The software developed in TiPES is available through GitHub and/or Zenodo via the links in table below and additional information is described especially in TiPES delivery “D5.4 Software: computational tools for identifying, classifying and predicting tipping“.

Research efforts into climate subsystems that may undergo rapid transitions due to slow variations in their forcing is the main focus of TiPES. Such transitions may be disrupting to society at both the local and regional scale. Several of these subsystems have been identified in the literature on tipping elements, in particular the Atlantic Meridional Overturning Circulation (AMOC), the polar ice sheets and the Amazon Rainforest. Critical thresholds for such tipping behaviour to occur, i.e. the tipping points, have been estimated in terms of Global Mean Surface Temperature (GMST) increase (with respect to pre-industrial). Computational tools are essential for the identification, classification and prediction of such tipping points. In deliverable D5.4 of TiPES, we report on the computational tools which have been developed in TiPES and describe their applications.

When identifying tipping behaviour, the situation is different when one has the equations of a model available or when only time series, such as from historical or proxy observations, are available. In the deterministic model case, one may be able to perform numerical bifurcation analysis to locate the steady states of the model versus parameters by continuation techniques. This will also allow us to classify the tipping points which arise through a crossing of bifurcation points. The bifurcation diagrams will also help to determine the parameter regimes in the stochastic version of the model where noise-or rate-induced tipping will occur. When only time series are available, one can locate the change in behaviour associated with a tipping event by using statistical techniques. The approach to a tipping point (even when the tipping behaviour is not in the time series) can also be determined by computing early warning signals.

The main results regarding software products obtained in TiPES are as follows.

A statistical toolbox was developed to detect tipping behaviour in paleoclimate time series. This toolbox was extensively described in D1.2 and the components of the toolbox will only be mentioned under ‘main results achieved’. A Julia toolbox was developed (TransitionsInTimeseries.jl) under the mentorship of TiPES and funded by another project. In TiPES, progress has been made to develop software for tipping in stochastic spatially extended systems, i.e. models governed by partial differential equations (PDEs). Software to analyse fragmented tipping was developed, where due to spatial heterogeneity, part of the spatial domain undergoes tipping whereas there is no tipping in the rest of this domain. Finally, software was further developed to compute transition probabilities of noise induced tipping both for models governed by ordinary differential equations (ODEs) and by PDEs. These new techniques were also applied to both conceptual and spatially extended models of the ocean circulation, in particular the AMOC and the wind-driven ocean circulation, and to a diverse set of conceptual models of tipping behaviour in the climate system. The latter included models of ocean convection and models of pattern formation in the atmosphere and models of vegetation patterns.

 Type of softwareDevelopersLink on GitGubLink on ZenodoTitle PaperAuthors
[paleojump]Statistical toolbox for determining tipping behavior in  paleoclimate dataKeno Riechers[EU127] Comprehensive uncertainty estimation of the timing of Greenland warmings in the Greenland ice core records. Climate of the Past, 18, 1275–1294. (2022)Myrvoll-Nilsen, E. Riechers, K., Rypdal, M.W. & Boers, N.:
[fragment]Fragmented tipping analysisRobbin Bastiaansen [EU110] Fragmented tipping in a spatially heterogeneous world, Environmental  Research Letters,  17, 045006, (2022)Bastiaansen/ Dijkstra/von der Heydt
[matrix]Matrix – DO methodRené van Westen[EU178] A New Method to Compute Transition Probabilities in Multi-Stable Stochastic Dynamical Systems: Application to the Wind-driven Ocean Circulation, Journal of Advances in Modeling Earth Systems,  15, e2022MS003456 (2023).  Westen van, R., Kotnala, S., Baars, S. Wubs, F. W. and  Henk A. Dijkstra
[TAMS]TAMS methodHenk Dijkstra methods to estimate the committor function in conceptual ocean models, Nonlinear Processes in Geophysics, 30, 195-216, (2023). Jacques-Dumas, V., Van Westen, R., Bouchet, F.  and  Henk A. Dijkstra
[Transitions]TransitionsInTimeseries.jl A Julia package for estimating transitions (from one dynamic regime or stable state to another) in timeseries and testing the statistical significance of found transitions.Swierczek-Jereczek, George Datseris  Jan Swierczek-Jereczek, George Datseris