Journal of Hydrology 248 (2001) 93±108
www.elsevier.com/locate/jhydrol
Validating the use of caesium-137 measurements to estimate soil
erosion rates in a small drainage basin in Calabria, Southern Italy
Paolo Porto a, Des. E. Walling a,*, Vito Ferro b
b
a
Department of Geography, University of Exeter, Amory Building, Rennes Drive, Exeter, EX4 4RJ, UK
Dipartimento di Ingegneria e Tecnologie Agro-Forestali, Universita' di Palermo, Viale delle Scienze, 90128 Palermo, Italy
Received 10 July 2000; revised 12 January 2001; accepted 2 April 2001
Abstract
Recent concern for problems of soil degradation and the offsite impacts of accelerated erosion has highlighted the need for
improved methods of estimating rates and patterns of soil erosion by water. The use of environmental radionuclides, particularly caesium-137 ( 137Cs), as a means of estimating rates of soil erosion and deposition is attracting increasing attention and the
approach has now been recognised as possessing several important advantages. However, one important uncertainty associated
with the use of 137Cs measurements to estimate soil erosion rates is the need to employ a calibration relationship to convert the
measured 137Cs inventory to an estimate of the erosion rate. Existing calibration procedures are commonly subdivided into
empirical relationships, based on independent measurements of soil loss, and theoretical models, that make use of existing
understanding of the fate and behaviour of fallout radionuclides in eroding soils to derive a relationship between erosion rate
and the reduction in the 137Cs inventory relative to the local reference value. There have been few attempts to validate these
theoretical calibration models and there is an important need for such validation if the 137Cs approach is to be more widely
applied. This paper reports the results of a study aimed at validating the use of a simple exponential pro®le distribution model to
convert measurements of 137Cs inventories on uncultivated soils to estimates of soil erosion rates. It is based on a small (1.38 ha)
catchment in Calabria, southern Italy, for which measurements of sediment output are available for the catchment outlet.
Because there is no evidence of signi®cant deposition within the catchment, a sediment delivery ratio close to 1.0 can be
assumed. It is therefore possible to make a direct comparison between the estimate of the mean annual erosion rate within the
catchment derived from 137Cs measurements and the measured sediment output. In undertaking this comparison, account was
taken of the different periods covered by the measured sediment output and the erosion rate estimated using 137Cs measurements. The results of the comparison show close agreement between the estimated and the measured erosion rates and therefore
provide an effective validation of the use of the 137Cs approach and, more particularly, a pro®le distribution calibration model,
to estimate soil erosion rates in this small catchment. Further studies are required to extend such independent validation to other
environments, including cultivated soils, and to different calibration procedures. q 2001 Elsevier Science B.V. All rights
reserved.
Keywords: Caesium-137; Radionuclides; Soil erosion; Sediment yield; Calibration models
1. Introduction
* Corresponding author. Tel.: 144-1392-263345; fax: 144-1392263342.
E-mail address: [email protected] (D.E. Walling).
Recent concern for problems of accelerated soil
erosion and associated land degradation in many
areas of the world (e.g. Pimentel, 1993) and recognition of the many adverse off-site impacts of soil
0022-1694/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.
PII: S 0022-169 4(01)00389-4
94
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
erosion (cf. Clark et al., 1985) have emphasised the
need for improved information on rates of soil loss
and thus for reliable means of assessing soil erosion
rates across a range of environments. Existing methods of quantifying soil loss, such as erosion plots,
possess many limitations in terms of cost, representativeness and the reliability of the resulting data (cf.
Loughran, 1989; Evans, 1995). These methods are
also generally unable to provide the detailed
spatially-distributed data required to verify the new
generation of distributed erosion and sediment yield
models (cf. Morgan et al., 1998; De Roo et al., 1989;
Nearing et al., 1989) and to interface with current
developments in the application of GIS and geostatistics to this ®eld (e.g. Ferro et al., 1994; Desmet and
Govers, 1995; Mitas and Mitasova, 1998; Molnar and
Julien, 1998). Recent work in exploring and exploiting the potential for using environmental radionuclides, and more particularly caesium-137 ( 137Cs), to
document rates and patterns of soil redistribution by
erosion processes (cf. Ritchie and McHenry, 1990;
Walling and Quine, 1993; Walling, 1998) can,
however, now be seen as offering important new
opportunities in this area.
In essence, the 137Cs technique makes use of the
global fallout of bomb-derived radiocaesium which
occurred during a period extending from the mid
1950s to the late 1970s. In most environments, the
137
Cs fallout reaching the land surface was rapidly
and strongly adsorbed by the surface soil and its
subsequent redistribution within the landscape will
have occurred in association with the erosion, transport and deposition of soil and sediment particles.
Caesium-137 has a half-life of 30.2 years and will
thus remain in soils and sediments in readily measurable amounts for the foreseeable future. Measurement
of the present spatial distribution of 137Cs inventories
in the landscape provides the basis for estimating
erosion and deposition rates. Where inventories are
depleted relative to the local reference, which re¯ects
the fallout input to an undisturbed site with no soil loss
and therefore no loss of 137Cs, signi®cant erosion can
be assumed to have occurred. The erosion rate can be
estimated from the degree of depletion of the 137Cs
inventory, relative to the reference, and this value will
represent an average value for the period extending
from the main period of bomb fallout to the time of
measurement. Equally, areas where deposition has
occurred will be marked by enhanced 137Cs inventories, relative to the reference value, and the average
rate of deposition over the period since the main
period of bomb fallout can be estimated from the
magnitude of the excess inventory.
The successful use of 137Cs to document rates of
soil erosion and sediment redistribution has now been
reported for a wide range of environments (cf.
McHenry and Ritchie, 1977; McIntyre et al., 1987;
Walling and Quine, 1991; Kachanoski, 1993; Loughran et al., 1993; Quine et al., 1993; Zhang et al., 1994;
Basher et al., 1995; Pennock et al., 1995; Ferro et al.,
1998). The key advantages of the 137Cs technique for
measuring soil erosion and sediment redistribution are
summarised in Table 1. These advantages are,
however, accompanied by a number of uncertainties.
The most important of these is undoubtedly the need
to establish a calibration relationship between the
degree of depletion or enhancement of the 137Cs
inventory, relative to the reference inventory, and
the erosion or deposition rate (cf. Walling and
Quine, 1990; Walling and He, 1999). Existing work
has demonstrated that the precise form of the calibration relationship will be quite different for cultivated
and uncultivated (e.g. pasture and rangeland) soils,
Table 1
Some advantages of the 137Cs technique for estimating rates of soil
erosion and deposition (based on Walling, 1998)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
The estimates relate to individual points within the landscape
and information relating to both rates and spatial patterns of
soil redistribution can be assembled
The technique is capable of providing spatially-distributed
data which are compatible with recent advances in physicallybased distributed modelling
The estimated rates of soil redistribution re¯ect the integration
of all landscape processes (e.g. water and wind erosion, tillage
effects etc.)
Estimated rates of soil redistribution relate to the past 40 years
and thus provide estimates of longer-term average rates of
erosion and deposition. Short-term measurements may be
unrepresentative
There are no major scale constraints apart from the number of
samples that can be processed. Areas studied can range from a
few m 2 to small drainage basins (e.g. 5 ha)
Application of the technique does not involve major
disturbance of the landscape under study
Estimates can be obtained on the basis of a single site visit
Estimates based on contemporary sampling are retrospective
and therefore avoid the need for establishment of long-term
monitoring programmes
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
137
since in the former case the
Cs will be mixed
throughout the plough layer, whereas in the latter
case it will be concentrated near the surface. Removal
of a given proportion of the 137Cs inventory will thus
be indicative of a much higher erosion rate for a cultivated soil, than for an uncultivated soil.
In their review of the various procedures that have
been used to establish calibration relationships,
Walling and Quine (1990) distinguished two distinct
approaches, namely empirical relationships and
theoretical models. The former involves collection
of independent information on erosion rates, such as
might be obtained from erosion plots, and the
development of a relationship between these rates
and measurements of the 137Cs inventory for the
same location (cf. Elliott et al., 1990; Loughran and
Campbell, 1995). In the latter case, the calibration
relationship is based on a theoretical model incorporating existing knowledge of the behaviour of 137Cs in
soils subject to both erosion and sediment accumulation. Such theoretical models range in complexity
from the simple proportional model, which assumes
that the depth of erosion since the beginning of 137Cs
fallout, expressed as a fraction of the total depth of the
plough layer, is directly proportional to the proportion
of the reference inventory that has been lost as a result
of erosion, to more complex mass balance models,
which attempt to incorporate a range of mechanisms
that will in¯uence the precise relationship between
soil loss or sediment deposition and the reduction or
increase in the 137Cs inventory (cf. Walling and He,
1999). In view of the general lack of data suitable
for the establishment of empirical calibration
relationships and the problems of extrapolating such
relationships to locations other than those for which
the relationship was developed, most calibration
procedures have been based on theoretical models.
However, such models necessarily suffer from the
limitation that they are dif®cult to test, since it
is generally impossible to obtain independent information on erosion and deposition rates, which is
directly compatible with the spatially distributed
point estimates of erosion and deposition rates
provided by the 137Cs measurements. As a result, it
could be suggested that the ability to produce complex
calibration models (e.g. Walling and He, 1999; Yang
et al., 1998) has moved ahead of the ability to test and
validate those models, and there is, therefore, an
95
important need to direct more attention to validation
exercises.
This paper reports such a validation exercise involving comparison of the estimates of soil erosion rates
within a small catchment, obtained using 137Cs
measurements, with information on sediment output
from the catchment. Although the measurements of
sediment output do not cover the entire period represented by the erosion rates estimated using the 137Cs
measurements, they are judged to provide a basis for
deriving a meaningful estimate of the sediment output
over the past 30±40 years covered by the 137Cs
measurements. However, any attempt to compare
estimates of erosion rates within a catchment derived
from 137Cs measurements with measurements of
sediment yield at the catchment outlet necessarily
faces uncertainties relating to the extent of sediment
redistribution or storage within the catchment and
thus the sediment delivery ratio (cf. Walling, 1983).
A signi®cant proportion of the sediment mobilised by
erosion may be redeposited within the catchment and
will not be transported to the basin outlet. It is therefore necessary to take account of both erosion and
deposition rates within the catchment and to use the
estimates of erosion and deposition rates obtained
from 137Cs measurements to calculate the net sediment ¯ux at the catchment outlet. This could,
however, introduce further uncertainties into the validation exercise, since close agreement between the
measured sediment output and the estimate of net
sediment ¯ux at the catchment outlet may not provide
a de®nitive validation of the calibration models
employed and of the resulting estimates of erosion
and deposition rates. It would be possible to obtain
an estimate of net sediment ¯ux that conformed
closely to measured sediment yield, even if the estimates of the erosion and deposition rates involved
signi®cant errors. For example, overestimation of
the erosion rates could be offset by overestimation
of the deposition rates. Equally, underestimation of
the erosion rates could be offset by underestimation
of the deposition rates. The catchment used for this
validation exercise is somewhat unique in affording a
means of overcoming this uncertainty. Field observations of sediment movement during storm events and
other ®eld evidence, as well as reconnaissance
measurements of 137Cs inventories at sites where
deposition might have been expected, provided no
96
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
indication of signi®cant sediment deposition within
the catchment. In this situation the delivery ratio can
be assumed to be close to 1.0 and it is possible to
directly compare the estimate of sediment mobilisation within the catchment, based on the erosion rates
estimated using the 137Cs measurements, with the
measured sediment ¯ux at the catchment outlet. The
study reported is thus seen to provide the basis for a
rigorous validation of the erosion rate estimates
derived from 137Cs measurements using a theoretical
calibration model and to meet the need for such independent validation exercises.
2. The study catchment
The study catchment (Fig. 1) is a small (1.38 ha)
basin (W2) located in the northern part of Calabria in
southern Italy. It forms part of the ephemeral network
of the larger Vallone del Crepacuore basin, that is
incised into the Upper Pliocene and Quaternary
clays, sandy clays and sands that are found in the
study area (Sorriso-Valvo et al., 1995). The altitude
of the study catchment ranges from 128 m a.s.l. at
the highest point to 85 m a.s.l. at the basin outlet,
providing a total relief of 43 m. Slopes are typically
in the range 12±69%. The predominant clay soils are
characterised by a silt 1 clay (d , 50 mm) content of
ca. 86%. The climate is typically Mediterranean, with
a mean annual rainfall of ca. 670 mm, most of which
is concentrated during the period extending from
October to March. The W2 basin has never been cultivated and originally supported a rangeland vegetation
cover (Avolio et al., 1980). In 1968 it was planted
with Eucalyptus occidentalis Engl and these trees
have been cut twice, in 1978 and 1990. The tree
cover is not uniformly distributed throughout the
basin and about 20% of the area, located on south
facing slopes (cf. Fig. 2), has few trees and retains a
sparse grass cover. Elsewhere the tree cover is relatively uniform. The soils under the eucalyptus trees
are largely devoid of ground cover and much of the
surface beneath the trees and under the sparse grass
cover is therefore bare. The bare soils are exposed to
rainsplash and surface runoff during periods of heavy
rainfall and signi®cant sheet erosion occurs at these
times. Visual observation during and immediately
after erosion events provides little evidence of
Fig. 1. The location of the study catchment.
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
signi®cant net deposition within the catchment and
most of the sediment mobilised by erosion appears
to be transported directly to the basin outlet. This
conclusion was con®rmed by reconnaissance
measurements of 137Cs inventories at a range of sites
within the catchment, where deposition might have
been expected. In all cases, the inventories were less
than the local reference inventory.
Rainfall has been recorded in the catchment
with a tipping bucket raingauge located in the
upper part of the basin (cf. Fig. 2) since 1978.
Flow has been monitored at the catchment outlet
by an H-¯ume structure (Brakensiek et al., 1979)
equipped with a mechanical stage recorder, since
the same time. The sediment load passing the
97
gauging structure has also been measured using
a Coshocton wheel sampler installed below the
H-¯ume. This sampler collects an aliquot of
ca.1/200th of the ¯ow, which is diverted to a
tank. After each storm event the sample collected
in the tank is well mixed and 1 l suspended sediment samples are collected from different depths
within the tank. The sediment concentrations associated with these samples are determined by oven
drying at 1058C and the mean sediment concentration of the samples is calculated. The sediment
yield of each event is calculated as the product
of the mean sediment concentration sampled in
the tank and the total runoff volume for the
event measured by the H-¯ume. The annual
Fig. 2. The study catchment, showing the relief, the forest cover, and the location of the
137
Cs sampling sites in the W2 basin.
98
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
sediment yield is in turn calculated as the sum of
the sediment loads for all storm events occurring
during a year. Sediment yield measurements have
been undertaken since 1978.
3. Soil sampling for
137
Cs analysis
In order to use 137Cs measurement to estimate rates
of soil loss within the study catchment, a programme
of soil coring was undertaken within basin W2 in
1998. Two soil cores were collected at the intersections of an approximate 20 £ 20 m grid using an
8.6 cm diameter steel core tube inserted to depth of
15 cm. The two cores were bulked. Previous studies
had indicated that signi®cant quantities of 137Cs were
unlikely to be found below a depth of ca. 15 cm in the
undisturbed ®ne textured soils that characterised the
catchment, and this was subsequently con®rmed by
collection of depth incremental samples from
representative sites (see below). Additional cores
were collected from areas characterised by marked
variability of vegetation cover or topography (cf.
Fig. 2), providing a total of 55 bulk cores.
Each bulk core sample was oven dried at 1058C
for 48 h, disaggregated and dry sieved to separate
the ,2 mm fraction. A representative sub-sample
of this fraction (ranging from 1 to 1.2 kg) was
packed into a 1 litre plastic Marinelli beaker for
determination of 137Cs activity by gamma spectroscopy. Caesium-137 activities were measured
using a high resolution HPGe detector in the
Laboratory of the Department of Nuclear Engineering at the University of Palermo, Italy.
Count times were ca. 30000 s, providing a
precision of ca. ^10% at the 95% level of con®dence. The total inventory (Bq m 22) of each bulk
core was calculated as the product of the
measured 137Cs activity (Bq g 21) and the dry
mass of the ,2 mm fraction of the bulk core
(g), divided by the surface area of the core (cm 2).
Additional sampling was carried out in the study
catchment and the adjacent area in late 1999, in order
to obtain information on the local reference inventory
and the depth distribution of 137Cs in the soil pro®le.
Since it was dif®cult to identify an undisturbed and
uneroded site within catchment W2, the samples used
to establish the reference inventory were obtained
from an area of permanent grassland with minimal
slope adjacent to the study catchment. In this case,
sampling was undertaken using a scraper plate
(Campbell et al., 1988). This provided a surface area
of 652 cm 2 and samples were collected at depth increments ranging from 1 to 4 cm to a depth of 50 cm. Six
additional 8.6 cm diameter soil cores were collected
from the reference site, in order to take account of
micro-scale variability in the reference inventory
(cf. Owens and Walling, 1996). Additional scraper
plate pro®les were also obtained from several
representative sites within catchment W2, using the
same procedure as employed at the reference site. The
samples collected during 1999 were prepared in the
same way as those collected in 1998 and their 137Cs
activity was measured by gamma spectrometry
using a high resolution HPGe detector in the
laboratory of the Department of Geography at
the University of Exeter, UK. Count times were
ca. 30000 s, providing a precision of ca. ^10% at
the 95% level of con®dence. In this case, Marinelli beakers of varying size were used to accommodate the smaller samples. The 137Cs
measurements undertaken at both laboratories
have been standardised to a ®xed date at the end
of 1998.
4. Results
4.1.
137
Cs measurements
The total 137Cs inventory obtained for the scraper
plate pro®le collected at the reference site was
2609 Bq m 22. This may be compared to the mean
inventory for the six cores collected in the immediate
vicinity of 2637 Bq m 22. The latter value con®rms the
representativeness of the former and the value
obtained for the scraper plate (2609 Bq m 22) has
been taken as the reference value for the study catchment, in view of the greater surface area associated
with the scraper plate samples. The depth distribution
of 137Cs associated with the scraper plate pro®le
collected from the reference site is illustrated in
Fig. 3(A). The depth scale in Fig. 3(A) has been
plotted in terms of cumulative mass, rather than
depth, in order to avoid the need to take account of
down core variations in soil bulk density. This depth
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
distribution is typical of an undisturbed site (Walling
and Quine, 1992), with ca. 86% of the total inventory
occurring in the top 10 cm and a sharp decline in
activity below this depth.
The values of 137Cs inventory obtained for the 55
bulk cores collected from the study catchment using
the network of sampling sites shown in Fig. 2 ranged
from 19 to 2602 Bq m 22. All these values are less than
the reference value of 2609 Bq m 22, indicating that
net soil loss has occurred at all of the sampling points.
The signi®cant reduction in inventory evident for
most cores indicates that most of the sampling points
have experienced appreciable net erosion over the
period since the commencement of 137Cs fallout in
the mid 1950s. A digital elevation model (DEM)
(3 £ 3 m) was created for the W2 basin, using a
kriging interpolation procedure (De Marsily, 1986)
and the surfer software plotting package, and an
interpolated map of 137Cs inventories produced
using the same kriging procedure has been overlaid
onto this DEM in Fig. 4. The pattern of 137Cs
inventories depicted in Fig. 4 clearly delineates the
areas with the highest rates of soil loss within
catchment W2. There is a trend of increasing erosion
severity from the north-facing hill slopes, with a
uniform cover of eucalyptus trees, to the south facing
hill slopes where the tree cover is discontinuous.
This trend emphasises the importance of vegetation
Fig. 3. The depth distribution of
137
99
cover in in¯uencing rates of soil loss in the study
catchment.
Fig. 3(B) provides a typical example of the depth
distribution of 137Cs for a sampling point within the
study catchment. The 137Cs inventory associated with
this depth pro®le is 456 Bq m 22 and is therefore
substantially less than the reference inventory. This
reduced inventory is indicative of signi®cant soil
loss over the period since the commencement of
137
Cs fallout and the occurrence of erosion at the
site is further con®rmed by the shape of the 137Cs
depth pro®le, which could be seen as re¯ecting the
removal of the surface horizon from that shown in
Fig. 3(A).
4.2. Estimating erosion rates from
measurements
137
Cs
As indicated above, estimation of rates of soil loss
from 137Cs measurements is generally based on a
comparison of the inventory measured at a speci®c
point with the reference inventory and thus the degree
of reduction of that inventory. For uncultivated soils,
the calibration relationship required to convert the
magnitude of the reduction in the 137Cs inventory to
an estimate of the rate of soil loss commonly employs
a theoretical pro®le distribution model (cf. Walling
and Quine, 1990; Zhang et al., 1990). This model
Cs activity at the reference site (A) and at an eroding site within the study catchment (B).
100
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
Fig. 4. The spatial distribution of
137
Cs inventories (Bq m 22) within the study catchment.
represents the vertical distribution of the 137Cs
inventory within the soil pro®le by a simple numerical
function, which in turn can be used to estimate the
depth of soil that would need to be removed to result
in the measured 137Cs inventory. In most cases an
exponential function is used to represent the downpro®le reduction in 137Cs activity (cf. Zhang et al.,
1990; Yang et al., 1998) viz.
A 0 …x† ˆ Aref …1 2 e2x=h0 †;
…1†
where, x is the mass depth from soil surface (kg m 22),
A 0 (x) the 137Cs inventory above depth x (Bq m 22), Aref
the local reference inventory (Bq m 22) and h0 the
relaxation depth describing the pro®le shape
(kg m 22).
The greater the value of the shape factor h0, the
deeper the 137Cs penetrates into the soil pro®le.
Assuming, as a simpli®cation, that the total 137Cs
fallout occurred in 1963, the year of maximum bomb
fallout, and that the depth distribution of 137Cs in the
soil pro®le is independent of time, the erosion rate Y
(for an eroding point, i.e. with a total inventory less
than the reference inventory) can be estimated (cf.
Walling and He, 1997, 1999) as:
10
X
h0 ln 1 2
;
Yˆ
t 2 1963
100
…2†
where, Y is the annual soil loss (t ha 21 yr 21) (negative
value), t the year of sample collection (yr), X the
percentage reduction in the 137Cs inventory in relation
to the local 137Cs reference value (de®ned as [(Aref 2
Au)/Aref]100) and Au the measured total 137Cs
inventory at the sampling point (Bq m 22).
Although this exponential pro®le distribution
model involves a number of simplifying assumptions
it is easy to apply and it has been widely used as a
means of estimating soil erosion rates from 137Cs
measurements in areas with undisturbed soils. Only
a single parameter h0, needs to be estimated and this
value can be derived from measurements of the
vertical distribution of 137Cs in the soil pro®le at the
reference site, by ®tting the following exponential
function to those data i.e.
A…x† ˆ A…0† e2x=h0 ;
…3†
where, x is the mass depth from soil surface (kg m 22),
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
137
21
A(x) the concentration of Cs at depth x (Bq kg )
and A(0) the concentration of 137Cs in the surface soil
(Bq kg 21).
Eq. (3) has been ®tted to the vertical distribution of
137
Cs activity documented in Fig. 3(A) for the
reference site, using linearised least squares regression (Figs. 5(A) and (B)). Values for the A(0) and h0
parameters are 41.3 (Bq kg 21) and 70.5 (kg m 22)
respectively. The exponential model provides a good
®t …r 2 ˆ 0:92† to the 137Cs pro®le for this location and
Eq. (2) has been used to derive estimates of soil
erosion rates from the measurements of 137Cs activity
undertaken on the bulk cores collected from the study
catchment. The values of soil loss estimated from the
values of 137Cs inventory associated with the 55 bulk
cores range from 0.053 to 101.16 t ha 21 yr 21. These
values represent mean values for the 44 year period
between 1955 and 1998 (i.e. between the beginning of
signi®cant 137Cs fallout and the time of sample
collection). The spatial pattern of erosion rates
within the study catchment, based on a kriging
interpolation of the 55 point values, is depicted in
Fig. 6. The pattern shown by Fig. 6 emphasises the
close relationship between erosion rates and the variations in vegetation cover density within the study
catchment, with maximum erosion rates occurring
on the south facing slopes with discontinuous tree
cover. The lowest erosion rates are found in the
101
north-facing hill slopes, where the tree cover is
more uniform.
4.3. Sediment yield at the catchment outlet
Measurements of sediment output from catchment
W2 are available for the period 1978±1994. Annual
sediment yields during this period varied markedly in
response to total rainfall input and its seasonal variability and ranged between 1.78 and 101.3 t ha 21 yr 21,
with a mean of 20.8 t ha 21 yr 21. Fig. 7 presents a
frequency distribution for these values and shows
the existence of two extreme outliers in 1990 and
1992. 1990 was associated with a particularly high
value of annual rainfall and both years were characterised by high values of the annual erosivity index
proposed by Arnoldus (1980). These years also coincided with a period of reduced vegetation cover as a
result of logging operations in 1990. These outliers
emphasise the importance of extreme events to
erosion and the total sediment output and this is
further demonstrated by consideration of the 52
signi®cant erosion events recorded at the basin outlet
during the study period. Four of the events accounted
for ca. 60% of the total sediment output (cf. Cantore et
al., 1994; Callegari et al., 1994; Cinnirella et al.,
1998). Other studies have reported similar trends for
annual soil loss that further emphasise the importance
Fig. 5. Fitting the exponential depth distribution function (Eq. (3)) to the 137Cs depth distribution documented for the reference site. (A) shows
how the estimates of A(0) and h0 were derived using least squares regression and (B) shows the function superimposed on the measured 137Cs
depth distribution.
102
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
Fig. 6. The spatial distribution of mean annual soil loss (t ha 21yr 21) within the study catchment estimated from the
of relatively large events in in¯uencing the longerterm average (cf. Edwards and Owens, 1991; Larson
et al., 1997).
Since the aim of this study was to compare the
estimates of soil loss obtained from the 137Cs measurements with the measured sediment output from the
study catchment, the different time periods involved
must be taken into account. In this context it is important to consider the extent to which the value of mean
annual sediment yield of 20.8 t ha 21 yr 21 calculated
using the records for the period 1978±1994 is likely to
be representative of the period 1955±1998 covered by
the estimates of erosional loss derived from the 137Cs
measurements. In the absence of long-term sediment
yield data for the study catchment or for other rivers in
the local area, precipitation data have been used to test
the representativeness of the shorter period. Monthly
rainfall data were obtained for two experimental
stations located near the study area that had been
monitored by the Servizio Idrogra®co e Mareogra®co
Italiano (SIMI) and by the Uf®cio Centrale di
Ecologia Agraria (UCEA). Two measures have been
137
Cs measurements.
used to characterise the rainfall received in individual
years. The ®rst is the total annual rainfall and the
second the Arnoldus annual erosivity index (cf.
Arnoldus, 1980). The latter is likely to be more
closely related to inter-annual variations in soil loss
and sediment yield. Mean values were calculated for
the two stations and the resulting values of annual
rainfall and erosivity index for the period 1954±
1993 are presented in Fig. 8. The close positive relationship between the erosivity index and the magnitude of the annual sediment yield is further con®rmed
by the high values of the annual erosivity index
recorded for 1990 and 1992, the years with very
high sediment yields (cf. Fig. 7). The data presented
in Fig. 8 suggest that the period 1978±1994 covered
by the sediment load measurements can be viewed as
being generally representative of the longer term. In
order to con®rm this conclusion, a Z-test was used to
test the signi®cance of the difference between the
means for the period 1978±1994 and the assumed
population means based on the longer period (cf.
Kanji, 1993). The resulting Z statistics (1.30 for
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
103
Fig. 7. The frequency distribution of annual sediment yield data for the study catchment.
annual rainfall and 1.181 for the annual erosivity
index) are less than the critical value at the 0.05
level of signi®cance, indicating that there is no significant difference between the two values. A similar
procedure has been employed to test for a signi®cant
difference between the assumed population variance
of the two parameters based on the longer period and
the variance calculated for the period 1978±1994.
Again, the resulting x 2 statistics (23.68 for annual
rainfall and 6.43 for the annual erosivity index) are
less than the critical value at the 0.05 level, indicating
that there is no signi®cant difference between the two
periods. It has therefore been assumed that the period
1978±1994 covered by the measurements undertaken
at the catchment outlet is generally representative of
the longer period covered by the erosion rate estimates
based on the 137Cs measurements.
Any comparison between the two periods must,
however, also take account of, ®rstly, potential
differences between the mean annual erosion rates
and sediment outputs for the shorter and longer periods consequent upon the natural variability of the
annual totals and, secondly, the possibility of nonstationarity in the erosion rate and sediment output
over the longer period. The ®rst problem has been
addressed by using a non-parametric approach,
based on the resampling (bootstrap) technique (cf.
Davison and Hinkley, 1997), to estimate the 95%
con®dence limits around the mean based on the
shorter 14 year period. Monte Carlo sampling, with
replacement, was used to generate 10 000 empirical
14 year series, that could be used to establish the
sampling distribution of the associated estimates of
mean annual sediment yield. The mean annual sediment output for the 14 year period of record is
20.8 t ha 21 yr 21 and the 95% bootstrap con®dence
limits around this mean were estimated to be 9.8
and 34.0 t ha 21 yr 21. Problems of potential non-stationarity in the longer period of record are more dif®cult
to address, but it is clearly important to take account
of changes in the vegetation cover within the study
catchment. The eucalyptus trees were planted in the
catchment in 1968 and cut in 1978 and 1990. Trees
were therefore absent from the study catchment for
the ®rst 12 years of the period covered by the 137Cs
measurements and during that time the catchment
would have been characterised by a sparse cover of
grass and by a higher erosion rate. Using values of
cover density within the catchment reported by
Avolio et al. (1980) and Cantore et al. (1994) and
assuming, as a simpli®cation, that over the period in
question the canopy cover of the trees was directly
proportional to their age, it is possible to produce a
schematic reconstruction of the changes in the cover
104
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
Fig. 8. Values of annual rainfall (A) and the annual erosivity index (B) for the period 1954±1993. The solid bars denote the period covered by
the sediment yield measurements.
density of the study catchment as shown in Fig. 9.
Assuming that erosion rates were signi®cantly higher
when the tree cover was initially absent and during the
period immediately following the cutting of the trees,
it can be suggested that the mean erosion rate for the
period covered by the 137Cs measurements (i.e. 1955±
1998) is likely to have been somewhat higher than that
associated with the shorter period covered by the
measurements of sediment yield at the catchment
outlet. However, the precise relationship between
the two values would clearly depend on the timing
of high magnitude erosion events during the longer
period.
4.4. Comparison of the estimates of soil loss derived
from the 137Cs measurements with the measurements
of sediment yield at the basin outlet
In order to make a direct comparison between the
estimates of soil loss derived from the 137Cs measurements and the measurements of sediment output from
the catchment, it is necessary to take account of both
conveyance losses and the spatial variability of
erosion within the catchment. As indicated
previously, there is no evidence of signi®cant
deposition within the study catchment and a sediment
delivery ratio close to 1.0 has been assumed. The
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
105
Fig. 9. A tentative reconstruction of the variation of vegetation cover density within the study catchment during the period 1955±1998.
erosion rate estimates and the sediment yield data can
therefore be directly compared. In order to obtain a
spatially-weighted mean value for the erosion rate
within the study catchment that can be compared
with the value of sediment yield at the catchment
outlet, three different procedures have been employed.
These are as follows:
1. Calculation of the mean erosion rate for the 55
points from which bulk cores were collected.
2. Areal integration of the map of erosion rates
presented in Fig. 6.
3. Discretisation of the study catchment into a series
of morphological units representing areas with
similar characteristics of aspect, slope length and
slope steepness (cf. Ferro and Porto, 2001), calculation of the mean erosion rate for each of these
areas by areal integration of Fig. 6, and ®nally
weighting of these values by the areal extent of
the units to obtain a mean erosion rate for the overall catchment. Thirty eight morphological units
were identi®ed in the study catchment.
The three estimates of the mean annual erosion rate
within the study catchment, calculated using the three
procedures outlined above, are presented in Table 2,
where they are compared with the mean annual sediment yield from the study catchment. There is little
difference between the three estimates of mean
erosion rate for the study catchment, indicating that
the precise method used to calculate the mean erosion
rate is of limited importance. The mean annual sedi-
ment yield measured at the catchment outlet for the
period 1978±1994 is less than the estimates of mean
annual erosion rate for the catchment derived from the
137
Cs measurements. However, the latter fall well
within the 95% bootstrap con®dence limits of the
measured mean annual sediment yield presented
above and are therefore not signi®cantly different
statistically. Furthermore, there are several reasons
why the measured sediment yield could be expected
to be less than the mean annual erosion rate estimated
using the 137Cs measurements. Firstly, although there
is no evidence of signi®cant deposition within the
study catchment and a sediment delivery ratio of
close to 1.0 has been assumed, some conveyance
loss with associated deposition is very likely to
occur. Local deposition could, for example, be
expected occur upslope of individual tree boles
(cf. Loughran et al., 1993). In this situation, the
sediment output should be less than the mean annual
erosion rate. Secondly, as indicated previously, the
mean annual erosion rate and therefore sediment
yield for the period covered by the 137Cs measurements (1955±1998) could be expected to be greater
than the measured sediment yield, due to the longerterm changes in vegetation cover density within the
catchment (Fig. 9). Thirdly, it is important to
recognise that the value for the measured sediment
output might itself also incorporate some uncertainty
associated with any malfunctioning of the sediment
sampling equipment. Such uncertainty is most likely
to be re¯ected in underestimation, through failing to
sample, or only partially sampling, some events.
106
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
Table 2
A comparison of the estimates of the mean annual erosion rate in the
study catchment obtained using 137Cs measurements and the
measured sediment output in the catchment
Criterion
Erosion rate (t ha 21 yr 21)
137
Cs Estimates
1
2
3
Measured output
29.0
29.5
28.4
20.8
Finally, it is likely that the pro®le distribution model
will overestimate the actual erosion rate, since, in the
case of very low inventories, use of the exponential
depth distribution could indicate removal of a greater
depth of soil than has actually been lost. For example,
the 137Cs depth distribution for the reference site
depicted in Fig. 3(A) indicates that removal of a
layer of soil equivalent to a mass depth of
167 kg m 22 would remove all the 137Cs from the
pro®le and thus result in a zero 137Cs inventory.
However, use of the exponential depth distribution
®tted to the measured 137Cs depth distribution in
Fig. 5(B), to estimate the depth of soil that would
need to be lost to result in a zero inventory, would
result in a value more than double that indicated
above. On this basis, the comparison of the estimates
of the mean annual erosion rate for the study catchment obtained from the 137Cs measurements with the
measured sediment output from the basin is seen to
demonstrate a high degree of consistency. It, therefore, provides an independent validation of the
erosion rate estimates derived from the 137Cs measurements and thus of both the overall 137Cs approach and,
more speci®cally, the pro®le distribution model
approach used here for calibration purposes.
5. Conclusion
The lack of studies aimed at comparing estimates of
erosion rates derived from 137Cs measurements
with equivalent independent data obtained using
other measurement techniques was highlighted in
the introduction to this paper. The paucity of such
studies is itself a re¯ection of the dif®culty of assembling independent information on erosion rates
stretching back to the mid 1950s, that is also directly
comparable with that obtained from the 137Cs
measurements.
In this study, use of information on the sediment
output from a small catchment overcomes many of
the potential problems associated with the spatial
variability of erosion rates and different scales of
measurement, by providing a spatially-integrated
value of sediment yield from a known area which
can be compared with a spatially-averaged estimate
of the erosion rate for the same area derived from
137
Cs measurements. Use of 55 soil-sampling points
within the study catchment is seen to provide a
meaningful basis for estimating the spatiallyaveraged erosion rate, although an increased
number of soil cores would undoubtedly increase
the precision of the resulting estimate. The availability of a small catchment with a sediment delivery ratio close to 1.0 also avoids the need to take
account of both erosion and deposition within the
catchment in calculating the net sediment output.
Use of a higher density of soil coring sites might
have revealed small areas of deposition missed by
the existing sampling network and the reconnaissance survey and in this situation the estimate of
net soil output derived from the 137Cs measurements
would be an overestimate and thus provide one
explanation of the higher values shown in Table 2
for the erosion rate based on 137Cs measurements.
One limitation of the study is undoubtedly the lack
of a full correspondence between the periods
covered by the two approaches and the likelihood
of changes in sediment mobilisation within the
study catchment consequent upon changes in vegetation cover density. However, the resulting uncertainties have been taken into account and the study
is seen to provide a effective basis for validating the
use of 137Cs measurements to estimate erosion rates
and more particularly the use of the simple exponential pro®le distribution model to estimate
erosion rates on uncultivated soils. Further studies
are, however, clearly required to extend the validation to other environments and terrain types, to
embrace the different calibration procedures
employed for cultivated soils and to provide a
basis for comparing the increasing number of calibration models that have been proposed in the
recent literature.
P. Porto et al. / Journal of Hydrology 248 (2001) 93±108
Acknowledgements
The ®rst author gratefully acknowledge the support of
an EC Marie Curie Fellowship (MCF1-2000-00096)
held at the University of Exeter. Thanks are also
extended to Dr G. Callegari for assistance with ®eldwork and to Professor R.J. Loughran and Professor E.
de Jong for valuable comments on an earlier draft of this
paper. This paper represents a contribution to the IAEA
Coordinated Research Programme D1.50.05 through
Technical Contract 9562/R2.
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