Forced versus coupled dynamics in Earth system modelling and prediction

International audienceWe compare coupled nonlinear climate models and their simplified forced counterparts with respect to predictability and phase space topology. Various types of uncertainty plague climate change simulation, which is, in turn, a crucial element of Earth System modelling. Since the currently preferred strategy for simulating the climate system, or the Earth System at large, is the coupling of sub-system modules (representing, e.g. atmosphere, oceans, global vegetation), this paper explicitly addresses the errors and indeterminacies generated by the coupling procedure. The focus is on a comparison of forced dynamics as opposed to fully, i.e. intrinsically, coupled dynamics. The former represents a particular type of simulation, where the time behaviour of one complex systems component is prescribed by data or some other external information source. Such a simplifying technique is often employed in Earth System models in order to save computing resources, in particular when massive model inter-comparisons need to be carried out. Our contribution to the debate is based on the investigation of two representative model examples, namely (i) a low-dimensional coupled atmosphere-ocean simulator, and (ii) a replica-like simulator embracing corresponding components.Whereas in general the forced version (ii) is able to mimic its fully coupled counterpart (i), we show in this paper that for a considerable fraction of parameter- and state-space, the two approaches qualitatively differ. Here we take up a phenomenon concerning the predictability of coupled versus forced models that was reported earlier in this journal: the observation that the time series of the forced version display artificial predictive skill. We present an explanation in terms of nonlinear dynamical theory. In particular we observe an intermittent version of artificial predictive skill, which we call on-off synchronization, and trace it back to the appearance of unstable periodic orbits. We also find it to be governed by a scaling law that allows us to estimate the probability of artificial predictive skill. In addition to artificial predictability we observe artificial bistability for the forced version, which has not been reported so far. The results suggest that bistability and intermittent predictability, when found in a forced model set-up, should always be cross-validated with alternative coupling designs before being taken for granted

Forecasting the El Ni\~no type well before the spring predictability barrier

The El Ni\~no Southern Oscillation (ENSO) is the most important driver of interannual global climate variability and can trigger extreme weather events and disasters in various parts of the globe. Depending on the region of maximal warming, El Ni\~no events can be partitioned into 2 types, Eastern Pacific (EP) and Central Pacific (CP) events. The type of an El Ni\~no has a major influence on its impact and can even lead to either dry or wet conditions in the same areas on the globe. Here we show that the zonal difference $\Delta T_{WP-CP}$ between the sea surface temperature anomalies (SSTA) in the equatorial western Pacific and central Pacific gives an early indication of the type of an upcoming El Ni\~no: When at the end of a year, $\Delta T_{WP-CP}$ is positive, an event in the following year will be probably an EP event, otherwise a CP event. Between 1950 and present, 3/4 of the EP forecasts and all CP forecasts are correct. When combining this approach with a previously introduced climate-network approach, we obtain reliable forecasts for both the onset and the type of an event: at a lead time of about one year, 2/3 of the EP forecasts and all CP forecasts in the regarded period are correct. The combined model has considerably more predictive power than the current operational type forecasts with a mean lead time of about 1 month and should allow early mitigation measures.Comment: 16 pages, 10 figure

Forced versus coupled dynamics in Earth system modelling and prediction

We compare coupled nonlinear climate models and their simplified forced counterparts with respect to predictability and phase space topology. Various types of uncertainty plague climate change simulation, which is, in turn, a crucial element of Earth System modelling. Since the currently preferred strategy for simulating the climate system, or the Earth System at large, is the coupling of sub-system modules (representing, e.g. atmosphere, oceans, global vegetation), this paper explicitly addresses the errors and indeterminacies generated by the coupling procedure. The focus is on a comparison of forced dynamics as opposed to fully, i.e. intrinsically, coupled dynamics. The former represents a particular type of simulation, where the time behaviour of one complex systems component is prescribed by data or some other external information source. Such a simplifying technique is often employed in Earth System models in order to save computing resources, in particular when massive model inter-comparisons need to be carried out. Our contribution to the debate is based on the investigation of two representative model examples, namely (i) a low-dimensional coupled atmosphere-ocean simulator, and (ii) a replica-like simulator embracing corresponding components.Whereas in general the forced version (ii) is able to mimic its fully coupled counterpart (i), we show in this paper that for a considerable fraction of parameter- and state-space, the two approaches qualitatively differ. Here we take up a phenomenon concerning the predictability of coupled versus forced models that was reported earlier in this journal: the observation that the time series of the forced version display artificial predictive skill. We present an explanation in terms of nonlinear dynamical theory. In particular we observe an intermittent version of artificial predictive skill, which we call on-off synchronization, and trace it back to the appearance of unstable periodic orbits. We also find it to be governed by a scaling law that allows us to estimate the probability of artificial predictive skill. In addition to artificial predictability we observe artificial bistability for the forced version, which has not been reported so far. The results suggest that bistability and intermittent predictability, when found in a forced model set-up, should always be cross-validated with alternative coupling designs before being taken for granted

Butterfly-like spectra and collective modes of antidot superlattices in magnetic fields

We calculate the energy band structure for electrons in an external periodic potential combined with a perpendicular magnetic field. Electron-electron interactions are included within a Hartree approximation. The calculated energy spectra display a considerable degree of self-similarity, just as the ``Hofstadter butterfly.'' However, screening affects the butterfly, most importantly the bandwidths oscillate with magnetic field in a characteristic way. We also investigate the dynamic response of the electron system in the far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectra can be interpreted mainly in semiclassical terms, while others originate from inter(sub)band transitions.Comment: 4 pages with 2 embeded eps figures. Uses revtex, multicol and graphicx styles. Accepted for publication in PRB Brief Report

The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment

A procedure is described for efficiently finding the ground state energy and configuration for a Frenkel-Kontorova model in a periodic potential, consisting of N parabolic segments of identical curvature in each period, through a numerical solution of the convex minimization problem described in the preceding paper. The key elements are the use of subdifferentials to describe the structure of the minimization problem; an intuitive picture of how to solve it, based on motion of quasiparticles; and a fast linear optimization method with a reduced memory requirement. The procedure has been tested for N up to 200.Comment: 9 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 3 Postscript figures, accepted by Phys.Rev.B to be published together with cond-mat/970722

Strong time dependence of ocean acidification mitigation by atmospheric carbon dioxide removal

In Paris in 2015, the global community agreed to limit global warming to well below 2 ∘C, aiming at even 1.5 ∘C. It is still uncertain whether these targets are sufficient to preserve marine ecosystems and prevent a severe alteration of marine biogeochemical cycles. Here, we show that stringent mitigation strategies consistent with the 1.5 ∘C scenario could, indeed, provoke a critical difference for the ocean’s carbon cycle and calcium carbonate saturation states. Favorable conditions for calcifying organisms like tropical corals and polar pteropods, both of major importance for large ecosystems, can only be maintained if CO2 emissions fall rapidly between 2025 and 2050, potentially requiring an early deployment of CO2 removal techniques in addition to drastic emissions reduction. Furthermore, this outcome can only be achieved if the terrestrial biosphere remains a carbon sink during the entire 21st century

Global climate models violate scaling of the observed atmospheric variability

We test the scaling performance of seven leading global climate models by using detrended fluctuation analysis. We analyse temperature records of six representative sites around the globe simulated by the models, for two different scenarios: (i) with greenhouse gas forcing only and (ii) with greenhouse gas plus aerosol forcing. We find that the simulated records for both scenarios fail to reproduce the universal scaling behavior of the observed records, and display wide performance differences. The deviations from the scaling behavior are more pronounced in the first scenario, where also the trends are clearly overestimated.Comment: Accepted for publishing in Physical Review Letter

Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?

We find that a 2D periodic potential with different modulation amplitudes in x- and y-direction and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization in the direction of weaker modulation. In the experimentally accessible regime we relate this new quantum transport phenomenon to avoided band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea