TSA-MC v1.0: A 30-m dataset of true surface area for China’s mountains to support SDG 15.4 indicators monitoring

Abstract

Traditional two-dimensional Projected Area (PA) calculations systematically underestimate area of mountain ecosystems, introducing significant uncertainty into resource management and sustainable development assessments. To address this critical data gap, we present the True Surface Area of China’s Mountains (TSA-MC v1.0), the first nationwide, 30-m resolution dataset providing a physically realistic three-dimensional land surface measure. Developed from ASTER GDEM V2 using a robust pixel decomposition algorithm, its reliability was confirmed through rigorous validation of its physical accuracy (e.g., TSA/PA ratio-slope correlation, ρ = 0.3917) and geomorphic consistency. The dataset, by accounting for three-dimensional topography, quantifies an additional 582,000 km² of surface area compared to traditional projected-area measurements. Consequently, this revision demonstrates that mountainous surface terrain is underestimated in previous assessments, with the updated estimate (67.25%, TSA-based) exceeding the Digital Map of China’s Mountains projection (64.9%, PA-based) by 2.35%. This foundational data layer enables more accurate area-dependent applications, including carbon stock accounting, hydrological modeling, habitat analysis, and the monitoring of SDGs. The complete dataset is openly available via the Zenodo repository to support further research.

Background & Summary

Mountains are critical ecosystems that play a vital role in global sustainable development, a fact underscored by their prominence in the United Nations’ 2030 Agenda, particularly Sustainable Development Goal 15 (SDG 15) which focuses on “Life on Land”^1,2. Acting as the “world’s water towers”, they provide essential freshwater for a large share of the global population, and they also support immense biodiversity, hosting over one-third of the world’s terrestrial species, making them irreplaceable hubs of life^3,4. However, these ecosystems are exceptionally sensitive to global threats such as climate change and land degradation⁵. Therefore, effective action on critical SDG indicators, from conserving mountain biodiversity and preventing land degradation to ensuring sustainable resource management, is fundamentally dependent on reliable data and accurate assessments of their spatial extent and carrying capacity⁶.

A fundamental flaw undermines the accuracy of current assessments: the near-universal reliance on the two-dimensional Projected Area (PA). This standard practice represents surface extent as a planar approximation and systematically ignores three-dimensional topographic complexity. In complex mountainous regions with steep slopes, this simplification leads to systematic underestimations of the True Surface Area (TSA), with discrepancies increasing as slope and terrain ruggedness intensify, thereby propagating substantial errors into a wide range of area-dependent calculations. The use of the term “TSA” in this study is intended to distinguish this quantity from the conventionally reported surface area, which is often implicitly planimetric, and is consistent with terminology adopted in previous studies. For example, Bian et al.⁷ reported an average global increase of approximately 12% in the Mountain Green Cover Index (MGCI) calculation when accounting for TSA. This directly impacts the reliability of key SDG-related indicators, including those for habitat capacity, soil erosion rates, and surface energy budgets^8,9, all of which are critical for gauging the health of mountain ecosystems. The absence of a reliable, high-resolution TSA dataset may therefore compromise the robustness of scientific assessments supporting conservation and management strategies.

This data gap is especially critical in China, where mountains cover approximately two-thirds of the national territory and are integral to the nation’s ecological security^10,11. The immense scale and topographic complexity of China’s mountain systems present a significant challenge for existing TSA estimation methods. While techniques based on Triangulated Irregular Networks (TINs) excel at preserving fine-scale terrain details, their significant computational overhead makes them impractical for national-scale analyses^12,13. Alternative approaches using fractal geometry, while conceptually elegant, often suffer from uncertainty and inconsistent performance across diverse landform types, limiting their reliability for producing a standardized, nationwide dataset^14,15. Consequently, China has lacked a high-resolution TSA dataset generated with a unified and computationally efficient method, representing a critical missing resource for robust SDG monitoring and national-level environmental management.

Although widely used Earth observation products, such as Landsat and Sentinel, apply DEM-based terrain corrections, these procedures mainly mitigate radiometric and geometric distortions during image acquisition and do not address the fundamental discrepancy between PA and TSA¹⁶. As a result, this limitation persists even with the availability of valuable regional datasets, such as the recent 30-m landform classification of the Loess Plateau¹⁷. To address this gap, we developed the True Surface Area of China’s Mountains (TSA-MC v1.0), the first nationwide, high-resolution (30-m) dataset that explicitly quantifies three-dimensional surface area. This foundational dataset provides a physically realistic measure of the three-dimensional land surface, generated from ASTER GDEM V2 using a robust and computationally efficient pixel decomposition algorithm¹⁸. The dataset’s quality and reliability have been confirmed through a rigorous, multi-faceted validation process, which demonstrated its consistency with fundamental geometric principles and its alignment with established geomorphological classifications.

The dataset’s core findings reveals that the TSA of its mountainous regions is 582,000 km² larger than estimates derived from the traditionally used PA. This substantial correction revises the national mountainous terrain estimate to 67.25% (TSA-based), representing a 2.35% increase relative to the 64.9% (PA-based) reported by the Digital Map of China’s Mountains. This area gain is highly heterogeneous, with the Qinghai-Tibet Plateau alone accounting for 45.95% of the increase, highlighting regions where PA-based assessments are most prone to uncertainty. The dataset provides an accurate baseline for applications including pasture capacity assessment, carbon stock accounting, and improved soil erosion and hydrological modeling^19–22. Furthermore, it functions as an analytical probe revealing complex vegetation-topography relationships, as demonstrated in a case study. As a foundational data layer, TSA-MC v1.0 offers critical support for scientific research and sustainable development assessments in mountainous regions worldwide^23–25.

Methods

Core data sources

The main data product of this study is the TSA dataset for China’s mountains, which was produced using a combination of trusted geospatial sources, including digital elevation models (DEMs), mountain range boundaries, and administrative boundary data. To ensure the results are accurate and repeatable, all spatial data were standardized under the WGS 1984 Albers equal-area conic projection, which is vital for maximizing the accuracy of area calculations. All core data sources used in this study are listed in Table 1. The specific datasets are detailed as follows:

Table 1.

Description of the primary datasets used in this study.

Dataset	Data Provider	Resolution	Year	Primary Use in This Study	Data Access / Identifier
ASTER GDEM V2	NASA/METI	1 arc-second (approx. 30-m)	2011	Calculate the true surface area and terrain factor	10.5067/ASTER/ASTGTM.00261
China Digital Mountain Map	Nan, X. et al.	N/A	2015	Defining mountainous areas, subdivisions, and classification statistics	https://data.tpdc.ac.cn/en/data/efa1dc3f-5f2d-4e60-8bf7-3ea4c6ec1929/31
Provincial administrative divisions of the People’s Republic of China	Ministry of Natural Resources Standard Map Service System	1:1,000,000 scale	2020	Summarize results and create maps by provincial administrative unit.	http://bzdt.ch.mnr.gov.cn/62

The DEM used was the ASTER Global Digital Elevation Model Version 2 (ASTER GDEM V2), jointly released by NASA and Japan’s Ministry of Economy, Trade and Industry (METI)²⁶. We selected this digital surface model (DSM) in this study due to three main reasons. First, with a spatial resolution of 1 arc second (approximately 30 m at the equator), ASTER GDEM V2 provides finer spatial detail than other widely used global DEMs, such as SRTM²⁷, which is particularly important for capturing terrain variability in mountainous regions. Second, previous comparative studies have demonstrated that ASTER GDEM V2 performs competitively in high-relief terrain and has been widely adopted in mountain-focused research⁷. Third, although recently developed Digital Terrain Model (DTM) datasets, including FABDEM²⁸, FathomDEM²⁹, and GEDTM30³⁰, show promise for geomorphic applications, their performance in steep and complex mountainous environments has not yet been fully evaluated and remains subject to additional uncertainties. Consequently, ASTER GDEM V2 was adopted as a digital surface model (DSM) to represent the three-dimensional topographic surface for generating the TSA dataset of China’s mountains. To delineate mountain boundaries and classify mountain types, we employed the Digital Map of China’s Mountains (DMC) as the primary geospatial framework³¹. This authoritative dataset provides two key vector layers: (1) Six major mountain regions, which serves as the framework for macro-scale spatial analysis (Fig. 1), and (2) a detailed geomorphic classification. While this classification system theoretically defines 21 mountain types based on elevation and surface relief, the provided dataset merges the “high-elevation, greatly undulating mountains” and “medium-elevation, greatly undulating mountains” into a single category under the code ‘DI’. This results in a total of 20 unique geomorphic type codes for analysis, offering a robust geomorphological basis for exploring the relationship between TSA and different landform types. Finally, for administrative division boundary data, we used the official boundaries for China’s 34 provincial-level administrative units, sourced from the standard map service system of the Ministry of Natural Resources, to summarize and visualize the results at the provincial level. All required data tiles were mosaicked and reprojected to ensure a consistent topographic foundation for subsequent analyses.

Fig. 1.

Spatial distribution of the mountainous study area in China. The map delineates the total extent of China’s mountains (black outline) and the six major geographic subregions used for analysis. This regionalization is adopted from the classification system of the Digital Map of China’s Mountains (DMC).

TSA calculation and data processing workflow

The calculation of the TSA addresses a fundamental limitation of the traditional two-dimensional PA: the omission of surface complexities introduced by topographic relief. The method calculates the TSA by discretizing the continuous DEM terrain into an array of three-dimensional facets and summing their individual areas. To implement this principle, this study adopts a widely used pixel-based algorithm that operates on a 3 × 3 moving window with a step size of one pixel, analyzing the elevation relationships between a central pixel and its eight neighbors¹⁸. Specifically, with this window, the TSA of the central pixel is calculated using the elevation data from its eight neighbors, and the window is moved across the raster one pixel at a time, ensuring that TSA is computed for every DEM pixel. As illustrated in Fig. 2, this process involves conceptually connecting the center point (O) of the central pixel to the center points (A–H) of the eight adjacent pixels, thereby decomposing the surface into eight three-dimensional triangles. This moving-window approach ensures full spatial coverage while preserving local topographic variability. The calculation of the final TSA involves two sequential steps. First, the lengths of the three sides ($a,\mathit{b},\mathit{c}$) of each triangle are calculated. The length of any given side ($L_{\mathit{SD}}$) is determined using the Pythagorean theorem in three dimensions:

$$L_{SD}=\sqrt{{\left(H_{DE}\right)}^2+{\left(L_{\mathit{PD}}\right)}^2}$$ 1

where$H_{\mathit{DE}}$ is the elevation difference between the two pixel centers, and $L_{\mathit{PD}}$ is the plane distance between them. The value of $L_{\mathit{PD}}$ is determined by the adjacency type: it is equivalent to the raster resolution for cardinally adjacent pixels (e.g., between pixel 5 and 6), and is determined by the Pythagorean theorem to be √2 times the resolution for diagonally adjacent pixels (e.g., between pixel 5 and 9).

Fig. 2.

Ground surface area calculation model based on the center pixel and surrounding eight pixels (modified from Jenness, 2004¹⁸).

Second, once the three side lengths ($a,\mathit{b},\mathit{c}$) are known, the area of the triangle $S_{\mathit{area}}$ is calculated using Heron’s formula:

$$S_{\mathit{area}}=\sqrt{p\left(p-a\right)\left(p-b\right)\left(p-c\right)}$$ 2

where $p$ is the semi-perimeter, calculated as $p=(a+b+c)/2$. The total TSA of the central pixel is then the sum of the areas of these eight constituent triangles.

Ecological validation case: data and methods

To validate the practical utility and ecological plausibility of the TSA-MC v1.0 dataset, an analytical case study for SDG 15.4.2 indicator, MGCI was designed for the Tibetan Plateau. The methodology for this validation is detailed below, involving an external data source and a derived ecological index. The external data source used was the China Land Use/Cover Dataset (CLCD) for the year 2022, which has a spatial resolution of 30-m³². Nine categories were extracted for analysis: Forest, Cropland, Shrub, Grassland, Wetland, Water, Snow/Ice, Barren, and Impervious surface. For the MGCI calculation, we first defined Forest, Cropland, Grassland, Shrub, and Wetland as “green vegetation”. The traditional MGCI is calculated based on PA using Eq. (3):

$$\mathit{MGCI}=\frac{\mathit{FA}+\mathit{SA}+\mathit{GA}+\mathit{CA}+\mathit{WA}}{\mathit{LA}}$$ 3

In the formula, $\mathit{FA}$, $\mathit{SA},\mathit{GA},\mathit{CA}$ and $\mathit{WA}$ represent the areas of Forest, Shrub, Grassland, Cropland, and Wetland, respectively, and $\mathit{LA}$ is the total mountainous area of the specified country.

To demonstrate the application of our dataset, we employed a Modified Mountain Green Cover Index (MGCI) based on the TSA. For any given mountain grid cell i, it is considered to contain m terrain‐rugged surface pixels, n terrain‐flat surface pixels, and k green vegetation pixels, all at a 30 m spatial resolution. The MGCI quantifies the proportion of the total true surface area within grid i that is covered by green vegetation. It is calculated as follows^7,33:

$${\mathit{MGCI}}_i=\frac{{\sum }_{j=1}^o{\sum }_{l=1}^k{\mathit{GC}}_{\mathit{jl}}\times {\mathit{TS}}_l}{{\sum }_{p=1}^m{\mathit{TS}}_p+{\sum }_{q=1}^n{\mathit{TS}}_q}$$ 4

where $\mathit{MGC}{I}_i$ is the MGCI value for the i-th mountain grid cell; $G{C}_{\mathit{jl}}$ denotes the j-th green vegetation class (o = 5) spatially corresponding to the $l$-th surface pixel within the grid; and $T{S}_l$ is the true surface area of the $l$-th green vegetation pixel. The denominator represents the total true surface area of all pixels inside grid $i$, including both rugged and flat terrain. The MGCI value of each mountain grid cell is computed at a 500 m spatial resolution, which is consistent with the resolution of the mountain classification dataset.

Data Records

This section details the structure and contents of the TSA-MC v1.0 dataset. The complete dataset, provided at a spatial resolution of 30 × 30 m, is permanently archived in the Zenodo repository³⁴ under a Creative Commons Attribution 4.0 International license (CC-BY 4.0) and is publicly available for download at 10.5281/zenodo.17098017. The dataset is provided as a single compressed archive (.zip) containing five primary data files: one main raster data file (.tif) and four tabular files (.csv). The technical specifications, format, and a detailed description of each file are provided in Table 2.

Table 2.

Description and technical specifications of the files included in the TSA-MC v1.0 data archive.

File name	Data description	Data type	Format	Resolution(m)	Coordinate system
TSA_MC_v1_0_raster.tif	True surface area grid map of the mountainous region of China	Raster	GeoTIFF	30	WGS 1984 Albers
TSA_MC_v1_0_stats_by_province.csv	Mountain area data statistics by 34 provincial administrative regions	Tabular	CSV	N/A	N/A
TSA_MC_v1_0_stats_by_subregion.csv	Mountain area statistics aggregated by the six major geographic subregions	Tabular	CSV	N/A	N/A
TSA_MC_v1_0_stats_by_mountain_type.csv	Area data calculated based on 20 types of mountainous terrain	Tabular	CSV	N/A	N/A
TSA_MC_v1_0_geomorphic_type_codes.csv	Descriptions and codes for the 20 geomorphic types (data dictionary)	Tabular	CSV	N/A	N/A

Spatial distribution and characteristics of the TSA dataset

The primary raster data product (TSA_MC_v1_0_raster.tif) reveals a distinct and highly heterogeneous spatial pattern, characterized by a clear west-east gradient of topographic complexity (Fig. 3A). High TSA values are concentrated in the rugged western ranges, while lower values characterize the gentler topography of eastern China.

Fig. 3.

Multi-scale visualization of the TSA-MC v1.0 dataset for China’s mountains. (A) National-scale map of the TSA raster data product at 30-meter resolution, where each pixel value represents the TSA in square meters (m²) for its corresponding 30×30 m grid cell. (B) The ratio of true surface area to projected area (TSA/PA) across China’s mountainous regions. (C) Comparison of real-world context (Google Earth imagery, hillshade) with the dataset’s core metrics (TSA/PA ratio, TSA) across six representative mountain ranges: (d) Himalayas, (e) Hengduan Mts, (f) Tianshan Mts, (g) Qinling Mts, (h) DaHingganLing Mts, and (i) Wuyi Mts.

This national-scale pattern is consistently reflected at the regional scale, as illustrated in a comparative analysis across a transect of six representative mountain ranges shown in Fig. 3B. This transect, from the extremely rugged Himalayas in the west to the gentler Wuyi Mountains in the east, directly compares real-world context (Google Earth imagery, hillshade) with the dataset’s core metrics. A strong visual correlation is evident: the complex western terrains, such as the Himalayas, correspond directly to high TSA and TSA/PA ratio values, whereas the smoother eastern ranges, like the Wuyi Mts, exhibit markedly lower values. This multi-scale consistency visually confirms the dataset’s robustness in accurately recording topographic complexity across diverse geomorphic settings.

Aggregated statistics by geographical and administrative units

Beyond the pixel-level spatial distribution, the dataset records a wealth of aggregated statistical information that characterizes China’s mountain landscapes. At the sub-national scale, the dataset reveals a highly heterogeneous distribution of TSA gain. The Qinghai-Tibet Mountain Region is the dominant contributor to the total area increase, and provincial-level analysis highlights a stark contrast between rugged western provinces like Tibet and Guizhou, and plains-dominated municipalities like Shanghai. Statistics aggregated by the 20 official geomorphic types further reveal that area gain is co-influenced by both a type’s spatial extent and its intrinsic ruggedness, with the highest proportional underestimation found in extremely undulating high-elevation units. Detailed statistics for all administrative units and geomorphic types are provided in the Supplementary Information (Tables S1-S3).

Furthermore, the fundamental geomorphic character of China’s mountains is detailed through the statistical distribution of the core derivative metric, the TSA/PA ratio. It should be noted that the TSA/PA ratio used in this study is conceptually equivalent to the Surface Area to Planimetric Area (SAPA) metric introduced by Jenness (2004)¹⁸. This distribution pattern quantitatively confirms the fundamental geomorphic character of China’s mountains: a landscape dominated by a vast expanse of relatively gentle terrain, punctuated by a small but significant fraction of extremely steep landforms Fig. 4a. The relationship between roughness and terrain factors reveals two key patterns. First, the TSA/PA ratio increases with slope in a positive and non-linear manner, indicating that steeper terrains tend to exhibit larger proportional surface area gains (Fig. 4d). In contrast, its relationship with elevation is more complex, showing a non-monotonic “increase-then-decrease” pattern, where surface roughness peaks in the 4000–5000 m elevation band (Fig. 4e).

Fig. 4.

Statistical properties of the surface roughness (TSA/PA ratio) in the TSA-MC v1.0 dataset. (a) Histogram and cumulative percentage curve of the TSA/PA ratio across all mountainous areas in China. (b) Area percentage of TSA values for each slope class. (c) Area percentage of TSA values across different elevation ranges. (d) Violin plots showing the relationship between the TSA/PA ratio and terrain slope. (e) Violin plots showing the relationship between the TSA/PA ratio and elevation, grouped by elevation bands.

Technical Validation

To establish the reliability and robustness of the TSA-MC v1.0 dataset, we performed a multi-faceted validation process designed to assess its quality at three distinct levels: (1) consistency with fundamental geometric and geomorphic principles; (2) practical utility and plausibility in a real-world ecological application; and (3) a transparent evaluation of inherent uncertainties and limitations.

Consistency with terrain slope

A fundamental validation of the dataset’s physical consistency check involves examining the relationship between the TSA/PA ratio and terrain slope (θ). For an idealized surface that is perfectly planar and uniformly inclined, basic geometry shows that the true surface area is related to its horizontal projection by TSA = PA / cos (θ). For natural terrain, which exhibits curvature and micro-topographic variability, this planar relationship should be interpreted as a lower bound, such that TSA ≥ PA / cos θ. This relationship is an exact geometric identity for planar surfaces and serves here as a theoretical reference, rather than a constraint, for real terrain. It should be noted that slope and TSA capture different geometric properties of terrain. Slope is a local measure of steepness, whereas TSA is an additive, physically meaningful surface measure that can be integrated across space. As a result, terrain with similar slope values may exhibit different surface areas due to curvature and micro-topographic complexity, which TSA explicitly represents.

Natural terrain surfaces are rarely planar and instead exhibit curvature and micro-topographic variability across multiple spatial scales. As a result, TSA values derived from high-resolution DEMs are not expected to strictly follow the planar relationship at individual pixels. However, if the TSA-MC dataset realistically represents surface geometry, the TSA/PA ratio should show a positive, monotonic, but non-linear relationship with slope when evaluated statistically across large samples. Based on this principle, we hypothesized that the TSA values generated by our algorithm should conform, in aggregate, to the theoretical relationship defined above.

To test this hypothesis while mitigating sampling bias, we employed a stratified sampling strategy of 10,000 points per 10° slope category. The results presented in Fig. 5, provide compelling support for our hypothesis. A visual inspection confirms an excellent alignment between the median values of our sampled data and the theoretical curve, validating the dataset’s adherence to this core physical principle. Furthermore, to characterize the correlation quantitatively, an analysis on a larger, unstratified sample of 5 million points was conducted. This yielded a Spearman’s rank coefficient (ρ = 0.3917) substantially higher than the Pearson coefficient (r = 0.3367), providing robust statistical evidence for the expected strong, monotonic, but distinctly non-linear positive correlation between the TSA/PA ratio and slope, accurately reflecting the underlying terrain geometry.

Fig. 5.

Consistency of the TSA/PA ratio with terrain slope. The figure displays violin plots of the TSA/PA ratio for a stratified random sample (n = 10,000) within each 10° slope category. White circles represent the median of the sampled data. The dashed red line represents the theoretical relationship for an idealized planar surface (TSA/PA = 1 / cos θ), which serves as a lower bound for natural terrain, such that TSA ≥ PA / cos θ.

Consistency with geomorphic classification

To further validate the dataset against established landform knowledge, we tested the relationship between the calculated surface roughness (TSA/PA ratio) and the 20 distinct geomorphic types defined in the DMC (see Supplementary Table S4 for code definitions). A stratified sampling strategy of 10,000 points per type was employed to ensure representative statistics. We hypothesized that the roughness values derived from this sample should align with the qualitative descriptions of surface relief in the official classification.

The results, presented in Fig. 6, provide compelling support for this hypothesis, revealing a perfect correspondence between our quantitatively derived roughness values and the established geomorphic hierarchy. This is most clearly demonstrated by the clear gradient observed in the figure, where the calculated roughness aligns perfectly with the descriptive classification, ranging from low roughness in “slightly undulating hills” (e.g., AH) to high roughness in “extremely undulating mountains” (e.g., EI). The distinct pattern (i.e., extremely undulating > greatly undulating > moderately undulating > slightly undulating mountains > slightly undulating hills) provides decisive evidence of the dataset’s logical consistency and its ability to accurately reflect inherent topographic characteristics.

Fig. 6.

Distribution of surface roughness (TSA/PA ratio) across 20 geomorphic types. Geomorphic types from the DMC are sorted on the y-axis by their median roughness value. Each type is represented by a boxplot showing the interquartile range (IQR) and jittered points visualizing the distribution of 10,000 stratified samples. For a complete list of geomorphic type codes, see Supplementary Table S4.

Validation of practical utility and ecological plausibility

To move beyond theoretical checks and validate the dataset’s performance in a real-world scientific application, we conducted a case study on the Tibetan Plateau by integrating the TSA-MC v1.0 dataset with the CLCD land cover product (see Methods for details). This validation was performed at two distinct levels: a macro-scale plausibility check and a micro-scale sensitivity analysis. In this context, the TSA/PA ratio was used as an indicator of surface roughness, consistent with previous studies (e.g., SAPA; Jenness, 2004). In contrast, the TSA–PA difference represents the absolute surface area gain (in m²) attributable to terrain relief and is relevant for area-based area accounting.

First, a macro-scale plausibility check was conducted to test whether the dataset produces ecologically plausible area corrections for different land cover types. We hypothesized that the calculated roughness index (TSA/PA) should align with the known topographic preferences driven by the ecological strategies of each class. The results, summarized in Table 3, provide qualitative support for this hypothesis. As a crucial ground-truth test, Impervious surfaces, located almost exclusively on flat terrain for human activities, exhibited a theoretically ideal roughness index of 1.00. Furthermore, the results align are consistent with established ecological patterns. Forest exhibits the highest roughness index (1.25), a finding consistent with the well-established principle that forest structure is strongly governed by fine-scale topography. This relationship is often driven by the preferential colonization of steep slopes, which can optimize abiotic conditions such as light exposure and soil drainage, ultimately influencing forest biomass³⁵. In contrast, Grassland shows a more moderate index (1.10), reflecting its prevalence on gentler, more stable plateau surfaces. Such topographic positions are known to foster deeper soils and more favorable soil water profiles, which are critical for supporting extensive root systems and enhancing ecosystem resilience³⁶. This differentiated correction suggests that the dataset captures meaningful terrain-related differences beyond uniform area scaling, but accurately captures the nuanced relationship between topography and ecosystem distribution.

Table 3.

TSA-corrected area statistics for major land cover types in the mountainous region of the Qinghai-Tibet Plateau.

Land Cover Type	True Surface Area (TSA) (×10⁴ km²)	Projected Area (PA) (×10⁴ km²)	Area Difference (TSA - PA) (×10⁴ km²)	Roughness Index (TSA/PA)
Cropland	0.73	0.68	0.05	1.07
Forest	29.93	24.00	5.93	1.25
Shrub	0.89	0.75	0.14	1.19
Grassland	149.60	135.89	13.71	1.10
Water	0.63	0.56	0.07	1.13
Snow/Ice	7.23	6.07	1.16	1.19
Barren	43.85	39.23	4.62	1.12
Impervious	0.01	0.01	0.00	1.00
Wetland	0.00*	0.00	0.00	NA
Total	232.87	207.19	25.68	1.12

^* The wetland area is non-zero but rounds to 0.00 at the current display precision (TSA: 37.83 km²; PA: 35.07 km²).

Second, a micro-scale sensitivity analysis was performed via MGCI revision to validate the dataset’s analytical fidelity. A quantitative assessment across the entire Tibetan Plateau reveals a small mean difference (+0.067) but a large standard deviation (2.81), strongly indicating that the calculation bias exhibits extreme spatial heterogeneity. This macro-scale statistical pattern reveals a small average difference coexisting with immense variability. This pattern is visualized in Fig. 7a, where widespread near-zero corrections (light blue) are punctuated by distinct hotspots of positive correction (red). To deconstruct the drivers of this heterogeneity and validate the dataset’s ability to capture underlying mechanisms, we analyzed two contrasting “vegetation-topography” coupling patterns from representative sites, as detailed in Fig. 7b.

Fig. 7.

Multi-scale validation of the dataset’s analytical sensitivity using the Mountain Green Cover Index (MGCI) difference on the Tibetan Plateau. The upper panel shows the pixel-wise MGCI difference (TSA_MGCI − PA_MGCI), with black boxes marking the locations of two representative sites. The lower panels present a comparative analysis of these sites with contrasting topography: (a) a steep, forested valley and (b) a high-altitude plateau. For each site, rows display Google Earth imagery, MGCI estimates derived from the TSA- and PA-based methods, and the corresponding MGCI difference map.

The first scenario, a steep, forested valley (Fig. 7a), reveals a strong positive correction bias, quantitatively confirmed by a significant mean difference of +0.130. This counter-intuitive but physically correct outcome provides a powerful validation of the dataset’s ability to handle complex ecological scenarios. The positive bias occurs because the vegetation in this valley, primarily forests, preferentially occupies the steepest slopes. Mechanistically, this means the average slope of the vegetated pixels is significantly higher than the average slope of the entire region. Consequently, according to the TSA/PA = 1/cos(slope) principle, the topographic correction applied to the numerator of the MGCI formula (the vegetated area) surpasses that of the denominator (the total area), leading to a net increase in the index value. This micro-level mechanism perfectly corroborates the macro-scale observation that the Forest category has the highest roughness index (Table 3).

The second scenario, a high-altitude plateau with incised valleys (Fig. 7b), is dominated by a near-zero correction bias, supported by a mean difference of approximately −0.01. This result is also mechanistically correct and serves as a crucial validation. In this landscape, vegetation is predominantly located on the gentler plateau surfaces, avoiding the steepest valley walls. This results in the average slope of the vegetated pixels being significantly lower than that of the entire region. Therefore, the topographic correction applied to the numerator is smaller than that applied to the denominator, leading to a slight net decrease in the MGCI value, which is correctly captured by our dataset.

This ability to simultaneously capture opposing, yet equally plausible correction patterns, is a testament to the dataset’s fidelity. First, it provides the ultimate explanation for the initial macro-scale statistics. The coexistence of positive and negative bias regimes across the landscape leads to a canceling-out effect, which produces the small overall mean difference. At the same time, their stark contrast generates the large standard deviation. Second, this result confirms the dual value of the TSA-MC v1.0 dataset. It is not only a tool for correcting area-dependent metrics but also a reliable analytical probe. Ultimately, it is capable of revealing the intricate coupling between ecosystems and topography.

Sources of uncertainty and limitations

While the validation tests confirm the dataset’s robustness for its intended macro-scale applications, users should be aware of several inherent sources of uncertainty that define the scope of its appropriate use. These limitations stem from both the source data and the methodological choices made during the dataset’s creation.

First, uncertainties arise from the foundational data and definitions used. (1) Error propagation from the source DEM: the primary source of uncertainty is the error propagated from the source ASTER GDEM³⁷. The vertical error inherent in the DEM is directly transferred into the TSA calculation, and in high-relief terrain, these errors can be exacerbated, leading to greater localized uncertainty³⁸. In this study, ASTER GDEM V2, as a DSM, was used based on its proven performance and widespread application in previous research. Nevertheless, newer DEM products, such as ASTER GDEM V3, may offer improved elevation accuracy^39–41 and could be employed in future updates. It should be noted that computing TSA from either a DTM or a DSM reflects fundamentally different surface definitions—bare-earth terrain versus land-cover–inclusive surfaces—and the choice should be guided by the application of interest. However, a systematic comparison of DTM- and DSM-derived TSA remains largely unexplored and warrants further investigation. (2) Dependency on mountain boundary definition: the spatial extent and subsequent statistical summaries are contingent upon the mountain boundaries defined by the DMC. The adoption of alternative delineation criteria would necessarily alter the total calculated mountain area, a classic example of the Modifiable Areal Unit Problem (MAUP) in spatial analysis⁴².

Second, further limitations are inherent to the raster-based methodology itself. (3) Underestimation due to spatial resolution: a key limitation is the landscape smoothing effect of the 30-m resolution, which omits sub-pixel features like narrow gullies. As a result, the calculated TSA should be considered a conservative estimate, a systematic tendency in raster-based terrain analysis⁴³. (4) Uncertainty from algorithmic choice: the 3×3 window algorithm employed is a standard, computationally efficient approach but represents an acknowledged methodological trade-off. Users should be aware that alternative frameworks (e.g., TINs) based on different geometric principles would produce minor but systematic discrepancies in TSA values, a fundamental source of uncertainty in all DEM-based terrain analysis^18,44.

Usage Notes

The TSA-MC v1.0 dataset, provided at a spatial resolution of 30 × 30 m, is designed as a foundational data layer for enhancing resource assessments and geomorphic-ecological studies. For effective application, users should consider two key characteristics. First, it is critical to differentiate between absolute area gain (TSA − PA) and the proportional TSA/PA ratio, as each metric is suited to different applications. Similar distinctions have been applied in previous studies, where absolute surface area was used to represent effective habitat⁴⁵, while TSA/PA ratio were used to adjust area-normalized variables such as forest carbon density⁸. Second, the non-monotonic relationship between surface roughness and elevation, which peaks in the 4000–5000 m band, is a crucial consideration for elevation-dependent process modeling (see Data Records).

The dataset’s physically accurate surface geometry makes it a valuable input for enhancing various surface process models. Key recommended application areas include: (1) Hydrological modeling, where it refines key parameters like canopy interception and evapotranspiration and improves calculations of hillslope flow lengths to enhance runoff simulations^46–48; (2) Soil erosion and geomorphology, where it corrects for the underestimation of potential soil loss in models like USLE/RUSLE and provides a geometric constraint for quantifying surface material fluxes^49–52; and (3) Surface energy balance and climate modeling, where it enables more accurate quantification of intercepted solar radiation and can improve land-atmosphere heat flux parameterizations in Regional Climate Models (RCMs)^53–55.

While robust for macro-scale assessments, users should be aware of the following limitations, which also point toward future research directions. (1) Higher resolution: the current 30-m resolution provides a conservative estimate, generally resulting in a slight underestimation due to unresolved sub-grid heterogeneity, and future work should integrate meter-scale DEMs for finer applications⁵⁶. (2) Dynamic monitoring: this dataset is a static snapshot; future versions could leverage multi-period DEMs to create a dynamic time-series for monitoring surface changes⁵⁷. (3) Deeper model integration: the next step is to formally integrate TSA into a wider range of earth system models to quantitatively assess its impact on simulation accuracy^58–60. Users are encouraged to build upon this foundational dataset, citing both this data descriptor and the dataset’s DOI to ensure reproducibility.

Author contributions

J.B. conceptualization, methodology, software, writing - review & editing, funding acquisition, generated the database. Y.W. writing - original draft, methodology, formal analysis. J.Z. methodology, formal analysis. A.L. conceptualization, supervision, writing - review & editing, funding acquisition. X.N. writing - review & editing, validation, resources. G.L. formal analysis. Z.Z. investigation. Y.D. validation. S.L. validation. A.N. validation, visualization, writing - review & editing.

Data availability

The complete dataset is permanently archived in the Zenodo repository under a Creative Commons Attribution 4.0 International license (CC-BY 4.0) and is publicly available for download at 10.5281/zenodo.17098017.

Code availability

The core True Surface Area calculations were performed using the DEM Surface Tools (v. 1.0) for ArcGIS, which were developed by Jeff Jenness and are freely available for download from the developer’s official website: https://www.jennessent.com/arcgis/surface_area.htm.

The custom python scripts used for the large-scale random sampling, all subsequent statistical analyses, and the generation of all figures presented in this paper are available from the first author (J.B.) upon reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41597-026-06880-6.