3.2 Spatial and temporal dynamics of gully topographical thresholds
All the topographical thresholds of the gully heads in the 12 main gully channels were approximated by the lines that represented power functions (Figure 4(a) for the Rift margin and Figure 4(b) for the Valley bottom); the coefficients of determination were 0.63−0.89 (the mean 0.76) for the Rift margin and 0.65−0.99 (the mean 0.84) for the Valley bottom. Besides the threshold lines for each main gully channel, the topographical thresholds of the gully heads categorised by gully head incision periods (before 1957, 1957−1972, and 1972−2005) in a sub-area can be approximated by the lines representing power functions (Figures 4(c)); the coefficients of determination were 0.82−0.88 for the Rift margin and 0.82−0.87 for the Valley bottom. It appeared that 2 data for the Rift margin and 3 data for the Valley bottom were outliers (rounded by solid red lines in Figures 4(a) and 4(b)). All of these gully heads were formed at lower threshold levels than those of each corresponding period. According to aerophoto-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 without the 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 one another, and as time passes, they shifted towards the origin, i.e., in equation (1), the exponent b values were rather static, whereas the threshold coefficient k values decreased over time. ANCOVA for the 3 subgroups of the (i) before 1957, (ii) 1957−1972, and (iii) 1972−2005 for the Rift margin found the hypothesis of no interaction between the 3 subgroups and the covariate s was rejected (α = 0.05), i.e., the 3 threshold lines cannot be paralleled with one another. However, ANCOVA for the 3 subgroups of the (iv) before 1957, (v) 1957−1972, and (vi) 1972−2005 for the Valley bottom found that all the ANCOVA-assumptions were fulfilled, indicating the 3 threshold lines can be paralleled with one another. The post hoc tests showed that there were significant difference between (i) before 1957 and (iii) 1972−2005 and between (ii) 1957−1972 and (iii) 1972−2005. Thus, the threshold lines representing gully head positions in the Valley bottom sub-area maintained almost the same exponent b while the threshold coefficient kdecreased as time passed from before 1957, to 1957−1972, and to 1972−2005.
The threshold lines that represented the land use items (forest, grassland, and farmland) around the position of the gully head in the two sub-areas (Figure 4(d)) can be approximated by power functions; the coefficients of determination were 0.62−0.95 for the Rift margin and 0.80−0.89 for the Valley bottom. ANCOVAs both for the 3 subgroups of the (i) forest, (ii) grassland, and (iii) farmland in the Rift margin and for the 3 subgroups of the (iv) forest, (v) grassland, and (vi) farmland in the Valley bottom found that all the ANCOVA-assumptions were fulfilled, indicating the 3 threshold lines in each sub-area can be paralleled with one another. The post hoc tests showed that there were significant differences between all pairs of the land use items for both the sub-areas. Thus, the threshold lines in both the Rift margin and Valley bottom sub-areas maintained almost the same exponent b(0.506−0.598 for the Rift margin and 0.286–0.354 for the Valley bottom) while the threshold coefficient k significantly decreased as the land use around the gully heads shifted from forest, to grassland, and to farmland in both the sub-areas.
Examination of land use/cover items around the gully heads formed before 1957, 1957−1972, and 1972−2005 found that, in both the sub-areas, forest had the highest frequencies (82% for the Rift margin and 60% for the Valley bottom) for the gully heads that began incision before 1957 (Table 2). Similarly, grassland had the highest (similarly, 100% and 71%) for the 1957−1972 gully heads, and farmland had the highest (97% and 100%) for the 1972−2005 gully heads. 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. 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, which can significantly influence a further increase in gully erosion and gully network expansion.
DISCUSSION
In the evolutionary process of the gully network, 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 network evolutionary processes specific to each sub-area. In the Valley floor catchments, gully incision started within the uppermost dense forests or grassland (all the main gullies except Hadaware) 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 (Figure 3 in Mukai (2017)). Because Hadaware (A = 6.1 km2 in 2005) had the dense forests and grassland at the middle reach of the catchment before 1957, the gully heads incised there had over 1.5 km2upslope drainage areas (three data rounded by red dot-line in Figure 4(b)). Then, from the middle reach gully channels formed before 1957, the Hadaware main gully extended to both upward and downward directions along slope. In contrast, no distinctive trend was observed in the starting points of gully incisions in the Rift margin catchments (Figure 3 in Mukai (2017)). In Figure 4(a), the gully heads incised before 1957 in the Rift margin sub-area can be categorised into two groups: one is the 8 gully heads that had narrow areas (7−67 ha) and steeper slopes (0.4−2.2 m/m) and another is 4 gully heads that had broader catchment areas (67−376 ha) and gentle slopes (0.04−0.08 m/m; rounded by red dot-line in the Figure). The former 8 gully heads incised in forest area (blue diamond-shaped markers in Figure (d)) in the southern margin of the Tebba Gersa mountainous area or fault scarp, while the latter 4 gully heads incised in grassland area at the middle or lower reaches of the catchments. Then, from these short short-distance discontinuous gully channels formed before 1957, the main gullies extended to both upward and downward directions along slope. The positions of gully head incision before 1957 in the Rift margin sub-area can be explained by the topographical threshold of the gully head induced by the land use/cover at that time. Thus, the catchment areas (A ), maximum catchment length (HL ), and the height difference between the outlet and the highest point (HDC ) of the Rift margin sub-area showed only slight increases over the three periods.
Gómez Gutiérrez, Schnabel, & Lavadzo (2009) determined topographical threshold equations of the gully heads in the 99.5 ha catchment over the 6 periods between 1945 and 2006, which had considerable land use/cover changes. The sequential topographical threshold equations showed that the values of the b exponent (equation (1)) were more or less regular for the entire period (0.46−0.68), while the kcoefficients varied almost in an order of magnitude (0.02−0.15) and seem to reflect land use changes. Torri & Poesen (2014) examined 63 reported topographical threshold equations from various parts of the world and found the exponent b varied slightly with land use while the median coefficient k increased from cropland to forest via grazing land/pasture. These findings were in line with the ones obtained from this study. The b exponent values for the Rift margin that oscillated between 0.51 and 0.60 were similar to ~0.5 for permanent channels and Hortonian overland flow proposed by Montgomery and Dietrich (1994). The b exponent values for the Valley bottom that oscillated between 0.29 and 0.35 were similar to 0.20 (Zucca et al., 2006) and low b -values (0.10−0.30) observed in some areas in Mediterranean Europe, which may indicate subsurface process (Vandekerckhove et al., 2006). In the Valley bottom sub-area, Vertisols dominate over a wide area in the lower reach of the catchments, where subsurface erosion represented by soil piping due to tunnelling (Bernatek-Jakiel & Poesen, 2018) are common.
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 Va (area-specific gully volume of a gully network) in the Rift margin sub-area. It is because the areal aspect of the catchment geomorphic parameters had a relatively strong or strong correlation with only V (volume of a gully network) over 1957, 1972, and 2005, whereas relief aspect of the catchment geomorphic parameters had a relatively strong or strong correlation with bothV and Va (Mukai, 2017). This agrees with Verstraeten & Poesen (2001), Tamene et al. (2006) and Haregeweyn et al. (2008). A previous study stated that 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). Thus, the temporal changes in the areal aspect of the catchment morphology and land use/cover in the catchments can be responsible for the continuous increases in V that had almost the same scale between the two sub-areas over time.
The combination of photogrammetric techniques, the VLrelation, and field measurements and interviews is probably a method that enables to assess spatial and temporal interactions between environmental changes and gully erosion/gully head positions.
CONCLUSIONS
As gully networks expand, catchment geomorphic parameters and indices change. The temporal changes in these parameters and indices are influenced by the temporal evolutionary processes of the gully networks specific to each sub-area. The temporal evolutionary process of the network depends on the positions of gully heads and discontinuous gullies formed particularly at the gully incision time. Those gully head positions were determined by the topographical threshold equations of the sub-area and land use/cover at that time because the threshold equations were a function of dominant erosion process specific to a sub-area and the topographical threshold levels significantly differed between land use/cover items.
Despite the difference observed in the gully network evolutionary process between the sub-areas, the areal aspect catchment geomorphic indices, which can have a significant impact on V , did not show any increasing or decreasing tendencies over time. The relief aspect catchment geomorphic indices, which can have a significant impact onVa , also have maintained similar patterns of spatial and temporal changes; their spatial difference inherent between the sub-areas has been maintained over time. Spatial variation and temporal changes in land use/cover items can be another driving force ofV . Since the initial gully incision, land use/cover items have changed to reduce vegetation cover continuously and to lower topographical threshold levels in both the sub-areas. Thus, the spatial variability and its temporal changes in relief aspect of the catchment morphology specific to each sub-area can be responsible for the different patterns of increases in Va between the sub-areas. The continuous reduction in vegetation cover induced by the changes in land use/cover over time can be the main driving force of the similar scale and changing patterns of V between the sub-areas.