Enhancing runoff predictions in data-sparse regions through hybrid deep learning and hydrologic modeling | Scientific Reports

Scientific Reports volume 14, Article number: 26450 (2024) Cite this article

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Amidst growing concerns over climate-induced extreme weather events, precise flood forecasting becomes imperative, especially in regions like the Chaersen Basin where data scarcity compounds the challenge. Traditional hydrologic models, while reliable, often fall short in areas with insufficient observational data. This study introduces a hybrid modeling approach that combines the deep learning capabilities of the Informer model with the robust hydrological simulation by the WRF-Hydro model to enhance runoff predictions in such data-sparse regions. Trained initially on the diverse and extensive CAMELS dataset in the United States, the Informer model successfully applied its learned insights to predict runoff in the Chaersen Basin, leveraging transfer learning to bridge data gaps. Concurrently, the WRF-Hydro model, when integrated with The Global Forecast System (GFS) data, provided a basis for comparison and further refinement of flood prediction accuracy. The integration of these models resulted in a significant improvement in prediction precision. The synergy between the Informer’s advanced pattern recognition and the physical modeling strength of the WRF-Hydro significantly enhanced the prediction accuracy. The final predictions for the years 2015 and 2016 demonstrated notable increases in the Nash–Sutcliffe Efficiency (NSE) and the Index of Agreement (IOA) metrics, confirming the effectiveness of the hybrid model in capturing complex hydrological dynamics during runoff predictions. Specifically, in 2015, the NSE improved from 0.5 with WRF-Hydro and 0.63 with the Informer model to 0.66 using the hybrid model, while in 2016, the NSE increased from 0.42 to 0.76. Similarly, the IOA in 2015 rose from 0.83 with WRF-Hydro and 0.84 with the Informer model to 0.87 using the hybrid approach, and in 2016, it increased from 0.78 to 0.92. Further investigation into the respective contributions of the WRF-Hydro and the Informer models revealed that the hybrid model achieved the optimal performance when the contribution of the Informer model was maintained between 60%-80%.

In recent decades, floods have been recognized as one of the most frequent and devastating natural disasters, inflicting significant damage on communities worldwide1,2. The increasing frequency and intensity of such events, driven by climate change and environmental degradation, have underscored the urgent need for improved flood prediction and management strategies especially in data-scarce regions. In these underserved areas, the lack of adequate hydrological data has particularly exacerbated the challenges of providing timely and accurate flood forecasting3,4,5. Enhancing the precision of flood forecasting in data-scarce regions has become a critical focus of contemporary hydrological research6.

Traditionally, the runoff prediction has heavily relied on hydrologic models that simulate the movement and distribution of water within a watershed7. Despite their sophistication, traditional hydrologic models, including advanced systems like WRF-Hydro, face several limitations and challenges in predicting runoff accurately8. To construct accurate hydrologic models, a comprehensive consideration of all aspects of the hydrological cycle was required, and appropriate mathematical equations were selected to describe these processes. This involved the calibration of multiple parameters, encompassing meteorological conditions, soil properties, land use, and vegetation cover. Extensive and high-quality data such as precipitation, temperature, and land use characteristics were utilized for the calibration and validation of these models to ensure their accuracy and reliability, before the models could be applied in practice9,10,11. For example, Xiang et al.12 utilized the WRF-Hydro model to simulate the atmospheric-hydrological interactions in Northwestern Mexico during the years 2004 and 2013, highlighting the challenges associated with tuning multiple parameters to accurately reflect the complex environmental and meteorological conditions; Silver et al.13 refined the accuracy of the simulations of five flood events in arid and semi-arid regions of the United States, by categorically calibrating parameters based on land use types. But in data-scarce regions, the absence of reliable and continuous observational data can significantly hinder the models’ accuracy and reliability.

Another challenge of hydrologic models is they often require complex calibration processes involving numerous parameters, which can be both time-consuming and computationally expensive14,15,16,17. This calibration is crucial as it adjusts the model to represent the actual conditions accurately, but the calibration becomes less effective without sufficient data. Additionally, physics-based models are inherently constrained by the assumptions embedded in their formulation18. For instance, they may not fully capture the nonlinear and dynamic interactions between different hydrological processes under extreme weather conditions. This limitation can lead to substantial errors during unusual or extreme hydrological events, such as flash floods or prolonged droughts, when the system behavior significantly deviates from the model’s standard settings.

The advancements in deep learning have provided novel alternatives for addressing the challenges of runoff prediction in data-scarce regions4,19,20,21. Techniques such as transfer learning (TL) have emerged as particularly promising, enabling the application of models trained on data-rich areas to regions lacking sufficient data. This approach leverages the generalized patterns learned from extensive datasets to make informed predictions in new environments, thus potentially overcoming the data dependency that limits traditional hydrologic models22. In data-scarce regions, transfer learning can enhance prediction accuracy by leveraging knowledge from data-rich areas. However, significant differences in climate, geology, land use, and other conditions between regions may affect the adaptability of model parameters. If the model fails to adequately adjust during the transfer process, it may lead to a decline in predictive performance. Neural networks (NNs), including long short-term memory (LSTM), Graph WaveNet, and convolutional networks, have proven effective in capturing hydrologic dynamics from extensive datasets23. These models are versatile, as they can be used for simulating not only streamflow but also other components of the hydrologic cycle24,25. However, while deep learning offers significant advantages, it also comes with its own set of challenges. One major issue is the “black box” nature of these models, where the decision-making process is not transparent, making it difficult to interpret the model outputs. Additionally, deep learning models require large amounts of data for training to achieve high accuracy, which can be a paradox in situations where they are specifically employed to overcome data limitations26. They are also sensitive to the quality of the training data, where biases in the dataset can lead to skewed or incorrect predictions27,28.

The integration of deep learning with traditional hydrologic models presents a synergistic approach that can harness the strengths of both methodologies29,30,31,32. Hydrologic models can compensate for the lack of interpretability in deep learning model results, by providing a physics-based framework that lends themselves to clearer understanding and validation of model behaviors. Furthermore, the robustness of physical models in terms of handling special cases not typically represented in the trained dataset can help mitigate the data quality issues faced by deep learning models. This combined approach could not only enhance the accuracy and reliability of runoff predictions but also expand the applicability of the hydrologic models to different conditions, making it useful for flood forecasting in underserved regions. Tsai et al.33 developed a NN-based parameterization pipeline to infer physical parameters for process-based models. Bhasme et al.30 replaced the empirical formulae previously employed in conceptual models with deep learning techniques to enhance the capability of hydrological predictions. Sezen et al.34 proposed a hybrid model combining a conceptual model with machine learning, which effectively enhances the performance of daily rainfall-runoff modeling in complex, nonhomogeneous catchments.

To enhance runoff predictions in regions lacking observation data, a hybrid model combining the deep learning model (Informer) and the hydrological model (WRF-Hydro) was employed in this study to predict runoff in the Chaersen Basin. The primary objectives of this study are threefold: (1) to develop a hybrid modeling approach that combines the Informer deep learning model with the WRF-Hydro hydrological model; (2) to evaluate the performance of this hybrid model using key metrics such as Nash–Sutcliffe Efficiency (NSE) and Index of Agreement (IOA); and (3) to demonstrate how this approach enhances the accuracy of flood prediction compared to conventional methods, including an investigation into the optimal contribution ratio of each model within the hybrid framework. The subsequent sections will explain the methodology behind the hybrid model, present the results from its application.

The Chaersen Basin, located within the territory of Horqin Right Wing Front Banner in Inner Mongolia, China, is characterized by a strip-shaped watershed35. The upstream watershed above the Chaersen Reservoir covers a mountainous area of 7,780 km2, known for its abundant water resources (Fig. 1b). The elevation of the watershed decreases from northwest to southeast, with the main river channel extending 239 km in length. This area is subjected to a temperate continental monsoon climate, characterized by dryness and scant rainfall. The average annual temperature is 4.2 °C, with the maximum temperature reaching 36 °C and the minimum temperature plummeting to -28 °C. The Chaersen Reservoir Basin receives an average annual rainfall of approximately 400 mm, unevenly distributed throughout the year. Most of the rainfall occurs between June and October, with floods most frequently occurring from June to August.

Study Areas. (a) Location of CAMELS catchments; (b) The Chaersen Basin in Inner Mongolia. The map was generated using ArcMap 10.8 (https://www.esri.com/en-us/arcgis/products/arcgis-desktop/overview).

Meteorological forecasts sourced from the Global Forecast System (GFS) forcing, which is maintained by the National Centers for Environmental Prediction (NCEP)36. This forcing features a temporal resolution of six hours, encompassing forecasts initiated at 00:00, 06:00, 12:00, and 18:00 Coordinated Universal Time (UTC), and a spatial resolution of 0.25° by 0.25°. For driving the daily hydrologic simulation, the 00:00 UTC meteorological forecasts were spaced at 3-h intervals producing eight forecasts per day. These GFS forecasts were specifically used to drive the WRF-Hydro model, providing the necessary meteorological inputs for accurately hydrological simulations. To derive daily mean discharge, these 3-hourly meteorological forecasts were first used to run the hydrological model at the corresponding temporal resolution. The resulting discharge outputs were then averaged over a 24-h period to obtain the daily mean discharge values used in the subsequent analysis. This process ensured that the model captured the diurnal variations in meteorological conditions, while providing a consistent daily output for comparison and further analysis37.

The Catchment Attributes and Meteorology for Large-sample Studies (CAMELS) dataset, as an integrated meteorological and hydrological dataset in the United States, were utilized for TL to learn the patterns and insights from the source watersheds, which were then applied to the Chaersen Basin as the targe watershed38. Developed collaboratively by institutions including the National Center for Atmospheric Research (NCAR) and the United States Geological Survey (USGS), the CAMELS dataset facilitates investigations into the intricate relationships among watershed characteristics, meteorological conditions, and hydrological responses. Comprising long-term, high-quality daily data of meteorology, flow, and watershed attributes from more than 670 basins across the United States, the dataset encompasses a variety of climate zones and geomorphic watershed types and spans from the 1980s to the present. In this study, to guarantee data integrity and reduce potential inaccuracies resulting from interpolation, not all watersheds within the CAMELS dataset were employed. Rather, a subset of 588 watersheds, characterized by continuous and comprehensive data from 1980 to 2014, was selected to serve as the source basins. The diversity of the U.S. basins included in the CAMELS dataset provided a solid foundation for the model, ensuring that a comprehensive understanding of hydrological dynamics was achieved. Consequently, this allowed for the accurate prediction of runoff data in the Chaersen Basin (Fig. 1). Previous studies have successfully employed the CAMELS dataset for transfer learning. Yao et al.21 demonstrated the utility of CAMELS in predicting hydrological responses in the Tibetan Plateau. Similarly, Khoshkalam et al.22 applied CAMELS data in a cross-regional study, highlighting its effectiveness in snow-dominated region. These studies underscore the relevance and applicability of the CAMELS dataset for diverse hydrological modeling contexts.

The China Meteorological Assimilation Driving Datasets for the Soil and Water Assessment Tool (CMADS) is a specialized meteorological assimilation dataset designed for the Soil and Water Assessment Tool, providing high-precision, high-resolution meteorological, surface, and hydrological data39. In this study, historical meteorological variables retrieved from CMADS was used to train the TL model for the target watershed. In comparison, while the GFS provides global-scale forcing with adequately temporal and spatial coverage for runoff prediction, CMADS offers more localized, historical and prediction forcing, making it particularly suitable for deep learning applications where the granularity and heterogeneity of the meteorological conditions are critical for prediction accuracy.

The transfer modeling process in this study was built upon a sequence of steps, including data collection, model training, and validation, as detailed in the Experiments section. Below was provided a summary of these key steps, followed by a detailed explanation of the methodologies used:

Data Collection: Data from CAMELS and CMADS datasets were collected.

Model Training: The Informer model was trained using data from CAMELS.

Transfer Learning: The trained model was applied to the Chaersen Basin based on CMADS.

Model Calibration: The WRF-Hydro model, driven by GFS forcing, was calibrated for Chaersen Basin.

Result Combination: Predictions from both TL and WRF-Hydro models were averaged.

In this research, the Informer, a model employing an encoder-decoder architecture, was utilized to address sequence prediction tasks40. In this architecture, the encoder is tasked with processing the input sequences, while the decoder is responsible for generating predictions (Fig. 2). This design is particularly adept at managing the intricate relationships between inputs and outputs inherent in such tasks. To enhance its efficiency further, a sparse attention mechanism was integrated into the Informer. This mechanism significantly decreased the number of key-value pairs involved in computations, thereby reducing computational complexity. This reduction is crucial for handling large datasets with temporal dependencies effectively, making the Informer particularly suitable for high-dimensional time-series forecasting.

The Informer model architecture.

The input data for the source domain consisted of meteorological variables from the CAMELS dataset, including temperature, precipitation, and radiation, collected across 588 watersheds in the United States. For the target domain, the input data were derived from the CMADS dataset, focusing on similar meteorological variables collected in the Chaersen Basin (Table 3).

During training, the Informer model was optimized by minimizing the prediction error, specifically using the Mean Squared Error (MSE) loss function. This approach allowed the model to learn the complex dependencies between the input meteorological variables and the corresponding observed runoff from the CAMELS dataset. By minimizing the MSE loss on the training dataset, the model was trained to accurately map the meteorological inputs to the predicted runoff values. For the Chaersen Basin, the trained Informer model used the input meteorological data from the CMADS dataset to generate predictions of daily runoff.

The hyperparameters for the Informer model were determined through tests and consistently maintained throughout the experiments. The settings included a learning rate of 0.001, a batch size of 32, training for 20 epochs, and early stopping with a patience of 3 and a tolerance of 0.

The Weather Research and Forecasting (WRF) model coupled with WRF-Hydro is an advanced computational tool designed for multiscale, multi-physics atmospheric research and operational hydrology41. WRF-Hydro, an extension of the core WRF model, has been specifically developed to improve the capability of hydrological simulations within a fully-coupled atmospheric-hydrological modeling framework. WRF-Hydro is designed to provide a flexible, extensible platform that can handle complex terrain and varying hydrological conditions. Its architecture allows for both standalone hydrological simulations and interactive coupling with atmospheric models, facilitating the analysis of hydro-meteorological interactions. The model integrates various hydrological components including surface runoff, subsurface flow, channel flow, and reservoir routing (Fig. 3).

Conceptual schematic of the WRF-Hydro architecture.

The subsurface flow simulations were based on the Dupuit-Forchheimer assumptions. For the simulation of overland flow, an unsteady, spatially explicit diffusive wave equation was employed. In this study, the diffusion wave method was selected for channel routing. Furthermore, the Noah-MP Land Surface Model (LSM) grids were generated at a spatial resolution of 1.5 km using the WRF Model Preprocessing System (WPS) as detailed by Skamarock et al.42.

WRF-Hydro was selected due to its ability to capture the complex spatial variability and detailed hydrological processes in the Chaersen Basin, which are critical for accurate flood prediction. Despite data scarcity, its distributed modeling approach, combined with the flexibility to integrate various data sources, ensures a more reliable and robust simulation compared to simpler models.

To assess the accuracy of the flood prediction models used in this study, three key performance metrics were employed: Nash–Sutcliffe Efficiency (NSE) and Index of Agreement (IOA). NSE is a normalized statistic that determines the relative magnitude of the residual variance compared to the measured data variance (Eq. 1).

IOA is a statistic that measures the degree of model prediction error and represents the ratio of the observed and predicted data variance. It is calculated as:

where \(O_{i}\) and \(P_{i}\) represent the observed and predicted values, respectively, and \(\overline{O}\) is the mean of observed values. IOA varied between 0 and 1, which reflected the degree of model prediction error. A value of 1 indicates a perfect match and 0 stands for no agreement at all.

Furthermore, the percentage error in predicting the top 2% segment of the flow duration curve high-segment volume (FHV) was examined, as it is indicative of the model’s precision in estimating extreme peak flows.

Initially, the Informer model was used to learn the relationships between meteorological data and runoff across various watersheds in the United States, utilizing comprehensive datasets (CAMELS) to capture the dynamics of hydrological responses under diverse climatic conditions. Subsequently, this trained model was applied to the Chaersen Basin in China to predict runoff based on meteorological data variables collected from CMADS, demonstrating the model’s capability to generalize and transfer knowledge to geographically distinct regions. Concurrently, runoff predictions were also generated using the WRF-Hydro model driven by GFS forcings, providing a comparative framework. The final runoff predictions were obtained by averaging the results from both the Informer and WRF-Hydro models, with each model contributing equally with a 50% weight. This innovative approach of combining predictions from a data-driven model and a physical-based model enhanced the robustness and accuracy of the final runoff predictions, particularly in capturing peak flow events and seasonal runoff trends (Fig. 4).

Experiments workflow.

The WRF-Hydro model, recognized as a distributed hydrologic model, incorporated a multitude of parameters that were pivotal in influencing the outcomes of flood simulations. These parameters were classified into two main categories based on their impact on runoff processes. The first category, directly influencing runoff generation, included parameters such as the surface infiltration rate (REFKDT), surface retention depth (RETDEPRT), and the coefficient for deep drainage (SLOPE). Conversely, the second category comprised parameters that indirectly affected runoff, including Manning’s coefficient (MannN) and surface roughness (OVROUGHRT). Throughout the calibration process, adjustments were made to these parameters, guided by insights gleaned from prior sensitivity analyses43,44, to optimize the model’s accuracy in simulating flood events.

To drive the WRF-Hydro model, we utilized eight key variables from the GFS dataset. These variables included surface pressure, 2-m temperature, 2-m specific humidity, 10-m wind speed components (U and V), surface downward shortwave radiation, surface downward longwave radiation, and precipitation rate. Each of these variables was essential in accurately representing the atmospheric conditions influencing the hydrological processes within the model, thus enabling more precise simulations of runoff and flood events.

Calibration was conducted on the five parameters identified as most sensitive: REFKDT, saturated soil lateral hydraulic conductivity (LKSATFAC), SLOPE, RETDEPRT, and MannN (Table 1). The calibration process was characterized by an iterative optimization approach, in which various combinations of parameter values were systematically adjusted. This method was aimed at identifying the combination that best matched the observed streamflow data.

All four historical events spanning from 2018 to 2020 were considered together in the calibration process, resulting in a single set of calibrated parameters (Fig. 5). To ensure the accuracy of the WRF model’s event-based simulations, each flood event was preceded by a two-month spin-up period. Following this calibration process, it was observed that the NSE for each event consistently exceeded 0.5, demonstrating an enhanced predictive accuracy of WRF-Hydro (Table 2).

WRF-Hydro calibration results.

A comprehensive dataset from CAMELS comprising extensive hydrological data from 588 watersheds across the United States ranging from 1980 to 2014 was assembled, serving as the source domains for TL training. Upon successful pre-training, the Informer model utilized the 2015–2016 meteorological data from CMADS to find the connections between the source and target basins (Table 3). Notably, runoff data was deliberately excluded from CMADS for the target basin during the training phase, thereby testing the capacity of Informer to generalize and predict runoff in data-scarce environments.

In this study, the effectiveness of three distinct flood prediction methodologies was assessed over two years, 2015 and 2016, employing two specific evaluation metrics: NSE, IOA and FHV. In 2015, the Hydro-Informer hybrid model was observed to achieve the highest NSE values at 0.66 (Table 4), outperforming both the WRF-Hydro and the standalone Informer models, which recorded NSE values of 0.50 and 0.63 respectively. Conversely, the WRF-Hydro model exhibited the lowest NSE values among the three. However, in 2016, both the Informer and the Hydro-Informer models shared similar high NSE values of 0.76, significantly surpassing that of the WRF-Hydro model which posted a lower score of 0.42. For the IOA metric, the Hydro-Informer model consistently showed the highest values in both years, with values of 0.87 in 2015 and 0.92 in 2016, as evident from Table 4. Specifically, in 2015, the Hydro-Informer’s performance markedly exceeded that of the other models, while in 2016, it paralleled the Informer model, which scored 0.93, both substantially outperforming the WRF-Hydro model. Regarding FHV, WRF-Hydro and Informer presented two extremes: in 2015, a year with high peak flows, WRF-Hydro significantly outperformed the Informer; whereas in 2016, with lower flows, the Informer notably outperformed WRF-Hydro. The Hydro-Informer model consistently remained in the middle position across both years.

The Hydro-Informer and Informer models consistently outperformed the WRF-Hydro model in most instances. Even in scenarios where the Hydro-Informer model exhibited the least favorable results, its performance was still observed to fall between that of the WRF-Hydro and Informer models, never dropping to the lowest observed levels. Similarly, in the study by Donnelly29 on inland floods, physics-informed neural networks were found to improve the RMSE by 3.5% over CNN models. The superior performance of the Hydro-Informer in terms of NSE and IOA suggests effective synergy between the Informer’s capability to capture complex nonlinear relationships in meteorological data and the hydrological processing strength of the WRF-Hydro. The consistent underperformance of the WRF-Hydro model in NSE and IOA metrics might be linked to its potential limitations in accurately capturing the specific hydrological dynamics of the target basins without the aid of advanced machine learning techniques, such as those employed by the Informer. The difficulty in calibrating physical models could also be a contributing factor to the suboptimal performance of the WRF-Hydro model. This complexity in parameter tuning often hinders its ability to accurately simulate hydrological dynamics in varied contexts.

Three flood prediction methodologies were compared against observed values (Fig. 6). In 2015, it was observed that the WRF-Hydro model approximated peak streamflow values more closely to the observed data than the other models. Conversely, significant deviations were noted in the Informer model’s predictions, particularly at peak values, where large discrepancies were evident. However, outside of these peak periods, the Informer model generally provided predictions that were closer to the observed data, with the Hydro-Informer model showing intermediate accuracy. This aligns with the conclusions drawn from the FHV values in Table 4.

Comparison of Predicted and Observed Streamflow for the Flood Season. (a) displays the streamflow curves for 2015, comparing three flood prediction methodologies against observed values; (b) displays the streamflow curves for 2016, comparing three flood prediction methodologies against observed values.

In 2016, both the Informer and Hydro-Informer models were found to closely approximate the observed values during two significant flood peak events, while the WRF-Hydro model displayed substantial deviations. Notably, during non-peak periods, the stability of the WRF-Hydro predictions was significantly lower, with the Hydro-Informer and Informer models demonstrating greater accuracy. This inconsistency in the WRF-Hydro’s performance might be attributed to the reduced rainfall that year, which led to lower overall streamflow, impacting the model’s predictive accuracy. Furthermore, while the Informer model occasionally overestimated peak flows, the hybrid Hydro-Informer approach mitigated this issue to a certain extent. The alleviation of peak overestimations by the Hydro-Informer model could be attributed to its integrated approach, combining the strengths of both the WRF-Hydro’s physical modeling capabilities and the Informer’s machine learning efficiency, thereby enhancing the overall prediction accuracy and reliability in varied hydrological conditions.

The outcomes of the hybrid model for the flood seasons of 2015 and 2016, tuned by different combinations of contributing proportions, were summarized (Fig. 7). Regardless of the metrics, the hybrid model consistently outperformed the WRF-Hydro standalone model across all proportion scenarios. However, the comparison between the hybrid model and the Informer standalone model demonstrated mixed results. Apart from the IOA index in 2015 when the hybrid model surpassed the Informer model, the performance of the former varied in other cases. Notably, the peak performance of the hybrid model was observed when the ratios of the WRF-Hydro weight over the Informer weight ranged from 20% over 80% to 40% over 60%. In other words, a TL model was found in this study to play a significant role in the hybrid runoff prediction, with a suggested 60% to 80% contribution of the TL prediction to the predicted runoff for achieving a decent overall performance.

The predictive performance of the hybrid models with different model proportions. Note: (a,b) represent the NSE values; (c,d) represent the IOA values; (a,c) predict the flood season of 2015; (b,d) predict the flood season of 2016.

Beyond this range, the performance of the model significantly declined, possibly due to the diminishing synergistic effect when the strengths of one individual model begin to overshadow those of the other. This optimal range likely represents a balance where the strengths of both models complement each other most effectively, avoiding the risks of overfitting with excessive Informer weight or underfitting with excessive WRF-Hydro weight. Therefore, it is imperative that the weight ratios in the hybrid model are optimally balanced to surpass the performance of standalone models under appropriate proportions.

This study’s approach of integrating a deep learning model with a traditional hydrological model aligns with and extends the findings of previous research in the field of hydrological modeling. Prior studies, such as Sezen et al.34, have demonstrated the effectiveness of hybrid models in capturing complex hydrological processes in nonhomogeneous catchments. While Sezen et al. focused on combining conceptual models with machine learning techniques, our study advances this approach by incorporating a transfer learning strategy to address the challenges of data scarcity in the Chaersen Basin. The results of our study corroborate previous findings that hybrid models can significantly enhance prediction accuracy, particularly in regions where traditional models alone may fall short due to insufficient observational data.

The integration of the Informer model with WRF-Hydro demonstrated several key benefits in this study, such as improved prediction accuracy for runoff events. However, one notable challenge was the Informer model’s limitation in accurately predicting extreme runoff values. This limitation in extreme value prediction was one of the factors contributing to the hybrid model’s reduced accuracy in peak flow predictions. Deep learning models like Informer, while powerful in recognizing complex patterns in data, can sometimes struggle with accurately predicting rare, extreme events due to their tendency to optimize for average performance rather than outliers. Similar conclusions were drawn by Xu et al.45 and Yao et al.21 who observed that Multilayer Perceptron (MLP) models also showed limited accuracy in peak flow predictions when applied in runoff transfer learning. Nevertheless, despite these challenges, our hybrid model still managed to elevate the predictive performance of the Informer model alone, offering improved overall accuracy in runoff predictions.

Another limitation of this study is that the simulations were conducted exclusively for the summer months. While summer is typically the season with the highest rainfall and runoff in the Chaersen Basin, limiting the study to this period may restrict the generalizability of the findings to other seasons. The absence of winter and spring simulations, which could include snowmelt and low-flow periods, means that the model’s performance in these conditions remains untested. This focus on the summer season might have led to an overestimation of the model’s robustness across different hydrological conditions. Future research should consider extending the simulations to a complete water year to offer a more comprehensive evaluation of the hybrid model’s performance across different seasons.

The prediction of runoff in data-scarce regions has long been a focal point in the field of hydrology. This study successfully integrated a deep learning-based transfer model with the physical WRF-Hydro model, significantly enhancing the accuracy of runoff predictions. Through the prediction of flood season runoff in the Chaersen basin from 2015 to 2016, and a comparison with predictions made using either the physical model or the transfer model alone, it was discovered that the Hydro-Informer hybrid model excelled in both years under the evaluation metrics NSE and IOA. The NSE and IOA values for 2015 and 2016 were found to be 0.66, 0.76 and 0.87, 0.92, respectively.

Further analysis of the three models’ performance in predicting peak runoff values revealed that both the WRF-Hydro and Informer models exhibited significant deviations during peak events in 2015 and 2016. Particularly in 2016, when runoff volumes were lower, the WRF-Hydro model displayed reduced stability in predictions outside of peak periods, whereas the Hydro-Informer and Informer models demonstrated higher accuracy. Although the Informer model occasionally overestimated peak flow volumes, the hybrid Hydro-Informer approach effectively mitigated this issue. The outcomes for the hybrid model across various proportions further emphasized its superior performance over standalone models. Notably, the model achieved peak performance when the ratios of the WRF-Hydro weight over the Informer weight ranged from 20% over 80% to 40% over 60%. Beyond this optimal range, performance significantly declined, highlighting the importance of maintaining a balanced integration of the two models to harness their complementary strengths. This optimal integration avoids the risks of overfitting with an excessive Informer weight and underfitting with excessive WRF-Hydro weight, ensuring the hybrid model’s superiority in terms of accuracy and stability across different hydrological scenarios.

Data for the CAMELS dataset is available for download at https://gdex.ucar.edu/dataset/camels/file.zip. Data for the CMADS can be downloaded from http://www.cmads.org/.

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The authors would like to thank the funding support from the Scientific Research Program of The Education Department of Jilin Province, China (JJKH20231179KJ).

Key Laboratory of Groundwater Resources and Environment, Ministry of Education, Jilin University, Changchun, 130021, China

Songliang Chen, Youcan Feng, Hongyan Li, Yilian Zhao & Junhui Liu

Jilin Provincial Key Laboratory of Water Resources and Environment, Jilin University, Changchun, 130021, China

Songliang Chen, Youcan Feng, Hongyan Li, Yilian Zhao & Junhui Liu

College of New Energy and Environment, Jilin University, Changchun, 130021, China

Songliang Chen, Youcan Feng, Hongyan Li, Yilian Zhao & Junhui Liu

China Water Northeastern Investigation, Design and Research Company, Changchun, 130021, China

Donghe Ma

School of Computer Science, Faculty of Science and Engineering, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo, 315100, China

Qinglin Mao

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S.C. and Y.F wrote the main manuscript text. S.C. prepared data for visualizations. All authors reviewed and contributed to the final manuscript.

Correspondence to Youcan Feng or Hongyan Li.

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Chen, S., Feng, Y., Li, H. et al. Enhancing runoff predictions in data-sparse regions through hybrid deep learning and hydrologic modeling. Sci Rep 14, 26450 (2024). https://doi.org/10.1038/s41598-024-77678-y

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Received: 24 May 2024

Accepted: 24 October 2024

Published: 02 November 2024

DOI: https://doi.org/10.1038/s41598-024-77678-y

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