A method for constructing a grain snow density profile model and a method for obtaining grain snow density

Abstract

The application discloses a construction method of a granular snow density profile model and a granular snow density acquisition method, and belongs to the technical field of granular snow density simulation; prior information related to the characteristics and mechanism of granular snow compaction is obtained and utilized, specifically, a granular snow compaction model is used to acquire the physical parameters of granular snow at different depths in different places, and then the characteristics of granular snow at different depths in the corresponding places are obtained; on this basis, considering that the deposition of granular snow is time-sequential and gradual, and the granular snow depth-density profile is different responses to the deposition characteristics of different strata, the whole has certain time-sequential characteristics, the application adopts a recurrent neural network to learn the complex mapping relationship between the granular snow characteristics and the granular snow density, can maximize the utilization and mining of the complex mapping relationship between the granular snow characteristics and the granular snow density, reduces the dependence of the granular snow compaction model on idealized assumptions, and can realize accurate acquisition of the granular snow density at different depths, and has relatively strong universality.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of granular snow density simulation, and more particularly relates to a method for constructing a granular snow density profile model and a method for obtaining granular snow density. BACKGROUND

[0002] Granular snow compaction is an intermediate process of new snow transforming into glacier ice. In this process, granular snow is continuously compacted under the stress of its own gravity and the overlying snow layer, and the crystal grains grow and deform, and the density increases with the increase of depth. In the process of granular snow compaction, obtaining the depth-density profile of granular snow and establishing the granular snow density profile model play an important role in the field of glaciology, such as glacier mass balance monitoring, ice core paleoclimate environment analysis, and glacier ice reserve estimation.

[0003] The method for constructing a granular snow density profile model mainly includes direct measurement method and indirect interpretation method. The direct measurement method obtains the granular snow density at a certain depth through ice core measurement. This method is the most accurate, but the cost of sampling and testing is high. Moreover, as the depth of the ice core increases, the difficulty of obtaining the granular snow density also increases. Therefore, the direct measurement method is limited to certain layers and certain regions, and it is difficult to obtain complete granular snow density in multiple regions and layers. The indirect interpretation method simulates the granular snow density at a certain depth according to known meteorological information through empirical / semi-empirical / physical models. This method can obtain good results for the simulation of granular snow density under the modeling background at that time. However, due to the complexity and strong heterogeneity of the underground, the numerous and complex relationships between the factors affecting the granular snow density, and the need for strong assumption conditions when constructing the model, i.e. the model is greatly simplified, this method cannot well explore the complex nonlinear relationship between the granular snow density and various parameters and the spatial continuity. At the same time, different models need to be selected for different meteorological information, and the selection process is easily dominated by thinking. Therefore, the granular snow density profile model constructed by the above methods cannot accurately obtain the granular snow density at different depths. SUMMARY

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

[0005] To achieve the above purpose, in a first aspect, the present application provides a method for constructing a granular snow density profile model, comprising:

[0006] obtaining granular snow density profile data and corresponding meteorological data at different locations; the granular snow density profile data includes measured results of granular snow density at different depths;

[0007] Each meteorological data point is input into the snow compaction model to calculate the snow physical property parameters at different depths at the corresponding location, thereby obtaining the snow characteristics at different depths at the corresponding location.

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

[0009] More preferably, the characteristics of snow pellets include one or more types of data in the snow pellet physical property parameters; the snow pellet physical property 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] More preferably, the method for obtaining the characteristics of snow grains at different depths at any location A includes:

[0011] Calculate X i The correlation coefficient between X and Y; i Y is a vector composed of the i-th type of data in the snow grain property parameters at different depths of location A; Y is a vector composed of the measured snow grain density results at different depths of location A; i = 1, 2, ..., M; M is the number of data categories in the snow grain property parameters;

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

[0013] For each depth, construct a snow feature that includes data from N candidate categories of snow grain properties at that depth.

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

[0015] More preferably, the above-mentioned snow density profile data is preprocessed snow density profile data;

[0016] The preprocessing methods include:

[0017] For any measured flake density ρ in the flake density profile data 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 in question is the surface snow layer, and ρ m When it is below the preset threshold, ρm Set to the density of the next layer of snow below it; when ρ m The snow layer in question is the bottom layer, and ρ m When it is below the preset threshold, ρ m Set to the density of the snow layer above it; when ρ m The snow layer in question is the intermediate snow layer, and ρ m When it is below the preset threshold, ρ m It is set to the average density of the snow layer above and below it.

[0018] More preferably, the preset threshold is Where 0 < α < 1 is a preset ratio; To input the meteorological data corresponding to the snow pellet density profile into the snow pellet densification model that does not consider the effect of liquid water, the simulated ρ m The density of snow grains in the snow layer.

[0019] More preferably, the method for constructing the above-mentioned snow grain density profile model further includes: normalizing the obtained snow grain features;

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

[0021] More preferably, the method for constructing the above-mentioned snow density profile model further includes: normalizing the measured snow density results;

[0022] The above-mentioned minimization of the difference between each snow grain density detection result and the corresponding measured result specifically includes minimizing the difference between each snow grain density detection result and the corresponding normalized measured result.

[0023] Secondly, the present invention provides a method for obtaining snow pellet density, comprising:

[0024] Meteorological data of the test site is obtained and input into the snow compaction model to calculate the snow physical property parameters at different depths of the test site, thereby obtaining the snow characteristics at different depths of the test site.

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

[0026] The snow density profile model is constructed using the snow density profile model construction method provided in the first aspect of this invention.

[0027] In a third aspect, the present application further provides a computer readable storage medium comprising a stored computer program, wherein the computer program, when executed by a processor, controls a device in which the storage medium is located to perform the method provided in the first aspect and / or the second aspect of the present application.

[0028] Overall, the above technical solutions conceived by the present application can achieve the following beneficial effects:

[0029] 1. The present application provides a method for constructing a grain snow density profile model, which utilizes prior information related to the characteristics and mechanisms of grain snow compaction. Specifically, the method obtains grain snow physical property parameters at different depths in different locations through a grain snow compaction model, and then obtains the grain snow characteristics at corresponding depths. Considering that the deposition of grain snow is a time-series change and the grain snow depth-density profile is a different response to the deposition characteristics of different strata, the present application uses a recurrent neural network to learn the complex mapping relationship between grain snow characteristics and grain snow density, which can maximize the use and mining of the complex mapping relationship between grain snow characteristics at different depths and grain snow density at corresponding depths, reduce the dependence of the grain snow compaction model on idealized assumptions, and achieve accurate acquisition of grain snow density at different depths with strong universality.

[0030] 2. Further, the method for constructing a grain snow density profile model provided by the present application selects class data in grain snow physical property parameters that are more sensitive to grain snow density to construct grain snow characteristics by analyzing the correlation between different data categories in grain snow physical property parameters and grain snow density, thereby further improving the accuracy of obtaining grain snow density. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 A flowchart of the method for constructing a grain snow density profile model provided by the present application is shown in the following figure:

[0032] Figure 2 A schematic diagram of the position and depth of the grain snow density profile collected at a certain ice cover is shown in the following figure:

[0033] Figure 3 A unit structure diagram of LSTM provided by the present application is shown in the following figure: DETAILED DESCRIPTION

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

[0035] To achieve the above object, in a first aspect, the present application provides a method for constructing a snow grain density profile model, as shown in the following formula (1): Figure 1

[0036] Obtaining snow grain density profile data and corresponding meteorological data at different locations; the snow grain density profile data comprises measured results of snow grain density at different depths;

[0037] Inputting each meteorological data into a snow grain densification model to calculate snow grain physical parameters at different depths of the corresponding location, and further obtaining snow grain characteristics at different depths of the corresponding location;

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

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

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

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

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

[0043] For each depth, constructing a snow grain characteristic including data in the N candidate categories in the snow grain physical parameters at the depth.

[0044] It should be noted that the correlation coefficient between X i and Y can be calculated by using the Kendall rank correlation coefficient calculation formula, the Spearman rank correlation coefficient calculation formula, the Pearson linear correlation coefficient calculation formula, etc. Preferably, X i ​The correlation coefficient between X and Y i A weighted average of the Kendall rank correlation coefficient, the Spearman rank correlation coefficient, and the Pearson linear correlation coefficient between X and Y.

[0045] In an optional implementation, the above-mentioned snow grain density profile data is pre-processed snow grain density profile data.

[0046] The pre-processing method comprises:

[0047] For any snow grain density measurement result ρ m When ρ m is higher than the density of pure ice, ρ m is set as the density of pure ice; when ρ m is in the surface snow layer and ρ m is lower than a preset threshold, ρ m is set as the density of the next layer of snow layer of the snow layer where ρ m is in the bottom snow layer and ρ m is lower than the preset threshold, ρ m is set as the density of the previous layer of snow layer of the snow layer where ρ m is in the middle snow layer and ρ m is lower than the preset threshold, ρ m is set as the average of the densities of the previous layer and the next layer of snow layer of the snow layer where ρ

[0048] Preferably, the above-mentioned preset threshold is wherein 0 < α < 1 is a preset proportion, and in an optional implementation, the value is 0.7. is the snow grain density of the snow layer where ρ m is located, which is simulated by inputting the meteorological data corresponding to the snow grain density profile data into a classical dry snow grain compaction model. The classical dry snow grain compaction model is a snow grain compaction model that does not consider the effect of liquid water.

[0049] In an optional implementation, the method for constructing the above-mentioned snow grain density profile model further comprises normalizing the obtained snow grain characteristics.

[0050] The above-mentioned inputting each snow grain characteristic into the recurrent neural network specifically comprises inputting each normalized snow grain characteristic into the recurrent neural network.

[0051] In an optional implementation, the method for constructing the above-mentioned snow grain density profile model further comprises normalizing the snow grain density measurement results.

[0052] The loss of minimizing the difference between each snow grain density detection result and the corresponding measured result specifically includes: the loss of minimizing the difference between each snow grain density detection result and the corresponding normalized measured result.

[0053] It should be noted that the existing snow grain compaction model often needs strong assumption conditions when building the model due to the lack of sufficient understanding of the physical mechanism, that is, the model is extremely simplified, so that there is a large difference between the simulated snow grain density and the measured density. In complex problems where the relationship between variables cannot be determined, the data-driven deep learning strategy is the best means to build its mapping relationship model at this stage, and is very suitable for problems that have complex mapping relationships but lack accurate physical models or empirical models. The problem we are facing now is as follows: the internal relationship between each parameter and the snow grain density is quite complex, is affected by factors such as depth, latitude, temperature, and shows strong nonlinearity and time sequence characteristics (the deposition of snow grain is time sequence gradual change, and the snow grain depth-density profile is different response to different stratum deposition characteristics, and has certain time sequence characteristics). Considering that the sampling interval of the snow grain density profile is small, and the thickness often reaches dozens of meters, that is, the sequence length of mutual influence contains hundreds of data points, the present application selects a recurrent neural network as a data-driven model.

[0054] However, since the snow grain density profile is often multi-source and complex, and the measured snow grain density profile is less, simply and directly using a recurrent neural network cannot guarantee the prediction effect of the model, the present application considers combining the data-driven characteristics of deep learning and the physical constraints of the snow grain compaction process to simulate the snow grain 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 snow grain density, and to reduce the dependence of the snow grain compaction model on idealized assumptions; on the other hand, the characteristics and mechanism of the snow grain compaction itself are used to feed back the algorithm and model, and are converted into constraint conditions or prior information of the model for use. The accurate acquisition of snow grain density of different depths can be realized, and the universality is relatively strong.

[0055] The present application combines the understanding of the snow grain compaction model for the compaction process and the powerful prediction ability of data-driven, considers the physical mechanism, and can partially reduce the snow grain density simulation uncertainty caused by complex physical mechanisms, improves the accuracy of the snow grain density acquisition, and has good generalization ability and robustness.

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

[0057] The method for constructing the snow grain density profile model provided by the present application includes the following steps:

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

[0059] Specifically, the snow density data measured from the ice core drilling and its corresponding depth, time, latitude and longitude are collected, and the data is spread over various depth ranges and liquid water-free, liquid water-poor and liquid water-rich regions, so as to train samples in different situations, so that the model has a certain generalization and robustness. For example, Figure 2 The range of the latitude and longitude corresponding to the snow density profile collected in a certain ice sheet and its maximum depth. Due to the influence of measurement method, stratum factor, instrument limitation and other factors, there may be certain abnormal values and blank values in the collected snow density profile, which need to be processed to reduce their influence on the later snow density prediction results. The abnormal value in this embodiment refers to the measured result of the snow density higher than the density of pure ice (917 kg / m -3 ) or the measured result of the snow density lower than 70% of the simulated snow density of the snow density compaction model. For overestimated abnormal values, this embodiment sets them to the density of pure ice. For underestimated abnormal values and blank values, set them to the average density of the adjacent snow segments above and below.

[0060] 2) Obtain the weather data of the corresponding place according to the latitude and longitude information of each snow density profile.

[0061] The weather data includes the surface temperature, snowfall, total liquid water, snowmelt and sublimation of each place per day within a period of time. The daily rainfall is the difference between the total daily precipitation and snowfall; the total liquid water entering the snow column per day is the sum of the daily snowmelt and rainfall.

[0062] 3) Input each weather data into the snow density compaction model to calculate the snow physical parameters at different depths of the corresponding place, and then obtain the snow characteristics at different depths of the corresponding place;

[0063] The snow characteristics include one or more types of data in the snow physical parameters; the snow physical parameters include the following types of data: the temperature of the snow layer, the pressure of the overlying snow layer, the liquid water content of 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 snow characteristics at different depths of any place A includes:

[0065] Calculate the correlation coefficient between X i and Y; X i is a vector composed of the i-th type of data in the snow physical parameters at different depths of place A; Y is a vector composed of the measured results of the snow density at different depths of place A; i=1, 2, …, M; M is the number of data categories in the 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 snow grain feature including data under the N candidate categories in the snow grain physical property parameters at the depth is constructed.

[0068] wherein, X i The correlation coefficient between X i and Y is a weighted average of the Kendall rank correlation coefficient, the Spearman rank correlation coefficient and the Pearson linear correlation coefficient between X i and Y; the weight values corresponding to the Kendall rank correlation coefficient, the Spearman rank correlation coefficient and the Pearson linear correlation coefficient can be set according to experience, considering that the snow grain physical property parameters and the snow grain density are generally non-normal distribution, the Kendall rank correlation coefficient and the Spearman rank correlation coefficient are given larger weights, and the specific weights can be adjusted according to test results. In the embodiment, the weight values corresponding to the Kendall rank correlation coefficient, the Spearman rank correlation coefficient and the Pearson linear correlation coefficient between X i and Y are 0.4, 0.4 and 0.2 respectively.

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

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

[0071] In the present embodiment, in order to eliminate the influence of the difference in the order of magnitude and dimension of each parameter on the model without affecting the data characteristics, reduce the training error, accelerate the convergence and improve the accuracy of the model, after the granular snow physical property parameters at different locations and depths are calculated, each category of data in the granular snow physical property parameters is normalized.

[0072] It should be noted that the normalization process for a certain category of data in the granular snow physical property parameters can be: normalizing the obtained category data at different locations and depths together; or can be: normalizing separately according to different locations, and normalizing the category data at different depths of the same location together. Here, no limitation is made.

[0073] There are many normalization methods, and in the present embodiment, the maximum and minimum normalization method is used to normalize each component data to 0-1:

[0074]

[0075] wherein y is the input or output component of the model, y * is the input or output component after normalization, y max and y min are the maximum and minimum values of the model input or output quantity, respectively.

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

[0077] In this embodiment, the firn densification model in patent CN202311200948.7 is taken as an example for detailed description. The process of obtaining the granular snow physical property parameters at different depths in a certain place by the firn densification model includes:

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

[0079] A32, establish the relationship between the temperature T and the density p of the granular snow in each granular snow layer by the one-dimensional heat conduction equation:

[0080]

[0081] where c f is the specific heat capacity of 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 and temperature of the granular snow, Since the present consideration is one-dimensional, the gradient operator Considering the effect of the phase change latent heat released during the refreezing of liquid water on the temperature of the granular snow, the temperature of the granular snow is updated after refreezing.

[0082] A33、according to the relationship, the surface temperature corresponding to each time step, the snow accumulation, the dry snow density of each snow layer in the snow column corresponding to the time step is obtained by the dry snow densification scheme. Specifically, the present application uses the stress-based CROCUS model developed for mountain snow as the dry snow densification scheme. The CROCUS model calculates the stress σ, snow viscosity η, snow density ρ and densification rate In connection with:

[0083]

[0084]

[0085] where T m is the melting point temperature (273.15K), η0=7.62237×106kg 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 of snow viscosity, which respectively consider the viscosity difference caused by the existence of liquid water and the grain size. According to previous studies, here f1=1 / (1+60θ w ), f2=4, where θ w represents the liquid water content in each snow layer.

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

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

[0088] (2) As liquid water percolates into the snow column, the pore space in each snow layer will contain air and liquid water. The maximum pore space that can be occupied by liquid water is called the saturated water content, which is expressed as: The saturated water content is θ s = V wm / dz. Assuming the amount of liquid water in a snow layer is V w , the volumetric water content of the layer is θ w = V w / dz. The capillary suction force of the snow grain causes some of the liquid water to be stored in the snow layer and cannot be refrozen or runoff, which is called the bound water. The water storage capacity of a snow layer is expressed as:

[0089]

[0090]

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

[0092] Thus, the effective degree of saturation in each snow layer is:

[0093]

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

[0095]

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

[0097] (3) In the jth layer of snow, the liquid water beyond the bound water can move downward. We denote the amount of liquid water that can flow as V av = V w - V wi To simplify the model, the present invention assumes that the liquid water is subjected to the action of gravity and capillary suction during the seepage process, and regards the liquid water as a Newtonian fluid with constant viscosity, whose flow in the snow column obeys the Newtonian 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 snow layers (m s -1 ), h is the pressure head (m), represents the vertical gradient of capillary suction, the +1 term represents the action of gravity, K w is the hydraulic conductivity of the snow layer (m s -1 ).

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

[0101] (4) With and V w * p wthe smaller value in the two as the mass m added by refreezing in each snow layer r , the snow density in the case of liquid water refreezing is calculated, and the overlying snow stress and porosity of each snow layer are further calculated. Wherein, Q cold is the cold content of each snow layer, is the latent heat of fusion of snow, and p w is the density of water.

[0102] Specifically, when there is liquid water in the pore space in addition to bound water and the refreezing temperature is met, phase transition of liquid water into ice will occur, and latent heat of phase transition is released in this process, increasing the energy of the snow column. At the same time, the ice formed will increase the mass of the snow layer, further affecting the density of the snow layer. The cold content of each snow layer is equal to the heat absorbed by the temperature T of the snow layer rising to the critical temperature T m :

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

[0104] Wherein, m is the mass of the snow layer before refreezing occurs in this time step. The refreezing capacity that can be caused by this cold content is:

[0105]

[0106] The actual refreezing amount in each snow layer is the smaller value of the refreezing capacity C r and the amount of liquid water available for refreezing in the snow layer, i.e. m r = min(C r , V w * p w ). Therefore, the latent heat of phase transition caused by refreezing is: Considering the effect of this latent heat on the temperature of the snow, the temperature of the snow after refreezing occurs is updated as:

[0107]

[0108] Finally, the snow density of each snow layer considering the effect of liquid water is calculated as p = (m + m r ) / dz. Thus, the porosity of each snow layer corresponding to the stress of the jth snow layer is σ j = (m + m r ) j g, then the overlying snow pressure of each snow layer is the sum of the stress of each snow layer above it, where g is the acceleration of gravity, (m + m r ) jThe mass of the jth snow grain layer is denoted as

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

[0110] In this embodiment, the physical property parameters output by the snow grain compaction model and the measured snow grain density profile are both resampled at a thickness interval of 0.01 m and arranged in depth order. It is assumed that the snow grain density profile to be predicted is output and denoted as y, and each physical property parameter is input and denoted as x1, x2, …, x p , where p is a natural number ≥ 2. For each ice core, it is assumed that there are n snow grain layers (i.e. n 0.01 m) in the snow grain column from the surface to the maximum depth of the ice core drilling, respectively denoted as vectors X1, X2, …, X n , where n is a natural number greater than 1, and the corresponding n outputs are denoted as a vector Y = [y1, y2, …, y n ] T , then the kth input is X k = [x 1k , x 2k , …, x pk ], k = 1, 2, …, N, and the corresponding kth output is y k ; p is a positive integer; T represents transposition in the above formulas.

[0111] The recurrent neural network used in this embodiment is LSTM, which is built based on the Tensorflow framework. Referring to Figure 3 , the LSTM network unit mainly consists of three gates, namely the forgetting gate f t , the input gate i t and the output gate O t . The forgetting gate is used to discard or retain information in the cell state, and determines how much information in the cell state at the previous time C t-1 is saved to the state C t at the current time, 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 fThe forget gate weight matrix has dimensions that depend on the dimensions of the hidden layer states and the unit states output at time t-1, as well as the dimensions of the input feature vectors at time t-1; b f For bias; [h t-1 ,x t [] is the output h at time t-1 t-1 x input at time t t Concatenation of eigenvectors; f t The output of the forget gate is a general value ranging from 0 to 1, multiplied by f for the cell state. t This determines how much of the hidden layer state information should be retained.

[0114] The input gate is used to update the cell state information. Its calculation is divided into two steps: the first step is to calculate h. t-1 and x t To determine which information needs to be strengthened or weakened, the hyperbolic tangent function tanh is used as the activation function, calculated as follows:

[0115]

[0116] Among them, W c b is the first weight matrix of the input gate; c For bias; The input state information is given at time t. The second step uses the sigmoid activation function to output probability values, which are used to determine... The formula for calculating how much information needs to be updated in the cell state is:

[0117] i t =σ(W i [h t-1 ,x t ]+b i )

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

[0119]

[0120] The output gate determines what information a cell in the LSTM network needs to output at time t, and the output value is O. t The information to be output is related to the cell state. The tanh activation function determines the information to be output, and the sigmoid function determines the amount of information to be output. The calculation formula is as follows:

[0121] O t = σ(W o [h t-1 ,x t ]+b o )

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

[0123] where h t represents the hidden layer state information of the LSTM network output at time t. In the above formulas, W f , W c , W i , W o , b f , b c , b i , b o parameters are obtained by 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, that is, 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 iterations, the learning rate, the batch size, etc. According to the common values of the LSTM network in predicting regression problems, the initial model parameters are set as follows in this embodiment: 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 learning rate to optimize and adjust 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 advantages of the RMSprop algorithm in processing non-stationary targets. It has the advantages of small required memory and high computational efficiency. The loss function is selected as Log-Cosh, which is similar to the mean square error, is less affected by individual values, is twice differentiable everywhere, and 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 core is divided into three types according to the amount of liquid water, i.e. no liquid water, less liquid water, and more liquid water. The proportion of the training set and 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 training, but is used to verify the stability and reliability of the LSTM network model.

[0127] The LSTM neural network model preliminarily determining the network parameters is trained by using the training set divided in each parameter combination, the network internal parameters are continuously adjusted to iteratively optimize the model during the training process, until the model training error reaches the target set in advance, 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 neuron of the LSTM is sequentially calculated along the forward propagation direction in the depth;

[0130] The output value calculated sequentially in the forward direction is compared with the true value, the error between the true value and the estimated value is calculated, and then the error between the hidden layers and the hidden layer cells is calculated along the back propagation direction according to the calculated error;

[0131] The corresponding weight gradient is calculated according to the calculated error between the hidden layers and the hidden layer cells;

[0132] According to the calculated weight gradient, the Adam algorithm is applied to update the corresponding weight, so that the prediction result gradually approaches the actual value;

[0133] The above steps are repeatedly performed, and when the total error is less than a given threshold or the maximum number of iterations is reached, the network training is completed.

[0134] Specifically, adjusting the network internal parameters includes determining the preferred network structure and super parameter combination of the LSTM model according to experimental debugging. The neural network structure has a significant influence on the prediction performance of the LSTM model, and selecting appropriate hidden layers and neuron numbers can make the model have the best comprehensive performance. Therefore, by changing the number of hidden layers and the number of neurons of the LSTM model, the prediction results of the LSTM model under the conditions of 1-4 hidden layers and 50-300 neurons are compared, and the preferred network structure is obtained. In addition to the network structure parameters, the super parameters of the model also affect the prediction accuracy and performance of the LSTM model, especially the learning rate, the number of iterations, the batch size and other super parameters. The network search method is selected to optimize the super parameters, the learning rate is set to 0.005, 0.010, 0.015 and 0.020 according to the general range of the parameters, the number of iterations is set to 100, 150, 200 and 250, and the batch size is set to 32, 64, 128 and 256, then the set parameters are calculated by loop traversal, and finally the super parameter with the smallest mean square error is selected as the optimized super parameter combination.

[0135] Finally, the performance of the model is verified by cross-validation (such as leave-one-out cross-validation) to determine the preferred parameter combination. Specifically, to determine whether the trained model is suitable for the current problem, leave-one-out cross-validation is used for verification. Taking the grain snow density profile in the area with more liquid water as an example, m grain snow density profiles in the area with more liquid water in the training set are cross-validated, that is, m-1 density profiles are used to train the model each time, and the remaining 1 density profile is used for verification, and the experiment is repeated m times to traverse all the density profiles in the training set. According to the results of the m experiments, the accuracy of the model is evaluated, and when the model results meet the requirements, it is considered that the model can solve the current problem, and then the model is trained with all m density profile data to obtain the corresponding weights and biases in each gate layer. When the training loss decreases and the validation set loss also decreases, it means that the model has not reached the optimal and is still in the training process; when the training loss decreases and the validation set loss tends to be constant, it means that the model has begun to overfit. When these two situations occur, the network parameters are adjusted again, and the model is configured and trained again. This step makes all samples in the training set become training data, and also has the opportunity to become a validation data, so as to better exploit the value of the training set data.

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

[0137] Obtain the meteorological data of the to-be-tested site and input it into the grain snow densification model to calculate the grain snow physical property parameters at different depths of the to-be-tested site, and then obtain the grain snow characteristics at different depths of the to-be-tested site;

[0138] Input the grain snow characteristics at different depths of the to-be-tested site into the grain snow density profile model respectively to obtain the grain snow density at different depths of the to-be-tested site;

[0139] The grain snow density profile model is constructed by the method for constructing a grain snow density profile model provided in the first aspect of the present application.

[0140] The related technical solution is the same as the method for constructing a grain snow density profile model provided in the first aspect of the present application, which is not repeated here.

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

[0142] It should be noted that the reverse normalization is a process of restoring the normalized data to the original data, and the method adopted by the reverse normalization depends on the method adopted by the normalization. Here, the reverse normalization method corresponding to the normalization method adopted in the construction stage of the grain snow density profile model is adopted. After obtaining the statistical information of the grain snow density curve, the reverse normalization operation can be performed on the normalized features based on the statistical information, so as to convert to obtain the corresponding grain snow density curve.

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

[0144] The related technical solutions are the same as the construction method of the grain snow density profile model provided in the first aspect of the present application and the method for obtaining the grain snow density provided in the second aspect of the present application, which will not be repeated here.

[0145] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the present application, and is not used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method of constructing a snow grain density profile model, characterized by, The method comprises: obtaining granular snow density profile data and corresponding meteorological data at different locations; the granular snow density profile data comprises measured granular snow density at different depths; inputting each meteorological data into a granular snow densification model to calculate granular snow physical property parameters at different depths of the corresponding location, and then obtaining granular snow characteristics at different depths of the corresponding location; the granular snow characteristics comprise one or more types of data in the granular snow physical property parameters; the granular snow physical property parameters comprise the following types of data: temperature of the snow layer, pressure of the overlying snow layer, liquid water content of the snow layer, porosity of the snow layer, thermal conductivity of the snow layer, and hydraulic conductivity of the snow layer; inputting each granular snow characteristic into a recurrent neural network to obtain a granular snow density detection result at the corresponding depth; training the recurrent neural network by minimizing the difference loss between each granular snow density detection result and the corresponding measured result to obtain a granular snow density profile model.

2. The method of claim 1, wherein The method for obtaining granular snow characteristics at different depths of any location A comprises: calculate The correlation coefficient between Y and; The first of the snow grain property parameters at different depths at location A i A vector composed of class data; Y is a vector composed of the measured snow density results at different depths of location A; M represents the number of data categories in the snow grain property parameters; The N categories with the largest correlation coefficients are taken as N candidate categories. ; For each depth, construct a granular snow characteristic comprising data in N candidate categories of granular snow physical property parameters at the depth.

3. The method of claim 2, wherein The The weighted average of the Kendall rank correlation coefficient, Spearman rank correlation coefficient, and Pearson linear correlation coefficient between X and Y. The weighted average of the Kendall rank correlation coefficient, Spearman rank correlation coefficient, and Pearson linear correlation coefficient between X and Y.

4. The method of claim 1-3, wherein The granular snow density profile data is pre-processed granular snow density profile data; The pre-processing method comprises: For any measured snow density result in the original snow density profile data ,when When the density is higher than that of pure ice, Set to the density of pure ice; when The snow layer in question is the surface snow layer, and When it is below the preset threshold, Set to the density of the next layer of snow below it; when The snow layer in question is the bottom layer, and When it is below the preset threshold, Set to the density of the snow layer above it; when The snow layer in question is the intermediate snow layer, and When it is below the preset threshold, It is set to the average density of the snow layer above and below it.

5. The method of claim 4, wherein The preset threshold is ; wherein, is a preset ratio; is the grain snow density profile data corresponding to the meteorological data input into the grain snow densification model without considering the effect of liquid water simulation The grain snow density of the snow layer.

6. The method of claim 1-3, wherein Further comprising: normalizing the obtained granular snow characteristics; The inputting each granular snow characteristic into a recurrent neural network specifically comprises: inputting each normalized granular snow characteristic into a recurrent neural network.

7. The method of claim 1-3, wherein Further comprising: normalizing the granular snow density measurement results; The minimizing the difference loss between each granular snow density detection result and the corresponding measured result specifically comprises: minimizing the difference loss between each granular snow density detection result and the corresponding normalized measured result.

8. A method of obtaining a density of granular snow, characterized by, The method comprises: obtaining meteorological data of the location to be measured and inputting it into a granular snow densification model to calculate granular snow physical property parameters at different depths of the location to be measured, and then obtaining granular snow characteristics at different depths of the location to be measured; inputting the granular snow characteristics at different depths of the location to be measured into the granular snow density profile model respectively to obtain the granular snow density at different depths of the location to be measured; The granular snow density profile model is constructed by the method for constructing a granular snow density profile model according to any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium comprises a stored computer program, wherein the computer program controls the device where the storage medium is located to execute the method according to any one of claims 1-8 when the computer program is run by a processor.

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