# Integrated Hydrological Analysis of Little Akaki Watershed Using SWAT-MODFLOW, Ethiopia
## 3 Results and Discussions
### Groundwater Modeling  
(a) MODFLOW Model Calibration  
The MODFLOW model was calibrated using automatic calibration tool, PEST for hydraulic conductivity in the range of 0.001 to 25 m/day using observed water table and estimated baseflow at the out late. The best fit simulation results were obtained while the model region was divided into different hydraulic conductivity zones through trial and error considering the hydrogeology and geomorphology of the area. The hydraulic conductivity zones and results of hydraulic conductivity values from the steady state calibrations are shown in Figure 9. The hydraulic conductivity result from calibration shows higher values below the Gefersa Lake which could be due to the presence of geological faults [11]. The plot of simulated steady-state hydraulic head values versus the measured water levels at the observation wells shows fit by comparison to a 1:1 line in Figure 10.  
Figure 9: Hydraulic conductivity zones and its values obtained through calibration process. * MODFLOW Model Performance Evaluation  
The simulation results of the calibration would be assessed both qualitatively and quantitatively [23]. The calibrated outcomes were appraised based on the calibration objective and calculation of the mass balance of the system. A scatter plot of measured heads against simulated heads showed the calibration performance (Figure 10). The scatter plots are observably examined to see how much the points in a plot differed from the straight line. Additionally, the calibrated model results were evaluated statistically by evaluating with the three common methods of error quantifications known as Mean error, Mean absolute error, and Root Mean Squared Error [26]. \[RMSE=\left[\frac{1}{n}\sum_{i=1}^{n}(h_{s}-h_{o})_{i}^{2}\right]^{0.5}, \tag{1}\]  
\[\text{ME}=\frac{1}{n}\sum_{i=1}^{n}(h_{s}-h_{o})_{i}\;, \tag{2}\]  
\[\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}(h_{s}-h_{o})_{i}\;, \tag{3}\]  
where \(n\) denotes to the number of observations considered, \(h_{s}\) to the simulated head [L], and ho to the observed head [L]. The mean error refers to the variation between the observed and simulated heads. The mean absolute error indicates the mean differences of the absolute values of observed and simulated heads. The calibration of the model was evaluated by applying all these objective functions (Table 3) highlighting the \(RMSE\) as it is the most reliable evaluation method as compared to the other two methods [26]. Therefore, the model performance evaluation to simulate the groundwater level shows statistically acceptable and unbiased. Figure 10: Scatter diagram of calculated and observed heads at the observation sites. The gains to and losses from streams indicate the interaction of the stream with an aquifer. The interactions were simulated using river and drain processes in the MODFLOW. Constant river stage was considered because the model is steady-state. The interaction between rivers and groundwater indicates that flow occurs from the rivers into aquifers above the Gefersa Lake in river 1 (R1) and above an elevation of 2375 masl in the second river (R2) (Figure 11), and from the aquifer to the rivers in the downstream courses of the rivers. (d) Sensitivity Analysis \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Evaluation Statistics**} & \multicolumn{3}{c}{**Error (m)**} \\ \cline{2-4}  & **ME** & **MAE** & **RMSE** \\ \hline Value & 1.99 & 3.812 & 4.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical values to evaluate MODFLOW model performance. Figure 11: Simulated groundwater head and the cross-section view. In groundwater modeling, there are unavoidable limitations that result in uncertainties in aquifer parameter estimation. Sensitivity analysis helps to understand the level of uncertainty in the calibrated model caused by those controls in the calculations of aquifer parameters. Aquifer hydraulic conductivity is one of the input parameters the groundwater models are sensitive to.