Nonlinear Processes in Geosciences

Nonlinear Processes in Geosciences

NPG Paper of the Month: “Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach”

Schematic map of spatial diversity of Indian precipitation teleconnections at different time scales. (a) ENSO, (b) IOD, (c) NAO, (d PDO, and (e) AMO. Colors are consistent with the Indian community shown in the right figure. Presence of color in community segment indicates significant synchronization between teleconnection and Indian precipitation. Every single segment of circle shows the temporal scale. Cardinal direction has been projected in the background of each circle.

Today’s we launch one of our promised activities: the NPG Paper of the Month.
This month the award is achieved by Jürgen Kurths and co-authors for their paper “Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach” (
Ankit Agarwal, one of the authors of the manuscript, tells us about the importance of the results achieved with this paper where the authors gained insights on spatial diversity of Indian precipitation teleconnections by studying the effects of global climate indices on Indian precipitation patterns at varying timescales.
Ankit is a hydro-climatologist at the Potsdam Institute for Climate Impact Research and Helmholtz Center for Geosciences, section 5.4 (Hydrology). He is interested in interdisciplinary research to understand multi-scale interactions among different components of Earth. He develops new methods and apply them in hydrology and climatology for advance understanding. His next position is due as an assistant professor at the Department of Hydrology, Indian Institute of Technology-Roorkee, India.

Atmospheric and oceanic phenomena are characterized by multi-scale behavior and their influence on precipitation varies across multiple timescales. Understanding the spatiotemporal variability of coupling between various global climate indices and precipitation is of great importance for accurate prediction of climatic variations on different time-scales. While this coupling has been investigated before, it has been a challenge to address its non-linear, scale-varying, and spatially diverse behavior. The study by Kurths et al., 2019 proposes a novel, and general, framework to disentangle the non-linear dependency structure between rainfall and climate patterns across space and temporal scales, by introducing the concept of multiscale event synchronization (Agarwal et al., 2017).
More specifically, the study examines the spatial diversity of Indian precipitation teleconnection at different time scales, first by identifying homogenous communities (Agarwal et al., 2018) and later by computing nonlinear linkages between the identified communities (spatial regions) and dominant climatic patterns, represented by climatic indices such as El-Nino Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), North Atlantic Oscillation (NAO), Pacific Decadal Oscillation (PDO) and Atlantic multi-decadal Oscillation (AMO). The results of the study unravel the spatial variation of the climate indices across India and across time scales. In particular, ENSO and the (IOD) exhibit precipitation teleconnections in the peninsular and southeast areas of India on interannual and decadal scales, respectively, whereas the North Atlantic Oscillation (NAO) has a strong connection to precipitation particularly in the northern regions (refer to the figure). The effect of PDO is seen across the entire country, while precipitation variations over the semi-arid and arid regions of Central India have linkages to the AMO. The proposed method provides a powerful approach for capturing the dynamics of influences of climatic indices on Indian precipitation and, hence, helps improving precipitation forecasting.

A comparison of the results with the state-of-the-art method, wavelet coherence, shows that the proposed method has much higher skill in detecting linkages between the Indian monsoon system and climate patterns. The authors believe that the findings presented in the paper will appeal to the broader society of Earth scientists and modelers given the problems they face in understanding the dynamics and forecasting Indian precipitation.


Kurths, J., Agarwal, A., Shukla, R., Marwan, N., Rathinasamy, M., Caesar, L., Krishnan, R., and Merz, B.: Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach, Nonlin. Processes Geophys., 26, 251-266,, 2019.

Agarwal, A., Marwan, N., Maheswaran, R., Merz, B., Kurths, J.: Quantifying the roles of single stations within homogeneous regions using complex network analysis, Journal of Hydrology, 563, 802-810,, 2018.

Agarwal, A., Marwan, N., Rathinasamy, M., Merz, B., Kurths, J.: Multi-scale event synchronization analysis for unravelling climate processes: a wavelet-based approach, Nonlin. Processes Geophys., 24, 599-611,, 2017.

Abrupt Warming could bring our planet a “Hothouse Earth” with catastrophic consequences for our economy and society

Abrupt Warming could bring our planet a “Hothouse Earth” with catastrophic consequences for our economy and society

Most of us have enjoyed swings in childhood. Some have even tried to swing faster and make a full 360 degrees’ loop. Those who succeeded had a very strange feeling of not being able to predict whether, increasing the energy of the swing, the transition from normal oscillations and 360 loops would happen. Indeed, there is an energy threshold such that the swing goes from oscillations to full loops and the change in the behavior is abrupt. Say now that the swing is our planet and the energy pumped in the Earth system are the anthropogenic emissions, in a recently published paper in the Proceedings of the National Academy of Sciences ( Will Steffen and co-authors found that increasing the emissions would push the earth towards an abrupt change in trajectory, leading in a very short time span to a 5 degrees’ warmer climate.

Up to now, scientists have predicted a fast but smooth increase of the planet temperature with increasing anthropogenic emissions. Although catastrophic, this scenario would leave enough time to adapt our society to a warmer climate and the associated consequences such as sea-level rise. This study has however identified a series of interconnected factors which could cause a chain reaction and push the Earth towards a “hothouse” state. Deforestation, permafrost thawing, relative weakening of land and ocean physiological CO2 sinks can drive further warming – even if we stop emitting greenhouse gases. Like going through the full loop could cause injuries, this process is likely to be unstoppable and irreversible and will lead to devastating consequences. The authors say: “a Hothouse Earth trajectory will likely exceed the limits of adaptation and result in a substantial overall decrease in agricultural production, increased prices, and even more disparity between wealthy and poor countries”. A Hothouse Earth trajectory would almost certainly flood deltaic environments, increase the risk of damage from coastal storms, and eliminate coral reefs (and all of the benefits that they provide for societies) by the end of this century or earlier.

The results of this study have animated a debate in the climate change community and there is actually a substantial disagreement about the possibility of crossing the tipping point described in the article. The non-linear geophysics community is working hard to understand these critical phenomena in simple systems which represents idealized climate.

Workshop report: Mathematics of the Economy and Climate

Workshop report: Mathematics of the Economy and Climate

Just before the summer a group of about 40 scientists gathered in an old Monastery in the Netherlands (Kontakt der Kontinenten, Soesterberg) for a rather special collaborative workshop entitled “Mathematics of the economy and climate”. Mathematicians, climate scientists and economists – a group of scientists that normally does not mix and are rather unfamiliar with each other’s research – joined together for three days to learn from each other and discuss the most pressing research questions around ongoing climate change and its connections with the development of economic systems (

The workshop included high-profile speakers from Imperial College, ENS Lyon, London School of Economics and Yale. Prof. Tony Smith from Yale reported on recent research using the integrated assessment model developed by his colleague William Nordhaus (Nobel prize 2018) and presented attempts to view the global economic system and its interaction with climate in a spatially resolved way. This and many other interesting talks triggered lively discussions on, e.g., the adequacy of models in general and in particular in the different fields of research. Uncertainty in both the climate response and the economic development was one issue that was extensively discussed as it appears that economists tend to assume future climate (measured by, e.g., the equilibrium or transient climate sensitivity) as relatively well-known and vice versa.

There is still a long way to go for a good understanding of the combined evolution and interaction of the climate and the economic system. This workshop was a starting point for the different disciplines to learn to talk to each other. Participants enjoyed discussing with academics from different areas in an open-minded atmosphere. Finally it became clear that there are exciting and novel mathematical techniques available such as numerical methods for stochastic differential equations and dynamical systems to tackle the challenges ahead.

June Heatwave 2019: can we attribute the event to anthropogenic emission?

June Heatwave 2019: can we attribute the event to anthropogenic emission?

If August Rodin had lived nowadays, he would have placed his gates of hell (la Porte de l’Enfer) in Gallargues-le-Montueux, where the absolute French temperature record (45.9 °C) was set on June 28th this year.

The last week of June has been very hot, not only in the south of France, but overall central Europe: in the Alps, some locations such as Chamonix (France) and Aosta (Italy) experienced temperatures close or above 40°C, setting absolute records. The atmospheric circulation responsible for this event consisted of a marked low pressure system centered on the Atlantic Ocean between France and Spain and a high pressure ridge extending from Morocco and Algeria up to central France and the Alpine regions. The strong Meridional wind caused exceptionally warm air advection from Africa and loads of Saharan dusts.

June heatwaves can have a large impact on professional and educational activities compared to July and August heatwaves, where most of the people are on holiday. It is therefore important to understand if greenhouse emissions have affected the intensity of such event and if similar heatwaves will be more likely in the future. A branch of climate science, termed attribution, tries to provide these answers via European collaborative projects (e.g. EUPHEME). The June 2019 heatwave is very interesting from this point of view because a quick attribution study has been published, at a record time, just few days after the events.

The first step for attributing the event to climate change is to provide its definition: which variable/indicator? Which spatial area? Which period of time? In their study the authors considered the three-day average of daily mean temperatures, as they are relevant for health impacts, and two spatial scales: the whole of France and one city, Toulouse. Only June heatwaves were analyzed because the atmospheric circulation is generally different in June than in July and August and the impacts are also different.

The study used a combination of high resolution observations and state-of-the-art climate models to highlight that the probability of this event has largely increased compared to the past and that similar events will be more likely in the future. The authors found that this event is about 4°C warmer than a century ago. They have however also recognized that the quantification of the increase in probability of this event under climate change strongly depends on the models/observations considered. They pointed out to the inadequacy of current models at simulating these events. This poses serious challenges both for the scientific community as well as for the decision makers: on one side, new techniques should be developed to improve the representation of extreme events in climate models. The non-linear geophysics community strongly contributes to this task by proposing bias correction algorithms to improve models output, and techniques issued from dynamical systems theory or statistical mechanics to simulate heatwaves with large deviations. On the other side, decision makers should be aware that uncertainty is a key feature of these studies and take action to prevent the worst possible scenarios both with adaption strategies (heat plans) and by reducing greenhouse gases emissions.