2.2 Field measurements
Aerial photographs of the study area taken in 1957, 1972, and 2005 (1:50,000 scale) were used for the analysis. Geometric rectification and photogrammetric restitutions were performed using ground control points, and a DEM (10 m pixel size) for the 2005 orthophotograph with positional accuracy in terms of root-mean-square errors (RMSExyz) of 2.4, 3.7, and 3.5 m was constructed. The geometric rectification performed by co-registration with the 2005 orthophotograph resulted in root-mean-square errors (RMSExy) of 3.7–3.8 and 3.2–3.4 m for the 1957 and 1972 aerial photographs. In the field surveys conducted in 2005, the dimensions of gully cross-sections and the length of each gully section were measured for 127 gully points selected from the Rift margin catchments and 139 gully points selected from the Valley floor catchments.
After the field measurement in the 12 study catchments, relationships between the volume of a gully network (V , 103m3) and the length of the gully network (L, km) (a V-L relation) was calculated as V = 0.870L 1.406 (n = 12,r 2 = 0.963). This power function was used to estimate the volumes of gully networks in 1957 and 1972. The area-specific volume of a gully network (Va , 103 m3 km-2) was estimated by the equation of Va = V /A where A (km2) is the catchment area of the gully network. A gully erosion rate in a mass unit for each of the catchments (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 and Y is year (1957, 1972, and 2005); the subscriptsstart and end represent the starting and ending years of estimation. Similarly, an area-specific gully erosion rate in a mass unit (AEM ; Mg ha-1 y-1) was estimated by the equation of AEM = (V endBD end / A endV start BD start /A start) / (Y endY start). Information on land use/cover in the 12 catchments was collected from the 2005 field survey, interviews, and aerophoto-interpretation.
Some geomorphic indices were used to analyse the temporal changes in areal and relief aspects of the study catchments in 1957, 1972, and 2005: (i) compactness coefficient (CC ; Gravelius, 1914);wherePe (km) is catchment perimeter. (ii) Form factor (FF ; Horton, 1932); FF = A /HL 2π where HL (km) is maximum catchment length. (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 ). The absolute elevation difference within the catchment (HDC ) represents the potential energy available for soil erosion (Verstraeten, & Poesen, 2001). A high relief ratio corresponds to a more pronounced topography and thus to a higher erosion risk (Verstraeten, & Poesen, 2001). (iv) Lemniscate ratio (LR ; Chorley, Malm, & Poaorzelski, 1957); LR = HL 2π / 4A . (v) Hypsometric integral (HI ; simplified equation of the elevation-relief ratio proposed by Pike & Wilson (1971) was used);HI = (HmeanHmin ) / (HmaxHmin ) whereHmean is the mean height in a catchment. The lower values of LR and CC and the higher value ofFF indicate the more compact shape of the catchment and hence the lesser time of concentration for runoff and the more soil erosion (Morgan, 1996). Strahler (1952) found that a catchment at a younger evolutionary stage is highly susceptible to erosion and has a largeHI 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). Values of the parameters that used to express the geomorphic indices, such asA , Pe , ground heights, HL , were obtained from the DEM for the 2005 orthophotograph using ArcGIS 10.1 (ESRI, Redlands) and the 2005 field survey.
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 of the sub-areas. Land use/cover in the 12 catchments was categorised into forest, grassland, and farmland on 1957 and 1972 aerial images and 2005 orthophotographs, and each polygon area was obtained by using ArcGIS.