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 V –L 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.