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

Stern's review and Dam's fallacy

The Stern Review has played an enormous role in making the world of business aware of the challenge of long-term climate change. In order to make real progress on the basis of this awareness, it is important to pay attention to the difference between human suffering and losses of gross domestic product (GDP). The Review has compared climate change to experiences of suffering like World War I. That war, however, hardly affected global GDP. The long-term damages to be expected from business-as-usual greenhouse gas emissions include loss of the coastal cities of the world over the next millennia. This would be an act of unprecedented barbarism, regardless of whether it would slow down economic growth or perhaps even accelerate it. Business leaders worried about climate change need to pay attention to the tensions between ethical and economic concerns. Otherwise, a credibility crisis threatens global climate policy. An important step to establish the credibility needed for effective climate policy will be to gradually move towards a regime where emission permits are auctioned, not handed out as hidden subsidies. The revenues generated by permit auctions should be used to establish a global system of regional climate funds. [References: 41

Analysis of rainfall records: possible relation to self-organized criticality

The hypothesis that rainfall might be a case of self-organized critical dynamics is tested using long-term data sets from weather stations around the world. It is found that the distribution of droughts in semi-arid regions obeys indeed a clear-cut power law. The statistics for rain intensity, on the other hand, exhibits two distinct scaring regimes. (C) 1998 Elsevier Science B.V. All rights reserved

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

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

The tolerable windows approach: Theoretical and methodological foundations

The tolerable windows (TW) approach is presented as a novel scheme for integrated assessment of climate change. The TW approach is based on the specification of a set of guardrails for climate evolution which refer to various climate-related attributes. These constraints, which define what we call tolerable windows, can be purely systemic in nature - like critical thresholds for the North Atlantic Deep Water formation - or of a normative type - like minimum standards for per-capita food production worldwide. Starting from this catalogue of knock-out criteria and using appropriate modeling techniques, those policy strategies which are compatible with all the constraints specified are sought to be identified. In addition to the discussion of the basic elements and the general theory of the TW approach, a modeling exercise is carried out, based on simple models and assumptions adopted from the German Advisory Council on Global Change (WBGU). The analysis shows that if the global mean temperature is restricted to 2 degrees C beyond the preindustrial level, the cumulative emissions of CO2 are asymptotically limited to about 1550 Gt C. Yet the temporal distribution of these emissions is also determined by the climate and socio-economic constraints: using, for example, a maximal tolerable rate of temperature change of 0.2 degrees C/ dec and a smoothly varying emissions profile, we obtain the maximal cumulative emissions, amounting to 370 Gt C in 2050 and 585 Gt C in 2100