Investigating conceptual model structure uncertainty
: Progress in large-sample comparative hydrology

  • Wouter Knoben

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Hydrological modelling is complicated by several sources of uncertainty: observations of climatic forcing and streamflow will have errors, model parameters are not always properly identifiable, and the choice of model structure itself can be difficult. A model structure, i.e. the collection of equations that represent certain hydrologic states and fluxes, can be seen as a hypothesis about how a given catchment behaves. Different models are different hypotheses and choosing the appropriate model is thus important for many applications, e.g. runoff prediction in ungauged basins, climate change impact assessment, and prediction of extremes such as floods and droughts. However, many different models have been created and differences and similarities between models are not well understood. In an ideal situation, we would (1) select a representative sample of testing conditions and (2) a representative sample of models (that are (3) implemented in
a coding framework that ensures an objective comparison between models can be made), (4) use an objective and extensive testing scheme to find between-model differences and similarities and thus improve our understanding of model structure uncertainty. None of these four steps are straightforward. Focussing on a sub-type of hydrologic models known as conceptual models, this thesis contributes to each of the steps in turn, although in every case many challenges remain.

The findings from any experiment are conditional on the study set-up and conclusions can only be generalised if it is clear how the tested sample relates to all possible cases. In hydrology, selecting a representative sample of catchments is difficult because it is not well known how hydrologic conditions vary across the world. Hydrologic conditions can be separated into climatic conditions and catchment attributes such as soil type and geology. Global data are available for several climatic variables that are hydrologically relevant (e.g. precipitation, temperature), but global data for hydrologically meaningful catchment attributes are more difficult to find. This thesis investigates the possibility of a hydrologically-informed climate classification and shows that a system based on three dimensionless numbers contains sufficient information to group hydrologically similar regimes on a global scale. These numbers do not account for a region’s annual number of rainfall seasons, even though this strongly influences within-year hydrologic behaviour. Further analysis shows that on a global scale, the number of rainfall seasons is a relevant indicator on approximately 7% of the Earth’s land surface. These results give us some idea of how representative a sample of catchments is of the global range of hydro-climatic conditions. An open challenge on this topic is expanding our approach to a global catchment classification that includes catchment attributes as well as climatic conditions, but, for now, data limitations place that out of reach.

In a model-comparison study, the next challenge is selecting a representative sample of models. There is however a wide variety of models available and no clear basis for defining both the total model space (i.e. all possible model configurations) and a representative selection within that space (i.e. several model structures that are in some way considered to cover different areas of the total model space). This thesis assumes that an iterative approach is appropriate, where a large number of models is used in a first model-comparison study. In a next pass, results from the first round can inform model selection to reduce the total number of structures and identify whether the first model sample leaves any obvious gaps in the total model space uncovered. To facilitate objective model comparison, a new open-source modelling framework has been created that currently includes 46 different conceptual hydrological models. The framework follows several best practices in model development and through its modular nature provides a stable ground for model comparison studies. Each modelling decision can be isolated in turn and its impact assessed. Expansion of the framework is straightforward, so that it can easily be used for iterative model-comparison studies.

Any large-sample study must necessarily sacrifice study depth to some extent, in return for larger sample sizes. This thesis investigates model structure uncertainty using 36 conceptual models, three different objective functions and 559 catchments (for which time series of climatic forcing and a variety of catchment attributes are known). To keep the analysis manageable, for each combination of model, catchment and objective function, only a single parameter set is calibrated. For the majority of cases at least two but up to 25 models achieve very similar efficiency values, although these are not the same models for each catchment. Contrary to expectations, there is no obvious relation between the number of model parameters and either calibration performance, evaluation performance and performance change between both periods. Instead, the model structure seems to dictate whether a model will do well for a given objective function and whether it will perform better or worse (relative to the other models) under certain flow regimes. The relation between model performance and catchment attributes is inconclusive, but models can be relatively neatly grouped based on their (weak) correlation with catchment attributes. This suggests that certain shared model structure elements lead to similar model performance in specific types of catchments, although this hypothesis remains untested. Taken together, several important steps towards a comprehensive and generalizable model-comparison study have been made in this thesis. A variety of challenges remain, from the need for a catchment classification scheme to a combined assessment of model structure, data and parameter uncertainty. However, these are grand challenges which the hydrologic community has been working on for several decades. The results presented here contribute to progress towards these goals and indicate several promising, practical next steps that can be taken in future work.
Date of Award26 Jun 2019
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorJim Freer (Supervisor) & Ross A Woods (Supervisor)

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