Data compression to define information content of hydrological time series

摘要

When inferring models from hydrological data or calibrating hydrologicalmodels, we are interested in the information content of those datato quantify how much can potentially be learned from them. In thiswork we take a perspective from (algorithmic) information theory,(A)IT, to discuss some underlying issues regarding this question.In the information-theoretical framework, there is a strong link betweeninformation content and data compression. We exploit this by usingdata compression performance as a time series analysis tool and highlightthe analogy to information content, prediction and learning (understandingis compression). The analysis is performed on time series of a setof catchments.We discuss both the deeper foundation from algorithmic informationtheory, some practical results and the inherent difficulties in answeringthe following question: "How much information is contained in this data set?".The conclusion is that the answer to this question can only be givenonce the following counter-questions have been answered: (1) informationabout which unknown quantities? and (2) what is your current state ofknowledge/beliefs about those quantities?Quantifying information content of hydrological data is closely linked to thequestion of separating aleatoric and epistemic uncertainty and quantifyingmaximum possible model performance, as addressed in the current hydrologicalliterature. The AIT perspective teaches us that it is impossible to answerthis question objectively without specifying prior beliefs.