arXiv subjects

Paul D. L. Ritchie

Publications and source records attributed to Paul D. L. Ritchie.

4 recordsLinked to original sources

arXiv2026

From trends to optimized forecasts: Quantifying the skill and advancing the utility of dynamics-based early warnings for tipping events

In this paper we explore and extend the state of the art for understanding the skill and utility of early warnings of critical transitions (tipping points) in forced nonlinear systems. We highlight some of the challenges and opportunities of transforming estimates of a dynamics-based early warning system, based on trends in stability or resilience into forecasts with high skill. We highlight the importance of (a) quantifying consequences of possible actions in response to warnings that may be false negatives or positives (b) considering finite time horizon predictions to give verifiable predictions (c) assumptions necessary for valid extrapolations of trends. We evaluate approaches to improving the skill and utility of the forecast.

math.DS↗

arXiv2026

The role of coupling and timescales for interacting tipping elements

Sudden and abrupt changes can occur in a nonlinear system within many fields of science when such a system crosses a tipping point; rapid changes of the system can then occur in response to slow changes in an external forcing. These can occur when time-varying inputs cross a bifurcation. If an upstream system loses stability in this way, it may cause a downstream system influenced by it to tip. This especially happens if the downstream system evolves on a much faster timescale, in what we call an accelerating cascade of tipping elements. In this paper, we identify the conditions on coupling and timescales of these systems that result in such tipping cascades and suggest a taxonomy to classify the different possible timings of tipping sequences. We also present a prototypical example of a unidirectionally coupled pair of simple tipping elements with hysteresis. This allows us to map out the various types of response as a function of system parameters and to link it to bifurcations of the underlying system that may have multiple timescales.

math.DS↗

arXiv2026

Evaluating the skill of a geometric early warning for tipping in a rapidly forced nonlinear system

The future behavioural fate of a forced nonlinear system can depend sensitively on the forcing profile as well as natural fluctuations within the system. This is especially the case for rate-induced tipping, where the forcing pushes the system to a basin boundary of a future behaviour and small changes in the forcing can lead to drastically different eventual behaviours. This sensitivity may be present only for a limited period of time, for example when the forcing is most rapidly changing. Moreover, critical slowing down based methods fail to be informative in such cases. We investigate a geometric early warning to evaluate when a system is in such a sensitive state. This involves computing the R-tipping indicator, namely the signed distance to an approximate R-tipping threshold. The latter is a dynamic state that embeds knowledge of the system and future behaviour of the forcing. We contrast this with early warnings of bifurcation-induced tipping, where tipping is associated with passing a threshold on slow variation of forcing. As an example, we consider methods of early prediction of the future state for a 3-box model of the Atlantic Meridional Overturning Circulation (AMOC) with specified rapid forcing. We show that the skill of the geometric early warning compares favourably with simple thresholds.

math.DS↗

arXiv2026

A Criterion for Safe Overshoot in Coupled Tipping Systems

Abrupt transitions are a central concern in climate and ecological research, and may arise when critical thresholds known as tipping points are crossed. However, previous work has shown that finite-time overshoots of tipping points can be safe, and that such behavior is captured by an inverse-square-law criterion when overshoots are sufficiently small and slow. So far studied in isolated systems with external drivers, (un)safe overshoots may also emerge from interactions between subsystems. Here, we investigate safe-overshoot phenomena in unidirectionally coupled slow-fast systems featuring both nonlinear interactions and coupling through time-derivatives. Specifically, we derive a criterion for the occurrence of safe overshoots analogous to the inverse-square law for isolated systems, but adapted to interactive settings, and expressed explicitly in terms of the timescale separation and coupling strength between subsystems. We illustrate these results using two conceptual models in which the Atlantic Meridional Overturning Circulation interacts with either the Amazon rainforest or the Greenland Ice Sheet.

nlin.CD↗