WINDMI Model Research Articles

The Growth of Ring Current/SYM‐H Under Northward IMF Bz Conditions Present During the 21–22 January 2005 Geomagnetic Storm

AbstractThe total energy transfer from the solar wind to the magnetosphere is governed by the reconnection rate at the magnetosphere edges as the Z‐component of interplanetary magnetic field (IMF Bz) turns southward. The geomagnetic storm on 21–22 January 2005 is considered to be anomalous as the SYM‐H index that signifies the strength of ring current, decreases and had a sustained trough value of −101 nT lasting more than 6 hr under northward IMF Bz conditions. In this work, the standard WINDMI model is utilized to estimate the growth and decay of magnetospheric currents by using several solar wind‐magnetosphere coupling functions. However, it is found that the WINDMI model driven by any of these coupling functions is not fully able to explain the decrease of SYM‐H under northward IMF Bz. A dense plasma sheet along with signatures of a highly stretched magnetosphere was observed during this storm. The SYM‐H variations during the entire duration of the storm were only reproduced after modifying the WINDMI model to account for the effects of the dense plasma sheet. The limitations of directly driven models relying purely on the solar wind parameters and not accounting for the state of the magnetosphere are highlighted by this work.

Global Energy Dynamics During Substorms on 9 March 2008 and 26 February 2008 Using Satellite Observations and the WINDMI Model

AbstractWe analyze three substorms that occur on (1) 9 March 2008 05:14 UT, (2) 26 February 2008 04:05 UT, and (3) 26 February 2008 04:55 UT. Using ACE solar wind velocity and interplanetary magnetic field Bz values, we calculate the rectified (southward Bz) solar wind voltage propagated to the magnetosphere. The solar wind conditions for the two events were vastly different, 300 kV for 9 March 2008 substorm, compared to 50 kV for 26 February 2008. The voltage is input to a nonlinear physics‐based model of the magnetosphere called WINDMI. The output is the westward auroral electrojet current which is proportional to the auroral electrojet (AL) index from World Data Center for Geomagnetism Kyoto and the SuperMAG auroral electrojet index (SML). Substorm onset times are obtained from the superMAG substorm database, Pu et al. (2010, https://doi.org/10.1029/2009JA014217), Lui (2011, https://doi.org/10.1029/2010JA016078) and synchronized to Time History of Events and Macroscale Interactions during Substorms satellite data. The timing of onset, model parameters, and intermediate state space variables are analyzed. The model onsets occurred about 5 to 10 min earlier than the reported onsets. Onsets occurred when the geotail current in the WINDMI model reached a critical threshold of 6.2 MA for the 9 March 2008 event, while, in contrast, a critical threshold of 2.1 MA was obtained for the two 26 February 2008 events. The model estimates 1.99 PJ of total energy transfer during the 9 March 2008 event, with 0.95 PJ deposited in the ionosphere. The smaller events on 26 February 2008 resulted in a total energy transfer of 0.37 PJ according to the model, with 0.095 PJ deposited in the ionosphere.

The dynamics of geomagnetic substorms with the WINDMI model

The global dynamics of substorms are controlled by several key magnetospheric parameters. In this work we obtain quantitative measures of these parameters from a low-order nonlinear model of the nightside magnetosphere called WINDMI. The model uses solar wind and IMF measurements from the ACE spacecraft as input into a system of 8 nonlinear ordinary differential equations. The state variables of the differential equations represent the energy stored in the geomagnetic tail, central plasma sheet, ring current and field-aligned currents. The output from the model is the geomagnetic westward auroral electrojet (AL) index and the Dst index. Intermediate variables of the model are the plasma sheet pressure, geotail current, cross-tail electric field, parallel ion velocity and the pressure gradient current. The values of these variables are controlled by physical parameters of the model, consisting of spatially averaged quantities that are analogous to electric circuit elements. We tune the model to re-produce substorm events, comparing model capability against observations of auroral brightening and the auroral electrojet indices AL from WDC Kyoto and SML from SuperMAG. The model is capable of capturing events within a 10–12-min interval of occurrence, with level of activity comparable to the measured indices.

Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI model

In this paper, we have improved the capabilities of a low dimensional nonlinear dynamical model called WINDMI to determine the state of the global magnetosphere by employing the magnetotail (MT) index as a measurement constraint during large geomagnetic storms. The MT index is derived from particle precipitation measurements made by the NOAA/POES satellites. This index indicates the location of the nightside ion isotropic boundary, which is then used as a proxy for the strength of the magnetotail current in the magnetosphere. In Asikainen et al. (2010), the contribution of the tail current to the Dst index is estimated from an empirical relationship based on the MT index. Here the WINDMI model is used as a substitute to arrive at the tail current and ring current contribution to the Dst index, for comparison purposes. We run the WINDMI model on 7 large geomagnetic storms, while optimizing the model state variables against the Dst index, the MT index, and the AL index simultaneously. Our results show that the contribution from the geotail current produced by the WINDMI model and the MT index are strongly correlated, except during some periods when storm time substorms are observed. The inclusion of the MT index as an optimization constraint in turn increases our confidence that the ring current contribution to the Dst index calculated by the WINDMI model is correct during large geomagnetic storms.

Influence of solar wind-magnetosphere coupling functions on theDstindex

[1] In this paper we investigate the role of different solar wind magnetosphere coupling functions on the Dst index calculated by the low-order nonlinear dynamical WINDMI model. In our previous work we have shown that the geotail current dynamics has a significant role in the two-phase decay of the Dst index. During that investigation we used the rectified solar wind electric field vxBz as a baseline for the simulations and analysis. Here we include an evaluation of four other coupling functions in addition to the rectified vBs. These coupling functions emphasize different physical mechanisms to explain the energy transfer into the magnetosphere due to solar wind velocity, dynamic pressure, magnetic field, and Mach number. One coupling function is due to Siscoe, another by Borovsky, and two by Newell. Our results indicate that for a majority of cases, at most only vx, By, and Bz are needed to sufficiently account for the supply of energy to the ring current and geotail current components that contribute to the Dst index. The more complex coupling functions sometimes perform extremely well on storm data sets but at other times do not reproduce the Dst index faithfully. The AL index was used as an additional constraint on the allowable geotail current dynamics and to further differentiate between coupling functions when the Dst performance was similar. The solar wind dynamic pressure contribution appears to be correctly accounted for through the calculation of the Dmp formula of Burton et al. (1975). The degree to which the By component affects the Dst index is not entirely clear from our results, but in most cases its inclusion slightly overemphasizes the ring current contribution and slightly underemphasizes the geotail current contribution.

Study ofDst/ring current recovery times using the WINDMI model

[1] We use the WINDMI model of the nightside magnetosphere to investigate the contributions of ring current, magnetotail current, and magnetopause current on the observed two-phase decay of the Dst index. For the analysis, several geomagnetic events in the period 2000–2007 were identified, during which the interplanetary magnetic field (IMF Bz) turns northward during the early recovery phase of the storm. The Dst recovery rate for these events were first estimated for either of two possible periods: by assuming an initial fast decay phase or by assuming an overall decay for the entire duration of storm. The recovery rates were estimated by matching Dst and Dst* data against WINDMI model predictions. We consistently found an increase in the Dst recovery times when a shorter initial decay phase was chosen as compared to an overall decay phase, thus, confirming the observations of two-phase decay and indicating the possibility of contributions from faster initial decay mechanisms. We then modified the Dst index as estimated by the WINDMI model to include contributions from the cross-tail current and magnetopause currents. The modified Dst was then optimized for all the events. The optimized results correlate very well to the Dst dynamics and indicate that under northward IMF Bz conditions and during the early recovery phase of a storm; contributions from the geotail currents to the fast initial decay of the Dst index are important, while the slower recovery of Dst in the later phases of the storm are due to the charge exchange dominated ring current decay.

Optimization of a Magnetosphere Model for Real-Time Space Weather Prediction Using a Modified Genetic Algorithm

A low-dimensional plasma physics based on the nonlinear dynamical model of the magnetosphere-ionosphere system called WINDMI is used as the basis for a real-time space weather prediction system. The input into the model is a driving voltage derived from solar wind parameters and the interplanetary magnetic field measured by the Advanced Composition Explorer satellite. The output is a field-aligned current proportional to the westward auroral electrojet AL index and the energy stored in the Earth's ring current which is proportional to the Dst index. In order to use the model for the real-time prediction of geomagnetic activity, the model parameters are required to update periodically. We developed a modified genetic algorithm (GA) with micromovement (MGAM) to train the parameters of the model in order to achieve the lowest mse against the measured AL and Dst indexes. The MGAM implements a particle-swarm-optimization-inspired movement phase that helps to improve the convergence rate while employing the efficient GA mechanism for maintaining the population diversity. The performance of the MGAM is compared to a basic real-valued GA (RGA) on five standard test functions and historical geomagnetic storm data sets. While the MGAM performs substantially better than the RGA when evaluating the standard test functions, the improvement is about 6%-12% when used on the 20-D nonlinear dynamical WINDMI model.

Localization of the attractor of the differential equations for the solar wind-magnetosphere-ionosphere model

The problem of localization of attractor of \solar wind-magnetosphere-ionosphere" (WINDMI) three-dimensional model has stimulated further development of method of conical nets. In the paper the development of this method is carried out and analytical localization of the attractor of WINDMI model is performed.

Real‐time predictions of geomagnetic storms and substorms: Use of the Solar Wind Magnetosphere‐Ionosphere System model

A low‐dimensional, plasma physics‐based, nonlinear dynamical model of the coupled magnetosphere‐ionosphere system, called Real‐Time Solar Wind Magnetosphere‐Ionosphere System (WINDMI), is used to predict AL and Dst values approximately 1 h before geomagnetic substorm and storm event. Subsequently, every 10 min ground‐based measurements compiled by World Data Center, Kyoto, are compared with model predictions (http://orion.ph.utexas.edu/∼windmi/realtime/). WINDMI model runs are also available at the Community Coordinated Modeling Center (http://ccmc.gsfc.nasa.gov/). The performance of the Real‐Time WINDMI model is quantitatively evaluated for 22 storm/substorm event predictions from February 2006 to August 2008. Three possible input solar wind‐magnetosphere coupling functions are considered: the standard rectified coupling function, a function due to Siscoe, and a recent function due to Newell. Model AL and Dst predictions are validated using the average relative variance (ARV), correlation coefficient (COR), and root mean squared error (RMSE). The Newell input function yielded the best model AL predictions by all three measures (mean ARV, COR, and RMSE), followed by the rectified, then Siscoe input functions. Model AL predictions correlate at least 1 standard deviation better with the AL index data than a direct correlation between the input coupling functions and the AL index. The mean Dst ARV results show better prediction performance for the rectified input than the Siscoe and Newell inputs. The mean Dst COR and RMSE measures do not readily distinguish between the three input coupling functions.

Evaluation of solar wind‐magnetosphere coupling functions during geomagnetic storms with the WINDMI model

We evaluate the performance of three solar wind‐magnetosphere coupling functions in training the physics‐based WINDMI model on the 3–7 October 2000 geomagnetic storm and predicting the geomagnetic Dst and AL indices during the 15–24 April 2002 geomagnetic storm. The rectified solar wind electric field, a coupling function by Siscoe, and a recent formula proposed by Newell are evaluated. The Newell coupling function performed best in both the training and prediction phases for Dst prediction. The Siscoe formula performed best during the training phase in reproducing the AL faithfully and capturing storm time events. The rectified driver was discovered to be the best in overall performance during both training as well as prediction phases, even though the other two coupling functions outperform it in the training phase. The results indicate that multiple drivers need to be concurrently employed in space weather models to yield different possible levels of geomagnetic activity.

Effect of Interplanetary Shocks on theALandDstIndices

[1] The question of how much interplanetary shock (IP) events contribute to the geoeffectiveness of solar wind drivers is assessed through numerical experiments using the WINDMI model, a physics-based model of the solar wind-driven magnetosphere-ionosphere system. Analytic fits to solar wind input parameters (B⊥IMF, usw, nsw) allowed shocks and associated shock-sheath plasma to be removed while leaving other features of the solar wind driver undisturbed. Percent changes in WINDMI-derived AL and Dst indices between runs with and without the observed shock and sheath signatures were taken as a measure of its relative contribution to the geoeffectiveness. The major magnetic storms during 15–24 April 2002 and 3–6 October 2000 were selected for this experiment. In both cases, the IP shock and sheath features contributed significantly to the geoeffectiveness of the solar wind driver. The magnetic field compressional jump is important to producing the changes in the AL during these two storm intervals.

The dynamics of storms and substorms with the WINDMI model

WINDMI is a physics based eight-dimensional state-space model that simulates the flow of energy between the dominant global energy components in the nightside magnetosphere. The model is intrinsically three-dimensional in configuration space, and uses the basic geometry of the Tsyganenko magnetic field model to define the physical quantities. The dynamical equations satisfy the laws of energy and charge conservation for the network of branches and nodes formed by the topology of the ambient magnetic field. The model includes energy coupled by injected plasma from the plasma sheet across the Alfvén layer into the ring current. The power input into the model is the electromotive plasma dynamo derived from solar wind parameters. The output of the model is the westward Auroral Electrojet current and the energy stored in the Earth’s ring current. The prediction of the model is compared to the geomagnetic AL and D st indices. These indices measure fluctuations of the earth’s magnetic field at its surface. The model parameters have been optimized using a genetic algorithm with the Average Relative Variance (ARV) as a performance metric for five of the seven designated Geospace Environment (GEM) storms. Results for the October 3–7 2000 GEM storm and the October 20–22 2001 GEM storm are given here. The optimized models appear to give a reliable method of making predictions from the solar wind for a range of auroral and ring current activity.

Analysis of the October 3-7 2000 GEM storm with the WINDMI model

[1] The 8 dimensional physics model WINDMI is used to analyze the October 3–7, 2000 geomagnetic storm using solar wind input data from the ACE satellite. This period was chosen because it contains an extended interval of well-defined and quasi-periodic auroral activations called sawtooth oscillations, a phenomena whose relationship to substorm processes and to upstream solar wind drivers is still under debate. The question of whether multiple sawtooth oscillations are triggered by periodic upstream solar wind features or by internal magnetospheric processes is addressed. The model predicts both the occurrence of 8 auroral activations identified as sawtooth events during the 24 hour period on the 4th of October, in agreement with the measured AL index, and also an earlier multiple sawtooth interval on the 3rd of October, in agreement with the measured AL index. These intervals occur during steady but moderate solar wind IMF Bz values and the periodicity of the sawtooth events was not directly related to any periodic features in the upstream solar wind. The model also predicts the geomagnetic Dst index through the main and recovery phase of the storm.

Substorm classification with the WINDMI model

Abstract. The results of a genetic algorithm optimization of the WINDMI model using the Blanchard-McPherron substorm data set is presented. A key result from the large-scale computations used to search for convergence in the predictions over the database is the finding that there are three distinct types of vx Bs -AL waveforms characterizing substorms. Type I and III substorms are given by the internally-triggered WINDMI model. The analysis reveals an additional type of event, called a type II substorm, that requires an external trigger as in the northward turning of the IMF model of Lyons (1995). We show that incorporating an external trigger, initiated by a fast northward turning of the IMF, into WINDMI, a low-dimensional model of substorms, yields improved predictions of substorm evolution in terms of the AL index. Intrinsic database uncertainties in the timing between the ground-based AL electrojet signal and the arrival time at the magnetopause of the IMF data measured by spacecraft in the solar wind prevent a sharp division between type I and II events. However, within these timing limitations we find that the fraction of events is roughly 40% type I, 40% type II, and 20% type III.

On the Horton-weigel-sprott model of the solar-wind-driven magnetosphere-ionosphere system

The solar-wind-driven magnetosphere-ionosphere is a system that exhibits a variety of dynamical states. These include low-level steady plasma convection, intermittent releases of stored plasma energy into the ionosphere that are known as sub-storms, and states of continuous strong unloading. The WINDMI model consisting of a set of six nonlinear coupled ordinary differential equations has been used to describe the energy flow through this system. This model has recently been reduced to a set of three nonlinear coupled ordinary differential equations that has been shown to admit chaotic solutions. The present calculation demonstrates that it is possible to synchronize this reduced nonlinear system with another system that may even be linear.

Geomagnetic transport in the solar wind driven nightside magnetosphere–ionosphere system

A spatially resolved nonlinear dynamical model of the solar wind driven geomagnetic tail plasma is developed for the purpose of space weather predictions. The model represents the fluctuating electromagnetic fields and high pressure central plasma sheet by a large number (2N≲200) of semiglobal coupled current loops ranging from the near-Earth geosynchronous orbit position for substorm dynamics to deep in the geotail. There is a spectrum of dynamical frequencies ranging from 1 h periods to 1 min and shorter periods. The low-frequency modes are global and lead to the dynamics of the low-dimensional (d=6) WINDMI model. The high-frequency dynamics are nonlinear compressional-rarefraction waves propagating up and down the geotail. The localized pulses start from sites of local reconnection set off either by the tearing mode unloading trigger or by localized solar wind disturbances acting on the nightside magnetopause. Larger unloading events lead to nonlinear steepening of the compressional pulsations which act to trigger secondary convection events under certain conditions.

Chaos and the limits of predictability for the solar-wind-driven magnetosphere–ionosphere system

The solar-wind-driven magnetosphere–ionosphere exhibits a variety of dynamical states including low-level steady plasma convection, episodic releases of geotail stored plasma energy into the ionospheric known broadly as substorms, and states of continuous strong unloading. The WINDMI model [J. P. Smith et al., J. Geophys. Res. 105, 12 983 (2000)] is a six-dimensional substorm model that uses a set of ordinary differential equations to describe the energy flow through the solar wind–magnetosphere–ionosphere system. This model has six major energy components, with conservation of energy and charge described by the coupling coefficients. The six-dimensional model is investigated by introducing reductions to derive a new minimal three-dimensional model for deterministic chaos. The reduced model is of the class of chaotic equations studied earlier [J. C. Sprott, Am. J. Phys. 68, 758 (2000)]. The bifurcation diagram remains similar, and the limited prediction time, which is in the range of three to five hours, occurs in the chaotic regime for both models. Determining all three Lyapunov exponents for the three-dimensional model allows one to determine the dimension of the chaotic attractor for the system.

Dynamical range of the WINDMI model: An exploration of possible magnetospheric plasma states

This paper explores the dynamical range of the WINDMI model (Horton and Doxas, 1998]. Such low‐dimensional models provide us with the tools to understand the relationships of simple physical quantities within the magnetosphere (such as energy deposition, macroscopic currents, cross‐tail voltage, etc.) without the necessity of coping with the more complete but unwieldy models (MHD or particle codes, for example). The model is highly versatile: certain regions of the parameter space support stable fixed points, while others contain periodic states that exhibit period doubling, and sometimes chaos. States in each of these regimes (stable, periodic, chaotic) are investigated for their ability to accurately describe the observed properties of the magnetosphere‐ionosphere system. A brief discussion of applications of this model to current space physics problems is included.

The solar-wind driven magnetosphere–ionosphere as a complex dynamical system

The solar-wind driven magnetosphere–ionosphere system is a classic example of a complex dynamical system (CDS). The defining properties of a CDS are (1) sensitivity to initial conditions; (2) multiple space-time scales; (3) bifurcation sequences with hysteresis in transitions between attractors; and (4) noncompositionality. Noncompositionality means that the behavior of the system as a whole is different from the dynamics of its subcomponents taken with passive or no couplings. In particular the dynamics of the geomagnetic tail plasma depends on its coupling to the dissipative ionospheric plasma and on the nature of the solar-wind driving electric field over a suitably long (many hours) previous time interval. These complex dynamical system features are shown here in detail using the known WINDMI model for the solar-wind driven magnetosphere–ionosphere (MI) system. Numerous features in the bifurcation sequence are identified with known substorm and storm characteristics.