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Abstract

Data analysis and model-data comparisons in the environmental sciences require diagnostic
measures that quantify time series dynamics and structure, and are robust to noise in
observational data. This paper investigates the temporal dynamics of environmental time
series using measures quantifying their information content and complexity. The measures
are used to classify natural processes on one hand, and to compare models with observations
on the other. The present analysis focuses on the global carbon cycle as an area of
research in which model-data integration and comparisons are key to improving our understanding
of natural phenomena. We investigate the dynamics of observed and simulated
time series of Gross Primary Productivity (GPP), a key variable in terrestrial ecosystems
that quantifies ecosystem carbon uptake. However, the dynamics, patterns and magnitudes
of GPP time series, both observed and simulated, vary substantially on different temporal
and spatial scales. We demonstrate here that information content and complexity, or
Information Theory Quantifiers (ITQ) for short, serve as robust and efficient data-analytical
and model benchmarking tools for evaluating the temporal structure and dynamical properties
of simulated or observed time series at various spatial scales. At continental scale, we
compare GPP time series simulated with two models and an observations-based product.
This analysis reveals qualitative differences between model evaluation based on ITQ compared
to traditional model performance metrics, indicating that good model performance in
terms of absolute or relative error does not imply that the dynamics of the observations is
captured well. Furthermore, we show, using an ensemble of site-scale measurements
obtained from the FLUXNET archive in the Mediterranean, that model-data or model-model
mismatches as indicated by ITQ can be attributed to and interpreted as differences in the temporal structure of the respective ecological time series. At global scale, our understanding of C fluxes relies on the use of consistently applied land models. Here, we
use ITQ to evaluate model structure: The measures are largely insensitive to climatic scenarios,
land use and atmospheric gas concentrations used to drive them, but clearly separate
the structure of 13 different land models taken from the CMIP5 archive and an
observations-based product. In conclusion, diagnostic measures of this kind provide dataanalytical
tools that distinguish different types of natural processes based solely on their
dynamics, and are thus highly suitable for environmental science applications such as
model structural diagnostics.