Glacier thickness inversion method fusing laminar flow model and random unit interpolation

Abstract

The invention relates to the technical field of glacier thickness inversion, particularly discloses a glacier thickness inversion method fusing a laminar flow model and random unit interpolation, and aims to solve the problems that a traditional glacier thickness estimation method based on the laminar flow model excessively depends on a glacier center streamline, and the glacier center streamline in a complex area is difficult to accurately obtain. A random unit interpolation method is introduced, the dependence of glacier thickness estimation on a central streamline is avoided, and glacier terrain and flow velocity data are fully utilized. Besides, the difference of different glacier shape factors is considered in the model, specific kinetic parameters are distributed for the glacier in combination with temperature information, and manual parameter determination can be effectively avoided. Experimental results show that glacier thickness distribution which is more practical can be obtained through the improved method.

Description

Technical Field

[0001] The present invention relates to the technical field of glacier thickness inversion, and in particular to a glacier thickness inversion method that integrates a laminar flow model and random unit interpolation. Background Art

[0002] In glacier research, glacier thickness is a crucial parameter for estimating glacier reserves and dynamic modeling. It also plays a key role in revealing the mechanisms that foster glacier instability hazards and simulating glacier instability hazard scenarios. Research has shown significant variations in glacier thickness across regions and types. This variation influences glacier responses to climate change, flow velocity, and meltwater flow. Accurately acquiring glacier thickness information is crucial for assessing glacier quality, predicting melting processes, and analyzing water resource contributions. While traditional ground drilling and ground-penetrating radar methods can provide relatively accurate point-level data, their widespread application is limited by cost and efficiency. Indirect estimates of glacier thickness distribution can be made by combining glacier physical models (such as laminar flow models), digital elevation models (DEMs), and ice surface geometric parameters. Earth observation techniques such as satellite photogrammetry and radar interferometry can systematically obtain key inputs such as glacier surface velocity fields and morphological parameters. This significantly improves the efficiency of glacier thickness estimation based on physical models, making it possible to estimate glacier thickness and volume over large areas and even globally. Combining glacier physical models with remote sensing observations to estimate glacier thickness has become a new research direction. Existing glacier thickness inversion methods based on physical models mainly fall into three categories: mass conservation-based methods, shear stress-based methods, and laminar flow model-based methods. However, these existing glacier thickness estimation methods based on physical models often rely on extracting central streamlines, which affects the models' adaptability and accuracy in complex areas. Summary of the Invention

[0003] The present invention aims to overcome the shortcomings of the existing technology and provide a glacier thickness inversion method that integrates the laminar flow model and random cell interpolation. The present invention combines air temperature data to determine the rate factor A, so that different rate factor parameters can be set for glaciers in different regions; the shape factor is determined by the glacier cross-sectional width and the thickness at the center streamline. ; By using the random cell interpolation method to avoid dependence on the streamlines in the center of the glacier, we can more effectively utilize the observation data from other parts of the glacier and generate a cross-section with a shape close to a parabola.

[0004] To achieve the above-mentioned purpose, the present invention provides a glacier thickness inversion method that integrates a laminar flow model and random unit interpolation. The ice thickness is calculated based on the laminar flow equation derived from Glen's flow law, and a random unit selection method is used to generate thickness samples. The global estimation of glacier thickness is then achieved through a spatial interpolation method. Among them: the laminar flow model is a physical model in glaciology, which is mainly used to describe the internal deformation movement of ice bodies inside glaciers driven by gravity; in this model, the flow of ice is analogous to the laminar flow of viscous fluid under the action of force, and its movement is controlled by factors such as shear stress, ice viscosity and ice thickness. Random unit interpolation is a spatial interpolation method based on randomly selected internal units of the glacier, combined with the statistical characteristics of the local buffer zone slope, through repeated thickness estimation and spatial interpolation and averaging of the results to obtain a stable glacier thickness distribution. The glacier thickness inversion method specifically includes the following steps:

[0005] Step 1: Obtain glacier surface velocity in the study area through remote sensing , digital elevation model, glacier boundary vector, glacier surface slope and glacier area mask data, and generate regular rasterized datasets;

[0006] Step 2: Use the glacier surface air temperature and the empirical temperature difference constant First, estimate the representative ice temperature of the glacier, and then dynamically calculate the flow rate factors of multiple different glacier areas using the empirical formula of the rate factor. ;

[0007] The present invention calculates the representative ice temperature based on the average annual temperature at the glacier mass balance line, and dynamically adjusts the flow rate factor in the Glen formula through an empirical formula. , improving adaptability to different glacier areas.

[0008] Step 3: Cross-section width across multiple different glacier regions Thickness of center streamline Estimate multiple sets of shape factors for valleys , and calculate the multiple sets of shape factors The corresponding glacier thickness values ​​are averaged to achieve the shape factor Dynamic correction of the shape factor; the present invention expresses the geometric shape of the glacier by introducing a shape factor calculated based on the cross-sectional width and central thickness of the glacier, thereby improving the adaptability of the laminar flow model to the cross-sectional shapes of different glaciers; by averaging the ice thickness results corresponding to multiple values, the uncertainty of the shape factor is dynamically corrected, thereby improving the accuracy and stability of the ice thickness inversion.

[0009] Step 4: Set the scale in the glacier interior unit Randomly select multiple sample units, build a buffer zone around each random sample unit, and determine whether the buffer zone meets the slope difference If the requirement of less than 50m is met, proceed to step 5; if not, continue to expand the buffer zone until the slope difference constraint condition is met;

[0010] Step 5: Calculate the average slope value for each buffer zone and calculate the ice thickness of the random sample unit corresponding to each buffer zone based on the laminar flow equation;

[0011] Step 6: Assign fixed or estimated boundary thickness values ​​to the glacier edge unit and adjacent units to ensure the rationality and continuity of boundary conditions;

[0012] Step 7: For the unselected internal glacier units, use the calculated sample unit thickness to complete the spatial thickness through the inverse distance weighted interpolation method to obtain the one-time glacier thickness distribution result. ;

[0013] Step 8: Repeat steps 4 to 7. times, record the glacier thickness distribution results generated each time, The results were averaged to obtain the final glacier thickness estimate.

[0014] The present invention combines the laminar flow model with gridded random cell interpolation technology. First, ice thickness is accurately inverted based on parameters such as flow velocity, slope and temperature at selected random cells. These points are then used for global interpolation, thereby improving the accuracy and rationality of the overall ice thickness estimation.

[0015] Furthermore, in step 2, the ice temperature at the glacier mass balance line is used as the representative temperature of the glacier, and the deviation between the annual average air temperature and the ice temperature of the glacier is assumed to be As a constant, the glacier surface air temperature is used Estimate the representative temperature of each glacier; then the flow rate factor The calculation formula is:

[0016]

[0017] in .

[0018] Furthermore, in step 3, the shape factor The calculation formula is:

[0019] .

[0020] Furthermore, in step 3, the central streamline thickness of the glacier Through the shear stress equation Please help.

[0021] Furthermore, in step 5, the laminar flow equation of glacier thickness is:

[0022]

[0023] In the above formula, is an empirically determined constant; is the basal flow velocity; is the glacier thickness, is the glacier density, is the acceleration due to gravity.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] (1) Rigorous theoretical basis and scientific parameter setting. This method is based on the laminar flow model derived from Glen's flow law, and its theoretical basis is mature and reliable. Unlike traditional methods that rely on manual experience to set parameters, the method of this invention dynamically calculates the flow rate factor and shape factor through physical quantities such as temperature and slope, achieving automated and physically driven setting of key parameters, enhancing the versatility and accuracy of the method.

[0026] (2) High computational efficiency and applicability to large areas. By dividing the glacier area into regular grids and adopting random cell selection and buffer zone construction, the proposed method can effectively reduce the amount of computation and avoid point-by-point modeling of the entire area. This significantly improves computational efficiency in large glacier areas, is highly adaptable, and is easy to promote.

[0027] (3) Avoid dependence on central streamlines and enhance spatial continuity. Traditional methods based on central streamlines are difficult to apply in complex terrain or areas with multiple flow directions. This paper estimates the ice thickness of unselected cells through a random cell interpolation method, avoiding the extraction and dependence on central streamlines and improving the spatial continuity and model robustness of ice thickness estimation.

[0028] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The accompanying drawings are used to provide a further understanding of the embodiments of the present invention and constitute a part of the specification. Together with the following detailed description, they are used to explain the embodiments of the present invention, but do not constitute a limitation of the embodiments of the present invention. In the accompanying drawings:

[0030] Figure 1 It is a schematic diagram of the research area model provided by the present invention;

[0031] Figure 2 Here is an idealized glacier cross section calculated using three different b values: Comparison of cross-sectional shapes obtained by inversion with different interpolation parameters;

[0032] Figure 3 It is the result of glacier flow velocity in the main peak area of ​​West Kunlun;

[0033] Figure 4 This is a glacier thickness map of the main peak area of ​​West Kunlun Mountains obtained by inversion using the method of the present invention. DETAILED DESCRIPTION

[0034] The present invention will be described in detail below with reference to the various embodiments shown in the accompanying drawings, but it should be noted that these embodiments are not limitations of the present invention, and any equivalent transformations or substitutions in functions, methods, or structures made by ordinary technicians in this field based on these embodiments are all within the scope of protection of the present invention.

[0035] This embodiment provides a glacier thickness inversion method that integrates a laminar flow model with random cell interpolation. Ice thickness is calculated based on the laminar flow equation derived from Glen's flow law, and thickness samples are generated using a random cell selection method. A spatial interpolation method is then used to estimate the entire glacier's thickness. This method uses the thickness of randomly selected glacier cells and the thickness of cells at the glacier's edge to interpolate the thickness across the entire glacier. The resulting ice thickness profile approximates the ideal shape. This glacier thickness inversion method specifically includes the following steps:

[0036] Step 1: Obtain glacier surface velocity in the study area through remote sensing , digital elevation model, glacier boundary vector, glacier surface slope and glacier area mask data, and generate a regular rasterized dataset.

[0037] Step 2: Use the glacier surface air temperature and the empirical temperature difference constant , estimate the representative ice temperature of the glacier, and dynamically calculate the flow rate factor by combining the empirical formula of the rate factor , and then obtain the flow rate factors of multiple different glacier regions ; that is, assigning spatially varying flow rate factors to different glacier regions , to reflect the difference in thermal state inside the glacier. In this step, the ice temperature at the glacier mass balance line is used as the representative temperature of the glacier, assuming that the empirical temperature difference between the annual average air temperature on the glacier surface and the ice temperature As a constant, the glacier surface air temperature is used Estimate the representative temperature of each glacier; the glacier surface air temperature data comes from the ERA5 reanalysis data, and the empirical temperature difference constant The setting method of is conventional in the art. The calculation formula is:

[0038]

[0039] Among them, when the empirical temperature difference constant When the temperature is 7℃ (this value is based on the statistical analysis of the difference between the borehole temperature of the active layer of glaciers in China and the surface air temperature), the mobility factor .

[0040] Step 3: Cross-section width across multiple different glacier regions Thickness of center streamline Multiple shape factors for valleys , and through multiple sets of shape factors Calculate the corresponding thickness values ​​and take the average value. The average thickness at the center streamline is recorded as , as the subsequent calculation shape factor Parameters, thereby achieving the shape factor Dynamic correction of the shape factor , calculated by the formula To calculate; the thickness value is obtained by selecting all shape factors within 0.6-1 with an interval of 0.01 The average thickness calculated from the value of . The central streamline thickness of the glacier Through the shear stress equation Please help.

[0041] Step 4: Set the scale in the glacier interior unit Randomly select multiple sample units and build a 3×3 buffer zone around each sample unit, and determine whether the buffer zone meets the slope difference If the requirement of less than 50m is met, proceed to step 5; if not, continue to expand the buffer zone until the slope difference limit is met.

[0042] Step 5: Calculate the average slope value for each buffer zone and calculate the ice thickness of the random cells based on the laminar flow equation for glacier thickness; the laminar flow equation for glacier thickness is:

[0043]

[0044] in, is an empirically determined constant; is the basal flow velocity; is the glacier thickness, is the glacier density, is the acceleration due to gravity.

[0045] Step 6: Assign fixed or estimated boundary thickness values ​​to the glacier edge cells and adjacent cells to ensure the rationality and continuity of the boundary conditions.

[0046] Step 7: For the unselected glacier internal units, use the calculated sample unit thickness to complete the spatial thickness through the inverse distance weighted interpolation method to obtain the one-time ice thickness distribution result ; Among them, the sample unit thickness includes the ice thickness of the random unit calculated in step 5 and the boundary thickness values ​​of the glacier edge unit and the adjacent unit in step 6.

[0047] Step 8: Repeat steps 4 to 7. times, record the ice thickness distribution results generated each time, The results are averaged to obtain the final ice thickness estimation result; According to the setting ratio in step 4 is determined by the value of .

[0048] The method of the present invention combines the laminar flow model with the random unit selection method, dynamically constructs a buffer zone and calculates the ice thickness of the sample unit under the condition that the slope difference is less than a preset threshold, taking into account the physical mechanism and computational efficiency of ice thickness inversion, thereby improving the reliability and spatial representativeness of the ice thickness estimation results.

[0049] Example 1

[0050] like Figure 1 As shown in the figure, the study area is divided into four categories: non-glacier units, glacier adjacent units, glacier edge units and glacier internal units; a certain proportion of glacier internal units are randomly selected A 3×3 buffer of cells is constructed around each randomly selected cell; the buffer size is allowed to grow until the slope difference between the lowest and highest cells in the buffer is Until it reaches 50m; the average slope of all cells in the buffer zone is used as the slope for calculating the thickness of the cell; the thickness of these random cells is calculated using the laminar flow equation. At the same time, thickness values ​​are assigned to the glacier adjacent cells and glacier edge cells; the thickness of the unselected glacier internal cells is interpolated using IDW to obtain the ice thickness distribution results within the glacier. Repeat the above steps times, get The ice thickness distribution results are The final ice thickness distribution result is obtained by averaging the ice thickness distribution results.

[0051] Figure 2 Here is an idealized glacier cross section calculated using three different b values: The cross-sectional shapes obtained by inversion with different interpolation parameters are compared to observe the correction ability of different parameter combinations on the cross-sectional shape; the glacier width range shown in the figure is 600m to 1500m. When the other inversion parameters are kept constant, the increase in width leads to an increase in the number of data points in the cross section, which increases the ratio of internal cells to edge cells, so the random cell ratio needs to be adjusted. The size of the two unit ratios is used to balance the two unit ratios. In this invention, the original cross section that has not been interpolated is called the 'uncorrected cross section', and the adjusted cross section is called the 'corrected cross section'. Often used to simulate the valley shape of a glacier. When the range is 1.5-2.5, the power law function curve is close to a parabola, which can represent the bottom of most glacial valley cross sections with nearly ideal shapes. The power law function describes the idealized cross-sectional morphology of the glacier. The changing data mainly include different surface flow velocities , different cross-sectional widths, and different random unit ratios .from Figure 2 It can be seen that the method of fusing the laminar flow model with random unit interpolation can generate a profile that is approximately in the ideal shape without relying on the generation of central streamlines and without fitting the cross-sectional shape of the vertical streamlines.

[0052] Figure 3 The results of glacier velocity in the main peak area of ​​West Kunlun are presented; Figure 4 The flow velocity results based on the main peak area of ​​West Kunlun are shown ( Figure 3 ), the glacier thickness result obtained by the inversion of the present invention. Figure 4 It can be seen that the method of the present invention can make full use of known glacier topography and flow velocity data to generate a more realistic glacier cross-section, to a certain extent correct the glacier thickness inverted by the laminar flow model itself, and improve the accuracy of glacier reserve estimation in large areas.

[0053] This invention addresses the problem that traditional glacier thickness estimation methods based on laminar flow models rely too heavily on the glacier's central streamline, which is difficult to accurately obtain in complex areas. By introducing a random unit interpolation method, this method eliminates this reliance on central streamlines while more fully utilizing glacier topography and flow velocity data. Furthermore, the model considers differences in glacier shape factors and, in combination with temperature information, assigns specific dynamic parameters to glaciers, avoiding artificial parameter determination. Experimental results demonstrate that this improved method can produce more realistic glacier thickness distributions.

[0054] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A glacier thickness inversion method that integrates a laminar flow model and random cell interpolation, characterized in that: The following steps are involved: Step 1: Obtain glacier surface velocity in the study area through remote sensing , digital elevation model, glacier boundary vector, glacier surface slope and glacier area mask data, and generate regular rasterized datasets; Step 2: Use the glacier surface air temperature and the empirical temperature difference constant First, estimate the representative ice temperature of the glacier, and then dynamically calculate the flow rate factors of multiple different glacier areas using the empirical formula of the rate factor. ; Step 3: Cross-section width across multiple different glacier regions Thickness of center streamline Estimate multiple sets of shape factors for valleys , and calculate the multiple sets of shape factors The corresponding glacier thickness values ​​were averaged; Step 4: Set the scale in the glacier interior unit Randomly select multiple sample units, build a buffer zone around each random sample unit, and determine whether the buffer zone meets the slope difference If the requirement of less than 50m is met, proceed to step 5; if not, continue to expand the buffer zone until the slope difference constraint condition is met; Step 5: Calculate the average slope value for each buffer zone and calculate the ice thickness of the random sample unit corresponding to each buffer zone based on the laminar flow equation; Step 6: Assign fixed or estimated boundary thickness values ​​to the glacier edge unit and adjacent units to ensure the rationality and continuity of boundary conditions; Step 7: For the unselected internal glacier units, use the calculated sample unit thickness to complete the spatial thickness through the inverse distance weighted interpolation method to obtain the one-time glacier thickness distribution result. ; Step 8: Repeat steps 4 to 7. times, record the glacier thickness distribution results generated each time, The results were averaged to obtain the final glacier thickness estimate.

2. The glacier thickness inversion method according to claim 1, characterized in that: In step 2, the ice temperature at the glacier mass balance line is used as the representative temperature of the glacier. It is assumed that the deviation between the annual average air temperature and the ice temperature of the glacier surface is As a constant, the glacier surface air temperature is used Estimate the representative temperature of each glacier; then the flow rate factor The calculation formula is: in .

3. The glacier thickness inversion method according to claim 1, characterized in that: In step 3, the shape factor The calculation formula is: 。 4. The glacier thickness inversion method according to claim 3, characterized in that: In step 3, the central streamline thickness of the glacier Through the shear stress equation Please solve.

5. The glacier thickness inversion method according to claim 1, characterized in that: In step 5, the laminar flow equation of glacier thickness is: In the above formula, is an empirically determined constant; is the basal flow velocity; is the glacier thickness, is the glacier density, is the acceleration due to gravity.

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