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).