*2.4. Arc SWAT Application*

Arc SWAT 2012 was used for the hydroclimatic impact assessment of the CRVB. Arc SWAT 2012 is an Arc GIS extension program used for watershed modeling. The Soil and Water Assessment Tool (SWAT) is a widely used model for analyzing the water balances of a basin using long-term meteorological and spatial data of the area [45]. It is a physicallybased, deterministic, continuous, watershed-scale simulation model developed by the U.S. Department of Agriculture—Agricultural Research Service (USDA) [45,46]. It is a model written in Fortran to analyze mainly water, nutrient, and sediment conditions in large basins and the behavior under climate changes [46]. It can also be applied to evaluate the impacts of various human, environmental, and infrastructural management interventions in basins. It involves systematic and interconnected spatial and weather data analyses to evaluate the intended goal at each hydraulic response unit (HRU).

In the application of the model, the Penman–Monteith method for evapotranspiration, the soil conservation service (SCS) curve number method for surface runoff determination, and the variable storage method to simulate channel water routing are employed to analyze the water balances.

### The Water Balance Equations

In the analysis of the impacts of climate change on water balance components, the model operates based on the water balance equation indicated in Arnold et al. (2011) which is defined as:

$$SWt = SW\_0 + \sum\_{i}^{t} (Rday\_i - Qsurf\_i - Ea\_i - Wsecp\_i - Qgw\_i) \tag{1}$$

where *SWt* is soil water content (mm) at time *t*, *SW*<sup>0</sup> is initial soil water content (mm), *t* is simulation period (days), *Rdayi* is amount of precipitation on the i-th day (mm), *Qsurfi* is amount of surface runoff on the i-th day (mm), *Eai* is amount of evapotranspiration on the i-th day (mm), *Wseepi* is amount of water entering the vadose zone from the soil profile on the i-th day (mm), and *Qgwi* is amount of base flow on the i-th day (mm) [45].

Moreover, one of the critical parameters that are evaluated for sustainable water resource management of the study area is the water yield. The water yield is the aggregate sum of water leaving the HRU and entering the principal channel during a time step [45]. The water yield within a basin is evaluated by the model based on Equation (2). Considering the hydrological processes taking place continuously in the basin, the water yield, i.e., the net amount of water flowing past a given point on a stream during a given period, can be described by a basic model equation:

$$\mathcal{W}\_{yld} = \mathcal{Q}\_{sur} + \mathcal{Q}\_{lat} + \mathcal{Q}\_{\mathcal{g}w} - T\_{loss} \tag{2}$$

where *Wyld* is the water yield (mm), *Qsur* is the surface runoff (mm), *Qlat* is the contribution of the lateral flow to the stream (mm), *Qgw* is the contribution of the groundwater to the streamflow (mm), and *Tloss* is the transmission losses (mm) from the tributary in the HRU by means of transmission through the bed.

### *2.5. Model Parameter Sensitivity Analysis*

For a particular area of interest (CRVB), Arc-SWAT contains many hydrological parameters that need to be considered. However, not all the parameters may be contributing significantly to the model output, and it is therefore necessary to identify the input parameters that are significant [46]. In addition, the heterogeneity of the area makes it difficult

for all SWAT parameters to be monitored simultaneously. Calibration and validation are required to identify the parameters to use for the specific area in a balanced way [47]. The parameter sensitivity scale developed by Lenhart et al. (2002) was used to classify the sensitivity of the parameters in the sub-basins [48]. It was scaled to the mean of index (I) values (Table 2).

**Table 2.** Parameter sensitivity scale classes assigned in SWAT as adapted from Lenhart et al. (2002) [48]).


In addition, the most sensitive parameters used for stream flow analyses in the CRVB were selected on the basis of a tropical nature environment review recommendations [49]. The sensitivity ranking of the parameters (mean of index) is defined through an analysis of the values of the "t-stat" and "*p*-value" indexes in SWAT-CUP during calibration. The "t-stat" values are the t statistics. The t statistic is a measure of how extreme a statistical estimate is, and is calculated as:

$$t = \frac{M - \mu}{S\_m} \tag{3}$$

Where *t* = t-stat, *M* = sample mean, μ = population mean and *Sm* = estimated standard error. The identified sensitive parameters are indicated in Table 3 with their descriptions.


**Table 3.** The most sensitive SWAT parameters identified in the CRV sub-basins, and their descriptions.

#### *2.6. Model Calibration and Validation*

Calibration and validation of the SWAT models were carried out using SWAT-CUP, a calibration uncertainty program for SWAT with the SUFI-2 algorithm, which is sequential uncertainty fitting, version 2. The program performed calibration, validation, sensitivity analysis (one at a time), and uncertainty analysis. In addition, the program links SUFI2, GLUE, ParaSol, MCMC, and PSO algorithms to SWAT [50]. The models were calibrated and validated using monitored stream flows from the outlets of the Ketar, Meki, and Jidu (Shalla) Rivers. The outlet locations were set at the flow gauging stations. The models were set to run for the baseline periods from 1984 to 2010 for each of the sub-basins (Ketar, Meki, and Shalla).

Calibration and validation help the model to resemble the study area in its operation by adjusting the sensitive model parameters. In this study, the observed stream flow data from 1990 to 2001, obtained from the Ministry of Water Resources of Ethiopia (MW), were used for calibration, and data from 2004 to 2010 were used for validation. The models of each of the sub-basins were calibrated and validated separately with their respective stream flow data from each sub-basin outlet (Figure 4). During calibration, the data from the first three years were kept as a warming-up period. These data allow the model to warm up, initialize, and approach reasonable initial values of the state variable of the model [50]. The adjusting values, as modified by SWAT-CUP to fit the values of the parameters to site-specific ranges, and the adjusting methods are presented in Table 4. The adjusting methods are indicated in the prefix of the parameter (V\_, R\_, and A\_) and they are described in the table caption.

**Table 4.** Adjusting values and methods as adjusted by SWAT-CUP for the parameters.


Note: R = relative, the parameter will be multiplied by the relative value as follows: value\* (1 + R); V = replace, the parameter value will be replaced by the new values in the model; A = absolute, the parameter value will be added to the values in the model as follows: value + A; NA\* = unchanged default values in the model.

### *2.7. Model Performance Evaluations*

Before applying for analysis, the models' performances were assessed. Three main statistical parameters were used to evaluate the performance of the models: the coefficient of determination (*R*2), the Nash–Sutcliffe efficiency *(NSE*), and the percentage of bias (*PBIAS*) [51]. *R*<sup>2</sup> is calculated as :

$$R^2 = \left[\frac{\sum\_{i=1}^{N} (O\_i - O)(S\_i - S)}{\left[\sum\_{i=0}^{N} (O\_i - O)^2\right]^{0.5} \left[\sum\_{i=0}^{N} (S\_i - S)^2\right]^{0.5}}\right]^2 \tag{4}$$

*R*<sup>2</sup> ranges from 0.0 to 1.0. A higher value of *R*<sup>2</sup> indicates better performance of the model. The formula for calculating *NSE* is:

$$NSE = 1 - \frac{\sum\_{i=1}^{N} \left(O\_i - S\_i\right)^2}{\sum\_{i=1}^{N} \left(O\_i - O\right)^2} \tag{5}$$

Nash–Sutcliffe Efficiency (*NSE*) is a normalized statistic, which measures the relative magnitude of the residual variance in comparison with the variance of the measured data. Like *R*2, the higher the value of *NSE*, the better the performance of the model. *NSE* indicates the statistical relationship between simulated model values and observed values. It was stated that the "values of *NSE* vary from − ∞ to 1" [51,52].

**Figure 4.** Calibration (**a**) and validation (**b**) results of the models for the CRV sub-basins.

*PBIAS* is calculated as:

$$\text{PBIAS} = \frac{\sum\_{i=1}^{N} \left(\mathcal{S}\_i - \mathcal{O}\_i\right)}{\sum\_{i=1}^{N} \mathcal{O}\_i} \times 100\tag{6}$$

*PBIAS* measures the average tendency of the simulated values to be larger or smaller than their respective observed values. Positive *PBIAS* values indicate underestimation by the model, and negative values indicate overestimation. From the general statistics, the range within ±25% is acceptable [52].

In Equations (4)–(6), *S* is the mean of the simulated stream flows, *O* is the mean of the observed stream flows, *Si* is the simulated stream flows, *Oi* is the observed stream flows, and *N* is the number of observations.
