To evaluate models as hypotheses, we developed the method of Flux Mapping to construct a hypothesis space based on dominant runoff generating mechanisms. Acceptable model runs, defined as total simulated flow with similar (and minimal) model error, are mapped to the hypothesis space given their simulated runoff components. In each modeling case, the hypothesis space is the result of an interplay of factors: model structure and parameterization, choice of error metric, and data information content. The aim of this study is to disentangle the role of each factor in model evaluation. We used two model structures (SACRAMENTO and SIMHYD), two parameter sampling approaches (Latin Hypercube Sampling of the parameter space and guided-search of the solution space), three widely used error metrics (Nash-Sutcliffe Efficiency – NSE, Kling-Gupta Efficiency skill score – KGEss, and Willmott’s refined Index of Agreement – WIA), and hydrological data from a large sample of Australian catchments. First, we characterized how the three error metrics behave under different error types and magnitudes independent of any modeling. We then conducted a series of controlled experiments to unpack the role of each factor in runoff generation hypotheses. We show that KGEss is a more reliable metric compared to NSE and WIA for model evaluation. We further demonstrate that only changing the error metric — while other factors remain constant — can change the model solution space and hence vary model performance, parameter sampling sufficiency, and/or the flux map. We show how unreliable error metrics and insufficient parameter sampling impair model-based inferences, particularly runoff generation hypotheses.

Equifinality is understood as one of the fundamental difficulties in the study of open complex systems, including catchment hydrology. A review of the hydrologic literature reveals that the term equifinality has been widely used, but in many cases inconsistently and without coherent recognition of the various facets of equifinality, which can lead to ambiguity but also methodological fallacies. Therefore, in this study we first characterise the term equifinality within the context of hydrological modelling by reviewing the genesis of the concept of equifinality and then presenting a theoretical framework. During past decades, equifinality has mainly been studied as a subset of aleatory (arising due to randomness) uncertainty and for the assessment of model parameter uncertainty. Although the connection between parameter uncertainty and equifinality is undeniable, we argue there is more to equifinality than just aleatory parameter uncertainty. That is, the importance of equifinality and epistemic uncertainty (arising due to lack of knowledge) and their implications is overlooked in our current practice of model evaluation. Equifinality and epistemic uncertainty in studying, modelling, and evaluating hydrologic processes are treated as if they can be simply discussed in (or often reduced to) probabilistic terms (as for aleatory uncertainty). The deficiencies of this approach to conceptual rainfall-runoff modelling are demonstrated for selected Australian catchments by examination of parameter and internal flux distributions and interactions within SIMHYD. On this basis, we present a new approach that expands equifinality concept beyond model parameters to inform epistemic uncertainty. The new approach potentially facilitates the identification and development of more physically plausible models and model evaluation schemes particularly within the multiple working hypotheses framework, and is generalisable to other fields of environmental modelling as well.

Water quality dynamics depend strongly on hydrologic flow paths and transit time within catchments. In this paper we use a travel time tracking method to simulate stream salinity (as measured by electrical conductivity) in the Duck River catchment, NW Tasmania, Australia. The approach couples the StorAge transit time modelling approach with two different approaches to model electrical conductivity. The first assumes the catchment has a cyclic salt balance (rainfall source, stream flow sink) that is in dynamic equilibrium and evapoconcentration of salt is the only process changing concentration. The second assumes that the salinity of water in catchment storages is a function of water age in those stores, without explicitly simulating salt mass balance processes. The paper compares these alternate approaches in terms of salinity simulation, simulated stream water age distributions, and simulated storage age distributions. Both salinity simulation approaches reproduce stream salinity with high fidelity under calibration and perform well under validation. The simulations using the age-related solute concentration approach produce less biased results and thus high model efficiencies for validation periods. This approach also produces more consistent model parameter estimates between periods. There are systematic differences in the resultant age distributions between models, particularly for the solute balance based simulations where parameters (catchment storage size) changed more between calibration periods. The effect of time varying versus static storage selection functions are compared, with clear evidence that time varying storage selection functions with parameters linked to catchment conditions (flow) are essential for adequate simulation of event concentration dynamics.