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Channel network morphology and sediment dynamics under
alternating periglacial and temperate regimes: a numerical
simulation study
Patrick W. Bogaarta,b,*, Gregory E. Tuckerc, J.J. de Vriesb
aNetherlands Centre for Geo-ecology ICG, The NetherlandsbFaculty of Earth and Life Sciences, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
cSchool of Geography and the Environment, Oxford University, Oxford, UK
Received 20 December 2001; received in revised form 12 November 2002; accepted 3 December 2002
Abstract
The occurrence of permafrost in a highly permeable catchment has a profound effect on runoff generation. The presence of
permafrost effectively makes the subsoil impermeable. Therefore, overland flow can be the dominant runoff-generating process
during periglacial conditions. The absence of permafrost will promote subsurface drainage and, therefore, saturation excess
overland flow can become the dominant runoff-generating process during temperate conditions. In this paper, we present a
numerical modelling study in which the effect of alternating climate-related phases of permafrost and nonpermafrost on
catchment hydrology and geomorphology is investigated. Special attention is given to the characteristics of the channel network
being formed, and the sediment yield from these catchments. We find that channel networks expand under permafrost
conditions and contract under nonpermafrost conditions. A change from permafrost to nonpermafrost conditions is
characterised by a decrease in sediment yield, while a change towards permafrost conditions is marked by a peak in sediment
yield. This peak is explained by the build-up of a reservoir of erodible sediment during the nonpermafrost phase. The driving
force behind this reservoir build-up may be local base-level change due to tectonic uplift or eustacy. We present a number of
experiments, which show the details of this process. The results are in line with existing reconstructions of climate and fluvial
dynamics during the Pleistocene in Europe and offer a new explanation to these observations.
D 2003 Elsevier Science B.V. All rights reserved.
Keywords: Quaternary; Permafrost; Geohydrology; Drainage networks; Landform evolution; Numerical models
1. Introduction
Unconsolidated Quaternary deposits of fluvial or
aeolian origin cover a significant portion of NW
Europe (Kasse, 1997). In these areas, the current
channel network appears to be in disequilibrium with
the valley network, which has a much larger extent
(Fig. 1). Numerous dry valleys occur and indicate that
0169-555X/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0169-555X(02)00360-4
* Corresponding author. Present address: Hydrology and
Quantitative Water Management Group, Department of Environ-
mental Sciences, Wageningen University, Nieuwe Kanaal 11,
Wageningen, 6709 PA, The Netherlands.
E-mail addresses: [email protected] (P.W. Bogaart),
[email protected] (G.E. Tucker), [email protected]
(J.J. de Vries).
www.elsevier.com/locate/geomorph
Geomorphology 54 (2003) 257–277
other hydrogeomorphological conditions existed dur-
ing the past. A number of hypotheses can be formu-
lated which are able to explain this former situation:
First, annual effective precipitation could have been
much higher, and fluvial geomorphological processes
would have been, thus, more intense. This explan-
ation can, however, be eliminated, since all palaeo-
climate reconstructions and modelling studies indicate
drier or similar conditions during the Last Glacial
(e.g. Renssen and Isarin, 2001). Second, runoff could
have been more peaked (fewer, but more intense
events) due to either a more peaked precipitation
regime or the distribution-moderating effects of snow
storage and melt dominance. As a result of this,
fluvial processes would have been more effective in
the past than they are now (Tucker and Slingerland,
1997; Tucker and Bras, 2000). Third, the hillslope
hydrological regime could have been different in the
past, e.g. switching between Hortonian (infiltration
excess) and saturation excess overland flow. In this
paper, we investigate the latter two hypotheses,
which deal with the way runoff is generated in low-
gradient, highly permeable catchments, under peri-
glacial conditions.
During interglacials or relative warm periods, the
subsoil is highly permeable and most runoff will occur
subsurface. Only in the lower parts of the catchment
will saturation excess overland flow occur (Dunne,
1978). This is also the current situation in most
temperate areas.
Fig. 1. Valley system in the southern Netherlands, as interpreted from the geomorphological map of The Netherlands. Map units indicating
fluvial activity during the Holocene, because of either an active floodplain or peat occurrences, are classified as ‘wet’ valleys. Map units
indicating no fluvial activity during the Holocene are classified as ‘dry’ valleys (after the 1:50,000 geomorphological map of The Netherlands,
Sheet 50: Breda, Stichting voor Bodemkartering, Wageningen, 1981).
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277258
During glacial or relative cold periods, the subsoil
is frozen for at least part of the year, and is no longer
capable of massive subsurface flow. Most runoff
would be taking place as overland flow and a more
Hortonian style of runoff generation prevails (e.g.
Dunne et al., 1976; FitzGibbon and Dunne, 1981).
A much more extended channel network is likely to
develop under these conditions. These changes in
runoff production are expected to have had a major
impact on the amount of sediment, which was deliv-
ered by catchments subject to these processes. This
sediment delivery is of special relevance to the study
of the Quaternary evolution of alluvial rivers since
these are, to a large extent, determined by water and
sediment input from the surrounding catchment.
The objective of this paper is to assess the impact
of alternating permafrost–nonpermafrost conditions
on channel network morphodynamics and the delivery
of sediment from upstream catchments to the main
river network, on glacial (stadial)–interglacial (inter-
stadial) time scales in lowland areas consisting of un-
consolidated, highly permeable sediments, by means
of numerical model experiments.
2. The periglacial environment
Periglacial and temperate geomorphology and
hydrology differ significantly in a number of ways.
Most, if not all, differences can be directly or indi-
rectly attributed to freezing and thawing of water on
or below the land surface. A brief overview of the
relevant hydrological and fluvial geomorphological
processes will be given in the next section.
2.1. Periglacial processes
In most temperate environments, saturation excess
is the dominant mode of storm runoff generation in
the vicinity of channels and channel heads (Dunne,
1978). The main factors that are responsible for this
are high-frequency, low-magnitude rainfall distribu-
tion, in combination with large values of infiltration
capacity and soil hydraulic conductivity, due to abun-
dant vegetation and soil fauna.
Under periglacial conditions, however, the situa-
tion is completely different. Vegetation and soil
fauna—if any—are scarce; soil hydraulic conductivity
is, therefore, more likely to be small, and infiltration
capacity may become a limiting factor. Hydraulic
conductivity and/or infiltration capacity is further
decreased by the presence of permafrost or seasonally
frozen soils. For example, steady-state infiltration rate
in a Vermont (USA) sandy-loam soil ranges from 8.0
cm/h for unfrozen conditions to 0.02 cm/h under
concrete frost (Dunne, 1978). Although there is some
evidence that permafrost systems are almost never
completely closed (even in ‘continuous’ permafrost
situations) (Woo, 1993), effective values for hydraulic
conductivity are much lower than under temperate
conditions. A more Hortonion-type of overland flow
can, therefore, be expected under periglacial condi-
tions. Fig. 2 shows the general hillslope hydrological
system under temperate and periglacial conditions.
Periglacial river flow regimes are extremely highly
peaked due to the springtime melting of snow (nival
regime; Woo, 1993). It is clear that climate-induced
changes in flow regime have a distinct impact on total
sediment transport, since (instantaneous) sediment
transport rate is a nonlinear function of (instantaneous)
river flow.
A large number of other hydrological processes are
active in the periglacial environment, such as inter-
hummock flow in the arctic tundra (Quinton and
Marsh, 1999) or slush flows and torrents (Gude and
Scherer, 1999). However, these processes are less
relevant for the issues dealt with in this paper, and
we will, therefore, ignore them for now.
Soil erodibility (defined here as the resistance
against erosion) is, in general, a function of soil
texture, vegetation cover, soil organic matter, etc.
Under temperate conditions, the vegetation will cover
most of surface, and soil organic matter content will
be high. Soils will, therefore, not be easily erodible.
(Palaeo) periglacial environments, on the other hand,
are generally characterised by much sparser vegeta-
tion. For example, the end of the Pleniglacial in NW
Europe was characterised by (relatively) dry condi-
tions with a sparse vegetation (Bohncke and Vanden-
berghe, 1991; Kasse, 1997). The response of
vegetation to climate change is also nonlinear and
lagged (e.g. because of nitrogen-deficiency induced
slow (primary) succession (van Geel, 1996)). In
addition, specific frost-related processes influence
erodibility. Freeze–thaw cycles weaken the soil and
riverbank strength (Gatto, 2000).
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277 259
Soil erodibility can, thus, be expected to be large
under temperate conditions, and low under periglacial
conditions. Whether or not soil erodibility has a major
impact on sediment production within the (unconso-
lidated, sandy) type of catchments that we are discus-
sing here is not certain. It can be argued that
erodibility during periglacial conditions is that of
loose sand because melt water derived from snow is
able to thaw enough soil to erode, and that it might be
higher during temperate conditions. However, under
temperate conditions, most overland flow will be
confined to small, incised channels, where vegetation
is more likely to be absent.
2.2. Reconstructed periglacial environments
Numerous workers have described the existence of
now dry valleys in formerly periglacial catchments.
Analysis of Polish fluvial valleys (Klatkowa, 1967)
suggest that the morphological evolution of fluvial
valleys is dependent on both scale and climate: the
larger, higher-order valleys were eroded during the
last interglacial (Eemian), and were filled by sediment
during the last glacial, while the smaller, lower-order
valleys (‘dells’) are the result of sheetwash erosion
under periglacial conditions.
Dry, incised valleys in ice-pushed ridges of the
Veluwe region (The Netherlands) are attributed to the
combined action of impervious soils and high snow-
melt discharges during the Weichselian (Maarleveld,
1949).
A reconstruction of the evolution of the Mark
(southern Netherlands) catchment (Vandenberghe et
al., 1987; Bohncke and Vandenberghe, 1991) suggests
a significant hydrological and geomorphological
response to climatic change. The interpreted river
response can be explained well by combining evi-
dence for soil frost and precipitation, as shown in
Table 1. The most prominent phase of river incision
occurred during the Weichselian Lateglacial, when
precipitation was high; a nival hydrological regime
prevailed and snowmelt peaked during springtime. In
Fig. 2. Cartoon illustrating the hillslope hydrological regime on a sandy subsoil under temperate conditions (top left and right) and under
periglacial conditions (bottom left and right).
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277260
combination with a (seasonally) frozen soil, high
overland flow discharges were generated.
A number of sections near the head of the present
drainage network show a relatively deep Lateglacial
incision and, thus, provides indirect evidence for a
more extended network during this period, compared
to the Holocene. The little activity during periods of
strong soil freezing, such as the Late Pleniglacial,
indicates that fluvial morphodynamics is forced by
both soil hydrological condition and total precipitation
and can, therefore, only be explained by taking both
hydrologic and precipitation regimes into account.
Analysis of drainage density and streamflow re-
gime properties in a number of catchments in the NE
United States (Carlston, 1963) showed that drainage
density (squared) is log-linearly related to both base
flow and mean annual flood, suggesting that drainage
density is controlled by transmissivity, and controls
flood discharge.
De Vries (1994) presented a conceptual model that
explains the relations between catchment morphology,
channel network structure and groundwater flow. This
model is valid for low-relief catchments in (thick)
unconsolidated, highly permeable substrate. Under
these conditions, groundwater and surface water are
tightly coupled, and it can be assumed that the
surficial channel network is adapted in such a way,
that precipitation surplus can be released through both
surface and subsurface drainages. Drainage density
can, therefore, be explained from geological, soil
physical and climatic parameters. The calculated rela-
tionships between stream density, channel morphol-
ogy, topography and groundwater dynamics compare
well with actual catchments from The Netherlands. In
a later study, it was shown that the seasonal expansion
and contraction of stream networks can be explained
by the seasonal changes in precipitation surplus and
the associated interplay of groundwater and stream
flow dynamics (de Vries, 1995). The mathematical
model describing this relation was shown to be in
agreement with the actual drainage density in the
Dutch Pleistocene area.
Kasse (1997) described the evolution of the Dutch
coversand areas during the Late Pleniglacial (OIS 2).
He attributed increased coversand deposition and
Table 1
Relation of climate, soil frost state, hydrology and morphodynamics for the Mark catchment, based on palynological, sedimentological and
geomorphological evidence (Bohncke and Vandenberghe, 1991)
Period Winter temperature (jC) Summer temperature (jC) Soil frost Total runoff Surface runoff Channel morphology
Early Holocene � 2 + 19 � + 0 very little activity
Younger Dryas � 20 + 10 + + � + minor activity
Lateglacial 2 � 13 + 12 + + ++ continuing incision
Lateglacial 1 � 6 + 15 + + + + ++ + major incision
Late Pleniglacial 2 � 12 + 12 + + � + filling
Late Pleniglacial 1 � 20 + 8 + + + + + ++ + incision
The number of (+) and (� ) symbols indicates the intensity of the process.
Table 2
Summary of changes in climate, hydrology and sedimentary
processes during the period of 20–12 ka, based on multiproxy
palaeo-climate (pollen, insects, periglacial features, etc.), sedimen-
tological and geomorphological evidence
Conditions Last Glacial
maximum
(20–15 14C kyr BP)
Late Pleniglacial
(14–12.4 14C kyr BP)
Climate/geology
Temperature (jC) <� 8 <� 1
Vegetation Tundra/absent Absent
Precipitation Low Very low
Permafrost Continuous No deep seasonal frost
Subsoil Frozen sand Unconsolidated sand
Hydrology
Infiltration Minimal Increased
Drainage density High Decreased
Overland flow Strong Absent
Surface moisture Wet Dry
Depositional processes
Aeolian activity Modest Strong
Preservation of
Aeolian sediments
Low High
Interfluves Erosion Aeolian accumulation
River valleys Aggradation Aggradation
Modified after Kasse (1997) and Huijzer and Vandenberghe (1998).
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277 261
preservation during the latter phase of this period to
the lower soil moisture content due to improved
drainage caused by permafrost degradation and chan-
nel network retreat. The reconstructed environmental
parameters are shown in Table 2.
3. Methodology
The Channel-Hillslope Integrated Landscape De-
velopment (CHILD) numerical landscape evolution
model (Tucker et al., 2001a,b) was used for the
following purposes. Firstly, to assess whether the
hypotheses put forward above are physically plausi-
ble, given a simple quantitative model. Secondly, to
examine the kind of dynamics that might be expected
to emerge, given reasonable variations in (climate-
induced) soil hydrology and rainfall or runoff varia-
bility, if the dynamics are expressed as changes in
drainage density and amounts of sediment yielded
from the catchment.
3.1. The CHILD landscape evolution model
CHILD (Tucker et al., 2001a,b) is a comprehensive
landscape evolution model in which the temporal
evolution of catchment topography is simulated by a
feedback between surface hydrology, regolith detach-
ment and sediment transport. In this, CHILD is com-
parable to earlier efforts (Willgoose et al., 1991;
Howard, 1994; Tucker and Slingerland, 1997; Tucker
and Bras, 1998).
As will be discussed in the next section, the CHILD
model will be applied to a geological setting charac-
terised by low-gradient, highly permeable, unconsoli-
dated substratum, such that the processes like bedrock
incision and slope failure do not apply, and only a
subset of the CHILD model will be outlined here, i.e.
transport-limited fluvial processes; slow, continuous
creep processes; and slow, continuous local base-level
changes. See Tucker et al. (2001b,a) for a full discus-
sion of the model.
The CHILD model calculates the spatially variable
rate of erosion/deposition Bz/Bt (m/year) as a sum of
contributions by these three different processes:
Bz
Bt¼ Bz
Bt
����fluvial
þ Bz
Bt
����mass wasting
þ Bz
Bt
����base�level
ð1Þ
which is numerically solved on a regular hexagonal
grid. The three terms in Eq. (1) are discussed below.
Erosion/deposition due to fluvial processes is mod-
elled as the spatial divergence of sediment transport
Qs (m3/year)
Bz
Bt
����fluvial
¼ �jqs ¼ � BqsxBx
þBqsy
By
� �ð2Þ
where qs is the sediment flux per unit width (m3/m/
year).
Eq. (2) is solved numerically by averaging local
erosion or deposition over the area of one grid cell, so
that the equation for elevation changes in a given cell
due to fluvial sediment transport is
Bz
Bt
����fluvial
¼ 1
Av
XðQsinÞ � Qsout
� �ð3Þ
where Av (m2) is the area of the computational cells,
and Qsinand Qsout
are total volumetric fluxes of sedi-
ment entering and leaving the grid cell, respectively.
Volumetric sediment transport per unit flow width,
qs (m2/year) is modelled by a generic power law
(Tucker et al., 2001b):
qs ¼1
qsð1� gÞ kf ðktqmf Snf � scÞp ð4Þ
where qs (kg/m3) is sediment mass density; g (m3/m3)
is sediment porosity; q (m2/year) is overland flow or
channel discharge per unit flow width; S (m/m) is
topographic gradient; sc (N/m2) is critical shear stress;
kf, kt, mf, nf and p are model parameters. As discussed
by Howard (1980), many common sediment transport
formulas can be cast into the general form of Eq. (4).
Overland flow discharge Q (m3/year) is modelled
using a simple saturation excess hillslope hydrological
scheme, assuming that subsurface flow capacity is a
function of topographic gradient S (m/m) and sub-
strate transmissivity (horizontal soil hydraulic con-
ductivity, vertically integrated to the surface) T (m2/
year) (O’Loughlin, 1986):
Q ¼AP � STx; if APzSTx;
0; otherwise
8<: ð5Þ
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277262
where A (m2) is upstream catchment area, P (m/year)
is runoff (precipitation or snowmelt) rate and x (m) is
the width of the interface between adjacent grid cells.
Because of the threshold values in this equation, it
effectively models the seepage of water within well-
defined channel heads.
Erosion/sedimentation due to slow, semicontinuous
mass wasting processes like soli- or gelifluction and
creep are modelled by a simple diffusion model:
Bz
Bt
����diffusion
¼ �Kdj2z ¼ �Kd
B2z
Bx2þ B
2z
By2
� �ð6Þ
where Kd (m2/year) is a diffusivity parameter. Fast
mass wasting processes like slope failure are not
considered here.
Finally, absolute elevation change due to direct
relief changing process like tectonic uplift or local
base-level change is modelled by the simple model
Bz
Bt
����base�level
¼ U ð7Þ
where U (m/year) is the rate of tectonic uplift or base-
level change. Within all the simulations described
here, U will be a constant boundary condition, which
is applied to all grid nodes, except those which are
outlet locations for the channel network (see also
Section 4.2). These outlet nodes are kept at an
elevation of z = 0. Effects of base-level change, thus,
propagate upstream through the catchment. It should
be noted that base level here means local base level,
i.e. for the modelled domain and, thus, not global (e.g.
sea level) base level.
4. Model application
4.1. Parameterisation
In this section, we derive parameter values, which
are reasonable estimates of the process magnitudes for
a typical locality under typical time scales, e.g. the
Pleistocene areas of The Netherlands, during the Late
Quaternary (Weichselian and Holocene).
It should be noted that even the best model
parameterisation is only a rough approximation of
reality, since some potentially relevant processes are
omitted from the model; most model assumptions
simplify physical reality, scale problems occur, and
initial conditions are unknown. See Haff (1996) for a
full discussion. In this case, these problems are of
second-order significance because our aim is not
precise reconstruction, but rather hypothesis evalua-
tion and insight into the relevant morphodynamical
processes.
4.1.1. Transmissivity
Thickness of the upper part of the Pleistocene
aquifer within The Netherlands is in the range of
25–250 m, and has an average horizontal hydraulic
conductivity of 20 m/day, leading to a transmissivity T
ranging from 500 to 5000 m2/day, or 182,500–
1,825,000 m2/year (de Vries, 1974, see Fig. 3).
Transmissivity in the coversand areas in the south-
ern Netherlands has an average value of 1000 m2/
day = 365,000 m2/year. This value is taken to repre-
sent average ‘warm’ conditions. Under periglacial
conditions, we assume that permafrost is continuous,
and that subsurface flow is limited to a summer time
active layer of c 1 m and, thus, T= 7300 m2/year.
4.1.2. Fluvial sediment transport
Parameter values for the generic transport model
(4) can be estimated using, e.g. the Einstein–Brown
transport equation (Brown, 1950), which relates non-
dimensional sediment transport:
U ¼ qs;m
qsFffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigðs� 1Þd350
p ð8Þ
where qs,m (kg/s) is sediment transport rate per unit
flow width, qs (kg/m3) is sediment density, F
(dimensionless) is a sediment grain fall velocity
parameter, g (m/s2) is gravity, s (dimensionless) is
specific sediment grain density qs/q and d50 (m) is
median sediment grain size, to nondimensional flow
intensity
1
W¼ s
qgðs� 1Þd50ð9Þ
where s (N/m2) is shear stress, and q (kg/m3) density
of water, by
U ¼ 401
W
� �3
: ð10Þ
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277 263
Sediment grain falling velocity parameter F in Eq.
(8) is defined as
F ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2
3þ 36m2
gd350ðs� 1Þ
s�
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi36m2
gd350ðs� 1Þ
sð11Þ
where m (m2/s) is the kinematic viscosity of water.
Using s = qgSR, where R (m) is hydraulic radius,
Eqs. (8)–(10) can be rewritten as
qs;m ¼ 40qsF
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigðs� 1Þd350
q1
ðs� 1Þd50
� �3
ðRSÞ3:
ð12Þ
Following Willgoose et al. (1991), by combining
the Manning’s equation V=R2/3 S1/2/n, where V (m/s)
Fig. 3. Map of The Netherlands showing average horizontal transmissivity for those parts of the Pleistocene aquifer that contribute to runoff
(after de Vries, 1974).
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277264
is depth-averaged flow velocity and n is Manning’s
resistance parameter, with the conservation of water
Q =WDV and the assumption that alluvial channels
are much wider than deep, such that RcD, one
yields
R ¼ Qn
WffiffiffiS
p� �3=5
¼ q0:6n0:6S�0:3 ð13Þ
which, after insertion in Eq. (12), gives
qs;m ¼ 40qsF
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigðs� 1Þd350
q1
ðs� 1Þd50
� �3
� q1:8n1:8S2:1: ð14Þ
Setting sediment density qs = 2650 kg/m3, water
density q = 1000 kg/m3, gravity g = 9.8 m/s2, kine-
matic viscosity m = 1.3� 10� 6 m2/s, sediment median
grain size d50 = 0.3 mm (typical sand), gives
qs;m ¼ 1:7381� 107q1:8S2:1 ð15Þ
if qs,m and q are measured in (kg/s/m) and (m3/s/m),
respectively, and
qs;m ¼ 17:4q1:8S2:1 ð16Þ
if qs,m and q are measured in (kg/year/m) and (m3/
year/m), respectively. A final expression gives volu-
metric unit sediment transport qs (m2/year) as (assum-
ing porosity g = 0.4)
qs ¼1
qsð1� gÞ qs;m ¼ 0:0109q1:8S2:1: ð17Þ
Thus, Eq. (4) can be parameterised as
kf ¼ 1 ð18Þ
kt ¼ 0:011 ð19Þ
mf ¼ 1:8 ð20Þ
nf ¼ 2:1 ð21Þ
sc ¼ 0 ð22Þ
pf ¼ 1: ð23Þ
4.1.3. Hydraulic geometry
Hydraulic geometry (Leopold and Maddock, 1953)
relates channel dimensions (width, depth) to flow
discharge. It is used in the CHILD model to dimen-
sionalise fluvial channels and to calculate flow char-
acteristics such as flow depth.
Downstream hydraulic geometry relates bankfull
channel width Wb (m) to bankfull discharge Qb (m3/s):
Wb ¼ kwbQmwb
b : ð24Þ
Analysis of published data for >300 rivers world-
wide (van den Berg, 1995) showed that good approx-
imations are given by,
Wb ¼ 3:65Q0:50b for meandering rivers ðmÞ ð25Þ
Wb ¼ 3:81Q0:69b for braided rivers ðbÞ ð26Þ
which gives
kwb ¼ 3:65 ðmÞ or 3:81 ðbÞ ð27Þ
mwb ¼ 0:50 ðmÞ or 0:69 ðbÞ: ð28Þ
Here, only the meandering (m) cases are used.
At-a-station hydraulic geometry relates instantane-
ous discharge Q to water-body width Wh:
Wh ¼ kwhQmwh : ð29Þ
Recognising that for Q =Qb and Wh =Wb, param-
eter kwh can be expressed as a function of the other
parameters and Qb, leading to
Wh ¼ kwbQmwb�mwh
b Qmwh ð30Þ
where mwh can be interpreted as a channel shape
parameter which essentially determines how fast the
water surface width Wh approaches bankfull (channel)
width Wb when discharge increases towards Qb. In
these simulations, we assume that channels are non-
cohesive, and that
mwh ¼ 0:25 ð31Þ
(Knighton, 1998). It should be further noted that
(bankfull) channel width W is independent from grid
cell interface width x.
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277 265
4.1.4. Bankfull discharge
Current mean precipitation within the southern
Netherlands is about 750 mm/year, about half of
which is lost by evapotranspiration. Mean discharge
hQi (m3/s) at a location within a catchment with
upstream area A (m2) is then
hQi ¼ 0:375A
31 536 000ð32Þ
where the factor 31,536,000 accounts for the conver-
sion between (year) and (s) time units.
The above assumptions were tested by taking the
Maas (Meuse, The Netherlands) catchment as an
example. For this catchment, with a size of 21,300
km2 upstream of station Borgharen, hQi, as calculatedfrom Eq. (32), is 253 m3/s, which compares well with
a measured value of hQi= 230 m3/s.
A general regression of bankfull discharge against
mean annual discharge, based on data presented by
van den Berg (1995) (see Fig. 4), reveals that the
model
Qb ¼ 25hQi0:75 ð33Þ
is a reasonable approximation of the underlying
hydrological regime processes.
Applied to the case of the river Maas, this yields
Qb = 1586 m3/s, which is also in good agreement with
present-day values of Q2.33 = 1616 m3/s (Passchier,
1995).
CHILD parameterises bankfull discharge as Pb (m/
year), which is the effective precipitation rate that
leads to bankfull discharge.
For a catchment with total area Ac, mean discharge
near the outlet is directly related to average precip-
itation rate P (m/year) as
hQi ¼ AcP=31; 536; 000 ð34Þ
and, thus, by definition
Qb ¼ AcPb: ð35Þ
The generic discharge scaling law Eq. (33) with Qb
and hQi in (m3/s), can be expressed for Qb and hQi in(m3/year) as
Qb ¼ 25NhQiN
� �0:75
ð36Þ
where N is the number of seconds within a year
(c 31,536,000). The bankfull event Pb is then
Pb ¼ Qb=Ac ð37Þ
Pb ¼25N
Ac
PAc
N
� �0:75
ð38Þ
Pb ¼ 25P0:75N 0:25
A0:25c
: ð39Þ
Applied to the case P= 0.375 m/year and for a
small catchment of Ac = 1205� 1250 m, this leads to
Pb ¼ 25:4 m=year: ð40Þ
Bankfull discharge events near the outlet are, thus,
generated by rainfall events that are 34 times the mean
rainfall rate. It should be noted that the units in which
Pb is expressed (m/year) do not imply that this effective
precipitation rate is valid on a yearly time scale, but
only for rare (once in 2.33 years) short-duration events.
4.1.5. Diffusional erosion/sedimentation
A number of studies have calculated hillslope dif-
fusivity values from the evolution of escarpments of
known age. For example, in a summary by Martin andFig. 4. Power law regression of bankfull discharge on mean annual
discharge, based on data in van den Berg (1995).
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277266
Church (1997), diffusivity due to slow, continuous
processes is estimated to be in the range 0.0001–0.01
m2/year. Rosenbloom and Anderson (1994) found a
rate of 0.01 m2/year for old marine terraces in Califor-
nia, while McKean et al. (1993) found 0.036 m2/year
for clay soils in California. Lacking better data, a value
of 0.01 m2/year is assigned to warm-phase diffusivity.
Diffusivity values for periglacial environments are
not explicitly listed in the literature. However, rea-
sonable values can be calculated from solifluction rate
measurements, as for example presented by French
(1996), using the following assumptions:
1. The mean movement rate can be approximated as
one quarter of the surface rate.
2. The active layer has a thickness of 50 cm.
Using the diffusional transport equation
qs ¼ KdS ð41Þ
where qs (m2/year) volumetric transport per unit slope
width, and S (m/m) slope gradient, the diffusion
coefficient Kd can then be calculated as
Kd ¼Dzv
Sð42Þ
where Dz (m) is the moving layer thickness and v (m/
year) is the mean downslope movement rate.
Table 3 presents the calculated diffusivity values.
The total range is about 0.01–0.06 m2/year. This
indicates that periglacial solifluction, as compared
with diffusional processes in more temperate environ-
ments, is less effective than one might expect. Given
the fact that solifluction acts in a spatially discontin-
uous manner (e.g. in ‘lobes’), areal average diffusivity
is even smaller. A value of 0.01 m2/year is, therefore,
assigned to cold-phase diffusivity also.
Using a more detailed, physically based temper-
ature- and topography-driven model for gelifluction,
Kirkby (1995) analysed the evolution of gelifluction
rate for Britain during the last 16 kyr. Model results
showed that total diffusivity peaked at c 0.3 m2/year
during the deglaciation, when mean annual temper-
ature passed the 0 jC isotherm. These temporary
effects during cold–warm transitions are not taken
into account here.
4.1.6. Base level changes
Changes in local base level of small rivers within
the Dutch Pleistocene areas depend on the dynamics
of the large river systems as the Maas and the Rhine.
The vertical movements of these rivers (incision and
aggradation) are controlled mainly by eustatic sea-
level change (leading to aggradation in the lower
reaches), climate-induced sediment supply (leading
to aggradation), tectonic uplift of the hinterland (lead-
ing to incision in the upper reaches) and overall
neotectonic activity in the area itself leading to a
complex variation of incising and aggrading stretches.
Local base-level lowering, however, is the driving
ultimate force behind all surface processes, since it
introduces relief and, thus, gradients within the mod-
elled catchment. Obtaining reliable estimates of base-
level change is often hindered by the coarse temporal
resolution of base-level indicators. On the glacial
cycle time scale, dated river terraces can be used to
derive an average rate on this time scale. For example,
the separation of Eemian and Holocene terraces in a
Maas tributary (Vandenberghe et al., 1987) leads to an
average base-level lowering rate of
U ¼ 20 mm=kyr ð43Þ
which is being used in our model experiments.
4.2. Transient evolution of an evolving drainage
network
In this numerical simulation, we investigate the
development of a drainage network in a highly per-
Table 3
Diffusivity values for periglacial areas, as calculated from
solifluction rates presented by French (1996)
Locality Gradient
(j)Rate
(cm/year)
Diffusivity
(m2/year)
Spitsbergen 3–4 1.0–3.0 0.024–0.054
Spitsbergen 7–15 5.0–12.0 0.051–0.056
Karkevagga, Sweden 15 4 0.019
Tarna area, Sweden 5 0.9–1.8 0.013–0.026
Norra Storfjell, Sweden 5 0.9–3.8 0.013–0.054
Okstindan, Norway 5–17 1.0–6.0 0.014–0.025
Ruby Range, YT, Canada 14–18 0.6–3.5 0.003–0.014
Sachs Harbour, Banks Island,
NWT, Canada
3 1.5–2.0 0.036–0.048
Garry Island, NWT, Canada 1–7 0.4–1.0 0.029–0.01
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277 267
meable catchment, under the constraints of alternating
phases of periglacial and temperate climates, repre-
sented as an alternation of high and low values for
transmissivity T (Fig. 5).
All other model parameters are as described in
Section 4.1. The catchment is modelled as a square
1250� 1250 m regular grid, with a grid node
spacing of 25 m. This grid resolution is chosen as
a compromise between the fine resolution required
to resolve for small-scale hillslope processes, and a
coarse grid required for numerical efficiency. Neither
sediment nor water is allowed to leave the grid,
except through the outlet node. Topography is
initialised as ‘random’ (uniformly distributed), with
a very small relief ( < 1 cm). Time step length is not
prescribed to the model. Instead, optimal time step
length is calculated for each time step to as large
possible without causing numerical instability prob-
lems.
Resulting characteristic channel networks during
‘cold’ and ‘warm’ phases, as predicted by CHILD are
shown in Figs. 6 and 7. The temporal evolution of the
drainage density is shown in Fig. 8. It can be clearly
seen that drainage density under cold conditions is
much higher than under warm conditions.
Fig. 9 shows the sediment yield as produced by
the evolving catchment. As can be seen from this
figure, the sediment yield is highly dynamic and
cannot be fully correlated to climate directly. The
course of events during this numerical experiment,
leading to the response in Fig. 9, can be explained as
follows:
0 year. The experiment starts within a cold phase.
Transmissivity is set very low. The landscape is an
initial peneplain with very low relief. Drainage
Fig. 5. Temporal changes in transmissivity, T. Low and high values
indicate ‘cold’ and ‘warm’ conditions, respectively.
Fig. 6. Channel network under ‘cold’ conditions (low trans-
missivity) at time t = 69 kyr. The black lines indicate the flow
network. Grey lines have subsurface discharge only. Line width is
proportional to discharge. The ‘loose’ ends are artefacts of the
runoff scheme and have no physical meaning.
Fig. 7. Channel network under ‘warm’ conditions (high trans-
missivity) at time t = 59 kyr.
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277268
density is very high (essentially l at time t = 0)
because of the swamp-like conditions associated with
this low relief.
0–10 kyr. The system is slowly starting to evolve
towards a dynamic equilibrium state in which all
uplift is compensated for by hillslope erosion. Total
sediment yield is, therefore, slowly rising towards an
equilibrium value (uplift rate times catchment area).
Note that equilibrium is not to be reached within this
simulation’s time span (70 kyr).
10–20 kyr. Onset of the first warm phase. Trans-
missivity increases suddenly, and —in theory—a high
portion of discharge could now be subsurface.
However, most (water table) gradients are too small
to support a large amount of subsurface flow. Surface
runoff, therefore, is only slightly lower than during the
previous phase and, consequently, sediment yield is
still rising, although with a somewhat slower rate.
This small change is in sharp contrast with the sudden
drop in drainage density. The explanation for this
contrast is that during this stage, most sediment is
derived from the lower branches of the channel
network, which do not experience much change in
discharge.
20–30 kyr. The second cold phase. Frozen soils and
low transmissivity cause the channel network to
extend over the whole catchment and sediment yield
is rising faster.
30–40 kyr. The second warm phase. Transmissivity
increases and a high fraction of discharge is now
drained subsurface. The upper parts of the channel
network, as established during the previous phase, no
longer have any surface runoff and, therefore, do not
contribute to fluvial erosion. Sediment yield, there-
fore, decreases significantly. This decrease in drainage
density may be associated with an infilling of (former)
channel heads, leading to a physical or morphological
reduction in drainage density. Alternatively, it may be
associated with a drying up of the former channel
heads, leading to a hydrological reduction in drainage
density. Here, we do not distinguish between the two
types. Uplift (or base-level lowering) is continuing
and the local relief in the catchment is increasing, due
to decoupling of the low-order hillslopes without any
overland flow, and the channels, which are linked to
the local base level.
40–50 kyr. The third cold phase. Again, the channel
network extends over the whole catchment and
sediment yield is rising. The upper parts of the
catchments, which were not affected by fluvial erosion
during the previous phase, are now subject to
temporary intensified erosion. This is due to the larger
gradients here, which were established during the
phase of decoupling of channels and hillslopes. This
causes a (small) peak in sediment yield during the first
part of this phase (indicated by an arrow in Fig. 9).
50–70 kyr. The same cycle as during the previous two
phases. Note that the peak in sediment yield during
Fig. 8. Temporal evolution of drainage density, expressed as the
fraction of computational nodes that have surface runoff. Grey
panels indicate warm phases.
Fig. 9. Sediment yield as modelled (solid line) and under eventual
dynamic equilibrium conditions (dashed line) for an evolving
drainage basin.
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277 269
the first part of the cold phase is larger than that
during interval 40–50 kyr.
A general trend worth noticing is that drainage
density (Fig. 8) is gradually decreasing. Over time,
catchment relief and overall gradients increase, more
water can be discharged subsurface, and fewer chan-
nels are needed to drain surface runoff. As noted
above, the system evolves towards a dynamic equili-
brium between hillslope erosion (or sediment yield)
and uplift (at tH70 kyr). Under these conditions, a
characteristic equilibrium hillslope form emerges,
leading to a characteristic equilibrium subsurface
discharge capacity. Therefore, the eventual equili-
brium drainage density will emerge as that drainage
density that is required to drain the runoff that cannot
be discharged subsurface. A further consequence of
these processes is that while sediment yield is increas-
ing over time, and drainage density is decreasing,
fluvial erosion processes are concentrating in a region
near the channels.
The most important feature of the catchment
response is the high peak in sediment yield, which
is produced during the onset of a cold phase. The
origin of this material is in fact the sediment, which
was not eroded during the preceding warm phase (a
more general analysis of the amount of this material
will be made in the next section).
The building up of this reservoir of erodible
material during the warm phase will be referred to
as the formation of a sediment source space. This
‘space’ should be thought of as an inverse analogue of
the term ‘accommodation space’, as used in basin
sedimentology. Where ‘accommodation space’
denotes (virtual) space where sediment can be stored
(and will, if there is supply), ‘sediment source space’
will denote (virtual) space where sediment can be
derived from (and will, if there is detachment/trans-
port capacity). It should be noted that the removal
of sediment from the ‘sediment source space’ is
not hindered by a too low erodibility, but by a lack
of sufficient overland flow, because of subsurface
drainage.
The ‘sediment source space’ is, thus, created or
‘filled’ by increasing relief near the channels, caused
by uplift-driven channel incision during warm peri-
ods, and ‘emptied’ by channel network expansion
during cold periods.
4.3. Analysis of the volume of the ‘sediment source
space’
As outlined in the previous section, a temporary
peak in sediment yield at the beginning of a cold period
is caused by the introduction of extra disequilibrium
during the preceding warm phase: the formation of the
‘sediment source space’ by gradual base-level low-
ering, which is emptied during the cold phase.
The volume of the ‘sediment source space’, or the
subsequent peak in sediment yield, is determined by
the depth and the areal extent of those areas within the
catchment that are subject to (fluvial) erosion during
cold phases, but not during warm phases. Adjacent
hillslopes (i.e. those parts of the catchment which are
not subject to fluvial erosion during both cold and
warm phases) do not contribute directly to the for-
mation of ‘sediment source space’.
During dynamic equilibrium conditions (not
reached during the model experiment discussed so
far), the depth of this volume is equal to the increase
in relief between hillslopes and channels during the
warm phase. Alluvial channels in dynamic equilibrium
are coupled to the catchment base level, and the
increase of relief is, thus, equal to the total rate of
base-level change or uplift U, times the length of the
warm phase Dtw. Depth of the ‘sediment source space’
is then UDtw.
Figs. 10 and 11 show the slope–area plots of the
catchment at the end of cold and warm phases,
respectively. It can be clearly seen which parts of
Fig. 10. Slope–area diagram of a typical ‘cold’ situation (t = 69
kyr).
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277270
the catchment (as expressed by contributing area) are
affected mostly by changes in transmissivity.
From Eq. (5), it follows that saturation occurs
where
A
SzTxP
ð44Þ
which is indicated in Figs. 10 and 11.
The channels, which are constrained to this satu-
ration domain, are approximated by (Tucker and Bras,
1998):
Seq ¼UA1�m
kfPm
� �1=n
ð45Þ
under dynamic equilibrium conditions. As can be seen
in Figs. 10 and 11, this equilibrium gradient is reached
during the simulations because (alluvial) channels have
a much shorter relaxation time than the hillslopes do.
The intersection of Eqs. (44) and (45) indicates the
position of the channel head (arrow). As shown by
Tucker and Bras (1998), this position is given by
As ¼T
nmþn�1ð ÞU 1
mþn�1ð Þ
k1
mþn1�ð ÞP mþnmþn�1ð Þ : ð46Þ
A comparison of Figs. 10 and 11 shows that (all
else being equal) the channel head position shifts in
time, as function of changes in transmissivity:
As;cold ¼ 2:8� 103 m2 ð47Þ
As;warm ¼ 2:9� 104 m2: ð48Þ
The area which is affected by alternating fluvial/
nonfluvial conditions is, thus, the range of locations
where
As;cold < A < Aswarm : ð49Þ
The total area for which Eq. (49) is valid is a
function of network structure, and can be determined
by analysing the cumulative distribution of contribu-
ting area. Fig. 12 shows this distribution as a cumu-
lative areal fraction P(A>a) plotted on logarithmic
axes.
The fraction A* of total catchment area which is
upstream of the channel heads then equals
1�P(A>As) and, thus, for cold and warm phase
channel heads:
Acold* ¼ 0:76 ð50Þ
Awarm* ¼ 0:89: ð51Þ
This indicates that 0.89–0.76 = 13% of the total
catchment contributes to the formation of a ‘sedi-
Fig. 11. Slope–area diagram of a typical ‘warm’ situation (t = 59
kyr).
Fig. 12. Cumulative distribution of contributing area, plotted as
cumulative areal fraction. Dotted lines indicate channel head
position during cold and warm phases.
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277 271
ment source space’, whose total volume is then
given by
Vs ¼ 0:13AcUDtw: ð52Þ
4.4. Impact of hydrological regime
As discussed above, the hydrological regime under
temperate conditions is significantly different from
that under periglacial conditions, the latter being more
‘flashy’ or ‘peaked’ than the former.
To investigate the role of hydrological regime, a
series of simple numerical model experiments were
designed. In reality, processes like snow pack for-
mation and melting are responsible for the highly
peaked nival regimes of periglacial climates. How-
ever, explicit modelling of these processes would
require additional model parameters and model input,
especially high-resolution temperature time series.
Here, we assume that (changes in) the resulting
probability distribution of water application to the
land surface is much more relevant than the details
on how it originates. Therefore, we directly change
this distribution. Four scenarios have been investi-
gated, spanning the continuum from a ‘flat’ regime,
where precipitation and/or channel flow occurs at an
equal rate throughout time, towards a highly peaked
regime, where channel flow occurs only 12% of the
time. Intermediate scenarios are where channel flow
occurs at 50% and 25%, respectively. Total annual
effective precipitation is kept constant at 375 mm/
year.
Fig. 13 shows the catchment response, in terms of
sediment yield, to these four scenarios. The impact of
hydrological regime is twofold:
Sediment yield is higher for more peaked
regimes. This can be explained by the more-
than-linear relation of overland flow discharge
and sediment detachment and transport. Since the
long-term average sediment yield is constrained
by uplift or local base-level lowering rate, this
also implies that equilibrium will be reached
much faster under peaked regimes than under a
flat regime. The peak in sediment yield during the first part of
cold phases is higher for more peaked regimes.
This can also be attributed to the greater effective-
ness of the concentrated flow events associated
with this regime.
Using a comparable (but stochastic, and for a
different runoff-generating mechanism) numerical
experimental setup, Tucker and Bras (2000) obtained
similar conclusions: they found that increased climatic
variability results in higher erosion rates, a higher
drainage density and reduced relief.
Fig. 14 and Table 4 show a comparison of the
area–slope diagrams of the catchment under typical
‘warm’ and ‘cold’ climates, for two extreme flow
regimes, i.e. the most flat and the most peaked of the
four regimes above. The immediate difference
between the two regimes is that the contributing area
for the channel head is, for the warm as well for the
cold climate, a factor of 5 smaller for the most peaked
regime, than for the flat regime. More importantly, if
we make the assumption that a flat hydrological
regime is typical for a warm climate, and a peaked
regime for a cold climate, the difference in warm/cold
channel head contributing area increases from a factor
of 15 to a factor of 85. The changes in hydrological
regime that can be expected under alternation between
temperate and periglacial climate, thus, has a large
impact on the total area affected by the ‘sediment
source space’ (Table 4).
Fig. 13. Sediment yield for different hydrological regimes. (a) ‘Flat’
regime with even discharge throughout the year. (b) All discharge
within 50% of time. (c) All discharge within 25% of time. (d) All
discharge within 12.5% of time. Grey bars indicate warm periods
(high transmissivity).
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277272
4.5. Long-term evolution
The modelling examples presented so far did not
drive the system towards a state of dynamic equi-
librium. Therefore, an additional experiment has
been set up, in which the model was run for 400
kyr, using alternating warm and cold periods of 10
kyr each. The results, shown in Fig. 15, indicate
that equilibrium is approached only after c 0.5
Myr.
This experiment further shows that the peak in
sediment yield at the beginning of cold periods is
increasing in magnitude during the first c 250 kyr.
The real-world relevance of this experiment as a case
study, however, is limited. Most unconsolidated sandy
deposits experiencing alternations of temperate and
periglacial temperature regimes also experience aeo-
lian disturbance during the cold, dry periods of the
Quaternary (e.g. Late Pleniglacial; Kasse, 1997). It
can, thus, be expected that local relief is smoothed out
by aeolian processes.
Fig. 14. Comparison of area-slope diagrams for a catchment subjected to ‘flat’ or ‘peaked’ discharge regimes, under ‘cold’ and ‘warm’ climatic
conditions. Arrows indicate the position of the channel head. See also Table 4.
Table 4
Statistics for channel head locations in Fig. 14
Regime, climate As P (A>As)
Flat, warm 5�104 0.09
Flat, cold 4�103 0.22
Peaked, warm 1�104 0.16
Peaked, cold 6�102 0.40
Fig. 15. Long-term evolution of a channel network system under
alternating temperate periglacial climates. The dashed line indicates
sediment yield under dynamic equilibrium conditions.
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277 273
5. Concluding remarks
The numerical model experiments presented show
clearly the response of (alluvial) channel networks and
associated sediment yield to climate induced changes
in subsurface hydrological parameters. Channel net-
works expand under periglacial conditions, and con-
tract under temperate conditions. A distinctive peak in
sediment yield is expected during a warm–cold tran-
sition, and is explained by the formation of a ‘sediment
source space’ in the upslope parts of the catchment. The
magnitude of this sediment yield peak is shown to be
controlled directly by the size of this ‘sediment source
space’, which itself is a function of relative uplift rate
and areal extent of those regions within the catchment
which have no surface runoff during the warm climatic
phase. A predictive equation for this sediment yield
peak is derived.
These results offer a good explanation for the
occurrence of dry valleys in many west and central
European catchments, and are in line with previous
field-based reconstructions of channel network loca-
tion and fluvial activity within these areas (Vanden-
berghe et al., 1987; Bohncke and Vandenberghe,
1991; Kasse, 1997). The presence of a thick uncon-
solidated Quaternary substratum, and the alternating
cold and warm phases of the Pleistocene provide
favourable conditions for these processes. The pro-
cesses described in this paper offer a good explanation
for the reconstructed changes in fluvial activity.
We have also shown that sediment yield from these
catchments is highly sensitive to the runoff regime. A
more peaked regime is associated with more effective
detachment and transport, resulting in higher sediment
yields and a shorter relaxation time of the system.
Although this paper is concerned primarily with
lower order catchments, it must be stressed that the
processes described here have a large impact beyond
these catchments. The dynamics of alluvial rivers is
determined by the amount of water and sediment
entering these rivers. Apart from within-catchment
sediment storage, the sediment yield from small catch-
ments will equal the sediment supply for a large-scale
river system. The periglacial extension of low order
networks, combined with peaked discharges is, there-
fore, a plausible explanation for river aggradation
under periglacial conditions, and incision under tem-
perate conditions. This type of behaviour is confirmed
in numerous studies (e.g. Budel, 1977; Huisink, 1999;
Mol, 1997).
These results further imply that the relationship
between climate and sediment yield/supply can be
highly nonlinear, and that the most pronounced sedi-
ment supply and fluvial activity can occur during a
climatic change, which is in line with previous model-
ling results (Tucker and Slingerland, 1997). This type
of response was previously recognised by, for example
Vandenberghe (1993), who attributed this enhanced
activity to time lags between climate and vegetation.
The results described here offer an alternative explan-
ation, although both factors may play a role.
A potentially important process, excluded from the
numerical experiments described here, is the impact of
aeolian processes. Aeolian activity is especially strong
in catchments consisting of sandy substrate during
Glacial periods because of the lack of vegetation and
the dry soil conditions (e.g. Kasse, 1997). One of the
central processes addressed in this paper is the alter-
nating active/inactive state of the first order segments
of the stream network. A possible mechanism is that
channel erosion within these segments during cold
periods (when they are active) is compensated by
aeolian input: these channel segments form local
depressions in the topography, and thus stimulate
aeolian deposition (because of air flowline diver-
gence) and prevent detachment by wind (because of
the wetness-induced aeolian erodibility). In fact, aeo-
lian infilling of fluvial channels has been found
(Kasse, 1997). A proper quantitative model-based
analysis of this aeolian–fluvial competition would
require the inclusion of process-based aeolian pro-
cesses within the model framework described.
In the model experiment described here, no consid-
eration is given to the form in which precipitation falls.
This can be as rain, as snow or as rain on snow. Instead,
a more simple approach has been adopted, in which it is
assumed that the exact source of water is less relevant
than the probability distribution of water supply to the
surface. Improvements of this approach can bemade by
using detailed process-based models for snowmelt and
storage and the water balance for the upper soil layers.
Such an enhanced model may better predict the prob-
ability distribution of water supply directly from cli-
mate and surface and soil properties data. However,
such a detailed modelling approach would require
additional data and model applications on a time scale
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277274
of days, which is beyond the scope of the present paper,
but may be the subject of further study. Furthermore,
(climate related) changes in evapotranspiration rates
are not taken into account yet.
Finally, it must be emphasised that although a
quantitative numerical model has been used in this
study, a precise quantitative relationship between soil
physical parameters, groundwater hydrology and (flu-
vial) erosion/deposition is not yet feasible. A number of
factors that were not accounted for in these numerical
experiments, for instance includes the impact of vege-
tation, soil erodibility, noncontinuous mass movement
processes and explicit groundwater tables. de Vries
(1994), for instance, showed that stream density in the
present warm phase is strongly related to average depth
of the groundwater table; the latter being a measure for
the groundwater storage capacity in this shallow aqui-
fer area. In addition, little is yet known of palaeo-
precipitation and -permafrost occurrence in a more than
indicative sense. These additional factors and a more
detailed model-data comparison will be the subject of
further study.
Notation
A Contributing area (m2)
Ac Total catchment area (m2)
As Threshold contributing area for saturation
(m2)
Av Grid cell area (m2)
D Channel depth (m)
Db Bankfull channel depth (m)
Dh Hydraulic channel depth (m)
d50 Median sediment grain size (m)
g Gravitational acceleration (m/s2)
Kd Hillslope diffusivity (m2/year)
kdb Downstream hydraulic geometry depth co-
efficient
kdh At-a-station hydraulic geometry depth coef-
ficient
kf Sediment transport coefficient
kt Sediment transport coefficient
kwb Downstream hydraulic geometry width co-
efficient
kwh At-a-station hydraulic geometry width coef-
ficient
mf Discharge exponent in sediment transport
equation
mdb Downstream hydraulic geometry depth ex-
ponent
mdh At-a-station hydraulic geometry depth ex-
ponent
mwb Downstream hydraulic geometry width ex-
ponent
mwh At-a-station hydraulic geometry width expo-
nent
N Number of days within 1 year
n Manning’s flow resistance factor
nf Slope exponent in sediment transport equa-
tion
P Precipitation rate (m/year)
Pb ‘Bankfull’ precipitation rate (m/year)
p Sediment transport exponent
Q Discharge (m3/s)
Qb Bankfull discharge (m3/s)
q Discharge per unit channel width (m2/s)
hQi Mean discharge (m3/s)
Qs Sediment transport rate (m3/year)
qs Sediment transport per unit channel width
(m2/year)
qs,m Mass unit sediment transport rate (kg/m/year)
R Hydraulic radius (m)
S Topographic gradient along flow path (m/m)
Seq Equilibrium gradient (m/m)
s Specific sediment density (qs/q)T Transmissivity (m2/year)
t Time (year)
U Uplift or base-level change rate (m/year)
V Depth averaged flow velocity (m/s)
Vs Volume of ‘sediment source space’ (m3)
v Average downslope gelifluction rate (m/year)
W Channel width (m)
Wb Bankfull channel width (m)
z Elevation above base level (m)
Dtw length of warm period (year)
Dz Thickness of active layer (m)
g Sediment porosity
q Mass density of water (kg/m3)
qs Sediment mass density (kg/m3)
s Shear stress (N/m2)
sc Critical shear stress (N/m2)
U Sediment transport number
W Flow number
m Kinematic viscosity of water (m2/s)
x Width of interface between adjacent grid
cells (m)
P.W. Bogaart et al. / Geomorphology 54 (2003) 257–277 275
Acknowledgements
The Netherlands Organisation for Scientific Re-
search (NWO) is thanked for providing a travel grant
to the first author. Prof. Dr. J. Vandenberghe, Dr. C.
Kasse, Dr. R.T. van Balen, Dr. T. Dunne and an
anonymous reviewer are thanked for constructive
comments on an earlier draft of this paper.
This is a contribution to the Netherlands Environ-
mental Earth System Dynamics Initiative (NEESDI)
programme, partly funded by the Netherlands
Organization for Scientific Research (NWO grant
750.296.01).
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