ICTS

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Linear decomposition techniques, such as Empirical Orthogonal Functions (EOFs) and Maximum Covariance Analysis (MCAs), have long been used to reveal spatial and temporal climate patterns, capturing relationships between climatic variables and large-scale drivers like the El Niño-Southern Oscillation (ENSO). However, these approaches often overlook complex, nonlinear interactions essential for understanding extreme events’ interconnectedness. To address these limitations, our work integrates a complex network framework capable of analyzing high-dimensional data without the assumptions inherent in traditional linear decomposition. Climate networks can reveal intricate interdependencies in the climate system, identifying nodes and links that represent statistically relevant associations. This network-based approach provides insights into synchronous extremes by quantifying linear and nonlinear relationships, enabling us to explore the dynamic nature of extreme event synchrony. We present findings from our recent work, which reveal central India as a key hub for synchronous extreme rainfall events during the Indian Summer Monsoon, characterized by persistent yet geographically localized connections. This “geographical trapping” of extremes is modulated by ENSO phases, with stronger localized synchronicity in El Niño periods and broader linkages in La Niña years. On a global scale, our drought analysis shows that temperature trends drive drought synchrony, while sea surface temperature variability imposes limits, maintaining drought clustering within certain bounds and safeguarding against widespread synchrony across key agricultural regions. Our approach underscores the critical role of synchrony for disaster preparedness and food security. By bridging linear and non-linear techniques, this framework provides actionable insights into extreme events' interconnected patterns, informing strategies for resilience and proactive risk management across multiple scales

I present the recurrence analysis of temperature and relative humidity data from various locations spread over India, including the mountainous region, coastal region, and central and north eastern parts of India. This study reveals the spatiotemporal pattern underlying the climate dynamics and captures the variations in the complexity of the dynamics over the period 1948 to 2022. By reconstructing the dynamics from data, the recurrence pattern is studied using recurrence networks and the measures of the networks computed using a sliding window analysis on the data sets. This brings out the climate variability in different spatial locations and the heterogeneity across the locations chosen. The variations observed in dynamics can be correlated with reported shifts in the climate related to strong and moderate El Niño–Southern Oscillation events.

Complex networks have revolutionised the way non-linear dynamical (deterministic and stochastic) systems are represented and analysed. This paradigm shift owes itself to the ability to encode non-linear relationships in a hierarchical manner from the skeletal structure to deeper and subtle spatio-temporal dependencies. This talk aims to provide an overview of a class of complex networks known as causal networks that draw ideas from various fields including econometrics, social sciences, neuroscience, sciences, ecology and engineering. Of specific interest and relevance are the causal climate networks. The first half of the talk shall be devoted the overview and mathematical formalism of different types of (climate) causal networks with focus on Granger causal and convergent cross-mapping (CCM) class of networks, both of which are constructed from time-series data. The second part of this talk is devoted to a presentation of applications to reconstructing climate networks from data and their analysis, which will include results from our cross-disciplinary research and glimpses from existing literature.

Over the past decade, climate networks have emerged as a powerful tool to characterise high dimensional weather and climate datasets. Climate networks are a sparse representation of the dynamical similarities between weather time series from different geographical locations. Nodes represent the locations themselves, and network edges represent high dynamical similarity between pairs of locations. The topology of the resulting complex network encodes information about how atmospheric and oceanic dynamics “connect” different locations. For instance, strong monsoon years might yield a different network structure than weak monsoon years. With the tools of graph theory and complex networks at our disposal, we can characterise climate dynamics in novel and interesting ways, which yield, in part, results that corroborate what meteorologists already know, and, in part, results that generate new hypotheses about how atmospheric and oceanic processes influence different weather patterns. In this talk, I will present a brief overview of how we estimate climate networks from data, the challenges involved in the estimation process, and finally a few examples of how we obtain new data-driven hypotheses about weather patterns using this tool.

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The main focus of these pedagogical talks will be on discussing the interplay between statistics and climate science as a two-way street. On one hand, thinking about the climate helps us understand many aspects of statistics, from the fundamental to conceptual to practical. On the other, statistical thinking is crucial and indispensable in studying climate. I will also emphasize that statistics plays an important role not just in climate studies, but more generally in understanding any complex system such as those from biological and social sciences as well. Another thread will be the discussion of interplay between uncertainty and dynamics, with an emphasis on the role of dynamical instabilities.

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Climate change is often related to the temporal variation of external driving forces, following a certain arbitrary trend. This poses difficulties to the analysis of complex dynamical systems under the impact of climate change, since all the analysis tools of nonlinear dynamics work only for autonomous systems or systems with periodic driving. To study the impact of climate change characterized by arbitrary time- dependence requires new methods to still use ideas of attractors, basins of attraction and bifurcations in the non-autonomous case. We discuss approaches which allow to study non-autonomous systems in the spirit of nonlinear dynamics: snapshot/pullback attractors, non-autonomous basins of attractions and bifurcations in non-autonomous systems like rate-induced transitions and basin boundary crossings. We use simple conceptual models of climate and ecosystem dynamics to illustrate these concepts.

The timing of monsoon season onset and withdrawal is of paramount importance to the population of the Indian subcontinent. Despite the rainy season occurring annually between June and September, the onset and withdrawal dates vary by up to a month from year to year, making accurate predictions a significant challenge.

However, a revolutionary approach has been developed those promises to transform our understanding of this phenomenon. By comprehending the core physical mechanisms involved in monsoon onset and withdrawal, spatial-temporal regularities have been discovered that can be used for forecasting. This approach fundamentally diverges from the traditional numerical weather and climate models by relying on the Nonlinear Dynamics and Nonlinear Phenomena in Statistical Physics.

This approach demonstrated successful results over a rigorous nine-year testing period, forecasting the onset date up to 40 days in advance and the withdrawal date up to 70 days in advance. It is also applicable to different regions of India, and other parts of the world in South Asia, Africa and South America.

This approach is the solution to mitigate the impact of climate change on human life and property in the region. The evidence is rock-solid, and it will revolutionize our understanding of monsoons, safeguarding the Indian subcontinent population.

The main focus of these pedagogical talks will be on discussing the interplay between statistics and climate science as a two-way street. On one hand, thinking about the climate helps us understand many aspects of statistics, from the fundamental to conceptual to practical. On the other, statistical thinking is crucial and indispensable in studying climate. I will also emphasize that statistics plays an important role not just in climate studies, but more generally in understanding any complex system such as those from biological and social sciences as well. Another thread will be the discussion of interplay between uncertainty and dynamics, with an emphasis on the role of dynamical instabilities.

Climate networks can be used to forecast some important climate phenomena, such as the monsoon, the North Atlantic Oscillation, El Niño events and cyclones. A percolation framework is used to study the cluster structure properties which brings out the global structural changes in the climate network.

Climate networks can be used to forecast some important climate phenomena, such as the monsoon, the North Atlantic Oscillation, El Niño events and cyclones. A percolation framework is used to study the cluster structure properties which brings out the global structural changes in the climate network.