Forecasting the underlying potential governing the time series of a dynamical system

Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for ‘potential analysis’ of tipping points which altogether serves anticipating, detecting and forecasting nonlinear changes including bifurcations using several independent techniques of time series analysis. Although being applied to climatological series in the present paper, the method is very general and can be used to forecast dynamics in time series of any origin.NERCAXA Research FundEuropean Commissio

Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data

Effects of atmospheric dynamics and ocean resolution on bi-stability of the thermohaline circulation examined using the Grid ENabled Integrated Earth system modelling (GENIE) framework

We have used the Grid ENabled Integrated Earth system modelling (GENIE) framework to undertake a systematic search for bi-stability of the ocean thermohaline circulation (THC) for different surface grids and resolutions of 3-D ocean (GOLDSTEIN) under a 3-D dynamical atmosphere model (IGCM). A total of 407,000 years were simulated over a three month period using Grid computing. We find bi-stability of the THC despite significant, quasi-periodic variability in its strength driven by variability in the dynamical atmosphere. The position and width of the hysteresis loop depends on the choice of surface grid (longitude-latitude or equal area), but is less sensitive to changes in ocean resolution. For the same ocean resolution, the region of bi-stability is broader with the IGCM than with a simple energy-moisture balance atmosphere model (EMBM). Feedbacks involving both ocean and atmospheric dynamics are found to promote THC bi-stability. THC switch-off leads to increased import of freshwater at the southern boundary of the Atlantic associated with meridional overturning circulation. This is counteracted by decreased freshwater import associated with gyre and diffusive transports. However, these are localised such that the density gradient between North and South is reduced tending to maintain the THC off state. THC switch-off can also generate net atmospheric freshwater input to the Atlantic that tends to maintain the off state. The ocean feedbacks are present in all resolutions, across most of the bi-stable region, whereas the atmosphere feedback is strongest in the longitude–latitude grid and around the transition where the THC off state is disappearing. Here the net oceanic freshwater import due to the overturning mode weakens, promoting THC switch-on, but the atmosphere counteracts this by increasing net freshwater input. This increases the extent of THC bi-stability in this version of the model

Optimisation of costs and carbon savings in relation to the economic dispatch problem as associated with power system operation

In this paper, the costs and carbon savings in the economic dispatch (ED) problem of the power system operation are optimised. Energy demands and generation are forecast and assimilated using ensemble Kalman filter (EnKF). Optimisation is performed using the ensemble-based closed-loop production optimisation scheme (EnOpt). The real energy parameters of thermal units with green generators (wind farm) are used to test the methodology. The ability of the EnKF to predict, and the robustness of the EnOpt to optimise costs and the resultant carbon emissions are demonstrated. The proposed approach addresses the complexity and diversity of the power system and may be implemented in operational conditions of energy suppliers