Akaki catchment is situated at the Northwestern Awash River between 8045’–9013’latitude and 38035’–39005’longitude (Figure 2). The climate condition of Akaki catchment is influenced by the movement of the ITCZ and the Indian Monsoon throughout the year (Romilly and Gebremichael, 2011). The annual climate of the study area may be classified as three seasons based on the movement of ITCZ. These are Kiremt, which is the main rainy season (June-September), Bega, which is the dry season (October-January), and Belg, the small rainy season (February-May) (Fazzini, Bisci and Billi, 2015). The annual rainfall in Akaki catchment varies from around 973.11 to 1266.04 mm whereas the mean annual temperature lies in a range between 13.19°C and 20.01°C with an overall mean value of 16.8°C (Getahun, 2015).

The total catchment area of Akaki is 1462 km2, divided into two sub-catchments Big Akaki (eastern) and the Little Akaki (figure 2). Land cover of the catchment is composed of cultivated land, urban area, water bodies, forest land, and grassland land. The most dominant soils in the catchment are Pellic Vertisols, Eutric nitisols, Orthic solonchaks, and Chromic luvisols. However, the entire watershed has undergone many anthropogenic changes potentially leading to expansion of urban land to the western and southern part of the catchment.

Daily precipitation data from nine stations ( Sebeta, Sendafa Add, Zequela, Ayertena, Dere Gidib, Boneya, Akaki, Addis Ababa Obs and Addiss Ababa Bole) was taken from National Meteorological Agency of Ethiopia ranging for the year 1987-2017, and daily flow data for three stations (big Akaki, little Akaki and Mutincha) were collected from Ministry of Water, Irrigation and Electricity of Ethiopia, for the period 1989-2004. Mean monthly evapotranspiration data was computed for three stations (Addis Ababa obs, Dire and Akaki) using Thornthwaite equation. Missing data in precipitation and flow data were filled using normal ratio method, and regression method respectively. Inverse distance weighted interpolation was used to determine the precipitation at the centroid of the sub catchments. Hydrologic model simulations are performed on daily time step basis.

## Methodology

Catchment Partitioning

The criteria used in the portioning are slope, hydrological soil group, land use, reservoir location and hydro-meteorological station availability. The hydrologic models were generated with the help of HEC-GeoHMS (US Army Corps of Engineers, 2015) using 30m by 30m DEM of the study area (Fig. 3). Using DEM terrain data, HEC-GeoHMS produces HMS input files, a stream network, sub-basin boundaries, and connectivity of various hydrologic elements in an ArcView GIS environment via a series of steps called terrain pre-processing and basin processing. The physical representation of catchments and rivers was configured in the basin models, and hydrologic elements were linked. During catchment delineation HMS input hydrological models were prepared, from partitioning of the sub catchments using multi-criteria considerations like gauging station, meteorological station, land use, location of reservoir and elevation. Which helps to identify the different land uses as well as different parts of the catchment contribution to discharge volume and peak.\n

Figure 2 Digital elevation model of Akaki catchment

### Model Calibration and Validation

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. The deficit constant method was employed to model infiltration loss. The SCS (Soil Conservation Service) unit hydrograph method was used to model the transformation of precipitation excess into direct surface runoff. The exponential recession model was employed to model baseflow. The Muskingum routing model was used to model the reaches. The catchment model incorporates three rainfall–runoff transformation processes. The first of these calculates the volume of runoff from a catchment as being the proportion of rainfall remaining in the system after “losses” have been subtracted.

The direct runoff (i.e. channel discharge) is modelled using the SCS (Soil Conservation Service) dimensionless unit hydrograph and the groundwater flow is transformed into base flow by exponential recession model. Each method in HEC-HMS has parameters and the values of these parameters should be entered as input to the model to obtain the simulated runoff hydrographs. Some of the parameters may be estimated by observation and measurements of stream and basin characteristics, but some of them cannot be estimated. When the required parameters cannot be estimated accurately, the model parameters are calibrated, i.e. in the presence of rainfall and runoff data the optimum parameters are found as a result of a systematic search process that yield the best fit between the observed runoff and the computed runoff. This systematic search process is called optimization.

For this study, initial values for all parameters (listed in Table 2) were obtained from geology, soil and land use maps and from published sources. The trial and error method, in which the hydrologist makes a subjective adjustment of parameter values in between simulations in order to arrive at the minimum values of objective function parameters that give the best fit between the observed and simulated hydrograph, was employed to calibrate the model. Although the model was calibrated manually, the HEC-HMS built-in automatic optimization procedure was used to authenticate the acceptability and suitability of the parameter values and their ranges as applicable to their uses in HEC-HMS.

The observed precipitation and discharge data were used to create the meteorological model using the Inverse Distance Weight method and, subsequently, the control specification model was created. The control specifications determine the time pattern for the simulation; its features are: a starting date and time, an ending date and time, and a computation time step. The observed historical data of nine rain gauge stations representing different sub-basin and three stream gauge stations in the Akaki basin, were used for model calibration and verification. A daily time step flow and precipitation data ranging from 1989 to 2004 was used for the simulation in which 1989-1991 was used as warm up period, 1992-2000 for calibration and 2001-2004 data was used for validation.

## MODEL PERFORMANCE EVALUATION METHODS

The criteria used to evaluate the performance of the models are the overall agreement between predicted and measured runoff discharges, and the models\' ability to predict time and magnitude of hydrograph peaks, and runoff volume. The choice of the objective function depends upon the need. The following statistical measures were used to quantify the performance accuracy of both models during each simulation periods, and combined over all periods. The objective function measures the goodness of fit between the computed outflow and observed stream flow at a selected element. Selection of objective function depends on the objectives of study. To evaluate the efficiency of the model two efficiency criteria are considered in this study. These are Nash Sutcliffe Efficiency (NSE and coefficient of determination (R2) which are widely applicable in hydrologic modelling. (Nash & Sutcliffe, 1970).

It is defined as: \nNSE=1-((∑_(i=1)^n▒(Qsim-Qobs)^2 )/(∑_(i=1)^n▒(Qobs-(Qobs) ̅ )^2 ))

NSE = Nash and Sutcliffe Efficiency, Qobs = observed value at the ith ime interval,

Qsim = simulated value at the ith time interval and = mean of the observed discharges.\nCoefficients of determination (R2) describe the degree of collinearity between simulated and measured data (Moriasi, Arnold, Van Liew, Bingner, Harmel and Veith, 2007).\nR^2=(∑▒〖(Qobs(t)-¯Qobs) ∑▒(Qsim(t)-¯Qsim) 〗)^2/(∑▒(Qobs(t)-(Q obs) ̅ )^2 ∑▒(Qsim(t)-(Qsim(t)) ̅ )^2 )

Where,

R2 = coefficient of determination, Qobs = observed value at the ith time interval, Qsim= simulated value at the ith time interval, ¯Qobs = mean of observed discharges and ¯Qsim= mean of simulated discharges.\nPercent error in peak flow (PEPF) ignores the entire hydrograph except for the single peak value:

PEPF=100|( Qo(peak)-Qs(peak) )/(Qo(peak))|\nWhere: PEPF=Percentage Error in Peak Flow, Qo= Observes discharge and Qs is simulated discharge \nPercent Error in volume considers computed volume, does not account for magnitude of the peak:

PEV=100|(Vo-Vs)/Vo|

Where: PEV=Percentage error in volume, Vo= observed volume and Vs is simulated volume