Medium-term gully headcut retreat rates in Southeast Spain determined from aerial photographs and ground measurements

Catena 50 (2003) 329 – 352 www.elsevier.com/locate/catena

Medium-term gully headcut retreat rates in Southeast Spain determined from aerial photographs and ground measurements L. Vandekerckhove, J. Poesen *, G. Govers Laboratory for Experimental Geomorphology, K.U. Leuven, Redingenstraat 16, B-3000 Leuven, Belgium Received 14 December 2000; received in revised form 31 January 2001; accepted 27 February 2002

Abstract This paper deals with gully retreat rates at different time scales, whereby the short-term time scale may span a time interval of 1 – 5 years, the medium-term time scale a time interval of 5 – 50 years, and the long-term time scale a time interval of more than 50 years. An analysis of high-altitude aerial photographs in combination with ground measurements allowed us to quantify volumetric gullyhead retreat rates for 12 permanent gullies in Southeast Spain (Guadalentin and Guadix study areas) over a 40 – 43 year time interval (medium-term time scale). This resulted in an average retreat rate (Ve) of 17.4 m3 year
1. A power relationship between drainage-basin area (A) and medium-term volumetric gully-head retreat rate, Ve = 0.069A0.380 (R2 = 0.51, n = 21), was found by combining the gully-head retreat rates obtained in this study with those obtained by a dendrochronological method. The exponent (b) and the coefficient of determination (R2) of the power relationships Ve = aAb increases from the short-term to the long-term time scale, expressing the increasing importance of drainage-basin area in gully development with time. Considerable differences between gully-head retreat rates measured at the short and medium-term time scales at individual gullies showed the importance of land-use changes and unsuccessful management practices on gully-head retreat, and the episodic nature of gully-head retreat when piping and tension cracking are involved. Higher gully-head retreat rates are obtained at the medium-term time scale compared to the short-term time scale but the differences are not significantly different at a = 10%. The medium-term methods tend to

* Corresponding author. Tel.: +32-16-326425; fax: +32-16-326400. E-mail address: [email protected] (J. Poesen). 0341-8162/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved PII: S 0 3 4 1 - 8 1 6 2 ( 0 2 ) 0 0 1 3 2 - 7

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measure proportionally more high gully retreat rates, but less extreme values compared to the shortterm method. This is explained by a more equal distribution of extreme rainfall events both in space and time at a longer-term time scale, and hence a higher probability of measuring the average effect of both small and extreme rainfall events at each gully. D 2003 Elsevier Science B.V. All rights reserved Keywords: Spain; Semi-arid region; Aerial photograph; Gully-head retreat; Drainage basin; Time scale

1. Introduction The use of aerial photography for measuring gully head retreat over a medium- to long-term time scale is a well-known method to determine gully retreat rates. Several means of measurements were used by different researchers, including linear measures (Thompson, 1964; Seginer, 1966; Burkard and Kostaschuk, 1995, 1997), area measures (Beer and Johnson, 1963; Burkard and Kostaschuk, 1995, 1997), volumetric measures (Stocking, 1980; Sneddon et al., 1988), and weight measures (Piest and Spomer, 1968). According to Stocking (1980), volumetric measures are the best compromise avoiding difficult considerations of bulk density of soils no longer in situ. Good estimations of volumetric gully retreat by remote sensing require a high spatial resolution of the images, which cannot be provided by conventional aerial photography. Therefore, alternative methods are being developed such as close-range photogrammetry by Sneddon et al. (1988) and large-scale aerial photography (Thomas and Welch, 1988), for instance taken from a hot air blimp (Ries and Marzloff, 1997). Another solution consists of combining high-altitude aerial photo data with field data. Vandaele et al. (1996) assessed ephemeral gully erosion volumes in central Belgium and Southern Portugal from measurements of gully length on aerial photographs and an average crosssection based on field measurements in the same study areas. Nachtergaele and Poesen (1999) calibrated this method for the assessment of ephemeral gully erosion volumes in the Belgian loess belt. In the absence of aerial photographs of high spatial resolution, this combination of methods provides an unexploited potential tool for an efficient and accurate determination of volumetric retreat rates of permanent gully systems at a medium-to long-term time scale. This paper deals with gully retreat rates at different time scales, whereby the shortterm time scale may span a time interval of 1 – 5 years, the medium-term time scale a time interval of 5– 50 years, and the long-term time scale a time interval of more than 50 years. The first objective of this study was to determine volumetric gully-head retreat rates based on linear retreat measurements from aerial photographs and volumetric field measurements for a number of large permanent gullies in Southeast Spain. The second objective was to relate the resulting retreat rates at a medium-term time scale to catchment and gully parameters. The third objective was to compare the statistical relationships and the gully-head retreat rates obtained in this study with those obtained by other methods at long-term, medium-term and short-term time scales.

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2. Methods 2.1. Aerial-photo analysis and related field measurements On aerial photographs, 17 gully heads with visible retreat or in some cases infilling between two different dates were selected. The photographs span a time interval between 1956 or 1957 (old photos) and 1978, 1981, 1984, 1985 or 1994 (recent photos), i.e. ranging from 21 to 38 years. The scale of photographs ranges between 1/18 000 and 1/ 32 000. Linear gully retreat rates (Rl, m year
1) were determined by a consultancy company (Soresma). From each stereoscopic pair of aerial photographs, topographical maps at scale 1/4000 were made by analytical restitution. The maps show contour lines with a height interval of 1 m, and indicate the aerial extent and the thalweg of the entire, often bifurcated gully system. Consequently, the relative change in position of each studied gully head, i.e. of the most upstream point of the gully contour, was determined in an orthogonal reference system (dX, dY) with an accuracy of 2 m. For each study site with headcut retreat, the gully volume eroded since the date of the first aerial photograph (1956 or 1957) until the date of fieldwork (1999) was measured in the field. This eroded volume corresponds to a gully length from the headcut location in 1956 or 1957 up to the headcut location in 1999, i.e. Lr-extr, (m) in Fig. 1. However, linear retreat was determined from the aerial photographs only until 1978, 1981, 1984, 1985 or

Fig. 1. Hypothetical gully retreat scenario with measured and predicted gully lengths and retreat distances.

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1994 (Lr-meas, m). Consequently, the studied gullies might have further extended between these dates and the date of field measurements in 1999 over Lr-diff (m) in Fig. 1. An extrapolated retreat distance (Lr-extr) was determined by assuming a linear extrapolation of the headcut retreat rate (Rl, m year
1) between the date of the recent air photos (1978, 1981, 1984, 1985 or 1994) and the date of the first field observations (the reference date: 1997 or 1999). In most cases, the reference date corresponds to the date of fieldwork in 1999. The year 1997 was taken as the reference date at gully heads where field monitoring between 1997 and 1999 indicated retreat rates different from those obtained from the airphoto analysis. The presumed headcut position in 1956 or 1957 was then located in the gully bed by measuring the extrapolated retreat distance (Lr-extr) from the actual headcut in downstream direction. Measuring the gully volume between the actual headcut and this point in the gully bed, using the method described by Vandekerckhove et al. (2000), allowed us to determine the volumetric retreat rate (Ve, m3 year
1). The accuracy of the extrapolation of gully retreat rates in time was verified at six gully sites. On the 1/4000 map of 1956 or 1957, the gully length between a clear bifurcation point of the gully system and the headcut (Lg0, m) was measured along the main gully thalweg. In the field, the gully length of 1999 was determined by means of a measuring tape, i.e. from the same bifurcation point until the actual gully head (Lg-meas, m). The difference between these two measured lengths (Lg-meas
Lg0, m) must be equal to the extrapolated retreat since 1956 or 1957 until 1999 (Lr-extr), as shown in Fig. 1. Hence, these measured and predicted parameters were compared with each other by linear regression. At each gully site, a number of parameters was measured describing local topography, gully morphology, land use and soil properties. Topographical parameters included the drainage-basin area (Ao, m2) of the studied gully, the local slope above the gully head (Slh, %), the average slope of the drainage basin (SAo, %), the average slope of the soil surface along the gully sides (Sag, %) and the average slope along the gully bed (Sab, %). The height of the headcut (Hhc, m) was measured to describe an important geometrical gully characteristic. Runoff curve number values (CN), i.e. empirical ratings of the runoff potential, for the individual bank gully catchments in 1999 were determined based on the actual vegetation cover type, agricultural treatment (if any), hydrologic condition and soil type. The CN rating system was developed by the USDA-SCS (1972), and adapted for Mediterranean environments by Lo`pez Cadenas (1994). The CN-values used in this study are given by Vandekerckhove et al. (2001a). Soil samples were taken in the selected gully heads. The rock fragment content (Rft, %) was determined by mass. The particle-size distribution of the fine earth fraction (Clay, Silt and Sand, %) was determined using the sieve-pipette method with addition of a dispersing agent. Each gully site was characterised by a USDA soil texture class (Soil Science Society of America, 1996). 2.2. Dendrochronological method A second method to determine gully retreat rates at the medium-term time scale makes use of trees or parts of a tree affected by gully erosion, revealing information on the history of the erosion process by datable deviations of their normal growth pattern. These ‘datable objects’ include roots exposed by erosion; browsing scars made by ungulates on exposed

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Fig. 2. Location of the field sites in the Guadalentin basin.

Fig. 3. Location of the field sites in the Guadix basin.

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Fig. 4. Prado 1, 2 and 3 in the Guadalentin study area.

roots or on above-ground parts of fallen trees; exposed and dead root ends; root suckers; stems, branches and leading shoots of fallen trees; and a sequence of trees within a gully. Three conditions are recognized. The first condition implies that the datable object was

Fig. 5. Belerda 1 in the Guadix study area.

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Table 1 Geological, lithological and land-use description of the studied gully sited Field site

Geological unit

Description

Soil texture class (USDA)

Rft (%)

Land use in 1999

Agua 1* Agua 2*

Bc T11

Tertiary loams, marls and calcareous sands

silt loam silt loam

0.6 0.8

n.a.

n.a.

matorral and grasses (abandonned) cultivated (small grain)/matorral

Agua 3* Santiago 1*

Q1 – 2 G

Quarternary gravels and red clay with calcareous crusts

clay loam

46.3

cultivated (small grain)/matorral (abandonned irrigated land)

Largo 1*

Q1 – 2 G

Quarternary gravels and red clay with calcareous crusts Tertiary to Quaternary conglomerates and sands

silt loam

0.3

cultivated (small grains and other crops)

Tertiary to Quaternary conglomerates and sands Tertiary to Quaternary silts, clays and conglomerates

silty clay loam

0.0

cultivated (small grain, almond and olive groves)/ abandonned agricultural fields

Quaternary deposits (loams) Tertiary marls

loam

0.0

cultivated (small grain, almond and olive groves in terraces)

Quaternary terrace deposits (loams) Tertiary marls and sands, with layers of conglomerate

silt

0.0

cultivated (irrigated vegetables)

TB2 – Q1s Belerda 1*

46 47

Estrecho 5 and 6**

Q Bc2 – Bc3 T11 – 11

Torrealvilla 14**

QT T12aBc

Prado 1,2 and 3**

T12aBc

Tertiary marls and sands, with layers of conglomerate

silt loam

0.2

matorral

Pen˜on 2**

C23 – T2Ab

Cretaceous to Tertiary marl – limestone; white to reddish marls

silt loam

0.2

cultivated (small grain)

Alcoluche 4 and 5**

C15 – 16

Cretaceous, dark green marls

silt loam

0.3

cultivated (small grain)

Salada 1**

C21 – T2Ab

Cretaceous to Tertiary, white to reddish marls and marl – limestone

silt loam

0.0

cultivated (almond)

Rft represents the rock fragment content by mass at the selected gully heads; sites where two geological units are given are located on the boundary of these units.

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created before erosion of the gully volume to be dated, e.g. exposed tree roots. According to the second condition, the datable object developed as an immediate consequence of the erosion event, e.g. growth reactions of a fallen tree. The third condition implies that the datable object was created some time after the erosion event took place, e.g. trees colonising the gully bed. Each principle has consequences for the accuracy and the correct interpretation of the estimated erosion rate, i.e. whether the true erosion rate is under-estimated, exact or over-estimated. Vandekerckhove et al. (2001b) give the full explanation of the method and apply it to nine gully sites in southeast Spain. The results of this dendrochronological study (n = 9) were used in the statistical analysis of the present paper. 2.3. Statistical analysis Correlation analysis between all measured gully parameters was applied to the mediumterm gully retreat datasets, obtained by air-photo analysis (this study, n = 12) and by combining the air-photo dataset with the dendrochronological dataset (n = 12 + 9 = 21). Stepwise multiple regression between gully-head retreat rate and all geomorphological site parameters was carried out using the combined dataset at the medium-term time scale. Furthermore, a statistical comparison between gully-head retreat rates measured at the short and medium-term time scales by three different methods was carried out.

3. Study areas and field sites The field sites are situated in the Guadalentin basin (Fig. 2) and in the Guadix basin (Fig. 3) in Southeast Spain. Fig. 4 illustrates a bifurcated gully system in the Guadalentin where three headcuts were studied (Prado 1, 2 and 3), and Fig. 5 shows the head of a large gully in Guadix (Belerda 1). The climate in both study areas is semi-arid. Annual average precipitation is 276 mm in the Guadalentin study area, measured over 25 years at four locations, and 325 mm in the Guadix study area, measured over 14.5 years at two locations. Mean daily temperatures are 16.4 and 14.9 jC, respectively (Casa ForestalZarcilla de Ramos; Andrade, 1990). Land use, geology and measured soil properties (USDA soil texture class and soil rock fragment content) of the field sites are given in Table 1. The geological units are taken from the geological map at scale 1/50 000 (Mapa Geologico de Espan˜a, Instituto Geologico y Minero de Espan˜a, 1978).

4. Results and discussion 4.1. Linear and volumetric retreat rates Table 2 summarises the results of the air-photo analysis and the field measurements. Linear retreat rates (Rl) were determined for the time interval between the dates of the old and recent air-photos, and extrapolated until 1997 or 1999 (the reference date). Volumetric

Table 2 Linear and volumetric headcut retreat rates by air-photo analysis and field measurements Site name

Alcoluche 4 Alcoluche 5 Salada 1 a

(1) (year)

(2) (year)

1956 1956 1956 1956 1956 1956 1956 1956 1956 1956 1956 1956 1956 1956 1978 1957 1957 1957

1994 1994 1994 1994 1994 1994 1994 1984 1984 1985 1985 1985 1985 1978 1999** 1978 1978 1981

Time interval (2)
(1) (years) 38 38 38 38 38 38 38 28 28 29 29 29 29 22 21 21 21 24

Linear headcut retreata Lr-meas (m)

Rl (m year
1)

Reference dateb (3) (year)

Extrapolated time interval (3)
(1) (years)

Extrapolated retreatc Lr-extr (m)

Eroded volumed (m3)

Volumetric retreat ratee Ve (m3 year
1)

14.32 18.87 0.00 25.61
166.15 6.40 31.06 11.66 0.00 22.56 10.77 2.00 6.00
30.53 18.00 12.21
122.07 0.00

0.38 0.50 0.00 0.67 – 0.17 0.82 0.42 0.00 0.78 0.37 0.07 0.21 – 0.86 0.58 – 0.00

1997 1999 1999 1997 – 1997 1997 1999 1999 1999 1999 1999 1999 – – – – 1997

41 43 43 41 – 41 41 43 43 43 43 43 43 – – – – 40

15.45 21.35 0.00 27.63 – 6.91 33.52 15.00* 0.00 33.45 15.97 2.97 8.90 – – – – 0.00

39.7 59.8 0.0 3554.5 – 29.8 3467.4 286.1 0.0 557.9 93.3 13.2 99.0 – 101.6 97.6 – 0.0

1.0 1.4 0.0 86.7 – 0.7 84.6 6.7 0.0 13.0 2.2 0.3 2.3 – 4.8*** 4.7*** – 0.0

Determined by air-photo analysis, i.e. for time interval (2)
(1) (negative retreat is due to infilling by tillage). 1999 for non-monitored sites, i.e. date of field work; 1997 for monitored sites where zero headcut retreat or another retreat rate was observed since 1997. c Linear headcut retreat rate  extrapolated time interval (3)
(1). d Field measurement (1999), starting at the head, in downstream direction over the length of the extrapolated retreat. e Eroded volume/extrapolated time interval (3)
(1). *Eroded volume since 1956 assumed over max 15 m. ** Field measurement. *** Eroded volume/time interval (2)
(1). – , not applicable.

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Agua 1 Agua 2 Agua 3 Santiago 1 Largo 1B Largo 1A Belerda 1 Estrecho 5 Estrecho 6 Torrealvilla 14 Prado 1 Prado 2 Prado 3 Penon 2

Data source air photo

b

337

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retreat rates (Ve) were determined for the extrapolated time interval between 1956 or 1957 and the reference date. For sites with negative headcut retreat due to infilling by tillage, no retreat rates were determined, except at Pen˜on 2. At this site, a linear headcut retreat of 18 m was observed between 1978 and 1999 by comparing the gully length measured on the 1/ 4000 map of 1978 (i.e. 116 m) with the gully length measured in the field in 1999 (i.e. 134 m). The corresponding eroded gully volume was measured and a volumetric retreat rate was calculated for the time interval between 1978 and 1999 (see Table 2). At Alcoluche 4, the linear retreat rate measured from the air photos between 1957 and 1978 was not extrapolated in time because the gully was partly erased by tillage and inactive at the time of field measurements in 1999. The volume eroded between 1957 and 1978 was estimated by measuring the dimensions from the remaining gully, allowing calculation of a volumetric retreat rate for this time interval. At Estrecho 5, a maximum extrapolated retreat of 15 m was assumed instead of the calculated value of 17.91 m (i.e. 0.42 m year
1  43 years). This was based on the difference in predicted gully length in 1999 (135.91 m) and the gully length measured in the field in 1999 (133 m), amounting 2.91 m. Moreover, the downstream 118 m of the gully was much older and more or less stabilised compared to the upstream 15 m. The location of the gully head in 1956 at the transition of the old and the recent gully part was suggested by the gully length measurement on the 1/ 4000 map of 1956 which also equalled 118 m. Given the total gully length of 133 m in 1999, the gully could not have retreated more than 15 m between 1956 and 1999. The results of the verification of the extrapolation procedure are shown in Table 3. A very good agreement between the (predicted) extrapolated retreat (Lr-extr) and its measured equivalent (Lg-meas
Lg0) for the test sites can be observed in Fig. 6 (R2 = 0.98). This suggests that the gullies had a more or less constant headcut retreat rate over the extrapolated time interval, so that the linear extrapolation of the measured retreat rates was justified. 4.2. Statistical analysis 4.2.1. Air-photo dataset Using the dataset obtained in this study, the highest positive correlations with volumetric retreat rate (Ve) was found with drainage basin area (Ao, R = 0.67; p = 0.0183), while linear retreat rate (Rl) was not correlated with Ao. Table 3 Verification of the extrapolation procedure (see also Fig. 1) Site name

Lg0a (m)

Lg-measb (m)

Lr-extrc (m)

Lg-meas
Lg0 (m)

Prado 1 Prado 2 Prado 3 Torrealvilla 14 Estrecho 5 Agua 2

48.00 40.00 28.00 124.00 118.00 52.50

64.00 43.00 36.00 158.00 133.00 75.50

15.97 2.97 8.90 33.45 17.91 21.35

16.00 3.00 8.00 34.00 15.00 23.00

a

Gully length in 1956 measured from air-photo derived map. Gully length measured in the field in 1999. c Extrapolated headcut retreat based on retreat rate determined by air-photo analysis. b

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Fig. 6. Extrapolated retreat (Lg-extr) versus the equivalent measured retreat (Lg-meas
Lg0) in 1999 for the test sites where the extrapolation of gully retreat rates was verified.

No correlation was found between linear or volumetric headcut retreat and runoff curve number (CN), in contrast with the short-term measurements of headcut retreat by Vandekerckhove et al. (2001a). The power relationship between drainage-basin area (Ao) and volumetric retreat rate (Ve) obtained in this study at a medium-term time scale is plotted with differentiation of three CN classes in Fig. 7. In this plot, no clear effect of the CN parameter can be discerned. This result is similar to that obtained for the entire gully volumes eroded at the long-term by Vandekerckhove et al. (2001a). Hence it can be

Fig. 7. Power relationship between drainage-basin area (Ao) and volumetric retreat rate (Ve) measured in this study with differentiation of three curve number (CN) classes.

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concluded that the CN values estimated in 1999 do not reflect the soil surface conditions during the time interval of 40 – 43 years over which the retreat rates were measured. In fact, the evolution of this parameter should be known for the entire period involved in the erosion measurements at any time scale. Gully headcut retreat rates determined by the dendrochronological method by Vandekerckhove et al. (2001b) were neither correlated to vegetation cover because this parameter reflected the soil surface conditions at the time of field measurement but not necessarily those during the medium-term time interval of erosion. Furthermore, volumetric retreat rate was positively correlated with clay content (Clay, R = 0.68, p = 0.0160) and with soil rock fragment content (Rft, R = 0.68, p = 0.0160). No direct explanations can be given for these correlations, as both clay and soil rock fragment contents are expected to increase the erosion resistance of the soil. However, a positive correlation was found between Hhc and Clay (R = 0.72, p = 0.0132) and Hhc and Rft (R = 0.70, p = 0.0169), indicating that these soil parameters have a stabilising effect which increases the critical headcut height, and therefore increases the eroded volume if headcut retreat takes place. This is confirmed by the finding that linear retreat rate was not correlated with any soil parameter. In contrast, volumetric headcut retreat rate determined by the dendrochronological method (Vandekerckhove et al., 2001b) was negatively correlated with soil rock fragment content. This correlation was only partly attributed to a lower soil erodibility because of intercorrelations with other parameters. Hence, it can be concluded that the ’pure’ effect of soil parameters is difficult to detect due to a large number of interactions with other site parameters. 4.2.2. Combined dataset Using the combined dataset of gully retreat rates obtained at the medium-term time scale by air-photo analysis (n = 12) and by the dendrochronological method (n = 9), comparable correlations are obtained. The power relationship between drainage-basin area (Ao) and volumetric retreat rate (Ve) is shown in Fig. 8 and given by Ve ¼ 0:069A0:380 o

ðR2 ¼ 0:51; n ¼ 21Þ

ð1Þ

Table 4 presents all available datasets of drainage-basin area versus gully head retreat at the short (Vandekerckhove et al., 2001a) and medium-term time scale (Vandekerckhove et al., 2001b, this study), and the datasets of drainage-basin area versus total gully erosion at the long-term time scale (Vandekerckhove et al., 2000). The exponent (b) and the coefficient of determination (R2) of the power relationships reflect the importance of drainage-basin area in gully head retreat. The evolution of these parameters from the shortterm, over the medium-term to the long-term time scale is visualised in Fig. 9a,b. A similar trend for b as well as for R2 can be observed from Table 4 and Fig. 9 when comparing the datasets at different time scales within the combined or the individual study areas. However, a statistical comparison of the relationships is necessary to verify the observed differences in b-value obtained at the three time scales. For the Guadalentin, the b-value (Fig. 9a) increases from 0.449 at the short term (dataset 1.a), 0.549 at the medium term (dataset 4.a) to 0.720 at the long term (dataset 6.a). For Guadix, the b-value increases from 0.363 at the short term (dataset 1.b), 0.495 at the

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Fig. 8. Power relationship between drainage-basin area (Ao) and volumetric retreat rate (Ve) measured at the medium-term time scale by air-photo analysis and by a dendrochronological method (Vandekerckhove et al., 2001b) with differentiation of the two methods.

medium term (dataset 2.b) to 0.698 at the long term (dataset 6.b). If the datasets of both study areas are amalgamated, the highest b-value is obtained at the long term (dataset 6, b = 0.592), but there is no increase of b between the short-term (dataset 1; b = 0.377) and the medium-term (dataset 4; b = 0.380) relationships. This is due to the low b-value obtained from dataset 2 (b = 0.262) based on the air-photo analysis resulting from this study. However, splitting up this dataset between the Guadalentin and Guadix results in higher b-values of the individual relationships for both study areas (dataset 2.a; b = 0.417 and dataset 2.b; b = 0.495, respectively). A similar effect was obtained when splitting up the dataset 6 (b = 0.592) according to the two study areas (datasets 6.a; b = 0.720 and 6.b; b = 0.698). The main reason is that on average in Guadix, larger drainage basin areas result in the same gully retreat rates or eroded gully volumes compared to the Guadalentin, which flattens the overall relationship while the individual relationships have steeper slopes. The difference in b-value between the different time scales as shown in Fig. 9a was statistically tested for both the combined datasets (i.e. combining the Guadalentin and Guadix data) and the individual datasets. The difference in b-value is the most pronounced between the short-term and the long-term relationships, i.e. significant at a = 2.5% for the combined datasets (i.e. 1 versus 6) and for the Guadalentin datasets (i.e. 1.a versus 6.a), but not significant for the Guadix datasets at a = 10% (i.e. 1.b versus 6.b). Comparing the medium-term with the long-term relationships, the difference in b-value is significant at a = 5% for the combined datasets (i.e. 4 versus 6) but not for the individual datasets at a = 10% (i.e. 4.a versus 6.a and 2.b versus 6.b). Between the short-term and the medium-

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Table 4 Comparison of datasets of drainage-basin area versus volumetric gully-head retreat rate at the short and mediumterm time scale, and datasets of drainage-basin area versus total gully erosion at the long-term time scale: number of observations (n), coefficient of determination (R2) and the exponent (b) of the power relationship of drainagebasin area versus gully-head retreat Dataset (method)

n

R2

b

Study areas

Reference

Short term headcut retreat 1. Field monitoring

46

0.394

0.377

39 7

0.432 0.298

0.449 0.363

Guadalentin + Guadix Guadalentin Guadix

Vandekerckhove et al. (2001a) this study this study

12

0.237

0.262

this study

7 5 9

0.504 0.232 0.929

0.417 0.495 0.570

Guadalentin + Guadix Guadalentin Guadix Guadalentin

21

0.511

0.380

16

0.792

0.549

55

0.658

0.592

42

0.714

0.720

Guadalentin + Guadix Guadalentin

13

0.584

0.698

Guadix

1.a 1.b Medium term headcut retreat 2. Air-photo analysis 2.a 2.b 3. Dendrochronological method 4. Combined dataset (2 + 3) 4.a (2.a + 3) Long term gully erosion 6. Total bank gully volume versus A: original dataset 6.a 6.b

Guadalentin + Guadix Guadalentin

this study this study Vandekerckhove et al. (2001b) this study this study

Vandekerckhove et al. (2000) Vandekerckhove et al. (2000) Vandekerckhove et al. (2000)

term relationships, the difference in b-value is not significant at a = 10% for both the combined and the individual datasets (i.e. 1 versus 4, 1.a versus 4.a and 1.b versus 2.b). The effect of extreme values for (Ap, Ve) and (Ao, V) on this comparison was verified for the combined datasets by leaving out the gullies Salada 1 and Belerda 1 at the short-term (b = 0.310 instead of 0.377) and at the long term (b = 0.570 instead of 0.592), and the gully Salada 1 at the medium term (b = 0.354 instead of 380). As a result the difference in bvalue is still significant between the short term and the long term at a = 2.5%, the significance between the medium term and the long term is reduced to a = 10%, and there is still no significant difference between the short term and the medium term at a = 10%. Hence, this minor effect indicates that these observations should not be considered as outliers in the overall relationships. Fig. 9b shows a general increase in R2 with time scale. At the medium-term time scale, relatively high and low values were obtained for the individual datasets, while these are averaged out by combining the datasets (dataset 4; R2 = 0.511). The high value for the Guadalentin (dataset 4.a; R2 = 0.792) is due to the exceptionally high value obtained by the dendrochronological method (dataset 3, R2 = 0.929). The low value for Guadix (dataset 2.b; R2 = 0.232) can be partly attributed to the small number of observations in this dataset (n = 5).

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Fig. 9. Evolution of the exponent (b) and the coefficient of determination (R2) of the power relationship between Ao and Ve from the short-term, over the medium-term to the long-term time scale.

From this analysis, it can be concluded that sub-dividing the datasets according to the individual study areas may lead to relatively small sample sizes (e.g. datasets 1.b, 2.b, 4.a and 6.b used in the comparison), reducing the significance of the relationships and hence obscuring the effect of time scale on the values of b and R2. Moreover, statistical comparison showed that by sub-dividing the field dataset (1), the air-photo dataset (2) and the long term dataset (6), no significant difference in b-value (a = 10%) was obtained between the Guadalentin and the Guadix datasets (i.e. 1.a versus 1.b, 2.a versus 2.b, and 6.a versus 6.b), nor between these individual datasets and the combined datasets (i.e. 1.a versus 1, 1.b versus 1, 2.a versus 2, 2.b versus 2, 6.a versus 6 and 6.b versus 6). Consequently, it seems better to use the combined datasets for the comparison of the relationships at different time scales. This comparison suggests an increasing importance of drainage-basin area in gully development with time. This is expressed by a general increase of both b-value and R2 of the Ap –Ve or Ao –V relationships with an increasing time scale, although there is no significant difference between the b-values of the short-term and the medium-term relationships. A partial explanation is given by a decreased variability in measured erosion rates with an increasing time scale. The physical reasons are that (i) the contribution of large erosion volumes by tension cracking, irrespective of runoff discharge and hence drainage-basin area, and (ii) spatial variations in rainfall

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intensities within the study areas, both average out at the longer term. An additional explanation is given by the increased contribution of extreme rainfall events implied in the measurements at a longer term. During such events, the entire drainage basin produces runoff, and transmission losses will be lower than at low intensity events. Consequently, the role of drainage-basin area in the long-term erosion process becomes more pronounced. Table 5 presents the equation explaining medium-term headcut retreat rates (Ve) obtained by stepwise multiple regression applied to the combined dataset (i.e. dataset 4 in Table 4). Only two parameters have been selected, including drainage-basin area (Ao) and height of the headcut (Hhc). As opposed to the multiple regression equations explaining short-term gully head retreat rates by Vandekerckhove et al. (2001a) and long-term gully erosion by Vandekerckhove et al. (2000), drainage-basin area is not the most important factor explaining medium-term headcut retreat rates. A higher partial coefficient of determination (Rp2) is obtained for the height of the headcut (Hhc). This is probably due to the low correlation of Ve with Ao resulting from the air-photo analysis (dataset 2). However, the equations explaining short-term and medium-term headcut retreat rates contain the same parameters with comparable coefficients. Only the curve number (CN) appears in the short-term and not in the medium-term equation. As already shown by simple correlation analysis and in Fig. 7, this actual parameter is not suited to explain past erosion, while it does have an explanatory value if it describes the surface conditions at the time of erosion measurements. 4.3. Comparison of gully-head retreat rates obtained by different methods at different time scales Gully head retreat rates obtained by field monitoring at a short-term time scale and by air-photo analysis at a medium-term time scale are compared for individual gully sites in Table 6. Differences between the individual sites are considerable. Three out of six gullies did not retreat at the short-term, but a retreat was measured at the medium-term time scale. The opposite situation was found at one other site. The difference was most pronounced for the sites Santiago 1 in Guadix and Salada 1 in the Guadalentin. At Santiago 1, an important headcut retreat rate of 86.7 m3 year
1 measured by air-photo analysis probably reflects the effect of irrigation water feeding the gully between 1956 and 1994. During the time interval of field monitoring, i.e. 1997 – 1999, the irrigation channels in the catchment area were not in use, resulting in relatively small discharges into the gully head and

Table 5 Multiple regression equation explaining volumetric retreat rate (Ve) as determined by air-photo analysis and by a dendrochronological method (n = 21)

R2 = coefficient of determination; Rp2 = partial R2; p = p-value of parameter estimate. Ve = volumetric retreat rate (m3 year
1); A = drainage-basin area (m2); Hhc = height of the headcut (m2).

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Table 6 Volumetric gully-head retreat rates obtained by field monitoring at a short-term time scale and by air-photo analysis at a medium-term time scale, measured at the same sites Site name

Agua 1 Penon 2 Salada 1 Santiago 1 Largo 1A Belerda 1

Short-term retreat

Medium-term retreat

DT

Ve (m3 year
1)

DT

Ve (m3 year
1)

1997 – 1999 1998 – 1999 1997 – 1999 1997 – 1999 1997 – 1999 1997 – 1999

0.0 1.5 117.9 0.0 0.0 12.5

1956 – 1994 1978 – 1999 1957 – 1981 1956 – 1994 1956 – 1994 1956 – 1994

1.0 4.8 0.0 86.7 0.7 84.6

consequently no headcut erosion. At Salada 1, failure of the gully head wall due to tension cracking caused an important soil loss of 245.2 m3 in 1998 while no retreat was measured in 1999 by field monitoring, and neither between 1957 and 1981 from the air-photos. In the latter period, erosion was prevented by an earth dam constructed around the gully head, deviating runoff away from the gully head. This dam is still visible as a bridge at about 8 m from the gully head in 1999 (Fig. 10). Given the result of the air-photo analysis, headcut retreat must have started after 1981. The development and collapse of several large pipes behind the dam are likely to have initiated a period of severe erosion. In comparison, the dendrochronological method suggested that the gully volume behind the dam eroded in less than 26 years before 1998, i.e. did not start before 1972. This resulted

Fig. 10. Salada 1 in the Guadalentin study area: the gully head is a collapsed pipe behind an old dam constructed around the former headcut; the dam now spans the gully head as a bridge from one bank to the other.

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in a minimum erosion rate of 39.2 m3 year
1. In fact, the estimation can now be improved by using a shorter maximum time interval for erosion of 17 years (i.e. between 1981 and 1999), bringing the minimum erosion rate to 56.6 m3 year
1. The first example (Santiago 1) shows the importance of land-use changes such as the use or inactivation of irrigation channels. The second example (Salada 1) illustrates the failure of an erosion prevention measure in situ, while no measures are taken to decrease runoff discharges from the catchment. Somehow, gully erosion takes place as runoff does find a way through pipes instead of flowing over the gully-head rim as overland flow. The important variations in headcut retreat rates measured at this site illustrate the episodic nature of erosion by piping and tension cracking. These processes imply that a gully can remain (apparently) inactive during a relatively long time interval in which pipes and tension cracks develop and widen, but can show a considerable activity when a single storm causes the collapse of the pipes or the cracked gully-head wall. At the remaining sites listed in Table 6, greater headcut retreat rates were measured over the medium-term time interval than at the short term. Table 7 shows a statistical summary of volumetric gully-head retreat rates measured at the short-term by field monitoring (Vandekerckhove et al., 2001a), and at the medium-term by a dendrochronological method (Vandekerckhove et al., 2001b) and by air-photo analysis (this study) in the Guadalentin and the Guadix study areas. The summary statistics are based on the datasets of original values (Ve), on the same datasets excluding the outliers measured at Salada 1 by field monitoring and by the dendrochronological method (Ve*), and on the datasets of transformed values representing volumetric retreat rates per unit drainage-basin area (Ve/A0.41). The transformed values take into account that a strong relationship between gully retreat rate (Ve) and drainage-basin area (A) exists, as shown for the different datasets in Table 4. Therefore, these values are better suited for a comparison of retreat rates measured at gullies with different drainage basin areas (and hence different gully dimensions). A general relationship between A and Ve, i.e. Ve = 0.035A0.410 (R2 = 0.49) was determined by combining all collected data (n = 67). This is statistically justified as no significant difference (a = 10%) was found between the relationships obtained by the three different measurement methods, testing the combined datasets for the field method (dataset 1) and for the air-photo method (dataset 2), and the Guadalentin dataset for the dendrochronological method (dataset 3). The transformed values are the projections according to this general relationship of the original values on the logarithmic Ve axis, i.e. assuming a drainage-basin area of 1 m2. Thus, the effect of drainage-basin area is filtered out and comparable values are obtained. A statistical comparison of the average values of Ve, Ve*, and Ve/A0.41 between the different data collection methods within the individual and the amalgamated study areas shows the following. .

.

There is no significant difference (a = 10%) for the three parameters between the field method and the dendrochronological method in the Guadalentin. It should be noticed that, while the average values of Ve and Ve* are smaller for the field method than for the dendrochronological method, the opposite is true for Ve/A0.41. There is no significant difference (a = 10%) for the three parameters between the field method and the air-photo method both in the individual and the amalgamated study

Table 7 Statistical summary of volumetric retreat rates of gully heads measured at the short-term by field monitoring (Vandekerckhove et al., 2001a), and at the medium-term by a dendrochronological method (Vandekerckhove et al., 2001b) and by air-photo analysis (this study) in the Guadalentin and the Guadix study areas Short term

Medium term

Field monitoring

Guadalentin

Guadix

Guadalentin + Guadix

a

Dendrochronology

Air-photo analysis

DT (year)

Ve (m3 year
1)

Vea (m3 year
1)

Ve/A0.41 (m3 year
1/m2)

DT (year)

Ve (m3 year
1)

Vea (m3 year
1)

Ve/A0.41 (m3 year
1/m2)

DT (year)

Ve (m3 year
1)

Ve/A0.41 (m3 year
1/m2)

average stdev max min n average stdev max min n average

2 0 2 2 39 2 0 2 2 7 2

4.1 18.8 117.9 0.0 39 3.6 4.7 12.5 0.1 7 4.0

1.1 2.0 10.7 0.0 38

18 14 46 3 9

5.6 12.8 39.2 0.3 9

1.4 2.4 7.2 0.3 8

0.062 0.044 0.155 0.022 9

1.5

0.072 0.126 0.691 0.002 39 0.039 0.053 0.149 0.001 7 0.067

37 11 43 21 7 41 1 43 41 5 39

4.8 4.2 13.0 0.3 7 34.9 46.3 86.7 0.7 5 17.4

0.121 0.076 0.226 0.021 7 0.106 0.172 0.406 0.002 5 0.115

stdev max min n

0 2 2 46

17.4 117.9 0.0 46

2.7 12.5 0.0 45

0.118 0.691 0.001 46

8 43 21 12

32.1 86.7 0.3 12

0.118 0.406 0.002 12

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Study areas

Without outlier Salada 1.

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areas, except between Ve*= 1.1 m3 year
1 obtained by the field method and Ve = 4.8 m3 year
1 obtained by the air-photo method in the Guadalentin (a = 10%). However, the average values of Ve, Ve* and Ve/A0.41 are smaller for the field method than for the airphoto method in all three datasets. There is no significant difference (a = 10%) for Ve between the dendrochronological method and the air-photo method in the Guadalentin, but the average values of Ve* and Ve/A0.41 obtained by the dendrochronological method are significantly smaller (a = 10%) than those obtained by the air-photo method. This finding confirms that the gully retreat rates obtained by the dendrochronological method should be considered as minimum estimates.

Combining all data collected at the medium term in the Guadalentin and in Guadix (n = 21), i.e. by the dendrochronological method (n = 9) and by the air-photo method (n = 12), results in higher average values for Ve (12.3 m3 year
1), Ve* (11.0 m3 year
1) and Ve/A0.41 (0.092 m3 year
1 m
2) (not tabulated) compared to the average values based on all data collected at the short term (n = 46). However, the differences are not significant at a = 10% for the three parameters, and the difference is the smallest between the transformed, i.e. the most comparable values. Partly, this is due to the large variation in Ve and Ve* at both time scales, and to the influence of the relatively small retreat rates estimated by the dendrochronological method. A similar result is obtained by comparing the corresponding A – Ve relationships at the short term and the medium term (Fig. 11, using datasets 1 and 4 in Table 4). This suggests that for a given drainage-basin area, higher gully retreat rates are measured at the medium term, but no significant difference in intercept was found (a = 10%).

Fig. 11. Comparison of the relationship between gully-head retreat rate (Ve) and drainage-basin area (Ap or Ao) at the short-term and at the medium-term time scale.

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The frequency distributions of the short-term and the medium-term values of Ve/A0.41 (Fig. 12) show that, from the short term to the medium term, there is a shift towards a normal distribution as expressed by a decrease in skewness and in kurtosis. This means that the medium-term methods tend to measure proportionally more high gully retreat

Fig. 12. Frequency distributions of the volumetric retreat rates per unit drainage-basin area (Ve /A0.41, m3 year
1 m
2) measured at the short-term and at the medium-term time scales.

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rates, but less extreme values compared to the short-term method. This can be explained by a more equal distribution of extreme rainfall events both in space and time at a longerterm time scale, and hence a higher probability of measuring the average effect of both small and extreme rainfall events at each gully. The high interannual rainfall variability typical for semi-arid environments implies that several years of drought may be alternated by relatively wet years including short periods of high intensity rainfall events. Hence, the shorter the time interval of gully-head retreat measurements, the higher the probability of missing an extreme rainfall event doing most of the geomorphological work. Consequently, proportionally more small gully retreat rates are measured at the short term, but only one or a few extreme observations may considerably increase the average retreat rate, as was the case for the short-term measurements in this study, resulting in a small difference compared to medium-term measurement methods.

5. Implications The average medium-term retreat rates, as given in Table 7 for the individual study areas, allowed us to calculate the total sediment production by headcut retreat in each area over the same past time interval, given a known spatial distribution of gullies with a similar erosion activity during this period. Such analysis was done by Oostwoud Wijdenes et al. (2000) for the catchment of the Puentes reservoir in the Guadalentin basin, using short-term retreat rates measured by Vandekerckhove et al. (2001a). Headcut retreat rates measured at the mediumterm time scale are better suited to be extrapolated in the past, but imply a more difficult task to assess the past activity of non-sampled gullies. This information can be derived from airphotos or, if possible, from local farmers or other sources.

6. Conclusions This study showed that the combined use of aerial photographs and field measurements is a valuable tool to determine volumetric gully-head retreat rates in Southeast Spain. Statistical analysis showed that these medium-term retreat rates are best correlated to drainage-basin area, reflecting the importance of runoff discharge entering the gully head. Curve numbers of the gully catchments are correlated to linear or volumetric headcut retreat rates only if the estimated values reflect the soil surface conditions during the time interval over which the retreat rates are measured. In this study, clay content and soil rock fragment content are thought to have a stabilising effect increasing the critical headcut height, and therefore increasing the eroded volume if headcut retreat takes place. However, the ‘pure’ effect of soil parameters is difficult to detect due to a large number of interactions with other site parameters. The exponent (b) and the coefficient of determination (R2) of the power relationships between drainage-basin area and volumetric gully-head retreat increases from the shortterm, over the medium-term to the long-term time scales, expressing the increasing importance of drainage-basin area in gully development with time. Increasing the time scale implies (1) a decreased variability in measured erosion rates as the effects of tension

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cracking and spatially variable rainfall intensities average out at a longer term; and (2) an increased contribution of extreme rainfall events whereby the role of drainage basin in the erosion process becomes more pronounced, as runoff is produced from the entire catchment and transmission losses are much lower than at low intensity events. Individual volumetric gully-head retreat rates obtained by field monitoring and by airphoto analysis showed the importance of land-use changes and (mis)management practices on gully-head retreat, and the episodic nature of gully-head retreat when piping and tension cracking are involved. At five out of six studied gully sites, greater headcut retreat rates were measured at the medium term than at the short term. A statistical comparison of average volumetric gully-head retreat rates obtained by the different data collection methods at the short term and at the medium term showed that (i) no significant difference exists between the average results of the field method and the average results of the dendrochronological method, (ii) smaller retreat rates are obtained with the field method compared to the air-photo method, but the difference is only significant when excluding an outlier from the field dataset; and (iii) the average retreat rate obtained by the dendrochronological method is significantly smaller than that obtained by the air-photo method when excluding an outlier from the dendrochronological dataset or when expressing the average retreat rate per unit drainage-basin area. Combining all data collected at the medium term results in a higher average retreat rate (per unit drainage-basin area) compared to the short term, but the difference is not significant. This finding is confirmed by a comparison of the corresponding A –Ve relationships, suggesting that for a given drainage-basin area, higher gully retreat rates are measured at the medium term while no significant difference in intercept was found. Frequency distributions of gully-head retreat rate per unit drainage-basin area at the short-term and the medium-term show that the medium-term methods tend to measure proportionally more high gully retreat rates, but less extreme values compared to the shortterm method. This can be explained by a more equal distribution of extreme rainfall events both in space and time at a longer-term time scale, and hence a higher probability of measuring the average effect of both small and extreme rainfall events at each gully. Acknowledgements This research was carried out as part of the MEDALUS (Mediterranean Desertification and Land Use) collaborative research project. MEDALUS was funded by the European Commission Environment and Climate Research Programme (contract: ENV4-CT950118, Climatology and Natural Hazards) and the support is gratefully acknowledged. Thanks are due to Dr. Karel Vandaele from Soresma nv., to Rafael Gimenez for his kind help to order the photogrammetric material, to Patriek Bleys for the soil-sample analysis, and to Mr. Arcas from Casa Forestal in Zarcilla de Ramos for providing rainfall data. References Andrade, J.L.A., 1990. Atlas fitoclimatico de Espan˜a, Taxonomias. Instituto Nacional de Investigationes Agrarias, Ministerio de Agricultura Pesca y Alimentacion, Madrid, p. 66.

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