The quantity and quality of information in hydrologic models

The role of models in science is to facilitate predictions from hypotheses. Although the idea that models provide information is widely reported and has been used as the basis for model evaluation, benchmarking, and updating strategies, this intuition has not been formally developed and current benchmarking strategies remain ad hoc at a fundamental level. Here we interpret what it means to say that a model provides information in the context of the formal inductive philosophy of science. We show how information theory can be used to measure the amount of information supplied by a model, and derive standard model benchmarking and evaluation activities in this context. We further demonstrate that, via a process of induction, dynamical models store information from hypotheses and observations about the systems that they represent, and that this stored information can be directly measured.