Data compression to define information content of hydrological time series

When inferring models from hydrological data or calibrating hydrological models, we might be interested in the information content of those data to quantify how much can potentially be learned from them. In this work we take a perspective from (algorithmic) information theory (AIT) to discuss some underlying issues regarding this question. In the information-theoretical framework, there is a strong link between information content and data compression. We exploit this by using data compression performance as a time series analysis tool and highlight the analogy to information content, prediction, and learning (understanding is compression). The analysis is performed on time series of a set of catchments, searching for the mechanisms behind compressibility. We discuss both the deeper foundation from algorithmic information theory, some practical results and the inherent difficulties in answering the question: "How much information is contained in this data?". The conclusion is that the answer to this question can only be given once the following counter-questions have been answered: (1) Information about which unknown quantities? (2) What is your current state of knowledge/beliefs about those quantities? Quantifying information content of hydrological data is closely linked to the question of separating aleatoric and epistemic uncertainty and quantifying maximum possible model performance, as addressed in current hydrological literature. The AIT perspective teaches us that it is impossible to answer this question objectively, without specifying prior beliefs. These beliefs are related to the maximum complexity one is willing to accept as a law and what is considered as random.