Fig 1.
Illustration of causal Information Theory quantifiers as data-analytical tools.
The causality entropy–complexity plane exhibits upper and lower limit curves, and the distances to these can be used to classify relevant processes. For all calculations, D = 6, τ = 1, and n = 104 were chosen.
Fig 2.
Illustration of the causality Shannon-Fisher plane plane () as data-analytical tool.
is used to classify relevant processes, such as constant/periodic signals, white and coloured noise (noise with a power spectrum proportional to 1/fk), and deterministic signals (e.g. chaotic maps), similar to Fig 1. For all calculations, D = 6, τ = 1, and n = 104 were chosen.
Fig 3.
ITQ derived from monthly time series from the JRC-TIP FAPAR dataset.
(top) Weighted Permutation Entropy, (bottom) RGB plot of weighted permutation entropy (, red channel), weighted complexity (
, green channel), and weighted Fisher Information (
, blue channel). An intense color indicates a high value of the respective ITQ.
Fig 4.
The effect of seasonal and diurnal oscillations on ITQ.
GPP dynamics at three flux tower measurement sites from half-hourly to monthly resolution as quantified by a) , and b)
.
Fig 5.
Model-Data comparison of simulated and observations-based GPP over the European continent.
Colour-coded (top right), as obtained from (top left) MTE-MR, (bottom left) JSBACH, and (bottom right) LPJmL. The causal information planes illustrating the point densities are given in the insets.
Fig 6.
Model-Data comparison of simulated and observations-based GPP over the European continent.
Colour-coded (bottom right), as obtained from (top left) MTE-MR, (bottom left) JSBACH, and (bottom right) LPJmL. The causal information planes illustrating the point densities are given in the insets.
Fig 7.
Model-Data comparison of simulated and observed GPP over the European continent.
Jensen-Shannon Divergence between (A) JSBACH and MTE-MR, and (B) LPJmL and MTE-MR. RMSE between (C) JSBACH and MTE-MR, and (D) LPJmL and MTE-MR.
Fig 8.
ITQ-based model-data comparison at site scale for Mediterranean flux tower sites.
(A) , and (B)
. (C) Time series of GPP at Puechabon, France.
Fig 9.
Differentiating model structure with statistical complexity measures.
The different models are coded by different colours, filling indicates the analyzed time period for all grid cells of the globe.