2.2. River Basin Water Balance
Water balance is the driving force behind all processes in the Soil and Water Assessment Tool (SWAT) model [
45]. SWAT simulates the hydrologic cycle as a function of the principle of water balance [
46].
where
is the soil water content (mm),
is the initial water content, t is the time in (days),
. is the rainfall amount on day I (mm),
. is the surface runoff quantity on day I (mm),
is the evapotranspiration amount on day I (mm),
. is the quantity of water entering the groundwater from the soil on day I (mm), and
is the quantity of return flow on day I (mm).
In the watershed, the SWAT model simulates runoff using the curve number method of the Soil Conservation Service (SCS) [
47]. It estimates the surface runoff using the following equation:
where
is the accumulated runoff or rainfall excess (mm),
is the daily rainfall depth (mm water),
is the initial abstraction before the runoff event (mm water), and
is the retention parameter (mm water).
The variation in land surface features such as land use, slope, and management measures causes spatial variation in retention parameters. This can be expressed mathematically as
where CN is the daily curve number, which is governed mainly by land use, soil permeability, and a hydraulic group of soils. The initial abstraction
is mostly taken as 0.2 S, and Equation (2) can be derived as
The SWAT model predicts the retention parameter with the help of two methods; the first method of calculation uses the soil moisture content in its profile, in which runoff is overestimated in shallow soil. CN is mainly governed by the antecedent climate, and the value is rarely governed by the soil storage. The CN estimation is based on evapotranspiration. The other method predicts the retention parameter using the accumulated plant evapotranspiration.
where S is the retention parameter for a specified day (mm), S
max is the maximum retention parameter on any specified day (mm), SW is the moisture content of the soil excluding the water held at wilting point (mm), and w
1 and w
2 are shape coefficients.
When evapotranspiration governs the retention parameter, the result of the retention parameter at the end of the day can be updated as
where S is the retention parameter for a given day (mm), S
prev is the previous day’s retention parameter (mm), E
o is the daily potential evapotranspiration (mm per day), cncoef is the average coefficient to estimate the retention coefficient for the daily curve number predictions, S
max is the daily higher retention parameter value (mm), R
day is the daily rainfall depth (mm), and Q
surf is the surface runoff (mm).
Evapotranspiration (PET) is one of the parameters for studying the water balance. In the SWAT model, three evapotranspiration prediction methods (the Penman–Monteith method [
48], the Priestley–Taylor method [
49], and the Hargreaves method [
50]) are integrated.
The Penman–Monteith method requires solar radiation, air temperature, relative humidity, and wind sped; the Priestley-Taylor method requires solar radiation, air temperature, and relative humidity; the Hargreaves method requires air temperature only. For this study, the Penman–Monteith method was used to estimate evapotranspiration.
The Penman–Monteith equation that estimates evapotranspiration is as follows:
where
is the daily reference crop evapotranspiration (mm·day
−1),
is the net radiation flux (MJ·m
−2·day
−1),
is the heat flux density in the soil (which is very small and can be neglected) (MJ·m
−2·day
−1),
is the mean daily air temperature (°C),
is the psychometric constant (kPa·°C
−1),
. is the wind speed measured at 2 m height (m·s
−1),
is the saturation vapor pressure (
=
× RH/100 (kPa)),
RH is the relative humidity (%), and
. is the slope of the saturation vapor pressure curve (a·°C
−1).
In a similar manner, the model estimates the ground water flow using Equation (8).
where
is the water accumulated in the shallow aquifer on day I (mm),
. is the water accumulated in the shallow aquifer on the previous day (mm),
is the recharge percolating to the aquifer on day I (mm),
is the water entering into the soil zone on day I (mm),
is the water percolating from the shallow to the deep aquifer on day I (mm), and
is the water removed from the shallow aquifer by pumping on day I (mm).
2.3. Sediment Balance
SWAT predicts soil erosion and sedimentation by applying the Modified Universal Soil Loss Equation (MUSLE) [
51]. In MUSLE, the rainfall energy factor used for USLE is replaced with a runoff factor to improve the sediment yield prediction, which eliminates the need for delivery ratios and allows the equation to be applied to individual storm events. Delivery ratios are not needed with MUSLE because the runoff factor represents energy used in detaching and transporting sediment.
where
is the sediment yield on a given day (metric tons),
is the surface runoff volume (mm /ha),
is the peak runoff rate (m
3/s),
is the area of the HRU (ha),
is the soil erodibility factor,
is the cover and management factor,
is the support practice factor,
is the topographic factor,
is the coarse fragment factor, and 0.56 is the delivery ratio.
SWAT simulates the sediment flow in channel networks using the following formula [
52]:
where
is the suspended sediment available in the reach,
is the suspended sediment provided in the reach at the beginning of the time period,
is the deposited sediment in the reach segment, and
is sediment amount reentering the reach segment.
According to [
52], SWAT simulates the quantity of sediment moved out of the channel as follows:
where
is the amount of sediment moved out of the channel,
is the suspended sediment available in the reach,
is the outflow volume, and
is the volume in the reach segment.
2.4. Model Development and Input Description
Two datasets describing watershed features and meteorological data are required to develop the SWAT model.
Land-use/cover data were obtained from Landsat-8 OLI (Operational Land Imager); for this study, Landsat-8 images from 2015 were used for land-use/cover classification. The satellite images of the watershed with high resolution and zero cloud cover were collected from the US Geological Survey (USGS) Center for Earth Resources Observation and Science (EROS) via
https://earthexplorer.usgs.gov (accessed on 5 January 2015). ERDAS IMAGINE was used for image classification purposes, and Arc GIS10.3 was used for mapping purposes.
In the processes of image classification, the main task is assigning pixels of a constant raster images to the predefined land-cover classes. In this study, supervised classification was applied. This is the most common type of classification method in which all pixels with comparable spectral values are automatically categorized into land-cover classes. Supervised classification, which depends on the prior knowledge of pattern recognition of the research area, was used. For this study, the land-cover map was produced depending on the pixel-based supervised classification. For the land-use/cover classification, a general correctness assessment and kappa coefficient of 95.7% and 0.9402, respectively, were realized, in agreement with the minimum accuracy level (85%) recommended by [
53].
The essential soil properties needed to set up the Soil and Water Assessment Tool Model are soil texture, size percentage, soil saturated hydraulic conductivity, grain, bulk density, texture class, and soil available water. These soil characteristics were obtained from laboratory analysis presented in the Rift Valley Lake Basin Master Plan study document [
44]. During the study of the Ethiopian Rift Valley Lake Basin Master Plan, soil samples were collected from all soil units of the basin, and physical and chemical laboratory analyses were conducted in the Ethiopia Water Works Design and Supervision Enterprise (WWDSE) laboratory. From 13 soil units in the basin, 203 soil samples were collected, and their physical and chemical properties were analyzed. Hence, the soil database of the SWAT model was set up for the basin using the analyzed soil properties. The basin’s soil erodibility (K) factor was calculated using the equation shown in EPIC [
54] from the analyzed soil parameters.
The meteorological data included daily precipitation, maximum and minimum temperature, daily wind speed, daily sunshine hours, and daily relative humidity, which were obtained from meteorological stations (
Table 1) available within and nearby the study area. Daily data over 27 years (1991–2017) were collected for the study.
To fill the missing values of climate elements, a weather generator model was used. The required statistical parameters were computed using the computer program developed by [
55]. As shown in
Table 1, in the river basin, only one meteorological station (Dilla) was used to establish the weather generator database.
2.5. The Hydrological Data
In the Gidabo river basin (total area of 3386 square kilometers), there are four stream gauging stations, namely, Aposto (area of 703 square kilometers), Kola (area of 145 square kilometers), Badessa (area of 76 square kilometers), and Measso (area of 2462 square kilometers) with data periods of 1997–2015 for Aposto, Kolla, and Badessa, whereas Measso has stream flow data from 1997–2006. As shown in
Figure 4, the gauging station Measso is located near to the outlet of the watershed, and it was selected for model calibration and validation. The daily flow data of all stations were collected from the Ministry of Water and Energy of Ethiopia. For all stations (except Measso), daily flow data were available up the year 2015, and a regression model (
r2 = 0.85) was used to generate the data of Measso from its upper station Aposto.
As shown in the
Figure 4, 27.3% of the catchment was ungauged. To predict the water and sediment budget of the ungauged regions, an empirical regression model relating sediment yield and flow of the gauged stations to several catchment characteristics, namely, drainage area, slope, and average annual rainfall, was used. Three explanatory factors were calculated for gauged and ungauged river catchments, i.e., areas of catchments and slopes were processed from the digital elevation model (DEM), and their mean annual area rainfall was calculated on the basis of the inverse distance-weighted interpolation (IDW) of the nearby meteorological stations (
Figure 2).
2.6. Sub-Catchment Delineation
Using the 30 × 30 m resolution DEM data, the contributing upstream area was delineated using ArcGIS 10.3 (Esri, Redlands, CA, USA). Accordingly, the entire study area was divided into 23 sub-watersheds. According to the model setup, the lowest area threshold values for land use, soil, and slope were set as 5%, 10%, and 10%, respectively, and 105 hydrological response units (HRUs) were identified, denoting unique combinations of land use, soil type, and slope.
2.7. Model Calibration and Validation
For the purposes of calibration and validation of the SWAT model, the daily discharge data of the river were obtained from the MoWE of Ethiopia, while the sediment data were generated using the sediment discharge rating curve from the Rift Valley Lake Basin Master Plan study [
44] with an
R2 value of 0.8. For calibration and validation of the model, the bed load component of the sediment was considered suspended as the model simulates total sediment load plus bed load, which was commonly overlooked in most studies in the country due to measurement limitations. In most streams, bed load to suspended load varies from 10% to 30% [
56]. For instance, a study in the Ziway Lake Basin in Ethiopia [
3] used 10% of the suspended sediment as bed load. Since Lake Ziway and Gidabo River are located in the Ethiopian Rift Valley, we assumed the bed load as 10% of the suspended sediment load gained from the rating curve, which was included for model calibration.
The SWAT model was calibrated and validated to ensure its ability to prioritize the sub-watershed according to sediment contribution. The model was run for the simulation period of 1 January 1998 through December 2015 for the Measso gauging station. River discharge and sediment data over 10 years from 2001 to 2010 were used for calibration, and data from the subsequent 5 years (2011–2015) were then used for the validation period. The first 3 years in the calibration run were used for model preparation. For this study, the duration lengths used for calibration and validation were fixed according to the observed data records. The sensitivity analyses were conducted automatically using the SUFI-2 program in SWATCUP software during calibration.