A comprehensive review on rainfall-runoff modelling using HEC-HMS

Introduction

Rainfall-runoff modeling is central to hydrological studies and plays a key role in watershed management, flood forecasting, and water resources planning. The HEC-HMS model, developed by the U.S. Army Corps of Engineers, provides a conceptual framework that enables the simulation of surface runoff generation and streamflow routing under different hydrological conditions. Its modular structure allows users to select appropriate physical representations of hydrological processes, such as infiltration, transformation, baseflow, and channel routing, according to data availability and basin characteristics (Verma et al., 2010; Fanta and Feyissa, 2021) [43,10] . Over the past decade, numerous studies have applied HEC-HMS across diverse climatic and geographic regions including India, Ethiopia, Vietnam, Malaysia, Morocco, and Greece (Anh and Canh, 2013; Bunganaen et al., 2021; Frysali et al., 2023) [1,5,11] . The model's versatility has been demonstrated for both gauged and ungauged watersheds, arid and humid environments, and small to large river basins. The objective of this review is to consolidate the methodological frameworks, calibration strategies, and performance evaluations used HEC-HMS applications to highlight the best-performing techniques and identify global trends in hydrological modeling.

Methodology of Review

The review compiled and analyzed various national and international studies that applied HEC-HMS for rainfall-runoff modeling. The papers were retrieved from peer-reviewed journals and conference proceedings. Each study was reviewed for key modeling parameters, including loss, transform, baseflow, and routing methods, simulation type (event-based or continuous), and performance metrics. The studies were further examined for model calibration, validation techniques, and acceptable parameter variation limits such as Curve Number (CN), lag time, and recession constant adjustments.

Common evaluation indicators across studies included NSE, R², RMSE, and Percent Bias (PBIAS). The synthesis was conducted by grouping studies according to their methodological similarities rather than geographical or chronological order.

HEC-HMS Simulation Methods 3.1 Loss Methods

The loss method in HEC-HMS determines the portion of precipitation that does not contribute to direct runoff.

Soil Conservation Service Curve Number (SCS-CN) Method

The SCS-CN method was the most frequently applied loss model across both event-based and continuous simulations (used in over 70% of the studies). Reviewed studies Belani et al. (2024) [3] , Namwade et al. (2023) [24] , Kencanawati et al. (2023) [17] , Belay et al. (2022) [4] , Daide et al. (2022) [8] , Obuya et al. (2022) [26] , Armain et al. (2021) [2] ,Bunganaen et al. (2021) [5] , Fanta and Feyissa (2021) [10] , Gopi and Rema (2021) [12] , Hamdan et al. (2021) [14] , Jabbar et al. (2021) [15] , Karna et al. (2021) [16] , Othman et al. (2021) [27] , Msaddek et al. (2020) [23] , Gunathilake et al. (2019) [13] , Khan et al. (2019) [18] , Paudel et al. (2019) [31] , Sarminingsih et al. (2019) [37] , Tassew et al. (2019)) [41] , Shaikh et al. (2018) [38] , Skhakhfa and Ouerdachi (2016) [40] and Choudhari et al. (2014) [7] . The CN value (ranging from 30-100) depends on soil type, land use, and antecedent moisture. Studies such as demonstrated that calibration of CN within ±10-15% of estimated values yielded optimal performance.

Equations

Initial and Constant Loss Method:

The Initial and Constant Loss (ICL) model is one of the simplest rainfall-loss (infiltration) models used in HEC-HMS to estimate the effective rainfall that contributes to runoff. Where:

= remaining portion of initial loss (I₀) if any. After initial loss becomes 0, only constant infiltration (C) is subtracted.

This method was applied by Frysali et al. (2023) [11] , Belay et al. (2022) [4] , and Sarminingsih et al. (2019) [37] . It assumes an initial abstraction followed by a constant infiltration rate. Performance ranged from Good to Satisfactory, with NSE values between 0.53-0.73, depending on watershed characteristics.

Deficit and Constant Loss Method:

The Deficit and Constant Loss (DCL) method is an infiltration model in HEC-HMS designed to represent the soil moisture accounting of a watershed. It calculates rainfall losses by tracking soil water deficit (unsatisfied soil moisture) and applying a constant rate of infiltration once the soil begins to saturate. Used for continuous simulation in Yilmaa and Kebede (2023) [44] , Matli and Hunashal (2021) [21] , Din et al. (2019) [9] and Chatterjee (2014) [6] . The results were typically very good, with R² values above 0.90 and NSE values up to 0.92, showing that this method performs reliably for long-term hydrologic studies.

Green-Ampt Method

The Green-Ampt (G-A) infiltration model is a physically-based method used in HEC-HMS to estimate infiltration losses during rainfall-runoff simulation. It represents infiltration as a sharp wetting front moving vertically downward into the soil. This method is best suited for event-based simulations, infiltrationexcess runoff conditions, and well-defined initial soil moisture. Cumulative infiltration (F): Used in event-based studies such as Prabha and Tapas (2020) [32] and Rathod et al. (2015) [34] . It applies physically-based infiltration parameters and produced very high accuracy, including R² reaching 0.97 and NSE 0.96, indicating excellent suitability for high-intensity rainfall events.

Soil Moisture Accounting (SMA)

The Soil Moisture Accounting (SMA) method is a physicallybased continuous infiltration and runoff model in HEC-HMS. It represents the watershed as a series of vertical storage layers, each with specific moisture capacities and percolation rules. Applied in Kumar and Pandey (2023) [19] , Msaddek et al. (2020) [23] ., Ouedraogo (2017, 2018) [28,29] , and Singh and Jain (2015) [39] . SMA provides detailed accounting of infiltration, percolation, storage, and evapotranspiration. Studies reported high to very high performance, with R² up to 0.96 and NSE up to 0.95, confirming the method's robustness for continuous simulations.

Transform Methods

The transform method converts excess precipitation into direct runoff at the subbasin outlet. It represents how rainfall moves over the watershed surface and through channels to generate streamflow.

SCS Unit Hydrograph

The dominant transform method across most studies. It was used in event and continuous simulations including Belani et al. (2024) [3] , Namwade et al. (2023) [24] , Kencanawati et al. (2023) [17] , Kumar and Pandey (2023) [19] , Daide et al. (2022) [8] , Belay et al. (2022) [4] , Obuya et al. (2022) [26] , Armain et al. (2021) [2] , Bunganaen et al. (2021) [5] , Fanta and Feyissa (2021) [10] , Gopi and Rema (2021) [12] , Hamdan et al. (2021) [14] , Jabbar et al. (2021) [15] , Karna et al. (2021) [16] , Matli and Hunashal (2021) [21] , Msaddek et al. (2020) [23] , Khan et al. (2019) [18] , Tassew et al. (2019) [41] , Paudel et al. (2019) [31] , Shaikh et al. (2018) [38] , Skhakhfa and Ouerdachi (2016) [40] , Rathod et al.( 2015) [34] , Choudhari et al. (2014) [7] . Reported performance was consistently strong, with NSE values often exceeding 0.80-0.90. The SCS-UH assumes a dimensionless hydrograph shape defined by: …( 14

Clark Unit Hydrograph

The Clark Unit Hydrograph (Clark UH) is a synthetic unit hydrograph method that combines two hydrologic processes: 1. Time-Area Histogram (Translation) 2. Linear Reservoir (Attenuation) It is widely used in HEC-HMS because it represents both runoff translation and runoff storage (attenuation) in a watershed. Applied in Din (2019) [9] , Gunathilake (2019) [13] , Ouedraogo (2017, 2018) [28,29] , Chatterjee (2014) [6] etc. The Clark UH combines translation and attenuation, explaining its good performance in mixed terrain basins, with R² commonly above 0.85.

Snyder Unit Hydrograph

The Snyder Unit Hydrograph (SUH) is one of the earliest synthetic unit hydrograph methods and is commonly used in HEC-HMS for rainfall-runoff modeling, especially when streamflow data is limited. The method was originally developed for watersheds in the Appalachian region and later generalized for other ungauged basins. Used in Belay (2022) [4] and Sarminingsih (2019) [37] Studies reported very good performance with NSE up to 0.94.

Baseflow Methods

HEC-HMS simulates baseflow as the slow component of streamflow emerging from groundwater storage. Baseflow accounts for the longer-term drainage of subsurface water, sustaining streamflow during inter-storm periods. The model provides several conceptual baseflow methods, each with different mathematical formulations.

Recession Method

The Recession Method is the most commonly used for baseflow estimation in HEC-HMS. Widely used in Belani et al. (2024) [3] , Gopi and Rema (2021) [12] , Gunathilake et al. (2019) [13] , Khan et al. (2019) [18] , Ouedraogo et al. (2018) [29] and Singh and Jain (2015) [39] . Models using recession baseflow achieved satisfactory to very good performance (NSE > 0.70).

Constant Monthly Baseflow Method

Assumes baseflow varies month-wise but is constant within each Where:

= baseflow at time = constant baseflow assigned for month Mostly apply in regions with predictable seasonal groundwater fluctuation. Applied in Karna (2021) [16] , Din (2019) [9] , Paudel (2019) [31] , Chatterjee (2014) [6] . These studies reported good consistency with R² above 0.80.

Linear Reservoir Baseflow Method

Groundwater is represented as one or more linear reservoirs. Outflow is proportional to the storage. Formula …(18) … (19) Where:

This is the same concept used in hydrogeology for linear aquifer drainage. Observed in Frysali (2023) [11] and Ouedraogo (2017) [28] . The method yielded good performance, with R² around 0.72-0.74.

Exponential Recession (Exponential Baseflow Method)

Represents baseflow using a two-term exponential curve with an asymptotic minimum baseflow.

…(20)

= maximum initial recession flow = minimum constant groundwater outflow = exponential decay coefficient It is used in Yilmaa and Kebede (2023) [44] , Bunganaen et al. (2021) [5] and Choudhari et al. (2014) [7] .

Routing Methods

Routing methods simulate how water flows through channels or river reaches after runoff is generated

Valid ranges

• •

Most widely used routing technique reviewed in Yilmaa and Kebede (2023) [44] , Daide et al. (2022) [8] , Obuya et al. (2022) [26] , Fanta and Feyissa (2021) [10] , Gopi and Rema (2021) [12] , Hamdan et al. (2021) [14] , Jabbar et al. (2021) [15] , Paudel et al. (2019) [31] , Skhakhfa and Ouerdachi (2016) [40] , Tassew et al. (2019) [41] , Choudhari et al. (2014) [7] . Performance ranged from good to very good, with R² up to 0.90.

Muskingum-Cunge Routing Method

Physically based routing that accounts for channel geometry, slope, and roughness. The diffusive wave approximation of the Saint-Venant equations. Storage is computed using: [11] and Karna et al. (2021) [16] . Calibration of routing parameters ensured that the simulated hydrograph matched peak timing and volume accurately.

Lag Routing

Very simple routing method used when limited data is available.

Outflow hydrograph (Ot)is simply the inflow hydrograph shifted by a fixed time lag (L):

No attenuation of peak is modeled. Used in Kencanawati (2023) [17] and Armain (2021) [2] , producing high accuracy, including R² up to 0.97.

Results and Discussion

HEC-HMS model provides strong and consistent performance across different climatic regions and watershed conditions. Most studies reported high model accuracy, with NSE values frequently between 0.80 and 0.95 and R² values commonly above 0.85, especially in event-based simulations. Continuous simulations also performed well, where NSE values ranged from moderate (0.63-0.75) to very high (0.90). Green-Ampt loss studies particularly high precision with NSE > 0.95. A few studies reported moderate accuracy indicating the challenges of long-term or data-limited conditions. The lowest performance appeared, where rainfall-runoff correlation was weak. In summary, the results clearly show that HEC-HMS consistently reproduces peak flows, runoff depth, and hydrograph shape with acceptable to excellent accuracy across a wide variety of watersheds. (2024) [3] Temporal analysis of rainfall-runoff models using HEC-HMS in semi-arid region: a case of the shetrunji river sub-basin, India (2023) [11] Hydrologic [24] Rainfall-Runoff modelling using HEC-HMS Model, Remote Sensing and GIS in Middle Gujarat, India Event SCS-CN

Clark unit hydrograph, SCS Unit Hydrograph --

Daily timescale calibration and validation result over the study area shown good performance with NSE, R² and Percent Bias PBIAS (%) 0.881, 0.913 and 9.76% respectively for calibration and 0.914, 0.947 and 14.8% respectively for validation. Whereas, The Nash-Sutcliffe efficiency, coefficient of determination, and 6statistical performance i7ndicators for the Clark unit hydrograph transform method were found to be 0.69, 0.77, 0.7461, and 0.9794, respectively. the model's results indicate a strong correlation between simulated and observed peak flows, suggesting that the water resource practices in the study area or similar basins are effective.

6

Yilmaa and Kebede (2023) [44] Application (2022) [8] Beht watershed (morocco) rainfallrunoff simulation with the HEC-HMS hydrological model

Continuous SCS-CN SCS Unit Hydrograph -Muskingum

Relative Error in peak: REP = 9.6%, Relative Error in volume: REV = 1.69%, Nash-Sutcliffe Efficiency: NSE = 0.63, coefficient of determination: R² = 0.870, and Ratio of standard deviation of observations to root mean square error: RSR = 0.36. 9

(2022) [26] Hydrodynamic modeling using HEC-HMS Model, river Kuja Basin, Kenya

Continuous SCS-CN SCS Unit Hydrograph

Exponential recession Muskingum

The regression analysis focusing on the relationship between rainfall and streamflow resulted in correlation coefficient value of 0.64 and coefficient of determinant value of 0.41.

10

(2021) [2] Development [5] Rainfall-Runoff Fanta and Feyissa (2021) [10] Performance (2021) [14] Rainfall-Runoff Modeling using the HEC-HMS Model for the Al-Adhaim River Catchment, Northern Iraq Event SCS-CN SCS Unit Hydrograph -Muskingum R² was 0.9 for both calibration and verification.

(2021) [15] HEC-HMS hydrological modelling for runoff estimation in cameron highlands, Malaysia Continuous SCS-CN SCS Unit Hydrograph -Muskingum (R²) = 0.90, Nash-sutcliffe Efficiency = 0.92, Root Mean Square Error = 0.1 and the Percent Bias = 0.77%. Thus, the model can be applied in the Cameron Highland Watershed. 16 Karna et al.

(2021) [16] Application of HEC-HMS model for runoff simulation: a case study of kankai river basin in Nepal Event

SCS-CN SCS Unit Hydrograph constant monthly

Muskingumcunge

The calculated value of both NSE and R² has found 0.805, 0.816 for the calibration period and 0.856, and 0.868 for the validation period, which indicates the finer accuracy of simulated outflow.

Matli and Hunashal (2021) [21] Hydrological (2021) [27] Calibration and validation of hydrological model using HEC-HMS for Kuantan River Basin Event

SCS-CN Clark unit hydrograph constant monthly Muskingum

The calibration result shows an acceptable model efficiency (ME) of 0.85 which is in agreement with observed data while the ME of 0.76, 0.83 and 0.81 are satisfactorily validated with HEC-HMSmodel. 19 Msaddek et al. (2020) [23] Hydrological (2019) [9] Runoff modelling using HEC-HMS for rural watershed

Continuous

Deficit and Constant

Clark unit hydrograph

Constant monthly Muskingum

Loss method, Deficit and Constant method with Clark transformation and constant monthly base flow perform well. This can be used as a decision support tool in the design and operation 22 Gunathilake et al. (2019) [13] Application (2019) [18] Hydrological Modeling of Upper Indus Basin Using HEC -HMS.

Continuous SCS-CN SCS Unit Hydrograph

Recession -While in the targeted watershed gave the value for Peak Discharge and Root Mean Square Method as 7.83 and R² value of 0.855 for the discharge. The performance of the HEC-HMS was found to be satisfactory for obtained square functions in the validated model during simulation. 24 Paudel et al.

(2019) [31] Application [38] Simulation of rainfallrunoff event using HEC-HMS model for rel sub-basin, Gujarat, India Event SCS-CN SCS Unit Hydrograph -

The comparison of observed and simulated hydrographs with high R² value (=0.86) shows the capability of the model to be used in hydrologic simulation in Rel watershed. 29 Ouedraogo et al. (2017) [28] HEC-HMS Model for Runoff Simulation in Ruiru Reservoir Watershed

Continuous Soil Moisture Accounting

Clark unit hydrograph linear reservoir -

The Efficiency of the model 0.74 and 0.72 respectively for the calibration and the validation indicating that the results of the simulation are good.

30

Skhakhfa and Ouerdachi (2016) [40] Hydrological modelling of wadi Ressoul Watershed, Algeria, by HEC-HMS model

Event

SCS-CN SCS Unit Hydrograph -Muskingum

The results of the measuring approved the results of the model and showed that the difference between the peak discharge observed and validated model was about 8.86 percent with R² value is 0.867 and Nash-Sutcliffe efficiency is at 0.99. The present study concludes that the model can be utilized for the wadi Ressoul.

(2015) [34] Simulation of Rainfall -Runoff process using Event Green-Ampt SCS unit hydrograph --Nash-Sutcliffe coefficient values come out to be more than 0.8 for all three sub basins.

HEC-HMS (Case Study: Tapi River, India)

Correlation coefficient between observed and simulated discharge is more than 0.9 for all three sub basins. Finally, study concludes that HEC-HMSmodel can be used with reasonable approximations on Tapi River. 32 Singh and Jain (2015) [39] Continuous hydrological modeling using Soil Moisture Accounting Algorithm in Vamsadhara River Basin, India

Continuous Soil Moisture Accounting

Clark unit hydrograph Recession -

The overall model efficiencies (EFF) given by Nash-Sutcliffe Efficiency criteria are 0.701 and 0.762 for the calibration and validation periods, respectively, indicating a good model fit. Percentage error in volume (PEV) for the calibration and validation periods was found to be 2.64% and 12.33%, respectively, which indicates good model fit.

On the basis of percentage error in peak (PEP) criteria, which gives an error of 0.21% and -15.2% for the calibration and validation periods, respectively, the performance of the model can be rated as good. The coefficient of determination (R²) for the calibration period was found to be 0.71 and 0.78 for the validation period, indicating good model fit.

Chatterjee et al. (2014) [6] Hydrological [7] Simulation of rainfallrunoff process using HEC-HMS model for Balijore Nala watershed, Odisha, India Event

SCS -CN SCS unit hydrograph

Exponential recession Muskingum

Final validation parameter was derived and considered as global values for the model.

The HEC-HMS model used for rainfallrunoff simulation in the selected watershed shows RMSE as 0.09 m3/sec and MARE as 0.06 for peak discharge and RMSE as 0.70 mm and MARE as 0.05 for runoff depth.

Conclusion

HEC-HMS is a highly reliable and versatile hydrological model capable of effectively simulating both event-based and continuous rainfall-runoff processes. The dominant use and consistently strong performance of the SCS-CN loss method, paired with the SCS Unit Hydrograph transform method, indicate that this combination is the most dependable approach across diverse catchments. The Muskingum routing and recession baseflow methods were also widely preferred due to their stability and realistic representation of channel storage and groundwater recession. Continuous modelling benefited significantly from the Deficit-Constant and Soil Accounting (SMA) methods, especially in studies targeting seasonal or annual hydrologic responses. The collective findings confirm that HEC-HMS can be confidently applied for flood forecasting, watershed assessment, reservoir inflow estimation, hydrologic design, and water resources planning. Overall, the table-based evidence clearly concludes that HEC-HMS delivers dependable simulation results when supported by proper parameterization, calibration, and method selection appropriate to watershed conditions.

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