® .Geomorphology 33 2000 37­58
Characteristics and controlling factors of bank gullies in two
semi-arid mediterranean environments
L. Vandekerckhove a,)
, J. Poesen a,b
, D. Oostwoud Wijdenes a
, G. Gyssels a
,
L. Beuselinck a
, E. de Luna a
a
Laboratory for Experimental Geomorphology, Instituut oor Aardwetenschappen, Katholieke Uniersiteit Leuen, Redingenstraat 16,
B-3000 Leuen, Belgium
b
Fund for Scientific Research-Flanders, Belgium
Received 9 February 1999; received in revised form 27 August 1999; accepted 12 September 1999
Abstract
Bank gullies are gullies that are formed due to a height drop caused by a terrace or a river bank, which develop by
® .headward retreat in erodible hillslopes. This study aims i to investigate the morphology of actively eroding bank gullies,
® .i.e., geometrical characteristics resulting from past erosion and active erosion processes shaping the gully, and, ii , to find
relationships with environmental site characteristics, such as topographical parameters, material properties and climate. The
ultimate goal is to identify the most important controlling factors of past and present bank gully erosion. Fifty-five active
bank gullies formed in different lithologies by various erosion processes have been selected in the Guadalentin basin and the
® .surroundings of Guadix Southeast Spain . For each bank gully site, geometrical and topographical parameters of both the
channel and the drainage basin were measured. Erosion features indicating activity at the gully head, such as tension cracks,
plunge pools, undercutting, fluting, piping and rill or sheet erosion on sloping side walls were mapped, and samples were
taken from distinct lithological layers that were considered to influence the type and intensity of erosion processes. A
relationship could be shown between the presence of piping and fluting and a number of material characteristics, including
particle size distribution, dispersion behaviour and electrical conductivity. On the other hand, lithology appeared not to be a
® .differentiating factor on gully development in the long run, as expressed by the total eroded volume V . This parameter was
® .most strongly related to the drainage basin area in which the entire bank gully had been formed A , explaining 66% of theo
variance. The relationship is Vs1.75)
A0.59
. No significant difference was found between regression lines througho
sub-datasets of different soil textural classes. Finally, multiple regression was used to include both topographical parameters
and material characteristics in an explanatory andror predictive equation for the total eroded bank gully volume. The results
of the analyses using the entire dataset, including the sites in the Guadalentin as well as in the Guadix area, have been
compared with the results for the separate study areas. Differences are not only related to topographical and lithological
characteristics, but may also be the consequence of a different climate in the two areas. q 2000 Elsevier Science B.V. All
rights reserved.
Keywords: bank gully; piping; fluting; lithology; southeast Spain
)
Corresponding author. Fax: q32-16326400.
® .E-mail address: liesbeth.vandekerckhove@geo.kuleuven.ac.be L. Vandekerckhove .
0169-555Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
® .PII: S0169-555X 99 00109-9
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­5838
1. Introduction
Bank gullies are gullies that are formed due to a
height drop caused by a terrace or a river bank
® .Poesen and Hooke, 1997 , in contrast to hillslope
gullies that are formed upon the exceedance of a
critical flow shear stress at the soil surface, as de-
® .scribed by Montgomery and Dietrich 1988 . Bank
gullies develop by headward retreat in erodible hill-
slopes. In this study, they occur as tributary gullies
®initiated at the bank of an ephemeral river rambla or
.barranco in a semi-arid environment in Southeast
® .Spain Fig. 1 . Eroding bank-gully heads decrease
the effective agricultural area of the surrounding
land, produce considerable amounts of sediment fill-
ing downstream reservoirs, and aggravate floods
® .Poesen and Hooke, 1997 .
Past research concentrated mainly on active gully
development in terms of headcut or sidewall retreat
and related erosion processes. Many descriptive stud-
ies exist on specific processes, such as piping or
®tunneling Harvey, 1982; Gutierrez et al., 1988, 1997;´
. ®Martin-Penela, 1994 , rill formation Gerits et al.,´
. ® .1987 , fluting Veness, 1980 , and badland develop-
® .ment Imeson et al., 1982 , relating these phenomena
to material characteristics or other factors. Some
studies provide an extensive description of the active
geomorphological processes by geomorphological
®mapping of entire gully systems La Roca Cervigon
.and Calvo-Cases, 1988 or along a gully wall
® .Jungerius and van den Brink, 1991 . Gullies have
been the object of intensive monitoring with respect
®to headcut retreat and active processes Leopold et
al., 1966; Malde and Scott, 1976; Crouch, 1983;
Sneddon et al., 1988; Oostwoud Wijdenes and Bryan,
1991, 1994; Palacio-Prieto and Lopez-Blanco, 1994;
Burkard and Kostaschuk, 1995; Archibold et al.,
.1996 . The majority of these studies make links with
controlling factors, but in qualitative terms. On the
other hand, quantitative prediction equations for
gully-head retreat have been established by relating
measured gully growth to different environmental
Fig. 1. Illustration of a bank gully in the Guadalentin basin.
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­58 39
® . ® . ® .Fig. 2. Location of the study sites in southeast Spain a ; b Guadix area; c Guadalentin basin.
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­5840
®factors Beer and Johnson, 1963; Thompson, 1964;
Seginer, 1966; Stocking, 1980; Burkard and
.Kostaschuk, 1997 . In fact, these relationships are
valid as long as the observed growth mechanisms
can be extrapolated in time, which probably repre-
sents only part of a gully's life span. Another group
®of studies uses a classification of gully types Heede,
.1970, 1974; Imeson and Kwaad, 1980 or gully
® .sidewalls Blong, 1985; Crouch and Blong, 1989 to
predict future gully behaviour and sediment produc-
tion, without providing quantitative estimates. The
idea is that understanding gully morphology as a
product of past and present gully processes is the
basis for predicting future gully events. However,
both the quantitative prediction equations and the
qualitative assessment of gully erosion hazard are
limited to projections to the near future. Measure-
ments andror observations of existing erosion phe-
nomena serve to predict their future evolution, but do
not predict nor help prevent gully erosion as such.
Consequently, there is a lack of knowledge on the
quantitative influence of factors controlling the pres-
ence, the prevailing processes and the severity of
gullying in a certain environment. This paper pre-
sents a contribution to this topic by investigating
quantitatively the relationship between the morphol-
ogy of a number of selected, active bank gullies and
some topographical parameters of the catchment as
well as some characteristics of the soil material in
which they have been formed. Both geometrical
characteristics resulting from past erosion, and spe-
cific processes shaping the gullies, such as piping
and fluting have been investigated. However, the
main focus is on the long-term effect of environmen-
Fig. 3. Measurement and calculation procedure of the total eroded
gully volume. O represent measured cross-sections. M are calcu-i i
lated cross-sections.
Fig. 4. Topographical parameters measured at a bank gully site.
tal factors on the presence and the final appearance
of bank gullies. No detailed process studies have
been undertaken, but different gully initiating mecha-
nisms have been considered.
The origin and progression of gullies has often
been related to piping or tunnel erosion where high
hydraulic gradients occur in dispersive materials. In
their gully classification scheme, Imeson and Kwaad
® .1980 distinguished a U-shaped gully type, in which
water is supplied from sub-surface sources in associ-
ation with piping, usually found on slope deposits
and pediments located on gently sloping lower slopes.
The dispersive nature of the lower soil horizons is an
essential condition for the formation of this gully
type. Duplex soils are also susceptible to this type of
® .gullying. Examples are given by Heede 1971 and
® . ® .Crouch 1976 . De Ploey 1974 also attributed the
generation of gullies in central Tunisia to progressive
® .pipe collapse, and Gutierrez et al. 1988 considered´
subsurface pipe networks as the initial cause of gully
development in alluvial fans and on debris slopes in
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­58 41
® . ® .the Ebro basin Spain . Crouch 1983 distinguished
three stages in gully-head advance in dispersive du-
plex soils by a combination of tunnel and overfall
erosion, and showed that gully heads advanced most
rapidly when tunneling was a dominant active me-
® .chanism. Harvey 1982 identified soil conditions in
which piping occurs, and showed a strong influence
of deep pipes on gully network development, mainly
on channel alignment in relation to tension cracks
and sub-surface veining. However, the progressive
development of piped areas may lead to the develop-
ment of poorly or non-piped badlands, where surface
or near surface processes dominate. No morpho-
metric distinction could be made between badlands
where pipe collapse had been important and areas
developed by surface or near surface processes. From
a study on the litho-structural control of pipe and
® .gully development, Martin-Penela 1994 also con-´
cluded that when mature gullies tend to become
stabilised, surface processes dominate their evolu-
tion. The general reduction of relief and hydraulic
gradients implies that piping activity is restricted to
small ducts in the sediments deposited in the gully
floors or near the heads. Especially in isolated linear
gullies, such as the bank gullies investigated within
this study, piping gradually decreases and eventually
disappears, or can be recognised only in relict mor-
phologies of inactive pipes. Hence, it may become
difficult to discern a previous stage of piping interac-
tion in the development of such gullies. In this study,
remnants of piping have been related to soil proper-
ties and are considered as an important indication of
® . ® .Fig. 5. Illustration of piping a , and fluting b at one of the studied bank gully heads in the Guadalentin basin.
()L.Vandekerckhoeetal.rGeomorphology33200037­5842
Table 1
Summary of the measured parameter values for all the studied bank gully sites and for the separate study areas
® . ® . ® .Variable Explanation All sites ns55 Guadalentin ns42 Guadix ns13 Significance level
a
of differenceUnits Mean Standard Minimum Maximum Mean Standard Mean Standard
deviation deviation deviation
UU3 ® .Vol Volume m 3149 11994 1.1 65172 1915 10016 7138 16795
UUU2 ® .A Present drainage m 359875 2140482 5.1 15832950 31146 146638 142192 4352455p
basin area
UUU2 ® .A Original drainage m 372537 2142229 11.9 15845776 32630 152913 147069 4342859o
basin area
A r A A ­ A ratio % 73.4 22.1 18.2 99.9 72.2 21.1 77.5 25.6p o p o
U
L A Length of A m 439.0 1319.0 2.5 8280 145.9 390.3 1386.0 2458.0­ p p
U
L A Length of A m 480.8 1342.0 4.4 8380 175.7 438.9 1467.0 2463.0­ o o
UUU
S Local slope at the % 12.7 8.8 2.0 38.5 15.4 8.4 4.3 2.0lh
gully head
UUU
S Average slope of the % 14.0 13.6 1.0 58.0 17.0 14.3 4.3 1.8Ap
present drainage basin
UUU
S Average slope of the % 12.2 8.6 1.5 36.0 14.6 8.4 4.4 2.0ag
soil surface along the gully
UUU
S Average slope of the % 24.5 19.4 2.0 100.0 29.9 19.1 7.1 4.8ab
gully bed
UUU
S Average slope of the % 13.8 11.5 1.3 49.1 16.7 11.7 4.5 1.6Ao
original drainage basin
UU
L Total gully length m 41.8 64.3 1.5 350.0 29.7 54.7 80.9 79.0
D Average gully depth m 3.5 2.1 0.6 10.3 3.3 1.8 4.0 3.0
W Average gully width m 5.0 5.3 0.8 31.6 4.9 5.1 5.6 6.0
WrD Width­Depth ratio r 1.45 0.71 0.23 3.07 1.44 0.70 1.48 0.74
UUU
WrL Width­Length ratio r 0.26 0.20 0.03 0.89 0.31 0.19 0.11 0.13
Hhc Height of the headcut m 2.1 2.2 0.1 12.0 2.2 2.0 1.8 2.6
Clay Clay content % 16.7 10.9 0.6 36.9 15.6 10.4 20.3 12.0
UU
Silt Silt content % 61.8 16.8 17.3 88.4 65.5 14.0 49.7 20.1
Sand Sand content % 21.5 16.2 2.6 63.1 18.9 12.6 30.0 23.2
ClayqSilt ClayqSilt content % 78.5 16.2 36.9 97.4 81.1 12.6 70.0 23.2
U
RFr Rock fragment content % 5.2 12.4 0.0 56.9 2.6 6.5 13.7 21.2
D clay Change in clay content % 13.6 10.3 y4.7 34.8 12.9 10.5 15.8 9.8­
b
after dispersion
D Silt Change in silt content % y9.0 10.6 y33.1 10.7 y8.4 11.0 y10.7 9.7­
c
after dispersion
D sand Change in sand content % y4.6 5.8 y36.9 0.6 y4.5 6.2 y5.0 4.5­
d
after dispersion
UUU
EC Electrical conductivity mSrcm 3.04 2.71 0.12 13.09 3.78 2.68 0.65 0.63
U
R Dispersion Ratio % 94.6 4.4 82.3 100.0 95.2 4.1 92.8 4.9
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­58 43
the potential role of this process in the initiation of
the respective bank gullies.
2. Study areas
Two study areas have been selected in Southeast
Spain, i.e., the Guadalentin basin and an area around
® .the town of Guadix Fig. 2a . Fig. 2b and 2c show
the location of the individual gully sites within each
area. The Guadalentin basin is a target area of the
Mediterranean Desertification and Land Use
® .MEDALUS project. The Guadix area has been
chosen to represent different environmental condi-
tions within the same climatic zone. Both areas have
a semi-arid climate; however, the area around Guadix
is slightly wetter and cooler than the Guadalentin
basin. The annual precipitation in the Guadalentin
study area, i.e., the average of the measurements
over 25 years at 4 locations near the gully sites
® .Zarcilla de Ramos, Vald'Infierno, Puentes, Lorca ,
amounts to 276 mm, and the mean daily temperature
®16.48C Casa Forestal-Zarcilla de Ramos; Andrade,
.1990 . Near Guadix, 14.5 years' measurements at
® .two meteorological stations Guadix and Esfiliana
give an annual average precipitation of 325 mm, and
® .a mean daily temperature of 14.98C Andrade, 1990 .
The main differences between the two study areas
result from the contrasting geological and lithologi-
cal situations, and the distinct topographical charac-
teristics of the landscape.
In the Guadalentin, the landscape can be de-
scribed as a basin and range topography. The inter-
mountain sedimentary basins consist of marls and
marly limestones of Cretaceous to Tertiary age, cov-
ered by Quaternary deposits. These basins were up-
lifted in the late Neogene and early Quaternary, and
consequently, the valley bottoms were incised by
ephemeral rivers from which the studied bank gullies
developed into the lower hillslopes. The Quaternary
sediments consist of alluvial and slope deposits, but
they often have an undifferentiated composition, and
are difficult to distinguish from each other. Some
Tertiary formations contain layers of conglomerate
and sandstone, occurring at a minority of the study
sites.
The Guadix basin is a wide inter-mountain sedi-
mentary basin between the Sierra Nevada, the Sierra
de Baza and the Sierra Arana, uplifted and dissected
by an ephemeral river network. The studied bank
gullies in this basin are located further from the
drainage divide in relatively flat surroundings, com-
pared to the Guadalentin, where the distance from
the bank-gully heads to the drainage divides is gen-
erally smaller and the slope of the land steeper. In
the Guadix area, Quaternary gravel and red clay is
the most frequently occurring formation at the stud-
ied gully sites. Other formations consist of a combi-
nation of Tertiary to Quaternary loams, marls, sands,
clays, and conglomerates.
Current land use in both study areas is a mixture
® .of arable land wheat and almond cultivation and
rangeland.
3. Materials and methods
Screening of aerial photographs covering the study
areas, followed by field prospection allowed the
identification of a set of 55 apparently active bank
gullies. 42 sites have been selected in the
Guadalentin, and 13 sites in the Guadix area. The
selection aimed at obtaining a representative range of
bank-gully types and sizes, and of material proper-
ties. Two years monitoring of these gullies allowed
the observation of active erosion processes. Pro-
cesses indicating activity and shaping a gully include
the formation of tension cracks at the rim of the
head- and the side-walls, promoting mass move-
ments by which the gully extends in length and
width, undercutting at the gully head by plunge-pool
Notes to Table 1:
a
Significance level of the difference between the mean parameter values for both study areas:
U
s10%;
UU
s5%;
UUU
s1%;
® .ssignificance level of the logged parameter.
b
% clay measured in dispersed sampley% clay measured in non-dispersed sample.
c
% silt measured in dispersed sampley% silt measured in non-dispersed sample.
d
% sand measured in dispersed sampley% sand measured in non-dispersed sample.
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­5844
activity and fluting, and, in case of sloping side
walls, sheet erosion and the formation of small rills
and headcuts. Although piping was expected to be an
active erosion process, a longer term observation
showed that the presence of pipes was not an indica-
tion of strong erosion activity. Subsurface flow as a
trigger for headcut erosion, e.g., by undercutting,
could, in the absence of water, only be assumed at
six gully sites. All bank gullies are linked either
®directly or indirectly with an ephemeral river rambla
.or barranco . Only first- or second-order channels
were selected. If necessary, the gully length was
considered only to the first or second bifurcation
instead of down to the outlet in the main river. Most
®gullies are continuous some have upstream rills or
.small headcuts , and both U- and V-shaped gullies
were included, as well as combinations of these
types. Often, the cross section varied from U-shaped
at the head to V-shaped further downstream, due to
the dominance of erosion activity at the head and the
accumulation and stabilisation of debris against the
downstream side-walls.
For each bank-gully site, geometrical and topo-
graphical parameters of both the channel and the
drainage basin were measured. The total eroded vol-
ume of each bank gully was determined by measur-
ing cross-sectional areas, mostly simplified as quad-
® .rangles or triangles areas `O ' in Fig. 3 , at regulari
intervals along the entire gully length. This was
carried out using measuring tapes. The total bank
® .gully volume V was then calculated according to
® .the formula Tysma et al., 1995
n 1
Vs l O qO q4M® ® .Ý i iy1 i i
6is1
where nsthe number of intervals at which a cross-
sectional area was measured, l s the distance be-i
tween the measured cross-sectional areas O andiy1
O ; and M s the area of the cross section betweeni i
the measured O and O , which can be geometri-iy1 i
cally derived. A related parameter is the total gully
length, LsÝn
l . From the basic measurements,is1 i
® . ® .an average depth D and width W of each gully,
® .and consequently, a width-depth ratio WrD and a
® .width-length ratio WrL were calculated.
® .The present drainage basin area A , i.e., thep
area draining to the present gully head, the original
® .drainage basin A , i.e., the area draining to theo
®gully mouth i.e., the original gully head assuming
.the gully was formed solely by surface processes ,
and several characteristic slopes of the catchments
® .and along the gully profile were measured Fig. 4 .
The drainage-basin area was delineated by visual
assessment of local topography and signs of overland
flow if these were still present. The area was subdi-
®vided into smaller polygons quadrangles and trian-
.gles that were measured with a measuring tape. The
total drainage-basin area was then calculated as the
sum of the areas of the individual polygons. The
parameter A rA was calculated to express a rela-p o
tive stage of development of the bank gullies: the
greater the difference in present and original catch-
® .ment area i.e., the smaller A rA , the more devel-p o
oped the gully must be. Characteristic slopes were
measured with a clinometer and include the local
slope above the gully head, measured over a distance
® .of 3 m or less S , the average slope of the presentlh
® .drainage basin S , the average slope of the origi-Ap
® .nal drainage basin S , the average slope of the soilAo
® .surface along the gully side S and the averageag
® .slope along the gully bed S .ab
Specific erosion processes in the bank gullies
were inventoried by means of geomorphological
mapping of the gully head and sketches of character-
istic gully-head or side-wall profiles. One to two soil
samples for each gully site were taken from distinct
soil layers associated with processes such as piping
® . ® .Fig. 5a and fluting Fig. 5b andror showing clear
differences in texture. As already mentioned, pipes
appeared to be relict features of past erosion activity.
No changes in shape took place during the monitor-
ing period. Vertical pipes were observed in side-walls
® .Fig. 5a , but seemed not active anymore. Sub-hori-
zontal pipes, most often formed in slumped and
non-evacuated sediment in the gully bed, could still
act as ducts for freshly eroded material from the
head. However, no roof collapse and consequent
deepening of the gully bed was observed.
Flutes are vertically elongated grooves, generally
tapering to the top, which furrow into the wall of the
gully. They result predominantly from the action of
® . ®running water Veness, 1980 or throughflow Blong,
.1985 , in combination with raindrop impact and
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­58 45
Fig. 6. USDA texture diagram for the fine earth fraction of all
® .studied bank gully sites ns55 .
splash. In the studied bank gullies, flutes were often
found in actively eroding heads, under an apparently
® .more resistant upper soil layer Fig. 5b . In the
Guadalentin, their development and consequent de-
struction were clearly responsible for undercutting of
the headwall as the first trigger of headcut retreat.
The extent of the soil layers with piping and
fluting, as well as the location where the samples
were taken, was indicated on the profile sketches.
From a total of 67 samples, rock fragment content
was determined as well as particle-size distribution
using the sieve-pipette method without and with
addition of a dispersing agent. The difference in clay
and silt content before and after dispersion is a
measure of the stability of the aggregates in which
these particles are `hidden'. Therefore, Middleton's
® .Fig. 7. Histogram of the dispersion ratio R for all studied bank
® .gullies ns55 .
® . ®®1930 ``dispersion ratio'', defined as Rs siltq
. . ®® . .clay r silt q clay , was calcu-non dispersed dispersed
lated for each sample. This erodibility index ex-
presses the relative amount of total silt and clay
®content that is easily dispersed by water without the
. ® .addition of a dispersing agent . Middleton 1930
classified soils with a ratio below 15% as `non-
erodible soils' and above 15% as `erodible soils'.
The data of the dispersed samples were used to
characterise each bank gully by a USDA soil texture
® .class Soil Science Society of America, 1996 . If
more than one sample was taken per gully, a weighted
average of the particle-size distribution according to
the depth of the sampled soil layers was used. Like-
wise, a depth-weighted average of the dispersion
® .ratio R was determined for each gully from the
values of R of the individual soil layers.
® .The electrical conductivity EC was measured
from the same soil samples on a mixture of 1:2.5 soil
Table 2
® . ® .Mean values of soil physical and chemical parameters for soil layers showing piping ns17 or fluting ns18 vs. those without
® U UU U UUU
.underlined values are significantly different: 5%, 1% , 0.1%
1® . ® . ® . ® . ® . ® .N Clay % Silt % Sand % RFr % R % EC mSrcm
UUU UUU UUU
Piping 17 17.0 71.2 11.8 3.4 93.6 4.7
UUU UUU UUU
No piping 50 16.8 55.4 27.8 6.1 93.2 2.1
U UU
Fluting 18 17.6 62.1 20.3 1.7 96.5 2.9
U UU
No fluting 49 16.6 58.0 25.4 6.6 92.4 2.6
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­5846
and distilled water. This parameter measures the
soluble salt content or electrolyte concentration, in-
fluencing the dispersion behaviour of the soil.
The relationship between soil material character-
istics and the presence of a specific erosion process
shaping the gully was studied, in particular for pip-
ing and fluting. For this purpose, mean values of the
measured soil parameters from the samples taken in
soil layers associated with the process were statisti-
cally compared with those from the samples taken in
soil layers were the process was not observed.
The dataset of all measured geometrical, topo-
graphical, and soil parameters for each bank-gully
site was statistically analysed. At each step in the
Table 3
® .Correlation matrix of measured topographical parameters and material characteristics ns55 , Correlation coefficient Rslarge font,
Significance level Pssmall font
Log Vol Log A Log A A rA Log S Log S Log S Log S Log S WrD­ ­ p ­ o p o ­ lh ­ A ­ ag ­ ab ­ Ap o
Log Vol 1.000 0.781 0.811 0.029 y0.580 y0.311 y0.376 y0.476 y0.340 0.463­
0 0.0001 0.0001 0.8339 0.0001 0.021 0.0046 0.0002 0.011 0.0004
Log A 1.000 0.993 0.426 y0.748 y0.428y0.668 y0.627 y0.523 0.365 y0.522­ p
0 0.0001 0.00012 0.0001 0.00011 0.0001 0.0001 0.0001 0.0062
Log A 1.000 0.319 y0.752 y0.437 y0.660 y0.636 y0.526 0.394­ o
0 0.0175 0.0001 0.0008 0.0001 0.0001 0.0001 0.0029
A rA 1.000 y0.265 y0.104 y0.342 y0.174 y0.194 y0.095p o
0 0.0509 0.4498 0.0107 0.2038 0.1563 0.4924
Log S 1.000 0.661 0.799 0.635 0.759 y0.193­ lh
0 0.0001 0.0001 0.0001 0.0001 0.158
Log S 1.000 0.535 0.296 0.958 y0.030­ Ap
0 0.0001 0.0283 0.0001 0.8307
Log S 1.000 0.648 0.701 y0.113­ ag
0 0.0001 0.0001 0.4121
Log S 1.000 0.409 y0.284­ ab
0 0.0019 0.0354
Log S 1.000 y0.045­ Ao
0 0.7442
WrD 1.000
0
WrL
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­58 47
analysis, the results for the entire dataset including
all the sites in both the Guadalentin and the Guadix
area were compared with those for the separate
areas. This involves differences in sample size. A
correlation matrix was constructed to study the rela-
tionships between all the parameters. Meaningful and
statistically significant relationships have been se-
lected and interpreted in more detail. Particular atten-
tion has been paid to environmental factors explain-
ing the geometrical characteristics of the bank gullies
resulting from past erosion, which is mainly reflected
in the total eroded volume. Therefore, statistical
relationships between these parameters were investi-
gated by simple and by multiple regression.
WrL Hhc Clay Silt Sand Rfr D Clay D Silt D Sand EC R­ ­ ­
y0.536 0.450 0.139 y0.245 0.161 0.368 0.146 y0.018 y0.229 y0.334 y0.228
0.0001 0.0006 0.3128 0.0715 0.24 0.0057 0.2866 0.8891 0.0932 0.0127 0.0944
0.222 0.189 y0.239 0.121 0.234 0.171 0.009 y0.322 y0.501 y0.245
0.0001 0.1029 0.166 0.0788 0.3793 0.0857 0.2111 0.9474 0.0165 0.0001 0.0711
y0.557 0.236 0.187 y0.246 0.130 0.266 0.165 0.016 y0.324 y0.517 y0.263
0.0001 0.0829 0.1708 0.0698 0.3445 0.0495 0.2275 0.908 0.0157 0.0001 0.0525
0.113 y0.001 0.121 y0.021 y0.059 y0.172 0.137 y0.072 y0.111 y0.076 0.066
0.4124 0.9934 0.3805 0.8791 0.6678 0.2081 0.3189 0.5993 0.4193 0.5806 0.6318
0.368 y0.193 y0.251 0.415 y0.263 y0.404 y0.232 0.083 0.261 0.537 0.140
0.0057 0.159 0.0649 0.0016 0.0527 0.0022 0.0888 0.5477 0.0543 0.0001 0.3078
0.145 y0.034 y0.106 0.471 y0.418 y0.507 y0.100 0.095 0.004 0.411 0.090
0.2904 0.806 0.4433 0.0003 0.0015 0.0001 0.4663 0.4887 0.9783 0.0018 0.5122
0.202 y0.030 y0.365 0.387 y0.157 y0.324 y0.325 0.181 0.248 0.497 0.223
0.1397 0.8293 0.0062 0.0035 0.252 0.0159 0.0154 0.1865 0.0678 0.0001 0.1021
0.337 y0.249 y0.174 0.214 y0.105 y0.286 y0.140 0.000 0.251 0.281 0.128
0.0118 0.0673 0.2042 0.1173 0.4456 0.0342 0.3067 0.9991 0.065 0.0378 0.3535
0.132 y0.003 y0.178 0.506 y0.405 y0.482 y0.169 0.131 0.060 0.479 0.139
0.3352 0.9803 0.1936 0.0001 0.0021 0.0002 0.2184 0.34 0.6636 0.0002 0.3109
y0.147 0.104 0.078 y0.233 0.189 0.158 0.096 0.077 y0.312 y0.214 y0.278
0.2836 0.4511 0.5728 0.0873 0.1661 0.2503 0.486 0.5767 0.0203 0.1163 0.0396
1.000 y0.011 y0.041 0.095 y0.071 y0.268 y0.024 y0.043 0.122 0.244 0.153
0 0.9369 0.7679 0.491 0.606 0.0476 0.8603 0.7552 0.3737 0.0727 0.2658
Hhc 1.000 0.122 y0.091 0.012 0.127 0.142 y0.219 0.149 0.092 0.110
0 0.3768 0.5108 0.9284 0.354 0.3016 0.108 0.276 0.5061 0.4248
Clay 1.000 y0.379 y0.278 0.152 0.983 y0.803 y0.277 y0.316 y0.124
0 0.0043 0.0398 0.2667 0.0001 0.0001 0.0405 0.0187 0.3687
Silt 1.000 y0.783 y0.641 y0.409 0.407 y0.018 0.487 0.298
0 0.0001 0.0001 0.0019 0.002 0.8982 0.0002 0.0273
Sand 1.000 0.563 y0.235 0.117 0.204 y0.293 y0.226
0 0.0001 0.0841 0.3952 0.1344 0.0298 0.097
Rfr 1.000 0.137 y0.138 0.010 y0.197 y0.256
0 0.32 0.3143 0.9406 0.1493 0.0588
D Clay 1.000 y0.848 y0.226 y0.285 y0.082­
0 0.0001 0.0966 0.0349 0.5502
D Silt 1.000 y0.325 0.229 y0.203­
0 0.0155 0.0923 0.1362
D Sand 1.000 0.087 0.520­
0 0.526 0.0001
EC 1.000 0.232
0 0.0887
R 1.000
0
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­5848
4. Results
A statistical summary of the data is given in Table
1, including the mean values, standard deviation and
range of the measured parameters for all the studied
bank-gully sites, as well as the values for the
Guadalentin and for the Guadix areas separately,
indicating significantly different parameters between
both areas.
® .The USDA texture diagram Fig. 6 shows that
most studied bank gullies are characterised by a fine
earth texture belonging to the silt, silt loam, silty
clay loam, loam and sandy loam class. The rock
fragment content in 91% of the gullies is lower than
7%. Only 5 sites, situated in Guadix, have a higher
rock fragment content ranging between 20% and
® .57%. According to Middleton's 1930 erodibility
classification, all sites are `erodible' with very high
values of the dispersion ratio R, ranging between
® .83% and 100% Fig. 7 . Electrical conductivity val-
® .ues EC indicate that this parameter is greatly vari-
able with, but not systematically related to the depth
at which the sample was taken. This soil parameter
also seemed to be dependent on changes in textural
composition, and on the topographical position of the
® .bank gully e.g., distance from the drainage divide .
In spite of the variations in EC values within the
separate study areas, there is a significant difference
between the mean value for the Guadalentin com-
® .pared to the Guadix area see Table 1 .
Table 2 shows the mean values of the measured
soil parameters for the samples taken in soil layers
with piping or fluting, in comparison with the results
for the samples from horizons where the processes
were not observed. This reveals significant differ-
ences in silt and sand content, and in EC for the soil
horizons showing piping versus those without, and in
® .gravel content and R dispersion ratio for the soil
layers showing fluting versus those without.
The correlation matrix of the entire dataset is
partly shown in Table 3. A significant topographical
relationship exists between the local slope at the
® .gully head S and the present catchment arealh
® . ®A , i.e., the area draining to the gully head Fig.p
.8 . The relationship has a correlation coefficient
® .Rsy0.748 Ps0.0001 , and is significant for the
® .Guadalentin Rsy0.688, Ps0.0001 but not for
® .Guadix Rsy0.258, Ps0.395 . Hence, the good
® . ® .Fig. 8. Local slope S ­drainage basin area A relationship atlh p
the head of the studied bank gullies in the Guadalentin basin
® . ® .ns42 and the Guadix area ns13 .
correlation for the entire dataset is based mainly on
that for the Guadalentin and also on the difference
between the study areas, i.e., significantly smaller
catchment areas and steeper slopes in the Guadalentin
compared to the Guadix area. The negative slope-
catchment area relationship at the bank-gully heads
results from the more pronounced topography of the
Guadalentin. In contrast, it is less evident in the
relatively flat Guadix basin, where there is little
variation in slope with distance from the drainage
divide. In addition, the poor significance for the
Guadix dataset may also result from its smaller
sample size. Nevertheless, this relationship indicates
the average topographical position of the studied
bank gully heads in the landscape.
Geometrical characteristics of the bank gullies
seem to be related to each other and to some envi-
ronmental parameters. For instance, the total eroded
® .bank-gully volume V is positively correlated to the
® . ® .width-depth ratio WrD Rs0.463, Ps0.0004
® . ®and negatively to the width-length ratio WrL Rs
.y0.536, Ps0.0001 . This indicates that in gully
® .growth increasing bank-gully volume , widening is
more important than deepening, but less important
than linear gully extension. Width-depth ratio is
® . ®negatively correlated to dispersion ratio R Rs
.y0.278, Ps0.0396 , indicating that bank gullies in
highly dispersive material are rather deep and nar-
row, and possibly have been formed as collapsed
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­58 49
® . ® . ® .Fig. 9. Bank gully volume V vs. original catchment area A for all study sites ns55 , differentiated by USDA texture class.o
pipes. A positive relationship exists between height
® .of the headcut Hhc and the present drainage basin
® . ® .area A Rs0.222, Ps0.1029 . However, thep
®correlation is significant for the Guadalentin Rs
.0.316, Ps0.0413 , but not for the Guadix area
® .Rs0.346, Ps0.247 . There is also a negative
® .correlation between height of the headcut Hhc and
® . ®average slope of the gully bed S Rsy0.249,ab
.Ps0.0673 , indicating that a steeper bed of a bank
gully results in a smaller headcut height. Again, this
®correlation is significant for the Guadalentin Rs
.y0.416, Ps0.0062 , but not for the Guadix area
® .Rsy0.242, Ps0.4265 . Also the differences in
significance of the correlation between these parame-
ters in the two study areas may partly result from the
difference in sample sizes. However, physical causes
®should not be excluded and are discussed below see
.Discussion .
The most significant correlation with total eroded
® .bank gully volume V is found with the original
® . ® . ® . ® .Fig. 10. Bank gully volume V vs. original catchment area A for the Guadalentin basin ns42 and the Guadix area ns13 .o
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­5850
® .catchment area A , i.e., the area draining to theo
gully mouth, explaining 66% of the variance. The
relationship is given by
Vs1.75U
A0.59
.o
This relationship is depicted in Fig. 9, where the
USDA texture classes for the individual gully sites
are indicated. Visually, points of the same texture
class do not cluster in a certain position relative to
the overall regression line. This was statistically
confirmed as no significant difference was found
between regression lines through the sub-datasets of
individual USDA texture classes. In contrast, when
® .comparing both study areas Fig. 10 , the V­Ao
regression line for the sites in the Guadalentin plots
parallel to, but above that of the Guadix area, ex-
® .pressing a significantly higher intercept as10% ,
but no significant difference in slope. This suggests
that, for a given catchment area, smaller gullies are
formed in the Guadix study area compared to the
Guadalentin.
Multiple regression analysis has been applied to
® .relate the total eroded bank-gully volume V to all
measured parameters listed in Table 1, apart from
Table 4
Results of the multiple regression analysis for the entire dataset and the sub-datasets of the Guadalentin and the Guadix area, using as input
® . ® . 2
all parameters A , and only predictive topographical parameters and material characteristics B , with R scoefficient of determination of
the multiple regression equation; R2
spartial R2
; psp-value of parameter estimatep
( )A Inputsall parameters
All gullies
2
R s0.7872
Log Vols y0.34q0.80 Log A y0.02 A rA q0.84 Log S q0.01 RFry0.01 D Siltq0.047EC­ ­ p p o ­ ag ­
p 0.5291 0.0001 0.0001 0.0080 0.0671 0.1277 0.1323
2
R 0.6095 0.1123 0.0282 0.0203 0.0065 0.0104p
Guadalentin
2
R s0.8236
Log Vols 0.87q0.92 Log A y0.02 A rA q0.02 RFrq0.02 D Sandq0.04EC­ ­ p p o ­
p 0.0025 0.0001 0.0001 0.0690 0.1361 0.1139
2
R 0.6602 0.1246 0.0166 0.0114 0.0108p
Guadix
2
R s0.8278
® .Log Vols 5.92q0.69 Log A y1.32 Log A rA y2.48 ClayqSilt q0.03 D Clay­ ­ o ­ p o ­
p 0.0277 0.0009 0.1477 0.0793 0.1582
2
R 0.5841 0.1470 0.0445 0.0521p
( )B Inputspredictie topographical parameters and material characteristics
All gullies
2
R s0.7228
Log Vols y0.67q1.20 Log L A q0.40 Log S q 0.02RFr­ ­ ­ o ­ Ao
p 0.1240 0.0001 0.1193 0.0051
2
R 0.6756 0.0336 0.0136p
Guadalentin
2
R s0.7510
Log Vols y0.51q1.41 Log L A q 0.02RFr­ ­ ­ o
p 0.0483 0.0001 0.1873
2
R 0.7395 0.0115p
Guadix
2
R s0.7647
Log Vols 0.67q0.68 Log A y0.02 Silt­ ­ o
p 0.4442 0.0007 0.0198
2
R 0.5841 0.1806p
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­58 51
those directly or indirectly used for the calculations
®of the volume itself i.e., total gully length, L,
average gully depth, D, average gully width, W,
width­depth ratio, WrD, width-length ratio, WrL,
.depth of the plunge pool, Hhc . The procedure re-
sulted in different but comparable relationships for
the entire dataset and the sub-datasets of the
Guadalentin and the Guadix area. The result also
depended on the combination variables used as input
for the stepwise regression procedure. The number of
variables in the relationships was further reduced to
remove the effect of multicollinearity, which was
detected by means of the variance inflation factors of
the parameter estimates, and the condition numbers
® .Freund and Littell, 1991 . The equations for both
the entire and the separate datasets are given in
Table 4, together with the model R2
, the partial R2
of the selected parameters, and the P-value of the
parameter estimates. First, all parameters have been
used as input, resulting in the highest R2
of the fitted
® .relationships Table 4A . Second, only variables with
® .a predictive value have been used Table 4B . There-
fore, topographical parameters related to or affected
by the gully itself, such as average slope along the
® . ® .gully bed S or along the gully side S , theab ag
® .present drainage-basin area A , the average slopep
® .of the present drainage-basin S and the localap
® .slope at the gully head S were omitted in thislh
input.
5. Discussion
5.1. Piping and fluting in relation to material prop-
erties
In our study, piping was observed in only 17 bank
gullies, and most pipes appeared to be fossil and
relatively inactive. However, the pipe remnants are
an indication that these and similar gullies have been
initiated from a collapsed pipe or pipe net, or at least
developed by a mixture of piping activity with over-
land flow processes. All bank gullies with pipes were
located in the Guadalentin, and no pipes were ob-
served in the studied bank gullies of the Guadix area.
Consequently, the initiation of the studied bank gul-
lies by pipe collapse is considered more likely in the
Guadalentin than in the Guadix area. Two reasons
® .may explain this unequal distribution: 1 related to
® .soil properties and 2 related to the influence of
local topography.
First, the physico-chemical analysis shows that
piping occurs in soil layers with a higher electrical
® .conductivity EC , and a higher silt and lower sand
® .content Table 2 . Although there is no significant
® .difference in dispersion ratio R between soil layers
® .with piping and those without Table 3 , EC is
® .positively correlated with R Table 3 , indicating
that higher EC values enhance dispersion behaviour
in the sampled soil horizons. Swelling and dispersion
depend on the relationship between electrical con-
® . ® .ductivity EC and sodium absorption ratio SAR
® .Kamphorst and Bolt, 1976 . Dispersion is usually
related to high SAR values, but may be inhibited by
® .too high soluble salt contents i.e., EC values . How-
ever, the average EC value of the soil horizons with
® .piping in this study 4.7 mSrcm is much lower than
® .values reported by Imeson et al. 1982 for saline
® . ® .EC 10­26 mSrcm and sodic SAR 20­35 soils,
resulting in a non-dispersive chemical environment.
® .Gutierrez et al. 1988 reported very high values for´
® . ® .both EC up to 26 mSrcm and SAR 48­67 in
soils showing severe piping. In that case, dispersion
was favoured by leaching of the soluble salts whereas
high levels of sodium saturation remained. Methods
® .for assessing soil dispersivity include i field disper-
®sion tests such as the Emerson test Loveday and
. ® . ® .Pyle, 1973 , used by Imeson et al. 1982 , ii disper-
sion thresholds with respect to the SAR and EC
®Agassi et al., 1981; Imeson and Verstraten, 1988;
. ® .Gerits, 1991 , and iii dispersion indices such as the
Middleton index or variations on this index, used by
® . ® .Imeson et al. 1982 , Gerits 1991 , Gerits et al.
® . ® .1987 and Gutierrez et al. 1988, 1997 . Besides´
chemical characterisation of the soil, several physical
properties are also related to its dispersion behaviour.
® .Gerits et al. 1987 used consistency parameters
indicating the capacity of material to withstand flow
or plastic deformation in terms of its moisture con-
tent, such as the plastic and liquid limits to calculate
®the plasticity index and the activity Young and
.Warkentin, 1975 , and determined the C -index5­10
® .developed by De Ploey and Mucher 1981 . They¨
also measured volumetric properties such as the
shrinkage limit, COLE and the dry bulk density.25
Most studies relate the presence of pipes to soil
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­5852
® .texture characteristics. Gutierrez et al. 1988 report´
a high silt and clay content and a low sand content of
piped soils, and the granulometric fraction smaller
than 4 mm was statistically correlated to piping by
® . ® .Gutierrez et al. 1997 . In a study of Harvey 1982 ,´
however, silt and clay percentages could not differ-
entiate between piped and non-piped sites. More
important was the nature of the material at depth,
particularly the presence of differential porosity, sol-
ubility and strength, together with surface features
allowing concentrated penetration of surface water
such as deep tension cracks or desiccation cracks,
and surface crusting over less consolidated sub-
® .surface layers. According to Martin-Penela 1994 ,´
the most decisive factors for piping are the presence
of poorly indurated silty­clayey materials containing
cracks, fractures or other discontinuities, such as
® .gypsum-filled joints and faults.
Compared to these studies, entirely dedicated to
piping processes, only a limited number of simple
physical­chemical parameters has been determined
in this study on bank-gully characteristics, but the
relationships found between piping and material
characteristics correspond relatively well, i.e., piping
was related to the more dispersive, silty soil hori-
zons. Consequently, the first reason for the absence
of piping at the study sites near Guadix vs. the
exclusive presence in the Guadalentin is also related
to the difference in material properties between these
two areas. Table 1 shows a lower EC value, a lower
silt content, a higher sand and a higher rock fragment
content for the Guadix area compared to the
Guadalentin, suggesting a lower soil dispersivity.
The second reason is probably related to the
difference in overall relief between the two study
areas. The wider and flatter drainage basins in the
Guadix area, as illustrated by their significantly
® .smaller slope gradients Table 1 , may imply that
pipe development was restricted by smaller hydraulic
gradients. Consequently, overland flow erosion might
have been more important in the Guadix area,
whereas in the Guadalentin, more gullies developed
from collapsed pipes.
The role of fluting in gully development in dis-
persible materials, in particular side-wall evolution,
® .has been extensively described by Veness 1980 and
® .Blong 1985 . The process of fluting is described in
a sequence of stages, starting with rilling in a fresh
planar face together with the transport of the dis-
lodged material by the channel, over the initiation
®and development of flutes, to their destruction by
.undercutting or slumping and eventually complete
drowning of the flutes by their own debris when the
channel is incapable of collecting and removing the
material. In short, gully side-wall development is
dominated by the growth, decay and stabilisation of
flutes. Whereas these authors stressed the importance
of fluting in gully sideward extension, flutes were
often observed in the head of the studied bank
gullies. In the Guadalentin, this process contributed
to headcut retreat by undercutting a more resistant
layer on top, when the action of overland flow or
plunge pool erosion destroyed the flutes. In the
Guadix area, the process appeared to be less active.
The frequency of fluting was about the same in the
Guadalentin as in the Guadix area, i.e., at 33% and
30% of the sites in the respective areas. Material
®characteristics of fluted vs. non-fluted horizons Ta-
.ble 2 show that fluting is related to a higher disper-
® . ® .sion ratio R and a lower gravel content RFr , and
therefore can be considered to accelerate the erosion
process and sediment production from the studied
bank-gully heads.
5.2. Topographical and geometrical relationships
The present topographical position of the heads of
the studied bank gullies is represented by the rela-
tionship between the local slope at the gully head
® . ® . ®S and the present drainage basin area A Fig.lh p
.8 . A topographical threshold for the initiation of
bank gullies would consist of a similar relationship
between topographical parameters at their original
initiation point, i.e., at the edge of the rambla banks
where the outlet of the present gullies is located. For
comparison, the initiation of gullies on hillslopes by
overland flow occurs where a critical flow shear
®stress at the soil surface is exceeded Montgomery
.and Dietrich, 1988 . This erosional threshold can be
expressed by a negative power relation between the
local slope and drainage basin area at the gully
® .initiation point Begin and Schumm, 1979 . Apply-
ing this concept to the studied bank gullies would
provide valuable information on the topographical
conditions of bank gully initiation. However, the
initiation of bank gullies is somehow different from
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­58 53
the incision of a gully into a continuous hillslope
® .without banks because of the sudden height drop at
the rambla bank. The main trigger for incision of the
headcut is more likely to be the overfall depth or the
hydraulic gradient at the rambla bank than the shear
force at the soil surface near the rambla bank as
determined by its local slope. Therefore, the original
® .catchment area A , substituting the runoff volume,o
®should be related to the overfall depth or the corre-
.sponding hydraulic gradient rather than to the local
slope of the soil surface at the original rambla bank
where the headcut was first formed. In the field,
however, it was impossible to accurately measure
these parameters because severe erosion destroyed
the original shape of the rambla bank at the outlet of
most gully sites, leading to a gradually sloping sur-
face instead of a sharp break. Consequently, the
assumed relationships could not be verified. Such a
study can only be undertaken at locations where
bank gully erosion has just started and the rambla
banks are still relatively intact, which was the case at
only a few of our study sites.
The positive correlation between height of the
® . ® .headcut Hhc and present drainage basin area Ap
for the bank gullies in the Guadalentin can be inter-
preted by the positive effect of discharge on plunge
pool erosion. A large drainage basin above the gully
head generates a large runoff discharge flowing over
the headcut, enhancing rapid downcutting and deep-
ening the plunge pool. This correlation is not signifi-
cant for the Guadix area. The difference between the
study areas can be explained by intrinsic differences
in channel geometry. Because at most studied bank-
® .gully sites 71% , the average slope of the gully bed
® .S is steeper than the average slope of the soilab
® .surface along the gully S , gully depth generallyag
decreases in upstream direction, i.e. with decreasing
drainage basin area. In the Guadalentin, S and Sab ag
are significantly steeper than in the Guadix area
® .Table 1 . Hence, comparing gullies of different
®length within one study area assuming the respec-
.tive mean values for S and S from Table 1 , theab ag
decrease in headcut height with increasing distance
from the rambla, or decreasing drainage basin area,
will be much more pronounced in the Guadalentin
compared to the Guadix area. The importance of
® .average slope of the gully bed S in relation to theab
® .height of the headcut Hhc is once more expressed
by the negative correlation between these two pa-
rameters, significant for the Guadalentin but not for
the Guadix area.
® .The greater average slope of the gully bed Sab
compared to the average slope of the soil surface
® .along the gully S illustrates that the studied bankag
gullies are situated in the lower part of a concave
slope profile, where the slope of the soil surface is
® .flattening out. If the slope of the gully bed S andab
® .the slope of the soil surface along the gully Sag
would remain constant while a bank gully retreats,
both would intersect at a certain point upstream.
Hence, it would be possible to predict the point
where bank gullies stop growing. However, the con-
cave slope profile of their catchments implies that
the slope of the soil surface increases much more
than that of the gully bed. Consequently, other mech-
anisms must be responsible for the future stabilisa-
tion of the bank gullies.
® .Heede 1970 associated low values of width-de-
pth ratio of a channel with a young stage of develop-
ment, in which all width changes are accompanied
by similar changes in depth. In this study, the posi-
® .tive correlation between width­depth ratio WrD
® .and gully volume V may express the same rela-
tionship, as a larger volume can be seen as a further
development stage, whereby width increases more
than depth. It also implies that for large gully vol-
umes, sidewall erosion becomes more important than
® .linear incision, as suggested by Blong 1985 and
® .Blong et al. 1982 .
A positive correlation between total bank-gully
® . ® .volume V and the original catchment area Ao
exists both for the entire dataset and for the sub-
datasets of the Guadalentin and the Guadix area. As
the original catchment area is a substitute for runoff
volume entering the entire bank gully, this relation-
ship expresses the physical effect of discharge as an
erosive force. The importance of drainage basin area
for gully growth has been shown by several authors
investigating the effects of catchment characteristics
®and hydrologic variables Beer and Johnson 1963;
Thompson, 1964; Seginer, 1966; Stocking, 1980;
.Burkard and Kostaschuk, 1997 . In most studies,
headcut retreat occurs by the action of overland flow.
® .Stocking 1980 , however, made a distinction be-
®tween gully growth by waterfall erosion overland
.flow , piping, or a combination of the two. Multiple
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­5854
regression analysis pointed out that catchment area
was highly significant for all heads that migrated at
least partly through waterfall erosion, but this param-
eter was not selected for headcut retreat by piping
® .alone. Also, Imeson et al. 1982 pointed out that
where piping occurs due to swelling and dispersion,
very high denudation rates can be expected that are
not just a function of mechanical laws, i.e., the
eroded volume may be extremely large compared to
the volume of water draining it. In contrast, where
interflow is responsible for undercutting by seepage
erosion, the progression of gully heads and sidewalls
is again related to contributing drainage area by
® .Sneddon et al. 1988 . Hence, the good correlation of
® .total bank-gully volume V with original catchment
® .area A resulting from this study suggests that ino
the long run, the total amount of water that has
reached the gully during its lifespan, through either
surface or sub-surface sources, determines its total
eroded volume. Differences in growth rate between
the first stages of development, possibly dominated
by piping and hence less related to catchment area,
and later stages when surface process become domi-
nant, are averaged out at this time scale. The final
extent of the gullies is determined by the volume of
overland flow that can still reach the head after
piping activity has disappeared. This explains the
nonlinear increase in total eroded volume with
drainage basin area, suggesting that gully growth is
limited by water transmission losses in the catch-
ment.
® .In the study of Seginer 1966 , the area draining
® 2 .into the gully head A, km appears as the single
most important factor explaining average annual gully
® .head retreat, E, mryear , measured over 15 years.
He obtained a relationship of the form EsaAb
with
b ranging from 0.36 to 0.75 for 3 different areas in
Southern Israel. Higher values for the exponent b
were associated with samples of smaller catchments
both within and between locations. This illustrates
the higher efficiency in surface runoff production for
smaller drainage basin areas. Finally, the average
value of 0.50 for the exponent b is proposed for use
in a practical prediction formula, valid for catchment
areas ranging between 0.01 and 1 km2
. This b value
is very close to the exponent of the relationship
® .between original drainage basin area A and totalo
® .eroded bank gully volume V , found in this study
® .bs0.57 . Apparently, the cumulative effect of the
original drainage basin area on gully growth, result-
ing in a certain eroded volume, is about the same as
the short-term effect of the drainage basin area enter-
ing the gully head on linear gully growth. Burkard
® .and Kostaschuk 1997 found a similar power rela-
® 2 .tion between gully area growth rate G , m ryearA
® 2 . 0.59
and drainage basin area D, m , G s0.4DA
® 2 .R s0.77 from measurements over 62 years. The
authors defined watershed area as the area that flows
into the gully through the headcut and over the side
slopes, because they measured the increase in plani-
metric area of the entire gully, including both head-
cut retreat and sidewall erosion. This parameter cor-
® .responds to the original drainage basin area Ao
used in this study, and the relationship expressing the
®short-term effect on gully growth in the order of
.decades corresponds very well with our relationship
expressing the long-term effect on total eroded vol-
®ume in the order of centuries, based on extrapola-
tion of actual gully retreat rates measured in the
.study areas .
The difference in regression lines between the two
study areas indicates smaller eroded volumes per
unit catchment area in the surroundings of Guadix.
Assuming that the gullies in Guadix are roughly the
same age as those in the Guadalentin, this can be
explained by topographical, lithological and climatic
factors. Table 1 shows that average catchment slopes
® .S and S as well as local slopes above the gullyA Ap o
® .heads S are steeper, on average, in thelh
Guadalentin. Consequently, larger bank gullies can
be formed with the same drainage basin area, be-
cause not only runoff volume, but also the flow
velocity influences the erosivity of concentrated
overland flow. Comparing material properties be-
® .tween the two study areas Table 1 , the Guadix area
is characterised by less dispersive soils compared to
® .the Guadalentin see 5.1 , and hence by an increased
stability and erosion resistance of the material in
which the studied bank gullies developed. Statisti-
cally, however, soil parameters were only poorly
correlated with bank-gully volume. This shows that
differences between the two study areas can only
partly be attributed to different material properties
and the main control of gully development in the
long run is topography. In addition, erosion activity
also depends on climatic factors. Although both ar-
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­58 55
eas have a semi-arid climate, the more humid condi-
tions in Guadix allow a higher vegetation cover
providing a higher erosion resistance.
5.3. Multiple regression
The multiple regression equations in Table 4 inte-
grate the effects of both topographical parameters
and soil material characteristics on the total eroded
bank-gully volume. If all parameters are used as
input, they provide a good reflection of the control-
® .ling factors A , whereas limiting the input to predic-
tive parameters provides a somewhat less accurate
but more simple and useful tool to predict the future
® .volume of bank gullies in a non-affected area B .
Drainage-basin area, A or A , or its length, L A ,­o p o
is represented in all equations, and explains the main
® .proportion )58% of the total variation. The pa-
rameter A appeared to be the most significant byo
simple regression both in this study and in previous
®studies Seginer, 1966; Burkard and Kostaschuk,
.1997 . In other studies using multiple regression to
estimate future rates of gully head retreat, drainage
basin area is always investigated as an input parame-
ter. Drainage basin area above the gully head was
represented in the equation proposed by Thompson
® .1964 with an exponent of 0.49. It was also highly
® .significant in equations obtained by Stocking 1980
for gully heads that migrate at least partly through
waterfall erosion. The exponent varies from 0.38 to
1.00 with an average of 0.68. In this study, exponent
values for A are between 0.68 and 1.20.o
The contribution of the remaining parameters
varies from about 1 to 18%. Although the parameter
A rA was not significantly correlated to V, neitherp o
for the entire or the separate datasets, it explains the
second largest proportion of the variation in the
® .multiple regression equations in A for all datasets.
Obviously, this parameter is not predictive as it
® .involves the present catchment area A . Its nega-p
tive coefficient in the equations corresponds to the
idea that, when bank gullies retreat and hence in-
® .crease in volume, the catchment at the headcut Ap
becomes smaller compared to the original catchment
® .A . Thus, smaller values for A rA imply greatero p o
bank gully volumes. The average slope along the
gully, S , and of the original drainage basin, S ,ag Ao
® .are represented in both types of equations A and B
for the entire dataset. Its positive coefficient reflects
decreasing transmission losses and increasing flow
velocity with steeper catchment slopes, resulting in
greater eroded volumes. In comparison, Thompson
® . ® .1964 and Stocking 1980 tested the slope above
® .the gully head equivalent with our S as an inputlh
parameter for their headcut retreat model, but ob-
tained rather poor results. The parameter was repre-
sented in the equation of Thompson with an expo-
nent of 0.14, but with a low significance. Stocking
did not withhold the parameter in his equations as it
was insignificant at the short-term while it improved
with longer-term measurements.
Material characteristics appearing in the equations
include clay, silt and rock fragment content, change
in clay, silt and sand content after dispersion, and
electrical conductivity. Clay and silt appear in the
® .equations both A and B for the Guadix area with a
negative coefficient. The cohesive influence of clay
contributes to the erosion resistance of the soil mate-
rial, and hence clay content has a negative effect on
the total eroded volume. Although silt can be consid-
ered as highly erodible, its negative coefficient is due
to the fact that the largest bank gullies in the Guadix
area were found in lithologies with a low silt content
but high gravel and sand content. This also explains
the positive coefficient of rock fragment content in
the equations. It can be concluded that, if bank
gullies in the Guadix area occur in gravels or litholo-
gies with a high rock fragment content, they tend to
be large, whereas in silty soils with few rock frag-
ments, relatively small gullies develop.
Changes in particle-size distribution upon addition
of a dispersing agent reflect the influence of soil
dispersivity on the total eroded gully volume. A low
®negative value for D silt a great reduction in silt­
.content after dispersion has the same relative effect
as a high positive value for D clay, and a negative­
®value for D sand closer to zero a small reduction in­
.sand content after dispersion , i.e., increasing the
total eroded volume. A great reduction of silt content
® .after dispersion implies that i a relatively large
proportion of the silt fraction consists of water-stable
aggregates that disintegrate into clay particles upon
® .addition of a dispersing agent, and ii a relatively
small proportion of the sand fraction disintegrates
into silt particles upon addition of a dispersing agent.
The latter is confirmed by the negative correlation
( )L. Vandekerckhoe et al.rGeomorphology 33 2000 37­5856
® .between D silt and D sand see Table 3 , and­ ­
indicates that there are few water-stable aggregates
of sand size, which can be considered as the least
erodible. In contrast, particles or aggregates of silt
size are generally considered to be highly erodible.
Hence, the parameters D silt, D clay and D sand­ ­ ­
in the multiple regression equations reflect relatively
well the effect of aggregates of silt and sand size on
the erodibility of the soil material in the estimations
of total eroded volume. Finally, electrical conducti-
® .vity EC also represents its influence on soil erodibi-
lity in some multiple regression equations. High EC
values may enhance dispersion of the soil material in
water, and therefore have a positive effect on bank
gully volume.
6. Conclusions
This study focused on the morphology and geo-
metrical characteristics of bank gullies resulting from
present and past erosion processes in two semi-arid
environments in Southeast Spain and revealed the
following conclusions.
® .1 Erosion processes shaping the bank gullies are
related to soil material characteristics. Piping occurs
in soil layers with a higher silt content, a lower sand
content and a higher electrical conductivity, whereas
horizons with fluting show a lower rock fragment
content and a higher dispersion ratio.
® .2 Correlation analysis of all measured bank-gully
parameters showed a negative relationship between
® .local slope at the gully head S and the presentlh
® .drainage basin area A , i.e., the area draining top
the gully head, indicating the average topographical
position of the studied bank gully-heads in the land-
scape. A similar relationship indicating the topo-
graphical threshold conditions for bank-gully initia-
tion could not be determined because erosion of the
original surface of the rambla banks inhibited accu-
rate measurement of the necessary parameters. Some
geometrical characteristics of the bank gullies, such
® .as total eroded bank gully volume V , width-depth
® . ® .ratio WrD , width-length ratio WrL and depth of
® .the plunge pool Hhc are related to each other. The
overall result of bank gully erosion over time, ex-
® .pressed by its total volume V , seems to be best
related to the topographical parameter `original
® .drainage basin area' A , explaining 66% of theo
variance of the relationship Vs1.75U A0.59
. Soil tex-o
ture had little impact on this relationship. The differ-
ence between the two study areas, indicating greater
eroded volumes for a given drainage basin area in
the Guadalentin compared to the Guadix area, may
be due to steeper drainage basin area slopes, a lower
erosion resistance of the soil material, and a higher
degree of degradation due to drier and more extreme
climatic conditions in this area. The implication of
these findings is that, in order to reduce the eroded
volume over time, conservation measures should fo-
cus on reducing the amount of overland flow drain-
ing into active gully heads. This could be achieved
either by mechanical structures diverting the flow
away from the headcut into stabilised channels, or by
adopting land-use practices which increase surface
®roughness and depression storage Oostwoud Wij-
.denes and Bryan, 1994 .
® .3 The effect of both topographical parameters
and soil material characteristics on total eroded bank
gully volume was integrated in multiple regression
equations. The models based on all measured para-
meters explain up to 83% of the variation in V. R2
is
limited to 76.5% for the strictly predictive models,
but these are more useful tools for erosion risk
assessment studies in potentially vulnerable areas.
Acknowledgements
This research was carried out as part of the
Mediterranean Desertification and Land Use
® .MEDALUS collaborative research project.
MEDALUS was funded by the European Commis-
sion Environment and Climate Research Programme
®contract: ENV4- CT95-0118, Climatology and Nat-
.ural Hazards and the support is gratefully acknowl-
edged. This study is also a contribution to the Soil
Erosion Network of the Global Change and Terres-
trial Ecosystems Core Research Programme, which
is part of the International Geosphere-Biosphere Pro-
gramme.
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