The Wang-Sheeley model is an empirical model that can predict the background solar wind speed and interplanetary magnetic field (IMF) polarity. We make a number of modifications to the basic technique that greatly improve the performance and reliability of the model. First, we establish a continuous empirical function that relates magnetic expansion factor to solar wind velocity at the source surface. Second, we propagate the wind from the source surface to the Earth using the assumption of radial streams and a simple scheme to account for their interactions. Third, we develop and apply a method for identifying and removing problematic magnetograms from the Wilcox Solar Observatory (WSO). Fourth, we correct WSO line-of-sight magnetograms for polar field strength modulation effects that result from the annual variation in the solar b angle. Fifth, we explore a number of techniques to optimize construction of daily updated synoptic maps from the WSO magnetograms. We report on a comprehensive statistical analysis comparing Wang-Sheeley model predictions with the WIND satellite data set during a 3-year period centered about the May 1996 solar minimum. The predicted and observed solar wind speeds have a statistically significant correlation (∼0.4) and an average fractional deviation of 0.15. When a single (6-month) period with large data gaps is excluded from the comparison, the solar wind speed is correctly predicted to within 10–15%. The IMF polarity is correctly predicted ∼75% of the time. The solar wind prediction technique presented here has direct applications to space weather research and forecasting.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JA000262

Improvement in the prediction of solar wind conditions using near‐real time solar magnetic field updates

By L I Sedov London: Cleaver-Hume Press Ltd Pp xvi + 363 Price 105s This is really two separate books within the same pair of covers First of all Chapters 1-3, some 145 pages, are devoted to the discussion of similarity and dimensional, methods and their application to a variety of problems in mechanics and fluid mechanics

http://iopscience.iop.org/article/10.1088/0031-9112/11/6/008/pdf

Similarity and Dimensional Methods in Mechanics

Around solar maximum, the dominant interplanetary phenomena causing intense magnetic storms (Dst<−100 nT) are the interplanetary manifestations of fast coronal mass ejections (CMEs). Two interplanetary structures are important for the development of storms, involving intense southward IMFs: the sheath region just behind the forward shock, and the CME ejecta itself. Whereas the initial phase of a storm is caused by the increase in plasma ram pressure associated with the increase in density and speed at and behind the shock (accompanied by a sudden impulse [SI] at Earth), the storm main phase is due to southward IMFs. If the fields are southward in both of the sheath and solar ejecta, two-step main phase storms can result and the storm intensity can be higher. The storm recovery phase begins when the IMF turns less southward, with delays of ≈1–2 hours, and has typically a decay time of 10 hours. For CMEs involving clouds the intensity of the core magnetic field and the amplitude of the speed of the cloud seems to be related, with a tendency that clouds which move at higher speeds also posses higher core magnetic field strengths, thus both contributing to the development of intense storms since those two parameters are important factors in genering the solar wind-magnetosphere coupling via the reconnection process. During solar minimum, high speed streams from coronal holes dominate the interplanetary medium activity. The high-density, low-speed streams associated with the heliospheric current sheet (HCS) plasma impinging upon the Earth's magnetosphere cause positive Dst values (storm initial phases if followed by main phases). In the absence of shocks, SIs are infrequent during this phase of the solar cycle. High-field regions called Corotating Interaction Regions (CIRs) are mainly created by the fast stream (emanating from a coronal hole) interaction with the HCS plasma sheet. However, because the Bz component is typically highly fluctuating within the CIRs, the main phases of the resultant magnetic storms typically have highly irregular profiles and are weaker. Storm recovery phases during this phase of the solar cycle are also quite different in that they can last from many days to weeks. The southward magnetic field (Bs) component of Alfven waves in the high speed stream proper cause intermittent reconnection, intermittent substorm activity, and sporadic injections of plasma sheet energy into the outer portion of the ring current, prolonging its final decay to quiet day values. This continuous auroral activity is called High Intensity Long Duration Continuous AE Activity (HILDCAAs). Possible interplanetary mechanisms for the creation of very intense magnetic storms are discussed. We examine the effects of a combination of a long-duration southward sheath magnetic field, followed by a magnetic cloud Bs event. We also consider the effects of interplanetary shock events on the sheath plasma. Examination of profiles of very intense storms from 1957 to the present indicate that double, and sometimes triple, IMF Bs events are important causes of such events. We also discuss evidence that magnetic clouds with very intense core magnetic fields tend to have large velocities, thus implying large amplitude interplanetary electric fields that can drive very intense storms. Finally, we argue that a combination of complex interplanetary structures, involving in rare occasions the interplanetary manifestations of subsequent CMEs, can lead to extremely intense storms.

Interplanetary origin of geomagnetic storms

We describe an empirical model to predict the 1-AU arrival of coronal mass ejections (CMEs). This model is based on an effective interplanetary (IP) acceleration described by Gopalswamy et al. [2000b] that the CMEs are subject to, as they propagate from the Sun to 1 AU. We have improved this model (1) by minimizing the projection effects (using data from spacecraft in quadrature) in determining the initial speed of CMEs, and (2) by allowing for the cessation of the interplanetary acceleration before 1 AU. The resulting effective IP acceleration was higher in magnitude than what was obtained from CME measurements from spacecraft along the Sun-Earth line. We evaluated the predictive capability of the CME arrival model using recent two-point measurements from the Solar and Heliospheric Observatory (SOHO), Wind, and ACE spacecraft. We found that an acceleration cessation distance of 0.76 AU is in reasonable agreement with the observations. The new prediction model reduces the average prediction error from 15.4 to 10.7 hours. The model is in good agreement with the observations for high-speed CMEs. For slow CMEs the model as well as observations show a flat arrival time of ∼4.3 days. Use of quadrature observations minimized the projection effects naturally without the need to assume the width of the CMEs. However, there is no simple way of estimating the projection effects based on the surface location of the Earth-directed CMEs observed by a spacecraft (such as SOHO) located along the Sun-Earth line because it is impossible to measure the width of these CMEs. The standard assumption that the CME is a rigid cone may not be correct. In fact, the predicted arrival times have a better agreement with the observed arrival times when no projection correction is applied to the SOHO CME measurements. The results presented in this work suggest that CMEs expand and accelerate near the Sun (inside 0.7 AU) more than our model supposes; these aspects will have to be included in future models.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2001JA000177

Predicting the 1‐AU arrival times of coronal mass ejections

This chapter provides an overview of current efforts in the theory and modeling of CMEs. Five key areas are discussed: (1) CME initiation; (2) CME evolution and propagation; (3) the structure of interplanetary CMEs derived from flux rope modeling; (4) CME shock formation in the inner corona; and (5) particle acceleration and transport at CME driven shocks. In the section on CME initiation three contemporary models are highlighted. Two of these focus on how energy stored in the coronal magnetic field can be released violently to drive CMEs. The third model assumes that CMEs can be directly driven by currents from below the photosphere. CMEs evolve considerably as they expand from the magnetically dominated lower corona into the advectively dominated solar wind. The section on evolution and propagation presents two approaches to the problem. One is primarily analytical and focuses on the key physical processes involved. The other is primarily numerical and illustrates the complexity of possible interactions between the CME and the ambient medium. The section on flux rope fitting reviews the accuracy and reliability of various methods. The section on shock formation considers the effect of the rapid decrease in the magnetic field and plasma density with height. Finally, in the section on particle acceleration and transport, some recent developments in the theory of diffusive particle acceleration at CME shocks are discussed. These include efforts to combine self-consistently the process of particle acceleration in the vicinity of the shock with the subsequent escape and transport of particles to distant regions.

CME Theory and Models

We present results of simulations of a magnetic cloud's evolution during its passage from the solar vicinity (18 solar radii) to approximately 1 AU using a two-dimensional MHD code. The cloud is a cylinder perpendicular to the ecliptic plane. The external flow is explicitly considered self-consistently. Our results show that the magnetic cloud retains its basic topology up to 1 AU, although it is distorted due to radially expanding solar wind and magnetic field lines bending. The magnetic cloud expands, faster near the Sun, and faster in the azimuthal direction than in the radial one; its extent is approximately 1.5–2× larger in the azimuthal direction. Magnetic clouds reach approximately the same asymptotic propagation velocity (higher than the background solar wind velocity) despite our assumptions of various initial conditions for their release. Recorded time profiles of the magnetic field magnitude, velocity, and temperature at one point, which would be measured by a hypothetical spacecraft, are qualitatively in agreement with observed profiles. The simulations qualitatively confirm the behavior of magnetic clouds derived from some observations, so they support the interpretations of some magnetic cloud phenomena as magnetically closed regions in the solar wind.

Simulation of magnetic cloud propagation in the inner heliosphere in two-dimensions: 1. A loop perpendicular to the ecliptic plane

[1] We describe a Sun-to-Earth system of coupled models. Our main goal is to create a real-time, three-dimensional (3-D), MHD-based system to aid in the operational forecasting of geomagnetic activity, but we expect the system to have other uses. We give here our initial survey of the system's characteristics. The Hybrid Heliospheric Modeling System (HHMS) is composed of two physics-based models, combined with two simple empirical models. The physics-based models are a source surface (potential field) current sheet model for the corona and a time-dependent 3-D MHD solar wind model. The system is driven by a sequence of photospheric magnetic maps composed from daily magnetograms. An empirical relationship between magnetic flux tube expansion factor and solar wind speed at 0.1 AU is a key element of the system. The solar wind model gives a predicted time series of MHD parameters at the location of Earth in the model grid; this is verified against Omni, Wind, or ACE satellite data, depending on the time period. The predicted solar wind at Earth is used as input to the second, data-based, empirical model to predict the geomagnetic Ap index. We compare test results for simulated 1 day ahead Ap forecasts for the years 1993 through 2002 with forecast skill of the official Ap forecasts that were issued by the NOAA Space Environment Center in that time interval. Results show the HHMS would have been useful to forecasters in some years. Simulations of transient events such as coronal mass ejections and interplanetary shocks with the HHMS will be reported on later.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2005JA011430

A hybrid heliospheric modeling system: Background solar wind

Interplanetary shock waves, propagating in the heliosphere faster than earlier-emitted coronal ejecta, penetrate them and modify their parameters during this interaction. Using two and one half dimensional MHD simulations, we show how a magnetic cloud (flux rope) propagating with a speed 3 times higher than the ambient solar wind is affected by an even faster traveling shock wave overtaking the cloud. The magnetic field increases inside the cloud during the interaction as it is compressed in the radial direction and becomes very oblate. The cloud is also accelerated and moves faster, as a whole, while both shocks (driven by the cloud and the faster interplanetary shock) merge upstream of the cloud. This interaction may be a rather common phenomenon due to the frequency of coronal mass ejections and occurrence of shock waves during periods of high solar activity.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JA01675

MHD simulation of an interaction of a shock wave with a magnetic cloud

This paper continues studies of the cylindrical magnetic clouds' propagation in the interplanetary medium. In our first paper devoted to this topic (Vandas et al., 1995) we dealt with the cloud with the axis perpendicular to the ecliptic plane and derived time dependencies of its velocity, field magnitude, and temperature as well as its shape for different initial conditions. Here, analogously, we present simulations for the cloud with the axis parallel to the ecliptic plane and show that the propagation of these clouds practically does not depend on the inclination of their axes to the ecliptic plane. We made a new conclusion concerning the helicity of the magnetic field inside the cloud. Because of the magnetic interaction with the background field, the cloud is shifted to the side where it meets with the external interplanetary magnetic field (IMF) polarity that is opposite to that within the cloud. The net effect of the time dependent Lorentz, inertial, and pressure gradient forces probably causes the complementary deformation of the whole cloud.

Simulation of magnetic cloud propagation in the inner heliosphere in two dimensions: 2. A loop parallel to the ecliptic plane and the role of helicity

Today a wide variety of techniques are available for nowcasting and forecasting magnetic storm activity. A brief review of linear time series prediction techniques, with examples, is used to lay a foundation for the description of newer non-linear techniques based on state-space reconstruction. We illustrate the state-space prediction technique in application to predict Dst from ISEE-3 solar wind data. Upstream solar wind data, such as from ISEE-3 or WIND close to the L 1 libration point, provide a prediction lead time of 0.5-1.5 hours. To go beyond the L 1 prediction lead time some information about the solar wind between the L 1 point and the Sun is required. Remote sensing is the measurement of something from a distance, like solar magnetograms or X-ray images. Both empirical and physically based models, driven by remote sensing data, promise a way to make forecasts a few days into the future. A combination of the statistical time series prediction techniques operating on the output of physically based models, driven by remote sensing data, may offer the first capability of predicting magnetic storms a few days in advance. We illustrate this combination of techniques using the output of a potential field model [Wang and Sheeley, 1988] as input to a linear prediction filter to forecast the planetary geomagnetic index. Finally, practical forecasting requires verification. We describe some of the standard measures of forecast performance: skill score, prediction efficiency, and correlation coefficient. The value of cross validation testing is emphasized.

Thomas Detman

Papers

Simulation of magnetic cloud propagation in the inner heliosphere in two-dimensions: 1. A loop perpendicular to the ecliptic plane

A hybrid heliospheric modeling system: Background solar wind

MHD simulation of an interaction of a shock wave with a magnetic cloud

Simulation of magnetic cloud propagation in the inner heliosphere in two dimensions: 2. A loop parallel to the ecliptic plane and the role of helicity

Review of techniques for magnetic storm forecasting