Evaluating statistical downscaling methods for future temperature and precipitation projections in the Qilian mountains

The Qilian Mountains, a crucial ecological security barrier and water conservation region in northwestern China, are highly sensitive to climate change. Reliable climate projections are essential for regional environmental management, yet the performance of statistical downscaling methods in this complex mountainous region remains inadequately evaluated. This study evaluates four statistical downscaling methods—Delta Change Method (DCM), Quantile Mapping (QM), Multiple Linear Regression (MLR), and Random Forest (RF)—using station-based observations (1951–2025) and outputs from 34 CMIP6 climate models. Validation results indicate that RF achieved the highest R 2 and the lowest RMSE for both temperature and precipitation, with superior stability across models, scenarios, and stations. Based on RF downscaling, future climate projections under SSP1–2.6, SSP2–4.5, SSP3–7.0, and SSP5–8.5 indicate a persistent warming and moderate wetting trend throughout the 21st century. Temperature is projected to increase at rates of 0.03 °C–0.31 °C/decade, while precipitation is projected to increase by approximately 3.2%–8.1% by the end of the century, although inter-model uncertainty remains substantial. Future climate change also exhibits pronounced seasonal and spatial heterogeneity, characterized by winter-dominated warming, reduced summer precipitation but increased autumn–winter precipitation, and strong elevation-dependent responses concentrated in high-elevation areas. The 0 °C isotherm is projected to rise by approximately 100–400 m by the late 21st century. These findings highlight the applicability of RF downscaling for station-scale climate projections in the Qilian Mountains and provide scientific support for regional climate adaptation, water resource management, and ecosystem conservation.

The Qilian Mountains, located on the northeastern margin of the Tibetan Plateau, constitute a critical ecological security barrier and water conservation region in northwestern China. As an important component of the Asian Water Tower, the region supplies water to the Yellow River, the Hexi inland river basins, and Qinghai Lake, thereby sustaining ecosystems and human activities in the surrounding arid and semi-arid regions (Chen et al., 2023; Yao et al., 2022). The Qilian Mountains are also characterized by extensive glaciers, seasonal snow cover, and permafrost, making the region highly sensitive to climate change (Pepin et al., 2015; Yao et al., 2022). In recent decades, the region has experienced significant warming and wetting, accompanied by glacier retreat, snow cover reduction, and substantial hydrological and ecological changes (Liu et al., 2022; Ding et al., 2023). Reliable projections of future climate change are therefore essential for understanding regional hydroclimatic processes and for supporting water resource management, ecosystem conservation, and climate adaptation. However, the complex terrain, large elevation gradients, and the combined influence of the mid-latitude westerlies and the Asian monsoon lead to pronounced spatial heterogeneity in temperature and precipitation, which increases the uncertainty of fine-scale climate projections, particularly for precipitation (Yao et al., 2019; Yang et al., 2023).

Global Climate Models (GCMs) from the Coupled Model Intercomparison Project Phase six (CMIP6) provide the primary basis for future climate projections (Eyring et al., 2016; Tebaldi et al., 2021). However, their coarse spatial resolution and structural differences among models introduce substantial uncertainty into regional projections, making downscaling necessary for regional and station-scale applications (Knutti et al., 2010; Pathak et al., 2023). Downscaling methods are commonly divided into dynamical and statistical approaches. Dynamical downscaling provides physically consistent simulations but is computationally demanding, especially in studies involving multiple climate models and emission scenarios. Statistical downscaling is more computationally efficient and has therefore been widely used for station-scale climate projections (Fowler et al., 2007; Maraun et al., 2010). Common statistical methods include the Delta Change Method (DCM), Quantile Mapping (QM), Multiple Linear Regression (MLR), and machine-learning approaches such as Random Forest (RF) (Cannon et al., 2015; Huth and Pokorná, 2023). Because these methods differ in their underlying assumptions and in their ability to capture nonlinear climate–terrain relationships, their performance may vary substantially in mountainous regions. However, their relative performance in the Qilian Mountains, where terrain is complex and meteorological stations are sparse and unevenly distributed, has not been systematically evaluated.

Several studies have investigated future climate change in the Qilian Mountains using CMIP6 simulations, regional climate models, and different downscaling approaches (Liu et al., 2022; Yang et al., 2023; Li and Yang, 2024). These studies generally project continued warming throughout the 21st century, accompanied by a modest increase in precipitation, with larger changes under higher emission scenarios (Liu et al., 2022; Yang et al., 2023; Li and Yang, 2024). Some studies have also reported stronger warming and larger increases in precipitation at higher elevations (Liu et al., 2022; Li and Yang, 2024). However, most previous studies have relied on a single downscaling method, and evaluations at the station scale based on long-term and recently updated observations remain limited (Liu et al., 2022; Yang et al., 2023). Consequently, the applicability of different statistical downscaling methods in the Qilian Mountains remains insufficiently understood.

In this study, station-based temperature and precipitation observations from 1951 to 2025, together with outputs from 34 CMIP6 climate models, were used to evaluate four statistical downscaling methods: DCM, QM, MLR, and RF. These methods were chosen because they represent commonly used statistical downscaling approaches with varying levels of complexity and underlying assumptions, including change-factor, bias-correction, regression-based, and machine-learning techniques. The objectives were to: (1) compare the performance and stability of these methods for station-scale temperature and precipitation simulations; (2) identify the most suitable method for climate projections in the Qilian Mountains and examine the reasons for its superior performance; and (3) project future changes in temperature and precipitation under four SSP scenarios (SSP1–2.6, SSP2–4.5, SSP3–7.0, and SSP5–8.5), with emphasis on seasonal redistribution, spatial heterogeneity, and elevation-dependent responses. This study fills a key gap in the evaluation of statistical downscaling methods for complex mountainous regions and provides scientific support for climate adaptation, water resource management, and ecosystem conservation in the Qilian Mountains.

Study area

The Qilian Mountains are located along the northeastern margin of the Qinghai–Tibet Plateau, extending in a southeast–northwest orientation (Figure 1). The region has a mean elevation of approximately 3,670 m. The cold and humid alpine climate supports the widespread development of cryospheric components, including glaciers, seasonal snow cover, and permafrost. Together with relatively abundant precipitation, these features make the Qilian Mountains a crucial water source for the Yellow River, the inland river systems of the Hexi Corridor, and the drainage basins feeding Qinghai Lake. In particular, for the inland river basins of northwestern China, the Qilian Mountains play a vital role in maintaining ecological stability and sustaining water resources for human activities in the arid and semi–arid downstream regions (Chen et al., 2023). Consequently, this region has long been a focal area of research in meteorology, hydrology, ecology, and related disciplines.

Data

Meteorological station data

Meteorological observations were obtained from the China Meteorological Administration National Meteorological Science Data Center (http://data.cma.cn/data). Stations were selected based on record length and data completeness. A total of 27 stations located within and around the Qilian Mountains were retained for analysis (Figure 1). Among them, nine stations are located within the mountainous region, with a mean elevation of approximately 3,066 m, and 18 stations are situated in surrounding areas, with a mean elevation of about 1,834 m. The average elevation of all stations is approximately 2,244 m. Although these stations record multiple meteorological variables, only air temperature and precipitation were used in this study. The observational records extend from 1951 to December 2025. Details of the meteorological stations are provided in Supplementary Table 1.

CMIP6 model data

The GCMs employed in this study were obtained from Phase six of the Coupled Model Intercomparison Project (CMIP6). To ensure consistency with station observations and enable robust comparative analysis, 34 GCMs providing outputs for both historical and future scenarios were selected (https://esgf.github.io/). Future projections were based on four Shared Socioeconomic Pathway (SSP) scenarios: SSP1–2.6, SSP2–4.5, SSP3–7.0, and SSP5–8.5. Historical simulations cover the period 1950–2014, and future projections extend from 2015 to 2100. Details of the selected CMIP6 models are provided in Supplementary Table 1.

Methods

Downscaling methods

In this study, four widely used statistical downscaling methods were selected to evaluate their applicability and associated uncertainties in station–scale projections over the Qilian Mountains. The principles of each method are briefly described below.

DCM

DCM is a simple bias-correction approach that assumes climate models can reliably simulate relative changes in temperature and precipitation (Fowler et al., 2007). Monthly additive correction factors for temperature and multiplicative correction factors for precipitation are derived from the baseline period and applied to future GCM projections. The mathematical formulations are as follows: For multiplicative variables such as precipitation: where m denotes the month, T o b s, h i s m and T G C M, h i s m represent the monthly mean temperatures from observations and GCM historical simulations during the baseline period, respectively, P o b s, h i s m and P G C M, h i s m represent the monthly mean precipitation values, where T G C M, f u t u r e and P G C M, f u t u r e represent the future temperature and precipitation simulated by the GCM, respectively (Lenderink et al., 2007).

QM

QM is a non-parametric bias-correction technique that adjusts systematic biases across the entire probability distribution by establishing a quantile-based transfer function between GCM outputs and observations (Panofsky and Brier, 1968; Cannon et al., 2015). The method aligns the cumulative distribution function (CDF) of model simulations with that of observations, expressed as: where F o b s and F G C M are the CDFs of observations and GCM historical simulations during the baseline period, respectively, and F o b s − 1 is the inverse CDF of observations (Cannon et al., 2015). This approach effectively corrects biases in the mean, variability, and extremes.

MLR

MLR establishes linear relationships between large-scale predictors and local climate variables. It assumes that these relationships are approximately linear and remain stable over time (Hessami et al., 2008). Regression models are calibrated during the baseline period and then applied to predictors from future GCM simulations to generate downscaled projections: where Y represents the local meteorological variable (e.g., temperature, precipitation), X i are large–scale predictors (e.g., pressure, temperature, humidity from GCMs), β i are regression coefficients, and ε is the random error term (Jiayi et al., 2018). In practical terms for climate downscaling, β 0 accounts for the baseline level of Y (e.g., temperature or log-transformed precipitation) that is not explained by the linear combination of the GCM-derived predictors. For precipitation, logarithmic transformation was applied prior to model fitting to reduce skewness and improve model performance.

RF

RF downscaling is a machine learning–based approach that captures complex nonlinear relationships between large–scale predictors and local variables through ensemble learning (Breiman, 2001). This method constructs multiple decision trees using bootstrap samples and aggregates their outputs, providing strong predictive performance, robustness to outliers, and the ability to handle high–dimensional datasets (Huth and Pokorná, 2023). The formulation is: where N is the number of decision trees, f k is the prediction function of the k –th tree, and X is the predictor vector. Final predictions are obtained by averaging (for regression) or majority voting (for classification) across all trees. In this study, the RF model was configured with 50 regression trees and a minimum leaf size of 10.

Baseline period selection

All methods were calibrated using the 1985–2014 baseline period, consistent with the reference period adopted in the IPCC Sixth Assessment Report (IPCC, 2021). Observations from 2015 to 2025 were used as an independent validation dataset. For the validation period, downscaling was performed separately for each SSP scenario and compared with the corresponding observations. Because the divergence among SSP1–2.6, SSP2–4.5, SSP3–7.0, and SSP5–8.5 remains minimal during 2015–2025, differences in validation results among scenarios were negligible. The selected optimal method was subsequently applied to project future climate change for 2026–2100.

Validation metrics for downscaling methods

The coefficient of determination (R 2) and the root mean square error (RMSE) are employed to evaluate the performance of the downscaling methods (Chai and Matsuura, 2014; Chicco et al., 2021). These metrics are defined as follows: where O i represents the observed values, P i represents the predicted values, O ˉ is the mean of observed values, and n is the number of observations.

Interpolation method

Following the validation of multiple downscaling methods, the optimal approach was selected to project future temperature and precipitation at observation stations in the Qilian Mountains. Based on these station–scale projections, spatial interpolation was then performed to characterize future climatic changes across the entire Qilian Mountains region. The interpolation method employed longitude, latitude, and elevation as independent variables within a multivariate nonlinear regression framework, which has been demonstrated to yield high interpolation accuracy over the Qilian Mountains (Wu et al., 2024). The interpolation was conducted at a monthly temporal resolution and a spatial resolution of 10 km × 10 km.

Comparison and validation of downscaling methods

Overall comparison of downscaling methods

For each downscaling method, validation statistics were calculated separately across the available combinations of CMIP6 models, SSP scenarios, and 27 meteorological stations. The boxplots summarize the distribution of R 2 and RMSE values across these combinations (Figure 2). For temperature downscaling, the R 2 values of the four methods all exceeded 0.95, with the RF method achieving the highest R 2 of approximately 0.98. In terms of RMSE, the superiority of the RF method was even more pronounced, with an RMSE of only 1.8 °C, while the other three methods all yielded RMSE values exceeding 2.0 °C. The downscaling accuracy for precipitation was considerably lower than that for temperature. For precipitation, the R 2 values of the DCM, QM, and MLR methods were all below 0.5, and only the RF method achieved an R 2 above 0.5, indicating marginal acceptability. Regarding RMSE, the RF method exhibited the lowest error at just 16.2 mm.

In terms of the dispersion of validation metrics, the RF and DCM methods exhibited relatively concentrated 25th–75th and fifth–95th percentile ranges for both R 2 and RMSE in temperature downscaling. In contrast, the corresponding ranges for precipitation downscaling were markedly more dispersed. For precipitation, the degree of dispersion in R 2 for the RF method was comparable to those of the DCM and QM methods, and all three were notably more concentrated than that of the MLR method.

To further investigate this, we conducted comparative analyses of the validation results for temperature and precipitation downscaling among different models, scenarios, and stations. The results show that for both temperature and precipitation, the RF method achieved the highest R 2 and the lowest RMSE across all climate models and four climate scenarios. Across different stations, the MLR method yielded the lowest RMSE for precipitation downscaling at only two stations, with differences of merely 6.3 mm and 0.2 mm compared to the RF method. For all remaining stations, regardless of whether temperature or precipitation was considered, the RF method consistently outperformed the other methods, achieving the highest R 2 and the lowest RMSE.

Monthly comparison of downscaling methods

The monthly validation results, aggregated across all models, scenarios, and stations (Figure 3), indicate that for temperature, higher temperatures correspond to higher R 2 and lower RMSE values. For precipitation, months with greater precipitation yield higher R 2 but also larger RMSE. Among the four downscaling methods, MLR and RF consistently achieved higher monthly R 2 for temperature than DCM and QM. Regarding RMSE, while differences among the four methods were marginal, RF exhibited the lowest RMSE in 6 months, particularly during colder months when its R 2 performance was relatively weaker. For precipitation downscaling, the superiority of RF was more evident. Except for the considerably drier months of April and November, where MLR yielded higher R 2, RF achieved the highest R 2 for all other months. During the dry season, all four methods showed low RMSE values with negligible differences; however, in the spring and summer months when precipitation is concentrated, RF demonstrated markedly lower RMSE. The relatively lower R 2 values of RF during colder months may be attributed to the reduced variability of winter temperatures. Under such conditions, even small prediction errors can substantially affect R 2, whereas RMSE remains low because the absolute errors are still limited. Therefore, the decline in R 2 during winter does not necessarily indicate a deterioration in model performance.

Selection of optimal methods

A comparative evaluation of the four downscaling methods—DCM, QM, MLR, and RF—reveals clear differences in their performance for temperature and precipitation downscaling over the Qilian Mountains. Although MLR performs comparably in the extremely dry months of April and November, RF demonstrates clear superiority during the spring and summer months when precipitation is concentrated. Furthermore, RF exhibits greater stability and more concentrated error distributions across different stations, models, and scenarios. Therefore, RF was selected as the optimal method for downscaling future temperature and precipitation over the Qilian Mountains.

Projection of future temperature and precipitation changes in the Qilian Mountains

Temperature and precipitation trends under different scenarios

Historical observations indicate a clear warming trend in the Qilian Mountains, which accelerated after the mid-1990s (Ding et al., 2023; Liu et al., 2022). From 1951 to 1995, temperature increased at approximately 0.1 °C/decade, rising to about 0.3 °C/decade during 1995–2025. Compared with the first decade (1951–1960, −2.77 °C), the mean temperature of the most recent decade (2016–2025, −1.24 °C) increased by 1.53 °C (Figure 4).

Future projections (Figure 4) suggest continued warming under all SSP scenarios during 2026–2100, although the magnitude varies substantially among scenarios. Under SSP1–2.6, temperatures remain relatively stable, with a change rate of 0.03 °C ± 0.10 °C/decade and an increase of only 0.20 °C ± 0.20 °C by the late 21st century relative to 2016–2025. Under SSP2–4.5 and SSP3–7.0, warming trends are similar before 2050 but diverge afterward, with SSP2–4.5 stabilizing and SSP3–7.0 continuing to rise. By the end of the century, mean temperature is projected to reach −0.42 °C ± 0.82 °C under SSP2–4.5 and 0.26 °C ± 1.18 °C under SSP3–7.0, corresponding to warming rates of 0.14 °C ± 0.09 °C/decade and 0.24 °C ± 0.11 °C/decade, respectively. Notably, under SSP3–7.0, annual mean temperature is projected to exceed 0 °C around 2085. Under the high-emission SSP5–8.5 scenario, warming intensifies further, reaching 0.31 °C ± 0.17 °C/decade, with mean temperature increasing to 0.75 °C ± 1.40 °C by the late 21st century.

Historical precipitation (1951–2025) exhibited substantial interannual variability but only a weak long-term increase after 1960, at a rate of approximately 5.9 mm/decade. Mean annual precipitation during 2016–2025 (437.52 mm) was 31.10 mm higher than that during 1961–1970 (Figure 5).

Compared with temperature, future precipitation changes (Figure 5) show limited scenario dependence (Figure 5). Before 2060, differences among SSP scenarios are minimal, with projected precipitation increases of only 12.00–14.35 mm relative to 2016–2025. By the late 21st century, precipitation is projected to increase under most scenarios, with stronger increases under higher emission pathways. Multi-model mean annual precipitation reaches 451.65 ± 19.51 mm, 458.71 ± 29.59 mm, 466.91 ± 49.27 mm, and 473.09 ± 86.27 mm under SSP1–2.6, SSP2–4.5, SSP3–7.0, and SSP5–8.5, respectively, corresponding to increases of 3.24%–8.13% relative to 2016–2025.

Seasonal differences in future temperature and precipitation

Under the combined influence of the westerlies and monsoon, the Qilian Mountains exhibit pronounced seasonal variability in temperature and precipitation. To reduce uncertainty caused by interannual extremes, multi-year monthly means during 2016–2025 and 2091–2100 were used to represent present and future conditions, respectively (Figure 6). Overall, the fundamental intra-annual patterns of temperature and precipitation are projected to remain stable by the end of the 21st century, with no substantial shifts in the timing of warm/cold or wet/dry seasons.

Future monthly temperature changes reveal a pattern of stronger warming in cold months and weaker warming or slight cooling in warm months (Figure 6a). Under all scenarios, temperatures in June, July, and August increase only slightly. Relative to the recent decade (2016–2025), the multi-model mean temperatures by the end of the 21st century are projected to increase by 0.70 °C, 0.18 °C, and 0.94 °C, respectively. In contrast, warming is much more pronounced during winter, particularly in February, November, and December, with multi-model mean increases of approximately 2.28 °C, 3.39 °C, and 2.05 °C, respectively. Under SSP5–8.5, temperature increases in these months exceed 3 °C, with the largest increase reaching 5.29 °C in November relative to the 2016–2025 baseline period. Consequently, annual temperature range decreases from the current 24.64 °C–23.75 °C, 23.01 °C, 22.03 °C, and 21.18 °C under SSP1–2.6, SSP2–4.5, SSP3–7.0, and SSP5–8.5, respectively, indicating a progressively weaker seasonal contrast under higher-emission scenarios.

Future precipitation shows limited differences among SSP scenarios but substantial monthly variation (Figure 6b). Relative to 2016–2025, precipitation in July and August decreases by 8.18 mm and 12.97 mm, respectively, whereas October and November increase by about 10 mm. Changes in other months are generally modest (∼5 mm). These shifts reduce annual precipitation range by approximately 11 mm relative to the current value (93.39 mm), with the wettest month shifting from August to July and the driest month from December to January. Overall, future precipitation is projected to show slight seasonal redistribution, characterized by modest decreases in summer precipitation and moderate increases during autumn and winter, while the overall intra-annual pattern remains broadly similar to present conditions.

Spatial distribution of future temperature and precipitation changes

Temperature in the Qilian Mountains is strongly controlled by latitude and elevation, with warmer conditions in the southeastern and low-elevation peripheral areas and colder conditions in the central high-elevation mountains (Figure 7a). Future projections indicate widespread warming across the region, with stronger warming under higher-emission scenarios (Figures 7a,b). Relative to 2016–2025, grid-scale temperature increases during 2091–2100 range from −0.19 °C–0.50 °C under SSP1–2.6, 0.42 °C–1.21 °C under SSP2–4.5, 1.03 °C–1.98 °C under SSP3–7.0, and 1.47 °C–2.53 °C under SSP5–8.5. Correspondingly, the 0 °C isotherm is projected to shift upward under all SSP scenarios, with the magnitude increasing from approximately 100 m under SSP1–2.6 to about 400 m under SSP5–8.5 by the end of the century.

Future warming exhibits clear spatial heterogeneity under different emission pathways (Figure 7b). Under SSP1–2.6, warming is spatially uniform, whereas under SSP2–4.5, SSP3–7.0, and SSP5–8.5, warming intensity gradually increases from southeast to northwest. In addition, warming shows a pronounced elevation-dependent pattern, with stronger warming at higher elevations. However, under high-emission scenarios, warming above 3,000 m becomes less sensitive to further elevation increases.

Precipitation shows a strong southeast–northwest gradient and increases with elevation (Figure 8a). Currently, the eastern high-elevation mountains form the wettest region (∼690 mm), while the southwestern lowlands receive less than 100 mm annually. By the end of the 21st century, precipitation is generally projected to increase across the Qilian Mountains, particularly in the central high-elevation region, suggesting a westward shift of the present wet center.

Future precipitation changes exhibit substantial spatial heterogeneity (Figure 8b). The largest increases occur in the central mountainous area, where annual precipitation may rise by approximately 110–140 mm by 2091–2100, with stronger increases under higher-emission scenarios. In contrast, surrounding valleys, piedmont lowlands, and basins show limited change, while the eastern wet zone experiences moderate decreases (approximately −70 to −50 mm). Elevation-dependent differences are also evident: precipitation generally decreases below 3,000 m but increases above this threshold, with larger increases at higher elevations and under stronger emission scenarios.

Overall, the spatiotemporal patterns of temperature and precipitation suggest that the Qilian Mountains will continue the long-term warming and wetting trend initiated in the mid-to-late 20th century. Both warming and precipitation increases intensify under higher-emission scenarios. Seasonally, future hydrothermal conditions are projected to become more moderate, characterized primarily by stronger winter warming and increased cold-season precipitation, while the fundamental seasonal cycle remains largely unchanged. Spatially, high-elevation regions emerge as hotspots of concurrent warming and wetting, whereas intermontane valleys and surrounding lowlands are likely to experience warming with limited precipitation change.

Comparison with existing studies

Comparison of statistical downscaling methods

Statistical downscaling methods are widely applied due to their efficiency and flexibility, but their performance depends strongly on model formulation and data quality (Fowler et al., 2007; Maraun et al., 2010). This issue is particularly important in the Qilian Mountains, where steep elevation gradients, complex terrain, and the combined influence of the westerlies and the Asian monsoon produce strong spatial heterogeneity in temperature and precipitation (Chen et al., 2023; Yao et al., 2022). In addition, the sparse and uneven distribution of meteorological stations, especially at high elevations, increases the difficulty of establishing robust statistical relationships. Under such conditions, different downscaling methods may produce substantially different results, particularly for precipitation (Maraun et al., 2010; Fowler et al., 2007).

Among commonly used methods, DCM assumes spatially uniform changes and therefore cannot adequately represent local climatic gradients in complex terrain (Hay et al., 2000; Wilby and Harris, 2006). QM effectively corrects biases in the probability distribution, but it is essentially a univariate bias-correction method and does not explicitly account for multivariate relationships among predictors (Piani et al., 2010; Gudmundsson et al., 2012; Cannon et al., 2015). MLR is constrained by its assumption of linear relationships and is less capable of representing the nonlinear responses of temperature and precipitation to topographic controls (Wilby et al., 2002; Hessami et al., 2008).

In contrast, RF can capture nonlinear relationships and higher-order interactions among predictors, making it well suited to high-dimensional and terrain-influenced environments (Breiman, 2001; Huth and Pokorná, 2023). Its ensemble structure also reduces the influence of multicollinearity and improves model robustness. Previous studies have similarly reported that RF outperforms traditional statistical methods in complex terrain (Hutengs and Vohland, 2016; Shen et al., 2019).

The results of this study further support these findings. RF consistently achieved the highest R 2 and lowest RMSE for both temperature and precipitation across climate models, SSP scenarios, and observation stations. Its advantage was particularly pronounced for precipitation, indicating that the ability to represent nonlinear terrain–climate relationships is critical for reliable downscaling in the Qilian Mountains.

Comparison of downscaling results for temperature and precipitation in the Qilian Mountains

Previous studies based on CMIP6 projections, CORDEX regional climate simulations, and dynamical downscaling consistently report a robust warming and weak wetting trend in the Qilian Mountains, together with pronounced elevation-dependent warming and limited changes in the seasonal cycle (Liu et al., 2022; Yang et al., 2023; Li and Yang, 2024). The results of this study are broadly consistent with these findings in terms of both the magnitude of warming and the overall increase in precipitation. Projected warming rates of 0.03 °C–0.31 °C decade −1 and total warming of approximately 1.5 °C–3.4 °C by the end of the century are comparable to previous CMIP6-based estimates. Similarly, the projected precipitation increase of 3.2%–8.1% falls within the range reported in earlier studies, although substantial inter-model uncertainty remains.

Beyond this general agreement, the RF-based downscaling provides a more detailed characterization of spatial heterogeneity. In particular, it reveals a clearer redistribution of precipitation, with increases concentrated in central high-elevation regions and decreases in wetter eastern areas, suggesting stronger spatial contrasts than those identified in previous CMIP6 and dynamical downscaling studies. This pattern indicates that local topographic controls may play a more important role than previously captured by coarser-resolution models. Compared with previous studies based primarily on a single downscaling method or coarser-resolution model outputs, the present study provides a more robust station-scale assessment and reveals finer spatial contrasts in future precipitation change.

In terms of seasonal variability, previous studies indicate that winter warming and changes in summer precipitation are the dominant seasonal features of projected climate change in the Qilian Mountains (Yang et al., 2023; Li et al., 2023). The present results support this conclusion, showing stronger winter warming (exceeding 3 °C–5 °C under SSP5–8.5) and a redistribution of precipitation from summer to autumn and winter, leading to a more balanced intra-annual hydrothermal pattern.

Earlier studies based on WRF and CMIP6 simulations have also highlighted elevation-dependent warming and enhanced climate sensitivity at high elevations (Li and Yang, 2024; Yang et al., 2023). This study further refines this pattern by quantifying a stronger elevation dependence of both temperature and precipitation, with warming intensifying toward higher elevations and precipitation increasing above 3,000 m while decreasing in lower-elevation basins. In addition, the projected upward shift of the 0 °C isotherm by approximately 100–400 m provides a more explicit representation of the potential cryospheric response to climate warming.

Overall, the present results are consistent with previous studies in showing a persistent warming and weak wetting trend. At the same time, the RF-based approach provides more detailed station-scale projections and reveals more pronounced spatial heterogeneity and elevation-dependent responses in the Qilian Mountains.

Uncertainty analysis

Uncertainty of GCMs

Despite the superior performance of the Random Forest (RF) downscaling approach, considerable uncertainties remain in future climate projections for the Qilian Mountains. One major source of uncertainty originates from differences among GCMs. CMIP6 models differ substantially in simulation mechanisms, initial condition settings, and parameterization schemes, resulting in varying representations of climate sensitivity, cloud feedback, atmospheric circulation, and land–atmosphere interactions (Eyring et al., 2016; Tebaldi et al., 2021). Consequently, projections of regional temperature and precipitation differ considerably among climate models.

Compared with temperature, precipitation projections exhibit substantially greater uncertainty because precipitation is strongly influenced by complex atmospheric circulation processes and internal climate variability (Fowler et al., 2007; Maraun et al., 2010). In the present study, the spread among individual model projections increased markedly under high–emission scenarios, particularly for precipitation under SSP5–8.5, indicating that uncertainty amplifies as warming intensifies. Similar findings have also been reported for High Mountain Asia and the Tibetan Plateau, where future precipitation changes show strong inter–model variability and remain highly sensitive to regional circulation dynamics (Yao et al., 2019).

Uncertainty of statistical downscaling methods

Uncertainty also arises from the inherent assumptions and limitations of statistical downscaling approaches. RF downscaling assumes that statistical relationships established during the historical period remain valid under future climate conditions (Maraun et al., 2010). However, under strong warming scenarios, future climate states may extend beyond the range represented in the historical training dataset, potentially reducing model reliability due to extrapolation beyond observed climate space.

Although RF has demonstrated superior performance in capturing nonlinear relationships and predictor interactions, its predictive performance may still be affected by predictor selection, parameter settings, and sample size (Breiman, 2001; Biau and Scornet, 2016). Such limitations may be particularly important in mountainous regions, where strong topographic gradients and pronounced environmental heterogeneity complicate climate–terrain relationships. Therefore, while RF generally outperforms conventional approaches, its future predictive skill should still be interpreted cautiously under extreme climate conditions.

Uncertainty from observational constraints

Observational uncertainty represents another important source of uncertainty in climate projections for the Qilian Mountains. Owing to harsh environmental conditions and limited accessibility, meteorological stations are mainly distributed in relatively low–elevation peripheral areas, whereas observations at high elevations remain sparse. This uneven station distribution may introduce uncertainties in both statistical model calibration and spatial interpolation processes (Pepin et al., 2015).

In addition, the temporal continuity and representativeness of historical observations may also influence statistical model performance. In this study (Figure 9), comparative analyses of downscaling accuracy across all stations revealed that, even when the same downscaling method was applied, high–elevation stations located in the interior Qilian Mountains exhibited larger R 2 for both temperature and precipitation. This result suggests that large-scale climate signals are more effectively captured at high-elevation sites, where climatic variability is often more strongly controlled by regional atmospheric circulation and long-term climate forcing. As a result, the RF model is able to reproduce temporal variations and long-term trends more effectively in these regions. Meanwhile, stations with higher temperatures and greater precipitation generally exhibited larger RMSE values. This pattern may be partly attributed to the sensitivity of RMSE to the absolute magnitude of climate variables. In regions with higher temperatures or precipitation amounts, similar relative errors can correspond to larger absolute deviations, resulting in increased RMSE values. Therefore, larger RMSE values do not necessarily indicate poorer model performance, but may instead reflect differences in the magnitude and variability of local climatic conditions. Multi–station validation is considered one of the most effective approaches to reduce such uncertainty; however, sparse observational coverage remains a major limitation for climate studies in High Mountain Asia and other high-altitude regions in or around Tibetan Plateau (Yao et al., 2019; Liu et al., 2023).

Multi-model uncertainty and implications for future climate projections

Although uncertainties are unavoidable, the warming trend projected across multiple models and emission scenarios exhibits strong consistency, suggesting that future warming in the Qilian Mountains is robust. In contrast, future precipitation changes should be interpreted more cautiously because of their greater inter–model variability and stronger dependence on regional circulation processes. Future efforts should therefore focus on improving high–elevation observations, integrating physically informed statistical downscaling approaches, and reducing uncertainties associated with regional climate dynamics.

The Multi–Model Ensemble Mean (MME) has been widely adopted in climate change projection studies because it effectively reduces random errors and suppresses systematic biases associated with individual climate models (Knutti et al., 2010). Numerous studies have demonstrated that, compared with single-model simulations, ensemble means generally provide more robust and stable projections of future climate change (Pathak et al., 2023). Therefore, this study primarily employs the MME to characterize future climate change patterns in the Qilian Mountains.

Nevertheless, the application of ensemble averaging also entails certain limitations. Averaging outputs from multiple climate models inevitably smooths interannual variability and attenuates extreme signals, thereby potentially obscuring physically meaningful features simulated by individual models. Particularly under future climate change scenarios, the MME may underestimate the intensity and frequency of extreme warming and precipitation events. Table 1 presents the standard deviations of temperature and precipitation projections in the Qilian Mountains during 2026–2100 for both individual climate models and the MME. The results indicate that, for both temperature and precipitation, the annual-scale standard deviations of the MME generally fall within the distribution range of individual model standard deviations, yet deviate substantially from their maximum values. Moreover, the dispersion among projections from individual models increases markedly under high-emission scenarios. These discrepancies suggest that relying solely on ensemble means may obscure critical information regarding potential high-risk climate outcomes. Consequently, simple arithmetic averaging may weaken regional signals with physical realism. In recent years, increasing attention has been directed toward the importance of model evaluation and weighting strategies in regional climate projection studies (Castaneda-Gonzalez et al., 2023).

In summary, although the MME provides an effective framework for assessing the overall future climate trends in the Qilian Mountains, future research should further explore model-weighting approaches, extreme event projections, and physically constrained ensemble techniques to better quantify regional climate risks. In particular, studies focusing on extreme climate events, such as heatwaves and heavy precipitation, may benefit from individual-model analyses or weighted ensemble approaches rather than relying solely on the MME.

This study systematically evaluated four statistical downscaling methods (DCM, QM, MLR, and RF) for station–scale temperature and precipitation projections in the Qilian Mountains using long–term meteorological observations (1951–2025) and outputs from 34 CMIP6 climate models. Comparative validation demonstrated that the Random Forest (RF) method consistently outperformed the other approaches, achieving the highest R 2 and lowest RMSE across climate models, SSP scenarios, and observation stations. Its superiority was particularly evident for precipitation downscaling, reflecting a stronger ability to capture nonlinear climate–terrain relationships in complex mountainous environments. Therefore, within the datasets, validation period, and methodological framework adopted in this study, RF was identified as the most suitable method for future climate projections in the Qilian Mountains.

Based on RF downscaling, future climate projections indicate that the Qilian Mountains will continue to experience a persistent warming and wetting trend throughout the 21st century, with stronger warming under higher emission scenarios. Annual mean temperature is projected to increase at rates of approximately 0.03 °C–0.31 °C/decade, while precipitation is projected to increase by 3.2%–8.1% by the end of the century. Seasonal redistribution is also evident, characterized by winter–dominated warming, reduced summer precipitation, and increased autumn–winter precipitation, resulting in a more moderate and symmetric intra–annual hydrothermal regime. Spatially, future climate change exhibits clear elevation dependence, with stronger warming and precipitation increases concentrated in high–elevation areas (>3,000 m), accompanied by an upward shift of the 0 °C isotherm ranging from approximately 100 m under SSP1–2.6 to about 400 m under SSP5–8.5. In contrast, low–elevation basins are projected to experience weaker hydroclimatic changes.

Despite the strong consistency of projected warming across models and scenarios, uncertainties remain, particularly for precipitation projections. These uncertainties mainly arise from differences among CMIP6 climate models, assumptions embedded in statistical downscaling methods, and the sparse distribution of high–elevation observations. Although the multi–model ensemble mean effectively reduces random model biases, it may smooth extreme climate signals and interannual variability. Overall, this study provides robust station–scale evidence for future climate change in the Qilian Mountains and offers scientific support for regional climate adaptation, water resource management, ecological conservation, and cryosphere risk assessment.