# Analysis of Hydrological Characteristics of Blue Nile Basin, Nishe Watershed
## 2 Materials and Methods
### Soil and Water Assessment Tool (SWAT) Model Description  
The SWAT is a semi-distributed hydrological model which depends on the daily time step and uses available spatio-temporal data to analyze hydrological parameters.  
Figure 1: Location map of the study area.  
The SWAT model interface of ArcGIS was used to assess the small and large catchments by discretizing them based on the principle of dividing the watershed into sub-basins and HRUs that consists of homogenous soil, slope, and land use [16]. The hydrological parameter modeling in SWAT was undertaken at two separate partitions. Land phase and routing phase which control the quantity and movement of water, sediments, nutrients and organic chemicals to the channel in individual sub-basins and to the catchment outlet through the network of channels, respectively [18]. The water balance equation is used to determine hydrologic cycle for the land phase as simulated by SWAT [19]:  
\[\text{SWt}=\text{SWo}+\sum_{\text{i}=1}^{\text{n}}(\text{Rday}-\text{QSurf}- \text{Ea}-\text{Wseep}-\text{Qgw}) \tag{1}\]  
where: SWt is the final soil water content (mm), SWo is the initial water content (mm), Rday is the amount of precipitation on day i (mm), Qsurf is the amount of surface runoff on day i (mm), Ea is the amount of evapotranspiration on day i (mm), Wseep is the amount of water entering the vadose zone from the soil profile on day i (mm) and Qgw is the amount of return flow on day i (mm), i and n is the initial and final day respectively.  
Surface run-off was calculated using the modified SCS-CN. The runoff in SWAT using SCS-CN method is determined by using the following equation:  
\[\text{Qsurf}=\frac{\left(\text{Rday}-0.2\text{S}\right)^{2}}{\left(\text{Rday }+0.8\text{S}\right)},\text{ R}>0.2\text{S} \tag{2}\]  
where: Qsurf: runoff accumulated, Rday: rainfall depth for the day, and S: retention parameter. The runoff will occur when R > 0.2S. The parameter of retention is:  
\[\text{S}=25.4*\left(\frac{100}{\text{CN}}-10\right) \tag{3}\]  
The peak runoff based on modified rational method [20] is given by:  
\[\text{q}_{\text{peak}}=\frac{\text{C.I.A}}{3.6} \tag{4}\]  
\(\text{q}_{\text{peak}}\): is the rate of peak runoff (m\({}^{3}\)/s), C: coefficient of runoff, i: is the rainfall intensity (mm/h), A: sub-basin area (km\({}^{2}\)) and 3.6 is utilized for unit conversion.  
The Penman-Monteith method is use to determine evapotranspiration using all climatic variables:  
\[\text{ET}=\frac{0.408\Delta(\text{Rn}-\text{G})+\gamma\frac{900}{\text{T}+2 \text{S}}\text{U}2(\text{es}-\text{ea})}{\Delta+\text{ }\gamma(1+0.34\text{U}2)} \tag{5}\]  
where ET--evapotranspirationiration (mm/day), Rn--net radiation (MJ/m\({}^{2}\)day), G--soil heat flux density (MJ/m\({}^{2}\)day), T--mean daily air temperature at 2 m height (\({}^{\circ}\)C), U2--wind speed at 2 m height (m/s), es--saturation vapor pressure (KPa), ea--actual vapor pressure (KPa), es--the deficit of saturation vapor pressure (KPa), \(\Delta\)--slope vapor pressure curve (KPa\({}^{\circ}\)C), #x3b3--psychometrics constant (KPa\({}^{\circ}\)C).  
For flow routing, the SWAT model uses the Manning's equation to estimate the velocity and amount of flow. The storage routing depends on the equation of continuity:  
\[\Delta\text{S}=\text{Sin}-\text{Sout} \tag{6}\]  
where: \(\Delta\)S--change in volume of storage, Sin--volume inflow, and Sout--volume outflow.  
The base flow is the volume of stream flow originating from ground water and it is assumed that 50% of the water percolates down to the shallow ground water.