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 endV start BD start) / (Y endY 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 endV startBD start / A start) / (Y endY 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 = (HmeanHmin ) / (HmaxHmin ) 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.