Comparing Hydrological Models in Configuration and Trajectory Space

Hydrological models often differ substantially in their internal structure, process representations, and parameterisations, even when calibrated against similar observations. Understanding how these structural differences manifest under both environmental forcing and management-driven forcing remains a central challenge for model intercomparison. Here, we explore a transformation-based diagnostic framework grounded in mass conservation and seasonal cyclic behaviour.

Rather than interpreting models in terms of static system states, we focus on admissible mass-conserving transformations defined by the balance among inputs, outputs, and storage changes. This relation defines an admissible envelope of possible transformations, which can be interpreted as a generalised configuration space. Within this space, seasonal cycles trace characteristic trajectories shaped by climatic variability and by model-specific representations of regulation, storage, and decision rules.

To facilitate comparison, we introduce the concept of “prints” and “scans” of these trajectories: visual representations that can be overlaid across models to reveal similarities, divergences, and systematic structural differences. This extension of the "water circles" allows model behaviour to be compared in terms of geometry and organisation of admissible transformations, rather than differences in isolated states or aggregated performance metrics.

Intended as a complementary and exploratory diagnostic, the framework provides a conservation-anchored reference to understand how environmental and anthropogenic forcings are encoded across hydrological models, offering insight into structural differences that traditional intercomparison approaches may obscure.