Enhancing river discharge inversion for the midstream Jialing River (China) using the Google Earth Engine platform

Rivers are complex systems where natural water flows through channels, playing a critical role in the water cycle. They serve as primary sources of water supply and mechanisms for transporting surface runoff from ecosystems to water bodies. Meybeck et al. (1996) categorized rivers based on flow characteristics, basin area, and width: small rivers (40–200 m wide), medium rivers (200–800 m wide), and large rivers (800–1,200 m wide). Rivers act as essential links between land and sea in the water cycle (Wohl 2015).

Runoff is a key hydrological parameter essential for flood forecasting and water resource management and serves as a critical climate variable in the hydrological cycle (Perry et al. 1996; Gleason et al. 2014; Yu et al. 2021). Despite its known importance, acquiring long-term runoff data is challenging in certain regions due to environmental, transportation, and economic constraints, leading to a scarcity of regional runoff data. Some basins remain unmeasured, and recently measured basins, particularly small and medium rivers, are decreasing (Meybeck et al. 1996).

The lack of runoff data significantly hampers water resource management, but remote sensing offers an alternative to obtain river flow information effectively, monitoring water resources based on water level and flow (Venkatalaxmi et al. 2004; Tang et al. 2009; Sun et al. 2012; Sulistioadi et al. 2015). Compared to traditional methods, remote sensing data have advantages like minimal ground limitations, wide coverage, and easy access, providing essential supplementary data for river runoff monitoring and estimation.

Remote sensing extraction of water body information is a prerequisite for river runoff inversion. Water extraction methods in remote sensing include optical and microwave techniques. Declaro & Kanae (2024) explores the potential and limitations of integrating Landsat 8/9, Sentinel-2, and Sentinel-1 SAR satellite data to enhance surface water monitoring. Liu et al. (2020) studied the characteristics of water area changes in Taihu Lake using Landsat imagery and the modified normalized difference water index (MNDWI). Generally, optical and microwave remote sensing have distinct advantages and disadvantages for water extraction. Optical remote sensing offers rich band information and established water index calculation methods; however, it is susceptible to cloud cover and weather conditions, reducing the number of available target water samples. Conversely, microwave remote sensing can penetrate clouds, is less affected by weather, and can obtain more target water samples.

On the basis of remote sensing extraction of water information, significant progress has been made in remote sensing inversion of river runoff. Bjerklie et al. (2003) proposed a runoff estimation model using remote sensing flow estimation techniques with flow velocity, river width, and depth as input parameters. Kebede et al. (2020) estimated river runoff in the high mountain regions of the Qinghai-Tibet Plateau using Landsat series data through the improved Manning's formula method, the empirical formula method, and the relationship fitting method. Tarpanelli et al. (2017) estimated and predicted the flow of the Benue River using MODIS and altimetry data. Lin et al. (2023) utilized Landsat imagery to extract multi-temporal river widths on a global scale and employed the Bayesian AMHG-Manning (BAM) algorithm, along with a geomorphology-enhanced variant (geoBAM), to estimate river discharge.

Google Earth Engine (GEE), a geospatial data analysis cloud platform developed by Google, provides global Sentinel-1/2, Landsat 8, MODIS, and other multi-source remote sensing data, transforming traditional remote sensing data processing methods. It can rapidly process large amounts of data, significantly facilitating water extraction research (Gorelick et al. 2017). Medium-sized rivers play crucial roles in various countries or regions, providing valuable water resources, supporting agricultural irrigation and industrial water needs, and serving as important transport routes. However, in economically underdeveloped countries or regions, the insufficient number of hydrological stations results in inadequate acquisition of river flow data. As a major river in Southwest China, the Jialing River significantly impacts the economic development and water resource supply of surrounding cities. The middle section of the Jialing River, the Jinxi segment, supports certain navigation and hydropower functions and shares common characteristics of medium-sized rivers. Its runoff data are vital for water resource management, flood forecasting, and defense. Therefore, validating the applicability of different models to medium-sized rivers and conducting runoff inversion studies in this area are of great practical significance.

Against this backdrop, this study selects the Jinxi segment of the Jialing River as the research area. Based on the Sentinel-2 and Landsat 8 remote sensing data provided by the GEE cloud platform, the study extracts water bodies using the MNDWI and performs runoff inversion using the relationship fitting method and the improved Manning's formula method. For MODIS remote sensing data provided by the GEE, the study uses the C/M signal method for runoff inversion. Finally, the study compares and analyzes the three methods to provide references for runoff monitoring of medium-sized rivers.

The Jialing River, originating from the Qinling Mountains in Shaanxi Province, China, traverses Gansu and Sichuan before converging with the Yangtze River at Chaotianmen in Chongqing. Spanning a total length of 1,345 km, the main stream encompasses a drainage area of approximately 156,000 km². Its average annual runoff measures 655.2 billion m³, with an average annual sediment transport of 9.67 million tons (Ministry of Water Resources 2020). Predominantly coursing through the Sichuan Basin, the region features a subtropical monsoon climate, characterized by abundant rainfall that averages 1,000 mm annually (Xu et al. 2008; Li & Wei 2016). The eastern, western, and northern segments of the Jialing River basin boast elevated terrains, sloping gradually toward the southeast. The upper reaches predominantly comprise mountainous terrain, characterized by narrow valleys and steep river beds.

The Jinxi Hydrological Station is located in Jinxi Town, Peng'an County, Nanchong City, Sichuan Province, China. The Jinxi section of the Jialing River is situated in the middle reaches of the Jialing River, with a basin area of 74,000 km², making it a medium-sized basin. According to statistics from the Jinxi Hydrological Station, the long-term average annual runoff is 15.23 billion m³, which is moderate and sufficient to meet the agricultural irrigation, industrial water, and domestic water needs of the surrounding areas.

The basin features significant topographical variations and diverse landforms, predominantly consisting of hills and mountains. The region is interspersed with numerous rivers and ravines, creating a rich ecological environment with a variety of aquatic flora and fauna. The climate is classified as subtropical monsoon, characterized by distinct seasonal changes. During the rainy season, the river flow increases significantly. The region's well-developed water system supports a certain scale of freight and navigation.

The remote sensing data utilized in this study were sourced from the GEE platform, comprising satellite imagery from Sentinel-2, MODIS, and Landsat 8.

The Sentinel-2 satellite constellation comprises two satellites, Sentinel-2A and Sentinel-2B, with a revisit period of 10 days for each satellite and a combined revisit period of up to 5 days. Sentinel-2 boasts 13 spectral bands, featuring varying spatial resolutions: bands B2, B3, B4, and B8 offer a resolution of 10 m; bands B5, B6, B7, B8a, B11, and B12 provide a resolution of 20 m; bands B1, B9, and B10 present a resolution of 60 m.

Landsat 8, with a revisit period of 16 days, is equipped with the Operational Land Imager and Thermal Infrared Sensor. It encompasses 11 spectral bands, with spatial resolutions as follows: bands B1 to B9 offer a resolution of 30 m; band B8 presents a resolution of 15 m; and bands B10 and B11 feature a resolution of 100 m.

MODIS, hosted aboard the Terra and Aqua satellites, serves as a moderate-resolution imaging spectroradiometer. It incorporates 36 spectral bands, characterized by diverse resolutions: bands B1 and B2 exhibit a resolution of 250 m; bands B3–B7 offer a resolution of 500 m; and bands B8–B36 provide a resolution of 1,000 m.

The data utilized in this study are radiometrically and geometrically corrected products accessible on the GEE platform. For water body extraction, the MNDWI was computed using bands B3 and B11 for Sentinel-2 and bands B3 and B6 for Landsat 8.

The figure indicates that cloud cover tends to remain high from November to March, while it is relatively lower from April to October. High cloud cover can affect the identification of water bodies and introduce errors in calculating hydraulic parameters.

To mitigate the impact of weather conditions on the quality of optical remote sensing images, only data from April to October of each year were processed and analyzed. Additionally, remote sensing images underwent careful selection and cloud removal based on the prevailing cloud cover within the study area. Landsat 8 and Sentinel-2 data were employed for the improved Manning's formula method and the relationship fitting method, while MODIS data were employed for the C/M signal method.

In situ gauge data of daily runoff from the Jialing River, recorded at the Jinxi hydrological station spanning the period from 2017 to 2020, were acquired from the Ministry of Water Resources of China. These datasets serve as the basis for calibrating and validating both the relationship fitting method and the C/M signal method. Unlike the improved Manning's formula method, which does not necessitate calibration, the relationship fitting method and the C/M signal method require rigorous calibration and validation procedures using observed data. To conduct the calibration and validation, the data from April to October 2017 to 2019 are designated as calibration datasets. Similarly, the data from April to October 2020 are earmarked as validation datasets. This division allows for the robust evaluation and refinement of the models, ensuring their reliability and accuracy in estimating runoff from the Jialing River.

Various satellite sensors are currently available for measuring river width, each offering different temporal and spatial resolutions. However, this approach can be susceptible to image artifacts, such as vegetation, wetland areas, and surrounding rocks, which can introduce measurement errors (Bjerklie et al. 2003). Moreover, the spatial resolution of the satellite plays a critical role in the accuracy of river width measurement. Hence, employing high-resolution images is essential for precise river width estimation.

Expanding on the computation of the MNDWI, the study employs the Otsu method for binarization of the target river segment (Otsu 1975), facilitating the quantification of the water body area. This technique establishes a threshold based on the grayscale characteristics of the image, partitioning it into background and target segments. This minimizes intra-class variance and maximizes inter-class variance, achieving optimal image binarization (Figure 3).

Roughness is a crucial parameter in hydraulic calculations, as it reflects the resistance encountered by flowing water. This resistance is influenced by factors such as vegetation, channel materials, obstacles, channel curvature, and irregularities (Coon 1998). Different methods exist for estimating roughness, including visual interpretation or assigning appropriate tabulated values (Table 1) (Chow 1959). Moreover, when measured data are unavailable, roughness values can be derived based on the specific conditions of the target river section (Chow 1959).

The research conducted by Moody & Troutman (2002) established regression relationships between river width, depth, and discharge, as depicted in Equations (5) and (6).

The C/M signal method operates under the assumption that natural environmental factors such as atmospheric water vapor content and surface temperature uniformly impact the brightness temperature data of each pixel. Based on this premise, it delineates C pixels and M pixels. Typically, all ‘dry pixels’ within the coverage area, representing entirely land areas, are classified as C pixels. These serve as calibration pixels within the observed area, positioned in close proximity to manually selected ‘wet pixels’. ‘Wet pixels,’ which partially or completely cover the river channel, are identified as M pixels, representing observed pixels for river discharge assessment.

In this study, MODIS satellite data were used to identify dry and wet pixels in the study area. A suitable wet pixel near the Jinxi hydrological station was selected as the center of the M pixel, ensuring that it did not include curved river channels or adjacent ponds, paddy fields, and other water bodies. A 3 × 3 pixel matrix was created with the M pixel at its center, and the average brightness temperature of this matrix was computed to represent the brightness temperature of the M pixel (Figure 5). Simultaneously, a 12 × 12 pixel matrix centered on the M pixel was constructed, and the pixel with the brightness temperature in the 95th percentile within this matrix was designated as the C pixel. The C/M ratio was then fitted with the measured discharge to develop a regression equation and establish a regression model, which was subsequently used to estimate the discharge (Figure 6).

The effective river width in this region is significantly influenced by seasonal fluctuations, with rainfall serving as a primary driver of changes in river flow and, consequently, river width. During periods of higher rainfall, increased water inflow expands the river channel, leading to substantial variations in width, particularly during high-flow seasons. Based on the observed variations in river width, the changes can be categorized into three distinct phases.

From 2017 to 2018, the river flow at the Jinxi section of the Jialing River exhibited an annual increase, marked by a significant rise in volume. This expansion of the river basin area led to pronounced fluctuations in river width, driven largely by cumulative regional precipitation events.

In 2019, river flow stabilized, with less variation compared to previous years. Reduced seasonal rainfall intensity resulted in smaller fluctuations in the river basin area and narrower changes in river width.

In 2020, flow dynamics were more variable, with low flow observed in May and high flow in September. These shifts caused notable fluctuations in the river basin area and substantial changes in river width, reflecting the sensitivity of width to seasonal flow variations.

Despite these fluctuations, river width generally ranged between 260 and 315 m throughout the study, with an overall increasing trend. This upward trajectory suggests evolving hydrological conditions at the Jinxi section, with potential implications for river management strategies. The findings highlight the importance of accounting for seasonal variability and selecting appropriate timeframes for accurate river width estimation.

The river depth calculation formula employed in this study emphasizes river flow as a key determinant. Given the region's pronounced precipitation from May to October, peak depth values are observed during this period. Although variations in river depth are less significant than changes in river width, depth remains a critical hydraulic parameter in the model.

From early 2017 to 2019, a steady increase in river flow significantly impacted river width. The increased flow volume also contributed to deepening certain river sections, though the depth changes were less pronounced than those in width.

By mid-2019, river flow stabilized, leading to reduced fluctuations in both river width and depth. Following this stabilization, depth variations remained within a narrower range.

From late 2019 to 2020, flow patterns became more variable, with notable differences observed in May and September. While May experienced relatively low flow, September saw a sharp increase, causing significant changes in both river width and depth. However, river depth variations generally remained within a 3–4 m range, indicating that while the variations in river depth were less pronounced than those in river width, the depth still responded to seasonal changes in flow.

Compared to river width, river depth appears more sensitive to long-term flow trends than short-term fluctuations. This suggests that while immediate flow changes cause less dramatic depth variations, seasonal and long-term flow dynamics exert a cumulative influence on depth.

The estimation of discharge for the Jinxi section of the Jialing River employed the improved Manning's formula, the relationship fitting method, and the C/M signal method, with their respective performance evaluated. River width calculations were conducted using Landsat 8 and Sentinel-2 imagery in conjunction with the river width calculation formula (2), while river depth estimations were derived from the discharge and effective depth formula (6). Slope determination utilized a 30 m resolution DEM elevation image through relationship fitting, and river roughness was established by integrating formula (4) with visual interpretation of remote sensing images.

From the figure, it can be observed that the river width–discharge model, established using the relationship fitting method combined with Landsat 8 and Sentinel-2 remote sensing images, performs well, with an R² value exceeding 0.869. The R² value of the C/M ratio–discharge model established using the C/M signal method is 0.8. The accuracy evaluation of the three methods is shown in Table 2.

The analysis highlights the superior performance of the improved Manning's formula method for flow estimation compared to the C/M signal and relationship fitting methods. The root mean square error (RMSE) of the improved Manning's formula method is 50.2, which is significantly lower than that of the C/M signal method (69.5) and the relationship fitting method (117.1). This indicates that flow estimates from the improved Manning's formula method align more closely with observed values. Lower RMSE values demonstrate higher model accuracy, and the improved Manning's formula method outperforms the other approaches in this regard.

Similarly, the relative RMSE (RRMSE) of 4.71 for the improved Manning's formula method is smaller than the RRMSEs of the C/M signal method (5.88) and the relationship fitting method (16.15). The normalized RRMSE highlights the improved Manning's formula's superior accuracy and reliability across varying flow conditions.

The Nash–Sutcliffe Efficiency (NSE) values further validate this method's effectiveness. The improved Manning's formula achieved an NSE of 0.956, which is higher than both the C/M signal method (0.931) and the relationship fitting method (0.954). The closer the NSE value is to 1, the better the model's predictive performance, reinforcing the improved Manning's formula as the most reliable option.

Additionally, the mean bias error (MBE) reveals nuanced performance differences. The improved Manning's formula and the C/M signal method exhibit minor underestimation tendencies, with the improved Manning's formula showing a smaller bias. Conversely, the relationship fitting method overestimates flow rates, particularly during high-flow conditions, making it less reliable for accurate discharge predictions.

Overall, the improved Manning's formula method offers the most precise and reliable flow estimates for the Jinxi section of the Jialing River, characterized by minimal error, high accuracy, and lower bias. While the C/M signal method is a dependable alternative, particularly with robust observational data, the relationship fitting method's tendency to overestimate flow limits its applicability, especially in high-flow scenarios.

The study utilized three models (the improved Manning's formula method, the relationship fitting method, and the C/M signal method) to estimate the flow rates of the Jialing River at the Jinxi section. The results indicate that all three methods are feasible for the daily flow estimation of medium-sized rivers (Kebede et al. 2020). The improved Manning's formula method and the C/M signal method are particularly reliable for flow estimation, with the former performing better than the latter.

Lin et al. (2023) employed satellite-derived river widths and a geomorphology-enhanced Bayesian model (geoBAM) to achieve accurate discharge estimations on a large scale. However, the improved Manning's formula offers greater stability in terms of parameters such as slope and roughness, making it more suitable for rivers with well-defined hydraulic characteristics. While Lin et al. (2023) highlighted the importance of river width in their model, this study demonstrates that the accuracy of both width and depth calculations is crucial for the performance of the improved Manning's formula as well as the relationship fitting method. Although the improved Manning's formula method and the relationship fitting method are influenced by various hydraulic parameters, these impacts can be mitigated using high-resolution remote sensing imagery and effective empirical formulas. The C/M signal method, on the other hand, requires a series of observed flow data to construct a regression model, which can be obtained by installing automatic flow recording devices to secure stable and reliable observation data (Shi et al. 2020).

To some extent, the improved Manning's formula and the C/M signal method tend to underestimate flow rates, while the relationship fitting method tends to overestimate them. For the relationship fitting method, the estimation of temporal changes in the flow rate is significantly affected by the average river width. The accuracy of the average river width calculation influences the overall precision of the model and the flow estimation results. For the improved Manning's formula method, the slope and roughness have a certain stability and do not significantly affect the model, while river depth and width are crucial hydraulic parameters. Therefore, the accurate calculation of average river width and depth is essential when using the improved Manning's formula method. Given the consideration of different river profiles, the improved Manning's formula method is suitable for rivers with clear channel conditions, while, for more complex rivers, the method can be used if the river width meets the requirements (LeFavour & Alsdorf 2005).

For the C/M signal method, the most critical parameters are the dry and wet pixels. The selection and range determination of these pixels should follow specific selection principles, and the constructed model must choose the appropriate fitting equation based on different situations (Xu et al. 2021).

Overall, the study of the Jialing River at the Jinxi section demonstrates that the improved Manning's formula method is the most suitable for this river section. This suitability arises because the improved Manning's formula method considers hydraulic parameters such as slope and roughness, which have a certain stability, and it also reduces the impact of inaccuracies in river width calculation. This makes the flow rate estimation using this method more reliable. For the relationship fitting method, the accuracy requirement for river width calculation is higher. When using this method for river flow estimation, choosing remote sensing imagery with higher spatial resolution can effectively reduce the impact of river width on flow estimation.

Finally, under conditions resembling those at the Jinxi section of the Jialing River – characterized by specific river width, slope, and depth – the three hydrological modeling approaches discussed in this study, namely the improved Manning's formula, the relationship fitting method, and the C/M signal method, prove effective for medium-sized river systems. These models offer reliable tools for simulating river runoff, which is critical for understanding and managing rivers in regions with dynamic hydrological conditions.

This study provides a comparative analysis of the strengths and limitations of each method in the context of medium-sized rivers. Key hydraulic parameters, such as river width and depth, significantly influence flow estimation accuracy. For the improved Manning's formula and relationship fitting methods, precise river width estimation is paramount, while the C/M signal method relies heavily on accurately distinguishing wet and dry pixels.

While these models demonstrate robust performance for medium-sized rivers, their scalability and adaptability to larger river systems remain areas for future exploration. Extending these approaches to broader spatial scales could enhance regional and global hydrological assessments, especially in regions with limited data and high spatial heterogeneity. Additionally, hybrid models that integrate the strengths of all three methods hold promise for improving accuracy and versatility, accommodating diverse variables like climate, topography, and human influences.

Future research should prioritize integrating remote sensing data with ground-based observations to enable real-time monitoring and more accurate model calibration. Emerging technologies, including satellite imagery, advanced remote sensing techniques, and machine learning, can further enhance the predictive power of these models. Recent findings (Lou et al. 2022; Huang et al. 2024) emphasize the potential of combining traditional hydrological models with modern technological innovations to improve river flow simulations.

In conclusion, this study underscores the feasibility and effectiveness of the three river flow inversion methods for medium-sized rivers, while highlighting the importance of key hydraulic parameters in determining model accuracy. As hydrological modeling continues to evolve, these findings contribute to advancing our understanding of river systems and support informed decision-making in sustainable water resource management.

To date, various techniques have been developed for estimating river discharge using remote sensing datasets, highlighting their potential for diverse hydrological applications. These methods rely heavily on accurately deriving surface hydraulic parameters from space, such as river width, depth, slope, flow velocity, and roughness, which are critical for understanding river dynamics and ensuring the precision of discharge estimations. In this study, the GEE platform was employed to process Landsat 8 and Sentinel-2 data for water body extraction and MODIS data for identifying dry and wet pixels, enabling the estimation of key hydraulic parameters. Three distinct models – the improved Manning's formula, the relationship fitting method, and the C/M signal method – were utilized to estimate discharge at the Jinxi section of the Jialing River. Model accuracy was assessed by comparing observed and estimated discharge values, while the influence of hydraulic parameters on model performance was systematically analyzed. This approach yielded the following key findings:

• (a). The accuracy of discharge inversion models, particularly the improved Manning's formula and the relationship fitting method, is strongly influenced by hydraulic parameters. For the improved Manning's formula, river width and depth are especially critical, as the model is highly sensitive to variations in these parameters. In contrast, the relationship fitting method relies more heavily on river width, underscoring the importance of precise width estimation when applying this approach. Consequently, the accurate determination of river width and depth is essential for achieving reliable discharge estimates using these models. Emphasizing the precise measurement of these key hydraulic parameters is crucial for ensuring the robustness and applicability of discharge inversion techniques.

• (b). While satellite altimetry data for estimating river depth are unavailable, empirical equations can be developed by integrating other hydraulic parameters to infer river discharge. These equations offer a practical solution, particularly in regions with limited observational data. However, their reliance on specific assumptions and simplifications can introduce uncertainties. When applied to rivers with complex hydraulic conditions or sparse data availability, the accuracy and reliability of these equations may be diminished. Improving the precision of hydraulic parameters – using higher-resolution remote sensing data or integrating ground-based observations – can help mitigate these errors and enhance overall model performance. In the Jinxi section of the Jialing River, the improved Manning's formula and the C/M signal method exhibit a slight tendency to underestimate discharge, whereas the relationship fitting method tends to overestimate it. Despite this, both the improved Manning's formula and the C/M signal method produce estimates closely aligned with observed field measurements, demonstrating their reliability for practical applications. Additionally, the NSE values further affirm the stability and accuracy of all three models for discharge estimation in this region.

• (c). The accuracy of discharge inversion using the C/M signal method is highly sensitive to the selection of dry and wet pixels. To optimize the selection of wet pixels, it is crucial to avoid pixels from curved river channels or adjacent areas such as ponds and paddy fields, as these can introduce significant errors. Additionally, to minimize the influence of local anomalies and variations in pixel reflectance, a more robust approach is recommended: averaging the wet pixel values within a matrix centered on the target pixel. This technique helps to mitigate the impact of outliers and provides a more reliable basis for discharge estimation. Enhancing pixel selection and processing techniques in this manner can substantially improve the accuracy and reliability of the C/M signal method.

This research was jointly supported by the Special Funds of the National Natural Science Foundation of China (Grant No. 42341102) and the National Science and Technology Basic Resource Investigation Program (Grant No. 2017FY100904).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.