3.3 Temporal changes in topographical thresholds of gully heads
All the s -a relationships for the 12 main gully channels were approximated by power functions (Figure 5); the coefficients of determination were 0.39−0.85 (the mean 0.65) for the Rift margin and 0.65−0.98 (the mean 0.84) for the Valley bottom.
Besides the threshold lines for each main gully channel, the topographical thresholds of the gully heads for each period (before 1957, 1957−1972, and 1972−2005) in a sub-area can be approximated by a line representing a power function (Figure 5). It appeared that 2 data for the Rift margin and 3 data for the Valley bottom were outliers (rounded by solid red lines in the figures). All of these gully heads were formed at lower threshold levels than those of each corresponding year. According to aerial photo interpretation and field observations, it was evident that the formation of these gully heads was influenced by roads (cattle passageway). Nyssen et al., (2002) found that the slope gradients of the gully heads influenced by the road were lower than those of without influence of the road (not statistically significant); lowering topographic threshold levels. Thus, these outliers were excluded from the subsequent analysis.
For both the sub-areas, 3 threshold lines for before 1957, 1957−1972, and 1972−2005 appear to be parallel with each others, and as time passes, they shift towards the origin, i.e., in equation (1), the exponent b values are rather static, whereas the threshold coefficient k values decrease over time. Univariate analysis of variance for the 6 sets of the s -a data of the threshold lines, such as (i) before 1957, (ii) 1957−1972, and (iii) 1972−2005 for the Rift margin, and (iv) before 1957, (v) 1957−1972, and (vi) 1972−2005 for the Valley bottom, found the hypothesis of no interaction between the factors (6 datasets) and covariate (upslope drainage area; a ) was rejected (α = 0.05), i.e., they cannot be paralleled. However; the analyses for (i), (ii), and (iii) and for (iv), (v), and (vi) proved that the s -a threshold lines of each sub-area could be parallel with each other. Thus, the threshold lines representing gully head positions in the three periods in each sub-area maintained almost the same exponent b specific to each sub-area while the threshold coefficient k decreased as time passed.
DISCUSSION
In the evolutionary processes, the values of the catchment geomorphic parameters generally increased; however, the main gully channels of both the sub-areas expanded maintaining almost the same risk of soil erosion hazard specific to each sub-area. The difference in dynamic movements of the catchment geomorphic indices observed between the sub-areas is likely to be reflected by the gully evolutionary processes specific to each of the sub-areas. In the Valley floor catchments, gully incision started within the uppermost dense forests before 1957, and then they extended downwards to flat farmlands via steep slope hillsides and gentle slope farmlands as a fierce land use/cover changes occurred during the subsequent periods by 2005. In contrast, no distinctive trend was observed in the starting points of gully incisions in the Rift margin catchments. In some catchments, gullies were found at the farmland close to the outlet of catchments in 1957. Thus, the catchment areas of the Rift margin sub-area showed a slight increase over the three periods (Mukai. 2017).
The steeper slopes inherent in the Rift margin catchments have contributed to a higher risk of soil erosion hazard in the sub-area since gully incision, which is likely to affect more rapid change particularly in area-specific gully volumes (Va ) in the sub-area. It is because areal aspect of the catchment morphological parameters had a relatively strong or strong correlation with only V , whereas relief aspect of the catchment morphological parameters had a relatively strong or strong correlation with bothV and Va (Tamene et al., 2006; Haregeweyn et al., 2008; Mukai, 2017).
In contrast, the rates of land use/cover changes in the catchments between the two periods significantly and relative strongly or strongly correlated with only V (Mukai, 2017). Torri & Poesen (2014) examined 63 reported s -a relationships data from various parts of the world and found the exponent b varied slightly with land use while the median coefficient k increases from cropland to forest via grazing land/pasture. Examination of land use/cover at the gully heads formed before 1957, 1957−1972, and 1972−2005 found that, in both the sub-areas, forest had the highest frequencies (94% for the Rift margin and 62% for the Valley bottom) among the land use/cover items in 1957 for the gully heads that began incision before 1957 (Table 2). Similarly, grazing land had the highest (similarly, 100% and 71%) in 1972 for the 1957−1972 gully heads, and cropland had the highest (97% and 100%) in 2005 for the 1972−2005 gully heads. Thus, the null hypotheses that the gully heads created before 1957, 1957−1972, and 1972−2005 had land use/cover of the forest, grazing land, and cropland, respectively, were tested by Mann-Whitney U tests. All the tests failed to reject the null hypotheses (α = 0.05). Thus the high threshold levels for gully heads incised before 1957 and 1957−1972 in both sub-areas can be best explained by the relatively high resistance to erosion due to the protective vegetation cover (Torri & Poesen, 2014). In both the sub-areas, land use/cover has continuously changed in the direction of reducing vegetation cover in the catchment since the initial gully incision. That induced reductions in the gully topographical threshold levels in the sub-areas, which can significantly influence further increase in gully volumes (V ).
Muňoz-Robles et al. (2010) stressed the importance of a quantitative analysis that assessed past land use/cover when gullies were initiated. Vandekerckhove et al. (2000) stated that, in rangelands, vegetation cover at the time of incision appears to be the most critical factor differentiating between topographical thresholds. In the study area, this principle can be applied to a wider land use/cover items, from forest to cropland. Thus, the combination of photogrammetric techniques, the VL relation, and field measurements and interviews is probably one of those methods that enable to assess temporal interactions between environmental changes and gully erosion/gully head positions.
Nyssen et al. (2004) found that the s -a relationship can be a guideline where structural measures, such as loose-rock and gabion check dams, are effective for gully control. This indicates that more than a certain topographic threshold level in a catchment, a gabion check dam should be selected. In the study area, the gully points formed earlier, e.g., before 1957, have higher topographic threshold levels. Thus, a historical survey on gully head formation guided from an on-site interview or aerial photo interpretation might provide a rough idea of what types of physical structures will be required on the spot; i.e., the site of a gully formed earlier have a higher level of topographical threshold and, therefore, more reliable structural measures will be needed.
CONCLUSIONS
As gully networks expand, catchment geomorphic parameters and indices change. The areal aspect catchment morphology showed a similar scale and pattern of temporal changes between the sub-areas. In contrast, relief aspect catchment morphology varied between the sub-areas, influenced by temporal evolutionary processes of the gully networks specific to each sub-area. Higher slopes inherent in the Rift margin sub-area represent the higher risk of soil erosion hazard and affect its higher area-specific gully volume in particular.
Besides the topographic thresholds of gully head positions for the study catchment, the topographic thresholds observed during the same individual period in each sub-area were approximated by a single power function. Transitions in these gully topographic threshold lines showed clear temporal and spatial patterns: the threshold lines maintained almost the same exponent b specific to each sub-area while the threshold coefficient k decreased as time passed. The land use/cover changes occurred in agroecology can influence these phenomena. The expansion of gully network induced by land use/cover changes lowered the gully topographic threshold levels in agroecology, which accelerated further gully expansion and influenced the exponential temporal increase in gully volumes in particular.