Diagnosing the Dynamics of Observed and Simulated Ecosystem Gross Primary Productivity with Time Causal Information Theory Quantifiers

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 data-analytical 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.

The intrinsic predictability of ecological time series and its potential to guide forecasting

“…, ), and in the environmental sciences it has provided insight into model‐data deviations of gross primary productivity to further understand the global carbon cycle (Sippel et al. ). In epidemiology, a recent study on the information‐theoretic limits to forecasting of infectious diseases concluded that, for most diseases, the forecast horizon is often well beyond the time scale of outbreaks, implying that prediction is likely to succeed (Scarpino and Petri ).…”

Refining multi-model projections of temperature extremes by evaluation against land–atmosphere coupling diagnostics

“…For example, empirical and/or physics-based criteria have been used to constrain snowalbedo feedbacks (Hall and Qu, 2006), constrain carbon cycle projections Wenzel et al, 2014;Mystakidis et al, 2016), or in the context of refining precipitation projections . Moreover, empirical diagnostics are applied to select models for event attribution analyses (Perkins et al, 2007;King et al, 2016;Otto et al, 2015) and analyses of drought projections based on model performance (Van Huijgevoort et al, 2014) or to resample large initialcondition ensembles to alleviate biases without distorting the multivariate structure of climate model output (Sippel et al, 2016b). In the context of land-atmosphere coupling, Fischer et al (2012) and Stegehuis et al (2013) have constrained a re- gional model ensemble over Europe using present-day interannual variability in summer temperature, and observationsbased estimates of summer sensible heat fluxes.…”

The intrinsic predictability of ecological time series and its potential to guide forecasting

“…Although the full potential of permutation entropy to guide forecasting is not yet realized, many other fields are starting to take advantage of its diagnostic potential. In paleoclimate science, permutation entropy has proven useful for detecting hidden data problems caused by outdated laboratory equipment (Garland et al 2016), and in the environmental sciences it has provided insight into model-data deviations of gross primary productivity to further understand the global carbon cycle (Sippel et al 2016). In epidemiology a recent study on the information-theoretic limits to forecasting of infectious diseases concluded that for most diseases the forecast horizon is often well beyond the time scale of outbreaks, implying prediction is likely to succeed (Scarpino & Petri 2017).…”