Geology Reference
In-Depth Information
convert any of them into the sediment fluxes (usu-
ally as mass per unit width per unit time: M L
−1
T
−1
)
which characterize erosion. However, standard
practice has been to convert these measurements
not
into fluxes, but into specific yields. A specific
yield calculates erosion as a function of upslope
contributing area [M L
−2
T
−1
]. At first glance, this
approach should account for scale, in that it directly
incorporates an upslope area. However, consider
again the soil particle moving on a slope. Its move-
ment is controlled by forces generated by local con-
ditions, some of which are independent of upslope
conditions (e.g. raindrop detachment in the absence
of flow), while others are complex functions of the
upslope conditions (e.g. raindrop detachment with
flow, flow hydraulics depending on surface micro-
topography and shape of the upslope area). Under
homogeneous conditions, these functions may be
reasonably predictable analytically, as discussed
below. On slopes and in catchments with varying
lithologies, soils, vegetation and land-use practices,
not to mention spatially variable rainfall intensi-
ties, the relationships tend to be more complicated,
and other approaches are required to address them.
Depending on whether measurements are made
on a hillslope or at a catchment outlet, it must also
be recognized that process domains change. On
shorter hillslopes, raindrop-driven processes such
as splash and unconcentrated overland-flow erosion
are dominant. As slopes get longer, concentrated
overland-flow erosion becomes more important,
and depending on soil type and land use, subsurface
erosion may also occur. Landslides will become
more important on steeper slopes, and in steep
catchments, undercutting by the channel can mean
that landslides are a significant source of sediment
reaching the channel system (Ergenzinger, 1992;
Korup, 2005). Catchment-based measurements
will also incorporate the effect of channel processes
such as lateral erosion of banks and floodplains, as
well as storage in channels and floodplains, and
remobilization of alluvial sediments. For these
process-related reasons, catchment-based measure-
ments may be a poor reflection of erosion flux on
and from slopes. From the 1950s, and largely
developing from empirical modelling approaches
to estimate erosion rates on slopes based on plot
data, there was a suggestion that catchment-based
measurements tended to underestimate hillslope
erosion rates systematically (e.g. Maner and Barnes,
1953; Glymph, 1954). The sediment delivery ratio
(SDR) was consequently defined as a way of scaling
between 'gross erosion' on slopes and sediment
yield at a point in the catchment, and subsequently
there has been a significant amount of research on
methods for predicting SDRs as a function of catch-
ment conditions (e.g. Roehl, 1962; Walling, 1983).
However, as will be discussed below, the SDR is an
artefact of the ways in which erosion has been
measured, and leads to erroneous understandings
of sediment transfers in catchments.
The use of SDRs demonstrates a fundamental
point: that data are not independent of the (con-
ceptual) models used in research designs. The
focus on measurement techniques and resulting
units above shows that not all measurements
relate to the same thing - even if they are gener-
ally considered to be identical. The failure to con-
sider how models and data relate to each other
has produced significant problems in estimating
erosion rates at different scales.
What exactly do we mean when we talk about
scale and scaling erosion rates and erosion models?
As suggested above, a simple consideration that
scale relates to different areas of measurement (or
different lengths of time) is too simplistic. A lack of
explicit consideration of what is meant by the
terms 'scale' and 'scaling' often leads to further
confusion (see reviews in Blöschl & Sivapalan,
1995; Zhang
et al
., 2002). Going beyond the carto-
graphic or geographical scales, we need to consider
operational or process scales (i.e. the scales over
which different processes are important - see
above), measurement or observational scale, and
modelling scale. Modelling scale relates to the rep-
resentation of space and time in the model. Different
models represent different elements of the land-
scape (e.g. slope segments, entire slopes, catchment
areas) more or less closely, and may integrate over a
range of timescales (e.g. event, annual, geological).
Measurement scales are characterized by triplets of
information (Blöschl, 1996): the extent of the data
(total area covered), data spacing or resolution (the
number and thus spacing of samples across the
