by the dry snow compaction scheme. Specifically, the present invention uses the stress-based CROCUS model developed for mountain snow as the dry snow compaction scheme. The CROCUS model converts the stress σ, snow viscosity η, snow density ρ and compaction rate of the overlying snow layer into the density of the snow. Get in touch:

[0083]

[0084]

[0085] Among them, T m is the melting point temperature (273.15K), η0 = 7.62237 × 106 kg s -1 m -1 , a η =0.1K -1 , b η =0.023m 3 kg -1 , c η =358kgm -3 f1 and f2 are two correction factors for snow viscosity, which take into account the viscosity difference caused by the presence of liquid water and the grain size, respectively. According to previous studies, f1 is taken here as 1 / (1+60θ w ), f2=4, where θ w Indicates the liquid water content in each snow particle layer.

[0086] A34, combined with the total liquid water volume at each time step and the saturated water volume V of each snow particle layer wm and bound water volume V wi , determine the liquid water volume V of each snow layer at this time step w Among them, the saturated water volume V wm is a function of the snow particle density ρ, the bound water volume V wi =V w *S wi , S wi The water storage capacity of each snow particle layer. Specifically, this sub-step includes the following steps:

[0087] (1) The snow column is simulated as a porous medium composed of a solid phase (snow, ice), a liquid phase (water), and a gas phase (air). Let P represent the porosity of the snow layer with a thickness of dz, that is, the ratio of the volume of the pore space in the snow layer to the total volume of the snow layer, expressed as: P = 1-ρ / ρ i , then the pore space corresponding to the snow layer is Among them, ρ iis the density of ice (917 kg m -3 ).

[0088] (2) As liquid water seeps into the snow column, the pore space in each snow layer will contain air and liquid water. The maximum pore space that liquid water can occupy is called the saturated water volume. Considering the volume that would expand if all the liquid water in the pore space were to refreeze into ice, the saturated water volume is expressed as: The saturated water content is θ s =V wm / dz. Assume that the amount of liquid water in the granular snow layer is V w , then the volume water content of this layer is θ w =V w / dz. The capillary suction of the granular snow crystals causes a portion of liquid water to be stored in the granular snow layer, which cannot refreeze or runoff. This portion of liquid water is called bound water. The water storage capacity of the granular snow layer is expressed as:

[0089]

[0090]

[0091] Then the bound water content in each snow layer is V wi =V w *S wi , the bound water content is θ i =V wi / dz. Among them, ρ w =1000kg·m -3 is the density of water.

[0092] Therefore, the effective saturation in each snow particle layer is:

[0093]

[0094] Here, at each time step, the amount of liquid water in the jth snow layer is expressed as:

[0095]

[0096] Among them, V' w V represents the amount of liquid water in the jth snow layer that can be re-frozen from the previous time step but is not re-frozen due to the limited cold content, tot is the total liquid water input at this time step, (V wm -V' w ) represents the amount of liquid water (including bound water) that can be contained in a granular snow layer. When an impermeable granular snow layer is encountered, all excess liquid water runs off, and the amount of liquid water below the layer is equal to its liquid water volume in the previous time step.

[0097] (3) In the jth snow layer, the liquid water exceeding the bound water volume can move downward. We express this part of the liquid water volume as: V av =V w -V wi To simplify the model, the present invention assumes that liquid water is affected by gravity and capillary suction during the seepage process, and regards liquid water as a Newtonian fluid with a constant viscosity. Its flow in the snow column follows Newton's viscosity law. The flow of water in the snow column is described by Darcy's law:

[0098]

[0099] Where q is the seepage velocity of liquid water between the snow particles (m·s -1 ), h is the pressure head (m), represents the vertical gradient of capillary suction, +1 represents the effect of gravity, K w is the hydraulic conductivity of the granular snow layer (m·s -1 ).

[0100] Based on the above information, the water transport in one Darcy time step is calculated as qdτ. Hirashima et al. pointed out that if the water transport in one Darcy time step is close to the water content, the model will be unstable. Therefore, the limit water transport in one Darcy time step is q lim It is determined by the amount of water required for two adjacent snow layers to reach equilibrium. The present invention assumes that the initial value of dτ is 60 s, and then continuously iterates and adjusts the value to approximately the time required to reach equilibrium. Finally, the water transport amount within a Darcy time step is calculated as Considering the amount of liquid water available for flow in a granular snow layer, the actual water transport in a granular snow layer should be and V av The amount of liquid water flowing into the jth snow layer is the water transport amount of the (j-1)th snow layer, then the amount of liquid water in the jth snow layer is updated to (V w ) j +u j-1 -u j -R j , where V w is the amount of liquid water before the water flow calculated in step c, R j It represents the amount of liquid water lost through lateral runoff in the j-th snow particle layer.

[0101] (4) With V w *ρ wThe smaller value is taken as the mass m added by refreezing in each snow layer r , calculate the density of snow particles under the action of liquid water refreezing, and further calculate the stress and porosity of the overlying snow layer of each snow particle layer. cold is the cold content of each snow particle layer, is the melting latent heat of snow particles, ρ w is the density of water.

[0102] Specifically, when there is liquid water other than bound water in the pore space and the refreezing temperature is met, a phase change of liquid water freezing into ice will occur, releasing the latent heat of phase change in the process, increasing the energy of the snow grain column. At the same time, the formed ice will increase the mass of the snow grain layer, further affecting the density of the snow grain layer. The cold content of each snow grain layer is equal to the temperature T of the snow grain layer rising to the critical temperature T m The amount of heat required to be absorbed:

[0103] Q cold =c i *m*ΔT=c i *m*(T m -T)

[0104] Where m is the mass of the snow layer before refreezing occurs at this time step. The refreezing capacity that may be caused by this cold content is:

[0105]

[0106] The actual refreezing amount in each snow layer is the refreezing capacity C. r The smaller value of the amount of liquid water available for refreezing in the snow layer, m r =min(C r ,V w *ρ w ). Therefore, the latent heat of phase change caused by refreezing is: Taking into account the influence of latent heat on the temperature of the granular snow, the temperature of the granular snow after refreezing is updated as:

[0107]

[0108] Finally, the density of each snow particle layer considering the effect of liquid water is calculated as ρ = (m + m r ) / dz. Thus, the porosity corresponding to each snow layer is obtained. The stress corresponding to the jth snow layer is σ j =(m+m r ) j g, then the pressure of the snow layer overlying each snow layer is the sum of the stresses of each snow layer above the snow layer, where g is the acceleration due to gravity, (m+m r ) jis the mass and of the jth snow particle layer.

[0109] 4) Each snow particle feature is input into the recurrent neural network to obtain the snow particle density detection result at the corresponding depth; by minimizing the difference loss between each snow particle density detection result and the corresponding measured result, the recurrent neural network is trained to obtain the snow particle density profile model.

[0110] In this embodiment, the physical parameters output by the particle snow densification model and the measured particle snow density profile are resampled to a thickness interval of 0.01m and arranged in depth order. Assume that the particle snow density profile to be predicted is the output and is represented by y, and the physical parameters are the input and are represented by x1, x2, ..., x p , where p is a natural number ≥ 2. For each ice core, it is assumed that there are n layers of granular snow from the surface to the maximum depth of the ice core borehole (i.e., there are n 0.01 m layers), represented by vectors X1, X2, …, X n represents the input, where n is a natural number greater than 1, and the corresponding n outputs are represented by the vector Y=[y1, y2, ..., y n ] T Indicates that the kth input is X k =[x 1k 、x 2k , …, x pk ], k = 1, 2, ..., N, the corresponding k-th output is y k ; p is a positive integer; in the above formulas, T represents transposition.

[0111] The recurrent neural network used in this embodiment is LSTM, which is built based on the Tensorflow framework. Figure 3 , the LSTM network unit is mainly composed of three gates, namely the forget gate f t , input gate i t and output gate O t The forget gate is used to discard or retain the information in the cell state, which determines the cell state C at the previous moment. t-1 How much information is saved to the current state C t , and its calculation formula is:

[0112] f t =σ(W f [h t-1 ,x t ]+b f )

[0113] Where σ is the sigmoid activation function; W fis the forget gate weight matrix, whose dimension depends on the dimension of the hidden layer state and the unit state output at time t-1, as well as the dimension of the feature vector input at time t-1; b f is the bias; [h t-1 ,x t ] is the h output at time t-1 t-1 and the input x at time t t Concatenation of feature vectors; f t is the output of the forget gate, which is a summary value ranging from 0 to 1. The unit state is multiplied by f t Determines how much of the input hidden layer state information needs to be retained.

[0114] The input gate is used to update the information of the unit state. Its calculation is divided into two steps. The first step is to calculate h t-1 and x t What information needs to be strengthened or weakened, so the activation function uses the hyperbolic tangent function tanh, and the calculation formula is:

[0115]

[0116] Among them, W c is the first weight matrix of the input gate; b c is bias; is the state information input at time t. The second step uses the sigmoid activation function to output the probability value, which is used to determine How much information needs to be updated to the unit state? The calculation formula is:

[0117] i t =σ(W i [h t-1 ,x t ]+b i )

[0118] Among them, W i is the second weight matrix of the input gate; b i is the bias; i t is the output of the input gate. At this time, the long-term state information can be combined with the current state information through the operation of the forget gate and the input gate to calculate the updated unit state at time t. The calculation formula is:

[0119]

[0120] The output gate determines what information the LSTM network unit needs to output at time t, and the output value is O t It is related to the unit state. The tanh activation function can determine the information that needs to be output, and then the sigmoid function determines the amount of output information. The calculation formula is:

[0121] O t =σ(W o [h t-1 ,x t ]+b o )

[0122] h t =O t tanh(C t )

[0123] Among them, h t Represents the hidden layer state information output by the LSTM network at time t. In the above formulas, W f , W c , W i , W o , b f , b c , b i , b o The parameters are obtained through network training, and the process of network training is also the process of obtaining these parameters.

[0124] Before training the LSTM network, the hyperparameters in the LSTM network are set, namely, the initial model parameters, wherein the hyperparameters include the number of hidden layers in the LSTM network, the number of neurons in each layer, the number of loop iterations, the learning rate, the batch size, etc. According to the common values ​​of the LSTM network in predicting regression problems, this embodiment sets the initial model parameters to: the number of hidden layers is 3, the number of neurons is 200, the batch size is 32, the learning rate is 0.005, and the number of training times is 200.

[0125] This embodiment uses the adaptive momentum estimation (Adam) algorithm with adaptive learning rate to optimize the LSTM network. This optimization algorithm integrates the first-order momentum of the stochastic gradient descent (SGD) algorithm and the second-order momentum of the RMSprop algorithm, and combines the advantages of the AdaGrad algorithm in processing sparse gradients and the RMSprop algorithm in processing non-stationary targets. It has the advantages of small memory requirements and high computational efficiency. The loss function uses Log-Cosh, which is similar to the mean square error, is less susceptible to individual numerical values, and is second-order differentiable everywhere. The training results are more stable and reliable. Its expression is: Where y represents the true value, Represents the predicted value.

[0126] When dividing the training set and the test set, the ice cores are divided into three types: no liquid water, less liquid water, and more liquid water. The ratio of the training set to the test set of each type is 7:3. The training set is used for network training, and the validation set is not involved in the training. It is used to verify the stability and reliability of the LSTM network model.

[0127] The LSTM neural network model with preliminarily determined network parameters is trained using the training sets divided from each parameter combination. During the training process, the internal parameters of the network are continuously adjusted to iteratively optimize the model until the model training error reaches the pre-set target, and then the model is saved.

[0128] Specifically, the training method adopts the error back propagation theory, including the following steps:

[0129] The output value of each LSTM neuron is calculated sequentially along the depth forward propagation direction;

[0130] Compare the output value obtained by sequential forward calculation with the true value, calculate the error between the true value and the estimated value, and then calculate the error between each hidden layer and between cells in the hidden layer along the back propagation direction based on the calculated error;

[0131] Calculate the corresponding weight gradients based on the calculated errors between hidden layers and between cells in the hidden layers;

[0132] According to the calculated weight gradient, the Adam algorithm is used to update the corresponding weights so that the prediction results gradually approach the actual values;

[0133] Repeat the above steps continuously. When the total error is less than the given threshold or the maximum number of iterations is reached, the network training ends.

[0134] Specifically, adjusting the internal parameters of the network includes determining the preferred network structure and hyperparameter combination of the LSTM model according to experimental debugging. The neural network structure has a significant impact on the prediction performance of the LSTM model. Selecting the appropriate hidden layer and number of neurons can make the model have the best overall performance. To this end, by changing the number of layers of the hidden layer of the LSTM model and the number of neurons in each layer, the prediction results of the particle snow density of the LSTM model under the conditions of 1 to 4 hidden layers and 50 to 300 neurons are compared, and the preferred network structure is obtained. In addition to the network structure parameters, the hyperparameters of the model will also affect the prediction accuracy and performance of the LSTM model, especially the hyperparameters such as the learning rate, number of iterations, and batch size of the model. The present invention selects the network search method for hyperparameter optimization. According to the general range of the parameters, the learning rate is set to 0.005, 0.010, 0.015 and 0.020, the number of iterations is 100, 150, 200 and 250, and the batch size is 32, 64, 128 and 256, and then the set parameters are cyclically traversed and calculated, and finally the hyperparameter with the smallest mean square error is selected as the optimized hyperparameter combination.

[0135] Finally, the model performance is verified by cross-checking (such as leave-one-out cross-checking) to determine the optimal parameter combination. Specifically, in order to determine whether the trained model is suitable for the current problem, the leave-one-out cross-checking is used for verification. Taking the density profile of snow particles in the area with more liquid water as an example, the m snow particles density profiles in the area with more liquid water in the training set are cross-checked, that is, each experiment uses m-1 density profiles to train the model, and uses the remaining 1 density profile for verification. Repeat the experiment m times to traverse all density profiles in the training set. The model accuracy is evaluated based on the results of m experiments. When the model results meet the requirements, it is considered that the model can solve the current problem. Then the model is trained with the data of all m density profiles to obtain the corresponding weights and biases in each gate layer, and the training is completed. When the training loss decreases and the validation set loss also decreases, it means that the model has not reached the optimal level and is still in the training process; when the training loss decreases and the validation set loss tends to remain unchanged, it means that the model begins to overfit. When these two situations occur, readjust the network parameters and reconfigure and train the model. This step ensures that all samples in the training set become training data and also have the opportunity to become verification data, thereby better exploring the use value of the training set data.

[0136] In a second aspect, the present invention provides a method for obtaining snow particle density, comprising:

[0137] Obtaining meteorological data of the test location and inputting it into the particle snow compaction model, calculating the particle snow physical parameters at different depths of the test location, and then obtaining the particle snow characteristics at different depths of the test location;

[0138] The snow grain characteristics at different depths of the test site are respectively input into the snow grain density profile model to obtain the snow grain density at different depths of the test site;

[0139] The particle snow density profile model is constructed by using the method for constructing the particle snow density profile model provided in the first aspect of the present invention.

[0140] The related technical solution is the same as the method for constructing the snow particle density profile model provided in the first aspect of the present invention, and will not be described in detail here.

[0141] It should be noted that the method for obtaining the grain snow characteristics in the process of obtaining the grain snow density is the same as the method for obtaining the grain snow characteristics in the method for constructing the grain snow density profile model. When the grain snow density profile model is trained based on the normalized grain snow density measured results, in the process of obtaining the grain snow density, the grain snow density output by the grain snow density profile model is denormalized.

[0142] It should be noted that denormalization is the process of restoring the normalized data to the original data. The denormalization method used depends on the normalization method used. Here, the denormalization method corresponding to the normalization method used in the construction stage of the particle snow density profile model is used. After obtaining the statistical information of the particle snow density curve, the normalized features can be denormalized based on the statistical information to convert the corresponding particle snow density curve.

[0143] In a third aspect, the present invention further provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the method provided in the first aspect and / or the second aspect of the present invention.

[0144] The related technical solutions are the same as the method for constructing the particle snow density profile model provided by the first aspect of the present invention and the method for obtaining the particle snow density provided by the second aspect of the present invention, which will not be described in detail here.

[0145] It will be easily understood by those skilled in the art that the above description is only 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 in the protection scope of the present invention.

Claims

1. A method for constructing a snow particle density profile model, characterized in that: include: Obtaining snow particle density profile data and corresponding meteorological data at different locations; the snow particle density profile data includes: actual measurement results of snow particle density at different depths; Each meteorological data is input into the snow particle compaction model to calculate the snow particle physical parameters at different depths at the corresponding location, and then obtain the snow particle characteristics at different depths at the corresponding location; Each snow particle feature is input into a recurrent neural network to obtain the snow particle density detection result at the corresponding depth; by minimizing the difference loss between each snow particle density detection result and the corresponding measured result, the recurrent neural network is trained to obtain a snow particle density profile model.

2. The method for constructing a particle snow density profile model according to claim 1, characterized in that: The granular snow characteristics include: one or more types of data in the granular snow physical parameters; the granular snow physical parameters include the following types of data: the temperature of the snow layer, the pressure of the overlying snow layer, the amount of liquid water in the snow layer, the porosity of the snow layer, the thermal conductivity of the snow layer and the hydraulic conductivity of the snow layer.

3. The method for constructing a snow particle density profile model according to claim 2, characterized in that: The method for obtaining the characteristics of snow particles at different depths at any location A includes: Calculate X i The correlation coefficient between X and Y i is a vector composed of the i-th type of data in the particle snow physical property parameters at different depths at the location A; Y is a vector composed of the actual measurement results of the particle snow density at different depths at the location A; i=1,2,…,M; M is the number of data categories in the particle snow physical property parameters; The N categories with the largest correlation coefficients are taken as N candidate categories; 1≤N <M; For each depth, a particle snow feature is constructed including data under N candidate categories of the particle snow physical property parameters at the depth.

4. The method for constructing a snow particle density profile model according to claim 3, characterized in that: The X i The correlation coefficient between X and Y is i The weighted average of the Kendall rank correlation coefficient, Spearman rank correlation coefficient, and Pearson linear correlation coefficient between it and Y.

5. The method for constructing a snow particle density profile model according to any one of claims 1 to 4, characterized in that: The particle snow density profile data is pre-processed particle snow density profile data; Among them, the preprocessing methods include: For the measured result of any snow particle density in the original snow particle density profile data, ρ m , when ρ m When the density is higher than that of pure ice, ρ m Set to the density of pure ice; when ρ m The snow layer is the surface snow layer, and ρ m When it is lower than the preset threshold, ρ m Set to the density of the next snow layer in the snow layer; when ρ m The snow layer is the bottom snow layer, and ρ m When it is lower than the preset threshold, ρ m Set to the density of the snow layer above the snow layer where it is located; when ρ m The snow layer is the middle snow layer, and ρ m When it is lower than the preset threshold, ρ m Set to the average density of the snow layer above and below it.

6. The method for constructing a particle snow density profile model according to claim 5, characterized in that: The preset threshold is Among them, 0<α<1 is the preset ratio; The ρ is obtained by inputting the meteorological data corresponding to the particle snow density profile data into the particle snow densification model without considering the effect of liquid water. m The density of snow particles in the snow layer.

7. The method for constructing a snow particle density profile model according to any one of claims 1 to 4, characterized in that: It also includes: normalizing the obtained snow particle characteristics; The step of inputting each snow particle feature into the recurrent neural network specifically includes: inputting each normalized snow particle feature into the recurrent neural network.

8. The method for constructing a snow particle density profile model according to any one of claims 1 to 4, characterized in that: It also includes: normalizing the measured results of snow particle density; The minimizing the difference loss between each snow particle density detection result and the corresponding measured result specifically includes: minimizing the difference loss between each snow particle density detection result and the corresponding normalized measured result.

9. A method for obtaining snow particle density, characterized in that: include: Obtaining meteorological data of the test location and inputting it into the particle snow compaction model, calculating the particle snow physical parameters at different depths of the test location, and then obtaining the particle snow characteristics at different depths of the test location; The snow grain characteristics at different depths of the test site are respectively input into the snow grain density profile model to obtain the snow grain density at different depths of the test site; Wherein, the particle snow density profile model is constructed by using the particle snow density profile model construction method described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the method according to any one of claims 1 to 9.

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