Rainfall-runoff Relationship Research Articles

Characterizing nonlinear, nonstationary, and heterogeneous hydrologic behavior using ensemble rainfall–runoff analysis (ERRA): proof of concept

Abstract. A classical approach to understanding hydrological behavior is the unit hydrograph and its many variants, but these often assume linearity (runoff response is proportional to effective precipitation), stationarity (runoff response to a given unit of rainfall is identical, regardless of when it falls), and spatial homogeneity (runoff response depends only on spatially averaged precipitation). In the real world, by contrast, runoff response is typically nonlinear, nonstationary, and spatially heterogeneous. Quantifying this nonlinearity, nonstationarity, and spatial heterogeneity is essential to unraveling the mechanisms and subsurface properties controlling hydrological behavior. Here, I present proof-of-concept demonstrations illustrating how nonlinear, nonstationary, and spatially heterogeneous rainfall–runoff behavior can be quantified, directly from data, using ensemble rainfall–runoff analysis (ERRA), a data-driven, model-independent method for quantifying rainfall–runoff relationships across a spectrum of time lags. I show how ERRA uses nonlinear deconvolution to quantify how catchments' runoff responses vary with precipitation intensity and to estimate their precipitation-weighted runoff response distributions. I further illustrate how ERRA combines nonlinear deconvolution with de-mixing techniques to reveal how runoff response depends jointly on precipitation intensity and nonstationary ambient conditions, including antecedent wetness and vapor pressure deficit. I demonstrate how ERRA's de-mixing techniques can be used to quantify spatially heterogeneous runoff responses in different parts of a catchment, even if those subcatchments are not separately gauged. I also illustrate how ERRA's broken-stick deconvolution capabilities can be used to quantify multiscale runoff responses that combine hydrograph peaks lasting for hours and recessions lasting for weeks, well beyond the average spacing between storms. ERRA can unscramble these multiple effects on runoff response even if they are overprinted on each other through time and even if they are corrupted by autoregressive moving average (ARMA) noise. Results from this approach may be informative for catchment characterization, process understanding, and model–data comparisons; they may also lead to a better understanding of storage dynamics and landscape-scale connectivity. An R script is provided to perform the necessary calculations, including uncertainty analysis.

Water sources and threshold behaviors of streamflow generation in a mountain headwater catchment

Numerous studies have analyzed the event-scale rainfall-runoff response of hillslopes and catchments. However, there are still knowledge gaps when it comes to understanding the spatiotemporal sources of headwater catchment runoff and the threshold behaviors of multiple runoff components. The aim of this study is to investigate the complex runoff generation mechanisms for 244 rainfall events in a humid headwater catchment of eastern China over five years (2011–2015). We employ a combined approach of isotopic tracing (δ2H and δ18O) and fully-integrated surface/subsurface flow modeling (HydroGeoSphere) to identify streamflow compositions and how the process chain of “rainfall infiltration, mixing with soil water, and subsequent exfiltration to the hillslope surface” impacts streamflow generation in headwater catchments. Our results show that the streamflow consists of event and pre-event water. Event water is composed of direct runoff from rainfall (2 % in the total streamflow) and indirect runoff from infiltrated rainfall (24 %). Pre-event water comprises the exfiltrated shallow soil water of indirect runoff (37 %) and subsurface flow (37 %). The study highlights the significant role of indirect runoff, comprising infiltrated rainfall and pre-event shallow soil water, in streamflow generation, reaching a peak proportion of 81.4 % during rainfall events. In addition, we quantify the threshold behaviors (including the generation threshold, and critical threshold from increasing to decreasing state) for surface and subsurface flow, based on the analysis of the non-linear rainfall-runoff relationships observed in the catchment. Results show that rainfall amount of 33 mm and rainfall intensity of 9 mm/d are generation thresholds for direct runoff and critical thresholds for proportion changes of exfiltrated shallow soil water. Critical thresholds of 55 mm for rainfall amount and 12 mm/d for rainfall intensity are identified for proportion changes of infiltrated rainfall and total indirect runoff. Our findings highlight that the combined analysis of hydrological modeling and isotopic tracing provides an effective solution for quantifying the roles of dominant water components in streamflow generation and elucidate the distinct threshold behaviors during rainfall events. Enhancing our comprehension of streamflow origins and their response mechanisms to rainfall events will improve the understanding of streamflow generation in headwater catchments.

The potential to reduce runoff generation through improving cropping and tillage practices in a sub-humid continental climate

Agricultural sustainability is threatened by both water deficit and water excess, especially at the presence of extreme meteorological events resulting from climate change. However, there has been lack of demonstrations on management options with long-term values for agricultural adaptation to runoff. Using 20 years of monitoring data (1993‒2012) for two experimental fields in the Canadian Prairies as a case study, we quantified the effects of rainfall characteristics, crop type and biomass, and tillage on growing-season runoff generation using regression analyses and thereafter scenario comparisons. With growing-season gross rainfall ranging between 183 and 456 mm, runoff responses varied between 0 and 59 mm. Over the 20-year study period, 70%‒74% of the growing-season runoff was generated by rainfall events > 100 mm. Compared to high-intensity tillage, long-term conservation tillage reduced both overall runoff and runoff in large events likely by improving water infiltration. Under both tillage methods, growing-season runoff significantly increased with increasing rainfall but decreased with increasing biomass (R2 range: 0.40‒0.58; p range: 0.0007‒0.02). At the event level, the rainfall-runoff relationship followed a piecewise regression model (Cd = 0.82; p < 0.0001; “breakpoint” rainfall event = 105 mm), in which runoff increased slowly before reaching the “breakpoint” but rose sharply afterwards. Due to a greater biomass, canola resulted in less runoff than wheat. Scenario analyses showed that increasing crop biomass by 50% under the current average rainfall conditions could reduce runoff by 81‒86% in wheat and 100% in canola. The reduction may be attributed to the combined effects of crop on interception, evapotranspiration, and infiltration. In conclusion, although in a sub-humid continental climate like the Canadian Prairies there are generally low amounts of rainfall runoff, this study demonstrates significant runoff in some years, especially following large rainfall events. Runoff generation can be significantly reduced through improving cropping and tillage practices, and such effects on regional water retention should be further assessed by considering the past and future changes in climate and management.

Application of SA-Conv1D-BiGRU model for streamflow prediction in southern Ethiopia

ABSTRACT Streamflow prediction offers crucial information for managing water resources, flood control, and hydropower generation. Yet, reliable streamflow prediction is challenging due to the complexity and nonlinearity of the rainfall-runoff relationship. This study investigated the comparative performance of the newly integrated self-attention-based deep learning (DL) model, SA-Conv1D-BiGRU with Conv1D-LSTM, and bidirectional long short-term memory (Bi-LSTM) models for streamflow prediction under different time-series conditions, and a range of variable input combinations based on flood events. All datasets passed quality control procedures, and the time lag for generating input series was established through Pearson correlation analysis. 80% of the data was used for training, whereas 20% was used to evaluate the model's performance. The performance of the models was evaluated using three metrics: mean absolute error (MAE), root mean square error (RMSE), and correlation coefficient (R2). The findings reveal the excellent potential of DL models for streamflow prediction, with the SA-Conv1D-BiGRU model outperforming other models under different time-series characteristics. Despite the complexity, the Conv1D-LSTM models did not outperform the Bi-LSTM model. In conclusion, the results are condensed into themes of model variability and time-series characteristics. Consequently, different architectures in DL models had a greater influence on streamflow prediction accuracy than input time lags and time-series features.

Region-scale decline in streamflow across New South Wales catchments

ABSTRACT Changing climate and its interactions with catchments may result in changes to water resources. This study examines the temporal trends in streamflow across New South Wales, Australia. Across 163 catchments with over 35 years of records up to September 2020, we used Mann-Kendall and Sen’s Slope methods to estimate trends in different flow indicators, including the annual, low and high flows, cease to flow, and the rainfall-–runoff relationship. Nearly all (160) catchments have decreasing trends in annual flow, with 62 of these being statistically significant, indicating an overall drying pattern. Most declines are 10–20% per decade relative to the mean annual flows of individual catchments. Trends in rainfall-–runoff relationship suggest that the flow declines are generally greater than expected with given rainfall, and likely due to region-scale processes such as groundwater and vegetation dynamics. Our finding has important implications for future water security for New South Wales and similar environments, such as planning for future reduction in water resources availability with likely increasing demands.

The influence of human activities on rainfall-runoff relationships at different time scales in the Minjiang River Basin

The influence of human activities on rainfall-runoff relationships at different time scales in the Minjiang River Basin

Prediction of runoff characteristics in permeable pavements using experimental data and intelligent models.

Considering the growing use of permeable pavements, the prediction of runoff passing through this pavement model is of considerable importance. The prediction of rainfall-runoff relationships can be a challenge because of several factors including data uncertainty, non-linear relationships, and high temporal and spatial variability. To deal with these challenges, intelligent algorithms are often used to predict such complex phenomena. In this research, runoff control parameters were investigated in two types of permeable pavements (permeable interlocking concrete pavement (PICP) and high strength clogging resistant permeable pavement (CRP)) using support vector machine (SVM), support vector machine-bat (SVM-BA) and support vector machine-grasshopper (SVM-GOA). Variables used in the models included percentage of coverage by permeable pavement (A), rainfall intensity (I), slope (S), and pavement type coefficient (K) as input data, and runoff coefficient (C), time to runoff (Tr), and peak discharge (Qp) as output data. In this research, from the total of 108 data extracted from the experimental results, 86 data were used in the training period, and 22 data were used in the test period. The results of the test period show that the SVM-BA model has the best performance with values of MAE = 0.010 in predicting C, MAE = 1.330 min in predicting Tr, and MAE = 0.029 lit/min in predicting Qp. The SVM-GOA model is ranked second with values of MAE = 0.051 in predicting C, MAE = 3.285 min in predicting Tr, and MAE = 0.097 lit/min in predicting Qp. Also, the SVM model is ranked third with values of MAE = 0.063 in predicting C, MAE = 4.470 min in predicting Tr, and MAE = 0.121 lit/min in predicting Qp. In summary, the SVM-BA algorithm showed the best performance and the SVM algorithm showed the weakest performance in predicting runoff characteristics in permeable pavements.

An artificial neural network and SCS–CN-based model for runoff estimation: a case study of the Peddavagu watershed

ABSTRACT The accurate prediction of runoff from rainfall events is crucial for effective water resource management, especially in regions with diverse climatic patterns like India. This study proposes a novel approach by integrating the soil conservation service (SCS)–curve number (CN) method with artificial neural networks (ANNs) to model rainfall–runoff relationships. In this research, an SCS–CN method is utilized to estimate initial runoff volumes, accounting for local soil and land-cover characteristics. Subsequently, an ANN-based model is developed to capture the complex nonlinear relationships between rainfall inputs and runoff outputs. Taking the rainfall of the watershed as the inputs, an ANN model was developed in MATLAB for runoff simulation at the main outlet of the Peddavagu watershed. A feed-forward back-propagation method is employed in the ANN model. The architecture with a 1-10-1 configuration based on tan–sig transfer function performed well in terms of MSE 0.019. The model efficiency was satisfactory with the coefficient of correlation (R), 0.96 for training, 0.98 for validation, and 0.98 for testing period. The overall value of R (0.96) indicates the utility of this ANN–SCS-based coupled model for rainfall–runoff simulation.

In-depth simulation of rainfall–runoff relationships using machine learning methods

ABSTRACT Measurement inaccuracies and the absence of precise parameters value in conceptual and analytical models pose challenges in simulating the rainfall–runoff modeling (RRM). Accurate prediction of water resources, especially in water scarcity conditions, plays a distinctive and pivotal role in decision-making within water resource management. The significance of machine learning models (MLMs) has become pronounced in addressing these issues. In this context, the forthcoming research endeavors to model the RRM utilizing four MLMs: Support Vector Machine, Gene Expression Programming (GEP), Multilayer Perceptron, and Multivariate Adaptive Regression Splines (MARS). The simulation was conducted within the Malwathu Oya watershed, employing a dataset comprising 4,765 daily observations spanning from July 18, 2005, to September 30, 2018, gathered from rainfall stations, and Kappachichiya hydrometric station. Of all input combinations, the model incorporating the input parameters Qt−1, Qt−2, and R̄t was identified as the optimal configuration among the considered alternatives. The models' performance was assessed through root mean square error (RMSE), mean average error (MAE), coefficient of determination (R2), and developed discrepancy ratio (DDR). The GEP model emerged as the superior choice, with corresponding index values (RMSE, MAE, R2, DDRmax) of (43.028, 9.991, 0.909, 0.736) during the training process and (40.561, 10.565, 0.832, 1.038) during the testing process.

A process-driven deep learning hydrological model for daily rainfall-runoff simulation

Although deep learning (DL) models, especially long-short-term memory (LSTM), demonstrate greater accuracy than process-based models in rainfall-runoff simulation, the predictions from process-based models are more physical than DL models. The main reason is that DL models have almost no process understanding capabilities like process-based models beyond their fitting capability. In this study, we developed a process-driven DL model under a unified DL architecture to improve the process awareness of DL models. To implement the model, a conceptual hydrological model (EXP-HYDRO) is implanted into a recurrent neural network (RNN) cell as a process driver for providing multi-sub-process variables related to the runoff process, and an Entity-Aware LSTM (EA-LSTM) cell is incorporated as a post-processor layer, resulting in the Process-driven RNN-EA-LSTM (PRNN-EA-LSTM). Under the assistance of the process driver, the model performance of PRNN-EA-LSTM on the 531 catchments from the Catchment Attributes and Meteorology for Large-sample Studies dataset is more robust than the pure DL model, and better than using only EXP-HYDRO as the input of EA-LSTM (i.e., EXP-HYDRO-EA-LSTM). Specifically, the median Nash-Sutcliffe efficiency (NSE) of PRNN-EA-LSTM in local and regional simulation is 0.03 and 0.02 higher than LSTM and 0.01 higher than EXP-HYDRO-EA-LSTM. Additionally, PRNN-EA-LSTM significantly enhances the low flow simulations and reduces the catchments number with negative NSE. This study demonstrates that process-based models can help DL models better represent the rainfall-runoff relationship under a unified architecture. Consequently, integrating the adaptability of process-based models into the DL architecture is anticipated to bolster the process understanding capabilities of DL models.

DEVELOPMENT AND ANALYSIS OF A GIS-BASED CURVE NUMBER MAP OF THE PHILIPPINES

Stormwater management requires quantitative methods to determine objective flood risk by estimating how much rainfall becomes runoff. With the absence of a locally generated runoff coefficient database in the Philippines, the standard model for surface runoff estimation is yet to be implemented using homegrown datasets. Traditionally, the empirical method is adapted from the National Resources Conservation Service (NRCS). The method quantifies rainfall-runoff relationships underscoring the combined effects of ground cover, soil hydraulic conductivity, and antecedent runoff condition (ARC) on runoff potential via a hydrologic parameter called the Curve Number (CN). Using geographic information system (GIS) tools, the Philippine CN map is developed by preprocessing and intersecting land use and land cover (LULC) and hydrologic soil group (HSG) with the CN look-up table. It was revealed that Group C soils dominate the Philippines. New data products—three raster CN maps at 25m spatial resolution—indicated the prevalence of medium to high runoff potential. National curve numbers were 61, 78, and 89 for dry, average, and wet ARCs, respectively. The outputs of this study provide access to spatially varied local runoff potential data in GIS format thus allowing direct GIS use for the swift simulation of flood damage mitigation models, among others.

Understanding the role of the spatial-temporal variability of catchment water storage capacity and its runoff response using deep learning networks

The land surface of a watershed acts as a large reservoir, with its catchment water storage capacity (CWSC) influencing rainfall-runoff relationship. Estimating CWSC at global grid scale is challenging due to calibration complexity, limited spatial continuity, and data scarcity. To address this, a deep learning-based approach incorporates spatial reconstruction and temporal transfer for capturing spatio-temporal variations in watershed characteristics. The study focuses on the Global Runoff Data Centre dataset and presents a grid-based hydrological model. Findings demonstrate accurate identification of CWSC distribution, with the model achieving an R 2 of 0.92 and the runoff Kling–Gupta efficiency of 0.71 during validation. According to the CMIP6 projections, the global CWSC is anticipated to undergo a significant increase at a rate of 1.7 mm per decade under the SSP5-8.5 emission scenario. Neglecting spatio-temporal CWSC variability globally overestimates climate change’s impact on runoff, potentially reducing the projected long-term increase by up to 41%.

Daily Simulation of the Rainfall–Runoff Relationship in the Sirba River Basin in West Africa: Insights from the HEC-HMS Model

This study focuses on the Sirba River Basin (SRB), a transboundary West African catchment of 38,950 km2 shared by Burkina Faso and Niger, which contributes to flooding downstream in Niamey (Niger). The study uses the HEC-HMS hydrological model to explore the dynamics of the daily rainfall–runoff relationship over the period 2006–2020. The model is calibrated using observed rainfall at 13 meteorological stations within the river basin and observed discharges at the Garbey Kourou hydrometric station outlet. Two types of simulation are compared: (i) a continuous simulation (CS) over the period 2006–2020 and (ii) an event-based simulation (ES) using selected major flood events in 2010, 2012, 2013, 2015 and 2020. The results showed satisfactory model performance under both modeling schemes (R2 = 0.84–0.87 for CS and R2 = 0.94–0.98 for ES), with a superior performance of ES over CS. Also, significant differences in the distribution of calibrated model parameters for the percent impervious and the attenuation flood wave factor were observed. A sensitivity analysis revealed that the curve number, initial abstraction, lag time and routing time factors were influential on the model outputs. The study therefore underscores the model’s robustness and contributes crucial insights for flood control management and infrastructure planning in the SRB.

Recession constants are non-stationary: Impacts of multi-annual drought on catchment recession behaviour and storage dynamics

Recession analysis is commonly adopted to characterise catchment behaviour, particularly in relation to the role of catchment storage in streamflow production. Recession techniques are data hungry and characterise average behaviour over long periods of recorded data, making them generally unsuitable in transient conditions. Nevertheless, in the context of multi-annual drought, sufficient data may be available to characterise temporal change by examining different subperiods. In this work, we assessed changes in recession behaviour of catchments affected by multi-annual drought in south-eastern Australia, focusing on how changes in recession patterns over time correlate to drought-induced shifts in annual rainfall-runoff relationships. We applied two methods, drawn from the vast methodological literature on recession analysis. They consider different information and entail different assumptions; one is based on average daily recession rates and the other on hourly recession slope plots. Despite the differences, their results are consistent: catchments that exhibited significant changes in rainfall-runoff relationship during the drought also display significantly steeper recessions during and after the drought. Subsequent investigation suggests that only a portion of the increases in recession speed are attributable to increased evaporative demand. Rather, they are likely caused by decreased connectivity between subsurface storage and catchment surface water and increased transmission losses through the streambed. With this work, we demonstrate the usefulness of recession analysis to investigate sources and effects of non-stationary behaviour, providing insights into the impacts of long-term drought on streamflow production and catchment storage dynamics.

Value of quality controlled citizen science data for rainfall-runoff characterization in a rapidly urbanizing catchment

The major concern of applying citizen science in water resources is the quality of the data. However, there are limited scientific studies addressing this concern and showing the data value. In this study, we established a citizen science program in the Akaki catchment which hosts Addis Ababa, Ethiopia. Citizen scientists monitored river stage at multiple gauging sites for multiple years. We evaluated the quality of citizen science data through a systematic quality control. Reference data was obtained from neighboring stations of the citizen science program and professionals while the evaluation involved graphical inspections and statistical methods. The quality-controlled data were applied to evaluate the spatial and temporal variation of rainfall-runoff relationships. Initially, large numbers of suspicious data were detected using single station data but that was significantly reduced when the data of multiple sites were compared. Further comparison against professional data revealed excellent agreement with high correlation coefficient (r >0.95), and low centered root mean square error (RMSE) <0.03–0.08 mm. The citizen science data indicated a large difference in rainfall-runoff relationship over the dominantly urban and rural sub-catchments. The citizen science data allowed comparison of runoff coefficient and base flow index for recent and historical periods where recent streamflow data is unavailable from a formal data source. This study illustrates the immense value of (i) multiple data quality assessment steps for building confidence on the quality of citizen science data, and (ii) citizen science for enhancing our understanding of rainfall-runoff relationships and change in a rapidly urbanizing catchment.

Designing of small water harvesting structures based on rainfall-runoff relationship for Dharashiv district of Maharashtra

Designing of small water harvesting structures based on rainfall-runoff relationship for Dharashiv district of Maharashtra

Ensemble rainfall–runoff modeling of physically based semi-distributed models using multi-source rainfall data fusion

Abstract This study was aimed at ensemble rainfall–runoff modeling by Soil and Water Analysis Tool (SWAT), the Hydrologic Engineering Center's Hydraulic Modeling System, and Hydrologiska Byråns Vattenbalansavdelning of Gilgel-Abay watershed, Blue Nile basin, Ethiopia. For modeling, daily rainfall datasets of five gauges and three satellites, streamflow, and spatial data were used. In the modeling stage, first, the runoff was simulated separately using the rainfall data of gauges, satellites, and their fusion. Second, ensemble rainfall–runoff simulation of the rainfall dataset fusion-based runoff result was conducted via the proposed weighted average, simple average, and neural network (NNE) ensemble techniques. The results exhibited that all models are good in capturing the rainfall–runoff relationship; however, SWAT showed slight superiority by Nash–Sutcliffe efficiency of 0.807 and 0.821 for gauge and fusion data, respectively. The rainfall fusion ensemble model revealed significant improvement over modeling by satellite rainfall owing to the bias-correcting gauge rainfall over satellite rainfall. The NNE technique enhanced the efficiency of the low-performing satellite-rainfall-based model by 17.5% and the rainfall fusion-based model by 13.3% at the validation stage. In general, the result of this study points out that the rainfall datasets’ fusion from multi-sources would be worthy for the rainfall–runoff simulation of ungauged basins.

The sanitary sewer unit hydrograph model: A comprehensive tool for wastewater flow modeling and inflow-infiltration simulations

Sanitary sewer systems are critical urban water infrastructure that protect both human and environmental health. Their design, operation, and monitoring require novel modeling techniques that capture dominant processes while allowing for computationally efficient simulations. Open water flow in sewers and rivers are intrinsically similar processes. With this in mind, we formulated a new parsimonious model inspired by the Width Function Instantaneous Unit Hydrograph (WFIUH) approach, widely used to predict rainfall-runoff relationships in watersheds, to a sanitary sewer system consisting of nearly 10,000 sewer conduits and 120,000 residential and commercial sewage connections in Northern Virginia, U.S.A. Model predictions for the three primary components of sanitary flow, including Base Wastewater Flow (BWF), Groundwater Infiltration (GWI), and Runoff Derived Infiltration and Inflow (RDII), compare favorably with the more computationally demanding industry-standard Storm Water Management Model (SWMM). This novel application of the WFIUH modeling framework should support a number of critical water quality endpoints, including (i) sewer hydrograph separation through the quantification of BWF, GWI, and RDII outflows, (ii) evaluation of the impact of new urban developments on sewage flow dynamics, (iii) monitoring and mitigation of sanitary sewer overflows, and (iv) design and interpretation of wastewater surveillance studies.

Unravelling the Impacts of Climate Variability on Surface Runoff in the Mouhoun River Catchment (West Africa)

This study assesses the impacts of climate variability on surface runoff generation in the Mouhoun River Catchment (MRC) in Burkina Faso, in the West African Sahel. The study uses a combination of observed and reanalysis data over the period 1983–2018 to develop a SWAT model (KGE = 0.77/0.89 in calibration/validation) further used to reconstitute the complete time series for surface runoff. Results show that annual rainfall and surface runoff follow a significant upward trend (rainfall: 4.98 mm·year−1, p-value = 0.029; runoff: 0.45 m3·s−1·year−1, p-value = 0.013). Also, rainfall appears to be the dominant driver of surface runoff (Spearman’s ρ = 0.732, p-value &lt; 0.0001), leading surface runoff at all timescales. Surface runoff is further modulated by potential evapotranspiration with quasi-decadal timescales fluctuations, although being less correlated to surface runoff (Spearman’s ρ = −0.148, p-value = 0.386). The study highlights the added value of the coupling of hydrological modeling and reanalysis datasets to analyze the rainfall–runoff relationship in data-scarce and poorly gauged environments and therefore raises pathways to improve knowledge and understanding of the impacts of climate variability in Sahelian hydrosystems.

A hybrid rainfall-runoff model: integrating initial loss and LSTM for improved forecasting

Accurate rainfall-runoff modeling is crucial for disaster prevention, mitigation, and water resource management. This study aims to enhance precision and reliability in predicting runoff patterns by integrating physical-based models like HEC-HMS with data-driven models, such as LSTM. We present a novel hybrid model, Ia-LSTM, which combines the strengths of HEC-HMS and LSTM to improve hydrological modeling. By optimizing the “initial loss” (Ia) with HEC-HMS and utilizing LSTM to capture the effective rainfall-runoff relationship, the model achieves a substantial improvement in precision. Tested in the Yufuhe basin in Jinan City, Shandong province, the Ia-LSTM consistently outperforms individual HEC-HMS and LSTM models, achieving notable average Nash-Sutcliffe Efficiency (NSE) values of 0.873 and 0.829, and average R2 values of 0.916 and 0.870 for calibration and validation, respectively. The study shows the potential of integrating physical mechanisms to enhance the efficiency of data-driven rainfall-runoff modeling. The Ia-LSTM model holds promise for more accurate runoff estimation, with wide applications in flood forecasting, water resource management, and infrastructure planning.