Conceptual environmental system models, such as
rainfall runoff models, generally rely on calibration for parameter
identification. Increasing complexity of this type of models for better
representation of hydrological process heterogeneity, typically makes
parameter identification more difficult. Although various, potentially
valuable, approaches for better parameter estimation have been developed,
strategies to impose general conceptual understanding of how a catchment
works into the process of parameter estimation has not been fully explored.
In this study we assess the effects of imposing semi-quantitative, relational
inequality constraints, based on expert-knowledge, for model development and
parameter specification, efficiently exploiting the complexity of a
semi-distributed model formulation. Making use of a topography driven
rainfall-runoff modeling (FLEX-TOPO) approach, a catchment was delineated
into three functional units, i.e., wetland, hillslope and plateau. Ranging
from simple to complex, three model setups, FLEX

Lumped conceptual and distributed physically based models are the two
endpoints of the modeling spectrum, ranging from simplicity to complexity,
which here is defined as the number of model parameters. Each modeling
strategy is characterized by advantages and limitations. In hydrology,
physically based models are typically applied under the assumptions that
(a) the spatial resolution and the complexity of the model are warranted by
the available data, and (b) the catchment response is a mere aggregation of
small scale processes. However, these two fundamental assumptions are
commonly violated. As a result, the predictive power and hydrological insight
achievable via these models is limited
(e.g.,

In contrast, lumped conceptual models require less data for model parameters
estimation. This advantage comes at the expense of considerable limitations.
Representing system integrated processes, model structures and parameters are
not directly linked to observable quantities. Their estimation therefore
strongly relies on calibration. To limit parameter identifiability issues
arising from calibration, these models are often oversimplified abstractions
of the system, and if inadequately tested they may act as

Various strategies have been suggested to allow for increased model
complexity and to thereby improve the physical realism of conceptual models.
These strategies included the attempt to incorporate different data sources
in the parameter estimation process, such as ground- and soil water dynamics

Traditional parameter estimation of conceptual models relies on the
availability of calibration data, which, however, are frequently not
available for the time period or the spatiotemporal resolution of interest.
A wide range of regionalization techniques for model parameters and
hydrological signatures have been developed to avoid calibration in such data
scarce environments

Related to these difficulties with parameter identifiability, the lack of
sufficient representation of processes heterogeneity (i.e., complexity) in
conceptual models limits the degree of realism of these models. The concept
of hydrological response units (HRUs) can be exploited as a strategy for an
efficient tradeoff between model simplicity, required for adequate parameter
identifiability, and a sufficient degree of process heterogeneity. HRUs are
units within a catchment, characterized by a different hydrological function
and can be represented by different model structures or parameters. In most
cases HRUs are defined based on soil types, land cover and other physical
catchment characteristics

A wide range of studies also points towards the potential value of using
topographical indices, readily available from digital elevation models (DEMs),
to account for process heterogeneity

Explicitly invoking the co-evolution of topography, vegetation and hydrology,

While HAND-based landscape classification can poten-tially show a way forward,
it does not solve the problem arising when moving from lumped to HRU-guided,
semi-distributed model formulations: multiple parallel model structures
typically result in an increased number of parameters, which, when not
adequately constrained, may increase equifinality and thereby limit
predictive uncertainty (e.g.,

In contrast to earlier attempts to constrain models using multiple evaluation
criteria or a priori information on catchment properties such as
land use or soil type

The objective of this paper is to test the hypothesis that application of model constraints based on expert knowledge (regarding relations between parameters, fluxes and states) to semi-distributed conceptual models defined by a hydrologically meaningful, topography-based, landscape classification system combined can (1) increase model internal consistency and thus the level of process realism as compared to lumped model setups, (2) increase the predictive power compared to lumped model setups and (3) reduce the need for model calibration.

The outlined methodology will be illustrated and tested with a case study
using data of the Wark catchment in the Grand Duchy of Luxembourg. The
catchment has an area of 82 km

The hydrological data used in this study include discharge measured at the
outlet of the Wark catchment, potential evaporation estimated by the Hamon
equation

Realizing the potential of “reading the landscape” in a

As the objective of FLEX-TOPO is to efficiently extract and use
hydrologically relevant information from worldwide readily available
topographic data, i.e., DEMs, the Height Above the Nearest Drainage

In this study a lumped conceptual model of the Wark catchment, hereafter
referred to as FLEX

This model setup represents the catchment in a lumped way. The
FLEX

The model structures for

The interception reservoir is characterized by its maximum storage capacity
(

The unsaturated reservoir is characterized by a parameter that loosely
reflects the maximum soil moisture capacity in the root zone
(

The proportion of effective rainfall which is not stored in the unsaturated
zone, i.e., 1

The fast reservoir is a linear reservoir characterized by reservoir
coefficient

The slow reservoir is a linear reservoir characterized by reservoir
coefficient

As discussed above, a range of process studies suggested that wetlands can
frequently exhibit storage–discharge dynamics that are decoupled from other
parts of a catchment, in particular due to their typically reduced storage
capacity and closeness to the stream. FLEX

This model setup offers a complete representation of the three HRUs in the
study catchment: wetland, hillslope and plateau (Fig. 2c). The formulation
of the wetland module in FLEX

The connection between the parallel structures of FLEX

Uniform prior parameter distributions for the three model setups.

Water balance equations and constitutive functions used in FLEX

With increasing process heterogeneity from FLEX

Inequality conditions between parameters of parallel model units, hereafter
referred to as

Different land cover proportions of individual landscape units, here
wetlands, hillslopes and plateaus, can be used to define the relation between
interception thresholds (

Preferential recharge (

Wetlands have shallower groundwater tables than the other two landscape
entities in this study. Therefore the unsaturated zone of wetland should have
a lower maximum soil moisture capacity (

The reservoir coefficient of the wetland fast reservoir (

In contrast to the parameters constraints discussed above, which are set
a priori,

The applicability of different parameter and process constraints for
the three different model structures, FLEX

Process constraints are defined for dry and wet periods as well as for peak,
high, and low flows. Here wet periods were defined to be the months from
November to April, while the dry periods in the study catchment occur between
May and October. The thresholds for distinguishing between high and low flow
were chosen to be 0.05 and 0.2 mm (3 h)

Transpiration typically exhibits a clear relationship with the normalized
difference vegetation index

Mean (

Based on the mean (

Similar constraints can be imposed between transpiration fluxes from wetland,
hillslope or plateau; however, the spatial resolution of LANDSAT 7 data with
resolution of 30 meters is coarser than the required 20 m DEM resolution
for distinguishing wetlands from other landscape entities

The runoff coefficient is a frequently used catchment signature

The slow reservoir can be recharged by both preferential and matrix
percolation from the unsaturated reservoirs. Here, hillslopes and plateaus
contribute to the slow reservoir by preferential recharge. It can be assumed
that in a realistic model setup the long term contribution volume of
preferential recharge ratio between hillslope and plateau should not be
unrealistically high or low. For example, it can be assumed unrealistic that
the ratio is zero or infinity, meaning that one landscape unit is constantly
feeding the slow reservoir while another one is not contributing at all. To
avoid such a problem, a loose and very conservative constraint was imposed on
the ratio of contribution of the two fluxes.

During dry periods, hillslopes and plateaus can exhibit significant soil
moisture deficits, limiting the amount of fast runoff generated from these
landscape elements. In contrast, due to their reduced storage capacity,
wetlands are likely to generate fast flows at lower moisture levels, thus
dominating event response during dry periods (cf.

Based on uniform prior parameter distributions as well as on the parameter
and process constraints the model was calibrated using MOSCEM-UA

The models were evaluated on the basis of three different objective functions
to emphasize different characteristics of the system response: (i) the
Nash–Sutcliffe efficiency of the flows

To assess the value of incorporating parameter and process constraints in increasingly complex models a four-step procedure was followed.

First, all parameter sets that satisfy all the applied constraints were
evaluated for their ability to reproduce the observed hydrograph; these
parameter sets are referred to as

To further study the effect of constraints on the performance and uncertainty
of

In the second step, the three models FLEX

Uncertainty intervals were evaluated based on the

Again, the results were compared to the calibrated but unconstrained benchmarks.

To assess the added value of incorporating constraints in higher complexity
models, the performance and uncertainties of the three models
FLEX

One of the main reasons for imposing constraints on model parameters is to
ensure realistic internal dynamics. Comparing different fluxes contributing
to the modeled hydrograph can provide insights into the performance of
imposed constraints on the model. The effect of imposing behavioral constraints
on fast and slow components of the three models structures,
FLEX

The median and the 95 % uncertainty intervals of the performance of modeled
hydrographs for

FLEX

The additional process heterogeneity and constraints allowed by
FLEX

These results clearly illustrate that the imposed relational constraints force the model and its parameters towards a more realistic behavior, which significantly improves model performance. Additionally, the comparison of result of the three models with their unconstrained benchmarks (Table 4) clearly shows that the incorporation of constraints improves the median performance and 95 % uncertainty intervals of all the models by rejecting parameter sets that violate the constraints and cannot reproduce certain aspects of the response patterns. In addition, the comparison between the unconstrained benchmark models themselves suggests that more complex model structures improve the performance, implying that model structures themselves already contain a considerable degree of information even in absence of any constraints or calibration attempts.

The 95 % uncertainty areas mapped by simulated hydrographs indicate that
FLEX

The median model performances (in brackets their corresponding 95 %
uncertainty intervals) and the area spanned by the 95 % uncertainty interval
of hydrograph derived from uncalibrated parameter sets which satisfy the complete
set of constraints for the three model setups FLEX

The observed hydrograph and the 95 % uncertainty interval of the
modeled hydrograph derived from the complete set of

The median model performances (in brackets their corresponding Pareto
uncertainty intervals) and the area spanned by the uncertainty interval of the
hydrograph derived from the Pareto optimal solutions of the

The observed hydrograph and the 95 % Pareto uncertainty interval
of the modeled hydrograph for

Flipping calibration and validation gave equivalent results, which are, for brevity, provided in Table S1; Fig. S1 in the Supplement.

The comparison of the

For the validation period, arguably more important for model assessment
because it provides independent information on model consistency

The following comparison of the performances of FLEX

Model performance (

Figure 5e compares model performance based on

Comparison between mean proportions of Pareto members for model
components of the three model setups in part of the validation periods
(August 2006–June 2007)

In addition, a second crucial aspect was revealed by comparing

The comparison of the fluxes generated from the individual model components in the three model setups helps to assess to which degree the model internal dynamics reflect the modeler's perception of the system and thus to a certain degree the realism of the models.

Fast and slow responses of each tested model setup have been visually
illustrated in Fig. 6. Predominance of slow responses of all the three models
are indicated by green color; predominance of fast responses of
FLEX

The colors in Fig. 6 are an illustration using three colors (red, green and
blue) for the models' responses based on their weight of contribution to the
modeled runoff. As it can be seen in Fig. 6a the fast component of
FLEX

In accordance with the perception of the system that wetlands are
predominantly responsible for peak flows during dry conditions, Fig. 6b and c
show that wetland fast responses in FLEX

The results of this study quite clearly indicate that discretizing the
catchment into hydrological response units (HRUs) and incorporating expert
knowledge in model development and testing is a potentially powerful strategy
for runoff prediction, even where insufficient data for model calibration

Typically it is expected that, if not warranted by data, models with higher
complexity suffer from higher predictive uncertainty. As stated by

A complex model may include many processes, i.e., hypotheses, which can
usually not be rigorously tested with the available data. However, a wide
range of previous studies has demonstrated that hydrologically meaningful
constraints can help to limit the increased uncertainty caused by
incorporating additional processes, i.e., parameters

In a similar attempt,

Including prior knowledge for parameters of physically based models for
estimating runoff in ungauged basins was quite successfully investigated in
the past

It should be kept in mind that the conclusions of this study remain at this
point only valid for the study catchment. To generalize the findings of this
study more rigorous tests should be set up

This study has tested whether a topography-driven semi-distributed formulation of a catchment-scale conceptual model, conditioned by expert knowledge based relational parameter and process constraints, can increase the level of process realism and predictive power while reducing the need for calibration.

It was found that

The performance of models,

Imposing relational parameter and process constraints improves the
performance of

Due to the reduced feasible parameter space, the search for behavioral parameter sets focuses on the feasible parameter space only.

Imposing constraints prevents the model from over-fitting on calibration time series and therefore enables the model to more reliably perform outside the calibration period.

The authors would like to thank Hoshin Gupta, Mojtaba Shafiei, Patrick Matgen, Rohini Kumar, Luis Samaniego and Thibault Mathevet for their constructive comments on this manuscript. Anke Luijben's assistance is appropriated for data analysis of the study area. We also thank the three anonymous reviewers; their comments improved our paper significantly. Shervan Gharari is funded during his PhD program by Fonds National de la Recherche (FNR) of Luxembourg with Aides à la Formation-Recherche (AFR) project number of 1383201. Edited by: F. Tian