2.3.1. HEC-HMS Model
The HEC-HMS model is physically based and conceptually semi-distributed model designed to simulate rainfall-runoff processes in a wide range of geographic areas, from large river basin water supplies and flood hydrology to small urban and natural watershed runoffs. It easily operates huge tasks in relation to hydrological studies, including losses, runoff transform, open channel routing, analysis of meteorological data, rainfall-runoff simulation, and parameter estimation [
21,
22]. Moreover, the HEC-HMS uses separate models that compute runoff volume, models of direct runoff, and models of baseflow. It has nine different loss methods, some of which are designed primarily for simulating events, while others are intended for continuous simulation. It also has seven different transformation methods. For example the Snyder Unit Hydrograph Yilma and Moges [
17] and Clark Unit Hydrograph Banitt [
23] methods have been applied successfully to simulate long-term stream flows elsewhere.
HEC-GeoHMS was used to create a basin model and a meteorological model, and to control specifications before running the model. The basin model and the basin features were taken as the background map file and imported to HEC-HMS 4.2. Since we do not have observation stations in each sub-basin, the precipitation values were estimated by the most commonly used Thiessen Polygon method and weights were worked out in HEC-GeoHMS software. The method was selected because of its easy application; accuracy depends on the sampling density. The boundaries are often oddly shaped, as transitions between polygons are often abrupt and continuous variables are often not well represented. During calibration, a daily simulation time step was used in estimating the parameters of the selected methods. Each model run combines a basin model, meteorological model, and control specifications with run options to obtain results. It contains four main components: (1) An analytical model to calculate overland flow runoff as well as channel routing, (2) an advanced graphical user interface illustrating hydrologic system components with interactive features, (3) a system for storing and managing data—specifically large, time variable data sets—and (4) a means for displaying and reporting model outputs [
24].
The Soil Conservation Service Curve Number, SCS Unit hydrograph, and Muskingum routing methods were selected for each component of the runoff process as runoff depth, direct runoff, and channel routing respectively. These methods were chosen on the basis of applicability and limitations of each method, availability of data, suitability for the same hydrologic condition, stability, wide acceptability, and well established researcher recommendations. The baseflow was not considered because in short duration event modelling and for small sub-basins the contribution of base flow is insignificant for flood flows [
25,
26].
(i) Loss Model
The loss models in HEC-HMS normally calculate the runoff volume by computing the volume of water that is intercepted, infiltrated, stored, evaporated, or transpired and subtracting it from the precipitation. In this study, the Soil Conservation Service Curve Number loss method was selected to estimate direct runoff from a specific or design rainfall [
27]. It has several advantages over other methods in that: It is a simple conceptual method for the estimation of the direct runoff amount from a storm rainfall event, and is well supported by empirical data; it relies only on the curve number, which is a function of the soil type and land use/cover that are the major runoff-producing watershed characteristics. However, there are several problems associated with the SCS-CN method. For example, it does not account for rainfall intensity and temporal variation of rainfall as well as for average ground slope [
28]. Despite the above problems, the SCS-CN loss method was chosen for HEC-HMS analysis in this study because of the following reasons: It is commonly used in different environments and provides better results compared to initial and constant loss rate method [
13]. Its calculation is made easier by the fact that only a few variables need to be estimated based on hydrologic soil group, land use and slope maps. And despite its simplicity, it yields results that are as good as those of complex models [
29].
The SCS-CN model assumes that the accumulated rainfall-excess depends upon the cumulative precipitation, soil type, land use and the previous moisture conditions as estimated in the following relationship [
21].
where Pe is the accumulated precipitation excess at time t (mm); P is the accumulated rainfall depth at time t (mm); Ia is the initial abstraction (initial loss) (mm) = αS, α is 0.2 as a standard; and S is the potential maximum retention (mm), a measure of the ability of a watershed to abstract and retain storm precipitation.
In the curve number method, the runoff is directly proportional to the precipitation with an assumption that the runoff is produced after the initial abstraction of 20% of the potential maximum storage [
30].
The maximum retention, S, and watershed characteristics are related through an intermediate dimensionless parameter, the curve number (CN) as:
where CN is the SCS curve number used to represent the combined effects of the primary characteristics of the catchment area, including soil type, land use, and the previous moisture condition. The CN values range from 100 (water bodies) to approximately 30 for permeable soils with high infiltration rates [
21].
(ii) The Transform Model
The transform prediction models in HEC-HMS simulate the process of the direct runoff of excess precipitation on the watershed, and they transform the precipitation excess in point runoff. In this study, the Soil Conservation Service Unit Hydrograph model was chosen to transform excess precipitation into runoff. It is a parametric model based on the average Unit Hydrograph (UH) derived from gauged rainfall and runoff data of a large number of small agricultural watersheds throughout the United States. The SCS proposed the Unit Hydrograph (UH) model, and it is included in the HEC-HMS program. The lag time (T
lag) is the only input for this method. It is the time from the center of mass of excess rainfall to the hydrograph peak and is calculated for each watershed based on the time of concentration Tc, as:
where T
lag and T
c are in minute.
The time of concentration can be estimated based on basin characteristics including topography and the length of the reach by Kirpich’s formula [
31].
where L is the reach length in feet, and S is the slope in (ft/ft).
(iii) Routing Model
As the flood runoff travels through the channel reach, it becomes attenuated due to channel storage effects. The routing models available in HEC-HMS account for this attenuation. The Muskingum method, which was developed by McCarthy [
32], is a popular lumped flow routing technique which was selected for this study.
The Muskingum routing method is a simple approximate method to calculate the outflow hydrograph at the downstream end of the channel reach from the inflow hydrograph at the upstream end. Among many models used for flood routing in rivers, it is a straightforward hydrological flood routing technique used in natural channels [
33], and it has been extensively applied in river engineering practice since its introduction in the 1930s [
34]. In this model calibration, two parameters are needed; travel time (K) of the flood wave through routing reach; and dimensionless weight (X) which corresponds to the attenuation of the flood wave as it moves through the reach. The routing parameters in the models are usually derived through calibration using measured discharge hydrographs [
35].
in which the prism storage in the reach is KQ, where K is a proportionality coefficient, and the volume of the wedge storage is equal to KX (I − Q), where X is a weighting factor having a range of 0 ≤ X ≤ 0.5.
2.3.2. HEC-GeoHMS Model
Background map files, basin model files, meteorological model files, and a grid cell parameter are created by HEC-GeoHMS which are input to a hydrological model HEC-HMS. The following steps adopted from Merwade [
36] were used to extract the basin model: (i) Data collection such as DEM, soil and land use/cover; (ii) data assembly; (iii) terrain preprocessing. This latter part of the HEC-GeoHMS processing step helps to drive the drainage network from the input DEM processing, such as flow direction, flow accumulation, stream definition and segmentation, catchment polygon processing, drainage line processing and adjoint catchment processing; (iv) Hydrologic Modelling System (HMS) Project Setup: The input files for the HEC-HMS project were developed using the HMS project set up menu in HEC-GeoHMS, this helps to copy all the terrain preprocessing data to the HEC-HMS project; (v) basin processing; (vi) the extraction of basin and stream characteristics such as length, upstream and downstream elevations, and river slopes. It can help to extract the physical characteristics of sub-basins, such as longest flow path, basin centroid, centroid elevation, centroidal longest flow lengths, and basin slopes; (vii) the estimation of hydrologic parameters, such as the curve numbers, the percentage impervious area and time of concentration initial values are estimated using HEC-GeoHMS model processing; (viii) the creation of HMS model files, such as background shapefile, the basin model, meteorological model file, and a project file.
HEC-GeoHMS extension in ArcGIS was used to delineate the boundary of the area by considering the geographical reference point of the hydrological gauging station as the outlet point of the Gilgel Abay Catchment. Further HEC-GeoHMS processing of the DEM produced four sub-basins, five routing reaches, five junctions, and the major physiographic characteristics of the catchment as shown in
Figure 1 and
Table 2.