Causal inference is at the heart of the scientific method as usually practiced. Still, Karl Popper (The Logic of Scientific Discovery, 1935/1959)  tells us that a theory in the empirical sciences can never be proven: it can only be falsified, meaning that it can, and should, be scrutinized with decisive experiments. Even so, nobody that I know writes or publishes papers to disprove one’s own theory, only an opposing theory. And the debate rages on.

At the heart of this session lies the question of whether, and how, one can prove, rather than just disprove, a causal link between phenomena in the empirical sciences. The session deals specifically with statistical, as opposed to dynamical methods. These methods have the advantage that they are essentially indifferent to any laws of, or other accumulated heuristic ideas on, the field to which they are being applied: whether the time series one considers are from the environmental sciences, biology or medicine does not matter, only their length and accuracy does.

Judea Pearl (e.g., Stat. Surveys, 2009) made an important observation on how to transcend the saying that “Correlation is not causation” by pointing out that standard methods of statistical analysis rely on the stationarity hypothesis of the phenomena being examined. Crucial questions, however, like the causal role of anthropogenic forcing in climate change, deal precisely with the causes of nonstationarity. In particular, Pearl suggested counterfactual analysis as an essential approach in establishing criteria for the necessary and sufficient character of a given cause for a given phenomenon. Thus, the common approach of detection and attribution in the climate sciences only covers the sufficiency aspect of anthropogenic forcing, and more can be done (Hannart et al., BAMS, 2016; Clim. Change, 2016).

The present talk will cover four specific aspects of these broad issues: (i) the distinction between information transfer, including both linear correlations and nonlinear extensions thereof, and true causation; (ii) the divergent results of some widely, and not so widely, used methods of studying information transfer (Krakovska et al., PRE, 2018; Kossakowski et al., Psychol. Methods, 2021; Delforge et al., HESS, 2022); (iii) shared variability of climatic time series (De Viron, GRL, 2013; ); and (iv) the uses of data assimilation in applying counterfactual theory to nonstationary phenomena (Carrassi, QJRMS, 2017; Metref et al., QJRMS, 2019).

Conclusions will include the obvious one that statistical studies of causal inference have to be complemented by dynamical ones.

How to cite: Ghil, M., Carrassi, A., and de Viron, O.: Some Thoughts on Causal Inference, the Scientific Method, and Data Assimilation, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-20548, https://doi.org/10.5194/egusphere-egu24-20548, 2024.

The talk discusses a critical topic in climate science: understanding how interventions on our climate system influence the likelihood of extreme events. The focus is on methodologies that enable causal attribution of such events to specific drivers, rather than merely predicting their occurrence. We discuss common practices and highlight the use of recent statistical methods that are applicable when only observational data is available, as opposed to model-based data. The talk defines the concept of a causal effect of a treatment (such as changes in flood infrastructure or increased CO2 emissions) on extreme outcomes (like a one in 100 year flood). We also cover the estimation of these effects amidst confounding factors and the assessment of associated uncertainties. Finally, we discuss the inherent challenges of applying causal inference to extreme climate events. 

How to cite: Engelke, S.: Causal methods for climate extremes, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-2948, https://doi.org/10.5194/egusphere-egu24-2948, 2024.

The present communication provides a contribution to an overarching cross-methodological causality investigation, encompassing a methodological synergy among physical, analytical, information-theoretic and systems intelligence approaches to causal discovery and quantification in complex system dynamics. These efforts methodologically lead to the emergence of a broader causal framework, valid not only in classical recurrence-based dynamical systems, but also on the generalized information physics of non-ergodic coevolutionary spatiotemporal complexity.

This study begins with a comprehensive cross-examination of causality metrics derived from these diverse domains, by synthesizing causality insights from information theory, which enables the quantification of information flow among variables; differential geometry, which captures the curvature and structure of causal relationships; dynamical systems, which analyze the temporal evolution of systems and associated kinematic geometric properties; and fundamental physical metrics, which elucidate causal connections in the physical world from fundamental thermodynamic principles. Through this analysis, we aim to deepen our understanding of causality in complex systems, with physical process understanding and geophysical applications in mind.

Having laid out some of the key methodological flavours of causality, the present communication introduces new metrics further contributing to a broader non-Shannonian information theoretic causality pool of methods, along with additional advances on quantum thermodymamical, nonlinear statistical mechanical, differential geometric and topologic approaches on causality. Positioning ourselves in a broader nonlinear non-Gaussian non-ergodic setting to tackle far-from-equilibrium structural-functional coevolution and synergistic emergence in complex system dynamics, our derivations further contribute to a new generation of information theoretic, dynamical systems and non-equilibrium thermodynamic causality approaches, along with their synergistic articulation towards a unified framework. This brings out further cross-methodological comparability, portability and complementary insights on dealing with the intricate causality of complex multiscale far-from-equilibrium Earth system dynamic phenomena.

By unveiling manifold flavours of causality and their interconnections, this study brings out their commonalities, synergies, and further potential synergistic applications across disciplines. This interdisciplinary approach not only enhances our theoretical understanding of causality but also provides practical implications for applications in fields such as data science, network theory, and complex systems analysis, with direct relevance across the Earth system sciences and beyond.

How to cite: Perdigão, R. A. P.: Unfolding the Manifold Flavours of Causality, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6535, https://doi.org/10.5194/egusphere-egu24-6535, 2024.

Causal inference is indeed a challenging endeavor, particularly when applied to observational studies of interacting systems. Perl's theory, along with the PC algorithm on directed acyclic graphs, and its extensions PCMCI and FCI, are powerful tools. However, their application to time series is time-consuming, and they still struggle to distinguish Markov-equivalent scenarios.

In our talk, we will present some methods based on principles that are partly or fully different from those underlying the aforementioned tools. Due to time constraints, we will focus on the main principles that allow the discovery of causal relations between a pair of systems, including hidden common causes (referred to as common drivers or confounders in different schools of thought). We won't delve into the numerous technical challenges due to the time limit.

How to cite: Telcs, A.: Some alternative metods for causal discovery, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12204, https://doi.org/10.5194/egusphere-egu24-12204, 2024.

We present a general theory for computing and estimating Shannon entropy-based information transfer in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises, by extending the Liang-Kleeman framework of causality inference to nonlinear cases. The method presents effective and computable formulas of the rates of information transfer between sets of causal and consequential system variables, relying on the evaluation of conditional expectations of the deterministic and stochastic forcings (Causal Sensitivity Method: CSM). The CSM can work with a) ensemble model runs, b) system time series in ergodic conditions and c) time series without a priori knowledge of model equations. The CSM also allows to express the information transfer parcels, which are attributable either to one-to-one interactions or to synergies across groups of variables and assess where the information is more relevant in the state space. The CSM is tested in two proof-of-concept low-order models: 1) a nonlinear model derived from a potential function and 2) the classical chaotic Lorenz model, both forced by additive and/or multiplicative noises. The CSM is also tested with a nonlinear regression model of the ice-cover time evolution, forced by radiation. The CSM estimation is much more robust and efficient than methods using the stochastic model’s full probability density function and its derivatives, whose estimation is rather unreliable in case of short data availability. The analysis also demonstrates that the CSM estimation is computationally cheap in the different experiments, providing evidence of the possibilities and generalizations offered by the method, thus opening new perspectives on real-world applications. This work was funded by the Portuguese Fundação para a Ciência e a Tecnologia (FCT) I.P./MCTES through national funds (PIDDAC) – UIDB/50019/2020(https://doi.org/10.54499/UIDB/50019/2020),UIDP/50019/2020(https://doi.org/10.54499/UIDP/50019/2020) and LA/P/0068/2020 (https://doi.org/10.54499/LA/P/0068/2020) and the project  JPIOCEANS/0001/2019 (ROADMAP).

How to cite: Pires, C., Vannitsem, S., and Docquier, D.: Evaluation of Shannon Entropy-based Information transfer in nonlinear systems , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4315, https://doi.org/10.5194/egusphere-egu24-4315, 2024.

Causality analysis is an important and old problem lying at the heart of scientific research. Causality analysis based on data, however, is a relatively recent development. Traditionally causal inference has been classified as a field in statistics. Motivated by the predictability problem in physical science, it is found that causality in terms of information flow/transfer is actually a real notion in physics that can be derived ab initio, rather than axiomatically proposed as an ansatz, and, moreover, can be quantified. A comprehensive study with generic systems (both deterministic and stochastic) has just been fulfilled, with explicit formulas attained in closed form (Liang, 2016). These formulas are invariant upon nonlinear coordinate transformation, indicating that the so-obtained information flow should be an intrinsic physical property. The principle of nil causality that reads, an event is not causal to another if the evolution of the latter is independent of the former, which all formalisms seek to verify in their respective applications, turns out to be a proven theorem here. In the linear limit, its maximum likelihood estimator is concise in form, involving only the commonly used statistics, i.e., sample covariances. An immediate corollary is that causation implies correlation, but the converse does not hold, expressing the long standing philosophical debate ever since Berkeley (1710) in a transparent mathematical expression.

The above rigorous formalism has been validated with benchmark systems like baker transformation, Hénon map, stochastic gradient system, and with causal networks in extreme situations such as those buried in heavy noises and those with nodes almost synchronized (e.g., Liang, 2021), to name a few. They have also been applied to real world problems in the diverse disciplines such as climate science, dynamic meteorology, turbulence, neuroscience, financial economics, quantum mechanics, etc., with interesting new findings. For example, Stips et al. (216) found that, while CO₂ emission does drive the recent global warming, on a paleoclimate scale, it is global warming that drives the CO₂ emission; PNA, a teleconnection pattern related to the inclement weather in North America, may trace a part of its origin to a rather limited local marginal sea far away in Asia. Besides, with the above causality analysis, pollution sourcing (particularly PM2.5) may be conducted in a rather effective way via causal graph reconstruction. If time permits, I will also present an ongoing application to the development of causal AI algorithms to overcome the interpretability crisis, and a recent remarkable exercise with such an algorithm in the forecasting of El Niño Modoki, a climate mode linked to hazards in far-flung regions of the globe.

References:

Liang, 2014: Unraveling the cause-effect relation between time series. Phy. Rev. E,  90, 052150.

Liang, 2016: Information flow and causality as rigorous notions ab initio. Phys. Rev. E, 94, 052201.

Liang, 2021: Normalized multivariate time series causality analysis and causal graph reconstruction. Entropy, 23, 679.

Liang et al., 2021: El Niño Modoki can be mostly predicted more than 10 years ahead of time. Nature Sci. Rep. 11:17860

How to cite: Liang, X. S.: Causality as a real physical notion ab initio, and its applications in Earth system sciences, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-2618, https://doi.org/10.5194/egusphere-egu24-2618, 2024.

Stips et al (2016) demonstrated the existing causal relationship between Green House Gases (GHG) concentrations and Global Mean Surface Temperature (GMTA) based on the Information Flow (IF) methodology. Critics on the application of the Information Flow concept as developed by Liang (2008, 2016) has focused on the underlying assumption of uncorrelated residuals (noise) between the time series. However, this assumption can only make sense for a system with two components, as for a multi-dimensional system unobserved noise may well exist. Fundamentally, there can be no such thing like correlated noise at all. It can seemingly only appear because of some hidden process(es). For investigating this in detail a multivariate information flow analysis has been developed. We will show that in our tests using processes with correlated noises, the preset causalities can be well reproduced. Further, it will be demonstrated that reducing autocorrelation within the time series by pre-whitening, confirms the achieved causality directions. Finally, we question the validity of the proposed alternative measure using forecast error variance decomposition based on vector autoregression by Goulet and Goebel (2021), because in their method causal directions can be simply reversed by reordering.  A physically faithful causal measure should be generally independent of ordering.

Coulombe, P. G. and Goebel, M. 2021. On Spurious Causality, CO2, and Global Temperature.  Econometrics, 9(3), 33.

Liang, X. S. 2008. Information Flow within Stochastic Dynamical System. Phys. Rev. E 78: 031113.

Liang, X. S. 2016. Information Flow and Causality as rigorous Notions ab initio. Physical Review E 94: 05220.

Stips, A., D. Macias, C. Coughlan, E. Garcia-Gorriz, and X. S. Liang. 2016. On the Causal Structure between CO2 and Global Temperature. Scientific Reports 6: 21691.

How to cite: Stips, A., Liang, S., and Macias-Moy, D.: A Reply to “On Spurious Causality, CO2, and Global Temperature”, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-20353, https://doi.org/10.5194/egusphere-egu24-20353, 2024.

In a world where climate change is rapidly accelerating, droughts are becoming more frequent and severe, posing a serious challenge to food security in the most vulnerable regions. The Horn of Africa has witnessed a rise in acute malnutrition, affecting 6.5 million people in 2022 [1]. Prolonged dry spells significantly contribute to this crisis [2], yet it is crucial to recognize that droughts are not the sole driver. Various factors, including hydrological conditions, food production capabilities, market access, insufficient humanitarian aid, conflicts, and displacement, play a significant role [3,4]. Understanding the underlying causes of food insecurity is pivotal for improving the effectiveness of humanitarian actions, yet in this context, the study proves to be complex, involving multiple variables, scales, and non-linear relationships. Predictive Machine Learning (ML) techniques are not suited to understanding the causes and estimating the causal effect by default [5,6], instead, this study focuses on causal inference to quantify the impacts of climate and socioeconomic factors on food insecurity. Our key contributions involve discerning causal relationships within the intricate food security system, integrating a comprehensive database including socio-economic, weather and remote sensing data, and estimating the causal effect of humanitarian interventions on the food security index, the outcome of interest. The causal discovery task is performed via time series methods accounting for nonlinear and nonstationary relations, like the PCMCI algorithm and nonlinear Granger causality [7,8], identifying the drivers in the data that are causally linked to the outcome. Besides, the causal effect estimation task is performed via a Conditional Average Treatment Effect (CATE), gaining insights into the spatiotemporal heterogeneity of the impact of humanitarian interventions on the outcome [9]. Such endeavors are crucial for facilitating more efficient future interventions and policies, thereby improving transparency and accountability in humanitarian aid.

References

[1] WFP, “Impacts of the Cost of Inaction on WFP Food Assistance in Eastern Africa (2021 & 2022),” https://docs.wfp.org/api/documents/WFP-0000148305/download/, 2023.

[2] Coughlan de Perez E., et al, “From rain to famine: assessing the utility of rainfall observations and seasonal forecasts to anticipate food insecurity in East Africa,” Food Secur., vol. 11, no. 1, pp. 57–68, 2019.

[3] Maxwell D. et al, “Viewpoint: Determining famine: Multi-dimensional analysis for the twenty-first century,” Food Policy, vol. 92, 2020.

[4] Guy A. J. et al, “Climate, conflict and forced migration” Global Environmental Change, vol. 54, no. 4, 2019.

[5] Pearl J., “Causality: Models, reasoning, and inference,” Cambridge University Press, vol. 19, 2000.

[6] Peters J., Janzing D., and Schlkopf B., Elements of Causal Inference: Foundations and Learning Algorithms, The MIT Press, 2017.

[7] Runge, J.. "Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets." Conference on Uncertainty in Artificial Intelligence. PMLR, 2020.

[8] Camps-Valls, G. et al, “Discovering causal relations and equations from data”, Physics Reports 1044 :1--68, 2023

[9] Giannarakis, G. et al, (2022). Personalizing sustainable agriculture with causal machine learning. arXiv preprint arXiv:2211.03179.

How to cite: Cerdà-Bautista, J., Tárraga, J. M., Sitokonstantinou, V., and Camps-Valls, G.: Causal evaluation of humanitarian aid on food security, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-17312, https://doi.org/10.5194/egusphere-egu24-17312, 2024.

Time series of in situ observations and remote sensing data suggest variability in epipelagic ecosystems at seasonal to multiannual time scales. These go along with changes in physical-biogeochemical conditions. While a consensus exists on the proximate causes of observed ecosystem variability (e.g. mixed layer variability, availability of nutrients, grazing pressure), the role of large-scale drivers (e.g. natural climate modes) still needs to be better understood. Moreover, differences in the implementation of marine ecosystem processes exist among Earth System Models, and it is important to understand the uncertainty around the representation of specific interactions via inter-model comparison.

We use output from 5 multi-centennial Earth system model simulations under pre-industrial climate to identify modes of low-frequency biogeochemical properties and the importance of individual drivers. The study focuses on the North Atlantic subpolar gyre (NASPG), a region of high primary productivity and considerable observed natural variability in physical and biogeochemical conditions. We explore causality between modes of climate variability, ocean physics and biogeochemistry by applying a Knowledge-Data-Discovery method, PCMCI. This method enables causal links with a potential time lag to be established between different domains. It proposes a novel way for the comparison of differences between model dynamics.

First, six geographic subregions are identified, based on their physical-biogeochemical characteristics (e.g. deep convection zones, intensity of spring bloom), followed by by the selection of physical and biogeochemical variables. These variables are the maximum winter mixed layer depth due to the role in supplying nutrients to the surface fueling the spring bloom, the North Atlantic Oscillation (NAO), a dominant natural mode climate variability, for its contribution to sea surface temperature (SST) and nutrient variability in the subpolar gyre, and the Gyre Strength, an index reflecting the response of the NASPG to wind forcing. We focus on one micronutrient (Iron) and one macronutrient (Nitrate). They were chosen because both can limit the primary production in this region. 

Next, PCMCI is applied to search for the temporal relationships (potentially lagged) between different regions and variables. These relationships are computed from partial correlations which, for gaussian distributed data, is equivalent to a causal link. The application of this method allows networks of causality to be identified, highlighting drivers of nutrient variability under varying natural climate forcing. The approach enables the quantification of intermodel differences either by analyzing one link after another or by looking directly at the entire causal graphs with a newly proposed method to quantify the dissimilarity between two models.

This method verified expected interactions such as the role of mixed layer depth for nutrient supply and quantified the strength of this interaction across the models. It also highlighted model-specific dynamics such as the role of temperature (via sea-ice formation) for iron in two biogeochemical models out of 5. 

How to cite: Bénard, G., Gehlen, M., and Vrac, M.: Multi-model comparison of causal relationships between atmospheric and marine biogeochemical variables, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-19242, https://doi.org/10.5194/egusphere-egu24-19242, 2024.

Causality is essential for understanding complex systems like the Earth and climate, where a plethora of intertwined variables and processes happen in the wild. Constructing causal graphs often relies on either data-driven or expert-driven approaches, both fraught with challenges. The former methods, like the celebrated Peter-Clark (PC) algorithm, face issues with data requirements and assumptions of causal sufficiency, while the latter demand substantial time and expertise.

This work explores the capabilities of Large Language Models (LLMs) as an alternative to domain experts for causal graph generation. We frame conditional independence queries as prompts to LLMs and employ the PC algorithm with the answers. The performances of the LLM-based conditional independence oracle on systems with known causal graphs show a high degree of variability. We improve the performance through a proposed statistical-inspired voting schema that allows control over false-positives and false-negatives rates. We apply our chatPC algorithm to understand the causal relations between complex sets of variables (social, economic, conflicts, environmental, and climatic factors) in two pressing problems: population displacement and food insecurity in Africa. We find plausible graphs as corroborated by experts in the humanitarian sector, finding traces of causal reasoning in the model's answers. We posit that LLM-based causality is a new, promising, alternative avenue for automated causality, especially indicated for rapid response and data-scarce regimes.

How to cite: Camps-Valls, G., Cohrs, K.-H., Diaz, E., Sitokonstantinou, V., and Varando, G.: Large Language Models for Causal Discovery in the Earth Sciences, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-21883, https://doi.org/10.5194/egusphere-egu24-21883, 2024.