Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives
Introduction
Application of numerical models in hydrological modelling generally requires estimation of model parameters through calibration with observed data. Lumped, conceptual type models, such as the Sacramento model [3], the HBV model [1], and the MIKE 11/NAM model [10] contain conceptual parameters that are related to aggregated hydrological process descriptions, which cannot, in general, be determined from physical characteristics of the catchment under consideration. In distributed, physically based models, such as MIKE SHE [22], model parameters should, in principle, be assessable from catchment data. In practice, however, determination of model parameters in each computational grid point is not possible due to scaling problems (i.e. differences between the measurement scale, model grid scale, and the scale at which the basic algorithmic process descriptions are derived) as well as experimental constraints. Thus, also distributed, physically based models need calibration.
In the calibration of lumped, conceptual models parameters are adjusted to match simulated and observed catchment runoff. In recent years, a great deal of research has been directed to develop automated calibration procedures based on numerical optimisation techniques. Efficient routines are the so-called population-evolution-based algorithms, such as genetic algorithms [30] and the shuffled complex evolution (SCE) algorithm [5]. Application of automatic routines has traditionally been based on a single objective measure of comparison, e.g. mean squared error or coefficient of determination [20]. A single measure, however, is often inadequate to properly take into account the simulation of all the characteristics of a system that are used by a hydrologist to evaluate the goodness-of-fit of the calibrated model. Automatic routines that use a multi-objective formulation of the calibration problem have been introduced [2], [9], [16] which allow a simultaneous optimisation of different response modes of the hydrograph. Recently, Madsen et al. [18] showed that calibration of the MIKE 11/NAM model based on a generic optimisation routine with multiple calibration criteria compares favourably with an expert system that is designed for the specific model and requires user intervention during the entire calibration process.
While much research has been devoted to developing automated procedures for calibration of lumped, conceptual models, automatic parameter estimation in distributed catchment models is an area with only very limited experience. As compared to lumped, conceptual models that have a more or less fixed model structure and relatively few calibration parameters (typically 5–10), a distributed model potentially includes a huge number of model structures and model parameters to be analysed. Therefore, a rigorous model parameterisation or conceptualisation is crucial for proper calibration of a distributed model [23]. And this aspect becomes even more important when automatic procedures are applied for parameter estimation.
Another important aspect that should be considered for parameter estimation in distributed models is the use of calibration data. It is important to evaluate the distributed model behaviour rather than just catchment-integrated behaviour by calibration against catchment runoff. Multi-site and multi-variable calibration should be performed if distributed predictions are needed for different state variables [21]. Thus, the calibration problem should be formulated using a general multi-objective framework. Such a framework should allow for specification of calibration criteria that are tailored to the specific model application being considered.
The objective of this paper is to formulate and evaluate a general framework for automatic calibration of a distributed and integrated hydrological catchment model based on the MIKE SHE modelling system. The framework focuses on the different steps in the estimation process, including model parameterisation and choice of calibration parameters, specification of calibration criteria and choice of optimisation algorithm. A test example is presented that illustrates the use of the proposed framework and comparison is made with an expert manual calibration.
Section snippets
Calibration framework
In automatic calibration, parameters are adjusted automatically according to a specific search scheme for optimisation of certain calibration criteria (objective functions). The process is repeated until a specified stopping criterion is satisfied, e.g. maximum number of model evaluations, convergence of the objective functions, or convergence of the parameter set.
Formulation of a proper framework for automatic calibration involves the following key elements:
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model parameterisation and choice of
Model setup
The automatic calibration framework is applied for calibration of the MIKE SHE model setup of the Danish Karup catchment used in [21] (see Fig. 1). The Karup catchment has an area of 440 km2 and is located in the western part of Denmark. The topography varies from about 20 to 100 m. The geology is relatively homogeneous with highly permeable sand and gravel deposits and small lenses of moraine clay. The aquifer is mainly unconfined and varies in thickness from about 10 m at the western and
Discussion and conclusions
A general framework for automatic calibration of a distributed and integrated hydrological model has been presented. The framework includes three basic elements: (1) model parameterisation and choice of calibration parameters, (2) specification of calibration criteria, and (3) choice of optimisation algorithm. The importance of a rigorous model parameterisation for calibration of distributed models has been emphasised. The calibration problem has been formulated in a general multi-objective
Acknowledgements
This work was in part funded by the Danish Technical Research Council under the Talent Project No. 9901671 “Data Assimilation in Hydrodynamic and Hydrological Modelling”. The comments by Tom Meixner and the second reviewer are gratefully acknowledged.
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