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.

The present study aims to quantify (estimate) the impact of human water consumption—as for irrigation, livestock, domestic, manufacturing, and thermal energy production—versus (natural) climatic variability on the water balance and storage of the Lake Urmia (LU) basin and consequently the lake desiccation during the past decades. This is indeed a curious question with high practical relevance, given the ongoing drying of the lake and scientific debates around possible causes and viable remedies. One of the strength of the study is incorporating multiple input data (both ground and remote sensing) in developing the basin’s hydrologic model. The authors have also attempted to include the groundwater data which is highly important in this basin, and has been ignored in many (not all) of the previous studies. I enjoyed reading the paper, however, as the other reviewers have already pointed out there are major shortcomings that call for a major revision. In the spirit of helping the authors to improve the manuscript, I’d like to further comment on a number of—I believe—major deficiencies and questionable assumptions of the study that undermine the reliability of their results and discussion, given my own (limited) knowledge/experience in studying the lake’s dynamics and desiccation [Khatami, 2013; Khatami and Berndtsson, 2013; Khazaei et al., in review]. I hope the authors would find my comments useful in highlighting the new insights and contribution of their study.

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.