Forecasting critical transitions using data-driven nonstationary dynamical modeling

This is the final version of the article. Available from American Physical Society via the DOI in this record.An approach to predicting critical transitions from time series is introduced. A nonstationary low-order stochastic dynamical model of appropriate complexity to capture the transition mechanism under consideration is estimated from data. In the simplest case, the model is a one-dimensional effective Langevin equation, but also higher-dimensional dynamical reconstructions based on time-delay embedding and local modeling are considered. Integrations with the nonstationary models are performed beyond the learning data window to predict the nature and timing of critical transitions. The technique is generic, not requiring detailed a priori knowledge about the underlying dynamics of the system. The method is demonstrated to successfully predict a fold and a Hopf bifurcation well beyond the learning data window

Enhanced regime predictability in atmospheric low-order models due to stochastic forcing.

PublishedJournal ArticleThis is the author accepted manuscript. The final version is available from The Royal Society via the DOI in this record.Regime predictability in atmospheric low-order models augmented with stochastic forcing is studied. Atmospheric regimes are identified as persistent or metastable states using a hidden Markov model analysis. A somewhat counterintuitive, coherence resonance-like effect is observed: regime predictability increases with increasing noise level up to an intermediate optimal value, before decreasing when further increasing the noise level. The enhanced regime predictability is due to increased persistence of the regimes. The effect is found in the Lorenz '63 model and a low-order model of barotropic flow over topography. The increased predictability is only present in the regime dynamics, that is, in a coarse-grained view of the system; predictability of individual trajectories decreases monotonically with increasing noise level. A possible explanation for the phenomenon is given and implications of the finding for weather and climate modelling and prediction are discussed

Predicting critical transitions in dynamical systems from time series using nonstationary probability density modeling

A time series analysis method for predicting the probability density of a dynamical system is proposed. A nonstationary parametric model of the probability density is estimated from data within a maximum likelihood framework and then extrapolated to forecast the future probability density and explore the system for critical transitions or tipping points. A full systematic account of parameter uncertainty is taken. The technique is generic, independent of the underlying dynamics of the system. The method is verified on simulated data and then applied to prediction of Arctic sea-ice extent. © 2013 American Physical Society

Vortex Erosion in a Shallow Water Model of the Polar Vortex

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The erosion of a model stratospheric polar vortex in response to bottom boundary forcing is investigated numerically. Stripping of filaments of air from the polar vortex has been implicated in the occurrence of stratospheric sudden warmings (SSWs) but it is not understood in detail what factors determine the rate and amount of stripping. Here a shallow water vortex forced by topography is used to investigate the factors initiating stripping and whether this leads the vortex to undergo an SSW. It is found that the amplitude of topographic forcing must exceed some threshold (of order 200–450 m) in order for significant stripping to occur. For larger forcing amplitudes significant stripping occurs, but not as an instantaneous response to the forcing; rather, the forcing appears to initiate a process that ultimately results in stripping several tens of days later. There appears to be no simple quantitative relationship between the amount of mass stripped and the topography amplitude. However, at least over the early stages of the experiments, there is a good correlation between the amount of mass stripped and the global integral of wave activity, which may be interpreted as a measure of the accumulated topographic forcing. Finally there does not appear to be a simple correspondence between amount of mass stripped and the occurrence of an SSW.Robin Beaumont was supported during this research with a PhD studentship funded by an EPSRC Doctoral Training Grant

Low-dimensional dynamical system model for observed coherent structures in ocean satellite data

The dynamics of coherent structures present in real-world environmental data is analyzed. The method developed in this Paper combines the power of the Proper Orthogonal Decomposition (POD) technique to identify these coherent structures in experimental data sets, and its optimality in providing Galerkin basis for projecting and reducing complex dynamical models. The POD basis used is the one obtained from the experimental data. We apply the procedure to analyze coherent structures in an oceanic setting, the ones arising from instabilities of the Algerian current, in the western Mediterranean Sea. Data are from satellite altimetry providing Sea Surface Height, and the model is a two-layer quasigeostrophic system. A four-dimensional dynamical system is obtained that correctly describe the observed coherent structures (moving eddies). Finally, a bifurcation analysis is performed on the reduced model.Comment: 23 pages, 7 figure

Fluctuations of finite-time Lyapunov exponents in an intermediate-complexity atmospheric model: a multivariate and large-deviation perspective

This is the final version. Available from European Geosciences Union via the DOI in this record.The data and codes relating to this paper are available upon request from the author. They are not publicly accessible, as they were created solely for the purpose of this research study.The stability properties as characterized by the fluctuations of finite-time Lyapunov exponents around their mean values are investigated in a three-level quasi-geostrophic atmospheric model with realistic mean state and variability. Firstly, the covariance structure of the fluctuation field is examined. In order to identify dominant patterns of collective excitation, an empirical orthogonal function (EOF) analysis of the fluctuation field of all of the finite-time Lyapunov exponents is performed. The three leading modes are patterns where the most unstable Lyapunov exponents fluctuate in phase. These modes are virtually independent of the integration time of the finite-time Lyapunov exponents. Secondly, large-deviation rate functions are estimated from time series of finite-time Lyapunov exponents based on the probability density functions and using the Legendre transform method. Serial correlation in the time series is properly accounted for. A large-deviation principle can be established for all of the Lyapunov exponents. Convergence is rather slow for the most unstable exponent, becomes faster when going further down in the Lyapunov spectrum, is very fast for the near-neutral and weakly dissipative modes, and becomes slow again for the strongly dissipative modes at the end of the Lyapunov spectrum. The curvature of the rate functions at the minimum is linked to the corresponding elements of the diffusion matrix. Also, the joint large-deviation rate function for the first and the second Lyapunov exponent is estimated

Early warnings and missed alarms for abrupt monsoon transitions

Journal ArticlePalaeo-records from China demonstrate that the East Asian Summer Monsoon (EASM) is dominated by abrupt and large magnitude monsoon shifts on millennial timescales, switching between periods of high and weak monsoon rains. It has been hypothesized that over these timescales, the EASM exhibits two stable states with bifurcation-Type tipping points between them. Here we test this hypothesis by looking for early warning signals of past bifurcations in speleothem δ18O records from Sanbao Cave and Hulu Cave, China, spanning the penultimate glacial cycle. We find that although there are increases in both autocorrelation and variance preceding some of the monsoon transitions during this period, it is only immediately prior to the abrupt monsoon shift at the penultimate deglaciation (Termination II) that statistically significant increases are detected. To supplement our data analysis, we produce and analyse multiple model simulations that we derive from these data. We find hysteresis behaviour in our model simulations with transitions directly forced by solar insolation. However, signals of critical slowing down, which occur on the approach to a bifurcation, are only detectable in the model simulations when the change in system stability is sufficiently slow to be detected by the sampling resolution of the data set. This raises the possibility that the early warning "alarms" were missed in the speleothem data over the period 224-150 kyr and it was only at the monsoon termination that the change in the system stability was sufficiently slow to detect early warning signals

Data assimilation in slow-fast systems using homogenized climate models

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization model is derived for the slow dynamics. The reliability of this reduced climate model in reproducing the statistics of the slow dynamics of the full deterministic model for finite values of the time scale separation is numerically established. The statistics however is sensitive to uncertainties in the parameters of the stochastic model. It is investigated whether the stochastic climate model can be beneficial as a forecast model in an ensemble data assimilation setting, in particular in the realistic setting when observations are only available for the slow variables. The main result is that reduced stochastic models can indeed improve the analysis skill, when used as forecast models instead of the perfect full deterministic model. The stochastic climate model is far superior at detecting transitions between regimes. The observation intervals for which skill improvement can be obtained are related to the characteristic time scales involved. The reason why stochastic climate models are capable of producing superior skill in an ensemble setting is due to the finite ensemble size; ensembles obtained from the perfect deterministic forecast model lacks sufficient spread even for moderate ensemble sizes. Stochastic climate models provide a natural way to provide sufficient ensemble spread to detect transitions between regimes. This is corroborated with numerical simulations. The conclusion is that stochastic parametrizations are attractive for data assimilation despite their sensitivity to uncertainties in the parameters.Comment: Accepted for publication in Journal of the Atmospheric Science

Regime‐dependent statistical post‐processing of ensemble forecasts

This is the final version. Available on open access from Wiley via the DOI in this recordA number of realisations of one or more numerical weather prediction (NWP) models, initialised at a variety of initial conditions, compose an ensemble forecast. These forecasts exhibit systematic errors and biases that can be corrected by statistical post‐processing. Post‐processing yields calibrated forecasts by analysing the statistical relationship between historical forecasts and their corresponding observations. This paper aims to extend post‐processing methodology to incorporate atmospheric circulation. The circulation, or flow, is largely responsible for the weather that we experience and it is hypothesised here that relationships between the NWP model and the atmosphere depend upon the prevailing flow. Numerous studies have focussed on the tendency of this flow to reduce to a set of recognisable arrangements, known as regimes, which recur and persist at fixed geographical locations. This dynamical phenomenon allows the circulation to be categorised into a small number of regime states. In a highly idealised model of the atmosphere, the Lorenz ’96 system, ensemble forecasts are subjected to well‐known post‐processing techniques conditional on the system's underlying regime. Two different variables, one of the state variables and one related to the energy of the system, are forecasted and considerable improvements in forecast skill upon standard post‐processing are seen when the distribution of the predictand varies depending on the regime. Advantages of this approach and its inherent challenges are discussed, along with potential extensions for operational forecasters.Natural Environment Research Council (NERC

Vortex dynamics of stratospheric sudden warmings: a reanalysis data study using PV contour integral diagnostics

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.ERA‐40 reanalysis dataset produced by the European Centre for Medium‐Range Weather Forecasts (ECMWF) and provided by the British Atmospheric Data Centre (BADC).The dynamics of the polar vortex underlying stratospheric sudden warming (SSW) events are investigated in a data-based diagnostic study. Potential vorticity (PV) contour integral quantities on isentropic surfaces are discussed in a unified framework; new expressions for their time evolution, particularly suitable for evaluation from data, are presented and related to previous work. Diagnostics of mass and circulation are calculated from ERA-40 reanalysis data for the stratosphere in case-studies of seven winters with different SSW behaviour. The edge of the polar vortex is easily identifiable in these diagnostics as an abrupt transition from high to low gradients of PV, and the warming events are clearly visible. The amount of air stripped from the vortex as part of a preconditioning leading up to the warming events is determined using the balance equation of the mass integral. Significant persistent removal of mass from the vortex is found, with several such stripping events identifiable throughout the winter, especially in those during which a major sudden warming event occurred. These stripping episodes are visible in corresponding PV maps, where tongues of high PV are being stripped from the vortex and mixed into the surrounding surf zone. An attempt is made to diagnose from the balance equation of the circulation the effect of frictional forces such as gravity wave dissipation on the polar vortex.EPSR