Hydrological process representation at the meso-scale:
the potential of a distributed, conceptual catchment model
Stefan Uhlenbrook*, Stefan Roser, Nils Tilch
Institute of Hydrology, University of Freiburg, Fahnenbergplatz, D-79098 Freiburg, Germany
Accepted 23 December 2003
Abstract
In order to achieve a process-oriented simulation of hydrological processes in a meso-scale basin (101–103 km2), the
spatially and temporally variable basin inputs (precipitation and energy) and runoff generation processes need to be adequately
addressed by the model. The catchment model TACD (tracer aided catchment model, distributed) is based on experimental
results including tracer studies at the mountainous Brugga basin (40 km2). This raster-based model (50 £ 50 m2) works on an
hourly basis, thus capturing the spatially and temporally variable inputs and processes. The model contains a process-realistic
description of the runoff generation mechanism, which is based on a spatial delineation of eight units with the same dominating
runoff generation processes. This defines the model structure and enables efficient model parameterisation. The model uses
linear and non-linear reservoir routines to conceptualise runoff generation processes, and includes a routing routine (kinematic
wave approach) to simulate surface runoff.
The model is successfully applied to a 1-year period following minimal calibration (model efficiency 0.94). In addition, the
runoff from both an independent 3-year period for the Brugga basin and a sub-basin (15.2 km2) is modelled well (model
efficiencies 0.80 and 0.85, respectively) without re-calibration. The use of tracer data (i.e. dissolved silica) measured in outlet
discharge demonstrates that the temporal mixing pattern of different runoff components is modelled correctly (multiple-
response validation). The results show that a validated process-based model that correctly simulates the origin of runoff
components and flow pathways must be the basis for integrating solute transport modelling of non-conservative species. Such a
model can serve as tool to make predictions and test hypotheses about the first-order controls on hydrological responses.
q 2004 Elsevier B.V. All rights reserved.
Keywords: Rainfall runoff modelling; Runoff generation; Dissolved silica; Tracer aided catchment model; Model validation; Tracer data
1. Introduction
The satisfactory modelling of hydrological
processes in meso-scale basins (approximately 101–
103 km2; Bloschl, 1996) is essential for optimal
protection and management of water resources at this
scale. If the aim of a modelling study is to reproduce
Journal of Hydrology 291 (2004) 278–296
www.elsevier.com/locate/jhydrol
0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.jhydrol.2003.12.038
* Corresponding author. Tel.: þ49-761-2033520; fax: þ49-761-
2033594.
E-mail address: [email protected]
(S. Uhlenbrook).
only the daily runoff dynamics, a simple lumped
model that can be calibrated to observed data is
sufficient (e.g. Jakeman and Hornberger, 1993;
Beven, 2001). However, if distributed calculations
are required as part of an environmental modelling
approach, a more complex and distributed model
needs to be applied. In particular, if estimations
(extrapolations) for the future under changed circum-
stances (i.e. altered land use, climate change) are
sought, purely statistical or lumped approaches reach
their limit and a model that contains process-realistic
descriptions for all hydrological processes is required.
The processes dominating hydrological response
differ at various spatial scales (e.g. Bloschl and
Sivapalan, 1995; Bloschl, 1996). Even if many
questions concerning scale issues remain unanswered,
the following generalized scheme can be assumed for
temperate zone catchments without large proportions
of urban land use. (i) In micro-scale catchments (i.e.
headwater catchments less than about 1 km2),
response to rainfall is dominated mainly by the runoff
generation processes at the hillslopes and near stream
areas (e.g. Anderson and Burt, 1990; McDonnell,
1990; Montgomery et al., 1997). All processes that
define the lateral movement of water on top of the soil,
or within the unsaturated and saturated zones are the
first-order controls. Thus, soil properties and land use
play key roles. Finally, the spatial distribution of
rainfall can be assumed to be much more uniform than
in larger basins. (ii) In meso-scale basins, processes
from smaller scales combine in a complex way to
produce an integrated response. Identifying basin
wide areas with the same dominating runoff gener-
ation processes is currently a major challenge in
runoff generation process research (e.g. Peschke et al.,
1999; Scherrer and Naef, 2003; Uhlenbrook, 2004).
Channel processes (i.e. runoff routing, groundwater–
surface water interactions) gain increasing importance
with increasing catchment area at this scale. (iii) At
the macro-scale (basins larger than 1000(0) km2), the
spatial and temporal distribution of rainfall or snow
melt and the routing of runoff are dominant. Recently,
Bardossy et al. (2002) showed the marginal influence
of different soil properties or land use covers (i.e.
increasing urbanization) on flood runoff of larger
events in the river Rhine.
In summary, the interesting challenge of working
at the meso-scale as an intermediate scale is
three-fold. First, the distributed runoff generation
processes need to be understood and captured by the
chosen model. Second, the spatial and temporal
variability of atmospheric forces and runoff concen-
tration is significant and needs to be included in the
model. Third, as this scale is crucial for water
management issues, addressing several societal
demands, it requires particular attention.
To capture the hydrological processes at the meso-
scale, different models with various ranges of
complexity were suggested (Singh, 1995). On one
hand, increased computer capabilities have made
possible the development and application of distrib-
uted and largely physically based models that work at
a highly detailed spatial and temporal resolution (e.g.
MIKE-SHE, Refsgaard and Storm, 1996; KINEROS,
Smith et al., 1995). However, the enormous data
requirements often prevent the extensive use of these
models, particularly in basins larger than experimen-
tal headwaters. In addition, further limitations of these
models are obvious, e.g. the application of small-scale
physical equations derived in laboratories to larger
heterogeneous areas, or the sub-grid variability (for
detailed discussion see Beven, 1996, 2001). On the
other hand, conceptual rainfall runoff models (e.g.
TOPMODEL, Beven and Kirkby, 1979; HBV,
Bergstrom, 1992) are less complex and the required
input data are available for most applications. Never-
theless, the model parameters are often not physically
based or clearly related to catchment properties and an
equifinality problem (different models or parameter
sets reach equally good simulation results) exists (e.g.
Beven and Binley, 1992). This makes model appli-
cation in ungauged basins difficult. In addition, a high
degree of model structure uncertainty exists (e.g.
Grayson et al., 1992; Seibert, 1999), as the structure
should be consistent with the perceptual (conceptual)
model of the investigated basin. The perceptual model
describes the ‘basin functioning’ and is based on
experimental investigations. Of course, this could be
different for every basin, thus the application of a
standard model and fitting by parameter calibration
might lead to models that ‘… are working right, but
for the wrong reasons’ (Klemes, 1986). Other sources
of model uncertainty, such as the error of input data
and its spatial regionalization to basin scale as well as
the lack of understanding of the dominant processes
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296 279
and their mathematical descriptions are discussed in
further detail by Beven (2001).
Because of these uncertainties it is clear that
calibrating model parameters to produce a close fit
between measured and simulated runoff is not a
rigorous enough test of the model, as it does not
guarantee accurate representation of internal hydro-
logical processes. This highlights the need for
additional data to evaluate model performance (e.g.
Kuczera and Mroczkowski, 1998). This additional
data can be, for instance, hydrochemical data
(Mroczkowski et al., 1997), groundwater levels
(Lamb et al., 1998; Seibert, 1999), environmental
isotopes sampled during events (Seibert and McDon-
nell, 2004), or sampled continuously (Uhlenbrook and
Leibundgut, 2002), and the distribution of saturated
areas (Ambroise et al., 1995; Franks et al., 1998;
Guntner et al., 1999a).
The objectives of this paper are, first, to introduce a
modelling approach able to translate runoff generation
process understanding into a catchment model for the
meso-scale. The second is to model continuously all
dominating hydrological processes (not only event
based), distributed (50 £ 50 m2) on an hourly resol-
ution using only minimal calibration. Third, this paper
seeks to use information in addition to total basin
discharge for analysing the model performance
(multiple-response validation). Therefore, runoff
data from a sub-basin is applied to test the model’s
ability to predict space–time variability of stream
flow. In addition, the concentration of a natural tracer
(i.e. dissolved silica) is used to check the temporally
variable composition of runoff components. Finally,
although this model is site-specific in its current form,
the applicability of the modelling approach to other
catchments based on knowledge of local processes is
discussed.
2. Study site
The study was performed in the meso-scale Brugga
basin (40 km2) and the sub-basin St. Wilhelmer
Talbach (15.4 km2; see Fig. 1), located in the southern
Black Forest in southwest Germany. The test site is
mountainous with elevations ranging from 438 to
1493 m a.m.s.l. and a nival runoff regime. The mean
annual precipitation amounts to approximately
1750 mm generating a mean annual discharge of
approximately 1220 mm. The gneiss bedrock is
Fig. 1. The meso-scale mountainous Brugga basin with monitoring network and land use.
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296280
covered by soils, debris, and drift of varying depths
(0–10 m). Soil hydraulic conductivity is generally
high: the infiltration capacity is too high to generate
infiltration excess except in some urban areas. Water
saturated areas cover 6.2% of the catchment and are
not considerably variable in their spatial extent
(Guntner et al., 1999a,b). Mostly, they are directly
connected to the river system. The study site is widely
forested (75%) and the remaining area is pastureland;
urban land use is less than 2% of the total area.
3. Previous investigations at the Brugga basin
3.1. Experimental process investigations
Detailed experimental investigations were carried
out using artificial and naturally occurring tracers.
This helped to identify runoff sources and flow
pathways, quantify runoff components, and date the
age of different water compartments (details are given
in Uhlenbrook et al., 2002). It was shown that surface
runoff is generated on sealed or saturated areas. In
addition, fast runoff components are generated on
steep highly permeable slopes covered by boulder
fields. Sub-surface storm flow components can also
be generated at hillslopes with permeable soil and
(peri-)glacial drift material, which is situated above
the almost impermeable bedrock, or at the drift cover
layers with significantly reduced permeability. Soil
water displacement takes place here, as mostly pre-
event water was observed at the bottom of hillslopes
during flood formation. Base flow components
originate from the fractured hard rock aquifer and
the deeper parts of the weathering zone. There is no
evidence that these components are important for
flood formation.
The contributions of (i) surface and near surface
runoff, (ii) shallow groundwater originating from the
hillslopes, and (iii) deep groundwater (deeper parts of
weathering layer and fissured aquifer) during a 3-year
period based on oxygen-18 and tritium measurements
were 11.1, 69.4 and 19.5%, respectively (Uhlenbrook
et al., 2002). Even if a relatively large uncertainty
should be considered for these numbers, this never-
theless demonstrates clearly the dominance of the
flow systems at the hillslopes. For short periods during
events, the proportion of surface and near surface
runoff components may increase to more than 50% as
shown by hydrograph separations for different events
in the Brugga and the neighbouring Zastler basin
(Uhlenbrook, 1999; Hoeg et al., 2000; Uhlenbrook
et al., 2002).
3.2. Modelling investigations
Different catchment models have been applied to
the Brugga basin, but none was able to capture
adequately the dominating runoff generation pro-
cesses. TOPMODEL (Beven and Kirkby, 1979)
yielded good simulations of total runoff, but required
a large spatial and temporal variation of simulated
saturated areas, which is not reasonable considering
the basin characteristics (Guntner et al., 1999a). The
HBV model (Bergstrom, 1992) also simulated
the overall runoff dynamics well, but the structure of
the classical response function did not agree with the
process understanding (Uhlenbrook et al., 1999).
Mehlhorn (1999) applied the PRMS/MMS model
(Leavesley et al., 1983) and Eisele et al. (2001) the
NPSM model (US-EPA, 1998) with reasonable
success for modelling total runoff. But similar
provisos had to be made, as the model structures
were often invalid and not in line with the results of
the experimental findings.
The process-oriented tracer aided catchment
(TAC) model, a previous version of the model
presented in this paper, was based on the experimental
findings in that the runoff generation routine was
designed in a way that captured the process under-
standing (Uhlenbrook and Leibundgut, 2002). Its
spatial discretization is based on a delineation of units
with the same dominating runoff generation pro-
cesses. Therefore, extensive field mapping was
carried out. For each of the units, a specific runoff
generation routine was developed using linear and
non-linear storage routines. The other model modules,
i.e. the evapotranspiration module or snow and soil
module, were adapted from other conceptual catch-
ment models (e.g. the HBV model). The model is
semi-distributed, as it uses 100-m intervals of
elevation and the proportional distribution of the
units within each interval. It was applied using daily
values with good success. In particular, the use of
tracer data showed that not only was the total runoff
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296 281
computed accurately, but the contribution of different
runoff components was also modelled correctly.
Comparison of the TAC model to an artificial
neutral network demonstrated that TAC utilizes a
larger amount of information from the input data set to
simulate daily discharge (Lischeid and Uhlenbrook,
2003). However, it was shown that the appropriate
modelling time step must be shorter than daily values
to be in line with the process time scale when
modelling dissolved silica at the basin outlet. Other-
wise, the hysteresis loops in the discharge–silica
concentration relationship will not be captured.
4. The TACD model
4.1. General structure and different modules
4.1.1. General
The TACD (tracer aided catchment model, dis-
tributed) model is a conceptual rainfall runoff model
with a modular structure. It can be applied on an hourly
basis, and is fully distributed, i.e. using 50 £ 50 m2
grid cells as spatial discretization. The water is routed
between the cells applying the single-flow direction
algorithm (D8), which is suitable for the mountainous
basin where the water flow direction is dominated by
the steepest gradient (Guntner et al., 1999b). It is
coded within the geographical information system
(GIS) PC-Raster (Karssenberg et al., 2001) that offers
a dynamic modelling language. The newly developed
runoff generation module, in combination with a
delineation of hydrological functional units, is the core
of the model (see Section 4.2); the other modules were
adapted from the literature and modified for the
specific circumstances at the mountainous test site.
4.1.2. Model input of meteorological parameters
Precipitation (mm h21) was observed at up to
seven stations in and around the Brugga catchment
(Fig. 1). Three stations collected data hourly or at
even higher resolution; four stations (daily values)
were disaggregated to hourly resolution by transfer-
ring the temporal pattern of the closest station. Due to
gaps in the records, an average of 5.9 and 6.3 values
per hour were available for the calibration and
validation period, respectively. The systematic error
caused by wind was corrected using an approach of
Schulla (1997)
Pcorr ¼ Pobsða þ buwÞ ð1Þ
with Pcorr (mm h21) as corrected precipitation, Pobs
(mm h21) as observed precipitation, uw (m s21) as
wind velocity, and the parameters a (–) and b (s m21)
with the parameter values of 1.01 and 0.01, respect-
ively. The wind velocity was measured at three stations
within the catchment and transferred to the other
stations by using the closed station directly. The
undercatch of solid precipitation was corrected in the
snow module (see below). A combined inverse
distance method (80%) and an elevation gradient
method (20%) were used for regionalization to
catchment scale. For this purpose, the non-linear long
term precipitation–elevation regression ðPrecip ¼
2100ð1 2 expð20:0027elevationÞÞwas used to extrap-
olate the basin precipitation per modelling time step to
the respective elevation of each grid cell. Thereupon a
weighted average was calculated to get the precipi-
tation for each cell and time step. Therefore, the value
obtained from the elevation was weighted with 20%
and the value obtained from the inverse distance
weighting method was weighted with 80%. This was
done because of an observed elevation dependence of
precipitation that was found for longer time intervals
(monthly, yearly), but which was not always observed
for shorter time steps in the mountainous test site.
During storms, the location of the rain cell is more
important than elevation. Consequently, the used
regionalisation scheme is a compromise to capture
the spatial distribution during shorter time intervals but
also to reproduce the long-term pattern.
Temperature (8C) was observed at seven locations
in and around the Brugga catchment, and data from
5.8 stations per hour, on average, were available. It
was regionalized with a temporal variable elevation
gradient whereby two different gradients were used
for the upper and lower parts of the catchment if a
temperature increase was found at higher elevations
(inversion).
4.1.3. Evapotranspiration
The potential evapotranspiration was calculated
using the approach from Turc-Wendling, as its results
are generally equal to that of the Penman formula
while using fewer parameters (DVWK, 1996). This
approach incorporates hourly temperature, sunshine
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296282
duration, and potential radiation (W m22). The latter
is calculated for every hour and raster cell using the
model POTRAD version 5 (van Dam, 2000), taking
into account the topography (slope, aspect, and
shadowing effects), solar geometry (declination of
the sun, latitude, and azimuth angle), and sunshine
duration. The estimated radiation was compared with
measured radiation at two locations for certain periods
with good success. The sunshine duration (–) is a
value between 0 and 1 that expresses the portion of
direct sunshine within the simulated hour. It was
measured at four stations and regionalized by the
inverse distance weighting method. The actual
evapotranspiration was computed depending on the
soil moisture availability at each cell. Evaporation of
snow was considered by monthly variable values of
0.01–0.3 mm d21 (DVWK, 1996).
4.1.4. Snow module
The precipitation input was processed through a
snow module, which is based on a temperature index
method. The present module was adapted from the
HBV model (Bergstrom, 1992). Precipitation is
modelled as snow if local air temperature is below
the threshold temperature TT (8C). This parameter was
varied for forested and non-forested areas to account
for different snow accumulation and melt conditions.
The other two parameters are CFMAX
(mm h21 8C21), which defines the melted water per
hour and per degree Celsius above the temperature
threshold. SFCF (–) (snow fall correction parameter)
accounts for the systematic error during snowfall
measurement by multiplying the fallen precipitation
at each cell with this parameter. Melted snow water
flows to the interception and soil module, but can be
stored in the snow cover with up to 10% of the water
equivalent. If the air temperature falls below TT, the
stored melt water can refreeze. The amount of
refreezed water melt is defined as 5% of CFMAX
multiplied with the difference of TT and the
temperature at the respective time step. Both percent
values were obtained from Bergstrom (1992).
4.1.5. Interception and soil water module
In unit types with a soil zone (all units except those
with dominating Hortonian or saturation overland
flow; see Section 4.1.6) a combined interception and
soil water module is used. The method was adopted
from the HBV model (Bergstrom, 1992), as it
realistically mirrors processes at the considered
scale, but has only two parameters: the maximal
stored water, FC (mm), and a parameter that describes
the water transfer to the runoff generation routine
BETA (–). The latter can be interpreted as a macro-
porosity parameter, and along with soil character-
istics, magnitudes of parameter values can be derived
if different soil types are compared to each other.
Parameter values of FC for each raster cell can be
estimated using soil and vegetation maps. The
realistic description of the soil processes is based on
the fact that deeper percolation is possible before field
capacity (defined by FC) is reached. This is calculated
depending on actual soil moisture using a non-linear
function that is defined by BETA (Bergstrom, 1992).
4.1.6. Routing module
TACD used the kinematic wave approach (Chow
et al., 1988) to simulate runoff routing in the stream
network. The differential equation for calculating flow
applies an iterative scheme by using finite differences
with an implicit non-linear approach. For the applied
cell size of 50 £ 50 m2, the suitable simulation time
step was found to be 60 s. This was examined through
numerical experiments checking the hydrograph
shape and the water balance.
The channel network was digitized from topo-
graphic maps (1:10,000), confirmed in the field, and
modified at some places due to local phenomena. The
routing module requires channel slope at each
location; this was derived from the digital elevation
model (DEM). The assumption that the slope of the
‘energy line’ equals the slope of the riverbed (i.e. not
having significant backwater effects) is appropriate for
the steep mountainous test site. To set a realistic
channel length for the often winding streamline, the
mean length of the digitized channel network per
channel cell was set to 60.6 m, also taking into account
the slope of the channel cells. Channel widths were
estimated by an empirical relationship that describes
the width as a function of the local drainage area at
each cell (Fig. 2). The empirical function ðr2 ¼ 0:90Þ
was derived from 30 measurements of channel widths
at different locations within the test site. The channel
width varies between 1 and 6 m for cells with a local
drainage area of more than 0.5 km2. For small streams,
the width was estimated by visual observation to 0.3,
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296 283
0.6, and 1 m for local drainage areas of less than 0.1,
0.1–0.3, and 0.3–0.5 km2, respectively. The rough-
ness coefficients (Manning’s n) were estimated
according to Barnes (1967) and amounted to about
0.08 for small mountainous streams and 0.06 for
somewhat larger streams near the outlet.
4.2. Runoff generation module and spatial delineation
of hydrological functional units
4.2.1. Spatial delineation of units with the same
dominating runoff generation processes
The characteristics of the land use, soil, and drift
cover determine the dominating runoff generation
processes, i.e. the storage and transmission of lateral
flow at the surface or the sub-surface. Uhlenbrook and
Leibundgut (2002) used an empirical approach to
delineate areas with the same dominating processes
by overlaying different spatially distributed data: a
forest habitat map (FVA, 1994), a map of saturated
areas (Guntner et al., 1999b), geological maps
(1:25,000 and 1:50,000), the drainage network, and
a DEM with a grid size of 50 £ 50 m2 (vertical
resolution: 0.1 m). In addition, the drift cover types
were mapped during a field survey (Rutenberg et al.,
1999; Uhlenbrook, 2004). Based on that and on
previous experimental process investigations (Hoeg
et al., 2000; Uhlenbrook et al., 2002), Tilch et al.
(2002) developed an objective approach delineating
units for which similar dominating runoff behaviour
can be assumed (Fig. 3). This approach is mainly
based on hillslope genesis and considers different
hydrogeological units, surface characteristics, and
topography:
(1) Areas with Horton overland flow, i.e. the
impervious part of settlements and bedrock
outcrops.
(2) Areas with saturation overland flow, i.e. the
stream network, continuously wet areas in the
riparian zones or near springs, and mires. These
Fig. 2. Empirical relation between stream width and local drainage
area; derived from 30 measurements.
Fig. 3. Spatial delineation of the units with the same dominating runoff generation processes at the Brugga basin using the objective approach
according to Tilch et al. (2002).
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296284
areas were mapped (Guntner et al., 1999b), but
can also be derived from LANDSAT TM data
(Vogt and Lenco, 1995). In general, all saturated
areas at the test site are directly connected to the
stream.
(3) Moraines are very heterogeneous in their struc-
ture and grain size distribution. Compared to
other peri-glacial deposits (see below) they have
a significant storage volume (GLA, 1981), and
because of their consolidated matrix they qualify
as mainly base flow contributing areas (Linden-
laub et al., 1997).
(4) At flat areas on the hilltops (slope less than 68)
loamy soils with a relatively deep weathering
profile are dominant. Water percolates to the
deeper parts of the weathering zone and the
fractured bedrock and runs off slowly, contribut-
ing to base flow.
(5) At very steep areas (slope more than 348) blocks
and boulder fields are dominant and the finer soil
material is washed out. Here, quick lateral flow
takes place, even in times of low antecedent
moisture contents (Mehlhorn et al., 1998).
(6) The soils and drift covers of hillslopes with a
slope angle of 6–258 are dominated by a
stratified soil cover with a base layer (dense,
adjusted stones) and a main layer (sandy loam
with stones), both covering the weathered bed-
rock. The stratification was caused by solifluc-
tion during the last glaciation. Lateral flow is
dominant in the main layer, and perched aquifers
can be established.
(7) At hillslopes with a steepness of 25–348 a coarse
boulder layer is located above a loose sandy
matrix, with high lateral hydraulic conductivities
(Mehlhorn et al., 1998).
(8) An accumulation and colluvium zone that the
hillslope water must pass through to reach the
stream is predominant at the toe of the slopes
(slope angle: 0–258). This material is character-
ized by highly conductive layers (macro-porous,
stony boulder layer) with finer sediments (loamy
layers) in between.
4.2.2. Conceptualisation of runoff processes
A reservoir-based approach was chosen to con-
ceptualise the runoff generation processes.
The reservoir systems with parallel, sequentially
connected, or ‘overflowing’ reservoirs (Fig. 4) were
designed for each of the units, based on knowledge of
the dominating runoff generation processes. The
outflow of each linear reservoir Q (mm h21) depends
on the reservoir content S (mm), the storage
coefficient k (h21), and the local slope at the
respective raster cell
Q ¼ k £ S £ ð1 þ tan b=tan bðmeanÞÞ ð2Þ
with b (8) as the slope at the modelled cell, and b
(mean) (8) as the mean slope of the runoff generation
unit of the modelled cell. The slope term was added to
the normal reservoir equation to account for the
variable slope within each unit class. The ‘1 þ ’ term
needed to be included as otherwise at flat areas (very
low tan b) the outflow Q becomes unrealistically low.
Single linear reservoirs (Fig. 4) were used for
the runoff generation unit types (3), (4), and (5). The
k-values for each unit were parameterised separately,
as the hydraulic conductivity of each unit is very
different (see above). Two sequential reservoirs were
used for unit types (6), (7), and (8) to conceptualize
the temporary preferential lateral flow at these layered
soil and drift cover types. The k-value of the upper
storage of unit (7) equals that of unit type (5), as the
hydraulic conductivity of both materials is similar.
The maximal storage capacity of the lower reservoir
of unit type (8) is limited, and additionally inflowing
water is transferred to the upper reservoir that drains
more rapidly. This causes a faster runoff response at
these units during higher antecedent moisture con-
ditions. Flow at saturated areas (unit type (2)) is
described by a single linear reservoir with an upper
overflow. The year-round discharging water is routed
through the lower outlet of the reservoir and
additional input from precipitation or snowmelt is
transferred directly (active overflow) if storage
capacity (defined by the parameter MTD) at these
areas is exceeded. The storage capacity of the
saturated area is defined by the interception and
water retention in micro-topographic depressions at
the saturated areas, and it can be estimated by
sprinkling experiments.
For simulating the runoff from urbanized areas, the
portion of sealed area in each urban raster cell was
distinguished from the portion of areas where
infiltration is still possible (open spaces, gardens,
etc.). For the latter, the soil and runoff generation
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296 285
routine of the respective runoff unit type was
calculated. The surface runoff from the sealed area
reaches the next cell or the stream, if the cell is
connected to the stream network, within the modelling
time step. This is suitable for the rural study basin that
contains only small settlements. For catchments with
larger urbanized areas that have designed urban
drainage systems, or for shorter modelling time
steps, a more detailed routing such as for channel
flow, using for instance, the kinematic flow equation,
would be required.
The percolation to the deeper groundwater was
equal for all units (defined by parameter cAll_P) since
no process data exists that allows a spatially detailed
recharge simulation. No deep percolation was allowed
for the saturated areas, as these are permanently
discharging areas that are also fed by deep
groundwater.
Fig. 4. Schematic sketch of the runoff generation module using distributed and interlinked reservoirs within the TACD model. HOF, Horton
overland flow; SOF, saturation overland flow.
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296286
Cells through which a stream flows were divided
into two parts. (i) The precipitation that falls to the
stream area (stream widths multiplied by mean stream
length) was added directly to the stream and
transferred with the routing module (see above). (ii)
Precipitation on the remaining area has to pass
through the runoff generation routine of the respective
runoff unit type. The outflow of this routine goes
directly into the stream (as a stream flow through
these cell) and was routed accordingly.
4.2.3. Modelling dissolved silica concentrations
Dissolved silica has been used as a tracer to
examine runoff sources and flow pathways at the
study site (Uhlenbrook et al., 2002; Uhlenbrook and
Hoeg, 2003). Different runoff components can be
separated using silica concentrations. To confirm the
temporal pattern of runoff components of the TACD
model, a simple mixing model was applied to simulate
concentrations of dissolved silica
Siconc ¼ Q21sim £
XðSirunoff-comp £ Qrunoff-compÞ ð3Þ
where Siconc (mg l21) is the simulated silica concen-
tration at any location of the stream, Sirunoff-comp
(mg l21) is the silica concentration of each runoff
component that enters the stream within the modelled
time step, Qrunoff-comp (mm h21) is the flow volume of
the respective runoff component, and Qsim (mm h21)
is the modelled discharge. The silica concentrations
for each runoff component are given in Table 1. These
are based on recent experimental investigations.
5. Modelling results
The model was calibrated for the period 01.08.95–
31.07.96, and the period 01.08.96–31.07.99 was used
for validation (split-sample test as suggested, e.g. by
Klemes, 1986). The model was initialized for 3
months to have realistic storage volumes at the
beginning of the calibration period. Some parameters
were estimated based on basin characteristics and
literature values. These parameters were not further
optimised during the model calibration. Other model
parameters had to be determined by calibration
(Table 2), but magnitudes of parameter values were
derived from other model applications within the study
site (PRMS, Mehlhorn, 1999; TOPMODEL, Guntner
et al., 1999a; HBV, Uhlenbrook et al., 1999; TAC,
Uhlenbrook and Leibundgut, 2002). The calibration
was performed manually with the goal of the best
agreement between simulated and observed runoff at
the Brugga basin outlet. Due to the long computation
times (about 2 h for the simulation of 1 year) only a
limited number of calibration runs (about 50 runs
including test runs) was executed. Extensive fine-
tuning to optimize parameter values by maximizing
the goodness of fit measures was not undertaken.
Monte Carlo simulations were not performed to
investigate the equifinality problem (e.g. Beven and
Binley, 1992). However, it is important to note that
some parameters are not well defined and different
parameters probably reach similar results. This was
even shown for the less highly parameterised HBV
model for this study site (Uhlenbrook et al., 1999).
A good agreement between the simulated and
observed discharge was reached (Fig. 5). The model
efficiency, ReffðQÞ (–) (Nash and Sutcliffe, 1970) and
the model efficiency using logarithmic runoff values,
Reff ðlog QÞ (–), as well as the volume errors, VE,
(observed minus simulated discharge) per year
(mm a21) are given in Table 3. The efficiency values
can be between 21 and 1.0; 1.0 signifies a perfect
agreement between simulated and observed dis-
charge. The runoff dynamics were described very
well during the calibration period ðReffðQÞ ¼ 0:94Þ
Table 1
Concentrations of dissolved silica in the runoff components
modelled by the TACD model
Runoff component Si (Si-mg l21)
Precipitation directly to water bodies 0
Runoff from saturated areas
(overflow) and urban areas
(unit types 1 and 2)
2.0
Runoff from hillslopes (unit types
5, 6, 7 and 8)
4.0
Runoff from saturated areas, lower
outflow (unit type 2)
4.3
Runoff from moraines (unit type 3) 5.0
Runoff from flat areas at the
hilltops (unit type 4)
6.0
Runoff from deep groundwater 6.2
For description of the unit types see Section 4.2.
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296 287
Table 2
Parameters of the TACD model and the respective estimation method
Parameter Unit Explanation Brugga Estimation method
Precipitation correction
CwindA – Correction of precip. measurement 1.01 Literature
CwindB s m21 Correction of precip. measurement 0.01 Literature
Snow routine
TT 8C Temperature threshold for snow fall 0.1 Calibrationa
TT_melt 8C TT for snow melt 0.5 Calibrationa
TT_meltforest 8C TT for snow melt in forests 1.5 Calibrationa
CFMAX mm 8C21 d21 Degree-hour factor 1.9 Calibrationa
CWH – Water holding capacity 0.1 Bergstrom (1992)
CFR – Refreezing coefficient 0.05 Bergstrom (1992)
Soil routine
CLP – Reduction of pot. evapotranspiration 0.6 Menzel (1997)
CFC_3 mm Field capacity at unit type 3 220 Soil map
CFC_4 mm Field capacity at unit type 4 250 Soil map
CFC_5 mm Field capacity at unit type 5 30 Soil map
CFC_6 mm Field capacity at unit type 6 130 Soil map
CFC_7 mm Field capacity at unit type 7 90 Soil map
CFC_8 mm Field capacity at unit type 8 200 Soil map
CBETA_3 – Beta parameter at unit type 3 3.5 Calibrationa
CBETA_4 – Beta parameter at unit type 4 3.6 Calibrationa
CBETA_5 – Beta parameter at unit type 5 2.0 Calibrationa
CBETA_6 – Beta parameter at unit type 6 3.0 Calibrationa
CBETA_7 – Beta parameter at unit type 7 2.5 Calibrationa
CBETA_8 – Beta parameter at unit type 8 3.0 Calibrationa
Runoff generation routine
CUrbanSplit – Portion of sealed areas in unit type 1 0.4 Peschke et al. (1999)
cMTD mm Micro-topographic depression storage at unit type 2 30 Sprinkling experiments
C2_K h21 Recession coefficient for unit type 2 0.01 Calibrationb
C3_K h21 Recession coefficient for unit type 3 0.002 Calibrationc
C4_K h21 Recession coefficient for unit type 4 0.001 Calibrationc
C5_K h21 Recession coefficient for unit type 5; same
as C7_K_u and C8_K_u
0.2 Calibrationb
C6_K_u h21 Upper recession coefficient for unit type 6; same as C7_K_l 0.024 Calibrationc
C6_K_l h21 Lower recession coefficient for unit type 6 0.005 Calibrationc
C6_T mm h21 Percolation from upper to lower reservoir at unit type 6r 0.2 Calibrationb
C6_H mm Maximal storage capacity of lower storage at unit type 6 400 Calibrationb
C7_K_u h21 Upper recession coefficient for unit type 7; same as
C5_K and C8_K_u
0.2 Calibrationc
C7_K_l h21 Lower recession coefficient for unit type 7; same as C6_K_u 0.024 Calibrationc
C7_T mm h21 Percolation from upper to lower reservoir at unit type 7 0.6 Calibrationb
C7_H mm Maximal storage capacity of lower storage at unit type 7 80 Calibrationb
C8_K_u h21 Upper recession coefficient for unit type 8; same as
C5_K and C7_K_u
0.2 Calibrationc
C8_K_l h21 Lower recession coefficient for unit type 8 0.007 Calibrationc
C8_T mm h21 Percolation from upper to lower reservoir at unit type 8 0.6 Calibrationb
C8_H mm Maximal storage capacity of lower storage at unit type 8 150 Calibrationb
CUpper_H mm Maximal storage capacity of all upper groundwaters 800 Calibrationb
CGW_K h21 Recession coefficient for hard rock aquifer 0.001 Calibrationc
CGW_H mm Maximal storage capacity of hard rock aquifer 1000 Calibrationb
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296288
and the volume error per year amounts to less than 3%
of the yearly precipitation. No systematic error during
high or low flow could be detected during the
calibration (Fig. 6a). During the validation period
(Fig. 6b), a larger scatter between simulated and
observed discharges was found, but the coefficient of
determination, r2; still amounts to 0.824. The runoff of
one flood, with the largest observed peak discharge,
was underestimated (see Fig. 6b with the line of
stringed dots). This flood was generated by rain on
snow and the error is caused by the precipitation input
that was not recorded well during particular storm.
The model outperformed in terms of the statistical
measures all models previously applied to the Brugga
basins, i.e. PRMS, TOPMODEL, HBV, WASIM-
ETH and TAC, using nearly the same data records.
The TACD results were aggregated to daily time steps
to illustrate the improvements of the new model
version compared to the old TAC model (semi-
distributed, daily time step). Both models were
Table 2 (continued)
Parameter Unit Explanation Brugga Estimation method
CGW_P mm h21 Percolation from upper reservoirs to hard rock aquifer 0.075 Environmental tracers
Runoff routing routine
cStreamWidth m Stream width 0.3–6.1 Field data
cStreamLength m Stream lengths per raster cell 60.6 Field data
CN m1/3 s21 Manning’s n (roughness coefficient) 0.06–0.08 Literature, field data
cBeta – Parameter for kinematic wave 0.6 Chow et al. (1988)
a Standard values can be found in the literature, exact determination by calibration.b Magnitudes of this parameter can be found in the literature (previous model applications), exact determination by calibration.c If the runoff formation in a sub-basin is only dominated by this unit type, this parameter can be estimated by recession analysis.
Fig. 5. Results of the discharge simulation using TACD for the calibration period (01.08.95–31.07.96).
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296 289
calibrated successfully for the period 01.08.95–
31.07.96, but TACD yielded a better agreement with
the observed discharge compared to TAC and the
coefficient of determination, r2; amounted to 0.97 and
0.80, respectively. High flows were modelled better in
all seasons and also the recession limbs and low flows
fit the observed hydrograph better (Fig. 7). This must
be caused by the distributed computation of the model
inputs and flow routing, which allows more realistic
simulations of all hydrological processes (see further
model tests below).
It is remarkable that the ReffðQÞ amounted already
to 0.75 using only first-estimates of all parameter
values without any calibration. This goodness of fit is
in the order of magnitude of other models applied to
the Brugga basin previously (see above) or to other
study basins after parameter optimization. It is
interesting to note that the number of parameters
required by previously applied distributed models
WASIM-ETH (52 parameters) and PRMS (60 par-
ameters, but some vary seasonally what increases the
number) is higher than is required by the TACD model
(38 parameters). The calibration efforts were even
more complete for the other models, but the modelling
results for discharge simulation were worse than those
provided by the TACD model.
The statistical measures were lower but still good
for the validation period (mean ReffðQÞ ¼ 0:8;
Table 3). Other previously applied models also had
problems with successful simulation of this period.
Two rain gauges in the southwest measured very high
Table 3
Results of the TACD applications in the Brugga basin (40 km2) and
the sub-basin St Wilhelmer Talbach (15.2 km2)
Brugga St Wilhelmer Talbach
Calibrationa period (1.8.95–31.7.96)
ReffðQÞ 0.94 0.85
Reffðlog QÞ 0.99 0.9
VE 244 249
Validation period (1.8.96–31.7.99)
ReffðQÞ 0.8 0.85
Reffðlog QÞ 0.83 0.87
VE 2175 258
As statistical measure the model efficiencies, ReffðQÞ and
Reffðlog QÞ (–), according to Nash and Sutcliffe (1970) and the
volume error per year, VE (mm a21), are given.a The model was only calibrated to Brugga data and not to the
St. Wilhelmer Talbach.
Fig. 6. Comparison of simulated and observed discharge at the outlet of the Brugga basin using TACD for (a) the calibration period (01.08.95–
31.07.96), and (b) the validation period (01.08.96–31.07.99).
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296290
precipitation, and this resulted in an overestimation of
runoff at Brugga for 1997–1998 (see very negative
volume error in Table 3 that amounts to about 10% of
the yearly precipitation). Analysis of simulations for
the St. Wilhelmer Talbach (sub-basin in the southeast)
confirmed that the overestimated discharge values at
the Brugga originated from this area in the southwest.
The volume error was smaller in the St. Wilhelmer
Talbach sub-basin; thus, the weaker simulations are
likely to be caused by incorrect precipitation data.
However, no systematic measurement error was
detected and the data were retained without
modification.
To evaluate the model performance in further
detail, model testing in addition to the classical split-
sample test was performed. The comparison between
simulated and observed runoff at the St. Wilhelmer
Talbach basin (15.2 km2) without re-calibrating the
model (Table 3) demonstrated the model’s ability to
capture internal runoff dynamics. Consequently, it can
be stated that the determined parameter set is suitable
both for the calibration period in the whole Brugga
basin as reasonable results were obtained for an
independent validation period, and for a sub-basin
without re-calibration.
Finally, the model was validated using tracer
data, i.e. dissolved silica. For the entire 4-year
investigation period correspondence between the
simulated and observed silica concentrations at the
basin outlet is not as accurate as runoff simulations.
The coefficient of determination, r2 (–), amounted
to 0.4. However, for shorter periods good silica
simulation could be obtained, as shown for two
summer storm events during the validation period
(Fig. 8). Here, the general variations of silica
concentrations were simulated well, only during
recession limb the concentrations are underesti-
mated. This is caused by an overestimation of
discharge during that time. The contributions of
delayed runoff components with lower silica
concentrations (generating the falling limb) are
overestimated for this particular storm, which might
be due to an overestimation of the spatial extent of
this convective rain storm. A good agreement
between simulated and observed silica concen-
trations was also found for a snowmelt period in
spring 1996. Thus, the plausibility of the temporal
mixing pattern of different runoff components
during the formation of different runoff events
was checked successfully.
Fig. 7. Comparison of the simulated hydrographs of the old TAC model (data from Uhlenbrook and Leibundgut, 2002) and the new model
version TACD at the outlet of the Brugga basin for the calibration period (01.08.95–31.07.96). The results of TACD were aggregated to daily
values. The log-scale at the y-axis enable a better comparison of mean and low flow periods.
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296 291
6. Discussion
Using tracer and discharge data from sub-basins
and a neighbouring basin, Uhlenbrook and Leibund-
gut (2002) showed that the previous version of TAC
not only computed the total runoff well, but also
correctly modelled the contribution of different runoff
components. However, flood generation was not
modelled in a process-realistic way due to the daily
time step, because the runoff generation dynamics and
runoff routing were not represented adequately; i.e.
the temporal resolution of the model did not agree
with process time scales. The precipitation in the
meso-scale test site is also very heterogeneous.
During the summer convective rain cells with limited
spatial extent dominate. During the winter, the
importance of snow varies significantly at different
elevations, and snowmelt contributions are variable
due to diurnal fluctuations and temperature variations
around 0 8C during many winter days. Widely
variable spatial patterns observed for the modelled
evapotranspiration were caused by the heterogeneity
of the climatic variables in the high-relief study area
(variable exposure and shadowing effects). Thus,
the use of the hourly time step in combination with the
raster-based model structure is significant progress
towards a better process representation within the
model. It enabled inclusion of the spatial and temporal
variability of the model input (i.e. precipitation and
temperature) as well as all subsequent processes
(snowmelt, infiltration, lateral flows, etc.) in a better,
more process-realistic way. Also, in order to capture
the temporal dynamics of the dissolved silica
concentrations at the basin outlet and to represent
the process timescale best, the modelling time step
must be more shorter than daily (Lischeid and
Uhlenbrook, 2003).
The concept of the runoff generation routine
describes the lateral flows of surface runoff and sub-
surface flows in a process-oriented way using different
reservoir concepts. In particular, lateral flows in the
soil and drift cover (shallow groundwater) are
modelled in detail, as these are the most important
turnover storages at the test site (Uhlenbrook et al.,
2002). Flow in the deep groundwater (deeper parts of
the weathering zone and fissured hard rock aquifer) is
conceptualized by simple linear reservoirs. This is
suitable for the present model version, which aims to
simulate correctly the runoff dynamics of discharge
from different sources. This is a pre-requisite for
simulation of solutes by conservative mixing of
different runoff components, as demonstrated for the
silica modelling in this paper. More complex reservoir
systems must be applied if the model is needed for
simulating real solute transport of, for instance,
environmental isotopes. In such cases, additional
mixing between mobile and immobile parts of each
flow system must be considered (Maloszewski and
Zuber, 1996). For modelling of solute transport of non-
conservative species such as nutrients or other weath-
ering products, the biogeochemical reactions must also
be included (Kendall and McDonnell, 1998). There-
fore, the TACD model offers a suitable framework
since the flowpaths and source areas of runoff are
modelled correctly, i.e. in a way that agrees with the
current knowledge of hydrological processes acquired
through experimental investigations. This is often not
the case for models that are technically able to simulate
even non-conservative solute transport, but are based
on runoff generation concepts that do not describe the
flow processes adequately. This shortcoming became
obvious when nitrate concentrations for the Brugga
Fig. 8. Simulated and observed discharge at the Brugga gauging
station (upper), and comparison of simulated and observed
dissolved silica concentrations (lower) for 7 days during the
validation period.
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296292
basin were simulated by the NPSM model (US-EPA,
1998; Eisele et al., 2001).
The tracer simulation accuracy is at least as good
as the results of other models using a comparable
solute transport module (e.g. Bergstrom et al., 1985;
Lundquist et al., 1990; Uhlenbrook and Leibundgut,
2002). The following three assumptions were made
for the silica simulation. (i) The last hydrogeological
unit from which the water enters the stream defines
the silica concentration of the respective runoff
component. This was found by Kienzler (2001) after
analyzing about 1000 samples taken at road cuts and
groundwater seeps at 69 locations within the Brugga
basin. (ii) The temporal variability of silica concen-
trations at a specific location in the stream is due to
mixing of different runoff components. This was also
corroborated by Kienzler (2001) who found constant
concentrations during floods at sites that drain a
specific runoff source area. Uhlenbrook et al. (2004)
demonstrated by end member mixing analyses
(Christophersen et al., 1990) and hydrograph separ-
ations at two springs draining a variety of source areas
that the variable concentrations could be explained by
mixing of different runoff components. (iii) Silica
remains constant as soon as it enters the stream. This
is reasonable, as uptake by diatoms is negligible for
rivers with little productivity (Hooper and Shoe-
maker, 1986), and other sinks are not important.
The TACD model is coded within the GIS PC
Raster using a dynamic environmental modelling
language (Karssenberg et al., 2001). This has several
technical advantages. (i) Pre- and post-processing of
the spatial data can be accomplished within the same
software environment, avoiding the time consuming
import and export of data. (ii) PC Raster contains
many coded sub-routines such as the inverse distance
weighting module, to regionalize point data (e.g.
precipitation measurements) or the linking of the
raster cells to route fluxes from one cell to the next.
(iii) All internal variables (e.g. fluxes and volumes of
different hydrological storages) can be reported as
time series and maps for the whole basin for each
modelling time step. This enables visualization of the
model performance in a spatially and temporally
distributed manner, and allows more detailed evalu-
ation of the plausibility of the input data and
modelling results. An extensive discussion of the
power and potential of dynamic environmental
modelling languages within GIS can be found in
Karssenberg (2004).
7. Conclusions and outlook
The TACD model is shown to be suitable for
representing hydrological processes at the meso-
scale Brugga basin. It reaches very good statistical
measures during the calibration period by needing
only a limited number of calibration runs since
many parameters could be estimated from field data
or previous investigations. Additionally, the model
is proved on different levels, and good model
performance is demonstrated for a sub-basin and an
independent validation period without re-cali-
bration. The temporal mixing pattern of different
runoff components is validated using the natural
tracer dissolved silica. Thus, the model goes
beyond the traditional mimicry of observed basin
outlet discharge, which can be obtained using
simpler models. The purpose of TACD is to include
a process-realistic description of the runoff gener-
ation processes, i.e. the origin of runoff components
and flow pathways. This is a pre-requisite for
integrating solute transport of non-conservative
species into a modelling system.
A validated process-based model can serve as
tool to test hypotheses about the most important
controls on hydrological responses to rainfall. This
study makes progress towards the development of
such a model for meso-scale mountainous basins.
The understanding of physical processes achieved
by previous investigations including tracer studies
is incorporated in a relatively simple way using
distributed, suitably designed reservoirs in the
runoff generation routine. This approach can also
be applied to other catchments if a perceptual
model of the study area can be formulated. This is
the aim of the spatial delineation of similar
landscape elements, which serves as spatial dis-
cretization within the model, defines the model
structure, and enables efficient model parameterisa-
tion. However, this procedure results in a model,
which is still exposed to the problem of equifinality
(even if not addressed particularly in this study).
The value of additional data such as discharge and
tracer data from sub-basins to constrain the model
S. Uhlenbrook et al. / Journal of Hydrology 291 (2004) 278–296 293
is demonstrated. The contribution of different
additional data to reduce model uncertainty caused
by the parameter uncertainty will be investigated in
a next step.
Future model developments will focus on the
incorporation of the Penman and Monteith approach
for estimating evapotranspiration in order to maxi-
mize the process-realistic predictions in this module.
For regions with large porous aquifers and spatially
and temporally variable flow between the surface
water and groundwater, an additional module needs to
be introduced into TACD. These processes need to be
simulated depending on the actual water levels and
hydraulic conductivities in each system. These model
enhancements will lead to a tool for testing hypoth-
eses in more complex environments with mixed land
use and diverse hydrogeological settings.
Acknowledgements
The authors thank the German Research Foun-
dation (Deutsche Forschungsgemeinschaft, DFG,
Bonn, Germany) for financial support, Grant no.
Le 698/12-1.
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