Evaluating the carbon dynamics of biogeochemical models using statistical complexity measures

Sebastian Sippel1, Miguel Mahecha1, Michael Hauhs2, Holger Lange3
1 Department for Biogeochemical Integration, Max Planck Institute for Biogeochemistry, Jena
2 Ecological Modelling, University of Bayreuth
3 Norwegian Institute of Bioeconomy Research, Norway

P 4.4 in Digging DATA, molding models: On the pursuit of patterns and correlations


A thorough evaluation and validation procedure („benchmarking“) of biosphere model simulations is a crucial task in order to improve earth system modelling. In this thesis, statistical complexity measures (SCM) were explored in the context of benchmarking land models and as empirical data-analytic indicators for environmental science applications.

Material and Methods

SCMs quantify the dynamical structure of a time series through its statistical complexity and information content. In particular, these tools -unlike conventional methods- are able to differentiate between deterministic-chaotic processes and correlated stochastic noise.

First, we addressed some application-relevant theoretical issues, namely to enhance and analytically understand the Fisher Information, a local, gradient-based complexity quantifier based on ordinal pattern statistics. Second, we applied the statistical methods to European carbon flux data.


The Fisher Information was refined through the development of a pattern-ordering scheme that maximizes the contrast between stochastic and deterministic-chaotic processes. This allows to target the complexity measure towards the distinction of particular classes of physical processes.

In the second part of the thesis, the statistical complexity measures were applied to simulated and observed time series of gross primary production (GPP). We find that the complexity quantifiers sensitively quantify inherent dynamical structure in models and observations, which is not the case for inter-scenario differences within one model structure.  This leads us to suggest that SCMs are very useful model benchmarking tools that distinguish models based on their dynamical structure and thus potentially superior to conventional model evaluation metrics.



In conclusion, statistical complexity measures are a promising data-analytic tool for model validation systems and, in general, to distinguish and describe different classes of processes.

Keywords: Model benchmarking, Statistical complexity, Carbon fluxes
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