A complete representation of uncertainties in layer-counted paleoclimatic archives

Accurate time series representation of paleoclimatic proxy records is challenging because such records involve dating errors in addition to proxy measurement errors. Rigorous attention is rarely given to age uncertainties in paleoclimatic research, although the latter can severely bias the results of proxy record analysis. Here, we introduce a Bayesian approach to represent layer-counted proxy records – such as ice cores, sediments, corals, or tree rings – as sequences of probability distributions on absolute, error-free time axes. The method accounts for both proxy measurement errors and uncertainties arising from layer-counting-based dating of the records. An application to oxygen isotope ratios from the North Greenland Ice Core Project (NGRIP) record reveals that the counting errors, although seemingly small, lead to substantial uncertainties in the final representation of the oxygen isotope ratios. In particular, for the older parts of the NGRIP record, our results show that the total uncertainty originating from dating errors has been seriously underestimated. Our method is next applied to deriving the overall uncertainties of the Suigetsu radiocarbon comparison curve, which was recently obtained from varved sediment cores at Lake Suigetsu, Japan. This curve provides the only terrestrial radiocarbon comparison for the time interval 12.5–52.8 kyr BP. The uncertainties derived here can be readily employed to obtain complete error estimates for arbitrary radiometrically dated proxy records of this recent part of the last glacial interval

A multi-modal representation of El Ni\~no Southern Oscillation Diversity

The El Ni\~no-Southern Oscillation (ENSO) is characterized by alternating periods of warm (El Ni\~no) and cold (La Ni\~na) sea surface temperature anomalies (SSTA) in the equatorial Pacific. Although El Ni\~no and La Ni\~na are well-defined climate patterns, no two events are alike. To date, ENSO diversity has been described primarily in terms of the longitudinal location of peak SSTA, used to define a bimodal classification of events in Eastern Pacific (EP) and Central Pacific (CP) types. Here, we use low-dimensional representations of Pacific SSTAs to argue that binary categorical memberships are unsuitable to describe ENSO events. Using fuzzy unsupervised clustering, we recover the four known ENSO categories, along with a fifth category: an Extreme El Ni\~no. We show that Extreme El Ni\~nos differ both in their intensity and temporal evolution from canonical EP El Ni\~nos. We also find that CP La Ni\~nas, EP El Ni\~nos, and Extreme El Ni\~nos contribute the most to interdecadal ENSO variability

A random interacting network model for complex networks

This paper was developed within the scope of the DAAD-DST PPP-Indien project 55516784 (INT/FRG/DAAD/P-215) which funded exchange visits between the two participating institutes. B.G. was supported by the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. J.K. acknowledges financial support from the Government of the Russian Federation (Agreement No. 14.Z50.31.0033). S.M.S. would like to thank University Grants Comission, New Delhi for the financial assistance as an SRF. B.G. and A.R. thank Niklas Boers for stimulating discussions and comments.Peer reviewedPublisher PD

Recurrence analysis of extreme event-like data

The identification of recurrences at various timescales in extreme event-like time series is challenging because of the rare occurrence of events which are separated by large temporal gaps. Most of the existing time series analysis techniques cannot be used to analyze an extreme event-like time series in its unaltered form. The study of the system dynamics by reconstruction of the phase space using the standard delay embedding method is not directly applicable to event-like time series as it assumes a Euclidean notion of distance between states in the phase space. The edit distance method is a novel approach that uses the point-process nature of events. We propose a modification of edit distance to analyze the dynamics of extreme event-like time series by incorporating a nonlinear function which takes into account the sparse distribution of extreme events and utilizes the physical significance of their temporal pattern. We apply the modified edit distance method to event-like data generated from point process as well as flood event series constructed from discharge data of the Mississippi River in the USA and compute their recurrence plots. From the recurrence analysis, we are able to quantify the deterministic properties of extreme event-like data. We also show that there is a significant serial dependency in the flood time series by using the random shuffle surrogate method

Inductive biases in deep learning models for weather prediction

Deep learning has recently gained immense popularity in the Earth sciences as it enables us to formulate purely data-driven models of complex Earth system processes. Deep learning-based weather prediction (DLWP) models have made significant progress in the last few years, achieving forecast skills comparable to established numerical weather prediction (NWP) models with comparatively lesser computational costs. In order to train accurate, reliable, and tractable DLWP models with several millions of parameters, the model design needs to incorporate suitable inductive biases that encode structural assumptions about the data and modelled processes. When chosen appropriately, these biases enable faster learning and better generalisation to unseen data. Although inductive biases play a crucial role in successful DLWP models, they are often not stated explicitly and how they contribute to model performance remains unclear. Here, we review and analyse the inductive biases of six state-of-the-art DLWP models, involving a deeper look at five key design elements: input data, forecasting objective, loss components, layered design of the deep learning architectures, and optimisation methods. We show how the design choices made in each of the five design elements relate to structural assumptions. Given recent developments in the broader DL community, we anticipate that the future of DLWP will likely see a wider use of foundation models -- large models pre-trained on big databases with self-supervised learning -- combined with explicit physics-informed inductive biases that allow the models to provide competitive forecasts even at the more challenging subseasonal-to-seasonal scales

Climatic and in-cave influences on δ18O and δ13C in a stalagmite from northeastern India through the last deglaciation

Northeastern (NE) India experiences extraordinarily pronounced seasonal climate, governed by the Indian summer monsoon (ISM). The vulnerability of this region to floods and droughts calls for detailed and highly resolved paleoclimate reconstructions to assess the recurrence rate and driving factors of ISM changes. We use stable oxygen and carbon isotope ratios (δ18O and δ13C) from stalagmite MAW-6 from Mawmluh Cave to infer climate and environmental conditions in NE India over the last deglaciation (16–6ka). We interpret stalagmite δ18O as reflecting ISM strength, whereas δ13C appears to be driven by local hydroclimate conditions. Pronounced shifts in ISM strength over the deglaciation are apparent from the δ18O record, similarly to other records from monsoonal Asia. The ISM is weaker during the late glacial (LG) period and the Younger Dryas, and stronger during the Bølling-Allerød and Holocene. Local conditions inferred from the δ13C record appear to have changed less substantially over time, possibly related to the masking effect of changing precipitation seasonality. Time series analysis of the δ18O record reveals more chaotic conditions during the late glacial and higher predictability during the Holocene, likely related to the strengthening of the seasonal recurrence of the ISM with the onset of the Holocene

A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots

Nonlinear time series analysis gained prominence from the late 1980s on, primarily because of its ability to characterize, analyze, and predict nontrivial features in data sets that stem from a wide range of fields such as finance, music, human physiology, cognitive science, astrophysics, climate, and engineering. More recently, recurrence plots, initially proposed as a visual tool for the analysis of complex systems, have proven to be a powerful framework to quantify and reveal nontrivial dynamical features in time series data. This tutorial review provides a brief introduction to the fundamentals of nonlinear time series analysis, before discussing in greater detail a few (out of the many existing) approaches of recurrence plot-based analysis of time series. In particular, it focusses on recurrence plot-based measures which characterize dynamical features such as determinism, synchronization, and regime changes. The concept of surrogate-based hypothesis testing, which is crucial to drawing any inference from data analyses, is also discussed. Finally, the presented recurrence plot approaches are applied to two climatic indices related to the equatorial and North Pacific regions, and their dynamical behavior and their interrelations are investigated

Teleconnection Patterns of Different El Niño Types Revealed by Climate Network Curvature

The diversity of El Niño events is commonly described by two distinct flavors, the Eastern Pacific (EP) and Central Pacific (CP) type. While the remote impacts, that is, teleconnections, of EP and CP events have been studied for different regions individually, a global picture of their structure is still lacking. Here, we use Forman‐Ricci curvature applied on climate networks constructed from surface air temperature data to distinguish regional links from teleconnections. Our results confirm that both El Niño types influence the teleconnection patterns, however, with different spatial manifestations. Our analysis suggests that EP El Niños alter the general circulation which changes the teleconnection structure to primarily tropical teleconnections. In contrast, the teleconnection pattern of CP El Niños show only subtle changes to normal conditions. Moreover, this work identifies the dynamics of the Eastern Pacific as a proxy for the remote impact of both El Niño types.Plain Language Summary: El Niño events, characterized by anomalous sea surface temperatures (SSTs) in the Tropical Pacific, come in two flavors; Eastern Pacific (EP) and Central Pacific (CP) types, depending on the longitudinal location of the strongest SST anomalies. Their remote impacts, known as teleconnections, differ. Although there are many studies investigating teleconnections of EP and CP events for individual target regions, a global analysis of the spatial distribution of their teleconnections is still lacking. In this study, we use the theory of complex networks to study EP and CP El Niño teleconnections. We construct “climate networks” from global surface air temperature data and use the notion of “curvature” of a network link to uncover their spatial organization. We show that the most negatively curved links highlight important teleconnection patterns that differ depending on the El Niño type. EP events change the teleconnection structure to the tropics while CP and Normal year conditions reveal teleconnections to all latitudes. Interestingly, the Central Pacific does not show many teleconnections, even during CP El Niño events which we attribute to the varying location of warm water anomalies in the Central Pacific. The Eastern Pacific changes more consistently allowing identifying remote impacts of both El Niños types.Key Points: Ricci curvature of boreal winter climate networks reveals long‐range teleconnection structure. Eastern Pacific (EP) El Niños show primarily teleconnections in tropical while Central Pacific El Niños teleconnections on all latitudes. The EP contains robust teleconnections for both El Niño types.Deutsche Forschungsgemeinschaft, DFG http://dx.doi.org/10.13039/501100001659researc