Progressive evaluation of incorporating information into a model building process: from scratch to FLEX-TOPO

Abstract:

Lumped conceptual and distributed physically based models are the two endpoints of the modelling spectrum in many environmental systems models, ranging from simplicity to complexity. These two approaches are characterized by their very own 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 is warranted by the available data, and (b) the catchment response is a mere aggregation of small-scale processes. However, these two fundamental assumptions are violated in many cases. As a result, not only the predictive power but also the hydrological insights that these models provide can be limited. In the case of conceptual models, parameter values are typically specified through a process of calibration that seeks to match the modelled runoff to observed hydrographs. Expert knowledge can be brought to bear implicitly, by the prior specification of parameter ranges that define the feasible parameter space. There have been various strategies proposed to find “better parameter sets” by introducing regularization, regionalization, multi-objective and multi-response calibration of hydrological models.

Although the above-mentioned strategies have demonstrated that incorporation of expert and a priori knowledge can help to improve the realism of models, no systematic strategy has been presented in the literature for constraining the model parameters to be consistent with the (sometimes) patchy understanding of a modeller regarding how the real system might work. Part of the difficulty in doing this is that expert knowledge may not always consist of explicitly quantifiable relationships between physical system characteristics and model parameters; rather, it may consist of conceptual understanding about consistency relationships that must exist between various model parameter or behavioural relationships that must exist among model state variables and/or fluxes. For example, the geology of a given catchment may suggest that the catchment response during intensive rainfall events is characterized by a slow responding groundwater component accompanied by fast responding Hortonian overland flow. In such a situation, any model results that imply that peak flows are composed of a strong groundwater response should be discarded or given lower importance. Such information can act as a constraint on the set of feasible model behaviours, and thus help to limit the feasible extent of the model parameter space, resulting in reduced parameter and predictive uncertainty.

Apart from aforementioned constraints, a unified strategy for measurement of information content in hierarchal model building considering both performance and uncertainty seems lacking. Firstly the model structure is built by its building blocks (control volumes or state variables) as well as interconnecting fluxes (formation of control volumes and fluxes). Secondly, parameterizations of model are designed, as an example the effect of a specific type of stage-discharge relation for a control volume can be explored. At the final stage, of the model building the parameter values are quantified. In each modelling layer, there is more and more information added to the model, based on assumptions and decisions.

In this study we try to construct (based on hierarchal model building scheme) and constrain parameters of different conceptual models built on landscape units classified according to their hydrological functions and based on our logical considerations and general lessons from previous studies across the globe for the Luxembourgish catchments. The classified landscapes, wetland, hillslope and plateau, were used to assign different model structures to the individual hydrological response units. As an example deep percolation was defined as dominant process for plateaus, while rapid subsurface flow as dominant process for hillslope, and saturation overland flow as dominant process for wetlands. The modelled runoffs from each hydrological unit were combined in a parallel set-up to proportionally contribute to the total catchment runoff. The hydrological units are, in addition, linked by a common groundwater reservoir. The parallel hydrological units, although increasing the number of parameters, have the benefit of separate calibration. By stepwise calibration different mechanisms can be calibrated at periods when these mechanisms are active in isolation. For instance, the groundwater module is calibrated during dry season recession and the wetland module during isolated summer storms when the hillslopes are below the activation threshold. Moreover, one can constrain parameters by realistic conditions. As an example, the lag time of wetlands is likely to be shorter than the lag time of water traveling to the outlet from a plateau. Moreover, due to the dominance of forest on hillslopes in this catchment, the interception threshold should be higher on hillslopes than on plateaus, which are mainly used for agriculture. Furthermore, fluxes and processes can be compared. For example, actual evaporation and transpiration from wetland can potentially be higher than from other entities within a catchment as wetlands are close to saturation for much of the year and evaporation and transpiration is thus less supply limited than on plateaus. To include all the comparisons and criteria in calibration, an evolutionary algorithm was used. The algorithm was adapted and applied in a way that in subsequent steps more and more comparative criteria are forced to be satisfied.

Based on the result, including landscape classification and our basic understanding of how a system may work into hydrological models appears to be a powerful tool to achieve higher model realism as it leads to models with higher performance. Progressive measurement of performance and uncertainty indicates which of the structural elements, parameterization or constraints contributes significantly in capturing the system behaviour. Moreover, this attempt can be seen as a platform which brings the opportunity for both modellers and experimentalists to better communicate and test their hypothesis and assumptions.