2.2 Field measurements
Aerial photographs from 1957 and 1972 at a 1:45,000 scale (ground
resolution of 1.25 m, scanned at 1200 dpi) were obtained from the
Ethiopia Mapping Agency. Aerial photographs (1:50,000) of the study area
(~25 km×20 km) were also taken in 2005 with
high-resolution panchromatic film. Geometric rectification and
photogrammetric restitutions were performed using ground control points,
and a digital elevation model (10 m pixel size) for the 2005
orthophotograph with positional accuracy in terms of root-mean-square
errors (RMSExyz; 2.4, 3.7, and 3.5 m) was constructed.
For the 1957 and 1972 aerial photographs, the geometric rectification
was performed by co-registration with the 2005 orthophotograph, which
resulted in root-mean-square errors (RMSExy; 3.7–3.8
and 3.2–3.4 m) for the 1957 and 1972 aerial photographs (Mukai, 2017).
In the field surveys conducted in 2005 and 2009, gully networks were
divided into homogeneous morphological sections of similar width and
depth (Mukai, 2017). The dimensions of gully cross-sections and the
length of each gully section were measured by using a tape and laser
distance meter (Leica DISTO A5, Leica Geosystems; with a measurement
accuracy of 1.5 mm), and then the area of the gully cross-section was
calculated by using Microsoft Excel. In total, 266 gully sections were
selected (127 and 139 sections from the Rift margin and Valley floor
catchments, respectively).
Based on the ground measurement values in the 12 study catchments,
relationships between the volume of a gully network (V ,
103 m3) and the length of the gully
network (L, km) (a V-L relation) in 2005 was calculated asV = 0.870L 1.406 (n = 12,r 2 = 0.963; Mukai, 2017). This power function
was used to estimate the volumes of gully networks in 1957 and 1972. For
each catchment and period, the area-specific volume of a gully network
(Va , 103 m3km-2) was estimated by the equation ofVa = V / A where V(103 m3) and A(km2) are the volume and catchment area of the gully
network, respectively. For each catchment and period, a gully erosion
rate in a mass unit (EM ; 103 Mg
y-1) was estimated by the equation of EM =
(V end BD end −V start BD start) /
(Y end – Y start) whereBD (Mg m-3) is the approximation of soil bulk
density (Mukai, 2017) and Y is year; the subscripts startand end represent the starting and ending years of estimation.
Similarly, an area-specific gully erosion rate in a mass unit for each
of the catchments (AEM ; Mg ha-1y-1) was estimated by the equation of AEM =
(V end BD end /A end − V startBD start / A start) /
(Y end – Y start).
Information on land use/cover in the 12 catchments was collected from
interviews with villagers, from aerial photos of 1957 and 1972 and from
a 2005 field survey (Mukai, 2017).
Some geomorphic indices were used to analyse the temporal changes in
areal and relief aspects of the study catchments: (i) compactness
coefficient (CC ; Gravelius, 1914);where Pe (km) is
catchment perimeter. (ii) Form factor (FF ; Horton, 1932);FF = A / HL 2π . (iii)
Relief ratio (RR ; Schumm, 1956); RR = HDC /HL where HDC (km) is a height difference between the
outlet (Hmin ) and the highest point in the
catchment (Hmax ). (iv) Lemniscate ratio
(LR ; Chorley, Malm, & Poaorzelski, 1957); LR =HL 2π / 4A where HL (km) is
maximum catchment length. (v) Hypsometric integral (HI ;
simplified equation of the elevation-relief ratio proposed by Pike &
Wilson (1971) was used; HI = (Hmean −Hmin ) / (Hmax −Hmin ) where Hmean is the
mean height in a catchment. The lower values of LR and CCand the higher value of FF indicate the more compact shape of the
catchment and hence the lesser time of concentration for runoff and the
more soil erosion (Morgan, 1996). Schumm (1956) found that sediment loss
per unit area is closely and positively correlated with RR .
Strahler (1952) found that a catchment at a younger evolutionary stage
is highly susceptible to erosion and has a large HI value, but it
decreases as the landscape is denuded towards a stage of maturity and
old age. The HI value can be used as an estimator of erosion
status of catchments (Singh, Sarangi, & Sharma, 2008), such as the
watershed is old and fully stabilized (HI ≤ 0.3); equilibrium or
mature stage (0.3≤ HI ≤0.6); and disequilibrium or young stage
(HI ≥ 0.6), in which the watershed is highly susceptible to
erosion (Strahler 1952).
Gully topographic thresholds, the relationships of the slopes at the
gully heads (s ) that were formed before 1957, between 1957 and
1972, and between 1972 and 2005 and the upslope drainage areas of the
gully heads (a ) were investigated for the main gully channels in
the sub-areas.