A geomorphic stage division and DEM construction method based on air time index

Abstract

The application discloses a geomorphologic stage division and DEM construction method based on space-time indexes, relates to the technical field of surveying and mapping, remote sensing and geographic information processing, and comprises the following steps: firstly, high-resolution DEM is spatially cropped, independent watershed samples are extracted, and topographic elements such as valley lines, ridge lines, gully lines and watershed boundary lines are extracted from the samples, which are spliced with the DEM to construct image pairs; secondly, four types of space-time indexes, including area-elevation integration, main gully branch gully ratio, gully density and surface roughness, are calculated for each sample, weights are assigned to the indexes in combination with expert knowledge, and the samples are divided into the juvenile stage, the mature stage and the old stage according to the weighted results to obtain a space-time dataset; finally, a CGAN network is trained in stages to generate high-resolution DEMs in different development stages; through scientific geomorphologic stage division, the expression ability of the model to terrain details is improved, and the adaptability and interpretability to different geomorphic evolution stages are also enhanced.

Description

Technical Field

[0001] This invention relates to the fields of surveying and mapping remote sensing and geographic information processing technology, and in particular to a method for geomorphic stage division and DEM construction based on spatial time indicators. Background Technology

[0002] Digital Elevation Models (DEMs) are core geographic information products that characterize the spatial structure of the Earth's surface. They are widely used in various geoscience research and engineering practice fields, such as watershed geomorphological analysis, soil erosion simulation, topographic mapping, and disaster risk assessment. Although high-resolution DEMs can accurately depict micro-topographic features, they often face problems of missing data or insufficient accuracy in practical applications due to high data acquisition costs and limited coverage of complex terrain areas.

[0003] In recent years, the application of deep learning technology in remote sensing image processing has developed rapidly. In particular, CGAN (Conditional Generative Adversarial Network), represented by Pix2Pix, has demonstrated good nonlinear modeling capabilities in image-to-image translation tasks, providing an effective path for generating corresponding DEMs from topographic feature maps. This type of method improves the spatial resolution and structural reconstruction capability of DEMs to a certain extent by learning the mapping relationship between topographic features and elevation. However, existing methods often use uniform datasets to train models, failing to consider the stage-specific differences in landform development, resulting in insufficient representation of topographic structures at different evolutionary stages.

[0004] On the other hand, Space-for-Time Substitution, as an important conceptual framework in geomorphological evolution research, emphasizes inferring the evolutionary trend of geomorphic systems by substituting time series observations of different watershed forms in space. By constructing quantifiable geomorphic index systems, such as elevation integral index, gully density, and surface roughness, the evolutionary stages of watersheds can be characterized and classified, providing a theoretical basis for cognitive modeling of geomorphic structural differences. Although these indicators have been widely used in geomorphic classification and evolution research, they still lack systematic integration and methodological support in deep learning-driven DEM construction. Summary of the Invention

[0005] To address the above technical problems, this invention provides a method for geomorphic stage division and DEM construction based on spatial temporal indices, comprising the following steps:

[0006] S1. Obtain the digital elevation model (DEM) data of the study area with a resolution of 5m and below, preprocess and manually crop it to extract batches of independent small watershed units; embed each small watershed unit into a standardized 256×256 pixel image to construct batches of DEM samples with uniform format.

[0007] S2. Based on hydrological analysis methods and automatic segmentation of positive and negative loess terrain, four types of terrain features are extracted from each DEM sample: gully line, ridge line, valley line, and watershed boundary line.

[0008] S3. Encode the gully line, ridge line, and valley line into the red, green, and blue channels of the RGB image respectively. The watershed boundary line is represented by grayscale overlay. This completes the fusion encoding of the four types of terrain elements and yields a terrain element map.

[0009] S4. Stitch the topographic feature map of each sample with the corresponding DEM sample in the horizontal direction to generate image pairs of 512×256 pixels, and obtain the topographic sample dataset.

[0010] S5. Based on the spatial-temporal theory of geomorphology, calculate four spatial-temporal indices for each image in the topographic sample dataset: area-elevation integral, main-to-branch ratio, gully density, and surface roughness.

[0011] S6. Standardize the four spatial time indicators, then assign weights to each indicator based on expert knowledge, perform weighted comprehensive scoring on all samples, and divide the terrain sample dataset into three different geomorphic development stage categories based on the scoring results: juvenile stage, mature stage and old age stage. Finally, the spatial time dataset is obtained, which includes the juvenile stage dataset, the mature stage dataset and the old age stage dataset.

[0012] S7. Using the juvenile stage dataset, the adult stage dataset, and the old age stage dataset respectively, train the conditional generative adversarial network Pix2Pix in stages to obtain three terrain generation models with the ability to perceive the features of the juvenile stage, the adult stage, and the old age stage respectively.

[0013] S8. Input each validation set into the terrain generation model trained in the corresponding stage to generate DEMs with a resolution of 5m or less, and verify the accuracy based on quantitative and qualitative indicators to evaluate the reconstruction performance of the three terrain generation models in the spatial time dataset.

[0014] The technical solution further defined in this invention is:

[0015] Furthermore, in step S1, manual cropping is based on DEMs with a resolution of 5m or less. Hydrological analysis methods are used to extract the river network and the initial watershed boundaries. Combined with manual review, watershed units with complete outlines and independent structures are selected, and the corresponding DEM regions are cropped through masking operations.

[0016] As described above, in the geomorphic stage division and DEM construction method based on spatial time index, step S2, extracting four topographic features from each DEM sample, specifically includes the following sub-steps:

[0017] S2.1 Based on the constructed batch DEM samples, hydrological analysis methods are used to calculate depression filling, flow direction and flow rate, and ridge lines are extracted by combining confluence thresholds;

[0018] S2.2 Construct a negative terrain model by elevation reversal and extract valley lines using hydrological analysis methods;

[0019] S2.3 Based on the automatic segmentation method of positive and negative loess terrain, construct a difference elevation map, extract local positive and negative terrain boundaries, and obtain the gully line;

[0020] S2.4. Combining slope and water system distribution, delineate closed watershed watersheds and extract watershed boundary lines.

[0021] As described above, in the geomorphic stage division and DEM construction method based on spatial-temporal indicators, step S5 involves using area-elevation integrals to reveal important indicators of valley landform morphology and development characteristics through statistical analysis of elevation combinations on the watershed surface. The specific calculation method for area-elevation integrals is as follows:

[0022] First, the normalized elevation values ​​are divided into n equal-width intervals:

[0023]

[0024] Then, count the number of pixels (a) in each elevation interval that are higher than the current segmented normalized elevation value. i And calculate the normalized area:

[0025]

[0026] Finally, the trapezoidal rule is used to approximate integration to calculate HI:

[0027]

[0028] Among them, H i z represents the normalized elevation value. i A(h) represents the original elevation value of the i-th elevation segment. i ) represents the normalized area higher than the current piecewise normalized elevation value, a j This indicates an elevation greater than h.i The number of pixels, A represents the total effective area, n represents the number of segments, and z min and z max Let h represent the minimum and maximum elevation values ​​in the DEM, respectively, where HI represents the area-elevation integral, and h represents the area-elevation integral. i and h i+1 These represent the normalized elevation values ​​of the i-th segment and the (i+1)-th segment, respectively.

[0029] As described above, in the geomorphic stage division and DEM construction method based on spatial time index, in step S5, the main gully-tributary ratio is defined as the ratio of the length of the main gully to the total length of the gullies within the watershed. This ratio reflects the development degree of tributaries in the gully system from the perspective of gully length. Its mathematical expression is:

[0030]

[0031] Where R represents the ratio of main gully to tributary gully, L0 represents the length of the main gully, and L represents the total length of the gully.

[0032] As described above, in the geomorphic stage division and DEM construction method based on spatial time index, in step S5, the gully density is defined as the total length of gullies per unit area, in km / km. 2 Its mathematical expression is:

[0033]

[0034] Among them, D s ∑L represents the gully density; ∑L represents the total length of gullies within the study area, in km; S represents the area of ​​a specific sample area, in km². 2 .

[0035] As described above, in a geomorphic stage division and DEM construction method based on spatial time index, in step S5, surface roughness is defined as the ratio of the surface area of ​​a surface element to its projected area on a horizontal plane, used to characterize the degree of surface erosion and undulation. Its mathematical formula is expressed as:

[0036]

[0037] Among them, S 曲面 S represents the surface area of ​​a cell. 平面 This represents the projected area of ​​a surface element onto a horizontal plane.

[0038] As described above, in the geomorphic stage division and DEM construction method based on spatial temporal indices, step S6 uses the Z-score standardization method to standardize the four spatial temporal indices. This method transforms the eigenvalues ​​into a distribution with a mean of 0 and a standard deviation of 1. Its mathematical expression is:

[0039]

[0040] Where x′ represents the standardized value of each spatial time index, x represents the original index value of each spatial time index, μ represents the average value of each spatial time index, and σ represents the average difference of each spatial time index.

[0041] As described above, in a method for geomorphic stage division and DEM construction based on spatial time indicators, in step S6, expert knowledge is used to reflect geomorphic development indicators, which include the size of the effective pixel area in each sample, the length of the main valley, geomorphological spatial time theory, and the Strahler classification method.

[0042] As described above, in the method for geomorphic stage division and DEM construction based on spatial time index, in step S7, the conditional generative adversarial network Pix2Pix includes a generator and a discriminator; the generator adopts a U-Net structure, which consists of an encoder and a decoder. The encoder is used to extract features of the image, and the decoder is used to generate the output image; the discriminator adopts a PatchGAN structure to perform local comparison and discrimination between the generated result and the real image.

[0043] The beneficial effects of this invention are:

[0044] (1) In this invention, the CGAN-based generative model is trained in stages and optimized specifically for the characteristics of different landform development stages, which significantly improves the spatial detail representation capability of high-resolution DEM. Compared with the coarse processing of terrain complexity by traditional DEM construction methods, this invention makes full use of key terrain element information such as valley lines and ridge lines, effectively enhancing the realistic restoration of terrain details, making the generated DEM more delicate and accurate in terms of water system morphology and landform cross sections. The high-resolution DEM not only provides a more reliable data foundation for applications such as geological exploration and flood simulation, but also creates conditions for refined terrain analysis and environmental monitoring.

[0045] (2) In this invention, the scientific division of geomorphic stages is achieved by combining multiple spatial and temporal indicators such as area-elevation integral and main-to-branch ratio with expert weighting. This stage division based on geomorphic evolution process breaks through the limitation of lacking geomorphic evolution background in previous DEM construction, making the model training and generation process more targeted and hierarchical. Through staged modeling, the model not only has better adaptability to the terrain features of different evolution stages, but also improves the geomorphological interpretability of the generated results, which is convenient for expert verification and subsequent analysis, and helps to promote the in-depth application of digital terrain products in geomorphology, environmental science and other fields.

[0046] (3) In this invention, a complete automated process is designed, from high-resolution DEM spatial clipping and terrain feature extraction to spatial time index calculation and stage division, and then to staged CGAN training. This process greatly reduces manual intervention, improves the efficiency of data preprocessing and model training, and ensures the standardization and repeatability of the method. At the same time, this invention has good adaptability and versatility, and can be quickly applied to different terrain regions and multiple watershed types, which facilitates the construction and updating of large-scale digital terrain products. Moreover, this invention has important engineering promotion value for improving the automation level of remote sensing and terrain data processing and promoting the intelligent generation of terrain data. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the overall process of the present invention;

[0048] Figure 2 This is a schematic diagram of 5-meter DEM data of the study area and DEM samples extracted from it in an embodiment of the present invention;

[0049] Figure 3 This is a flowchart illustrating the creation process of terrain feature image pairs in an embodiment of the present invention.

[0050] Figure 4 This is a schematic diagram of the time-space dataset in an embodiment of the present invention; each column from left to right in the figure is a schematic diagram of a portion of the dataset for the juvenile, adult, and old age stages, and from top to bottom are schematic diagrams of image pairs of samples from different independent small watersheds in each stage;

[0051] Figure 5 This is a principal component analysis distribution map of samples from the geomorphic development stage in an embodiment of the present invention;

[0052] Figure 6 This is a schematic diagram of the pix2pix network structure of the conditional generative adversarial network in an embodiment of the present invention;

[0053] Figure 7 This is a comparison of the DEM construction results for each developmental stage in the spatial time dataset of this invention. From left to right and from top to bottom, the figures show a schematic diagram of the reference DEM, a schematic diagram of the generated virtual DEM, a reference DEM mountain shadow map, and a generated virtual DEM mountain shadow map, representing three independent small watersheds at the juvenile, mature, and old stages, respectively. Detailed Implementation

[0054] This embodiment provides a geomorphic stage division and DEM construction method based on spatial-temporal indices, which is applicable to application scenarios such as terrain modeling, geomorphic evolution research and reconstruction of terrain data in complex areas. The geomorphic stages are divided by spatial-temporal indices such as area-elevation integral and main-to-branch ratio, and the CGAN network is combined for staged training to improve the model's ability to express terrain structures at different developmental stages and the accuracy of reconstruction.

[0055] like Figure 1 As shown, a method for geomorphic stage division and DEM construction based on spatial time index includes the following steps:

[0056] S1, First obtain as follows Figure 2 The 5-meter high-resolution DEM (Digital Elevation Model) data of the Jiuyuangou watershed in the Loess Plateau of northern Shaanxi, as shown, underwent preprocessing including projection transformation and filtering for denoising. Subsequently, based on hydrological analysis methods, the river network and initial sub-watershed boundaries were extracted. Sub-watershed units with complete outlines and independent structures were selected through manual review, and the corresponding DEM regions were manually cropped using masking operations. The cropped batches of sub-watersheds were then centered and embedded into 256×256 pixel images, surrounded by NoData values, and batch-constructed as shown. Figure 2 The DEM sample shown is in a uniform format.

[0057] S2. Based on the constructed batch DEM samples, hydrological analysis methods are used to calculate depression filling, flow direction, and flow rate. A confluence threshold of 200 is set to extract ridge lines. By subtracting the original DEM value from the maximum elevation value in the region, a negative terrain model is constructed. The same hydrological analysis method with the same threshold is applied to the negative terrain to extract valley lines. Based on the automatic segmentation method of loess positive and negative terrain, a difference elevation map is constructed to extract local positive and negative terrain boundaries and obtain gully lines. Combining slope and water system distribution, closed watershed watersheds are delineated, and watershed boundary lines are extracted.

[0058] S3. Encode the processed terrain features (gully edges, ridge lines, valley lines, and watershed boundaries) into a three-channel RGB image, where valley lines are encoded to the blue channel, ridge lines to the green channel, gully edges to the red channel, and watershed boundaries are overlaid in gray (220, 220, 220) to obtain a terrain feature map.

[0059] S4, such as Figure 3 As shown, the topographic feature map of each sample is stitched with the corresponding DEM image in the horizontal direction to generate a 512×256 pixel image pair sample, thus obtaining the topographic sample dataset.

[0060] S5. Based on the spatial time theory of geomorphology, calculate four spatial time indices for each image in the topographic sample dataset: area-elevation integral, main-to-branch ratio, gully density, and surface roughness.

[0061] HI (Hypsometric Integral) is an important indicator that reveals the morphology and development characteristics of valley landforms by statistically combining elevation information of the watershed surface. Its specific calculation method is as follows:

[0062] First, the normalized elevation values ​​are divided into n equal-width intervals:

[0063]

[0064] Then, count the number of pixels (a) in each elevation interval that are higher than the current segmented normalized elevation value. i And calculate the normalized area:

[0065]

[0066] Finally, the trapezoidal rule is used to approximate integration to calculate HI:

[0067]

[0068] Among them, H i z represents the normalized elevation value. i A(h) represents the original elevation value of the i-th elevation segment. i ) represents the normalized area higher than the current piecewise normalized elevation value, a j This indicates an elevation greater than h. i The number of pixels, A represents the total effective area, n represents the number of segments, and z min and z max Let h represent the minimum and maximum elevation values ​​in the DEM, respectively, where HI represents the area-elevation integral, and h represents the area-elevation integral. i and h i+1 These represent the normalized elevation values ​​of the i-th segment and the (i+1)-th segment, respectively.

[0069] The main-to-tributary ratio, also known as the ratio of the length of the main gully to the total length of the gullies within a watershed, reflects the development level of the tributaries in the gully system from the perspective of gully length. Its mathematical expression is:

[0070]

[0071] Where R represents the ratio of main gully to tributary gully, L0 represents the length of the main gully, and L represents the total length of the gully.

[0072] Gully density, also known as gully density or channel density, refers to the total length of gullies per unit area, measured in km / km. 2Its mathematical expression is:

[0073]

[0074] Among them, D s ∑L represents the gully density; ∑L represents the total length of gullies within the study area, in km; S represents the area of ​​a specific sample area, in km². 2 .

[0075] Surface roughness is an indicator of the degree of surface erosion and undulation. It is usually defined as the ratio of the surface area of ​​a surface element to its projected area on a horizontal plane, and its mathematical formula is expressed as:

[0076]

[0077] Among them, S 曲面 S represents the surface area of ​​a cell. 平面 This represents the projected area of ​​a surface element onto a horizontal plane.

[0078] The calculation results of the terrain indices of the sample images in the study area in this embodiment are shown in Table 1 below.

[0079] Table 1 Calculation results of spatial-temporal indices in small watersheds of the study area

[0080]

[0081] S6. First, the calculated values ​​of the four time-varying indices are Z-score standardized (standard deviation normalized) to convert them into a standard normal distribution with a mean of 0 and a standard deviation of 1. The mathematical expression is as follows:

[0082]

[0083] Where x′ represents the standardized value of each spatial time index, x represents the original index value of each spatial time index, μ represents the average value of each spatial time index, and σ represents the average difference of each spatial time index.

[0084] Secondly, based on expert knowledge, the ratio of main gullies to tributaries and surface roughness were assigned a weight of 0.4, while gully density and area-elevation integral were assigned a weight of 0.1. A weighted comprehensive score was calculated for all samples. The expert knowledge was based on indicators reflecting geomorphic development, such as the size of the effective pixel area in each sample, the length of the main gully, geomorphological spatial-temporal theory, and the Strahler classification method. Subsequently, based on the scoring results, the topographic sample dataset was divided into three equal geomorphic development stages: juvenile, mature, and senile. The results are as follows: Figure 4 The dataset shown has three developmental stages.

[0085] To visually demonstrate the distribution characteristics of each sample across multiple index dimensions, this embodiment performs PCA (Principal Component Analysis) dimensionality reduction on the standardized indicators. Figure 5 The image shows the distribution of the samples in the principal component space (PC1 and PC2). Each dot represents a sample, and its position reflects its combined features in the two principal component dimensions.

[0086] S7. Divide the samples from the three developmental stages in the spatial time dataset into training and validation sets according to the ratio of 80% and 20% respectively. Then train the conditional generative adversarial network pix2pix respectively to obtain three terrain generation models with different stage feature perception capabilities.

[0087] The network structure of the conditional generative adversarial network pix2pix is ​​as follows: Figure 6 As shown, it includes a generator and a discriminator; the generator adopts a U-Net structure, which consists of an encoder and a decoder. The encoder is used to extract the features of the image, and the decoder is used to generate the output image; the discriminator adopts a PatchGAN structure, which performs local comparison and discrimination between the generated result and the real image to improve the detail quality and structural consistency of the generated image.

[0088] S8. Input the validation sets of the three stages into the corresponding terrain generation models to generate high-resolution virtual DEMs. Quantitative evaluation is performed based on the root mean square error (RMSE) of elevation and slope, and qualitative evaluation is performed based on mountain shadows. The performance differences of the models at each stage in the spatial-temporal dataset at different geomorphic development stages are compared. The spatial-temporal terrain modeling accuracy validation results are shown in Table 2 below. The DEM construction results for each development stage are compared... Figure 7 As shown.

[0089] Table 2. Verification of the accuracy of spatial terrain modeling

[0090]

[0091] Experimental results show that geomorphic stage division based on spatial-temporal indices significantly improves the ability of DEM modeling to express stage-specific features. Among them, the old-age stage model has the best accuracy, and its DEM mountain shadow fully presents the typical features of wide and gentle valleys and smooth watersheds, with the best texture continuity. The mature stage model accurately depicts the balanced development of the valley system, and the transition between the main and branch gullies is natural. Although the juvenile stage model is limited by the complexity of the terrain, it still effectively preserves the initial development features of steep valleys and sharp watersheds. The above results confirm the scientificity and practicality of the spatial-temporal index system and provide a new technical paradigm for DEM modeling oriented towards geomorphic evolution stages.

[0092] This embodiment introduces a geomorphic development stage division mechanism to construct a DEM construction system with stage awareness capabilities. It not only focuses on the model's overall elevation prediction accuracy, but also emphasizes its structural expression ability, morphological adaptability, and generalization stability in different geomorphic stages, thereby providing more scientific technical support for high-quality DEM construction and geomorphic process simulation in complex terrain areas.

[0093] In addition to the embodiments described above, the present invention may have other implementations. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. A method for geomorphic stage division and DEM construction based on spatial temporal indices, characterized in that: Includes the following steps: S1. Obtain the digital elevation model (DEM) data of the study area with a resolution of 5m and below, preprocess and manually crop it to extract batches of independent small watershed units; embed each small watershed unit into a standardized 256×256 pixel image to construct batches of DEM samples with uniform format. S2. Based on hydrological analysis methods and automatic segmentation of positive and negative loess terrain, four types of terrain features are extracted from each DEM sample: gully line, ridge line, valley line, and watershed boundary line. S3. Encode the gully line, ridge line, and valley line into the red, green, and blue channels of the RGB image respectively. The watershed boundary line is represented by grayscale overlay. This completes the fusion encoding of the four types of terrain elements and yields a terrain element map. S4. Stitch the topographic feature map of each sample with the corresponding DEM sample in the horizontal direction to generate image pairs of 512×256 pixels, and obtain the topographic sample dataset. S5. Based on the spatial-temporal theory of geomorphology, calculate four spatial-temporal indices for each image in the topographic sample dataset: area-elevation integral, main-to-branch ratio, gully density, and surface roughness. S6. Standardize the four spatial time indicators, then assign weights to each indicator based on expert knowledge, perform weighted comprehensive scoring on all samples, and divide the terrain sample dataset into three different geomorphic development stage categories based on the scoring results: juvenile stage, mature stage and old age stage. Finally, the spatial time dataset is obtained, which includes the juvenile stage dataset, the mature stage dataset and the old age stage dataset. S7. Using the juvenile stage dataset, the adult stage dataset, and the old age stage dataset respectively, train the conditional generative adversarial network Pix2Pix in stages to obtain three terrain generation models with the ability to perceive the features of the juvenile stage, the adult stage, and the old age stage respectively. S8. Input each validation set into the terrain generation model trained in the corresponding stage to generate DEMs with a resolution of 5m or less, and verify the accuracy based on quantitative and qualitative indicators to evaluate the reconstruction performance of the three terrain generation models in the spatial time dataset.

2. The method for geomorphic stage division and DEM construction based on spatial temporal indices according to claim 1, characterized in that: In step S1, manual cropping is based on a DEM with a resolution of 5m or less. Hydrological analysis methods are used to extract the river network and the initial watershed boundary. Combined with manual review, watershed units with complete outlines and independent structures are selected, and the corresponding DEM regions are cropped through masking operations.

3. The method for geomorphic stage division and DEM construction based on spatial temporal indices according to claim 1, characterized in that: In step S2, extracting four terrain features from each DEM sample specifically includes the following sub-steps: S2.1 Based on the constructed batch DEM samples, hydrological analysis methods are used to calculate depression filling, flow direction and flow rate, and ridge lines are extracted by combining confluence thresholds; S2.2 Construct a negative terrain model by elevation reversal and extract valley lines using hydrological analysis methods; S2.3 Based on the automatic segmentation method of positive and negative loess terrain, construct a difference elevation map, extract local positive and negative terrain boundaries, and obtain the gully line; S2.

4. Combining slope and water system distribution, delineate closed watershed watersheds and extract watershed boundary lines.

4. The method for geomorphic stage division and DEM construction based on spatial temporal indices according to claim 1, characterized in that: In step S5, the area-elevation integral reveals important indicators of valley landform morphology and development characteristics by statistically analyzing the elevation combination information of the watershed surface; the specific calculation method of the area-elevation integral is as follows: First, the normalized elevation values ​​are divided into n equal-width intervals: Then, count the number of pixels (a) in each elevation interval that are higher than the current segmented normalized elevation value. i And calculate the normalized area: Finally, the trapezoidal rule is used to approximate integration to calculate HI: Among them, H i z represents the normalized elevation value. i A(h) represents the original elevation value of the i-th elevation segment. i ) represents the normalized area higher than the current piecewise normalized elevation value, a j This indicates an elevation greater than h. i The number of pixels, A represents the total effective area, n represents the number of segments, and z min and z max Let h represent the minimum and maximum elevation values ​​in the DEM, respectively, where HI represents the area-elevation integral, and h represents the area-elevation integral. i and h i+1 These represent the normalized elevation values ​​of the i-th segment and the (i+1)-th segment, respectively.

5. The method for geomorphic stage division and DEM construction based on spatial temporal indices according to claim 1, characterized in that: In step S5, the main gully-tributary ratio is defined as the ratio of the length of the main gully to the total length of the gullies within the watershed. It reflects the development degree of the tributaries in the gully system from the perspective of gully length, and its mathematical expression is: Where R represents the ratio of main gully to tributary gully, L0 represents the length of the main gully, and L represents the total length of the gully.

6. The method for geomorphic stage division and DEM construction based on spatial temporal indices according to claim 1, characterized in that: In step S5, the gully density is defined as the total length of gullies per unit area, expressed in km / km. 2 Its mathematical expression is: Among them, D s ∑L represents the gully density; ∑L represents the total length of gullies within the study area, in km; S represents the area of ​​a specific sample area, in km². 2 .

7. The method for geomorphic stage division and DEM construction based on spatial temporal indices according to claim 1, characterized in that: In step S5, surface roughness is defined as the ratio of the surface area of ​​a surface element to its projected area on a horizontal plane, used to characterize the degree of surface erosion and undulation. Its mathematical formula is expressed as: Among them, S 曲面 S represents the surface area of ​​a cell. 平面 This represents the projected area of ​​a surface element onto a horizontal plane.

8. The method for geomorphic stage division and DEM construction based on spatial temporal indices according to claim 1, characterized in that: In step S6, the four spatial time indicators are standardized using the Z-score standardization method. This method transforms the eigenvalues ​​into a distribution with a mean of 0 and a standard deviation of 1. Its mathematical expression is: Where x′ represents the standardized value of each spatial time index, x represents the original index value of each spatial time index, μ represents the average value of each spatial time index, and σ represents the average difference of each spatial time index.

9. The method for geomorphic stage division and DEM construction based on spatial temporal indices according to claim 1, characterized in that: In step S6, expert knowledge is based on indicators used to reflect landform development, including the size of the effective pixel area in each sample, the length of the main valley, the geomorphological spatial-temporal theory, and the Strahler classification method.

10. The method for geomorphic stage division and DEM construction based on spatial temporal indices according to claim 1, characterized in that: In step S7, the conditional generative adversarial network Pix2Pix includes a generator and a discriminator; the generator adopts a U-Net structure, which consists of an encoder and a decoder. The encoder is used to extract features of the image, and the decoder is used to generate the output image. The discriminator uses a PatchGAN structure to perform local comparison and discrimination between the generated results and the real images.

Images