Quantitative Assessment of Drought Impact on Grassland Productivity in Inner Mongolia Using SPI and Biome-BGC

Abstract

Drought poses a severe threat to grassland biodiversity and ecosystem function. However, quantitative frameworks that capture the interactive effects of drought intensity and duration on productivity remain scarce, limiting impact assessment accuracy. To bridge this gap, we developed and validated a novel hybrid modeling framework to quantify drought impacts on net primary productivity (NPP) across Inner Mongolia’s major grasslands (1961–2012). Drought was characterized using the Standardized Precipitation Index (SPI), and ecosystem productivity was simulated with the Biome-BGC model. Our core innovation is the hybrid model, which integrates linear and nonlinear components to explicitly capture the compounded, nonlinear influence of combined drought intensity and duration. This represents a significant advance over conventional single-perspective approaches. Key results demonstrate that the hybrid model substantially outperforms linear and nonlinear models alone, yielding highly significant regression equations for all grassland types (meadow, typical, desert; all p < 0.001). Independent validation confirmed its robustness and high predictive skill (NSE ≈ 0.868, RMSE = 20.09 gC/m²/yr). The analysis reveals two critical findings: (1) drought duration is a stronger driver of productivity decline than instantaneous intensity, and (2) desert grasslands are the most vulnerable, followed by typical and meadow grasslands. The hybrid model serves as a practical tool for estimating site-specific productivity loss, directly informing grassland management priorities, adaptive grazing strategies, and early-warning system design. Beyond immediate applications, this framework provides a transferable methodology for assessing drought-induced vulnerability in biodiverse ecosystems, supporting conservation and climate-adaptive management.

1. Introduction

Drought is one of the most widespread and extensive natural disasters affecting human society [1,2,3,4]. Current interference patterns and global changes have significantly impacted ecosystem resources, severely affecting ecosystem productivity [5,6,7] and drawing widespread attention from countries worldwide. China is particularly vulnerable to frequent droughts, especially in arid and semi-arid regions [8,9,10,11]. Currently, drought impact evaluations primarily focus on agriculture, including crop production and livestock [12,13], while research on other critical dimensions, particularly those related to ecological resilience, socioeconomic vulnerability, and urban water security, remains limited [14,15], despite their fundamental importance for sustainable land management and ecosystem conservation.

Within ecological studies, recent research has increasingly examined climate change impacts from a functional perspective. Substantial efforts have been made to quantify the effects of drought on ecosystem productivity [16,17,18,19,20,21], with a particular emphasis on terrestrial net primary productivity (NPP) as a key indicator [22,23,24,25]. For instance, Chen et al. employed an ecological process model to analyze drought impacts on ecosystem functions in the southern United States, revealing a 40% NPP reduction under extreme drought conditions [26]. Xie et al. explored the combined effects of drought and drought-flood abrupt alternation on vegetation, revealing that while drought events intensified, the NPP showed an upward trend [27]. Hao et al. examined drought impacts on carbon exchange using long-term observational data from Inner Mongolian grasslands, comparing arid and humid years [28]. Gao et al. utilized land use data and climatic data to drive ecosystem process models, quantitatively estimating the impacts of land use change and climate change on NPP in the cropping–grazing transitional zone in China [29]. Similarly, Peng et al. developed an integrated regression model to assess drought impacts on grassland productivity through precipitation patterns [30]. Lei et al. presented a valuable framework for evaluating the impacts of droughts (single factor) on grassland ecosystems, demonstrating significantly increased NPP losses along a gradient of increasing drought levels [31]. More recently, Luo et al. detected drought-related temporal effects on global NPP, revealing that the effects of drought on vegetation NPP varied according to climate zones and vegetation types [32].

While the studies cited above have significantly advanced our understanding of drought impacts, a critical methodological gap persists. Research has effectively addressed precipitation patterns [30], single drought characteristics [31], and broad spatiotemporal effects [32]. However, models that simultaneously and mechanistically integrate the two defining characteristics of drought—intensity and duration—to quantify their synergistic, nonlinear interaction on ecosystem productivity are notably lacking. Precisely because drought severity is co-determined by intensity and duration, and their impact is cumulative over time, a comprehensive assessment must account for these interactive relationships (Figure 1). To bridge this gap, this study aims to develop a quantitative model that explicitly integrates these dimensions to elucidate drought’s impact on grassland ecosystems.

However, most existing approaches rely on conventional models or isolated correlations, which often fail to capture the nonlinear and cumulative effects arising from the interaction between drought intensity and duration across different ecosystems [33]. Furthermore, rigorous frameworks for validating such integrated assessments in critical yet vulnerable grasslands are scarce.

To directly address this gap, our study has three clear objectives:

• To develop a hybrid quantitative model that explicitly integrates drought intensity and duration to predict productivity (NPP) loss;
• To calibrate and validate this model using ecological process modeling (Biome-BGC) and independent data across major grassland types in Inner Mongolia;
• To apply the model to quantify the relative importance of drought characteristics and identify ecosystem-specific vulnerability gradients.

By achieving these objectives, this work provides a novel, transferable tool for assessing drought impacts, moving beyond single-factor analyses toward a more mechanistic understanding of compounded drought stress.

2. Materials and Methods

2.1. Study Area

Inner Mongolia, situated in northern China (Figure 2), forms the core distribution area of China’s temperate grasslands. Its natural grasslands cover approximately 86.667 million hectares, accounting for about 25% of the nation’s total grassland area. As the dominant natural vegetation, these grasslands are characterized by extensive spatial coverage and high typological diversity [34,35,36], which exhibit a distinct east-to-west zonation pattern shaped by gradients in topography, climate, and soil types. Corresponding to this spatial transition from Chernozem through Chestnut to Brown Calcic soils, three primary grassland ecosystems are distributed: meadow grassland, typical grassland, and desert grassland. These ecosystems support the livelihoods of local pastoral communities while functioning as critical ecological barriers that regulate regional climate, mitigate wind erosion, and stabilize sandy lands [37,38]. Moreover, they harbor high biodiversity, providing essential habitats for a variety of wildlife species. This ecological configuration underpins the region’s indispensable role in sustaining livestock production, maintaining socioeconomic stability, and preserving regional ecological integrity.

2.2. Data

The meteorological data used in this study were obtained from the China Meteorological Data Sharing Network (http://data.cma.cn, accessed on 8 January 2026). These daily records span the period from 1961 to 2012 and are provided at a spatial resolution of 0.25° × 0.25°, meeting the input requirements of the ecological process model applied in this research. The dataset includes maximum temperature (Tmax, °C), minimum temperature (Tmin, °C), average temperature (Tavg, °C), precipitation (Prec, cm), saturated vapor pressure deficit (VPD, Pa), shortwave radiation flux density (Srad, W·m⁻²), and day length (Daylen, s). Drought conditions were characterized using the Standardized Precipitation Index (SPI), which was calculated based on monthly precipitation data.

Soil properties, including sand, silt, and clay contents, as well as soil depth, were derived from the International Soil Reference and Information Center (http://www.isric.org). These soil parameters are considered invariant over the simulation period. Vegetation type information was extracted from the high-resolution 1:1,000,000 Vegetation Atlas of China (http://www.geodata.cn). The potential natural vegetation distribution was assumed constant for the historical climate impact analysis. Nitrogen deposition and atmospheric CO₂ concentration data were obtained from the UK Air Pollution Information System (http://www.apis.ac.uk) and the Mauna Loa Observatory (NASA, Hawaii; http://www.co2now.org), respectively.

Model validation was performed using biomass data compiled from the literature and flux observations obtained from the China Flux Observation Network (ChinaFLUX and COIRAS). Key validation sites included Tongyu (Meadow Steppe), Xilinhot (Typical Steppe), and Sunite Left Banner (Desert Steppe), which represent the three dominant grassland types in Inner Mongolia.

2.3. Methodology

To assess the impact of drought on grassland ecosystem productivity, this study employed an integrated methodology combining flux observations, field measurements, and ecological process modeling. This multi-method approach enables a consistent analysis of ecosystem drought stress from site-level mechanisms to regional and global patterns.

Within this framework, NPP serves as the central quantitative indicator. It reflects the productive capacity of vegetation under natural conditions and indicates the functional integrity of terrestrial ecosystems under environmental stress. As a synthetic measure of ecosystem function, NPP not only captures the overall provisioning capacity of ecosystem services but also provides an integrated response signal to external drivers such as drought.

2.3.1. Drought Identification

The Standardized Precipitation Index (SPI) is commonly used for drought identification. Developed by McKee et al. in 1993 [39], this meteorological drought index is more sensitive to short-term rainfall than the Palmer Drought Severity Index (PDSI) and demonstrates superior spatiotemporal adaptability. The SPI can effectively characterize drought duration and intensity while reflecting drought conditions across different regions and temporal scales, making it valuable for global drought monitoring and forecasting. Compared with other drought indices, the SPI provides a more accurate characterization of drought severity. Since precipitation serves as the primary limiting factor for vegetation growth in Inner Mongolia’s grasslands, and given that global climate and land ecosystem studies examine drought impacts from meteorological perspectives, we selected the SPI for drought event identification in this study.

SPI Calculation: The calculation of SPI involves two main steps. First, long-term precipitation records are fitted to a probability distribution, typically the Gamma distribution. The Gamma probability density function is defined as follows:

$$g(x)={\displaystyle \frac{1}{{\beta }^{\alpha }\Gamma \left(\alpha \right)}}{x}^{\alpha -1}{e}^{-x/\beta } for x>0$$

(1)

where x is the monthly precipitation amount, α > 0 is the shape parameter, β > 0 is the scale parameter, and Γ(α) is the Gamma function. Parameters α and β are estimated from historical precipitation time series using the maximum likelihood method.

Second, the cumulative probability G(x) of the observed precipitation is calculated and then adjusted to account for the probability of zero precipitation (since the Gamma distribution is undefined for x = 0). The cumulative probability is given by H(x) = q + (1 − q)G(x), where q is the probability of zero precipitation. Finally, H(x) is transformed into a standard normal variate Z to obtain the SPI value:

$$\mathrm{S}\mathrm{P}\mathrm{I}=Z={\mathsf{\Phi }}^{-1}\left[H\right(x\left)\right]$$

(2)

where Φ⁻¹ is the inverse of the standard normal cumulative distribution function. This transformation standardizes SPI values across different regions and time scales, enabling consistent interpretation: positive values indicate wetter conditions, while negative values signify drier conditions (drought). An SPI of zero corresponds to the long-term mean precipitation.

We employed SPI at 1-, 3-, 6-, and 12-month scales to represent short-term, seasonal, growth-period, and annual drought conditions, respectively. The selection of these specific scales is grounded in their direct ecological relevance to grassland growth cycles and productivity dynamics in Inner Mongolia.

• The 1-month SPI captures short-term soil moisture stress relevant to vegetation greening-up and leaf expansion at the start of the growing season.
• The 3-month SPI aligns with the critical period of peak biomass accumulation for many grass species, making it sensitive to seasonal droughts that most directly affect yield.
• The 6-month SPI corresponds approximately to the length of the entire growing season in this temperate region, thereby integrating moisture conditions that govern total annual forage production.
• The 12-month SPI reflects the annual water balance, which influences deeper soil water reserves, perennial plant survival, and long-term ecosystem carbon sequestration capacity.

This multi-scale approach allows us to examine how droughts of different temporal extents, from transient moisture deficits to persistent multi-seasonal anomalies, impact grassland productivity. The standard SPI drought classification levels used in this study are presented in

Table 1. Drought classification levels based on the SPI.

SPI Value	Class
SPI > 2.0	Extremely wet
1.5 < SPI ≤ 2.0	Very wet
1.0 < SPI ≤ 1.5	Moderately wet
0 < SPI ≤ 1.0	Mild wet (near normal)
−1.0 < SPI ≤ 0	Mild dry (near normal)
−1.5 < SPI ≤ −1.0	Moderately dry
−2.0 < SPI ≤ −1.5	Severely dry
SPI ≤ −2.0	Extremely dry

.

Operational Definition of Regional Drought Characteristics:

To characterize drought at the regional scale for correlation with modeled grassland productivity, drought intensity and duration were derived from a synthesized monthly SPI series representing the most severe condition across Inner Mongolia.

• Regional Monthly Drought Intensity: For each month, the drought intensity was defined as the minimum SPI value across the study region. This approach captures the spatial extremity of drought stress in any given month.
• Drought Duration: A drought month was identified when the regional monthly drought intensity (i.e., the minimum SPI) was ≤−1.0 (indicating at least moderate drought somewhere in the region). The drought duration for a specific drought episode was then calculated as the number of consecutive months meeting this criterion.
• Drought Episode Identification: A discrete drought episode was considered to have started in the first month of such a consecutive sequence and to have ended in the last month before the regional intensity rose above −1.0. Only episodes with a duration of at least 1 month were considered.
• Episode Intensity Assignment: For each identified drought episode, its overall intensity was characterized by the most severe (minimum) value of the regional monthly drought intensity within that episode.

2.3.2. Productivity Simulation

Biome-BGC Ecosystem Process Model

The Biome-BGC ecosystem process model was employed to simulate ecosystem productivity. This model systematically accounts for the impacts of spatiotemporal variations in grassland vegetation morphology and environmental factors on plant growth, with particular emphasis on the regulatory role of water cycling and moisture availability in carbon assimilation and storage. The model simulated daily productivity changes in grassland ecosystems throughout the growing season under drought conditions, quantitatively characterizing the processes of vegetation growth, development, and yield formation, along with their dynamic responses to progressive drought stress.

Model Calibration and Localization: For model calibration, we used a randomly selected subset (approximately 70%) of the available observational data. This included flux data from the ChinaFLUX network sites and published biomass data. The key parameters calibrated included: the canopy average specific leaf area (SLA), leaf carbon to nitrogen ratio (C:N), fine root C:N, the stomatal conductance slope, the fraction of labile carbon in litter, and the lignin-to-cellulose ratio in litter. The objective was to minimize the difference between simulated and observed NPP and biomass for the calibration periods. This process resulted in a calibrated, localized version of the Biome-BGC model specific to our study region.

Discussion of Uncertainties: Several sources of uncertainty are acknowledged. First, uncertainty arises from the calibrated physiological parameters, although our multi-site calibration aimed to capture representative values. Second, uncertainties in the input meteorological data (spatial interpolation) and soil properties affect the simulated water and nitrogen cycles. Third, the model simplifies certain ecophysiological processes (e.g., dynamic vegetation composition, detailed microbial feedbacks), which may introduce structural uncertainty, particularly under extreme drought conditions outside the calibration range. Despite these uncertainties, the model demonstrated sufficient skill for its intended purpose: to provide a consistent, process-based estimate of drought-induced NPP variations at a regional scale. The flux simulation procedures and input/output parameters of the Biome-BGC model are presented in

Table 2. The input and output parameters of the Biome-BGC model.

Input Data	Parameter Contents	Spatial Resolution	Time Resolution	Output Result
Meteorological data	Daily maximum/minimum/average temperature, precipitation, vapor pressure deficit, shortwave radiation, etc.	Partial to regional/global scale	Daily, monthly, yearly	Annual precipitation, annual average temperature, maximum leaf area index, annual evapotranspiration, annual runoff, annual NPP, and annual net biomass productivity.
Initialization file	Longitude, latitude, altitude, soil depth, CO2 concentration (interannual variation), vegetation type selection, input/output file settings, etc.
Physiological and ecological parameters	Including 44 parameters, such as the carbon-to-nitrogen ratio in leaves, the carbon-to-nitrogen ratio in roots, stomatal conductance, canopy extinction coefficient, canopy specific leaf area, nitrogen content in leaf carboxylase tissue, etc.

.

Quantification of NPP Variations

Following the established framework for quantifying drought impact [31], the core response variable in this study—drought-induced NPP loss (also termed NPP variation)—is defined as the reduction in productivity during a drought year relative to the expected productivity under normal climatic conditions.

The NPP loss (ΔNPP) is calculated as the absolute difference between the long-term average of simulated NPP and the simulated NPP for a specific drought year:

ΔNPP = NPP_long-term_mean − NPP_drought_year (gC/m²/yr)

(3)

NPP_long-term_mean is the arithmetic mean of annual NPP simulated by the Biome-BGC model over the entire study period, representing the expected productivity under average (non-drought) climatic conditions.

NPP_drought_year is the annual NPP simulated for a specific year identified as experiencing drought.

This approach provides a robust metric that isolates the drought-induced component of interannual productivity variability by utilizing a long-term climatological baseline.

2.3.3. Model Validation and Accuracy Evaluation

The calibrated Biome-BGC model was validated against the remaining independent subset of observational data (approximately 30%), which was withheld from the calibration process. Model performance was quantitatively assessed using the following statistical metrics, which evaluate the agreement between simulated values (y_i) and observed values (x_i) across N paired samples:

1. Root Mean Square Error (RMSE): Measures the average magnitude of the prediction errors, giving higher weight to large errors. It is in the same units as the variable.

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{\left(y_i-x_i\right)}^2}$$

(4)

2. Mean Absolute Error (MAE): Measures the average magnitude of errors without considering their direction, providing a linear score.

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N \left|y_i-x_i\right|$$

(5)

3. Nash–Sutcliffe Efficiency (NSE): Assesses the predictive skill of the model relative to the mean of the observations. An NSE of 1 indicates a perfect match, 0 indicates the model is as accurate as the mean of the observed data, and values <0 indicate poorer performance than the mean.

$$\mathrm{N}\mathrm{S}\mathrm{E}=1-{\displaystyle \frac{{\sum }_{i=1}^N {\left(x_i-y_i\right)}^2}{{\sum }_{i=1}^N {\left(x_i-\bar{x}\right)}^2}}$$

(6)

4. Relative Error (RE): Measures the average magnitude of errors relative to the observed values.

$$\mathrm{R}\mathrm{E}={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N {\displaystyle \frac{\left|y_i-x_i\right|}{x_i}}\times 100\%$$

(7)

y_i: the simulated value for the i-th sample.

x_i: the observed value for the i-th sample.

N: the total number of samples in the validation dataset.

$\bar{x}$: the arithmetic mean of the observed values.

This multi-metric approach provides a robust evaluation of the model’s accuracy and reliability for simulating grassland productivity under drought conditions.

3. Results

3.1. Correlation Between Drought Characteristics and NPP Variations

Drought incidents are extreme events characterized by multiple feature variables, including intensity, duration, and impacts (e.g., affected area, population exposure, crop yield reduction, and NPP variations). Therefore, comprehensive drought analysis should focus on three key aspects: intensity, duration, and spatial extent. This study aims to quantify the relationships between drought characteristics (intensity and duration) and NPP loss. We first established the statistical correlations for the three major grassland types in Inner Mongolia: meadow, typical, and desert grasslands (

Table 3. Correlation analysis between NPP variations and drought characteristics (intensity and duration) in meadow grasslands.

			Drought Intensity	Duration	NPP Losses
Pearson correlation coefficient	Drought intensity	Correlation	1	−0.583 **	0.143 **
		Significant	-	0.000	0.000
		N	1920	1920	1920
	Duration	Correlation	−0.583 **	1	−0.309 **
		Significant	0.000	-	0.000
		N	1920	1920	1920
	NPP losses	Correlation	0.143 **	−0.309 **	1
		Significant	0.000	0.000	-
		N	1920	1920	1920
Kendall correlation coefficient	Drought intensity	Correlation	1.000	−0.436 **	0.101 **
		Significant	-	0.000	0.000
		N	1920	1920	1920
	Duration	Correlation	−0.436 **	1.000	−0.241 **
		Significant	0.000	-	0.000
		N	1920	1920	1920
	NPP losses	Correlation	0.101 **	−0.241 **	1.000
		Significant	0.000	0.000	-
		N	1920	1920	1920
Spearman correlation coefficient	Drought intensity	Correlation	1.000	−0.585 **	0.146 **
		Significant	-	0.000	0.000
		N	1920	1920	1920
	Duration	Correlation	−0.585 **	1.000	−0.328 **
		Significant	0.000	-	0.000
		N	1920	1920	1920
	NPP losses	Correlation	0.146 **	−0.328 **	1.000
		Significant	0.000	0.000	-
		N	1920	1920	1920

** The correlation is significant at the 0.01 level (p < 0.01).

,

Table 4. Correlation analysis between NPP variations and drought characteristics (intensity and duration) in typical grasslands.

			Drought Intensity	Duration	NPP Losses
Pearson correlation coefficient	Drought intensity	Correlation	1	−0.648 **	0.155 **
		Significant	-	0.000	0.000
		N	2174	2174	2174
	Duration	Correlation	−0.648 **	1	−0.282 **
		Significant	0.000	-	0.000
		N	2174	2174	2174
	NPP losses	Correlation	0.155 **	−0.282**	1
		Significant	0.000	0.000	-
		N	2174	2174	2174
Kendall correlation coefficient	Drought intensity	Correlation	1.000	−0.517 **	0.124 **
		Significant	-	0.000	0.000
		N	2174	2174	2174
	Duration	Correlation	−0.517 **	1.000	−0.225 **
		Significant	0.000	-	0.000
		N	2174	2174	2174
	NPP losses	Correlation	0.124 **	−0.225 **	1.000
		Significant	0.000	0.000	-
		N	2174	2174	2174
Spearman correlation coefficient	Drought intensity	Correlation	1.000	−0.678 **	0.187 **
		Significant	-	0.000	0.000
		N	2174	2174	2174
	Duration	Correlation	−0.678 **	1.000	−0.304 **
		Significant	0.000	-	0.000
		N	2174	2174	2174
	NPP losses	Correlation	0.187 **	−0.304 **	1.000
		Significant	0.000	0.000	-
		N	2174	2174	2174

** The correlation is significant at the 0.01 level (p < 0.01).

and

Table 5. Correlation analysis between NPP variations and drought characteristics (intensity and duration) in desert grasslands.

			Drought Intensity	Duration	NPP Losses
Pearson correlation coefficient	Drought intensity	Correlation	1	−0.553 **	0.252 **
		Significant	-	0.000	0.000
		N	434	434	434
	Duration	Correlation	−0.553 **	1	−0.533 **
		Significant	0.000	-	0.000
		N	434	434	434
	NPP losses	Correlation	0.252 **	−0.533 **	1
		Significant	0.000	0.000	-
		N	434	434	434
Kendall correlation coefficient	Drought intensity	Correlation	1.000	−0.419 **	0.160 **
		Significant	-	0.000	0.000
		N	434	434	434
	Duration	Correlation	−0.419 **	1.000	−0.306 **
		Significant	0.000	-	0.000
		N	434	434	434
	NPP losses	Correlation	0.160 **	−0.306 **	1.000
		Significant	0.000	0.000	-
		N	434	434	434
Spearman correlation coefficient	Drought intensity	Correlation	1.000	−0.569 **	0.251 **
		Significant	-	0.000	0.000
		N	434	434	434
	Duration	Correlation	−0.569 **	1.000	−0.421 **
		Significant	0.000	-	0.000
		N	434	434	434
	NPP losses	Correlation	0.251 **	−0.421 **	1.000
		Significant	0.000	0.000	-
		N	434	434	434

** The correlation is significant at the 0.01 level (p < 0.01).

).

A central finding emerges from the correlation analyses: across all grassland types, NPP loss exhibited a significantly stronger correlation with drought duration than with drought intensity (p < 0.01 for all reported correlations). This result directly addresses a core objective of our study, providing statistical evidence that drought duration is the primary driver of productivity decline in these ecosystems.

The analyses further revealed two additional consistent patterns:

• Inverse Relationship between Intensity and Duration: Drought intensity and duration were themselves significantly negatively correlated, indicating that longer-lasting droughts tend to have lower peak intensity.
• Spatial Gradient in Correlation Strength: The strength of the correlations, particularly between NPP loss and drought characteristics, followed a clear geographical gradient. They were strongest in desert grasslands and weakest in meadow grasslands, suggesting an increase in ecosystem sensitivity to drought along the west-to-east aridification gradient.

These correlational findings not only establish the primacy of drought duration as a driver but also underscore the necessity of integrating both characteristics. They provide a robust statistical foundation for the development of the quantitative, process-informed evaluation models in the following sections.

3.2. Development of a Quantitative Evaluation Model for NPP Variations

Drought intensity and duration exhibit independent, inclusive, and interactive relationships that may affect grassland ecosystems through separate or combined mechanisms. The quantitative evaluation model for NPP variations was developed through the following steps: (1) initial construction using both linear and nonlinear regression models, followed by (2) application of a hybrid relationship model to assess drought variable impacts on NPP variations.

3.2.1. Linear Evaluation of Drought Impacts on NPP Variations

NPP variations showed linear response relationships with both drought intensity and duration (Figure 3). Significant differences were observed in these linear relationships among total grassland, meadow grassland, typical grassland, and desert grassland, demonstrating grassland-type-dependent responses to drought. The response slopes decreased sequentially from desert to typical to meadow grasslands, indicating progressively reduced drought impacts on NPP.

For total grasslands, the linear regression model of NPP variations with drought intensity and duration is shown in Formula (8), with a correlation coefficient of 0.31 and significance at the 0.001 level.

$$z = 2.28x + 3.024y + 4.278$$

(8)

where z represents NPP variations in total grasslands, x denotes drought intensity, and y indicates duration.

For meadow grasslands, the linear regression model of NPP variations with drought intensity and duration is shown in Formula (9), with a correlation coefficient of 0.32 and significance at the 0.001 level.

$$z= 1.584x + 2.804y + 5.755$$

(9)

where z represents NPP variations in meadow grasslands, x denotes drought intensity, and y indicates duration.

For typical grasslands, the linear regression model of NPP variations with drought intensity and duration is shown in Formula (10), with a correlation coefficient of 0.24 and significance at the 0.001 level.

$$z= 4.034x + 2.386y + 10.156$$

(10)

where z represents NPP variations in typical grasslands, x denotes drought intensity, and y indicates duration.

For desert grasslands, the linear regression model of NPP variations with drought intensity and duration is shown in Formula (11), with a correlation coefficient of 0.554 and significance at the 0.001 level.

$$z= -0.123x + 6.34y - 15.487$$

(11)

where z represents NPP variations in desert grasslands, x denotes drought intensity, and y indicates duration.

3.2.2. Nonlinear Evaluation of Drought Impacts on NPP Variations

Table 3, Table 4 and Table 5 demonstrate that drought intensity and duration are not independent but interact significantly. These findings suggest a potential nonlinear relationship between NPP variations and drought characteristics (intensity × duration). Existing research confirms that NPP responses to drought are typically nonlinear, implying that drought intensity and duration likely interact synergistically to affect ecosystem productivity. The ecological impacts of drought emerge through cumulative effects of intensity over time, supporting our hypothesis of a nonlinear NPP response to combined drought stressors. Further investigation of drought intensity–duration interactions on NPP variations is therefore warranted.

NPP variations were significantly influenced by the interaction between drought intensity and duration (Figure 4). Stronger responses of NPP to drought intensity and duration corresponded to more pronounced NPP variations, demonstrating the compounding effects of these drought characteristics. A nonlinear relationship was observed between NPP variations and drought intensity/duration, with NPP showing progressive changes in response to increasing drought severity. Among grassland types, desert grasslands exhibited the strongest NPP response to drought, while typical grasslands showed the weakest response. For total grasslands (aggregating all three types), the NPP response to drought intensity and duration showed intermediate sensitivity between desert and typical grasslands.

For total grasslands, the nonlinear regression model of NPP variations with drought intensity and duration is shown in Formula (12), with a correlation coefficient of 0.28 and significance at the 0.001 level.

$$z=-0.67x\times y^{1.118}+0.738$$

(12)

where z represents NPP variations in total grasslands, x denotes drought intensity, and y indicates duration.

For meadow grasslands, the nonlinear regression model of NPP variations with drought intensity and duration is shown in Formula (13), with a correlation coefficient of 0.27 and significance at the 0.001 level.

$$z=-0.479x\times y^{1.202}-2.108$$

(13)

where z represents NPP variations in meadow grasslands, x denotes drought intensity, and y indicates duration.

For typical grasslands, the nonlinear regression model of NPP variations with drought intensity and duration is shown in Formula (14), with a correlation coefficient of 0.25 and significance at the 0.001 level.

$$z=-0.973x\times y^{0.911}+0.854$$

(14)

where z represents NPP variations in typical grasslands, x denotes drought intensity, and y indicates duration.

For desert grasslands, the nonlinear regression model of NPP variations with drought intensity and duration is shown in Formula (15), with a correlation coefficient of 0.53 and significance at the 0.001 level.

$$z=-0.236x\times y^{2.02}-2.387$$

(15)

where z represents NPP variations in desert grasslands, x denotes drought intensity, and y indicates duration.

3.2.3. Hybrid Model Evaluation of Drought Impacts on NPP Variations

Both linear and nonlinear drought evaluation models can effectively assess and predict drought impacts on NPP variations to a certain extent, with the combined model demonstrating superior performance over individual models in capturing the average effects of drought intensity and duration. Validation tests using independent datasets confirmed that the hybrid evaluation model more accurately quantifies drought impacts on NPP compared to single-model approaches, justifying the use of this modified integrated framework for assessing drought-NPP relationships.

NPP variations exhibited both linear and nonlinear response relationships with drought intensity and duration within specific ranges (Figure 5). Overall, a hybrid linear–nonlinear relationship best characterized drought impacts on NPP variations. Figure 4 demonstrates that desert grasslands showed the strongest NPP response to drought, while meadow grasslands exhibited the weakest response. Desert grasslands displayed the greatest drought resistance, with NPP responding in an approximately linear fashion to drought progression, though the response rate accelerated from slow to fast, ultimately resulting in the most serious NPP losses. Sample statistics revealed that drought durations exceeding six months consistently caused severe NPP reductions in desert grasslands across all drought intensity levels. In contrast, meadow and typical grasslands initially showed rapid NPP declines that peaked before transitioning to downward trends. Moderate and severe droughts caused relatively greater losses in meadow and typical grasslands due to their higher frequency of occurrence. Meadow grasslands demonstrated relatively weak drought sensitivity, with short-duration severe and extreme droughts demonstrating comparatively minor impacts on NPP. Typical grasslands exhibited enhanced drought sensitivity, with short-duration droughts paradoxically increasing NPP. This may reflect a known ecological phenomenon where mild water stress can reduce leaf area, thereby improving water-use efficiency of the remaining foliage, or trigger a compensatory photosynthetic response upon rehydration.

For total grasslands, the hybrid regression model of NPP variations with drought intensity and duration is shown in Formula (16), with a correlation coefficient of 0.57 and significance at the 0.001 level.

$$z=-4.294x+5.282y+0.001x\times y^{3.84}-14.513$$

(16)

where z represents NPP variations in total grasslands, x denotes drought intensity, and y indicates duration.

For meadow grasslands, the hybrid regression model of NPP variations with drought intensity and duration is shown in Formula (17), with a correlation coefficient of 0.37 and significance at the 0.001 level.

$$z=-1.873x+4.152y+0.007x\times y^{3.081}-2.719$$

(17)

where z represents NPP variations in meadow grassland, x denotes drought intensity, and y indicates duration.

For typical grasslands, the hybrid regression model of NPP variations with drought intensity and duration is shown in Formula (18), with a correlation coefficient of 0.54 and significance at the 0.001 level.

$$z=-8.077x+6.541y+0.121x\times y^{2.02}-22.898$$

(18)

where z represents NPP variations in typical grasslands, x denotes drought intensity, and y indicates duration.

For desert grasslands, the hybrid regression model of NPP variations with drought intensity and duration is shown in Formula (19), with a correlation coefficient of 0.58 and significance at the 0.001 level.

$$z=2.195x+7.698y-6.135x\times y^{-1.366}-20.053$$

(19)

where z represents NPP variations in desert grasslands, x denotes drought intensity, and y indicates duration.

In summary, the hybrid evaluation model more accurately assesses drought impacts on NPP variations, with significantly improved correlation coefficients across all grassland ecosystem types (p < 0.001).

3.3. Model Validation and Accuracy Evaluation

To validate model applicability, we utilized an independent dataset that was excluded from the initial model development. The confusion matrix method was applied to randomly evaluate the accuracy of the hybrid model in assessing NPP losses. Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Nash–Sutcliffe Efficiency (NSE), and Relative Error (RE) were calculated between observed and simulated values across the independent validation sites. Model performance was further quantitatively evaluated by analyzing the distribution patterns of errors between observed and simulated values within specified error intervals.

Overall Validation Metrics:

The hybrid model demonstrated robust predictive performance on the independent validation data. The NSE reached approximately 0.868, indicating that the model explains about 86.8% of the variance in the observed NPP data, which signifies a very good agreement between simulations and observations. The RMSE was 20.09 gC/m²/yr, and the MAE was 21.24 gC/m²/yr, quantifying the average magnitude of prediction errors. The RE was 22.3%. According to the validation standards established by Soler et al., RE values between 20% and 30% are considered acceptable [40], confirming that our evaluation method yields reliable results.

Error Distribution Analysis:

For rigorous validation, we selected completely independent sample data—not involved in the model training process—to evaluate prediction accuracy across three grassland ecosystem types. The distribution of errors is summarized in

Table 6. Error distribution intervals between observed and simulated values.

Error Interval (gC/m2/yr)	0–10	10–20	20–30	30–50	Total
Number	16	12	15	10	53

.

Table 6 demonstrates that 81.13% of data errors fall within the acceptable range of 0–30 gC/m²/yr, which aligns with and complements the aggregated metrics (RMSE, MAE).

Validation for Extreme Droughts:

Furthermore, while the hybrid model was developed using drought impact data with durations ≤ 12 months, its applicability to multi-year droughts (>12 months) was also validated. As shown in

Table 7. Model applicability evaluation for consecutive extreme drought events.

Grassland Type	Drought Intensity	Duration (Month)	Observed Value (gC/m2/yr)	Simulated Value (gC/m2/yr)	The Error (gC/m2/yr)
Meadow grassland	−1.79	15.6	58.567	35.69904	22.86796
Meadow grassland	−2.525	14.5	29.487	25.01667	4.470332
Meadow grassland	−2.88	12	27.495	39.61448	−12.1195
Typical grassland	−1.7881	15.6	133.39	175.0036	−41.6136
Typical grassland	−2.4925	14.25	169.71	180.8234	−11.1134
Typical grassland	−2.515	14.5	229	185.5535	43.44649
Desert grassland	−2.685	12.5	58.565	70.87139	−12.3064
Desert grassland	−2.495	13	53.106	75.07639	−21.9704

, the model yields reasonable errors in estimating NPP changes even for these prolonged events, demonstrating its robustness. Nevertheless, due to the limited sample size of such extreme cases, further validation is recommended to fully ensure model generalizability.

4. Discussion

4.1. Key Findings and Their Novelty

A principal and novel finding of this study is that drought duration, rather than intensity, is the primary driver of grassland productivity decline. Correlation analyses (Table 3, Table 4 and Table 5) reveal that NPP loss exhibits a significantly stronger negative correlation with drought duration than with intensity across all grassland types. This indicates that prolonged water stress inflicts more severe cumulative damage to ecosystems than short-term, intense droughts—a distinction that is often overlooked in assessments focusing solely on precipitation deficits. Furthermore, we identified a distinct sensitivity gradient: desert grasslands are the most vulnerable, followed by typical and meadow grasslands. These findings not only establish drought as a critical factor in NPP variation but also provide a new, nuanced understanding that is crucial for developing accurate quantitative evaluation models. The originality of this work lies in its systematic dissection of these two drought characteristics (intensity vs. duration) and their interactive effects, moving beyond the common approach of treating drought as a monolithic stressor.

4.2. Mechanistic Interpretation and Advancement over Previous Studies

The varied drought responses among different grassland types (Figure 3, Figure 4 and Figure 5) are primarily driven by a regional gradient in water availability, which is further mediated by differences in plant traits and soil properties. As precipitation decreases from east to west, ecosystems become more dependent on limited water and thus more sensitive to drought, a pattern consistent with previous studies [41,42,43,44]. Specifically, meadow grasslands, benefiting from better hydrological conditions and typically deeper, more water-retentive soils (e.g., Chernozems), exhibit a greater buffering capacity through deeper root systems that can access subsurface water reserves.

In contrast, desert grasslands are characterized by a suite of traits that predispose them to high drought sensitivity. These ecosystems typically occur on shallow, coarse-textured soils (e.g., Brown Calcic soils) with low water-holding capacity, which rapidly lose moisture after limited rainfall events. The vegetation often comprises shallow-rooted annuals or stress-tolerant perennials with limited root depth, constraining their access to deeper soil water. Consequently, they rely heavily on recent precipitation and have minimal reserves to buffer against water deficit. This combination of resource-limiting edaphic conditions and constrained plant foraging strategies results in fragile stability and low resilience, making desert grasslands acutely susceptible to severe productivity losses even from prolonged, low-intensity droughts. These patterns reflect distinct survival strategies forged through long-term adaptation to local hydrological environments.

While ecosystem responses to environmental stress are inherently complex and nonlinear, many previous studies have oversimplified them by focusing on linear relationships between NPP and annual precipitation [45,46]. The nonlinearity is supported by ecophysiological evidence, such as the inverted U-shaped curve of photosynthetic rates under soil moisture stress [47,48]. Our study represents a significant methodological advance in explicitly rejecting this simplification. To capture the true complexity, we developed a hybrid model that integrates both linear and nonlinear components, thereby representing the hybrid physiological response of NPP to drought.

The nonlinear relationships captured by our hybrid model likely arise from several key ecological processes. First, threshold effects in plant physiology are common: beyond a certain level of water deficit, stomatal closure becomes severe, photosynthesis declines precipitously, and carbon allocation may shift from growth to maintenance, leading to a disproportionate drop in NPP. Second, prolonged drought can induce plant mortality, particularly of shallow-rooted annuals or drought-sensitive species in desert grasslands, causing a stepwise reduction in ecosystem productivity that linear models cannot capture. Third, changes in community composition over time—such as a shift towards more drought-tolerant species under recurring stress—can alter the ecosystem’s aggregate response function. Finally, soil moisture dynamics exhibit strong nonlinearities; as soil dries, hydraulic conductivity drops sharply, further limiting water availability to plants. While our current model does not explicitly resolve all these fine-scale mechanisms, the success of the nonlinear hybrid formulation underscores the importance of representing such higher-order ecological feedbacks in drought impact assessments.

This hybrid modeling framework is a core contribution of our work, as it provides a robust, transferable tool for quantifying drought impacts that is more mechanistically informed than conventional statistical models. The model’s superiority and reliability are empirically confirmed by its high predictive skill and accuracy on independent validation data. Specifically, it achieved an NSE of approximately 0.868, explaining a large proportion of the variance in observed productivity. The low magnitude of error was evidenced by an RMSE of 20.09 gC/m²/yr and an MAE of 21.24 gC/m²/yr, with a RE of 22.3%, which falls within the acceptable range for ecological models. Furthermore, all fitted regression equations exhibited significantly high correlation coefficients (p < 0.001). This comprehensive suite of validation metrics substantiates the model’s effectiveness across all major grassland types in Inner Mongolia.

4.3. Relevance and Practical Implications

The relevance of our research extends beyond theoretical ecology into practical management and conservation. First, the quantitative models we developed (Equations (12)–(15)) translate standard climatic drought indices (SPI) into tangible metrics of ecosystem function loss (NPP). This provides land managers and policymakers with a directly applicable tool for assessing drought vulnerability across different grassland types, addressing a recognized need for more ecologically grounded decision-support systems [49,50]. Second, the identified sensitivity gradient (desert > typical > meadow) offers a scientific basis for prioritizing conservation resources and adaptive interventions—such as grazing pressure adjustments or restoration efforts—in the most vulnerable regions. This approach aligns with the understanding that building resilience in grassland systems requires tailored strategies rather than one-size-fits-all solutions [51], and is supported by evidence that adaptive management practices can effectively deliver ecosystem services and enhance socio-ecological stability [52]. This is particularly critical for biodiversity conservation, as grassland degradation directly threatens habitat integrity and species diversity [38].

Finally, and most fundamentally, by highlighting the paramount importance of drought duration, our findings advocate for a paradigm shift in drought early-warning and management. Moving beyond the monitoring of short-term rainfall deficits toward the assessment of developing long-term water deficits is essential. This aligns with the evolving concept of “ecological drought,” which emphasizes the cumulative impacts of water shortage on ecosystems over time [53] and requires monitoring frameworks sensitive to cumulative water balance across multiple temporal scales [54]. Our study provides the quantitative evidence and modeling framework necessary to operationalize this shift, thereby enabling more proactive, risk-based, and ecologically informed management strategies.

4.4. Limitations and Future Directions

However, this study has several limitations that should be acknowledged. First, the Biome-BGC model and statistical hybrid approach capture drought–NPP relationships primarily through climate forcing variables such as precipitation-derived SPI, while explicit representation of key ecophysiological mechanisms—including stomatal regulation, shifts in carbon allocation, and belowground microbial feedbacks under prolonged water stress—remains unresolved [55,56,57]. This may limit the model’s ability to predict nonlinear responses or threshold behavior during extreme multi-year droughts.

Second, a significant limitation of this study is the exclusion of anthropogenic factors, particularly grazing intensity and land use/land cover change. In reality, these human activities interact strongly with climatic drivers, often exacerbating or mitigating drought impacts, and jointly shape grassland productivity, structure, and resilience [58,59,60]. Our model estimates, therefore, reflect the potential climatic impacts of drought in a ‘natural’ state, rather than the realized outcomes under the pervasive and varying pressures of livestock grazing and other land management practices. This omission is important because, in many regions, anthropogenic pressures may be the dominant driver of grassland degradation, operating synergistically with drought.

Future studies should prioritize the integration of these critical human drivers through specific, actionable pathways:

• Grazing Integration: Incorporate spatially explicit datasets on livestock distribution (e.g., from statistical yearbooks [38], the Gridded Livestock of the World (GLW) database [61], or regional stocking rate surveys) to dynamically modify key vegetation parameters in process models. Model algorithms could be refined using data from long-term grazing exclusion experiments [62] to better represent biomass removal and plant compensatory growth.
• Land Use Change Integration: Utilize high-resolution remote sensing time series (e.g., Landsat or Sentinel-2 archives) and existing land use/land cover change products (e.g., FROM-GLC [63] or China’s National Land Cover Datasets [64]) to reconstruct historical vegetation transitions. These timelines can be used to dynamically update the land cover and initial state files within the Biome-BGC model across the simulation period.
• Socio-Ecological Coupling: Apply coupled modeling frameworks that formally link ecological process models (like Biome-BGC) with models of human decision-making. For example, agent-based models (ABMs) could simulate herder adaptive behaviors (e.g., mobility, herd size adjustment) in response to drought forecasts and pasture conditions [65], with their collective actions feeding back into the ecological model via modified grazing pressure.

Such integrative approaches are essential for developing more realistic predictions, targeting effective management interventions, and advancing towards a holistic drought-risk early-warning system that accounts for both climatic and socioeconomic forcings.

Third, the regional-scale and decadal-level analysis, while revealing broad spatial patterns, may obscure finer-scale heterogeneity in drought responses related to micro-topography, soil moisture redistribution, and sub-seasonal vegetation dynamics [66,67,68,69]. Consequently, direct application of the model for site-specific management requires further downscaling and validation with higher-resolution data.

Importantly, these limitations do not diminish the validity of our core findings or the utility of our modeling framework. Instead, they chart a clear path for future research: coupling process-based models with multi-source observations (e.g., remote sensing, flux towers), integrating human-activity datasets, and conducting cross-scale assessments. Our study provides the essential foundation and a validated methodological toolkit for the next step toward a more mechanistic and operational drought-risk early-warning system.

5. Conclusions

Based on the drought index SPI and the Biome-BGC ecological process models, this study obtained gridded sample data of drought events and productivity during growing seasons across Inner Mongolia grasslands over the past 50 years. A hybrid evaluation model was developed to assess drought impacts on NPP variations across different grassland types. By integrating drought characteristics (intensity and duration) with NPP responses, the model systematically quantifies their correlations and evaluates per-unit-area NPP variations, with performance validated via a confusion matrix. Compared with conventional methods, the proposed model demonstrates superior accuracy and broader applicability.

Our analysis revealed significant correlations between NPP variations and both drought intensity and duration, along with notable intensity–duration interaction effects. The complex response patterns reflected grassland-type-dependent drought sensitivities. Key findings are as follows: (1) Linear evaluation models demonstrated distinct NPP–drought relationships across grassland types (desert > typical > meadow in slope steepness). (2) The nonlinear evaluation model revealed progressively reduced drought impacts on NPP along the grassland gradient: desert > meadow > typical. (3) Drought intensity–duration interactions exerted the strongest impact on NPP variations in desert grasslands and the weakest in meadow grasslands. The hybrid evaluation model confirmed this sensitivity hierarchy and achieved superior simulation accuracy (NSE ≈ 0.868, RMSE = 20.09 gC/m²/yr, MAE = 21.24 gC/m²/yr, RE = 22.3%), demonstrating that ecosystem-scale drought impacts are ultimately determined by compounded drought severity.