Estimating Discharge Time Series in Data-Scarce Mountainous Areas Using Remote Sensing Inversion and Regionalization Methods

Highlights

What are the main findings?

• Combined UAV and satellite imagery-based flow inversion with a spatial regionalization method to estimate river discharge time series in the data-scarce mountainous region of the Tianshan–Pamir.
• Spatial regionalization facilitated high-precision reconstruction of long-term discharge series (NSE up to 0.88) spanning 1989 to 2020.

What are the implications of the main findings?

• This study provides new insights into long-term river discharge estimation in remote or data-scarce regions.
• This approach demonstrates accurate discharge estimation in ungauged basins, supporting water resource management and hydrological studies.

Abstract

The Tianshan–Pamir mountain region, serving as the core “water tower” for countries in Central Asia east of the Aral Sea, is a critical bulwark for sustaining downstream socioeconomic systems. However, constrained by complex topography and harsh climatic conditions, this region suffers from a severe scarcity of long-term, continuous hydrological observation data. This study focuses on a typical data-scarce mountainous area, coupling UAV and satellite imagery-based (e.g., Landsat/Sentinel) flow inversion with a hybrid spatial regionalization method—integrating spatial proximity, basin similarity, and regression-based hydrograph reconstruction—to quantitatively estimate long-term discharge time series. The results indicate that, for the validation of instantaneous discharge inversion, the Nash–Sutcliffe efficiency coefficient (NSE) at 29 river cross-sections was consistently greater than 0.80, with the coefficient of determination (R²) reached 0.94 (p < 0.01). Subsequently, for the long-term discharge series reconstructed using the regionalization method, the NSE values at three representative verification sites—each corresponding to a distinct basin type—were 0.88, 0.84, and 0.86, respectively. These findings exhibit higher precision compared to direct temporal upscaling, confirming the reliability of the regionalization method across varying temporal scales. An analysis of monthly discharge trends from 1989 to 2020 revealed a decreasing trend in the discharge of glacier-dominated rivers, with an average rate of change of −2.89 ± 2.54% (p < 0.05); the Pamir Plateau experienced the largest decline (−4.89 ± 6.58%), which is closely linked to large-scale glacial retreat within the basins. Conversely, the discharge of non-glacier-dominated rivers showed an increasing trend, with a multi-year average rate of change of +0.32 ± 8.43% (n.s.), primarily driven by shifts in precipitation and vegetation cover. This research introduces a new approach for hydrological monitoring in data-scarce regions and provides essential data and methodological support for water resource management decisions in arid zones.

1. Introduction

Driven by the intensification of global climate change, the global water cycle has undergone significant alterations, leading to a severe spatio-temporal imbalance in water resources [1,2]. As the source of numerous inland rivers, often referred to as “water towers,” mountainous regions, as the source of numerous inland rivers (often referred to as “water towers”), play a decisive role in determining the water resource distribution and ecological security of mid- and downstream areas through their upstream runoff generation and concentration processes [3]. However, complex topography, harsh climatic conditions, and high maintenance costs in high mountainous areas have resulted in an extreme scarcity and uneven distribution of traditional hydrological observation stations. This “data-scarce” reality severely restricts our understanding of mountain hydrological processes. Particularly under global warming, the accelerated retreat of the cryosphere (glaciers, snow cover, and permafrost) has dramatically increased the volatility and uncertainty of mountain runoff. Therefore, how to scientifically and accurately reconstruct long-term runoff series in data-scarce mountainous regions has become a core challenge urgently needing resolution in current international hydrological sciences (e.g., Predictions in Ungauged Basins, PUB) [4].

In recent years, with the development of Earth observation technologies, significant progress has been made in runoff estimation for data-scarce regions. On the one hand, discharge inversion methods based on unmanned aerial vehicles (UAVs) and remote sensing technologies have been widely applied [5,6,7]. By extracting high-precision topographical information of the river channel and combining it with hydraulic models, these methods effectively overcome the difficulty of obtaining discharge in ungauged areas, and their accuracy has been validated in regions such as Northwest China and the Qinghai–Tibet Plateau [8,9,10,11,12,13]. However, limited by satellite revisit cycles and UAV flight frequencies, remote sensing retrieval methods typically only acquire discrete, instantaneous discharge data. For small mountainous catchments characterized by strong diurnal variations and seasonal fluctuations, instantaneous discharge fails to reflect continuous temporal runoff evolution patterns and cannot directly meet the requirements of long-term water resource management. On the other hand, spatial regionalization represents a classical approach for runoff simulation in ungauged basins, which estimates hydrological parameters by establishing statistical relationships of topographical, geomorphological, and climatic characteristics between gauged and ungauged basins [14]. Studies by Oudin et al. [15], Sellami et al. [16], and Bao et al. [17] have confirmed the applicability of this method at larger spatial scales. Nevertheless, for high-altitude mountainous areas and small catchment scales, traditional regionalization methods face significant limitations. High mountainous regions feature dramatic topographic relief, strong micro-climate variations, and are heavily influences from glacier and snowmelt, resulting in extreme spatial heterogeneity in hydrological processes. Consequently, the hydrological “similarity” between small catchments is difficult to accurately quantify accurately using conventional hydroclimatic indices alone, and relying solely on regionalization methods often leads to large simulation biases.

Against this background, breaking the limitations of single methods and coupling the high-precision “instantaneous discharge” from remote sensing retrieval with the “continuous simulation” capability of regionalization methods provides a critical breakthrough for converting discrete data into continuous, standardized runoff series. As the core “water tower” for countries in Central Asia east of the Aral Sea [18], the Tianshan–Pamir mountain region is essential for maintaining regional water stability and the supporting downstream socioeconomic systems [19]. Climate observations over the past half-century indicate that this region is warming at a rate of 0.1–0.42 °C per decade [20,21], accompanied by accelerated glacier ablation [22,23], making future water resource evolution highly uncertain. Previous studies on runoff responses in this region have mostly relied on limited data from hydrological stations on large mainstem rivers [23,24], whereas small headwater catchments—the core areas for water conservation and runoff generation—have received severely insufficient attention. Due to the lack of long-term continuous observation data, there remains a substantial knowledge gap regarding runoff changes in headwater regions and their potential impacts downstream impacts. Therefore, taking typical data-scarce, high-altitude mountainous catchments in the Tianshan–Pamir region as the study area, this research proposes a long-term runoff reconstruction framework that couples remote sensing discharge retrieval with spatial regionalization methods. This study aims to: (1) explore the cross-scale feasibility of coupling UAV/remote sensing-derived discharge estimation with aspatial regionalization method; (2) quantitatively reconstruct the long-term runoff evolution patterns of small headwater catchments in this region; and (3) provide a novel theoretical perspective and methodological support for addressing the challenge of acquiring hydrological data acquisition in high-altitude, data-scarce regions.

2. Materials and Methods

2.1. Study Area

This study selected three typically representative data-scarce regions for a systematic investigation of river discharge estimation: the Ebinur Lake Basin, the central section of the Tianshan Mountains, and the Eastern Pamir Plateau (Figure 1).

The Ebinur Lake Basin, located in the heart of the Eurasian continent, experiences scarce precipitation and intense evaporation, with hydrological processes characteristic of arid inland rivers. Due to its remote geographical location, weak infrastructure, and vast area, the distribution of traditional hydrological monitoring stations is sparse, making it difficult to obtain continuous and complete hydrological observation data over the long term. This situation has severely constrained water resource management and ecological protection efforts in the region, making the basin a hotspot for research on environmental evolution and water resources in recent years.

The central Tianshan and Eastern Pamir Plateau, as typical high-altitude cold regions, exhibit even more pronounced ecological fragility. The unique geographical environment makes the construction and maintenance of conventional hydrological observation stations difficult. Concurrently, extreme climatic conditions and complex topography pose significant challenges to field investigations. It is noteworthy that as integral parts of Asia’s vital “water towers,” changes in the water resources of these high-altitude cold regions have profound impacts on downstream ecosystems and human societies. Against the backdrop of global warming, processes such as glacial retreat and changes in snow cover are profoundly altering regional hydrological cycle characteristics. In response to the severe lack of fundamental hydrological data in these areas, this study employs remote sensing technology to conduct dynamic discharge monitoring.

2.2. Data

2.2.1. UAV and Field Measurement Data

This study utilized the DJI Phantom 4 Pro drone (Dajiang Company, Shenzhen, China, https://www.dji.com/cn, accessed on 19 November 2024) for low-altitude remote sensing data acquisition. This model is equipped with a high-performance FC300X camera (DJI, Shenzhen, China) featuring a 1-inch, 20-megapixel CMOS sensor, providing excellent image acquisition capabilities that meet the demands of high-precision aerial surveys. Its compact design (total weight 1380 g) ensures portability for fieldwork, while its ability to operate at altitudes up to 6000 m and a cruising speed of 72 km/h makes it suitable for aerial survey tasks in complex terrain. The drone’s front and rear dual-vision obstacle avoidance systems effectively ensure flight safety in mountainous areas.

The research team conducted aerial surveys at 33 key hydrological cross-sections in typical areas, including the Ebinur Lake Basin, the central Tianshan, and the Pamir Plateau. These included 29 upstream control sections for flow inversion and 4 reference sections for accuracy validation (Figure 1). The raw image data was processed using Pix4Dmapper (Pix4D S.A., Prilly, Switzerland, https://pix4d.com/, accessed on 19 November 2024) professional photogrammetry software. Through processes including image matching, point cloud generation, and 3D reconstruction, high-precision Digital Orthophoto Maps (DOM) and Digital Surface Models (DSM) were ultimately generated, providing a reliable data foundation for subsequent river channel morphology analysis and flow inversion.

Since the UAV only carries a visible-light camera sensor which cannot directly measure the underwater topography [25], essential hydrological data for discharge estimation were measured concurrently with the UAV flights, including flow velocity, river discharge, water depth, and underwater topography. Flow velocity was measured using a surface velocity radar (SVR, USA), river discharge was measured with a portable Ponolflow-VA Doppler flow instrument (depth range 0–5 m), and water depth was surveyed using a staff gauge. These measured data provide inputs for the discharge calculation formulas and were used to validate the estimation results.

2.2.2. Satellite Remote Sensing Data

Multi-temporal and multi-resolution satellite remote sensing imagery was used to extract water surface width. Specifically, two types of satellite data sources were employed: first, Landsat series images (including TM, ETM+, and OLI sensors) from 1989 to 2020, with a spatial resolution of 30 m; second, Sentinel-2A satellite images acquired from 2016 to 2020, with a spatial resolution of 10 m. All satellite imagery was accessed and preprocessed utilizing the Google Earth Engine (GEE) cloud platform. To ensure data quality and reliability, we directly employed the Level-2 Surface Reflectance (SR) products for both datasets. Specifically, the Landsat data were atmospherically corrected by the USGS using the LEDAPS (for TM/ETM+) and LaSRC (for OLI) algorithms. The Sentinel-2A Level-2A products were atmospherically corrected using the Sen2Cor processor. Furthermore, rigorous cloud masking was applied to eliminate the interference of clouds and cloud shadows prior to water body extraction. For Landsat imagery, the Quality Assessment (QA) band (QA_PIXEL) was used for masking, while the QA60 band was utilized for the Sentinel-2A data. Following these preprocessing steps, the Normalized Difference Water Index (NDWI) was calculated using the Green and Near-Infrared bands to extract the water surface width of the study river sections. All satellite imagery used covered the catchment areas of the control sections identified by the UAV surveys, ensuring spatial consistency across the multi-source data.

2.2.3. Hydrological Station Data

To validate the accuracy of the regionalization-based discharge estimation method, measured monthly discharge data from 2017 to 2018 were collected from the Wenquan and Bole hydrological stations in the Ebinur Lake Basin, and the Kalabeili station in the Kashgar River Basin. These data were used to evaluate the accuracy of the cross-sectional discharge estimations. Additionally, daily flow observation series from different seasons between 2002 and 2018 from the Jinghe Shankou station, Tianshan Glacier station, and Tongguziluoke station were used to construct hydrological response relationship models for correcting the instantaneous flow data derived from remote sensing.

2.3. Methods

2.3.1. Remote Sensing Flow Inversion Method

The remote sensing flow inversion method consists of five key steps: First, high-resolution imagery from UAV aerial photography is used to generate a Digital Orthophoto Map (DOM) and a Digital Surface Model (DSM). Combined with field hydrological measurements, river cross-section morphological parameters are extracted. Second, a digital river section model is established based on the cross-sectional morphological characteristics to define the relationship between discharge, water surface width, and water depth. The third step involves using the Manning–Strickler hydraulic formula to calculate instantaneous discharge and validate its accuracy as a baseline for regionalization. Fourth, the Google Earth Engine platform is used to batch-process remote sensing imagery to obtain the NDWI for the study sections. This, combined with prior knowledge—specifically, the spatial constraints of the river channel boundaries and morphological parameters previously extracted from the high-precision UAV DOM and DSM—is used to extract multi-temporal water surface width data, effectively avoiding misclassification of adjacent non-river water bodies or terrain shadows. By integrating this with the digital river channel model, a long-term time series of instantaneous discharge is inverted. Finally, the regionalization method for ungauged basins is employed to upscale instantaneous data to a scientific reconstruction of monthly discharge series (Figure 2).

The Manning–Strickler formula is written as [26]:

$$Q=V·A$$

(1)

$$V={\displaystyle \frac{k}{n}}{R}^{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{J}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$$

(2)

where Q is the river discharge, m³/s; V is the velocity, m/s; and A is the area of the river cross-section, m², which is determined by the water depth and the water surface width; v is the average velocity of the flow; k is a conversion factor, m^1/3/s, regarded as 1 in this study; n is the roughness coefficient; R is the hydraulic radius; and J is the hydraulic gradient.

2.3.2. Extraction of Water Surface Width

By integrating low-altitude UAV remote sensing with field measurements, the Manning–Strickler formula is employed to estimate instantaneous discharge at monitored cross-sections during flight times, establishing a robust baseline for hydrological analysis. However, since UAV observations are constrained by low temporal resolution and cannot capture continuous river dynamics, obtaining time-series data of water surface width is essential for achieving sustained discharge estimation. The introduction of high-temporal-resolution satellite remote sensing data effectively addresses this challenge by enabling continuous monitoring of width changes, thereby extending the remote sensing flow inversion method from discrete points in time to long-term monitoring series.

For accurate inversion of river surface width, the NDWI is used to enhance the water spectral signature of water while reducing interference from land surfaces. Given that mountain rivers are often narrower than the resolution of standard satellite pixels, Linear Spectral Unmixing (LSU) is adopted to estimate the fractional water coverage, assuming that each cross-sections consists mainly of stable water and land endmembers [27]. Four training regions—Water, Land, Valley, and Length—are defined to ensure the purity of endmembers. Water bodies are finally identified using a threshold criterion: pixels with water fraction > 70% and land fraction < 30% are classified as water, enabling high-precision width calculations.

Its expression is as follows:

$$NDWI=\left(Green-NIR\right)/\left(Green+NIR\right)$$

(3)

where Green and NIR are the surface reflectance of the green band and near-infrared band, respectively.

2.3.3. Application of Regionalization Method to Derive Long-Term Discharge

By applying the previously established Manning–Strickler baseline to the long-term width series extracted from satellite data, multi-temporal instantaneous discharges for the target cross-sections are derived. Following the estimation of multi-temporal instantaneous discharge via remote sensing inversion, a spatial regionalization method is implemented to reconstruct continuous series for the ungauged target basins. The selection of our regionalization method is supported by established studies in diverse hydrological contexts. Specifically, research in French and Mediterranean catchments has demonstrated that spatial proximity and geo-climatic similarity yield high consistency in hydrological responses [15]. Furthermore, comparative analyses across 55 catchments in China confirmed that the spatial proximity method often achieves optimal performance in regionalization applications, providing the scientific justification for our hybrid approach [17].

The core methodology involves identifying a reference basin with analogous hydrological attributes to establish a response model for the target study area. This model facilitates the systematic correction of discrete remote sensing-derived flow into reliable long-term data through the following steps: ① select a reference basin based on the principles of spatial proximity and basin similarity, ensuring comparability by referring to authoritative sources such as the Hydrological Regionalization of China [28] and River Hydrology of China [29]; ② establish a functional relationship for instantaneous discharge between the two basins and use the reference basin’s seasonal daily hydrograph to correct the discharge; and ③ conduct a polynomial regression analysis using MATLAB R2021b (The MathWorks, Inc., Natick, MA, USA) to reconstruct the continuous daily hydrograph. A second-degree (quadratic) polynomial regression was selected because it effectively captures the inherent nonlinear hydrological responses between the basins—often caused by varying topography and antecedent moisture—without the overfitting risks associated with higher-order polynomials or complex machine learning models under limited sample sizes. In this model, the daily discharge of the reference basin serves as the independent variable (X), and the remote sensing-derived instantaneous discharge of the study basin acts as the dependent variable (Y). The model parameters were optimized and trained using the Ordinary Least Squares (OLS) method to minimize the sum of squared residuals. ④ Finally, obtain the monthly discharge series through temporal integration and perform an accuracy validation.

The functional relationship for discharge between a reference basin and the study basin can generally be expressed as [30]:

$$Q_L=H_R\left({\displaystyle \frac{Q_R}{\phi }}\right)+V_R$$

(4)

where Q_L is the estimated hydrological variable (discharge) for the ungauged basin; Q_R is the observed discharge of the reference basin; $\phi$ represents the basin characteristic attributes; H_R is the functional relationship between Q_R and $\phi$; and V_R is the error term.

2.3.4. Performance Evaluation

The accuracy of river discharge estimates was evaluated using the relative accuracy (RA), root mean square error (RMSE), and the Nash–Sutcliffe efficiency coefficient (NSE) [31] as the evaluation criteria:

$$RA={\displaystyle \frac{|Q_C-Q_m|}{Q_m}}$$

(5)

$$RMSE=\sqrt{({{\displaystyle \frac{\sum \left(Q_c-Q_m\right)}{n}})}^2}$$

(6)

$$NSE=1-{\displaystyle \frac{{\sum }_{t=1}^T{\left(Q_m^t-Q_c^t\right)}^2}{{\sum }_{t=1}^T{\left(Q_m^t-\overline{Q_m}\right)}^2}}$$

(7)

where Q_m is the in situ discharge, Q_c is the estimated discharge, $\overline{Q_m}$ denotes the mean value of the in situ discharge, T is the number of simulation calculations, and n represents the total number of observations. The NSE varies from −∞ to 1, and 1 indicates the optimal status where the simulated discharge equals the in situ measurements.

3. Results

3.1. River Discharge Estimation and Accuracy Validation

Following the completion of the UAV aerial survey missions, the acquired high-resolution imagery was processed using the professional software Pix4Dmapper (Pix4D S.A., Prilly, Switzerland, https://pix4d.com/, accessed on 19 November,2024). Through preprocessing steps including image stitching and point cloud densification, high-precision Digital Orthophoto Maps (DOM) and Digital Surface Models (DSM) were successfully generated. In conjunction with field-measured hydrological data, key morphological parameters for each river cross-section were extracted. Based on the hydraulic geometry relationships among discharge, water surface width, and water depth, digital river section models were constructed (as shown in Figure 3). The cross-sectional shapes of the 29 typical tributaries in the study area were predominantly U-shaped, characteristic of maturely developed mountain river valleys.

Based on the digital river channel models, the Manning–Strickler formula was used to calculate the instantaneous discharge for each key cross-section during the UAV survey period. To validate the accuracy of the estimations, the results were compared with in situ measurement data. The results show a good consistency between the estimated and measured discharge values (Figure 4).

Table 1. Results of accuracy evaluation.

Location of Cross-Section	RMSE	NSE
Ebinur Lake Basin	1.42	0.98
Central Tianshan	4.43	0.98
Eastern Pamir Plateau	12.50	0.84

presents the accuracy evaluation of the river cross-section discharge estimations, categorized by geographical unit. The accuracy analysis indicates that the RMSE values between the estimated and measured discharge for the Ebinur Lake Basin, the central Tianshan, and the Eastern Pamir Plateau were 1.42, 4.43, and 12.50, respectively. The corresponding NSE were 0.98, 0.98, and 0.84. The NSE values for all regions exceeded the acceptable threshold of 0.80. To further verify the reliability of the estimation results, a point-scale correlation analysis was conducted for all monitored cross-sections (Figure 5). The results show a highly significant positive correlation between the estimated and measured discharge (R² = 0.94, p < 0.01). This finding fully demonstrates that the UAV remote sensing-based flow inversion method possesses high accuracy and reliability, meeting the precision requirements for hydrological monitoring.

The accuracy assessment results indicate regional differences in the precision of discharge estimations across the three study areas. The Ebinur Lake Basin and the central Tianshan demonstrated higher estimation accuracy, whereas the Eastern Pamir Plateau showed relatively lower precision, with a noticeable deviation between estimated and measured values. This discrepancy is primarily due to the unique hydrological characteristics of the river sections in the Eastern Pamir Plateau: first, the discharge in this region is significantly larger than in the other two areas, reaching several times the flow of the Ebinur Lake Basin and central Tianshan; second, as an error metric sensitive to extreme values, the RMSE remained within an acceptable range even under the extreme flow conditions of the Eastern Pamir Plateau (where maximum and minimum values differ by an order of magnitude). This suggests that the remote sensing-based flow inversion method still holds practical value in this region.

3.2. Derivation of Discharge Using the Regionalization Method

3.2.1. Selection of Reference Basins

After obtaining instantaneous discharge data for the study cross-sections via remote sensing inversion, the regionalization method was employed to upscale the instantaneous data to monthly discharge data. For the selection of reference basins, following the technical requirements of the PUB initiative and the relevant provisions of the Hydrological Calculation Code for Water Resources and Hydropower Engineering (SL278-2002), factors such as geographical location and similarity in hydro-meteorological conditions were comprehensively considered. Ultimately, the Jinghe River Basin, the Tianshan Glacier No. 1 area, and the Yurungkash River Basin were selected as the reference basins corresponding to the three target study areas: the Ebinur Lake Basin, the central Tianshan, and the Eastern Pamir Plateau, respectively (Figure 6).

From a geospatial perspective, the Jinghe River Basin, Tianshan Glacier No. 1 area, and Yurungkash River Basin exhibit significant spatial proximity to the Ebinur Lake Basin, central Tianshan, and Eastern Pamir Plateau, respectively, and belong to similar natural geographical units and climatic zones. According to the Hydrological Regionalization of China, the Ebinur Lake Basin and central Tianshan, along with the Jinghe River Basin and Tianshan Glacier No. 1 area, all belong to the Tianshan Hydrological Region (a secondary hydrological region). The Yurungkash River Basin and the catchments controlled by the Pamir Plateau cross-sections both belong to the Pamir Plateau Hydrological Region. This classification confirms that the spatial distribution of the study and reference areas strictly adheres to the principle of spatial proximity in hydrological regionalization. From the perspective of basin hydrological response mechanisms, since the study and reference areas are within the same hydrological region, their key hydrological attributes, such as precipitation-discharge relationships and snowmelt-glacial meltwater supply characteristics, are highly consistent. Therefore, the selected reference basins fully meet the application conditions of the regionalization method. Based on the long-term hydrological observation data from these basins, reliable hydrological response models can be established to scientifically reconstruct the long-term discharge series for the study areas.

3.2.2. Typical Daily Hydrographs

Figure 7 illustrates the daily discharge characteristics of the Jinghe River Basin, Tianshan Glacier No. 1 area, and Yurungkash River Basin during different seasons. Considering that some cross-sections have zero estimated discharge during the winter low-flow period, this study focuses on analyzing the hydrographs for spring, summer, and autumn. The results show that all three regions exhibit distinct diurnal discharge fluctuations, with summer displaying a typical “single-peak” daily variation pattern. The Jinghe River Basin reaches its daily peak (approx. 62 m³/s) between 16:00 and 17:00 in summer and its daily trough (approx. 9.42 m³/s) at 00:00 in spring. The Tianshan Glacier No. 1 area peaks between 15:00 and 18:00 in summer and autumn (0.65 m³/s in summer, 0.2 m³/s in autumn) and reaches its trough between 08:00 and 09:00. The diurnal variation in the Yurungkash River Basin is relatively gentle, but its discharge is significantly higher than in the other regions (peaking at 768 m³/s at 16:00 in summer). Seasonally, all three regions show the highest discharge in summer, followed by autumn, and the lowest in spring. The diurnal discharge variation in the Tianshan Glacier No. 1 area is most subdued in spring. The Yurungkash River Basin exhibits a unique dual-peak characteristic (at 10:00 and 16:00).

Based on the seasonal daily discharge patterns of the Jinghe River Basin, Tianshan Glacier No. 1 area, and Yurungkash River Basin, the instantaneous discharge data obtained from multi-period remote sensing inversions were temporally corrected to establish the complete daily hydrograph for the study basins.This specific time correction process was achieved by applying the established instantaneous discharge functional relationship (Equation (4)) and mapping the remote-sensing derived instantaneous flow onto the polynomial equations fitted to the reference basin’s daily hydrographs. Subsequently, the daily discharge was calculated by temporal integration of the daily discharge data, and the total monthly discharge was obtained by daily accumulation. This process was repeated to construct a continuous monthly discharge series for the study basins. This method fully considers the differences in discharge generation mechanisms across seasons and uses the measured diurnal variations from the reference basins to constrain the remote sensing inversion results. This ensures the physical rationality of the calculation process and significantly improves the spatiotemporal representativeness of the discharge estimations, providing a reliable technical pathway for hydrological simulation in data-scarce regions.

3.3. Trend Analysis of Long-Term River Discharge

3.3.1. Long-Term (Inter-Annual) Trends in River Discharge

River discharge variation primarily depends on the river’s supply sources and the underlying surface characteristics of the catchment. In the arid region of Northwest China, due to scarce precipitation, the discharge changes in most rivers are closely related to glacial meltwater [32]. In this study, based on the geographic location of the monitored cross-sections, the elevation gradient and the underlying surface characteristics of their controlling catchments, the 29 monitored sections were classified into two types: “Glacier-dominated” and “Non-glacier-dominated” [33,34,35] (

Table 2. The types of studied river sections.

Types	Location	Cross-Sections
Glacier-dominated	Ebinur Lake Basin	B1/B2/B3/W5
	Central Tianshan	TS-3/TS-4/TS-5/TS-6/TS-7
	Pamir Plateau	K1/K2/K3/K4/T1/T2/T3/T4/T5/T6
Non-glacier-dominated	Ebinur Lake Basin	B4/B5/B6/W1/W2/W3/W4/W6
	Central Tianshan	TS-1/TS-2
	Pamir Plateau	-

). Among them, 19 are located at high altitude headwater areas downstream of glaciers, with elevations significantly higher than those of other sections. Specifically, the 10 sections in the Eastern Pamir Plateau (K1–K4, T1–T6) exhibit extremely strong glacial recharge characteristics, where the elevations of sections T1–T6 range from 3484 to 4270 m, placing them under the direct control of the perennial snow and ice zone; the mean elevation of the catchment controlled by section K1 reaches 3825 m, belonging to the typical high-mountain zone. Additionally, the catchments controlled by sections B1, B2, B3, and W5 in the Ebinur Lake Basin, as well as the 5 sections in the central Tianshan Mountains, all feature large-scale modern glaciers or perennial snow cover. In contrast, the 10 Non-glacier-dominated sections are primarily located at the mountain outlets, with generally lower elevations (mostly concentrated between 1000 and 2000 m) and almost no modern glacier distribution in their controlling catchments. This includes several outlet sections flowing into the Bortala River (such as sections B4–B6 with elevations of 1891–2373 m) and sections TS-1 and TS-2 in the central Tianshan Mountains, where glacier areas are minimal. The discharge dynamics of these sections are primarily driven by a combination of seasonal snowmelt, precipitation, and groundwater recharge.

During the process of monitoring river width, some cross-sections had abnormal width extraction results for certain months due to factors such as drying up or winter surface freezing (e.g., abnormally low estimated discharge or zero values). To ensure data accuracy, these abnormal width values were excluded. Consequently, complete monthly data for the entire study period (January to December) were not available for all cross-sections. Given this data discontinuity at the monthly level, this study ultimately chose to analyze the characteristics of discharge changes on a monthly scale.

From 1989 to 2020, the discharge at the 19 cross-sections dominated by glacial meltwater showed minor fluctuations. With the exception of T3 and T4, which exhibited a slight increasing trend, the discharge at the remaining 17 cross-sections showed a decreasing trend, with an average rate of change of −2.89 ± 2.54% (p < 0.05, Figure 8). There were significant regional differences in discharge changes: the change was gentle in the Ebinur Lake Basin (−0.62 ± 1.59%) and the central Tianshan (−0.74%), while the Pamir Plateau experienced the largest decline (−4.89 ± 6.58%). Similarly, there were marked differences among cross-sections. The minimum discharge was observed at section W5 in the Ebinur Lake Basin (0.002 to 0.32 × 10⁶ m³), while the maximum discharge was at section K1 on the Pamir Plateau (0 to 109.83 × 10⁶ m³).

Discharge and its variation are primarily determined by the catchment area controlled by the river cross-section, underlying surface characteristics, and climatic factors. Taking the Ebinur Lake Basin as an example, section B1 recorded its maximum discharge in June 1991 (33.87 × 10⁶ m³), which is directly related to its 260 km² catchment area—a larger catchment area leads to more abundant groundwater storage and deeper river incision, resulting in significantly higher discharge compared to other sections in the basin. The Pamir Plateau exhibited the maximum discharge and rate of change precisely because the catchment areas of its sections (e.g., K1 at 1497.19 km²) are several times larger than those in other regions (e.g., B1 at 260 km²). This significant difference in catchment area directly leads to regional disparities in discharge characteristics. Furthermore, discharge changes also vary markedly among different catchments within the same region. On the Pamir Plateau, the discharge reduction rate in the Kashgar River Basin (sections K1–K4) was −6.5 ± 4.14%, much higher than the −3.79 ± 4.86% in the Tashkurgan River Basin (sections T1–T6). This difference stems from the unique characteristics of each section’s catchment: for instance, section K1, with a discharge range of 0 to 109.83 × 10⁶ m³ and the most significant rate of change among all sections (−15.02 ± 6.93%, p < 0.01), controls a 1497.19 km² catchment at an elevation of 1850–5885 m. It is not only the largest catchment among the four sections in the Kashgar River Basin but also has the highest glacier coverage. The glacier area in its catchment was 179.31 km² in 1989 and had retreated to only 15.82 km² by 2020. Based on the changes in discharge and glacier area, this section exhibits both the most significant discharge decrease and glacial retreat, confirming the decisive impact of glacial ablation on discharge changes.

In the catchments of sections dominated by glacial meltwater, modern glaciers are widely distributed and constitute the main water source for the rivers. Against the backdrop of climate warming, these glaciers are showing a significant retreat, with their areas continuously shrinking and some smaller glaciers disappearing completely. Therefore, it can be concluded that the large-scale retreat of glaciers within these catchments is the key driving factor for the reduction in discharge at the glacier-dominated river sections.

From 1989 to 2020, the discharge at the 10 non-glacier-dominated cross-sections in the study area showed an overall increasing trend (Figure 9), with a multi-year average monthly rate of change of +0.32 ± 8.43% (n.s.). Eight of these sections are located in the Ebinur Lake Basin, with an average rate of change of +0.18 ± 0.46%; the other two sections (TS-1, TS-2) are in the central Tianshan, with a rate of change of +0.89 ± 3.77%. Among the eight sections in the Ebinur Lake Basin, section B4 showed the most significant increasing trend in discharge (p < 0.05), with a discharge ranging from 0.06 to 6.16 × 10⁶ m³ (mean 1.01 × 10⁶ m³), and a multi-year rate of change of +0.38 ± 0.32% (p < 0.05). In contrast, section W3 showed smaller changes in discharge (ranging from 0.05 to 1.30 × 10⁶ m³, mean 0.59 × 10⁶ m³), with a rate of change of only +0.05%, the least significant among all sections. Section TS-1 in the central Tianshan had a discharge ranging from 2.89 to 4.83 × 10⁶ m³ (mean 30.97 × 10⁶ m³) during the monitoring period, with a multi-year rate of change of +1.62 ± 5.53%. Between 1989 and 2006, the underlying surface characteristics of the catchment controlled by this section remained relatively stable, and discharge changes were gentle. However, after 2007, due to a continuous decrease in vegetation cover and an increase in precipitation within the catchment, the river discharge showed a clear increasing trend. Section TS-2 controls a larger catchment area, with a discharge ranging from 0.10 to 42.05 × 10⁶ m³ (mean 14.59 × 10⁶ m³), and a multi-year rate of change of +0.17 ± 0.28% (n.s.).

The discharge changes at non-glacier-dominated sections are influenced by complex mixed recharge processes. While these river sections are sustained by a combination of precipitation, seasonal snowmelt, and groundwater contributions (baseflow), their long-term variability is primarily sensitive to regional precipitation changes. Relevant studies indicate that the climate in the study area has recently been transitioning from warm-dry to warm-wet, with an increasing trend in annual precipitation. This climatic shift has led to a corresponding increase in the discharge of non-glacier-dominated rivers, where precipitation serves as a major driver of discharge fluctuations [36]. In addition to precipitation, changes in vegetation cover within the catchment also play an important regulatory role in surface discharge. For example, visual interpretation of multi-temporal high-resolution Google Earth imagery identifies marked meadow degradation within the B4 catchment after 2008, consistent with observations of localized habitat shrinkage in the Ebinur Lake Basin [37]. This study confirmed that localized habitat shrinkage resulted from anthropogenic activities. These alterations in the underlying surface modify the regional water balance by diminishing canopy interception and reducing the characteristically high evapotranspiration (ET) losses typical of arid zones, thereby physically enhancing the process of surface runoff generation.

It is important to note that since all monitored sections on the Pamir Plateau are located in high-altitude headwater regions where glacial meltwater is the primary component of total discharge, this water source composition significantly weakens the impact of precipitation changes on discharge. Furthermore, the increase in evaporation caused by rising temperatures also partially offsets the hydrological effects of increased precipitation. Based on these characteristics, this study classifies all sections on the Pamir Plateau as glacier-dominated. Therefore, an in-depth discussion of the impact of precipitation on the discharge of these sections is not included in the analysis.

3.3.2. Seasonal (Intra-Annual) Dynamics and Variations

To systematically investigate the seasonal distribution of river discharge, this study analyzed the multi-year average monthly discharge from March to November. Given that mountainous rivers generally enter a low-flow period in winter, the analysis focuses on the intra-annual distribution characteristics during the ablation and flood seasons (March–November). To reveal the patterns of geographical differentiation, the hydrological characteristics of each cross-section are elaborated by individual drainage basin units as follows.

In the Ebinur Lake Basin (Figure 10a), glacier-dominated cross-sections exhibit pronounced seasonal rhythms, with stable low-flow stability is observed in March, April, and November. Discharge rises rapidly from May onwards, with increasing temperatures, peaking in July and August, representing a typical ablation-driven unimodal regime. Due to the regulatory effects of alpine glaciers and perennial snowpack, spring floods in these rivers are less significant. Instead, summer discharge is highly concentrated, accounting for approximately 47% of the annual total, with autumn discharge generally exceeding that of spring discharge due to the sustained contribution of glacier meltwater. Notably, section B1 reaches its maximum discharge in August (23.17 × 10⁶ m³). In contrast, non-glacier-dominated cross-sections show distinct bimodal characteristics (Figure 10b). Discharge begins to increase in March, and several cross-sections (e.g., B4, B6, and W1) displaying a clear bimodal evolution pattern consisting of spring floods (April–May) and summer/autumn floods (June and September), reflecting the combined effects of seasonal snowmelt and precipitation. The intra-annual distributions for cross-sections W2, W3, and W4 are relatively stable but remains susceptible to disturbances from extreme weather events.

The intra-annual distribution of discharge in the central Tianshan Mountains is highly uneven, strongly governed by altitude and recharge sources (Figure 10c). Monthly discharge in glacier-dominated cross-sections generally follows a unimodal distribution, with runoff concentrated mainly in summer, followed by spring. Cross-section TS-7 peaks in July (9.38 × 10⁶ m³). Owing to the deep snowpack in this region (often persisting for more than six months), rising spring temperatures trigger substantial snowmelt, resulting in a prominent spring flood. Non-glacier-dominated cross-sections (e.g., TS-1 and TS-2) exhibit multimodal distributions (Figure 10d). The peaks of TS-1 occur in May, July, and September, with the maximum discharge in July at 18.38 × 10⁶ m³, indicating a precipitation-driven response. The peak of TS-2 appears approximately one month earlier than that of TS-1 (April and June), reflecting the earlier hydrological response of lower-altitude areas to seasonal snowmelt.

The ten cross-sections on the Pamir Plateau are all highly glacier-dominated, with seasonal discharge following a “summer-concentrated” pattern (Figure 10e,f), where summer runoff accounts for about 45% of the annual total. In the Kashgar River Basin, the four cross-sections (K1–K4) show an extremely significant unimodal trend, with peaks occurring between June and July. Among them, K1 records a maximum discharge of 57.87 × 10⁶ m³ in June, the highest value in the region. In the Taxkorgan River Basin, all cross-sections except T4 conform to the unimodal pattern. T6 reaches its peak in July (53.23 × 10⁶ m³), while T1 shows its minimum discharge in November. This high degree of consistency underscores the strong dependence of rivers in the Pamir Plateau on glacial ablation and highlights an increased risk of water resource volatility under the context of climate warming.

4. Discussion

4.1. Accuracy Evaluation of Discharge Estimation Results

To assess the accuracy of the discharge estimation results derived from the regionalization method, a comparative validation was conducted using measured discharge data against two estimation outcomes: one based on the regionalization method and the other on an estimation based on temporal upscaling of instantaneous flow (Figure 11). In the temporal upscaling method, the instantaneous flow obtained from remote sensing inversion was treated as the average flow for that month, and the monthly discharge was calculated through temporal integration.

The measured discharge data were sourced from the Wenquan and Bole hydrological stations in the Ebinur Lake Basin, and the Kalabeili hydrological station in the Kashgar River Basin. The Wenquan station corresponds to river cross-section B7, and the Bole station corresponds to section B8. The upstream inflow to the Kalabeili station is controlled by sections K0, K1, and K5, with no other tributaries in between; therefore, the sum of the discharge from these three sections represents the measured discharge at this station. Regarding the validation period, continuous measured data from 2017 to 2019 were used for the Wenquan and Kalabeili stations. However, due to data availability constraints, only partial measured data from 2017 to 2018 were available for the Bole station, making its validation period inconsistent with the other two stations. Although this shorter validation period at the Bole station limits our ability to fully capture inter-annual hydrological variations and long-term extreme events, its impact on the overall validation results is considered minimal. The available data still covers complete seasonal hydrological cycles, and the evaluation metrics achieved at this station (NSE = 0.84) remain highly consistent with the robust performance observed at the Wenquan and Kalabeili stations over longer periods. Therefore, while this objective limitation introduces slight uncertainty regarding the long-term validation at section B8, it does not undermine the overall conclusion regarding the reliability and superiority of the regionalization method.

A comparison between the measured discharge and the results from the two estimation methods reveals that the overall fluctuation trends of the measured data align well with both the regionalization method and the temporal upscaling estimation. However, the regionalization method provides a better fit. The accuracy evaluation results (

Table 3. Comparison of calculation accuracy between regionalization discharge and time process discharge.

River Section	NSE		RMSE
	Regionalization	Time Process	Regionalization	Time Process
B7	0.88	0.72	4.31	6.58
B8	0.84	0.62	3.14	7.70
K0, K1, K5	0.86	0.68	52.87	80.64

) show that the NSEs for the discharge estimated by the regionalization method were 0.88, 0.84, and 0.86, which are significantly higher than the 0.72, 0.62, and 0.68 obtained from the temporal upscaling estimation. Concurrently, the RMSE values for the regionalization method (4.31, 3.14, and 52.87 × 10⁶ m³) were also markedly lower than those of the temporal upscaling estimation (6.58, 7.70, and 80.64 × 10⁶ m³), indicating a smaller estimation bias. This validation demonstrates that, for monthly discharge estimation, the regionalization method holds a significant accuracy advantage over the temporal upscaling method. Specifically: (1) The NSE increased by an average of 0.18, showing a significant enhancement in simulation capability; (2) The RMSE decreased by an average of 35.7%, reflecting a considerable reduction in estimation error. This difference in accuracy primarily stems from the regionalization method’s ability to better account for the spatial heterogeneity of the catchments, whereas the temporal upscaling estimation, relying solely on the assumption of instantaneous flow, may introduce systematic errors. Therefore, the discharge estimation based on the regionalization method demonstrated more reliable applicability in this study.

From the river cross-sections monitored by remote sensing, sections B1 in the Ebinur Lake Basin, TS-1 in the central Tianshan, and K1 in the Pamir Plateau were selected as representative cases to compare the long-term discharge series estimated by the regionalization method and the temporal upscaling method (Figure 12). The results show that the discharge variation trends from both methods are generally consistent, but there are significant differences in their numerical ranges. Specifically, for section B1, the monthly discharge estimated by the temporal upscaling method ranged from 0 to 26.46 × 10⁶ m³, while the regionalization method yielded a range of 0 to 33.87 × 10⁶ m³, with the latter being 1.28 times higher on average. For section TS-1, the temporal upscaling results were 2.22 to 42.22 × 10⁶ m³, whereas the regionalization results were 2.89 to 54.83 × 10⁶ m³, an average of 0.77 times higher. For section K1, the temporal upscaling results ranged from 0 to 87.17 × 10⁶ m³, while the regionalization method gave a range of 0 to 109.83 × 10⁶ m³, an average of 1.26 times higher.

A comprehensive analysis indicates that the temporal upscaling estimation method systematically underestimates discharge but does not affect the overall trend of variation. The regionalization method, by integrating hydrological information from reference basins, can more accurately reflect the actual discharge conditions. This further illustrates the clear advantage of the regionalization method in estimating discharge in ungauged basins.

4.2. Divergent Responses of Mountain Catchments to Climate Warming

4.2.1. Scale Effects and the “Peak Water” Tipping Point

Numerous scholars, both domestically and internationally, have conducted extensive research on the changes in glacial discharge in various basins using a multitude of methods, yielding a series of important findings. Most studies indicate that glacial retreat significantly increases river recharge, thereby leading to a sustained increase in river discharge. Duethmann et al. [38] found through hydrological model simulations that the discharge in the headwaters of the Tarim River increased by 30% between 1957 and 2004, with the primary driver being accelerated glacial melt due to rising temperatures. The research by Yin et al. [39] showed that over the past five years, the total discharge and glacial meltwater discharge in the Yarkant River Basin have been continuously increasing at rates of 0.031 × 10⁹ m³·a⁻¹ and 0.011 × 10⁹ m³·a⁻¹, respectively. For the three regions studied in this paper—the Ebinur Lake Basin, the central Tianshan, and the Pamir Plateau—previous research has drawn similar conclusions. Qiao et al. [40], through the analysis of long-term hydrological data, pointed out that the annual discharge of the Bo and Jing rivers in the Ebinur Lake Basin both show a significant increasing trend over a long time scale. Shen et al. [41], using the Mann–Kendall method on four typical basins on the southern slopes of the Tianshan, showed that the annual discharge in these areas has significantly increased in recent decades, with rising temperatures being the main cause of increased discharge in glacial basins. Chevallier et al. [42] found that the discharge from the Pamir Plateau, a vital freshwater resource in Central Asia, has shown a continuous increasing trend in the past, while Kure et al. [43] further predicted that the river discharge in this region will continue to grow over the next 60 years.

However, the present study reaches a conclusion that contrasts with much of the existing literature—specifically, that the discharge in small mountain headwater catchments has exhibited a continuous decreasing trend in recent years. This discrepancy is not arbitrary but stems from fundamental differences in two key aspects: research scale and the dominant recharge sources. Specifically, previous studies [44] have predominantly focused on long-term discharge trends in large-scale river basins, where the hydrological regime is a complex composite of multiple water sources, including glacial meltwater, precipitation, and groundwater. In such large-scale systems, the localized declines in glacial meltwater can be temporarily masked or compensated by increased rainfall-runoff or enhanced baseflow from downstream reaches. In contrast, the small headwater catchments targeted in this study are characterized by a singular, glacier-dominant recharge structure. At this micro-scale, the catchments lack extensive downstream areas that could provide additional rainfall compensation or baseflow supplementation. Consequently, the hydrological response to glacier shrinkage is more direct and immediate: once the finite glacier storage of glacial ice is depleted, there are no alternative water sources to offset the deficit, resulting in a sustained decline in streamflow.

In addition to this study, several scholars have reached conclusions consistent with ours in their discharge research in different regions. Kogutenko et al. [45], analyzing three typical sub-basins of the Ili River Basin, found that since 1980, drastic glacial retreat has led to a continuous decline in flow in each sub-basin, with the contribution of glacial meltwater to total discharge decreasing annually. Zhang et al. [46] showed that the discharge of the Toshkan and Kumalak rivers in the Tianshan Mountains trended upward from 1979 to 2002 but shifted to a significant negative growth after 2002. Zhao et al. [3] using the VIC-CAS model to simulate five upstream basins on the Tibetan Plateau, found that by the end of the 21st century, glacier area will shrink by over 50%. Except for the headwaters of the Yangtze River, the glacial discharge in the remaining basins crossed a critical point (glacier loss > 20%) in the early 21st century and is expected to show a systematic decline after the 2030s. Deng et al. [19] based on long-term observations, pointed out that the discharge at the outlets of the Aksu, Kaidu, and Urumqi rivers has generally shown an increasing trend over the past 50 years but entered a decreasing phase after the 1990s. These studies collectively reveal that in the initial phase of climate warming, glacier-dominated basins experience an increase in discharge due to accelerated melting. However, in the long term, this process comes at the cost of consuming finite glacier storage. As highlighted in existing research [47], when glacier area loss exceeds a critical threshold (typically 20–30% of the original area), the contribution of glacial meltwater to river discharge will begin a continuous decline, triggering a “peak water” tipping point in discharge dynamics. This tipping point mechanisms is particularly pronounced in small catchments due to their limited water storage capacity and high dependence on glacial meltwater. Unlike large river basins that may still be in a “melt-increasing” phase due to their vast glacier reserves, the small headwater catchments in the Pamir and Tianshan regions studiees here have likely already crossed the critical threshold. Notably, the slight increasing discharge trend observed at certain cross-sections (e.g., T3 and T4) may reflect cases where glacial retreat is still contribution, and discharge has not yet reached its peak. Nevertheless, as glacial storage in these catchments continues to diminish in the future, their discharge trends are expected to align with the decreasing pattern observed in the other glacier-dominated cross-sections.

4.2.2. Diverse Hydrological Mechanisms: Glacier-Dominated vs. Non-Glacier-Dominated

By dividing the river sections into glacier-dominated and non-glacier-dominated types, this study provides a relatively clear physical framework for analyzing long-term runoff variations. The glacier-dominated sections are mainly distributed in high-alpine regions at elevations of approximately 3484–4270 m. The continuous increase in discharge at these sections primarily reflects the promoting effect of enhanced ice and snow melt on discharge under the background of rising temperatures, exhibiting strong temperature sensitivity. In contrast, the non-glacier-dominated cross-sections located near the mountain outlets (approximately 1000–2000 m) lack the regulatory effect of large-area glaciers. Their discharge variations are more influenced by precipitation and vegetation cover changes, exhibiting greater volatility and more complex underlying causes.

This binary division reveals the differential responses of various recharge mechanisms to climate warming. In glacier-dominated regions, continuous glacier ablation masks the negative impacts of regional aridification. The current discharge increase indicates an accelerated depletion of glacier mass storage, approaching or currently in the “peak water” phase. Without spatial differentiation, the signal of high-altitude glacier mass loss would be masked by the overall increase in runoff. Conversely, non-glacier-dominated sections are more susceptible to extreme precipitation and changes in underlying infiltration conditions. The focus for non-glacier-dominated regions is coping with adjustments in seasonal discharge distribution caused by earlier snowmelt and precipitation phase shifts (e.g., snow to rain). Overall, this classification significantly enhances the targeted accuracy of future hydrological regime predictions and risk assessments in arid regions.

4.3. Methodological Robustness, Uncertainties and Limitations

4.3.1. Rationale and Robustness of Method Selection

In reconstructing long-term streamflow series, this study utilizes quadratic polynomial regression as a spatial transfer function linking the reference basin to target basin. Within this framework, the pronounced seasonal and nonstationary nature of hydrological processes is primarily captured by observed daily discharge in reference basins, while the polynomial model transfers these characteristics to data-sparse target basins. Regarding regression methods, although harmonic regression, Fourier series, and spline interpolation offer theoretical advantages in capturing periodic fluctuations, they face significant limitations here. Harmonic regression and Fourier series heavily rely on high-frequency, continuous calibration data—unavailable due to the discrete nature of remote sensing retrievals. Applying high-order methods under such conditions can easily lead to overfitting and unrealistic numerical oscillations [48,49]. Similarly, spline interpolation is highly sensitive to outliers inherent in remote sensing data. Low-order polynomials therefore demonstrate greater robustness, ensuring reconstructed results remain physically reasonable under sparse sampling conditions. In future work, with enhanced observation networks, we plan to incorporate machine learning approaches (e.g., random forests or LSTM) or hybrid physics-based models to better capture extreme nonlinear responses.

4.3.2. Error Propagation from Remote Sensing to Long-Term River Discharge

It is important to acknowledge the propagation of methodological uncertainties throughout our framework. In mountainous regions like Tianshan–Pamir, the spectral signatures of topographic shadows mimic water bodies, posing challenges for NDWI-based retrievals. To address this, we employed Linear Spectral Unmixing (LSU). By defining a “Valley” training area, LSU identifies and eliminates topographic shadow interference. Our sensitivity analysis demonstrates that the 70% water-fraction threshold is highly robust: ±10% variations result in marginal width fluctuations relative to long-term trends. However, in extreme cases of steep terrain where shadows completely cover the river, LSU may still misclassify water components.

These initial width errors propagate and are nonlinearly amplified when converted to instantaneous discharge via the Manning–Strickler formula. This amplification stems primarily from the equation’s high sensitivity to channel roughness (n) and geometric parameters. In this study, the roughness values (n) were initially determined based on field observations (bed material, channel morphology, riparian vegetation) and referenced to the Table of Roughness Values for Natural Rivers [3]. Subsequently, these uncertainties propagate through the polynomial regression used for daily reconstruction. During temporal integration to monthly discharge, while high-frequency random errors are effectively smoothed out, systematic biases from the initial inversion persist in the final estimations. To characterize this cumulative uncertainty, we employed non-parametric Sen’s slope confidence intervals (CIs), offering a scientifically rigorous range that reflects the robustness of our results.

4.3.3. Sensitivity to Reference Basin Selection

The core of the spatial regionalization method hinges on the consistency of hydrological characteristics between reference and ungauged basins, making discharge reconstruction results highly sensitive to reference basin selection. Although this study strictly followed principles of spatial proximity and hydrological similarity in selecting three high-quality reference basins (e.g., the Jinghe River Basin), pronounced spatial heterogeneity—driven by complex topography and steep vertical climate gradients in high-alpine regions—still introduces uncertainties. Even within the same macro-hydrological region, variations in glacier coverage and microclimates persist. The model is highly sensitive to the unique discharge generation signals of the reference basin: for instance, if the reference basin has a higher proportion of ice meltwater, it may systematically overestimate summer discharge peaks in the target catchment. Conversely, for non-glacier-dominated cross-sections, if the reference basin fails to capture localized extreme precipitation, reconstructed fluctuation may be overly smoothed. While matching with a single reference basin is reasonable under data constraints, future studies could adopt an ensemble approach using multiple reference basins or integrate remote sensing-derived physical variables to construct dynamic similarity weights.

4.3.4. Limitations in Long-Term Validation

The shortage of hydrological records in the Tianshan–Pamir region inherently limits our ability to validate long-term discharge results. Our current assessment relies on three specific stations providing only 2 to 3 years of observation data. We used a cross-validation strategy to ensure the independence of the validation process and avoid “circular validation”.

Specifically, the Bole station only has data from 2017 to 2018. While this shorter period restricts our ability to capture inter-annual hydrological variability and long-term extreme events, its influence on the overall validation is deemed minimal. The available data still covers complete seasonal hydrological cycles (including extreme high and low flows), providing a robust baseline for the model. Furthermore, the performance metric achieved at the Bole station (NSE = 0.84) remains highly consistent with the robust results observed at the Wenquan and Kalabeili stations over longer timeframes. However, we emphasize that the 31-year reconstruction sequence is far longer than our validation period, implying the data may not fully capture the impacts of decadal climatic shifts. While these limitations introduce slight uncertainty at specific sections, they do not undermine the overall conclusion regarding the reliability of the regionalization method; we interpret these results as reliable estimations under data-constrained conditions rather than absolute historical records.

5. Conclusions

This study integrated UAV and satellite imagery-based flow inversion with a spatial regionalization method to systematically estimate discharge time series in the data-scarce Tianshan–Pamir regions. Leveraging digital river channel models derived from high-precision UAV data and field measurements, the instantaneous discharge inversion exhibited excellent validation performance across the three study areas: Ebinur Lake Basin (RMSE = 1.42, NSE = 0.98), central Tianshan (RMSE = 4.43, NSE = 0.98), and Eastern Pamir Plateau (RMSE = 12.50, NSE = 0.84). The overall correlation between estimated and measured instantaneous discharge reached (R² = 0.94, p < 0.01), confirming the reliability of this baseline for regionalization.

Through the selection of reference basins guided by spatial proximity and hydrological similarity, the regionalization method successfully reconstructed monthly discharge series from 1989 to 2020. Compared with the traditional temporal upscaling approach, this method significantly improved accuracy, with the NSE increased by 0.18, and the RMSE decreasing by an average 35.7%. An analysis of the 31-year discharge evolution revealed that the discharge from glacier-dominated cross-sections showed a significant decreasing trend (average rate of change −4.05%), with the Pamir Plateau experiencing the largest decline (−7.09%) attributed to large-scale glacial retreat. In contrast, non-glacier-dominated cross-sections exhibited a slight increasing trend (+0.32%), primarily driven by shifts in regional precipitation and vegetation cover.

The remote sensing-regionalization integration method developed in this study offers a reliable technical approach for estimating long-term discharge series in data-scarce regions. More importantly, this study not only validates the reliability of the “remote sensing regionalization” method for runoff reconstruction in ungauged basins, but also uncovers the profound complexity of hydrological responses across watersheds with distinct recharge types and spatial scales under climate change. Ultimately, these findings underscore the critical importance of implementing independent monitoring and targeted assessments of small watersheds to safeguard sustainable water resource management in arid regions amid global change.