Toward more reliable, complete, and equitable global urban land use efficiency assessments

Abstract

Improving Urban Land Use Efficiency (LUE) can curb urban sprawl, protect farmland and ecological spaces, and promote low-carbon, intensive development models. Although numerous studies have been conducted, uncertainty and bias in LUE assessments—stemming from data sources, LUE calculations, and trend analysis methodology—has rarely been investigated. After a series of tests, here we propose a reliable, comprehensive, and equitable framework, which uses Built-Up Area per capita (BUP) metrics and provincial population data, along with time-series analysis tools, to assess LUE trends. Our global evaluation reveals that 79.6% of provinces saw significant BUP growth from 1985 to 2020, with an average increase of 15 m² per capita per five years - a trend that challenges progress toward Sustainable Development Goal 11.3. Considerable—and widening—disparities in BUP are observed across provinces and countries. In 2020, the BUP in some high-income countries was thirty times greater than in low-income countries, while the latter exhibited higher BUP growth rates—likely due to their smaller initial base. However, they could still be considered inefficient in land use if assessed solely based on growth rate metrics. The study highlights the importance of reliability, completeness, and equity in global assessments and in building global criteria.

Introduction

Urbanization—the large-scale migration of populations from rural to urban areas—is reshaping the world at an unprecedented pace. By 2050, 68% of the global population is projected to live in cities¹, driving rapid urban expansion into previously undeveloped or rural landscapes^2,3,4. This trend brings substantial economic and social benefits, including heightened productivity, improved living standards, and greater access to healthcare, education, and services⁵. Cities, as hubs of innovation and industry, making urbanization a key driver of development. However, unplanned urban sprawl has severe environmental consequences. It is a leading cause of arable land loss, habitat destruction, and biodiversity decline^6,7,8, while cities contribute 70% of global CO₂ emissions due to concentrated energy use and transportation³. Without sustainable interventions, these challenges will intensify as urban populations grow. To balance development with ecological preservation, cities must adopt effective land-use policies, green infrastructure, and compact urban planning⁹.

Recognizing the significance of cities and urban areas, along with the challenges they confront, the United Nations (UN) has expressly incorporated their sustainability into its 2030 Agenda for Sustainable Development¹⁰. Specifically, SDG indicator 11.3.1 recommends the ratio of land consumption rate to population growth rate (LCRPGR) as the primary metric for evaluating urban land-use efficiency^11,12. Tracking the trajectory of this indicator can provide policymakers and urban planners with a nuanced understanding of the dynamics between urbanization, population growth, and land use. Additionally, it enables projections regarding the demand for ecosystem goods and services, the identification of emerging areas for expansion, and the proactive development of sustainable urban development strategies¹³. Using this indicator, numerous studies have been conducted to investigate urban land use efficiency across various scales and regions^{14,15,16,17,18,19}. Jiang et al. examined the sustainability of urbanization in China using the LCRPGR, and their findings indicate a positive trend towards improved efficiency in national-level urbanization²⁰. Additionally, Estoque et al. evaluated global land use efficiency at the country level by utilizing data from the Global Human Settlement Layer (GHSL)²¹. Schiavina et al. depicted the profile of the LUE across several territorial scales between 1990 and 2015, highlighting diverse development trajectories and the land take efficiency of different human settlements¹⁹. In a later study, Schiavina et al. investigated the global pattern and evolution of development trajectories of land use efficiency of functional urban areas (FUA), using population and built-up area data extracted from the GHSL dataset²².

As LUE has become a fundamental tool in global policy evaluation and formulation, the uncertainties associated with it—stemming from both input data and error propagation during indicator calculations—urgently require in-depth examination. There has been considerable analysis and comparison of uncertainties in global built-up area and population data, confirming they are subject to substantial uncertainties from both interpretation/allocation models and source data errors^{23,24,25,26,27,28,29}. However, little research has been conducted on uncertainty propagation analysis or sensitivity assessment in the context of LCRPGR calculations. In fact, the complex operations involved in LCRPGR calculations—such as logarithmic transformations and division—are likely to amplify data sources uncertainties according to error propagation laws, potentially compromising the reliability of the results. Consequently, trend estimations based on simplistic inter-annual LCRPGR comparisons may become unreliable due to these compounded uncertainties. Furthermore, the LCRPGR metric fails to incorporate absolute increments or current urban land use conditions, which could lead to incomplete or systematically biased assessments. This oversight may disproportionately disadvantage low-income cities in policy evaluations.

To address these challenges, this study conducts a series of tests to examine uncertainties arising from data sources, LUE calculations, and trend estimation. We then estimate refined global LUE patterns from 1985 to 2020 using rigorously evaluated datasets, LUE metrics, analytical scales, and trend estimation methods. Through these comprehensive, context-specific investigations, we aim to assess LUE trends across global urban systems in a reliable, rational, and equitable manner. The study’s new findings provide a basis for crafting targeted policy suggestions to improve LUE in varied urban settings.

Results

Uncertainty analysis of LUE indicators

First, we test the sensitivity of LCRPGR to minimum population change and data errors at the provincial level, where downscaling errors of population data can be neglected. When examining the maximum absolute LCRPGR values, 49.5% of provinces have at least one value exceeding 10, indicating that LCRPGR frequently reaches high values due to minimal population changes. Consequently, LCRPGR can vary sharply between efficient and inefficient land use ranges, leading to completely opposite LUE judgments despite negligible population changes. Fig. 1b reveals that at least two sharp transitions occur in 1,130 provinces, with several hundred provinces experiencing three or more transitions. These frequent fluctuations make it difficult to establish reliable LUE estimates or discern long-term trends, as demonstrated in Fig. 1c. When introducing minor errors to population data, dramatic changes in LCRPGR values are observed (Fig. 1d). This high sensitivity to errors indicates that the method cannot produce reliable assessments with estimated population data or the derived built-up land data.

Fig. 1: The sensitivity tests of LCRPGR.

a The maximum absolute LCRPGR for each province during the study period. b The frequency of provinces that experienced multiple sharp changes in LCRPGR. c Samples exhibiting multiple sharp changes. d The sensitivity to minor random errors. In (d) the red point represents the reference LCRPGR, while the cyan points indicate values generated by incorporating random errors ($\mu =1$ and ${\sigma }^{2}=0.01$).

In contrast, the BUP curves of provinces show no sharp changes (Fig. 2c), indicating that long-term trends can be more easily estimated from them. Furthermore, random errors have negligible impact on ${{{{\rm{BUP}}}}}_{{{{\rm{grow}}}}}$ (Fig. 2d), demonstrating its robustness to data inaccuracies. However, slight BUP fluctuations in Fig. 2c suggest that data noise or short-term variations may still affect BUP calculations to some degree. Therefore, trend estimation methods are required to mitigate the influence of sporadic outliers and obtain more robust trend estimates. When applying the MK tests and Sen’s slope, a clear monotonic trend is observed in 3,654 provinces (79.5% of the total), providing reliable assessment of their long-term progress toward SDG targets (Fig. 2a).

Fig. 2: Sensitivity tests of BUP.

a Trend assessment using Mann-Kendall tests and Sen’s slope. b. The median ${{{{\rm{BUP}}}}}_{{slope}}$ of 15 countries. c. BUP curves of samples. d Error sensitivity of ${{{{\rm{BUP}}}}}_{{grow}}$. In Panel a, gray indicates insignificant change or missing data. The samples in (c, d) are the same as those in Fig. 1c and Fig. 1d, respectively. ${{{{\rm{BUP}}}}}_{{slope}}$ represents the results of the MK test and Sen’s slope.

To assess the impacts of uncertainty introduced by population data gridding (from census units to 1 km grids), we analyze BUP variations across adjacent cities. Notably, many provinces simultaneously exhibit both extremely low (< 50 m²per person) and high (> 400 m²per person) city-level LCRPGR values (Fig. 3d, 3h, 3i). This pattern is clearly implausible since, theoretically, BUP within homogeneous context should not vary so dramatically, and developing regions cannot realistically reach developed-country levels. Notably, similar discrepancies exist in North America and Australia, though the lack of classification beyond >400 m²per person in the visualization masks these differences. These variations stem from uncertainties in both impervious surface extraction algorithms and population data rasterization processes, making city-scale BUP calculations fundamentally unreliable. While some existing studies calculate BUP or LCRPGR at city scales, their analyses typically aggregate results to national levels to mitigate errors. Since provincial population statistics are more reliable and impervious surface data (as the denominator) contribute less to computational errors, we recommend using provincial units for BUP analysis. This approach can better balance spatial granularity with analytical reliability.

Fig. 3: BUP of global cities in 2020.

a The BUP of approximately 8000 cities. b–i Enlarged regional details corresponding to (a). Due to BUP’s lower sensitivity to errors, this study employs it to assess the reliability of LUE calculations at the city level.

LUE assessment using BUP metrics

Based on the above uncertainty analysis, we preferred to estimate the global LUE trend using BUP metrics at the provincial level. The MK test and Sen’s slope indicate that only 215 provinces (4.7%) experienced a BUP decrease (${{{{\rm{BUP}}}}}_{{slope}}$ < 0 m², primarily concentrated in Africa and Western Asia (Fig. 2a). 1,328 provinces (28.9%) showed ${{{{\rm{BUP}}}}}_{{slope}}$ values between [0,5] m², mainly distributed across Africa and South-Central Asia. Another 661 provinces (14.4%) exhibited ${{{{\rm{BUP}}}}}_{{slope}}$ values within [5,10] m², with widespread distribution across all regions. Meanwhile, 1,453 provinces (31.6%) demonstrated ${{{{\rm{BUP}}}}}_{{slope}}$ values exceeding 10 m², predominantly located in North America, Europe, East Asia, and the Pacific region. Overall, North America and Europe displayed higher ${{{{\rm{BUP}}}}}_{{slope}}$ values than other regions, followed by East Asia and the Pacific. Latin America, Western Asia & North Africa, and Sub-Saharan Africa showed intermediate values, while South Asia recorded the lowest ${{{{\rm{BUP}}}}}_{{slope}}$ values. Figure 2b also indicates that economically developed or rapidly developing countries (e.g., United States, France, Japan, China) exhibit faster ${{{{\rm{BUP}}}}}_{{slope}}$ growth, while low- and middle-income countries (e.g., India, Philippines, Egypt, Ethiopia) show relatively slower ${{{{\rm{BUP}}}}}_{{slope}}$ increases.

Figure 4 illustrates 430 provinces (9.4%) exhibited a ${{{{\rm{BUP}}}}}_{{grow}}$ > 1.3, primarily observed in Sub-Saharan Africa, followed by East and Southeast Asia (Fig. 4). A total of 1547 provinces (33.96%) had a ${{{{\rm{BUP}}}}}_{{grow}}$ between 1.1 and 1.3, widely distributed across Sub-Saharan Africa and Asia. Meanwhile, 1,687 cities (36.71%) had a ${{{{\rm{BUP}}}}}_{{grow}}$ below 1.1, mainly found in North America and Europe, followed by South America and Western Asia. Consequently, when focusing solely on growth rate, global LUE evaluations primarily attribute inefficient land use to Sub-Saharan Africa and Asia. A similar conclusion can be drawn from LCRPGR, as it also considers only the growth rate.

Fig. 4: Global distribution of BUP in 2020 and median BUP_grow from 1985 to 2020.

BUP (2020) is classified into ranges: [0, 100), [100, 200), [200, 400), and ≥400. ${{{{\rm{BUP}}}}}_{{grow}}$ is categorized as: <1, 1–1.1, 1.1–1.3, and >1.3.

Figure 4 also shows that 1,244 provinces (27.1%) had a BUP below 50 m² per person, primarily located in Sub-Saharan Africa, South Asia, and Southeast Asia. Additionally, 873 provinces (19.0%) had a BUP between 50 and 100 m² per person, widely distributed across the Global South. Another 981 provinces (21.3%) had a BUP ranging from 100 to 200 m² per person, mainly concentrated in Latin America, Eastern Europe, and East Asia. Meanwhile, 979 provinces (21.3%) had a BUP between 200 and 400 m² per person, predominantly found in Europe, North America, and North Africa. Finally, 298 provinces (6.5%) had a BUP exceeding 400 m² per person, mostly in North America, Australia, and Western Europe. Generally, developed countries (e.g., the USA, France, and Japan) exhibit substantially higher BUP values (>300 m² per person) than developing countries (e.g., China, Mexico, and Brazil), while the least developed regions (e.g., Nigeria and Ethiopia) have the lowest BUP (< 50 m² per person). If land use efficiency is considered in terms of urban land per capita, developed countries are the least efficient.

Notably, the study clearly reveals variations between provinces within countries. For example, in the United States and Australia, eastern states exhibit higher ${{{{\rm{BUP}}}}}_{{slope}}$ and ${{{{\rm{BUP}}}}}_{{grow}}$, whereas in China, eastern provinces show a higher ${{{{\rm{BUP}}}}}_{{slope}}$ but lower ${{{{\rm{BUP}}}}}_{{grow}}$ compared to their western counterparts (Figs. 2, 4)). These findings provide finer spatial details than national-level statistics while maintaining strong reliability.

Socio-economic influences

We further investigated the influence of socio-economic development on LUE trends. The country-level analysis results are presented in Fig. 5, while provincial-level analyses for the U.S., China, and India are shown in Fig. 6. To minimize errors, countries or provinces with populations below 1 million were excluded from the analysis.

Fig. 5: Country-level analysis.

a–c Correlation between GDP per capita and BUP metrics. d–f Correlation between population and BUP metrics. Here, “slope” represents long-term trends estimated using the Mann-Kendall (MK) test and Sen’s slope estimator, while “Growth” refers to the rate calculated using these slope values. Countries are classified by World Bank income group.

Fig. 6: Province-level analysis in selected countries.

a–c Correlation between GDP per capita and BUP metrics. d–f Correlation between population and BUP metrics.

In Fig. 5a, distinct disparities in per capita GDP are evident across income groups, with minimal overlap. Although some overlap exists in 2020 BUP values, the overall distribution aligns with income levels—higher-income countries generally exhibit higher 2020 BUP. Fig. 5b reveals that ${{{{\rm{GDP}}}}}_{{slope}}$ and ${{{{\rm{BUP}}}}}_{{slope}}$ also follow income-based trends, with wealthier nations showing greater absolute growth. Notably, upper-middle-income countries approach high-income levels in ${{{{\rm{BUP}}}}}_{{slope}}$, while certain lower-middle-income countries also demonstrate relatively high ${{{{\rm{BUP}}}}}_{{slope}}$. Both figures highlight stark inequalities: low-income countries score poorly across all metrics, lagging far behind high-income nations. The only higher performance metric in low-income countries is ${{{{\rm{BUP}}}}}_{{grow}}$; however, this may be attributed to inefficient land use. Fig. 5d and e demonstrate that countries with higher 2020 BUP and ${{{{\rm{BUP}}}}}_{{slope}}$ typically have smaller populations and slower population growth, with few exceptions (e.g., the U.S.). Conversely, Fig. 5f shows that lower-income countries tend to have higher ${{{{\rm{POP}}}}}_{{grow}}$ and ${{{{\rm{BUP}}}}}_{{grow}}$, while higher-income countries score lower on both metrics. Additionally, the range of provincial-level indicators and their interconnections within representative countries are visually demonstrated in Fig. 6a–f. The variability in LUE metrics and their socio-economic influences across nations and provinces underscores the limitations of relying on single indicators or simplistic analyses, as such approaches may lead to biased conclusions.

Discussions

In the era of big data, the proliferation of diverse geospatial data sources has introduced substantial challenges: (1) selecting high-quality, applicable data from heterogeneous sources, and (2) reliably utilizing these data while minimizing uncertainty—both inherent in the data sources themselves and arising from subsequent calculations or modeling processes³⁰. Notably, while existing studies typically examine general uncertainty using statistical indicators (e.g., means, standard deviations, maximum absolute values, and correlation coefficients), uncertainties related to specific characteristics—such as object definitions, processing methods, spatial distributions, and spatiotemporal scales—are rarely considered in practical applications²⁸.

For instance, new data sources often feature improved spatial resolution (e.g., population data downscaled to 1-km grids), however, this apparent precision frequently masks increased uncertainty. Gridded population datasets inherit uncertainties from source data and modeling approaches, compromising their reliability in fine-scale analyses²³. Moreover, validation remains challenging due to the lack of ground-truth population data at the 1 km scale. Existing validations are typically limited to specific countries or urban areas with abundant reference data. In contrast, spatially heterogeneous rural regions suffer from data scarcity and methodological constraints, leading to critically understudied accuracy and reliability²⁹—a gap that also applies to other datasets, such as impervious surfaces in sparsely populated areas²⁷.

Comparative analyses of geospatial datasets remain scarce, and even fewer studies examine the propagation or amplification of dataset uncertainties. In the context of land use efficiency (LUE) assessment, the UN-Habitat guidelines recommend LCRPGR as the primary indicator¹². Many studies rely on remote sensing-derived urban area data and gridded population datasets as key inputs^21,22. Despite extensive research, the uncertainty in LUE assessments—stemming from data inconsistencies and indicator choices—has rarely been investigated. Consequently, the reliability and accuracy of most findings remain unclear.

In this study, we conducted a series of tests to examine these issues and found that the LCRPGR—which involves multiple divisions and logarithmic operations—has the potential to amplify errors, leading to biased assessments and trends. Additionally, city-level analysis is substantially affected by population allocation errors. To enhance the reliability, this study adopts the following approaches: (1) incorporating BUP alongside its growth rate and absolute increments for a robust and comprehensive evaluation; (2) using provinces as the unit of analysis to reduce spatial inaccuracies while maintaining fine-scale; (3) applying the MK test and Sen’s slope estimator mitigates the impacts of uncertainty and identifies reliable trends.

The study revealed that a substantial majority (79.6%) of global provinces have undergone a significant increase in BUP, as supported by previous studies^31,32. Anticipating population growth, projections indicate that the overall global urban land area could surge by a factor of 1.8–5.9, and the BUP could rise by a factor of 1.1–4.9, under various socioeconomic scenarios throughout the century³³. This prevailing global trend poses a challenge in enhancing land use efficiency required by SDG which specifically advocates for BUP maintenance or decline. The increase in BUP stems primarily from growing demand for larger living spaces and the financial capacity to accommodate this demand. This is underscored by a significant positive correlation between BUP change and GDP per capita growth (Figs. 5, 6). Specifically, provinces in developed regions, with greater financial capabilities, can expand urban areas more extensively, resulting in higher BUP and faster growth³². Conversely, provinces in low-income regions generally face financial constraints, leading to lower BUP and smaller increments.

Substantial and widening disparities in BUP across countries are observed in the study, which aligns to some extent with existing studies^34,35,36. These variations stem from multiple factors, including economic conditions, land-use policies, and divergent urbanization processes. In sub-Saharan African countries, urbanization is driven less by economic development and more by factors such as civil conflicts, political instability, ethnic tensions, and momentum effects³⁷. South Asian urbanization is primarily fueled by rural-to-urban migration. Both regions struggle to accommodate these population inflows due to limited financial resources, leaving millions trapped in poverty and confined to informal settlements. Meanwhile, cities in high-income nations benefit from stronger economic foundations, which enable residents to access proper housing.

The substantial disparities raise concerns about the feasibility and equity of applying uniform indicators and criteria in the United Nations’ SDG guidelines. The existing indicators (e.g., LCRPGR) focus solely on growth rates while neglecting basic living conditions. The existing criteria inadvertently permit high-income cities to maintain unsustainable low-density sprawl—a pattern known to exacerbate habitat loss and climate emissions. Second, cities in rapidly developing middle-income countries, such as China and India, have been criticized for very low land-use efficiency due to their high growth rates^19,21,22. However, their increment and ultimate values of BUP remain lower, particularly in South Asian countries, where BUP accounts for less than one-tenth of that in high-income countries. Many residents still live in informal settlements (e.g., “slums” or “urban villages”), which may not necessarily be more compact³⁸. While high-rise residential construction could improve living space and reduce land consumption, affordability constraints persist in many cities. Third, the only higher performance metric in low-income countries is the BUP growth rate, primarily due to the small baseline value. However, this may reflect inefficient land use rather than progress. The modest BUP slope suggests that these cities still struggle to improve—or even maintain—extremely limited living space, especially given the impracticality of constructing high-rise buildings. Moreover, strict adherence to SDG requirements in these regions could hinder efforts to enhance living conditions. Such criteria are not only unrealistic but also inequitable.

Given that urbanization directly or indirectly influences most of the SDG targets³⁹, the substantial variation in BUP presents formidable challenges for sustainable development. In addition to disparities among countries, disparities within countries are also noteworthy. Filling this gap demands a substantial global consumption of construction materials and natural land, subsequently leading to an increase in greenhouse gas emissions and environmental degradation. This concern is particularly relevant when considering that the top BUP still continues to increase, leading to widening gaps. In this century, although the most rapid urban land expansion is anticipated to occur in Africa and Asia, the developed world continues to experience a substantial amount of new development³³. This trend intensifies the demand for land for incoming urban residents, surpassing the current total amounts of global built-up infrastructure, even under the assumption of no population growth. Given this, further investigation is imperative to identify efficient, effective, and economical solutions for mitigating BUP inequality in a manner aligned with Sustainable Development Goals.

Methods

Datasets

Built-up and population data are fundamental for calculating LUE indicators. Within the context of SDG Indicator 11.3.1, built-up areas are defined as all impervious surfaces occupied by buildings and infrastructure. Impervious surfaces serve as both direct manifestations of human-modified landscapes and critical parameters for urbanization monitoring and environmental assessment⁴⁰. Landsat data, with over 50 years of observations, have supported long term global impervious surface products like GISA⁴¹, GAIA⁴², GlobeLand30⁴³, GAUD⁴⁴ and GHSL⁴⁵. While all datasets depict a rapidly urbanizing world—with global urban land area nearly tripling since 1985—substantial discrepancies persist among the estimates due to variations in scale, differing urban definitions, and methodological approaches²⁸. Accuracy assessments across 45 global cities using ZY-3 samples show GISA achieves the highest overall accuracy (OA = 88.56%), followed by GAUD (88.06%), GAIA (86.03%), and GHSL (83.72%)²⁷. This superior performance of GISA has been further corroborated by other studies^46,47.

Several 1 km global population products have been released, including the Gridded Population of the World (GPWv4.11) provided by the Center for International Earth Science Information Network (CIESIN)⁴⁸, the Global Human Settlement Population Layer (GHS-POP) provided by the European Commission Joint Research Centre (JRC)⁴⁹, LandScan from Oak Ridge National Laboratory (https://landscan.ornl.gov/), and the WorldPop datasets⁵⁰. The production process of gridded population products essentially involves redistributing population estimates from census or administrative units to potential human settlement grids. Crucially, uncertainties from census data, ancillary data (e.g., built-up area), data processing stages are not isolated but rather propagate through conversion, integration, and other steps, forming an intricate error chain that is difficult to trace²³.

Studies based on non-administrative units have demonstrated significant uncertainties in gridded population datasets. Láng-Ritter et al. systematically validated global gridded population data in rural areas, revealing substantial negative biases: −53% (WorldPop), −65% (GWP), −67% (GRUMP), −68% (LandScan), and −84% (GHS-POP)²⁹. A pixel-level evaluation in Sweden showed that WorldPop, GPWv4, and GRUMP correctly identified only 18% of cells as populated or unpopulated on average, whereas GHS-POP and LandScan achieved 78% and 81% accuracy, respectively⁵¹. In contrast, comparisons based on census units indicate strong correlations between all gridded population data and official statistics (R² ≈ 1)^25,52. Therefore, for applications requiring precise population data (such as land use efficiency calculations), original census units should be used instead of urban boundaries that are independent of statistical units (e.g., GUB)⁵³ to ensure reliability.

GDP per capita, a critical indicator of economic development, is an important factor influencing urban land use efficiency. However, gridded GDP data - produced through methodologies similar to population grids^54,55 - are subject to comparable uncertainties. Crucially, when deriving GDP per capita by combining two such spatial datasets, these uncertainties become compounded. Therefore, for applications requiring precise data, original census units should be prioritized over urban boundaries that lack statistical unit correspondence.

Notably, the accuracy differences among the datasets are minor (e.g., ~1%), so selecting one over another (when comparable) has little impact on the results. What matters more is how the data are used—particularly the formulas applied—as flawed methodologies can propagate or even greatly amplify errors.

LUE indicators

Within the UN 2030 Agenda, SDG 11.3 seeks to promote inclusive and sustainable urbanization while strengthening capacities for participatory, integrated, and sustainable human settlement planning and management across all countries by 2030¹⁰. In alignment with this objective, UN-Habitat established SDG Indicator 11.3.1 (LCRPGR) as the core metric for evaluating land-use efficiency^11,12. The LCRPGR is calculated as follows

$${{{\rm{L}}}}{{{\rm{CRPGR}}}}={{{\rm{LCR}}}}/{{{\rm{PGR}}}}$$

(1)

Here, LCR denotes Land Consumption Rate, and PGR represents Population Growth Rate, which are calculated as follows:

$${{{\rm{LCR}}}}={{{\mathrm{ln}}}}({{{\rm{UrBU}}}}_{{{{\rm{t}}}}2}/{{{{\rm{UrBU}}}}}_{{{{\rm{t}}}}1})/y$$

$${{{\rm{PGR}}}}={{{\mathrm{ln}}}}({{{\rm{POP}}}}_{{{{\rm{t}}}}2}/{{{{\rm{POP}}}}}_{{{{\rm{t}}}}1})/y$$

Where ${{{{\rm{U}}}}{{{\rm{rBU}}}}}_{{{{\rm{t}}}}1}$ and ${{{{\rm{U}}}}{{{\rm{rBU}}}}}_{{{{\rm{t}}}}2}$ refer to the total built-up area at times ${{{\rm{t}}}}1$ and ${{{\rm{t}}}}2$, respectively$.\,{{{{\rm{P}}}}{{{\rm{OP}}}}}_{{{{\rm{t}}}}1}$ and ${{{{\rm{P}}}}{{{\rm{OP}}}}}_{{{{\rm{t}}}}2}$ denote the total urban population at times ${{{\rm{t}}}}1$ and ${{{\rm{t}}}}2$, respectively. y stands for the number of years between t1 and t2. According to UN-Habitat guidelines, 0 < LCRPGR < 1 indicates efficient land use, as it means built-up areas grow more slowly than the population. An LCRPGR > 1 suggests inefficient LUE due to built-up areas growing faster than the population, while an LCRPGR < 0 indicates inefficient LUE resulting from population decline.

Using this indicator, previous studies have assessed LUE at multiple scales, including individual cities^14,15,16,17, larger geographical regions^18,20, and even global analyses^19,22. However, its mathematical formulation - combining logarithmic and division operations - renders it acutely vulnerable to source data inaccuracies. When population change is minimal (i.e., when ${{{{\rm{P}}}}{{{\rm{OP}}}}}_{{{{\rm{t}}}}2}$ is nearly equal to ${{{{\rm{P}}}}{{{\rm{OP}}}}}_{{{{\rm{t}}}}1}$), the PGR approaches zero, resulting in an extremely large LCRPGR. In such cases, even minor errors in population data can lead to substantial misjudgments. This dramatic variation makes it difficult to determine a reasonable confidence interval for LUE assessment, potentially leading to entirely opposite conclusions. While SDG Indicator 11.3.1 guidelines require accurate data for calculations, large-scale studies often face challenges as they typically rely on global estimated data.

Additionally, UN-Habitat recommends built-up area per capita (BUP) as a metric to measure the average built-up area allocated per person in an urban area for a given analysis year¹². The BUP is calculated by dividing the total built-up area by the corresponding urban population within a city or urban area for a specific year, using the following formula:

$${{{{\rm{BUP}}}}}_{t}={{{{\rm{UrBU}}}}}_{t}/{{{{\rm{POP}}}}}_{t}$$

(2)

Where ${{{{\rm{U}}}}{{{\rm{rBU}}}}}_{{{{\rm{t}}}}}$ and ${{{{\rm{P}}}}{{{\rm{OP}}}}}_{{{{\rm{t}}}}}$ refer to the total built-up area and total urban population of a city at times ${{{\rm{t}}}}$, respectively$.\,$BUP has been used to quantify the relationship between urban land consumption and population in numerous studies^31,32,34. Temporal variations in BUP further enable evaluation of whether built-up area expansion outpaces or lags behind population growth, similar to LCRPGR. Indeed, the BUP growth rate can be mathematically formulated in a manner analogous to LCRPGR, as demonstrated below:

$${{{{\rm{BUP}}}}}_{{grow}}={{{{\rm{BUP}}}}}_{t2}/{{{{\rm{BUP}}}}}_{t1}=(\frac{{{{{\rm{UrBU}}}}}_{t2}}{{{{{\rm{POP}}}}}_{t2}})/(\frac{{{{{\rm{UrBU}}}}}_{t1}}{{{{{\rm{POP}}}}}_{t1}})=(\frac{{{{{\rm{UrBU}}}}}_{t2}}{{{{{\rm{UrBU}}}}}_{t1}})/\left(\frac{{{{{\rm{POP}}}}}_{t2}}{{{{{\rm{POP}}}}}_{t1}}\right)$$

(3)

Due to their similar form, ${{{{\rm{BUP}}}}}_{{grow}}$ can serve as a substitute for LCRPGR to some extent. For instance, values of 0 <${{{{\rm{BUP}}}}}_{{grow}}\,$< 1 indicate efficient urban land use (analogous to LCRPGR), while ${{{{\rm{BUP}}}}}_{{grow}} > 1$ suggests inefficient land use where built-up areas expand faster than population growth. Notably, ${{{{\rm{BUP}}}}}_{{grow}}$ does not significantly amplify data source errors since it avoids logarithmic operations. For instance, consider a city with one million population and 100 km² built-up area that experiences an actual increase of 100 people and 1 km² in built-up area: the true PGR would be 0.0001 and LCRPGR would be 100. However, if gridded population data inaccurately shows a decrease of 100 people, the PGR becomes −0.0001 and LCRPGR drops to −100. Regarding BUP, accurate data yield ${{{{\rm{BUP}}}}}_{t2}$ = 100.1 m²per person and ${{{{\rm{BUP}}}}}_{{grow}}$ = 1.001, biased population data produce only slight deviations to 101.01 m²per person and 1.010.

Beyond this, the increment in BUP can also quantify changes in the relationship between urban land consumption and population, reflecting additional dimensions of urban land use efficiency.

$${{{{\rm{BUP}}}}}_{{slope}}={{{{\rm{BUP}}}}}_{t2}-{{{{\rm{BUP}}}}}_{t1}$$

(4)

BUP metrics possess clear physical meanings and can comprehensively reflect multiple aspects of the urban land-population relationship. In contrast, the logarithmic transformations involved in LCRPGR render it both error-sensitive and lacking in intuitive physical meaning. Furthermore, this indicator exclusively measures growth rates while failing to account for either static conditions or absolute magnitude changes, potentially resulting in incomplete or skewed assessments.

Uncertainty analysis

Big data has emerged as a cutting-edge tool for addressing global challenges—from climate change mitigation to sustainable urban development⁵⁶. The accurate and precise interpretation of big data is critical, necessitating a thorough understanding of the uncertainties inherent in such analyses³⁰. A deeper comprehension of uncertainties in big data will unlock the full potential of datasets and analytical research, driving progress in both theoretical and applied studies⁵⁷. These uncertainties stem from multiple factors, including the definition of research objectives and boundaries, as well as the entire workflow of data collection, processing, and analysis. They hinder our ability to leverage big data effectively for scientific decision-making and accurate predictions. In principle, every measurement should be accompanied by an uncertainty assessment. Yet, in many applications, researchers often analyze collected or self-generated data without accounting for source data uncertainties (which frequently exhibit less than 80% accuracy) or the propagation—and potential amplification—of uncertainties during analysis. Even dedicated uncertainty analyses tend to focus on observational datasets (e.g., buildings and population)^25,27,29,51, while the propagation or magnification of uncertainties through LUE indicator calculations remains understudied.

This study designed a series of tests to address these challenges. First, we examine the extreme values and sharp changes—the sudden transitions between efficient and inefficient land use at adjacent time points in indicator curves). Both cases deviate substantially from true conditions and will result in challenges when estimating the trend. An indicator with fewer such cases is considered less sensitive to minimal population changes and potential errors, making it a more reliable metrics. In addition, we introducing random errors into population data (the denominator in both LCRPGR and BUP) to compare the metrics’ error susceptibility. In contrast, minimal changes in the numerator (built-up area) are unlikely to generate extreme errors and are therefore excluded from these tests.

Second, we assess whether the city unit is suitable for LUE evaluation, leveraging the hypothesis that cities within homogeneous regions (e.g., a single province) should exhibit comparable LUE values. For instance, Chengdu’s LUE in Sichuan Province, China, would reasonably cluster around the provincial mean rather than approximate values observed in New York State, USA. A substantial divergence between city-level estimates and provincial statistical averages would quantitatively reveal uncertainties introduced by gridded data. Since provinces (or states) are often the original units used to disaggregate census population²⁹, provincial population data should be more reliable. Totally, 4596 provinces (Sates) are involved in the study. In total, 7875 cities and 4,596 provinces (or states) are included in the study.

In these tests, we used the GISA dataset⁵⁸ to track built-up area changes due to its superior accuracy. Earlier records (1972, 1978) were excluded because their lower accuracy, resulting from poorer image quality. For population data, we selected GHS-POP due to longer temporal alignment with GISA and demonstrated strong correlation (R² ≈ 1) with official statistics at the census unit level²⁵. Regarding GDP data, we utilized the downscaled gridded global dataset⁵⁹, which provides reported subnational GDP per capita values (serving as ground truth).

Robust trend estimation

We employ the Mann-Kendall (MK) test and Sen’s slope estimator to characterize reliable long-term urban LUE trends, rather than relying on simplistic comparisons of discrete time points. At each time point, LUE contains substantial uncertainty from data sources and calculation processes. Direct interannual comparisons risk generating erroneous trend interpretations due to error propagation effects. In comparison, the MK test and Sen’s slope estimator are particularly valuable for obtaining reliable estimates as they are resilient to skewed distributions and outlier contamination. This methodological combination has proven particularly effective across environmental and climatic studies, and we adapt its rigorous analytical capabilities to urban LUE assessment for more reliable land management insights. Specifically, the MK test provides statistical significance assessment (p-value and direction), while Sen’s slope quantifies the actual rate of change, together offering a comprehensive trend analysis framework.

First, we establish the hypotheses: (1) No monotonic trend exists (${{{{\rm{H}}}}}_{0}$); (2) A significant increasing or decreasing trend exists (${{{{\rm{H}}}}}_{1}$). For data pairs (${x}_{i},\,{x}_{j}$) where $i < j$,

$$S={\sum }_{i=1}^{n-1}{\sum }_{j=i+1}^{n}{{\mathrm{sgn}}}\left({x}_{j}-{x}_{i}\right),{where}\,{{\mathrm{sgn}}}\left(z\right)=\left\{\begin{array}{c}1\\ 0\\ -1\end{array}{if}\begin{array}{c}z > 0\\ z=0\\ z < 0\end{array}\right.\,$$

(5)

The variance of $S$ can be calculated as below,

$${{{\mathrm{var}}}}\left(S\right)=\frac{1}{18}(n\left(n-1\right)\left(2n+5\right)-{\sum }_{k=1}^{p}{t}_{k}({t}_{k}-1)(2{t}_{k}+5))$$

(6)

where $p$ is the number of tied groups and ${t}_{k}$ is the size of the k-th tied group.

Then, compute standardized test statistic

$${Z}_{{MK}}=\left\{\begin{array}{c}\frac{S-1}{{{{\mathrm{var}}}}\left(S\right)}\\ 0\\ \frac{S+1}{{{{\mathrm{var}}}}\left(S\right)}\end{array}{if}\begin{array}{c}S > 0\\ S=0\\ S < 0\end{array}\right.$$

(7)

Reject ${{{{\rm{H}}}}}_{0}$ if $\left|{Z}_{{MK}}\right|\ge {Z}_{1-a/2}$ (e.g., 1.96 for $a$=0.05).

For the pairs (${x}_{i},\,{x}_{j}$) where $i < j$, the Sen’s slope $\beta$ is calculated as:

$$\beta ={Median}\left(\frac{{x}_{j}-{x}_{i}}{j-i}\right),\,i=1,\ldots ,\,N$$

(8)