A brief history of equifinality in hydrological modelling: from GST to GLUE to ML

Keith Beven, Yang Eric Hong 

AbstractEquifinality has shaped hydrological modelling for five decades. The equifinality thesis rejects the concept of an “optimal” model in favour of the possibility that different model structures or parameter sets can provide similarly acceptable representations of a system when uncertainties in the forcing and evaluation data are considered, especially when those data are subject to epistemic uncertainties and disinformation. We trace the concept from General Systems Theory and geomorphology to its adoption in hydrology, the development of GLUE, and subsequent limits-of-acceptability approaches to model evaluation. We then examine its emerging relevance to machine learning. High-dimensional and flexible ML models can achieve similar high predictive performance through different architectures and training realizations while encoding different internal representations, giving rise to a form of neural equifinality. Improved predictive skill therefore does not necessarily resolve questions of process attribution, identifiability or robustness under extrapolation and change. We argue that the ML era extends and amplifies, rather than resolves, the equifinality problem, highlighting the need for hypothesis testing, informative observations and fitness-for-purpose evaluation of alternative model representations.