A monthly soil freezing depth mapping method considering spatiotemporal heterogeneity

Abstract

The application discloses a monthly soil freezing depth mapping method considering spatial and temporal heterogeneity, and belongs to the technical field of soil freezing depth. The monthly soil freezing depth mapping method comprises the following steps: collecting daily multi-layer soil temperature and air temperature of each station, and collecting various environmental factor data and monthly air temperature data of a target region; calculating monthly heat transfer factors of each station, and calculating monthly cumulative average value distribution of each environmental factor and monthly air freezing index distribution in the target region; determining the monthly heat transfer factor distribution of the target region through a regression model; and calculating the monthly soil freezing depth distribution based on the monthly heat transfer factor distribution and the monthly air freezing index distribution of the target region. The monthly soil freezing depth mapping method considering spatial and temporal heterogeneity can accurately reflect the spatial and temporal differences of soil freezing depth, and improves the reliability of the monthly soil freezing depth mapping method.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of soil freezing depth, and particularly relates to a monthly soil freezing depth mapping method considering spatial and temporal heterogeneity. BACKGROUND

[0002] Soil freezing depth refers to the vertical distance from the ground surface to the freezing front in the seasonally frozen layer (including the active layer above the seasonal and permafrost) of frozen soil. Soil freezing depth affects local climate, hydrological processes, vegetation dynamics, soil carbon cycle and infrastructure stability. Correspondingly, monthly soil freezing depth mapping has wide application value in the fields of geography, cryosphere science and climate change, which not only helps to understand the response of frozen soil to climate change, but also serves the ecological assessment and engineering planning of frozen soil.

[0003] However, the existing soil freezing depth mapping mainly faces the annual maximum value, ignores the monthly dynamics, and is difficult to accurately characterize the influence of environmental factors on soil freezing depth, so that the soil freezing depth mapping cannot accurately reflect the spatial and temporal differences of soil freezing depth, resulting in that the reliability of the final monthly soil freezing depth mapping method is greatly reduced. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the application provides a monthly soil freezing depth mapping method considering spatial and temporal heterogeneity, which aims to not only consider the time dynamics under the month, but also consider the spatial dynamics caused by the influence of environmental factors on heat transfer, so as to accurately reflect the spatial and temporal differences of soil freezing depth and improve the reliability of the monthly soil freezing depth mapping method.

[0005] To achieve the above purpose, the application provides a monthly soil freezing depth mapping method considering spatial and temporal heterogeneity, which comprises:

[0006] Determine a target area with coordinate data, the target area has a plurality of stations, collect daily multi-layer soil temperature and air temperature of each station, and collect a plurality of environmental factor data and monthly air temperature data corresponding to the target area;

[0007] Based on the multi-layer soil temperature and air temperature, the monthly soil freezing depth and the monthly air freezing index of each station are calculated, and the monthly heat transfer factor of each station is calculated through the monthly soil freezing depth and the monthly air freezing index; based on the plurality of environmental factor data corresponding to the target area, the monthly cumulative average value distribution of each environmental factor in the freezing period in the target area is calculated, and based on the monthly air temperature data corresponding to the target area, the monthly air freezing index distribution of the target area is calculated;

[0008] The monthly cumulative average values of the environmental factors at each of the stations are extracted from the monthly cumulative average value distribution, and the monthly heat transfer factor distribution is determined in combination with the monthly heat transfer factors of each of the stations, so as to calculate the monthly heat transfer factor distribution of the target region;

[0009] Based on the monthly heat transfer factor distribution of the target region and the monthly air freezing index distribution of the target region, the monthly soil freezing depth distribution is calculated, so as to obtain the monthly soil freezing depth map of the target region.

[0010] Optionally, the monthly soil freezing depth of each of the stations is calculated by the following formula:

[0011] ;

[0012] ;

[0013] Wherein, F is the soil freezing depth of the corresponding month of the station; F i is the daily soil freezing depth of the corresponding month of the station; i is the soil temperature at the depth of i days in the corresponding month; m is the total number of days in the corresponding month, T F is the freezing temperature; D + is the soil depth closest to the upper layer and having a temperature higher than the freezing temperature, T + is the soil temperature at the depth of D + ; D_ is the soil depth further above and having a temperature lower than the freezing temperature, T − is the soil temperature at the depth of D_

[0014] Optionally, from the calculation of the monthly soil freezing depth of each of the stations, the month in which the number of days of the soil freezing depth of the corresponding month is greater than or equal to 15 days is selected as the required soil freezing depth of the corresponding month of the station.

[0015] Optionally, from the calculation of the monthly soil freezing depth of each of the stations in the freezing period, at least three months in which the soil freezing depth is greater than the soil freezing depth of the previous month are selected as the required soil freezing depth of the corresponding month of the station.

[0016] Optionally, the monthly air freezing index of each of the stations is calculated by the following formula: ​

[0017] ;

[0018] wherein, I is the air freeze index of the corresponding month of the site; T i is the daily air temperature, T i T F ; T F is the freezing temperature; N 1 is the number of days from the first month of the freezing period to the corresponding month that satisfy T i T F .

[0019] Optionally, the monthly heat transfer factor of each of the sites is calculated by the soil freezing depth of each month and the air freeze index of each month, and is obtained by the following formula:

[0020] ;

[0021] wherein, E is the monthly heat transfer factor of the site, F is the soil freezing depth of the corresponding month of the site, I is the air freeze index of the corresponding month of the site.

[0022] Optionally, the monthly cumulative average value distribution of each environmental factor in the target area during the freezing period is calculated by the following formula:

[0023] ;

[0024] wherein, is the monthly cumulative average value distribution of each environmental factor in the target area during the freezing period, M is the number of months from the first month of the freezing period to each month; X i,x,y is the environmental factor value corresponding to the i month from the first month of the freezing period; x, y ) is the coordinate in the target area.

[0025] Optionally, the monthly air freeze index distribution of the target area is calculated by the following formula:

[0026] ;

[0027] wherein, I x,y is the monthly air freeze index distribution of the target area;​​T i,x,y is the average temperature of the target area in the first month of the freeze period; i N 2 is the number of months from the first month of the freeze period to the corresponding month in the period; T i,x,y T F is the number of months from the first month of the freeze period to the corresponding month in the period, T F is the freezing temperature; n i is the number of days in the first month of the freeze period; i x, y is the coordinate in the target area.

[0028] Optionally, the environmental factor is snow depth, precipitation, average vegetation leaf area index in the growing season, soil water content, soil organic carbon content, soil bulk density, soil saturated water content, soil sand content, soil silt content, soil clay content, slope or aspect.

[0029] Optionally, the monthly heat transfer factor distribution in the target area is calculated by the following formula:

[0030]

[0031] wherein, E x,y is the monthly heat transfer factor distribution of the target area, f( ) is a regression model of the monthly heat transfer factor distribution with respect to the monthly cumulative average value distribution of the various environmental factors in the freeze period, is the monthly cumulative average value distribution of the corresponding environmental factor; ( x, y n is the category corresponding to the environmental factor.

[0032] The above technical features can be combined with each other as long as they do not conflict with each other.

[0033] Overall, the above technical solutions conceived by the present application have the following beneficial effects compared with the prior art:

[0034] ​​​​​For the monthly soil freezing depth mapping method considering spatial and temporal heterogeneity provided by the embodiment of the application, to obtain the monthly soil freezing depth distribution map, first, the target area with coordinate data is determined, the target area has a plurality of stations, the daily multi-layer soil temperature and air temperature of each station are collected, and a plurality of environmental factor data and monthly air temperature data corresponding to the target area are collected, so that the above data are used as sample data of the method, and the sample data not only combines daily data and monthly data, but also determines the monthly dynamics of the station and the target area data; meanwhile, a plurality of environmental factors in the target area are combined, so that the spatial dynamics caused by the influence of the environmental factors on heat transfer can be determined; and then the spatial and temporal differences of the soil freezing depth can be accurately reflected, and the reliability of the subsequent monthly soil freezing depth mapping method is improved.

[0035] Then, on the one hand, based on the multi-layer soil temperature and air temperature, the monthly soil freezing depth and the monthly air freezing index of each station are calculated, and the monthly heat transfer factor of each station is calculated through the monthly soil freezing depth and the monthly air freezing index. On the other hand, based on the plurality of environmental factor data corresponding to the target area, the monthly cumulative average value distribution of each environmental factor in the target area during the freezing period is calculated, and based on the monthly air temperature data corresponding to the target area, the monthly air freezing index distribution of the target area is calculated. On this basis, the monthly cumulative average value of each environmental factor at each station is extracted in the monthly cumulative average value distribution, and the monthly heat transfer factor distribution is determined in combination with the monthly heat transfer factor of each station, and a regression model of the monthly heat transfer factor distribution with respect to the monthly cumulative average value distribution of the plurality of environmental factors is determined, which can be used to calculate the monthly heat transfer factor distribution through the monthly cumulative average value distribution of the plurality of environmental factors in the target area.

[0036] Finally, based on the monthly heat transfer factor distribution of the target area and the monthly air freezing index distribution of the target area, the monthly soil freezing depth distribution is calculated, so that the monthly soil freezing depth mapping of the target area is obtained.

[0037] That is, the monthly soil freezing depth mapping method considering spatial and temporal heterogeneity provided by the embodiment of the application not only considers the time dynamics under the month, but also considers the spatial dynamics caused by the influence of the environmental factors on heat transfer, can accurately reflect the spatial and temporal differences of the soil freezing depth, and improves the reliability of the monthly soil freezing depth mapping method. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is a flowchart of the monthly soil freezing depth mapping method considering spatial and temporal heterogeneity provided by the embodiment of the application;

[0039] Figure 2 is a principle flowchart of the monthly soil freezing depth mapping method considering spatial and temporal heterogeneity provided by the embodiment of the application. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0041] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0042] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0043] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0044] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0045] Example:

[0046] Figure 1 This is a flowchart of a monthly soil freezing depth mapping method considering spatiotemporal heterogeneity provided by an embodiment of the present invention. Figure 2 This is a flowchart illustrating the principle of a monthly soil freezing depth mapping method considering spatiotemporal heterogeneity, provided by an embodiment of the present invention. Figure 1 and Figure 2 As shown, the method for mapping the monthly soil freezing depth includes:

[0047] S1. Determine the target area with coordinate data. The target area contains multiple stations. Collect daily multi-layer soil temperature and air temperature data for each station, and collect various environmental factor data and monthly air temperature data corresponding to the target area.

[0048] Each type of environmental factor data corresponds to one environmental factor.

[0049] S2. Based on multi-layer soil temperature and air temperature, the monthly soil freezing depth at each station was calculated. F ) and monthly air freezing index ( I The monthly heat transfer factor for each station was calculated using the monthly soil freezing depth and the monthly air freezing index. E Based on data from various environmental factors in the target area, the monthly cumulative average distribution of each environmental factor in the target area during the freezing period was calculated. Based on the monthly temperature data of the target area, the monthly air freezing index distribution of the target area is calculated. I x,y );

[0050] S3. Extract the monthly cumulative average of each environmental factor at each station from the monthly cumulative average distribution. Combine this with the monthly heat transfer factor at each station to determine the regression model of the monthly heat transfer factor distribution with respect to the monthly cumulative average distribution of multiple environmental factors during the freezing period. This allows for the calculation of the monthly heat transfer factor distribution in the target area. E x,y ).

[0051] S4, calculate the monthly soil freezing depth distribution of the target area based on the monthly heat transfer factor distribution of the target area and the monthly air freezing index distribution of the target area F x,y , so as to obtain the monthly soil freezing depth map of the target area.

[0052] For the monthly soil freezing depth mapping method considering spatial and temporal heterogeneity provided by the embodiment of the application, to obtain the monthly soil freezing depth distribution map, first, a target area with coordinate data is determined, the target area has a plurality of stations, daily multi-layer soil temperature and air temperature of each station are collected, and a plurality of environmental factor data and monthly air temperature data corresponding to the target area are collected, so that the above data are used as sample data of the method, and the sample data not only combines daily data and monthly data, but also determines the monthly dynamics of the station and the target area data; at the same time, a plurality of environmental factors in the target area are combined, so that the spatial dynamics caused by the environmental factors affecting heat transfer can be determined; and then the spatial and temporal differences of the soil freezing depth can be accurately reflected, and the reliability of the subsequent monthly soil freezing depth mapping method is improved.

[0053] Then, on the one hand, based on the multi-layer soil temperature and the air temperature, the monthly soil freezing depth and the monthly air freezing index of each station are calculated, and the monthly heat transfer factor of each station is calculated through the monthly soil freezing depth and the monthly air freezing index. On the other hand, based on the plurality of environmental factor data corresponding to the target area, the monthly cumulative average value distribution of each environmental factor in the target area during the freezing period is calculated, and based on the monthly air temperature data corresponding to the target area, the monthly air freezing index distribution of the target area is calculated. On this basis, the monthly cumulative average value of each environmental factor at each station is extracted in the monthly cumulative average value distribution, and the monthly heat transfer factor distribution is determined in combination with the monthly heat transfer factor of each station, and a regression model of the monthly heat transfer factor distribution about the monthly cumulative average value distribution of the plurality of environmental factors is determined, which can be used to calculate the monthly heat transfer factor distribution of the target area through the monthly cumulative average value distribution of the plurality of environmental factors.

[0054] Finally, the monthly soil freezing depth distribution is calculated based on the monthly heat transfer factor distribution of the target area and the monthly air freezing index distribution of the target area, so as to obtain the monthly soil freezing depth map of the target area.

[0055] That is, the monthly soil freezing depth mapping method considering spatial and temporal heterogeneity provided by the embodiment of the application not only considers the time dynamics under the month, but also considers the spatial dynamics caused by the environmental factors affecting heat transfer, can accurately reflect the spatial and temporal differences of the soil freezing depth, and improves the reliability of the monthly soil freezing depth mapping method.

[0056] In addition, the method considers the change of the heat transfer factor with time and space, predicts the monthly heat transfer factor distribution through a regression model, realizes the monthly soil freezing depth mapping with precise characterization of spatial and temporal heterogeneity, and facilitates the depiction of the spatial and temporal dynamics of the monthly soil freezing depth distribution on a large scale and over a long time series. The method has simple principles, is easy to implement, has strong adaptability, high automation, and wide applicability.

[0057] It should be noted that in the present embodiment, for the target region, the required environmental factor data and monthly air temperature data can be obtained from remote sensing or reanalysis data, which will not be described here. The daily multi-layer soil temperature and air temperature of each site can be obtained directly from the database of each site. In addition, in the present method, the data calculation period is usually a hydrological year, i.e. from July to June of the previous year, which covers a complete freezing period. In the present embodiment, the cold season months (defined as October to May, i.e. a freezing period) of the hydrological year (2004-2023) in the pan-Arctic region (target region) north of 60°N are taken as an example to illustrate the present method, covering 60 sites.

[0058] Illustratively, the environmental factors are snow depth, precipitation, average vegetation leaf area index in the growing season, soil water content, soil organic carbon content, soil bulk density, soil saturated water content, soil sand content, soil silt content, soil clay content, slope or aspect.

[0059] It should be noted that in other embodiments of the present application, the environmental factors corresponding to different target regions are different, and therefore the environmental factors can also be of other types or in combination, which are not limited by the present application.

[0060] In the present embodiment, for step S2, the monthly soil freezing depth of each site is calculated, which is obtained by the following formula:

[0061] ; (1)

[0062] ; (2)

[0063] wherein, F is the soil freezing depth of the site in the corresponding month; F i is the daily soil freezing depth of the site; i is the i day in the corresponding month, m is the total number of days in the corresponding month, T F is the freezing temperature (usually 0℃); D + is the soil depth closest to the upper layer and having a temperature higher than the freezing temperature, T + is the D+ the soil temperature at the depth; D_ the soil depth at which the temperature is lower than the freezing temperature, T − the soil temperature at the depth; D_ the soil temperature at the depth.

[0064] It should be noted that the above formula (1) can be understood as determining the adjacent two layers in the multi-layer soil temperature, the temperature of the upper layer (the depth is known) is negative, the temperature of the lower layer (the depth is known) is positive, and the depth corresponding to the freezing temperature is calculated by the above interpolation, which is the corresponding daily soil freezing depth. In addition, for the daily multi-layer soil temperature that cannot be obtained D + and D_ , the daily multi-layer soil temperature is discarded at this time, and the corresponding daily soil freezing depth is empty.

[0065] Further, after step S2, it further includes: a, selecting the months in which the number of days corresponding to the soil freezing depth of each month is greater than or equal to 15 from the calculated soil freezing depths of each month of each site, as the required soil freezing depth of the corresponding month of the site.

[0066] That is, the number of daily soil freezing depths of a month is greater than 15, at this time, the data is more complete and reliable, the corresponding soil freezing depth of the month is regarded as the required effective value and should be retained. On the contrary, it is invalid (i.e. the number of soil freezing days of the month is less, or the data error is large), and should be discarded.

[0067] Further, after step S2, it further includes: b, selecting at least three months in which the soil freezing depth is greater than the soil freezing depth of the previous month from the calculated soil freezing depths of each month of each site in the freezing period, as the required soil freezing depth of the corresponding month of the site.

[0068] It is easy to understand that the step b processing is more in line with the rule that the soil freezing gradually deepens, so that the soil freezing depths of these months (together with the first month) can be selected for the subsequent steps, and the reliability is higher.

[0069] Exemplarily, when the corresponding soil freezing depths of each month are 10, 20, 30, 20, 40, 50, after the step b processing, 10, 20, 30, 40, and 50 months are selected, and the remaining months are discarded; when the corresponding soil freezing depths of each month are 10, 9, 15, 12, 20, 16, after the step b processing, 10, 15, and 20 are selected, and the remaining months are discarded; when the corresponding soil freezing depths of each month are 10, 30, 10, 15, 20, 25, after the step b processing, all are discarded.

[0070] It should be noted that step a and step b can be used simultaneously, or only one of them can be used. In addition, in step b, the larger the value of the selected multiple months, the more stringent the quality control.

[0071] In addition, the air freezing index of each site in each month is calculated, and the following formula is obtained:

[0072] ; (3)

[0073] Among them, I is the air freezing index of the site corresponding to the month; T i is the daily air temperature, T i T F ; T F is the freezing temperature; N 1 is the number of days from the first month of the freezing period to the corresponding month period that meets T i T F

[0074] Therefore, the monthly heat transfer factor of each site is calculated by the monthly soil freezing depth F and the monthly air freezing index I , and the following formula is obtained:

[0075] ; (4)

[0076] Among them, E is the monthly heat transfer factor of the site, F is the soil freezing depth of the site corresponding to the month, I is the air freezing index of the site corresponding to the month.

[0077] It should be noted that formula (4) is obtained by corresponding simplification of Stefan equation, which can show the relationship between soil freezing depth F , air freezing index I and monthly heat transfer factor E .

[0078] In step S2, the monthly cumulative average value distribution of each environmental factor in the target area during the freezing period is calculated, and the following formula is obtained:

[0079] ; (5)

[0080] Among them, is the monthly cumulative average value distribution of each environmental factor in the target area during the freezing period, M ​​​This refers to the number of months from the first month of the freeze period to the next month. X i,x,y From the first month of the freeze period i The environmental factor value corresponding to the month ( X 1 、X 2 、X The three levels represent different types of environmental factors. x, y () represents the coordinates within the target area.

[0081] In the above implementation, formula (5) can be used to calculate the average value after monthly accumulation, thereby determining the corresponding time period of environmental factors and the monthly heat transfer factor in the simplified Stefan equation. E The corresponding time period is consistent and can be used as the independent variable in the subsequent heat transfer factor distribution regression model.

[0082] In this embodiment, the monthly air freezing index distribution of the target area is calculated using the following formula:

[0083] (6)

[0084] in, I x,y The monthly air freezing factor distribution for the target area; T i,x,y For the first i The average temperature over the past month; N 2. To meet the requirements from the first month of the freeze period to the corresponding month. T i,x,y < T F number of months, T F This is the freezing temperature; n i For the first i The number of days in a month; x, y () represents the coordinates within the target area.

[0085] It is easy to understand that, I The air freezing index for the corresponding month at the site. I x,y The monthly air freezing index distribution for the target area corresponds to the entire target area, which facilitates the subsequent calculation of the monthly soil freezing depth at various locations within the entire target area.

[0086] In step S3, the monthly heat transfer factor distribution in the target area is calculated using the following formula:

[0087] (7)

[0088] in, Ex,y a monthly heat transfer factor distribution of the target region, f( ) a regression model of the monthly heat transfer factor distribution with respect to the monthly cumulative average value distribution of the plurality of environmental factors in the freezing period, a monthly cumulative average value distribution corresponding to the environmental factors; x, y a coordinate within the target region; n a category corresponding to the environmental factors.

[0089] In the above embodiment, based on the monthly heat transfer factor and the monthly cumulative average value of the plurality of environmental factors on each site, a function relationship of the monthly heat transfer factor distribution with respect to the monthly cumulative average value distribution of the plurality of environmental factors in the entire target region is fitted by a regression model.

[0090] Exemplarily, the regression model can be a random forest regression model, and the regression model can also be selected in other forms, which is not limited in the present application.

[0091] In addition, step S3 can specifically include: first selecting key environmental factors by feature recursive elimination. In feature recursive elimination, the number of candidate features is set to half (rounded down) of the input features, and 1 feature is removed each iteration, which is the feature with the lowest feature importance. Thus, the key environmental factors for constructing the random forest regression model of the monthly heat transfer factor distribution with respect to the monthly cumulative average value distribution of the plurality of environmental factors in this case are: precipitation, soil moisture content, average vegetation leaf area index in growing season, soil bulk density, soil clay content, and soil organic carbon content. The monthly cumulative average value distribution of the key environmental factors is unified in spatial resolution in the form of mean aggregation, which is 0.1° in this case, and is input into the random forest regression model of the monthly heat transfer factor distribution with respect to the monthly cumulative average value distribution of the plurality of environmental factors, to obtain the heat transfer factor distribution of the cold season (defined as October-May) in the Pan-Arctic region during the hydrological years 2004-2023.

[0092] For step S4, based on the heat transfer factor distribution of the target region and the monthly air freezing index distribution of the target region, the monthly soil freezing depth distribution is calculated, specifically:

[0093] (8)

[0094] wherein, F x,y a monthly soil freezing depth distribution of the target region, E x,y a heat transfer factor distribution of the target region; I x,y a monthly air freezing index distribution of the target region, which is also obtained by using the corresponding simplified Stefan equation.

[0095] Specifically, the monthly heat transfer factor of each position in the target area can be calculated by formula (5) and formula (7), the monthly air freezing index of each position in the target area can be calculated by formula (6), and the monthly soil freezing depth of each position in the target area can be finally determined by substituting the monthly heat transfer factor and the monthly air freezing index of each position into formula (8), so as to obtain the monthly soil freezing depth mapping of the target area (i.e., the distribution of soil freezing depth in each month of the cold season in the pan-Arctic region during the hydrological year 2004-2023).

[0096] The monthly soil freezing depth mapping method has the following characteristics:

[0097] (1) Simple principle and easy to implement. The soil freezing depth mapping method is based on the simplified Stefan equation, and the spatial and temporal heterogeneity of soil freezing depth can be accurately characterized by optimizing the calculation of the heat transfer factor distribution. The method only needs multi-layer soil temperature and air temperature observations, and the required environmental factor data and monthly air temperature data of the target area can be obtained from remote sensing or reanalysis data.

[0098] (2) Strong adaptability, suitable for monthly soil freezing depth mapping in different regions.

[0099] (3) High degree of automation. A regression model of monthly heat transfer factor is constructed based on the station observations in the target area, which can automatically calculate the distribution of monthly heat transfer factor in the target area, and then automatically realize the monthly soil freezing depth mapping combined with the monthly air freezing index.

[0100] (4) Wide application range, which can be widely applied in the fields of geography, cryosphere science, climate change, etc.

[0101] Those skilled in the art will readily understand that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. 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 for mapping monthly soil freezing depth considering spatiotemporal heterogeneity, characterized in that, The method for mapping monthly soil freezing depth includes: A target area with coordinate data is identified, which contains multiple stations. Daily multi-layer soil temperature and air temperature data are collected for each station, and various environmental factor data and monthly air temperature data corresponding to the target area are also collected. Based on multi-layer soil temperature and air temperature, the monthly soil freezing depth and monthly air freezing index of each station are calculated, and the monthly heat transfer factor of each station is calculated using the monthly soil freezing depth and monthly air freezing index. Based on the data of multiple environmental factors corresponding to the target area, the monthly cumulative average distribution of each environmental factor in the target area during the freezing period is calculated, and the monthly air freezing index distribution of the target area is calculated based on the monthly air temperature data corresponding to the target area. The monthly cumulative average value of each environmental factor at each of the aforementioned sites is extracted from the monthly cumulative average value distribution. Combined with the monthly heat transfer factor of each of the aforementioned sites, a regression model is determined on the monthly cumulative average value distribution of multiple environmental factors during the freezing period, thereby calculating the monthly heat transfer factor distribution in the target area. Based on the monthly heat transfer factor distribution and the monthly air freezing index distribution of the target area, the monthly soil freezing depth distribution is calculated, thereby obtaining a monthly soil freezing depth map of the target area.

2. The method for mapping monthly soil freezing depth considering spatiotemporal heterogeneity according to claim 1, characterized in that, The monthly soil freezing depth at each of the aforementioned sites is calculated using the following formula: ； ； in, F The soil freezing depth for the corresponding month at the site; F i The daily soil freezing depth corresponding to the site; i For the corresponding month's first i sky, m This represents the total number of days in the corresponding month. T F This is the freezing temperature; D + This refers to the soil depth closest to the upper layer and where the temperature is above the freezing point. T + for D + Soil temperature at the location; D_ represents the depth of the uppermost soil layer where the temperature is below the freezing point. T − D Soil temperature at _.

3. The method for mapping monthly soil freezing depth considering spatiotemporal heterogeneity according to claim 2, characterized in that, From the calculated monthly soil freezing depths of each of the aforementioned sites, select the months in which the number of days with soil freezing depth is ≥15 days, and use these months as the required monthly soil freezing depths for the respective sites.

4. The method for mapping monthly soil freezing depth considering spatiotemporal heterogeneity according to claim 2, characterized in that, From the calculated soil freezing depths for each site during the freezing period, select at least three months in which the soil freezing depth is greater than that of the previous months, and use these as the required soil freezing depths for the corresponding months of the site.

5. The method for mapping monthly soil freezing depth considering spatiotemporal heterogeneity according to claim 2, characterized in that, The monthly air freezing index for each of the aforementioned stations is calculated using the following formula: ； in, I The air freezing index for the corresponding month at the site; T i For daily temperature, T i < T F ; T F This is the freezing temperature; N 1. To meet the requirements from the first month of the freeze period to the corresponding month. T i < T F The number of days.

6. The method for mapping monthly soil freezing depth considering spatiotemporal heterogeneity according to claim 5, characterized in that, The monthly heat transfer factor for each station is calculated using the monthly soil freezing depth and the monthly air freezing index, and is obtained through the following formula: ； in, E The monthly heat transfer factor of the site. F The soil freezing depth for the corresponding month at the site. I The air freezing index for the corresponding month at the site.

7. The method for mapping monthly soil freezing depth considering spatiotemporal heterogeneity according to claim 1, characterized in that, The monthly cumulative average distribution of various environmental factors within the target area during the freezing period is calculated using the following formula: ； in, This represents the monthly cumulative average distribution of various environmental factors within the target area during the freezing period. M This refers to the number of months from the first month of the freeze period to the next month. X i,x,y From the first month of the freeze period i The corresponding environmental factor values ​​for the month; x,y () represents the coordinates within the target area.

8. The method for mapping monthly soil freezing depth considering spatiotemporal heterogeneity according to claim 1, characterized in that, The monthly air freezing index distribution of the target area is calculated using the following formula: ； in, I x,y The monthly air freezing factor distribution for the target area; T i,x,y For the first i The average temperature over the past month; N 2. To meet the requirements from the first month of the freeze period to the corresponding month. T i,x,y < T F the number of months, T F This is the freezing temperature; n i For the first i The number of days in a month; x, y () represents the coordinates within the target area.

9. The method for mapping monthly soil freezing depth considering spatiotemporal heterogeneity according to claim 1, characterized in that, The environmental factors mentioned are snow cover thickness, precipitation, average leaf area index of vegetation during the growing season, soil moisture content, soil organic carbon content, soil bulk density, soil saturated moisture content, soil sand content, soil silt content, soil clay content, and slope or aspect.

10. A method for mapping monthly soil freezing depth considering spatiotemporal heterogeneity according to any one of claims 1-9, characterized in that, The monthly heat transfer factor distribution in the target area is calculated using the following formula: ； in, E x,y The monthly heat transfer factor distribution of the target region. f( ) This is a regression model for the monthly distribution of heat transfer factors with respect to the monthly cumulative average distribution of various environmental factors during the freezing period. This represents the monthly cumulative average distribution of the corresponding environmental factors; x,y () represents the coordinates within the target area; n These are the categories corresponding to environmental factors.

Images