Abstract
Abstract. When inferring models from hydrological data or calibrating hydrological models, we are 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, (A)IT, 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. We discuss both the deeper foundation from algorithmic information theory, some practical results and the inherent difficulties in answering the following question: "How much information is contained in this data set?". 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? and (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 the current hydrological literature. The AIT perspective teaches us that it is impossible to answer this question objectively without specifying prior beliefs.
Highlights
IntroductionThis question is not often explicitly asked, but is underlying many challenges in hydrological modeling and monitoring
How much information is contained in hydrological time series? This question is not often explicitly asked, but is underlying many challenges in hydrological modeling and monitoring
The file sizes after quantization are exactly equal to the number of values in the series, as each value is encoded by 1 byte (8 bits), allowing for 28 = 256 different values, and stored in binary raw format
Summary
This question is not often explicitly asked, but is underlying many challenges in hydrological modeling and monitoring. The information content of hydrological time series is, for example, relevant for decisions regarding what to measure and where in order to achieve optimal monitoring network designs (Alfonso et al, 2010a,b; Mishra and Coulibaly, 2010; Li et al, 2012). In hydrological model inference and calibration, the above question can be asked in order to decide how much model complexity is warranted by the data (Jakeman and Hornberger, 1993; Vrugt et al, 2002; Schoups et al, 2008; Laio et al, 2010; Beven et al, 2011). The question seems straightforward, the answer is not This is partly due to the fact that the question is not completely specified. An objective assessment of information content is only possible when prior knowledge is explicitly specified
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