hydrological process representation at the meso-scale: the potential of a distributed, conceptual...

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).

http://www.elsevier.com/locate/jhydrol

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


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


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,


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).


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


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.


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.


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






CBETA_3 – Beta parameter at unit type 3 3.5 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


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


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


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).


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).


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.


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.


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


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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