Simulation of the rainfall–runoff relationship using an HEC-HMS hydrological model for Dabus Subbasin, Blue Nile Basin, Ethiopia

The derivation of relationships between the rainfall over a catchment area and the resulting flow in a river is a fundamental problem for the hydrologist. In most countries, there are usually plenty of rainfall records, but the more elaborate and expensive stream flow measurements, which are what the engineer needs for the assessment of water resources or damaging flood peaks, are often limited. Evaluating river discharges from rainfall has stimulated the imagination and ingenuity of engineers for many years, and more recently has been the inspiration of many researchers (Sarminingsih et al. 2019; Hamdan et al. 2021; Ranjan & Singh 2022; Guduru et al. 2023).

The surface subsystem of the hydrologic cycle is where the rainfall and runoff interaction takes place. The input to this system is the rainfall and the output is taken as the stream flow at the outlet of the system (Neitsch et al. 2002). Hydrological modeling is a typical approach for predicting the hydrological response of a basin to rainfall. It enables the prediction of the hydrologic response to various watershed management methods as well as a better understanding of their implications (Kadem 2011).

The wide analysis of the literature reveals that studies on the use of watershed models for hydrologic simulations in underdeveloped countries are severely restricted due to the limitation of data (Kumar & Bhattacharya 2011; Derdour et al. 2018). As a result, a study of hydrologic simulation through the development of an appropriate watershed model is very necessary. Since it is impossible to assess all characteristics that affect runoff, selecting a model with a basic structure, minimal input data needs, and adequate precision is critical (Ramesh 2017). Hydrologic Modeling System (HEC_HMS), which has been used extensively in many research works, is one of the hydrologic models that meet these criteria.

HEC-HMS is a physically based semidistributed hydrological model that represents a basin with interconnected hydrologic and hydraulic components to simulate the surface runoff response to precipitation. The HEC-HMS model uses three basic data sets for the modeling work, viz. meteorological data (rainfall, temperature, evapotranspiration); hydrological data (streamflow); and geospatial data (digital elevation model (DEM), soil, land use land cover). The computation of stream flow hydrographs at the basin outlet is the result of the modeling process.

The HEC-HMS model has been applied in wide geographical areas (Majidi & Shahedi 2012; Haddad 2022; Ranjan & Singh 2022; Guduru et al. 2023). The current version of HEC-HMS 4.2.1 is a highly flexible package. It includes different methods to simulate runoff volume, transforming excess precipitation, base flow estimation, and channel routing. The user can choose a suitable combination of models depending on the availability of data, the purpose of modeling; and the required spatial and temporal scales.

This study was, therefore, conducted to simulate the rainfall–runoff relationship for the Dabus subbasin in the Blue Nile Basin using HEC-HMS hydrological model to give useful information for future water resource planning and management. As the meteorological and gauging stations installed in the Blue Nile Basin in particular and in the country, in general, are very limited, the main motive of the study was to investigate hydrologic responses to precipitation under these data-scarce conditions.

The daily historical hydrological and meteorological data for the subbasin were obtained from the Department of Hydrology and National Meteorological Agency of the Ministry of Water, Irrigation and Energy (MoWIE) for the period from 2002 to 2019. The data were collected from 10 rainfall stations (Table 1). The hydrologic gauging stations in the Dabus subbasin with automatic water level recordings are very limited. There are seven gauged stations but the stream flow data used in the model are from three stations, namely Dabus, Aleltu, and Dilla owing to the availability of rainfall recording stations in or near the boundary of the stream-gauged catchments (Table 2).

The reliability of the collected raw meteorological and hydrological data significantly affects the quality of the model input data and, consequently, the model simulation. Screening of the daily rainfall and stream flow data was first done by visual inspection. Filling of missed data and consistent checking were then made using the normal ratio and double mass curve analysis, respectively (Wang et al. 2002).

The collected spatial and time series hydrological and metrological data were arranged in a manner suited to HEC-HMS hydrological model for rainfall–runoff modeling.

The first step in doing any kind of hydrologic modeling is terrain preprocessing which involves delineating streams and watersheds and getting some basic watershed properties such as area, slope, flow length, and stream network density. Arc Hydro (a tool that works with Arc-GIS) was used to process a DEM to delineate the subbasin, watersheds, stream network, and drainage patterns of the subbasin. The results from terrain preprocessing were used to create input files for the HEC-HMS model using HEC-GeoHMS. HEC-GeoHMS provides the connection for translating GIS spatial information into model files for HEC-HMS.

Diverse methods are included in HEC-HMS to simulate various hydrologic processes (USACE-HEC 2008). In this study, the deficit constant loss method was employed to calculate rainfall losses by infiltration; the Clark unit hydrograph transformation method to compute direct runoff; the exponential recession method to estimate base flow; and the Muskingum method for channel routing. These methods were selected based on the applicability and limitations of each method, availability of data, suitability for the same hydrologic condition, well-established, stable, and widely acceptable, and recommendation by various studies (Ramesh 2017; Trivedi et al. 2019; Jaiswal 2020).

The deficit constant loss method assumes a single soil layer to account for continuous changes in moisture content. The potential evapotranspiration computed by the model was used to dry out the soil layer between precipitation events. Infiltration is assumed to occur only when the soil layer is saturated.

Runoff transformations convert excess precipitation on a subbasin to direct runoff at the subbasin outlet. The HEC-HMS is a conceptual model in which the process during simulation cannot be observed. It only gives the final output from the given input. The surface runoff calculations were performed using the Clark Unit Hydrograph method which requires time of concentration and storage coefficient to be computed for implementation.

The Muskingum method for channel routing was chosen. In this method, X and K parameters must be evaluated. Theoretically, the K parameter is the time of passing of a wave in reach length and the X parameter is a constant coefficient and its value varies between 0 and 0.5. Therefore, parameters can be estimated with the help of observed inflow and outflow hydrographs. Parameter K was estimated as the interval between similar points on the inflow and outflow hydrographs. Once K was estimated, X was estimated by trial and error method (USACE-HEC 2008).

Sensitivity analysis in hydrological modeling helps to reduce uncertainty by identifying the factors that have the greatest influence on output variation as a result of input variability. It also offers suggestions for parameter estimates at the model's calibration step (Haibo et al. 2018). The HEC-HMS model's built-in sensitivity analysis tool offers suggested parameter adjustment ranges. To improve the simulation result and thus understand the behavior of hydrologic systems in Dabus subbasin, sensitivity analyses were conducted using the entire flow parameters for HEC-HMS model. While all other parameters stayed constant at their nominal starting values, the model was run repeatedly with each parameter's initial baseline value increasing and decreasing by 25% (Lenhart et al. 2002). The hydrographs generated by the various model parameter values were then compared with the hydrograph from the base model. The effect of each model parameter was analyzed based on the objective function (model performance). Those model parameters having steep slopes (having high variation between intervals) were considered most sensitive, while those having moderate to gentle slopes (having low variation between intervals) were considered as less sensitive.

Model calibration is a process of changing model parameter values until the output of the model satisfactorily corresponds to the observed data (Madsen 2000). In this study, a peak-weighted root mean square error (PWRMSE) function was used to assess the degree of fit between the computed and observed hydrographs. Two search methods are available in the HEC-HMS model to find the best parameter value (USACE-HEC 2008). The first is known as the univariate gradient method, which only evaluates and modifies one parameter at a time while maintaining the other parameter values constant. The second technique is the Nelder and Mead (NM) method, which uses a downhill simplex to assess all parameters simultaneously and decide which one should be changed. For this study, PWRMSE with NM method was used to search for the optimal parameter value.

The comparison of the model outputs with an independent data set without any further alterations is known as model validation. The values of calibrated model parameters are neither changed nor remain constant during this process. The degree of variation between estimated and observed hydrographs is the quantitative measure of the match.

Based on 18 years of historical streamflow data from 2002 to 2019, the HEC-HMS model was calibrated and validated. Data from 2002 to 2014 were utilized for calibration, and data from 2015 to 2019 were used for validation.

To evaluate the performance of the HEC-HMS model, the quality and dependability of simulated values were compared with observed values using statistical tools. The Nash-Sutcliffe simulation efficiency (NSE), the observation standard deviation ratio (RSR), and the coefficient of determination (R²) were applied for the purpose.

R² values again range between 0 and 1, with higher values suggesting less error variance and values larger than 0.5 are commonly regarded as acceptable (Moriasi et al. 2007).

The sensitivity analysis was performed on two event model parameters (loss method and transform method). Parameters such as the base flow and relative loss percentages were not included in the sensitivity analysis due to their linear relationship with runoff production.

In the current study, the rainfall–runoff relationship was simulated for the data-scarce Dabus subbasin of the Blue Nile River Basin using the HEC-HMS hydrologic model. Daily precipitation and stream flow data from 2002 to 2019 were used as input data for the model, together with soil and land use/land cover data, and a DEM of the study area. When model parameters were subjected to sensitivity analysis, parameters like time of concentration and storage coefficient were found much more sensitive than loss parameters like initial deficit, maximum deficit, and constant rate. The model was calibrated and validated for its simulation of stream flow. The model predicted stream flow with reasonable accuracy with NSE, RSR, and R² values of 0.784, 0.334, and 0.818 during calibration, and 0.793, 0.323, and 0.875 during validation, respectively. This suggests that HEC-HMS modeling for daily stream flow in the Dabus subbasin is reliable and acceptable. As a result, the model can be used to obtain runoff data from measured precipitation on the studied subbasin. It can also be used to model runoff in ungauged watersheds having similar features to the study area.

This research was funded by the Ministry of Education of the Federal Government of Ethiopia.

The authors would like to thank the Ethiopian Roads Authority for the financial support to conduct the study; and the Ethiopian Ministry of Water, Irrigation and Energy for providing the necessary data.

All relevant data are included in the paper and any supplementary information, if required, can be provided upon reasonable request.

The authors declare there is no conflict.