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Severe geomagnetic storms caused by the solar wind disturbances have harmful influences on the operation of modern equipment and systems. The modelling and forecasting of AE index are extremely useful to understand the geomagnetic substorms. This study presents a novel cloud‐NARX model to predict AE index 1 hour ahead. The cloud‐NARX model provides AE index forecasting results, with a correlation coefficient of 0.87 on the data of whole year 2015. The benchmarks on the data of the two interested periods of 17‐21 March 2015 and 22‐26 June 2015 are presented. The presented model uses uncertainty ‘cloud’ model and cloud transformation to quantify the uncertainty throughout the structure detection, parameter estimation and model prediction. The new predicted band can be generated to forecast AE index with confidence interval. The proposed method provides a new way to evaluate the model based on uncertainty analysis, revealing the reliability of model and visualize the bias of model prediction.

Severe geomagnetic disturbances can be hazardous for modern technological systems. The reliable forecast of parameters related to the state of the magnetosphere can facilitate the mitigation of adverse effects of space weather. This study is devoted to the modeling and forecasting of the evolution of the Kp index related to global geomagnetic disturbances. Throughout this work the Nonlinear AutoRegressive with eXogenous inputs (NARX) methodology is applied. Two approaches are presented: i) a recursive sliding window approach, and ii) a direct approach. These two approaches are studied separately and are then compared to evaluate their performances. It is shown that the direct approach outperforms the recursive approach, but both tend to produce predictions slightly biased from the true values for low and high disturbances.

[1] This paper reports the metrics-based results of the Dst index part of the 2008–2009 GEM Metrics Challenge. The 2008–2009 GEM Metrics Challenge asked modelers to submit results for four geomagnetic storm events and five different types of observations that can be modeled by statistical, climatological or physics-based models of the magnetosphere-ionosphere system. We present the results of 30 model settings that were run at the Community Coordinated Modeling Center and at the institutions of various modelers for these events. To measure the performance of each of the models against the observations, we use comparisons of 1 hour averaged model data with the Dst index issued by the World Data Center for Geomagnetism, Kyoto, Japan, and direct comparison of 1 minute model data with the 1 minute Dst index calculated by the United States Geological Survey. The latter index can be used to calculate spectral variability of model outputs in comparison to the index. We find that model rankings vary widely by skill score used. None of the models consistently perform best for all events. We find that empirical models perform well in general. Magnetohydrodynamics-based models of the global magnetosphere with inner magnetosphere physics (ring current model) included and stand-alone ring current models with properly defined boundary conditions perform well and are able to match or surpass results from empirical models. Unlike in similar studies, the statistical models used in this study found their challenge in the weakest events rather than the strongest events.

[1] Recently published data from Reeves et al. (2011) on the fluxes of 1.8–3.5 MeV electrons at geostationary orbit are subjected to Error Reduction Ratio (ERR) analysis in order to identify the parameters that control variance of these fluxes. ERR shows that it is the solar wind density not the velocity that controls most of the variance of the energetic electrons fluxes. High fluxes are observed under the conditions of low density in absolute majority of cases. Under the condition of fixed density the dependence of fluxes upon the velocity is the following: fluxes increase with the velocity reaching some saturation level. Both the level of saturation and the value of the velocity where it is achieved decrease with the increase of solar wind density.

[1] The NARMAX OLS-ERR algorithm, which is widely used in the study of systems dynamics, is able to determine the causal relationship between the input and output variables for nonlinear systems. This technique has been applied to measurements of the solar wind from ACE at L1 and the Dst index in order to find the best solar wind–magnetosphere coupling function, i.e., which combination of solar wind parameters provides the best predictive capabilities of the Dst index. The data-deduced coupling functions were then compared to those suggested in previous analytical and data-based studies. The most appropriate coupling function was found to be n1/2VαBT sin6(θ/2), where the power of velocity, α, was inconclusive but should be in the range 2–3.

[1] The NARMAX (Nonlinear Autoregressive Moving Average with eXogenous inputs) modeling based approach is used to identify the relations for Solar wind Magnetosphere Coupling Functions in order to identify the one with the best Dst index forecasting abilities. It is argued that the Error Reduction Ratio which is a cornerstone concept in the NARMAX system identification methodology is more appropriate for such nonlinear system as the terrestrial magnetosphere than correlation function analysis which has often been used in the past. It is shown that the identified relationships for coupling functions are proportional to , where is the clock angle, and not to as was suggested in earlier studies. It is shown that the factor appears naturally within the analytical model of Kan and Lee (1979) as the dependence on the clock angle.

[1] A new identification approach is introduced for predicting the Dst index using multiresolution B-spline wavelet models based on an observational data set consisting of VBs, the solar wind parameter, as the input and the Dst index as the output. The relationship between the input VBs and output Dst is initially described using a B-spline wavelet model. This model is then simplified using an orthogonal least squares and error reduction ratio (OLS-ERR) algorithm by selecting the significant model terms to produce a parsimonious wavelet model. Forecasts of the Dst index are then computed based on this model.