2.1.2 Materials and input datasets
A topographic map 1:50,000 scales (EMA, 1987) were used to delineate the boundary of the study watershed. ArcGIS 10.3 software was used for mapping and a GPS (Garmin 60, ~2 m accuracy) was used to collect the outlet point of the watershed and gully locations. Satellite imageries were used to estimate the past and the current surface area coverage of the studied 22 gullies and to quantify the changes in gully dimensions. To measure the current annual development rate of gullies, one-year gully expansion measurement was done from eight gullies (i.e. three gullies on cultivated land, two gullies on grazing land and three gullies on both cultivated and grazing land) before and after the rainy season of the year 2017. Hand meter was used to measure gully geometrical dimensions (gully length, width, and depth). Erosion pins were installed around the studied gullies before the rainy season and the annual rate of expansion was determined after the rainy season calculating the difference in dimensions.
2.1.3 Field measurement
Gully cross-sectional geometry was surveyed by dividing the cross-section into trapezoidal segments at abrupt changes in gully banks and then measuring the width and depth of the gully at each segment (Figure 2).
To calculate the cross-sectional area (A), the surface area occupied by gullies (S), the volume of soil loss (V), dry mass of soil loss (Dm), gully density (Gd) and long term gully erosion (LTGE ), Eq.1; Eq.2; Eq.3; Eq.4; Eq.5 and Eq.6 were used, respectively (Tebebu etal ., 2010; Gebreslassie et al., 2014; Zegeye et al., 2014; M. Mekonnen et al ., 2015).
The gully cross-sectional area (A; m2) and the total surface area (S; m2) occupied by gullies were calculated using Eq.1 and Eq.2, respectively. The volume of soil loss over the monitoring period was obtained by Eq.3. The dry mass of soil loss was calculated by multiplying the volume of soil loss with the average bulk density of the soils (Eq.4). Gully density (m; ha-1) was calculated dividing gully length by watershed area using Eq.5.
A\(=1/2\sum_{i-1}^{N-1}{(wi*hi+1-wi+1*hi)}\)……………………………………….Eq. 1
Where A is the cross-sectional area of the gully; i is a trapezoidal segment index; w is gully cross-section width; h is the height of gully; N is the number of trapezoidal segment sides of height hi and located a distance w from the gully edge in a cross-section (Figure 3).
The total surface area occupied by gullies was calculated using Eq.2:
\(S=\sum_{j-1}^{N-1}{\ \ \ Lj(\frac{\left(wj+wj+1\right)}{2})}\)……………………………………………………………Eq. 2
Where S is the surface area of the gully; j is cross-sectional width index; w is cross-sectional width; N is the number of cross-sections; L is the length of the gully section between cross-sections j and j+1.
The total volume of soil loss was calculated using Eq. 3:
V=Σj-1N-1 Lj(\(\frac{\left(Aj+Aj+1\right)}{2})\)…………………………………………………………………Eq. 3
Where V is the volume of soil loss; j is the cross-sectional width index; Aj is the cross-sectional area of the gully at j; Aj+1 is the cross-sectional area of the gully at j+1, and Lj is the length of the gully between Aj and A j+1.
The dry mass (Dm) of soil loss was calculated using Eq.4:
Dm = V*Bd……………………………………………………………………………………..Eq.4
Where Dm is the dry soil mass; V is the volume of soil loss; BD is soil bulk density.
Gd = L/A………………………………………………………………………………Eq.5
Where Gd is gully density; L is the length of the gully, and A is an area of the watershed.
The historical gullies’ surface dimension was delineated using Google Earth Imagery and aerial photograph to quantify gully surface area coverage and assess changes. Since gully volume can’t be obtained from the Google Earth Imagery/ aerial photograph, it was derived from the digitized gully surface area through a regression of the surface area measurements of gullies (Eq.8).
V = 0.54S1.226……………………………………………………………………..Eq.6
TSL =Vend*Bd - Vstart*Bd/ (Yend-Ystart)*A) ………………………………..Eq.7
Where V (m3) is the volume of gully /soil loss; S is the gully surface area (m2) obtained from Google Earth/ aerial photograph; TSL is total soil loss (ha-1yr-1); Vend is the volume of gully calculated at the end of the investigation year (2017); Vstart is the volume of gully calculated at the beginning of the investigation year (2007); Bd is Bulk density, and A is an area of the watershed; Yend is the final year of investigation (the year 2017) and Ystart is the starting year of investigation (the year 2007).